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Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/A-technical-drawing.html", "source2": "./usr/share/doc/sketch-doc/sketch/A-technical-drawing.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/About-sketch.html", "source2": "./usr/share/doc/sketch-doc/sketch/About-sketch.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Affine-arithmetic.html", "source2": "./usr/share/doc/sketch-doc/sketch/Affine-arithmetic.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Arithmetic.html", "source2": "./usr/share/doc/sketch-doc/sketch/Arithmetic.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Blocks.html", "source2": "./usr/share/doc/sketch-doc/sketch/Blocks.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Bugs-and-anomalies.html", "source2": "./usr/share/doc/sketch-doc/sketch/Bugs-and-anomalies.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Building-a-drawing.html", "source2": "./usr/share/doc/sketch-doc/sketch/Building-a-drawing.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Camera.html", "source2": "./usr/share/doc/sketch-doc/sketch/Camera.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Caveats.html", "source2": "./usr/share/doc/sketch-doc/sketch/Caveats.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Clipping.html", "source2": "./usr/share/doc/sketch-doc/sketch/Clipping.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Command-line.html", "source2": "./usr/share/doc/sketch-doc/sketch/Command-line.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Contributions.html", "source2": "./usr/share/doc/sketch-doc/sketch/Contributions.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Curves.html", "source2": "./usr/share/doc/sketch-doc/sketch/Curves.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Definitions.html", "source2": "./usr/share/doc/sketch-doc/sketch/Definitions.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Dots-in-TikZ_002fPGF.html", "source2": "./usr/share/doc/sketch-doc/sketch/Dots-in-TikZ_002fPGF.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Dots.html", "source2": "./usr/share/doc/sketch-doc/sketch/Dots.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Drawables.html", "source2": "./usr/share/doc/sketch-doc/sketch/Drawables.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Drawing-a-solid.html", "source2": "./usr/share/doc/sketch-doc/sketch/Drawing-a-solid.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Drawing-options.html", "source2": "./usr/share/doc/sketch-doc/sketch/Drawing-options.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Forms-of-definitions.html", "source2": "./usr/share/doc/sketch-doc/sketch/Forms-of-definitions.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Forms-of-references.html", "source2": "./usr/share/doc/sketch-doc/sketch/Forms-of-references.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Frame.html", "source2": "./usr/share/doc/sketch-doc/sketch/Frame.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Global-environment.html", "source2": "./usr/share/doc/sketch-doc/sketch/Global-environment.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Global-options.html", "source2": "./usr/share/doc/sketch-doc/sketch/Global-options.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Helix-with-cull-set-false-then-true.html", "source2": "./usr/share/doc/sketch-doc/sketch/Helix-with-cull-set-false-then-true.html", "unified_diff": "@@ -3,15 +3,15 @@\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <!-- This file redirects to the location of a node or anchor -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Hello-world.html", "source2": "./usr/share/doc/sketch-doc/sketch/Hello-world.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Hidden-surface-removal.html", "source2": "./usr/share/doc/sketch-doc/sketch/Hidden-surface-removal.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Identifiers.html", "source2": "./usr/share/doc/sketch-doc/sketch/Identifiers.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Index-of-syntax.html", "source2": "./usr/share/doc/sketch-doc/sketch/Index-of-syntax.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Index.html", "source2": "./usr/share/doc/sketch-doc/sketch/Index.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Input-language.html", "source2": "./usr/share/doc/sketch-doc/sketch/Input-language.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Installing-sketch.html", "source2": "./usr/share/doc/sketch-doc/sketch/Installing-sketch.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Internal-options.html", "source2": "./usr/share/doc/sketch-doc/sketch/Internal-options.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Introduction-by-example.html", "source2": "./usr/share/doc/sketch-doc/sketch/Introduction-by-example.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Key-and-reserved-words.html", "source2": "./usr/share/doc/sketch-doc/sketch/Key-and-reserved-words.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Language-basics.html", "source2": "./usr/share/doc/sketch-doc/sketch/Language-basics.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Language.html", "source2": "./usr/share/doc/sketch-doc/sketch/Language.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Limits-on-error-detection.html", "source2": "./usr/share/doc/sketch-doc/sketch/Limits-on-error-detection.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Lines.html", "source2": "./usr/share/doc/sketch-doc/sketch/Lines.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Literals.html", "source2": "./usr/share/doc/sketch-doc/sketch/Literals.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/More-to-learn.html", "source2": "./usr/share/doc/sketch-doc/sketch/More-to-learn.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Nested-sweeps.html", "source2": "./usr/share/doc/sketch-doc/sketch/Nested-sweeps.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Object-transforms.html", "source2": "./usr/share/doc/sketch-doc/sketch/Object-transforms.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Options.html", "source2": "./usr/share/doc/sketch-doc/sketch/Options.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Overview.html", "source2": "./usr/share/doc/sketch-doc/sketch/Overview.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/PSTricks-options.html", "source2": "./usr/share/doc/sketch-doc/sketch/PSTricks-options.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Picture-box.html", "source2": "./usr/share/doc/sketch-doc/sketch/Picture-box.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Point-and-vector-literals.html", "source2": "./usr/share/doc/sketch-doc/sketch/Point-and-vector-literals.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Point-sweeps.html", "source2": "./usr/share/doc/sketch-doc/sketch/Point-sweeps.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Polygon-sweeps.html", "source2": "./usr/share/doc/sketch-doc/sketch/Polygon-sweeps.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Polygons.html", "source2": "./usr/share/doc/sketch-doc/sketch/Polygons.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Polyline-sweeps-with-closure.html", "source2": "./usr/share/doc/sketch-doc/sketch/Polyline-sweeps-with-closure.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Polyline-sweeps.html", "source2": "./usr/share/doc/sketch-doc/sketch/Polyline-sweeps.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Puts.html", "source2": "./usr/share/doc/sketch-doc/sketch/Puts.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Repeated-objects.html", "source2": "./usr/share/doc/sketch-doc/sketch/Repeated-objects.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Repeats.html", "source2": "./usr/share/doc/sketch-doc/sketch/Repeats.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Reporting-bugs.html", "source2": "./usr/share/doc/sketch-doc/sketch/Reporting-bugs.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Right-hand-rule.html", "source2": "./usr/share/doc/sketch-doc/sketch/Right-hand-rule.html", "unified_diff": "@@ -3,15 +3,15 @@\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <!-- This file redirects to the location of a node or anchor -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Scalar-literals.html", "source2": "./usr/share/doc/sketch-doc/sketch/Scalar-literals.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Solid-coil-example.html", "source2": "./usr/share/doc/sketch-doc/sketch/Solid-coil-example.html", "unified_diff": "@@ -3,15 +3,15 @@\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <!-- This file redirects to the location of a node or anchor -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Special-objects.html", "source2": "./usr/share/doc/sketch-doc/sketch/Special-objects.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Specials.html", "source2": "./usr/share/doc/sketch-doc/sketch/Specials.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Statistics.html", "source2": "./usr/share/doc/sketch-doc/sketch/Statistics.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Sweep-face-splitting.html", "source2": "./usr/share/doc/sketch-doc/sketch/Sweep-face-splitting.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Sweeps.html", "source2": "./usr/share/doc/sketch-doc/sketch/Sweeps.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Swept-blocks.html", "source2": "./usr/share/doc/sketch-doc/sketch/Swept-blocks.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Swept-lines.html", "source2": "./usr/share/doc/sketch-doc/sketch/Swept-lines.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Swept-objects.html", "source2": "./usr/share/doc/sketch-doc/sketch/Swept-objects.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Swept-points.html", "source2": "./usr/share/doc/sketch-doc/sketch/Swept-points.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Swept-polygons.html", "source2": "./usr/share/doc/sketch-doc/sketch/Swept-polygons.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/TikZ_002fPGF-options.html", "source2": "./usr/share/doc/sketch-doc/sketch/TikZ_002fPGF-options.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/TikZ_002fPGF-user_002ddefined-styles.html", "source2": "./usr/share/doc/sketch-doc/sketch/TikZ_002fPGF-user_002ddefined-styles.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Transform-literals.html", "source2": "./usr/share/doc/sketch-doc/sketch/Transform-literals.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Transparency.html", "source2": "./usr/share/doc/sketch-doc/sketch/Transparency.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Two_002doperand-_0028binary_0029-forms.html", "source2": "./usr/share/doc/sketch-doc/sketch/Two_002doperand-_0028binary_0029-forms.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/Unary-forms.html", "source2": "./usr/share/doc/sketch-doc/sketch/Unary-forms.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n"}, {"source1": "./usr/share/doc/sketch-doc/sketch/index.html", "source2": "./usr/share/doc/sketch-doc/sketch/index.html", "unified_diff": "@@ -2,15 +2,15 @@\n <html>\n <!-- Created by GNU Texinfo 6.8, https://www.gnu.org/software/texinfo/ -->\n <head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\">\n <!-- Copyright (C) 2005 to 2012 Eugene K. Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n PSTricks or PGF/TikZ code suitable for use with the\n TeX document processing system.\n \n Sketch is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n@@ -78,15 +78,15 @@\n </div>\n <hr>\n <span id=\"Sketch\"></span><h1 class=\"top\">Sketch</h1>\n \n <p>Copyright &copy; 2005 to 2012 Eugene K. Ressler.\n </p>\n <p>This manual is for <code>sketch</code>, version 0.3 (build 7),\n-Sunday, January 07, 2024, a program that converts descriptions of simple\n+Saturday, February 08, 2025, a program that converts descriptions of simple\n three-dimensional scenes into line drawings. This version generates\n <code>PSTricks</code> or <code>PGF/TikZ</code> code suitable for use with the\n TeX document processing system.\n </p>\n <p><code>Sketch</code> is free software. You can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 3, or (at your option)\n", "details": [{"source1": "html2text {}", "source2": "html2text {}", "unified_diff": "@@ -11,18 +11,18 @@\n \n \n                              ****** Sketch ******\n Next: About_sketch, Previous: (dir), Up: (dir) \u00a0 [Contents][Index]\n ===============================================================================\n ****** Sketch ******\n Copyright \u00a9 2005 to 2012 Eugene K. Ressler.\n-This manual is for sketch, version 0.3 (build 7), Sunday, January 07, 2024, a\n-program that converts descriptions of simple three-dimensional scenes into line\n-drawings. This version generates PSTricks or PGF/TikZ code suitable for use\n-with the TeX document processing system.\n+This manual is for sketch, version 0.3 (build 7), Saturday, February 08, 2025,\n+a program that converts descriptions of simple three-dimensional scenes into\n+line drawings. This version generates PSTricks or PGF/TikZ code suitable for\n+use with the TeX document processing system.\n Sketch is free software. You can redistribute it and/or modify it under the\n terms of the GNU General Public License as published by the Free Software\n Foundation; either version 3, or (at your option) any later version.\n Sketch is distributed in the hope that it will be useful, but WITHOUT ANY\n WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A\n PARTICULAR PURPOSE. See the GNU General Public License for more details.\n You should have received a copy of the GNU General Public License along with\n"}]}, {"source1": "./usr/share/doc/sketch-doc/sketch.pdf.gz", "source2": "./usr/share/doc/sketch-doc/sketch.pdf.gz", "unified_diff": null, "details": [{"source1": "sketch.pdf", "source2": "sketch.pdf", "unified_diff": null, "details": [{"source1": "pdftotext {} -", "source2": "pdftotext {} -", "unified_diff": "@@ -1,18 +1,17 @@\n Sketch\n Simple 3D sketching\n-Version 0.3 (build 7), Sunday, January 07, 2024\n+Version 0.3 (build 7), Saturday, February 08, 2025\n \n Gene Ressler\n \n \fCopyright c 2005 to 2012 Eugene K. Ressler.\n-This manual is for sketch, version 0.3 (build 7), Sunday, January 07, 2024, a program that\n-converts descriptions of simple three-dimensional scenes into line drawings. This version\n-generates PSTricks or PGF/TikZ code suitable for use with the TEX document processing\n-system.\n+This manual is for sketch, version 0.3 (build 7), Saturday, February 08, 2025, a program that converts descriptions of simple three-dimensional scenes into line drawings. This\n+version generates PSTricks or PGF/TikZ code suitable for use with the TEX document\n+processing system.\n Sketch is free software. You can redistribute it and/or modify it under the terms of the\n GNU General Public License as published by the Free Software Foundation; either version\n 3, or (at your option) any later version.\n Sketch is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;\n without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.\n You should have received a copy of the GNU General Public License along with sketch;\n see the file COPYING.txt. If not, see http://www.gnu.org/copyleft.\n"}]}]}, {"source1": "./usr/share/info/sketch.info.gz", "source2": "./usr/share/info/sketch.info.gz", "unified_diff": null, "details": [{"source1": "sketch.info", "source2": "sketch.info", "has_internal_linenos": true, "unified_diff": "@@ -5,9618 +5,9619 @@\n 00000040: 682e 7465 7869 2e0a 0a43 6f70 7972 6967  h.texi...Copyrig\n 00000050: 6874 2028 4329 2032 3030 3520 746f 2032  ht (C) 2005 to 2\n 00000060: 3031 3220 4575 6765 6e65 204b 2e20 5265  012 Eugene K. Re\n 00000070: 7373 6c65 722e 0a0a 2020 2054 6869 7320  ssler...   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See the\n-00000330: 2047 4e55 2047 656e 6572 616c 2050 7562   GNU General Pub\n-00000340: 6c69 6320 4c69 6365 6e73 6520 666f 720a  lic License for.\n-00000350: 6d6f 7265 2064 6574 6169 6c73 2e0a 0a20  more details... \n-00000360: 2020 596f 7520 7368 6f75 6c64 2068 6176    You should hav\n-00000370: 6520 7265 6365 6976 6564 2061 2063 6f70  e received a cop\n-00000380: 7920 6f66 2074 6865 2047 4e55 2047 656e  y of the GNU Gen\n-00000390: 6572 616c 2050 7562 6c69 6320 4c69 6365  eral Public Lice\n-000003a0: 6e73 650a 616c 6f6e 6720 7769 7468 2027  nse.along with '\n-000003b0: 736b 6574 6368 273b 2073 6565 2074 6865  sketch'; see the\n-000003c0: 2066 696c 6520 434f 5059 494e 472e 7478   file COPYING.tx\n-000003d0: 742e 2020 4966 206e 6f74 2c20 7365 650a  t.  If not, see.\n-000003e0: 6874 7470 3a2f 2f77 7777 2e67 6e75 2e6f  http://www.gnu.o\n-000003f0: 7267 2f63 6f70 796c 6566 742e 0a0a 494e  rg/copyleft...IN\n-00000400: 464f 2d44 4952 2d53 4543 5449 4f4e 2054  FO-DIR-SECTION T\n-00000410: 6558 0a53 5441 5254 2d49 4e46 4f2d 4449  eX.START-INFO-DI\n-00000420: 522d 454e 5452 590a 2a20 536b 6574 6368  R-ENTRY.* Sketch\n-00000430: 3a20 2873 6b65 7463 6829 2e20 2020 2020  : (sketch).     \n-00000440: 2020 2020 2020 2020 5369 6d70 6c65 2033          Simple 3\n-00000450: 4420 736b 6574 6368 696e 6720 666f 7220  D sketching for \n-00000460: 5465 580a 454e 442d 494e 464f 2d44 4952  TeX.END-INFO-DIR\n-00000470: 2d45 4e54 5259 0a0a 1f0a 4669 6c65 3a20  -ENTRY....File: \n-00000480: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n-00000490: 6465 3a20 546f 702c 2020 4e65 7874 3a20  de: Top,  Next: \n-000004a0: 4162 6f75 7420 736b 6574 6368 2c20 2050  About sketch,  P\n-000004b0: 7265 763a 2028 6469 7229 2c20 2055 703a  rev: (dir),  Up:\n-000004c0: 2028 6469 7229 0a0a 536b 6574 6368 0a2a   (dir)..Sketch.*\n-000004d0: 2a2a 2a2a 2a0a 0a43 6f70 7972 6967 6874  *****..Copyright\n-000004e0: 2028 4329 2032 3030 3520 746f 2032 3031   (C) 2005 to 201\n-000004f0: 3220 4575 6765 6e65 204b 2e20 5265 7373  2 Eugene K. 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Lines::\n-00001430: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00001440: 2020 2020 2020 2044 7261 7720 706f 6c79         Draw poly\n-00001450: 6c69 6e65 732e 0a2a 2043 7572 7665 733a  lines..* Curves:\n-00001460: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00001470: 2020 2020 2020 2044 7261 7720 6375 7276         Draw curv\n-00001480: 6573 2e0a 2a20 506f 6c79 676f 6e73 3a3a  es..* Polygons::\n-00001490: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000014a0: 2020 2020 4472 6177 2070 6f6c 7967 6f6e      Draw polygon\n-000014b0: 732e 0a2a 2053 7065 6369 616c 733a 3a20  s..* Specials:: \n-000014c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000014d0: 2020 2045 6d62 6564 2072 6177 204c 6154     Embed raw LaT\n-000014e0: 6558 2061 6e64 2027 5053 5472 6963 6b73  eX and 'PSTricks\n-000014f0: 272e 0a2a 2053 7765 6570 733a 3a20 2020  '..* Sweeps::   \n-00001500: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00001510: 2020 2044 7261 7720 7377 6565 7073 206f     Draw sweeps o\n-00001520: 6620 646f 7473 2061 6e64 2070 6f6c 796c  f dots and polyl\n-00001530: 696e 6573 2e0a 2a20 426c 6f63 6b73 3a3a  ines..* Blocks::\n-00001540: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00001550: 2020 2020 2020 4772 6f75 7020 6f74 6865        Group othe\n-00001560: 7220 6472 6177 6162 6c65 732e 0a2a 2052  r drawables..* R\n-00001570: 6570 6561 7473 3a3a 2020 2020 2020 2020  epeats::        \n-00001580: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n-00001590: 7720 7472 616e 7366 6f72 6d65 6420 636f  w transformed co\n-000015a0: 7069 6573 206f 6620 6f62 6a65 6374 732e  pies of objects.\n-000015b0: 0a2a 2050 7574 733a 3a20 2020 2020 2020  .* Puts::       \n+000000b0: 6174 7572 6461 792c 0a46 6562 7275 6172  aturday,.Februar\n+000000c0: 7920 3038 2c20 3230 3235 2c20 6120 7072  y 08, 2025, a pr\n+000000d0: 6f67 7261 6d20 7468 6174 2063 6f6e 7665  ogram that conve\n+000000e0: 7274 7320 6465 7363 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This ve\n+00000130: 7273 696f 6e20 6765 6e65 7261 7465 730a  rsion generates.\n+00000140: 2750 5354 7269 636b 7327 206f 7220 2750  'PSTricks' or 'P\n+00000150: 4746 2f54 696b 5a27 2063 6f64 6520 7375  GF/TikZ' code su\n+00000160: 6974 6162 6c65 2066 6f72 2075 7365 2077  itable for use w\n+00000170: 6974 6820 7468 6520 5465 5820 646f 6375  ith the TeX docu\n+00000180: 6d65 6e74 0a70 726f 6365 7373 696e 6720  ment.processing \n+00000190: 7379 7374 656d 2e0a 0a20 2020 2753 6b65  system...   'Ske\n+000001a0: 7463 6827 2069 7320 6672 6565 2073 6f66  tch' is free sof\n+000001b0: 7477 6172 652e 2020 596f 7520 6361 6e20  tware.  You can \n+000001c0: 7265 6469 7374 7269 6275 7465 2069 7420  redistribute it \n+000001d0: 616e 642f 6f72 206d 6f64 6966 7920 6974  and/or modify it\n+000001e0: 0a75 6e64 6572 2074 6865 2074 6572 6d73  .under the terms\n+000001f0: 206f 6620 7468 6520 474e 5520 4765 6e65   of the GNU Gene\n+00000200: 7261 6c20 5075 626c 6963 204c 6963 656e  ral Public Licen\n+00000210: 7365 2061 7320 7075 626c 6973 6865 6420  se as published \n+00000220: 6279 2074 6865 0a46 7265 6520 536f 6674  by the.Free Soft\n+00000230: 7761 7265 2046 6f75 6e64 6174 696f 6e3b  ware Foundation;\n+00000240: 2065 6974 6865 7220 7665 7273 696f 6e20   either version \n+00000250: 332c 206f 7220 2861 7420 796f 7572 206f  3, or (at your o\n+00000260: 7074 696f 6e29 2061 6e79 0a6c 6174 6572  ption) any.later\n+00000270: 2076 6572 7369 6f6e 2e0a 0a20 2020 536b   version...   Sk\n+00000280: 6574 6368 2069 7320 6469 7374 7269 6275  etch is distribu\n+00000290: 7465 6420 696e 2074 6865 2068 6f70 6520  ted in the hope \n+000002a0: 7468 6174 2069 7420 7769 6c6c 2062 6520  that it will be \n+000002b0: 7573 6566 756c 2c20 6275 7420 5749 5448  useful, but WITH\n+000002c0: 4f55 540a 414e 5920 5741 5252 414e 5459  OUT.ANY WARRANTY\n+000002d0: 3b20 7769 7468 6f75 7420 6576 656e 2074  ; without even t\n+000002e0: 6865 2069 6d70 6c69 6564 2077 6172 7261  he implied warra\n+000002f0: 6e74 7920 6f66 204d 4552 4348 414e 5441  nty of MERCHANTA\n+00000300: 4249 4c49 5459 206f 720a 4649 544e 4553  BILITY or.FITNES\n+00000310: 5320 464f 5220 4120 5041 5254 4943 554c  S FOR A PARTICUL\n+00000320: 4152 2050 5552 504f 5345 2e20 5365 6520  AR PURPOSE. See \n+00000330: 7468 6520 474e 5520 4765 6e65 7261 6c20  the GNU General \n+00000340: 5075 626c 6963 204c 6963 656e 7365 2066  Public License f\n+00000350: 6f72 0a6d 6f72 6520 6465 7461 696c 732e  or.more details.\n+00000360: 0a0a 2020 2059 6f75 2073 686f 756c 6420  ..   You should \n+00000370: 6861 7665 2072 6563 6569 7665 6420 6120  have received a \n+00000380: 636f 7079 206f 6620 7468 6520 474e 5520  copy of the GNU \n+00000390: 4765 6e65 7261 6c20 5075 626c 6963 204c  General Public L\n+000003a0: 6963 656e 7365 0a61 6c6f 6e67 2077 6974  icense.along wit\n+000003b0: 6820 2773 6b65 7463 6827 3b20 7365 6520  h 'sketch'; see \n+000003c0: 7468 6520 6669 6c65 2043 4f50 5949 4e47  the file COPYING\n+000003d0: 2e74 7874 2e20 2049 6620 6e6f 742c 2073  .txt.  If not, s\n+000003e0: 6565 0a68 7474 703a 2f2f 7777 772e 676e  ee.http://www.gn\n+000003f0: 752e 6f72 672f 636f 7079 6c65 6674 2e0a  u.org/copyleft..\n+00000400: 0a49 4e46 4f2d 4449 522d 5345 4354 494f  .INFO-DIR-SECTIO\n+00000410: 4e20 5465 580a 5354 4152 542d 494e 464f  N TeX.START-INFO\n+00000420: 2d44 4952 2d45 4e54 5259 0a2a 2053 6b65  -DIR-ENTRY.* Ske\n+00000430: 7463 683a 2028 736b 6574 6368 292e 2020  tch: (sketch).  \n+00000440: 2020 2020 2020 2020 2020 2053 696d 706c             Simpl\n+00000450: 6520 3344 2073 6b65 7463 6869 6e67 2066  e 3D sketching f\n+00000460: 6f72 2054 6558 0a45 4e44 2d49 4e46 4f2d  or TeX.END-INFO-\n+00000470: 4449 522d 454e 5452 590a 0a1f 0a46 696c  DIR-ENTRY....Fil\n+00000480: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n+00000490: 204e 6f64 653a 2054 6f70 2c20 204e 6578   Node: Top,  Nex\n+000004a0: 743a 2041 626f 7574 2073 6b65 7463 682c  t: About sketch,\n+000004b0: 2020 5072 6576 3a20 2864 6972 292c 2020    Prev: (dir),  \n+000004c0: 5570 3a20 2864 6972 290a 0a53 6b65 7463  Up: (dir)..Sketc\n+000004d0: 680a 2a2a 2a2a 2a2a 0a0a 436f 7079 7269  h.******..Copyri\n+000004e0: 6768 7420 2843 2920 3230 3035 2074 6f20  ght (C) 2005 to \n+000004f0: 3230 3132 2045 7567 656e 6520 4b2e 2052  2012 Eugene K. R\n+00000500: 6573 736c 6572 2e0a 0a20 2020 5468 6973  essler...   This\n+00000510: 206d 616e 7561 6c20 6973 2066 6f72 2027   manual is for '\n+00000520: 736b 6574 6368 272c 2076 6572 7369 6f6e  sketch', version\n+00000530: 2030 2e33 2028 6275 696c 6420 3729 2c20   0.3 (build 7), \n+00000540: 5361 7475 7264 6179 2c0a 4665 6272 7561  Saturday,.Februa\n+00000550: 7279 2030 382c 2032 3032 352c 2061 2070  ry 08, 2025, a p\n+00000560: 726f 6772 616d 2074 6861 7420 636f 6e76  rogram that conv\n+00000570: 6572 7473 2064 6573 6372 6970 7469 6f6e  erts description\n+00000580: 7320 6f66 2073 696d 706c 650a 7468 7265  s of simple.thre\n+00000590: 652d 6469 6d65 6e73 696f 6e61 6c20 7363  e-dimensional sc\n+000005a0: 656e 6573 2069 6e74 6f20 6c69 6e65 2064  enes into line d\n+000005b0: 7261 7769 6e67 732e 2020 5468 6973 2076  rawings.  This v\n+000005c0: 6572 7369 6f6e 2067 656e 6572 6174 6573  ersion generates\n+000005d0: 0a27 5053 5472 6963 6b73 2720 6f72 2027  .'PSTricks' or '\n+000005e0: 5047 462f 5469 6b5a 2720 636f 6465 2073  PGF/TikZ' code s\n+000005f0: 7569 7461 626c 6520 666f 7220 7573 6520  uitable for use \n+00000600: 7769 7468 2074 6865 2054 6558 2064 6f63  with the TeX doc\n+00000610: 756d 656e 740a 7072 6f63 6573 7369 6e67  ument.processing\n+00000620: 2073 7973 7465 6d2e 0a0a 2020 2027 536b   system...   'Sk\n+00000630: 6574 6368 2720 6973 2066 7265 6520 736f  etch' is free so\n+00000640: 6674 7761 7265 2e20 2059 6f75 2063 616e  ftware.  You can\n+00000650: 2072 6564 6973 7472 6962 7574 6520 6974   redistribute it\n+00000660: 2061 6e64 2f6f 7220 6d6f 6469 6679 2069   and/or modify i\n+00000670: 740a 756e 6465 7220 7468 6520 7465 726d  t.under the term\n+00000680: 7320 6f66 2074 6865 2047 4e55 2047 656e  s of the GNU Gen\n+00000690: 6572 616c 2050 7562 6c69 6320 4c69 6365  eral Public Lice\n+000006a0: 6e73 6520 6173 2070 7562 6c69 7368 6564  nse as published\n+000006b0: 2062 7920 7468 650a 4672 6565 2053 6f66   by the.Free Sof\n+000006c0: 7477 6172 6520 466f 756e 6461 7469 6f6e  tware Foundation\n+000006d0: 3b20 6569 7468 6572 2076 6572 7369 6f6e  ; either version\n+000006e0: 2033 2c20 6f72 2028 6174 2079 6f75 7220   3, or (at your \n+000006f0: 6f70 7469 6f6e 2920 616e 790a 6c61 7465  option) any.late\n+00000700: 7220 7665 7273 696f 6e2e 0a0a 2020 2053  r version...   S\n+00000710: 6b65 7463 6820 6973 2064 6973 7472 6962  ketch is distrib\n+00000720: 7574 6564 2069 6e20 7468 6520 686f 7065  uted in the hope\n+00000730: 2074 6861 7420 6974 2077 696c 6c20 6265   that it will be\n+00000740: 2075 7365 6675 6c2c 2062 7574 2057 4954   useful, but WIT\n+00000750: 484f 5554 0a41 4e59 2057 4152 5241 4e54  HOUT.ANY WARRANT\n+00000760: 593b 2077 6974 686f 7574 2065 7665 6e20  Y; without even \n+00000770: 7468 6520 696d 706c 6965 6420 7761 7272  the implied warr\n+00000780: 616e 7479 206f 6620 4d45 5243 4841 4e54  anty of MERCHANT\n+00000790: 4142 494c 4954 5920 6f72 0a46 4954 4e45  ABILITY or.FITNE\n+000007a0: 5353 2046 4f52 2041 2050 4152 5449 4355  SS FOR A PARTICU\n+000007b0: 4c41 5220 5055 5250 4f53 452e 2053 6565  LAR PURPOSE. See\n+000007c0: 2074 6865 2047 4e55 2047 656e 6572 616c   the GNU General\n+000007d0: 2050 7562 6c69 6320 4c69 6365 6e73 6520   Public License \n+000007e0: 666f 720a 6d6f 7265 2064 6574 6169 6c73  for.more details\n+000007f0: 2e0a 0a20 2020 596f 7520 7368 6f75 6c64  ...   You should\n+00000800: 2068 6176 6520 7265 6365 6976 6564 2061   have received a\n+00000810: 2063 6f70 7920 6f66 2074 6865 2047 4e55   copy of the GNU\n+00000820: 2047 656e 6572 616c 2050 7562 6c69 6320   General Public \n+00000830: 4c69 6365 6e73 650a 616c 6f6e 6720 7769  License.along wi\n+00000840: 7468 2027 736b 6574 6368 273b 2073 6565  th 'sketch'; see\n+00000850: 2074 6865 2066 696c 6520 434f 5059 494e   the file COPYIN\n+00000860: 472e 7478 742e 2020 4966 206e 6f74 2c20  G.txt.  If not, \n+00000870: 7365 650a 6874 7470 3a2f 2f77 7777 2e67  see.http://www.g\n+00000880: 6e75 2e6f 7267 2f63 6f70 796c 6566 742e  nu.org/copyleft.\n+00000890: 0a0a 2a20 4d65 6e75 3a0a 0a2a 2041 626f  ..* Menu:..* Abo\n+000008a0: 7574 2073 6b65 7463 683a 3a20 2020 2020  ut sketch::     \n+000008b0: 2020 2020 2020 2020 2020 2057 6879 2073             Why s\n+000008c0: 6b65 7463 6820 6578 6973 7473 2061 6e64  ketch exists and\n+000008d0: 2077 6861 7420 6974 2064 6f65 732e 0a2a   what it does..*\n+000008e0: 2049 6e74 726f 6475 6374 696f 6e20 6279   Introduction by\n+000008f0: 2065 7861 6d70 6c65 3a3a 2020 2020 204d   example::     M\n+00000900: 6f73 7420 6665 6174 7572 6573 2073 686f  ost features sho\n+00000910: 776e 2061 7320 776f 726b 696e 6720 636f  wn as working co\n+00000920: 6465 2e0a 2a20 496e 7075 7420 6c61 6e67  de..* Input lang\n+00000930: 7561 6765 3a3a 2020 2020 2020 2020 2020  uage::          \n+00000940: 2020 2020 5379 6e74 6178 2061 6e64 2073      Syntax and s\n+00000950: 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6f66 2073 796e 7461  * Index of synta\n+00000a40: 783a 3a0a 2a20 496e 6465 783a 3a0a 0a20  x::.* Index::.. \n+00000a50: 2d2d 2054 6865 2044 6574 6169 6c65 6420  -- The Detailed \n+00000a60: 4e6f 6465 204c 6973 7469 6e67 202d 2d0a  Node Listing --.\n+00000a70: 0a41 626f 7574 2073 6b65 7463 680a 0a2a  .About sketch..*\n+00000a80: 2052 6570 6f72 7469 6e67 2062 7567 733a   Reporting bugs:\n+00000a90: 3a20 2020 2020 2020 2020 2020 2020 204c  :              L\n+00000aa0: 6574 2075 7365 206b 6e6f 7720 7768 6174  et use know what\n+00000ab0: 2773 2077 726f 6e67 210a 2a20 436f 6e74  's wrong!.* Cont\n+00000ac0: 7269 6275 7469 6f6e 733a 3a20 2020 2020  ributions::     \n+00000ad0: 2020 2020 2020 2020 2020 486f 7720 796f            How yo\n+00000ae0: 7520 6361 6e20 6865 6c70 2e2e 2e2e 0a0a  u can help......\n+00000af0: 496e 7472 6f64 7563 7469 6f6e 2062 7920  Introduction by \n+00000b00: 6578 616d 706c 650a 0a2a 2048 656c 6c6f  example..* Hello\n+00000b10: 2077 6f72 6c64 3a3a 2020 2020 2020 2020   world::        \n+00000b20: 2020 2020 2020 2020 2053 696d 706c 6573           Simples\n+00000b30: 7420 706f 7373 6962 6c65 2027 736b 6574  t possible 'sket\n+00000b40: 6368 2720 7072 6f67 7261 6d2e 0a2a 2044  ch' program..* D\n+00000b50: 7261 7769 6e67 206f 7074 696f 6e73 3a3a  rawing options::\n+00000b60: 2020 2020 2020 2020 2020 2020 2043 6f6e               Con\n+00000b70: 7472 6f6c 6c69 6e67 206f 626a 6563 7420  trolling object \n+00000b80: 6170 7065 6172 616e 6365 2e0a 2a20 4472  appearance..* Dr\n+00000b90: 6177 696e 6720 6120 736f 6c69 643a 3a20  awing a solid:: \n+00000ba0: 2020 2020 2020 2020 2020 2020 4472 6177              Draw\n+00000bb0: 696e 6720 616e 206f 626a 6563 7420 7769  ing an object wi\n+00000bc0: 7468 2033 6420 6170 7065 6172 616e 6365  th 3d appearance\n+00000bd0: 2e0a 2a20 5370 6563 6961 6c20 6f62 6a65  ..* Special obje\n+00000be0: 6374 733a 3a20 2020 2020 2020 2020 2020  cts::           \n+00000bf0: 2020 4c61 7969 6e67 2054 6558 206f 7665    Laying TeX ove\n+00000c00: 722c 2069 6e2c 206f 7220 756e 6465 7220  r, in, or under \n+00000c10: 6472 6177 696e 6773 2e0a 2a20 4f62 6a65  drawings..* Obje\n+00000c20: 6374 2074 7261 6e73 666f 726d 733a 3a20  ct transforms:: \n+00000c30: 2020 2020 2020 2020 2020 526f 7461 7465            Rotate\n+00000c40: 2c20 7472 616e 736c 6174 652c 2073 6361  , translate, sca\n+00000c50: 6c65 2c20 616e 6420 6f74 6865 7273 2e0a  le, and others..\n+00000c60: 2a20 5265 7065 6174 6564 206f 626a 6563  * Repeated objec\n+00000c70: 7473 3a3a 2020 2020 2020 2020 2020 2020  ts::            \n+00000c80: 4d61 6b69 6e67 2074 7261 6e73 666f 726d  Making transform\n+00000c90: 6564 2063 6f70 6965 732e 0a2a 2053 7765  ed copies..* Swe\n+00000ca0: 7074 206f 626a 6563 7473 3a3a 2020 2020  pt objects::    \n+00000cb0: 2020 2020 2020 2020 2020 2053 7765 6570             Sweep\n+00000cc0: 696e 6720 6f62 6a65 6374 7320 696e 2073  ing objects in s\n+00000cd0: 7061 6365 2074 6f20 6d61 6b65 206e 6577  pace to make new\n+00000ce0: 2073 6861 7065 732e 0a0a 5377 6570 7420   shapes...Swept \n+00000cf0: 6f62 6a65 6374 730a 0a2a 2050 6f69 6e74  objects..* Point\n+00000d00: 2073 7765 6570 733a 3a20 2020 2020 2020   sweeps::       \n+00000d10: 2020 2020 2020 2020 2053 7765 7074 2070           Swept p\n+00000d20: 6f69 6e74 7320 6d61 6b65 206c 696e 6573  oints make lines\n+00000d30: 2061 6e64 2070 6f6c 7967 6f6e 732e 0a2a   and polygons..*\n+00000d40: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n+00000d50: 3a3a 2020 2020 2020 2020 2020 2020 2053  ::             S\n+00000d60: 7765 7074 206c 696e 6573 206d 616b 6520  wept lines make \n+00000d70: 7375 7266 6163 6573 2e0a 2a20 4e65 7374  surfaces..* Nest\n+00000d80: 6564 2073 7765 6570 733a 3a20 2020 2020  ed sweeps::     \n+00000d90: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n+00000da0: 7377 6565 7073 2061 7265 2075 7365 6675  sweeps are usefu\n+00000db0: 6c21 0a2a 2050 6f6c 7967 6f6e 2073 7765  l!.* Polygon swe\n+00000dc0: 6570 733a 3a20 2020 2020 2020 2020 2020  eps::           \n+00000dd0: 2020 2053 7765 7074 2070 6f6c 7967 6f6e     Swept polygon\n+00000de0: 7320 6d61 6b65 2073 6f6c 6964 732e 2e2e  s make solids...\n+00000df0: 0a2a 2050 6f6c 796c 696e 6520 7377 6565  .* Polyline swee\n+00000e00: 7073 2077 6974 6820 636c 6f73 7572 653a  ps with closure:\n+00000e10: 3a20 2061 6e64 2073 6f20 646f 2063 6c6f  :  and so do clo\n+00000e20: 7365 6420 706f 6c79 6c69 6e65 2073 7765  sed polyline swe\n+00000e30: 6570 732e 0a2a 2041 6666 696e 6520 6172  eps..* Affine ar\n+00000e40: 6974 686d 6574 6963 3a3a 2020 2020 2020  ithmetic::      \n+00000e50: 2020 2020 2053 6b65 7463 6820 7573 6566       Sketch usef\n+00000e60: 756c 206d 6174 6820 6578 7072 6573 7369  ul math expressi\n+00000e70: 6f6e 2e0a 2a20 4d6f 7265 2074 6f20 6c65  on..* More to le\n+00000e80: 6172 6e3a 3a20 2020 2020 2020 2020 2020  arn::           \n+00000e90: 2020 2020 4368 6563 6b20 6f75 7420 7468      Check out th\n+00000ea0: 6520 4d6f 6269 7573 2073 7472 6970 210a  e Mobius strip!.\n+00000eb0: 0a49 6e70 7574 206c 616e 6775 6167 650a  .Input language.\n+00000ec0: 0a2a 204c 616e 6775 6167 6520 6261 7369  .* Language basi\n+00000ed0: 6373 3a3a 2020 2020 2020 2020 2020 2020  cs::            \n+00000ee0: 2043 6173 652c 2073 7061 6365 2c20 636f   Case, space, co\n+00000ef0: 6d6d 656e 7473 2c20 696e 636c 7564 6520  mments, include \n+00000f00: 6669 6c65 732e 0a2a 2044 7261 7761 626c  files..* Drawabl\n+00000f10: 6573 3a3a 2020 2020 2020 2020 2020 2020  es::            \n+00000f20: 2020 2020 2020 2054 6869 6e67 7320 7468         Things th\n+00000f30: 6174 2063 616e 2062 6520 6472 6177 6e2e  at can be drawn.\n+00000f40: 0a2a 2044 6566 696e 6974 696f 6e73 3a3a  .* Definitions::\n+00000f50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00000f60: 2047 6976 696e 6720 7468 696e 6773 206e   Giving things n\n+00000f70: 616d 6573 2e0a 2a20 476c 6f62 616c 2065  ames..* Global e\n+00000f80: 6e76 6972 6f6e 6d65 6e74 3a3a 2020 2020  nvironment::    \n+00000f90: 2020 2020 2020 4166 6665 6374 2074 6865        Affect the\n+00000fa0: 2065 6e74 6972 6520 6472 6177 696e 672e   entire drawing.\n+00000fb0: 0a0a 4261 7369 6373 0a0a 2a20 4964 656e  ..Basics..* Iden\n+00000fc0: 7469 6669 6572 733a 3a20 2020 2020 2020  tifiers::       \n+00000fd0: 2020 2020 2020 2020 2020 4e61 6d65 7320            Names \n+00000fe0: 666f 7220 7468 696e 6773 2e0a 2a20 4b65  for things..* Ke\n+00000ff0: 7920 616e 6420 7265 7365 7276 6564 2077  y and reserved w\n+00001000: 6f72 6473 3a3a 2020 2020 2020 4e61 6d65  ords::      Name\n+00001010: 7320 796f 7520 7368 6f75 6c64 6e27 7420  s you shouldn't \n+00001020: 7573 652e 0a2a 204c 6974 6572 616c 733a  use..* Literals:\n+00001030: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00001040: 2020 2020 2043 6f6e 7374 616e 7473 2061       Constants a\n+00001050: 6e64 2063 6f6e 7374 7275 6374 6f72 732e  nd constructors.\n+00001060: 0a2a 2041 7269 7468 6d65 7469 633a 3a20  .* Arithmetic:: \n+00001070: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00001080: 2052 756c 6573 2066 6f72 2065 7870 7265   Rules for expre\n+00001090: 7373 696f 6e73 2e0a 2a20 4f70 7469 6f6e  ssions..* Option\n+000010a0: 733a 3a20 2020 2020 2020 2020 2020 2020  s::             \n+000010b0: 2020 2020 2020 2020 4d6f 6469 6679 696e          Modifyin\n+000010c0: 6720 6f62 6a65 6374 2061 7070 6561 7261  g object appeara\n+000010d0: 6e63 652e 0a0a 4c69 7465 7261 6c73 0a0a  nce...Literals..\n+000010e0: 2a20 5363 616c 6172 206c 6974 6572 616c  * Scalar literal\n+000010f0: 733a 3a20 2020 2020 2020 2020 2020 2020  s::             \n+00001100: 4a75 7374 2074 6865 206e 756d 6265 7273  Just the numbers\n+00001110: 2e0a 2a20 506f 696e 7420 616e 6420 7665  ..* Point and ve\n+00001120: 6374 6f72 206c 6974 6572 616c 733a 3a20  ctor literals:: \n+00001130: 2020 3364 2071 7561 6e74 6974 6965 732e    3d quantities.\n+00001140: 0a2a 2054 7261 6e73 666f 726d 206c 6974  .* Transform lit\n+00001150: 6572 616c 733a 3a20 2020 2020 2020 2020  erals::         \n+00001160: 204d 6174 7269 7820 666f 726d 2e0a 0a41   Matrix form...A\n+00001170: 7269 7468 6d65 7469 6320 6578 7072 6573  rithmetic expres\n+00001180: 7369 6f6e 730a 0a2a 2054 776f 2d6f 7065  sions..* Two-ope\n+00001190: 7261 6e64 2028 6269 6e61 7279 2920 666f  rand (binary) fo\n+000011a0: 726d 733a 3a20 2041 206f 7020 420a 2a20  rms::  A op B.* \n+000011b0: 556e 6172 7920 666f 726d 733a 3a20 2020  Unary forms::   \n+000011c0: 2020 2020 2020 2020 2020 2020 2020 6f70                op\n+000011d0: 2041 2028 616e 6420 6f74 6865 7273 290a   A (and others).\n+000011e0: 0a4f 7074 696f 6e73 0a0a 2a20 5053 5472  .Options..* PSTr\n+000011f0: 6963 6b73 206f 7074 696f 6e73 3a3a 2020  icks options::  \n+00001200: 2020 2020 2020 2020 2020 4f70 7469 6f6e            Option\n+00001210: 7320 696e 6865 7269 7465 6420 6672 6f6d  s inherited from\n+00001220: 2027 5053 5472 6963 6b73 272e 0a2a 2054   'PSTricks'..* T\n+00001230: 696b 5a2f 5047 4620 6f70 7469 6f6e 733a  ikZ/PGF options:\n+00001240: 3a20 2020 2020 2020 2020 2020 204f 7074  :            Opt\n+00001250: 696f 6e73 2069 6e68 6572 6974 6564 2066  ions inherited f\n+00001260: 726f 6d20 2754 696b 5a2f 5047 4627 2e0a  rom 'TikZ/PGF'..\n+00001270: 2a20 446f 7473 2069 6e20 5469 6b5a 2f50  * Dots in TikZ/P\n+00001280: 4746 3a3a 2020 2020 2020 2020 2020 2020  GF::            \n+00001290: 536b 6574 6368 2075 7365 7320 2754 696b  Sketch uses 'Tik\n+000012a0: 5a2f 5047 4627 2063 6972 636c 6573 2066  Z/PGF' circles f\n+000012b0: 6f72 2064 6f74 732e 0a2a 2054 696b 5a2f  or dots..* TikZ/\n+000012c0: 5047 4620 7573 6572 2d64 6566 696e 6564  PGF user-defined\n+000012d0: 2073 7479 6c65 733a 3a20 2053 7570 706f   styles::  Suppo\n+000012e0: 7274 2066 6f72 2027 5469 6b5a 2f50 4746  rt for 'TikZ/PGF\n+000012f0: 2720 6e61 6d65 642c 2075 7365 722d 6465  ' named, user-de\n+00001300: 6669 6e65 6420 7374 796c 6573 2e0a 2a20  fined styles..* \n+00001310: 5472 616e 7370 6172 656e 6379 3a3a 2020  Transparency::  \n+00001320: 2020 2020 2020 2020 2020 2020 2020 5365                Se\n+00001330: 652d 7468 726f 7567 6820 706f 6c79 676f  e-through polygo\n+00001340: 6e73 2e0a 2a20 496e 7465 726e 616c 206f  ns..* Internal o\n+00001350: 7074 696f 6e73 3a3a 2020 2020 2020 2020  ptions::        \n+00001360: 2020 2020 4f70 7469 6f6e 7320 7573 6564      Options used\n+00001370: 2062 7920 2773 6b65 7463 6827 2e0a 0a50   by 'sketch'...P\n+00001380: 6f69 6e74 206c 6973 7473 0a0a 2a20 4472  oint lists..* Dr\n+00001390: 6177 6162 6c65 733a 3a20 2020 2020 2020  awables::       \n+000013a0: 2020 2020 2020 2020 2020 2020 5468 696e              Thin\n+000013b0: 6773 2074 6861 7420 6172 6520 6472 6177  gs that are draw\n+000013c0: 6e2e 0a2a 2044 6566 696e 6974 696f 6e73  n..* Definitions\n+000013d0: 3a3a 2020 2020 2020 2020 2020 2020 2020  ::              \n+000013e0: 2020 2054 6869 6e67 7320 7769 7468 206e     Things with n\n+000013f0: 616d 6573 2e0a 0a44 7261 7761 626c 6573  ames...Drawables\n+00001400: 0a0a 2a20 446f 7473 3a3a 2020 2020 2020  ..* Dots::      \n+00001410: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00001420: 2020 4472 6177 2064 6f74 732e 0a2a 204c    Draw dots..* L\n+00001430: 696e 6573 3a3a 2020 2020 2020 2020 2020  ines::          \n+00001440: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n+00001450: 7720 706f 6c79 6c69 6e65 732e 0a2a 2043  w polylines..* C\n+00001460: 7572 7665 733a 3a20 2020 2020 2020 2020  urves::         \n+00001470: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n+00001480: 7720 6375 7276 6573 2e0a 2a20 506f 6c79  w curves..* Poly\n+00001490: 676f 6e73 3a3a 2020 2020 2020 2020 2020  gons::          \n+000014a0: 2020 2020 2020 2020 2020 4472 6177 2070            Draw p\n+000014b0: 6f6c 7967 6f6e 732e 0a2a 2053 7065 6369  olygons..* Speci\n+000014c0: 616c 733a 3a20 2020 2020 2020 2020 2020  als::           \n+000014d0: 2020 2020 2020 2020 2045 6d62 6564 2072           Embed r\n+000014e0: 6177 204c 6154 6558 2061 6e64 2027 5053  aw LaTeX and 'PS\n+000014f0: 5472 6963 6b73 272e 0a2a 2053 7765 6570  Tricks'..* Sweep\n+00001500: 733a 3a20 2020 2020 2020 2020 2020 2020  s::             \n+00001510: 2020 2020 2020 2020 2044 7261 7720 7377           Draw sw\n+00001520: 6565 7073 206f 6620 646f 7473 2061 6e64  eeps of dots and\n+00001530: 2070 6f6c 796c 696e 6573 2e0a 2a20 426c   polylines..* Bl\n+00001540: 6f63 6b73 3a3a 2020 2020 2020 2020 2020  ocks::          \n+00001550: 2020 2020 2020 2020 2020 2020 4772 6f75              Grou\n+00001560: 7020 6f74 6865 7220 6472 6177 6162 6c65  p other drawable\n+00001570: 732e 0a2a 2052 6570 6561 7473 3a3a 2020  s..* Repeats::  \n+00001580: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00001590: 2020 2044 7261 7720 7472 616e 7366 6f72     Draw transfor\n+000015a0: 6d65 6420 636f 7069 6573 206f 6620 6f62  med copies of ob\n+000015b0: 6a65 6374 732e 0a2a 2050 7574 733a 3a20  jects..* Puts:: \n 000015c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000015d0: 2044 7261 7720 6f6e 6520 6f62 6a65 6374   Draw one object\n-000015e0: 2074 7261 6e73 666f 726d 6564 2e0a 0a53   transformed...S\n-000015f0: 7765 6570 730a 0a2a 2053 7765 7074 2070  weeps..* Swept p\n-00001600: 6f69 6e74 733a 3a20 2020 2020 2020 2020  oints::         \n-00001610: 2020 2020 2020 2053 7765 7074 2070 6f69         Swept poi\n-00001620: 6e74 7320 6d61 6b65 206c 696e 6573 206f  nts make lines o\n-00001630: 7220 706f 6c79 676f 6e73 2e0a 2a20 5377  r polygons..* Sw\n-00001640: 6570 7420 6c69 6e65 733a 3a20 2020 2020  ept lines::     \n-00001650: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n-00001660: 7420 6c69 6e65 7320 6d61 6b65 206f 7065  t lines make ope\n-00001670: 6e20 6f72 2063 6c6f 7365 6420 7375 7266  n or closed surf\n-00001680: 6163 6573 2e0a 2a20 5377 6570 7420 706f  aces..* Swept po\n-00001690: 6c79 676f 6e73 3a3a 2020 2020 2020 2020  lygons::        \n-000016a0: 2020 2020 2020 5377 6570 7420 706f 6c79        Swept poly\n-000016b0: 676f 6e73 206d 616b 6520 636c 6f73 6564  gons make closed\n-000016c0: 2073 7572 6661 6365 732e 0a2a 2053 7765   surfaces..* Swe\n-000016d0: 7074 2062 6c6f 636b 733a 3a20 2020 2020  pt blocks::     \n-000016e0: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-000016f0: 2062 6c6f 636b 203d 3d20 626c 6f63 6b20   block == block \n-00001700: 6f66 2073 7765 6570 732e 0a2a 2053 7765  of sweeps..* Swe\n-00001710: 6570 2066 6163 6520 7370 6c69 7474 696e  ep face splittin\n-00001720: 673a 3a20 2020 2020 2020 2046 6978 696e  g::        Fixin\n-00001730: 6720 7761 7270 6564 2066 6163 6573 2077  g warped faces w\n-00001740: 6974 6820 7472 6961 6e67 6c65 732e 0a0a  ith triangles...\n-00001750: 4465 6669 6e69 7469 6f6e 730a 0a2a 2046  Definitions..* F\n-00001760: 6f72 6d73 206f 6620 6465 6669 6e69 7469  orms of definiti\n-00001770: 6f6e 733a 3a20 2020 2020 2020 2044 6966  ons::        Dif\n-00001780: 6665 7265 6e74 2064 6566 7320 666f 7220  ferent defs for \n-00001790: 6469 6666 6572 656e 7420 7075 7270 6f73  different purpos\n-000017a0: 6573 2e0a 2a20 466f 726d 7320 6f66 2072  es..* Forms of r\n-000017b0: 6566 6572 656e 6365 733a 3a20 2020 2020  eferences::     \n-000017c0: 2020 2020 486f 7720 7265 6665 7265 6e63      How referenc\n-000017d0: 6573 2064 656e 6f74 6520 7479 7065 732e  es denote types.\n-000017e0: 0a0a 476c 6f62 616c 2065 6e76 6972 6f6e  ..Global environ\n-000017f0: 6d65 6e74 0a0a 2a20 476c 6f62 616c 206f  ment..* Global o\n-00001800: 7074 696f 6e73 3a3a 2020 2020 2020 2020  ptions::        \n-00001810: 2020 2020 2020 4174 7472 6962 7574 6573        Attributes\n-00001820: 206f 6620 7468 6520 656e 7469 7265 2064   of the entire d\n-00001830: 7261 7769 6e67 2e0a 2a20 4361 6d65 7261  rawing..* Camera\n-00001840: 3a3a 2020 2020 2020 2020 2020 2020 2020  ::              \n-00001850: 2020 2020 2020 2020 4120 6669 6e61 6c20          A final \n-00001860: 6361 6d65 7261 2074 7261 6e73 666f 726d  camera transform\n-00001870: 6174 696f 6e20 6f66 2074 6865 2073 6365  ation of the sce\n-00001880: 6e65 2e0a 2a20 5069 6374 7572 6520 626f  ne..* Picture bo\n-00001890: 783a 3a20 2020 2020 2020 2020 2020 2020  x::             \n-000018a0: 2020 2020 5365 7474 696e 6720 7468 6520      Setting the \n-000018b0: 626f 756e 6469 6e67 2062 6f78 2061 6e64  bounding box and\n-000018c0: 2032 6420 636c 6970 7069 6e67 2e0a 2a20   2d clipping..* \n-000018d0: 4672 616d 653a 3a20 2020 2020 2020 2020  Frame::         \n-000018e0: 2020 2020 2020 2020 2020 2020 2020 4164                Ad\n-000018f0: 6469 6e67 2061 2062 6f78 2061 726f 756e  ding a box aroun\n-00001900: 6420 7468 6520 6472 6177 696e 672e 0a2a  d the drawing..*\n-00001910: 204c 616e 6775 6167 653a 3a20 2020 2020   Language::     \n-00001920: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n-00001930: 6574 7469 6e67 2074 6865 206f 7574 7075  etting the outpu\n-00001940: 7420 6c61 6e67 7561 6765 2e0a 0a42 7569  t language...Bui\n-00001950: 6c64 696e 6720 6120 6472 6177 696e 670a  lding a drawing.\n-00001960: 0a2a 204f 7665 7276 6965 773a 3a20 2020  .* Overview::   \n-00001970: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00001980: 2042 7569 6c64 696e 6720 6120 7375 6273   Building a subs\n-00001990: 7461 6e74 6961 6c20 6472 6177 696e 672e  tantial drawing.\n-000019a0: 0a2a 2041 2074 6563 686e 6963 616c 2064  .* A technical d\n-000019b0: 7261 7769 6e67 3a3a 2020 2020 2020 2020  rawing::        \n-000019c0: 2041 6e20 6578 616d 706c 6520 7769 7468   An example with\n-000019d0: 2066 696e 6520 706c 6163 656d 656e 742e   fine placement.\n-000019e0: 0a2a 2041 2068 6965 7261 7263 6869 6361  .* A hierarchica\n-000019f0: 6c20 6d6f 6465 6c3a 3a20 2020 2020 2020  l model::       \n-00001a00: 2041 6e20 6578 616d 706c 6520 7769 7468   An example with\n-00001a10: 2073 7765 6570 7320 616e 6420 7075 7473   sweeps and puts\n-00001a20: 2e0a 2a20 4361 7665 6174 733a 3a20 2020  ..* Caveats::   \n-00001a30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00001a40: 2020 5768 6572 6520 7472 6f75 626c 6520    Where trouble \n-00001a50: 6361 6e20 6f63 6375 722e 0a0a 4361 7665  can occur...Cave\n-00001a60: 6174 730a 0a2a 204c 696d 6974 7320 6f6e  ats..* Limits on\n-00001a70: 2065 7272 6f72 2064 6574 6563 7469 6f6e   error detection\n-00001a80: 3a3a 2020 2057 6861 7420 736b 6574 6368  ::   What sketch\n-00001a90: 2064 6f65 736e 2774 2064 6f2e 0a2a 2043   doesn't do..* C\n-00001aa0: 6c69 7070 696e 673a 3a20 2020 2020 2020  lipping::       \n-00001ab0: 2020 2020 2020 2020 2020 2020 204e 6f20               No \n-00001ac0: 636c 6970 7069 6e67 2061 7420 7072 6573  clipping at pres\n-00001ad0: 656e 742e 0a2a 2048 6964 6465 6e20 7375  ent..* Hidden su\n-00001ae0: 7266 6163 6520 7265 6d6f 7661 6c3a 3a20  rface removal:: \n-00001af0: 2020 2020 2049 6d70 6572 6665 6374 696f       Imperfectio\n-00001b00: 6e73 2074 6f20 6669 782e 0a0a 4869 6464  ns to fix...Hidd\n-00001b10: 656e 2073 7572 6661 6365 2072 656d 6f76  en surface remov\n-00001b20: 616c 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6c6f 636b 203d 3d20   Swept block == \n+00001700: 626c 6f63 6b20 6f66 2073 7765 6570 732e  block of sweeps.\n+00001710: 0a2a 2053 7765 6570 2066 6163 6520 7370  .* Sweep face sp\n+00001720: 6c69 7474 696e 673a 3a20 2020 2020 2020  litting::       \n+00001730: 2046 6978 696e 6720 7761 7270 6564 2066   Fixing warped f\n+00001740: 6163 6573 2077 6974 6820 7472 6961 6e67  aces with triang\n+00001750: 6c65 732e 0a0a 4465 6669 6e69 7469 6f6e  les...Definition\n+00001760: 730a 0a2a 2046 6f72 6d73 206f 6620 6465  s..* Forms of de\n+00001770: 6669 6e69 7469 6f6e 733a 3a20 2020 2020  finitions::     \n+00001780: 2020 2044 6966 6665 7265 6e74 2064 6566     Different def\n+00001790: 7320 666f 7220 6469 6666 6572 656e 7420  s for different \n+000017a0: 7075 7270 6f73 6573 2e0a 2a20 466f 726d  purposes..* Form\n+000017b0: 7320 6f66 2072 6566 6572 656e 6365 733a  s of references:\n+000017c0: 3a20 2020 2020 2020 2020 486f 7720 7265  :         How re\n+000017d0: 6665 7265 6e63 6573 2064 656e 6f74 6520  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Performance numb\n+00001b70: 6572 7320 6f6e 2064 6570 7468 2073 6f72  ers on depth sor\n+00001b80: 742e 0a2a 2042 7567 7320 616e 6420 616e  t..* Bugs and an\n+00001b90: 6f6d 616c 6965 733a 3a20 2020 2020 2020  omalies::       \n+00001ba0: 2020 2049 6d70 6572 6665 6374 696f 6e73     Imperfections\n+00001bb0: 2069 6e20 7468 6973 2069 6d70 6c65 6d65   in this impleme\n+00001bc0: 6e74 6174 696f 6e2e 0a0a 0a1f 0a46 696c  ntation......Fil\n+00001bd0: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n+00001be0: 204e 6f64 653a 2041 626f 7574 2073 6b65   Node: About ske\n+00001bf0: 7463 682c 2020 4e65 7874 3a20 496e 7472  tch,  Next: Intr\n+00001c00: 6f64 7563 7469 6f6e 2062 7920 6578 616d  oduction by exam\n+00001c10: 706c 652c 2020 5072 6576 3a20 546f 702c  ple,  Prev: Top,\n+00001c20: 2020 5570 3a20 546f 700a 0a31 2041 626f    Up: Top..1 Abo\n+00001c30: 7574 2073 6b65 7463 680a 2a2a 2a2a 2a2a  ut sketch.******\n+00001c40: 2a2a 2a2a 2a2a 2a2a 0a0a 2a20 4d65 6e75  ********..* 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It began as\n+00001d40: 2061 2077 6179 2074 6f20 6d61 6b65 0a69   a way to make.i\n+00001d50: 6c6c 7573 7472 6174 696f 6e73 2066 6f72  llustrations for\n+00001d60: 2061 2074 6578 7462 6f6f 6b20 6166 7465   a textbook afte\n+00001d70: 7220 7765 2063 6f75 6c64 2066 696e 6420  r we could find \n+00001d80: 6e6f 2073 7569 7461 626c 6520 746f 6f6c  no suitable tool\n+00001d90: 2066 6f72 0a74 6869 7320 7075 7270 6f73   for.this purpos\n+00001da0: 652e 2020 4578 6973 7469 6e67 2073 6365  e.  Existing sce\n+00001db0: 6e65 2070 726f 6365 7373 6f72 7320 656d  ne processors em\n+00001dc0: 7068 6173 697a 6564 2047 5549 7320 616e  phasized GUIs an\n+00001dd0: 642f 6f72 0a70 686f 746f 2d72 6561 6c69  d/or.photo-reali\n+00001de0: 736d 2c20 626f 7468 2075 6e2d 7573 6566  sm, both un-usef\n+00001df0: 756c 2074 6f20 7573 2e20 2057 6520 7761  ul to us.  We wa\n+00001e00: 6e74 6564 2074 6f20 7072 6f64 7563 6520  nted to produce \n+00001e10: 6669 6e65 6c79 0a77 726f 7567 6874 2c20  finely.wrought, \n+00001e20: 6d61 7468 656d 6174 6963 616c 6c79 2d62  mathematically-b\n+00001e30: 6173 6564 2069 6c6c 7573 7472 6174 696f  ased illustratio\n+00001e40: 6e73 2077 6974 6820 6e6f 2065 7874 7261  ns with no extra\n+00001e50: 6e65 6f75 7320 6465 7461 696c 2e0a 0a20  neous detail... \n+00001e60: 2020 2753 6b65 7463 6827 2061 6363 6570    'Sketch' accep\n+00001e70: 7473 2061 2074 696e 7920 7363 656e 6520  ts a tiny scene \n+00001e80: 6465 7363 7269 7074 696f 6e20 6c61 6e67  description lang\n+00001e90: 7561 6765 2061 6e64 2067 656e 6572 6174  uage and generat\n+00001ea0: 6573 0a27 5053 5472 6963 6b73 2720 6f72  es.'PSTricks' or\n+00001eb0: 2027 5469 6b5a 2f50 4746 2720 636f 6465   'TikZ/PGF' code\n+00001ec0: 2066 6f72 204c 6154 6558 2e20 2054 6865   for LaTeX.  The\n+00001ed0: 2027 736b 6574 6368 2720 6c61 6e67 7561   'sketch' langua\n+00001ee0: 6765 2069 730a 7369 6d69 6c61 7220 746f  ge is.similar to\n+00001ef0: 2027 5053 5472 6963 6b73 272c 206d 616b   'PSTricks', mak\n+00001f00: 696e 6720 6974 2065 6173 7920 746f 206c  ing it easy to l\n+00001f10: 6561 726e 2066 6f72 2063 7572 7265 6e74  earn for current\n+00001f20: 2027 5053 5472 6963 6b73 270a 7573 6572   'PSTricks'.user\n+00001f30: 732e 2020 5365 6520 7777 772e 7073 7472  s.  See www.pstr\n+00001f40: 6963 6b73 2e64 6520 666f 7220 696e 666f  icks.de for info\n+00001f50: 726d 6174 696f 6e20 6f6e 2027 5053 5472  rmation on 'PSTr\n+00001f60: 6963 6b73 272e 2020 2754 696b 5a2f 5047  icks'.  'TikZ/PG\n+00001f70: 4627 0a69 7320 7369 6d69 6c61 722e 2020  F'.is similar.  \n+00001f80: 5365 6520 6874 7470 3a2f 2f73 6f75 7263  See http://sourc\n+00001f90: 6566 6f72 6765 2e6e 6574 2f70 726f 6a65  eforge.net/proje\n+00001fa0: 6374 732f 7067 662e 2020 4f6e 6520 6361  cts/pgf.  One ca\n+00001fb0: 6e20 6561 7369 6c79 0a69 6e63 6c75 6465  n easily.include\n+00001fc0: 2061 7262 6974 7261 7279 2027 5053 5472   arbitrary 'PSTr\n+00001fd0: 6963 6b73 2720 6f72 2027 5469 6b5a 2f50  icks' or 'TikZ/P\n+00001fe0: 4746 2720 6472 6177 696e 6773 2061 6e64  GF' drawings and\n+00001ff0: 2074 6578 7420 6f76 6572 2c20 696e 2c0a   text over, in,.\n+00002000: 6f72 2075 6e64 6572 2027 736b 6574 6368  or under 'sketch\n+00002010: 2720 6472 6177 696e 6773 2c20 7072 6f76  ' drawings, prov\n+00002020: 6964 696e 6720 6163 6365 7373 2074 6f20  iding access to \n+00002030: 7468 6520 6675 6c6c 2070 6f77 6572 206f  the full power o\n+00002040: 6620 4c61 5465 580a 7465 7874 2061 6e64  f LaTeX.text and\n+00002050: 206d 6174 6865 6d61 7469 6373 2066 6f72   mathematics for\n+00002060: 6d61 7474 696e 6720 696e 2061 2074 6872  matting in a thr\n+00002070: 6565 2d64 696d 656e 7369 6f6e 616c 2073  ee-dimensional s\n+00002080: 6574 7469 6e67 2e0a 0a1f 0a46 696c 653a  etting.....File:\n+00002090: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n+000020a0: 6f64 653a 2052 6570 6f72 7469 6e67 2062  ode: Reporting b\n+000020b0: 7567 732c 2020 4e65 7874 3a20 436f 6e74  ugs,  Next: Cont\n+000020c0: 7269 6275 7469 6f6e 732c 2020 5072 6576  ributions,  Prev\n+000020d0: 3a20 4162 6f75 7420 736b 6574 6368 2c20  : About sketch, \n+000020e0: 2055 703a 2041 626f 7574 2073 6b65 7463   Up: About sketc\n+000020f0: 680a 0a31 2e31 2052 6570 6f72 7469 6e67  h..1.1 Reporting\n+00002100: 2062 7567 7320 616e 6420 7265 636f 6d6d   bugs and recomm\n+00002110: 656e 6469 6e67 2069 6d70 726f 7665 6d65  ending improveme\n+00002120: 6e74 732e 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d  nts..===========\n 00002130: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n 00002140: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n-00002150: 0a0a 5468 6520 6772 6f75 7020 6874 7470  ..The group http\n-00002160: 3a2f 2f67 726f 7570 732e 676f 6f67 6c65  ://groups.google\n-00002170: 2e63 6f6d 2f67 726f 7570 2f73 6b65 7463  .com/group/sketc\n-00002180: 682d 7573 6572 7320 6973 2074 6865 2062  h-users is the b\n-00002190: 6573 7420 706c 6163 650a 746f 2072 6570  est place.to rep\n-000021a0: 6f72 7420 6275 6773 2061 6e64 206d 616b  ort bugs and mak\n-000021b0: 6520 696d 7072 6f76 656d 656e 7473 2e20  e improvements. \n-000021c0: 2041 2073 6563 6f6e 6420 6d65 7468 6f64   A second method\n-000021d0: 2074 6861 7420 7769 6c6c 0a70 726f 6261   that will.proba\n-000021e0: 626c 7920 7072 6f64 7563 6520 6120 736c  bly produce a sl\n-000021f0: 6f77 6572 2072 6573 706f 6e73 6520 6973  ower response is\n-00002200: 2065 6d61 696c 2074 6f20 736b 6574 6368   email to sketch\n-00002210: 4066 726f 6e74 6965 726e 6574 2e6e 6574  @frontiernet.net\n-00002220: 2e0a 5765 2077 696c 6c20 7472 7920 746f  ..We will try to\n-00002230: 2072 6573 706f 6e64 2c20 6275 7420 6361   respond, but ca\n-00002240: 6e27 7420 7072 6f6d 6973 652e 2020 496e  n't promise.  In\n-00002250: 2061 6e79 2065 7665 6e74 2c20 646f 6e27   any event, don'\n-00002260: 7420 6265 0a6f 6666 656e 6465 6420 6966  t be.offended if\n-00002270: 2061 2072 6570 6c79 2069 7320 6e6f 7420   a reply is not \n-00002280: 666f 7274 6863 6f6d 696e 672e 2020 5765  forthcoming.  We\n-00002290: 2772 6520 6a75 7374 2062 7573 7920 616e  're just busy an\n-000022a0: 6420 7769 6c6c 2067 6574 2074 6f0a 796f  d will get to.yo\n-000022b0: 7572 2073 7567 6765 7374 696f 6e20 6576  ur suggestion ev\n-000022c0: 656e 7475 616c 6c79 2e0a 0a20 2020 466f  entually...   Fo\n-000022d0: 7220 6275 6773 2c20 6174 7461 6368 2061  r bugs, attach a\n-000022e0: 2027 736b 6574 6368 2720 696e 7075 7420   'sketch' input \n-000022f0: 6669 6c65 2074 6861 7420 6361 7573 6573  file that causes\n-00002300: 2074 6865 2062 6164 2062 6568 6176 696f   the bad behavio\n-00002310: 722e 0a45 6d62 6564 2063 6f6d 6d65 6e74  r..Embed comment\n-00002320: 7320 7468 6174 2065 7870 6c61 696e 2077  s that explain w\n-00002330: 6861 7420 746f 206c 6f6f 6b20 666f 7220  hat to look for \n-00002340: 696e 2074 6865 2062 6568 6176 696f 7220  in the behavior \n-00002350: 6f66 2027 736b 6574 6368 270a 6f72 2069  of 'sketch'.or i\n-00002360: 7473 206f 7574 7075 742e 0a0a 2020 2041  ts output...   A\n-00002370: 2072 6563 6f6d 6d65 6e64 6174 696f 6e20   recommendation \n-00002380: 666f 7220 696d 7072 6f76 656d 656e 7420  for improvement \n-00002390: 6672 6f6d 206f 6e65 2075 6e6b 6e6f 776e  from one unknown\n-000023a0: 2070 6572 736f 6e20 636f 756e 7473 2061   person counts a\n-000023b0: 730a 6f6e 6520 766f 7465 2e20 2057 6520  s.one vote.  We \n-000023c0: 7573 6520 6f76 6572 616c 6c20 766f 7465  use overall vote\n-000023d0: 2074 616c 6c69 6573 2074 6f20 6465 6369   tallies to deci\n-000023e0: 6465 2077 6861 7420 746f 2064 6f20 6e65  de what to do ne\n-000023f0: 7874 2061 730a 7265 736f 7572 6365 7320  xt as.resources \n-00002400: 7065 726d 6974 2e20 2057 6520 7265 7365  permit.  We rese\n-00002410: 7276 6520 7468 6520 7269 6768 7420 746f  rve the right to\n-00002420: 2061 7373 6967 6e20 616e 7920 6e75 6d62   assign any numb\n-00002430: 6572 206f 6620 766f 7465 7320 746f 0a73  er of votes to.s\n-00002440: 7567 6765 7374 696f 6e73 2066 726f 6d20  uggestions from \n-00002450: 7065 6f70 6c65 2077 686f 2068 6176 6520  people who have \n-00002460: 6265 656e 2068 656c 7066 756c 2061 6e64  been helpful and\n-00002470: 2073 7570 706f 7274 6976 6520 696e 2074   supportive in t\n-00002480: 6865 0a70 6173 742e 0a0a 1f0a 4669 6c65  he.past.....File\n-00002490: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n-000024a0: 4e6f 6465 3a20 436f 6e74 7269 6275 7469  Node: Contributi\n-000024b0: 6f6e 732c 2020 5072 6576 3a20 5265 706f  ons,  Prev: Repo\n-000024c0: 7274 696e 6720 6275 6773 2c20 2055 703a  rting bugs,  Up:\n-000024d0: 2041 626f 7574 2073 6b65 7463 680a 0a31   About sketch..1\n-000024e0: 2e32 2043 6f6e 7472 6962 7574 696f 6e73  .2 Contributions\n-000024f0: 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  .===============\n-00002500: 3d3d 0a0a 4966 2079 6f75 2069 6e74 656e  ==..If you inten\n-00002510: 6420 746f 2069 6d70 6c65 6d65 6e74 2061  d to implement a\n-00002520: 6e20 656e 6861 6e63 656d 656e 7420 6f66  n enhancement of\n-00002530: 2079 6f75 7220 6f77 6e2c 2074 6861 7427   your own, that'\n-00002540: 7320 7465 7272 6966 6963 210a 436f 6e73  s terrific!.Cons\n-00002550: 6964 6572 2063 6f6c 6c61 626f 7261 7469  ider collaborati\n-00002560: 6e67 2077 6974 6820 7573 2066 6972 7374  ng with us first\n-00002570: 2074 6f20 7365 6520 6966 2077 6527 7265   to see if we're\n-00002580: 2061 6c72 6561 6479 2077 6f72 6b69 6e67   already working\n-00002590: 206f 6e0a 796f 7572 2069 6465 6120 6f72   on.your idea or\n-000025a0: 2069 6620 7765 2063 616e 2075 7365 2079   if we can use y\n-000025b0: 6f75 7220 776f 726b 2069 6e20 7468 6520  our work in the \n-000025c0: 6f66 6669 6369 616c 2072 656c 6561 7365  official release\n-000025d0: 2e0a 0a00 085b 696d 6167 6520 7372 633d  .....[image src=\n-000025e0: 2265 7830 3030 2e70 6e67 2220 7465 7874  \"ex000.png\" text\n-000025f0: 3d22 496d 6167 6520 6578 3030 3020 6f6d  =\"Image ex000 om\n-00002600: 6974 7465 6420 696e 2074 6578 7420 7665  itted in text ve\n-00002610: 7273 696f 6e20 6f66 2074 6869 7320 646f  rsion of this do\n-00002620: 6375 6d65 6e74 2e22 0008 5d0a 0a1f 0a46  cument.\"..]....F\n-00002630: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n-00002640: 2c20 204e 6f64 653a 2049 6e74 726f 6475  ,  Node: Introdu\n-00002650: 6374 696f 6e20 6279 2065 7861 6d70 6c65  ction by example\n-00002660: 2c20 204e 6578 743a 2049 6e70 7574 206c  ,  Next: Input l\n-00002670: 616e 6775 6167 652c 2020 5072 6576 3a20  anguage,  Prev: \n-00002680: 4162 6f75 7420 736b 6574 6368 2c20 2055  About sketch,  U\n-00002690: 703a 2054 6f70 0a0a 3220 496e 7472 6f64  p: Top..2 Introd\n-000026a0: 7563 7469 6f6e 2062 7920 6578 616d 706c  uction by exampl\n-000026b0: 650a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  e.**************\n-000026c0: 2a2a 2a2a 2a2a 2a2a 2a2a 2a0a 0a54 6865  ***********..The\n-000026d0: 2027 736b 6574 6368 2720 696e 7075 7420   'sketch' input \n-000026e0: 6c61 6e67 7561 6765 2077 696c 6c20 7365  language will se\n-000026f0: 656d 2066 616d 696c 6961 7220 746f 2075  em familiar to u\n-00002700: 7365 7273 206f 6620 7468 650a 2750 5354  sers of the.'PST\n-00002710: 7269 636b 7327 2070 6163 6b61 6765 2066  ricks' package f\n-00002720: 6f72 204c 6154 6558 2e20 2054 6865 2066  or LaTeX.  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world.======\n-00002ac0: 3d3d 3d3d 3d3d 3d3d 3d0a 0a54 6865 2027  =========..The '\n-00002ad0: 736b 6574 6368 2720 7072 6f67 7261 6d20  sketch' program \n-00002ae0: 6162 6f76 6520 6973 206e 6561 726c 7920  above is nearly \n-00002af0: 7468 6520 7369 6d70 6c65 7374 206f 6e65  the simplest one\n-00002b00: 2070 6f73 7369 626c 652c 2074 6865 0a65   possible, the.e\n-00002b10: 7175 6976 616c 656e 7420 6f66 2061 2022  quivalent of a \"\n-00002b20: 6865 6c6c 6f20 776f 726c 6422 2070 726f  hello world\" pro\n-00002b30: 6772 616d 2079 6f75 206d 6967 6874 2066  gram you might f\n-00002b40: 696e 6420 6174 2074 6865 2073 7461 7274  ind at the start\n-00002b50: 206f 6620 610a 7072 6f67 7261 6d6d 696e   of a.programmin\n-00002b60: 6720 6c61 6e67 7561 6765 2074 6578 742e  g language text.\n-00002b70: 2020 4966 2069 7420 6973 2073 6176 6564    If it is saved\n-00002b80: 2069 6e20 7468 6520 6669 6c65 2027 7369   in the file 'si\n-00002b90: 6d70 6c65 2e73 6b27 2c20 7468 656e 0a74  mple.sk', then.t\n-00002ba0: 6865 2063 6f6d 6d61 6e64 0a20 2073 6b65  he command.  ske\n-00002bb0: 7463 6820 7369 6d70 6c65 2e73 6b20 2d6f  tch simple.sk -o\n-00002bc0: 2073 696d 706c 652e 7465 780a 6372 6561   simple.tex.crea\n-00002bd0: 7465 7320 6120 6669 6c65 2027 7369 6d70  tes a file 'simp\n-00002be0: 6c65 2e74 6578 2720 636f 6e74 6169 6e69  le.tex' containi\n-00002bf0: 6e67 2027 5053 5472 6963 6b73 2720 636f  ng 'PSTricks' co\n-00002c00: 6d6d 616e 6473 2074 6f20 6472 6177 2074  mmands to draw t\n-00002c10: 6865 7365 0a6f 626a 6563 7473 206f 6e20  hese.objects on \n-00002c20: 7061 7065 722e 2020 5468 6520 636f 6e74  paper.  The cont\n-00002c30: 656e 7473 206f 6620 2773 696d 706c 652e  ents of 'simple.\n-00002c40: 7465 7827 206c 6f6f 6b20 6c69 6b65 2074  tex' look like t\n-00002c50: 6869 732e 0a20 205c 6265 6769 6e7b 7073  his..  \\begin{ps\n-00002c60: 7069 6374 7572 657d 282d 312c 2d31 2928  picture}(-1,-1)(\n-00002c70: 322c 3229 0a20 205c 7073 7456 6572 627b  2,2).  \\pstVerb{\n-00002c80: 3120 7365 746c 696e 656a 6f69 6e7d 0a20  1 setlinejoin}. \n-00002c90: 205c 7073 6c69 6e65 282d 312c 2d31 2928   \\psline(-1,-1)(\n-00002ca0: 2e33 3333 2c2e 3333 3329 0a20 205c 7073  .333,.333).  \\ps\n-00002cb0: 706f 6c79 676f 6e5b 6669 6c6c 7374 796c  polygon[fillstyl\n-00002cc0: 653d 736f 6c69 642c 6669 6c6c 636f 6c6f  e=solid,fillcolo\n-00002cd0: 723d 7768 6974 655d 2830 2c30 2928 312c  r=white](0,0)(1,\n-00002ce0: 3029 2830 2c31 290a 2020 5c70 736c 696e  0)(0,1).  \\pslin\n-00002cf0: 6528 2e33 3333 2c2e 3333 3329 2832 2c32  e(.333,.333)(2,2\n-00002d00: 290a 2020 5c65 6e64 7b70 7370 6963 7475  ).  \\end{pspictu\n-00002d10: 7265 7d0a 5468 6520 6869 6464 656e 2073  re}.The hidden s\n-00002d20: 7572 6661 6365 2061 6c67 6f72 6974 686d  urface algorithm\n-00002d30: 206f 6620 2773 6b65 7463 6827 2068 6173   of 'sketch' has\n-00002d40: 2073 706c 6974 2074 6865 206c 696e 6520   split the line \n-00002d50: 696e 746f 2074 776f 0a70 6965 6365 7320  into two.pieces \n-00002d60: 616e 6420 6f72 6465 7265 6420 7468 6520  and ordered the \n-00002d70: 7468 7265 6520 7265 7375 6c74 696e 6720  three resulting \n-00002d80: 6f62 6a65 6374 7320 736f 2074 6861 7420  objects so that \n-00002d90: 7468 6520 636f 7272 6563 740a 706f 7274  the correct.port\n-00002da0: 696f 6e20 6f66 2074 6865 206c 696e 6520  ion of the line \n-00002db0: 6973 2068 6964 6465 6e2e 0a0a 2020 2049  is hidden...   I\n-00002dc0: 6620 796f 7527 7665 206e 6f74 6963 6564  f you've noticed\n-00002dd0: 2074 6861 7420 7468 6520 7072 6f6a 6563   that the projec\n-00002de0: 7469 6f6e 2077 6520 6172 6520 7573 696e  tion we are usin\n-00002df0: 6720 7365 656d 7320 6571 7569 7661 6c65  g seems equivale\n-00002e00: 6e74 0a74 6f20 6572 6173 696e 6720 7468  nt.to erasing th\n-00002e10: 6520 7a2d 636f 6f72 6469 6e61 7465 206f  e z-coordinate o\n-00002e20: 6620 7468 6520 7468 7265 652d 6469 6d65  f the three-dime\n-00002e30: 6e73 696f 6e61 6c20 696e 7075 7420 706f  nsional input po\n-00002e40: 696e 7473 2c20 7061 740a 796f 7572 7365  ints, pat.yourse\n-00002e50: 6c66 206f 6e20 7468 6520 6261 636b 2e20  lf on the back. \n-00002e60: 2059 6f75 2061 7265 2063 6f72 7265 6374   You are correct\n-00002e70: 2e20 2054 6869 7320 6973 2063 616c 6c65  .  This is calle\n-00002e80: 6420 6120 2270 6172 616c 6c65 6c0a 7072  d a \"parallel.pr\n-00002e90: 6f6a 6563 7469 6f6e 222e 2020 5468 6520  ojection\".  The \n-00002ea0: 7a2d 636f 6f72 6469 6e61 7465 2061 7869  z-coordinate axi\n-00002eb0: 7320 6973 2070 6f69 6e74 696e 6720 7374  s is pointing st\n-00002ec0: 7261 6967 6874 206f 7574 206f 6620 7468  raight out of th\n-00002ed0: 650a 7061 7065 7220 6174 2075 732c 2077  e.paper at us, w\n-00002ee0: 6869 6c65 2074 6865 2078 2d20 616e 6420  hile the x- and \n-00002ef0: 792d 6178 6573 2070 6f69 6e74 2074 6f20  y-axes point to \n-00002f00: 7468 6520 7269 6768 7420 616e 6420 7570  the right and up\n-00002f10: 2061 7320 7573 7561 6c2e 0a0a 2020 2054   as usual...   T\n-00002f20: 6865 2072 6573 756c 7469 6e67 2070 6963  he resulting pic\n-00002f30: 7475 7265 2066 696c 6520 6361 6e20 6265  ture file can be\n-00002f40: 2069 6e63 6c75 6465 6420 696e 2061 204c   included in a L\n-00002f50: 6154 6558 2064 6f63 756d 656e 7420 7769  aTeX document wi\n-00002f60: 7468 0a5c 696e 7075 747b 7369 6d70 6c65  th.\\input{simple\n-00002f70: 7d2e 2020 416c 7465 726e 6174 656c 792c  }.  Alternately,\n-00002f80: 2061 6464 696e 6720 7468 6520 636f 6d6d   adding the comm\n-00002f90: 616e 6420 6c69 6e65 206f 7074 696f 6e20  and line option \n-00002fa0: 272d 5427 2831 290a 6361 7573 6573 2074  '-T'(1).causes t\n-00002fb0: 6865 2027 7073 7069 6374 7572 6527 2074  he 'pspicture' t\n-00002fc0: 6f20 6265 2077 7261 7070 6564 2069 6e20  o be wrapped in \n-00002fd0: 6120 7368 6f72 7420 6275 7420 636f 6d70  a short but comp\n-00002fe0: 6c65 7465 2064 6f63 756d 656e 742c 0a72  lete document,.r\n-00002ff0: 6561 6479 2074 6f20 7275 6e20 7468 6f75  eady to run thou\n-00003000: 6768 204c 6154 6558 2e20 2049 6e20 6120  gh LaTeX.  In a \n-00003010: 6669 6e69 7368 6564 2c20 7479 7065 7365  finished, typese\n-00003020: 7420 646f 6375 6d65 6e74 2c20 7468 6520  t document, the \n-00003030: 7069 6374 7572 650a 6c6f 6f6b 7320 6c69  picture.looks li\n-00003040: 6b65 2074 6869 732e 2020 2854 6865 2061  ke this.  (The a\n-00003050: 7865 7320 6861 7665 2062 6565 6e20 6164  xes have been ad\n-00003060: 6465 6420 696e 206c 6967 6874 2067 7261  ded in light gra\n-00003070: 792e 290a 0a00 085b 696d 6167 6520 7372  y.)....[image sr\n-00003080: 633d 2265 7830 3230 2e70 6e67 2220 7465  c=\"ex020.png\" te\n-00003090: 7874 3d22 496d 6167 6520 6578 3032 3020  xt=\"Image ex020 \n-000030a0: 6f6d 6974 7465 6420 696e 2074 6578 7420  omitted in text \n-000030b0: 7665 7273 696f 6e20 6f66 2074 6869 7320  version of this \n-000030c0: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a49  document.\"..]..I\n-000030d0: 7420 6973 2069 6d70 6f72 7461 6e74 2074  t is important t\n-000030e0: 6f20 6b6e 6f77 2074 6861 7420 6f6e 6c79  o know that only\n-000030f0: 2074 6865 2022 6f75 7473 6964 6522 206f   the \"outside\" o\n-00003100: 6620 6120 706f 6c79 676f 6e20 6973 206e  f a polygon is n\n-00003110: 6f72 6d61 6c6c 790a 6472 6177 6e2e 2020  ormally.drawn.  \n-00003120: 5468 6520 226f 7574 7369 6465 2220 6973  The \"outside\" is\n-00003130: 2077 6865 7265 2074 6865 2076 6572 7469   where the verti\n-00003140: 6365 7320 6769 7665 6e20 696e 2074 6865  ces given in the\n-00003150: 2027 706f 6c79 676f 6e27 0a63 6f6d 6d61   'polygon'.comma\n-00003160: 6e64 2061 7070 6561 7220 696e 205f 636f  nd appear in _co\n-00003170: 756e 7465 722d 636c 6f63 6b77 6973 655f  unter-clockwise_\n-00003180: 206f 7264 6572 2e20 2054 6875 732c 2069   order.  Thus, i\n-00003190: 6620 7468 6520 636f 6d6d 616e 6420 6162  f the command ab\n-000031a0: 6f76 650a 6861 6420 6265 656e 0a20 2070  ove.had been.  p\n-000031b0: 6f6c 7967 6f6e 2830 2c31 2c30 2928 312c  olygon(0,1,0)(1,\n-000031c0: 302c 3029 2830 2c30 2c31 290a 7468 6520  0,0)(0,0,1).the \n-000031d0: 706f 6c79 676f 6e20 776f 756c 6420 6e6f  polygon would no\n-000031e0: 7420 6170 7065 6172 2069 6e20 7468 6520  t appear in the \n-000031f0: 7069 6374 7572 6520 6174 2061 6c6c 2e20  picture at all. \n-00003200: 2049 7420 776f 756c 6420 6861 7665 2062   It would have b\n-00003210: 6565 6e0a 2263 756c 6c65 6422 2066 726f  een.\"culled\" fro\n-00003220: 6d20 7468 6520 7363 656e 652e 2020 5468  m the scene.  Th\n-00003230: 6973 2063 756c 6c69 6e67 2062 6568 6176  is culling behav\n-00003240: 696f 7220 6d61 7920 7365 656d 2073 7472  ior may seem str\n-00003250: 616e 6765 2c20 6275 740a 7374 6179 2074  ange, but.stay t\n-00003260: 756e 6564 2e0a 0a20 2020 2d2d 2d2d 2d2d  uned...   ------\n-00003270: 2d2d 2d2d 2046 6f6f 746e 6f74 6573 202d  ---- Footnotes -\n-00003280: 2d2d 2d2d 2d2d 2d2d 2d0a 0a20 2020 2831  ---------..   (1\n-00003290: 2920 4f72 2066 6f72 2045 7572 6f70 6561  ) Or for Europea\n-000032a0: 6e20 7573 6572 7320 6f66 2041 3420 7369  n users of A4 si\n-000032b0: 7a65 2070 6170 6572 2c20 272d 5465 272e  ze paper, '-Te'.\n-000032c0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n-000032d0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4472  .info,  Node: Dr\n-000032e0: 6177 696e 6720 6f70 7469 6f6e 732c 2020  awing options,  \n-000032f0: 4e65 7874 3a20 4472 6177 696e 6720 6120  Next: Drawing a \n-00003300: 736f 6c69 642c 2020 5072 6576 3a20 4865  solid,  Prev: He\n-00003310: 6c6c 6f20 776f 726c 642c 2020 5570 3a20  llo world,  Up: \n-00003320: 496e 7472 6f64 7563 7469 6f6e 2062 7920  Introduction by \n-00003330: 6578 616d 706c 650a 0a32 2e32 204f 7074  example..2.2 Opt\n-00003340: 696f 6e73 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d  ions.===========\n-00003350: 0a0a 4d61 6e79 2027 5053 5472 6963 6b73  ..Many 'PSTricks\n-00003360: 2720 616e 6420 2754 696b 5a2f 5047 4627  ' and 'TikZ/PGF'\n-00003370: 206f 7074 696f 6e73 2077 6f72 6b20 6a75   options work ju\n-00003380: 7374 2066 696e 6520 696e 2027 736b 6574  st fine in 'sket\n-00003390: 6368 272e 2020 4966 0a67 656e 6572 6174  ch'.  If.generat\n-000033a0: 696e 6720 2750 5354 7269 636b 7327 2c20  ing 'PSTricks', \n-000033b0: 7468 6520 636f 6465 0a20 2070 6f6c 7967  the code.  polyg\n-000033c0: 6f6e 5b66 696c 6c63 6f6c 6f72 3d6c 6967  on[fillcolor=lig\n-000033d0: 6874 6772 6179 2c6c 696e 6577 6964 7468  htgray,linewidth\n-000033e0: 3d33 7074 5d28 302c 302c 3129 2831 2c30  =3pt](0,0,1)(1,0\n-000033f0: 2c30 2928 302c 312c 3029 0a20 206c 696e  ,0)(0,1,0).  lin\n-00003400: 655b 6c69 6e65 7374 796c 653d 646f 7474  e[linestyle=dott\n-00003410: 6564 5d28 2d31 2c2d 312c 2d31 2928 322c  ed](-1,-1,-1)(2,\n-00003420: 322c 3229 0a70 726f 6475 6365 730a 0a00  2,2).produces...\n-00003430: 085b 696d 6167 6520 7372 633d 2265 7830  .[image src=\"ex0\n-00003440: 3330 2e70 6e67 2220 7465 7874 3d22 496d  30.png\" text=\"Im\n-00003450: 6167 6520 6578 3033 3020 6f6d 6974 7465  age ex030 omitte\n-00003460: 6420 696e 2074 6578 7420 7665 7273 696f  d in text versio\n-00003470: 6e20 6f66 2074 6869 7320 646f 6375 6d65  n of this docume\n-00003480: 6e74 2e22 0008 5d0a 0a20 2020 546f 2070  nt.\"..]..   To p\n-00003490: 726f 6475 6365 2027 5469 6b5a 2f50 4746  roduce 'TikZ/PGF\n-000034a0: 272c 2074 6865 2063 6f72 7265 7370 6f6e  ', the correspon\n-000034b0: 6469 6e67 2063 6f64 6520 6973 0a20 2070  ding code is.  p\n-000034c0: 6f6c 7967 6f6e 5b66 696c 6c3d 6c69 6768  olygon[fill=ligh\n-000034d0: 7467 7261 792c 6c69 6e65 2077 6964 7468  tgray,line width\n-000034e0: 3d33 7074 5d28 302c 302c 3129 2831 2c30  =3pt](0,0,1)(1,0\n-000034f0: 2c30 2928 302c 312c 3029 0a20 206c 696e  ,0)(0,1,0).  lin\n-00003500: 655b 7374 796c 653d 646f 7474 6564 5d28  e[style=dotted](\n-00003510: 2d31 2c2d 312c 2d31 2928 322c 322c 3229  -1,-1,-1)(2,2,2)\n-00003520: 0a20 2067 6c6f 6261 6c20 7b20 6c61 6e67  .  global { lang\n-00003530: 7561 6765 2074 696b 7a20 7d0a 5468 6520  uage tikz }.The \n-00003540: 6669 6e61 6c20 2767 6c6f 6261 6c27 2069  final 'global' i\n-00003550: 6e73 7472 7563 7473 2027 736b 6574 6368  nstructs 'sketch\n-00003560: 2720 746f 2070 726f 6475 6365 2027 5469  ' to produce 'Ti\n-00003570: 6b5a 2f50 4746 2720 636f 6465 2061 730a  kZ/PGF' code as.\n-00003580: 6f75 7470 7574 2072 6174 6865 7220 7468  output rather th\n-00003590: 616e 2074 6865 2064 6566 6175 6c74 2c20  an the default, \n-000035a0: 2750 5354 7269 636b 7327 2e20 204e 6f74  'PSTricks'.  Not\n-000035b0: 6520 7468 6174 2027 706f 6c79 676f 6e27  e that 'polygon'\n-000035c0: 2066 696c 6c0a 636f 6c6f 7220 616e 6420   fill.color and \n-000035d0: 276c 696e 6527 2073 7479 6c65 206f 7074  'line' style opt\n-000035e0: 696f 6e73 2062 6f74 6820 636f 6e66 6f72  ions both confor\n-000035f0: 6d20 746f 2027 5469 6b5a 2720 7379 6e74  m to 'TikZ' synt\n-00003600: 6178 2072 756c 6573 2e20 2054 6865 0a72  ax rules.  The.r\n-00003610: 6573 756c 7469 6e67 2027 5469 6b5a 2f50  esulting 'TikZ/P\n-00003620: 4746 2720 6f75 7470 7574 2069 730a 2020  GF' output is.  \n-00003630: 5c62 6567 696e 7b74 696b 7a70 6963 7475  \\begin{tikzpictu\n-00003640: 7265 7d5b 6a6f 696e 3d72 6f75 6e64 5d0a  re}[join=round].\n-00003650: 2020 5c64 7261 775b 646f 7474 6564 5d28    \\draw[dotted](\n-00003660: 2d31 2c2d 3129 2d2d 282e 3333 332c 2e33  -1,-1)--(.333,.3\n-00003670: 3333 293b 0a20 205c 6669 6c6c 6472 6177  33);.  \\filldraw\n-00003680: 5b66 696c 6c3d 6c69 6768 7467 7261 792c  [fill=lightgray,\n-00003690: 6c69 6e65 2077 6964 7468 3d33 7074 5d28  line width=3pt](\n-000036a0: 302c 3029 2d2d 2831 2c30 292d 2d28 302c  0,0)--(1,0)--(0,\n-000036b0: 3129 2d2d 6379 636c 653b 0a20 205c 6472  1)--cycle;.  \\dr\n-000036c0: 6177 5b64 6f74 7465 645d 282e 3333 332c  aw[dotted](.333,\n-000036d0: 2e33 3333 292d 2d28 322c 3229 3b0a 2020  .333)--(2,2);.  \n-000036e0: 5c65 6e64 7b74 696b 7a70 6963 7475 7265  \\end{tikzpicture\n-000036f0: 7d0a 5468 6520 7265 6d61 696e 696e 6720  }.The remaining \n-00003700: 6578 616d 706c 6573 206f 6620 7468 6973  examples of this\n-00003710: 206d 616e 7561 6c20 6172 6520 696e 2050   manual are in P\n-00003720: 5354 7269 636b 7320 7374 796c 652e 0a0a  STricks style...\n-00003730: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n-00003740: 6e66 6f2c 2020 4e6f 6465 3a20 4472 6177  nfo,  Node: Draw\n-00003750: 696e 6720 6120 736f 6c69 642c 2020 4e65  ing a solid,  Ne\n-00003760: 7874 3a20 5370 6563 6961 6c20 6f62 6a65  xt: Special obje\n-00003770: 6374 732c 2020 5072 6576 3a20 4472 6177  cts,  Prev: Draw\n-00003780: 696e 6720 6f70 7469 6f6e 732c 2020 5570  ing options,  Up\n-00003790: 3a20 496e 7472 6f64 7563 7469 6f6e 2062  : Introduction b\n-000037a0: 7920 6578 616d 706c 650a 0a32 2e33 2044  y example..2.3 D\n-000037b0: 7261 7769 6e67 2061 2073 6f6c 6964 0a3d  rawing a solid.=\n-000037c0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n-000037d0: 3d3d 0a0a 4c65 7427 7320 7472 7920 736f  ==..Let's try so\n-000037e0: 6d65 7468 696e 6720 6d6f 7265 2065 7863  mething more exc\n-000037f0: 6974 696e 672e 2020 2753 6b65 7463 6827  iting.  'Sketch'\n-00003800: 2068 6173 206e 6f20 6e6f 7469 6f6e 206f   has no notion o\n-00003810: 6620 6120 736f 6c69 642c 0a62 7574 2070  f a solid,.but p\n-00003820: 6f6c 7967 6f6e 616c 2022 6661 6365 7322  olygonal \"faces\"\n-00003830: 2063 616e 2062 6520 7573 6564 2074 6f20   can be used to \n-00003840: 7265 7072 6573 656e 7420 7468 6520 626f  represent the bo\n-00003850: 756e 6461 7279 206f 6620 6120 736f 6c69  undary of a soli\n-00003860: 642e 0a54 6f20 7468 6520 7072 6576 696f  d..To the previo\n-00003870: 7573 2065 7861 6d70 6c65 2c20 6c65 7427  us example, let'\n-00003880: 7320 6164 6420 7468 7265 6520 6d6f 7265  s add three more\n-00003890: 2074 7269 616e 6775 6c61 7220 706f 6c79   triangular poly\n-000038a0: 676f 6e73 2074 6f0a 6d61 6b65 2074 6865  gons to.make the\n-000038b0: 2066 6163 6573 206f 6620 616e 2069 7272   faces of an irr\n-000038c0: 6567 756c 6172 2074 6574 7261 6865 6472  egular tetrahedr\n-000038d0: 6f6e 2e0a 2020 2520 7665 7274 6963 6573  on..  % vertices\n-000038e0: 206f 6620 7468 6520 7465 7472 6168 6564   of the tetrahed\n-000038f0: 726f 6e0a 2020 6465 6620 7031 2028 302c  ron.  def p1 (0,\n-00003900: 302c 3129 2064 6566 2070 3220 2831 2c30  0,1) def p2 (1,0\n-00003910: 2c30 290a 2020 6465 6620 7033 2028 302c  ,0).  def p3 (0,\n-00003920: 312c 3029 2064 6566 2070 3420 282d 2e33  1,0) def p4 (-.3\n-00003930: 2c2d 2e35 2c2d 2e38 290a 0a20 2025 2066  ,-.5,-.8)..  % f\n-00003940: 6163 6573 206f 6620 7468 6520 7465 7472  aces of the tetr\n-00003950: 6168 6564 726f 6e2e 0a20 2070 6f6c 7967  ahedron..  polyg\n-00003960: 6f6e 2870 3129 2870 3229 2870 3329 2025  on(p1)(p2)(p3) %\n-00003970: 206f 7269 6769 6e61 6c20 6672 6f6e 7420   original front \n-00003980: 706f 6c79 676f 6e0a 2020 706f 6c79 676f  polygon.  polygo\n-00003990: 6e28 7031 2928 7034 2928 7032 2920 2520  n(p1)(p4)(p2) % \n-000039a0: 626f 7474 6f6d 0a20 2070 6f6c 7967 6f6e  bottom.  polygon\n-000039b0: 2870 3129 2870 3329 2870 3429 2025 206c  (p1)(p3)(p4) % l\n-000039c0: 6566 740a 2020 706f 6c79 676f 6e28 7033  eft.  polygon(p3\n-000039d0: 2928 7032 2928 7034 2920 2520 7265 6172  )(p2)(p4) % rear\n-000039e0: 0a0a 2020 2520 6c69 6e65 2074 6f20 7069  ..  % line to pi\n-000039f0: 6572 6365 2074 6865 2074 6574 7261 6865  erce the tetrahe\n-00003a00: 6472 6f6e 0a20 206c 696e 655b 6c69 6e65  dron.  line[line\n-00003a10: 636f 6c6f 723d 7265 645d 282d 312c 2d31  color=red](-1,-1\n-00003a20: 2c2d 3129 2832 2c32 2c32 290a 5468 6973  ,-1)(2,2,2).This\n-00003a30: 2065 7861 6d70 6c65 2075 7365 7320 2264   example uses \"d\n-00003a40: 6566 696e 6974 696f 6e73 222c 2077 6869  efinitions\", whi\n-00003a50: 6368 2062 6567 696e 2077 6974 6820 2764  ch begin with 'd\n-00003a60: 6566 272e 2020 5468 6573 6520 2264 6566  ef'.  These \"def\n-00003a70: 696e 6522 0a6f 7220 6769 7665 206e 616d  ine\".or give nam\n-00003a80: 6573 2074 6f20 706f 696e 7473 2c20 7768  es to points, wh\n-00003a90: 6963 6820 6172 6520 7468 656e 2061 7661  ich are then ava\n-00003aa0: 696c 6162 6c65 2061 7320 2272 6566 6572  ilable as \"refer\n-00003ab0: 656e 6365 7322 2062 790a 656e 636c 6f73  ences\" by.enclos\n-00003ac0: 696e 6720 7468 6520 6e61 6d65 7320 696e  ing the names in\n-00003ad0: 2070 6172 656e 7468 6573 6573 2c20 652e   parentheses, e.\n-00003ae0: 672e 2028 666f 6f29 2e20 2054 6865 2070  g. (foo).  The p\n-00003af0: 6172 656e 7468 6573 6573 2064 656e 6f74  arentheses denot\n-00003b00: 650a 7468 6174 2074 6865 206e 616d 6573  e.that the names\n-00003b10: 2072 6566 6572 2074 6f20 706f 696e 7473   refer to points\n-00003b20: 3b20 7468 6579 2061 7265 2072 6571 7569  ; they are requi\n-00003b30: 7265 642e 2020 5468 6572 6520 6361 6e20  red.  There can \n-00003b40: 6265 206e 6f0a 7768 6974 6520 7370 6163  be no.white spac\n-00003b50: 6520 6265 7477 6565 6e20 7468 656d 2061  e between them a\n-00003b60: 6e64 2074 6865 206e 616d 652e 0a0a 2020  nd the name...  \n-00003b70: 2041 7320 796f 7520 6361 6e20 7365 652c   As you can see,\n-00003b80: 2063 6f6d 6d65 6e74 7320 7374 6172 7420   comments start \n-00003b90: 7769 7468 2025 2061 7320 696e 2054 6558  with % as in TeX\n-00003ba0: 2061 6e64 2065 7874 656e 6420 746f 2074   and extend to t\n-00003bb0: 6865 2065 6e64 0a6f 6620 7468 6520 6c69  he end.of the li\n-00003bc0: 6e65 2028 7468 6f75 6768 2023 2077 696c  ne (though # wil\n-00003bd0: 6c20 776f 726b 2061 7320 7765 6c6c 292e  l work as well).\n-00003be0: 2020 5768 6974 6520 7370 6163 652c 2069    White space, i\n-00003bf0: 6e63 6c75 6469 6e67 0a73 7061 6365 732c  ncluding.spaces,\n-00003c00: 2074 6162 7320 616e 6420 626c 616e 6b20   tabs and blank \n-00003c10: 6c69 6e65 732c 2068 6173 206e 6f20 6566  lines, has no ef\n-00003c20: 6665 6374 2069 6e20 7468 6520 2773 6b65  fect in the 'ske\n-00003c30: 7463 6827 206c 616e 6775 6167 652e 0a0a  tch' language...\n-00003c40: 0008 5b69 6d61 6765 2073 7263 3d22 6578  ..[image src=\"ex\n-00003c50: 3034 302e 706e 6722 2074 6578 743d 2249  040.png\" text=\"I\n-00003c60: 6d61 6765 2065 7830 3430 206f 6d69 7474  mage ex040 omitt\n-00003c70: 6564 2069 6e20 7465 7874 2076 6572 7369  ed in text versi\n-00003c80: 6f6e 206f 6620 7468 6973 2064 6f63 756d  on of this docum\n-00003c90: 656e 742e 2200 085d 0a0a 4966 2077 6520  ent.\"..]..If we \n-00003ca0: 6c6f 6f6b 2069 6e73 6964 6520 7468 6520  look inside the \n-00003cb0: 5465 5820 6669 6c65 2070 726f 6475 6365  TeX file produce\n-00003cc0: 6420 6279 2027 736b 6574 6368 272c 2074  d by 'sketch', t\n-00003cd0: 6865 7265 2077 696c 6c20 6265 206f 6e6c  here will be onl\n-00003ce0: 790a 7468 7265 6520 706f 6c79 676f 6e73  y.three polygons\n-00003cf0: 2e20 2054 6865 2066 6f75 7274 6820 6861  .  The fourth ha\n-00003d00: 7320 6265 656e 2063 756c 6c65 6420 6265  s been culled be\n-00003d10: 6361 7573 6520 6974 2069 7320 6120 2262  cause it is a \"b\n-00003d20: 6163 6b20 6661 6365 220a 6f66 2074 6865  ack face\".of the\n-00003d30: 2074 6574 7261 6865 6472 6f6e 2c20 696e   tetrahedron, in\n-00003d40: 7669 7369 626c 6520 746f 206f 7572 2076  visible to our v\n-00003d50: 6965 772e 2020 4974 2069 7320 756e 6e65  iew.  It is unne\n-00003d60: 6365 7373 6172 792c 2061 6e64 2073 6f20  cessary, and so \n-00003d70: 6974 0a69 7320 7265 6d6f 7665 642e 0a0a  it.is removed...\n-00003d80: 2020 2049 6e20 736f 6d65 2064 7261 7769     In some drawi\n-00003d90: 6e67 732c 2070 6f6c 7967 6f6e 7320 6163  ngs, polygons ac\n-00003da0: 7420 6173 207a 6572 6f2d 7468 6963 6b6e  t as zero-thickn\n-00003db0: 6573 7320 736f 6c69 6420 7375 7266 6163  ess solid surfac\n-00003dc0: 6573 2077 6974 680a 626f 7468 2073 6964  es with.both sid\n-00003dd0: 6573 2076 6973 6962 6c65 2072 6174 6865  es visible rathe\n-00003de0: 7220 7468 616e 2061 7320 7468 6520 6661  r than as the fa\n-00003df0: 6365 7320 6f66 2073 6f6c 6964 206f 626a  ces of solid obj\n-00003e00: 6563 7473 2c20 7768 6572 6520 6261 636b  ects, where back\n-00003e10: 0a66 6163 6573 2063 616e 2062 6520 6375  .faces can be cu\n-00003e20: 6c6c 6564 2e20 2046 6f72 207a 6572 6f2d  lled.  For zero-\n-00003e30: 7468 6963 6b6e 6573 7320 736f 6c69 6473  thickness solids\n-00003e40: 2c20 6375 6c6c 696e 6720 6973 2061 2070  , culling is a p\n-00003e50: 726f 626c 656d 2e0a 4f6e 6520 736f 6c75  roblem..One solu\n-00003e60: 7469 6f6e 2069 7320 746f 2075 7365 2061  tion is to use a\n-00003e70: 2070 6169 7220 6f66 2027 736b 6574 6368   pair of 'sketch\n-00003e80: 2720 706f 6c79 676f 6e73 2066 6f72 2065  ' polygons for e\n-00003e90: 6163 680a 7a65 726f 2d74 6869 636b 6e65  ach.zero-thickne\n-00003ea0: 7373 2066 6163 652c 2069 6465 6e74 6963  ss face, identic\n-00003eb0: 616c 2065 7863 6570 7420 7769 7468 206f  al except with o\n-00003ec0: 7070 6f73 6974 6520 7665 7274 6578 206f  pposite vertex o\n-00003ed0: 7264 6572 732e 2020 5468 6973 0a69 7320  rders.  This.is \n-00003ee0: 756e 7769 656c 6479 2061 6e64 2065 7870  unwieldy and exp\n-00003ef0: 656e 7369 7665 2e20 2041 2062 6574 7465  ensive.  A bette\n-00003f00: 7220 7761 7920 6973 2074 6f20 7365 7420  r way is to set \n-00003f10: 7468 6520 2773 6b65 7463 6827 2069 6e74  the 'sketch' int\n-00003f20: 6572 6e61 6c0a 6f70 7469 6f6e 2027 6375  ernal.option 'cu\n-00003f30: 6c6c 2720 746f 2027 6661 6c73 6527 2069  ll' to 'false' i\n-00003f40: 6e20 7468 6520 7573 7561 6c20 2750 5354  n the usual 'PST\n-00003f50: 7269 636b 7327 206d 616e 6e65 722e 0a20  ricks' manner.. \n-00003f60: 2070 6f6c 7967 6f6e 5b63 756c 6c3d 6661   polygon[cull=fa\n-00003f70: 6c73 655d 2870 3129 2870 3229 2870 3329  lse](p1)(p2)(p3)\n-00003f80: 0a54 6865 2066 6f6c 6c6f 7769 6e67 2073  .The following s\n-00003f90: 686f 7773 2074 6865 2073 616d 6520 6865  hows the same he\n-00003fa0: 6c69 7820 7368 6170 6520 6472 6177 6e20  lix shape drawn \n-00003fb0: 6669 7273 7420 7769 7468 2063 756c 6c3d  first with cull=\n-00003fc0: 7472 7565 2028 7468 650a 6465 6661 756c  true (the.defaul\n-00003fd0: 7429 2061 6e64 2074 6865 6e20 6375 6c6c  t) and then cull\n-00003fe0: 3d66 616c 7365 2e0a 0a00 085b 696d 6167  =false.....[imag\n-00003ff0: 6520 7372 633d 2265 7830 3435 2e70 6e67  e src=\"ex045.png\n-00004000: 2220 7465 7874 3d22 496d 6167 6520 6578  \" text=\"Image ex\n-00004010: 3034 3520 6f6d 6974 7465 6420 696e 2074  045 omitted in t\n-00004020: 6578 7420 7665 7273 696f 6e20 6f66 2074  ext version of t\n-00004030: 6869 7320 646f 6375 6d65 6e74 2e22 0008  his document.\"..\n-00004040: 5d0a 0a57 6527 6c6c 2073 6f6f 6e20 7365  ]..We'll soon se\n-00004050: 6520 686f 7720 746f 2070 726f 6475 6365  e how to produce\n-00004060: 2074 6865 7365 2068 656c 6978 6573 2077   these helixes w\n-00004070: 6974 6820 6120 6665 7720 6c69 6e65 7320  ith a few lines \n-00004080: 6f66 2027 736b 6574 6368 270a 6c61 6e67  of 'sketch'.lang\n-00004090: 7561 6765 2063 6f64 652e 0a0a 2020 2049  uage code...   I\n-000040a0: 7420 6d61 7920 6265 2074 656d 7074 696e  t may be temptin\n-000040b0: 6720 746f 2074 7572 6e20 6375 6c6c 696e  g to turn cullin\n-000040c0: 6720 6f66 6620 6772 6174 7569 746f 7573  g off gratuitous\n-000040d0: 6c79 2073 6f20 7468 6174 2076 6572 7465  ly so that verte\n-000040e0: 780a 6f72 6465 7220 6361 6e20 6265 2069  x.order can be i\n-000040f0: 676e 6f72 6564 2e20 2054 6869 7320 6973  gnored.  This is\n-00004100: 206e 6f74 2061 2067 6f6f 6420 6964 6561   not a good idea\n-00004110: 2062 6563 6175 7365 206f 7574 7075 7420   because output \n-00004120: 6669 6c65 2073 697a 650a 616e 6420 5465  file size.and Te\n-00004130: 5820 616e 6420 506f 7374 7363 7269 7074  X and Postscript\n-00004140: 2070 726f 6365 7373 696e 6720 7469 6d65   processing time\n-00004150: 2062 6f74 6820 6465 7065 6e64 206f 6e20   both depend on \n-00004160: 7468 6520 6e75 6d62 6572 206f 660a 6f75  the number of.ou\n-00004170: 7470 7574 2070 6f6c 7967 6f6e 732e 2020  tput polygons.  \n-00004180: 4375 6c6c 696e 6720 7573 7561 6c6c 7920  Culling usually \n-00004190: 696d 7072 6f76 6573 2070 6572 666f 726d  improves perform\n-000041a0: 616e 6365 2062 7920 6120 6661 6374 6f72  ance by a factor\n-000041b0: 206f 660a 7477 6f2e 2020 4f6e 2074 6865   of.two.  On the\n-000041c0: 206f 7468 6572 2068 616e 642c 2067 6c6f   other hand, glo\n-000041d0: 6261 6c6c 7920 7365 7474 696e 6720 2763  bally setting 'c\n-000041e0: 756c 6c3d 6661 6c73 6527 2069 7320 7265  ull=false' is re\n-000041f0: 6173 6f6e 6162 6c65 0a77 6869 6c65 2064  asonable.while d\n-00004200: 6562 7567 6769 6e67 2e20 2053 6565 202a  ebugging.  See *\n-00004210: 6e6f 7465 2047 6c6f 6261 6c20 6f70 7469  note Global opti\n-00004220: 6f6e 733a 3a20 616e 6420 2a6e 6f74 6520  ons:: and *note \n-00004230: 4c69 6d69 7473 206f 6e20 6572 726f 720a  Limits on error.\n-00004240: 6465 7465 6374 696f 6e3a 3a2e 0a0a 1f0a  detection::.....\n-00004250: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n-00004260: 6f2c 2020 4e6f 6465 3a20 5370 6563 6961  o,  Node: Specia\n-00004270: 6c20 6f62 6a65 6374 732c 2020 4e65 7874  l objects,  Next\n-00004280: 3a20 4f62 6a65 6374 2074 7261 6e73 666f  : Object transfo\n-00004290: 726d 732c 2020 5072 6576 3a20 4472 6177  rms,  Prev: Draw\n-000042a0: 696e 6720 6120 736f 6c69 642c 2020 5570  ing a solid,  Up\n-000042b0: 3a20 496e 7472 6f64 7563 7469 6f6e 2062  : Introduction b\n-000042c0: 7920 6578 616d 706c 650a 0a32 2e34 2053  y example..2.4 S\n-000042d0: 7065 6369 616c 206f 626a 6563 7473 0a3d  pecial objects.=\n-000042e0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n-000042f0: 3d3d 0a0a 5765 2063 616e 2061 6464 206c  ==..We can add l\n-00004300: 6162 656c 7320 746f 2061 2064 7261 7769  abels to a drawi\n-00004310: 6e67 2062 7920 7573 696e 6720 7370 6563  ng by using spec\n-00004320: 6961 6c20 6f62 6a65 6374 732c 2077 6869  ial objects, whi\n-00004330: 6368 2070 726f 7669 6465 2061 0a77 6179  ch provide a.way\n-00004340: 2074 6f20 656d 6265 6420 7261 7720 4c61   to embed raw La\n-00004350: 5465 5820 616e 6420 2750 5354 7269 636b  TeX and 'PSTrick\n-00004360: 7327 2063 6f64 652e 2020 4164 6469 6e67  s' code.  Adding\n-00004370: 2074 6869 7320 746f 2074 6865 0a74 6574   this to the.tet\n-00004380: 7261 6865 6472 6f6e 2064 6f65 7320 7468  rahedron does th\n-00004390: 6520 7472 6963 6b2e 0a20 2073 7065 6369  e trick..  speci\n-000043a0: 616c 207c 5c66 6f6f 746e 6f74 6573 697a  al |\\footnotesiz\n-000043b0: 650a 2020 2020 2020 2020 2020 205c 7570  e.           \\up\n-000043c0: 7574 7b32 7074 7d5b 7572 5d23 317b 2450  ut{2pt}[ur]#1{$P\n-000043d0: 3124 7d0a 2020 2020 2020 2020 2020 205c  1$}.           \\\n-000043e0: 7570 7574 5b72 5d23 327b 2450 3224 7d0a  uput[r]#2{$P2$}.\n-000043f0: 2020 2020 2020 2020 2020 205c 7570 7574             \\uput\n-00004400: 5b75 5d23 337b 2450 3324 7d0a 2020 2020  [u]#3{$P3$}.    \n-00004410: 2020 2020 2020 205c 7570 7574 5b64 5d23         \\uput[d]#\n-00004420: 347b 2450 3424 7d7c 0a20 2020 2028 7031  4{$P4$}|.    (p1\n-00004430: 2928 7032 2928 7033 2928 7034 290a 4865  )(p2)(p3)(p4).He\n-00004440: 7265 2069 7320 7468 6520 7265 7375 6c74  re is the result\n-00004450: 2e0a 0a00 085b 696d 6167 6520 7372 633d  .....[image src=\n-00004460: 2265 7830 3432 2e70 6e67 2220 7465 7874  \"ex042.png\" text\n-00004470: 3d22 496d 6167 6520 6578 3034 3220 6f6d  =\"Image ex042 om\n-00004480: 6974 7465 6420 696e 2074 6578 7420 7665  itted in text ve\n-00004490: 7273 696f 6e20 6f66 2074 6869 7320 646f  rsion of this do\n-000044a0: 6375 6d65 6e74 2e22 0008 5d0a 0a20 2020  cument.\"..]..   \n-000044b0: 5468 6572 6520 6172 6520 7365 7665 7261  There are severa\n-000044c0: 6c20 6465 7461 696c 7320 746f 206e 6f74  l details to not\n-000044d0: 6520 6865 7265 2e20 2046 6972 7374 2c20  e here.  First, \n-000044e0: 7468 6520 7175 6f74 696e 670a 636f 6e76  the quoting.conv\n-000044f0: 656e 7469 6f6e 2066 6f72 2074 6865 2072  ention for the r\n-00004500: 6177 2063 6f64 6520 6973 2073 696d 696c  aw code is simil\n-00004510: 6172 2074 6f20 7468 6520 4c61 5465 5820  ar to the LaTeX \n-00004520: 5c76 6572 6220 636f 6d6d 616e 642e 2020  \\verb command.  \n-00004530: 5468 650a 6669 7273 7420 6e6f 6e2d 7768  The.first non-wh\n-00004540: 6974 6520 7370 6163 6520 6368 6172 6163  ite space charac\n-00004550: 7465 7220 666f 6c6c 6f77 696e 6720 7370  ter following sp\n-00004560: 6563 6961 6c20 6973 2075 6e64 6572 7374  ecial is underst\n-00004570: 6f6f 6420 746f 2062 650a 7468 6520 7175  ood to be.the qu\n-00004580: 6f74 6520 6368 6172 6163 7465 722c 2069  ote character, i\n-00004590: 6e20 7468 6973 2063 6173 6520 277c 272e  n this case '|'.\n-000045a0: 2020 5468 6520 7261 7720 7465 7874 2063    The raw text c\n-000045b0: 6f6e 7469 6e75 6573 2075 6e74 696c 0a74  ontinues until.t\n-000045c0: 6869 7320 6368 6172 6163 7465 7220 7265  his character re\n-000045d0: 6375 7273 2e0a 0a20 2020 5365 636f 6e64  curs...   Second\n-000045e0: 2c20 7468 6520 6172 6775 6d65 6e74 2072  , the argument r\n-000045f0: 6566 6572 656e 6365 7320 2331 2c20 2332  eferences #1, #2\n-00004600: 2c20 2333 2c20 616e 6420 2334 2072 6566  , #3, and #4 ref\n-00004610: 6572 2074 6f20 706f 696e 742c 0a76 6563  er to point,.vec\n-00004620: 746f 722c 206f 7220 7363 616c 6172 2076  tor, or scalar v\n-00004630: 616c 7565 7320 696e 2074 6865 206c 6973  alues in the lis\n-00004640: 7420 7468 6174 2066 6f6c 6c6f 772e 2020  t that follow.  \n-00004650: 5468 6973 2069 7320 7369 6d69 6c61 7220  This is similar \n-00004660: 746f 0a54 6558 206d 6163 726f 2073 796e  to.TeX macro syn\n-00004670: 7461 782e 2020 5468 6520 7472 616e 7366  tax.  The transf\n-00004680: 6f72 6d65 6420 616e 6420 7477 6f2d 6469  ormed and two-di\n-00004690: 6d65 6e73 696f 6e61 6c20 7072 6f6a 6563  mensional projec\n-000046a0: 7469 6f6e 7320 6f66 0a74 6865 7365 2074  tions of.these t\n-000046b0: 6872 6565 2d64 696d 656e 7369 6f6e 616c  hree-dimensional\n-000046c0: 2070 6f69 6e74 7320 6172 6520 7375 6273   points are subs\n-000046d0: 7469 7475 7465 6420 696e 2074 6865 2066  tituted in the f\n-000046e0: 696e 616c 206f 7574 7075 742e 2020 416e  inal output.  An\n-000046f0: 0a61 7267 756d 656e 7420 7265 6665 7265  .argument refere\n-00004700: 6e63 6520 6f66 2074 6865 2066 6f72 6d20  nce of the form \n-00004710: 2331 2d32 2069 7320 7265 706c 6163 6564  #1-2 is replaced\n-00004720: 2077 6974 6820 7468 6520 616e 676c 6520   with the angle \n-00004730: 696e 0a64 6567 7265 6573 206f 6620 7468  in.degrees of th\n-00004740: 6520 7477 6f2d 6469 6d65 6e73 696f 6e61  e two-dimensiona\n-00004750: 6c20 7665 6374 6f72 2074 6861 7420 636f  l vector that co\n-00004760: 6e6e 6563 7473 2074 6865 2070 726f 6a65  nnects the proje\n-00004770: 6374 696f 6e73 206f 660a 7468 6520 7477  ctions of.the tw\n-00004780: 6f20 7265 7370 6563 7469 7665 2061 7267  o respective arg\n-00004790: 756d 656e 7420 706f 696e 7473 2c20 6865  ument points, he\n-000047a0: 7265 2023 3120 616e 6420 2332 2e20 2054  re #1 and #2.  T\n-000047b0: 6865 2073 7562 7374 6974 7574 6564 0a61  he substituted.a\n-000047c0: 6e67 6c65 2069 7320 656e 636c 6f73 6564  ngle is enclosed\n-000047d0: 2069 6e20 6375 726c 7920 6272 6163 6573   in curly braces\n-000047e0: 2027 7b20 7d27 2e20 2057 6865 6e20 2754   '{ }'.  When 'T\n-000047f0: 696b 5a2f 5047 4627 206f 7574 7075 7420  ikZ/PGF' output \n-00004800: 6973 0a62 6569 6e67 2067 656e 6572 6174  is.being generat\n-00004810: 6564 2c20 7468 6520 616e 676c 6520 6973  ed, the angle is\n-00004820: 2072 6f75 6e64 6564 2074 6f20 7468 6520   rounded to the \n-00004830: 6e65 6172 6573 7420 6465 6772 6565 2062  nearest degree b\n-00004840: 6563 6175 7365 0a6e 6f6e 2d69 6e74 6567  ecause.non-integ\n-00004850: 6572 2061 6e67 6c65 7320 6172 6520 6e6f  er angles are no\n-00004860: 7420 616c 6c6f 7765 6420 6279 2027 5469  t allowed by 'Ti\n-00004870: 6b5a 2f50 4746 2720 7072 696d 6974 6976  kZ/PGF' primitiv\n-00004880: 6573 2e0a 0a20 2020 4173 206f 6620 5665  es...   As of Ve\n-00004890: 7273 696f 6e20 302e 3320 6f66 2027 736b  rsion 0.3 of 'sk\n-000048a0: 6574 6368 272c 2073 7065 6369 616c 2061  etch', special a\n-000048b0: 7267 756d 656e 7473 206d 6179 2062 6520  rguments may be \n-000048c0: 7363 616c 6172 7320 6f72 0a76 6563 746f  scalars or.vecto\n-000048d0: 7273 2069 6e20 6164 6469 7469 6f6e 2074  rs in addition t\n-000048e0: 6f20 706f 696e 7473 2e20 2052 6566 6572  o points.  Refer\n-000048f0: 656e 6365 7320 746f 2073 6361 6c61 7220  ences to scalar \n-00004900: 6172 6775 6d65 6e74 7320 6172 650a 6d65  arguments are.me\n-00004910: 7265 6c79 2072 6570 6c61 6365 6420 7769  rely replaced wi\n-00004920: 7468 2061 206e 756d 6265 7220 666f 726d  th a number form\n-00004930: 6174 7465 6420 6a75 7374 2061 7320 616e  atted just as an\n-00004940: 7920 706f 696e 7420 636f 6f72 6469 6e61  y point coordina\n-00004950: 7465 2e0a 5265 6665 7265 6e63 6573 2074  te..References t\n-00004960: 6f20 7665 6374 6f72 7320 6265 636f 6d65  o vectors become\n-00004970: 2074 776f 2d64 696d 656e 7369 6f6e 616c   two-dimensional\n-00004980: 2070 6f69 6e74 732e 2020 5468 6520 7469   points.  The ti\n-00004990: 636b 206f 7065 7261 746f 720a 7468 6174  ck operator.that\n-000049a0: 2073 656c 6563 7473 2069 6e64 6976 6964   selects individ\n-000049b0: 7561 6c20 636f 6d70 6f6e 656e 7473 206f  ual components o\n-000049c0: 6620 706f 696e 7473 2061 6e64 2076 6563  f points and vec\n-000049d0: 746f 7273 2065 6c73 6577 6865 7265 2069  tors elsewhere i\n-000049e0: 6e0a 2773 6b65 7463 6827 2028 7365 6520  n.'sketch' (see \n-000049f0: 666f 7220 6578 616d 706c 6520 2a6e 6f74  for example *not\n-00004a00: 6520 4166 6669 6e65 2061 7269 7468 6d65  e Affine arithme\n-00004a10: 7469 633a 3a29 2063 616e 2061 6c73 6f20  tic::) can also \n-00004a20: 6265 2061 7070 6c69 6564 0a74 6f20 706f  be applied.to po\n-00004a30: 696e 7420 616e 6420 7665 6374 6f72 2061  int and vector a\n-00004a40: 7267 756d 656e 7420 7265 6665 7265 6e63  rgument referenc\n-00004a50: 6573 2e20 2041 6c6c 2074 6872 6565 2064  es.  All three d\n-00004a60: 696d 656e 7369 6f6e 7320 6f66 2061 0a74  imensions of a.t\n-00004a70: 7261 6e73 666f 726d 6564 2070 6f69 6e74  ransformed point\n-00004a80: 206f 7220 7665 6374 6f72 2063 616e 2061   or vector can a\n-00004a90: 6c73 6f20 6265 2073 7562 7374 6974 7565  lso be substitue\n-00004aa0: 6420 7769 7468 2027 2733 272e 2020 5365  d with ''3'.  Se\n-00004ab0: 6520 2a6e 6f74 650a 5370 6563 6961 6c73  e *note.Specials\n-00004ac0: 3a3a 2066 6f72 2064 6574 6169 6c73 2e0a  :: for details..\n-00004ad0: 0a20 2020 4279 2064 6566 6175 6c74 2c20  .   By default, \n-00004ae0: 2773 7065 6369 616c 2720 6f62 6a65 6374  'special' object\n-00004af0: 7320 6172 6520 7072 696e 7465 6420 6c61  s are printed la\n-00004b00: 7374 2c20 6f76 6572 6c61 7969 6e67 2061  st, overlaying a\n-00004b10: 6c6c 206f 7468 6572 0a6f 626a 6563 7473  ll other.objects\n-00004b20: 2069 6e20 7468 6520 7363 656e 652e 2020   in the scene.  \n-00004b30: 4966 2079 6f75 2073 7065 6369 6679 2074  If you specify t\n-00004b40: 6865 2069 6e74 6572 6e61 6c20 6f70 7469  he internal opti\n-00004b50: 6f6e 2027 6c61 793d 696e 272c 2074 6865  on 'lay=in', the\n-00004b60: 0a68 6964 6465 6e20 7375 7266 6163 6520  .hidden surface \n-00004b70: 616c 676f 7269 7468 6d20 636f 6e73 6964  algorithm consid\n-00004b80: 6572 7320 7468 6520 656e 7469 7265 2073  ers the entire s\n-00004b90: 7065 6369 616c 206f 626a 6563 7420 746f  pecial object to\n-00004ba0: 2062 6520 7468 650a 6669 7273 7420 706f   be the.first po\n-00004bb0: 696e 7420 2823 3129 2069 6e20 7468 6520  int (#1) in the \n-00004bc0: 6172 6775 6d65 6e74 206c 6973 742e 2020  argument list.  \n-00004bd0: 4966 2074 6861 7420 706f 696e 7420 6973  If that point is\n-00004be0: 2062 6568 696e 6420 286f 660a 736d 616c   behind (of.smal\n-00004bf0: 6c65 7220 7a2d 636f 6d70 6f6e 656e 7420  ler z-component \n-00004c00: 7468 616e 2920 616e 7920 6472 6177 6162  than) any drawab\n-00004c10: 6c65 2c20 7468 656e 2074 6865 2065 6e74  le, then the ent\n-00004c20: 6972 6520 7370 6563 6961 6c20 6f62 6a65  ire special obje\n-00004c30: 6374 0a69 7320 6472 6177 6e20 6265 666f  ct.is drawn befo\n-00004c40: 7265 2074 6861 7420 6472 6177 6162 6c65  re that drawable\n-00004c50: 2c20 736f 2074 6865 2064 7261 7761 626c  , so the drawabl\n-00004c60: 6520 6f62 7363 7572 6573 2070 6172 7473  e obscures parts\n-00004c70: 206f 6620 7468 650a 7370 6563 6961 6c20   of the.special \n-00004c80: 6f62 6a65 6374 2074 6861 7420 6f76 6572  object that over\n-00004c90: 6c61 7073 2069 742e 2020 496e 206f 7572  laps it.  In our\n-00004ca0: 2065 7861 6d70 6c65 2c20 7031 2069 7320   example, p1 is \n-00004cb0: 7468 6520 6672 6f6e 742d 6d6f 7374 0a70  the front-most.p\n-00004cc0: 6f69 6e74 2069 6e20 7468 6520 7363 656e  oint in the scen\n-00004cd0: 6520 2868 6173 2074 6865 206c 6172 6765  e (has the large\n-00004ce0: 7374 207a 2d63 6f6d 706f 6e65 6e74 292c  st z-component),\n-00004cf0: 2073 6f20 6164 6469 6e67 2027 6c61 793d   so adding 'lay=\n-00004d00: 696e 2720 6861 730a 6e6f 2065 6666 6563  in' has.no effec\n-00004d10: 742e 0a0a 2020 2057 6974 6820 6f70 7469  t...   With opti\n-00004d20: 6f6e 2027 6c61 793d 756e 6465 7227 2c20  on 'lay=under', \n-00004d30: 6120 7370 6563 6961 6c20 6973 2064 7261  a special is dra\n-00004d40: 776e 205f 6265 666f 7265 5f2c 2068 656e  wn _before_, hen\n-00004d50: 6365 2061 7070 6561 7273 0a5f 756e 6465  ce appears._unde\n-00004d60: 725f 2061 6e79 206f 6620 7468 6520 6f62  r_ any of the ob\n-00004d70: 6a65 6374 7320 6861 6e64 6c65 6420 6279  jects handled by\n-00004d80: 2074 6865 2068 6964 6465 6e20 7375 7266   the hidden surf\n-00004d90: 6163 6520 616c 676f 7269 7468 6d2e 0a54  ace algorithm..T\n-00004da0: 6869 7320 6973 2068 6f77 2074 6865 206c  his is how the l\n-00004db0: 6967 6874 2067 7261 7920 6178 6573 2077  ight gray axes w\n-00004dc0: 6572 6520 6164 6465 6420 746f 2074 6865  ere added to the\n-00004dd0: 2022 6865 6c6c 6f20 776f 726c 6422 2065   \"hello world\" e\n-00004de0: 7861 6d70 6c65 0a2a 6e6f 7465 2048 656c  xample.*note Hel\n-00004df0: 6c6f 2077 6f72 6c64 3a3a 2e0a 0a20 2020  lo world::...   \n-00004e00: 5370 6563 6961 6c20 6f62 6a65 6374 7320  Special objects \n-00004e10: 6172 6520 706f 7765 7266 756c 2c20 7769  are powerful, wi\n-00004e20: 7468 206d 616e 7920 706f 7373 6962 6c65  th many possible\n-00004e30: 2075 7365 732e 0a0a 1f0a 4669 6c65 3a20   uses.....File: \n-00004e40: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n-00004e50: 6465 3a20 4f62 6a65 6374 2074 7261 6e73  de: Object trans\n-00004e60: 666f 726d 732c 2020 4e65 7874 3a20 5265  forms,  Next: Re\n-00004e70: 7065 6174 6564 206f 626a 6563 7473 2c20  peated objects, \n-00004e80: 2050 7265 763a 2053 7065 6369 616c 206f   Prev: Special o\n-00004e90: 626a 6563 7473 2c20 2055 703a 2049 6e74  bjects,  Up: Int\n-00004ea0: 726f 6475 6374 696f 6e20 6279 2065 7861  roduction by exa\n-00004eb0: 6d70 6c65 0a0a 322e 3520 5472 616e 7366  mple..2.5 Transf\n-00004ec0: 6f72 6d73 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d  orms.===========\n-00004ed0: 3d3d 3d0a 0a4e 6f77 206c 6574 2773 2061  ===..Now let's a\n-00004ee0: 6464 2061 2073 6563 6f6e 6420 636f 7079  dd a second copy\n-00004ef0: 206f 6620 7468 6520 7069 6572 6365 6420   of the pierced \n-00004f00: 7465 7472 6168 6564 726f 6e2e 2020 5765  tetrahedron.  We\n-00004f10: 276c 6c20 726f 7461 7465 0a74 6865 2063  'll rotate.the c\n-00004f20: 6f70 7920 3930 2064 6567 7265 6573 2061  opy 90 degrees a\n-00004f30: 626f 7574 2074 6865 2078 2d61 7869 7320  bout the x-axis \n-00004f40: 7769 7468 2074 6865 206f 7269 6769 6e20  with the origin \n-00004f50: 6173 2022 6365 6e74 6572 206f 660a 726f  as \"center of.ro\n-00004f60: 7461 7469 6f6e 2220 736f 2077 6520 6361  tation\" so we ca\n-00004f70: 6e20 7365 6520 7468 6520 6261 636b 2c20  n see the back, \n-00004f80: 7468 656e 2074 7261 6e73 6c61 7465 2069  then translate i\n-00004f90: 7420 746f 2074 6865 2072 6967 6874 2d2d  t to the right--\n-00004fa0: 696e 2074 6865 0a70 6f73 6974 6976 6520  in the.positive \n-00004fb0: 782d 6469 7265 6374 696f 6e2d 2d73 6f20  x-direction--so \n-00004fc0: 6974 2064 6f65 736e 2774 2063 6f6c 6c69  it doesn't colli\n-00004fd0: 6465 2077 6974 6820 7468 6520 6f72 6967  de with the orig\n-00004fe0: 696e 616c 2e20 2054 6f20 6865 6c70 0a75  inal.  To help.u\n-00004ff0: 7320 7365 6520 7768 6174 2773 2067 6f69  s see what's goi\n-00005000: 6e67 206f 6e2c 206d 616b 6520 7468 6520  ng on, make the \n-00005010: 6261 636b 2073 6964 6520 6772 6179 2e0a  back side gray..\n-00005020: 2020 6465 6620 7069 6572 6365 645f 7465    def pierced_te\n-00005030: 7472 6168 6564 726f 6e20 7b0a 2020 2020  trahedron {.    \n-00005040: 6465 6620 7031 2028 302c 302c 3129 2064  def p1 (0,0,1) d\n-00005050: 6566 2070 3220 2831 2c30 2c30 290a 2020  ef p2 (1,0,0).  \n-00005060: 2020 6465 6620 7033 2028 302c 312c 3029    def p3 (0,1,0)\n-00005070: 2064 6566 2070 3420 282d 2e33 2c2d 2e35   def p4 (-.3,-.5\n-00005080: 2c2d 2e38 290a 2020 2020 706f 6c79 676f  ,-.8).    polygo\n-00005090: 6e28 7031 2928 7032 2928 7033 2920 2020  n(p1)(p2)(p3)   \n-000050a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000050b0: 2020 2025 206f 7269 6769 6e61 6c0a 2020     % original.  \n-000050c0: 2020 706f 6c79 676f 6e28 7031 2928 7034    polygon(p1)(p4\n-000050d0: 2928 7032 2920 2020 2020 2020 2020 2020  )(p2)           \n-000050e0: 2020 2020 2020 2020 2020 2025 2062 6f74             % bot\n-000050f0: 746f 6d0a 2020 2020 706f 6c79 676f 6e28  tom.    polygon(\n-00005100: 7031 2928 7033 2928 7034 2920 2020 2020  p1)(p3)(p4)     \n-00005110: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00005120: 2025 206c 6566 740a 2020 2020 706f 6c79   % left.    poly\n-00005130: 676f 6e5b 6669 6c6c 636f 6c6f 723d 6c69  gon[fillcolor=li\n-00005140: 6768 7467 7261 795d 2870 3329 2870 3229  ghtgray](p3)(p2)\n-00005150: 2870 3429 2025 2072 6561 720a 2020 2020  (p4) % rear.    \n-00005160: 6c69 6e65 5b6c 696e 6563 6f6c 6f72 3d72  line[linecolor=r\n-00005170: 6564 5d28 2d31 2c2d 312c 2d31 2928 322c  ed](-1,-1,-1)(2,\n-00005180: 322c 3229 0a20 207d 0a20 207b 7069 6572  2,2).  }.  {pier\n-00005190: 6365 645f 7465 7472 6168 6564 726f 6e7d  ced_tetrahedron}\n-000051a0: 2020 2520 7465 7472 6168 6564 726f 6e20    % tetrahedron \n-000051b0: 696e 206f 7269 6769 6e61 6c20 706f 7369  in original posi\n-000051c0: 7469 6f6e 0a20 2070 7574 207b 2072 6f74  tion.  put { rot\n-000051d0: 6174 6528 3930 2c20 2830 2c30 2c30 292c  ate(90, (0,0,0),\n-000051e0: 205b 312c 302c 305d 2920 2520 636f 7079   [1,0,0]) % copy\n-000051f0: 2069 6e20 6e65 7720 706f 7369 7469 6f6e   in new position\n-00005200: 0a20 2020 2020 2020 2074 6865 6e20 7472  .        then tr\n-00005210: 616e 736c 6174 6528 5b32 2e35 2c30 2c30  anslate([2.5,0,0\n-00005220: 5d29 207d 207b 7069 6572 6365 645f 7465  ]) } {pierced_te\n-00005230: 7472 6168 6564 726f 6e7d 0a48 6572 6520  trahedron}.Here \n-00005240: 7468 6520 656e 7469 7265 2063 6f64 6520  the entire code \n-00005250: 6f66 2074 6865 2070 7265 7669 6f75 7320  of the previous \n-00005260: 6578 616d 706c 6520 6861 7320 6265 656e  example has been\n-00005270: 2077 7261 7070 6564 2069 6e20 610a 6465   wrapped in a.de\n-00005280: 6669 6e69 7469 6f6e 2062 7920 666f 726d  finition by form\n-00005290: 696e 6720 6120 2262 6c6f 636b 2220 7769  ing a \"block\" wi\n-000052a0: 7468 2062 7261 6365 7320 2861 2073 696e  th braces (a sin\n-000052b0: 676c 6520 6974 656d 2077 6f75 6c64 206e  gle item would n\n-000052c0: 6f74 0a6e 6565 6420 7468 656d 292e 2020  ot.need them).  \n-000052d0: 5468 6520 706f 696e 7420 6465 6669 6e69  The point defini\n-000052e0: 7469 6f6e 7320 6e65 7374 6564 2069 6e73  tions nested ins\n-000052f0: 6964 6520 7468 6520 6272 6163 6573 2061  ide the braces a\n-00005300: 7265 0a22 6c65 7869 6361 6c6c 7920 7363  re.\"lexically sc\n-00005310: 6f70 6564 222e 2020 5468 6569 7220 6d65  oped\".  Their me\n-00005320: 616e 696e 6720 6578 7465 6e64 7320 6f6e  aning extends on\n-00005330: 6c79 2074 6f20 7468 6520 656e 6420 6f66  ly to the end of\n-00005340: 2074 6865 2062 6c6f 636b 2e0a 5468 6520   the block..The \n-00005350: 6f75 7465 7220 6465 6620 6973 2063 616c  outer def is cal\n-00005360: 6c65 6420 6120 2264 7261 7761 626c 6522  led a \"drawable\"\n-00005370: 2064 6566 696e 6974 696f 6e20 6265 6361   definition beca\n-00005380: 7573 6520 6974 2064 6573 6372 6962 6573  use it describes\n-00005390: 0a73 6f6d 6574 6869 6e67 2074 6861 7420  .something that \n-000053a0: 6361 6e20 6265 2064 7261 776e 2e0a 0a20  can be drawn... \n-000053b0: 2020 4120 6472 6177 6162 6c65 2064 6566    A drawable def\n-000053c0: 696e 6974 696f 6e20 6279 2069 7473 656c  inition by itsel\n-000053d0: 6620 6361 7573 6573 206e 6f74 6869 6e67  f causes nothing\n-000053e0: 2074 6f20 6861 7070 656e 2075 6e74 696c   to happen until\n-000053f0: 2069 7473 0a6e 616d 6520 6973 2072 6566   its.name is ref\n-00005400: 6572 656e 6365 642e 2020 4472 6177 6162  erenced.  Drawab\n-00005410: 6c65 2072 6566 6572 656e 6365 7320 6d75  le references mu\n-00005420: 7374 2062 6520 656e 636c 6f73 6564 2069  st be enclosed i\n-00005430: 6e20 6375 726c 790a 6272 6163 6573 2c20  n curly.braces, \n-00005440: 652e 672e 207b 666f 6f7d 2c20 7769 7468  e.g. {foo}, with\n-00005450: 206e 6f20 696e 7465 7276 656e 696e 6720   no intervening \n-00005460: 7768 6974 6520 7370 6163 652e 2020 496e  white space.  In\n-00005470: 2074 6865 2063 6f64 6520 6162 6f76 652c   the code above,\n-00005480: 0a74 6865 2066 6972 7374 2072 6566 6572  .the first refer\n-00005490: 656e 6365 207b 7069 6572 6365 645f 7465  ence {pierced_te\n-000054a0: 7472 6168 6564 726f 6e7d 2069 7320 6120  trahedron} is a \n-000054b0: 706c 6169 6e20 6f6e 652e 2020 4974 7320  plain one.  Its \n-000054c0: 6566 6665 6374 2069 730a 6d65 7265 6c79  effect is.merely\n-000054d0: 2074 6f20 6475 706c 6963 6174 6520 7468   to duplicate th\n-000054e0: 6520 6561 726c 6965 7220 6472 6177 696e  e earlier drawin\n-000054f0: 672e 2020 416c 6d6f 7374 2061 6e79 2073  g.  Almost any s\n-00005500: 6572 6965 7320 6f66 2027 736b 6574 6368  eries of 'sketch\n-00005510: 270a 636f 6d6d 616e 6473 2073 7475 6666  '.commands stuff\n-00005520: 206d 6179 2062 6520 7265 706c 6163 6564   may be replaced\n-00005530: 2077 6974 6820 6465 6620 666f 6f20 7b20   with def foo { \n-00005540: 7374 7566 6620 7d20 7b66 6f6f 7d20 7769  stuff } {foo} wi\n-00005550: 7468 6f75 740a 6368 616e 6769 6e67 2069  thout.changing i\n-00005560: 7473 206d 6561 6e69 6e67 2e0a 0a20 2020  ts meaning...   \n-00005570: 5468 6520 7075 7420 636f 6d6d 616e 6420  The put command \n-00005580: 7375 7070 6c69 6573 2061 2073 6563 6f6e  supplies a secon\n-00005590: 6420 7265 6665 7265 6e63 652c 2074 6869  d reference, thi\n-000055a0: 7320 7469 6d65 2077 6974 6820 610a 2274  s time with a.\"t\n-000055b0: 7261 6e73 666f 726d 2220 6170 706c 6965  ransform\" applie\n-000055c0: 6420 6669 7273 742e 2020 5468 6520 726f  d first.  The ro\n-000055d0: 7461 7465 2074 7261 6e73 666f 726d 2074  tate transform t\n-000055e0: 7572 6e73 2074 6865 2074 6574 7261 6865  urns the tetrahe\n-000055f0: 6472 6f6e 0a39 3020 6465 6772 6565 7320  dron.90 degrees \n-00005600: 6162 6f75 7420 7468 6520 6f72 6967 696e  about the origin\n-00005610: 2e20 2054 6865 2061 7869 7320 6f66 2072  .  The axis of r\n-00005620: 6f74 6174 696f 6e20 6973 2074 6865 2076  otation is the v\n-00005630: 6563 746f 720a 5b31 2c30 2c30 5d2e 2020  ector.[1,0,0].  \n-00005640: 4279 2074 6865 2022 7269 6768 7420 6861  By the \"right ha\n-00005650: 6e64 2072 756c 6522 2c20 7468 6973 2063  nd rule\", this c\n-00005660: 6175 7365 7320 7468 6520 746f 7020 6f66  auses the top of\n-00005670: 2074 6865 0a74 6574 7261 6865 6472 6f6e   the.tetrahedron\n-00005680: 2074 6f20 726f 7461 7465 2074 6f77 6172   to rotate towar\n-00005690: 6420 7468 6520 7669 6577 6572 2061 6e64  d the viewer and\n-000056a0: 2074 6865 2062 6f74 746f 6d20 6177 6179   the bottom away\n-000056b0: 2e20 2054 6865 2072 756c 650a 7265 6365  .  The rule.rece\n-000056c0: 6976 6573 2069 7473 206e 616d 6520 6672  ives its name fr\n-000056d0: 6f6d 2074 6865 2066 6f6c 6c6f 7769 6e67  om the following\n-000056e0: 2064 6566 696e 6974 696f 6e3a 0a20 2020   definition:.   \n-000056f0: 2020 2a52 6967 6874 2068 616e 6420 7275    *Right hand ru\n-00005700: 6c65 2e2a 2020 4966 2074 6865 2072 6967  le.*  If the rig\n-00005710: 6874 2068 616e 6420 6973 2077 7261 7070  ht hand is wrapp\n-00005720: 6564 2061 726f 756e 6420 616e 7920 6178  ed around any ax\n-00005730: 6973 0a20 2020 2020 7769 7468 2074 6865  is.     with the\n-00005740: 2074 6875 6d62 2070 6f69 6e74 696e 6720   thumb pointing \n-00005750: 696e 2074 6865 2061 7869 7320 6469 7265  in the axis dire\n-00005760: 6374 696f 6e2c 2074 6865 6e20 7468 6520  ction, then the \n-00005770: 6669 6e67 6572 730a 2020 2020 2063 7572  fingers.     cur\n-00005780: 6c20 696e 2074 6865 2064 6972 6563 7469  l in the directi\n-00005790: 6f6e 206f 6620 706f 7369 7469 7665 2072  on of positive r\n-000057a0: 6f74 6174 696f 6e20 6162 6f75 7420 7468  otation about th\n-000057b0: 6174 2061 7869 732e 0a20 2020 5468 6520  at axis..   The \n-000057c0: 7472 616e 736c 6174 6520 7472 616e 7366  translate transf\n-000057d0: 6f72 6d20 6d6f 7665 7320 7468 6520 7079  orm moves the py\n-000057e0: 7261 6d69 6420 6c61 7465 7261 6c6c 7920  ramid laterally \n-000057f0: 746f 2074 6865 2072 6967 6874 2062 790a  to the right by.\n-00005800: 6164 6469 6e67 2074 6865 2076 6563 746f  adding the vecto\n-00005810: 7220 5b32 2e35 2c30 2c30 5d20 746f 2065  r [2.5,0,0] to e\n-00005820: 6163 6820 7665 7274 6578 2063 6f6f 7264  ach vertex coord\n-00005830: 696e 6174 652e 2020 5468 6520 7265 7375  inate.  The resu\n-00005840: 6c74 2069 730a 7368 6f77 6e20 6865 7265  lt is.shown here\n-00005850: 2e0a 0a00 085b 696d 6167 6520 7372 633d  .....[image src=\n-00005860: 2265 7830 3530 2e70 6e67 2220 7465 7874  \"ex050.png\" text\n-00005870: 3d22 496d 6167 6520 6578 3035 3020 6f6d  =\"Image ex050 om\n-00005880: 6974 7465 6420 696e 2074 6578 7420 7665  itted in text ve\n-00005890: 7273 696f 6e20 6f66 2074 6869 7320 646f  rsion of this do\n-000058a0: 6375 6d65 6e74 2e22 0008 5d0a 0a1f 0a46  cument.\"..]....F\n-000058b0: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n-000058c0: 2c20 204e 6f64 653a 2052 6570 6561 7465  ,  Node: Repeate\n-000058d0: 6420 6f62 6a65 6374 732c 2020 4e65 7874  d objects,  Next\n-000058e0: 3a20 5377 6570 7420 6f62 6a65 6374 732c  : Swept objects,\n-000058f0: 2020 5072 6576 3a20 4f62 6a65 6374 2074    Prev: Object t\n-00005900: 7261 6e73 666f 726d 732c 2020 5570 3a20  ransforms,  Up: \n-00005910: 496e 7472 6f64 7563 7469 6f6e 2062 7920  Introduction by \n-00005920: 6578 616d 706c 650a 0a32 2e36 2052 6570  example..2.6 Rep\n-00005930: 6561 7465 6420 6f62 6a65 6374 730a 3d3d  eated objects.==\n-00005940: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n-00005950: 3d3d 0a0a 546f 2064 7261 7720 7365 7665  ==..To draw seve\n-00005960: 6e20 696e 7374 616e 6365 7320 6f66 2074  n instances of t\n-00005970: 6865 2074 6574 7261 6865 6472 6f6e 2c20  he tetrahedron, \n-00005980: 6561 6368 2064 6966 6665 7269 6e67 2066  each differing f\n-00005990: 726f 6d20 7468 6520 6c61 7374 0a62 7920  rom the last.by \n-000059a0: 7468 6520 7361 6d65 2074 7261 6e73 666f  the same transfo\n-000059b0: 726d 2c20 7265 706c 6163 6520 7468 6520  rm, replace the \n-000059c0: 6c61 7374 2074 776f 2063 6f6d 6d61 6e64  last two command\n-000059d0: 7320 6f66 2074 6865 2070 7265 7669 6f75  s of the previou\n-000059e0: 730a 6578 616d 706c 6520 7769 7468 0a20  s.example with. \n-000059f0: 2072 6570 6561 7420 7b20 372c 2072 6f74   repeat { 7, rot\n-00005a00: 6174 6528 3135 2c20 2830 2c30 2c30 292c  ate(15, (0,0,0),\n-00005a10: 205b 312c 302c 305d 2920 2520 636f 7079   [1,0,0]) % copy\n-00005a20: 2069 6e20 6e65 7720 706f 7369 7469 6f6e   in new position\n-00005a30: 0a20 2020 2020 2020 2020 2020 2020 2074  .              t\n-00005a40: 6865 6e20 7472 616e 736c 6174 6528 5b32  hen translate([2\n-00005a50: 2c30 2c30 5d29 207d 207b 7069 6572 6365  ,0,0]) } {pierce\n-00005a60: 645f 7465 7472 6168 6564 726f 6e7d 0a41  d_tetrahedron}.A\n-00005a70: 6e64 2074 6865 2072 6573 756c 742e 2e2e  nd the result...\n-00005a80: 0a0a 0008 5b69 6d61 6765 2073 7263 3d22  ....[image src=\"\n-00005a90: 6578 3036 302e 706e 6722 2074 6578 743d  ex060.png\" text=\n-00005aa0: 2249 6d61 6765 2065 7830 3630 206f 6d69  \"Image ex060 omi\n-00005ab0: 7474 6564 2069 6e20 7465 7874 2076 6572  tted in text ver\n-00005ac0: 7369 6f6e 206f 6620 7468 6973 2064 6f63  sion of this doc\n-00005ad0: 756d 656e 742e 2200 085d 0a0a 1f0a 4669  ument.\"..]....Fi\n-00005ae0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n-00005af0: 2020 4e6f 6465 3a20 5377 6570 7420 6f62    Node: Swept ob\n-00005b00: 6a65 6374 732c 2020 5072 6576 3a20 5265  jects,  Prev: Re\n-00005b10: 7065 6174 6564 206f 626a 6563 7473 2c20  peated objects, \n-00005b20: 2055 703a 2049 6e74 726f 6475 6374 696f   Up: Introductio\n-00005b30: 6e20 6279 2065 7861 6d70 6c65 0a0a 322e  n by example..2.\n-00005b40: 3720 5377 6570 7420 6f62 6a65 6374 730a  7 Swept objects.\n-00005b50: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n-00005b60: 3d0a 0a4d 616e 7920 6661 6d69 6c69 6172  =..Many familiar\n-00005b70: 2073 6861 7065 7320 6361 6e20 6265 2067   shapes can be g\n-00005b80: 656e 6572 6174 6564 2062 7920 7377 6565  enerated by swee\n-00005b90: 7069 6e67 2073 696d 706c 6572 206f 6e65  ping simpler one\n-00005ba0: 7320 7468 726f 7567 680a 7370 6163 6520  s through.space \n-00005bb0: 616e 6420 636f 6e73 6964 6572 696e 6720  and considering \n-00005bc0: 7468 6520 7265 7375 6c74 696e 6720 7061  the resulting pa\n-00005bd0: 7468 2c20 7375 7266 6163 652c 206f 7220  th, surface, or \n-00005be0: 766f 6c75 6d65 2e20 2027 536b 6574 6368  volume.  'Sketch\n-00005bf0: 270a 696d 706c 656d 656e 7473 2074 6869  '.implements thi\n-00005c00: 7320 6964 6561 2069 6e20 7468 6520 7377  s idea in the sw\n-00005c10: 6565 7020 636f 6d6d 616e 642e 0a20 2064  eep command..  d\n-00005c20: 6566 206e 5f73 6567 7320 380a 2020 7377  ef n_segs 8.  sw\n-00005c30: 6565 7020 7b20 6e5f 7365 6773 2c20 726f  eep { n_segs, ro\n-00005c40: 7461 7465 2831 3830 202f 206e 5f73 6567  tate(180 / n_seg\n-00005c50: 732c 2028 302c 302c 3029 2c20 5b30 2c30  s, (0,0,0), [0,0\n-00005c60: 2c31 5d29 207d 2028 312c 302c 3029 0a54  ,1]) } (1,0,0).T\n-00005c70: 6869 7320 636f 6465 2073 7765 6570 7320  his code sweeps \n-00005c80: 7468 6520 706f 696e 7420 2831 2c30 2c30  the point (1,0,0\n-00005c90: 2920 6569 6768 7420 7469 6d65 7320 6279  ) eight times by\n-00005ca0: 2072 6f74 6174 696e 6720 6974 2031 3830   rotating it 180\n-00005cb0: 2f38 203d 0a32 322e 3520 6465 6772 6565  /8 =.22.5 degree\n-00005cc0: 7320 6561 6368 2074 696d 6520 616e 6420  s each time and \n-00005cd0: 636f 6e6e 6563 7469 6e67 2074 6865 2072  connecting the r\n-00005ce0: 6573 756c 7469 6e67 2070 6f69 6e74 7320  esulting points \n-00005cf0: 7769 7468 206c 696e 650a 7365 676d 656e  with line.segmen\n-00005d00: 7473 2e20 2054 6865 2064 6566 2075 7365  ts.  The def use\n-00005d10: 6420 6865 7265 2069 7320 6120 2273 6361  d here is a \"sca\n-00005d20: 6c61 7222 2064 6566 696e 6974 696f 6e2e  lar\" definition.\n-00005d30: 2020 5265 6665 7265 6e63 6573 2074 6f0a    References to.\n-00005d40: 7363 616c 6172 7320 6861 7665 206e 6f20  scalars have no \n-00005d50: 656e 636c 6f73 696e 6720 6272 6163 6b65  enclosing bracke\n-00005d60: 7473 2061 7420 616c 6c2e 0a0a 2a20 4d65  ts at all...* Me\n-00005d70: 6e75 3a0a 0a2a 2050 6f69 6e74 2073 7765  nu:..* Point swe\n-00005d80: 6570 733a 3a20 2020 2020 2020 2020 2020  eps::           \n-00005d90: 2020 2020 2053 7765 7074 2070 6f69 6e74       Swept point\n-00005da0: 7320 6d61 6b65 206c 696e 6573 2061 6e64  s make lines and\n-00005db0: 2070 6f6c 7967 6f6e 732e 0a2a 2050 6f6c   polygons..* Pol\n-00005dc0: 796c 696e 6520 7377 6565 7073 3a3a 2020  yline sweeps::  \n-00005dd0: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-00005de0: 206c 696e 6573 206d 616b 6520 7375 7266   lines make surf\n-00005df0: 6163 6573 2e0a 2a20 4e65 7374 6564 2073  aces..* Nested s\n-00005e00: 7765 6570 733a 3a20 2020 2020 2020 2020  weeps::         \n-00005e10: 2020 2020 2020 5377 6570 7420 7377 6565        Swept swee\n-00005e20: 7073 2061 7265 2075 7365 6675 6c21 0a2a  ps are useful!.*\n-00005e30: 2050 6f6c 7967 6f6e 2073 7765 6570 733a   Polygon sweeps:\n-00005e40: 3a20 2020 2020 2020 2020 2020 2020 2053  :              S\n-00005e50: 7765 7074 2070 6f6c 7967 6f6e 7320 6d61  wept polygons ma\n-00005e60: 6b65 2073 6f6c 6964 732e 2e2e 0a2a 2050  ke solids....* P\n-00005e70: 6f6c 796c 696e 6520 7377 6565 7073 2077  olyline sweeps w\n-00005e80: 6974 6820 636c 6f73 7572 653a 3a20 2061  ith closure::  a\n-00005e90: 6e64 2073 6f20 646f 2063 6c6f 7365 6420  nd so do closed \n-00005ea0: 706f 6c79 6c69 6e65 2073 7765 6570 732e  polyline sweeps.\n-00005eb0: 0a2a 2041 6666 696e 6520 6172 6974 686d  .* Affine arithm\n-00005ec0: 6574 6963 3a3a 2020 2020 2020 2020 2020  etic::          \n-00005ed0: 2053 6b65 7463 6820 7573 6566 756c 206d   Sketch useful m\n-00005ee0: 6174 6820 6578 7072 6573 7369 6f6e 2e0a  ath expression..\n-00005ef0: 2a20 4d6f 7265 2074 6f20 6c65 6172 6e3a  * More to learn:\n-00005f00: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00005f10: 4368 6563 6b20 6f75 7420 7468 6520 4d6f  Check out the Mo\n-00005f20: 6269 7573 2073 7472 6970 210a 0a1f 0a46  bius strip!....F\n-00005f30: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n-00005f40: 2c20 204e 6f64 653a 2050 6f69 6e74 2073  ,  Node: Point s\n-00005f50: 7765 6570 732c 2020 4e65 7874 3a20 506f  weeps,  Next: Po\n-00005f60: 6c79 6c69 6e65 2073 7765 6570 732c 2020  lyline sweeps,  \n-00005f70: 5072 6576 3a20 5377 6570 7420 6f62 6a65  Prev: Swept obje\n-00005f80: 6374 732c 2020 5570 3a20 5377 6570 7420  cts,  Up: Swept \n-00005f90: 6f62 6a65 6374 730a 0a32 2e37 2e31 2050  objects..2.7.1 P\n-00005fa0: 6f69 6e74 2073 7765 6570 730a 2d2d 2d2d  oint sweeps.----\n-00005fb0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a  --------------..\n-00005fc0: 5377 6565 7069 6e67 2061 2070 6f69 6e74  Sweeping a point\n-00005fd0: 206d 616b 6573 2061 206f 6e65 2d64 696d   makes a one-dim\n-00005fe0: 656e 7369 6f6e 616c 2070 6174 682c 2077  ensional path, w\n-00005ff0: 6869 6368 2069 7320 6120 706f 6c79 6c69  hich is a polyli\n-00006000: 6e65 2e0a 5369 6e63 6520 7765 2068 6176  ne..Since we hav\n-00006010: 6520 7377 6570 7420 7769 7468 2061 2072  e swept with a r\n-00006020: 6f74 6174 696f 6e2c 2074 6865 2072 6573  otation, the res\n-00006030: 756c 7420 6973 2061 2063 6972 6375 6c61  ult is a circula\n-00006040: 7220 6172 632e 2020 4865 7265 0a69 7320  r arc.  Here.is \n-00006050: 7768 6174 2069 7420 6c6f 6f6b 7320 6c69  what it looks li\n-00006060: 6b65 2e0a 0a00 085b 696d 6167 6520 7372  ke.....[image sr\n-00006070: 633d 2265 7830 3730 2e70 6e67 2220 7465  c=\"ex070.png\" te\n-00006080: 7874 3d22 496d 6167 6520 6578 3037 3020  xt=\"Image ex070 \n-00006090: 6f6d 6974 7465 6420 696e 2074 6578 7420  omitted in text \n-000060a0: 7665 7273 696f 6e20 6f66 2074 6869 7320  version of this \n-000060b0: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a20  document.\"..].. \n-000060c0: 2020 5468 6973 2069 7320 7468 6520 6669    This is the fi\n-000060d0: 7273 7420 6578 616d 706c 6520 7765 2068  rst example we h\n-000060e0: 6176 6520 7365 656e 206f 6620 2773 6b65  ave seen of 'ske\n-000060f0: 7463 6827 2061 7269 7468 6d65 7469 632e  tch' arithmetic.\n-00006100: 2020 5468 650a 6578 7072 6573 7369 6f6e    The.expression\n-00006110: 2031 3830 202f 206e 5f73 6567 7320 6361   180 / n_segs ca\n-00006120: 7573 6573 2074 6865 2065 6967 6874 2072  uses the eight r\n-00006130: 6f74 6174 696f 6e73 2074 6f20 6164 6420  otations to add \n-00006140: 746f 2031 3830 2e20 2049 660a 796f 7527  to 180.  If.you'\n-00006150: 7265 2070 6179 696e 6720 6174 7465 6e74  re paying attent\n-00006160: 696f 6e2c 2079 6f75 276c 6c20 6861 7665  ion, you'll have\n-00006170: 2061 6c72 6561 6479 206e 6f74 6564 2074   already noted t\n-00006180: 6861 7420 7468 6572 6520 6172 6520 5f6e  hat there are _n\n-00006190: 696e 655f 0a70 6f69 6e74 732c 2070 726f  ine_.points, pro\n-000061a0: 6475 6369 6e67 2065 6967 6874 206c 696e  ducing eight lin\n-000061b0: 6520 7365 676d 656e 7473 2e0a 0a20 2020  e segments...   \n-000061c0: 596f 7520 6361 6e20 6361 7573 6520 7468  You can cause th\n-000061d0: 6520 7377 6570 7420 706f 696e 7420 746f  e swept point to\n-000061e0: 2067 656e 6572 6174 6520 6120 7369 6e67   generate a sing\n-000061f0: 6c65 2070 6f6c 7967 6f6e 2072 6174 6865  le polygon rathe\n-00006200: 720a 7468 616e 2061 2070 6f6c 796c 696e  r.than a polylin\n-00006210: 6520 6279 2075 7369 6e67 2074 6865 2022  e by using the \"\n-00006220: 636c 6f73 7572 6520 7461 6722 203c 3e20  closure tag\" <> \n-00006230: 6166 7465 7220 7468 6520 6e75 6d62 6572  after the number\n-00006240: 206f 6620 7377 6570 740a 6f62 6a65 6374   of swept.object\n-00006250: 732e 2020 436f 6465 2061 6e64 2072 6573  s.  Code and res\n-00006260: 756c 7420 666f 6c6c 6f77 0a20 2064 6566  ult follow.  def\n-00006270: 206e 5f73 6567 7320 380a 2020 7377 6565   n_segs 8.  swee\n-00006280: 7020 7b20 6e5f 7365 6773 3c3e 2c20 726f  p { n_segs<>, ro\n-00006290: 7461 7465 2831 3830 202f 206e 5f73 6567  tate(180 / n_seg\n-000062a0: 732c 2028 302c 302c 3029 2c20 5b30 2c30  s, (0,0,0), [0,0\n-000062b0: 2c31 5d29 207d 2028 312c 302c 3029 0a00  ,1]) } (1,0,0)..\n-000062c0: 085b 696d 6167 6520 7372 633d 2265 7830  .[image src=\"ex0\n-000062d0: 3830 2e70 6e67 2220 7465 7874 3d22 496d  80.png\" text=\"Im\n-000062e0: 6167 6520 6578 3038 3020 6f6d 6974 7465  age ex080 omitte\n-000062f0: 6420 696e 2074 6578 7420 7665 7273 696f  d in text versio\n-00006300: 6e20 6f66 2074 6869 7320 646f 6375 6d65  n of this docume\n-00006310: 6e74 2e22 0008 5d0a 0a1f 0a46 696c 653a  nt.\"..]....File:\n-00006320: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n-00006330: 6f64 653a 2050 6f6c 796c 696e 6520 7377  ode: Polyline sw\n-00006340: 6565 7073 2c20 204e 6578 743a 204e 6573  eeps,  Next: Nes\n-00006350: 7465 6420 7377 6565 7073 2c20 2050 7265  ted sweeps,  Pre\n-00006360: 763a 2050 6f69 6e74 2073 7765 6570 732c  v: Point sweeps,\n-00006370: 2020 5570 3a20 5377 6570 7420 6f62 6a65    Up: Swept obje\n-00006380: 6374 730a 0a32 2e37 2e32 2050 6f6c 796c  cts..2.7.2 Polyl\n-00006390: 696e 6520 7377 6565 7073 0a2d 2d2d 2d2d  ine sweeps.-----\n-000063a0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-000063b0: 0a0a 5377 6565 7069 6e67 2061 2070 6f6c  ..Sweeping a pol\n-000063c0: 796c 696e 6520 7072 6f64 7563 6573 2061  yline produces a\n-000063d0: 2073 7572 6661 6365 2063 6f6d 706f 7365   surface compose\n-000063e0: 6420 6f66 206d 616e 7920 6661 6365 732e  d of many faces.\n-000063f0: 2020 5468 650a 756e 6272 6f6b 656e 2068    The.unbroken h\n-00006400: 656c 6978 2069 6e20 7468 6520 6578 616d  elix in the exam\n-00006410: 706c 6520 2a6e 6f74 6520 4865 6c69 7820  ple *note Helix \n-00006420: 7769 7468 2063 756c 6c20 7365 7420 6661  with cull set fa\n-00006430: 6c73 6520 7468 656e 0a74 7275 653a 3a20  lse then.true:: \n-00006440: 6973 2070 726f 6475 6365 6420 6279 2074  is produced by t\n-00006450: 6869 7320 636f 6465 2028 706c 7573 2061  his code (plus a\n-00006460: 2073 7572 726f 756e 6469 6e67 2070 7574   surrounding put\n-00006470: 2072 6f74 6174 696f 6e20 746f 206d 616b   rotation to mak\n-00006480: 650a 616e 2069 6e74 6572 6573 7469 6e67  e.an interesting\n-00006490: 2076 6965 773b 2074 6869 7320 6861 7320   view; this has \n-000064a0: 6265 656e 206f 6d69 7474 6564 292e 0a20  been omitted).. \n-000064b0: 2064 6566 204b 205b 302c 302c 315d 0a20   def K [0,0,1]. \n-000064c0: 2073 7765 6570 5b63 756c 6c3d 6661 6c73   sweep[cull=fals\n-000064d0: 655d 207b 0a20 2020 2036 302c 200a 2020  e] {.    60, .  \n-000064e0: 2020 726f 7461 7465 2831 302c 2028 302c    rotate(10, (0,\n-000064f0: 302c 3029 2c20 5b4b 5d29 2074 6865 6e20  0,0), [K]) then \n-00006500: 7472 616e 736c 6174 6528 312f 3620 2a20  translate(1/6 * \n-00006510: 5b4b 5d29 200a 2020 7d20 6c69 6e65 5b6c  [K]) .  } line[l\n-00006520: 696e 6577 6964 7468 3d32 7074 5d28 2d31  inewidth=2pt](-1\n-00006530: 2c30 2928 312c 3029 0a41 6761 696e 2c20  ,0)(1,0).Again, \n-00006540: 3630 2073 6567 6d65 6e74 7320 6f66 2074  60 segments of t\n-00006550: 6865 2068 656c 6978 2061 7265 2070 726f  he helix are pro\n-00006560: 6475 6365 6420 6279 2063 6f6e 6e65 6374  duced by connect\n-00006570: 696e 6720 3631 2069 6e73 7461 6e63 6573  ing 61 instances\n-00006580: 0a6f 6620 7468 6520 7377 6570 7420 6c69  .of the swept li\n-00006590: 6e65 2e20 204f 7074 696f 6e73 2061 7070  ne.  Options app\n-000065a0: 6c69 6564 2074 6f20 7468 6520 7377 6565  lied to the swee\n-000065b0: 702c 2068 6572 6520 6375 6c6c 3d66 616c  p, here cull=fal\n-000065c0: 7365 2c20 6172 650a 7472 6561 7465 6420  se, are.treated \n-000065d0: 6173 206f 7074 696f 6e73 2066 6f72 2074  as options for t\n-000065e0: 6865 2067 656e 6572 6174 6564 2070 6f6c  he generated pol\n-000065f0: 7967 6f6e 206f 7220 706f 6c79 6c69 6e65  ygon or polyline\n-00006600: 2e20 204f 7074 696f 6e73 206f 660a 7468  .  Options of.th\n-00006610: 6520 7377 6570 7420 6c69 6e65 2069 7473  e swept line its\n-00006620: 656c 662c 2068 6572 6520 6c69 6e65 7769  elf, here linewi\n-00006630: 6474 683d 3270 742c 2061 7265 2069 676e  dth=2pt, are ign\n-00006640: 6f72 6564 2c20 7468 6f75 6768 2077 6974  ored, though wit\n-00006650: 6820 610a 7761 726e 696e 672e 2020 5468  h a.warning.  Th\n-00006660: 6973 2064 6566 2069 7320 6120 2276 6563  is def is a \"vec\n-00006670: 746f 7222 2064 6566 696e 6974 696f 6e2c  tor\" definition,\n-00006680: 2077 6869 6368 206d 7573 7420 6265 2072   which must be r\n-00006690: 6566 6572 656e 6365 640a 7769 7468 2073  eferenced.with s\n-000066a0: 7175 6172 6520 6272 6163 6b65 7473 2c20  quare brackets, \n-000066b0: 652e 672e 205b 666f 6f5d 2e0a 0a1f 0a46  e.g. [foo].....F\n-000066c0: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n-000066d0: 2c20 204e 6f64 653a 204e 6573 7465 6420  ,  Node: Nested \n-000066e0: 7377 6565 7073 2c20 204e 6578 743a 2050  sweeps,  Next: P\n-000066f0: 6f6c 7967 6f6e 2073 7765 6570 732c 2020  olygon sweeps,  \n-00006700: 5072 6576 3a20 506f 6c79 6c69 6e65 2073  Prev: Polyline s\n-00006710: 7765 6570 732c 2020 5570 3a20 5377 6570  weeps,  Up: Swep\n-00006720: 7420 6f62 6a65 6374 730a 0a32 2e37 2e33  t objects..2.7.3\n-00006730: 204e 6573 7465 6420 7377 6565 7073 0a2d   Nested sweeps.-\n-00006740: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-00006750: 2d2d 0a0a 5768 656e 2074 6865 2063 656e  --..When the cen\n-00006760: 7465 7220 706f 696e 7420 6f66 2072 6f74  ter point of rot\n-00006770: 6174 696f 6e20 6973 206f 6d69 7474 6564  ation is omitted\n-00006780: 2c20 7468 6520 6f72 6967 696e 2069 7320  , the origin is \n-00006790: 6173 7375 6d65 642e 0a57 6865 6e20 6120  assumed..When a \n-000067a0: 706f 696e 7420 6861 7320 6f6e 6c79 2074  point has only t\n-000067b0: 776f 2063 6f6f 7264 696e 6174 6573 2c20  wo coordinates, \n-000067c0: 7468 6579 2061 7265 2074 616b 656e 2061  they are taken a\n-000067d0: 7320 7820 616e 6420 792c 2077 6974 680a  s x and y, with.\n-000067e0: 7a3d 3020 6173 7375 6d65 642e 2020 4120  z=0 assumed.  A \n-000067f0: 746f 726f 6964 2069 7320 7468 6572 6566  toroid is theref\n-00006800: 6f72 6520 6f62 7461 696e 6564 2077 6974  ore obtained wit\n-00006810: 6820 7468 6973 2063 6f64 652e 0a20 2064  h this code..  d\n-00006820: 6566 206e 5f74 6f72 6f69 645f 7365 6773  ef n_toroid_segs\n-00006830: 2032 3020 2020 6465 6620 6e5f 6369 7263   20   def n_circ\n-00006840: 6c65 5f73 6567 7320 3136 0a20 2064 6566  le_segs 16.  def\n-00006850: 2072 5f6d 696e 6f72 2031 2020 2020 2020   r_minor 1      \n-00006860: 2020 2020 6465 6620 725f 6d61 6a6f 7220      def r_major \n-00006870: 312e 350a 2020 7377 6565 7020 7b20 6e5f  1.5.  sweep { n_\n-00006880: 746f 726f 6964 5f73 6567 732c 2072 6f74  toroid_segs, rot\n-00006890: 6174 6528 3336 3020 2f20 6e5f 746f 726f  ate(360 / n_toro\n-000068a0: 6964 5f73 6567 732c 205b 302c 312c 305d  id_segs, [0,1,0]\n-000068b0: 2920 7d0a 2020 2020 7377 6565 7020 7b20  ) }.    sweep { \n-000068c0: 6e5f 6369 7263 6c65 5f73 6567 732c 2072  n_circle_segs, r\n-000068d0: 6f74 6174 6528 3336 3020 2f20 6e5f 6369  otate(360 / n_ci\n-000068e0: 7263 6c65 5f73 6567 732c 2028 725f 6d61  rcle_segs, (r_ma\n-000068f0: 6a6f 722c 302c 3029 2920 7d20 0a20 2020  jor,0,0)) } .   \n-00006900: 2020 2028 725f 6d61 6a6f 7220 2b20 725f     (r_major + r_\n-00006910: 6d69 6e6f 722c 2030 290a 2020 2046 6f72  minor, 0).   For\n-00006920: 2069 6e74 7569 7469 6f6e 2c20 7468 6520   intuition, the \n-00006930: 6964 6561 206f 6620 7468 6520 636f 6465  idea of the code\n-00006940: 2069 7320 746f 2073 6b65 7463 6820 6120   is to sketch a \n-00006950: 6369 7263 6c65 2074 6f20 7468 650a 7269  circle to the.ri\n-00006960: 6768 7420 6f66 2074 6865 206f 7269 6769  ght of the origi\n-00006970: 6e20 696e 2074 6865 2078 792d 706c 616e  n in the xy-plan\n-00006980: 652c 2074 6865 6e20 726f 7461 7465 2074  e, then rotate t\n-00006990: 6861 7420 6369 7263 6c65 2022 6f75 7420  hat circle \"out \n-000069a0: 6f66 2074 6865 0a70 6c61 6e65 2220 6162  of the.plane\" ab\n-000069b0: 6f75 7420 7468 6520 792d 6178 6973 2074  out the y-axis t\n-000069c0: 6f20 6d61 6b65 2074 6865 2066 696e 616c  o make the final\n-000069d0: 2066 6967 7572 652e 2020 5468 6973 2070   figure.  This p\n-000069e0: 726f 6475 6365 7320 7468 650a 666f 6c6c  roduces the.foll\n-000069f0: 6f77 696e 672e 2020 2841 2076 6965 7720  owing.  (A view \n-00006a00: 726f 7461 7469 6f6e 2061 6e64 2073 6f6d  rotation and som\n-00006a10: 6520 6178 6573 2068 6176 6520 6265 656e  e axes have been\n-00006a20: 2061 6464 6564 2e29 0a0a 0008 5b69 6d61   added.)....[ima\n-00006a30: 6765 2073 7263 3d22 6578 3039 302e 706e  ge src=\"ex090.pn\n-00006a40: 6722 2074 6578 743d 2249 6d61 6765 2065  g\" text=\"Image e\n-00006a50: 7830 3930 206f 6d69 7474 6564 2069 6e20  x090 omitted in \n-00006a60: 7465 7874 2076 6572 7369 6f6e 206f 6620  text version of \n-00006a70: 7468 6973 2064 6f63 756d 656e 742e 2200  this document.\".\n-00006a80: 085d 0a0a 2020 2054 6869 7320 6578 616d  .]..   This exam\n-00006a90: 706c 6520 616c 736f 2073 686f 7773 2074  ple also shows t\n-00006aa0: 6861 7420 7468 6520 7377 6570 7420 6f62  hat the swept ob\n-00006ab0: 6a65 6374 206d 6179 2069 7473 656c 6620  ject may itself \n-00006ac0: 6265 2061 6e6f 7468 6572 0a27 7377 6565  be another.'swee\n-00006ad0: 7027 2e20 2049 6e20 6661 6374 2c20 6974  p'.  In fact, it\n-00006ae0: 206d 6179 2062 6520 5f61 6e79 5f20 2773   may be _any_ 's\n-00006af0: 6b65 7463 6827 2065 7870 7265 7373 696f  ketch' expressio\n-00006b00: 6e20 7468 6174 2072 6573 756c 7473 2069  n that results i\n-00006b10: 6e20 610a 6c69 7374 206f 6620 6f6e 6520  n a.list of one \n-00006b20: 6f72 206d 6f72 6520 706f 696e 7473 206f  or more points o\n-00006b30: 722c 2061 6c74 6572 6e61 7465 6c79 2c20  r, alternately, \n-00006b40: 6120 6c69 7374 206f 6620 6f6e 6520 6f72  a list of one or\n-00006b50: 206d 6f72 650a 706f 6c79 6c69 6e65 7320   more.polylines \n-00006b60: 616e 6420 706f 6c79 676f 6e73 2e20 2054  and polygons.  T\n-00006b70: 6865 206c 6174 7465 7220 6b69 6e64 206f  he latter kind o\n-00006b80: 6620 6c69 7374 2063 616e 2062 6520 6372  f list can be cr\n-00006b90: 6561 7465 6420 7769 7468 2061 0a7b 207d  eated with a.{ }\n-00006ba0: 2d65 6e63 6c6f 7365 6420 626c 6f63 6b2c  -enclosed block,\n-00006bb0: 2070 6572 6861 7073 2066 6f6c 6c6f 7769   perhaps followi\n-00006bc0: 6e67 2061 2070 7574 206f 7220 7265 7065  ng a put or repe\n-00006bd0: 6174 2e0a 0a1f 0a46 696c 653a 2073 6b65  at.....File: ske\n-00006be0: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n-00006bf0: 2050 6f6c 7967 6f6e 2073 7765 6570 732c   Polygon sweeps,\n-00006c00: 2020 4e65 7874 3a20 506f 6c79 6c69 6e65    Next: Polyline\n-00006c10: 2073 7765 6570 7320 7769 7468 2063 6c6f   sweeps with clo\n-00006c20: 7375 7265 2c20 2050 7265 763a 204e 6573  sure,  Prev: Nes\n-00006c30: 7465 6420 7377 6565 7073 2c20 2055 703a  ted sweeps,  Up:\n-00006c40: 2053 7765 7074 206f 626a 6563 7473 0a0a   Swept objects..\n-00006c50: 322e 372e 3420 506f 6c79 676f 6e20 7377  2.7.4 Polygon sw\n-00006c60: 6565 7073 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d  eeps.-----------\n-00006c70: 2d2d 2d2d 2d2d 2d2d 2d0a 0a53 7765 6570  ---------..Sweep\n-00006c80: 696e 6720 6120 706f 6c79 676f 6e20 6372  ing a polygon cr\n-00006c90: 6561 7465 7320 6120 636c 6f73 6564 2073  eates a closed s\n-00006ca0: 7572 6661 6365 2077 6974 6820 706f 6c79  urface with poly\n-00006cb0: 676f 6e73 2061 7420 7468 6520 656e 6473  gons at the ends\n-00006cc0: 2c0a 7768 6963 6820 6172 6520 6a75 7374  ,.which are just\n-00006cd0: 2063 6f70 6965 7320 6f66 2074 6865 206f   copies of the o\n-00006ce0: 7269 6769 6e61 6c2c 2061 7070 726f 7072  riginal, appropr\n-00006cf0: 6961 7465 6c79 2070 6f73 6974 696f 6e65  iately positione\n-00006d00: 642e 2020 2a4e 6f74 650a 536f 6c69 6420  d.  *Note.Solid \n-00006d10: 636f 696c 2065 7861 6d70 6c65 3a3a 2e20  coil example::. \n-00006d20: 204f 7074 696f 6e73 206f 6e20 7468 6520   Options on the \n-00006d30: 7377 6570 7420 706f 6c79 676f 6e2c 2069  swept polygon, i\n-00006d40: 6620 7468 6579 2065 7869 7374 2c20 6172  f they exist, ar\n-00006d50: 650a 6170 706c 6965 6420 746f 2074 6865  e.applied to the\n-00006d60: 2065 6e64 732e 2020 4f74 6865 7277 6973   ends.  Otherwis\n-00006d70: 6520 7468 6520 7377 6565 7020 6f70 7469  e the sweep opti\n-00006d80: 6f6e 7320 6172 6520 7573 6564 2074 6872  ons are used thr\n-00006d90: 6f75 6768 6f75 742e 0a0a 1f0a 4669 6c65  oughout.....File\n-00006da0: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n-00006db0: 4e6f 6465 3a20 506f 6c79 6c69 6e65 2073  Node: Polyline s\n-00006dc0: 7765 6570 7320 7769 7468 2063 6c6f 7375  weeps with closu\n-00006dd0: 7265 2c20 204e 6578 743a 2041 6666 696e  re,  Next: Affin\n-00006de0: 6520 6172 6974 686d 6574 6963 2c20 2050  e arithmetic,  P\n-00006df0: 7265 763a 2050 6f6c 7967 6f6e 2073 7765  rev: Polygon swe\n-00006e00: 6570 732c 2020 5570 3a20 5377 6570 7420  eps,  Up: Swept \n-00006e10: 6f62 6a65 6374 730a 0a32 2e37 2e35 2050  objects..2.7.5 P\n-00006e20: 6f6c 796c 696e 6520 7377 6565 7073 2077  olyline sweeps w\n-00006e30: 6974 6820 636c 6f73 7572 650a 2d2d 2d2d  ith closure.----\n-00006e40: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-00006e50: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a  --------------..\n-00006e60: 4120 706f 6c79 6c69 6e65 2073 7765 6570  A polyline sweep\n-00006e70: 2077 6974 6820 6120 636c 6f73 7572 6520   with a closure \n-00006e80: 7461 6720 6372 6561 7465 7320 616e 6f74  tag creates anot\n-00006e90: 6865 7220 6b69 6e64 206f 6620 636c 6f73  her kind of clos\n-00006ea0: 6564 0a73 7572 6661 6365 2e20 2046 6972  ed.surface.  Fir\n-00006eb0: 7374 2c20 7468 6520 706f 6c79 6c69 6e65  st, the polyline\n-00006ec0: 2073 6567 6d65 6e74 7320 6172 6520 636f   segments are co\n-00006ed0: 6e6e 6563 7465 6420 6279 2066 6163 6573  nnected by faces\n-00006ee0: 2c20 6a75 7374 2061 730a 7769 7468 6f75  , just as.withou\n-00006ef0: 7420 7468 6520 636c 6f73 7572 6520 7461  t the closure ta\n-00006f00: 672e 2020 5468 656e 2c20 6561 6368 2073  g.  Then, each s\n-00006f10: 6574 206f 6620 656e 6420 706f 696e 7473  et of end points\n-00006f20: 2069 7320 6a6f 696e 6564 2074 6f20 6d61   is joined to ma\n-00006f30: 6b65 0a61 2070 6f6c 7967 6f6e 2c20 6f6e  ke.a polygon, on\n-00006f40: 6520 666f 7220 6561 6368 2065 6e64 2e20  e for each end. \n-00006f50: 2041 2063 6f64 6520 666f 7220 7365 7665   A code for seve\n-00006f60: 7261 6c20 7669 6577 7320 6f66 2061 2063  ral views of a c\n-00006f70: 796c 696e 6472 6963 616c 0a70 7269 736d  ylindrical.prism\n-00006f80: 2066 6f6c 6c6f 7773 2e0a 2020 6465 6620   follows..  def \n-00006f90: 6e5f 6379 6c5f 7365 6773 2032 3020 2064  n_cyl_segs 20  d\n-00006fa0: 6566 206e 5f76 6965 7773 2035 2020 6465  ef n_views 5  de\n-00006fb0: 6620 4920 5b31 2c30 2c30 5d0a 2020 6465  f I [1,0,0].  de\n-00006fc0: 6620 656e 646f 7074 7320 5b66 696c 6c63  f endopts [fillc\n-00006fd0: 6f6c 6f72 3d6c 6967 6874 6772 6179 5d0a  olor=lightgray].\n-00006fe0: 2020 7265 7065 6174 207b 206e 5f76 6965    repeat { n_vie\n-00006ff0: 7773 2c20 726f 7461 7465 2831 3830 2f6e  ws, rotate(180/n\n-00007000: 5f76 6965 7773 2c20 5b49 5d29 2074 6865  _views, [I]) the\n-00007010: 6e20 7472 616e 736c 6174 6528 5b49 5d20  n translate([I] \n-00007020: 2a20 322e 3129 207d 200a 2020 2020 7377  * 2.1) } .    sw\n-00007030: 6565 705b 656e 646f 7074 735d 7b20 6e5f  eep[endopts]{ n_\n-00007040: 6379 6c5f 7365 6773 3c3e 2c20 726f 7461  cyl_segs<>, rota\n-00007050: 7465 2833 3630 2f6e 5f63 796c 5f73 6567  te(360/n_cyl_seg\n-00007060: 732c 205b 302c 312c 305d 2920 7d20 0a20  s, [0,1,0]) } . \n-00007070: 2020 2020 206c 696e 655b 6669 6c6c 636f       line[fillco\n-00007080: 6c6f 723d 7768 6974 655d 2831 2c2d 3129  lor=white](1,-1)\n-00007090: 2831 2c31 290a 4974 2070 726f 6475 6365  (1,1).It produce\n-000070a0: 7320 7468 6973 2064 7261 7769 6e67 2e0a  s this drawing..\n-000070b0: 0a00 085b 696d 6167 6520 7372 633d 2265  ...[image src=\"e\n-000070c0: 7831 3130 2e70 6e67 2220 7465 7874 3d22  x110.png\" text=\"\n-000070d0: 496d 6167 6520 6578 3131 3020 6f6d 6974  Image ex110 omit\n-000070e0: 7465 6420 696e 2074 6578 7420 7665 7273  ted in text vers\n-000070f0: 696f 6e20 6f66 2074 6869 7320 646f 6375  ion of this docu\n-00007100: 6d65 6e74 2e22 0008 5d0a 0a54 6865 206f  ment.\"..]..The o\n-00007110: 7074 696f 6e73 206f 6620 7468 6520 7377  ptions of the sw\n-00007120: 6570 7420 6c69 6e65 2c20 6966 2061 6e79  ept line, if any\n-00007130: 2c20 6172 6520 6170 706c 6965 6420 746f  , are applied to\n-00007140: 2074 6865 2066 6163 6573 2070 726f 6475   the faces produ\n-00007150: 6365 640a 6279 2073 7765 6570 696e 6720  ced.by sweeping \n-00007160: 7468 6520 6c69 6e65 2c20 6275 7420 6e6f  the line, but no\n-00007170: 7420 7468 6520 656e 6420 706f 6c79 676f  t the end polygo\n-00007180: 6e73 2e20 204f 7468 6572 7769 7365 2c20  ns.  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(1) Or for E\n+000032a0: 7572 6f70 6561 6e20 7573 6572 7320 6f66  uropean users of\n+000032b0: 2041 3420 7369 7a65 2070 6170 6572 2c20   A4 size paper, \n+000032c0: 272d 5465 272e 0a0a 1f0a 4669 6c65 3a20  '-Te'.....File: \n+000032d0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n+000032e0: 6465 3a20 4472 6177 696e 6720 6f70 7469  de: Drawing opti\n+000032f0: 6f6e 732c 2020 4e65 7874 3a20 4472 6177  ons,  Next: Draw\n+00003300: 696e 6720 6120 736f 6c69 642c 2020 5072  ing a solid,  Pr\n+00003310: 6576 3a20 4865 6c6c 6f20 776f 726c 642c  ev: Hello world,\n+00003320: 2020 5570 3a20 496e 7472 6f64 7563 7469    Up: Introducti\n+00003330: 6f6e 2062 7920 6578 616d 706c 650a 0a32  on by example..2\n+00003340: 2e32 204f 7074 696f 6e73 0a3d 3d3d 3d3d  .2 Options.=====\n+00003350: 3d3d 3d3d 3d3d 0a0a 4d61 6e79 2027 5053  ======..Many 'PS\n+00003360: 5472 6963 6b73 2720 616e 6420 2754 696b  Tricks' and 'Tik\n+00003370: 5a2f 5047 4627 206f 7074 696f 6e73 2077  Z/PGF' options w\n+00003380: 6f72 6b20 6a75 7374 2066 696e 6520 696e  ork just fine in\n+00003390: 2027 736b 6574 6368 272e 2020 4966 0a67   'sketch'.  If.g\n+000033a0: 656e 6572 6174 696e 6720 2750 5354 7269  enerating 'PSTri\n+000033b0: 636b 7327 2c20 7468 6520 636f 6465 0a20  cks', the code. \n+000033c0: 2070 6f6c 7967 6f6e 5b66 696c 6c63 6f6c   polygon[fillcol\n+000033d0: 6f72 3d6c 6967 6874 6772 6179 2c6c 696e  or=lightgray,lin\n+000033e0: 6577 6964 7468 3d33 7074 5d28 302c 302c  ewidth=3pt](0,0,\n+000033f0: 3129 2831 2c30 2c30 2928 302c 312c 3029  1)(1,0,0)(0,1,0)\n+00003400: 0a20 206c 696e 655b 6c69 6e65 7374 796c  .  line[linestyl\n+00003410: 653d 646f 7474 6564 5d28 2d31 2c2d 312c  e=dotted](-1,-1,\n+00003420: 2d31 2928 322c 322c 3229 0a70 726f 6475  -1)(2,2,2).produ\n+00003430: 6365 730a 0a00 085b 696d 6167 6520 7372  ces....[image sr\n+00003440: 633d 2265 7830 3330 2e70 6e67 2220 7465  c=\"ex030.png\" te\n+00003450: 7874 3d22 496d 6167 6520 6578 3033 3020  xt=\"Image ex030 \n+00003460: 6f6d 6974 7465 6420 696e 2074 6578 7420  omitted in text \n+00003470: 7665 7273 696f 6e20 6f66 2074 6869 7320  version of this \n+00003480: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a20  document.\"..].. \n+00003490: 2020 546f 2070 726f 6475 6365 2027 5469    To produce 'Ti\n+000034a0: 6b5a 2f50 4746 272c 2074 6865 2063 6f72  kZ/PGF', the cor\n+000034b0: 7265 7370 6f6e 6469 6e67 2063 6f64 6520  responding code \n+000034c0: 6973 0a20 2070 6f6c 7967 6f6e 5b66 696c  is.  polygon[fil\n+000034d0: 6c3d 6c69 6768 7467 7261 792c 6c69 6e65  l=lightgray,line\n+000034e0: 2077 6964 7468 3d33 7074 5d28 302c 302c   width=3pt](0,0,\n+000034f0: 3129 2831 2c30 2c30 2928 302c 312c 3029  1)(1,0,0)(0,1,0)\n+00003500: 0a20 206c 696e 655b 7374 796c 653d 646f  .  line[style=do\n+00003510: 7474 6564 5d28 2d31 2c2d 312c 2d31 2928  tted](-1,-1,-1)(\n+00003520: 322c 322c 3229 0a20 2067 6c6f 6261 6c20  2,2,2).  global \n+00003530: 7b20 6c61 6e67 7561 6765 2074 696b 7a20  { language tikz \n+00003540: 7d0a 5468 6520 6669 6e61 6c20 2767 6c6f  }.The final 'glo\n+00003550: 6261 6c27 2069 6e73 7472 7563 7473 2027  bal' instructs '\n+00003560: 736b 6574 6368 2720 746f 2070 726f 6475  sketch' to produ\n+00003570: 6365 2027 5469 6b5a 2f50 4746 2720 636f  ce 'TikZ/PGF' co\n+00003580: 6465 2061 730a 6f75 7470 7574 2072 6174  de as.output rat\n+00003590: 6865 7220 7468 616e 2074 6865 2064 6566  her than the def\n+000035a0: 6175 6c74 2c20 2750 5354 7269 636b 7327  ault, 'PSTricks'\n+000035b0: 2e20 204e 6f74 6520 7468 6174 2027 706f  .  Note that 'po\n+000035c0: 6c79 676f 6e27 2066 696c 6c0a 636f 6c6f  lygon' fill.colo\n+000035d0: 7220 616e 6420 276c 696e 6527 2073 7479  r and 'line' sty\n+000035e0: 6c65 206f 7074 696f 6e73 2062 6f74 6820  le options both \n+000035f0: 636f 6e66 6f72 6d20 746f 2027 5469 6b5a  conform to 'TikZ\n+00003600: 2720 7379 6e74 6178 2072 756c 6573 2e20  ' syntax rules. \n+00003610: 2054 6865 0a72 6573 756c 7469 6e67 2027   The.resulting '\n+00003620: 5469 6b5a 2f50 4746 2720 6f75 7470 7574  TikZ/PGF' output\n+00003630: 2069 730a 2020 5c62 6567 696e 7b74 696b   is.  \\begin{tik\n+00003640: 7a70 6963 7475 7265 7d5b 6a6f 696e 3d72  zpicture}[join=r\n+00003650: 6f75 6e64 5d0a 2020 5c64 7261 775b 646f  ound].  \\draw[do\n+00003660: 7474 6564 5d28 2d31 2c2d 3129 2d2d 282e  tted](-1,-1)--(.\n+00003670: 3333 332c 2e33 3333 293b 0a20 205c 6669  333,.333);.  \\fi\n+00003680: 6c6c 6472 6177 5b66 696c 6c3d 6c69 6768  lldraw[fill=ligh\n+00003690: 7467 7261 792c 6c69 6e65 2077 6964 7468  tgray,line width\n+000036a0: 3d33 7074 5d28 302c 3029 2d2d 2831 2c30  =3pt](0,0)--(1,0\n+000036b0: 292d 2d28 302c 3129 2d2d 6379 636c 653b  )--(0,1)--cycle;\n+000036c0: 0a20 205c 6472 6177 5b64 6f74 7465 645d  .  \\draw[dotted]\n+000036d0: 282e 3333 332c 2e33 3333 292d 2d28 322c  (.333,.333)--(2,\n+000036e0: 3229 3b0a 2020 5c65 6e64 7b74 696b 7a70  2);.  \\end{tikzp\n+000036f0: 6963 7475 7265 7d0a 5468 6520 7265 6d61  icture}.The rema\n+00003700: 696e 696e 6720 6578 616d 706c 6573 206f  ining examples o\n+00003710: 6620 7468 6973 206d 616e 7561 6c20 6172  f this manual ar\n+00003720: 6520 696e 2050 5354 7269 636b 7320 7374  e in PSTricks st\n+00003730: 796c 652e 0a0a 1f0a 4669 6c65 3a20 736b  yle.....File: sk\n+00003740: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n+00003750: 3a20 4472 6177 696e 6720 6120 736f 6c69  : Drawing a soli\n+00003760: 642c 2020 4e65 7874 3a20 5370 6563 6961  d,  Next: Specia\n+00003770: 6c20 6f62 6a65 6374 732c 2020 5072 6576  l objects,  Prev\n+00003780: 3a20 4472 6177 696e 6720 6f70 7469 6f6e  : Drawing option\n+00003790: 732c 2020 5570 3a20 496e 7472 6f64 7563  s,  Up: Introduc\n+000037a0: 7469 6f6e 2062 7920 6578 616d 706c 650a  tion by example.\n+000037b0: 0a32 2e33 2044 7261 7769 6e67 2061 2073  .2.3 Drawing a s\n+000037c0: 6f6c 6964 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d  olid.===========\n+000037d0: 3d3d 3d3d 3d3d 3d3d 0a0a 4c65 7427 7320  ========..Let's \n+000037e0: 7472 7920 736f 6d65 7468 696e 6720 6d6f  try something mo\n+000037f0: 7265 2065 7863 6974 696e 672e 2020 2753  re exciting.  'S\n+00003800: 6b65 7463 6827 2068 6173 206e 6f20 6e6f  ketch' has no no\n+00003810: 7469 6f6e 206f 6620 6120 736f 6c69 642c  tion of a solid,\n+00003820: 0a62 7574 2070 6f6c 7967 6f6e 616c 2022  .but polygonal \"\n+00003830: 6661 6365 7322 2063 616e 2062 6520 7573  faces\" can be us\n+00003840: 6564 2074 6f20 7265 7072 6573 656e 7420  ed to represent \n+00003850: 7468 6520 626f 756e 6461 7279 206f 6620  the boundary of \n+00003860: 6120 736f 6c69 642e 0a54 6f20 7468 6520  a solid..To the \n+00003870: 7072 6576 696f 7573 2065 7861 6d70 6c65  previous example\n+00003880: 2c20 6c65 7427 7320 6164 6420 7468 7265  , let's add thre\n+00003890: 6520 6d6f 7265 2074 7269 616e 6775 6c61  e more triangula\n+000038a0: 7220 706f 6c79 676f 6e73 2074 6f0a 6d61  r polygons to.ma\n+000038b0: 6b65 2074 6865 2066 6163 6573 206f 6620  ke the faces of \n+000038c0: 616e 2069 7272 6567 756c 6172 2074 6574  an irregular tet\n+000038d0: 7261 6865 6472 6f6e 2e0a 2020 2520 7665  rahedron..  % ve\n+000038e0: 7274 6963 6573 206f 6620 7468 6520 7465  rtices of the te\n+000038f0: 7472 6168 6564 726f 6e0a 2020 6465 6620  trahedron.  def \n+00003900: 7031 2028 302c 302c 3129 2064 6566 2070  p1 (0,0,1) def p\n+00003910: 3220 2831 2c30 2c30 290a 2020 6465 6620  2 (1,0,0).  def \n+00003920: 7033 2028 302c 312c 3029 2064 6566 2070  p3 (0,1,0) def p\n+00003930: 3420 282d 2e33 2c2d 2e35 2c2d 2e38 290a  4 (-.3,-.5,-.8).\n+00003940: 0a20 2025 2066 6163 6573 206f 6620 7468  .  % faces of th\n+00003950: 6520 7465 7472 6168 6564 726f 6e2e 0a20  e tetrahedron.. \n+00003960: 2070 6f6c 7967 6f6e 2870 3129 2870 3229   polygon(p1)(p2)\n+00003970: 2870 3329 2025 206f 7269 6769 6e61 6c20  (p3) % original \n+00003980: 6672 6f6e 7420 706f 6c79 676f 6e0a 2020  front polygon.  \n+00003990: 706f 6c79 676f 6e28 7031 2928 7034 2928  polygon(p1)(p4)(\n+000039a0: 7032 2920 2520 626f 7474 6f6d 0a20 2070  p2) % bottom.  p\n+000039b0: 6f6c 7967 6f6e 2870 3129 2870 3329 2870  olygon(p1)(p3)(p\n+000039c0: 3429 2025 206c 6566 740a 2020 706f 6c79  4) % left.  poly\n+000039d0: 676f 6e28 7033 2928 7032 2928 7034 2920  gon(p3)(p2)(p4) \n+000039e0: 2520 7265 6172 0a0a 2020 2520 6c69 6e65  % rear..  % line\n+000039f0: 2074 6f20 7069 6572 6365 2074 6865 2074   to pierce the t\n+00003a00: 6574 7261 6865 6472 6f6e 0a20 206c 696e  etrahedron.  lin\n+00003a10: 655b 6c69 6e65 636f 6c6f 723d 7265 645d  e[linecolor=red]\n+00003a20: 282d 312c 2d31 2c2d 3129 2832 2c32 2c32  (-1,-1,-1)(2,2,2\n+00003a30: 290a 5468 6973 2065 7861 6d70 6c65 2075  ).This example u\n+00003a40: 7365 7320 2264 6566 696e 6974 696f 6e73  ses \"definitions\n+00003a50: 222c 2077 6869 6368 2062 6567 696e 2077  \", which begin w\n+00003a60: 6974 6820 2764 6566 272e 2020 5468 6573  ith 'def'.  Thes\n+00003a70: 6520 2264 6566 696e 6522 0a6f 7220 6769  e \"define\".or gi\n+00003a80: 7665 206e 616d 6573 2074 6f20 706f 696e  ve names to poin\n+00003a90: 7473 2c20 7768 6963 6820 6172 6520 7468  ts, which are th\n+00003aa0: 656e 2061 7661 696c 6162 6c65 2061 7320  en available as \n+00003ab0: 2272 6566 6572 656e 6365 7322 2062 790a  \"references\" by.\n+00003ac0: 656e 636c 6f73 696e 6720 7468 6520 6e61  enclosing the na\n+00003ad0: 6d65 7320 696e 2070 6172 656e 7468 6573  mes in parenthes\n+00003ae0: 6573 2c20 652e 672e 2028 666f 6f29 2e20  es, e.g. (foo). \n+00003af0: 2054 6865 2070 6172 656e 7468 6573 6573   The parentheses\n+00003b00: 2064 656e 6f74 650a 7468 6174 2074 6865   denote.that the\n+00003b10: 206e 616d 6573 2072 6566 6572 2074 6f20   names refer to \n+00003b20: 706f 696e 7473 3b20 7468 6579 2061 7265  points; they are\n+00003b30: 2072 6571 7569 7265 642e 2020 5468 6572   required.  Ther\n+00003b40: 6520 6361 6e20 6265 206e 6f0a 7768 6974  e can be no.whit\n+00003b50: 6520 7370 6163 6520 6265 7477 6565 6e20  e space between \n+00003b60: 7468 656d 2061 6e64 2074 6865 206e 616d  them and the nam\n+00003b70: 652e 0a0a 2020 2041 7320 796f 7520 6361  e...   As you ca\n+00003b80: 6e20 7365 652c 2063 6f6d 6d65 6e74 7320  n see, comments \n+00003b90: 7374 6172 7420 7769 7468 2025 2061 7320  start with % as \n+00003ba0: 696e 2054 6558 2061 6e64 2065 7874 656e  in TeX and exten\n+00003bb0: 6420 746f 2074 6865 2065 6e64 0a6f 6620  d to the end.of \n+00003bc0: 7468 6520 6c69 6e65 2028 7468 6f75 6768  the line (though\n+00003bd0: 2023 2077 696c 6c20 776f 726b 2061 7320   # will work as \n+00003be0: 7765 6c6c 292e 2020 5768 6974 6520 7370  well).  White sp\n+00003bf0: 6163 652c 2069 6e63 6c75 6469 6e67 0a73  ace, including.s\n+00003c00: 7061 6365 732c 2074 6162 7320 616e 6420  paces, tabs and \n+00003c10: 626c 616e 6b20 6c69 6e65 732c 2068 6173  blank lines, has\n+00003c20: 206e 6f20 6566 6665 6374 2069 6e20 7468   no effect in th\n+00003c30: 6520 2773 6b65 7463 6827 206c 616e 6775  e 'sketch' langu\n+00003c40: 6167 652e 0a0a 0008 5b69 6d61 6765 2073  age.....[image s\n+00003c50: 7263 3d22 6578 3034 302e 706e 6722 2074  rc=\"ex040.png\" t\n+00003c60: 6578 743d 2249 6d61 6765 2065 7830 3430  ext=\"Image ex040\n+00003c70: 206f 6d69 7474 6564 2069 6e20 7465 7874   omitted in text\n+00003c80: 2076 6572 7369 6f6e 206f 6620 7468 6973   version of this\n+00003c90: 2064 6f63 756d 656e 742e 2200 085d 0a0a   document.\"..]..\n+00003ca0: 4966 2077 6520 6c6f 6f6b 2069 6e73 6964  If we look insid\n+00003cb0: 6520 7468 6520 5465 5820 6669 6c65 2070  e the TeX file p\n+00003cc0: 726f 6475 6365 6420 6279 2027 736b 6574  roduced by 'sket\n+00003cd0: 6368 272c 2074 6865 7265 2077 696c 6c20  ch', there will \n+00003ce0: 6265 206f 6e6c 790a 7468 7265 6520 706f  be only.three po\n+00003cf0: 6c79 676f 6e73 2e20 2054 6865 2066 6f75  lygons.  The fou\n+00003d00: 7274 6820 6861 7320 6265 656e 2063 756c  rth has been cul\n+00003d10: 6c65 6420 6265 6361 7573 6520 6974 2069  led because it i\n+00003d20: 7320 6120 2262 6163 6b20 6661 6365 220a  s a \"back face\".\n+00003d30: 6f66 2074 6865 2074 6574 7261 6865 6472  of the tetrahedr\n+00003d40: 6f6e 2c20 696e 7669 7369 626c 6520 746f  on, invisible to\n+00003d50: 206f 7572 2076 6965 772e 2020 4974 2069   our view.  It i\n+00003d60: 7320 756e 6e65 6365 7373 6172 792c 2061  s unnecessary, a\n+00003d70: 6e64 2073 6f20 6974 0a69 7320 7265 6d6f  nd so it.is remo\n+00003d80: 7665 642e 0a0a 2020 2049 6e20 736f 6d65  ved...   In some\n+00003d90: 2064 7261 7769 6e67 732c 2070 6f6c 7967   drawings, polyg\n+00003da0: 6f6e 7320 6163 7420 6173 207a 6572 6f2d  ons act as zero-\n+00003db0: 7468 6963 6b6e 6573 7320 736f 6c69 6420  thickness solid \n+00003dc0: 7375 7266 6163 6573 2077 6974 680a 626f  surfaces with.bo\n+00003dd0: 7468 2073 6964 6573 2076 6973 6962 6c65  th sides visible\n+00003de0: 2072 6174 6865 7220 7468 616e 2061 7320   rather than as \n+00003df0: 7468 6520 6661 6365 7320 6f66 2073 6f6c  the faces of sol\n+00003e00: 6964 206f 626a 6563 7473 2c20 7768 6572  id objects, wher\n+00003e10: 6520 6261 636b 0a66 6163 6573 2063 616e  e back.faces can\n+00003e20: 2062 6520 6375 6c6c 6564 2e20 2046 6f72   be culled.  For\n+00003e30: 207a 6572 6f2d 7468 6963 6b6e 6573 7320   zero-thickness \n+00003e40: 736f 6c69 6473 2c20 6375 6c6c 696e 6720  solids, culling \n+00003e50: 6973 2061 2070 726f 626c 656d 2e0a 4f6e  is a problem..On\n+00003e60: 6520 736f 6c75 7469 6f6e 2069 7320 746f  e solution is to\n+00003e70: 2075 7365 2061 2070 6169 7220 6f66 2027   use a pair of '\n+00003e80: 736b 6574 6368 2720 706f 6c79 676f 6e73  sketch' polygons\n+00003e90: 2066 6f72 2065 6163 680a 7a65 726f 2d74   for each.zero-t\n+00003ea0: 6869 636b 6e65 7373 2066 6163 652c 2069  hickness face, i\n+00003eb0: 6465 6e74 6963 616c 2065 7863 6570 7420  dentical except \n+00003ec0: 7769 7468 206f 7070 6f73 6974 6520 7665  with opposite ve\n+00003ed0: 7274 6578 206f 7264 6572 732e 2020 5468  rtex orders.  Th\n+00003ee0: 6973 0a69 7320 756e 7769 656c 6479 2061  is.is unwieldy a\n+00003ef0: 6e64 2065 7870 656e 7369 7665 2e20 2041  nd expensive.  A\n+00003f00: 2062 6574 7465 7220 7761 7920 6973 2074   better way is t\n+00003f10: 6f20 7365 7420 7468 6520 2773 6b65 7463  o set the 'sketc\n+00003f20: 6827 2069 6e74 6572 6e61 6c0a 6f70 7469  h' internal.opti\n+00003f30: 6f6e 2027 6375 6c6c 2720 746f 2027 6661  on 'cull' to 'fa\n+00003f40: 6c73 6527 2069 6e20 7468 6520 7573 7561  lse' in the usua\n+00003f50: 6c20 2750 5354 7269 636b 7327 206d 616e  l 'PSTricks' man\n+00003f60: 6e65 722e 0a20 2070 6f6c 7967 6f6e 5b63  ner..  polygon[c\n+00003f70: 756c 6c3d 6661 6c73 655d 2870 3129 2870  ull=false](p1)(p\n+00003f80: 3229 2870 3329 0a54 6865 2066 6f6c 6c6f  2)(p3).The follo\n+00003f90: 7769 6e67 2073 686f 7773 2074 6865 2073  wing shows the s\n+00003fa0: 616d 6520 6865 6c69 7820 7368 6170 6520  ame helix shape \n+00003fb0: 6472 6177 6e20 6669 7273 7420 7769 7468  drawn first with\n+00003fc0: 2063 756c 6c3d 7472 7565 2028 7468 650a   cull=true (the.\n+00003fd0: 6465 6661 756c 7429 2061 6e64 2074 6865  default) and the\n+00003fe0: 6e20 6375 6c6c 3d66 616c 7365 2e0a 0a00  n cull=false....\n+00003ff0: 085b 696d 6167 6520 7372 633d 2265 7830  .[image src=\"ex0\n+00004000: 3435 2e70 6e67 2220 7465 7874 3d22 496d  45.png\" text=\"Im\n+00004010: 6167 6520 6578 3034 3520 6f6d 6974 7465  age ex045 omitte\n+00004020: 6420 696e 2074 6578 7420 7665 7273 696f  d in text versio\n+00004030: 6e20 6f66 2074 6869 7320 646f 6375 6d65  n of this docume\n+00004040: 6e74 2e22 0008 5d0a 0a57 6527 6c6c 2073  nt.\"..]..We'll s\n+00004050: 6f6f 6e20 7365 6520 686f 7720 746f 2070  oon see how to p\n+00004060: 726f 6475 6365 2074 6865 7365 2068 656c  roduce these hel\n+00004070: 6978 6573 2077 6974 6820 6120 6665 7720  ixes with a few \n+00004080: 6c69 6e65 7320 6f66 2027 736b 6574 6368  lines of 'sketch\n+00004090: 270a 6c61 6e67 7561 6765 2063 6f64 652e  '.language code.\n+000040a0: 0a0a 2020 2049 7420 6d61 7920 6265 2074  ..   It may be t\n+000040b0: 656d 7074 696e 6720 746f 2074 7572 6e20  empting to turn \n+000040c0: 6375 6c6c 696e 6720 6f66 6620 6772 6174  culling off grat\n+000040d0: 7569 746f 7573 6c79 2073 6f20 7468 6174  uitously so that\n+000040e0: 2076 6572 7465 780a 6f72 6465 7220 6361   vertex.order ca\n+000040f0: 6e20 6265 2069 676e 6f72 6564 2e20 2054  n be ignored.  T\n+00004100: 6869 7320 6973 206e 6f74 2061 2067 6f6f  his is not a goo\n+00004110: 6420 6964 6561 2062 6563 6175 7365 206f  d idea because o\n+00004120: 7574 7075 7420 6669 6c65 2073 697a 650a  utput file size.\n+00004130: 616e 6420 5465 5820 616e 6420 506f 7374  and TeX and Post\n+00004140: 7363 7269 7074 2070 726f 6365 7373 696e  script processin\n+00004150: 6720 7469 6d65 2062 6f74 6820 6465 7065  g time both depe\n+00004160: 6e64 206f 6e20 7468 6520 6e75 6d62 6572  nd on the number\n+00004170: 206f 660a 6f75 7470 7574 2070 6f6c 7967   of.output polyg\n+00004180: 6f6e 732e 2020 4375 6c6c 696e 6720 7573  ons.  Culling us\n+00004190: 7561 6c6c 7920 696d 7072 6f76 6573 2070  ually improves p\n+000041a0: 6572 666f 726d 616e 6365 2062 7920 6120  erformance by a \n+000041b0: 6661 6374 6f72 206f 660a 7477 6f2e 2020  factor of.two.  \n+000041c0: 4f6e 2074 6865 206f 7468 6572 2068 616e  On the other han\n+000041d0: 642c 2067 6c6f 6261 6c6c 7920 7365 7474  d, globally sett\n+000041e0: 696e 6720 2763 756c 6c3d 6661 6c73 6527  ing 'cull=false'\n+000041f0: 2069 7320 7265 6173 6f6e 6162 6c65 0a77   is reasonable.w\n+00004200: 6869 6c65 2064 6562 7567 6769 6e67 2e20  hile debugging. \n+00004210: 2053 6565 202a 6e6f 7465 2047 6c6f 6261   See *note Globa\n+00004220: 6c20 6f70 7469 6f6e 733a 3a20 616e 6420  l options:: and \n+00004230: 2a6e 6f74 6520 4c69 6d69 7473 206f 6e20  *note Limits on \n+00004240: 6572 726f 720a 6465 7465 6374 696f 6e3a  error.detection:\n+00004250: 3a2e 0a0a 1f0a 4669 6c65 3a20 736b 6574  :.....File: sket\n+00004260: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n+00004270: 5370 6563 6961 6c20 6f62 6a65 6374 732c  Special objects,\n+00004280: 2020 4e65 7874 3a20 4f62 6a65 6374 2074    Next: Object t\n+00004290: 7261 6e73 666f 726d 732c 2020 5072 6576  ransforms,  Prev\n+000042a0: 3a20 4472 6177 696e 6720 6120 736f 6c69  : Drawing a soli\n+000042b0: 642c 2020 5570 3a20 496e 7472 6f64 7563  d,  Up: Introduc\n+000042c0: 7469 6f6e 2062 7920 6578 616d 706c 650a  tion by example.\n+000042d0: 0a32 2e34 2053 7065 6369 616c 206f 626a  .2.4 Special obj\n+000042e0: 6563 7473 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d  ects.===========\n+000042f0: 3d3d 3d3d 3d3d 3d3d 0a0a 5765 2063 616e  ========..We can\n+00004300: 2061 6464 206c 6162 656c 7320 746f 2061   add labels to a\n+00004310: 2064 7261 7769 6e67 2062 7920 7573 696e   drawing by usin\n+00004320: 6720 7370 6563 6961 6c20 6f62 6a65 6374  g special object\n+00004330: 732c 2077 6869 6368 2070 726f 7669 6465  s, which provide\n+00004340: 2061 0a77 6179 2074 6f20 656d 6265 6420   a.way to embed \n+00004350: 7261 7720 4c61 5465 5820 616e 6420 2750  raw LaTeX and 'P\n+00004360: 5354 7269 636b 7327 2063 6f64 652e 2020  STricks' code.  \n+00004370: 4164 6469 6e67 2074 6869 7320 746f 2074  Adding this to t\n+00004380: 6865 0a74 6574 7261 6865 6472 6f6e 2064  he.tetrahedron d\n+00004390: 6f65 7320 7468 6520 7472 6963 6b2e 0a20  oes the trick.. \n+000043a0: 2073 7065 6369 616c 207c 5c66 6f6f 746e   special |\\footn\n+000043b0: 6f74 6573 697a 650a 2020 2020 2020 2020  otesize.        \n+000043c0: 2020 205c 7570 7574 7b32 7074 7d5b 7572     \\uput{2pt}[ur\n+000043d0: 5d23 317b 2450 3124 7d0a 2020 2020 2020  ]#1{$P1$}.      \n+000043e0: 2020 2020 205c 7570 7574 5b72 5d23 327b       \\uput[r]#2{\n+000043f0: 2450 3224 7d0a 2020 2020 2020 2020 2020  $P2$}.          \n+00004400: 205c 7570 7574 5b75 5d23 337b 2450 3324   \\uput[u]#3{$P3$\n+00004410: 7d0a 2020 2020 2020 2020 2020 205c 7570  }.           \\up\n+00004420: 7574 5b64 5d23 347b 2450 3424 7d7c 0a20  ut[d]#4{$P4$}|. \n+00004430: 2020 2028 7031 2928 7032 2928 7033 2928     (p1)(p2)(p3)(\n+00004440: 7034 290a 4865 7265 2069 7320 7468 6520  p4).Here is the \n+00004450: 7265 7375 6c74 2e0a 0a00 085b 696d 6167  result.....[imag\n+00004460: 6520 7372 633d 2265 7830 3432 2e70 6e67  e src=\"ex042.png\n+00004470: 2220 7465 7874 3d22 496d 6167 6520 6578  \" text=\"Image ex\n+00004480: 3034 3220 6f6d 6974 7465 6420 696e 2074  042 omitted in t\n+00004490: 6578 7420 7665 7273 696f 6e20 6f66 2074  ext version of t\n+000044a0: 6869 7320 646f 6375 6d65 6e74 2e22 0008  his document.\"..\n+000044b0: 5d0a 0a20 2020 5468 6572 6520 6172 6520  ]..   There are \n+000044c0: 7365 7665 7261 6c20 6465 7461 696c 7320  several details \n+000044d0: 746f 206e 6f74 6520 6865 7265 2e20 2046  to note here.  F\n+000044e0: 6972 7374 2c20 7468 6520 7175 6f74 696e  irst, the quotin\n+000044f0: 670a 636f 6e76 656e 7469 6f6e 2066 6f72  g.convention for\n+00004500: 2074 6865 2072 6177 2063 6f64 6520 6973   the raw code is\n+00004510: 2073 696d 696c 6172 2074 6f20 7468 6520   similar to the \n+00004520: 4c61 5465 5820 5c76 6572 6220 636f 6d6d  LaTeX \\verb comm\n+00004530: 616e 642e 2020 5468 650a 6669 7273 7420  and.  The.first \n+00004540: 6e6f 6e2d 7768 6974 6520 7370 6163 6520  non-white space \n+00004550: 6368 6172 6163 7465 7220 666f 6c6c 6f77  character follow\n+00004560: 696e 6720 7370 6563 6961 6c20 6973 2075  ing special is u\n+00004570: 6e64 6572 7374 6f6f 6420 746f 2062 650a  nderstood to be.\n+00004580: 7468 6520 7175 6f74 6520 6368 6172 6163  the quote charac\n+00004590: 7465 722c 2069 6e20 7468 6973 2063 6173  ter, in this cas\n+000045a0: 6520 277c 272e 2020 5468 6520 7261 7720  e '|'.  The raw \n+000045b0: 7465 7874 2063 6f6e 7469 6e75 6573 2075  text continues u\n+000045c0: 6e74 696c 0a74 6869 7320 6368 6172 6163  ntil.this charac\n+000045d0: 7465 7220 7265 6375 7273 2e0a 0a20 2020  ter recurs...   \n+000045e0: 5365 636f 6e64 2c20 7468 6520 6172 6775  Second, the argu\n+000045f0: 6d65 6e74 2072 6566 6572 656e 6365 7320  ment references \n+00004600: 2331 2c20 2332 2c20 2333 2c20 616e 6420  #1, #2, #3, and \n+00004610: 2334 2072 6566 6572 2074 6f20 706f 696e  #4 refer to poin\n+00004620: 742c 0a76 6563 746f 722c 206f 7220 7363  t,.vector, or sc\n+00004630: 616c 6172 2076 616c 7565 7320 696e 2074  alar values in t\n+00004640: 6865 206c 6973 7420 7468 6174 2066 6f6c  he list that fol\n+00004650: 6c6f 772e 2020 5468 6973 2069 7320 7369  low.  This is si\n+00004660: 6d69 6c61 7220 746f 0a54 6558 206d 6163  milar to.TeX mac\n+00004670: 726f 2073 796e 7461 782e 2020 5468 6520  ro syntax.  The \n+00004680: 7472 616e 7366 6f72 6d65 6420 616e 6420  transformed and \n+00004690: 7477 6f2d 6469 6d65 6e73 696f 6e61 6c20  two-dimensional \n+000046a0: 7072 6f6a 6563 7469 6f6e 7320 6f66 0a74  projections of.t\n+000046b0: 6865 7365 2074 6872 6565 2d64 696d 656e  hese three-dimen\n+000046c0: 7369 6f6e 616c 2070 6f69 6e74 7320 6172  sional points ar\n+000046d0: 6520 7375 6273 7469 7475 7465 6420 696e  e substituted in\n+000046e0: 2074 6865 2066 696e 616c 206f 7574 7075   the final outpu\n+000046f0: 742e 2020 416e 0a61 7267 756d 656e 7420  t.  An.argument \n+00004700: 7265 6665 7265 6e63 6520 6f66 2074 6865  reference of the\n+00004710: 2066 6f72 6d20 2331 2d32 2069 7320 7265   form #1-2 is re\n+00004720: 706c 6163 6564 2077 6974 6820 7468 6520  placed with the \n+00004730: 616e 676c 6520 696e 0a64 6567 7265 6573  angle in.degrees\n+00004740: 206f 6620 7468 6520 7477 6f2d 6469 6d65   of the two-dime\n+00004750: 6e73 696f 6e61 6c20 7665 6374 6f72 2074  nsional vector t\n+00004760: 6861 7420 636f 6e6e 6563 7473 2074 6865  hat connects the\n+00004770: 2070 726f 6a65 6374 696f 6e73 206f 660a   projections of.\n+00004780: 7468 6520 7477 6f20 7265 7370 6563 7469  the two respecti\n+00004790: 7665 2061 7267 756d 656e 7420 706f 696e  ve argument poin\n+000047a0: 7473 2c20 6865 7265 2023 3120 616e 6420  ts, here #1 and \n+000047b0: 2332 2e20 2054 6865 2073 7562 7374 6974  #2.  The substit\n+000047c0: 7574 6564 0a61 6e67 6c65 2069 7320 656e  uted.angle is en\n+000047d0: 636c 6f73 6564 2069 6e20 6375 726c 7920  closed in curly \n+000047e0: 6272 6163 6573 2027 7b20 7d27 2e20 2057  braces '{ }'.  W\n+000047f0: 6865 6e20 2754 696b 5a2f 5047 4627 206f  hen 'TikZ/PGF' o\n+00004800: 7574 7075 7420 6973 0a62 6569 6e67 2067  utput is.being g\n+00004810: 656e 6572 6174 6564 2c20 7468 6520 616e  enerated, the an\n+00004820: 676c 6520 6973 2072 6f75 6e64 6564 2074  gle is rounded t\n+00004830: 6f20 7468 6520 6e65 6172 6573 7420 6465  o the nearest de\n+00004840: 6772 6565 2062 6563 6175 7365 0a6e 6f6e  gree because.non\n+00004850: 2d69 6e74 6567 6572 2061 6e67 6c65 7320  -integer angles \n+00004860: 6172 6520 6e6f 7420 616c 6c6f 7765 6420  are not allowed \n+00004870: 6279 2027 5469 6b5a 2f50 4746 2720 7072  by 'TikZ/PGF' pr\n+00004880: 696d 6974 6976 6573 2e0a 0a20 2020 4173  imitives...   As\n+00004890: 206f 6620 5665 7273 696f 6e20 302e 3320   of Version 0.3 \n+000048a0: 6f66 2027 736b 6574 6368 272c 2073 7065  of 'sketch', spe\n+000048b0: 6369 616c 2061 7267 756d 656e 7473 206d  cial arguments m\n+000048c0: 6179 2062 6520 7363 616c 6172 7320 6f72  ay be scalars or\n+000048d0: 0a76 6563 746f 7273 2069 6e20 6164 6469  .vectors in addi\n+000048e0: 7469 6f6e 2074 6f20 706f 696e 7473 2e20  tion to points. \n+000048f0: 2052 6566 6572 656e 6365 7320 746f 2073   References to s\n+00004900: 6361 6c61 7220 6172 6775 6d65 6e74 7320  calar arguments \n+00004910: 6172 650a 6d65 7265 6c79 2072 6570 6c61  are.merely repla\n+00004920: 6365 6420 7769 7468 2061 206e 756d 6265  ced with a numbe\n+00004930: 7220 666f 726d 6174 7465 6420 6a75 7374  r formatted just\n+00004940: 2061 7320 616e 7920 706f 696e 7420 636f   as any point co\n+00004950: 6f72 6469 6e61 7465 2e0a 5265 6665 7265  ordinate..Refere\n+00004960: 6e63 6573 2074 6f20 7665 6374 6f72 7320  nces to vectors \n+00004970: 6265 636f 6d65 2074 776f 2d64 696d 656e  become two-dimen\n+00004980: 7369 6f6e 616c 2070 6f69 6e74 732e 2020  sional points.  \n+00004990: 5468 6520 7469 636b 206f 7065 7261 746f  The tick operato\n+000049a0: 720a 7468 6174 2073 656c 6563 7473 2069  r.that selects i\n+000049b0: 6e64 6976 6964 7561 6c20 636f 6d70 6f6e  ndividual compon\n+000049c0: 656e 7473 206f 6620 706f 696e 7473 2061  ents of points a\n+000049d0: 6e64 2076 6563 746f 7273 2065 6c73 6577  nd vectors elsew\n+000049e0: 6865 7265 2069 6e0a 2773 6b65 7463 6827  here in.'sketch'\n+000049f0: 2028 7365 6520 666f 7220 6578 616d 706c   (see for exampl\n+00004a00: 6520 2a6e 6f74 6520 4166 6669 6e65 2061  e *note Affine a\n+00004a10: 7269 7468 6d65 7469 633a 3a29 2063 616e  rithmetic::) can\n+00004a20: 2061 6c73 6f20 6265 2061 7070 6c69 6564   also be applied\n+00004a30: 0a74 6f20 706f 696e 7420 616e 6420 7665  .to point and ve\n+00004a40: 6374 6f72 2061 7267 756d 656e 7420 7265  ctor argument re\n+00004a50: 6665 7265 6e63 6573 2e20 2041 6c6c 2074  ferences.  All t\n+00004a60: 6872 6565 2064 696d 656e 7369 6f6e 7320  hree dimensions \n+00004a70: 6f66 2061 0a74 7261 6e73 666f 726d 6564  of a.transformed\n+00004a80: 2070 6f69 6e74 206f 7220 7665 6374 6f72   point or vector\n+00004a90: 2063 616e 2061 6c73 6f20 6265 2073 7562   can also be sub\n+00004aa0: 7374 6974 7565 6420 7769 7468 2027 2733  stitued with ''3\n+00004ab0: 272e 2020 5365 6520 2a6e 6f74 650a 5370  '.  See *note.Sp\n+00004ac0: 6563 6961 6c73 3a3a 2066 6f72 2064 6574  ecials:: for det\n+00004ad0: 6169 6c73 2e0a 0a20 2020 4279 2064 6566  ails...   By def\n+00004ae0: 6175 6c74 2c20 2773 7065 6369 616c 2720  ault, 'special' \n+00004af0: 6f62 6a65 6374 7320 6172 6520 7072 696e  objects are prin\n+00004b00: 7465 6420 6c61 7374 2c20 6f76 6572 6c61  ted last, overla\n+00004b10: 7969 6e67 2061 6c6c 206f 7468 6572 0a6f  ying all other.o\n+00004b20: 626a 6563 7473 2069 6e20 7468 6520 7363  bjects in the sc\n+00004b30: 656e 652e 2020 4966 2079 6f75 2073 7065  ene.  If you spe\n+00004b40: 6369 6679 2074 6865 2069 6e74 6572 6e61  cify the interna\n+00004b50: 6c20 6f70 7469 6f6e 2027 6c61 793d 696e  l option 'lay=in\n+00004b60: 272c 2074 6865 0a68 6964 6465 6e20 7375  ', the.hidden su\n+00004b70: 7266 6163 6520 616c 676f 7269 7468 6d20  rface algorithm \n+00004b80: 636f 6e73 6964 6572 7320 7468 6520 656e  considers the en\n+00004b90: 7469 7265 2073 7065 6369 616c 206f 626a  tire special obj\n+00004ba0: 6563 7420 746f 2062 6520 7468 650a 6669  ect to be the.fi\n+00004bb0: 7273 7420 706f 696e 7420 2823 3129 2069  rst point (#1) i\n+00004bc0: 6e20 7468 6520 6172 6775 6d65 6e74 206c  n the argument l\n+00004bd0: 6973 742e 2020 4966 2074 6861 7420 706f  ist.  If that po\n+00004be0: 696e 7420 6973 2062 6568 696e 6420 286f  int is behind (o\n+00004bf0: 660a 736d 616c 6c65 7220 7a2d 636f 6d70  f.smaller z-comp\n+00004c00: 6f6e 656e 7420 7468 616e 2920 616e 7920  onent than) any \n+00004c10: 6472 6177 6162 6c65 2c20 7468 656e 2074  drawable, then t\n+00004c20: 6865 2065 6e74 6972 6520 7370 6563 6961  he entire specia\n+00004c30: 6c20 6f62 6a65 6374 0a69 7320 6472 6177  l object.is draw\n+00004c40: 6e20 6265 666f 7265 2074 6861 7420 6472  n before that dr\n+00004c50: 6177 6162 6c65 2c20 736f 2074 6865 2064  awable, so the d\n+00004c60: 7261 7761 626c 6520 6f62 7363 7572 6573  rawable obscures\n+00004c70: 2070 6172 7473 206f 6620 7468 650a 7370   parts of the.sp\n+00004c80: 6563 6961 6c20 6f62 6a65 6374 2074 6861  ecial object tha\n+00004c90: 7420 6f76 6572 6c61 7073 2069 742e 2020  t overlaps it.  \n+00004ca0: 496e 206f 7572 2065 7861 6d70 6c65 2c20  In our example, \n+00004cb0: 7031 2069 7320 7468 6520 6672 6f6e 742d  p1 is the front-\n+00004cc0: 6d6f 7374 0a70 6f69 6e74 2069 6e20 7468  most.point in th\n+00004cd0: 6520 7363 656e 6520 2868 6173 2074 6865  e scene (has the\n+00004ce0: 206c 6172 6765 7374 207a 2d63 6f6d 706f   largest z-compo\n+00004cf0: 6e65 6e74 292c 2073 6f20 6164 6469 6e67  nent), so adding\n+00004d00: 2027 6c61 793d 696e 2720 6861 730a 6e6f   'lay=in' has.no\n+00004d10: 2065 6666 6563 742e 0a0a 2020 2057 6974   effect...   Wit\n+00004d20: 6820 6f70 7469 6f6e 2027 6c61 793d 756e  h option 'lay=un\n+00004d30: 6465 7227 2c20 6120 7370 6563 6961 6c20  der', a special \n+00004d40: 6973 2064 7261 776e 205f 6265 666f 7265  is drawn _before\n+00004d50: 5f2c 2068 656e 6365 2061 7070 6561 7273  _, hence appears\n+00004d60: 0a5f 756e 6465 725f 2061 6e79 206f 6620  ._under_ any of \n+00004d70: 7468 6520 6f62 6a65 6374 7320 6861 6e64  the objects hand\n+00004d80: 6c65 6420 6279 2074 6865 2068 6964 6465  led by the hidde\n+00004d90: 6e20 7375 7266 6163 6520 616c 676f 7269  n surface algori\n+00004da0: 7468 6d2e 0a54 6869 7320 6973 2068 6f77  thm..This is how\n+00004db0: 2074 6865 206c 6967 6874 2067 7261 7920   the light gray \n+00004dc0: 6178 6573 2077 6572 6520 6164 6465 6420  axes were added \n+00004dd0: 746f 2074 6865 2022 6865 6c6c 6f20 776f  to the \"hello wo\n+00004de0: 726c 6422 2065 7861 6d70 6c65 0a2a 6e6f  rld\" example.*no\n+00004df0: 7465 2048 656c 6c6f 2077 6f72 6c64 3a3a  te Hello world::\n+00004e00: 2e0a 0a20 2020 5370 6563 6961 6c20 6f62  ...   Special ob\n+00004e10: 6a65 6374 7320 6172 6520 706f 7765 7266  jects are powerf\n+00004e20: 756c 2c20 7769 7468 206d 616e 7920 706f  ul, with many po\n+00004e30: 7373 6962 6c65 2075 7365 732e 0a0a 1f0a  ssible uses.....\n+00004e40: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n+00004e50: 6f2c 2020 4e6f 6465 3a20 4f62 6a65 6374  o,  Node: Object\n+00004e60: 2074 7261 6e73 666f 726d 732c 2020 4e65   transforms,  Ne\n+00004e70: 7874 3a20 5265 7065 6174 6564 206f 626a  xt: Repeated obj\n+00004e80: 6563 7473 2c20 2050 7265 763a 2053 7065  ects,  Prev: Spe\n+00004e90: 6369 616c 206f 626a 6563 7473 2c20 2055  cial objects,  U\n+00004ea0: 703a 2049 6e74 726f 6475 6374 696f 6e20  p: Introduction \n+00004eb0: 6279 2065 7861 6d70 6c65 0a0a 322e 3520  by example..2.5 \n+00004ec0: 5472 616e 7366 6f72 6d73 0a3d 3d3d 3d3d  Transforms.=====\n+00004ed0: 3d3d 3d3d 3d3d 3d3d 3d0a 0a4e 6f77 206c  =========..Now l\n+00004ee0: 6574 2773 2061 6464 2061 2073 6563 6f6e  et's add a secon\n+00004ef0: 6420 636f 7079 206f 6620 7468 6520 7069  d copy of the pi\n+00004f00: 6572 6365 6420 7465 7472 6168 6564 726f  erced tetrahedro\n+00004f10: 6e2e 2020 5765 276c 6c20 726f 7461 7465  n.  We'll rotate\n+00004f20: 0a74 6865 2063 6f70 7920 3930 2064 6567  .the copy 90 deg\n+00004f30: 7265 6573 2061 626f 7574 2074 6865 2078  rees about the x\n+00004f40: 2d61 7869 7320 7769 7468 2074 6865 206f  -axis with the o\n+00004f50: 7269 6769 6e20 6173 2022 6365 6e74 6572  rigin as \"center\n+00004f60: 206f 660a 726f 7461 7469 6f6e 2220 736f   of.rotation\" so\n+00004f70: 2077 6520 6361 6e20 7365 6520 7468 6520   we can see the \n+00004f80: 6261 636b 2c20 7468 656e 2074 7261 6e73  back, then trans\n+00004f90: 6c61 7465 2069 7420 746f 2074 6865 2072  late it to the r\n+00004fa0: 6967 6874 2d2d 696e 2074 6865 0a70 6f73  ight--in the.pos\n+00004fb0: 6974 6976 6520 782d 6469 7265 6374 696f  itive x-directio\n+00004fc0: 6e2d 2d73 6f20 6974 2064 6f65 736e 2774  n--so it doesn't\n+00004fd0: 2063 6f6c 6c69 6465 2077 6974 6820 7468   collide with th\n+00004fe0: 6520 6f72 6967 696e 616c 2e20 2054 6f20  e original.  To \n+00004ff0: 6865 6c70 0a75 7320 7365 6520 7768 6174  help.us see what\n+00005000: 2773 2067 6f69 6e67 206f 6e2c 206d 616b  's going on, mak\n+00005010: 6520 7468 6520 6261 636b 2073 6964 6520  e the back side \n+00005020: 6772 6179 2e0a 2020 6465 6620 7069 6572  gray..  def pier\n+00005030: 6365 645f 7465 7472 6168 6564 726f 6e20  ced_tetrahedron \n+00005040: 7b0a 2020 2020 6465 6620 7031 2028 302c  {.    def p1 (0,\n+00005050: 302c 3129 2064 6566 2070 3220 2831 2c30  0,1) def p2 (1,0\n+00005060: 2c30 290a 2020 2020 6465 6620 7033 2028  ,0).    def p3 (\n+00005070: 302c 312c 3029 2064 6566 2070 3420 282d  0,1,0) def p4 (-\n+00005080: 2e33 2c2d 2e35 2c2d 2e38 290a 2020 2020  .3,-.5,-.8).    \n+00005090: 706f 6c79 676f 6e28 7031 2928 7032 2928  polygon(p1)(p2)(\n+000050a0: 7033 2920 2020 2020 2020 2020 2020 2020  p3)             \n+000050b0: 2020 2020 2020 2020 2025 206f 7269 6769           % origi\n+000050c0: 6e61 6c0a 2020 2020 706f 6c79 676f 6e28  nal.    polygon(\n+000050d0: 7031 2928 7034 2928 7032 2920 2020 2020  p1)(p4)(p2)     \n+000050e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000050f0: 2025 2062 6f74 746f 6d0a 2020 2020 706f   % bottom.    po\n+00005100: 6c79 676f 6e28 7031 2928 7033 2928 7034  lygon(p1)(p3)(p4\n+00005110: 2920 2020 2020 2020 2020 2020 2020 2020  )               \n+00005120: 2020 2020 2020 2025 206c 6566 740a 2020         % left.  \n+00005130: 2020 706f 6c79 676f 6e5b 6669 6c6c 636f    polygon[fillco\n+00005140: 6c6f 723d 6c69 6768 7467 7261 795d 2870  lor=lightgray](p\n+00005150: 3329 2870 3229 2870 3429 2025 2072 6561  3)(p2)(p4) % rea\n+00005160: 720a 2020 2020 6c69 6e65 5b6c 696e 6563  r.    line[linec\n+00005170: 6f6c 6f72 3d72 6564 5d28 2d31 2c2d 312c  olor=red](-1,-1,\n+00005180: 2d31 2928 322c 322c 3229 0a20 207d 0a20  -1)(2,2,2).  }. \n+00005190: 207b 7069 6572 6365 645f 7465 7472 6168   {pierced_tetrah\n+000051a0: 6564 726f 6e7d 2020 2520 7465 7472 6168  edron}  % tetrah\n+000051b0: 6564 726f 6e20 696e 206f 7269 6769 6e61  edron in origina\n+000051c0: 6c20 706f 7369 7469 6f6e 0a20 2070 7574  l position.  put\n+000051d0: 207b 2072 6f74 6174 6528 3930 2c20 2830   { rotate(90, (0\n+000051e0: 2c30 2c30 292c 205b 312c 302c 305d 2920  ,0,0), [1,0,0]) \n+000051f0: 2520 636f 7079 2069 6e20 6e65 7720 706f  % copy in new po\n+00005200: 7369 7469 6f6e 0a20 2020 2020 2020 2074  sition.        t\n+00005210: 6865 6e20 7472 616e 736c 6174 6528 5b32  hen translate([2\n+00005220: 2e35 2c30 2c30 5d29 207d 207b 7069 6572  .5,0,0]) } {pier\n+00005230: 6365 645f 7465 7472 6168 6564 726f 6e7d  ced_tetrahedron}\n+00005240: 0a48 6572 6520 7468 6520 656e 7469 7265  .Here the entire\n+00005250: 2063 6f64 6520 6f66 2074 6865 2070 7265   code of the pre\n+00005260: 7669 6f75 7320 6578 616d 706c 6520 6861  vious example ha\n+00005270: 7320 6265 656e 2077 7261 7070 6564 2069  s been wrapped i\n+00005280: 6e20 610a 6465 6669 6e69 7469 6f6e 2062  n a.definition b\n+00005290: 7920 666f 726d 696e 6720 6120 2262 6c6f  y forming a \"blo\n+000052a0: 636b 2220 7769 7468 2062 7261 6365 7320  ck\" with braces \n+000052b0: 2861 2073 696e 676c 6520 6974 656d 2077  (a single item w\n+000052c0: 6f75 6c64 206e 6f74 0a6e 6565 6420 7468  ould not.need th\n+000052d0: 656d 292e 2020 5468 6520 706f 696e 7420  em).  The point \n+000052e0: 6465 6669 6e69 7469 6f6e 7320 6e65 7374  definitions nest\n+000052f0: 6564 2069 6e73 6964 6520 7468 6520 6272  ed inside the br\n+00005300: 6163 6573 2061 7265 0a22 6c65 7869 6361  aces are.\"lexica\n+00005310: 6c6c 7920 7363 6f70 6564 222e 2020 5468  lly scoped\".  Th\n+00005320: 6569 7220 6d65 616e 696e 6720 6578 7465  eir meaning exte\n+00005330: 6e64 7320 6f6e 6c79 2074 6f20 7468 6520  nds only to the \n+00005340: 656e 6420 6f66 2074 6865 2062 6c6f 636b  end of the block\n+00005350: 2e0a 5468 6520 6f75 7465 7220 6465 6620  ..The outer def \n+00005360: 6973 2063 616c 6c65 6420 6120 2264 7261  is called a \"dra\n+00005370: 7761 626c 6522 2064 6566 696e 6974 696f  wable\" definitio\n+00005380: 6e20 6265 6361 7573 6520 6974 2064 6573  n because it des\n+00005390: 6372 6962 6573 0a73 6f6d 6574 6869 6e67  cribes.something\n+000053a0: 2074 6861 7420 6361 6e20 6265 2064 7261   that can be dra\n+000053b0: 776e 2e0a 0a20 2020 4120 6472 6177 6162  wn...   A drawab\n+000053c0: 6c65 2064 6566 696e 6974 696f 6e20 6279  le definition by\n+000053d0: 2069 7473 656c 6620 6361 7573 6573 206e   itself causes n\n+000053e0: 6f74 6869 6e67 2074 6f20 6861 7070 656e  othing to happen\n+000053f0: 2075 6e74 696c 2069 7473 0a6e 616d 6520   until its.name \n+00005400: 6973 2072 6566 6572 656e 6365 642e 2020  is referenced.  \n+00005410: 4472 6177 6162 6c65 2072 6566 6572 656e  Drawable referen\n+00005420: 6365 7320 6d75 7374 2062 6520 656e 636c  ces must be encl\n+00005430: 6f73 6564 2069 6e20 6375 726c 790a 6272  osed in curly.br\n+00005440: 6163 6573 2c20 652e 672e 207b 666f 6f7d  aces, e.g. {foo}\n+00005450: 2c20 7769 7468 206e 6f20 696e 7465 7276  , with no interv\n+00005460: 656e 696e 6720 7768 6974 6520 7370 6163  ening white spac\n+00005470: 652e 2020 496e 2074 6865 2063 6f64 6520  e.  In the code \n+00005480: 6162 6f76 652c 0a74 6865 2066 6972 7374  above,.the first\n+00005490: 2072 6566 6572 656e 6365 207b 7069 6572   reference {pier\n+000054a0: 6365 645f 7465 7472 6168 6564 726f 6e7d  ced_tetrahedron}\n+000054b0: 2069 7320 6120 706c 6169 6e20 6f6e 652e   is a plain one.\n+000054c0: 2020 4974 7320 6566 6665 6374 2069 730a    Its effect is.\n+000054d0: 6d65 7265 6c79 2074 6f20 6475 706c 6963  merely to duplic\n+000054e0: 6174 6520 7468 6520 6561 726c 6965 7220  ate the earlier \n+000054f0: 6472 6177 696e 672e 2020 416c 6d6f 7374  drawing.  Almost\n+00005500: 2061 6e79 2073 6572 6965 7320 6f66 2027   any series of '\n+00005510: 736b 6574 6368 270a 636f 6d6d 616e 6473  sketch'.commands\n+00005520: 2073 7475 6666 206d 6179 2062 6520 7265   stuff may be re\n+00005530: 706c 6163 6564 2077 6974 6820 6465 6620  placed with def \n+00005540: 666f 6f20 7b20 7374 7566 6620 7d20 7b66  foo { stuff } {f\n+00005550: 6f6f 7d20 7769 7468 6f75 740a 6368 616e  oo} without.chan\n+00005560: 6769 6e67 2069 7473 206d 6561 6e69 6e67  ging its meaning\n+00005570: 2e0a 0a20 2020 5468 6520 7075 7420 636f  ...   The put co\n+00005580: 6d6d 616e 6420 7375 7070 6c69 6573 2061  mmand supplies a\n+00005590: 2073 6563 6f6e 6420 7265 6665 7265 6e63   second referenc\n+000055a0: 652c 2074 6869 7320 7469 6d65 2077 6974  e, this time wit\n+000055b0: 6820 610a 2274 7261 6e73 666f 726d 2220  h a.\"transform\" \n+000055c0: 6170 706c 6965 6420 6669 7273 742e 2020  applied first.  \n+000055d0: 5468 6520 726f 7461 7465 2074 7261 6e73  The rotate trans\n+000055e0: 666f 726d 2074 7572 6e73 2074 6865 2074  form turns the t\n+000055f0: 6574 7261 6865 6472 6f6e 0a39 3020 6465  etrahedron.90 de\n+00005600: 6772 6565 7320 6162 6f75 7420 7468 6520  grees about the \n+00005610: 6f72 6967 696e 2e20 2054 6865 2061 7869  origin.  The axi\n+00005620: 7320 6f66 2072 6f74 6174 696f 6e20 6973  s of rotation is\n+00005630: 2074 6865 2076 6563 746f 720a 5b31 2c30   the vector.[1,0\n+00005640: 2c30 5d2e 2020 4279 2074 6865 2022 7269  ,0].  By the \"ri\n+00005650: 6768 7420 6861 6e64 2072 756c 6522 2c20  ght hand rule\", \n+00005660: 7468 6973 2063 6175 7365 7320 7468 6520  this causes the \n+00005670: 746f 7020 6f66 2074 6865 0a74 6574 7261  top of the.tetra\n+00005680: 6865 6472 6f6e 2074 6f20 726f 7461 7465  hedron to rotate\n+00005690: 2074 6f77 6172 6420 7468 6520 7669 6577   toward the view\n+000056a0: 6572 2061 6e64 2074 6865 2062 6f74 746f  er and the botto\n+000056b0: 6d20 6177 6179 2e20 2054 6865 2072 756c  m away.  The rul\n+000056c0: 650a 7265 6365 6976 6573 2069 7473 206e  e.receives its n\n+000056d0: 616d 6520 6672 6f6d 2074 6865 2066 6f6c  ame from the fol\n+000056e0: 6c6f 7769 6e67 2064 6566 696e 6974 696f  lowing definitio\n+000056f0: 6e3a 0a20 2020 2020 2a52 6967 6874 2068  n:.     *Right h\n+00005700: 616e 6420 7275 6c65 2e2a 2020 4966 2074  and rule.*  If t\n+00005710: 6865 2072 6967 6874 2068 616e 6420 6973  he right hand is\n+00005720: 2077 7261 7070 6564 2061 726f 756e 6420   wrapped around \n+00005730: 616e 7920 6178 6973 0a20 2020 2020 7769  any axis.     wi\n+00005740: 7468 2074 6865 2074 6875 6d62 2070 6f69  th the thumb poi\n+00005750: 6e74 696e 6720 696e 2074 6865 2061 7869  nting in the axi\n+00005760: 7320 6469 7265 6374 696f 6e2c 2074 6865  s direction, the\n+00005770: 6e20 7468 6520 6669 6e67 6572 730a 2020  n the fingers.  \n+00005780: 2020 2063 7572 6c20 696e 2074 6865 2064     curl in the d\n+00005790: 6972 6563 7469 6f6e 206f 6620 706f 7369  irection of posi\n+000057a0: 7469 7665 2072 6f74 6174 696f 6e20 6162  tive rotation ab\n+000057b0: 6f75 7420 7468 6174 2061 7869 732e 0a20  out that axis.. \n+000057c0: 2020 5468 6520 7472 616e 736c 6174 6520    The translate \n+000057d0: 7472 616e 7366 6f72 6d20 6d6f 7665 7320  transform moves \n+000057e0: 7468 6520 7079 7261 6d69 6420 6c61 7465  the pyramid late\n+000057f0: 7261 6c6c 7920 746f 2074 6865 2072 6967  rally to the rig\n+00005800: 6874 2062 790a 6164 6469 6e67 2074 6865  ht by.adding the\n+00005810: 2076 6563 746f 7220 5b32 2e35 2c30 2c30   vector [2.5,0,0\n+00005820: 5d20 746f 2065 6163 6820 7665 7274 6578  ] to each vertex\n+00005830: 2063 6f6f 7264 696e 6174 652e 2020 5468   coordinate.  Th\n+00005840: 6520 7265 7375 6c74 2069 730a 7368 6f77  e result is.show\n+00005850: 6e20 6865 7265 2e0a 0a00 085b 696d 6167  n here.....[imag\n+00005860: 6520 7372 633d 2265 7830 3530 2e70 6e67  e src=\"ex050.png\n+00005870: 2220 7465 7874 3d22 496d 6167 6520 6578  \" text=\"Image ex\n+00005880: 3035 3020 6f6d 6974 7465 6420 696e 2074  050 omitted in t\n+00005890: 6578 7420 7665 7273 696f 6e20 6f66 2074  ext version of t\n+000058a0: 6869 7320 646f 6375 6d65 6e74 2e22 0008  his document.\"..\n+000058b0: 5d0a 0a1f 0a46 696c 653a 2073 6b65 7463  ]....File: sketc\n+000058c0: 682e 696e 666f 2c20 204e 6f64 653a 2052  h.info,  Node: R\n+000058d0: 6570 6561 7465 6420 6f62 6a65 6374 732c  epeated objects,\n+000058e0: 2020 4e65 7874 3a20 5377 6570 7420 6f62    Next: Swept ob\n+000058f0: 6a65 6374 732c 2020 5072 6576 3a20 4f62  jects,  Prev: Ob\n+00005900: 6a65 6374 2074 7261 6e73 666f 726d 732c  ject transforms,\n+00005910: 2020 5570 3a20 496e 7472 6f64 7563 7469    Up: Introducti\n+00005920: 6f6e 2062 7920 6578 616d 706c 650a 0a32  on by example..2\n+00005930: 2e36 2052 6570 6561 7465 6420 6f62 6a65  .6 Repeated obje\n+00005940: 6374 730a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  cts.============\n+00005950: 3d3d 3d3d 3d3d 3d3d 0a0a 546f 2064 7261  ========..To dra\n+00005960: 7720 7365 7665 6e20 696e 7374 616e 6365  w seven instance\n+00005970: 7320 6f66 2074 6865 2074 6574 7261 6865  s of the tetrahe\n+00005980: 6472 6f6e 2c20 6561 6368 2064 6966 6665  dron, each diffe\n+00005990: 7269 6e67 2066 726f 6d20 7468 6520 6c61  ring from the la\n+000059a0: 7374 0a62 7920 7468 6520 7361 6d65 2074  st.by the same t\n+000059b0: 7261 6e73 666f 726d 2c20 7265 706c 6163  ransform, replac\n+000059c0: 6520 7468 6520 6c61 7374 2074 776f 2063  e the last two c\n+000059d0: 6f6d 6d61 6e64 7320 6f66 2074 6865 2070  ommands of the p\n+000059e0: 7265 7669 6f75 730a 6578 616d 706c 6520  revious.example \n+000059f0: 7769 7468 0a20 2072 6570 6561 7420 7b20  with.  repeat { \n+00005a00: 372c 2072 6f74 6174 6528 3135 2c20 2830  7, rotate(15, (0\n+00005a10: 2c30 2c30 292c 205b 312c 302c 305d 2920  ,0,0), [1,0,0]) \n+00005a20: 2520 636f 7079 2069 6e20 6e65 7720 706f  % copy in new po\n+00005a30: 7369 7469 6f6e 0a20 2020 2020 2020 2020  sition.         \n+00005a40: 2020 2020 2074 6865 6e20 7472 616e 736c       then transl\n+00005a50: 6174 6528 5b32 2c30 2c30 5d29 207d 207b  ate([2,0,0]) } {\n+00005a60: 7069 6572 6365 645f 7465 7472 6168 6564  pierced_tetrahed\n+00005a70: 726f 6e7d 0a41 6e64 2074 6865 2072 6573  ron}.And the res\n+00005a80: 756c 742e 2e2e 0a0a 0008 5b69 6d61 6765  ult.......[image\n+00005a90: 2073 7263 3d22 6578 3036 302e 706e 6722   src=\"ex060.png\"\n+00005aa0: 2074 6578 743d 2249 6d61 6765 2065 7830   text=\"Image ex0\n+00005ab0: 3630 206f 6d69 7474 6564 2069 6e20 7465  60 omitted in te\n+00005ac0: 7874 2076 6572 7369 6f6e 206f 6620 7468  xt version of th\n+00005ad0: 6973 2064 6f63 756d 656e 742e 2200 085d  is document.\"..]\n+00005ae0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n+00005af0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5377  .info,  Node: Sw\n+00005b00: 6570 7420 6f62 6a65 6374 732c 2020 5072  ept objects,  Pr\n+00005b10: 6576 3a20 5265 7065 6174 6564 206f 626a  ev: Repeated obj\n+00005b20: 6563 7473 2c20 2055 703a 2049 6e74 726f  ects,  Up: Intro\n+00005b30: 6475 6374 696f 6e20 6279 2065 7861 6d70  duction by examp\n+00005b40: 6c65 0a0a 322e 3720 5377 6570 7420 6f62  le..2.7 Swept ob\n+00005b50: 6a65 6374 730a 3d3d 3d3d 3d3d 3d3d 3d3d  jects.==========\n+00005b60: 3d3d 3d3d 3d3d 3d0a 0a4d 616e 7920 6661  =======..Many fa\n+00005b70: 6d69 6c69 6172 2073 6861 7065 7320 6361  miliar shapes ca\n+00005b80: 6e20 6265 2067 656e 6572 6174 6564 2062  n be generated b\n+00005b90: 7920 7377 6565 7069 6e67 2073 696d 706c  y sweeping simpl\n+00005ba0: 6572 206f 6e65 7320 7468 726f 7567 680a  er ones through.\n+00005bb0: 7370 6163 6520 616e 6420 636f 6e73 6964  space and consid\n+00005bc0: 6572 696e 6720 7468 6520 7265 7375 6c74  ering the result\n+00005bd0: 696e 6720 7061 7468 2c20 7375 7266 6163  ing path, surfac\n+00005be0: 652c 206f 7220 766f 6c75 6d65 2e20 2027  e, or volume.  '\n+00005bf0: 536b 6574 6368 270a 696d 706c 656d 656e  Sketch'.implemen\n+00005c00: 7473 2074 6869 7320 6964 6561 2069 6e20  ts this idea in \n+00005c10: 7468 6520 7377 6565 7020 636f 6d6d 616e  the sweep comman\n+00005c20: 642e 0a20 2064 6566 206e 5f73 6567 7320  d..  def n_segs \n+00005c30: 380a 2020 7377 6565 7020 7b20 6e5f 7365  8.  sweep { n_se\n+00005c40: 6773 2c20 726f 7461 7465 2831 3830 202f  gs, rotate(180 /\n+00005c50: 206e 5f73 6567 732c 2028 302c 302c 3029   n_segs, (0,0,0)\n+00005c60: 2c20 5b30 2c30 2c31 5d29 207d 2028 312c  , [0,0,1]) } (1,\n+00005c70: 302c 3029 0a54 6869 7320 636f 6465 2073  0,0).This code s\n+00005c80: 7765 6570 7320 7468 6520 706f 696e 7420  weeps the point \n+00005c90: 2831 2c30 2c30 2920 6569 6768 7420 7469  (1,0,0) eight ti\n+00005ca0: 6d65 7320 6279 2072 6f74 6174 696e 6720  mes by rotating \n+00005cb0: 6974 2031 3830 2f38 203d 0a32 322e 3520  it 180/8 =.22.5 \n+00005cc0: 6465 6772 6565 7320 6561 6368 2074 696d  degrees each tim\n+00005cd0: 6520 616e 6420 636f 6e6e 6563 7469 6e67  e and connecting\n+00005ce0: 2074 6865 2072 6573 756c 7469 6e67 2070   the resulting p\n+00005cf0: 6f69 6e74 7320 7769 7468 206c 696e 650a  oints with line.\n+00005d00: 7365 676d 656e 7473 2e20 2054 6865 2064  segments.  The d\n+00005d10: 6566 2075 7365 6420 6865 7265 2069 7320  ef used here is \n+00005d20: 6120 2273 6361 6c61 7222 2064 6566 696e  a \"scalar\" defin\n+00005d30: 6974 696f 6e2e 2020 5265 6665 7265 6e63  ition.  Referenc\n+00005d40: 6573 2074 6f0a 7363 616c 6172 7320 6861  es to.scalars ha\n+00005d50: 7665 206e 6f20 656e 636c 6f73 696e 6720  ve no enclosing \n+00005d60: 6272 6163 6b65 7473 2061 7420 616c 6c2e  brackets at all.\n+00005d70: 0a0a 2a20 4d65 6e75 3a0a 0a2a 2050 6f69  ..* Menu:..* Poi\n+00005d80: 6e74 2073 7765 6570 733a 3a20 2020 2020  nt sweeps::     \n+00005d90: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n+00005da0: 2070 6f69 6e74 7320 6d61 6b65 206c 696e   points make lin\n+00005db0: 6573 2061 6e64 2070 6f6c 7967 6f6e 732e  es and polygons.\n+00005dc0: 0a2a 2050 6f6c 796c 696e 6520 7377 6565  .* Polyline swee\n+00005dd0: 7073 3a3a 2020 2020 2020 2020 2020 2020  ps::            \n+00005de0: 2053 7765 7074 206c 696e 6573 206d 616b   Swept lines mak\n+00005df0: 6520 7375 7266 6163 6573 2e0a 2a20 4e65  e surfaces..* Ne\n+00005e00: 7374 6564 2073 7765 6570 733a 3a20 2020  sted sweeps::   \n+00005e10: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n+00005e20: 7420 7377 6565 7073 2061 7265 2075 7365  t sweeps are use\n+00005e30: 6675 6c21 0a2a 2050 6f6c 7967 6f6e 2073  ful!.* Polygon s\n+00005e40: 7765 6570 733a 3a20 2020 2020 2020 2020  weeps::         \n+00005e50: 2020 2020 2053 7765 7074 2070 6f6c 7967       Swept polyg\n+00005e60: 6f6e 7320 6d61 6b65 2073 6f6c 6964 732e  ons make solids.\n+00005e70: 2e2e 0a2a 2050 6f6c 796c 696e 6520 7377  ...* Polyline sw\n+00005e80: 6565 7073 2077 6974 6820 636c 6f73 7572  eeps with closur\n+00005e90: 653a 3a20 2061 6e64 2073 6f20 646f 2063  e::  and so do c\n+00005ea0: 6c6f 7365 6420 706f 6c79 6c69 6e65 2073  losed polyline s\n+00005eb0: 7765 6570 732e 0a2a 2041 6666 696e 6520  weeps..* Affine \n+00005ec0: 6172 6974 686d 6574 6963 3a3a 2020 2020  arithmetic::    \n+00005ed0: 2020 2020 2020 2053 6b65 7463 6820 7573         Sketch us\n+00005ee0: 6566 756c 206d 6174 6820 6578 7072 6573  eful math expres\n+00005ef0: 7369 6f6e 2e0a 2a20 4d6f 7265 2074 6f20  sion..* More to \n+00005f00: 6c65 6172 6e3a 3a20 2020 2020 2020 2020  learn::         \n+00005f10: 2020 2020 2020 4368 6563 6b20 6f75 7420        Check out \n+00005f20: 7468 6520 4d6f 6269 7573 2073 7472 6970  the Mobius strip\n+00005f30: 210a 0a1f 0a46 696c 653a 2073 6b65 7463  !....File: sketc\n+00005f40: 682e 696e 666f 2c20 204e 6f64 653a 2050  h.info,  Node: P\n+00005f50: 6f69 6e74 2073 7765 6570 732c 2020 4e65  oint sweeps,  Ne\n+00005f60: 7874 3a20 506f 6c79 6c69 6e65 2073 7765  xt: Polyline swe\n+00005f70: 6570 732c 2020 5072 6576 3a20 5377 6570  eps,  Prev: Swep\n+00005f80: 7420 6f62 6a65 6374 732c 2020 5570 3a20  t objects,  Up: \n+00005f90: 5377 6570 7420 6f62 6a65 6374 730a 0a32  Swept objects..2\n+00005fa0: 2e37 2e31 2050 6f69 6e74 2073 7765 6570  .7.1 Point sweep\n+00005fb0: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  s.--------------\n+00005fc0: 2d2d 2d2d 0a0a 5377 6565 7069 6e67 2061  ----..Sweeping a\n+00005fd0: 2070 6f69 6e74 206d 616b 6573 2061 206f   point makes a o\n+00005fe0: 6e65 2d64 696d 656e 7369 6f6e 616c 2070  ne-dimensional p\n+00005ff0: 6174 682c 2077 6869 6368 2069 7320 6120  ath, which is a \n+00006000: 706f 6c79 6c69 6e65 2e0a 5369 6e63 6520  polyline..Since \n+00006010: 7765 2068 6176 6520 7377 6570 7420 7769  we have swept wi\n+00006020: 7468 2061 2072 6f74 6174 696f 6e2c 2074  th a rotation, t\n+00006030: 6865 2072 6573 756c 7420 6973 2061 2063  he result is a c\n+00006040: 6972 6375 6c61 7220 6172 632e 2020 4865  ircular arc.  He\n+00006050: 7265 0a69 7320 7768 6174 2069 7420 6c6f  re.is what it lo\n+00006060: 6f6b 7320 6c69 6b65 2e0a 0a00 085b 696d  oks like.....[im\n+00006070: 6167 6520 7372 633d 2265 7830 3730 2e70  age src=\"ex070.p\n+00006080: 6e67 2220 7465 7874 3d22 496d 6167 6520  ng\" text=\"Image \n+00006090: 6578 3037 3020 6f6d 6974 7465 6420 696e  ex070 omitted in\n+000060a0: 2074 6578 7420 7665 7273 696f 6e20 6f66   text version of\n+000060b0: 2074 6869 7320 646f 6375 6d65 6e74 2e22   this document.\"\n+000060c0: 0008 5d0a 0a20 2020 5468 6973 2069 7320  ..]..   This is \n+000060d0: 7468 6520 6669 7273 7420 6578 616d 706c  the first exampl\n+000060e0: 6520 7765 2068 6176 6520 7365 656e 206f  e we have seen o\n+000060f0: 6620 2773 6b65 7463 6827 2061 7269 7468  f 'sketch' arith\n+00006100: 6d65 7469 632e 2020 5468 650a 6578 7072  metic.  The.expr\n+00006110: 6573 7369 6f6e 2031 3830 202f 206e 5f73  ession 180 / n_s\n+00006120: 6567 7320 6361 7573 6573 2074 6865 2065  egs causes the e\n+00006130: 6967 6874 2072 6f74 6174 696f 6e73 2074  ight rotations t\n+00006140: 6f20 6164 6420 746f 2031 3830 2e20 2049  o add to 180.  I\n+00006150: 660a 796f 7527 7265 2070 6179 696e 6720  f.you're paying \n+00006160: 6174 7465 6e74 696f 6e2c 2079 6f75 276c  attention, you'l\n+00006170: 6c20 6861 7665 2061 6c72 6561 6479 206e  l have already n\n+00006180: 6f74 6564 2074 6861 7420 7468 6572 6520  oted that there \n+00006190: 6172 6520 5f6e 696e 655f 0a70 6f69 6e74  are _nine_.point\n+000061a0: 732c 2070 726f 6475 6369 6e67 2065 6967  s, producing eig\n+000061b0: 6874 206c 696e 6520 7365 676d 656e 7473  ht line segments\n+000061c0: 2e0a 0a20 2020 596f 7520 6361 6e20 6361  ...   You can ca\n+000061d0: 7573 6520 7468 6520 7377 6570 7420 706f  use the swept po\n+000061e0: 696e 7420 746f 2067 656e 6572 6174 6520  int to generate \n+000061f0: 6120 7369 6e67 6c65 2070 6f6c 7967 6f6e  a single polygon\n+00006200: 2072 6174 6865 720a 7468 616e 2061 2070   rather.than a p\n+00006210: 6f6c 796c 696e 6520 6279 2075 7369 6e67  olyline by using\n+00006220: 2074 6865 2022 636c 6f73 7572 6520 7461   the \"closure ta\n+00006230: 6722 203c 3e20 6166 7465 7220 7468 6520  g\" <> after the \n+00006240: 6e75 6d62 6572 206f 6620 7377 6570 740a  number of swept.\n+00006250: 6f62 6a65 6374 732e 2020 436f 6465 2061  objects.  Code a\n+00006260: 6e64 2072 6573 756c 7420 666f 6c6c 6f77  nd result follow\n+00006270: 0a20 2064 6566 206e 5f73 6567 7320 380a  .  def n_segs 8.\n+00006280: 2020 7377 6565 7020 7b20 6e5f 7365 6773    sweep { n_segs\n+00006290: 3c3e 2c20 726f 7461 7465 2831 3830 202f  <>, rotate(180 /\n+000062a0: 206e 5f73 6567 732c 2028 302c 302c 3029   n_segs, (0,0,0)\n+000062b0: 2c20 5b30 2c30 2c31 5d29 207d 2028 312c  , [0,0,1]) } (1,\n+000062c0: 302c 3029 0a00 085b 696d 6167 6520 7372  0,0)...[image sr\n+000062d0: 633d 2265 7830 3830 2e70 6e67 2220 7465  c=\"ex080.png\" te\n+000062e0: 7874 3d22 496d 6167 6520 6578 3038 3020  xt=\"Image ex080 \n+000062f0: 6f6d 6974 7465 6420 696e 2074 6578 7420  omitted in text \n+00006300: 7665 7273 696f 6e20 6f66 2074 6869 7320  version of this \n+00006310: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a1f  document.\"..]...\n+00006320: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n+00006330: 666f 2c20 204e 6f64 653a 2050 6f6c 796c  fo,  Node: Polyl\n+00006340: 696e 6520 7377 6565 7073 2c20 204e 6578  ine sweeps,  Nex\n+00006350: 743a 204e 6573 7465 6420 7377 6565 7073  t: Nested sweeps\n+00006360: 2c20 2050 7265 763a 2050 6f69 6e74 2073  ,  Prev: Point s\n+00006370: 7765 6570 732c 2020 5570 3a20 5377 6570  weeps,  Up: Swep\n+00006380: 7420 6f62 6a65 6374 730a 0a32 2e37 2e32  t objects..2.7.2\n+00006390: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n+000063a0: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  .---------------\n+000063b0: 2d2d 2d2d 2d2d 0a0a 5377 6565 7069 6e67  ------..Sweeping\n+000063c0: 2061 2070 6f6c 796c 696e 6520 7072 6f64   a polyline prod\n+000063d0: 7563 6573 2061 2073 7572 6661 6365 2063  uces a surface c\n+000063e0: 6f6d 706f 7365 6420 6f66 206d 616e 7920  omposed of many \n+000063f0: 6661 6365 732e 2020 5468 650a 756e 6272  faces.  The.unbr\n+00006400: 6f6b 656e 2068 656c 6978 2069 6e20 7468  oken helix in th\n+00006410: 6520 6578 616d 706c 6520 2a6e 6f74 6520  e example *note \n+00006420: 4865 6c69 7820 7769 7468 2063 756c 6c20  Helix with cull \n+00006430: 7365 7420 6661 6c73 6520 7468 656e 0a74  set false then.t\n+00006440: 7275 653a 3a20 6973 2070 726f 6475 6365  rue:: is produce\n+00006450: 6420 6279 2074 6869 7320 636f 6465 2028  d by this code (\n+00006460: 706c 7573 2061 2073 7572 726f 756e 6469  plus a surroundi\n+00006470: 6e67 2070 7574 2072 6f74 6174 696f 6e20  ng put rotation \n+00006480: 746f 206d 616b 650a 616e 2069 6e74 6572  to make.an inter\n+00006490: 6573 7469 6e67 2076 6965 773b 2074 6869  esting view; thi\n+000064a0: 7320 6861 7320 6265 656e 206f 6d69 7474  s has been omitt\n+000064b0: 6564 292e 0a20 2064 6566 204b 205b 302c  ed)..  def K [0,\n+000064c0: 302c 315d 0a20 2073 7765 6570 5b63 756c  0,1].  sweep[cul\n+000064d0: 6c3d 6661 6c73 655d 207b 0a20 2020 2036  l=false] {.    6\n+000064e0: 302c 200a 2020 2020 726f 7461 7465 2831  0, .    rotate(1\n+000064f0: 302c 2028 302c 302c 3029 2c20 5b4b 5d29  0, (0,0,0), [K])\n+00006500: 2074 6865 6e20 7472 616e 736c 6174 6528   then translate(\n+00006510: 312f 3620 2a20 5b4b 5d29 200a 2020 7d20  1/6 * [K]) .  } \n+00006520: 6c69 6e65 5b6c 696e 6577 6964 7468 3d32  line[linewidth=2\n+00006530: 7074 5d28 2d31 2c30 2928 312c 3029 0a41  pt](-1,0)(1,0).A\n+00006540: 6761 696e 2c20 3630 2073 6567 6d65 6e74  gain, 60 segment\n+00006550: 7320 6f66 2074 6865 2068 656c 6978 2061  s of the helix a\n+00006560: 7265 2070 726f 6475 6365 6420 6279 2063  re produced by c\n+00006570: 6f6e 6e65 6374 696e 6720 3631 2069 6e73  onnecting 61 ins\n+00006580: 7461 6e63 6573 0a6f 6620 7468 6520 7377  tances.of the sw\n+00006590: 6570 7420 6c69 6e65 2e20 204f 7074 696f  ept line.  Optio\n+000065a0: 6e73 2061 7070 6c69 6564 2074 6f20 7468  ns applied to th\n+000065b0: 6520 7377 6565 702c 2068 6572 6520 6375  e sweep, here cu\n+000065c0: 6c6c 3d66 616c 7365 2c20 6172 650a 7472  ll=false, are.tr\n+000065d0: 6561 7465 6420 6173 206f 7074 696f 6e73  eated as options\n+000065e0: 2066 6f72 2074 6865 2067 656e 6572 6174   for the generat\n+000065f0: 6564 2070 6f6c 7967 6f6e 206f 7220 706f  ed polygon or po\n+00006600: 6c79 6c69 6e65 2e20 204f 7074 696f 6e73  lyline.  Options\n+00006610: 206f 660a 7468 6520 7377 6570 7420 6c69   of.the swept li\n+00006620: 6e65 2069 7473 656c 662c 2068 6572 6520  ne itself, here \n+00006630: 6c69 6e65 7769 6474 683d 3270 742c 2061  linewidth=2pt, a\n+00006640: 7265 2069 676e 6f72 6564 2c20 7468 6f75  re ignored, thou\n+00006650: 6768 2077 6974 6820 610a 7761 726e 696e  gh with a.warnin\n+00006660: 672e 2020 5468 6973 2064 6566 2069 7320  g.  This def is \n+00006670: 6120 2276 6563 746f 7222 2064 6566 696e  a \"vector\" defin\n+00006680: 6974 696f 6e2c 2077 6869 6368 206d 7573  ition, which mus\n+00006690: 7420 6265 2072 6566 6572 656e 6365 640a  t be referenced.\n+000066a0: 7769 7468 2073 7175 6172 6520 6272 6163  with square brac\n+000066b0: 6b65 7473 2c20 652e 672e 205b 666f 6f5d  kets, e.g. [foo]\n+000066c0: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463  .....File: sketc\n+000066d0: 682e 696e 666f 2c20 204e 6f64 653a 204e  h.info,  Node: N\n+000066e0: 6573 7465 6420 7377 6565 7073 2c20 204e  ested sweeps,  N\n+000066f0: 6578 743a 2050 6f6c 7967 6f6e 2073 7765  ext: Polygon swe\n+00006700: 6570 732c 2020 5072 6576 3a20 506f 6c79  eps,  Prev: Poly\n+00006710: 6c69 6e65 2073 7765 6570 732c 2020 5570  line sweeps,  Up\n+00006720: 3a20 5377 6570 7420 6f62 6a65 6374 730a  : Swept objects.\n+00006730: 0a32 2e37 2e33 204e 6573 7465 6420 7377  .2.7.3 Nested sw\n+00006740: 6565 7073 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d  eeps.-----------\n+00006750: 2d2d 2d2d 2d2d 2d2d 0a0a 5768 656e 2074  --------..When t\n+00006760: 6865 2063 656e 7465 7220 706f 696e 7420  he center point \n+00006770: 6f66 2072 6f74 6174 696f 6e20 6973 206f  of rotation is o\n+00006780: 6d69 7474 6564 2c20 7468 6520 6f72 6967  mitted, the orig\n+00006790: 696e 2069 7320 6173 7375 6d65 642e 0a57  in is assumed..W\n+000067a0: 6865 6e20 6120 706f 696e 7420 6861 7320  hen a point has \n+000067b0: 6f6e 6c79 2074 776f 2063 6f6f 7264 696e  only two coordin\n+000067c0: 6174 6573 2c20 7468 6579 2061 7265 2074  ates, they are t\n+000067d0: 616b 656e 2061 7320 7820 616e 6420 792c  aken as x and y,\n+000067e0: 2077 6974 680a 7a3d 3020 6173 7375 6d65   with.z=0 assume\n+000067f0: 642e 2020 4120 746f 726f 6964 2069 7320  d.  A toroid is \n+00006800: 7468 6572 6566 6f72 6520 6f62 7461 696e  therefore obtain\n+00006810: 6564 2077 6974 6820 7468 6973 2063 6f64  ed with this cod\n+00006820: 652e 0a20 2064 6566 206e 5f74 6f72 6f69  e..  def n_toroi\n+00006830: 645f 7365 6773 2032 3020 2020 6465 6620  d_segs 20   def \n+00006840: 6e5f 6369 7263 6c65 5f73 6567 7320 3136  n_circle_segs 16\n+00006850: 0a20 2064 6566 2072 5f6d 696e 6f72 2031  .  def r_minor 1\n+00006860: 2020 2020 2020 2020 2020 6465 6620 725f            def r_\n+00006870: 6d61 6a6f 7220 312e 350a 2020 7377 6565  major 1.5.  swee\n+00006880: 7020 7b20 6e5f 746f 726f 6964 5f73 6567  p { n_toroid_seg\n+00006890: 732c 2072 6f74 6174 6528 3336 3020 2f20  s, rotate(360 / \n+000068a0: 6e5f 746f 726f 6964 5f73 6567 732c 205b  n_toroid_segs, [\n+000068b0: 302c 312c 305d 2920 7d0a 2020 2020 7377  0,1,0]) }.    sw\n+000068c0: 6565 7020 7b20 6e5f 6369 7263 6c65 5f73  eep { n_circle_s\n+000068d0: 6567 732c 2072 6f74 6174 6528 3336 3020  egs, rotate(360 \n+000068e0: 2f20 6e5f 6369 7263 6c65 5f73 6567 732c  / n_circle_segs,\n+000068f0: 2028 725f 6d61 6a6f 722c 302c 3029 2920   (r_major,0,0)) \n+00006900: 7d20 0a20 2020 2020 2028 725f 6d61 6a6f  } .      (r_majo\n+00006910: 7220 2b20 725f 6d69 6e6f 722c 2030 290a  r + r_minor, 0).\n+00006920: 2020 2046 6f72 2069 6e74 7569 7469 6f6e     For intuition\n+00006930: 2c20 7468 6520 6964 6561 206f 6620 7468  , the idea of th\n+00006940: 6520 636f 6465 2069 7320 746f 2073 6b65  e code is to ske\n+00006950: 7463 6820 6120 6369 7263 6c65 2074 6f20  tch a circle to \n+00006960: 7468 650a 7269 6768 7420 6f66 2074 6865  the.right of the\n+00006970: 206f 7269 6769 6e20 696e 2074 6865 2078   origin in the x\n+00006980: 792d 706c 616e 652c 2074 6865 6e20 726f  y-plane, then ro\n+00006990: 7461 7465 2074 6861 7420 6369 7263 6c65  tate that circle\n+000069a0: 2022 6f75 7420 6f66 2074 6865 0a70 6c61   \"out of the.pla\n+000069b0: 6e65 2220 6162 6f75 7420 7468 6520 792d  ne\" about the y-\n+000069c0: 6178 6973 2074 6f20 6d61 6b65 2074 6865  axis to make the\n+000069d0: 2066 696e 616c 2066 6967 7572 652e 2020   final figure.  \n+000069e0: 5468 6973 2070 726f 6475 6365 7320 7468  This produces th\n+000069f0: 650a 666f 6c6c 6f77 696e 672e 2020 2841  e.following.  (A\n+00006a00: 2076 6965 7720 726f 7461 7469 6f6e 2061   view rotation a\n+00006a10: 6e64 2073 6f6d 6520 6178 6573 2068 6176  nd some axes hav\n+00006a20: 6520 6265 656e 2061 6464 6564 2e29 0a0a  e been added.)..\n+00006a30: 0008 5b69 6d61 6765 2073 7263 3d22 6578  ..[image src=\"ex\n+00006a40: 3039 302e 706e 6722 2074 6578 743d 2249  090.png\" text=\"I\n+00006a50: 6d61 6765 2065 7830 3930 206f 6d69 7474  mage ex090 omitt\n+00006a60: 6564 2069 6e20 7465 7874 2076 6572 7369  ed in text versi\n+00006a70: 6f6e 206f 6620 7468 6973 2064 6f63 756d  on of this docum\n+00006a80: 656e 742e 2200 085d 0a0a 2020 2054 6869  ent.\"..]..   Thi\n+00006a90: 7320 6578 616d 706c 6520 616c 736f 2073  s example also s\n+00006aa0: 686f 7773 2074 6861 7420 7468 6520 7377  hows that the sw\n+00006ab0: 6570 7420 6f62 6a65 6374 206d 6179 2069  ept object may i\n+00006ac0: 7473 656c 6620 6265 2061 6e6f 7468 6572  tself be another\n+00006ad0: 0a27 7377 6565 7027 2e20 2049 6e20 6661  .'sweep'.  In fa\n+00006ae0: 6374 2c20 6974 206d 6179 2062 6520 5f61  ct, it may be _a\n+00006af0: 6e79 5f20 2773 6b65 7463 6827 2065 7870  ny_ 'sketch' exp\n+00006b00: 7265 7373 696f 6e20 7468 6174 2072 6573  ression that res\n+00006b10: 756c 7473 2069 6e20 610a 6c69 7374 206f  ults in a.list o\n+00006b20: 6620 6f6e 6520 6f72 206d 6f72 6520 706f  f one or more po\n+00006b30: 696e 7473 206f 722c 2061 6c74 6572 6e61  ints or, alterna\n+00006b40: 7465 6c79 2c20 6120 6c69 7374 206f 6620  tely, a list of \n+00006b50: 6f6e 6520 6f72 206d 6f72 650a 706f 6c79  one or more.poly\n+00006b60: 6c69 6e65 7320 616e 6420 706f 6c79 676f  lines and polygo\n+00006b70: 6e73 2e20 2054 6865 206c 6174 7465 7220  ns.  The latter \n+00006b80: 6b69 6e64 206f 6620 6c69 7374 2063 616e  kind of list can\n+00006b90: 2062 6520 6372 6561 7465 6420 7769 7468   be created with\n+00006ba0: 2061 0a7b 207d 2d65 6e63 6c6f 7365 6420   a.{ }-enclosed \n+00006bb0: 626c 6f63 6b2c 2070 6572 6861 7073 2066  block, perhaps f\n+00006bc0: 6f6c 6c6f 7769 6e67 2061 2070 7574 206f  ollowing a put o\n+00006bd0: 7220 7265 7065 6174 2e0a 0a1f 0a46 696c  r repeat.....Fil\n+00006be0: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n+00006bf0: 204e 6f64 653a 2050 6f6c 7967 6f6e 2073   Node: Polygon s\n+00006c00: 7765 6570 732c 2020 4e65 7874 3a20 506f  weeps,  Next: Po\n+00006c10: 6c79 6c69 6e65 2073 7765 6570 7320 7769  lyline sweeps wi\n+00006c20: 7468 2063 6c6f 7375 7265 2c20 2050 7265  th closure,  Pre\n+00006c30: 763a 204e 6573 7465 6420 7377 6565 7073  v: Nested sweeps\n+00006c40: 2c20 2055 703a 2053 7765 7074 206f 626a  ,  Up: Swept obj\n+00006c50: 6563 7473 0a0a 322e 372e 3420 506f 6c79  ects..2.7.4 Poly\n+00006c60: 676f 6e20 7377 6565 7073 0a2d 2d2d 2d2d  gon sweeps.-----\n+00006c70: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a  ---------------.\n+00006c80: 0a53 7765 6570 696e 6720 6120 706f 6c79  .Sweeping a poly\n+00006c90: 676f 6e20 6372 6561 7465 7320 6120 636c  gon creates a cl\n+00006ca0: 6f73 6564 2073 7572 6661 6365 2077 6974  osed surface wit\n+00006cb0: 6820 706f 6c79 676f 6e73 2061 7420 7468  h polygons at th\n+00006cc0: 6520 656e 6473 2c0a 7768 6963 6820 6172  e ends,.which ar\n+00006cd0: 6520 6a75 7374 2063 6f70 6965 7320 6f66  e just copies of\n+00006ce0: 2074 6865 206f 7269 6769 6e61 6c2c 2061   the original, a\n+00006cf0: 7070 726f 7072 6961 7465 6c79 2070 6f73  ppropriately pos\n+00006d00: 6974 696f 6e65 642e 2020 2a4e 6f74 650a  itioned.  *Note.\n+00006d10: 536f 6c69 6420 636f 696c 2065 7861 6d70  Solid coil examp\n+00006d20: 6c65 3a3a 2e20 204f 7074 696f 6e73 206f  le::.  Options o\n+00006d30: 6e20 7468 6520 7377 6570 7420 706f 6c79  n the swept poly\n+00006d40: 676f 6e2c 2069 6620 7468 6579 2065 7869  gon, if they exi\n+00006d50: 7374 2c20 6172 650a 6170 706c 6965 6420  st, are.applied \n+00006d60: 746f 2074 6865 2065 6e64 732e 2020 4f74  to the ends.  Ot\n+00006d70: 6865 7277 6973 6520 7468 6520 7377 6565  herwise the swee\n+00006d80: 7020 6f70 7469 6f6e 7320 6172 6520 7573  p options are us\n+00006d90: 6564 2074 6872 6f75 6768 6f75 742e 0a0a  ed throughout...\n+00006da0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n+00006db0: 6e66 6f2c 2020 4e6f 6465 3a20 506f 6c79  nfo,  Node: Poly\n+00006dc0: 6c69 6e65 2073 7765 6570 7320 7769 7468  line sweeps with\n+00006dd0: 2063 6c6f 7375 7265 2c20 204e 6578 743a   closure,  Next:\n+00006de0: 2041 6666 696e 6520 6172 6974 686d 6574   Affine arithmet\n+00006df0: 6963 2c20 2050 7265 763a 2050 6f6c 7967  ic,  Prev: Polyg\n+00006e00: 6f6e 2073 7765 6570 732c 2020 5570 3a20  on sweeps,  Up: \n+00006e10: 5377 6570 7420 6f62 6a65 6374 730a 0a32  Swept objects..2\n+00006e20: 2e37 2e35 2050 6f6c 796c 696e 6520 7377  .7.5 Polyline sw\n+00006e30: 6565 7073 2077 6974 6820 636c 6f73 7572  eeps with closur\n+00006e40: 650a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  e.--------------\n+00006e50: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n+00006e60: 2d2d 2d2d 0a0a 4120 706f 6c79 6c69 6e65  ----..A polyline\n+00006e70: 2073 7765 6570 2077 6974 6820 6120 636c   sweep with a cl\n+00006e80: 6f73 7572 6520 7461 6720 6372 6561 7465  osure tag create\n+00006e90: 7320 616e 6f74 6865 7220 6b69 6e64 206f  s another kind o\n+00006ea0: 6620 636c 6f73 6564 0a73 7572 6661 6365  f closed.surface\n+00006eb0: 2e20 2046 6972 7374 2c20 7468 6520 706f  .  First, the po\n+00006ec0: 6c79 6c69 6e65 2073 6567 6d65 6e74 7320  lyline segments \n+00006ed0: 6172 6520 636f 6e6e 6563 7465 6420 6279  are connected by\n+00006ee0: 2066 6163 6573 2c20 6a75 7374 2061 730a   faces, just as.\n+00006ef0: 7769 7468 6f75 7420 7468 6520 636c 6f73  without the clos\n+00006f00: 7572 6520 7461 672e 2020 5468 656e 2c20  ure tag.  Then, \n+00006f10: 6561 6368 2073 6574 206f 6620 656e 6420  each set of end \n+00006f20: 706f 696e 7473 2069 7320 6a6f 696e 6564  points is joined\n+00006f30: 2074 6f20 6d61 6b65 0a61 2070 6f6c 7967   to make.a polyg\n+00006f40: 6f6e 2c20 6f6e 6520 666f 7220 6561 6368  on, one for each\n+00006f50: 2065 6e64 2e20 2041 2063 6f64 6520 666f   end.  A code fo\n+00006f60: 7220 7365 7665 7261 6c20 7669 6577 7320  r several views \n+00006f70: 6f66 2061 2063 796c 696e 6472 6963 616c  of a cylindrical\n+00006f80: 0a70 7269 736d 2066 6f6c 6c6f 7773 2e0a  .prism follows..\n+00006f90: 2020 6465 6620 6e5f 6379 6c5f 7365 6773    def n_cyl_segs\n+00006fa0: 2032 3020 2064 6566 206e 5f76 6965 7773   20  def n_views\n+00006fb0: 2035 2020 6465 6620 4920 5b31 2c30 2c30   5  def I [1,0,0\n+00006fc0: 5d0a 2020 6465 6620 656e 646f 7074 7320  ].  def endopts \n+00006fd0: 5b66 696c 6c63 6f6c 6f72 3d6c 6967 6874  [fillcolor=light\n+00006fe0: 6772 6179 5d0a 2020 7265 7065 6174 207b  gray].  repeat {\n+00006ff0: 206e 5f76 6965 7773 2c20 726f 7461 7465   n_views, rotate\n+00007000: 2831 3830 2f6e 5f76 6965 7773 2c20 5b49  (180/n_views, [I\n+00007010: 5d29 2074 6865 6e20 7472 616e 736c 6174  ]) then translat\n+00007020: 6528 5b49 5d20 2a20 322e 3129 207d 200a  e([I] * 2.1) } .\n+00007030: 2020 2020 7377 6565 705b 656e 646f 7074      sweep[endopt\n+00007040: 735d 7b20 6e5f 6379 6c5f 7365 6773 3c3e  s]{ n_cyl_segs<>\n+00007050: 2c20 726f 7461 7465 2833 3630 2f6e 5f63  , rotate(360/n_c\n+00007060: 796c 5f73 6567 732c 205b 302c 312c 305d  yl_segs, [0,1,0]\n+00007070: 2920 7d20 0a20 2020 2020 206c 696e 655b  ) } .      line[\n+00007080: 6669 6c6c 636f 6c6f 723d 7768 6974 655d  fillcolor=white]\n+00007090: 2831 2c2d 3129 2831 2c31 290a 4974 2070  (1,-1)(1,1).It p\n+000070a0: 726f 6475 6365 7320 7468 6973 2064 7261  roduces this dra\n+000070b0: 7769 6e67 2e0a 0a00 085b 696d 6167 6520  wing.....[image \n+000070c0: 7372 633d 2265 7831 3130 2e70 6e67 2220  src=\"ex110.png\" \n+000070d0: 7465 7874 3d22 496d 6167 6520 6578 3131  text=\"Image ex11\n+000070e0: 3020 6f6d 6974 7465 6420 696e 2074 6578  0 omitted in tex\n+000070f0: 7420 7665 7273 696f 6e20 6f66 2074 6869  t version of thi\n+00007100: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a  s document.\"..].\n+00007110: 0a54 6865 206f 7074 696f 6e73 206f 6620  .The options of \n+00007120: 7468 6520 7377 6570 7420 6c69 6e65 2c20  the swept line, \n+00007130: 6966 2061 6e79 2c20 6172 6520 6170 706c  if any, are appl\n+00007140: 6965 6420 746f 2074 6865 2066 6163 6573  ied to the faces\n+00007150: 2070 726f 6475 6365 640a 6279 2073 7765   produced.by swe\n+00007160: 6570 696e 6720 7468 6520 6c69 6e65 2c20  eping the line, \n+00007170: 6275 7420 6e6f 7420 7468 6520 656e 6420  but not the end \n+00007180: 706f 6c79 676f 6e73 2e20 204f 7468 6572  polygons.  Other\n+00007190: 7769 7365 2c20 7468 6520 7377 6565 700a  wise, the sweep.\n+000071a0: 6f70 7469 6f6e 7320 6172 6520 6170 706c  options are appl\n+000071b0: 6965 6420 7468 726f 7567 686f 7574 2e20  ied throughout. \n+000071c0: 2054 6865 2064 6566 2069 6e20 7468 6973   The def in this\n+000071d0: 2065 7861 6d70 6c65 2069 7320 616e 2022   example is an \"\n+000071e0: 6f70 7469 6f6e 220a 6465 6669 6e69 7469  option\".definiti\n+000071f0: 6f6e 2e20 2052 6566 6572 656e 6365 7320  on.  References \n+00007200: 746f 206f 7074 696f 6e73 206d 7573 7420  to options must \n+00007210: 6265 2065 6e63 6c6f 7365 6420 696e 2073  be enclosed in s\n+00007220: 7175 6172 6520 6272 6163 6b65 7473 2c0a  quare brackets,.\n+00007230: 652e 672e 2020 205b 666f 6f5d 2e20 2059  e.g.   [foo].  Y\n+00007240: 6f75 2063 616e 2063 6f6e 6361 7465 6e61  ou can concatena\n+00007250: 7465 2073 6576 6572 616c 2073 6574 7320  te several sets \n+00007260: 6f66 206f 7074 696f 6e73 2077 6974 6820  of options with \n+00007270: 6120 7369 6e67 6c65 0a72 6566 6572 656e  a single.referen\n+00007280: 6365 2c20 652e 672e 2020 205b 636f 6c6f  ce, e.g.   [colo\n+00007290: 722c 2073 697a 652c 2073 7479 6c65 5d20  r, size, style] \n+000072a0: 776f 756c 6420 6361 7573 6520 7468 6520  would cause the \n+000072b0: 6f70 7469 6f6e 0a64 6566 696e 6974 696f  option.definitio\n+000072c0: 6e73 2066 6f72 2027 636f 6c6f 7227 2c20  ns for 'color', \n+000072d0: 2773 697a 6527 2c20 616e 6420 2773 7479  'size', and 'sty\n+000072e0: 6c65 2720 746f 2061 7070 6561 7220 696e  le' to appear in\n+000072f0: 2073 6571 7565 6e63 6520 696e 0a74 6865   sequence in.the\n+00007300: 206f 7574 7075 7420 6372 6561 7465 6420   output created \n+00007310: 6279 2074 6865 2027 736b 6574 6368 2720  by the 'sketch' \n+00007320: 636f 6d6d 616e 6420 636f 6e74 6169 6e69  command containi\n+00007330: 6e67 2074 6865 2072 6566 6572 656e 6365  ng the reference\n+00007340: 2e0a 4861 7070 696c 792c 2074 6865 2073  ..Happily, the s\n+00007350: 796e 7461 7820 6f66 2027 736b 6574 6368  yntax of 'sketch\n+00007360: 2720 6973 2073 7563 6820 7468 6174 206f  ' is such that o\n+00007370: 7074 696f 6e73 2072 6566 6572 656e 6365  ptions reference\n+00007380: 7320 6361 6e0a 6e65 7665 7220 6265 2063  s can.never be c\n+00007390: 6f6e 6675 7365 6420 7769 7468 2076 6563  onfused with vec\n+000073a0: 746f 7220 7265 6665 7265 6e63 6573 2e20  tor references. \n+000073b0: 2057 6869 6c65 206e 6f74 2061 7070 6172   While not appar\n+000073c0: 656e 7420 696e 2074 6869 730a 6578 616d  ent in this.exam\n+000073d0: 706c 652c 206f 7074 696f 6e73 2072 6566  ple, options ref\n+000073e0: 6572 656e 6365 7320 6172 6520 7573 6566  erences are usef\n+000073f0: 756c 2077 6865 6e20 6465 6669 6e69 6e67  ul when defining\n+00007400: 206d 616e 7920 6f62 6a65 6374 7320 7769   many objects wi\n+00007410: 7468 2061 0a73 696d 696c 6172 2061 7070  th a.similar app\n+00007420: 6561 7261 6e63 652e 0a0a 1f0a 4669 6c65  earance.....File\n+00007430: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n+00007440: 4e6f 6465 3a20 4166 6669 6e65 2061 7269  Node: Affine ari\n+00007450: 7468 6d65 7469 632c 2020 4e65 7874 3a20  thmetic,  Next: \n+00007460: 4d6f 7265 2074 6f20 6c65 6172 6e2c 2020  More to learn,  \n+00007470: 5072 6576 3a20 506f 6c79 6c69 6e65 2073  Prev: Polyline s\n+00007480: 7765 6570 7320 7769 7468 2063 6c6f 7375  weeps with closu\n+00007490: 7265 2c20 2055 703a 2053 7765 7074 206f  re,  Up: Swept o\n+000074a0: 626a 6563 7473 0a0a 322e 372e 3620 4166  bjects..2.7.6 Af\n+000074b0: 6669 6e65 2061 7269 7468 6d65 7469 630a  fine arithmetic.\n 000074c0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-000074d0: 2d0a 0a54 6865 2061 7269 7468 6d65 7469  -..The arithmeti\n-000074e0: 6320 5b49 5d20 2a20 322e 3120 6162 6f76  c [I] * 2.1 abov\n-000074f0: 6520 6869 6e74 7320 6174 2061 206c 6172  e hints at a lar\n-00007500: 6765 7220 7472 7574 682e 2020 2753 6b65  ger truth.  'Ske\n-00007510: 7463 6827 0a6f 7065 7261 746f 7273 2077  tch'.operators w\n-00007520: 6f72 6b20 6f6e 2073 6361 6c61 7273 2c20  ork on scalars, \n-00007530: 7665 6374 6f72 732c 2070 6f69 6e74 732c  vectors, points,\n-00007540: 2061 6e64 2074 7261 6e73 666f 726d 7320   and transforms \n-00007550: 6163 636f 7264 696e 6720 746f 0a74 6865  according to.the\n-00007560: 2067 656e 6572 616c 2072 756c 6573 206f   general rules o\n-00007570: 6620 2261 6666 696e 6520 616c 6765 6272  f \"affine algebr\n-00007580: 6122 2e20 2054 6869 7320 6361 6e20 6265  a\".  This can be\n-00007590: 2068 656c 7066 756c 2066 6f72 2073 6574   helpful for set\n-000075a0: 7469 6e67 0a75 7020 6469 6167 7261 6d73  ting.up diagrams\n-000075b0: 2077 6974 6820 636f 6d70 7574 6564 2067   with computed g\n-000075c0: 656f 6d65 7472 792e 2020 466f 7220 6578  eometry.  For ex\n-000075d0: 616d 706c 652c 2069 6620 796f 7520 6861  ample, if you ha\n-000075e0: 7665 2074 7269 616e 676c 650a 7665 7274  ve triangle.vert\n-000075f0: 6963 6573 2028 7031 2920 7468 726f 7567  ices (p1) throug\n-00007600: 6820 2870 3329 2061 6e64 206e 6565 6420  h (p3) and need \n-00007610: 746f 2064 7261 7720 6120 756e 6974 206e  to draw a unit n\n-00007620: 6f72 6d61 6c20 7665 6374 6f72 0a70 6f69  ormal vector.poi\n-00007630: 6e74 696e 6720 6f75 7420 6f66 2074 6865  nting out of the\n-00007640: 2063 656e 7465 7220 6f66 2074 6865 2074   center of the t\n-00007650: 7269 616e 676c 652c 2074 6869 7320 636f  riangle, this co\n-00007660: 6465 2064 6f65 7320 7468 6520 7472 6963  de does the tric\n-00007670: 6b2e 0a20 2064 6566 2070 3120 2831 2c30  k..  def p1 (1,0\n-00007680: 2c30 2920 2064 6566 2070 3220 2830 2c30  ,0)  def p2 (0,0\n-00007690: 2e35 2c30 2920 2064 6566 2070 3320 282d  .5,0)  def p3 (-\n-000076a0: 302e 352c 2d31 2c32 290a 2020 6465 6620  0.5,-1,2).  def \n-000076b0: 4f20 2830 2c30 2c30 290a 2020 6465 6620  O (0,0,0).  def \n-000076c0: 4e20 756e 6974 2820 2828 7033 2920 2d20  N unit( ((p3) - \n-000076d0: 2870 3229 2920 2a20 2828 7031 2920 2d20  (p2)) * ((p1) - \n-000076e0: 2870 3229 2920 290a 2020 6465 6620 6e31  (p2)) ).  def n1\n-000076f0: 2028 2870 3129 2d28 4f29 202b 2028 7032   ((p1)-(O) + (p2\n-00007700: 292d 284f 2920 2b20 2870 3329 2d28 4f29  )-(O) + (p3)-(O)\n-00007710: 2920 2f20 3320 2b20 284f 290a 2020 6465  ) / 3 + (O).  de\n-00007720: 6620 6e32 2028 6e31 292b 5b4e 5d0a 2020  f n2 (n1)+[N].  \n-00007730: 706f 6c79 676f 6e28 7031 2928 7032 2928  polygon(p1)(p2)(\n-00007740: 7033 290a 2020 6c69 6e65 5b61 7272 6f77  p3).  line[arrow\n-00007750: 733d 2a2d 3e5d 286e 3129 286e 3229 0a54  s=*->](n1)(n2).T\n-00007760: 6865 2066 6972 7374 206c 696e 6520 636f  he first line co\n-00007770: 6d70 7574 6573 2074 6865 2063 726f 7373  mputes the cross\n-00007780: 2070 726f 6475 6374 206f 6620 7477 6f20   product of two \n-00007790: 6564 6765 2076 6563 746f 7273 206f 6620  edge vectors of \n-000077a0: 7468 650a 7472 6961 6e67 6c65 2061 6e64  the.triangle and\n-000077b0: 2073 6361 6c65 7320 6974 2074 6f20 756e   scales it to un\n-000077c0: 6974 206c 656e 6774 682e 2020 5468 6520  it length.  The \n-000077d0: 7365 636f 6e64 2063 6f6d 7075 7465 7320  second computes \n-000077e0: 7468 6520 6176 6572 6167 650a 6f66 2074  the average.of t\n-000077f0: 6865 2076 6572 7469 6365 732e 2020 4e6f  he vertices.  No\n-00007800: 7465 2074 6861 7420 7375 6274 7261 6374  te that subtract\n-00007810: 696f 6e20 616e 6420 6164 6469 7469 6f6e  ion and addition\n-00007820: 206f 6620 7468 6520 6f72 6967 696e 0a65   of the origin.e\n-00007830: 6666 6563 7469 7665 6c79 2063 6f6e 7665  ffectively conve\n-00007840: 7274 2076 6563 746f 7273 2074 6f20 706f  rt vectors to po\n-00007850: 696e 7473 2061 6e64 205f 7669 6365 2076  ints and _vice v\n-00007860: 6572 7361 5f2e 2020 5468 6520 6c69 6e65  ersa_.  The line\n-00007870: 0a63 6f6d 6d61 6e64 2064 7261 7773 2074  .command draws t\n-00007880: 6865 206e 6f72 6d61 6c20 6174 2074 6865  he normal at the\n-00007890: 2063 6f72 7265 6374 2073 706f 742e 0a0a   correct spot...\n-000078a0: 0008 5b69 6d61 6765 2073 7263 3d22 6578  ..[image src=\"ex\n-000078b0: 3130 302e 706e 6722 2074 6578 743d 2249  100.png\" text=\"I\n-000078c0: 6d61 6765 2065 7831 3030 206f 6d69 7474  mage ex100 omitt\n-000078d0: 6564 2069 6e20 7465 7874 2076 6572 7369  ed in text versi\n-000078e0: 6f6e 206f 6620 7468 6973 2064 6f63 756d  on of this docum\n-000078f0: 656e 742e 2200 085d 0a0a 2020 2054 776f  ent.\"..]..   Two\n-00007900: 2063 6176 6561 7473 2072 6567 6172 6469   caveats regardi\n-00007910: 6e67 2074 6869 7320 6578 616d 706c 6520  ng this example \n-00007920: 7265 6d61 696e 2e20 2046 6972 7374 2c20  remain.  First, \n-00007930: 7468 6520 6f6e 6c79 2077 6179 2074 6f0a  the only way to.\n-00007940: 7573 6520 2750 5354 7269 636b 7327 2d73  use 'PSTricks'-s\n-00007950: 7479 6c65 2061 7272 6f77 7320 6973 2077  tyle arrows is w\n-00007960: 6974 6820 6172 726f 7773 3d2e 2020 5468  ith arrows=.  Th\n-00007970: 6520 616c 7465 726e 6174 6976 6520 7379  e alternative sy\n-00007980: 6e74 6178 2066 6f72 0a27 5053 5472 6963  ntax for.'PSTric\n-00007990: 6b73 2720 6172 726f 7773 2069 7320 6e6f  ks' arrows is no\n-000079a0: 7420 616c 6c6f 7765 6420 696e 2073 6b65  t allowed in ske\n-000079b0: 7463 682e 2020 5365 636f 6e64 2c20 796f  tch.  Second, yo\n-000079c0: 7520 6d69 6768 7420 6c69 6b65 2074 6f0a  u might like to.\n-000079d0: 656c 696d 696e 6174 6520 7468 6520 7468  eliminate the th\n-000079e0: 6972 6420 6465 6620 616e 6420 7772 6974  ird def and writ\n-000079f0: 6520 696e 7374 6561 6420 7468 6520 666f  e instead the fo\n-00007a00: 6c6c 6f77 696e 672e 0a20 206c 696e 655b  llowing..  line[\n-00007a10: 6172 726f 7773 3d2a 2d3e 5d28 6e31 2920  arrows=*->](n1) \n-00007a20: 286e 3129 2b5b 4e5d 0a54 6869 7320 6973  (n1)+[N].This is\n-00007a30: 206e 6f74 2061 6c6c 6f77 6564 2e20 2054   not allowed.  T\n-00007a40: 6865 2070 6f69 6e74 206c 6973 7473 2069  he point lists i\n-00007a50: 6e20 6472 6177 6162 6c65 7320 6d61 7920  n drawables may \n-00007a60: 636f 6e73 6973 7420 6f6e 6c79 206f 660a  consist only of.\n-00007a70: 6578 706c 6963 6974 2070 6f69 6e74 7320  explicit points \n-00007a80: 6f72 2070 6f69 6e74 2072 6566 6572 656e  or point referen\n-00007a90: 6365 732e 2020 596f 7520 6d61 792c 2068  ces.  You may, h\n-00007aa0: 6f77 6576 6572 2c20 7573 6520 6172 6974  owever, use arit\n-00007ab0: 686d 6574 6963 0a74 6f20 6361 6c63 756c  hmetic.to calcul\n-00007ac0: 6174 6520 706f 696e 7420 636f 6d70 6f6e  ate point compon\n-00007ad0: 656e 7473 2e20 2054 6865 2066 6f6c 6c6f  ents.  The follo\n-00007ae0: 7769 6e67 2077 6f72 6b73 2c20 7468 6f75  wing works, thou\n-00007af0: 6768 2069 7427 7320 610a 6c69 7474 6c65  gh it's a.little\n-00007b00: 2063 756d 6265 7273 6f6d 652e 0a20 206c   cumbersome..  l\n-00007b10: 696e 655b 6172 726f 7773 3d2a 2d3e 5d28  ine[arrows=*->](\n-00007b20: 6e31 2928 286e 3129 2778 2b28 4e29 2778  n1)((n1)'x+(N)'x\n-00007b30: 2c20 286e 3129 2779 2b28 4e29 2779 2c20  , (n1)'y+(N)'y, \n-00007b40: 286e 3129 277a 2b28 4e29 277a 290a 4f62  (n1)'z+(N)'z).Ob\n-00007b50: 7669 6f75 736c 792c 2074 6865 2022 7469  viously, the \"ti\n-00007b60: 636b 206f 7065 7261 746f 7222 2027 2778  ck operator\" ''x\n-00007b70: 2720 6578 7472 6163 7473 2063 6f6d 706f  ' extracts compo\n-00007b80: 6e65 6e74 7320 6f66 2070 6f69 6e74 7320  nents of points \n-00007b90: 616e 640a 7665 6374 6f72 732e 0a0a 1f0a  and.vectors.....\n-00007ba0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n-00007bb0: 6f2c 2020 4e6f 6465 3a20 4d6f 7265 2074  o,  Node: More t\n-00007bc0: 6f20 6c65 6172 6e2c 2020 5072 6576 3a20  o learn,  Prev: \n-00007bd0: 4166 6669 6e65 2061 7269 7468 6d65 7469  Affine arithmeti\n-00007be0: 632c 2020 5570 3a20 5377 6570 7420 6f62  c,  Up: Swept ob\n-00007bf0: 6a65 6374 730a 0a32 2e37 2e37 204d 6f72  jects..2.7.7 Mor\n-00007c00: 6520 746f 206c 6561 726e 0a2d 2d2d 2d2d  e to learn.-----\n-00007c10: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a  --------------..\n-00007c20: 5468 6973 2069 7320 6e6f 7420 7468 6520  This is not the \n-00007c30: 656e 6420 6f66 2074 6865 2073 746f 7279  end of the story\n-00007c40: 206f 6e20 7377 6565 7073 2120 2057 6520   on sweeps!  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In\n-00008850: 2061 6464 6974 696f 6e2c 2074 6865 7265   addition, there\n-00008860: 2061 7265 2072 6573 6572 7665 6420 776f   are reserved wo\n-00008870: 7264 7320 7468 6174 2063 616e 2063 7572  rds that can cur\n-00008880: 7265 6e74 6c79 2062 6520 6465 6669 6e65  rently be define\n-00008890: 640a 6279 2074 6865 2075 7365 722c 2062  d.by the user, b\n-000088a0: 7574 2077 6974 6820 7468 6520 7269 736b  ut with the risk\n-000088b0: 2074 6861 7420 6675 7475 7265 2076 6572   that future ver\n-000088c0: 7369 6f6e 7320 6f66 2027 736b 6574 6368  sions of 'sketch\n-000088d0: 2720 7769 6c6c 0a72 656a 6563 7420 7468  ' will.reject th\n-000088e0: 6f73 6520 6465 6669 6e69 7469 6f6e 732e  ose definitions.\n-000088f0: 2020 5468 6520 7265 7365 7276 6564 2077    The reserved w\n-00008900: 6f72 6473 2061 7265 2027 6163 6f73 2720  ords are 'acos' \n-00008910: 2761 7369 6e27 2027 6174 616e 3227 0a27  'asin' 'atan2'.'\n-00008920: 636f 7327 2027 696e 7665 7273 6527 2027  cos' 'inverse' '\n-00008930: 7065 7273 7065 6374 6976 6527 2027 7072  perspective' 'pr\n-00008940: 6f6a 6563 7427 2027 726f 7461 7465 2720  oject' 'rotate' \n-00008950: 2773 6361 6c65 2720 2773 696e 2720 2773  'scale' 'sin' 's\n-00008960: 7065 6369 616c 270a 2773 7172 7427 2027  pecial'.'sqrt' '\n-00008970: 7472 616e 736c 6174 6527 2027 756e 6974  translate' 'unit\n-00008980: 2720 616e 6420 2776 6965 7727 2e0a 0a1f  ' and 'view'....\n-00008990: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n-000089a0: 666f 2c20 204e 6f64 653a 204c 6974 6572  fo,  Node: Liter\n-000089b0: 616c 732c 2020 4e65 7874 3a20 4172 6974  als,  Next: Arit\n-000089c0: 686d 6574 6963 2c20 2050 7265 763a 204b  hmetic,  Prev: K\n-000089d0: 6579 2061 6e64 2072 6573 6572 7665 6420  ey and reserved \n-000089e0: 776f 7264 732c 2020 5570 3a20 4c61 6e67  words,  Up: Lang\n-000089f0: 7561 6765 2062 6173 6963 730a 0a33 2e31  uage basics..3.1\n-00008a00: 2e33 204c 6974 6572 616c 730a 2d2d 2d2d  .3 Literals.----\n-00008a10: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 4c69 7465  ----------..Lite\n-00008a20: 7261 6c73 2069 6e20 2773 6b65 7463 6827  rals in 'sketch'\n-00008a30: 2069 6e63 6c75 6465 2073 6361 6c61 7273   include scalars\n-00008a40: 2c20 706f 696e 7473 2c20 7665 6374 6f72  , points, vector\n-00008a50: 732c 2061 6e64 2074 7261 6e73 666f 726d  s, and transform\n-00008a60: 732e 0a4c 6974 6572 616c 732c 2061 6c6f  s..Literals, alo\n-00008a70: 6e67 2077 6974 6820 6465 6669 6e65 6420  ng with defined \n-00008a80: 6f62 6a65 6374 2072 6566 6572 656e 6365  object reference\n-00008a90: 732c 2061 7265 2075 7365 6420 696e 2061  s, are used in a\n-00008aa0: 7269 7468 6d65 7469 630a 6578 7072 6573  rithmetic.expres\n-00008ab0: 7369 6f6e 732e 2020 2a4e 6f74 6520 4172  sions.  *Note Ar\n-00008ac0: 6974 686d 6574 6963 3a3a 2e0a 0a2a 204d  ithmetic::...* M\n-00008ad0: 656e 753a 0a0a 2a20 5363 616c 6172 206c  enu:..* Scalar l\n-00008ae0: 6974 6572 616c 733a 3a20 2020 2020 2020  iterals::       \n-00008af0: 2020 2020 2020 4a75 7374 2074 6865 206e        Just the n\n-00008b00: 756d 6265 7273 2e0a 2a20 506f 696e 7420  umbers..* Point \n-00008b10: 616e 6420 7665 6374 6f72 206c 6974 6572  and vector liter\n-00008b20: 616c 733a 3a20 2020 3364 2071 7561 6e74  als::   3d quant\n-00008b30: 6974 6965 732e 0a2a 2054 7261 6e73 666f  ities..* Transfo\n-00008b40: 726d 206c 6974 6572 616c 733a 3a20 2020  rm literals::   \n-00008b50: 2020 2020 2020 204d 6174 7269 7820 666f         Matrix fo\n-00008b60: 726d 2e0a 0a1f 0a46 696c 653a 2073 6b65  rm.....File: ske\n-00008b70: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n-00008b80: 2053 6361 6c61 7220 6c69 7465 7261 6c73   Scalar literals\n-00008b90: 2c20 204e 6578 743a 2050 6f69 6e74 2061  ,  Next: Point a\n-00008ba0: 6e64 2076 6563 746f 7220 6c69 7465 7261  nd vector litera\n-00008bb0: 6c73 2c20 2050 7265 763a 204c 6974 6572  ls,  Prev: Liter\n-00008bc0: 616c 732c 2020 5570 3a20 4c69 7465 7261  als,  Up: Litera\n-00008bd0: 6c73 0a0a 332e 312e 332e 3120 5363 616c  ls..3.1.3.1 Scal\n-00008be0: 6172 206c 6974 6572 616c 730a 2e2e 2e2e  ar literals.....\n-00008bf0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-00008c00: 2e2e 2e0a 0a53 6361 6c61 7220 6c69 7465  .....Scalar lite\n-00008c10: 7261 6c73 2061 7265 2070 6f73 6974 6976  rals are positiv\n-00008c20: 6520 666c 6f61 7469 6e67 2070 6f69 6e74  e floating point\n-00008c30: 206e 756d 6265 7273 2077 6974 6820 7379   numbers with sy\n-00008c40: 6e74 6178 0a61 6363 6f72 6469 6e67 2074  ntax.according t\n-00008c50: 6f20 4320 636f 6e76 656e 7469 6f6e 732e  o C conventions.\n-00008c60: 2020 5468 6520 666f 6c6c 6f77 696e 6720    The following \n-00008c70: 6172 6520 736f 6d65 2065 7861 6d70 6c65  are some example\n-00008c80: 732e 0a20 2020 2020 3020 3130 3034 202e  s..     0 1004 .\n-00008c90: 3030 3120 382e 3331 3433 2033 2e20 312e  001 8.3143 3. 1.\n-00008ca0: 3630 452d 3139 2036 2e30 3265 2b32 330a  60E-19 6.02e+23.\n-00008cb0: 5363 616c 6172 206c 6974 6572 616c 7320  Scalar literals \n-00008cc0: 6d61 7920 6e6f 7420 636f 6e74 6169 6e20  may not contain \n-00008cd0: 656d 6265 6464 6564 2073 7061 6365 732e  embedded spaces.\n-00008ce0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n-00008cf0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 506f  .info,  Node: Po\n-00008d00: 696e 7420 616e 6420 7665 6374 6f72 206c  int and vector l\n-00008d10: 6974 6572 616c 732c 2020 4e65 7874 3a20  iterals,  Next: \n-00008d20: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n-00008d30: 6c73 2c20 2050 7265 763a 2053 6361 6c61  ls,  Prev: Scala\n-00008d40: 7220 6c69 7465 7261 6c73 2c20 2055 703a  r literals,  Up:\n-00008d50: 204c 6974 6572 616c 730a 0a33 2e31 2e33   Literals..3.1.3\n-00008d60: 2e32 2050 6f69 6e74 2061 6e64 2076 6563  .2 Point and vec\n-00008d70: 746f 7220 6c69 7465 7261 6c73 0a2e 2e2e  tor literals....\n-00008d80: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-00008d90: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a  ................\n-00008da0: 506f 696e 7473 2061 6e64 2076 6563 746f  Points and vecto\n-00008db0: 7220 6c69 7465 7261 6c73 2068 6176 6520  r literals have \n-00008dc0: 7468 6573 6520 666f 726d 7320 7265 7370  these forms resp\n-00008dd0: 6563 7469 7665 6c79 2e0a 2020 2020 2028  ectively..     (\n-00008de0: 582c 592c 5a29 2020 5b58 2c59 2c5a 5d0a  X,Y,Z)  [X,Y,Z].\n-00008df0: 4561 6368 206f 6620 7468 6520 636f 6d70  Each of the comp\n-00008e00: 6f6e 656e 7473 2069 7320 6974 7365 6c66  onents is itself\n-00008e10: 2061 2073 6361 6c61 7220 6578 7072 6573   a scalar expres\n-00008e20: 7369 6f6e 2e20 2054 6865 207a 2d63 6f6d  sion.  The z-com\n-00008e30: 706f 6e65 6e74 730a 6172 6520 6f70 7469  ponents.are opti\n-00008e40: 6f6e 616c 2061 6e64 2064 6566 6175 6c74  onal and default\n-00008e50: 2074 6f20 7a65 726f 2e0a 0a1f 0a46 696c   to zero.....Fil\n-00008e60: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n-00008e70: 204e 6f64 653a 2054 7261 6e73 666f 726d   Node: Transform\n-00008e80: 206c 6974 6572 616c 732c 2020 5072 6576   literals,  Prev\n-00008e90: 3a20 506f 696e 7420 616e 6420 7665 6374  : Point and vect\n-00008ea0: 6f72 206c 6974 6572 616c 732c 2020 5570  or literals,  Up\n-00008eb0: 3a20 4c69 7465 7261 6c73 0a0a 332e 312e  : Literals..3.1.\n-00008ec0: 332e 3320 5472 616e 7366 6f72 6d20 6c69  3.3 Transform li\n-00008ed0: 7465 7261 6c73 0a2e 2e2e 2e2e 2e2e 2e2e  terals..........\n+000074d0: 2d2d 2d2d 2d2d 2d0a 0a54 6865 2061 7269  -------..The ari\n+000074e0: 7468 6d65 7469 6320 5b49 5d20 2a20 322e  thmetic [I] * 2.\n+000074f0: 3120 6162 6f76 6520 6869 6e74 7320 6174  1 above hints at\n+00007500: 2061 206c 6172 6765 7220 7472 7574 682e   a larger truth.\n+00007510: 2020 2753 6b65 7463 6827 0a6f 7065 7261    'Sketch'.opera\n+00007520: 746f 7273 2077 6f72 6b20 6f6e 2073 6361  tors work on sca\n+00007530: 6c61 7273 2c20 7665 6374 6f72 732c 2070  lars, vectors, p\n+00007540: 6f69 6e74 732c 2061 6e64 2074 7261 6e73  oints, and trans\n+00007550: 666f 726d 7320 6163 636f 7264 696e 6720  forms according \n+00007560: 746f 0a74 6865 2067 656e 6572 616c 2072  to.the general r\n+00007570: 756c 6573 206f 6620 2261 6666 696e 6520  ules of \"affine \n+00007580: 616c 6765 6272 6122 2e20 2054 6869 7320  algebra\".  This \n+00007590: 6361 6e20 6265 2068 656c 7066 756c 2066  can be helpful f\n+000075a0: 6f72 2073 6574 7469 6e67 0a75 7020 6469  or setting.up di\n+000075b0: 6167 7261 6d73 2077 6974 6820 636f 6d70  agrams with comp\n+000075c0: 7574 6564 2067 656f 6d65 7472 792e 2020  uted geometry.  \n+000075d0: 466f 7220 6578 616d 706c 652c 2069 6620  For example, if \n+000075e0: 796f 7520 6861 7665 2074 7269 616e 676c  you have triangl\n+000075f0: 650a 7665 7274 6963 6573 2028 7031 2920  e.vertices (p1) \n+00007600: 7468 726f 7567 6820 2870 3329 2061 6e64  through (p3) and\n+00007610: 206e 6565 6420 746f 2064 7261 7720 6120   need to draw a \n+00007620: 756e 6974 206e 6f72 6d61 6c20 7665 6374  unit normal vect\n+00007630: 6f72 0a70 6f69 6e74 696e 6720 6f75 7420  or.pointing out \n+00007640: 6f66 2074 6865 2063 656e 7465 7220 6f66  of the center of\n+00007650: 2074 6865 2074 7269 616e 676c 652c 2074   the triangle, t\n+00007660: 6869 7320 636f 6465 2064 6f65 7320 7468  his code does th\n+00007670: 6520 7472 6963 6b2e 0a20 2064 6566 2070  e trick..  def p\n+00007680: 3120 2831 2c30 2c30 2920 2064 6566 2070  1 (1,0,0)  def p\n+00007690: 3220 2830 2c30 2e35 2c30 2920 2064 6566  2 (0,0.5,0)  def\n+000076a0: 2070 3320 282d 302e 352c 2d31 2c32 290a   p3 (-0.5,-1,2).\n+000076b0: 2020 6465 6620 4f20 2830 2c30 2c30 290a    def O (0,0,0).\n+000076c0: 2020 6465 6620 4e20 756e 6974 2820 2828    def N unit( ((\n+000076d0: 7033 2920 2d20 2870 3229 2920 2a20 2828  p3) - (p2)) * ((\n+000076e0: 7031 2920 2d20 2870 3229 2920 290a 2020  p1) - (p2)) ).  \n+000076f0: 6465 6620 6e31 2028 2870 3129 2d28 4f29  def n1 ((p1)-(O)\n+00007700: 202b 2028 7032 292d 284f 2920 2b20 2870   + (p2)-(O) + (p\n+00007710: 3329 2d28 4f29 2920 2f20 3320 2b20 284f  3)-(O)) / 3 + (O\n+00007720: 290a 2020 6465 6620 6e32 2028 6e31 292b  ).  def n2 (n1)+\n+00007730: 5b4e 5d0a 2020 706f 6c79 676f 6e28 7031  [N].  polygon(p1\n+00007740: 2928 7032 2928 7033 290a 2020 6c69 6e65  )(p2)(p3).  line\n+00007750: 5b61 7272 6f77 733d 2a2d 3e5d 286e 3129  [arrows=*->](n1)\n+00007760: 286e 3229 0a54 6865 2066 6972 7374 206c  (n2).The first l\n+00007770: 696e 6520 636f 6d70 7574 6573 2074 6865  ine computes the\n+00007780: 2063 726f 7373 2070 726f 6475 6374 206f   cross product o\n+00007790: 6620 7477 6f20 6564 6765 2076 6563 746f  f two edge vecto\n+000077a0: 7273 206f 6620 7468 650a 7472 6961 6e67  rs of the.triang\n+000077b0: 6c65 2061 6e64 2073 6361 6c65 7320 6974  le and scales it\n+000077c0: 2074 6f20 756e 6974 206c 656e 6774 682e   to unit length.\n+000077d0: 2020 5468 6520 7365 636f 6e64 2063 6f6d    The second com\n+000077e0: 7075 7465 7320 7468 6520 6176 6572 6167  putes the averag\n+000077f0: 650a 6f66 2074 6865 2076 6572 7469 6365  e.of the vertice\n+00007800: 732e 2020 4e6f 7465 2074 6861 7420 7375  s.  Note that su\n+00007810: 6274 7261 6374 696f 6e20 616e 6420 6164  btraction and ad\n+00007820: 6469 7469 6f6e 206f 6620 7468 6520 6f72  dition of the or\n+00007830: 6967 696e 0a65 6666 6563 7469 7665 6c79  igin.effectively\n+00007840: 2063 6f6e 7665 7274 2076 6563 746f 7273   convert vectors\n+00007850: 2074 6f20 706f 696e 7473 2061 6e64 205f   to points and _\n+00007860: 7669 6365 2076 6572 7361 5f2e 2020 5468  vice versa_.  Th\n+00007870: 6520 6c69 6e65 0a63 6f6d 6d61 6e64 2064  e line.command d\n+00007880: 7261 7773 2074 6865 206e 6f72 6d61 6c20  raws the normal \n+00007890: 6174 2074 6865 2063 6f72 7265 6374 2073  at the correct s\n+000078a0: 706f 742e 0a0a 0008 5b69 6d61 6765 2073  pot.....[image s\n+000078b0: 7263 3d22 6578 3130 302e 706e 6722 2074  rc=\"ex100.png\" t\n+000078c0: 6578 743d 2249 6d61 6765 2065 7831 3030  ext=\"Image ex100\n+000078d0: 206f 6d69 7474 6564 2069 6e20 7465 7874   omitted in text\n+000078e0: 2076 6572 7369 6f6e 206f 6620 7468 6973   version of this\n+000078f0: 2064 6f63 756d 656e 742e 2200 085d 0a0a   document.\"..]..\n+00007900: 2020 2054 776f 2063 6176 6561 7473 2072     Two caveats r\n+00007910: 6567 6172 6469 6e67 2074 6869 7320 6578  egarding this ex\n+00007920: 616d 706c 6520 7265 6d61 696e 2e20 2046  ample remain.  F\n+00007930: 6972 7374 2c20 7468 6520 6f6e 6c79 2077  irst, the only w\n+00007940: 6179 2074 6f0a 7573 6520 2750 5354 7269  ay to.use 'PSTri\n+00007950: 636b 7327 2d73 7479 6c65 2061 7272 6f77  cks'-style arrow\n+00007960: 7320 6973 2077 6974 6820 6172 726f 7773  s is with arrows\n+00007970: 3d2e 2020 5468 6520 616c 7465 726e 6174  =.  The alternat\n+00007980: 6976 6520 7379 6e74 6178 2066 6f72 0a27  ive syntax for.'\n+00007990: 5053 5472 6963 6b73 2720 6172 726f 7773  PSTricks' arrows\n+000079a0: 2069 7320 6e6f 7420 616c 6c6f 7765 6420   is not allowed \n+000079b0: 696e 2073 6b65 7463 682e 2020 5365 636f  in sketch.  Seco\n+000079c0: 6e64 2c20 796f 7520 6d69 6768 7420 6c69  nd, you might li\n+000079d0: 6b65 2074 6f0a 656c 696d 696e 6174 6520  ke to.eliminate \n+000079e0: 7468 6520 7468 6972 6420 6465 6620 616e  the third def an\n+000079f0: 6420 7772 6974 6520 696e 7374 6561 6420  d write instead \n+00007a00: 7468 6520 666f 6c6c 6f77 696e 672e 0a20  the following.. \n+00007a10: 206c 696e 655b 6172 726f 7773 3d2a 2d3e   line[arrows=*->\n+00007a20: 5d28 6e31 2920 286e 3129 2b5b 4e5d 0a54  ](n1) (n1)+[N].T\n+00007a30: 6869 7320 6973 206e 6f74 2061 6c6c 6f77  his is not allow\n+00007a40: 6564 2e20 2054 6865 2070 6f69 6e74 206c  ed.  The point l\n+00007a50: 6973 7473 2069 6e20 6472 6177 6162 6c65  ists in drawable\n+00007a60: 7320 6d61 7920 636f 6e73 6973 7420 6f6e  s may consist on\n+00007a70: 6c79 206f 660a 6578 706c 6963 6974 2070  ly of.explicit p\n+00007a80: 6f69 6e74 7320 6f72 2070 6f69 6e74 2072  oints or point r\n+00007a90: 6566 6572 656e 6365 732e 2020 596f 7520  eferences.  You \n+00007aa0: 6d61 792c 2068 6f77 6576 6572 2c20 7573  may, however, us\n+00007ab0: 6520 6172 6974 686d 6574 6963 0a74 6f20  e arithmetic.to \n+00007ac0: 6361 6c63 756c 6174 6520 706f 696e 7420  calculate point \n+00007ad0: 636f 6d70 6f6e 656e 7473 2e20 2054 6865  components.  The\n+00007ae0: 2066 6f6c 6c6f 7769 6e67 2077 6f72 6b73   following works\n+00007af0: 2c20 7468 6f75 6768 2069 7427 7320 610a  , though it's a.\n+00007b00: 6c69 7474 6c65 2063 756d 6265 7273 6f6d  little cumbersom\n+00007b10: 652e 0a20 206c 696e 655b 6172 726f 7773  e..  line[arrows\n+00007b20: 3d2a 2d3e 5d28 6e31 2928 286e 3129 2778  =*->](n1)((n1)'x\n+00007b30: 2b28 4e29 2778 2c20 286e 3129 2779 2b28  +(N)'x, (n1)'y+(\n+00007b40: 4e29 2779 2c20 286e 3129 277a 2b28 4e29  N)'y, (n1)'z+(N)\n+00007b50: 277a 290a 4f62 7669 6f75 736c 792c 2074  'z).Obviously, t\n+00007b60: 6865 2022 7469 636b 206f 7065 7261 746f  he \"tick operato\n+00007b70: 7222 2027 2778 2720 6578 7472 6163 7473  r\" ''x' extracts\n+00007b80: 2063 6f6d 706f 6e65 6e74 7320 6f66 2070   components of p\n+00007b90: 6f69 6e74 7320 616e 640a 7665 6374 6f72  oints and.vector\n+00007ba0: 732e 0a0a 1f0a 4669 6c65 3a20 736b 6574  s.....File: sket\n+00007bb0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n+00007bc0: 4d6f 7265 2074 6f20 6c65 6172 6e2c 2020  More to learn,  \n+00007bd0: 5072 6576 3a20 4166 6669 6e65 2061 7269  Prev: Affine ari\n+00007be0: 7468 6d65 7469 632c 2020 5570 3a20 5377  thmetic,  Up: Sw\n+00007bf0: 6570 7420 6f62 6a65 6374 730a 0a32 2e37  ept objects..2.7\n+00007c00: 2e37 204d 6f72 6520 746f 206c 6561 726e  .7 More to learn\n+00007c10: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  .---------------\n+00007c20: 2d2d 2d2d 0a0a 5468 6973 2069 7320 6e6f  ----..This is no\n+00007c30: 7420 7468 6520 656e 6420 6f66 2074 6865  t the end of the\n+00007c40: 2073 746f 7279 206f 6e20 7377 6565 7073   story on sweeps\n+00007c50: 2120 2057 6520 696e 7669 7465 2074 6865  !  We invite the\n+00007c60: 2072 6561 6465 7220 696e 746f 0a74 6865   reader into.the\n+00007c70: 206d 6169 6e20 626f 6479 206f 6620 7468   main body of th\n+00007c80: 6973 2064 6f63 756d 656e 7461 7469 6f6e  is documentation\n+00007c90: 202a 6e6f 7465 2053 7765 6570 733a 3a20   *note Sweeps:: \n+00007ca0: 746f 206c 6561 726e 206d 6f72 652e 0a0a  to learn more...\n+00007cb0: 0008 5b69 6d61 6765 2073 7263 3d22 6578  ..[image src=\"ex\n+00007cc0: 3132 302e 706e 6722 2074 6578 743d 2249  120.png\" text=\"I\n+00007cd0: 6d61 6765 2065 7831 3230 206f 6d69 7474  mage ex120 omitt\n+00007ce0: 6564 2069 6e20 7465 7874 2076 6572 7369  ed in text versi\n+00007cf0: 6f6e 206f 6620 7468 6973 2064 6f63 756d  on of this docum\n+00007d00: 656e 742e 2200 085d 0a0a 5768 6f20 6b6e  ent.\"..]..Who kn\n+00007d10: 6f77 7320 7768 6572 6520 796f 7527 6c6c  ows where you'll\n+00007d20: 2066 696e 6973 683f 0a0a 1f0a 4669 6c65   finish?....File\n+00007d30: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n+00007d40: 4e6f 6465 3a20 496e 7075 7420 6c61 6e67  Node: Input lang\n+00007d50: 7561 6765 2c20 204e 6578 743a 2042 7569  uage,  Next: Bui\n+00007d60: 6c64 696e 6720 6120 6472 6177 696e 672c  lding a drawing,\n+00007d70: 2020 5072 6576 3a20 496e 7472 6f64 7563    Prev: Introduc\n+00007d80: 7469 6f6e 2062 7920 6578 616d 706c 652c  tion by example,\n+00007d90: 2020 5570 3a20 546f 700a 0a33 2049 6e70    Up: Top..3 Inp\n+00007da0: 7574 206c 616e 6775 6167 650a 2a2a 2a2a  ut language.****\n+00007db0: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 0a0a 5468  ************..Th\n+00007dc0: 6973 2063 6861 7074 6572 2064 6573 6372  is chapter descr\n+00007dd0: 6962 6573 2074 6865 2027 736b 6574 6368  ibes the 'sketch\n+00007de0: 2720 696e 7075 7420 6c61 6e67 7561 6765  ' input language\n+00007df0: 2069 6e20 6465 7461 696c 2e0a 0a2a 204d   in detail...* M\n+00007e00: 656e 753a 0a0a 2a20 4c61 6e67 7561 6765  enu:..* Language\n+00007e10: 2062 6173 6963 733a 3a20 2020 2020 2020   basics::       \n+00007e20: 2020 2020 2020 4361 7365 2c20 7370 6163        Case, spac\n+00007e30: 652c 2063 6f6d 6d65 6e74 732c 2069 6e63  e, comments, inc\n+00007e40: 6c75 6465 2066 696c 6573 2e0a 2a20 4472  lude files..* Dr\n+00007e50: 6177 6162 6c65 733a 3a20 2020 2020 2020  awables::       \n+00007e60: 2020 2020 2020 2020 2020 2020 5468 696e              Thin\n+00007e70: 6773 2074 6861 7420 6361 6e20 6265 2064  gs that can be d\n+00007e80: 7261 776e 2e0a 2a20 4465 6669 6e69 7469  rawn..* Definiti\n+00007e90: 6f6e 733a 3a20 2020 2020 2020 2020 2020  ons::           \n+00007ea0: 2020 2020 2020 4769 7669 6e67 2074 6869        Giving thi\n+00007eb0: 6e67 7320 6e61 6d65 732e 0a2a 2047 6c6f  ngs names..* Glo\n+00007ec0: 6261 6c20 656e 7669 726f 6e6d 656e 743a  bal environment:\n+00007ed0: 3a20 2020 2020 2020 2020 2041 6666 6563  :          Affec\n+00007ee0: 7420 7468 6520 656e 7469 7265 2064 7261  t the entire dra\n+00007ef0: 7769 6e67 2e0a 0a1f 0a46 696c 653a 2073  wing.....File: s\n+00007f00: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n+00007f10: 653a 204c 616e 6775 6167 6520 6261 7369  e: Language basi\n+00007f20: 6373 2c20 204e 6578 743a 2044 7261 7761  cs,  Next: Drawa\n+00007f30: 626c 6573 2c20 2050 7265 763a 2049 6e70  bles,  Prev: Inp\n+00007f40: 7574 206c 616e 6775 6167 652c 2020 5570  ut language,  Up\n+00007f50: 3a20 496e 7075 7420 6c61 6e67 7561 6765  : Input language\n+00007f60: 0a0a 332e 3120 4261 7369 6373 0a3d 3d3d  ..3.1 Basics.===\n+00007f70: 3d3d 3d3d 3d3d 3d0a 0a27 536b 6574 6368  =======..'Sketch\n+00007f80: 2720 696e 7075 7420 6973 2070 6c61 696e  ' input is plain\n+00007f90: 2041 5343 4949 2074 6578 742c 2075 7375   ASCII text, usu\n+00007fa0: 616c 6c79 2073 746f 7265 6420 696e 2061  ally stored in a\n+00007fb0: 6e20 696e 7075 7420 6669 6c65 2e20 2049  n input file.  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The comman\n+000082c0: 640a 2020 696e 7075 747b 6f74 6865 7266  d.  input{otherf\n+000082d0: 696c 652e 736b 7d0a 6361 7573 6573 2074  ile.sk}.causes t\n+000082e0: 6865 2063 6f6e 7465 6e74 7320 6f66 2027  he contents of '\n+000082f0: 6f74 6865 7266 696c 652e 736b 2720 746f  otherfile.sk' to\n+00008300: 2062 6520 696e 7365 7274 6564 2061 7320   be inserted as \n+00008310: 7468 6f75 6768 2074 6865 7920 7765 7265  though they were\n+00008320: 0a70 6172 7420 6f66 2074 6865 2063 7572  .part of the cur\n+00008330: 7265 6e74 2066 696c 652e 0a0a 2a20 4d65  rent file...* Me\n+00008340: 6e75 3a0a 0a2a 2049 6465 6e74 6966 6965  nu:..* Identifie\n+00008350: 7273 3a3a 2020 2020 2020 2020 2020 2020  rs::            \n+00008360: 2020 2020 204e 616d 6573 2066 6f72 2074       Names for t\n+00008370: 6869 6e67 732e 0a2a 204b 6579 2061 6e64  hings..* Key and\n+00008380: 2072 6573 6572 7665 6420 776f 7264 733a   reserved words:\n+00008390: 3a20 2020 2020 204e 616d 6573 2079 6f75  :      Names you\n+000083a0: 2073 686f 756c 646e 2774 2075 7365 2e0a   shouldn't use..\n+000083b0: 2a20 4c69 7465 7261 6c73 3a3a 2020 2020  * Literals::    \n+000083c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000083d0: 436f 6e73 7461 6e74 7320 616e 6420 636f  Constants and co\n+000083e0: 6e73 7472 7563 746f 7273 2e0a 2a20 4172  nstructors..* Ar\n+000083f0: 6974 686d 6574 6963 3a3a 2020 2020 2020  ithmetic::      \n+00008400: 2020 2020 2020 2020 2020 2020 5275 6c65              Rule\n+00008410: 7320 666f 7220 6578 7072 6573 7369 6f6e  s for expression\n+00008420: 732e 0a2a 204f 7074 696f 6e73 3a3a 2020  s..* Options::  \n+00008430: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00008440: 2020 204d 6f64 6966 7969 6e67 206f 626a     Modifying obj\n+00008450: 6563 7420 6170 7065 6172 616e 6365 2e0a  ect appearance..\n+00008460: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n+00008470: 696e 666f 2c20 204e 6f64 653a 2049 6465  info,  Node: Ide\n+00008480: 6e74 6966 6965 7273 2c20 204e 6578 743a  ntifiers,  Next:\n+00008490: 204b 6579 2061 6e64 2072 6573 6572 7665   Key and reserve\n+000084a0: 6420 776f 7264 732c 2020 5072 6576 3a20  d words,  Prev: \n+000084b0: 4c61 6e67 7561 6765 2062 6173 6963 732c  Language basics,\n+000084c0: 2020 5570 3a20 4c61 6e67 7561 6765 2062    Up: Language b\n+000084d0: 6173 6963 730a 0a33 2e31 2e31 2049 6465  asics..3.1.1 Ide\n+000084e0: 6e74 6966 6965 7273 0a2d 2d2d 2d2d 2d2d  ntifiers.-------\n+000084f0: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 4964 656e  ----------..Iden\n+00008500: 7469 6669 6572 7320 696e 2027 736b 6574  tifiers in 'sket\n+00008510: 6368 2720 6172 6520 7265 6665 7265 6e63  ch' are referenc\n+00008520: 6573 2074 6f20 6561 726c 6965 722d 6465  es to earlier-de\n+00008530: 6669 6e65 6420 6f70 7469 6f6e 732c 0a73  fined options,.s\n+00008540: 6361 6c61 7273 2c20 706f 696e 7473 2c20  calars, points, \n+00008550: 7665 6374 6f72 732c 2074 7261 6e73 666f  vectors, transfo\n+00008560: 726d 732c 2064 7261 7761 626c 6573 2c20  rms, drawables, \n+00008570: 616e 6420 7461 6773 2e20 2044 6566 696e  and tags.  Defin\n+00008580: 6974 696f 6e73 0a61 7265 2065 7870 6c61  itions.are expla\n+00008590: 696e 6564 2069 6e20 2a6e 6f74 6520 4465  ined in *note De\n+000085a0: 6669 6e69 7469 6f6e 733a 3a2e 0a0a 2020  finitions::...  \n+000085b0: 2041 6e20 6964 656e 7469 6669 6572 2063   An identifier c\n+000085c0: 6f6e 7369 7374 7320 6f66 2061 206c 6561  onsists of a lea\n+000085d0: 6469 6e67 206c 6574 7465 7220 666f 6c6c  ding letter foll\n+000085e0: 6f77 6564 2062 7920 6c65 7474 6572 732c  owed by letters,\n+000085f0: 0a6e 756d 6265 7273 2061 6e64 2075 6e64  .numbers and und\n+00008600: 6572 7363 6f72 6573 2e20 2054 6865 206c  erscores.  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The 'sk\n+000087f0: 6574 6368 2720 7061 7273 6572 2077 696c  etch' parser wil\n+00008800: 6c20 6e6f 7465 2061 2073 796e 7461 7820  l note a syntax \n+00008810: 6572 726f 7220 6966 2061 6e79 206f 6620  error if any of \n+00008820: 7468 6573 650a 6172 6520 7573 6564 2069  these.are used i\n+00008830: 6e20 706c 6163 6520 6f66 2061 2070 726f  n place of a pro\n+00008840: 7065 7220 6964 656e 7469 6669 6572 2e0a  per identifier..\n+00008850: 0a20 2020 496e 2061 6464 6974 696f 6e2c  .   In addition,\n+00008860: 2074 6865 7265 2061 7265 2072 6573 6572   there are reser\n+00008870: 7665 6420 776f 7264 7320 7468 6174 2063  ved words that c\n+00008880: 616e 2063 7572 7265 6e74 6c79 2062 6520  an currently be \n+00008890: 6465 6669 6e65 640a 6279 2074 6865 2075  defined.by the u\n+000088a0: 7365 722c 2062 7574 2077 6974 6820 7468  ser, but with th\n+000088b0: 6520 7269 736b 2074 6861 7420 6675 7475  e risk that futu\n+000088c0: 7265 2076 6572 7369 6f6e 7320 6f66 2027  re versions of '\n+000088d0: 736b 6574 6368 2720 7769 6c6c 0a72 656a  sketch' will.rej\n+000088e0: 6563 7420 7468 6f73 6520 6465 6669 6e69  ect those defini\n+000088f0: 7469 6f6e 732e 2020 5468 6520 7265 7365  tions.  The rese\n+00008900: 7276 6564 2077 6f72 6473 2061 7265 2027  rved words are '\n+00008910: 6163 6f73 2720 2761 7369 6e27 2027 6174  acos' 'asin' 'at\n+00008920: 616e 3227 0a27 636f 7327 2027 696e 7665  an2'.'cos' 'inve\n+00008930: 7273 6527 2027 7065 7273 7065 6374 6976  rse' 'perspectiv\n+00008940: 6527 2027 7072 6f6a 6563 7427 2027 726f  e' 'project' 'ro\n+00008950: 7461 7465 2720 2773 6361 6c65 2720 2773  tate' 'scale' 's\n+00008960: 696e 2720 2773 7065 6369 616c 270a 2773  in' 'special'.'s\n+00008970: 7172 7427 2027 7472 616e 736c 6174 6527  qrt' 'translate'\n+00008980: 2027 756e 6974 2720 616e 6420 2776 6965   'unit' and 'vie\n+00008990: 7727 2e0a 0a1f 0a46 696c 653a 2073 6b65  w'.....File: ske\n+000089a0: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n+000089b0: 204c 6974 6572 616c 732c 2020 4e65 7874   Literals,  Next\n+000089c0: 3a20 4172 6974 686d 6574 6963 2c20 2050  : Arithmetic,  P\n+000089d0: 7265 763a 204b 6579 2061 6e64 2072 6573  rev: Key and res\n+000089e0: 6572 7665 6420 776f 7264 732c 2020 5570  erved words,  Up\n+000089f0: 3a20 4c61 6e67 7561 6765 2062 6173 6963  : Language basic\n+00008a00: 730a 0a33 2e31 2e33 204c 6974 6572 616c  s..3.1.3 Literal\n+00008a10: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  s.--------------\n+00008a20: 0a0a 4c69 7465 7261 6c73 2069 6e20 2773  ..Literals in 's\n+00008a30: 6b65 7463 6827 2069 6e63 6c75 6465 2073  ketch' include s\n+00008a40: 6361 6c61 7273 2c20 706f 696e 7473 2c20  calars, points, \n+00008a50: 7665 6374 6f72 732c 2061 6e64 2074 7261  vectors, and tra\n+00008a60: 6e73 666f 726d 732e 0a4c 6974 6572 616c  nsforms..Literal\n+00008a70: 732c 2061 6c6f 6e67 2077 6974 6820 6465  s, along with de\n+00008a80: 6669 6e65 6420 6f62 6a65 6374 2072 6566  fined object ref\n+00008a90: 6572 656e 6365 732c 2061 7265 2075 7365  erences, are use\n+00008aa0: 6420 696e 2061 7269 7468 6d65 7469 630a  d in arithmetic.\n+00008ab0: 6578 7072 6573 7369 6f6e 732e 2020 2a4e  expressions.  *N\n+00008ac0: 6f74 6520 4172 6974 686d 6574 6963 3a3a  ote Arithmetic::\n+00008ad0: 2e0a 0a2a 204d 656e 753a 0a0a 2a20 5363  ...* Menu:..* Sc\n+00008ae0: 616c 6172 206c 6974 6572 616c 733a 3a20  alar literals:: \n+00008af0: 2020 2020 2020 2020 2020 2020 4a75 7374              Just\n+00008b00: 2074 6865 206e 756d 6265 7273 2e0a 2a20   the numbers..* \n+00008b10: 506f 696e 7420 616e 6420 7665 6374 6f72  Point and vector\n+00008b20: 206c 6974 6572 616c 733a 3a20 2020 3364   literals::   3d\n+00008b30: 2071 7561 6e74 6974 6965 732e 0a2a 2054   quantities..* T\n+00008b40: 7261 6e73 666f 726d 206c 6974 6572 616c  ransform literal\n+00008b50: 733a 3a20 2020 2020 2020 2020 204d 6174  s::          Mat\n+00008b60: 7269 7820 666f 726d 2e0a 0a1f 0a46 696c  rix form.....Fil\n+00008b70: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n+00008b80: 204e 6f64 653a 2053 6361 6c61 7220 6c69   Node: Scalar li\n+00008b90: 7465 7261 6c73 2c20 204e 6578 743a 2050  terals,  Next: P\n+00008ba0: 6f69 6e74 2061 6e64 2076 6563 746f 7220  oint and vector \n+00008bb0: 6c69 7465 7261 6c73 2c20 2050 7265 763a  literals,  Prev:\n+00008bc0: 204c 6974 6572 616c 732c 2020 5570 3a20   Literals,  Up: \n+00008bd0: 4c69 7465 7261 6c73 0a0a 332e 312e 332e  Literals..3.1.3.\n+00008be0: 3120 5363 616c 6172 206c 6974 6572 616c  1 Scalar literal\n+00008bf0: 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  s...............\n+00008c00: 2e2e 2e2e 2e2e 2e2e 2e0a 0a53 6361 6c61  ...........Scala\n+00008c10: 7220 6c69 7465 7261 6c73 2061 7265 2070  r literals are p\n+00008c20: 6f73 6974 6976 6520 666c 6f61 7469 6e67  ositive floating\n+00008c30: 2070 6f69 6e74 206e 756d 6265 7273 2077   point numbers w\n+00008c40: 6974 6820 7379 6e74 6178 0a61 6363 6f72  ith syntax.accor\n+00008c50: 6469 6e67 2074 6f20 4320 636f 6e76 656e  ding to C conven\n+00008c60: 7469 6f6e 732e 2020 5468 6520 666f 6c6c  tions.  The foll\n+00008c70: 6f77 696e 6720 6172 6520 736f 6d65 2065  owing are some e\n+00008c80: 7861 6d70 6c65 732e 0a20 2020 2020 3020  xamples..     0 \n+00008c90: 3130 3034 202e 3030 3120 382e 3331 3433  1004 .001 8.3143\n+00008ca0: 2033 2e20 312e 3630 452d 3139 2036 2e30   3. 1.60E-19 6.0\n+00008cb0: 3265 2b32 330a 5363 616c 6172 206c 6974  2e+23.Scalar lit\n+00008cc0: 6572 616c 7320 6d61 7920 6e6f 7420 636f  erals may not co\n+00008cd0: 6e74 6169 6e20 656d 6265 6464 6564 2073  ntain embedded s\n+00008ce0: 7061 6365 732e 0a0a 1f0a 4669 6c65 3a20  paces.....File: \n+00008cf0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n+00008d00: 6465 3a20 506f 696e 7420 616e 6420 7665  de: Point and ve\n+00008d10: 6374 6f72 206c 6974 6572 616c 732c 2020  ctor literals,  \n+00008d20: 4e65 7874 3a20 5472 616e 7366 6f72 6d20  Next: Transform \n+00008d30: 6c69 7465 7261 6c73 2c20 2050 7265 763a  literals,  Prev:\n+00008d40: 2053 6361 6c61 7220 6c69 7465 7261 6c73   Scalar literals\n+00008d50: 2c20 2055 703a 204c 6974 6572 616c 730a  ,  Up: Literals.\n+00008d60: 0a33 2e31 2e33 2e32 2050 6f69 6e74 2061  .3.1.3.2 Point a\n+00008d70: 6e64 2076 6563 746f 7220 6c69 7465 7261  nd vector litera\n+00008d80: 6c73 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ls..............\n+00008d90: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+00008da0: 2e2e 2e2e 0a0a 506f 696e 7473 2061 6e64  ......Points and\n+00008db0: 2076 6563 746f 7220 6c69 7465 7261 6c73   vector literals\n+00008dc0: 2068 6176 6520 7468 6573 6520 666f 726d   have these form\n+00008dd0: 7320 7265 7370 6563 7469 7665 6c79 2e0a  s respectively..\n+00008de0: 2020 2020 2028 582c 592c 5a29 2020 5b58       (X,Y,Z)  [X\n+00008df0: 2c59 2c5a 5d0a 4561 6368 206f 6620 7468  ,Y,Z].Each of th\n+00008e00: 6520 636f 6d70 6f6e 656e 7473 2069 7320  e components is \n+00008e10: 6974 7365 6c66 2061 2073 6361 6c61 7220  itself a scalar \n+00008e20: 6578 7072 6573 7369 6f6e 2e20 2054 6865  expression.  The\n+00008e30: 207a 2d63 6f6d 706f 6e65 6e74 730a 6172   z-components.ar\n+00008e40: 6520 6f70 7469 6f6e 616c 2061 6e64 2064  e optional and d\n+00008e50: 6566 6175 6c74 2074 6f20 7a65 726f 2e0a  efault to zero..\n+00008e60: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n+00008e70: 696e 666f 2c20 204e 6f64 653a 2054 7261  info,  Node: Tra\n+00008e80: 6e73 666f 726d 206c 6974 6572 616c 732c  nsform literals,\n+00008e90: 2020 5072 6576 3a20 506f 696e 7420 616e    Prev: Point an\n+00008ea0: 6420 7665 6374 6f72 206c 6974 6572 616c  d vector literal\n+00008eb0: 732c 2020 5570 3a20 4c69 7465 7261 6c73  s,  Up: Literals\n+00008ec0: 0a0a 332e 312e 332e 3320 5472 616e 7366  ..3.1.3.3 Transf\n+00008ed0: 6f72 6d20 6c69 7465 7261 6c73 0a2e 2e2e  orm literals....\n 00008ee0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-00008ef0: 2e0a 0a4d 6f73 7420 7472 616e 7366 6f72  ...Most transfor\n-00008f00: 6d20 6c69 7465 7261 6c73 2061 7265 2066  m literals are f\n-00008f10: 6f72 6d65 6420 6279 2022 636f 6e73 7472  ormed by \"constr\n-00008f20: 7563 746f 7273 222e 2020 5468 6573 6520  uctors\".  These \n-00008f30: 6172 650a 7375 6d6d 6172 697a 6564 2069  are.summarized i\n-00008f40: 6e20 7468 6520 666f 6c6c 6f77 696e 6720  n the following \n-00008f50: 7461 626c 652e 0a43 6f6e 7374 7275 6374  table..Construct\n-00008f60: 6f72 2020 2020 2020 2020 2020 2020 2020  or              \n-00008f70: 2020 2020 2020 2020 2020 2050 6172 616d             Param\n-00008f80: 2074 7970 6573 2020 2020 2020 2020 2020   types          \n-00008f90: 2044 6573 6372 6970 7469 6f6e 0a2d 2d2d   Description.---\n-00008fa0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n+00008ef0: 2e2e 2e2e 2e2e 2e0a 0a4d 6f73 7420 7472  .........Most tr\n+00008f00: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n+00008f10: 2061 7265 2066 6f72 6d65 6420 6279 2022   are formed by \"\n+00008f20: 636f 6e73 7472 7563 746f 7273 222e 2020  constructors\".  \n+00008f30: 5468 6573 6520 6172 650a 7375 6d6d 6172  These are.summar\n+00008f40: 697a 6564 2069 6e20 7468 6520 666f 6c6c  ized in the foll\n+00008f50: 6f77 696e 6720 7461 626c 652e 0a43 6f6e  owing table..Con\n+00008f60: 7374 7275 6374 6f72 2020 2020 2020 2020  structor        \n+00008f70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00008f80: 2050 6172 616d 2074 7970 6573 2020 2020   Param types    \n+00008f90: 2020 2020 2020 2044 6573 6372 6970 7469         Descripti\n+00008fa0: 6f6e 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  on.-------------\n 00008fb0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 00008fc0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 00008fd0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 00008fe0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 00008ff0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-00009000: 2d2d 2d2d 2d2d 2d2d 0a27 726f 7461 7465  --------.'rotate\n-00009010: 2841 2c50 2c58 2927 2020 2020 2020 2020  (A,P,X)'        \n-00009020: 2020 2020 2020 2020 2020 2020 2073 6361               sca\n-00009030: 6c61 722c 706f 696e 742c 7665 6374 6f72  lar,point,vector\n-00009040: 2020 2052 6f74 6174 6520 2741 2720 6465     Rotate 'A' de\n-00009050: 6772 6565 7320 6162 6f75 7420 706f 696e  grees about poin\n-00009060: 7420 2750 2720 7769 7468 2061 7869 730a  t 'P' with axis.\n-00009070: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009000: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a27  --------------.'\n+00009010: 726f 7461 7465 2841 2c50 2c58 2927 2020  rotate(A,P,X)'  \n+00009020: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009030: 2020 2073 6361 6c61 722c 706f 696e 742c     scalar,point,\n+00009040: 7665 6374 6f72 2020 2052 6f74 6174 6520  vector   Rotate \n+00009050: 2741 2720 6465 6772 6565 7320 6162 6f75  'A' degrees abou\n+00009060: 7420 706f 696e 7420 2750 2720 7769 7468  t point 'P' with\n+00009070: 2061 7869 730a 2020 2020 2020 2020 2020   axis.          \n 00009080: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009090: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000090a0: 2020 2020 2020 2020 2020 2758 2720 6163            'X' ac\n-000090b0: 636f 7264 696e 6720 746f 2074 6865 2072  cording to the r\n-000090c0: 6967 6874 2068 616e 6420 7275 6c65 2e0a  ight hand rule..\n-000090d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000090a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000090b0: 2758 2720 6163 636f 7264 696e 6720 746f  'X' according to\n+000090c0: 2074 6865 2072 6967 6874 2068 616e 6420   the right hand \n+000090d0: 7275 6c65 2e0a 2020 2020 2020 2020 2020  rule..          \n 000090e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000090f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009100: 2020 2020 2020 2020 2020 2a4e 6f74 6520            *Note \n-00009110: 5269 6768 7420 6861 6e64 2072 756c 653a  Right hand rule:\n-00009120: 3a2e 2020 2750 2720 616e 6420 2758 2720  :.  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'P' an\n+00009130: 6420 2758 2720 6172 6520 626f 7468 0a20  d 'X' are both. \n 00009140: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009150: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009160: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009170: 2020 206f 7074 696f 6e61 6c20 616e 6420     optional and \n-00009180: 6465 6661 756c 7420 746f 2074 6865 206f  default to the o\n-00009190: 7269 6769 6e20 616e 6420 7468 650a 2020  rigin and the.  \n-000091a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009170: 2020 2020 2020 2020 206f 7074 696f 6e61           optiona\n+00009180: 6c20 616e 6420 6465 6661 756c 7420 746f  l and default to\n+00009190: 2074 6865 206f 7269 6769 6e20 616e 6420   the origin and \n+000091a0: 7468 650a 2020 2020 2020 2020 2020 2020  the.            \n 000091b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000091c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000091d0: 2020 2020 2020 2020 7a2d 6178 6973 2072          z-axis r\n-000091e0: 6573 7065 6374 6976 656c 792e 0a27 7472  espectively..'tr\n-000091f0: 616e 736c 6174 6528 5829 2720 2020 2020  anslate(X)'     \n-00009200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009210: 2076 6563 746f 7220 2020 2020 2020 2020   vector         \n-00009220: 2020 2020 2020 2054 7261 6e73 6c61 7465         Translate\n-00009230: 2062 7920 2758 272e 0a27 7363 616c 6528   by 'X'..'scale(\n-00009240: 5329 2720 2020 2020 2020 2020 2020 2020  S)'             \n-00009250: 2020 2020 2020 2020 2020 2020 2073 6361               sca\n-00009260: 6c61 7220 2020 2020 2020 2020 2020 2020  lar             \n-00009270: 2020 2053 6361 6c65 2075 6e69 666f 726d     Scale uniform\n-00009280: 6c79 2062 7920 6661 6374 6f72 2027 5327  ly by factor 'S'\n-00009290: 2e0a 2773 6361 6c65 2856 2927 2020 2020  ..'scale(V)'    \n-000092a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000092b0: 2020 2020 2020 7665 6374 6f72 2020 2020        vector    \n-000092c0: 2020 2020 2020 2020 2020 2020 5363 616c              Scal\n-000092d0: 6520 616c 6f6e 6720 6561 6368 2061 7869  e along each axi\n-000092e0: 7320 6279 2063 6f6d 706f 6e65 6e74 7320  s by components \n-000092f0: 6f66 2027 5627 2e0a 2770 726f 6a65 6374  of 'V'..'project\n-00009300: 2829 2720 2020 2020 2020 2020 2020 2020  ()'             \n-00009310: 2020 2020 2020 2020 2020 2020 2d2d 2020              --  \n-00009320: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009330: 2020 5361 6d65 2061 7320 2773 6361 6c65    Same as 'scale\n-00009340: 285b 312c 312c 305d 2927 2e0a 2770 726f  ([1,1,0])'..'pro\n-00009350: 6a65 6374 2853 2927 2020 2020 2020 2020  ject(S)'        \n+000091d0: 2020 2020 2020 2020 2020 2020 2020 7a2d                z-\n+000091e0: 6178 6973 2072 6573 7065 6374 6976 656c  axis respectivel\n+000091f0: 792e 0a27 7472 616e 736c 6174 6528 5829  y..'translate(X)\n+00009200: 2720 2020 2020 2020 2020 2020 2020 2020  '               \n+00009210: 2020 2020 2020 2076 6563 746f 7220 2020         vector   \n+00009220: 2020 2020 2020 2020 2020 2020 2054 7261               Tra\n+00009230: 6e73 6c61 7465 2062 7920 2758 272e 0a27  nslate by 'X'..'\n+00009240: 7363 616c 6528 5329 2720 2020 2020 2020  scale(S)'       \n+00009250: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009260: 2020 2073 6361 6c61 7220 2020 2020 2020     scalar       \n+00009270: 2020 2020 2020 2020 2053 6361 6c65 2075           Scale u\n+00009280: 6e69 666f 726d 6c79 2062 7920 6661 6374  niformly by fact\n+00009290: 6f72 2027 5327 2e0a 2773 6361 6c65 2856  or 'S'..'scale(V\n+000092a0: 2927 2020 2020 2020 2020 2020 2020 2020  )'              \n+000092b0: 2020 2020 2020 2020 2020 2020 7665 6374              vect\n+000092c0: 6f72 2020 2020 2020 2020 2020 2020 2020  or              \n+000092d0: 2020 5363 616c 6520 616c 6f6e 6720 6561    Scale along ea\n+000092e0: 6368 2061 7869 7320 6279 2063 6f6d 706f  ch axis by compo\n+000092f0: 6e65 6e74 7320 6f66 2027 5627 2e0a 2770  nents of 'V'..'p\n+00009300: 726f 6a65 6374 2829 2720 2020 2020 2020  roject()'       \n+00009310: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009320: 2020 2d2d 2020 2020 2020 2020 2020 2020    --            \n+00009330: 2020 2020 2020 2020 5361 6d65 2061 7320          Same as \n+00009340: 2773 6361 6c65 285b 312c 312c 305d 2927  'scale([1,1,0])'\n+00009350: 2e0a 2770 726f 6a65 6374 2853 2927 2020  ..'project(S)'  \n 00009360: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009370: 7363 616c 6172 2020 2020 2020 2020 2020  scalar          \n-00009380: 2020 2020 2020 5065 7273 7065 6374 6976        Perspectiv\n-00009390: 6520 7072 6f6a 6563 7469 6f6e 2077 6974  e projection wit\n-000093a0: 6820 7669 6577 2063 656e 7465 7220 6174  h view center at\n-000093b0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+00009370: 2020 2020 2020 7363 616c 6172 2020 2020        scalar    \n+00009380: 2020 2020 2020 2020 2020 2020 5065 7273              Pers\n+00009390: 7065 6374 6976 6520 7072 6f6a 6563 7469  pective projecti\n+000093a0: 6f6e 2077 6974 6820 7669 6577 2063 656e  on with view cen\n+000093b0: 7465 7220 6174 0a20 2020 2020 2020 2020  ter at.         \n 000093c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000093d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000093e0: 2020 2020 2020 2020 2020 206f 7269 6769             origi\n-000093f0: 6e20 616e 6420 7072 6f6a 6563 7469 6f6e  n and projection\n-00009400: 2070 6c61 6e65 207a 3d2d 2753 272e 0a27   plane z=-'S'..'\n-00009410: 7065 7273 7065 6374 6976 6528 5329 2720  perspective(S)' \n-00009420: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009430: 2020 2073 6361 6c61 7220 2020 2020 2020     scalar       \n-00009440: 2020 2020 2020 2020 2050 6572 7370 6563           Perspec\n-00009450: 7469 7665 205f 7472 616e 7366 6f72 6d5f  tive _transform_\n-00009460: 2069 6465 6e74 6963 616c 2074 6f0a 2020   identical to.  \n-00009470: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000093e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000093f0: 206f 7269 6769 6e20 616e 6420 7072 6f6a   origin and proj\n+00009400: 6563 7469 6f6e 2070 6c61 6e65 207a 3d2d  ection plane z=-\n+00009410: 2753 272e 0a27 7065 7273 7065 6374 6976  'S'..'perspectiv\n+00009420: 6528 5329 2720 2020 2020 2020 2020 2020  e(S)'           \n+00009430: 2020 2020 2020 2020 2073 6361 6c61 7220           scalar \n+00009440: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n+00009450: 6572 7370 6563 7469 7665 205f 7472 616e  erspective _tran\n+00009460: 7366 6f72 6d5f 2069 6465 6e74 6963 616c  sform_ identical\n+00009470: 2074 6f0a 2020 2020 2020 2020 2020 2020   to.            \n 00009480: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009490: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000094a0: 2020 2020 2020 2020 2770 726f 6a65 6374          'project\n-000094b0: 2853 2927 2065 7863 6570 7420 7468 6174  (S)' except that\n-000094c0: 2074 6865 207a 2d63 6f6f 7264 696e 6174   the z-coordinat\n-000094d0: 6520 6f66 0a20 2020 2020 2020 2020 2020  e of.           \n+000094a0: 2020 2020 2020 2020 2020 2020 2020 2770                'p\n+000094b0: 726f 6a65 6374 2853 2927 2065 7863 6570  roject(S)' excep\n+000094c0: 7420 7468 6174 2074 6865 207a 2d63 6f6f  t that the z-coo\n+000094d0: 7264 696e 6174 6520 6f66 0a20 2020 2020  rdinate of.     \n 000094e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000094f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009500: 2020 2020 2020 2020 2020 2020 2020 2074                 t\n-00009510: 6865 2074 7261 6e73 666f 726d 6564 2072  he transformed r\n-00009520: 6573 756c 7420 6973 2022 7073 6575 646f  esult is \"pseudo\n-00009530: 6465 7074 6822 2c0a 2020 2020 2020 2020  depth\",.        \n+00009500: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009510: 2020 2020 2074 6865 2074 7261 6e73 666f       the transfo\n+00009520: 726d 6564 2072 6573 756c 7420 6973 2022  rmed result is \"\n+00009530: 7073 6575 646f 6465 7074 6822 2c0a 2020  pseudodepth\",.  \n 00009540: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009550: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009560: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009570: 2020 7573 6162 6c65 2062 7920 7468 6520    usable by the \n-00009580: 6869 6464 656e 2073 7572 6661 6365 2061  hidden surface a\n-00009590: 6c67 6f72 6974 686d 2e0a 2776 6965 7728  lgorithm..'view(\n-000095a0: 452c 442c 5529 2720 2020 2020 2020 2020  E,D,U)'         \n-000095b0: 2020 2020 2020 2020 2020 2020 2020 706f                po\n-000095c0: 696e 742c 7665 6374 6f72 2c76 6563 746f  int,vector,vecto\n-000095d0: 7220 2020 5669 6577 2074 7261 6e73 666f  r   View transfo\n-000095e0: 726d 2073 696d 696c 6172 2074 6f20 7468  rm similar to th\n-000095f0: 6174 206f 6620 274f 7065 6e47 4c27 2773  at of 'OpenGL''s\n-00009600: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+00009570: 2020 2020 2020 2020 7573 6162 6c65 2062          usable b\n+00009580: 7920 7468 6520 6869 6464 656e 2073 7572  y the hidden sur\n+00009590: 6661 6365 2061 6c67 6f72 6974 686d 2e0a  face algorithm..\n+000095a0: 2776 6965 7728 452c 442c 5529 2720 2020  'view(E,D,U)'   \n+000095b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000095c0: 2020 2020 706f 696e 742c 7665 6374 6f72      point,vector\n+000095d0: 2c76 6563 746f 7220 2020 5669 6577 2074  ,vector   View t\n+000095e0: 7261 6e73 666f 726d 2073 696d 696c 6172  ransform similar\n+000095f0: 2074 6f20 7468 6174 206f 6620 274f 7065   to that of 'Ope\n+00009600: 6e47 4c27 2773 2e0a 2020 2020 2020 2020  nGL''s..        \n 00009610: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009620: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009630: 2020 2020 2020 2020 2020 2020 5468 6520              The \n-00009640: 5f65 7965 2070 6f69 6e74 5f20 2745 2720  _eye point_ 'E' \n-00009650: 6973 2074 7261 6e73 6c61 7465 6420 746f  is translated to\n-00009660: 2074 6865 0a20 2020 2020 2020 2020 2020   the.           \n+00009630: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009640: 2020 5468 6520 5f65 7965 2070 6f69 6e74    The _eye point\n+00009650: 5f20 2745 2720 6973 2074 7261 6e73 6c61  _ 'E' is transla\n+00009660: 7465 6420 746f 2074 6865 0a20 2020 2020  ted to the.     \n 00009670: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009680: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009690: 2020 2020 2020 2020 2020 2020 2020 206f                 o\n-000096a0: 7269 6769 6e20 7768 696c 6520 6120 726f  rigin while a ro\n-000096b0: 7461 7469 6f6e 2069 7320 616c 736f 2061  tation is also a\n-000096c0: 7070 6c69 6564 2074 6861 740a 2020 2020  pplied that.    \n-000096d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009690: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000096a0: 2020 2020 206f 7269 6769 6e20 7768 696c       origin whil\n+000096b0: 6520 6120 726f 7461 7469 6f6e 2069 7320  e a rotation is \n+000096c0: 616c 736f 2061 7070 6c69 6564 2074 6861  also applied tha\n+000096d0: 740a 2020 2020 2020 2020 2020 2020 2020  t.              \n 000096e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000096f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009700: 2020 2020 2020 6d61 6b65 7320 7468 6520        makes the \n-00009710: 5f76 6965 7720 6469 7265 6374 696f 6e20  _view direction \n-00009720: 7665 6374 6f72 5f20 2744 2720 616e 6420  vector_ 'D' and \n-00009730: 7468 650a 2020 2020 2020 2020 2020 2020  the.            \n+00009700: 2020 2020 2020 2020 2020 2020 6d61 6b65              make\n+00009710: 7320 7468 6520 5f76 6965 7720 6469 7265  s the _view dire\n+00009720: 6374 696f 6e20 7665 6374 6f72 5f20 2744  ction vector_ 'D\n+00009730: 2720 616e 6420 7468 650a 2020 2020 2020  ' and the.      \n 00009740: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009750: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009760: 2020 2020 2020 2020 2020 2020 2020 5f76                _v\n-00009770: 6965 7720 2275 7022 2076 6563 746f 725f  iew \"up\" vector_\n-00009780: 2027 5527 2070 6f69 6e74 2069 6e20 7468   'U' point in th\n-00009790: 6520 6e65 6761 7469 7665 0a20 2020 2020  e negative.     \n-000097a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009760: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009770: 2020 2020 5f76 6965 7720 2275 7022 2076      _view \"up\" v\n+00009780: 6563 746f 725f 2027 5527 2070 6f69 6e74  ector_ 'U' point\n+00009790: 2069 6e20 7468 6520 6e65 6761 7469 7665   in the negative\n+000097a0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n 000097b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000097c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000097d0: 2020 2020 207a 2d20 616e 6420 7468 6520       z- and the \n-000097e0: 792d 6469 7265 6374 696f 6e73 2072 6573  y-directions res\n-000097f0: 7065 6374 6976 656c 792e 2020 4966 2027  pectively.  If '\n-00009800: 5527 0a20 2020 2020 2020 2020 2020 2020  U'.             \n+000097d0: 2020 2020 2020 2020 2020 207a 2d20 616e             z- an\n+000097e0: 6420 7468 6520 792d 6469 7265 6374 696f  d the y-directio\n+000097f0: 6e73 2072 6573 7065 6374 6976 656c 792e  ns respectively.\n+00009800: 2020 4966 2027 5527 0a20 2020 2020 2020    If 'U'.       \n 00009810: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009820: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009830: 2020 2020 2020 2020 2020 2020 2069 7320               is \n-00009840: 6f6d 6974 7465 642c 2069 7420 6465 6661  omitted, it defa\n-00009850: 756c 7473 2074 6f20 5b30 2c31 2c30 5d2e  ults to [0,1,0].\n-00009860: 2020 5768 656e 2027 5527 0a20 2020 2020    When 'U'.     \n-00009870: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009830: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009840: 2020 2069 7320 6f6d 6974 7465 642c 2069     is omitted, i\n+00009850: 7420 6465 6661 756c 7473 2074 6f20 5b30  t defaults to [0\n+00009860: 2c31 2c30 5d2e 2020 5768 656e 2027 5527  ,1,0].  When 'U'\n+00009870: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n 00009880: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009890: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000098a0: 2020 2020 2069 7320 6f6d 6974 7465 642c       is omitted,\n-000098b0: 2027 4427 206d 6179 2062 6520 616c 736f   'D' may be also\n-000098c0: 3b20 6974 2064 6566 6175 6c74 7320 746f  ; it defaults to\n-000098d0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+000098a0: 2020 2020 2020 2020 2020 2069 7320 6f6d             is om\n+000098b0: 6974 7465 642c 2027 4427 206d 6179 2062  itted, 'D' may b\n+000098c0: 6520 616c 736f 3b20 6974 2064 6566 6175  e also; it defau\n+000098d0: 6c74 7320 746f 0a20 2020 2020 2020 2020  lts to.         \n 000098e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000098f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009900: 2020 2020 2020 2020 2020 2027 2830 2c30             '(0,0\n-00009910: 2c30 292d 2845 2927 2c20 6120 7665 6374  ,0)-(E)', a vect\n-00009920: 6f72 2070 6f69 6e74 696e 6720 6672 6f6d  or pointing from\n-00009930: 2074 6865 2065 7965 0a20 2020 2020 2020   the eye.       \n+00009900: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009910: 2027 2830 2c30 2c30 292d 2845 2927 2c20   '(0,0,0)-(E)', \n+00009920: 6120 7665 6374 6f72 2070 6f69 6e74 696e  a vector pointin\n+00009930: 6720 6672 6f6d 2074 6865 2065 7965 0a20  g from the eye. \n 00009940: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009950: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009960: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009970: 2020 2074 6f77 6172 6420 7468 6520 6f72     toward the or\n-00009980: 6967 696e 2e0a 2776 6965 7728 452c 4c2c  igin..'view(E,L,\n-00009990: 5529 2720 2020 2020 2020 2020 2020 2020  U)'             \n-000099a0: 2020 2020 2020 2020 2020 706f 696e 742c            point,\n-000099b0: 706f 696e 742c 7665 6374 6f72 2020 2020  point,vector    \n-000099c0: 416e 2061 6c74 6572 6e61 7465 2066 6f72  An alternate for\n-000099d0: 6d20 6f66 2027 7669 6577 2845 2c44 2c55  m of 'view(E,D,U\n-000099e0: 2927 2061 626f 7665 2077 6865 7265 0a20  )' above where. \n-000099f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009970: 2020 2020 2020 2020 2074 6f77 6172 6420           toward \n+00009980: 7468 6520 6f72 6967 696e 2e0a 2776 6965  the origin..'vie\n+00009990: 7728 452c 4c2c 5529 2720 2020 2020 2020  w(E,L,U)'       \n+000099a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000099b0: 706f 696e 742c 706f 696e 742c 7665 6374  point,point,vect\n+000099c0: 6f72 2020 2020 416e 2061 6c74 6572 6e61  or    An alterna\n+000099d0: 7465 2066 6f72 6d20 6f66 2027 7669 6577  te form of 'view\n+000099e0: 2845 2c44 2c55 2927 2061 626f 7665 2077  (E,D,U)' above w\n+000099f0: 6865 7265 0a20 2020 2020 2020 2020 2020  here.           \n 00009a00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009a10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009a20: 2020 2020 2020 2020 2074 6865 2076 6965           the vie\n-00009a30: 7720 6469 7265 6374 696f 6e20 7061 7261  w direction para\n-00009a40: 6d65 7465 7220 2744 2720 6973 2072 6570  meter 'D' is rep\n-00009a50: 6c61 6365 640a 2020 2020 2020 2020 2020  laced.          \n+00009a20: 2020 2020 2020 2020 2020 2020 2020 2074                 t\n+00009a30: 6865 2076 6965 7720 6469 7265 6374 696f  he view directio\n+00009a40: 6e20 7061 7261 6d65 7465 7220 2744 2720  n parameter 'D' \n+00009a50: 6973 2072 6570 6c61 6365 640a 2020 2020  is replaced.    \n 00009a60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009a70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009a80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009a90: 7769 7468 2061 2022 6c6f 6f6b 2061 7422  with a \"look at\"\n-00009aa0: 2070 6f69 6e74 2027 4c27 2c20 692e 652e   point 'L', i.e.\n-00009ab0: 2c20 6120 706f 696e 740a 2020 2020 2020  , a point.      \n+00009a90: 2020 2020 2020 7769 7468 2061 2022 6c6f        with a \"lo\n+00009aa0: 6f6b 2061 7422 2070 6f69 6e74 2027 4c27  ok at\" point 'L'\n+00009ab0: 2c20 692e 652e 2c20 6120 706f 696e 740a  , i.e., a point.\n 00009ac0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009ad0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009ae0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009af0: 2020 2020 7768 6572 6520 7468 6520 7669      where the vi\n-00009b00: 6577 6572 2069 7320 666f 6375 7369 6e67  ewer is focusing\n-00009b10: 2068 6572 2061 7474 656e 7469 6f6e 2e0a   her attention..\n-00009b20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009af0: 2020 2020 2020 2020 2020 7768 6572 6520            where \n+00009b00: 7468 6520 7669 6577 6572 2069 7320 666f  the viewer is fo\n+00009b10: 6375 7369 6e67 2068 6572 2061 7474 656e  cusing her atten\n+00009b20: 7469 6f6e 2e0a 2020 2020 2020 2020 2020  tion..          \n 00009b30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009b40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009b50: 2020 2020 2020 2020 2020 5468 6973 2066            This f\n-00009b60: 6f72 6d20 6f66 2076 6965 7720 6973 2065  orm of view is e\n-00009b70: 7175 6976 616c 656e 7420 746f 2027 7669  quivalent to 'vi\n-00009b80: 6577 2845 2c0a 2020 2020 2020 2020 2020  ew(E,.          \n+00009b50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009b60: 5468 6973 2066 6f72 6d20 6f66 2076 6965  This form of vie\n+00009b70: 7720 6973 2065 7175 6976 616c 656e 7420  w is equivalent \n+00009b80: 746f 2027 7669 6577 2845 2c0a 2020 2020  to 'view(E,.    \n 00009b90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009ba0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009bb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009bc0: 284c 292d 2845 292c 2055 2927 2c20 7768  (L)-(E), U)', wh\n-00009bd0: 6572 6520 2728 4c29 2d28 4529 2720 6973  ere '(L)-(E)' is\n-00009be0: 2061 2064 6972 6563 7469 6f6e 0a20 2020   a direction.   \n-00009bf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009bc0: 2020 2020 2020 284c 292d 2845 292c 2055        (L)-(E), U\n+00009bd0: 2927 2c20 7768 6572 6520 2728 4c29 2d28  )', where '(L)-(\n+00009be0: 4529 2720 6973 2061 2064 6972 6563 7469  E)' is a directi\n+00009bf0: 6f6e 0a20 2020 2020 2020 2020 2020 2020  on.             \n 00009c00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009c10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009c20: 2020 2020 2020 2076 6563 746f 722e 2020         vector.  \n-00009c30: 2755 2720 6973 206f 7074 696f 6e61 6c20  'U' is optional \n-00009c40: 616e 6420 6465 6661 756c 7473 2074 6f0a  and defaults to.\n-00009c50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009c20: 2020 2020 2020 2020 2020 2020 2076 6563               vec\n+00009c30: 746f 722e 2020 2755 2720 6973 206f 7074  tor.  'U' is opt\n+00009c40: 696f 6e61 6c20 616e 6420 6465 6661 756c  ional and defaul\n+00009c50: 7473 2074 6f0a 2020 2020 2020 2020 2020  ts to.          \n 00009c60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00009c70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009c80: 2020 2020 2020 2020 2020 5b30 2c31 2c30            [0,1,0\n-00009c90: 5d2e 0a27 5b5b 615f 7b31 317d 2c61 5f7b  ]..'[[a_{11},a_{\n-00009ca0: 3132 7d2c 615f 7b31 337d 2c61 5f7b 3134  12},a_{13},a_{14\n-00009cb0: 7d5d 2720 2020 2031 3620 7363 616c 6172  }]'    16 scalar\n-00009cc0: 7320 2020 2020 2020 2020 2020 2044 6972  s            Dir\n-00009cd0: 6563 7420 7472 616e 7366 6f72 6d20 6d61  ect transform ma\n-00009ce0: 7472 6978 2064 6566 696e 6974 696f 6e2e  trix definition.\n-00009cf0: 2020 4561 6368 206f 660a 2720 5b61 5f7b    Each of.' [a_{\n-00009d00: 3231 7d2c 615f 7b32 327d 2c61 5f7b 3233  21},a_{22},a_{23\n-00009d10: 7d2c 615f 7b32 347d 5d27 2020 2020 2020  },a_{24}]'      \n+00009c80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009c90: 5b30 2c31 2c30 5d2e 0a27 5b5b 615f 7b31  [0,1,0]..'[[a_{1\n+00009ca0: 317d 2c61 5f7b 3132 7d2c 615f 7b31 337d  1},a_{12},a_{13}\n+00009cb0: 2c61 5f7b 3134 7d5d 2720 2020 2031 3620  ,a_{14}]'    16 \n+00009cc0: 7363 616c 6172 7320 2020 2020 2020 2020  scalars         \n+00009cd0: 2020 2044 6972 6563 7420 7472 616e 7366     Direct transf\n+00009ce0: 6f72 6d20 6d61 7472 6978 2064 6566 696e  orm matrix defin\n+00009cf0: 6974 696f 6e2e 2020 4561 6368 206f 660a  ition.  Each of.\n+00009d00: 2720 5b61 5f7b 3231 7d2c 615f 7b32 327d  ' [a_{21},a_{22}\n+00009d10: 2c61 5f7b 3233 7d2c 615f 7b32 347d 5d27  ,a_{23},a_{24}]'\n 00009d20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009d30: 2020 2020 7468 6520 615f 7b69 6a7d 2069      the a_{ij} i\n-00009d40: 7320 6120 7363 616c 6172 2065 7870 7265  s a scalar expre\n-00009d50: 7373 696f 6e2e 2020 5365 6520 7465 7874  ssion.  See text\n-00009d60: 0a27 205b 615f 7b33 317d 2c61 5f7b 3332  .' [a_{31},a_{32\n-00009d70: 7d2c 615f 7b33 337d 2c61 5f7b 3334 7d5d  },a_{33},a_{34}]\n-00009d80: 2720 2020 2020 2020 2020 2020 2020 2020  '               \n-00009d90: 2020 2020 2020 2020 2020 2066 6f72 2064             for d\n-00009da0: 6574 6169 6c73 2e0a 2720 5b61 5f7b 3431  etails..' [a_{41\n-00009db0: 7d2c 615f 7b34 327d 2c61 5f7b 3433 7d2c  },a_{42},a_{43},\n-00009dc0: 615f 7b34 347d 5d5d 270a 5468 6520 2770  a_{44}]]'.The 'p\n-00009dd0: 726f 6a65 6374 2720 636f 6e73 7472 7563  roject' construc\n-00009de0: 746f 7220 6973 206e 6f74 2067 656e 6572  tor is not gener\n-00009df0: 616c 6c79 2075 7365 6675 6c20 6265 6361  ally useful beca\n-00009e00: 7573 6520 6974 2064 6566 6561 7473 0a68  use it defeats.h\n-00009e10: 6964 6465 6e20 7375 7266 6163 6520 7265  idden surface re\n-00009e20: 6d6f 7661 6c20 6279 2063 6f6c 6c61 7073  moval by collaps\n-00009e30: 696e 6720 7468 6520 7363 656e 6520 6f6e  ing the scene on\n-00009e40: 746f 2061 2073 696e 676c 6520 706c 616e  to a single plan\n-00009e50: 652e 2020 4974 0a69 7320 6120 7370 6563  e.  It.is a spec\n-00009e60: 6961 6c20 7075 7270 6f73 6520 7472 616e  ial purpose tran\n-00009e70: 7366 6f72 6d20 666f 7220 6472 6177 696e  sform for drawin\n-00009e80: 6720 7069 6374 7572 6573 206f 6620 7363  g pictures of sc\n-00009e90: 656e 6573 2077 6865 7265 0a74 6872 6565  enes where.three\n-00009ea0: 2d64 696d 656e 7369 6f6e 616c 206f 626a  -dimensional obj\n-00009eb0: 6563 7473 2061 7265 2062 6569 6e67 2070  ects are being p\n-00009ec0: 726f 6a65 6374 6564 206f 6e74 6f20 706c  rojected onto pl\n-00009ed0: 616e 6573 2e20 2053 6565 2c20 666f 720a  anes.  See, for.\n-00009ee0: 6578 616d 706c 652c 202a 6e6f 7465 204f  example, *note O\n-00009ef0: 7665 7276 6965 773a 3a2e 0a0a 2020 2054  verview::...   T\n-00009f00: 6865 2064 6972 6563 7420 7472 616e 7366  he direct transf\n-00009f10: 6f72 6d20 636f 6e73 7472 7563 746f 7220  orm constructor \n-00009f20: 616c 6c6f 7773 2064 6972 6563 7420 656e  allows direct en\n-00009f30: 7472 7920 6f66 2061 2034 7834 0a74 7261  try of a 4x4.tra\n-00009f40: 6e73 666f 726d 6174 696f 6e20 6d61 7472  nsformation matr\n-00009f50: 6978 2e20 204d 6f73 7420 3364 2067 7261  ix.  Most 3d gra\n-00009f60: 7068 6963 7320 7379 7374 656d 732c 2069  phics systems, i\n-00009f70: 6e63 6c75 6469 6e67 2027 736b 6574 6368  ncluding 'sketch\n-00009f80: 272c 0a75 7365 2034 2d64 696d 656e 7369  ',.use 4-dimensi\n-00009f90: 6f6e 616c 2068 6f6d 6f67 656e 656f 7573  onal homogeneous\n-00009fa0: 2063 6f6f 7264 696e 6174 6573 2069 6e74   coordinates int\n-00009fb0: 6572 6e61 6c6c 792e 2020 5468 6573 6520  ernally.  These \n-00009fc0: 6172 650a 7472 616e 7366 6f72 6d65 6420  are.transformed \n-00009fd0: 6279 206d 756c 7469 706c 6963 6174 696f  by multiplicatio\n-00009fe0: 6e20 7769 7468 2034 7834 206d 6174 7269  n with 4x4 matri\n-00009ff0: 6365 732e 2020 5468 6520 6275 696c 742d  ces.  The built-\n-0000a000: 696e 0a63 6f6e 7374 7275 6374 6f72 7320  in.constructors \n-0000a010: 2827 726f 7461 7465 272c 2027 7363 616c  ('rotate', 'scal\n-0000a020: 6527 2c20 6574 632e 2920 2061 7265 2061  e', etc.)  are a\n-0000a030: 6c6c 2074 7261 6e73 6c61 7465 6420 696e  ll translated in\n-0000a040: 7465 726e 616c 6c79 2074 6f0a 7375 6368  ternally to.such\n-0000a050: 2034 7834 206d 6174 7269 6365 732e 2020   4x4 matrices.  \n-0000a060: 466f 7220 6d6f 7265 2069 6e66 6f72 6d61  For more informa\n-0000a070: 7469 6f6e 206f 6e20 686f 6d6f 6765 6e65  tion on homogene\n-0000a080: 6f75 7320 636f 6f72 6469 6e61 7465 0a74  ous coordinate.t\n-0000a090: 7261 6e73 666f 726d 6174 696f 6e73 2c20  ransformations, \n-0000a0a0: 7365 6520 616e 7920 676f 6f64 2063 6f6d  see any good com\n-0000a0b0: 7075 7465 7220 6772 6170 6869 6373 2074  puter graphics t\n-0000a0c0: 6578 7462 6f6f 6b2e 2020 5468 6520 6469  extbook.  The di\n-0000a0d0: 7265 6374 0a74 7261 6e73 666f 726d 2066  rect.transform f\n-0000a0e0: 6561 7475 7265 206f 6620 2773 6b65 7463  eature of 'sketc\n-0000a0f0: 6827 2061 6c6c 6f77 7320 796f 7520 746f  h' allows you to\n-0000a100: 2065 6e74 6572 2061 206d 6174 7269 7820   enter a matrix \n-0000a110: 6f66 2079 6f75 7220 6f77 6e0a 6368 6f69  of your own.choi\n-0000a120: 6365 2e20 2054 6865 7265 2061 7265 206e  ce.  There are n\n-0000a130: 6f74 206d 616e 7920 6361 7365 7320 7768  ot many cases wh\n-0000a140: 6572 6520 7468 6973 2069 7320 7573 6566  ere this is usef\n-0000a150: 756c 2c20 6275 7420 6966 2079 6f75 2064  ul, but if you d\n-0000a160: 6f0a 6e65 6564 2069 742c 2079 6f75 206e  o.need it, you n\n-0000a170: 6565 6420 6974 2062 6164 6c79 210a 0a1f  eed it badly!...\n-0000a180: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n-0000a190: 666f 2c20 204e 6f64 653a 2041 7269 7468  fo,  Node: Arith\n-0000a1a0: 6d65 7469 632c 2020 4e65 7874 3a20 4f70  metic,  Next: Op\n-0000a1b0: 7469 6f6e 732c 2020 5072 6576 3a20 4c69  tions,  Prev: Li\n-0000a1c0: 7465 7261 6c73 2c20 2055 703a 204c 616e  terals,  Up: Lan\n-0000a1d0: 6775 6167 6520 6261 7369 6373 0a0a 332e  guage basics..3.\n-0000a1e0: 312e 3420 4172 6974 686d 6574 6963 2065  1.4 Arithmetic e\n-0000a1f0: 7870 7265 7373 696f 6e73 0a2d 2d2d 2d2d  xpressions.-----\n-0000a200: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-0000a210: 2d2d 2d2d 2d2d 2d0a 0a41 7269 7468 6d65  -------..Arithme\n-0000a220: 7469 6320 6578 7072 6573 7369 6f6e 7320  tic expressions \n-0000a230: 6f76 6572 2027 736b 6574 6368 2720 6c69  over 'sketch' li\n-0000a240: 7465 7261 6c73 2061 6e64 2064 6566 696e  terals and defin\n-0000a250: 6564 2069 6465 6e74 6966 6965 7273 0a61  ed identifiers.a\n-0000a260: 7265 2073 756d 6d61 7269 7a65 6420 696e  re summarized in\n-0000a270: 2074 6865 2066 6f6c 6c6f 7769 6e67 2074   the following t\n-0000a280: 6162 6c65 732e 0a0a 2a20 4d65 6e75 3a0a  ables...* Menu:.\n-0000a290: 0a2a 2054 776f 2d6f 7065 7261 6e64 2028  .* Two-operand (\n-0000a2a0: 6269 6e61 7279 2920 666f 726d 733a 3a20  binary) forms:: \n-0000a2b0: 2041 206f 7020 420a 2a20 556e 6172 7920   A op B.* Unary \n-0000a2c0: 666f 726d 733a 3a20 2020 2020 2020 2020  forms::         \n-0000a2d0: 2020 2020 2020 2020 6f70 2041 2028 616e          op A (an\n-0000a2e0: 6420 6f74 6865 7273 290a 0a1f 0a46 696c  d others)....Fil\n-0000a2f0: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n-0000a300: 204e 6f64 653a 2054 776f 2d6f 7065 7261   Node: Two-opera\n-0000a310: 6e64 2028 6269 6e61 7279 2920 666f 726d  nd (binary) form\n-0000a320: 732c 2020 4e65 7874 3a20 556e 6172 7920  s,  Next: Unary \n-0000a330: 666f 726d 732c 2020 5072 6576 3a20 4172  forms,  Prev: Ar\n-0000a340: 6974 686d 6574 6963 2c20 2055 703a 2041  ithmetic,  Up: A\n-0000a350: 7269 7468 6d65 7469 630a 0a33 2e31 2e34  rithmetic..3.1.4\n-0000a360: 2e31 2054 776f 2d6f 7065 7261 6e64 2028  .1 Two-operand (\n-0000a370: 6269 6e61 7279 2920 666f 726d 7320 616e  binary) forms an\n-0000a380: 6420 7072 6563 6564 656e 6365 0a2e 2e2e  d precedence....\n-0000a390: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+00009d30: 2020 2020 2020 2020 2020 7468 6520 615f            the a_\n+00009d40: 7b69 6a7d 2069 7320 6120 7363 616c 6172  {ij} is a scalar\n+00009d50: 2065 7870 7265 7373 696f 6e2e 2020 5365   expression.  Se\n+00009d60: 6520 7465 7874 0a27 205b 615f 7b33 317d  e text.' [a_{31}\n+00009d70: 2c61 5f7b 3332 7d2c 615f 7b33 337d 2c61  ,a_{32},a_{33},a\n+00009d80: 5f7b 3334 7d5d 2720 2020 2020 2020 2020  _{34}]'         \n+00009d90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009da0: 2066 6f72 2064 6574 6169 6c73 2e0a 2720   for details..' \n+00009db0: 5b61 5f7b 3431 7d2c 615f 7b34 327d 2c61  [a_{41},a_{42},a\n+00009dc0: 5f7b 3433 7d2c 615f 7b34 347d 5d5d 270a  _{43},a_{44}]]'.\n+00009dd0: 5468 6520 2770 726f 6a65 6374 2720 636f  The 'project' co\n+00009de0: 6e73 7472 7563 746f 7220 6973 206e 6f74  nstructor is not\n+00009df0: 2067 656e 6572 616c 6c79 2075 7365 6675   generally usefu\n+00009e00: 6c20 6265 6361 7573 6520 6974 2064 6566  l because it def\n+00009e10: 6561 7473 0a68 6964 6465 6e20 7375 7266  eats.hidden surf\n+00009e20: 6163 6520 7265 6d6f 7661 6c20 6279 2063  ace removal by c\n+00009e30: 6f6c 6c61 7073 696e 6720 7468 6520 7363  ollapsing the sc\n+00009e40: 656e 6520 6f6e 746f 2061 2073 696e 676c  ene onto a singl\n+00009e50: 6520 706c 616e 652e 2020 4974 0a69 7320  e plane.  It.is \n+00009e60: 6120 7370 6563 6961 6c20 7075 7270 6f73  a special purpos\n+00009e70: 6520 7472 616e 7366 6f72 6d20 666f 7220  e transform for \n+00009e80: 6472 6177 696e 6720 7069 6374 7572 6573  drawing pictures\n+00009e90: 206f 6620 7363 656e 6573 2077 6865 7265   of scenes where\n+00009ea0: 0a74 6872 6565 2d64 696d 656e 7369 6f6e  .three-dimension\n+00009eb0: 616c 206f 626a 6563 7473 2061 7265 2062  al objects are b\n+00009ec0: 6569 6e67 2070 726f 6a65 6374 6564 206f  eing projected o\n+00009ed0: 6e74 6f20 706c 616e 6573 2e20 2053 6565  nto planes.  See\n+00009ee0: 2c20 666f 720a 6578 616d 706c 652c 202a  , for.example, *\n+00009ef0: 6e6f 7465 204f 7665 7276 6965 773a 3a2e  note Overview::.\n+00009f00: 0a0a 2020 2054 6865 2064 6972 6563 7420  ..   The direct \n+00009f10: 7472 616e 7366 6f72 6d20 636f 6e73 7472  transform constr\n+00009f20: 7563 746f 7220 616c 6c6f 7773 2064 6972  uctor allows dir\n+00009f30: 6563 7420 656e 7472 7920 6f66 2061 2034  ect entry of a 4\n+00009f40: 7834 0a74 7261 6e73 666f 726d 6174 696f  x4.transformatio\n+00009f50: 6e20 6d61 7472 6978 2e20 204d 6f73 7420  n matrix.  Most \n+00009f60: 3364 2067 7261 7068 6963 7320 7379 7374  3d graphics syst\n+00009f70: 656d 732c 2069 6e63 6c75 6469 6e67 2027  ems, including '\n+00009f80: 736b 6574 6368 272c 0a75 7365 2034 2d64  sketch',.use 4-d\n+00009f90: 696d 656e 7369 6f6e 616c 2068 6f6d 6f67  imensional homog\n+00009fa0: 656e 656f 7573 2063 6f6f 7264 696e 6174  eneous coordinat\n+00009fb0: 6573 2069 6e74 6572 6e61 6c6c 792e 2020  es internally.  \n+00009fc0: 5468 6573 6520 6172 650a 7472 616e 7366  These are.transf\n+00009fd0: 6f72 6d65 6420 6279 206d 756c 7469 706c  ormed by multipl\n+00009fe0: 6963 6174 696f 6e20 7769 7468 2034 7834  ication with 4x4\n+00009ff0: 206d 6174 7269 6365 732e 2020 5468 6520   matrices.  The \n+0000a000: 6275 696c 742d 696e 0a63 6f6e 7374 7275  built-in.constru\n+0000a010: 6374 6f72 7320 2827 726f 7461 7465 272c  ctors ('rotate',\n+0000a020: 2027 7363 616c 6527 2c20 6574 632e 2920   'scale', etc.) \n+0000a030: 2061 7265 2061 6c6c 2074 7261 6e73 6c61   are all transla\n+0000a040: 7465 6420 696e 7465 726e 616c 6c79 2074  ted internally t\n+0000a050: 6f0a 7375 6368 2034 7834 206d 6174 7269  o.such 4x4 matri\n+0000a060: 6365 732e 2020 466f 7220 6d6f 7265 2069  ces.  For more i\n+0000a070: 6e66 6f72 6d61 7469 6f6e 206f 6e20 686f  nformation on ho\n+0000a080: 6d6f 6765 6e65 6f75 7320 636f 6f72 6469  mogeneous coordi\n+0000a090: 6e61 7465 0a74 7261 6e73 666f 726d 6174  nate.transformat\n+0000a0a0: 696f 6e73 2c20 7365 6520 616e 7920 676f  ions, see any go\n+0000a0b0: 6f64 2063 6f6d 7075 7465 7220 6772 6170  od computer grap\n+0000a0c0: 6869 6373 2074 6578 7462 6f6f 6b2e 2020  hics textbook.  \n+0000a0d0: 5468 6520 6469 7265 6374 0a74 7261 6e73  The direct.trans\n+0000a0e0: 666f 726d 2066 6561 7475 7265 206f 6620  form feature of \n+0000a0f0: 2773 6b65 7463 6827 2061 6c6c 6f77 7320  'sketch' allows \n+0000a100: 796f 7520 746f 2065 6e74 6572 2061 206d  you to enter a m\n+0000a110: 6174 7269 7820 6f66 2079 6f75 7220 6f77  atrix of your ow\n+0000a120: 6e0a 6368 6f69 6365 2e20 2054 6865 7265  n.choice.  There\n+0000a130: 2061 7265 206e 6f74 206d 616e 7920 6361   are not many ca\n+0000a140: 7365 7320 7768 6572 6520 7468 6973 2069  ses where this i\n+0000a150: 7320 7573 6566 756c 2c20 6275 7420 6966  s useful, but if\n+0000a160: 2079 6f75 2064 6f0a 6e65 6564 2069 742c   you do.need it,\n+0000a170: 2079 6f75 206e 6565 6420 6974 2062 6164   you need it bad\n+0000a180: 6c79 210a 0a1f 0a46 696c 653a 2073 6b65  ly!....File: ske\n+0000a190: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n+0000a1a0: 2041 7269 7468 6d65 7469 632c 2020 4e65   Arithmetic,  Ne\n+0000a1b0: 7874 3a20 4f70 7469 6f6e 732c 2020 5072  xt: Options,  Pr\n+0000a1c0: 6576 3a20 4c69 7465 7261 6c73 2c20 2055  ev: Literals,  U\n+0000a1d0: 703a 204c 616e 6775 6167 6520 6261 7369  p: Language basi\n+0000a1e0: 6373 0a0a 332e 312e 3420 4172 6974 686d  cs..3.1.4 Arithm\n+0000a1f0: 6574 6963 2065 7870 7265 7373 696f 6e73  etic expressions\n+0000a200: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  .---------------\n+0000a210: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a41  -------------..A\n+0000a220: 7269 7468 6d65 7469 6320 6578 7072 6573  rithmetic expres\n+0000a230: 7369 6f6e 7320 6f76 6572 2027 736b 6574  sions over 'sket\n+0000a240: 6368 2720 6c69 7465 7261 6c73 2061 6e64  ch' literals and\n+0000a250: 2064 6566 696e 6564 2069 6465 6e74 6966   defined identif\n+0000a260: 6965 7273 0a61 7265 2073 756d 6d61 7269  iers.are summari\n+0000a270: 7a65 6420 696e 2074 6865 2066 6f6c 6c6f  zed in the follo\n+0000a280: 7769 6e67 2074 6162 6c65 732e 0a0a 2a20  wing tables...* \n+0000a290: 4d65 6e75 3a0a 0a2a 2054 776f 2d6f 7065  Menu:..* Two-ope\n+0000a2a0: 7261 6e64 2028 6269 6e61 7279 2920 666f  rand (binary) fo\n+0000a2b0: 726d 733a 3a20 2041 206f 7020 420a 2a20  rms::  A op B.* \n+0000a2c0: 556e 6172 7920 666f 726d 733a 3a20 2020  Unary forms::   \n+0000a2d0: 2020 2020 2020 2020 2020 2020 2020 6f70                op\n+0000a2e0: 2041 2028 616e 6420 6f74 6865 7273 290a   A (and others).\n+0000a2f0: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n+0000a300: 696e 666f 2c20 204e 6f64 653a 2054 776f  info,  Node: Two\n+0000a310: 2d6f 7065 7261 6e64 2028 6269 6e61 7279  -operand (binary\n+0000a320: 2920 666f 726d 732c 2020 4e65 7874 3a20  ) forms,  Next: \n+0000a330: 556e 6172 7920 666f 726d 732c 2020 5072  Unary forms,  Pr\n+0000a340: 6576 3a20 4172 6974 686d 6574 6963 2c20  ev: Arithmetic, \n+0000a350: 2055 703a 2041 7269 7468 6d65 7469 630a   Up: Arithmetic.\n+0000a360: 0a33 2e31 2e34 2e31 2054 776f 2d6f 7065  .3.1.4.1 Two-ope\n+0000a370: 7261 6e64 2028 6269 6e61 7279 2920 666f  rand (binary) fo\n+0000a380: 726d 7320 616e 6420 7072 6563 6564 656e  rms and preceden\n+0000a390: 6365 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ce..............\n 0000a3a0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000a3b0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a  ................\n-0000a3c0: 4d6f 7374 2074 776f 2d6f 7065 7261 6e64  Most two-operand\n-0000a3d0: 2062 696e 6172 7920 666f 726d 7320 6861   binary forms ha\n-0000a3e0: 7665 206d 6561 6e69 6e67 7320 6465 7065  ve meanings depe\n-0000a3f0: 6e64 656e 7420 6f6e 2074 6865 2074 7970  ndent on the typ\n-0000a400: 6573 206f 660a 7468 6569 7220 6172 6775  es of.their argu\n-0000a410: 6d65 6e74 732e 2020 416e 2065 7868 6175  ments.  An exhau\n-0000a420: 7374 6976 6520 7375 6d6d 6172 7920 6f66  stive summary of\n-0000a430: 2074 6865 2070 6f73 7369 6269 6c69 7469   the possibiliti\n-0000a440: 6573 2069 7320 6769 7665 6e20 696e 0a74  es is given in.t\n-0000a450: 6865 2066 6f6c 6c6f 7769 6e67 2074 6162  he following tab\n-0000a460: 6c65 2e0a 4c65 6674 2020 2020 2020 2020  le..Left        \n-0000a470: 4f70 2020 2020 2020 2052 6967 6874 2020  Op       Right  \n-0000a480: 2020 2020 2052 6573 756c 7420 2020 2020       Result     \n-0000a490: 2044 6573 6372 6970 7469 6f6e 0a2d 2d2d   Description.---\n-0000a4a0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n+0000a3b0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+0000a3c0: 2e2e 2e2e 0a0a 4d6f 7374 2074 776f 2d6f  ......Most two-o\n+0000a3d0: 7065 7261 6e64 2062 696e 6172 7920 666f  perand binary fo\n+0000a3e0: 726d 7320 6861 7665 206d 6561 6e69 6e67  rms have meaning\n+0000a3f0: 7320 6465 7065 6e64 656e 7420 6f6e 2074  s dependent on t\n+0000a400: 6865 2074 7970 6573 206f 660a 7468 6569  he types of.thei\n+0000a410: 7220 6172 6775 6d65 6e74 732e 2020 416e  r arguments.  An\n+0000a420: 2065 7868 6175 7374 6976 6520 7375 6d6d   exhaustive summ\n+0000a430: 6172 7920 6f66 2074 6865 2070 6f73 7369  ary of the possi\n+0000a440: 6269 6c69 7469 6573 2069 7320 6769 7665  bilities is give\n+0000a450: 6e20 696e 0a74 6865 2066 6f6c 6c6f 7769  n in.the followi\n+0000a460: 6e67 2074 6162 6c65 2e0a 4c65 6674 2020  ng table..Left  \n+0000a470: 2020 2020 2020 4f70 2020 2020 2020 2052        Op       R\n+0000a480: 6967 6874 2020 2020 2020 2052 6573 756c  ight       Resul\n+0000a490: 7420 2020 2020 2044 6573 6372 6970 7469  t      Descripti\n+0000a4a0: 6f6e 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  on.-------------\n 0000a4b0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000a4c0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000a4d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000a4e0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000a4f0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000a500: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-0000a510: 2d2d 2d0a 7363 616c 6172 2020 2020 2020  ---.scalar      \n-0000a520: 272b 2720 2020 2020 2073 6361 6c61 7220  '+'      scalar \n-0000a530: 2020 2020 2073 6361 6c61 7220 2020 2020       scalar     \n-0000a540: 2053 6361 6c61 7220 7375 6d2e 0a76 6563   Scalar sum..vec\n-0000a550: 746f 7220 2020 2020 2027 2b27 2020 2020  tor      '+'    \n-0000a560: 2020 7665 6374 6f72 2020 2020 2020 7665    vector      ve\n-0000a570: 6374 6f72 2020 2020 2020 5665 6374 6f72  ctor      Vector\n-0000a580: 2073 756d 2e0a 706f 696e 7420 2020 2020   sum..point     \n-0000a590: 2020 272b 2720 2020 2020 2076 6563 746f    '+'      vecto\n-0000a5a0: 7220 2020 2020 2070 6f69 6e74 2020 2020  r      point    \n-0000a5b0: 2020 2050 6f69 6e74 2d76 6563 746f 7220     Point-vector \n-0000a5c0: 6166 6669 6e65 2073 756d 2e0a 7665 6374  affine sum..vect\n-0000a5d0: 6f72 2020 2020 2020 272b 2720 2020 2020  or      '+'     \n-0000a5e0: 2070 6f69 6e74 2020 2020 2020 2022 2020   point       \"  \n-0000a5f0: 2020 2020 2020 2020 2022 0a73 6361 6c61           \".scala\n-0000a600: 7220 2020 2020 2027 2d27 2020 2020 2020  r      '-'      \n-0000a610: 7363 616c 6172 2020 2020 2020 7363 616c  scalar      scal\n-0000a620: 6172 2020 2020 2020 5363 616c 6172 2064  ar      Scalar d\n-0000a630: 6966 6665 7265 6e63 652e 0a76 6563 746f  ifference..vecto\n-0000a640: 7220 2020 2020 2027 2d27 2020 2020 2020  r      '-'      \n-0000a650: 7665 6374 6f72 2020 2020 2020 7665 6374  vector      vect\n-0000a660: 6f72 2020 2020 2020 5665 6374 6f72 2064  or      Vector d\n-0000a670: 6966 6665 7265 6e63 652e 0a70 6f69 6e74  ifference..point\n-0000a680: 2020 2020 2020 2027 2d27 2020 2020 2020         '-'      \n-0000a690: 706f 696e 7420 2020 2020 2020 7665 6374  point       vect\n-0000a6a0: 6f72 2020 2020 2020 506f 696e 742d 706f  or      Point-po\n-0000a6b0: 696e 7420 6166 6669 6e65 2064 6966 6665  int affine diffe\n-0000a6c0: 7265 6e63 652e 0a70 6f69 6e74 2020 2020  rence..point    \n-0000a6d0: 2020 2027 2d27 2020 2020 2020 7665 6374     '-'      vect\n-0000a6e0: 6f72 2020 2020 2020 706f 696e 7420 2020  or      point   \n-0000a6f0: 2020 2020 506f 696e 742d 7665 6374 6f72      Point-vector\n-0000a700: 2061 6666 696e 6520 6469 6666 6572 656e   affine differen\n-0000a710: 6365 2e0a 7363 616c 6172 2020 2020 2020  ce..scalar      \n-0000a720: 272a 2720 6f72 2020 2073 6361 6c61 7220  '*' or   scalar \n-0000a730: 2020 2020 2073 6361 6c61 7220 2020 2020       scalar     \n-0000a740: 2053 6361 6c61 7220 7072 6f64 7563 742e   Scalar product.\n-0000a750: 0a20 2020 2020 2020 2020 2020 2027 2e27  .            '.'\n-0000a760: 0a73 6361 6c61 7220 2020 2020 2027 2a27  .scalar      '*'\n-0000a770: 206f 7220 2020 7665 6374 6f72 2020 2020   or   vector    \n-0000a780: 2020 7665 6374 6f72 2020 2020 2020 5363    vector      Sc\n-0000a790: 616c 6172 2d76 6563 746f 7220 7072 6f64  alar-vector prod\n-0000a7a0: 7563 742e 0a20 2020 2020 2020 2020 2020  uct..           \n-0000a7b0: 2027 2e27 0a76 6563 746f 7220 2020 2020   '.'.vector     \n-0000a7c0: 2027 2a27 206f 7220 2020 7363 616c 6172   '*' or   scalar\n-0000a7d0: 2020 2020 2020 2220 2020 2020 2020 2020        \"         \n-0000a7e0: 2020 220a 2020 2020 2020 2020 2020 2020    \".            \n-0000a7f0: 272e 270a 7665 6374 6f72 2020 2020 2020  '.'.vector      \n-0000a800: 272a 2720 2020 2020 2076 6563 746f 7220  '*'      vector \n-0000a810: 2020 2020 2076 6563 746f 7220 2020 2020       vector     \n-0000a820: 2056 6563 746f 7220 6372 6f73 732d 7072   Vector cross-pr\n-0000a830: 6f64 7563 742e 0a76 6563 746f 7220 2020  oduct..vector   \n-0000a840: 2020 2027 2e27 2020 2020 2020 7665 6374     '.'      vect\n-0000a850: 6f72 2020 2020 2020 7363 616c 6172 2020  or      scalar  \n-0000a860: 2020 2020 5665 6374 6f72 2064 6f74 2070      Vector dot p\n-0000a870: 726f 6475 6374 2e0a 7363 616c 6172 2020  roduct..scalar  \n-0000a880: 2020 2020 275e 2720 2020 2020 2073 6361      '^'      sca\n-0000a890: 6c61 7220 2020 2020 2073 6361 6c61 7220  lar      scalar \n-0000a8a0: 2020 2020 2052 6169 7365 2073 6361 6c61       Raise scala\n-0000a8b0: 7220 746f 2073 6361 6c61 7220 706f 7765  r to scalar powe\n-0000a8c0: 722e 0a74 7261 6e73 666f 726d 2020 2027  r..transform   '\n-0000a8d0: 5e27 2020 2020 2020 696e 7465 6765 7220  ^'      integer \n-0000a8e0: 2020 2020 7472 616e 7366 6f72 6d20 2020      transform   \n-0000a8f0: 5261 6973 6520 7472 616e 7366 6f72 6d20  Raise transform \n-0000a900: 746f 2069 6e74 6567 6572 2070 6f77 6572  to integer power\n-0000a910: 2e0a 7472 616e 7366 6f72 6d20 2020 272a  ..transform   '*\n-0000a920: 2720 6f72 2020 2070 6f69 6e74 2020 2020  ' or   point    \n-0000a930: 2020 2070 6f69 6e74 2020 2020 2020 2041     point       A\n-0000a940: 6666 696e 6520 706f 696e 7420 7472 616e  ffine point tran\n-0000a950: 7366 6f72 6d20 2872 6967 6874 2d74 6f2d  sform (right-to-\n-0000a960: 6c65 6674 292e 0a20 2020 2020 2020 2020  left)..         \n-0000a970: 2020 2027 2e27 0a74 7261 6e73 666f 726d     '.'.transform\n-0000a980: 2020 2027 2a27 206f 7220 2020 7665 6374     '*' or   vect\n-0000a990: 6f72 2020 2020 2020 7665 6374 6f72 2020  or      vector  \n-0000a9a0: 2020 2020 4166 6669 6e65 2076 6563 746f      Affine vecto\n-0000a9b0: 7220 7472 616e 7366 6f72 6d20 2872 6967  r transform (rig\n-0000a9c0: 6874 2d74 6f2d 6c65 6674 292e 0a20 2020  ht-to-left)..   \n-0000a9d0: 2020 2020 2020 2020 2027 2e27 0a74 7261           '.'.tra\n-0000a9e0: 6e73 666f 726d 2020 2027 2a27 206f 7220  nsform   '*' or \n-0000a9f0: 2020 7472 616e 7366 6f72 6d20 2020 7472    transform   tr\n-0000aa00: 616e 7366 6f72 6d20 2020 5472 616e 7366  ansform   Transf\n-0000aa10: 6f72 6d20 636f 6d70 6f73 6974 696f 6e20  orm composition \n-0000aa20: 2872 6967 6874 2d74 6f2d 6c65 6674 292e  (right-to-left).\n-0000aa30: 0a20 2020 2020 2020 2020 2020 2027 2e27  .            '.'\n-0000aa40: 0a70 6f69 6e74 2020 2020 2020 2027 7468  .point       'th\n-0000aa50: 656e 2720 2020 7472 616e 7366 6f72 6d20  en'   transform \n-0000aa60: 2020 706f 696e 7420 2020 2020 2020 4166    point       Af\n-0000aa70: 6669 6e65 2070 6f69 6e74 2074 7261 6e73  fine point trans\n-0000aa80: 666f 726d 2028 6c65 6674 2d74 6f2d 7269  form (left-to-ri\n-0000aa90: 6768 7429 2e0a 7665 6374 6f72 2020 2020  ght)..vector    \n-0000aaa0: 2020 2774 6865 6e27 2020 2074 7261 6e73    'then'   trans\n-0000aab0: 666f 726d 2020 2076 6563 746f 7220 2020  form   vector   \n-0000aac0: 2020 2041 6666 696e 6520 7665 6374 6f72     Affine vector\n-0000aad0: 2074 7261 6e73 666f 726d 2028 6c65 6674   transform (left\n-0000aae0: 2d74 6f2d 7269 6768 7429 2e0a 7472 616e  -to-right)..tran\n-0000aaf0: 7366 6f72 6d20 2020 2774 6865 6e27 2020  sform   'then'  \n-0000ab00: 2074 7261 6e73 666f 726d 2020 2074 7261   transform   tra\n-0000ab10: 6e73 666f 726d 2020 2054 7261 6e73 666f  nsform   Transfo\n-0000ab20: 726d 2063 6f6d 706f 7369 7469 6f6e 2028  rm composition (\n-0000ab30: 6c65 6674 2d74 6f2d 7269 6768 7429 2e0a  left-to-right)..\n-0000ab40: 7363 616c 6172 2020 2020 2020 272f 2720  scalar      '/' \n-0000ab50: 2020 2020 2073 6361 6c61 7220 2020 2020       scalar     \n-0000ab60: 2073 6361 6c61 7220 2020 2020 2053 6361   scalar      Sca\n-0000ab70: 6c61 7220 6469 7669 7369 6f6e 2e0a 7665  lar division..ve\n-0000ab80: 6374 6f72 2020 2020 2020 272f 2720 2020  ctor      '/'   \n-0000ab90: 2020 2073 6361 6c61 7220 2020 2020 2076     scalar      v\n-0000aba0: 6563 746f 7220 2020 2020 2056 6563 746f  ector      Vecto\n-0000abb0: 7220 636f 6d70 6f6e 656e 742d 7769 7365  r component-wise\n-0000abc0: 2064 6976 6973 696f 6e20 6279 2073 6361   division by sca\n-0000abd0: 6c61 722e 0a70 6f69 6e74 2020 2020 2020  lar..point      \n-0000abe0: 2027 2727 2020 2020 2020 2778 272c 2027   '''      'x', '\n-0000abf0: 7927 2c20 2020 7363 616c 6172 2020 2020  y',   scalar    \n-0000ac00: 2020 506f 696e 7420 636f 6d70 6f6e 656e    Point componen\n-0000ac10: 7420 6578 7472 6163 7469 6f6e 2e0a 2020  t extraction..  \n-0000ac20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000ac30: 2020 206f 7220 277a 270a 7665 6374 6f72     or 'z'.vector\n-0000ac40: 2020 2020 2020 2727 2720 2020 2020 2027        '''      '\n-0000ac50: 7827 2c20 2779 272c 2020 2073 6361 6c61  x', 'y',   scala\n-0000ac60: 7220 2020 2020 2056 6563 746f 7220 636f  r      Vector co\n-0000ac70: 6d70 6f6e 656e 7420 6578 7472 6163 7469  mponent extracti\n-0000ac80: 6f6e 2e0a 2020 2020 2020 2020 2020 2020  on..            \n-0000ac90: 2020 2020 2020 2020 206f 7220 277a 270a           or 'z'.\n-0000aca0: 0a4f 7065 7261 746f 7220 7072 6563 6564  .Operator preced\n-0000acb0: 656e 6365 2069 7320 7368 6f77 6e20 696e  ence is shown in\n-0000acc0: 2074 6869 7320 7461 626c 652e 0a4f 7020   this table..Op \n-0000acd0: 2020 2020 2020 5072 6563 6564 656e 6365        Precedence\n-0000ace0: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  .---------------\n+0000a510: 2d2d 2d2d 2d2d 2d2d 2d0a 7363 616c 6172  ---------.scalar\n+0000a520: 2020 2020 2020 272b 2720 2020 2020 2073        '+'      s\n+0000a530: 6361 6c61 7220 2020 2020 2073 6361 6c61  calar      scala\n+0000a540: 7220 2020 2020 2053 6361 6c61 7220 7375  r      Scalar su\n+0000a550: 6d2e 0a76 6563 746f 7220 2020 2020 2027  m..vector      '\n+0000a560: 2b27 2020 2020 2020 7665 6374 6f72 2020  +'      vector  \n+0000a570: 2020 2020 7665 6374 6f72 2020 2020 2020      vector      \n+0000a580: 5665 6374 6f72 2073 756d 2e0a 706f 696e  Vector sum..poin\n+0000a590: 7420 2020 2020 2020 272b 2720 2020 2020  t       '+'     \n+0000a5a0: 2076 6563 746f 7220 2020 2020 2070 6f69   vector      poi\n+0000a5b0: 6e74 2020 2020 2020 2050 6f69 6e74 2d76  nt       Point-v\n+0000a5c0: 6563 746f 7220 6166 6669 6e65 2073 756d  ector affine sum\n+0000a5d0: 2e0a 7665 6374 6f72 2020 2020 2020 272b  ..vector      '+\n+0000a5e0: 2720 2020 2020 2070 6f69 6e74 2020 2020  '      point    \n+0000a5f0: 2020 2022 2020 2020 2020 2020 2020 2022     \"           \"\n+0000a600: 0a73 6361 6c61 7220 2020 2020 2027 2d27  .scalar      '-'\n+0000a610: 2020 2020 2020 7363 616c 6172 2020 2020        scalar    \n+0000a620: 2020 7363 616c 6172 2020 2020 2020 5363    scalar      Sc\n+0000a630: 616c 6172 2064 6966 6665 7265 6e63 652e  alar difference.\n+0000a640: 0a76 6563 746f 7220 2020 2020 2027 2d27  .vector      '-'\n+0000a650: 2020 2020 2020 7665 6374 6f72 2020 2020        vector    \n+0000a660: 2020 7665 6374 6f72 2020 2020 2020 5665    vector      Ve\n+0000a670: 6374 6f72 2064 6966 6665 7265 6e63 652e  ctor difference.\n+0000a680: 0a70 6f69 6e74 2020 2020 2020 2027 2d27  .point       '-'\n+0000a690: 2020 2020 2020 706f 696e 7420 2020 2020        point     \n+0000a6a0: 2020 7665 6374 6f72 2020 2020 2020 506f    vector      Po\n+0000a6b0: 696e 742d 706f 696e 7420 6166 6669 6e65  int-point affine\n+0000a6c0: 2064 6966 6665 7265 6e63 652e 0a70 6f69   difference..poi\n+0000a6d0: 6e74 2020 2020 2020 2027 2d27 2020 2020  nt       '-'    \n+0000a6e0: 2020 7665 6374 6f72 2020 2020 2020 706f    vector      po\n+0000a6f0: 696e 7420 2020 2020 2020 506f 696e 742d  int       Point-\n+0000a700: 7665 6374 6f72 2061 6666 696e 6520 6469  vector affine di\n+0000a710: 6666 6572 656e 6365 2e0a 7363 616c 6172  fference..scalar\n+0000a720: 2020 2020 2020 272a 2720 6f72 2020 2073        '*' or   s\n+0000a730: 6361 6c61 7220 2020 2020 2073 6361 6c61  calar      scala\n+0000a740: 7220 2020 2020 2053 6361 6c61 7220 7072  r      Scalar pr\n+0000a750: 6f64 7563 742e 0a20 2020 2020 2020 2020  oduct..         \n+0000a760: 2020 2027 2e27 0a73 6361 6c61 7220 2020     '.'.scalar   \n+0000a770: 2020 2027 2a27 206f 7220 2020 7665 6374     '*' or   vect\n+0000a780: 6f72 2020 2020 2020 7665 6374 6f72 2020  or      vector  \n+0000a790: 2020 2020 5363 616c 6172 2d76 6563 746f      Scalar-vecto\n+0000a7a0: 7220 7072 6f64 7563 742e 0a20 2020 2020  r product..     \n+0000a7b0: 2020 2020 2020 2027 2e27 0a76 6563 746f         '.'.vecto\n+0000a7c0: 7220 2020 2020 2027 2a27 206f 7220 2020  r      '*' or   \n+0000a7d0: 7363 616c 6172 2020 2020 2020 2220 2020  scalar      \"   \n+0000a7e0: 2020 2020 2020 2020 220a 2020 2020 2020          \".      \n+0000a7f0: 2020 2020 2020 272e 270a 7665 6374 6f72        '.'.vector\n+0000a800: 2020 2020 2020 272a 2720 2020 2020 2076        '*'      v\n+0000a810: 6563 746f 7220 2020 2020 2076 6563 746f  ector      vecto\n+0000a820: 7220 2020 2020 2056 6563 746f 7220 6372  r      Vector cr\n+0000a830: 6f73 732d 7072 6f64 7563 742e 0a76 6563  oss-product..vec\n+0000a840: 746f 7220 2020 2020 2027 2e27 2020 2020  tor      '.'    \n+0000a850: 2020 7665 6374 6f72 2020 2020 2020 7363    vector      sc\n+0000a860: 616c 6172 2020 2020 2020 5665 6374 6f72  alar      Vector\n+0000a870: 2064 6f74 2070 726f 6475 6374 2e0a 7363   dot product..sc\n+0000a880: 616c 6172 2020 2020 2020 275e 2720 2020  alar      '^'   \n+0000a890: 2020 2073 6361 6c61 7220 2020 2020 2073     scalar      s\n+0000a8a0: 6361 6c61 7220 2020 2020 2052 6169 7365  calar      Raise\n+0000a8b0: 2073 6361 6c61 7220 746f 2073 6361 6c61   scalar to scala\n+0000a8c0: 7220 706f 7765 722e 0a74 7261 6e73 666f  r power..transfo\n+0000a8d0: 726d 2020 2027 5e27 2020 2020 2020 696e  rm   '^'      in\n+0000a8e0: 7465 6765 7220 2020 2020 7472 616e 7366  teger     transf\n+0000a8f0: 6f72 6d20 2020 5261 6973 6520 7472 616e  orm   Raise tran\n+0000a900: 7366 6f72 6d20 746f 2069 6e74 6567 6572  sform to integer\n+0000a910: 2070 6f77 6572 2e0a 7472 616e 7366 6f72   power..transfor\n+0000a920: 6d20 2020 272a 2720 6f72 2020 2070 6f69  m   '*' or   poi\n+0000a930: 6e74 2020 2020 2020 2070 6f69 6e74 2020  nt       point  \n+0000a940: 2020 2020 2041 6666 696e 6520 706f 696e       Affine poin\n+0000a950: 7420 7472 616e 7366 6f72 6d20 2872 6967  t transform (rig\n+0000a960: 6874 2d74 6f2d 6c65 6674 292e 0a20 2020  ht-to-left)..   \n+0000a970: 2020 2020 2020 2020 2027 2e27 0a74 7261           '.'.tra\n+0000a980: 6e73 666f 726d 2020 2027 2a27 206f 7220  nsform   '*' or \n+0000a990: 2020 7665 6374 6f72 2020 2020 2020 7665    vector      ve\n+0000a9a0: 6374 6f72 2020 2020 2020 4166 6669 6e65  ctor      Affine\n+0000a9b0: 2076 6563 746f 7220 7472 616e 7366 6f72   vector transfor\n+0000a9c0: 6d20 2872 6967 6874 2d74 6f2d 6c65 6674  m (right-to-left\n+0000a9d0: 292e 0a20 2020 2020 2020 2020 2020 2027  )..            '\n+0000a9e0: 2e27 0a74 7261 6e73 666f 726d 2020 2027  .'.transform   '\n+0000a9f0: 2a27 206f 7220 2020 7472 616e 7366 6f72  *' or   transfor\n+0000aa00: 6d20 2020 7472 616e 7366 6f72 6d20 2020  m   transform   \n+0000aa10: 5472 616e 7366 6f72 6d20 636f 6d70 6f73  Transform compos\n+0000aa20: 6974 696f 6e20 2872 6967 6874 2d74 6f2d  ition (right-to-\n+0000aa30: 6c65 6674 292e 0a20 2020 2020 2020 2020  left)..         \n+0000aa40: 2020 2027 2e27 0a70 6f69 6e74 2020 2020     '.'.point    \n+0000aa50: 2020 2027 7468 656e 2720 2020 7472 616e     'then'   tran\n+0000aa60: 7366 6f72 6d20 2020 706f 696e 7420 2020  sform   point   \n+0000aa70: 2020 2020 4166 6669 6e65 2070 6f69 6e74      Affine point\n+0000aa80: 2074 7261 6e73 666f 726d 2028 6c65 6674   transform (left\n+0000aa90: 2d74 6f2d 7269 6768 7429 2e0a 7665 6374  -to-right)..vect\n+0000aaa0: 6f72 2020 2020 2020 2774 6865 6e27 2020  or      'then'  \n+0000aab0: 2074 7261 6e73 666f 726d 2020 2076 6563   transform   vec\n+0000aac0: 746f 7220 2020 2020 2041 6666 696e 6520  tor      Affine \n+0000aad0: 7665 6374 6f72 2074 7261 6e73 666f 726d  vector transform\n+0000aae0: 2028 6c65 6674 2d74 6f2d 7269 6768 7429   (left-to-right)\n+0000aaf0: 2e0a 7472 616e 7366 6f72 6d20 2020 2774  ..transform   't\n+0000ab00: 6865 6e27 2020 2074 7261 6e73 666f 726d  hen'   transform\n+0000ab10: 2020 2074 7261 6e73 666f 726d 2020 2054     transform   T\n+0000ab20: 7261 6e73 666f 726d 2063 6f6d 706f 7369  ransform composi\n+0000ab30: 7469 6f6e 2028 6c65 6674 2d74 6f2d 7269  tion (left-to-ri\n+0000ab40: 6768 7429 2e0a 7363 616c 6172 2020 2020  ght)..scalar    \n+0000ab50: 2020 272f 2720 2020 2020 2073 6361 6c61    '/'      scala\n+0000ab60: 7220 2020 2020 2073 6361 6c61 7220 2020  r      scalar   \n+0000ab70: 2020 2053 6361 6c61 7220 6469 7669 7369     Scalar divisi\n+0000ab80: 6f6e 2e0a 7665 6374 6f72 2020 2020 2020  on..vector      \n+0000ab90: 272f 2720 2020 2020 2073 6361 6c61 7220  '/'      scalar \n+0000aba0: 2020 2020 2076 6563 746f 7220 2020 2020       vector     \n+0000abb0: 2056 6563 746f 7220 636f 6d70 6f6e 656e   Vector componen\n+0000abc0: 742d 7769 7365 2064 6976 6973 696f 6e20  t-wise division \n+0000abd0: 6279 2073 6361 6c61 722e 0a70 6f69 6e74  by scalar..point\n+0000abe0: 2020 2020 2020 2027 2727 2020 2020 2020         '''      \n+0000abf0: 2778 272c 2027 7927 2c20 2020 7363 616c  'x', 'y',   scal\n+0000ac00: 6172 2020 2020 2020 506f 696e 7420 636f  ar      Point co\n+0000ac10: 6d70 6f6e 656e 7420 6578 7472 6163 7469  mponent extracti\n+0000ac20: 6f6e 2e0a 2020 2020 2020 2020 2020 2020  on..            \n+0000ac30: 2020 2020 2020 2020 206f 7220 277a 270a           or 'z'.\n+0000ac40: 7665 6374 6f72 2020 2020 2020 2727 2720  vector      ''' \n+0000ac50: 2020 2020 2027 7827 2c20 2779 272c 2020       'x', 'y',  \n+0000ac60: 2073 6361 6c61 7220 2020 2020 2056 6563   scalar      Vec\n+0000ac70: 746f 7220 636f 6d70 6f6e 656e 7420 6578  tor component ex\n+0000ac80: 7472 6163 7469 6f6e 2e0a 2020 2020 2020  traction..      \n+0000ac90: 2020 2020 2020 2020 2020 2020 2020 206f                 o\n+0000aca0: 7220 277a 270a 0a4f 7065 7261 746f 7220  r 'z'..Operator \n+0000acb0: 7072 6563 6564 656e 6365 2069 7320 7368  precedence is sh\n+0000acc0: 6f77 6e20 696e 2074 6869 7320 7461 626c  own in this tabl\n+0000acd0: 652e 0a4f 7020 2020 2020 2020 5072 6563  e..Op       Prec\n+0000ace0: 6564 656e 6365 0a2d 2d2d 2d2d 2d2d 2d2d  edence.---------\n 0000acf0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-0000ad00: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 2727 2720  -----------.''' \n-0000ad10: 2020 2020 2068 6967 6865 7374 2028 6d6f       highest (mo\n-0000ad20: 7374 2074 6967 6874 6c79 2062 696e 6469  st tightly bindi\n-0000ad30: 6e67 290a 275e 270a 272d 2720 2020 2020  ng).'^'.'-'     \n-0000ad40: 2028 756e 6172 7920 6e65 6761 7469 6f6e   (unary negation\n-0000ad50: 290a 272a 270a 272e 270a 272f 270a 272b  ).'*'.'.'.'/'.'+\n-0000ad60: 270a 272d 270a 2774 6865 6e27 2020 206c  '.'-'.'then'   l\n-0000ad70: 6f77 6573 7420 286c 6561 7374 2074 6967  owest (least tig\n-0000ad80: 6874 6c79 2062 696e 6469 6e67 290a 0a41  htly binding)..A\n-0000ad90: 6c6c 206f 7065 7261 7469 6f6e 7320 6172  ll operations ar\n-0000ada0: 6520 6c65 6674 2d61 7373 6f63 6961 7469  e left-associati\n-0000adb0: 7665 2065 7863 6570 7420 666f 7220 275e  ve except for '^\n-0000adc0: 272e 2020 5061 7265 6e74 6865 7365 7320  '.  Parentheses \n-0000add0: 2728 2029 270a 6172 6520 7573 6564 2066  '( )'.are used f\n-0000ade0: 6f72 2067 726f 7570 696e 6720 746f 206f  or grouping to o\n-0000adf0: 7665 7272 6964 6520 7072 6563 6564 656e  verride preceden\n-0000ae00: 6365 2069 6e20 7468 6520 7573 7561 6c20  ce in the usual \n-0000ae10: 7761 792e 0a0a 2020 2041 7320 796f 7520  way...   As you \n-0000ae20: 6361 6e20 7365 652c 2074 6865 2064 6f74  can see, the dot\n-0000ae30: 206f 7065 7261 746f 7220 272e 2720 6973   operator '.' is\n-0000ae40: 2075 7375 616c 6c79 2061 2073 796e 6f6e   usually a synon\n-0000ae50: 796d 2066 6f72 0a72 756e 2d6f 662d 7468  ym for.run-of-th\n-0000ae60: 652d 6d69 6c6c 206d 756c 7469 706c 6963  e-mill multiplic\n-0000ae70: 6174 696f 6e2c 2027 2a27 2e20 2054 6865  ation, '*'.  The\n-0000ae80: 206d 6561 6e69 6e67 7320 6469 6666 6572   meanings differ\n-0000ae90: 206f 6e6c 7920 666f 720a 7665 6374 6f72   only for.vector\n-0000aea0: 206f 7065 7261 6e64 732e 2020 5468 6520   operands.  The \n-0000aeb0: 2774 6865 6e27 206f 7065 7261 746f 7220  'then' operator \n-0000aec0: 6d65 7265 6c79 2072 6576 6572 7365 7320  merely reverses \n-0000aed0: 7468 6520 6f70 6572 616e 6420 6f72 6465  the operand orde\n-0000aee0: 720a 7769 7468 2072 6573 7065 6374 2074  r.with respect t\n-0000aef0: 6f20 6e6f 726d 616c 206d 756c 7469 706c  o normal multipl\n-0000af00: 6963 6174 696f 6e20 272a 272e 2020 5468  ication '*'.  Th\n-0000af10: 6520 696e 7465 6e74 2068 6572 6520 6973  e intent here is\n-0000af20: 2074 6f20 6d61 6b65 0a63 6f6d 706f 7369   to make.composi\n-0000af30: 7469 6f6e 7320 7265 6164 206d 6f72 6520  tions read more \n-0000af40: 6e61 7475 7261 6c6c 792e 2020 5468 6520  naturally.  The \n-0000af50: 636f 6465 0a20 2020 2020 2831 2c32 2c33  code.     (1,2,3\n-0000af60: 2920 7468 656e 2073 6361 6c65 2832 2920  ) then scale(2) \n-0000af70: 7468 656e 2072 6f74 6174 6528 3330 2920  then rotate(30) \n-0000af80: 7468 656e 2074 7261 6e73 6c61 7465 285b  then translate([\n-0000af90: 312c 332c 305d 290a 6578 7072 6573 7365  1,3,0]).expresse\n-0000afa0: 7320 6120 7365 7269 6573 206f 6620 7375  s a series of su\n-0000afb0: 6363 6573 7369 7665 206d 6f64 6966 6963  ccessive modific\n-0000afc0: 6174 696f 6e73 2074 6f20 7468 6520 706f  ations to the po\n-0000afd0: 696e 742c 2077 6865 7265 6173 2074 6865  int, whereas the\n-0000afe0: 0a65 7175 6976 616c 656e 7420 666f 726d  .equivalent form\n-0000aff0: 0a20 2020 2020 7472 616e 736c 6174 6528  .     translate(\n-0000b000: 5b31 2c33 2c30 5d29 202a 2072 6f74 6174  [1,3,0]) * rotat\n-0000b010: 6528 3330 2920 2a20 7363 616c 6528 3229  e(30) * scale(2)\n-0000b020: 202a 2028 312c 322c 3329 0a77 696c 6c20   * (1,2,3).will \n-0000b030: 6265 2069 6e74 7569 7469 7665 206f 6e6c  be intuitive onl\n-0000b040: 7920 746f 206d 6174 6865 6d61 7469 6369  y to mathematici\n-0000b050: 616e 7320 2861 6e64 2070 6572 6861 7073  ans (and perhaps\n-0000b060: 2041 7261 6269 6320 6c61 6e67 7561 6765   Arabic language\n-0000b070: 0a72 6561 6465 7273 292e 0a0a 1f0a 4669  .readers).....Fi\n-0000b080: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n-0000b090: 2020 4e6f 6465 3a20 556e 6172 7920 666f    Node: Unary fo\n-0000b0a0: 726d 732c 2020 5072 6576 3a20 5477 6f2d  rms,  Prev: Two-\n-0000b0b0: 6f70 6572 616e 6420 2862 696e 6172 7929  operand (binary)\n-0000b0c0: 2066 6f72 6d73 2c20 2055 703a 2041 7269   forms,  Up: Ari\n-0000b0d0: 7468 6d65 7469 630a 0a33 2e31 2e34 2e32  thmetic..3.1.4.2\n-0000b0e0: 2055 6e61 7279 2066 6f72 6d73 0a2e 2e2e   Unary forms....\n-0000b0f0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000b100: 0a0a 556e 6172 7920 6f72 206f 6e65 2d6f  ..Unary or one-o\n-0000b110: 7065 7261 6e64 2066 6f72 6d73 2061 7265  perand forms are\n-0000b120: 2073 756d 6d61 7269 7a65 6420 696e 2074   summarized in t\n-0000b130: 6865 2066 6f6c 6c6f 7769 6e67 2074 6162  he following tab\n-0000b140: 6c65 2c20 7768 6572 650a 2758 2720 7374  le, where.'X' st\n-0000b150: 616e 6473 2066 6f72 2074 6865 206f 7065  ands for the ope\n-0000b160: 7261 6e64 2e0a 4f70 2020 2020 2020 2020  rand..Op        \n-0000b170: 2020 2020 204f 7065 7261 6e64 2020 2020       Operand    \n-0000b180: 2052 6573 756c 7420 2020 2020 2044 6573   Result      Des\n-0000b190: 6372 6970 7469 6f6e 0a2d 2d2d 2d2d 2d2d  cription.-------\n+0000ad00: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n+0000ad10: 2d0a 2727 2720 2020 2020 2068 6967 6865  -.'''      highe\n+0000ad20: 7374 2028 6d6f 7374 2074 6967 6874 6c79  st (most tightly\n+0000ad30: 2062 696e 6469 6e67 290a 275e 270a 272d   binding).'^'.'-\n+0000ad40: 2720 2020 2020 2028 756e 6172 7920 6e65  '      (unary ne\n+0000ad50: 6761 7469 6f6e 290a 272a 270a 272e 270a  gation).'*'.'.'.\n+0000ad60: 272f 270a 272b 270a 272d 270a 2774 6865  '/'.'+'.'-'.'the\n+0000ad70: 6e27 2020 206c 6f77 6573 7420 286c 6561  n'   lowest (lea\n+0000ad80: 7374 2074 6967 6874 6c79 2062 696e 6469  st tightly bindi\n+0000ad90: 6e67 290a 0a41 6c6c 206f 7065 7261 7469  ng)..All operati\n+0000ada0: 6f6e 7320 6172 6520 6c65 6674 2d61 7373  ons are left-ass\n+0000adb0: 6f63 6961 7469 7665 2065 7863 6570 7420  ociative except \n+0000adc0: 666f 7220 275e 272e 2020 5061 7265 6e74  for '^'.  Parent\n+0000add0: 6865 7365 7320 2728 2029 270a 6172 6520  heses '( )'.are \n+0000ade0: 7573 6564 2066 6f72 2067 726f 7570 696e  used for groupin\n+0000adf0: 6720 746f 206f 7665 7272 6964 6520 7072  g to override pr\n+0000ae00: 6563 6564 656e 6365 2069 6e20 7468 6520  ecedence in the \n+0000ae10: 7573 7561 6c20 7761 792e 0a0a 2020 2041  usual way...   A\n+0000ae20: 7320 796f 7520 6361 6e20 7365 652c 2074  s you can see, t\n+0000ae30: 6865 2064 6f74 206f 7065 7261 746f 7220  he dot operator \n+0000ae40: 272e 2720 6973 2075 7375 616c 6c79 2061  '.' is usually a\n+0000ae50: 2073 796e 6f6e 796d 2066 6f72 0a72 756e   synonym for.run\n+0000ae60: 2d6f 662d 7468 652d 6d69 6c6c 206d 756c  -of-the-mill mul\n+0000ae70: 7469 706c 6963 6174 696f 6e2c 2027 2a27  tiplication, '*'\n+0000ae80: 2e20 2054 6865 206d 6561 6e69 6e67 7320  .  The meanings \n+0000ae90: 6469 6666 6572 206f 6e6c 7920 666f 720a  differ only for.\n+0000aea0: 7665 6374 6f72 206f 7065 7261 6e64 732e  vector operands.\n+0000aeb0: 2020 5468 6520 2774 6865 6e27 206f 7065    The 'then' ope\n+0000aec0: 7261 746f 7220 6d65 7265 6c79 2072 6576  rator merely rev\n+0000aed0: 6572 7365 7320 7468 6520 6f70 6572 616e  erses the operan\n+0000aee0: 6420 6f72 6465 720a 7769 7468 2072 6573  d order.with res\n+0000aef0: 7065 6374 2074 6f20 6e6f 726d 616c 206d  pect to normal m\n+0000af00: 756c 7469 706c 6963 6174 696f 6e20 272a  ultiplication '*\n+0000af10: 272e 2020 5468 6520 696e 7465 6e74 2068  '.  The intent h\n+0000af20: 6572 6520 6973 2074 6f20 6d61 6b65 0a63  ere is to make.c\n+0000af30: 6f6d 706f 7369 7469 6f6e 7320 7265 6164  ompositions read\n+0000af40: 206d 6f72 6520 6e61 7475 7261 6c6c 792e   more naturally.\n+0000af50: 2020 5468 6520 636f 6465 0a20 2020 2020    The code.     \n+0000af60: 2831 2c32 2c33 2920 7468 656e 2073 6361  (1,2,3) then sca\n+0000af70: 6c65 2832 2920 7468 656e 2072 6f74 6174  le(2) then rotat\n+0000af80: 6528 3330 2920 7468 656e 2074 7261 6e73  e(30) then trans\n+0000af90: 6c61 7465 285b 312c 332c 305d 290a 6578  late([1,3,0]).ex\n+0000afa0: 7072 6573 7365 7320 6120 7365 7269 6573  presses a series\n+0000afb0: 206f 6620 7375 6363 6573 7369 7665 206d   of successive m\n+0000afc0: 6f64 6966 6963 6174 696f 6e73 2074 6f20  odifications to \n+0000afd0: 7468 6520 706f 696e 742c 2077 6865 7265  the point, where\n+0000afe0: 6173 2074 6865 0a65 7175 6976 616c 656e  as the.equivalen\n+0000aff0: 7420 666f 726d 0a20 2020 2020 7472 616e  t form.     tran\n+0000b000: 736c 6174 6528 5b31 2c33 2c30 5d29 202a  slate([1,3,0]) *\n+0000b010: 2072 6f74 6174 6528 3330 2920 2a20 7363   rotate(30) * sc\n+0000b020: 616c 6528 3229 202a 2028 312c 322c 3329  ale(2) * (1,2,3)\n+0000b030: 0a77 696c 6c20 6265 2069 6e74 7569 7469  .will be intuiti\n+0000b040: 7665 206f 6e6c 7920 746f 206d 6174 6865  ve only to mathe\n+0000b050: 6d61 7469 6369 616e 7320 2861 6e64 2070  maticians (and p\n+0000b060: 6572 6861 7073 2041 7261 6269 6320 6c61  erhaps Arabic la\n+0000b070: 6e67 7561 6765 0a72 6561 6465 7273 292e  nguage.readers).\n+0000b080: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n+0000b090: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 556e  .info,  Node: Un\n+0000b0a0: 6172 7920 666f 726d 732c 2020 5072 6576  ary forms,  Prev\n+0000b0b0: 3a20 5477 6f2d 6f70 6572 616e 6420 2862  : Two-operand (b\n+0000b0c0: 696e 6172 7929 2066 6f72 6d73 2c20 2055  inary) forms,  U\n+0000b0d0: 703a 2041 7269 7468 6d65 7469 630a 0a33  p: Arithmetic..3\n+0000b0e0: 2e31 2e34 2e32 2055 6e61 7279 2066 6f72  .1.4.2 Unary for\n+0000b0f0: 6d73 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ms..............\n+0000b100: 2e2e 2e2e 2e2e 0a0a 556e 6172 7920 6f72  ........Unary or\n+0000b110: 206f 6e65 2d6f 7065 7261 6e64 2066 6f72   one-operand for\n+0000b120: 6d73 2061 7265 2073 756d 6d61 7269 7a65  ms are summarize\n+0000b130: 6420 696e 2074 6865 2066 6f6c 6c6f 7769  d in the followi\n+0000b140: 6e67 2074 6162 6c65 2c20 7768 6572 650a  ng table, where.\n+0000b150: 2758 2720 7374 616e 6473 2066 6f72 2074  'X' stands for t\n+0000b160: 6865 206f 7065 7261 6e64 2e0a 4f70 2020  he operand..Op  \n+0000b170: 2020 2020 2020 2020 2020 204f 7065 7261             Opera\n+0000b180: 6e64 2020 2020 2052 6573 756c 7420 2020  nd     Result   \n+0000b190: 2020 2044 6573 6372 6970 7469 6f6e 0a2d     Description.-\n 0000b1a0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000b1b0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000b1c0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000b1d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-0000b1e0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 272d  -------------.'-\n-0000b1f0: 5827 2020 2020 2020 2020 2020 2073 6361  X'           sca\n-0000b200: 6c61 7220 2020 2020 2073 6361 6c61 7220  lar      scalar \n-0000b210: 2020 2020 2055 6e61 7279 2073 6361 6c61       Unary scala\n-0000b220: 7220 6e65 6761 7469 6f6e 2e0a 272d 5827  r negation..'-X'\n-0000b230: 2020 2020 2020 2020 2020 2076 6563 746f             vecto\n-0000b240: 7220 2020 2020 2076 6563 746f 7220 2020  r      vector   \n-0000b250: 2020 2055 6e61 7279 2076 6563 746f 7220     Unary vector \n-0000b260: 6e65 6761 7469 6f6e 2e0a 277c 587c 2720  negation..'|X|' \n-0000b270: 2020 2020 2020 2020 2076 6563 746f 7220           vector \n-0000b280: 2020 2020 2073 6361 6c61 7220 2020 2020       scalar     \n-0000b290: 2056 6563 746f 7220 6c65 6e67 7468 2e0a   Vector length..\n-0000b2a0: 2775 6e69 7428 5829 2720 2020 2020 2076  'unit(X)'      v\n-0000b2b0: 6563 746f 7220 2020 2020 2076 6563 746f  ector      vecto\n-0000b2c0: 7220 2020 2020 2055 6e69 7420 7665 6374  r      Unit vect\n-0000b2d0: 6f72 2077 6974 6820 7361 6d65 2064 6972  or with same dir\n-0000b2e0: 6563 7469 6f6e 2e0a 2773 7172 7428 5829  ection..'sqrt(X)\n-0000b2f0: 2720 2020 2020 2073 6361 6c61 7220 2020  '      scalar   \n-0000b300: 2020 2073 6361 6c61 7220 2020 2020 2053     scalar      S\n-0000b310: 6361 6c61 7220 7371 7561 7265 2072 6f6f  calar square roo\n-0000b320: 742e 0a27 7369 6e28 5829 2720 2020 2020  t..'sin(X)'     \n-0000b330: 2020 7363 616c 6172 2020 2020 2020 7363    scalar      sc\n-0000b340: 616c 6172 2020 2020 2020 5472 6967 6f6e  alar      Trigon\n-0000b350: 6f6d 6574 7269 6320 7369 6e65 2028 2758  ometric sine ('X\n-0000b360: 2720 696e 2064 6567 7265 6573 292e 0a27  ' in degrees)..'\n-0000b370: 636f 7328 5829 2720 2020 2020 2020 7363  cos(X)'       sc\n-0000b380: 616c 6172 2020 2020 2020 7363 616c 6172  alar      scalar\n-0000b390: 2020 2020 2020 5472 6967 6f6e 6f6d 6574        Trigonomet\n-0000b3a0: 7269 6320 636f 7369 6e65 2028 2758 2720  ric cosine ('X' \n-0000b3b0: 696e 2064 6567 7265 6573 292e 0a27 6173  in degrees)..'as\n-0000b3c0: 696e 2858 2927 2020 2020 2020 7363 616c  in(X)'      scal\n-0000b3d0: 6172 2020 2020 2020 7363 616c 6172 2020  ar      scalar  \n-0000b3e0: 2020 2020 496e 7665 7273 6520 7369 6e65      Inverse sine\n-0000b3f0: 2028 2758 2720 696e 2064 6567 7265 6573   ('X' in degrees\n-0000b400: 292e 0a27 6163 6f73 2858 2927 2020 2020  )..'acos(X)'    \n-0000b410: 2020 7363 616c 6172 2020 2020 2020 7363    scalar      sc\n-0000b420: 616c 6172 2020 2020 2020 496e 7665 7273  alar      Invers\n-0000b430: 6520 636f 7369 6e65 2028 2758 2720 696e  e cosine ('X' in\n-0000b440: 2064 6567 7265 6573 292e 0a27 6174 616e   degrees)..'atan\n-0000b450: 3228 582c 5929 2720 2020 7363 616c 6172  2(X,Y)'   scalar\n-0000b460: 2020 2020 2020 7363 616c 6172 2020 2020        scalar    \n-0000b470: 2020 506f 6c61 7220 616e 676c 6520 696e    Polar angle in\n-0000b480: 2064 6567 7265 6573 206f 6620 7665 6374   degrees of vect\n-0000b490: 6f72 205b 582c 595d 2e0a 2769 6e76 6572  or [X,Y]..'inver\n-0000b4a0: 7365 2858 2927 2020 2074 7261 6e73 666f  se(X)'   transfo\n-0000b4b0: 726d 2020 2074 7261 6e73 666f 726d 2020  rm   transform  \n-0000b4c0: 2049 6e76 6572 7365 2074 7261 6e73 666f   Inverse transfo\n-0000b4d0: 726d 2e0a 0a45 7272 6f72 7320 6172 6520  rm...Errors are \n-0000b4e0: 7265 706f 7274 6564 2077 6865 6e20 277c  reported when '|\n-0000b4f0: 587c 272c 2027 756e 6974 272c 2027 6173  X|', 'unit', 'as\n-0000b500: 696e 272c 2027 6163 6f73 272c 2027 7371  in', 'acos', 'sq\n-0000b510: 7274 272c 2027 6174 616e 3227 2c0a 616e  rt', 'atan2',.an\n-0000b520: 6420 2769 6e76 6572 7365 2720 6661 696c  d 'inverse' fail\n-0000b530: 2064 7565 2074 6f20 6f70 6572 616e 6473   due to operands\n-0000b540: 206f 7574 7369 6465 2074 6865 6972 2072   outside their r\n-0000b550: 6573 7065 6374 6976 6520 646f 6d61 696e  espective domain\n-0000b560: 732e 0a0a 1f0a 4669 6c65 3a20 736b 6574  s.....File: sket\n-0000b570: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n-0000b580: 4f70 7469 6f6e 732c 2020 5072 6576 3a20  Options,  Prev: \n-0000b590: 4172 6974 686d 6574 6963 2c20 2055 703a  Arithmetic,  Up:\n-0000b5a0: 204c 616e 6775 6167 6520 6261 7369 6373   Language basics\n-0000b5b0: 0a0a 332e 312e 3520 4f70 7469 6f6e 730a  ..3.1.5 Options.\n-0000b5c0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a  -------------..*\n-0000b5d0: 5379 6e74 6178 3a2a 0a20 2020 2020 5b4b  Syntax:*.     [K\n-0000b5e0: 4559 313d 5641 4c31 2c4b 4559 323d 5641  EY1=VAL1,KEY2=VA\n-0000b5f0: 4c32 2c2e 2e2e 5d0a 4f70 7469 6f6e 7320  L2,...].Options \n-0000b600: 6172 6520 7573 6564 2074 6f20 7370 6563  are used to spec\n-0000b610: 6966 7920 6465 7461 696c 7320 6f66 2074  ify details of t\n-0000b620: 6865 2061 7070 6561 7261 6e63 6520 6f66  he appearance of\n-0000b630: 2064 7261 7761 626c 6573 2e20 2041 730a   drawables.  As.\n-0000b640: 7368 6f77 6e20 6162 6f76 652c 2074 6865  shown above, the\n-0000b650: 7920 6172 6520 6769 7665 6e20 6173 2063  y are given as c\n-0000b660: 6f6d 6d61 2d73 6570 6172 6174 6564 206b  omma-separated k\n-0000b670: 6579 2d76 616c 7565 2070 6169 7273 2e0a  ey-value pairs..\n-0000b680: 0a2a 204d 656e 753a 0a0a 2a20 5053 5472  .* Menu:..* PSTr\n-0000b690: 6963 6b73 206f 7074 696f 6e73 3a3a 2020  icks options::  \n-0000b6a0: 2020 2020 2020 2020 2020 4f70 7469 6f6e            Option\n-0000b6b0: 7320 696e 6865 7269 7465 6420 6672 6f6d  s inherited from\n-0000b6c0: 2027 5053 5472 6963 6b73 272e 0a2a 2054   'PSTricks'..* T\n-0000b6d0: 696b 5a2f 5047 4620 6f70 7469 6f6e 733a  ikZ/PGF options:\n-0000b6e0: 3a20 2020 2020 2020 2020 2020 204f 7074  :            Opt\n-0000b6f0: 696f 6e73 2069 6e68 6572 6974 6564 2066  ions inherited f\n-0000b700: 726f 6d20 2754 696b 5a2f 5047 4627 2e0a  rom 'TikZ/PGF'..\n-0000b710: 2a20 446f 7473 2069 6e20 5469 6b5a 2f50  * Dots in TikZ/P\n-0000b720: 4746 3a3a 2020 2020 2020 2020 2020 2020  GF::            \n-0000b730: 536b 6574 6368 2075 7365 7320 2754 696b  Sketch uses 'Tik\n-0000b740: 5a2f 5047 4627 2063 6972 636c 6573 2066  Z/PGF' circles f\n-0000b750: 6f72 2064 6f74 732e 0a2a 2054 696b 5a2f  or dots..* TikZ/\n-0000b760: 5047 4620 7573 6572 2d64 6566 696e 6564  PGF user-defined\n-0000b770: 2073 7479 6c65 733a 3a20 2053 7570 706f   styles::  Suppo\n-0000b780: 7274 2066 6f72 2027 5469 6b5a 2f50 4746  rt for 'TikZ/PGF\n-0000b790: 2720 6e61 6d65 642c 2075 7365 722d 6465  ' named, user-de\n-0000b7a0: 6669 6e65 6420 7374 796c 6573 2e0a 2a20  fined styles..* \n-0000b7b0: 5472 616e 7370 6172 656e 6379 3a3a 2020  Transparency::  \n-0000b7c0: 2020 2020 2020 2020 2020 2020 2020 5365                Se\n-0000b7d0: 652d 7468 726f 7567 6820 706f 6c79 676f  e-through polygo\n-0000b7e0: 6e73 2e0a 2a20 496e 7465 726e 616c 206f  ns..* Internal o\n-0000b7f0: 7074 696f 6e73 3a3a 2020 2020 2020 2020  ptions::        \n-0000b800: 2020 2020 4f70 7469 6f6e 7320 7573 6564      Options used\n-0000b810: 2062 7920 2773 6b65 7463 6827 2e0a 0a1f   by 'sketch'....\n-0000b820: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n-0000b830: 666f 2c20 204e 6f64 653a 2050 5354 7269  fo,  Node: PSTri\n-0000b840: 636b 7320 6f70 7469 6f6e 732c 2020 4e65  cks options,  Ne\n-0000b850: 7874 3a20 5469 6b5a 2f50 4746 206f 7074  xt: TikZ/PGF opt\n-0000b860: 696f 6e73 2c20 2050 7265 763a 204f 7074  ions,  Prev: Opt\n-0000b870: 696f 6e73 2c20 2055 703a 204f 7074 696f  ions,  Up: Optio\n-0000b880: 6e73 0a0a 332e 312e 352e 3120 2750 5354  ns..3.1.5.1 'PST\n-0000b890: 7269 636b 7327 206f 7074 696f 6e73 0a2e  ricks' options..\n-0000b8a0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000b8b0: 2e2e 2e2e 2e2e 2e2e 2e0a 0a57 6865 6e20  ...........When \n-0000b8c0: 276c 616e 6775 6167 6520 7073 7472 6963  'language pstric\n-0000b8d0: 6b73 2720 6973 2073 656c 6563 7465 6420  ks' is selected \n-0000b8e0: 2874 6865 2064 6566 6175 6c74 292c 2070  (the default), p\n-0000b8f0: 6572 6d69 7373 6962 6c65 0a6b 6579 2d76  ermissible.key-v\n-0000b900: 616c 7565 2070 6169 7273 2069 6e63 6c75  alue pairs inclu\n-0000b910: 6465 2061 6c6c 2074 686f 7365 2066 6f72  de all those for\n-0000b920: 2073 696d 696c 6172 2027 5053 5472 6963   similar 'PSTric\n-0000b930: 6b73 2720 6f62 6a65 6374 732e 2020 466f  ks' objects.  Fo\n-0000b940: 720a 6578 616d 706c 652c 2061 2070 6f6c  r.example, a pol\n-0000b950: 7967 6f6e 206d 6967 6874 2068 6176 6520  ygon might have \n-0000b960: 7468 6520 6f70 7469 6f6e 730a 2020 5b6c  the options.  [l\n-0000b970: 696e 6577 6964 7468 3d31 7074 2c6c 696e  inewidth=1pt,lin\n-0000b980: 6563 6f6c 6f72 3d62 6c75 652c 6669 6c6c  ecolor=blue,fill\n-0000b990: 636f 6c6f 723d 6379 616e 5d0a 2753 6b65  color=cyan].'Ske\n-0000b9a0: 7463 6827 206d 6572 656c 7920 7061 7373  tch' merely pass\n-0000b9b0: 6573 2074 6865 7365 206f 6e20 746f 2027  es these on to '\n-0000b9c0: 5053 5472 6963 6b73 2720 7769 7468 6f75  PSTricks' withou\n-0000b9d0: 7420 6368 6563 6b69 6e67 206f 720a 6d6f  t checking or.mo\n-0000b9e0: 6469 6669 6361 7469 6f6e 2e20 204f 7074  dification.  Opt\n-0000b9f0: 696f 6e20 6c69 7374 7320 6172 6520 616c  ion lists are al\n-0000ba00: 7761 7973 206f 7074 696f 6e61 6c2e 2020  ways optional.  \n-0000ba10: 4120 6d69 7373 696e 6720 6f70 7469 6f6e  A missing option\n-0000ba20: 7320 6c69 7374 0a69 7320 6571 7569 7661  s list.is equiva\n-0000ba30: 6c65 6e74 2074 6f20 616e 2065 6d70 7479  lent to an empty\n-0000ba40: 206f 6e65 2027 5b5d 272e 0a0a 2020 2057   one '[]'...   W\n-0000ba50: 6865 6e20 6120 2770 6f6c 7967 6f6e 2720  hen a 'polygon' \n-0000ba60: 6861 7320 6f70 7469 6f6e 7320 666f 7220  has options for \n-0000ba70: 626f 7468 2069 7473 2066 6163 6520 616e  both its face an\n-0000ba80: 6420 6974 7320 6564 6765 732c 2061 6e64  d its edges, and\n-0000ba90: 2074 6865 0a70 6f6c 7967 6f6e 2069 7320   the.polygon is \n-0000baa0: 7370 6c69 7420 6279 2074 6865 2068 6964  split by the hid\n-0000bab0: 6465 6e20 7375 7266 6163 6520 616c 676f  den surface algo\n-0000bac0: 7269 7468 6d2c 2027 736b 6574 6368 2720  rithm, 'sketch' \n-0000bad0: 6d75 7374 2063 6f70 7920 7468 650a 6564  must copy the.ed\n-0000bae0: 6765 206f 7074 696f 6e73 2074 6f20 2770  ge options to 'p\n-0000baf0: 736c 696e 6527 7320 666f 7220 7468 6520  sline's for the \n-0000bb00: 6564 6765 2073 6567 6d65 6e74 7320 616e  edge segments an\n-0000bb10: 6420 7468 6520 6661 6365 206f 7074 696f  d the face optio\n-0000bb20: 6e73 2074 6f0a 2770 7370 6f6c 7967 6f6e  ns to.'pspolygon\n-0000bb30: 2773 2e20 204f 7074 696f 6e73 206b 6e6f  's.  Options kno\n-0000bb40: 776e 2074 6f20 2773 6b65 7463 6827 2066  wn to 'sketch' f\n-0000bb50: 6f72 2070 7572 706f 7365 7320 6f66 2074  or purposes of t\n-0000bb60: 6869 7320 7370 6c69 7474 696e 670a 6f70  his splitting.op\n-0000bb70: 6572 6174 696f 6e20 696e 636c 7564 6520  eration include \n-0000bb80: 2761 7272 6f77 7327 2c20 2764 6173 6827  'arrows', 'dash'\n-0000bb90: 2c20 2764 6f74 7365 7027 2c20 2766 696c  , 'dotsep', 'fil\n-0000bba0: 6c63 6f6c 6f72 272c 2027 6669 6c6c 7374  lcolor', 'fillst\n-0000bbb0: 796c 6527 2c0a 276c 696e 6563 6f6c 6f72  yle',.'linecolor\n-0000bbc0: 272c 2027 6c69 6e65 7374 796c 6527 2c20  ', 'linestyle', \n-0000bbd0: 276c 696e 6577 6964 7468 272c 2027 6f70  'linewidth', 'op\n-0000bbe0: 6163 6974 7927 2c20 2773 686f 7770 6f69  acity', 'showpoi\n-0000bbf0: 6e74 7327 2c0a 2773 7472 6f6b 656f 7061  nts',.'strokeopa\n-0000bc00: 6369 7479 272c 2061 6e64 2027 7472 616e  city', and 'tran\n-0000bc10: 7370 616c 7068 6127 2e0a 0a1f 0a46 696c  spalpha'.....Fil\n-0000bc20: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n-0000bc30: 204e 6f64 653a 2054 696b 5a2f 5047 4620   Node: TikZ/PGF \n-0000bc40: 6f70 7469 6f6e 732c 2020 4e65 7874 3a20  options,  Next: \n-0000bc50: 446f 7473 2069 6e20 5469 6b5a 2f50 4746  Dots in TikZ/PGF\n-0000bc60: 2c20 2050 7265 763a 2050 5354 7269 636b  ,  Prev: PSTrick\n-0000bc70: 7320 6f70 7469 6f6e 732c 2020 5570 3a20  s options,  Up: \n-0000bc80: 4f70 7469 6f6e 730a 0a33 2e31 2e35 2e32  Options..3.1.5.2\n-0000bc90: 2027 5469 6b5a 2f50 4746 2720 6f70 7469   'TikZ/PGF' opti\n-0000bca0: 6f6e 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ons.............\n-0000bcb0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a  ................\n-0000bcc0: 2754 696b 5a2f 5047 4627 206f 7074 696f  'TikZ/PGF' optio\n-0000bcd0: 6e73 2061 7265 2068 616e 646c 6564 206d  ns are handled m\n-0000bce0: 7563 6820 6173 2066 6f72 2027 5053 5472  uch as for 'PSTr\n-0000bcf0: 6963 6b73 272e 2020 5468 6f75 6768 0a27  icks'.  Though.'\n-0000bd00: 5469 6b5a 2f50 4746 2720 6f66 7465 6e20  TikZ/PGF' often \n-0000bd10: 616c 6c6f 7773 2063 6f6c 6f72 7320 616e  allows colors an\n-0000bd20: 6420 7374 796c 6573 2074 6f20 6265 2067  d styles to be g\n-0000bd30: 6976 656e 2077 6974 686f 7574 0a63 6f72  iven without.cor\n-0000bd40: 7265 7370 6f6e 6469 6e67 206b 6579 732c  responding keys,\n-0000bd50: 2066 6f72 2065 7861 6d70 6c65 2c0a 2020   for example,.  \n-0000bd60: 5c64 7261 775b 7265 642c 756c 7472 6120  \\draw[red,ultra \n-0000bd70: 7468 6963 6b5d 2830 2c30 292d 2d28 312c  thick](0,0)--(1,\n-0000bd80: 3129 3b0a 7468 6973 2069 7320 6e6f 7420  1);.this is not \n-0000bd90: 7065 726d 6974 7465 6420 696e 2027 736b  permitted in 'sk\n-0000bda0: 6574 6368 272e 2020 546f 2064 7261 7720  etch'.  To draw \n-0000bdb0: 6120 7265 642c 2075 6c74 7261 2d74 6869  a red, ultra-thi\n-0000bdc0: 636b 206c 696e 6520 696e 0a27 736b 6574  ck line in.'sket\n-0000bdd0: 6368 272c 2074 6865 2066 6f72 6d20 6973  ch', the form is\n-0000bde0: 0a20 206c 696e 655b 6472 6177 3d72 6564  .  line[draw=red\n-0000bdf0: 2c73 7479 6c65 3d75 6c74 7261 2074 6869  ,style=ultra thi\n-0000be00: 636b 5d28 302c 3029 2831 2c31 290a 0a20  ck](0,0)(1,1).. \n-0000be10: 2020 4a75 7374 2061 7320 666f 7220 2750    Just as for 'P\n-0000be20: 5354 7269 636b 7327 2c20 7768 656e 2061  STricks', when a\n-0000be30: 2027 706f 6c79 676f 6e27 2068 6173 206f   'polygon' has o\n-0000be40: 7074 696f 6e73 2066 6f72 2062 6f74 6820  ptions for both \n-0000be50: 6974 730a 6661 6365 2061 6e64 2069 7473  its.face and its\n-0000be60: 2065 6467 6573 2c20 616e 6420 7468 6520   edges, and the \n-0000be70: 706f 6c79 676f 6e20 6973 2073 706c 6974  polygon is split\n-0000be80: 2062 7920 7468 6520 6869 6464 656e 2073   by the hidden s\n-0000be90: 7572 6661 6365 0a61 6c67 6f72 6974 686d  urface.algorithm\n-0000bea0: 2c20 2773 6b65 7463 6827 206d 7573 7420  , 'sketch' must \n-0000beb0: 636f 7079 2074 6865 2065 6467 6520 6f70  copy the edge op\n-0000bec0: 7469 6f6e 7320 746f 2027 7073 6c69 6e65  tions to 'psline\n-0000bed0: 2773 2066 6f72 2074 6865 2065 6467 650a  's for the edge.\n-0000bee0: 7365 676d 656e 7473 2061 6e64 2074 6865  segments and the\n-0000bef0: 2066 6163 6520 6f70 7469 6f6e 7320 746f   face options to\n-0000bf00: 2027 7073 706f 6c79 676f 6e27 732e 2020   'pspolygon's.  \n-0000bf10: 2754 696b 5a2f 5047 4627 206f 7074 696f  'TikZ/PGF' optio\n-0000bf20: 6e73 206b 6e6f 776e 0a74 6f20 2773 6b65  ns known.to 'ske\n-0000bf30: 7463 6827 2066 6f72 2070 7572 706f 7365  tch' for purpose\n-0000bf40: 7320 6f66 2074 6869 7320 7370 6c69 7474  s of this splitt\n-0000bf50: 696e 6720 6f70 6572 6174 696f 6e20 696e  ing operation in\n-0000bf60: 636c 7564 6520 2761 7272 6f77 7327 2c0a  clude 'arrows',.\n-0000bf70: 2763 6170 272c 2027 636f 6c6f 7227 2c20  'cap', 'color', \n-0000bf80: 2764 6173 6820 7061 7474 6572 6e27 2c20  'dash pattern', \n-0000bf90: 2764 6173 6820 7068 6173 6527 2c20 2764  'dash phase', 'd\n-0000bfa0: 6f75 626c 6527 2c20 2764 6f75 626c 650a  ouble', 'double.\n-0000bfb0: 6469 7374 616e 6365 272c 2027 6472 6177  distance', 'draw\n-0000bfc0: 272c 2027 6472 6177 206f 7061 6369 7479  ', 'draw opacity\n-0000bfd0: 272c 2027 6669 6c6c 272c 2027 6669 6c6c  ', 'fill', 'fill\n-0000bfe0: 206f 7061 6369 7479 272c 2027 6a6f 696e   opacity', 'join\n-0000bff0: 272c 2027 6c69 6e65 0a77 6964 7468 272c  ', 'line.width',\n-0000c000: 2027 6d69 7465 7220 6c69 6d69 7427 2c20   'miter limit', \n-0000c010: 2770 6174 7465 726e 272c 2027 7061 7474  'pattern', 'patt\n-0000c020: 6572 6e20 636f 6c6f 7227 2c20 616e 6420  ern color', and \n-0000c030: 2773 7479 6c65 272e 0a0a 2020 2054 6865  'style'...   The\n-0000c040: 2027 7374 796c 6527 206f 7074 696f 6e20   'style' option \n-0000c050: 6361 6e20 636f 6e74 6169 6e20 626f 7468  can contain both\n-0000c060: 2066 6163 6520 616e 6420 6564 6765 2069   face and edge i\n-0000c070: 6e66 6f72 6d61 7469 6f6e 2c20 736f 0a27  nformation, so.'\n-0000c080: 736b 6574 6368 2720 6d75 7374 2063 6865  sketch' must che\n-0000c090: 636b 2074 6865 2073 7479 6c65 2076 616c  ck the style val\n-0000c0a0: 7565 2e20 2056 616c 7565 7320 6b6e 6f77  ue.  Values know\n-0000c0b0: 6e20 746f 2027 736b 6574 6368 2720 696e  n to 'sketch' in\n-0000c0c0: 636c 7564 650a 2764 6173 6865 6427 2c20  clude.'dashed', \n-0000c0d0: 2764 656e 7365 6c79 2064 6173 6865 6427  'densely dashed'\n-0000c0e0: 2c20 2764 656e 7365 6c79 2064 6f74 7465  , 'densely dotte\n-0000c0f0: 6427 2c20 2764 6f74 7465 6427 2c20 2764  d', 'dotted', 'd\n-0000c100: 6f75 626c 6527 2c0a 276c 6f6f 7365 6c79  ouble',.'loosely\n-0000c110: 2064 6173 6865 6427 2c20 276c 6f6f 7365   dashed', 'loose\n-0000c120: 6c79 2064 6f74 7465 6427 2c20 276e 6561  ly dotted', 'nea\n-0000c130: 726c 7920 6f70 6171 7565 272c 2027 6e65  rly opaque', 'ne\n-0000c140: 6172 6c79 0a74 7261 6e73 7061 7265 6e74  arly.transparent\n-0000c150: 272c 2027 7365 6d69 7468 6963 6b27 2c20  ', 'semithick', \n-0000c160: 2773 656d 6974 7261 6e73 7061 7265 6e74  'semitransparent\n-0000c170: 272c 2027 736f 6c69 6427 2c20 2774 6869  ', 'solid', 'thi\n-0000c180: 636b 272c 2027 7468 696e 272c 0a27 7472  ck', 'thin',.'tr\n-0000c190: 616e 7370 6172 656e 7427 2c20 2775 6c74  ansparent', 'ult\n-0000c1a0: 7261 206e 6561 726c 7920 7472 616e 7370  ra nearly transp\n-0000c1b0: 6172 656e 7427 2c20 2775 6c74 7261 2074  arent', 'ultra t\n-0000c1c0: 6869 636b 272c 2027 756c 7472 6120 7468  hick', 'ultra th\n-0000c1d0: 696e 272c 0a27 7665 7279 206e 6561 726c  in',.'very nearl\n-0000c1e0: 7920 7472 616e 7370 6172 656e 7427 2c20  y transparent', \n-0000c1f0: 2776 6572 7920 7468 6963 6b27 2c20 616e  'very thick', an\n-0000c200: 6420 2776 6572 7920 7468 696e 272e 0a0a  d 'very thin'...\n-0000c210: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n-0000c220: 6e66 6f2c 2020 4e6f 6465 3a20 446f 7473  nfo,  Node: Dots\n-0000c230: 2069 6e20 5469 6b5a 2f50 4746 2c20 204e   in TikZ/PGF,  N\n-0000c240: 6578 743a 2054 696b 5a2f 5047 4620 7573  ext: TikZ/PGF us\n-0000c250: 6572 2d64 6566 696e 6564 2073 7479 6c65  er-defined style\n-0000c260: 732c 2020 5072 6576 3a20 5469 6b5a 2f50  s,  Prev: TikZ/P\n-0000c270: 4746 206f 7074 696f 6e73 2c20 2055 703a  GF options,  Up:\n-0000c280: 204f 7074 696f 6e73 0a0a 332e 312e 352e   Options..3.1.5.\n-0000c290: 3320 446f 7473 2069 6e20 2754 696b 5a2f  3 Dots in 'TikZ/\n-0000c2a0: 5047 4627 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e  PGF'............\n-0000c2b0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a  ................\n-0000c2c0: 0a27 5469 6b5a 2f50 4746 2720 646f 6573  .'TikZ/PGF' does\n-0000c2d0: 206e 6f74 2068 6176 6520 6120 2764 6f74   not have a 'dot\n-0000c2e0: 7327 2063 6f6d 6d61 6e64 2061 7320 646f  s' command as do\n-0000c2f0: 6573 2050 5354 7269 636b 732e 2020 496e  es PSTricks.  In\n-0000c300: 7374 6561 642c 0a27 536b 6574 6368 2720  stead,.'Sketch' \n-0000c310: 656d 6974 7320 646f 7473 2061 7320 2766  emits dots as 'f\n-0000c320: 696c 6c64 7261 7727 2063 6972 636c 6573  illdraw' circles\n-0000c330: 2e20 2054 6865 2064 6961 6d65 7465 7220  .  The diameter \n-0000c340: 6d61 7920 6265 2073 6574 0a75 7369 6e67  may be set.using\n-0000c350: 2074 6865 206f 7074 696f 6e20 2764 6f74   the option 'dot\n-0000c360: 7369 7a65 2720 626f 7272 6f77 6564 2066  size' borrowed f\n-0000c370: 726f 6d20 5053 5472 6963 6b73 2e20 2054  rom PSTricks.  T\n-0000c380: 6865 2027 646f 7473 697a 6527 206f 7074  he 'dotsize' opt\n-0000c390: 696f 6e0a 7769 6c6c 2062 6520 7265 6d6f  ion.will be remo\n-0000c3a0: 7665 6420 6672 6f6d 2074 6865 206f 7074  ved from the opt\n-0000c3b0: 696f 6e20 6c69 7374 2069 6e20 7468 6520  ion list in the \n-0000c3c0: 6f75 7470 7574 2027 6669 6c6c 6472 6177  output 'filldraw\n-0000c3d0: 2720 636f 6d6d 616e 642e 0a4f 7468 6572  ' command..Other\n-0000c3e0: 206f 7074 696f 6e73 2077 6f72 6b20 696e   options work in\n-0000c3f0: 2074 6865 2065 7870 6563 7465 6420 7761   the expected wa\n-0000c400: 792e 2020 466f 7220 6578 616d 706c 652c  y.  For example,\n-0000c410: 2027 6669 6c6c 2720 7365 7473 2066 696c   'fill' sets fil\n-0000c420: 6c0a 636f 6c6f 7220 616e 6420 2763 6f6c  l.color and 'col\n-0000c430: 6f72 2720 7365 7473 206c 696e 6520 636f  or' sets line co\n-0000c440: 6c6f 7220 6f66 2074 6865 2063 6972 636c  lor of the circl\n-0000c450: 6573 2e0a 0a1f 0a46 696c 653a 2073 6b65  es.....File: ske\n-0000c460: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n-0000c470: 2054 696b 5a2f 5047 4620 7573 6572 2d64   TikZ/PGF user-d\n-0000c480: 6566 696e 6564 2073 7479 6c65 732c 2020  efined styles,  \n-0000c490: 4e65 7874 3a20 5472 616e 7370 6172 656e  Next: Transparen\n-0000c4a0: 6379 2c20 2050 7265 763a 2044 6f74 7320  cy,  Prev: Dots \n-0000c4b0: 696e 2054 696b 5a2f 5047 462c 2020 5570  in TikZ/PGF,  Up\n-0000c4c0: 3a20 4f70 7469 6f6e 730a 0a33 2e31 2e35  : Options..3.1.5\n-0000c4d0: 2e34 2027 5469 6b5a 2f50 4746 2720 7573  .4 'TikZ/PGF' us\n-0000c4e0: 6572 2d64 6566 696e 6564 2073 7479 6c65  er-defined style\n-0000c4f0: 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  s...............\n+0000b1e0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n+0000b1f0: 2d2d 2d0a 272d 5827 2020 2020 2020 2020  ---.'-X'        \n+0000b200: 2020 2073 6361 6c61 7220 2020 2020 2073     scalar      s\n+0000b210: 6361 6c61 7220 2020 2020 2055 6e61 7279  calar      Unary\n+0000b220: 2073 6361 6c61 7220 6e65 6761 7469 6f6e   scalar negation\n+0000b230: 2e0a 272d 5827 2020 2020 2020 2020 2020  ..'-X'          \n+0000b240: 2076 6563 746f 7220 2020 2020 2076 6563   vector      vec\n+0000b250: 746f 7220 2020 2020 2055 6e61 7279 2076  tor      Unary v\n+0000b260: 6563 746f 7220 6e65 6761 7469 6f6e 2e0a  ector negation..\n+0000b270: 277c 587c 2720 2020 2020 2020 2020 2076  '|X|'          v\n+0000b280: 6563 746f 7220 2020 2020 2073 6361 6c61  ector      scala\n+0000b290: 7220 2020 2020 2056 6563 746f 7220 6c65  r      Vector le\n+0000b2a0: 6e67 7468 2e0a 2775 6e69 7428 5829 2720  ngth..'unit(X)' \n+0000b2b0: 2020 2020 2076 6563 746f 7220 2020 2020       vector     \n+0000b2c0: 2076 6563 746f 7220 2020 2020 2055 6e69   vector      Uni\n+0000b2d0: 7420 7665 6374 6f72 2077 6974 6820 7361  t vector with sa\n+0000b2e0: 6d65 2064 6972 6563 7469 6f6e 2e0a 2773  me direction..'s\n+0000b2f0: 7172 7428 5829 2720 2020 2020 2073 6361  qrt(X)'      sca\n+0000b300: 6c61 7220 2020 2020 2073 6361 6c61 7220  lar      scalar \n+0000b310: 2020 2020 2053 6361 6c61 7220 7371 7561       Scalar squa\n+0000b320: 7265 2072 6f6f 742e 0a27 7369 6e28 5829  re root..'sin(X)\n+0000b330: 2720 2020 2020 2020 7363 616c 6172 2020  '       scalar  \n+0000b340: 2020 2020 7363 616c 6172 2020 2020 2020      scalar      \n+0000b350: 5472 6967 6f6e 6f6d 6574 7269 6320 7369  Trigonometric si\n+0000b360: 6e65 2028 2758 2720 696e 2064 6567 7265  ne ('X' in degre\n+0000b370: 6573 292e 0a27 636f 7328 5829 2720 2020  es)..'cos(X)'   \n+0000b380: 2020 2020 7363 616c 6172 2020 2020 2020      scalar      \n+0000b390: 7363 616c 6172 2020 2020 2020 5472 6967  scalar      Trig\n+0000b3a0: 6f6e 6f6d 6574 7269 6320 636f 7369 6e65  onometric cosine\n+0000b3b0: 2028 2758 2720 696e 2064 6567 7265 6573   ('X' in degrees\n+0000b3c0: 292e 0a27 6173 696e 2858 2927 2020 2020  )..'asin(X)'    \n+0000b3d0: 2020 7363 616c 6172 2020 2020 2020 7363    scalar      sc\n+0000b3e0: 616c 6172 2020 2020 2020 496e 7665 7273  alar      Invers\n+0000b3f0: 6520 7369 6e65 2028 2758 2720 696e 2064  e sine ('X' in d\n+0000b400: 6567 7265 6573 292e 0a27 6163 6f73 2858  egrees)..'acos(X\n+0000b410: 2927 2020 2020 2020 7363 616c 6172 2020  )'      scalar  \n+0000b420: 2020 2020 7363 616c 6172 2020 2020 2020      scalar      \n+0000b430: 496e 7665 7273 6520 636f 7369 6e65 2028  Inverse cosine (\n+0000b440: 2758 2720 696e 2064 6567 7265 6573 292e  'X' in degrees).\n+0000b450: 0a27 6174 616e 3228 582c 5929 2720 2020  .'atan2(X,Y)'   \n+0000b460: 7363 616c 6172 2020 2020 2020 7363 616c  scalar      scal\n+0000b470: 6172 2020 2020 2020 506f 6c61 7220 616e  ar      Polar an\n+0000b480: 676c 6520 696e 2064 6567 7265 6573 206f  gle in degrees o\n+0000b490: 6620 7665 6374 6f72 205b 582c 595d 2e0a  f vector [X,Y]..\n+0000b4a0: 2769 6e76 6572 7365 2858 2927 2020 2074  'inverse(X)'   t\n+0000b4b0: 7261 6e73 666f 726d 2020 2074 7261 6e73  ransform   trans\n+0000b4c0: 666f 726d 2020 2049 6e76 6572 7365 2074  form   Inverse t\n+0000b4d0: 7261 6e73 666f 726d 2e0a 0a45 7272 6f72  ransform...Error\n+0000b4e0: 7320 6172 6520 7265 706f 7274 6564 2077  s are reported w\n+0000b4f0: 6865 6e20 277c 587c 272c 2027 756e 6974  hen '|X|', 'unit\n+0000b500: 272c 2027 6173 696e 272c 2027 6163 6f73  ', 'asin', 'acos\n+0000b510: 272c 2027 7371 7274 272c 2027 6174 616e  ', 'sqrt', 'atan\n+0000b520: 3227 2c0a 616e 6420 2769 6e76 6572 7365  2',.and 'inverse\n+0000b530: 2720 6661 696c 2064 7565 2074 6f20 6f70  ' fail due to op\n+0000b540: 6572 616e 6473 206f 7574 7369 6465 2074  erands outside t\n+0000b550: 6865 6972 2072 6573 7065 6374 6976 6520  heir respective \n+0000b560: 646f 6d61 696e 732e 0a0a 1f0a 4669 6c65  domains.....File\n+0000b570: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n+0000b580: 4e6f 6465 3a20 4f70 7469 6f6e 732c 2020  Node: Options,  \n+0000b590: 5072 6576 3a20 4172 6974 686d 6574 6963  Prev: Arithmetic\n+0000b5a0: 2c20 2055 703a 204c 616e 6775 6167 6520  ,  Up: Language \n+0000b5b0: 6261 7369 6373 0a0a 332e 312e 3520 4f70  basics..3.1.5 Op\n+0000b5c0: 7469 6f6e 730a 2d2d 2d2d 2d2d 2d2d 2d2d  tions.----------\n+0000b5d0: 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a 0a20  ---..*Syntax:*. \n+0000b5e0: 2020 2020 5b4b 4559 313d 5641 4c31 2c4b      [KEY1=VAL1,K\n+0000b5f0: 4559 323d 5641 4c32 2c2e 2e2e 5d0a 4f70  EY2=VAL2,...].Op\n+0000b600: 7469 6f6e 7320 6172 6520 7573 6564 2074  tions are used t\n+0000b610: 6f20 7370 6563 6966 7920 6465 7461 696c  o specify detail\n+0000b620: 7320 6f66 2074 6865 2061 7070 6561 7261  s of the appeara\n+0000b630: 6e63 6520 6f66 2064 7261 7761 626c 6573  nce of drawables\n+0000b640: 2e20 2041 730a 7368 6f77 6e20 6162 6f76  .  As.shown abov\n+0000b650: 652c 2074 6865 7920 6172 6520 6769 7665  e, they are give\n+0000b660: 6e20 6173 2063 6f6d 6d61 2d73 6570 6172  n as comma-separ\n+0000b670: 6174 6564 206b 6579 2d76 616c 7565 2070  ated key-value p\n+0000b680: 6169 7273 2e0a 0a2a 204d 656e 753a 0a0a  airs...* Menu:..\n+0000b690: 2a20 5053 5472 6963 6b73 206f 7074 696f  * PSTricks optio\n+0000b6a0: 6e73 3a3a 2020 2020 2020 2020 2020 2020  ns::            \n+0000b6b0: 4f70 7469 6f6e 7320 696e 6865 7269 7465  Options inherite\n+0000b6c0: 6420 6672 6f6d 2027 5053 5472 6963 6b73  d from 'PSTricks\n+0000b6d0: 272e 0a2a 2054 696b 5a2f 5047 4620 6f70  '..* TikZ/PGF op\n+0000b6e0: 7469 6f6e 733a 3a20 2020 2020 2020 2020  tions::         \n+0000b6f0: 2020 204f 7074 696f 6e73 2069 6e68 6572     Options inher\n+0000b700: 6974 6564 2066 726f 6d20 2754 696b 5a2f  ited from 'TikZ/\n+0000b710: 5047 4627 2e0a 2a20 446f 7473 2069 6e20  PGF'..* Dots in \n+0000b720: 5469 6b5a 2f50 4746 3a3a 2020 2020 2020  TikZ/PGF::      \n+0000b730: 2020 2020 2020 536b 6574 6368 2075 7365        Sketch use\n+0000b740: 7320 2754 696b 5a2f 5047 4627 2063 6972  s 'TikZ/PGF' cir\n+0000b750: 636c 6573 2066 6f72 2064 6f74 732e 0a2a  cles for dots..*\n+0000b760: 2054 696b 5a2f 5047 4620 7573 6572 2d64   TikZ/PGF user-d\n+0000b770: 6566 696e 6564 2073 7479 6c65 733a 3a20  efined styles:: \n+0000b780: 2053 7570 706f 7274 2066 6f72 2027 5469   Support for 'Ti\n+0000b790: 6b5a 2f50 4746 2720 6e61 6d65 642c 2075  kZ/PGF' named, u\n+0000b7a0: 7365 722d 6465 6669 6e65 6420 7374 796c  ser-defined styl\n+0000b7b0: 6573 2e0a 2a20 5472 616e 7370 6172 656e  es..* Transparen\n+0000b7c0: 6379 3a3a 2020 2020 2020 2020 2020 2020  cy::            \n+0000b7d0: 2020 2020 5365 652d 7468 726f 7567 6820      See-through \n+0000b7e0: 706f 6c79 676f 6e73 2e0a 2a20 496e 7465  polygons..* Inte\n+0000b7f0: 726e 616c 206f 7074 696f 6e73 3a3a 2020  rnal options::  \n+0000b800: 2020 2020 2020 2020 2020 4f70 7469 6f6e            Option\n+0000b810: 7320 7573 6564 2062 7920 2773 6b65 7463  s used by 'sketc\n+0000b820: 6827 2e0a 0a1f 0a46 696c 653a 2073 6b65  h'.....File: ske\n+0000b830: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n+0000b840: 2050 5354 7269 636b 7320 6f70 7469 6f6e   PSTricks option\n+0000b850: 732c 2020 4e65 7874 3a20 5469 6b5a 2f50  s,  Next: TikZ/P\n+0000b860: 4746 206f 7074 696f 6e73 2c20 2050 7265  GF options,  Pre\n+0000b870: 763a 204f 7074 696f 6e73 2c20 2055 703a  v: Options,  Up:\n+0000b880: 204f 7074 696f 6e73 0a0a 332e 312e 352e   Options..3.1.5.\n+0000b890: 3120 2750 5354 7269 636b 7327 206f 7074  1 'PSTricks' opt\n+0000b8a0: 696f 6e73 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e  ions............\n+0000b8b0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a  ................\n+0000b8c0: 0a57 6865 6e20 276c 616e 6775 6167 6520  .When 'language \n+0000b8d0: 7073 7472 6963 6b73 2720 6973 2073 656c  pstricks' is sel\n+0000b8e0: 6563 7465 6420 2874 6865 2064 6566 6175  ected (the defau\n+0000b8f0: 6c74 292c 2070 6572 6d69 7373 6962 6c65  lt), permissible\n+0000b900: 0a6b 6579 2d76 616c 7565 2070 6169 7273  .key-value pairs\n+0000b910: 2069 6e63 6c75 6465 2061 6c6c 2074 686f   include all tho\n+0000b920: 7365 2066 6f72 2073 696d 696c 6172 2027  se for similar '\n+0000b930: 5053 5472 6963 6b73 2720 6f62 6a65 6374  PSTricks' object\n+0000b940: 732e 2020 466f 720a 6578 616d 706c 652c  s.  For.example,\n+0000b950: 2061 2070 6f6c 7967 6f6e 206d 6967 6874   a polygon might\n+0000b960: 2068 6176 6520 7468 6520 6f70 7469 6f6e   have the option\n+0000b970: 730a 2020 5b6c 696e 6577 6964 7468 3d31  s.  [linewidth=1\n+0000b980: 7074 2c6c 696e 6563 6f6c 6f72 3d62 6c75  pt,linecolor=blu\n+0000b990: 652c 6669 6c6c 636f 6c6f 723d 6379 616e  e,fillcolor=cyan\n+0000b9a0: 5d0a 2753 6b65 7463 6827 206d 6572 656c  ].'Sketch' merel\n+0000b9b0: 7920 7061 7373 6573 2074 6865 7365 206f  y passes these o\n+0000b9c0: 6e20 746f 2027 5053 5472 6963 6b73 2720  n to 'PSTricks' \n+0000b9d0: 7769 7468 6f75 7420 6368 6563 6b69 6e67  without checking\n+0000b9e0: 206f 720a 6d6f 6469 6669 6361 7469 6f6e   or.modification\n+0000b9f0: 2e20 204f 7074 696f 6e20 6c69 7374 7320  .  Option lists \n+0000ba00: 6172 6520 616c 7761 7973 206f 7074 696f  are always optio\n+0000ba10: 6e61 6c2e 2020 4120 6d69 7373 696e 6720  nal.  A missing \n+0000ba20: 6f70 7469 6f6e 7320 6c69 7374 0a69 7320  options list.is \n+0000ba30: 6571 7569 7661 6c65 6e74 2074 6f20 616e  equivalent to an\n+0000ba40: 2065 6d70 7479 206f 6e65 2027 5b5d 272e   empty one '[]'.\n+0000ba50: 0a0a 2020 2057 6865 6e20 6120 2770 6f6c  ..   When a 'pol\n+0000ba60: 7967 6f6e 2720 6861 7320 6f70 7469 6f6e  ygon' has option\n+0000ba70: 7320 666f 7220 626f 7468 2069 7473 2066  s for both its f\n+0000ba80: 6163 6520 616e 6420 6974 7320 6564 6765  ace and its edge\n+0000ba90: 732c 2061 6e64 2074 6865 0a70 6f6c 7967  s, and the.polyg\n+0000baa0: 6f6e 2069 7320 7370 6c69 7420 6279 2074  on is split by t\n+0000bab0: 6865 2068 6964 6465 6e20 7375 7266 6163  he hidden surfac\n+0000bac0: 6520 616c 676f 7269 7468 6d2c 2027 736b  e algorithm, 'sk\n+0000bad0: 6574 6368 2720 6d75 7374 2063 6f70 7920  etch' must copy \n+0000bae0: 7468 650a 6564 6765 206f 7074 696f 6e73  the.edge options\n+0000baf0: 2074 6f20 2770 736c 696e 6527 7320 666f   to 'psline's fo\n+0000bb00: 7220 7468 6520 6564 6765 2073 6567 6d65  r the edge segme\n+0000bb10: 6e74 7320 616e 6420 7468 6520 6661 6365  nts and the face\n+0000bb20: 206f 7074 696f 6e73 2074 6f0a 2770 7370   options to.'psp\n+0000bb30: 6f6c 7967 6f6e 2773 2e20 204f 7074 696f  olygon's.  Optio\n+0000bb40: 6e73 206b 6e6f 776e 2074 6f20 2773 6b65  ns known to 'ske\n+0000bb50: 7463 6827 2066 6f72 2070 7572 706f 7365  tch' for purpose\n+0000bb60: 7320 6f66 2074 6869 7320 7370 6c69 7474  s of this splitt\n+0000bb70: 696e 670a 6f70 6572 6174 696f 6e20 696e  ing.operation in\n+0000bb80: 636c 7564 6520 2761 7272 6f77 7327 2c20  clude 'arrows', \n+0000bb90: 2764 6173 6827 2c20 2764 6f74 7365 7027  'dash', 'dotsep'\n+0000bba0: 2c20 2766 696c 6c63 6f6c 6f72 272c 2027  , 'fillcolor', '\n+0000bbb0: 6669 6c6c 7374 796c 6527 2c0a 276c 696e  fillstyle',.'lin\n+0000bbc0: 6563 6f6c 6f72 272c 2027 6c69 6e65 7374  ecolor', 'linest\n+0000bbd0: 796c 6527 2c20 276c 696e 6577 6964 7468  yle', 'linewidth\n+0000bbe0: 272c 2027 6f70 6163 6974 7927 2c20 2773  ', 'opacity', 's\n+0000bbf0: 686f 7770 6f69 6e74 7327 2c0a 2773 7472  howpoints',.'str\n+0000bc00: 6f6b 656f 7061 6369 7479 272c 2061 6e64  okeopacity', and\n+0000bc10: 2027 7472 616e 7370 616c 7068 6127 2e0a   'transpalpha'..\n+0000bc20: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n+0000bc30: 696e 666f 2c20 204e 6f64 653a 2054 696b  info,  Node: Tik\n+0000bc40: 5a2f 5047 4620 6f70 7469 6f6e 732c 2020  Z/PGF options,  \n+0000bc50: 4e65 7874 3a20 446f 7473 2069 6e20 5469  Next: Dots in Ti\n+0000bc60: 6b5a 2f50 4746 2c20 2050 7265 763a 2050  kZ/PGF,  Prev: P\n+0000bc70: 5354 7269 636b 7320 6f70 7469 6f6e 732c  STricks options,\n+0000bc80: 2020 5570 3a20 4f70 7469 6f6e 730a 0a33    Up: Options..3\n+0000bc90: 2e31 2e35 2e32 2027 5469 6b5a 2f50 4746  .1.5.2 'TikZ/PGF\n+0000bca0: 2720 6f70 7469 6f6e 730a 2e2e 2e2e 2e2e  ' options.......\n+0000bcb0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+0000bcc0: 2e2e 2e2e 0a0a 2754 696b 5a2f 5047 4627  ......'TikZ/PGF'\n+0000bcd0: 206f 7074 696f 6e73 2061 7265 2068 616e   options are han\n+0000bce0: 646c 6564 206d 7563 6820 6173 2066 6f72  dled much as for\n+0000bcf0: 2027 5053 5472 6963 6b73 272e 2020 5468   'PSTricks'.  Th\n+0000bd00: 6f75 6768 0a27 5469 6b5a 2f50 4746 2720  ough.'TikZ/PGF' \n+0000bd10: 6f66 7465 6e20 616c 6c6f 7773 2063 6f6c  often allows col\n+0000bd20: 6f72 7320 616e 6420 7374 796c 6573 2074  ors and styles t\n+0000bd30: 6f20 6265 2067 6976 656e 2077 6974 686f  o be given witho\n+0000bd40: 7574 0a63 6f72 7265 7370 6f6e 6469 6e67  ut.corresponding\n+0000bd50: 206b 6579 732c 2066 6f72 2065 7861 6d70   keys, for examp\n+0000bd60: 6c65 2c0a 2020 5c64 7261 775b 7265 642c  le,.  \\draw[red,\n+0000bd70: 756c 7472 6120 7468 6963 6b5d 2830 2c30  ultra thick](0,0\n+0000bd80: 292d 2d28 312c 3129 3b0a 7468 6973 2069  )--(1,1);.this i\n+0000bd90: 7320 6e6f 7420 7065 726d 6974 7465 6420  s not permitted \n+0000bda0: 696e 2027 736b 6574 6368 272e 2020 546f  in 'sketch'.  To\n+0000bdb0: 2064 7261 7720 6120 7265 642c 2075 6c74   draw a red, ult\n+0000bdc0: 7261 2d74 6869 636b 206c 696e 6520 696e  ra-thick line in\n+0000bdd0: 0a27 736b 6574 6368 272c 2074 6865 2066  .'sketch', the f\n+0000bde0: 6f72 6d20 6973 0a20 206c 696e 655b 6472  orm is.  line[dr\n+0000bdf0: 6177 3d72 6564 2c73 7479 6c65 3d75 6c74  aw=red,style=ult\n+0000be00: 7261 2074 6869 636b 5d28 302c 3029 2831  ra thick](0,0)(1\n+0000be10: 2c31 290a 0a20 2020 4a75 7374 2061 7320  ,1)..   Just as \n+0000be20: 666f 7220 2750 5354 7269 636b 7327 2c20  for 'PSTricks', \n+0000be30: 7768 656e 2061 2027 706f 6c79 676f 6e27  when a 'polygon'\n+0000be40: 2068 6173 206f 7074 696f 6e73 2066 6f72   has options for\n+0000be50: 2062 6f74 6820 6974 730a 6661 6365 2061   both its.face a\n+0000be60: 6e64 2069 7473 2065 6467 6573 2c20 616e  nd its edges, an\n+0000be70: 6420 7468 6520 706f 6c79 676f 6e20 6973  d the polygon is\n+0000be80: 2073 706c 6974 2062 7920 7468 6520 6869   split by the hi\n+0000be90: 6464 656e 2073 7572 6661 6365 0a61 6c67  dden surface.alg\n+0000bea0: 6f72 6974 686d 2c20 2773 6b65 7463 6827  orithm, 'sketch'\n+0000beb0: 206d 7573 7420 636f 7079 2074 6865 2065   must copy the e\n+0000bec0: 6467 6520 6f70 7469 6f6e 7320 746f 2027  dge options to '\n+0000bed0: 7073 6c69 6e65 2773 2066 6f72 2074 6865  psline's for the\n+0000bee0: 2065 6467 650a 7365 676d 656e 7473 2061   edge.segments a\n+0000bef0: 6e64 2074 6865 2066 6163 6520 6f70 7469  nd the face opti\n+0000bf00: 6f6e 7320 746f 2027 7073 706f 6c79 676f  ons to 'pspolygo\n+0000bf10: 6e27 732e 2020 2754 696b 5a2f 5047 4627  n's.  'TikZ/PGF'\n+0000bf20: 206f 7074 696f 6e73 206b 6e6f 776e 0a74   options known.t\n+0000bf30: 6f20 2773 6b65 7463 6827 2066 6f72 2070  o 'sketch' for p\n+0000bf40: 7572 706f 7365 7320 6f66 2074 6869 7320  urposes of this \n+0000bf50: 7370 6c69 7474 696e 6720 6f70 6572 6174  splitting operat\n+0000bf60: 696f 6e20 696e 636c 7564 6520 2761 7272  ion include 'arr\n+0000bf70: 6f77 7327 2c0a 2763 6170 272c 2027 636f  ows',.'cap', 'co\n+0000bf80: 6c6f 7227 2c20 2764 6173 6820 7061 7474  lor', 'dash patt\n+0000bf90: 6572 6e27 2c20 2764 6173 6820 7068 6173  ern', 'dash phas\n+0000bfa0: 6527 2c20 2764 6f75 626c 6527 2c20 2764  e', 'double', 'd\n+0000bfb0: 6f75 626c 650a 6469 7374 616e 6365 272c  ouble.distance',\n+0000bfc0: 2027 6472 6177 272c 2027 6472 6177 206f   'draw', 'draw o\n+0000bfd0: 7061 6369 7479 272c 2027 6669 6c6c 272c  pacity', 'fill',\n+0000bfe0: 2027 6669 6c6c 206f 7061 6369 7479 272c   'fill opacity',\n+0000bff0: 2027 6a6f 696e 272c 2027 6c69 6e65 0a77   'join', 'line.w\n+0000c000: 6964 7468 272c 2027 6d69 7465 7220 6c69  idth', 'miter li\n+0000c010: 6d69 7427 2c20 2770 6174 7465 726e 272c  mit', 'pattern',\n+0000c020: 2027 7061 7474 6572 6e20 636f 6c6f 7227   'pattern color'\n+0000c030: 2c20 616e 6420 2773 7479 6c65 272e 0a0a  , and 'style'...\n+0000c040: 2020 2054 6865 2027 7374 796c 6527 206f     The 'style' o\n+0000c050: 7074 696f 6e20 6361 6e20 636f 6e74 6169  ption can contai\n+0000c060: 6e20 626f 7468 2066 6163 6520 616e 6420  n both face and \n+0000c070: 6564 6765 2069 6e66 6f72 6d61 7469 6f6e  edge information\n+0000c080: 2c20 736f 0a27 736b 6574 6368 2720 6d75  , so.'sketch' mu\n+0000c090: 7374 2063 6865 636b 2074 6865 2073 7479  st check the sty\n+0000c0a0: 6c65 2076 616c 7565 2e20 2056 616c 7565  le value.  Value\n+0000c0b0: 7320 6b6e 6f77 6e20 746f 2027 736b 6574  s known to 'sket\n+0000c0c0: 6368 2720 696e 636c 7564 650a 2764 6173  ch' include.'das\n+0000c0d0: 6865 6427 2c20 2764 656e 7365 6c79 2064  hed', 'densely d\n+0000c0e0: 6173 6865 6427 2c20 2764 656e 7365 6c79  ashed', 'densely\n+0000c0f0: 2064 6f74 7465 6427 2c20 2764 6f74 7465   dotted', 'dotte\n+0000c100: 6427 2c20 2764 6f75 626c 6527 2c0a 276c  d', 'double',.'l\n+0000c110: 6f6f 7365 6c79 2064 6173 6865 6427 2c20  oosely dashed', \n+0000c120: 276c 6f6f 7365 6c79 2064 6f74 7465 6427  'loosely dotted'\n+0000c130: 2c20 276e 6561 726c 7920 6f70 6171 7565  , 'nearly opaque\n+0000c140: 272c 2027 6e65 6172 6c79 0a74 7261 6e73  ', 'nearly.trans\n+0000c150: 7061 7265 6e74 272c 2027 7365 6d69 7468  parent', 'semith\n+0000c160: 6963 6b27 2c20 2773 656d 6974 7261 6e73  ick', 'semitrans\n+0000c170: 7061 7265 6e74 272c 2027 736f 6c69 6427  parent', 'solid'\n+0000c180: 2c20 2774 6869 636b 272c 2027 7468 696e  , 'thick', 'thin\n+0000c190: 272c 0a27 7472 616e 7370 6172 656e 7427  ',.'transparent'\n+0000c1a0: 2c20 2775 6c74 7261 206e 6561 726c 7920  , 'ultra nearly \n+0000c1b0: 7472 616e 7370 6172 656e 7427 2c20 2775  transparent', 'u\n+0000c1c0: 6c74 7261 2074 6869 636b 272c 2027 756c  ltra thick', 'ul\n+0000c1d0: 7472 6120 7468 696e 272c 0a27 7665 7279  tra thin',.'very\n+0000c1e0: 206e 6561 726c 7920 7472 616e 7370 6172   nearly transpar\n+0000c1f0: 656e 7427 2c20 2776 6572 7920 7468 6963  ent', 'very thic\n+0000c200: 6b27 2c20 616e 6420 2776 6572 7920 7468  k', and 'very th\n+0000c210: 696e 272e 0a0a 1f0a 4669 6c65 3a20 736b  in'.....File: sk\n+0000c220: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n+0000c230: 3a20 446f 7473 2069 6e20 5469 6b5a 2f50  : Dots in TikZ/P\n+0000c240: 4746 2c20 204e 6578 743a 2054 696b 5a2f  GF,  Next: TikZ/\n+0000c250: 5047 4620 7573 6572 2d64 6566 696e 6564  PGF user-defined\n+0000c260: 2073 7479 6c65 732c 2020 5072 6576 3a20   styles,  Prev: \n+0000c270: 5469 6b5a 2f50 4746 206f 7074 696f 6e73  TikZ/PGF options\n+0000c280: 2c20 2055 703a 204f 7074 696f 6e73 0a0a  ,  Up: Options..\n+0000c290: 332e 312e 352e 3320 446f 7473 2069 6e20  3.1.5.3 Dots in \n+0000c2a0: 2754 696b 5a2f 5047 4627 0a2e 2e2e 2e2e  'TikZ/PGF'......\n+0000c2b0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+0000c2c0: 2e2e 2e2e 2e0a 0a27 5469 6b5a 2f50 4746  .......'TikZ/PGF\n+0000c2d0: 2720 646f 6573 206e 6f74 2068 6176 6520  ' does not have \n+0000c2e0: 6120 2764 6f74 7327 2063 6f6d 6d61 6e64  a 'dots' command\n+0000c2f0: 2061 7320 646f 6573 2050 5354 7269 636b   as does PSTrick\n+0000c300: 732e 2020 496e 7374 6561 642c 0a27 536b  s.  Instead,.'Sk\n+0000c310: 6574 6368 2720 656d 6974 7320 646f 7473  etch' emits dots\n+0000c320: 2061 7320 2766 696c 6c64 7261 7727 2063   as 'filldraw' c\n+0000c330: 6972 636c 6573 2e20 2054 6865 2064 6961  ircles.  The dia\n+0000c340: 6d65 7465 7220 6d61 7920 6265 2073 6574  meter may be set\n+0000c350: 0a75 7369 6e67 2074 6865 206f 7074 696f  .using the optio\n+0000c360: 6e20 2764 6f74 7369 7a65 2720 626f 7272  n 'dotsize' borr\n+0000c370: 6f77 6564 2066 726f 6d20 5053 5472 6963  owed from PSTric\n+0000c380: 6b73 2e20 2054 6865 2027 646f 7473 697a  ks.  The 'dotsiz\n+0000c390: 6527 206f 7074 696f 6e0a 7769 6c6c 2062  e' option.will b\n+0000c3a0: 6520 7265 6d6f 7665 6420 6672 6f6d 2074  e removed from t\n+0000c3b0: 6865 206f 7074 696f 6e20 6c69 7374 2069  he option list i\n+0000c3c0: 6e20 7468 6520 6f75 7470 7574 2027 6669  n the output 'fi\n+0000c3d0: 6c6c 6472 6177 2720 636f 6d6d 616e 642e  lldraw' command.\n+0000c3e0: 0a4f 7468 6572 206f 7074 696f 6e73 2077  .Other options w\n+0000c3f0: 6f72 6b20 696e 2074 6865 2065 7870 6563  ork in the expec\n+0000c400: 7465 6420 7761 792e 2020 466f 7220 6578  ted way.  For ex\n+0000c410: 616d 706c 652c 2027 6669 6c6c 2720 7365  ample, 'fill' se\n+0000c420: 7473 2066 696c 6c0a 636f 6c6f 7220 616e  ts fill.color an\n+0000c430: 6420 2763 6f6c 6f72 2720 7365 7473 206c  d 'color' sets l\n+0000c440: 696e 6520 636f 6c6f 7220 6f66 2074 6865  ine color of the\n+0000c450: 2063 6972 636c 6573 2e0a 0a1f 0a46 696c   circles.....Fil\n+0000c460: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n+0000c470: 204e 6f64 653a 2054 696b 5a2f 5047 4620   Node: TikZ/PGF \n+0000c480: 7573 6572 2d64 6566 696e 6564 2073 7479  user-defined sty\n+0000c490: 6c65 732c 2020 4e65 7874 3a20 5472 616e  les,  Next: Tran\n+0000c4a0: 7370 6172 656e 6379 2c20 2050 7265 763a  sparency,  Prev:\n+0000c4b0: 2044 6f74 7320 696e 2054 696b 5a2f 5047   Dots in TikZ/PG\n+0000c4c0: 462c 2020 5570 3a20 4f70 7469 6f6e 730a  F,  Up: Options.\n+0000c4d0: 0a33 2e31 2e35 2e34 2027 5469 6b5a 2f50  .3.1.5.4 'TikZ/P\n+0000c4e0: 4746 2720 7573 6572 2d64 6566 696e 6564  GF' user-defined\n+0000c4f0: 2073 7479 6c65 730a 2e2e 2e2e 2e2e 2e2e   styles.........\n 0000c500: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000c510: 2e2e 2e2e 2e2e 2e2e 0a0a 2754 696b 5a2f  ..........'TikZ/\n-0000c520: 5047 4627 2061 6c6c 6f77 7320 6e61 6d65  PGF' allows name\n-0000c530: 6420 7374 796c 6573 2064 6566 696e 6564  d styles defined\n-0000c540: 2062 7920 7468 6520 7573 6572 2c20 666f   by the user, fo\n-0000c550: 7220 6578 616d 706c 650a 2020 5c74 696b  r example.  \\tik\n-0000c560: 7a73 7479 6c65 7b6d 7970 6f6c 7967 6f6e  zstyle{mypolygon\n-0000c570: 7374 796c 657d 203d 205b 6669 6c6c 3d62  style} = [fill=b\n-0000c580: 6c75 6521 3230 2c66 696c 6c20 6f70 6163  lue!20,fill opac\n-0000c590: 6974 793d 302e 385d 2020 0a20 205c 7469  ity=0.8]  .  \\ti\n-0000c5a0: 6b7a 7374 796c 657b 6d79 6c69 6e65 7374  kzstyle{mylinest\n-0000c5b0: 796c 657d 203d 205b 7265 6421 3230 2c64  yle} = [red!20,d\n-0000c5c0: 6173 6865 645d 0a53 696e 6365 2027 736b  ashed].Since 'sk\n-0000c5d0: 6574 6368 2720 6861 7320 6e6f 2069 6e66  etch' has no inf\n-0000c5e0: 6f72 6d61 7469 6f6e 206f 6e20 7468 6520  ormation on the \n-0000c5f0: 636f 6e74 656e 7473 206f 6620 7375 6368  contents of such\n-0000c600: 2073 7479 6c65 732c 2069 740a 6f6d 6974   styles, it.omit\n-0000c610: 7320 7468 656d 2065 6e74 6972 656c 7920  s them entirely \n-0000c620: 6672 6f6d 206c 696e 6573 2c20 706f 6c79  from lines, poly\n-0000c630: 676f 6e73 2c20 616e 6420 7468 6569 7220  gons, and their \n-0000c640: 6564 6765 7320 6475 7269 6e67 206f 7074  edges during opt\n-0000c650: 696f 6e0a 7370 6c69 7474 696e 672e 2020  ion.splitting.  \n-0000c660: 466f 7220 6578 616d 706c 652c 0a20 2070  For example,.  p\n-0000c670: 6f6c 7967 6f6e 5b73 7479 6c65 3d6d 7970  olygon[style=myp\n-0000c680: 6f6c 7967 6f6e 7374 796c 652c 7374 796c  olygonstyle,styl\n-0000c690: 653d 7468 6963 6b5d 2830 2c30 2c31 2928  e=thick](0,0,1)(\n-0000c6a0: 312c 302c 3029 2830 2c31 2c30 290a 2020  1,0,0)(0,1,0).  \n-0000c6b0: 6c69 6e65 5b73 7479 6c65 3d6d 796c 696e  line[style=mylin\n-0000c6c0: 6573 7479 6c65 5d28 2d31 2c2d 312c 2d31  estyle](-1,-1,-1\n-0000c6d0: 2928 322c 322c 3229 0a70 726f 6475 6365  )(2,2,2).produce\n-0000c6e0: 7320 7468 6520 2754 696b 5a27 206f 7574  s the 'TikZ' out\n-0000c6f0: 7075 740a 2020 5c64 7261 7728 2d31 2c2d  put.  \\draw(-1,-\n-0000c700: 3129 2d2d 282e 3333 332c 2e33 3333 293b  1)--(.333,.333);\n-0000c710: 0a20 205c 6669 6c6c 6472 6177 5b74 6869  .  \\filldraw[thi\n-0000c720: 636b 2c66 696c 6c3d 7768 6974 655d 2830  ck,fill=white](0\n-0000c730: 2c30 292d 2d28 312c 3029 2d2d 2830 2c31  ,0)--(1,0)--(0,1\n-0000c740: 292d 2d63 7963 6c65 3b0a 2020 5c64 7261  )--cycle;.  \\dra\n-0000c750: 7728 2e33 3333 2c2e 3333 3329 2d2d 2832  w(.333,.333)--(2\n-0000c760: 2c32 293b 0a4e 6f74 6520 7468 6174 2074  ,2);.Note that t\n-0000c770: 6865 2075 7365 722d 6465 6669 6e65 6420  he user-defined \n-0000c780: 7374 796c 6573 2061 7265 206e 6f74 2070  styles are not p\n-0000c790: 7265 7365 6e74 2e20 2053 6b65 7463 6820  resent.  Sketch \n-0000c7a0: 616c 736f 2069 7373 7565 730a 7761 726e  also issues.warn\n-0000c7b0: 696e 6773 3a0a 2020 7761 726e 696e 672c  ings:.  warning,\n-0000c7c0: 2075 6e6b 6e6f 776e 2070 6f6c 7967 6f6e   unknown polygon\n-0000c7d0: 206f 7074 696f 6e20 7374 796c 653d 6d79   option style=my\n-0000c7e0: 706f 6c79 676f 6e73 7479 6c65 2077 696c  polygonstyle wil\n-0000c7f0: 6c20 6265 2069 676e 6f72 6564 0a20 2077  l be ignored.  w\n-0000c800: 6172 6e69 6e67 2c20 756e 6b6e 6f77 6e20  arning, unknown \n-0000c810: 6c69 6e65 206f 7074 696f 6e20 7374 796c  line option styl\n-0000c820: 653d 6d79 6c69 6e65 7374 796c 6520 7769  e=mylinestyle wi\n-0000c830: 6c6c 2062 6520 6967 6e6f 7265 640a 0a20  ll be ignored.. \n-0000c840: 2020 5468 6520 7265 6d65 6479 2069 7320    The remedy is \n-0000c850: 746f 2073 7461 7465 2065 7870 6c69 6369  to state explici\n-0000c860: 746c 7920 7768 6574 6865 7220 6120 7573  tly whether a us\n-0000c870: 6572 2d64 6566 696e 6564 2073 7479 6c65  er-defined style\n-0000c880: 2073 686f 756c 640a 6265 2061 7474 6368   should.be attch\n-0000c890: 6564 2074 6f20 706f 6c79 676f 6e73 206f  ed to polygons o\n-0000c8a0: 7220 6c69 6e65 7320 696e 2074 6865 2027  r lines in the '\n-0000c8b0: 5469 6b5a 2720 6f75 7470 7574 2075 7369  TikZ' output usi\n-0000c8c0: 6e67 0a5f 7073 6575 646f 2d6f 7074 696f  ng._pseudo-optio\n-0000c8d0: 6e73 5f20 2766 696c 6c20 7374 796c 6527  ns_ 'fill style'\n-0000c8e0: 2061 6e64 2027 6c69 6e65 2073 7479 6c65   and 'line style\n-0000c8f0: 272c 0a20 2070 6f6c 7967 6f6e 5b66 696c  ',.  polygon[fil\n-0000c900: 6c20 7374 796c 653d 6d79 706f 6c79 676f  l style=mypolygo\n-0000c910: 6e73 7479 6c65 2c73 7479 6c65 3d74 6869  nstyle,style=thi\n-0000c920: 636b 5d28 302c 302c 3129 2831 2c30 2c30  ck](0,0,1)(1,0,0\n-0000c930: 2928 302c 312c 3029 0a20 206c 696e 655b  )(0,1,0).  line[\n-0000c940: 6c69 6e65 2073 7479 6c65 3d6d 796c 696e  line style=mylin\n-0000c950: 6573 7479 6c65 5d28 2d31 2c2d 312c 2d31  estyle](-1,-1,-1\n-0000c960: 2928 322c 322c 3229 0a4e 6f77 2c20 7468  )(2,2,2).Now, th\n-0000c970: 6520 6f75 7470 7574 2069 730a 2020 5c64  e output is.  \\d\n-0000c980: 7261 775b 6d79 6c69 6e65 7374 796c 655d  raw[mylinestyle]\n-0000c990: 282d 312c 2d31 292d 2d28 2e33 3333 2c2e  (-1,-1)--(.333,.\n-0000c9a0: 3333 3329 3b0a 2020 5c66 696c 6c64 7261  333);.  \\filldra\n-0000c9b0: 775b 6d79 706f 6c79 676f 6e73 7479 6c65  w[mypolygonstyle\n-0000c9c0: 2c74 6869 636b 5d28 302c 3029 2d2d 2831  ,thick](0,0)--(1\n-0000c9d0: 2c30 292d 2d28 302c 3129 2d2d 6379 636c  ,0)--(0,1)--cycl\n-0000c9e0: 653b 0a20 205c 6472 6177 5b6d 796c 696e  e;.  \\draw[mylin\n-0000c9f0: 6573 7479 6c65 5d28 2e33 3333 2c2e 3333  estyle](.333,.33\n-0000ca00: 3329 2d2d 2832 2c32 293b 0a0a 2020 2041  3)--(2,2);..   A\n-0000ca10: 2075 7365 6675 6c20 7465 6368 6e69 7175   useful techniqu\n-0000ca20: 6520 6973 2074 6f20 696e 636c 7564 6520  e is to include \n-0000ca30: 7573 6572 2d64 6566 696e 6564 2073 7479  user-defined sty\n-0000ca40: 6c65 2064 6566 696e 6974 696f 6e73 2069  le definitions i\n-0000ca50: 6e0a 2773 6b65 7463 6827 2063 6f64 6520  n.'sketch' code \n-0000ca60: 6173 2027 7370 6563 6961 6c27 7320 7769  as 'special's wi\n-0000ca70: 7468 206f 7074 696f 6e20 275b 6c61 793d  th option '[lay=\n-0000ca80: 756e 6465 725d 2720 746f 2065 6e73 7572  under]' to ensur\n-0000ca90: 6520 7468 6174 2074 6865 0a73 7479 6c65  e that the.style\n-0000caa0: 7320 6172 6520 656d 6974 7465 6420 6669  s are emitted fi\n-0000cab0: 7273 7420 696e 2074 6865 206f 7574 7075  rst in the outpu\n-0000cac0: 742c 2062 6566 6f72 6520 616e 7920 7573  t, before any us\n-0000cad0: 6573 206f 6620 7468 6520 7374 796c 650a  es of the style.\n-0000cae0: 6e61 6d65 732e 2020 2831 2920 2046 6f72  names.  (1)  For\n-0000caf0: 2065 7861 6d70 6c65 2c0a 2020 7370 6563   example,.  spec\n-0000cb00: 6961 6c7c 5c74 696b 7a73 7479 6c65 7b6d  ial|\\tikzstyle{m\n-0000cb10: 7970 6f6c 7967 6f6e 7374 796c 657d 203d  ypolygonstyle} =\n-0000cb20: 205b 6669 6c6c 3d62 6c75 6521 3230 2c66   [fill=blue!20,f\n-0000cb30: 696c 6c20 6f70 6163 6974 793d 302e 385d  ill opacity=0.8]\n-0000cb40: 7c5b 6c61 793d 756e 6465 725d 0a20 2073  |[lay=under].  s\n-0000cb50: 7065 6369 616c 7c5c 7469 6b7a 7374 796c  pecial|\\tikzstyl\n-0000cb60: 657b 6d79 6c69 6e65 7374 796c 657d 203d  e{mylinestyle} =\n-0000cb70: 205b 7265 6421 3230 2c64 6173 6865 645d   [red!20,dashed]\n-0000cb80: 7c5b 6c61 793d 756e 6465 725d 0a54 6865  |[lay=under].The\n-0000cb90: 2061 7574 686f 7220 6973 2072 6573 706f   author is respo\n-0000cba0: 6e73 6962 6c65 2066 6f72 2075 7369 6e67  nsible for using\n-0000cbb0: 2074 6865 206b 6579 2c20 276c 696e 6520   the key, 'line \n-0000cbc0: 7374 796c 6527 206f 7220 2766 696c 6c0a  style' or 'fill.\n-0000cbd0: 7374 796c 6527 2c20 7468 6174 206d 6174  style', that mat\n-0000cbe0: 6368 6573 2074 6865 2063 6f6e 7465 6e74  ches the content\n-0000cbf0: 206f 6620 7468 6520 7374 796c 6520 6465   of the style de\n-0000cc00: 6669 6e69 7469 6f6e 2e0a 0a20 2020 2d2d  finition...   --\n-0000cc10: 2d2d 2d2d 2d2d 2d2d 2046 6f6f 746e 6f74  -------- Footnot\n-0000cc20: 6573 202d 2d2d 2d2d 2d2d 2d2d 2d0a 0a20  es ----------.. \n-0000cc30: 2020 2831 2920 5468 6973 2063 6c65 7665    (1) This cleve\n-0000cc40: 7220 7472 6963 6b20 6973 2064 7565 2074  r trick is due t\n-0000cc50: 6f20 4b6a 656c 6c20 4d61 676e 6520 4661  o Kjell Magne Fa\n-0000cc60: 7573 6b65 2e0a 0a1f 0a46 696c 653a 2073  uske.....File: s\n-0000cc70: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n-0000cc80: 653a 2054 7261 6e73 7061 7265 6e63 792c  e: Transparency,\n-0000cc90: 2020 4e65 7874 3a20 496e 7465 726e 616c    Next: Internal\n-0000cca0: 206f 7074 696f 6e73 2c20 2050 7265 763a   options,  Prev:\n-0000ccb0: 2054 696b 5a2f 5047 4620 7573 6572 2d64   TikZ/PGF user-d\n-0000ccc0: 6566 696e 6564 2073 7479 6c65 732c 2020  efined styles,  \n-0000ccd0: 5570 3a20 4f70 7469 6f6e 730a 0a33 2e31  Up: Options..3.1\n-0000cce0: 2e35 2e35 2054 7261 6e73 7061 7265 6e63  .5.5 Transparenc\n-0000ccf0: 790a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  y...............\n-0000cd00: 2e2e 2e2e 2e2e 0a0a 426f 7468 2027 5053  ........Both 'PS\n-0000cd10: 5472 6963 6b73 2720 616e 6420 2754 696b  Tricks' and 'Tik\n-0000cd20: 5a2f 5047 4627 2073 7570 706f 7274 2070  Z/PGF' support p\n-0000cd30: 6f6c 7967 6f6e 206f 7074 696f 6e73 2074  olygon options t\n-0000cd40: 6861 7420 6861 7665 2074 6865 0a65 6666  hat have the.eff\n-0000cd50: 6563 7420 6f66 206d 616b 696e 6720 7468  ect of making th\n-0000cd60: 6520 706f 6c79 676f 6e20 6170 7065 6172  e polygon appear\n-0000cd70: 2074 7261 6e73 7061 7265 6e74 2e20 2046   transparent.  F\n-0000cd80: 6f72 2027 5053 5472 6963 6b73 272c 0a6b  or 'PSTricks',.k\n-0000cd90: 6579 776f 7264 2027 7472 616e 7370 616c  eyword 'transpal\n-0000cda0: 7068 6127 2077 6173 2075 7365 6420 6475  pha' was used du\n-0000cdb0: 7269 6e67 2069 6e69 7469 616c 2064 6576  ring initial dev\n-0000cdc0: 656c 6f70 6d65 6e74 206f 660a 7472 616e  elopment of.tran\n-0000cdd0: 7370 6172 656e 6379 2066 6561 7475 7265  sparency feature\n-0000cde0: 732c 2061 6e64 2027 6f70 6163 6974 7927  s, and 'opacity'\n-0000cdf0: 2077 6173 2061 646f 7074 6564 206c 6174   was adopted lat\n-0000ce00: 6572 2e20 2027 536b 6574 6368 2720 686f  er.  'Sketch' ho\n-0000ce10: 6e6f 7273 0a62 6f74 682e 2020 2754 696b  nors.both.  'Tik\n-0000ce20: 5a2f 5047 4627 2075 7365 7320 276f 7061  Z/PGF' uses 'opa\n-0000ce30: 6369 7479 2720 6f6e 6c79 2e20 2057 6865  city' only.  Whe\n-0000ce40: 6e20 7472 616e 7370 6172 656e 7420 706f  n transparent po\n-0000ce50: 6c79 676f 6e73 2061 7265 2069 6e0a 7468  lygons are in.th\n-0000ce60: 6520 666f 7265 6772 6f75 6e64 2c20 6f62  e foreground, ob\n-0000ce70: 6a65 6374 7320 6265 6869 6e64 2074 6865  jects behind the\n-0000ce80: 6d20 2864 7261 776e 2065 6172 6c69 6572  m (drawn earlier\n-0000ce90: 2920 6172 6520 7669 7369 626c 6520 7769  ) are visible wi\n-0000cea0: 7468 0a63 6f6c 6f72 2073 7562 6475 6564  th.color subdued\n-0000ceb0: 2061 6e64 2074 696e 7465 642e 2020 5468   and tinted.  Th\n-0000cec0: 6520 6869 6464 656e 2073 7572 6661 6365  e hidden surface\n-0000ced0: 2061 6c67 6f72 6974 686d 206f 6620 2773   algorithm of 's\n-0000cee0: 6b65 7463 6827 0a77 6f72 6b73 2077 656c  ketch'.works wel\n-0000cef0: 6c20 7769 7468 2073 7563 6820 7472 616e  l with such tran\n-0000cf00: 7370 6172 656e 7420 706f 6c79 676f 6e73  sparent polygons\n-0000cf10: 2e0a 0a20 2020 4e6f 7465 2074 6861 7420  ...   Note that \n-0000cf20: 6375 6c6c 3d66 616c 7365 206d 7573 7420  cull=false must \n-0000cf30: 6265 2075 7365 6420 666f 7220 7265 6172  be used for rear\n-0000cf40: 2d66 6163 696e 6720 706f 6c79 676f 6e73  -facing polygons\n-0000cf50: 2074 6f20 6265 0a76 6973 6962 6c65 2077   to be.visible w\n-0000cf60: 6865 6e20 706f 7369 7469 6f6e 6564 2062  hen positioned b\n-0000cf70: 6568 696e 6420 6f74 6865 7220 7472 616e  ehind other tran\n-0000cf80: 7370 6172 656e 7420 7375 7266 6163 6573  sparent surfaces\n-0000cf90: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463  .....File: sketc\n-0000cfa0: 682e 696e 666f 2c20 204e 6f64 653a 2049  h.info,  Node: I\n-0000cfb0: 6e74 6572 6e61 6c20 6f70 7469 6f6e 732c  nternal options,\n-0000cfc0: 2020 5072 6576 3a20 5472 616e 7370 6172    Prev: Transpar\n-0000cfd0: 656e 6379 2c20 2055 703a 204f 7074 696f  ency,  Up: Optio\n-0000cfe0: 6e73 0a0a 332e 312e 352e 3620 496e 7465  ns..3.1.5.6 Inte\n-0000cff0: 726e 616c 206f 7074 696f 6e73 0a2e 2e2e  rnal options....\n-0000d000: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000d010: 2e2e 2e2e 2e0a 0a54 6865 7265 2061 7265  .......There are\n-0000d020: 2061 6c73 6f20 5f69 6e74 6572 6e61 6c5f   also _internal_\n-0000d030: 206f 7074 696f 6e73 2075 7365 6420 6f6e   options used on\n-0000d040: 6c79 2062 7920 2773 6b65 7463 6827 2061  ly by 'sketch' a\n-0000d050: 6e64 206e 6f74 2070 6173 7365 640a 6f6e  nd not passed.on\n-0000d060: 2074 6f20 2750 5354 7269 636b 7327 2e20   to 'PSTricks'. \n-0000d070: 2054 6865 7365 2061 7265 2073 756d 6d61   These are summa\n-0000d080: 7269 7a65 6420 696e 2074 6865 2066 6f6c  rized in the fol\n-0000d090: 6c6f 7769 6e67 2074 6162 6c65 2e0a 4b65  lowing table..Ke\n-0000d0a0: 7920 2020 2020 2020 506f 7373 6962 6c65  y       Possible\n-0000d0b0: 2076 616c 7565 7320 2020 2020 2020 2020   values         \n-0000d0c0: 4465 7363 7269 7074 696f 6e0a 2d2d 2d2d  Description.----\n-0000d0d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n+0000c510: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a  ................\n+0000c520: 2754 696b 5a2f 5047 4627 2061 6c6c 6f77  'TikZ/PGF' allow\n+0000c530: 7320 6e61 6d65 6420 7374 796c 6573 2064  s named styles d\n+0000c540: 6566 696e 6564 2062 7920 7468 6520 7573  efined by the us\n+0000c550: 6572 2c20 666f 7220 6578 616d 706c 650a  er, for example.\n+0000c560: 2020 5c74 696b 7a73 7479 6c65 7b6d 7970    \\tikzstyle{myp\n+0000c570: 6f6c 7967 6f6e 7374 796c 657d 203d 205b  olygonstyle} = [\n+0000c580: 6669 6c6c 3d62 6c75 6521 3230 2c66 696c  fill=blue!20,fil\n+0000c590: 6c20 6f70 6163 6974 793d 302e 385d 2020  l opacity=0.8]  \n+0000c5a0: 0a20 205c 7469 6b7a 7374 796c 657b 6d79  .  \\tikzstyle{my\n+0000c5b0: 6c69 6e65 7374 796c 657d 203d 205b 7265  linestyle} = [re\n+0000c5c0: 6421 3230 2c64 6173 6865 645d 0a53 696e  d!20,dashed].Sin\n+0000c5d0: 6365 2027 736b 6574 6368 2720 6861 7320  ce 'sketch' has \n+0000c5e0: 6e6f 2069 6e66 6f72 6d61 7469 6f6e 206f  no information o\n+0000c5f0: 6e20 7468 6520 636f 6e74 656e 7473 206f  n the contents o\n+0000c600: 6620 7375 6368 2073 7479 6c65 732c 2069  f such styles, i\n+0000c610: 740a 6f6d 6974 7320 7468 656d 2065 6e74  t.omits them ent\n+0000c620: 6972 656c 7920 6672 6f6d 206c 696e 6573  irely from lines\n+0000c630: 2c20 706f 6c79 676f 6e73 2c20 616e 6420  , polygons, and \n+0000c640: 7468 6569 7220 6564 6765 7320 6475 7269  their edges duri\n+0000c650: 6e67 206f 7074 696f 6e0a 7370 6c69 7474  ng option.splitt\n+0000c660: 696e 672e 2020 466f 7220 6578 616d 706c  ing.  For exampl\n+0000c670: 652c 0a20 2070 6f6c 7967 6f6e 5b73 7479  e,.  polygon[sty\n+0000c680: 6c65 3d6d 7970 6f6c 7967 6f6e 7374 796c  le=mypolygonstyl\n+0000c690: 652c 7374 796c 653d 7468 6963 6b5d 2830  e,style=thick](0\n+0000c6a0: 2c30 2c31 2928 312c 302c 3029 2830 2c31  ,0,1)(1,0,0)(0,1\n+0000c6b0: 2c30 290a 2020 6c69 6e65 5b73 7479 6c65  ,0).  line[style\n+0000c6c0: 3d6d 796c 696e 6573 7479 6c65 5d28 2d31  =mylinestyle](-1\n+0000c6d0: 2c2d 312c 2d31 2928 322c 322c 3229 0a70  ,-1,-1)(2,2,2).p\n+0000c6e0: 726f 6475 6365 7320 7468 6520 2754 696b  roduces the 'Tik\n+0000c6f0: 5a27 206f 7574 7075 740a 2020 5c64 7261  Z' output.  \\dra\n+0000c700: 7728 2d31 2c2d 3129 2d2d 282e 3333 332c  w(-1,-1)--(.333,\n+0000c710: 2e33 3333 293b 0a20 205c 6669 6c6c 6472  .333);.  \\filldr\n+0000c720: 6177 5b74 6869 636b 2c66 696c 6c3d 7768  aw[thick,fill=wh\n+0000c730: 6974 655d 2830 2c30 292d 2d28 312c 3029  ite](0,0)--(1,0)\n+0000c740: 2d2d 2830 2c31 292d 2d63 7963 6c65 3b0a  --(0,1)--cycle;.\n+0000c750: 2020 5c64 7261 7728 2e33 3333 2c2e 3333    \\draw(.333,.33\n+0000c760: 3329 2d2d 2832 2c32 293b 0a4e 6f74 6520  3)--(2,2);.Note \n+0000c770: 7468 6174 2074 6865 2075 7365 722d 6465  that the user-de\n+0000c780: 6669 6e65 6420 7374 796c 6573 2061 7265  fined styles are\n+0000c790: 206e 6f74 2070 7265 7365 6e74 2e20 2053   not present.  S\n+0000c7a0: 6b65 7463 6820 616c 736f 2069 7373 7565  ketch also issue\n+0000c7b0: 730a 7761 726e 696e 6773 3a0a 2020 7761  s.warnings:.  wa\n+0000c7c0: 726e 696e 672c 2075 6e6b 6e6f 776e 2070  rning, unknown p\n+0000c7d0: 6f6c 7967 6f6e 206f 7074 696f 6e20 7374  olygon option st\n+0000c7e0: 796c 653d 6d79 706f 6c79 676f 6e73 7479  yle=mypolygonsty\n+0000c7f0: 6c65 2077 696c 6c20 6265 2069 676e 6f72  le will be ignor\n+0000c800: 6564 0a20 2077 6172 6e69 6e67 2c20 756e  ed.  warning, un\n+0000c810: 6b6e 6f77 6e20 6c69 6e65 206f 7074 696f  known line optio\n+0000c820: 6e20 7374 796c 653d 6d79 6c69 6e65 7374  n style=mylinest\n+0000c830: 796c 6520 7769 6c6c 2062 6520 6967 6e6f  yle will be igno\n+0000c840: 7265 640a 0a20 2020 5468 6520 7265 6d65  red..   The reme\n+0000c850: 6479 2069 7320 746f 2073 7461 7465 2065  dy is to state e\n+0000c860: 7870 6c69 6369 746c 7920 7768 6574 6865  xplicitly whethe\n+0000c870: 7220 6120 7573 6572 2d64 6566 696e 6564  r a user-defined\n+0000c880: 2073 7479 6c65 2073 686f 756c 640a 6265   style should.be\n+0000c890: 2061 7474 6368 6564 2074 6f20 706f 6c79   attched to poly\n+0000c8a0: 676f 6e73 206f 7220 6c69 6e65 7320 696e  gons or lines in\n+0000c8b0: 2074 6865 2027 5469 6b5a 2720 6f75 7470   the 'TikZ' outp\n+0000c8c0: 7574 2075 7369 6e67 0a5f 7073 6575 646f  ut using._pseudo\n+0000c8d0: 2d6f 7074 696f 6e73 5f20 2766 696c 6c20  -options_ 'fill \n+0000c8e0: 7374 796c 6527 2061 6e64 2027 6c69 6e65  style' and 'line\n+0000c8f0: 2073 7479 6c65 272c 0a20 2070 6f6c 7967   style',.  polyg\n+0000c900: 6f6e 5b66 696c 6c20 7374 796c 653d 6d79  on[fill style=my\n+0000c910: 706f 6c79 676f 6e73 7479 6c65 2c73 7479  polygonstyle,sty\n+0000c920: 6c65 3d74 6869 636b 5d28 302c 302c 3129  le=thick](0,0,1)\n+0000c930: 2831 2c30 2c30 2928 302c 312c 3029 0a20  (1,0,0)(0,1,0). \n+0000c940: 206c 696e 655b 6c69 6e65 2073 7479 6c65   line[line style\n+0000c950: 3d6d 796c 696e 6573 7479 6c65 5d28 2d31  =mylinestyle](-1\n+0000c960: 2c2d 312c 2d31 2928 322c 322c 3229 0a4e  ,-1,-1)(2,2,2).N\n+0000c970: 6f77 2c20 7468 6520 6f75 7470 7574 2069  ow, the output i\n+0000c980: 730a 2020 5c64 7261 775b 6d79 6c69 6e65  s.  \\draw[myline\n+0000c990: 7374 796c 655d 282d 312c 2d31 292d 2d28  style](-1,-1)--(\n+0000c9a0: 2e33 3333 2c2e 3333 3329 3b0a 2020 5c66  .333,.333);.  \\f\n+0000c9b0: 696c 6c64 7261 775b 6d79 706f 6c79 676f  illdraw[mypolygo\n+0000c9c0: 6e73 7479 6c65 2c74 6869 636b 5d28 302c  nstyle,thick](0,\n+0000c9d0: 3029 2d2d 2831 2c30 292d 2d28 302c 3129  0)--(1,0)--(0,1)\n+0000c9e0: 2d2d 6379 636c 653b 0a20 205c 6472 6177  --cycle;.  \\draw\n+0000c9f0: 5b6d 796c 696e 6573 7479 6c65 5d28 2e33  [mylinestyle](.3\n+0000ca00: 3333 2c2e 3333 3329 2d2d 2832 2c32 293b  33,.333)--(2,2);\n+0000ca10: 0a0a 2020 2041 2075 7365 6675 6c20 7465  ..   A useful te\n+0000ca20: 6368 6e69 7175 6520 6973 2074 6f20 696e  chnique is to in\n+0000ca30: 636c 7564 6520 7573 6572 2d64 6566 696e  clude user-defin\n+0000ca40: 6564 2073 7479 6c65 2064 6566 696e 6974  ed style definit\n+0000ca50: 696f 6e73 2069 6e0a 2773 6b65 7463 6827  ions in.'sketch'\n+0000ca60: 2063 6f64 6520 6173 2027 7370 6563 6961   code as 'specia\n+0000ca70: 6c27 7320 7769 7468 206f 7074 696f 6e20  l's with option \n+0000ca80: 275b 6c61 793d 756e 6465 725d 2720 746f  '[lay=under]' to\n+0000ca90: 2065 6e73 7572 6520 7468 6174 2074 6865   ensure that the\n+0000caa0: 0a73 7479 6c65 7320 6172 6520 656d 6974  .styles are emit\n+0000cab0: 7465 6420 6669 7273 7420 696e 2074 6865  ted first in the\n+0000cac0: 206f 7574 7075 742c 2062 6566 6f72 6520   output, before \n+0000cad0: 616e 7920 7573 6573 206f 6620 7468 6520  any uses of the \n+0000cae0: 7374 796c 650a 6e61 6d65 732e 2020 2831  style.names.  (1\n+0000caf0: 2920 2046 6f72 2065 7861 6d70 6c65 2c0a  )  For example,.\n+0000cb00: 2020 7370 6563 6961 6c7c 5c74 696b 7a73    special|\\tikzs\n+0000cb10: 7479 6c65 7b6d 7970 6f6c 7967 6f6e 7374  tyle{mypolygonst\n+0000cb20: 796c 657d 203d 205b 6669 6c6c 3d62 6c75  yle} = [fill=blu\n+0000cb30: 6521 3230 2c66 696c 6c20 6f70 6163 6974  e!20,fill opacit\n+0000cb40: 793d 302e 385d 7c5b 6c61 793d 756e 6465  y=0.8]|[lay=unde\n+0000cb50: 725d 0a20 2073 7065 6369 616c 7c5c 7469  r].  special|\\ti\n+0000cb60: 6b7a 7374 796c 657b 6d79 6c69 6e65 7374  kzstyle{mylinest\n+0000cb70: 796c 657d 203d 205b 7265 6421 3230 2c64  yle} = [red!20,d\n+0000cb80: 6173 6865 645d 7c5b 6c61 793d 756e 6465  ashed]|[lay=unde\n+0000cb90: 725d 0a54 6865 2061 7574 686f 7220 6973  r].The author is\n+0000cba0: 2072 6573 706f 6e73 6962 6c65 2066 6f72   responsible for\n+0000cbb0: 2075 7369 6e67 2074 6865 206b 6579 2c20   using the key, \n+0000cbc0: 276c 696e 6520 7374 796c 6527 206f 7220  'line style' or \n+0000cbd0: 2766 696c 6c0a 7374 796c 6527 2c20 7468  'fill.style', th\n+0000cbe0: 6174 206d 6174 6368 6573 2074 6865 2063  at matches the c\n+0000cbf0: 6f6e 7465 6e74 206f 6620 7468 6520 7374  ontent of the st\n+0000cc00: 796c 6520 6465 6669 6e69 7469 6f6e 2e0a  yle definition..\n+0000cc10: 0a20 2020 2d2d 2d2d 2d2d 2d2d 2d2d 2046  .   ---------- F\n+0000cc20: 6f6f 746e 6f74 6573 202d 2d2d 2d2d 2d2d  ootnotes -------\n+0000cc30: 2d2d 2d0a 0a20 2020 2831 2920 5468 6973  ---..   (1) This\n+0000cc40: 2063 6c65 7665 7220 7472 6963 6b20 6973   clever trick is\n+0000cc50: 2064 7565 2074 6f20 4b6a 656c 6c20 4d61   due to Kjell Ma\n+0000cc60: 676e 6520 4661 7573 6b65 2e0a 0a1f 0a46  gne Fauske.....F\n+0000cc70: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n+0000cc80: 2c20 204e 6f64 653a 2054 7261 6e73 7061  ,  Node: Transpa\n+0000cc90: 7265 6e63 792c 2020 4e65 7874 3a20 496e  rency,  Next: In\n+0000cca0: 7465 726e 616c 206f 7074 696f 6e73 2c20  ternal options, \n+0000ccb0: 2050 7265 763a 2054 696b 5a2f 5047 4620   Prev: TikZ/PGF \n+0000ccc0: 7573 6572 2d64 6566 696e 6564 2073 7479  user-defined sty\n+0000ccd0: 6c65 732c 2020 5570 3a20 4f70 7469 6f6e  les,  Up: Option\n+0000cce0: 730a 0a33 2e31 2e35 2e35 2054 7261 6e73  s..3.1.5.5 Trans\n+0000ccf0: 7061 7265 6e63 790a 2e2e 2e2e 2e2e 2e2e  parency.........\n+0000cd00: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 426f  ..............Bo\n+0000cd10: 7468 2027 5053 5472 6963 6b73 2720 616e  th 'PSTricks' an\n+0000cd20: 6420 2754 696b 5a2f 5047 4627 2073 7570  d 'TikZ/PGF' sup\n+0000cd30: 706f 7274 2070 6f6c 7967 6f6e 206f 7074  port polygon opt\n+0000cd40: 696f 6e73 2074 6861 7420 6861 7665 2074  ions that have t\n+0000cd50: 6865 0a65 6666 6563 7420 6f66 206d 616b  he.effect of mak\n+0000cd60: 696e 6720 7468 6520 706f 6c79 676f 6e20  ing the polygon \n+0000cd70: 6170 7065 6172 2074 7261 6e73 7061 7265  appear transpare\n+0000cd80: 6e74 2e20 2046 6f72 2027 5053 5472 6963  nt.  For 'PSTric\n+0000cd90: 6b73 272c 0a6b 6579 776f 7264 2027 7472  ks',.keyword 'tr\n+0000cda0: 616e 7370 616c 7068 6127 2077 6173 2075  anspalpha' was u\n+0000cdb0: 7365 6420 6475 7269 6e67 2069 6e69 7469  sed during initi\n+0000cdc0: 616c 2064 6576 656c 6f70 6d65 6e74 206f  al development o\n+0000cdd0: 660a 7472 616e 7370 6172 656e 6379 2066  f.transparency f\n+0000cde0: 6561 7475 7265 732c 2061 6e64 2027 6f70  eatures, and 'op\n+0000cdf0: 6163 6974 7927 2077 6173 2061 646f 7074  acity' was adopt\n+0000ce00: 6564 206c 6174 6572 2e20 2027 536b 6574  ed later.  'Sket\n+0000ce10: 6368 2720 686f 6e6f 7273 0a62 6f74 682e  ch' honors.both.\n+0000ce20: 2020 2754 696b 5a2f 5047 4627 2075 7365    'TikZ/PGF' use\n+0000ce30: 7320 276f 7061 6369 7479 2720 6f6e 6c79  s 'opacity' only\n+0000ce40: 2e20 2057 6865 6e20 7472 616e 7370 6172  .  When transpar\n+0000ce50: 656e 7420 706f 6c79 676f 6e73 2061 7265  ent polygons are\n+0000ce60: 2069 6e0a 7468 6520 666f 7265 6772 6f75   in.the foregrou\n+0000ce70: 6e64 2c20 6f62 6a65 6374 7320 6265 6869  nd, objects behi\n+0000ce80: 6e64 2074 6865 6d20 2864 7261 776e 2065  nd them (drawn e\n+0000ce90: 6172 6c69 6572 2920 6172 6520 7669 7369  arlier) are visi\n+0000cea0: 626c 6520 7769 7468 0a63 6f6c 6f72 2073  ble with.color s\n+0000ceb0: 7562 6475 6564 2061 6e64 2074 696e 7465  ubdued and tinte\n+0000cec0: 642e 2020 5468 6520 6869 6464 656e 2073  d.  The hidden s\n+0000ced0: 7572 6661 6365 2061 6c67 6f72 6974 686d  urface algorithm\n+0000cee0: 206f 6620 2773 6b65 7463 6827 0a77 6f72   of 'sketch'.wor\n+0000cef0: 6b73 2077 656c 6c20 7769 7468 2073 7563  ks well with suc\n+0000cf00: 6820 7472 616e 7370 6172 656e 7420 706f  h transparent po\n+0000cf10: 6c79 676f 6e73 2e0a 0a20 2020 4e6f 7465  lygons...   Note\n+0000cf20: 2074 6861 7420 6375 6c6c 3d66 616c 7365   that cull=false\n+0000cf30: 206d 7573 7420 6265 2075 7365 6420 666f   must be used fo\n+0000cf40: 7220 7265 6172 2d66 6163 696e 6720 706f  r rear-facing po\n+0000cf50: 6c79 676f 6e73 2074 6f20 6265 0a76 6973  lygons to be.vis\n+0000cf60: 6962 6c65 2077 6865 6e20 706f 7369 7469  ible when positi\n+0000cf70: 6f6e 6564 2062 6568 696e 6420 6f74 6865  oned behind othe\n+0000cf80: 7220 7472 616e 7370 6172 656e 7420 7375  r transparent su\n+0000cf90: 7266 6163 6573 2e0a 0a1f 0a46 696c 653a  rfaces.....File:\n+0000cfa0: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n+0000cfb0: 6f64 653a 2049 6e74 6572 6e61 6c20 6f70  ode: Internal op\n+0000cfc0: 7469 6f6e 732c 2020 5072 6576 3a20 5472  tions,  Prev: Tr\n+0000cfd0: 616e 7370 6172 656e 6379 2c20 2055 703a  ansparency,  Up:\n+0000cfe0: 204f 7074 696f 6e73 0a0a 332e 312e 352e   Options..3.1.5.\n+0000cff0: 3620 496e 7465 726e 616c 206f 7074 696f  6 Internal optio\n+0000d000: 6e73 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ns..............\n+0000d010: 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a54 6865  .............The\n+0000d020: 7265 2061 7265 2061 6c73 6f20 5f69 6e74  re are also _int\n+0000d030: 6572 6e61 6c5f 206f 7074 696f 6e73 2075  ernal_ options u\n+0000d040: 7365 6420 6f6e 6c79 2062 7920 2773 6b65  sed only by 'ske\n+0000d050: 7463 6827 2061 6e64 206e 6f74 2070 6173  tch' and not pas\n+0000d060: 7365 640a 6f6e 2074 6f20 2750 5354 7269  sed.on to 'PSTri\n+0000d070: 636b 7327 2e20 2054 6865 7365 2061 7265  cks'.  These are\n+0000d080: 2073 756d 6d61 7269 7a65 6420 696e 2074   summarized in t\n+0000d090: 6865 2066 6f6c 6c6f 7769 6e67 2074 6162  he following tab\n+0000d0a0: 6c65 2e0a 4b65 7920 2020 2020 2020 506f  le..Key       Po\n+0000d0b0: 7373 6962 6c65 2076 616c 7565 7320 2020  ssible values   \n+0000d0c0: 2020 2020 2020 4465 7363 7269 7074 696f        Descriptio\n+0000d0d0: 6e0a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  n.--------------\n 0000d0e0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000d0f0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000d100: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 0000d110: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-0000d120: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a27 6375  ------------.'cu\n-0000d130: 6c6c 2720 2020 2027 7472 7565 272c 2027  ll'    'true', '\n-0000d140: 6661 6c73 6527 2020 2020 2020 2020 2054  false'         T\n-0000d150: 7572 6e20 6375 6c6c 696e 6720 6f66 2062  urn culling of b\n-0000d160: 6163 6b66 6163 6573 206f 6e20 616e 6420  ackfaces on and \n-0000d170: 6f66 6620 7265 7370 6563 7469 7665 6c79  off respectively\n-0000d180: 2066 6f72 2074 6869 730a 2020 2020 2020   for this.      \n+0000d120: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n+0000d130: 2d2d 0a27 6375 6c6c 2720 2020 2027 7472  --.'cull'    'tr\n+0000d140: 7565 272c 2027 6661 6c73 6527 2020 2020  ue', 'false'    \n+0000d150: 2020 2020 2054 7572 6e20 6375 6c6c 696e       Turn cullin\n+0000d160: 6720 6f66 2062 6163 6b66 6163 6573 206f  g of backfaces o\n+0000d170: 6e20 616e 6420 6f66 6620 7265 7370 6563  n and off respec\n+0000d180: 7469 7665 6c79 2066 6f72 2074 6869 730a  tively for this.\n 0000d190: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d1a0: 2020 2020 2020 2020 2020 2020 6f62 6a65              obje\n-0000d1b0: 6374 2e20 2054 6865 2064 6566 6175 6c74  ct.  The default\n-0000d1c0: 2076 616c 7565 2069 7320 2774 7275 6527   value is 'true'\n-0000d1d0: 2e0a 276c 6179 2720 2020 2020 276f 7665  ..'lay'     'ove\n-0000d1e0: 7227 2c20 2769 6e27 2c20 2775 6e64 6572  r', 'in', 'under\n-0000d1f0: 2720 2020 466f 7263 6520 7468 6973 206f  '   Force this o\n-0000d200: 626a 6563 7420 746f 2062 6520 2775 6e64  bject to be 'und\n-0000d210: 6572 2720 6f72 2027 6f76 6572 2720 616c  er' or 'over' al\n-0000d220: 6c20 6f74 6865 7220 6f62 6a65 6374 730a  l other objects.\n-0000d230: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000d1a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000d1b0: 2020 6f62 6a65 6374 2e20 2054 6865 2064    object.  The d\n+0000d1c0: 6566 6175 6c74 2076 616c 7565 2069 7320  efault value is \n+0000d1d0: 2774 7275 6527 2e0a 276c 6179 2720 2020  'true'..'lay'   \n+0000d1e0: 2020 276f 7665 7227 2c20 2769 6e27 2c20    'over', 'in', \n+0000d1f0: 2775 6e64 6572 2720 2020 466f 7263 6520  'under'   Force \n+0000d200: 7468 6973 206f 626a 6563 7420 746f 2062  this object to b\n+0000d210: 6520 2775 6e64 6572 2720 6f72 2027 6f76  e 'under' or 'ov\n+0000d220: 6572 2720 616c 6c20 6f74 6865 7220 6f62  er' all other ob\n+0000d230: 6a65 6374 730a 2020 2020 2020 2020 2020  jects.          \n 0000d240: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d250: 2020 696e 2074 6865 2064 6570 7468 2073    in the depth s\n-0000d260: 6f72 7420 6f72 6465 7220 6372 6561 7465  ort order create\n-0000d270: 6420 6279 2074 6865 2068 6964 6465 6e20  d by the hidden \n-0000d280: 7375 7266 6163 650a 2020 2020 2020 2020  surface.        \n+0000d250: 2020 2020 2020 2020 696e 2074 6865 2064          in the d\n+0000d260: 6570 7468 2073 6f72 7420 6f72 6465 7220  epth sort order \n+0000d270: 6372 6561 7465 6420 6279 2074 6865 2068  created by the h\n+0000d280: 6964 6465 6e20 7375 7266 6163 650a 2020  idden surface.  \n 0000d290: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d2a0: 2020 2020 2020 2020 2020 616c 676f 7269            algori\n-0000d2b0: 7468 6d2e 2020 5468 6520 6465 6661 756c  thm.  The defaul\n-0000d2c0: 7420 7661 6c75 6520 276f 7665 7227 2067  t value 'over' g\n-0000d2d0: 7561 7261 6e74 6565 7320 7468 6174 206f  uarantees that o\n-0000d2e0: 7574 7075 740a 2020 2020 2020 2020 2020  utput.          \n+0000d2a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000d2b0: 616c 676f 7269 7468 6d2e 2020 5468 6520  algorithm.  The \n+0000d2c0: 6465 6661 756c 7420 7661 6c75 6520 276f  default value 'o\n+0000d2d0: 7665 7227 2067 7561 7261 6e74 6565 7320  ver' guarantees \n+0000d2e0: 7468 6174 206f 7574 7075 740a 2020 2020  that output.    \n 0000d2f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d300: 2020 2020 2020 2020 6475 6520 746f 2074          due to t\n-0000d310: 6865 2027 7370 6563 6961 6c27 2077 696c  he 'special' wil\n-0000d320: 6c20 6265 2076 6973 6962 6c65 2e0a 2773  l be visible..'s\n-0000d330: 706c 6974 2720 2020 2774 7275 6527 2c20  plit'   'true', \n-0000d340: 2766 616c 7365 2720 2020 2020 2020 2020  'false'         \n-0000d350: 5475 726e 2073 706c 6974 7469 6e67 206f  Turn splitting o\n-0000d360: 6620 7377 6565 702d 6765 6e65 7261 7465  f sweep-generate\n-0000d370: 6420 626f 6479 2070 6f6c 7967 6f6e 7320  d body polygons \n-0000d380: 6f6e 2061 6e64 206f 6666 0a20 2020 2020  on and off.     \n-0000d390: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d3a0: 2020 2020 2020 2020 2020 2020 2072 6573               res\n-0000d3b0: 7065 6374 6976 656c 792e 2020 2a4e 6f74  pectively.  *Not\n-0000d3c0: 6520 5377 6565 7073 3a3a 2e20 2054 6865  e Sweeps::.  The\n-0000d3d0: 2064 6566 6175 6c74 2076 616c 7565 2027   default value '\n-0000d3e0: 7472 7565 270a 2020 2020 2020 2020 2020  true'.          \n+0000d300: 2020 2020 2020 2020 2020 2020 2020 6475                du\n+0000d310: 6520 746f 2074 6865 2027 7370 6563 6961  e to the 'specia\n+0000d320: 6c27 2077 696c 6c20 6265 2076 6973 6962  l' will be visib\n+0000d330: 6c65 2e0a 2773 706c 6974 2720 2020 2774  le..'split'   't\n+0000d340: 7275 6527 2c20 2766 616c 7365 2720 2020  rue', 'false'   \n+0000d350: 2020 2020 2020 5475 726e 2073 706c 6974        Turn split\n+0000d360: 7469 6e67 206f 6620 7377 6565 702d 6765  ting of sweep-ge\n+0000d370: 6e65 7261 7465 6420 626f 6479 2070 6f6c  nerated body pol\n+0000d380: 7967 6f6e 7320 6f6e 2061 6e64 206f 6666  ygons on and off\n+0000d390: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+0000d3a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000d3b0: 2020 2072 6573 7065 6374 6976 656c 792e     respectively.\n+0000d3c0: 2020 2a4e 6f74 6520 5377 6565 7073 3a3a    *Note Sweeps::\n+0000d3d0: 2e20 2054 6865 2064 6566 6175 6c74 2076  .  The default v\n+0000d3e0: 616c 7565 2027 7472 7565 270a 2020 2020  alue 'true'.    \n 0000d3f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d400: 2020 2020 2020 2020 6361 7573 6573 2022          causes \"\n-0000d410: 7761 7270 6564 2220 706f 6c79 676f 6e73  warped\" polygons\n-0000d420: 2074 6f20 6265 2073 706c 6974 2069 6e74   to be split int\n-0000d430: 6f20 7472 6961 6e67 6c65 732c 2077 6869  o triangles, whi\n-0000d440: 6368 0a20 2020 2020 2020 2020 2020 2020  ch.             \n+0000d400: 2020 2020 2020 2020 2020 2020 2020 6361                ca\n+0000d410: 7573 6573 2022 7761 7270 6564 2220 706f  uses \"warped\" po\n+0000d420: 6c79 676f 6e73 2074 6f20 6265 2073 706c  lygons to be spl\n+0000d430: 6974 2069 6e74 6f20 7472 6961 6e67 6c65  it into triangle\n+0000d440: 732c 2077 6869 6368 0a20 2020 2020 2020  s, which.       \n 0000d450: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d460: 2020 2020 2061 766f 6964 7320 6d69 7374       avoids mist\n-0000d470: 616b 6573 2062 7920 7468 6520 6869 6464  akes by the hidd\n-0000d480: 656e 2073 7572 6661 6365 2061 6c67 6f72  en surface algor\n-0000d490: 6974 686d 2e0a 0a33 2e31 2e36 2050 6f69  ithm...3.1.6 Poi\n-0000d4a0: 6e74 206c 6973 7473 0a2d 2d2d 2d2d 2d2d  nt lists.-------\n-0000d4b0: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e  ----------..*Syn\n-0000d4c0: 7461 783a 2a0a 2020 2020 2028 5831 2c59  tax:*.     (X1,Y\n-0000d4d0: 312c 5a31 2928 5832 2c59 322c 5a32 292e  1,Z1)(X2,Y2,Z2).\n-0000d4e0: 2e2e 0a41 2073 6571 7565 6e63 6520 6f66  ...A sequence of\n-0000d4f0: 206f 6e65 206f 7220 6d6f 7265 2070 6f69   one or more poi\n-0000d500: 6e74 7320 6d61 6b65 7320 6120 706f 696e  nts makes a poin\n-0000d510: 7420 6c69 7374 2c20 6120 6665 6174 7572  t list, a featur\n-0000d520: 6520 636f 6d6d 6f6e 2074 6f0a 616c 6c20  e common to.all \n-0000d530: 6472 6177 6162 6c65 732e 2020 4561 6368  drawables.  Each\n-0000d540: 206f 6620 7468 6520 706f 696e 7420 636f   of the point co\n-0000d550: 6d70 6f6e 656e 7473 2069 7320 6120 7363  mponents is a sc\n-0000d560: 616c 6172 2061 7269 7468 6d65 7469 630a  alar arithmetic.\n-0000d570: 6578 7072 6573 7369 6f6e 2e20 2041 6e79  expression.  Any\n-0000d580: 2070 6f69 6e74 206d 6179 2068 6176 6520   point may have \n-0000d590: 7468 6520 7a2d 636f 6d70 6f6e 656e 7420  the z-component \n-0000d5a0: 6f6d 6974 7465 643b 2069 7420 7769 6c6c  omitted; it will\n-0000d5b0: 2064 6566 6175 6c74 0a74 6f20 7a3d 302e   default.to z=0.\n-0000d5c0: 0a0a 2a20 4d65 6e75 3a0a 0a2a 2044 7261  ..* Menu:..* Dra\n-0000d5d0: 7761 626c 6573 3a3a 2020 2020 2020 2020  wables::        \n-0000d5e0: 2020 2020 2020 2020 2020 2054 6869 6e67             Thing\n-0000d5f0: 7320 7468 6174 2061 7265 2064 7261 776e  s that are drawn\n-0000d600: 2e0a 2a20 4465 6669 6e69 7469 6f6e 733a  ..* Definitions:\n-0000d610: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0000d620: 2020 5468 696e 6773 2077 6974 6820 6e61    Things with na\n-0000d630: 6d65 732e 0a0a 1f0a 4669 6c65 3a20 736b  mes.....File: sk\n-0000d640: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n-0000d650: 3a20 4472 6177 6162 6c65 732c 2020 4e65  : Drawables,  Ne\n-0000d660: 7874 3a20 4465 6669 6e69 7469 6f6e 732c  xt: Definitions,\n-0000d670: 2020 5072 6576 3a20 4c61 6e67 7561 6765    Prev: Language\n-0000d680: 2062 6173 6963 732c 2020 5570 3a20 496e   basics,  Up: In\n-0000d690: 7075 7420 6c61 6e67 7561 6765 0a0a 332e  put language..3.\n-0000d6a0: 3220 4472 6177 6162 6c65 730a 3d3d 3d3d  2 Drawables.====\n-0000d6b0: 3d3d 3d3d 3d3d 3d3d 3d0a 0a44 7261 7761  =========..Drawa\n-0000d6c0: 626c 6573 2061 7265 2073 696d 706c 7920  bles are simply \n-0000d6d0: 2773 6b65 7463 6827 206f 626a 6563 7473  'sketch' objects\n-0000d6e0: 2074 6861 7420 6d69 6768 7420 6170 7065   that might appe\n-0000d6f0: 6172 2069 6e20 7468 6520 6472 6177 696e  ar in the drawin\n-0000d700: 672e 0a54 6865 7920 696e 636c 7564 6520  g..They include \n-0000d710: 646f 7473 2c20 706f 6c79 6c69 6e65 732c  dots, polylines,\n-0000d720: 2063 7572 7665 732c 2070 6f6c 7967 6f6e   curves, polygon\n-0000d730: 732c 2061 6e64 206d 6f72 6520 636f 6d70  s, and more comp\n-0000d740: 6c65 7820 6f62 6a65 6374 730a 7468 6174  lex objects.that\n-0000d750: 2061 7265 2062 7569 6c74 2075 7020 6672   are built up fr\n-0000d760: 6f6d 2073 696d 706c 6572 206f 6e65 7320  om simpler ones \n-0000d770: 696e 2076 6172 696f 7573 2077 6179 732e  in various ways.\n-0000d780: 2020 4669 6e61 6c6c 792c 2022 7370 6563    Finally, \"spec\n-0000d790: 6961 6c22 0a6f 626a 6563 7473 2061 7265  ial\".objects are\n-0000d7a0: 2074 686f 7365 2063 6f6d 706f 7365 6420   those composed \n-0000d7b0: 6f66 204c 6154 6558 206f 7220 2750 5354  of LaTeX or 'PST\n-0000d7c0: 7269 636b 7327 2063 6f64 652c 2070 6572  ricks' code, per\n-0000d7d0: 6861 7073 0a69 6e63 6c75 6469 6e67 2063  haps.including c\n-0000d7e0: 6f6f 7264 696e 6174 6573 2061 6e64 2061  oordinates and a\n-0000d7f0: 6e67 6c65 7320 636f 6d70 7574 6564 2062  ngles computed b\n-0000d800: 7920 2773 6b65 7463 6827 2e0a 0a2a 204d  y 'sketch'...* M\n-0000d810: 656e 753a 0a0a 2a20 446f 7473 3a3a 2020  enu:..* Dots::  \n-0000d820: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d830: 2020 2020 2020 4472 6177 2064 6f74 732e        Draw dots.\n-0000d840: 0a2a 204c 696e 6573 3a3a 2020 2020 2020  .* Lines::      \n+0000d460: 2020 2020 2020 2020 2020 2061 766f 6964             avoid\n+0000d470: 7320 6d69 7374 616b 6573 2062 7920 7468  s mistakes by th\n+0000d480: 6520 6869 6464 656e 2073 7572 6661 6365  e hidden surface\n+0000d490: 2061 6c67 6f72 6974 686d 2e0a 0a33 2e31   algorithm...3.1\n+0000d4a0: 2e36 2050 6f69 6e74 206c 6973 7473 0a2d  .6 Point lists.-\n+0000d4b0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n+0000d4c0: 0a0a 2a53 796e 7461 783a 2a0a 2020 2020  ..*Syntax:*.    \n+0000d4d0: 2028 5831 2c59 312c 5a31 2928 5832 2c59   (X1,Y1,Z1)(X2,Y\n+0000d4e0: 322c 5a32 292e 2e2e 0a41 2073 6571 7565  2,Z2)....A seque\n+0000d4f0: 6e63 6520 6f66 206f 6e65 206f 7220 6d6f  nce of one or mo\n+0000d500: 7265 2070 6f69 6e74 7320 6d61 6b65 7320  re points makes \n+0000d510: 6120 706f 696e 7420 6c69 7374 2c20 6120  a point list, a \n+0000d520: 6665 6174 7572 6520 636f 6d6d 6f6e 2074  feature common t\n+0000d530: 6f0a 616c 6c20 6472 6177 6162 6c65 732e  o.all drawables.\n+0000d540: 2020 4561 6368 206f 6620 7468 6520 706f    Each of the po\n+0000d550: 696e 7420 636f 6d70 6f6e 656e 7473 2069  int components i\n+0000d560: 7320 6120 7363 616c 6172 2061 7269 7468  s a scalar arith\n+0000d570: 6d65 7469 630a 6578 7072 6573 7369 6f6e  metic.expression\n+0000d580: 2e20 2041 6e79 2070 6f69 6e74 206d 6179  .  Any point may\n+0000d590: 2068 6176 6520 7468 6520 7a2d 636f 6d70   have the z-comp\n+0000d5a0: 6f6e 656e 7420 6f6d 6974 7465 643b 2069  onent omitted; i\n+0000d5b0: 7420 7769 6c6c 2064 6566 6175 6c74 0a74  t will default.t\n+0000d5c0: 6f20 7a3d 302e 0a0a 2a20 4d65 6e75 3a0a  o z=0...* Menu:.\n+0000d5d0: 0a2a 2044 7261 7761 626c 6573 3a3a 2020  .* Drawables::  \n+0000d5e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000d5f0: 2054 6869 6e67 7320 7468 6174 2061 7265   Things that are\n+0000d600: 2064 7261 776e 2e0a 2a20 4465 6669 6e69   drawn..* Defini\n+0000d610: 7469 6f6e 733a 3a20 2020 2020 2020 2020  tions::         \n+0000d620: 2020 2020 2020 2020 5468 696e 6773 2077          Things w\n+0000d630: 6974 6820 6e61 6d65 732e 0a0a 1f0a 4669  ith names.....Fi\n+0000d640: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n+0000d650: 2020 4e6f 6465 3a20 4472 6177 6162 6c65    Node: Drawable\n+0000d660: 732c 2020 4e65 7874 3a20 4465 6669 6e69  s,  Next: Defini\n+0000d670: 7469 6f6e 732c 2020 5072 6576 3a20 4c61  tions,  Prev: La\n+0000d680: 6e67 7561 6765 2062 6173 6963 732c 2020  nguage basics,  \n+0000d690: 5570 3a20 496e 7075 7420 6c61 6e67 7561  Up: Input langua\n+0000d6a0: 6765 0a0a 332e 3220 4472 6177 6162 6c65  ge..3.2 Drawable\n+0000d6b0: 730a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a  s.=============.\n+0000d6c0: 0a44 7261 7761 626c 6573 2061 7265 2073  .Drawables are s\n+0000d6d0: 696d 706c 7920 2773 6b65 7463 6827 206f  imply 'sketch' o\n+0000d6e0: 626a 6563 7473 2074 6861 7420 6d69 6768  bjects that migh\n+0000d6f0: 7420 6170 7065 6172 2069 6e20 7468 6520  t appear in the \n+0000d700: 6472 6177 696e 672e 0a54 6865 7920 696e  drawing..They in\n+0000d710: 636c 7564 6520 646f 7473 2c20 706f 6c79  clude dots, poly\n+0000d720: 6c69 6e65 732c 2063 7572 7665 732c 2070  lines, curves, p\n+0000d730: 6f6c 7967 6f6e 732c 2061 6e64 206d 6f72  olygons, and mor\n+0000d740: 6520 636f 6d70 6c65 7820 6f62 6a65 6374  e complex object\n+0000d750: 730a 7468 6174 2061 7265 2062 7569 6c74  s.that are built\n+0000d760: 2075 7020 6672 6f6d 2073 696d 706c 6572   up from simpler\n+0000d770: 206f 6e65 7320 696e 2076 6172 696f 7573   ones in various\n+0000d780: 2077 6179 732e 2020 4669 6e61 6c6c 792c   ways.  Finally,\n+0000d790: 2022 7370 6563 6961 6c22 0a6f 626a 6563   \"special\".objec\n+0000d7a0: 7473 2061 7265 2074 686f 7365 2063 6f6d  ts are those com\n+0000d7b0: 706f 7365 6420 6f66 204c 6154 6558 206f  posed of LaTeX o\n+0000d7c0: 7220 2750 5354 7269 636b 7327 2063 6f64  r 'PSTricks' cod\n+0000d7d0: 652c 2070 6572 6861 7073 0a69 6e63 6c75  e, perhaps.inclu\n+0000d7e0: 6469 6e67 2063 6f6f 7264 696e 6174 6573  ding coordinates\n+0000d7f0: 2061 6e64 2061 6e67 6c65 7320 636f 6d70   and angles comp\n+0000d800: 7574 6564 2062 7920 2773 6b65 7463 6827  uted by 'sketch'\n+0000d810: 2e0a 0a2a 204d 656e 753a 0a0a 2a20 446f  ...* Menu:..* Do\n+0000d820: 7473 3a3a 2020 2020 2020 2020 2020 2020  ts::            \n+0000d830: 2020 2020 2020 2020 2020 2020 4472 6177              Draw\n+0000d840: 2064 6f74 732e 0a2a 204c 696e 6573 3a3a   dots..* Lines::\n 0000d850: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d860: 2044 7261 7720 706f 6c79 6c69 6e65 732e   Draw polylines.\n-0000d870: 0a2a 2043 7572 7665 733a 3a20 2020 2020  .* Curves::     \n-0000d880: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d890: 2044 7261 7720 6375 7276 6573 2e0a 2a20   Draw curves..* \n-0000d8a0: 506f 6c79 676f 6e73 3a3a 2020 2020 2020  Polygons::      \n-0000d8b0: 2020 2020 2020 2020 2020 2020 2020 4472                Dr\n-0000d8c0: 6177 2070 6f6c 7967 6f6e 732e 0a2a 2053  aw polygons..* S\n-0000d8d0: 7065 6369 616c 733a 3a20 2020 2020 2020  pecials::       \n-0000d8e0: 2020 2020 2020 2020 2020 2020 2045 6d62               Emb\n-0000d8f0: 6564 2072 6177 204c 6154 6558 2061 6e64  ed raw LaTeX and\n-0000d900: 2027 5053 5472 6963 6b73 272e 0a2a 2053   'PSTricks'..* S\n-0000d910: 7765 6570 733a 3a20 2020 2020 2020 2020  weeps::         \n-0000d920: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n-0000d930: 7720 7377 6565 7073 206f 6620 646f 7473  w sweeps of dots\n-0000d940: 2061 6e64 2070 6f6c 796c 696e 6573 2e0a   and polylines..\n-0000d950: 2a20 426c 6f63 6b73 3a3a 2020 2020 2020  * Blocks::      \n+0000d860: 2020 2020 2020 2044 7261 7720 706f 6c79         Draw poly\n+0000d870: 6c69 6e65 732e 0a2a 2043 7572 7665 733a  lines..* Curves:\n+0000d880: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0000d890: 2020 2020 2020 2044 7261 7720 6375 7276         Draw curv\n+0000d8a0: 6573 2e0a 2a20 506f 6c79 676f 6e73 3a3a  es..* Polygons::\n+0000d8b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000d8c0: 2020 2020 4472 6177 2070 6f6c 7967 6f6e      Draw polygon\n+0000d8d0: 732e 0a2a 2053 7065 6369 616c 733a 3a20  s..* Specials:: \n+0000d8e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000d8f0: 2020 2045 6d62 6564 2072 6177 204c 6154     Embed raw LaT\n+0000d900: 6558 2061 6e64 2027 5053 5472 6963 6b73  eX and 'PSTricks\n+0000d910: 272e 0a2a 2053 7765 6570 733a 3a20 2020  '..* Sweeps::   \n+0000d920: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000d930: 2020 2044 7261 7720 7377 6565 7073 206f     Draw sweeps o\n+0000d940: 6620 646f 7473 2061 6e64 2070 6f6c 796c  f dots and polyl\n+0000d950: 696e 6573 2e0a 2a20 426c 6f63 6b73 3a3a  ines..* Blocks::\n 0000d960: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d970: 4772 6f75 7020 6f74 6865 7220 6472 6177  Group other draw\n-0000d980: 6162 6c65 732e 0a2a 2052 6570 6561 7473  ables..* Repeats\n-0000d990: 3a3a 2020 2020 2020 2020 2020 2020 2020  ::              \n-0000d9a0: 2020 2020 2020 2044 7261 7720 7472 616e         Draw tran\n-0000d9b0: 7366 6f72 6d65 6420 636f 7069 6573 206f  sformed copies o\n-0000d9c0: 6620 6f62 6a65 6374 732e 0a2a 2050 7574  f objects..* Put\n-0000d9d0: 733a 3a20 2020 2020 2020 2020 2020 2020  s::             \n-0000d9e0: 2020 2020 2020 2020 2020 2044 7261 7720             Draw \n-0000d9f0: 6f6e 6520 6f62 6a65 6374 2074 7261 6e73  one object trans\n-0000da00: 666f 726d 6564 2e0a 0a1f 0a46 696c 653a  formed.....File:\n-0000da10: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n-0000da20: 6f64 653a 2044 6f74 732c 2020 4e65 7874  ode: Dots,  Next\n-0000da30: 3a20 4c69 6e65 732c 2020 5072 6576 3a20  : Lines,  Prev: \n-0000da40: 4472 6177 6162 6c65 732c 2020 5570 3a20  Drawables,  Up: \n-0000da50: 4472 6177 6162 6c65 730a 0a33 2e32 2e31  Drawables..3.2.1\n-0000da60: 2044 6f74 730a 2d2d 2d2d 2d2d 2d2d 2d2d   Dots.----------\n-0000da70: 0a0a 2a53 796e 7461 783a 2a0a 2020 2020  ..*Syntax:*.    \n-0000da80: 2064 6f74 735b 4f50 5449 4f4e 535d 2050   dots[OPTIONS] P\n-0000da90: 4f49 4e54 5f4c 4953 540a 5468 6973 2063  OINT_LIST.This c\n-0000daa0: 6f6d 6d61 6e64 2069 7320 7468 6520 7468  ommand is the th\n-0000dab0: 7265 652d 6469 6d65 6e73 696f 6e61 6c20  ree-dimensional \n-0000dac0: 6571 7569 7661 6c65 6e74 206f 6620 7468  equivalent of th\n-0000dad0: 6520 2750 5354 7269 636b 7327 0a63 6f6d  e 'PSTricks'.com\n-0000dae0: 6d61 6e64 2027 5c70 7364 6f74 7327 2e0a  mand '\\psdots'..\n-0000daf0: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n-0000db00: 696e 666f 2c20 204e 6f64 653a 204c 696e  info,  Node: Lin\n-0000db10: 6573 2c20 204e 6578 743a 2043 7572 7665  es,  Next: Curve\n-0000db20: 732c 2020 5072 6576 3a20 446f 7473 2c20  s,  Prev: Dots, \n-0000db30: 2055 703a 2044 7261 7761 626c 6573 0a0a   Up: Drawables..\n-0000db40: 332e 322e 3220 4c69 6e65 730a 2d2d 2d2d  3.2.2 Lines.----\n-0000db50: 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178  -------..*Syntax\n-0000db60: 3a2a 0a20 2020 2020 6c69 6e65 5b4f 5054  :*.     line[OPT\n-0000db70: 494f 4e53 5d20 504f 494e 545f 4c49 5354  IONS] POINT_LIST\n-0000db80: 0a54 6869 7320 636f 6d6d 616e 6420 6973  .This command is\n-0000db90: 2074 6865 2074 6872 6565 2d64 696d 656e   the three-dimen\n-0000dba0: 7369 6f6e 616c 2065 7175 6976 616c 656e  sional equivalen\n-0000dbb0: 7420 6f66 2074 6865 2027 5053 5472 6963  t of the 'PSTric\n-0000dbc0: 6b73 270a 636f 6d6d 616e 6420 275c 7073  ks'.command '\\ps\n-0000dbd0: 6c69 6e65 272e 0a0a 1f0a 4669 6c65 3a20  line'.....File: \n-0000dbe0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n-0000dbf0: 6465 3a20 4375 7276 6573 2c20 204e 6578  de: Curves,  Nex\n-0000dc00: 743a 2050 6f6c 7967 6f6e 732c 2020 5072  t: Polygons,  Pr\n-0000dc10: 6576 3a20 4c69 6e65 732c 2020 5570 3a20  ev: Lines,  Up: \n-0000dc20: 4472 6177 6162 6c65 730a 0a33 2e32 2e33  Drawables..3.2.3\n-0000dc30: 2043 7572 7665 730a 2d2d 2d2d 2d2d 2d2d   Curves.--------\n-0000dc40: 2d2d 2d2d 0a0a 2a53 796e 7461 783a 2a0a  ----..*Syntax:*.\n-0000dc50: 2020 2020 2063 7572 7665 5b4f 5054 494f       curve[OPTIO\n-0000dc60: 4e53 5d20 504f 494e 545f 4c49 5354 0a54  NS] POINT_LIST.T\n-0000dc70: 6869 7320 636f 6d6d 616e 6420 6973 2074  his command is t\n-0000dc80: 6865 2074 6872 6565 2d64 696d 656e 7369  he three-dimensi\n-0000dc90: 6f6e 616c 2065 7175 6976 616c 656e 7420  onal equivalent \n-0000dca0: 6f66 2074 6865 2027 5053 5472 6963 6b73  of the 'PSTricks\n-0000dcb0: 270a 636f 6d6d 616e 6420 275c 7073 6375  '.command '\\pscu\n-0000dcc0: 7276 6527 2e20 2049 7420 6973 206e 6f74  rve'.  It is not\n-0000dcd0: 2069 6d70 6c65 6d65 6e74 6564 2069 6e20   implemented in \n-0000dce0: 7468 6520 6375 7272 656e 7420 7665 7273  the current vers\n-0000dcf0: 696f 6e20 6f66 0a27 736b 6574 6368 272e  ion of.'sketch'.\n-0000dd00: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n-0000dd10: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 506f  .info,  Node: Po\n-0000dd20: 6c79 676f 6e73 2c20 204e 6578 743a 2053  lygons,  Next: S\n-0000dd30: 7065 6369 616c 732c 2020 5072 6576 3a20  pecials,  Prev: \n-0000dd40: 4375 7276 6573 2c20 2055 703a 2044 7261  Curves,  Up: Dra\n-0000dd50: 7761 626c 6573 0a0a 332e 322e 3420 506f  wables..3.2.4 Po\n-0000dd60: 6c79 676f 6e73 0a2d 2d2d 2d2d 2d2d 2d2d  lygons.---------\n-0000dd70: 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a  -----..*Syntax:*\n-0000dd80: 0a20 2020 2020 706f 6c79 676f 6e5b 4f50  .     polygon[OP\n-0000dd90: 5449 4f4e 535d 2050 4f49 4e54 5f4c 4953  TIONS] POINT_LIS\n-0000dda0: 540a 5468 6973 2063 6f6d 6d61 6e64 2069  T.This command i\n-0000ddb0: 7320 7468 6520 7468 7265 652d 6469 6d65  s the three-dime\n-0000ddc0: 6e73 696f 6e61 6c20 6571 7569 7661 6c65  nsional equivale\n-0000ddd0: 6e74 206f 6620 7468 6520 2750 5354 7269  nt of the 'PSTri\n-0000dde0: 636b 7327 0a63 6f6d 6d61 6e64 2027 5c70  cks'.command '\\p\n-0000ddf0: 7370 6f6c 7967 6f6e 272e 2020 5468 6520  spolygon'.  The \n-0000de00: 2773 6b65 7463 6827 2068 6964 6465 6e20  'sketch' hidden \n-0000de10: 7375 7266 6163 6520 616c 676f 7269 7468  surface algorith\n-0000de20: 6d20 6173 7375 6d65 730a 7468 6174 2070  m assumes.that p\n-0000de30: 6f6c 7967 6f6e 7320 6172 6520 636f 6e76  olygons are conv\n-0000de40: 6578 2061 6e64 2070 6c61 6e61 722e 2020  ex and planar.  \n-0000de50: 496e 2070 7261 6374 6963 652c 2064 7261  In practice, dra\n-0000de60: 7769 6e67 7320 6d61 7920 7765 6c6c 0a74  wings may well.t\n-0000de70: 7572 6e20 6f75 7420 636f 7272 6563 746c  urn out correctl\n-0000de80: 7920 6576 656e 2069 6620 7468 6573 6520  y even if these \n-0000de90: 6173 7375 6d70 7469 6f6e 7320 6172 6520  assumptions are \n-0000dea0: 7669 6f6c 6174 6564 2e0a 0a1f 0a46 696c  violated.....Fil\n-0000deb0: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n-0000dec0: 204e 6f64 653a 2053 7065 6369 616c 732c   Node: Specials,\n-0000ded0: 2020 4e65 7874 3a20 5377 6565 7073 2c20    Next: Sweeps, \n-0000dee0: 2050 7265 763a 2050 6f6c 7967 6f6e 732c   Prev: Polygons,\n-0000def0: 2020 5570 3a20 4472 6177 6162 6c65 730a    Up: Drawables.\n-0000df00: 0a33 2e32 2e35 2053 7065 6369 616c 730a  .3.2.5 Specials.\n-0000df10: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a  --------------..\n-0000df20: 2a53 796e 7461 783a 2a0a 2020 2020 2073  *Syntax:*.     s\n-0000df30: 7065 6369 616c 2024 5241 575f 5445 5854  pecial $RAW_TEXT\n-0000df40: 245b 4f50 5449 4f4e 535d 2041 5247 5f4c  $[OPTIONS] ARG_L\n-0000df50: 4953 540a 4865 7265 2027 2427 2063 616e  IST.Here '$' can\n-0000df60: 2062 6520 616e 7920 6368 6172 6163 7465   be any characte\n-0000df70: 7220 616e 6420 6973 2075 7365 6420 746f  r and is used to\n-0000df80: 2064 656c 696d 6974 2074 6865 2073 7461   delimit the sta\n-0000df90: 7274 2061 6e64 2065 6e64 0a6f 6620 5241  rt and end.of RA\n-0000dfa0: 575f 5445 5854 2e20 2054 6865 2063 6f6d  W_TEXT.  The com\n-0000dfb0: 6d61 6e64 2065 6d62 6564 7320 5241 575f  mand embeds RAW_\n-0000dfc0: 5445 5854 2069 6e20 7468 6520 2773 6b65  TEXT in the 'ske\n-0000dfd0: 7463 6827 206f 7574 7075 7420 6166 7465  tch' output afte\n-0000dfe0: 720a 7065 7266 6f72 6d69 6e67 2073 7562  r.performing sub\n-0000dff0: 7374 6974 7574 696f 6e73 2061 7320 666f  stitutions as fo\n-0000e000: 6c6c 6f77 732e 0a20 2020 2a20 2723 4927  llows..   * '#I'\n-0000e010: 2077 6865 7265 2049 2069 7320 6120 706f   where I is a po\n-0000e020: 7369 7469 7665 2069 6e74 6567 6572 2069  sitive integer i\n-0000e030: 7320 7265 706c 6163 6564 2062 7920 7468  s replaced by th\n-0000e040: 6520 4927 7468 2076 616c 7565 2069 6e0a  e I'th value in.\n-0000e050: 2020 2020 2041 5247 5f4c 4953 542e 2020       ARG_LIST.  \n-0000e060: 506f 696e 7420 616e 6420 7665 6374 6f72  Point and vector\n-0000e070: 2061 7267 756d 656e 7473 2062 6563 6f6d   arguments becom\n-0000e080: 6520 7477 6f2d 6469 6d65 6e73 696f 6e61  e two-dimensiona\n-0000e090: 6c0a 2020 2020 2070 6f69 6e74 732c 2077  l.     points, w\n-0000e0a0: 6869 6368 2061 7265 2074 6865 2074 7261  hich are the tra\n-0000e0b0: 6e73 666f 726d 6564 2033 6420 6172 6775  nsformed 3d argu\n-0000e0c0: 6d65 6e74 7320 7072 6f6a 6563 7465 6420  ments projected \n-0000e0d0: 6f6e 746f 2074 6865 0a20 2020 2020 582d  onto the.     X-\n-0000e0e0: 5920 706c 616e 652e 2020 5468 6973 2061  Y plane.  This a\n-0000e0f0: 6c6c 6f77 7320 7477 6f2d 6469 6d65 6e74  llows two-diment\n-0000e100: 696f 6e61 6c20 6f75 7470 7574 2065 6c65  ional output ele\n-0000e110: 6d65 6e74 7320 7375 6368 2061 730a 2020  ments such as.  \n-0000e120: 2020 206c 6162 656c 7320 746f 2062 6520     labels to be \n-0000e130: 6561 7369 6c79 2070 6f73 6974 696f 6e65  easily positione\n-0000e140: 6420 7769 7468 2072 6573 7065 6374 2074  d with respect t\n-0000e150: 6f20 7468 7265 652d 6469 6d65 6e73 696f  o three-dimensio\n-0000e160: 6e61 6c0a 2020 2020 2066 6561 7475 7265  nal.     feature\n-0000e170: 7320 696e 2074 6865 2064 7261 7769 6e67  s in the drawing\n-0000e180: 2e20 2053 6361 6c61 7220 6172 6775 6d65  .  Scalar argume\n-0000e190: 6e74 7320 6172 6520 7375 6273 6974 7574  nts are subsitut\n-0000e1a0: 6564 2064 6972 6563 746c 792e 0a20 2020  ed directly..   \n-0000e1b0: 2020 4e6f 2074 7261 6e73 666f 726d 6174    No transformat\n-0000e1c0: 696f 6e20 6973 2061 7070 6c69 6564 2e0a  ion is applied..\n-0000e1d0: 2020 202a 2027 237b 497d 2720 6973 2061     * '#{I}' is a\n-0000e1e0: 6c73 6f20 7265 706c 6163 6564 2061 7320  lso replaced as \n-0000e1f0: 6162 6f76 652e 0a20 2020 2a20 2723 4927  above..   * '#I'\n-0000e200: 3227 2069 7320 7265 706c 6163 6564 2061  2' is replaced a\n-0000e210: 7320 6162 6f76 6520 666f 7220 706f 696e  s above for poin\n-0000e220: 7473 206f 7220 7665 6374 6f72 732e 2020  ts or vectors.  \n-0000e230: 4974 2069 7320 616e 2065 7272 6f72 0a20  It is an error. \n-0000e240: 2020 2020 666f 7220 7468 6520 4927 7468      for the I'th\n-0000e250: 2061 7267 756d 656e 7420 746f 2062 6520   argument to be \n-0000e260: 6120 7363 616c 6172 2e0a 2020 202a 2027  a scalar..   * '\n-0000e270: 2349 2778 272c 2027 2349 2779 272c 206f  #I'x', '#I'y', o\n-0000e280: 7220 2723 4927 7a27 2069 7320 7265 706c  r '#I'z' is repl\n-0000e290: 6163 6564 2c20 7265 7370 6563 7469 7665  aced, respective\n-0000e2a0: 6c79 2c20 6279 2074 6865 2073 6361 6c61  ly, by the scala\n-0000e2b0: 720a 2020 2020 2058 2c20 592c 206f 7220  r.     X, Y, or \n-0000e2c0: 5a2d 636f 6f72 6469 6e61 7465 206f 6620  Z-coordinate of \n-0000e2d0: 7468 6520 6172 6775 6d65 6e74 2070 6f69  the argument poi\n-0000e2e0: 6e74 206f 7220 7665 6374 6f72 2e20 2049  nt or vector.  I\n-0000e2f0: 7420 6973 2061 6e0a 2020 2020 2065 7272  t is an.     err\n-0000e300: 6f72 2066 6f72 2074 6865 2049 2774 6820  or for the I'th \n-0000e310: 6172 6775 6d65 6e74 2074 6f20 6265 2061  argument to be a\n-0000e320: 2073 6361 6c61 722e 0a20 2020 2a20 2723   scalar..   * '#\n-0000e330: 4927 3327 2069 7320 7265 706c 6163 6564  I'3' is replaced\n-0000e340: 2062 7920 7468 6520 7468 7265 652d 6469   by the three-di\n-0000e350: 6d65 6e73 696f 6e61 6c20 7472 616e 7366  mensional transf\n-0000e360: 6f72 6d65 6420 6172 6775 6d65 6e74 2e0a  ormed argument..\n-0000e370: 2020 2020 204e 6f74 6520 7468 6174 2069       Note that i\n-0000e380: 6620 6120 7065 7273 7065 6374 6976 6520  f a perspective \n-0000e390: 7472 616e 7366 6f72 6d61 7469 6f6e 2068  transformation h\n-0000e3a0: 6173 2062 6565 6e20 6170 706c 6965 642c  as been applied,\n-0000e3b0: 2074 6865 0a20 2020 2020 5a2d 636f 6f72   the.     Z-coor\n-0000e3c0: 6469 6e61 7465 2068 6173 206c 6974 746c  dinate has littl\n-0000e3d0: 6520 6765 6f6d 6574 7269 6320 7369 676e  e geometric sign\n-0000e3e0: 6966 6963 616e 6365 2c20 7468 6f75 6768  ificance, though\n-0000e3f0: 2069 740a 2020 2020 2061 6363 7572 6174   it.     accurat\n-0000e400: 656c 7920 696e 6469 6361 7465 7320 7265  ely indicates re\n-0000e410: 6c61 7469 7665 2064 6570 7468 2e0a 2020  lative depth..  \n-0000e420: 202a 2027 2349 2d4a 2720 7768 6572 6520   * '#I-J' where \n-0000e430: 4920 616e 6420 4a20 6172 6520 706f 7369  I and J are posi\n-0000e440: 7469 7665 2069 6e74 6567 6572 7320 6973  tive integers is\n-0000e450: 2072 6570 6c61 6365 6420 6279 2061 2073   replaced by a s\n-0000e460: 7472 696e 670a 2020 2020 2027 7b41 4e47  tring.     '{ANG\n-0000e470: 4c45 7d27 2077 6865 7265 2041 4e47 4c45  LE}' where ANGLE\n-0000e480: 2069 7320 7468 6520 706f 6c61 7220 616e   is the polar an\n-0000e490: 676c 6520 6f66 2061 2076 6563 746f 7220  gle of a vector \n-0000e4a0: 6672 6f6d 2074 6865 2049 2774 680a 2020  from the I'th.  \n-0000e4b0: 2020 2070 6f69 6e74 2069 6e20 504f 494e     point in POIN\n-0000e4c0: 545f 4c49 5354 2074 6f20 7468 6520 4a27  T_LIST to the J'\n-0000e4d0: 7468 2070 6f69 6e74 2070 726f 6a65 6374  th point project\n-0000e4e0: 6564 2069 6e74 6f20 7468 6520 782d 7920  ed into the x-y \n-0000e4f0: 706c 616e 652e 0a20 2020 2020 4974 2069  plane..     It i\n-0000e500: 7320 616e 2065 7272 6f72 2066 6f72 2074  s an error for t\n-0000e510: 6865 2049 2774 6820 6f72 204a 2774 6820  he I'th or J'th \n-0000e520: 6172 6775 6d65 6e74 2074 6f20 6265 2061  argument to be a\n-0000e530: 2073 6361 6c61 7220 6f72 2061 0a20 2020   scalar or a.   \n-0000e540: 2020 7665 6374 6f72 2e0a 2020 202a 2027    vector..   * '\n-0000e550: 237b 492d 4a7d 2720 6973 2061 6c73 6f20  #{I-J}' is also \n-0000e560: 7265 706c 6163 6564 2061 7320 6162 6f76  replaced as abov\n-0000e570: 652e 0a20 2020 2a20 2723 2327 2069 7320  e..   * '##' is \n-0000e580: 7265 706c 6163 6564 2077 6974 6820 2723  replaced with '#\n-0000e590: 272e 0a54 6865 2066 6f72 6d73 2077 6974  '..The forms wit\n-0000e5a0: 6820 6272 6163 6573 2027 7b20 7d27 2061  h braces '{ }' a\n-0000e5b0: 7265 2075 7365 6675 6c20 7768 656e 2074  re useful when t\n-0000e5c0: 6865 2061 7267 756d 656e 7420 6973 2069  he argument is i\n-0000e5d0: 6d6d 6564 6961 7465 6c79 0a66 6f6c 6c6f  mmediately.follo\n-0000e5e0: 7765 6420 6279 2061 2064 6967 6974 206f  wed by a digit o\n-0000e5f0: 7220 6120 7469 636b 2063 6861 7261 6374  r a tick charact\n-0000e600: 6572 2074 6861 7420 6973 2070 6172 7420  er that is part \n-0000e610: 6f66 2074 6865 2054 6558 2063 6f64 652e  of the TeX code.\n-0000e620: 0a0a 2020 2054 6865 206f 6e6c 7920 7573  ..   The only us\n-0000e630: 6566 756c 206f 7074 696f 6e20 6f66 2027  eful option of '\n-0000e640: 7370 6563 6961 6c27 2069 7320 276c 6179  special' is 'lay\n-0000e650: 272c 2077 6869 6368 2064 6574 6572 6d69  ', which determi\n-0000e660: 6e65 7320 6966 2074 6865 0a73 7562 7374  nes if the.subst\n-0000e670: 6974 7565 6420 7261 7720 7465 7874 2069  itued raw text i\n-0000e680: 7320 656d 6974 7465 6420 6265 666f 7265  s emitted before\n-0000e690: 2c20 6166 7465 722c 206f 7220 7573 696e  , after, or usin\n-0000e6a0: 6720 7468 6520 6669 7273 7420 706f 696e  g the first poin\n-0000e6b0: 740a 696e 2050 4f49 4e54 5f4c 4953 5420  t.in POINT_LIST \n-0000e6c0: 6173 2061 6e20 696e 6469 6361 746f 7220  as an indicator \n-0000e6d0: 6f66 2064 6570 7468 2e20 2054 6865 7365  of depth.  These\n-0000e6e0: 206f 6363 7572 2c20 7265 7370 6563 7469   occur, respecti\n-0000e6f0: 7665 6c79 2c20 7769 7468 0a27 6c61 793d  vely, with.'lay=\n-0000e700: 756e 6465 7227 2c20 276c 6179 3d6f 7665  under', 'lay=ove\n-0000e710: 7227 2c20 616e 6420 276c 6179 3d69 6e27  r', and 'lay=in'\n-0000e720: 2e20 2053 6565 202a 6e6f 7465 2053 7065  .  See *note Spe\n-0000e730: 6369 616c 206f 626a 6563 7473 3a3a 2061  cial objects:: a\n-0000e740: 6e64 0a2a 6e6f 7465 2054 696b 5a2f 5047  nd.*note TikZ/PG\n-0000e750: 4620 7573 6572 2d64 6566 696e 6564 2073  F user-defined s\n-0000e760: 7479 6c65 733a 3a20 666f 7220 6578 616d  tyles:: for exam\n-0000e770: 706c 6573 2e20 202a 4e6f 7465 2049 6e74  ples.  *Note Int\n-0000e780: 6572 6e61 6c0a 6f70 7469 6f6e 733a 3a2e  ernal.options::.\n-0000e790: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n-0000e7a0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5377  .info,  Node: Sw\n-0000e7b0: 6565 7073 2c20 204e 6578 743a 2042 6c6f  eeps,  Next: Blo\n-0000e7c0: 636b 732c 2020 5072 6576 3a20 5370 6563  cks,  Prev: Spec\n-0000e7d0: 6961 6c73 2c20 2055 703a 2044 7261 7761  ials,  Up: Drawa\n-0000e7e0: 626c 6573 0a0a 332e 322e 3620 5377 6565  bles..3.2.6 Swee\n-0000e7f0: 7073 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a  ps.------------.\n-0000e800: 0a2a 5379 6e74 6178 3a2a 0a20 2020 2020  .*Syntax:*.     \n-0000e810: 7377 6565 7020 7b20 4e2c 2054 5f31 2c20  sweep { N, T_1, \n-0000e820: 545f 322c 202e 2e2e 2c20 545f 5220 7d5b  T_2, ..., T_R }[\n-0000e830: 4f50 5449 4f4e 535d 2053 5745 5054 5f4f  OPTIONS] SWEPT_O\n-0000e840: 424a 4543 540a 2020 2020 2073 7765 6570  BJECT.     sweep\n-0000e850: 207b 204e 3c3e 2c20 545f 312c 2054 5f32   { N<>, T_1, T_2\n-0000e860: 2c20 2e2e 2e2c 2054 5f52 207d 5b4f 5054  , ..., T_R }[OPT\n-0000e870: 494f 4e53 5d20 5357 4550 545f 4f42 4a45  IONS] SWEPT_OBJE\n-0000e880: 4354 0a54 6865 2073 7765 6570 2063 6f6e  CT.The sweep con\n-0000e890: 6e65 6374 7320 4e20 286f 7220 7065 7268  nects N (or perh\n-0000e8a0: 6170 7320 4e2b 3129 2063 6f70 6965 7320  aps N+1) copies \n-0000e8b0: 6f66 2053 5745 5054 5f4f 424a 4543 5420  of SWEPT_OBJECT \n-0000e8c0: 696e 206f 7264 6572 2074 6f0a 6372 6561  in order to.crea\n-0000e8d0: 7465 2061 206e 6577 206f 626a 6563 7420  te a new object \n-0000e8e0: 6f66 2068 6967 6865 7220 6469 6d65 6e73  of higher dimens\n-0000e8f0: 696f 6e2e 2020 5468 6520 545f 4920 2866  ion.  The T_I (f\n-0000e900: 6f72 2069 2062 6574 7765 656e 2031 2061  or i between 1 a\n-0000e910: 6e64 0a72 2920 6172 6520 7472 616e 7366  nd.r) are transf\n-0000e920: 6f72 6d73 2e20 2054 6865 206b 2774 6820  orms.  The k'th \n-0000e930: 636f 7079 206f 6620 5357 4550 545f 4f42  copy of SWEPT_OB\n-0000e940: 4a45 4354 2069 7320 7072 6f64 7563 6564  JECT is produced\n-0000e950: 2062 790a 6170 706c 7969 6e67 2074 6865   by.applying the\n-0000e960: 2066 6f6c 6c6f 7769 6e67 2074 7261 6e73   following trans\n-0000e970: 666f 726d 2074 6f20 7468 6520 6f72 6967  form to the orig\n-0000e980: 696e 616c 2e0a 2020 2020 2054 5f31 5e6b  inal..     T_1^k\n-0000e990: 2074 6865 6e20 545f 325e 6b20 7468 656e   then T_2^k then\n-0000e9a0: 202e 2e2e 2074 6865 6e20 545f 525e 6b0a   ... then T_R^k.\n-0000e9b0: 4865 7265 2054 5e6b 206d 6561 6e73 2022  Here T^k means \"\n-0000e9c0: 7472 616e 7366 6f72 6d20 5420 6170 706c  transform T appl\n-0000e9d0: 6965 6420 6b20 7469 6d65 732e 2220 2054  ied k times.\"  T\n-0000e9e0: 6865 206f 7269 6769 6e61 6c20 6f62 6a65  he original obje\n-0000e9f0: 6374 2069 730a 7468 6520 7a65 726f 2774  ct is.the zero't\n-0000ea00: 6820 636f 7079 2c20 7769 7468 206b 3d30  h copy, with k=0\n-0000ea10: 2061 6e64 2065 6666 6563 7469 7665 6c79   and effectively\n-0000ea20: 206e 6f20 7472 616e 7366 6f72 6d20 6170   no transform ap\n-0000ea30: 706c 6965 6420 2854 5e30 3d49 2c0a 7468  plied (T^0=I,.th\n-0000ea40: 6520 6964 656e 7469 7479 2074 7261 6e73  e identity trans\n-0000ea50: 666f 726d 292e 0a0a 2020 2054 6865 206d  form)...   The m\n-0000ea60: 6574 686f 6420 6f66 2063 6f6e 6e65 6374  ethod of connect\n-0000ea70: 696e 6720 7468 6520 636f 7069 6573 2064  ing the copies d\n-0000ea80: 6570 656e 6473 206f 6e20 7468 6520 7479  epends on the ty\n-0000ea90: 7065 206f 660a 5357 4550 545f 4f42 4a45  pe of.SWEPT_OBJE\n-0000eaa0: 4354 2061 6e64 206f 6e20 7768 6574 6865  CT and on whethe\n-0000eab0: 7220 7468 6520 636c 6f73 7572 6520 7461  r the closure ta\n-0000eac0: 6720 273c 3e27 2069 7320 7072 6573 656e  g '<>' is presen\n-0000ead0: 7420 6f72 206e 6f74 2e0a 0a20 2020 416e  t or not...   An\n-0000eae0: 2065 7861 6d70 6c65 206f 6620 6120 7377   example of a sw\n-0000eaf0: 6565 7020 7768 6572 6520 723d 3220 6973  eep where r=2 is\n-0000eb00: 2074 6865 204d 6f62 6975 7320 6669 6775   the Mobius figu\n-0000eb10: 7265 2061 7420 2a6e 6f74 6520 4d6f 7265  re at *note More\n-0000eb20: 2074 6f0a 6c65 6172 6e3a 3a2e 0a0a 2a20   to.learn::...* \n-0000eb30: 4d65 6e75 3a0a 0a2a 2053 7765 7074 2070  Menu:..* Swept p\n-0000eb40: 6f69 6e74 733a 3a20 2020 2020 2020 2020  oints::         \n-0000eb50: 2020 2020 2020 2053 7765 7074 2070 6f69         Swept poi\n-0000eb60: 6e74 7320 6d61 6b65 206c 696e 6573 206f  nts make lines o\n-0000eb70: 7220 706f 6c79 676f 6e73 2e0a 2a20 5377  r polygons..* Sw\n-0000eb80: 6570 7420 6c69 6e65 733a 3a20 2020 2020  ept lines::     \n-0000eb90: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n-0000eba0: 7420 6c69 6e65 7320 6d61 6b65 206f 7065  t lines make ope\n-0000ebb0: 6e20 6f72 2063 6c6f 7365 6420 7375 7266  n or closed surf\n-0000ebc0: 6163 6573 2e0a 2a20 5377 6570 7420 706f  aces..* Swept po\n-0000ebd0: 6c79 676f 6e73 3a3a 2020 2020 2020 2020  lygons::        \n-0000ebe0: 2020 2020 2020 5377 6570 7420 706f 6c79        Swept poly\n-0000ebf0: 676f 6e73 206d 616b 6520 636c 6f73 6564  gons make closed\n-0000ec00: 2073 7572 6661 6365 732e 0a2a 2053 7765   surfaces..* Swe\n-0000ec10: 7074 2062 6c6f 636b 733a 3a20 2020 2020  pt blocks::     \n-0000ec20: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-0000ec30: 2062 6c6f 636b 203d 3d20 626c 6f63 6b20   block == block \n-0000ec40: 6f66 2073 7765 6570 732e 0a2a 2053 7765  of sweeps..* Swe\n-0000ec50: 6570 2066 6163 6520 7370 6c69 7474 696e  ep face splittin\n-0000ec60: 673a 3a20 2020 2020 2020 2046 6978 696e  g::        Fixin\n-0000ec70: 6720 7761 7270 6564 2066 6163 6573 2077  g warped faces w\n-0000ec80: 6974 6820 7472 6961 6e67 6c65 732e 0a0a  ith triangles...\n-0000ec90: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n-0000eca0: 6e66 6f2c 2020 4e6f 6465 3a20 5377 6570  nfo,  Node: Swep\n-0000ecb0: 7420 706f 696e 7473 2c20 204e 6578 743a  t points,  Next:\n-0000ecc0: 2053 7765 7074 206c 696e 6573 2c20 2050   Swept lines,  P\n-0000ecd0: 7265 763a 2053 7765 6570 732c 2020 5570  rev: Sweeps,  Up\n-0000ece0: 3a20 5377 6565 7073 0a0a 332e 322e 362e  : Sweeps..3.2.6.\n-0000ecf0: 3120 5377 6570 7420 706f 696e 7473 0a2e  1 Swept points..\n-0000ed00: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000ed10: 2e2e 2e0a 0a49 6620 5357 4550 545f 4f42  .....If SWEPT_OB\n-0000ed20: 4a45 4354 2069 7320 6120 706f 696e 7420  JECT is a point \n-0000ed30: 6c69 7374 2061 6e64 2074 6865 7265 2069  list and there i\n-0000ed40: 7320 6e6f 2063 6c6f 7375 7265 2074 6167  s no closure tag\n-0000ed50: 2c20 7468 656e 0a27 7377 6565 7027 2063  , then.'sweep' c\n-0000ed60: 6f6e 6e65 6374 7320 4e2b 3120 7375 6363  onnects N+1 succ\n-0000ed70: 6573 7369 7665 2063 6f70 6965 7320 6f66  essive copies of\n-0000ed80: 2065 6163 6820 706f 696e 7420 2869 6e63   each point (inc\n-0000ed90: 6c75 6469 6e67 2074 6865 0a6f 7269 6769  luding the.origi\n-0000eda0: 6e61 6c29 2077 6974 6820 7374 7261 6967  nal) with straig\n-0000edb0: 6874 206c 696e 6520 7365 676d 656e 7473  ht line segments\n-0000edc0: 2074 6f20 666f 726d 2061 2070 6f6c 796c   to form a polyl\n-0000edd0: 696e 652e 2020 4966 2074 6865 7265 2061  ine.  If there a\n-0000ede0: 7265 0a6d 2070 6f69 6e74 7320 696e 2074  re.m points in t\n-0000edf0: 6865 206f 7269 6769 6e61 6c20 706f 696e  he original poin\n-0000ee00: 7420 6c69 7374 2c20 7468 656e 206d 2070  t list, then m p\n-0000ee10: 6f6c 796c 696e 6573 2077 6974 6820 4e20  olylines with N \n-0000ee20: 7365 676d 656e 7473 0a65 6163 6820 6172  segments.each ar\n-0000ee30: 6520 666f 726d 6564 2062 7920 7468 6520  e formed by the \n-0000ee40: 7377 6565 702e 2020 496e 2074 6869 7320  sweep.  In this \n-0000ee50: 6d61 6e6e 6572 2c20 2773 7765 6570 2720  manner, 'sweep' \n-0000ee60: 666f 726d 7320 6120 7365 7420 6f66 0a6f  forms a set of.o\n-0000ee70: 6e65 2d64 696d 656e 7369 6f6e 616c 206f  ne-dimensional o\n-0000ee80: 626a 6563 7473 2028 706f 6c79 6c69 6e65  bjects (polyline\n-0000ee90: 7329 2066 726f 6d20 7a65 726f 2d64 696d  s) from zero-dim\n-0000eea0: 656e 7369 6f6e 616c 206f 6e65 7320 2870  ensional ones (p\n-0000eeb0: 6f69 6e74 7329 2e0a 0a20 2020 5768 656e  oints)...   When\n-0000eec0: 2074 6865 7265 205f 6973 5f20 6120 636c   there _is_ a cl\n-0000eed0: 6f73 7572 6520 7461 672c 2027 7377 6565  osure tag, 'swee\n-0000eee0: 7027 2063 6f6e 6e65 6374 7320 4e20 7375  p' connects N su\n-0000eef0: 6363 6573 7369 7665 2063 6f70 6965 730a  ccessive copies.\n-0000ef00: 6f66 2065 6163 6820 706f 696e 7420 2869  of each point (i\n-0000ef10: 6e63 6c75 6469 6e67 2074 6865 206f 7269  ncluding the ori\n-0000ef20: 6769 6e61 6c29 2077 6974 6820 7374 7261  ginal) with stra\n-0000ef30: 6967 6874 206c 696e 6520 7365 676d 656e  ight line segmen\n-0000ef40: 7473 2061 6e64 0a66 696e 616c 6c79 2063  ts and.finally c\n-0000ef50: 6f6e 6e65 6374 7320 7468 6520 6c61 7374  onnects the last\n-0000ef60: 2063 6f70 7920 6261 636b 2074 6f20 7468   copy back to th\n-0000ef70: 6520 6f72 6967 696e 616c 2074 6f20 666f  e original to fo\n-0000ef80: 726d 2061 2070 6f6c 7967 6f6e 0a77 6974  rm a polygon.wit\n-0000ef90: 6820 4e20 7369 6465 732e 2020 4966 2074  h N sides.  If t\n-0000efa0: 6865 7265 2061 7265 206d 2070 6f69 6e74  here are m point\n-0000efb0: 7320 696e 2074 6865 206f 7269 6769 6e61  s in the origina\n-0000efc0: 6c20 706f 696e 7420 6c69 7374 2c20 7468  l point list, th\n-0000efd0: 656e 206d 0a70 6f6c 7967 6f6e 7320 7769  en m.polygons wi\n-0000efe0: 7468 204e 2073 6964 6573 2065 6163 6820  th N sides each \n-0000eff0: 6172 6520 666f 726d 6564 2062 7920 7468  are formed by th\n-0000f000: 6520 7377 6565 702e 2020 496e 2074 6869  e sweep.  In thi\n-0000f010: 7320 6d61 6e6e 6572 2c0a 2773 7765 6570  s manner,.'sweep\n-0000f020: 2720 666f 726d 7320 6120 7365 7420 6f66  ' forms a set of\n-0000f030: 2074 776f 2d64 696d 656e 7369 6f6e 616c   two-dimensional\n-0000f040: 206f 626a 6563 7473 2028 706f 6c79 676f   objects (polygo\n-0000f050: 6e73 2920 6672 6f6d 0a7a 6572 6f2d 6469  ns) from.zero-di\n-0000f060: 6d65 6e73 696f 6e61 6c20 6f6e 6573 2028  mensional ones (\n-0000f070: 706f 696e 7473 292e 0a0a 2020 204f 7074  points)...   Opt\n-0000f080: 696f 6e73 206f 6620 7468 6520 2773 7765  ions of the 'swe\n-0000f090: 6570 2720 6172 6520 636f 7069 6564 2064  ep' are copied d\n-0000f0a0: 6972 6563 746c 7920 746f 2074 6865 2072  irectly to the r\n-0000f0b0: 6573 756c 7469 6e67 0a70 6f6c 796c 696e  esulting.polylin\n-0000f0c0: 6528 7329 2e0a 0a1f 0a46 696c 653a 2073  e(s).....File: s\n-0000f0d0: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n-0000f0e0: 653a 2053 7765 7074 206c 696e 6573 2c20  e: Swept lines, \n-0000f0f0: 204e 6578 743a 2053 7765 7074 2070 6f6c   Next: Swept pol\n-0000f100: 7967 6f6e 732c 2020 5072 6576 3a20 5377  ygons,  Prev: Sw\n-0000f110: 6570 7420 706f 696e 7473 2c20 2055 703a  ept points,  Up:\n-0000f120: 2053 7765 6570 730a 0a33 2e32 2e36 2e32   Sweeps..3.2.6.2\n-0000f130: 2053 7765 7074 206c 696e 6573 0a2e 2e2e   Swept lines....\n-0000f140: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000f150: 0a0a 4966 2053 5745 5054 5f4f 424a 4543  ..If SWEPT_OBJEC\n-0000f160: 5420 6973 2061 2070 6f6c 796c 696e 6520  T is a polyline \n-0000f170: 616e 6420 7468 6572 6520 6973 206e 6f20  and there is no \n-0000f180: 636c 6f73 7572 6520 7461 672c 2074 6865  closure tag, the\n-0000f190: 6e20 2773 7765 6570 270a 636f 6e6e 6563  n 'sweep'.connec\n-0000f1a0: 7473 204e 2b31 2073 7563 6365 7373 6976  ts N+1 successiv\n-0000f1b0: 6520 636f 7069 6573 206f 6620 7468 6520  e copies of the \n-0000f1c0: 706f 6c79 6c69 6e65 2028 696e 636c 7564  polyline (includ\n-0000f1d0: 696e 6720 7468 6520 6f72 6967 696e 616c  ing the original\n-0000f1e0: 290a 7769 7468 2066 6f75 722d 7369 6465  ).with four-side\n-0000f1f0: 6420 706f 6c79 676f 6e73 2c20 6561 6368  d polygons, each\n-0000f200: 2070 6169 7220 6f66 2063 6f70 6965 7320   pair of copies \n-0000f210: 6769 7669 6e67 2072 6973 6520 746f 2061  giving rise to a\n-0000f220: 2022 706f 6c79 676f 6e0a 7374 7269 702e   \"polygon.strip.\n-0000f230: 2220 2049 6620 7468 6572 6520 6172 6520  \"  If there are \n-0000f240: 6d20 706f 696e 7473 2069 6e20 7468 6520  m points in the \n-0000f250: 6f72 6967 696e 616c 2070 6f6c 796c 696e  original polylin\n-0000f260: 652c 2074 6865 6e20 286d 2d31 294e 0a70  e, then (m-1)N.p\n-0000f270: 6f6c 7967 6f6e 7320 6172 6520 666f 726d  olygons are form\n-0000f280: 6564 2062 7920 7468 6520 7377 6565 702e  ed by the sweep.\n-0000f290: 2020 5765 2063 616c 6c20 7468 6573 6520    We call these \n-0000f2a0: 2262 6f64 7920 706f 6c79 676f 6e73 222e  \"body polygons\".\n-0000f2b0: 2020 496e 0a74 6869 7320 6d61 6e6e 6572    In.this manner\n-0000f2c0: 2c20 2773 7765 6570 2720 666f 726d 7320  , 'sweep' forms \n-0000f2d0: 6120 7477 6f2d 6469 6d65 6e73 696f 6e61  a two-dimensiona\n-0000f2e0: 6c20 7375 7266 6163 6520 6672 6f6d 2066  l surface from f\n-0000f2f0: 726f 6d20 610a 6f6e 652d 6469 6d65 6e73  rom a.one-dimens\n-0000f300: 696f 6e61 6c20 706f 6c79 6c69 6e65 2e0a  ional polyline..\n-0000f310: 0a20 2020 5468 6520 6f72 6465 7220 6f66  .   The order of\n-0000f320: 2076 6572 7469 6365 7320 7072 6f64 7563   vertices produc\n-0000f330: 6564 2062 7920 2773 7765 6570 2720 6973  ed by 'sweep' is\n-0000f340: 2069 6d70 6f72 7461 6e74 2e20 2049 6620   important.  If \n-0000f350: 610a 706f 6c79 676f 6e27 7320 7665 7274  a.polygon's vert\n-0000f360: 6963 6573 2064 6f20 6e6f 7420 6170 7065  ices do not appe\n-0000f370: 6172 2069 6e20 636f 756e 7465 722d 636c  ar in counter-cl\n-0000f380: 6f63 6b77 6973 6520 6f72 6465 7220 696e  ockwise order in\n-0000f390: 2074 6865 2066 696e 616c 0a69 6d61 6765   the final.image\n-0000f3a0: 2c20 7468 6520 706f 6c79 676f 6e20 7769  , the polygon wi\n-0000f3b0: 6c6c 2062 6520 6375 6c6c 6564 2028 756e  ll be culled (un\n-0000f3c0: 6c65 7373 2027 6375 6c6c 3d66 616c 7365  less 'cull=false\n-0000f3d0: 2720 6973 2073 6574 292e 2020 4966 2074  ' is set).  If t\n-0000f3e0: 6865 0a70 6f69 6e74 7320 696e 2074 6865  he.points in the\n-0000f3f0: 206b 2774 6820 636f 7079 206f 6620 7468   k'th copy of th\n-0000f400: 6520 706f 6c79 6c69 6e65 2061 7265 2050  e polyline are P\n-0000f410: 5f31 2c20 505f 322c 202e 2e2e 2c20 505f  _1, P_2, ..., P_\n-0000f420: 6d2c 2061 6e64 2074 6865 0a70 6f69 6e74  m, and the.point\n-0000f430: 7320 696e 2074 6865 206e 6578 7420 636f  s in the next co\n-0000f440: 7079 2c20 7468 6520 286b 2b31 2973 742c  py, the (k+1)st,\n-0000f450: 2061 7265 2050 5f31 272c 2050 5f32 272c   are P_1', P_2',\n-0000f460: 202e 2e2e 2c20 505f 6d27 2c20 7468 656e   ..., P_m', then\n-0000f470: 0a74 6865 2076 6572 7465 7820 6f72 6465  .the vertex orde\n-0000f480: 7220 6f66 2074 6865 2067 656e 6572 6174  r of the generat\n-0000f490: 6564 2070 6f6c 7967 6f6e 7320 6973 0a20  ed polygons is. \n-0000f4a0: 2020 2020 426f 6479 2070 6f6c 7967 6f6e      Body polygon\n-0000f4b0: 2031 3a20 505f 3220 505f 3120 505f 3127   1: P_2 P_1 P_1'\n-0000f4c0: 2050 5f32 270a 2020 2020 2042 6f64 7920   P_2'.     Body \n-0000f4d0: 706f 6c79 676f 6e20 323a 2050 5f33 2050  polygon 2: P_3 P\n-0000f4e0: 5f32 2050 5f32 2720 505f 3327 0a20 2020  _2 P_2' P_3'.   \n-0000f4f0: 2020 2e2e 2e0a 2020 2020 2042 6f64 7920    ....     Body \n-0000f500: 706f 6c79 676f 6e20 6d2d 313a 2050 5f6d  polygon m-1: P_m\n-0000f510: 2050 5f7b 6d2d 317d 2050 5f7b 6d2d 317d   P_{m-1} P_{m-1}\n-0000f520: 2720 505f 6d27 0a0a 2020 204f 7074 696f  ' P_m'..   Optio\n-0000f530: 6e73 206f 6620 756e 636c 6f73 6564 206c  ns of unclosed l\n-0000f540: 696e 6520 7377 6565 7073 2061 7265 2063  ine sweeps are c\n-0000f550: 6f70 6965 6420 746f 2065 6163 6820 6f75  opied to each ou\n-0000f560: 7470 7574 2070 6f6c 7967 6f6e 2e0a 4f70  tput polygon..Op\n-0000f570: 7469 6f6e 7320 6f66 2074 6865 2073 7765  tions of the swe\n-0000f580: 7074 206c 696e 6520 6172 6520 6967 6e6f  pt line are igno\n-0000f590: 7265 642e 0a0a 2020 2057 6865 6e20 7468  red...   When th\n-0000f5a0: 6572 6520 5f69 735f 2061 2063 6c6f 7375  ere _is_ a closu\n-0000f5b0: 7265 2074 6167 2c20 7468 656e 2027 7377  re tag, then 'sw\n-0000f5c0: 6565 7027 2063 6f6e 6e65 6374 7320 4e20  eep' connects N \n-0000f5d0: 7375 6363 6573 7369 7665 0a63 6f70 6965  successive.copie\n-0000f5e0: 7320 6f66 2074 6865 2070 6f6c 796c 696e  s of the polylin\n-0000f5f0: 6520 2869 6e63 6c75 6469 6e67 2074 6865  e (including the\n-0000f600: 206f 7269 6769 6e61 6c29 2077 6974 6820   original) with \n-0000f610: 666f 7572 2d73 6964 6564 2062 6f64 790a  four-sided body.\n-0000f620: 706f 6c79 676f 6e73 206a 7573 7420 6173  polygons just as\n-0000f630: 2074 6865 2063 6173 6520 7769 7468 206e   the case with n\n-0000f640: 6f20 636c 6f73 7572 6520 7461 672e 2020  o closure tag.  \n-0000f650: 4974 2074 6865 6e20 636f 6e6e 6563 7473  It then connects\n-0000f660: 2074 6865 0a6c 6173 7420 636f 7079 2062   the.last copy b\n-0000f670: 6163 6b20 746f 2074 6865 206f 7269 6769  ack to the origi\n-0000f680: 6e61 6c20 746f 2066 6f72 6d20 6120 7269  nal to form a ri\n-0000f690: 6262 6f6e 2d73 6861 7065 6420 7375 7266  bbon-shaped surf\n-0000f6a0: 6163 6520 7468 6174 0a63 6c6f 7365 7320  ace that.closes \n-0000f6b0: 6f6e 2069 7473 656c 6620 7769 7468 2074  on itself with t\n-0000f6c0: 776f 2068 6f6c 6573 2072 656d 6169 6e69  wo holes remaini\n-0000f6d0: 6e67 2e0a 0a20 2020 4669 6e61 6c6c 792c  ng...   Finally,\n-0000f6e0: 2074 6865 2073 7765 6570 2061 6464 7320   the sweep adds \n-0000f6f0: 7477 6f20 6d6f 7265 2070 6f6c 7967 6f6e  two more polygon\n-0000f700: 7320 746f 2073 6561 6c20 7468 6520 686f  s to seal the ho\n-0000f710: 6c65 7320 616e 6420 666f 726d 0a61 2063  les and form.a c\n-0000f720: 6c6f 7365 6420 7375 7266 6163 6520 7468  losed surface th\n-0000f730: 6174 2c20 6465 7065 6e64 696e 6720 6f6e  at, depending on\n-0000f740: 2074 6865 2073 7765 6570 2074 7261 6e73   the sweep trans\n-0000f750: 666f 726d 732c 206d 6179 2072 6570 7265  forms, may repre\n-0000f760: 7365 6e74 0a74 6865 2062 6f75 6e64 6172  sent.the boundar\n-0000f770: 7920 6f66 2061 2073 6f6c 6964 2e20 2049  y of a solid.  I\n-0000f780: 6e20 7468 6973 206d 616e 6e65 722c 2027  n this manner, '\n-0000f790: 7377 6565 7027 2066 6f72 6d73 2074 6865  sweep' forms the\n-0000f7a0: 2062 6f75 6e64 6172 7920 6f66 0a61 2074   boundary of.a t\n-0000f7b0: 6872 6565 2d64 696d 656e 7369 6f6e 616c  hree-dimensional\n-0000f7c0: 206f 626a 6563 7420 6672 6f6d 2061 206f   object from a o\n-0000f7d0: 6e65 2d64 696d 656e 7369 6f6e 616c 2070  ne-dimensional p\n-0000f7e0: 6f6c 796c 696e 652e 2020 5765 2063 616c  olyline.  We cal\n-0000f7f0: 6c0a 7468 6573 6520 686f 6c65 2d66 696c  l.these hole-fil\n-0000f800: 6c69 6e67 2070 6f6c 7967 6f6e 7320 2265  ling polygons \"e\n-0000f810: 6e64 7322 2e0a 0a20 2020 5468 6520 6f72  nds\"...   The or\n-0000f820: 6465 7220 6f66 2076 6572 7469 6365 7320  der of vertices \n-0000f830: 6f66 2065 6e64 2070 6f6c 7967 6f6e 7320  of end polygons \n-0000f840: 6973 2069 6d70 6f72 7461 6e74 2066 6f72  is important for\n-0000f850: 2063 6f72 7265 6374 0a63 756c 6c69 6e67   correct.culling\n-0000f860: 2061 7320 6465 7363 7269 6265 6420 6162   as described ab\n-0000f870: 6f76 652e 2020 4966 2050 5f31 5e31 2c20  ove.  If P_1^1, \n-0000f880: 505f 315e 322c 202e 2e2e 2c20 505f 315e  P_1^2, ..., P_1^\n-0000f890: 6e20 6172 6520 7468 6520 4e0a 636f 7069  n are the N.copi\n-0000f8a0: 6573 206f 6620 7468 6520 6669 7273 7420  es of the first \n-0000f8b0: 706f 6c79 6c69 6e65 2070 6f69 6e74 2061  polyline point a\n-0000f8c0: 6e64 2050 5f6d 5e31 2c20 505f 6d5e 322c  nd P_m^1, P_m^2,\n-0000f8d0: 202e 2e2e 202c 505f 6d5e 6e20 6172 6520   ... ,P_m^n are \n-0000f8e0: 7468 650a 4e20 636f 7069 6573 206f 6620  the.N copies of \n-0000f8f0: 7468 6520 6c61 7374 2070 6f6c 796c 696e  the last polylin\n-0000f900: 6520 706f 696e 742c 2074 6865 6e20 7468  e point, then th\n-0000f910: 6520 656e 6420 706f 6c79 676f 6e20 7665  e end polygon ve\n-0000f920: 7274 6578 206f 7264 6572 0a69 730a 2020  rtex order.is.  \n-0000f930: 2020 2045 6e64 2070 6f6c 7967 6f6e 2031     End polygon 1\n-0000f940: 3a20 505f 315e 6e2c 2050 5f31 5e7b 6e2d  : P_1^n, P_1^{n-\n-0000f950: 317d 2c20 2e2e 2e20 2c50 5f31 5e31 0a20  1}, ... ,P_1^1. \n-0000f960: 2020 2020 456e 6420 706f 6c79 676f 6e20      End polygon \n-0000f970: 323a 2050 5f6d 5e31 2c20 505f 6d5e 322c  2: P_m^1, P_m^2,\n-0000f980: 202e 2e2e 202c 505f 6d5e 6e0a 0a20 2020   ... ,P_m^n..   \n-0000f990: 4966 2074 6865 7265 2061 7265 206e 6f20  If there are no \n-0000f9a0: 6f70 7469 6f6e 7320 6f6e 2074 6865 2073  options on the s\n-0000f9b0: 7765 7074 206c 696e 652c 2074 6865 6e20  wept line, then \n-0000f9c0: 7468 6520 2773 7765 6570 2720 6f70 7469  the 'sweep' opti\n-0000f9d0: 6f6e 730a 6172 6520 636f 7069 6564 2074  ons.are copied t\n-0000f9e0: 6f20 6561 6368 206f 7574 7075 7420 706f  o each output po\n-0000f9f0: 6c79 676f 6e2e 2020 4966 2074 6865 2073  lygon.  If the s\n-0000fa00: 7765 7074 206c 696e 6520 646f 6573 2068  wept line does h\n-0000fa10: 6176 6520 6f70 7469 6f6e 732c 0a74 6865  ave options,.the\n-0000fa20: 7365 2061 7265 2063 6f70 6965 6420 746f  se are copied to\n-0000fa30: 2063 6f72 7265 7370 6f6e 6469 6e67 2062   corresponding b\n-0000fa40: 6f64 7920 706f 6c79 676f 6e73 3b20 7468  ody polygons; th\n-0000fa50: 6520 7377 6565 7020 6f70 7469 6f6e 7320  e sweep options \n-0000fa60: 6172 650a 636f 7069 6564 2074 6f20 7468  are.copied to th\n-0000fa70: 6520 656e 6420 706f 6c79 676f 6e73 2e20  e end polygons. \n-0000fa80: 2049 6e20 7468 6973 206d 616e 6e65 722c   In this manner,\n-0000fa90: 2062 6f64 7920 616e 6420 656e 6473 206d   body and ends m\n-0000faa0: 6179 2062 6520 6472 6177 6e0a 7769 7468  ay be drawn.with\n-0000fab0: 2064 6966 6665 7265 6e74 2063 6861 7261   different chara\n-0000fac0: 6374 6572 6973 7469 6373 2073 7563 6820  cteristics such \n-0000fad0: 6173 2027 6669 6c6c 636f 6c6f 7227 2e0a  as 'fillcolor'..\n-0000fae0: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n-0000faf0: 696e 666f 2c20 204e 6f64 653a 2053 7765  info,  Node: Swe\n-0000fb00: 7074 2070 6f6c 7967 6f6e 732c 2020 4e65  pt polygons,  Ne\n-0000fb10: 7874 3a20 5377 6570 7420 626c 6f63 6b73  xt: Swept blocks\n-0000fb20: 2c20 2050 7265 763a 2053 7765 7074 206c  ,  Prev: Swept l\n-0000fb30: 696e 6573 2c20 2055 703a 2053 7765 6570  ines,  Up: Sweep\n-0000fb40: 730a 0a33 2e32 2e36 2e33 2053 7765 7074  s..3.2.6.3 Swept\n-0000fb50: 2070 6f6c 7967 6f6e 730a 2e2e 2e2e 2e2e   polygons.......\n+0000d970: 2020 2020 2020 4772 6f75 7020 6f74 6865        Group othe\n+0000d980: 7220 6472 6177 6162 6c65 732e 0a2a 2052  r drawables..* R\n+0000d990: 6570 6561 7473 3a3a 2020 2020 2020 2020  epeats::        \n+0000d9a0: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n+0000d9b0: 7720 7472 616e 7366 6f72 6d65 6420 636f  w transformed co\n+0000d9c0: 7069 6573 206f 6620 6f62 6a65 6374 732e  pies of objects.\n+0000d9d0: 0a2a 2050 7574 733a 3a20 2020 2020 2020  .* Puts::       \n+0000d9e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000d9f0: 2044 7261 7720 6f6e 6520 6f62 6a65 6374   Draw one object\n+0000da00: 2074 7261 6e73 666f 726d 6564 2e0a 0a1f   transformed....\n+0000da10: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n+0000da20: 666f 2c20 204e 6f64 653a 2044 6f74 732c  fo,  Node: Dots,\n+0000da30: 2020 4e65 7874 3a20 4c69 6e65 732c 2020    Next: Lines,  \n+0000da40: 5072 6576 3a20 4472 6177 6162 6c65 732c  Prev: Drawables,\n+0000da50: 2020 5570 3a20 4472 6177 6162 6c65 730a    Up: Drawables.\n+0000da60: 0a33 2e32 2e31 2044 6f74 730a 2d2d 2d2d  .3.2.1 Dots.----\n+0000da70: 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 783a  ------..*Syntax:\n+0000da80: 2a0a 2020 2020 2064 6f74 735b 4f50 5449  *.     dots[OPTI\n+0000da90: 4f4e 535d 2050 4f49 4e54 5f4c 4953 540a  ONS] POINT_LIST.\n+0000daa0: 5468 6973 2063 6f6d 6d61 6e64 2069 7320  This command is \n+0000dab0: 7468 6520 7468 7265 652d 6469 6d65 6e73  the three-dimens\n+0000dac0: 696f 6e61 6c20 6571 7569 7661 6c65 6e74  ional equivalent\n+0000dad0: 206f 6620 7468 6520 2750 5354 7269 636b   of the 'PSTrick\n+0000dae0: 7327 0a63 6f6d 6d61 6e64 2027 5c70 7364  s'.command '\\psd\n+0000daf0: 6f74 7327 2e0a 0a1f 0a46 696c 653a 2073  ots'.....File: s\n+0000db00: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n+0000db10: 653a 204c 696e 6573 2c20 204e 6578 743a  e: Lines,  Next:\n+0000db20: 2043 7572 7665 732c 2020 5072 6576 3a20   Curves,  Prev: \n+0000db30: 446f 7473 2c20 2055 703a 2044 7261 7761  Dots,  Up: Drawa\n+0000db40: 626c 6573 0a0a 332e 322e 3220 4c69 6e65  bles..3.2.2 Line\n+0000db50: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a  s.-----------..*\n+0000db60: 5379 6e74 6178 3a2a 0a20 2020 2020 6c69  Syntax:*.     li\n+0000db70: 6e65 5b4f 5054 494f 4e53 5d20 504f 494e  ne[OPTIONS] POIN\n+0000db80: 545f 4c49 5354 0a54 6869 7320 636f 6d6d  T_LIST.This comm\n+0000db90: 616e 6420 6973 2074 6865 2074 6872 6565  and is the three\n+0000dba0: 2d64 696d 656e 7369 6f6e 616c 2065 7175  -dimensional equ\n+0000dbb0: 6976 616c 656e 7420 6f66 2074 6865 2027  ivalent of the '\n+0000dbc0: 5053 5472 6963 6b73 270a 636f 6d6d 616e  PSTricks'.comman\n+0000dbd0: 6420 275c 7073 6c69 6e65 272e 0a0a 1f0a  d '\\psline'.....\n+0000dbe0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n+0000dbf0: 6f2c 2020 4e6f 6465 3a20 4375 7276 6573  o,  Node: Curves\n+0000dc00: 2c20 204e 6578 743a 2050 6f6c 7967 6f6e  ,  Next: Polygon\n+0000dc10: 732c 2020 5072 6576 3a20 4c69 6e65 732c  s,  Prev: Lines,\n+0000dc20: 2020 5570 3a20 4472 6177 6162 6c65 730a    Up: Drawables.\n+0000dc30: 0a33 2e32 2e33 2043 7572 7665 730a 2d2d  .3.2.3 Curves.--\n+0000dc40: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e  ----------..*Syn\n+0000dc50: 7461 783a 2a0a 2020 2020 2063 7572 7665  tax:*.     curve\n+0000dc60: 5b4f 5054 494f 4e53 5d20 504f 494e 545f  [OPTIONS] POINT_\n+0000dc70: 4c49 5354 0a54 6869 7320 636f 6d6d 616e  LIST.This comman\n+0000dc80: 6420 6973 2074 6865 2074 6872 6565 2d64  d is the three-d\n+0000dc90: 696d 656e 7369 6f6e 616c 2065 7175 6976  imensional equiv\n+0000dca0: 616c 656e 7420 6f66 2074 6865 2027 5053  alent of the 'PS\n+0000dcb0: 5472 6963 6b73 270a 636f 6d6d 616e 6420  Tricks'.command \n+0000dcc0: 275c 7073 6375 7276 6527 2e20 2049 7420  '\\pscurve'.  It \n+0000dcd0: 6973 206e 6f74 2069 6d70 6c65 6d65 6e74  is not implement\n+0000dce0: 6564 2069 6e20 7468 6520 6375 7272 656e  ed in the curren\n+0000dcf0: 7420 7665 7273 696f 6e20 6f66 0a27 736b  t version of.'sk\n+0000dd00: 6574 6368 272e 0a0a 1f0a 4669 6c65 3a20  etch'.....File: \n+0000dd10: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n+0000dd20: 6465 3a20 506f 6c79 676f 6e73 2c20 204e  de: Polygons,  N\n+0000dd30: 6578 743a 2053 7065 6369 616c 732c 2020  ext: Specials,  \n+0000dd40: 5072 6576 3a20 4375 7276 6573 2c20 2055  Prev: Curves,  U\n+0000dd50: 703a 2044 7261 7761 626c 6573 0a0a 332e  p: Drawables..3.\n+0000dd60: 322e 3420 506f 6c79 676f 6e73 0a2d 2d2d  2.4 Polygons.---\n+0000dd70: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a 5379  -----------..*Sy\n+0000dd80: 6e74 6178 3a2a 0a20 2020 2020 706f 6c79  ntax:*.     poly\n+0000dd90: 676f 6e5b 4f50 5449 4f4e 535d 2050 4f49  gon[OPTIONS] POI\n+0000dda0: 4e54 5f4c 4953 540a 5468 6973 2063 6f6d  NT_LIST.This com\n+0000ddb0: 6d61 6e64 2069 7320 7468 6520 7468 7265  mand is the thre\n+0000ddc0: 652d 6469 6d65 6e73 696f 6e61 6c20 6571  e-dimensional eq\n+0000ddd0: 7569 7661 6c65 6e74 206f 6620 7468 6520  uivalent of the \n+0000dde0: 2750 5354 7269 636b 7327 0a63 6f6d 6d61  'PSTricks'.comma\n+0000ddf0: 6e64 2027 5c70 7370 6f6c 7967 6f6e 272e  nd '\\pspolygon'.\n+0000de00: 2020 5468 6520 2773 6b65 7463 6827 2068    The 'sketch' h\n+0000de10: 6964 6465 6e20 7375 7266 6163 6520 616c  idden surface al\n+0000de20: 676f 7269 7468 6d20 6173 7375 6d65 730a  gorithm assumes.\n+0000de30: 7468 6174 2070 6f6c 7967 6f6e 7320 6172  that polygons ar\n+0000de40: 6520 636f 6e76 6578 2061 6e64 2070 6c61  e convex and pla\n+0000de50: 6e61 722e 2020 496e 2070 7261 6374 6963  nar.  In practic\n+0000de60: 652c 2064 7261 7769 6e67 7320 6d61 7920  e, drawings may \n+0000de70: 7765 6c6c 0a74 7572 6e20 6f75 7420 636f  well.turn out co\n+0000de80: 7272 6563 746c 7920 6576 656e 2069 6620  rrectly even if \n+0000de90: 7468 6573 6520 6173 7375 6d70 7469 6f6e  these assumption\n+0000dea0: 7320 6172 6520 7669 6f6c 6174 6564 2e0a  s are violated..\n+0000deb0: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n+0000dec0: 696e 666f 2c20 204e 6f64 653a 2053 7065  info,  Node: Spe\n+0000ded0: 6369 616c 732c 2020 4e65 7874 3a20 5377  cials,  Next: Sw\n+0000dee0: 6565 7073 2c20 2050 7265 763a 2050 6f6c  eeps,  Prev: Pol\n+0000def0: 7967 6f6e 732c 2020 5570 3a20 4472 6177  ygons,  Up: Draw\n+0000df00: 6162 6c65 730a 0a33 2e32 2e35 2053 7065  ables..3.2.5 Spe\n+0000df10: 6369 616c 730a 2d2d 2d2d 2d2d 2d2d 2d2d  cials.----------\n+0000df20: 2d2d 2d2d 0a0a 2a53 796e 7461 783a 2a0a  ----..*Syntax:*.\n+0000df30: 2020 2020 2073 7065 6369 616c 2024 5241       special $RA\n+0000df40: 575f 5445 5854 245b 4f50 5449 4f4e 535d  W_TEXT$[OPTIONS]\n+0000df50: 2041 5247 5f4c 4953 540a 4865 7265 2027   ARG_LIST.Here '\n+0000df60: 2427 2063 616e 2062 6520 616e 7920 6368  $' can be any ch\n+0000df70: 6172 6163 7465 7220 616e 6420 6973 2075  aracter and is u\n+0000df80: 7365 6420 746f 2064 656c 696d 6974 2074  sed to delimit t\n+0000df90: 6865 2073 7461 7274 2061 6e64 2065 6e64  he start and end\n+0000dfa0: 0a6f 6620 5241 575f 5445 5854 2e20 2054  .of RAW_TEXT.  T\n+0000dfb0: 6865 2063 6f6d 6d61 6e64 2065 6d62 6564  he command embed\n+0000dfc0: 7320 5241 575f 5445 5854 2069 6e20 7468  s RAW_TEXT in th\n+0000dfd0: 6520 2773 6b65 7463 6827 206f 7574 7075  e 'sketch' outpu\n+0000dfe0: 7420 6166 7465 720a 7065 7266 6f72 6d69  t after.performi\n+0000dff0: 6e67 2073 7562 7374 6974 7574 696f 6e73  ng substitutions\n+0000e000: 2061 7320 666f 6c6c 6f77 732e 0a20 2020   as follows..   \n+0000e010: 2a20 2723 4927 2077 6865 7265 2049 2069  * '#I' where I i\n+0000e020: 7320 6120 706f 7369 7469 7665 2069 6e74  s a positive int\n+0000e030: 6567 6572 2069 7320 7265 706c 6163 6564  eger is replaced\n+0000e040: 2062 7920 7468 6520 4927 7468 2076 616c   by the I'th val\n+0000e050: 7565 2069 6e0a 2020 2020 2041 5247 5f4c  ue in.     ARG_L\n+0000e060: 4953 542e 2020 506f 696e 7420 616e 6420  IST.  Point and \n+0000e070: 7665 6374 6f72 2061 7267 756d 656e 7473  vector arguments\n+0000e080: 2062 6563 6f6d 6520 7477 6f2d 6469 6d65   become two-dime\n+0000e090: 6e73 696f 6e61 6c0a 2020 2020 2070 6f69  nsional.     poi\n+0000e0a0: 6e74 732c 2077 6869 6368 2061 7265 2074  nts, which are t\n+0000e0b0: 6865 2074 7261 6e73 666f 726d 6564 2033  he transformed 3\n+0000e0c0: 6420 6172 6775 6d65 6e74 7320 7072 6f6a  d arguments proj\n+0000e0d0: 6563 7465 6420 6f6e 746f 2074 6865 0a20  ected onto the. \n+0000e0e0: 2020 2020 582d 5920 706c 616e 652e 2020      X-Y plane.  \n+0000e0f0: 5468 6973 2061 6c6c 6f77 7320 7477 6f2d  This allows two-\n+0000e100: 6469 6d65 6e74 696f 6e61 6c20 6f75 7470  dimentional outp\n+0000e110: 7574 2065 6c65 6d65 6e74 7320 7375 6368  ut elements such\n+0000e120: 2061 730a 2020 2020 206c 6162 656c 7320   as.     labels \n+0000e130: 746f 2062 6520 6561 7369 6c79 2070 6f73  to be easily pos\n+0000e140: 6974 696f 6e65 6420 7769 7468 2072 6573  itioned with res\n+0000e150: 7065 6374 2074 6f20 7468 7265 652d 6469  pect to three-di\n+0000e160: 6d65 6e73 696f 6e61 6c0a 2020 2020 2066  mensional.     f\n+0000e170: 6561 7475 7265 7320 696e 2074 6865 2064  eatures in the d\n+0000e180: 7261 7769 6e67 2e20 2053 6361 6c61 7220  rawing.  Scalar \n+0000e190: 6172 6775 6d65 6e74 7320 6172 6520 7375  arguments are su\n+0000e1a0: 6273 6974 7574 6564 2064 6972 6563 746c  bsituted directl\n+0000e1b0: 792e 0a20 2020 2020 4e6f 2074 7261 6e73  y..     No trans\n+0000e1c0: 666f 726d 6174 696f 6e20 6973 2061 7070  formation is app\n+0000e1d0: 6c69 6564 2e0a 2020 202a 2027 237b 497d  lied..   * '#{I}\n+0000e1e0: 2720 6973 2061 6c73 6f20 7265 706c 6163  ' is also replac\n+0000e1f0: 6564 2061 7320 6162 6f76 652e 0a20 2020  ed as above..   \n+0000e200: 2a20 2723 4927 3227 2069 7320 7265 706c  * '#I'2' is repl\n+0000e210: 6163 6564 2061 7320 6162 6f76 6520 666f  aced as above fo\n+0000e220: 7220 706f 696e 7473 206f 7220 7665 6374  r points or vect\n+0000e230: 6f72 732e 2020 4974 2069 7320 616e 2065  ors.  It is an e\n+0000e240: 7272 6f72 0a20 2020 2020 666f 7220 7468  rror.     for th\n+0000e250: 6520 4927 7468 2061 7267 756d 656e 7420  e I'th argument \n+0000e260: 746f 2062 6520 6120 7363 616c 6172 2e0a  to be a scalar..\n+0000e270: 2020 202a 2027 2349 2778 272c 2027 2349     * '#I'x', '#I\n+0000e280: 2779 272c 206f 7220 2723 4927 7a27 2069  'y', or '#I'z' i\n+0000e290: 7320 7265 706c 6163 6564 2c20 7265 7370  s replaced, resp\n+0000e2a0: 6563 7469 7665 6c79 2c20 6279 2074 6865  ectively, by the\n+0000e2b0: 2073 6361 6c61 720a 2020 2020 2058 2c20   scalar.     X, \n+0000e2c0: 592c 206f 7220 5a2d 636f 6f72 6469 6e61  Y, or Z-coordina\n+0000e2d0: 7465 206f 6620 7468 6520 6172 6775 6d65  te of the argume\n+0000e2e0: 6e74 2070 6f69 6e74 206f 7220 7665 6374  nt point or vect\n+0000e2f0: 6f72 2e20 2049 7420 6973 2061 6e0a 2020  or.  It is an.  \n+0000e300: 2020 2065 7272 6f72 2066 6f72 2074 6865     error for the\n+0000e310: 2049 2774 6820 6172 6775 6d65 6e74 2074   I'th argument t\n+0000e320: 6f20 6265 2061 2073 6361 6c61 722e 0a20  o be a scalar.. \n+0000e330: 2020 2a20 2723 4927 3327 2069 7320 7265    * '#I'3' is re\n+0000e340: 706c 6163 6564 2062 7920 7468 6520 7468  placed by the th\n+0000e350: 7265 652d 6469 6d65 6e73 696f 6e61 6c20  ree-dimensional \n+0000e360: 7472 616e 7366 6f72 6d65 6420 6172 6775  transformed argu\n+0000e370: 6d65 6e74 2e0a 2020 2020 204e 6f74 6520  ment..     Note \n+0000e380: 7468 6174 2069 6620 6120 7065 7273 7065  that if a perspe\n+0000e390: 6374 6976 6520 7472 616e 7366 6f72 6d61  ctive transforma\n+0000e3a0: 7469 6f6e 2068 6173 2062 6565 6e20 6170  tion has been ap\n+0000e3b0: 706c 6965 642c 2074 6865 0a20 2020 2020  plied, the.     \n+0000e3c0: 5a2d 636f 6f72 6469 6e61 7465 2068 6173  Z-coordinate has\n+0000e3d0: 206c 6974 746c 6520 6765 6f6d 6574 7269   little geometri\n+0000e3e0: 6320 7369 676e 6966 6963 616e 6365 2c20  c significance, \n+0000e3f0: 7468 6f75 6768 2069 740a 2020 2020 2061  though it.     a\n+0000e400: 6363 7572 6174 656c 7920 696e 6469 6361  ccurately indica\n+0000e410: 7465 7320 7265 6c61 7469 7665 2064 6570  tes relative dep\n+0000e420: 7468 2e0a 2020 202a 2027 2349 2d4a 2720  th..   * '#I-J' \n+0000e430: 7768 6572 6520 4920 616e 6420 4a20 6172  where I and J ar\n+0000e440: 6520 706f 7369 7469 7665 2069 6e74 6567  e positive integ\n+0000e450: 6572 7320 6973 2072 6570 6c61 6365 6420  ers is replaced \n+0000e460: 6279 2061 2073 7472 696e 670a 2020 2020  by a string.    \n+0000e470: 2027 7b41 4e47 4c45 7d27 2077 6865 7265   '{ANGLE}' where\n+0000e480: 2041 4e47 4c45 2069 7320 7468 6520 706f   ANGLE is the po\n+0000e490: 6c61 7220 616e 676c 6520 6f66 2061 2076  lar angle of a v\n+0000e4a0: 6563 746f 7220 6672 6f6d 2074 6865 2049  ector from the I\n+0000e4b0: 2774 680a 2020 2020 2070 6f69 6e74 2069  'th.     point i\n+0000e4c0: 6e20 504f 494e 545f 4c49 5354 2074 6f20  n POINT_LIST to \n+0000e4d0: 7468 6520 4a27 7468 2070 6f69 6e74 2070  the J'th point p\n+0000e4e0: 726f 6a65 6374 6564 2069 6e74 6f20 7468  rojected into th\n+0000e4f0: 6520 782d 7920 706c 616e 652e 0a20 2020  e x-y plane..   \n+0000e500: 2020 4974 2069 7320 616e 2065 7272 6f72    It is an error\n+0000e510: 2066 6f72 2074 6865 2049 2774 6820 6f72   for the I'th or\n+0000e520: 204a 2774 6820 6172 6775 6d65 6e74 2074   J'th argument t\n+0000e530: 6f20 6265 2061 2073 6361 6c61 7220 6f72  o be a scalar or\n+0000e540: 2061 0a20 2020 2020 7665 6374 6f72 2e0a   a.     vector..\n+0000e550: 2020 202a 2027 237b 492d 4a7d 2720 6973     * '#{I-J}' is\n+0000e560: 2061 6c73 6f20 7265 706c 6163 6564 2061   also replaced a\n+0000e570: 7320 6162 6f76 652e 0a20 2020 2a20 2723  s above..   * '#\n+0000e580: 2327 2069 7320 7265 706c 6163 6564 2077  #' is replaced w\n+0000e590: 6974 6820 2723 272e 0a54 6865 2066 6f72  ith '#'..The for\n+0000e5a0: 6d73 2077 6974 6820 6272 6163 6573 2027  ms with braces '\n+0000e5b0: 7b20 7d27 2061 7265 2075 7365 6675 6c20  { }' are useful \n+0000e5c0: 7768 656e 2074 6865 2061 7267 756d 656e  when the argumen\n+0000e5d0: 7420 6973 2069 6d6d 6564 6961 7465 6c79  t is immediately\n+0000e5e0: 0a66 6f6c 6c6f 7765 6420 6279 2061 2064  .followed by a d\n+0000e5f0: 6967 6974 206f 7220 6120 7469 636b 2063  igit or a tick c\n+0000e600: 6861 7261 6374 6572 2074 6861 7420 6973  haracter that is\n+0000e610: 2070 6172 7420 6f66 2074 6865 2054 6558   part of the TeX\n+0000e620: 2063 6f64 652e 0a0a 2020 2054 6865 206f   code...   The o\n+0000e630: 6e6c 7920 7573 6566 756c 206f 7074 696f  nly useful optio\n+0000e640: 6e20 6f66 2027 7370 6563 6961 6c27 2069  n of 'special' i\n+0000e650: 7320 276c 6179 272c 2077 6869 6368 2064  s 'lay', which d\n+0000e660: 6574 6572 6d69 6e65 7320 6966 2074 6865  etermines if the\n+0000e670: 0a73 7562 7374 6974 7565 6420 7261 7720  .substitued raw \n+0000e680: 7465 7874 2069 7320 656d 6974 7465 6420  text is emitted \n+0000e690: 6265 666f 7265 2c20 6166 7465 722c 206f  before, after, o\n+0000e6a0: 7220 7573 696e 6720 7468 6520 6669 7273  r using the firs\n+0000e6b0: 7420 706f 696e 740a 696e 2050 4f49 4e54  t point.in POINT\n+0000e6c0: 5f4c 4953 5420 6173 2061 6e20 696e 6469  _LIST as an indi\n+0000e6d0: 6361 746f 7220 6f66 2064 6570 7468 2e20  cator of depth. \n+0000e6e0: 2054 6865 7365 206f 6363 7572 2c20 7265   These occur, re\n+0000e6f0: 7370 6563 7469 7665 6c79 2c20 7769 7468  spectively, with\n+0000e700: 0a27 6c61 793d 756e 6465 7227 2c20 276c  .'lay=under', 'l\n+0000e710: 6179 3d6f 7665 7227 2c20 616e 6420 276c  ay=over', and 'l\n+0000e720: 6179 3d69 6e27 2e20 2053 6565 202a 6e6f  ay=in'.  See *no\n+0000e730: 7465 2053 7065 6369 616c 206f 626a 6563  te Special objec\n+0000e740: 7473 3a3a 2061 6e64 0a2a 6e6f 7465 2054  ts:: and.*note T\n+0000e750: 696b 5a2f 5047 4620 7573 6572 2d64 6566  ikZ/PGF user-def\n+0000e760: 696e 6564 2073 7479 6c65 733a 3a20 666f  ined styles:: fo\n+0000e770: 7220 6578 616d 706c 6573 2e20 202a 4e6f  r examples.  *No\n+0000e780: 7465 2049 6e74 6572 6e61 6c0a 6f70 7469  te Internal.opti\n+0000e790: 6f6e 733a 3a2e 0a0a 1f0a 4669 6c65 3a20  ons::.....File: \n+0000e7a0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n+0000e7b0: 6465 3a20 5377 6565 7073 2c20 204e 6578  de: Sweeps,  Nex\n+0000e7c0: 743a 2042 6c6f 636b 732c 2020 5072 6576  t: Blocks,  Prev\n+0000e7d0: 3a20 5370 6563 6961 6c73 2c20 2055 703a  : Specials,  Up:\n+0000e7e0: 2044 7261 7761 626c 6573 0a0a 332e 322e   Drawables..3.2.\n+0000e7f0: 3620 5377 6565 7073 0a2d 2d2d 2d2d 2d2d  6 Sweeps.-------\n+0000e800: 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a  -----..*Syntax:*\n+0000e810: 0a20 2020 2020 7377 6565 7020 7b20 4e2c  .     sweep { N,\n+0000e820: 2054 5f31 2c20 545f 322c 202e 2e2e 2c20   T_1, T_2, ..., \n+0000e830: 545f 5220 7d5b 4f50 5449 4f4e 535d 2053  T_R }[OPTIONS] S\n+0000e840: 5745 5054 5f4f 424a 4543 540a 2020 2020  WEPT_OBJECT.    \n+0000e850: 2073 7765 6570 207b 204e 3c3e 2c20 545f   sweep { N<>, T_\n+0000e860: 312c 2054 5f32 2c20 2e2e 2e2c 2054 5f52  1, T_2, ..., T_R\n+0000e870: 207d 5b4f 5054 494f 4e53 5d20 5357 4550   }[OPTIONS] SWEP\n+0000e880: 545f 4f42 4a45 4354 0a54 6865 2073 7765  T_OBJECT.The swe\n+0000e890: 6570 2063 6f6e 6e65 6374 7320 4e20 286f  ep connects N (o\n+0000e8a0: 7220 7065 7268 6170 7320 4e2b 3129 2063  r perhaps N+1) c\n+0000e8b0: 6f70 6965 7320 6f66 2053 5745 5054 5f4f  opies of SWEPT_O\n+0000e8c0: 424a 4543 5420 696e 206f 7264 6572 2074  BJECT in order t\n+0000e8d0: 6f0a 6372 6561 7465 2061 206e 6577 206f  o.create a new o\n+0000e8e0: 626a 6563 7420 6f66 2068 6967 6865 7220  bject of higher \n+0000e8f0: 6469 6d65 6e73 696f 6e2e 2020 5468 6520  dimension.  The \n+0000e900: 545f 4920 2866 6f72 2069 2062 6574 7765  T_I (for i betwe\n+0000e910: 656e 2031 2061 6e64 0a72 2920 6172 6520  en 1 and.r) are \n+0000e920: 7472 616e 7366 6f72 6d73 2e20 2054 6865  transforms.  The\n+0000e930: 206b 2774 6820 636f 7079 206f 6620 5357   k'th copy of SW\n+0000e940: 4550 545f 4f42 4a45 4354 2069 7320 7072  EPT_OBJECT is pr\n+0000e950: 6f64 7563 6564 2062 790a 6170 706c 7969  oduced by.applyi\n+0000e960: 6e67 2074 6865 2066 6f6c 6c6f 7769 6e67  ng the following\n+0000e970: 2074 7261 6e73 666f 726d 2074 6f20 7468   transform to th\n+0000e980: 6520 6f72 6967 696e 616c 2e0a 2020 2020  e original..    \n+0000e990: 2054 5f31 5e6b 2074 6865 6e20 545f 325e   T_1^k then T_2^\n+0000e9a0: 6b20 7468 656e 202e 2e2e 2074 6865 6e20  k then ... then \n+0000e9b0: 545f 525e 6b0a 4865 7265 2054 5e6b 206d  T_R^k.Here T^k m\n+0000e9c0: 6561 6e73 2022 7472 616e 7366 6f72 6d20  eans \"transform \n+0000e9d0: 5420 6170 706c 6965 6420 6b20 7469 6d65  T applied k time\n+0000e9e0: 732e 2220 2054 6865 206f 7269 6769 6e61  s.\"  The origina\n+0000e9f0: 6c20 6f62 6a65 6374 2069 730a 7468 6520  l object is.the \n+0000ea00: 7a65 726f 2774 6820 636f 7079 2c20 7769  zero'th copy, wi\n+0000ea10: 7468 206b 3d30 2061 6e64 2065 6666 6563  th k=0 and effec\n+0000ea20: 7469 7665 6c79 206e 6f20 7472 616e 7366  tively no transf\n+0000ea30: 6f72 6d20 6170 706c 6965 6420 2854 5e30  orm applied (T^0\n+0000ea40: 3d49 2c0a 7468 6520 6964 656e 7469 7479  =I,.the identity\n+0000ea50: 2074 7261 6e73 666f 726d 292e 0a0a 2020   transform)...  \n+0000ea60: 2054 6865 206d 6574 686f 6420 6f66 2063   The method of c\n+0000ea70: 6f6e 6e65 6374 696e 6720 7468 6520 636f  onnecting the co\n+0000ea80: 7069 6573 2064 6570 656e 6473 206f 6e20  pies depends on \n+0000ea90: 7468 6520 7479 7065 206f 660a 5357 4550  the type of.SWEP\n+0000eaa0: 545f 4f42 4a45 4354 2061 6e64 206f 6e20  T_OBJECT and on \n+0000eab0: 7768 6574 6865 7220 7468 6520 636c 6f73  whether the clos\n+0000eac0: 7572 6520 7461 6720 273c 3e27 2069 7320  ure tag '<>' is \n+0000ead0: 7072 6573 656e 7420 6f72 206e 6f74 2e0a  present or not..\n+0000eae0: 0a20 2020 416e 2065 7861 6d70 6c65 206f  .   An example o\n+0000eaf0: 6620 6120 7377 6565 7020 7768 6572 6520  f a sweep where \n+0000eb00: 723d 3220 6973 2074 6865 204d 6f62 6975  r=2 is the Mobiu\n+0000eb10: 7320 6669 6775 7265 2061 7420 2a6e 6f74  s figure at *not\n+0000eb20: 6520 4d6f 7265 2074 6f0a 6c65 6172 6e3a  e More to.learn:\n+0000eb30: 3a2e 0a0a 2a20 4d65 6e75 3a0a 0a2a 2053  :...* Menu:..* S\n+0000eb40: 7765 7074 2070 6f69 6e74 733a 3a20 2020  wept points::   \n+0000eb50: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n+0000eb60: 7074 2070 6f69 6e74 7320 6d61 6b65 206c  pt points make l\n+0000eb70: 696e 6573 206f 7220 706f 6c79 676f 6e73  ines or polygons\n+0000eb80: 2e0a 2a20 5377 6570 7420 6c69 6e65 733a  ..* Swept lines:\n+0000eb90: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0000eba0: 2020 5377 6570 7420 6c69 6e65 7320 6d61    Swept lines ma\n+0000ebb0: 6b65 206f 7065 6e20 6f72 2063 6c6f 7365  ke open or close\n+0000ebc0: 6420 7375 7266 6163 6573 2e0a 2a20 5377  d surfaces..* Sw\n+0000ebd0: 6570 7420 706f 6c79 676f 6e73 3a3a 2020  ept polygons::  \n+0000ebe0: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n+0000ebf0: 7420 706f 6c79 676f 6e73 206d 616b 6520  t polygons make \n+0000ec00: 636c 6f73 6564 2073 7572 6661 6365 732e  closed surfaces.\n+0000ec10: 0a2a 2053 7765 7074 2062 6c6f 636b 733a  .* Swept blocks:\n+0000ec20: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0000ec30: 2053 7765 7074 2062 6c6f 636b 203d 3d20   Swept block == \n+0000ec40: 626c 6f63 6b20 6f66 2073 7765 6570 732e  block of sweeps.\n+0000ec50: 0a2a 2053 7765 6570 2066 6163 6520 7370  .* Sweep face sp\n+0000ec60: 6c69 7474 696e 673a 3a20 2020 2020 2020  litting::       \n+0000ec70: 2046 6978 696e 6720 7761 7270 6564 2066   Fixing warped f\n+0000ec80: 6163 6573 2077 6974 6820 7472 6961 6e67  aces with triang\n+0000ec90: 6c65 732e 0a0a 1f0a 4669 6c65 3a20 736b  les.....File: sk\n+0000eca0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n+0000ecb0: 3a20 5377 6570 7420 706f 696e 7473 2c20  : Swept points, \n+0000ecc0: 204e 6578 743a 2053 7765 7074 206c 696e   Next: Swept lin\n+0000ecd0: 6573 2c20 2050 7265 763a 2053 7765 6570  es,  Prev: Sweep\n+0000ece0: 732c 2020 5570 3a20 5377 6565 7073 0a0a  s,  Up: Sweeps..\n+0000ecf0: 332e 322e 362e 3120 5377 6570 7420 706f  3.2.6.1 Swept po\n+0000ed00: 696e 7473 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e  ints............\n+0000ed10: 2e2e 2e2e 2e2e 2e2e 2e0a 0a49 6620 5357  ...........If SW\n+0000ed20: 4550 545f 4f42 4a45 4354 2069 7320 6120  EPT_OBJECT is a \n+0000ed30: 706f 696e 7420 6c69 7374 2061 6e64 2074  point list and t\n+0000ed40: 6865 7265 2069 7320 6e6f 2063 6c6f 7375  here is no closu\n+0000ed50: 7265 2074 6167 2c20 7468 656e 0a27 7377  re tag, then.'sw\n+0000ed60: 6565 7027 2063 6f6e 6e65 6374 7320 4e2b  eep' connects N+\n+0000ed70: 3120 7375 6363 6573 7369 7665 2063 6f70  1 successive cop\n+0000ed80: 6965 7320 6f66 2065 6163 6820 706f 696e  ies of each poin\n+0000ed90: 7420 2869 6e63 6c75 6469 6e67 2074 6865  t (including the\n+0000eda0: 0a6f 7269 6769 6e61 6c29 2077 6974 6820  .original) with \n+0000edb0: 7374 7261 6967 6874 206c 696e 6520 7365  straight line se\n+0000edc0: 676d 656e 7473 2074 6f20 666f 726d 2061  gments to form a\n+0000edd0: 2070 6f6c 796c 696e 652e 2020 4966 2074   polyline.  If t\n+0000ede0: 6865 7265 2061 7265 0a6d 2070 6f69 6e74  here are.m point\n+0000edf0: 7320 696e 2074 6865 206f 7269 6769 6e61  s in the origina\n+0000ee00: 6c20 706f 696e 7420 6c69 7374 2c20 7468  l point list, th\n+0000ee10: 656e 206d 2070 6f6c 796c 696e 6573 2077  en m polylines w\n+0000ee20: 6974 6820 4e20 7365 676d 656e 7473 0a65  ith N segments.e\n+0000ee30: 6163 6820 6172 6520 666f 726d 6564 2062  ach are formed b\n+0000ee40: 7920 7468 6520 7377 6565 702e 2020 496e  y the sweep.  In\n+0000ee50: 2074 6869 7320 6d61 6e6e 6572 2c20 2773   this manner, 's\n+0000ee60: 7765 6570 2720 666f 726d 7320 6120 7365  weep' forms a se\n+0000ee70: 7420 6f66 0a6f 6e65 2d64 696d 656e 7369  t of.one-dimensi\n+0000ee80: 6f6e 616c 206f 626a 6563 7473 2028 706f  onal objects (po\n+0000ee90: 6c79 6c69 6e65 7329 2066 726f 6d20 7a65  lylines) from ze\n+0000eea0: 726f 2d64 696d 656e 7369 6f6e 616c 206f  ro-dimensional o\n+0000eeb0: 6e65 7320 2870 6f69 6e74 7329 2e0a 0a20  nes (points)... \n+0000eec0: 2020 5768 656e 2074 6865 7265 205f 6973    When there _is\n+0000eed0: 5f20 6120 636c 6f73 7572 6520 7461 672c  _ a closure tag,\n+0000eee0: 2027 7377 6565 7027 2063 6f6e 6e65 6374   'sweep' connect\n+0000eef0: 7320 4e20 7375 6363 6573 7369 7665 2063  s N successive c\n+0000ef00: 6f70 6965 730a 6f66 2065 6163 6820 706f  opies.of each po\n+0000ef10: 696e 7420 2869 6e63 6c75 6469 6e67 2074  int (including t\n+0000ef20: 6865 206f 7269 6769 6e61 6c29 2077 6974  he original) wit\n+0000ef30: 6820 7374 7261 6967 6874 206c 696e 6520  h straight line \n+0000ef40: 7365 676d 656e 7473 2061 6e64 0a66 696e  segments and.fin\n+0000ef50: 616c 6c79 2063 6f6e 6e65 6374 7320 7468  ally connects th\n+0000ef60: 6520 6c61 7374 2063 6f70 7920 6261 636b  e last copy back\n+0000ef70: 2074 6f20 7468 6520 6f72 6967 696e 616c   to the original\n+0000ef80: 2074 6f20 666f 726d 2061 2070 6f6c 7967   to form a polyg\n+0000ef90: 6f6e 0a77 6974 6820 4e20 7369 6465 732e  on.with N sides.\n+0000efa0: 2020 4966 2074 6865 7265 2061 7265 206d    If there are m\n+0000efb0: 2070 6f69 6e74 7320 696e 2074 6865 206f   points in the o\n+0000efc0: 7269 6769 6e61 6c20 706f 696e 7420 6c69  riginal point li\n+0000efd0: 7374 2c20 7468 656e 206d 0a70 6f6c 7967  st, then m.polyg\n+0000efe0: 6f6e 7320 7769 7468 204e 2073 6964 6573  ons with N sides\n+0000eff0: 2065 6163 6820 6172 6520 666f 726d 6564   each are formed\n+0000f000: 2062 7920 7468 6520 7377 6565 702e 2020   by the sweep.  \n+0000f010: 496e 2074 6869 7320 6d61 6e6e 6572 2c0a  In this manner,.\n+0000f020: 2773 7765 6570 2720 666f 726d 7320 6120  'sweep' forms a \n+0000f030: 7365 7420 6f66 2074 776f 2d64 696d 656e  set of two-dimen\n+0000f040: 7369 6f6e 616c 206f 626a 6563 7473 2028  sional objects (\n+0000f050: 706f 6c79 676f 6e73 2920 6672 6f6d 0a7a  polygons) from.z\n+0000f060: 6572 6f2d 6469 6d65 6e73 696f 6e61 6c20  ero-dimensional \n+0000f070: 6f6e 6573 2028 706f 696e 7473 292e 0a0a  ones (points)...\n+0000f080: 2020 204f 7074 696f 6e73 206f 6620 7468     Options of th\n+0000f090: 6520 2773 7765 6570 2720 6172 6520 636f  e 'sweep' are co\n+0000f0a0: 7069 6564 2064 6972 6563 746c 7920 746f  pied directly to\n+0000f0b0: 2074 6865 2072 6573 756c 7469 6e67 0a70   the resulting.p\n+0000f0c0: 6f6c 796c 696e 6528 7329 2e0a 0a1f 0a46  olyline(s).....F\n+0000f0d0: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n+0000f0e0: 2c20 204e 6f64 653a 2053 7765 7074 206c  ,  Node: Swept l\n+0000f0f0: 696e 6573 2c20 204e 6578 743a 2053 7765  ines,  Next: Swe\n+0000f100: 7074 2070 6f6c 7967 6f6e 732c 2020 5072  pt polygons,  Pr\n+0000f110: 6576 3a20 5377 6570 7420 706f 696e 7473  ev: Swept points\n+0000f120: 2c20 2055 703a 2053 7765 6570 730a 0a33  ,  Up: Sweeps..3\n+0000f130: 2e32 2e36 2e32 2053 7765 7074 206c 696e  .2.6.2 Swept lin\n+0000f140: 6573 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  es..............\n+0000f150: 2e2e 2e2e 2e2e 0a0a 4966 2053 5745 5054  ........If SWEPT\n+0000f160: 5f4f 424a 4543 5420 6973 2061 2070 6f6c  _OBJECT is a pol\n+0000f170: 796c 696e 6520 616e 6420 7468 6572 6520  yline and there \n+0000f180: 6973 206e 6f20 636c 6f73 7572 6520 7461  is no closure ta\n+0000f190: 672c 2074 6865 6e20 2773 7765 6570 270a  g, then 'sweep'.\n+0000f1a0: 636f 6e6e 6563 7473 204e 2b31 2073 7563  connects N+1 suc\n+0000f1b0: 6365 7373 6976 6520 636f 7069 6573 206f  cessive copies o\n+0000f1c0: 6620 7468 6520 706f 6c79 6c69 6e65 2028  f the polyline (\n+0000f1d0: 696e 636c 7564 696e 6720 7468 6520 6f72  including the or\n+0000f1e0: 6967 696e 616c 290a 7769 7468 2066 6f75  iginal).with fou\n+0000f1f0: 722d 7369 6465 6420 706f 6c79 676f 6e73  r-sided polygons\n+0000f200: 2c20 6561 6368 2070 6169 7220 6f66 2063  , each pair of c\n+0000f210: 6f70 6965 7320 6769 7669 6e67 2072 6973  opies giving ris\n+0000f220: 6520 746f 2061 2022 706f 6c79 676f 6e0a  e to a \"polygon.\n+0000f230: 7374 7269 702e 2220 2049 6620 7468 6572  strip.\"  If ther\n+0000f240: 6520 6172 6520 6d20 706f 696e 7473 2069  e are m points i\n+0000f250: 6e20 7468 6520 6f72 6967 696e 616c 2070  n the original p\n+0000f260: 6f6c 796c 696e 652c 2074 6865 6e20 286d  olyline, then (m\n+0000f270: 2d31 294e 0a70 6f6c 7967 6f6e 7320 6172  -1)N.polygons ar\n+0000f280: 6520 666f 726d 6564 2062 7920 7468 6520  e formed by the \n+0000f290: 7377 6565 702e 2020 5765 2063 616c 6c20  sweep.  We call \n+0000f2a0: 7468 6573 6520 2262 6f64 7920 706f 6c79  these \"body poly\n+0000f2b0: 676f 6e73 222e 2020 496e 0a74 6869 7320  gons\".  In.this \n+0000f2c0: 6d61 6e6e 6572 2c20 2773 7765 6570 2720  manner, 'sweep' \n+0000f2d0: 666f 726d 7320 6120 7477 6f2d 6469 6d65  forms a two-dime\n+0000f2e0: 6e73 696f 6e61 6c20 7375 7266 6163 6520  nsional surface \n+0000f2f0: 6672 6f6d 2066 726f 6d20 610a 6f6e 652d  from from a.one-\n+0000f300: 6469 6d65 6e73 696f 6e61 6c20 706f 6c79  dimensional poly\n+0000f310: 6c69 6e65 2e0a 0a20 2020 5468 6520 6f72  line...   The or\n+0000f320: 6465 7220 6f66 2076 6572 7469 6365 7320  der of vertices \n+0000f330: 7072 6f64 7563 6564 2062 7920 2773 7765  produced by 'swe\n+0000f340: 6570 2720 6973 2069 6d70 6f72 7461 6e74  ep' is important\n+0000f350: 2e20 2049 6620 610a 706f 6c79 676f 6e27  .  If a.polygon'\n+0000f360: 7320 7665 7274 6963 6573 2064 6f20 6e6f  s vertices do no\n+0000f370: 7420 6170 7065 6172 2069 6e20 636f 756e  t appear in coun\n+0000f380: 7465 722d 636c 6f63 6b77 6973 6520 6f72  ter-clockwise or\n+0000f390: 6465 7220 696e 2074 6865 2066 696e 616c  der in the final\n+0000f3a0: 0a69 6d61 6765 2c20 7468 6520 706f 6c79  .image, the poly\n+0000f3b0: 676f 6e20 7769 6c6c 2062 6520 6375 6c6c  gon will be cull\n+0000f3c0: 6564 2028 756e 6c65 7373 2027 6375 6c6c  ed (unless 'cull\n+0000f3d0: 3d66 616c 7365 2720 6973 2073 6574 292e  =false' is set).\n+0000f3e0: 2020 4966 2074 6865 0a70 6f69 6e74 7320    If the.points \n+0000f3f0: 696e 2074 6865 206b 2774 6820 636f 7079  in the k'th copy\n+0000f400: 206f 6620 7468 6520 706f 6c79 6c69 6e65   of the polyline\n+0000f410: 2061 7265 2050 5f31 2c20 505f 322c 202e   are P_1, P_2, .\n+0000f420: 2e2e 2c20 505f 6d2c 2061 6e64 2074 6865  .., P_m, and the\n+0000f430: 0a70 6f69 6e74 7320 696e 2074 6865 206e  .points in the n\n+0000f440: 6578 7420 636f 7079 2c20 7468 6520 286b  ext copy, the (k\n+0000f450: 2b31 2973 742c 2061 7265 2050 5f31 272c  +1)st, are P_1',\n+0000f460: 2050 5f32 272c 202e 2e2e 2c20 505f 6d27   P_2', ..., P_m'\n+0000f470: 2c20 7468 656e 0a74 6865 2076 6572 7465  , then.the verte\n+0000f480: 7820 6f72 6465 7220 6f66 2074 6865 2067  x order of the g\n+0000f490: 656e 6572 6174 6564 2070 6f6c 7967 6f6e  enerated polygon\n+0000f4a0: 7320 6973 0a20 2020 2020 426f 6479 2070  s is.     Body p\n+0000f4b0: 6f6c 7967 6f6e 2031 3a20 505f 3220 505f  olygon 1: P_2 P_\n+0000f4c0: 3120 505f 3127 2050 5f32 270a 2020 2020  1 P_1' P_2'.    \n+0000f4d0: 2042 6f64 7920 706f 6c79 676f 6e20 323a   Body polygon 2:\n+0000f4e0: 2050 5f33 2050 5f32 2050 5f32 2720 505f   P_3 P_2 P_2' P_\n+0000f4f0: 3327 0a20 2020 2020 2e2e 2e0a 2020 2020  3'.     ....    \n+0000f500: 2042 6f64 7920 706f 6c79 676f 6e20 6d2d   Body polygon m-\n+0000f510: 313a 2050 5f6d 2050 5f7b 6d2d 317d 2050  1: P_m P_{m-1} P\n+0000f520: 5f7b 6d2d 317d 2720 505f 6d27 0a0a 2020  _{m-1}' P_m'..  \n+0000f530: 204f 7074 696f 6e73 206f 6620 756e 636c   Options of uncl\n+0000f540: 6f73 6564 206c 696e 6520 7377 6565 7073  osed line sweeps\n+0000f550: 2061 7265 2063 6f70 6965 6420 746f 2065   are copied to e\n+0000f560: 6163 6820 6f75 7470 7574 2070 6f6c 7967  ach output polyg\n+0000f570: 6f6e 2e0a 4f70 7469 6f6e 7320 6f66 2074  on..Options of t\n+0000f580: 6865 2073 7765 7074 206c 696e 6520 6172  he swept line ar\n+0000f590: 6520 6967 6e6f 7265 642e 0a0a 2020 2057  e ignored...   W\n+0000f5a0: 6865 6e20 7468 6572 6520 5f69 735f 2061  hen there _is_ a\n+0000f5b0: 2063 6c6f 7375 7265 2074 6167 2c20 7468   closure tag, th\n+0000f5c0: 656e 2027 7377 6565 7027 2063 6f6e 6e65  en 'sweep' conne\n+0000f5d0: 6374 7320 4e20 7375 6363 6573 7369 7665  cts N successive\n+0000f5e0: 0a63 6f70 6965 7320 6f66 2074 6865 2070  .copies of the p\n+0000f5f0: 6f6c 796c 696e 6520 2869 6e63 6c75 6469  olyline (includi\n+0000f600: 6e67 2074 6865 206f 7269 6769 6e61 6c29  ng the original)\n+0000f610: 2077 6974 6820 666f 7572 2d73 6964 6564   with four-sided\n+0000f620: 2062 6f64 790a 706f 6c79 676f 6e73 206a   body.polygons j\n+0000f630: 7573 7420 6173 2074 6865 2063 6173 6520  ust as the case \n+0000f640: 7769 7468 206e 6f20 636c 6f73 7572 6520  with no closure \n+0000f650: 7461 672e 2020 4974 2074 6865 6e20 636f  tag.  It then co\n+0000f660: 6e6e 6563 7473 2074 6865 0a6c 6173 7420  nnects the.last \n+0000f670: 636f 7079 2062 6163 6b20 746f 2074 6865  copy back to the\n+0000f680: 206f 7269 6769 6e61 6c20 746f 2066 6f72   original to for\n+0000f690: 6d20 6120 7269 6262 6f6e 2d73 6861 7065  m a ribbon-shape\n+0000f6a0: 6420 7375 7266 6163 6520 7468 6174 0a63  d surface that.c\n+0000f6b0: 6c6f 7365 7320 6f6e 2069 7473 656c 6620  loses on itself \n+0000f6c0: 7769 7468 2074 776f 2068 6f6c 6573 2072  with two holes r\n+0000f6d0: 656d 6169 6e69 6e67 2e0a 0a20 2020 4669  emaining...   Fi\n+0000f6e0: 6e61 6c6c 792c 2074 6865 2073 7765 6570  nally, the sweep\n+0000f6f0: 2061 6464 7320 7477 6f20 6d6f 7265 2070   adds two more p\n+0000f700: 6f6c 7967 6f6e 7320 746f 2073 6561 6c20  olygons to seal \n+0000f710: 7468 6520 686f 6c65 7320 616e 6420 666f  the holes and fo\n+0000f720: 726d 0a61 2063 6c6f 7365 6420 7375 7266  rm.a closed surf\n+0000f730: 6163 6520 7468 6174 2c20 6465 7065 6e64  ace that, depend\n+0000f740: 696e 6720 6f6e 2074 6865 2073 7765 6570  ing on the sweep\n+0000f750: 2074 7261 6e73 666f 726d 732c 206d 6179   transforms, may\n+0000f760: 2072 6570 7265 7365 6e74 0a74 6865 2062   represent.the b\n+0000f770: 6f75 6e64 6172 7920 6f66 2061 2073 6f6c  oundary of a sol\n+0000f780: 6964 2e20 2049 6e20 7468 6973 206d 616e  id.  In this man\n+0000f790: 6e65 722c 2027 7377 6565 7027 2066 6f72  ner, 'sweep' for\n+0000f7a0: 6d73 2074 6865 2062 6f75 6e64 6172 7920  ms the boundary \n+0000f7b0: 6f66 0a61 2074 6872 6565 2d64 696d 656e  of.a three-dimen\n+0000f7c0: 7369 6f6e 616c 206f 626a 6563 7420 6672  sional object fr\n+0000f7d0: 6f6d 2061 206f 6e65 2d64 696d 656e 7369  om a one-dimensi\n+0000f7e0: 6f6e 616c 2070 6f6c 796c 696e 652e 2020  onal polyline.  \n+0000f7f0: 5765 2063 616c 6c0a 7468 6573 6520 686f  We call.these ho\n+0000f800: 6c65 2d66 696c 6c69 6e67 2070 6f6c 7967  le-filling polyg\n+0000f810: 6f6e 7320 2265 6e64 7322 2e0a 0a20 2020  ons \"ends\"...   \n+0000f820: 5468 6520 6f72 6465 7220 6f66 2076 6572  The order of ver\n+0000f830: 7469 6365 7320 6f66 2065 6e64 2070 6f6c  tices of end pol\n+0000f840: 7967 6f6e 7320 6973 2069 6d70 6f72 7461  ygons is importa\n+0000f850: 6e74 2066 6f72 2063 6f72 7265 6374 0a63  nt for correct.c\n+0000f860: 756c 6c69 6e67 2061 7320 6465 7363 7269  ulling as descri\n+0000f870: 6265 6420 6162 6f76 652e 2020 4966 2050  bed above.  If P\n+0000f880: 5f31 5e31 2c20 505f 315e 322c 202e 2e2e  _1^1, P_1^2, ...\n+0000f890: 2c20 505f 315e 6e20 6172 6520 7468 6520  , P_1^n are the \n+0000f8a0: 4e0a 636f 7069 6573 206f 6620 7468 6520  N.copies of the \n+0000f8b0: 6669 7273 7420 706f 6c79 6c69 6e65 2070  first polyline p\n+0000f8c0: 6f69 6e74 2061 6e64 2050 5f6d 5e31 2c20  oint and P_m^1, \n+0000f8d0: 505f 6d5e 322c 202e 2e2e 202c 505f 6d5e  P_m^2, ... ,P_m^\n+0000f8e0: 6e20 6172 6520 7468 650a 4e20 636f 7069  n are the.N copi\n+0000f8f0: 6573 206f 6620 7468 6520 6c61 7374 2070  es of the last p\n+0000f900: 6f6c 796c 696e 6520 706f 696e 742c 2074  olyline point, t\n+0000f910: 6865 6e20 7468 6520 656e 6420 706f 6c79  hen the end poly\n+0000f920: 676f 6e20 7665 7274 6578 206f 7264 6572  gon vertex order\n+0000f930: 0a69 730a 2020 2020 2045 6e64 2070 6f6c  .is.     End pol\n+0000f940: 7967 6f6e 2031 3a20 505f 315e 6e2c 2050  ygon 1: P_1^n, P\n+0000f950: 5f31 5e7b 6e2d 317d 2c20 2e2e 2e20 2c50  _1^{n-1}, ... ,P\n+0000f960: 5f31 5e31 0a20 2020 2020 456e 6420 706f  _1^1.     End po\n+0000f970: 6c79 676f 6e20 323a 2050 5f6d 5e31 2c20  lygon 2: P_m^1, \n+0000f980: 505f 6d5e 322c 202e 2e2e 202c 505f 6d5e  P_m^2, ... ,P_m^\n+0000f990: 6e0a 0a20 2020 4966 2074 6865 7265 2061  n..   If there a\n+0000f9a0: 7265 206e 6f20 6f70 7469 6f6e 7320 6f6e  re no options on\n+0000f9b0: 2074 6865 2073 7765 7074 206c 696e 652c   the swept line,\n+0000f9c0: 2074 6865 6e20 7468 6520 2773 7765 6570   then the 'sweep\n+0000f9d0: 2720 6f70 7469 6f6e 730a 6172 6520 636f  ' options.are co\n+0000f9e0: 7069 6564 2074 6f20 6561 6368 206f 7574  pied to each out\n+0000f9f0: 7075 7420 706f 6c79 676f 6e2e 2020 4966  put polygon.  If\n+0000fa00: 2074 6865 2073 7765 7074 206c 696e 6520   the swept line \n+0000fa10: 646f 6573 2068 6176 6520 6f70 7469 6f6e  does have option\n+0000fa20: 732c 0a74 6865 7365 2061 7265 2063 6f70  s,.these are cop\n+0000fa30: 6965 6420 746f 2063 6f72 7265 7370 6f6e  ied to correspon\n+0000fa40: 6469 6e67 2062 6f64 7920 706f 6c79 676f  ding body polygo\n+0000fa50: 6e73 3b20 7468 6520 7377 6565 7020 6f70  ns; the sweep op\n+0000fa60: 7469 6f6e 7320 6172 650a 636f 7069 6564  tions are.copied\n+0000fa70: 2074 6f20 7468 6520 656e 6420 706f 6c79   to the end poly\n+0000fa80: 676f 6e73 2e20 2049 6e20 7468 6973 206d  gons.  In this m\n+0000fa90: 616e 6e65 722c 2062 6f64 7920 616e 6420  anner, body and \n+0000faa0: 656e 6473 206d 6179 2062 6520 6472 6177  ends may be draw\n+0000fab0: 6e0a 7769 7468 2064 6966 6665 7265 6e74  n.with different\n+0000fac0: 2063 6861 7261 6374 6572 6973 7469 6373   characteristics\n+0000fad0: 2073 7563 6820 6173 2027 6669 6c6c 636f   such as 'fillco\n+0000fae0: 6c6f 7227 2e0a 0a1f 0a46 696c 653a 2073  lor'.....File: s\n+0000faf0: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n+0000fb00: 653a 2053 7765 7074 2070 6f6c 7967 6f6e  e: Swept polygon\n+0000fb10: 732c 2020 4e65 7874 3a20 5377 6570 7420  s,  Next: Swept \n+0000fb20: 626c 6f63 6b73 2c20 2050 7265 763a 2053  blocks,  Prev: S\n+0000fb30: 7765 7074 206c 696e 6573 2c20 2055 703a  wept lines,  Up:\n+0000fb40: 2053 7765 6570 730a 0a33 2e32 2e36 2e33   Sweeps..3.2.6.3\n+0000fb50: 2053 7765 7074 2070 6f6c 7967 6f6e 730a   Swept polygons.\n 0000fb60: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000fb70: 0a0a 4966 2053 5745 5054 5f4f 424a 4543  ..If SWEPT_OBJEC\n-0000fb80: 5420 6973 2061 2070 6f6c 7967 6f6e 2c20  T is a polygon, \n-0000fb90: 7468 6520 2773 7765 6570 2720 636f 6e6e  the 'sweep' conn\n-0000fba0: 6563 7473 204e 2b31 2073 7563 6365 7373  ects N+1 success\n-0000fbb0: 6976 6520 636f 7069 6573 0a6f 6620 7468  ive copies.of th\n-0000fbc0: 6520 636c 6f73 6564 2070 6f6c 796c 696e  e closed polylin\n-0000fbd0: 6520 626f 7264 6572 206f 6620 7468 6520  e border of the \n-0000fbe0: 706f 6c79 676f 6e20 746f 2066 6f72 6d20  polygon to form \n-0000fbf0: 626f 6479 2070 6f6c 7967 6f6e 730a 6578  body polygons.ex\n-0000fc00: 6163 746c 7920 6173 2074 686f 7567 6820  actly as though \n-0000fc10: 7468 6520 626f 7264 6572 2077 6572 6520  the border were \n-0000fc20: 6120 7377 6570 7420 706f 6c79 6c69 6e65  a swept polyline\n-0000fc30: 2061 7320 6465 7363 7269 6265 6420 696e   as described in\n-0000fc40: 202a 6e6f 7465 0a53 7765 7074 206c 696e   *note.Swept lin\n-0000fc50: 6573 3a3a 2e20 2049 6620 7468 6572 6520  es::.  If there \n-0000fc60: 6172 6520 6d20 706f 696e 7473 2069 6e20  are m points in \n-0000fc70: 7468 6520 6f72 6967 696e 616c 2070 6f6c  the original pol\n-0000fc80: 7967 6f6e 2c20 7468 656e 206d 4e0a 626f  ygon, then mN.bo\n-0000fc90: 6479 2070 6f6c 7967 6f6e 7320 6172 6520  dy polygons are \n-0000fca0: 666f 726d 6564 2062 7920 7468 6973 2073  formed by this s\n-0000fcb0: 7765 6570 2e20 2054 6865 2062 6f64 7920  weep.  The body \n-0000fcc0: 706f 6c79 676f 6e73 2066 6f72 6d20 616e  polygons form an\n-0000fcd0: 0a22 6578 7472 7573 696f 6e22 206f 6620  .\"extrusion\" of \n-0000fce0: 7468 6520 626f 756e 6461 7279 206f 6620  the boundary of \n-0000fcf0: 7468 6520 6f72 6967 696e 616c 2070 6f6c  the original pol\n-0000fd00: 7967 6f6e 2077 6974 6820 7477 6f20 686f  ygon with two ho\n-0000fd10: 6c65 7320 6174 0a74 6865 206f 7065 6e20  les at.the open \n-0000fd20: 656e 6473 2e0a 0a20 2020 4669 6e61 6c6c  ends...   Finall\n-0000fd30: 792c 2074 6865 2073 7765 6570 2061 6464  y, the sweep add\n-0000fd40: 7320 7477 6f20 636f 7069 6573 206f 6620  s two copies of \n-0000fd50: 7468 6520 6f72 6967 696e 616c 2070 6f6c  the original pol\n-0000fd60: 7967 6f6e 2074 6f20 636f 7665 720a 7468  ygon to cover.th\n-0000fd70: 6520 686f 6c65 732e 2020 5765 2063 616c  e holes.  We cal\n-0000fd80: 6c20 7468 6573 6520 686f 6c65 2d66 696c  l these hole-fil\n-0000fd90: 6c69 6e67 2070 6f6c 7967 6f6e 7320 2265  ling polygons \"e\n-0000fda0: 6e64 7322 2e20 2049 6e20 7468 6973 206d  nds\".  In this m\n-0000fdb0: 616e 6e65 722c 0a27 7377 6565 7027 2066  anner,.'sweep' f\n-0000fdc0: 6f72 6d73 2074 6865 2062 6f75 6e64 6172  orms the boundar\n-0000fdd0: 7920 6f66 2061 2074 6872 6565 2d64 696d  y of a three-dim\n-0000fde0: 656e 7369 6f6e 616c 206f 626a 6563 7420  ensional object \n-0000fdf0: 6672 6f6d 2061 0a74 776f 2d64 696d 656e  from a.two-dimen\n-0000fe00: 7369 6f6e 616c 2070 6f6c 7967 6f6e 2e0a  sional polygon..\n-0000fe10: 0a20 2020 5468 6520 6f72 6465 7220 6f66  .   The order of\n-0000fe20: 2076 6572 7469 6365 7320 6f66 2065 6e64   vertices of end\n-0000fe30: 2070 6f6c 7967 6f6e 7320 6973 2069 6d70   polygons is imp\n-0000fe40: 6f72 7461 6e74 2066 6f72 2063 6f72 7265  ortant for corre\n-0000fe50: 6374 0a63 756c 6c69 6e67 2061 7320 6465  ct.culling as de\n-0000fe60: 7363 7269 6265 6420 6162 6f76 652e 2020  scribed above.  \n-0000fe70: 416e 2065 7861 6374 2063 6f70 7920 6f66  An exact copy of\n-0000fe80: 2074 6865 206f 7269 6769 6e61 6c20 706f   the original po\n-0000fe90: 6c79 676f 6e20 7769 7468 0a76 6572 7465  lygon with.verte\n-0000fea0: 7820 6f72 6465 7220 696e 7461 6374 2066  x order intact f\n-0000feb0: 6f72 6d73 2074 6865 2066 6972 7374 2065  orms the first e\n-0000fec0: 6e64 2070 6f6c 7967 6f6e 2e20 2054 6865  nd polygon.  The\n-0000fed0: 206f 7468 6572 2065 6e64 2070 6f6c 7967   other end polyg\n-0000fee0: 6f6e 0a72 6573 756c 7473 2066 726f 6d20  on.results from \n-0000fef0: 7472 616e 7366 6f72 6d69 6e67 2061 6e64  transforming and\n-0000ff00: 2074 6865 2072 6576 6572 7369 6e67 2074   the reversing t\n-0000ff10: 6865 206f 7264 6572 206f 6620 7665 7274  he order of vert\n-0000ff20: 6963 6573 2069 6e20 7468 650a 6f72 6967  ices in the.orig\n-0000ff30: 696e 616c 2e20 2054 6865 2074 7261 6e73  inal.  The trans\n-0000ff40: 666f 726d 2070 6c61 6365 7320 7468 6520  form places the \n-0000ff50: 6f72 6967 696e 616c 2070 6f6c 7967 6f6e  original polygon\n-0000ff60: 2061 7420 7468 6520 756e 636f 7665 7265   at the uncovere\n-0000ff70: 640a 686f 6c65 3b20 6974 2069 730a 2020  d.hole; it is.  \n-0000ff80: 2020 2054 5f31 5e6e 2074 6865 6e20 545f     T_1^n then T_\n-0000ff90: 325e 6e20 7468 656e 202e 2e2e 2074 6865  2^n then ... the\n-0000ffa0: 6e20 545f 525e 6e2e 0a49 6620 7468 6572  n T_R^n..If ther\n-0000ffb0: 6520 6172 6520 6e6f 206f 7074 696f 6e73  e are no options\n-0000ffc0: 206f 6e20 7468 6520 7377 6570 7420 706f   on the swept po\n-0000ffd0: 6c79 676f 6e2c 2074 6865 6e20 7468 6520  lygon, then the \n-0000ffe0: 2773 7765 6570 2720 6f70 7469 6f6e 730a  'sweep' options.\n-0000fff0: 6172 6520 636f 7069 6564 2074 6f20 6561  are copied to ea\n-00010000: 6368 206f 7574 7075 7420 706f 6c79 676f  ch output polygo\n-00010010: 6e2e 2020 4966 2074 6865 2073 7765 7074  n.  If the swept\n-00010020: 2070 6f6c 7967 6f6e 2064 6f65 7320 6861   polygon does ha\n-00010030: 7665 0a6f 7074 696f 6e73 2c20 7468 6573  ve.options, thes\n-00010040: 6520 6172 6520 636f 7069 6564 2074 6f20  e are copied to \n-00010050: 7468 6520 656e 6473 3b20 7468 6520 7377  the ends; the sw\n-00010060: 6565 7020 6f70 7469 6f6e 7320 6172 6520  eep options are \n-00010070: 636f 7069 6564 2074 6f0a 7468 6520 626f  copied to.the bo\n-00010080: 6479 2070 6f6c 7967 6f6e 732e 2020 496e  dy polygons.  In\n-00010090: 2074 6869 7320 6d61 6e6e 6572 2c20 626f   this manner, bo\n-000100a0: 6479 2061 6e64 2065 6e64 7320 6d61 7920  dy and ends may \n-000100b0: 6265 2064 7261 776e 2077 6974 680a 6469  be drawn with.di\n-000100c0: 6666 6572 656e 7420 6368 6172 6163 7465  fferent characte\n-000100d0: 7269 7374 6963 7320 7375 6368 2061 7320  ristics such as \n-000100e0: 2766 696c 6c63 6f6c 6f72 272e 0a0a 1f0a  'fillcolor'.....\n-000100f0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n-00010100: 6f2c 2020 4e6f 6465 3a20 5377 6570 7420  o,  Node: Swept \n-00010110: 626c 6f63 6b73 2c20 204e 6578 743a 2053  blocks,  Next: S\n-00010120: 7765 6570 2066 6163 6520 7370 6c69 7474  weep face splitt\n-00010130: 696e 672c 2020 5072 6576 3a20 5377 6570  ing,  Prev: Swep\n-00010140: 7420 706f 6c79 676f 6e73 2c20 2055 703a  t polygons,  Up:\n-00010150: 2053 7765 6570 730a 0a33 2e32 2e36 2e34   Sweeps..3.2.6.4\n-00010160: 2053 7765 7074 2062 6c6f 636b 730a 2e2e   Swept blocks...\n-00010170: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-00010180: 2e2e 0a0a 5468 6520 7377 6570 7420 6f62  ....The swept ob\n-00010190: 6a65 6374 2053 5745 5054 5f4f 424a 4543  ject SWEPT_OBJEC\n-000101a0: 5420 6d61 7920 616c 736f 2062 6520 616e  T may also be an\n-000101b0: 7920 636f 6c6c 6563 7469 6f6e 206f 6620  y collection of \n-000101c0: 706f 6c79 6c69 6e65 730a 616e 6420 706f  polylines.and po\n-000101d0: 6c79 676f 6e73 2e20 2054 6869 7320 6d61  lygons.  This ma\n-000101e0: 7920 6265 2061 2062 6c6f 636b 2063 6f6d  y be a block com\n-000101f0: 706f 7365 6420 6f66 2027 6c69 6e65 2720  posed of 'line' \n-00010200: 616e 642f 6f72 2027 706f 6c79 676f 6e27  and/or 'polygon'\n-00010210: 0a63 6f6d 6d61 6e64 7320 696e 2062 7261  .commands in bra\n-00010220: 6365 7320 277b 207d 272c 206f 7220 6974  ces '{ }', or it\n-00010230: 206d 6179 2062 6520 7468 6520 7265 7375   may be the resu\n-00010240: 6c74 206f 6620 6120 2772 6570 6561 7427  lt of a 'repeat'\n-00010250: 2c20 616e 6f74 6865 720a 2773 7765 6570  , another.'sweep\n-00010260: 272c 2065 7463 2e20 2054 6865 2073 7765  ', etc.  The swe\n-00010270: 6570 2061 6374 7320 696e 6465 7065 6e64  ep acts independ\n-00010280: 656e 746c 7920 6f6e 2065 6163 6820 6f62  ently on each ob\n-00010290: 6a65 6374 2069 6e20 7468 6520 626c 6f63  ject in the bloc\n-000102a0: 6b0a 6578 6163 746c 7920 6173 2069 6620  k.exactly as if \n-000102b0: 6974 2077 6572 6520 6120 7369 6e67 6c65  it were a single\n-000102c0: 2073 7765 7074 206f 626a 6563 7420 6465   swept object de\n-000102d0: 7363 7269 6265 6420 6162 6f76 6520 696e  scribed above in\n-000102e0: 202a 6e6f 7465 0a53 7765 7074 206c 696e   *note.Swept lin\n-000102f0: 6573 3a3a 2061 6e64 202a 6e6f 7465 2053  es:: and *note S\n-00010300: 7765 7074 2070 6f6c 7967 6f6e 733a 3a2e  wept polygons::.\n-00010310: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n-00010320: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5377  .info,  Node: Sw\n-00010330: 6565 7020 6661 6365 2073 706c 6974 7469  eep face splitti\n-00010340: 6e67 2c20 2050 7265 763a 2053 7765 7074  ng,  Prev: Swept\n-00010350: 2062 6c6f 636b 732c 2020 5570 3a20 5377   blocks,  Up: Sw\n-00010360: 6565 7073 0a0a 332e 322e 362e 3520 5377  eeps..3.2.6.5 Sw\n-00010370: 6565 7020 6661 6365 2073 706c 6974 7469  eep face splitti\n-00010380: 6e67 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ng..............\n-00010390: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a  ................\n-000103a0: 0a42 6566 6f72 6520 7365 6e64 696e 6720  .Before sending \n-000103b0: 6561 6368 2066 6f75 722d 7369 6465 6420  each four-sided \n-000103c0: 626f 6479 2070 6f6c 7967 6f6e 206f 6620  body polygon of \n-000103d0: 6120 2773 7765 6570 2720 746f 2074 6865  a 'sweep' to the\n-000103e0: 206f 7574 7075 742c 0a27 736b 6574 6368   output,.'sketch\n-000103f0: 2720 7465 7374 7320 746f 2073 6565 2069  ' tests to see i\n-00010400: 6620 6974 2069 7320 726f 7567 686c 7920  f it is roughly \n-00010410: 706c 616e 6172 2e20 2053 696e 6365 2070  planar.  Since p\n-00010420: 6c61 6e61 7269 7479 2069 730a 6e65 6365  lanarity is.nece\n-00010430: 7373 6172 7920 666f 7220 7072 6f70 6572  ssary for proper\n-00010440: 2066 756e 6374 696f 6e69 6e67 206f 6620   functioning of \n-00010450: 7468 6520 6869 6464 656e 2073 7572 6661  the hidden surfa\n-00010460: 6365 2061 6c67 6f72 6974 686d 2c0a 2277  ce algorithm,.\"w\n-00010470: 6172 7065 6422 2070 6f6c 7967 6f6e 7320  arped\" polygons \n-00010480: 6172 6520 6175 746f 6d61 7469 6361 6c6c  are automaticall\n-00010490: 7920 7370 6c69 7420 696e 746f 2074 776f  y split into two\n-000104a0: 2074 7269 616e 676c 6573 2e0a 0a20 2020   triangles...   \n-000104b0: 486f 6c65 2d66 696c 6c69 6e67 2070 6f6c  Hole-filling pol\n-000104c0: 7967 6f6e 7320 7072 6f64 7563 6564 2062  ygons produced b\n-000104d0: 7920 636c 6f73 7572 652d 7461 6767 6564  y closure-tagged\n-000104e0: 206c 696e 6520 7377 6565 7073 2061 7265   line sweeps are\n-000104f0: 206e 6f74 0a73 706c 6974 2e20 204e 6f72   not.split.  Nor\n-00010500: 2061 7265 206f 7269 6769 6e61 6c20 706f   are original po\n-00010510: 6c79 676f 6e73 2069 6e20 706f 6c79 676f  lygons in polygo\n-00010520: 6e20 7377 6565 7073 2e20 2049 7420 6973  n sweeps.  It is\n-00010530: 2074 6865 2075 7365 7227 730a 7265 7370   the user's.resp\n-00010540: 6f6e 7369 6269 6c69 7479 2074 6f20 656e  onsibility to en\n-00010550: 7375 7265 2074 6865 7365 2061 7265 2070  sure these are p\n-00010560: 6c61 6e61 722e 0a0a 1f0a 4669 6c65 3a20  lanar.....File: \n-00010570: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n-00010580: 6465 3a20 426c 6f63 6b73 2c20 204e 6578  de: Blocks,  Nex\n-00010590: 743a 2052 6570 6561 7473 2c20 2050 7265  t: Repeats,  Pre\n-000105a0: 763a 2053 7765 6570 732c 2020 5570 3a20  v: Sweeps,  Up: \n-000105b0: 4472 6177 6162 6c65 730a 0a33 2e32 2e37  Drawables..3.2.7\n-000105c0: 2042 6c6f 636b 730a 2d2d 2d2d 2d2d 2d2d   Blocks.--------\n-000105d0: 2d2d 2d2d 0a0a 416e 7920 7365 7175 656e  ----..Any sequen\n-000105e0: 6365 206f 6620 6472 6177 6162 6c65 7320  ce of drawables \n-000105f0: 6d61 7920 6265 2067 726f 7570 6564 2069  may be grouped i\n-00010600: 6e20 6120 2262 6c6f 636b 2220 6d65 7265  n a \"block\" mere\n-00010610: 6c79 2062 790a 656e 636c 6f73 696e 6720  ly by.enclosing \n-00010620: 7468 656d 2069 6e20 6272 6163 6573 2027  them in braces '\n-00010630: 7b20 7d27 2e20 2041 2062 6c6f 636b 2069  { }'.  A block i\n-00010640: 7320 6974 7365 6c66 2064 7261 7761 626c  s itself drawabl\n-00010650: 652e 2020 4120 6b65 7920 7573 650a 6f66  e.  A key use.of\n-00010660: 2062 6c6f 636b 7320 6973 2074 6f20 6578   blocks is to ex\n-00010670: 7465 6e64 2074 6865 2065 6666 6563 7420  tend the effect \n-00010680: 6f66 2061 2073 696e 676c 6520 2764 6566  of a single 'def\n-00010690: 272c 202a 6e6f 7465 0a44 6566 696e 6974  ', *note.Definit\n-000106a0: 696f 6e73 3a3a 2c20 2770 7574 2720 2a6e  ions::, 'put' *n\n-000106b0: 6f74 6520 5075 7473 3a3a 2c20 2773 7765  ote Puts::, 'swe\n-000106c0: 6570 2720 2a6e 6f74 6520 5377 6565 7073  ep' *note Sweeps\n-000106d0: 3a3a 2c20 6f72 2027 7265 7065 6174 270a  ::, or 'repeat'.\n-000106e0: 2a6e 6f74 6520 5265 7065 6174 733a 3a20  *note Repeats:: \n-000106f0: 746f 2069 6e63 6c75 6465 2073 6576 6572  to include sever\n-00010700: 616c 206f 626a 6563 7473 2072 6174 6865  al objects rathe\n-00010710: 7220 7468 616e 206f 6e65 2e0a 0a20 2020  r than one...   \n-00010720: 4465 6669 6e69 7469 6f6e 7320 282a 4e6f  Definitions (*No\n-00010730: 7465 2044 6566 696e 6974 696f 6e73 3a3a  te Definitions::\n-00010740: 2e29 2020 696e 7369 6465 2061 2062 6c6f  .)  inside a blo\n-00010750: 636b 2068 6176 6520 226c 6578 6963 616c  ck have \"lexical\n-00010760: 0a73 636f 7065 2220 6578 7465 6e64 696e  .scope\" extendin\n-00010770: 6720 6672 6f6d 2074 6865 2070 6c61 6365  g from the place\n-00010780: 206f 6620 6465 6669 6e69 7469 6f6e 2074   of definition t\n-00010790: 6f20 7468 6520 656e 6420 6f66 2074 6865  o the end of the\n-000107a0: 2062 6c6f 636b 2e0a 0a1f 0a46 696c 653a   block.....File:\n-000107b0: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n-000107c0: 6f64 653a 2052 6570 6561 7473 2c20 204e  ode: Repeats,  N\n-000107d0: 6578 743a 2050 7574 732c 2020 5072 6576  ext: Puts,  Prev\n-000107e0: 3a20 426c 6f63 6b73 2c20 2055 703a 2044  : Blocks,  Up: D\n-000107f0: 7261 7761 626c 6573 0a0a 332e 322e 3820  rawables..3.2.8 \n-00010800: 5265 7065 6174 730a 2d2d 2d2d 2d2d 2d2d  Repeats.--------\n-00010810: 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a  -----..*Syntax:*\n-00010820: 0a20 2020 2020 7265 7065 6174 207b 204e  .     repeat { N\n-00010830: 2c20 545f 312c 2054 5f32 2c20 2e2e 2e2c  , T_1, T_2, ...,\n-00010840: 2054 5f52 207d 2052 4550 4541 5445 445f   T_R } REPEATED_\n-00010850: 4f42 4a45 4354 0a54 6865 2072 6570 6561  OBJECT.The repea\n-00010860: 7420 6d61 6b65 7320 4e20 7472 616e 7366  t makes N transf\n-00010870: 6f72 6d65 6420 636f 7069 6573 206f 6620  ormed copies of \n-00010880: 5245 5045 4154 4544 5f4f 424a 4543 5420  REPEATED_OBJECT \n-00010890: 2869 6e63 6c75 6469 6e67 2074 6865 0a6f  (including the.o\n-000108a0: 7269 6769 6e61 6c29 2e20 2054 6865 2054  riginal).  The T\n-000108b0: 5f49 2061 7265 2074 7261 6e73 666f 726d  _I are transform\n-000108c0: 732e 2020 5468 6520 6b27 7468 2063 6f70  s.  The k'th cop\n-000108d0: 7920 6f66 2074 6865 0a52 4550 4541 5445  y of the.REPEATE\n-000108e0: 445f 4f42 4a45 4354 2028 666f 7220 6b3d  D_OBJECT (for k=\n-000108f0: 302c 312c 2e2e 2e2c 6e2d 3129 2069 7320  0,1,...,n-1) is \n-00010900: 7072 6f64 7563 6564 2069 6e20 7468 6520  produced in the \n-00010910: 7361 6d65 206d 616e 6e65 7220 6173 0a66  same manner as.f\n-00010920: 6f72 2027 7377 6565 7027 7320 6465 7363  or 'sweep's desc\n-00010930: 7269 6265 6420 696e 202a 6e6f 7465 2053  ribed in *note S\n-00010940: 7765 6570 733a 3a2e 2020 5468 6973 2069  weeps::.  This i\n-00010950: 7320 7265 7065 6174 6564 2068 6572 6520  s repeated here \n-00010960: 286e 6f20 7075 6e0a 696e 7465 6e64 6564  (no pun.intended\n-00010970: 2920 666f 7220 636f 6e76 656e 6965 6e63  ) for convenienc\n-00010980: 652e 2020 546f 206d 616b 6520 7468 6520  e.  To make the \n-00010990: 6b27 7468 2063 6f70 792c 2074 6865 2066  k'th copy, the f\n-000109a0: 6f6c 6c6f 7769 6e67 0a74 7261 6e73 666f  ollowing.transfo\n-000109b0: 726d 2069 7320 6170 706c 6965 6420 746f  rm is applied to\n-000109c0: 2074 6865 206f 7269 6769 6e61 6c20 6f62   the original ob\n-000109d0: 6a65 6374 2e0a 2020 2020 2054 5f31 5e6b  ject..     T_1^k\n-000109e0: 2074 6865 6e20 545f 325e 6b20 7468 656e   then T_2^k then\n-000109f0: 202e 2e2e 2074 6865 6e20 545f 525e 6b0a   ... then T_R^k.\n-00010a00: 4865 7265 2054 5e6b 206d 6561 6e73 2022  Here T^k means \"\n-00010a10: 7472 616e 7366 6f72 6d20 5420 6170 706c  transform T appl\n-00010a20: 6965 6420 6b20 7469 6d65 732e 220a 0a1f  ied k times.\"...\n-00010a30: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n-00010a40: 666f 2c20 204e 6f64 653a 2050 7574 732c  fo,  Node: Puts,\n-00010a50: 2020 5072 6576 3a20 5265 7065 6174 732c    Prev: Repeats,\n-00010a60: 2020 5570 3a20 4472 6177 6162 6c65 730a    Up: Drawables.\n-00010a70: 0a33 2e32 2e39 2050 7574 730a 2d2d 2d2d  .3.2.9 Puts.----\n-00010a80: 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 783a  ------..*Syntax:\n-00010a90: 2a0a 2020 2020 2070 7574 207b 2054 207d  *.     put { T }\n-00010aa0: 2050 5554 5f4f 424a 4543 540a 5075 7420   PUT_OBJECT.Put \n-00010ab0: 6d65 7265 6c79 2061 7070 6c69 6573 2074  merely applies t\n-00010ac0: 7261 6e73 666f 726d 2054 2074 6f20 7468  ransform T to th\n-00010ad0: 6520 6472 6177 6162 6c65 2050 5554 5f4f  e drawable PUT_O\n-00010ae0: 424a 4543 542e 0a0a 1f0a 4669 6c65 3a20  BJECT.....File: \n-00010af0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n-00010b00: 6465 3a20 4465 6669 6e69 7469 6f6e 732c  de: Definitions,\n-00010b10: 2020 4e65 7874 3a20 476c 6f62 616c 2065    Next: Global e\n-00010b20: 6e76 6972 6f6e 6d65 6e74 2c20 2050 7265  nvironment,  Pre\n-00010b30: 763a 2044 7261 7761 626c 6573 2c20 2055  v: Drawables,  U\n-00010b40: 703a 2049 6e70 7574 206c 616e 6775 6167  p: Input languag\n-00010b50: 650a 0a33 2e33 2044 6566 696e 6974 696f  e..3.3 Definitio\n-00010b60: 6e73 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ns.=============\n-00010b70: 3d3d 0a0a 4465 6669 6e69 7469 6f6e 7320  ==..Definitions \n-00010b80: 6769 7665 206e 616d 6573 2074 6f20 2773  give names to 's\n-00010b90: 6b65 7463 6827 206f 626a 6563 7473 2e20  ketch' objects. \n-00010ba0: 2044 6566 696e 6974 696f 6e73 2061 6c6f   Definitions alo\n-00010bb0: 6e65 2061 7265 0a62 656e 6967 6e2e 2020  ne are.benign.  \n-00010bc0: 4120 2773 6b65 7463 6827 2069 6e70 7574  A 'sketch' input\n-00010bd0: 2066 696c 6520 636f 6e73 6973 7469 6e67   file consisting\n-00010be0: 2065 6e74 6972 656c 7920 6f66 2064 6566   entirely of def\n-00010bf0: 696e 6974 696f 6e73 2077 696c 6c0a 6765  initions will.ge\n-00010c00: 6e65 7261 7465 206e 6f20 6472 6177 696e  nerate no drawin\n-00010c10: 672e 2020 4f6e 6c79 2077 6865 6e20 6465  g.  Only when de\n-00010c20: 6669 6e69 7469 6f6e 7320 6172 6520 2272  finitions are \"r\n-00010c30: 6566 6572 656e 6365 6422 2064 6f20 7468  eferenced\" do th\n-00010c40: 6579 0a70 6f74 656e 7469 616c 6c79 206c  ey.potentially l\n-00010c50: 6561 6420 746f 2069 6e6b 206f 6e20 7468  ead to ink on th\n-00010c60: 6520 6472 6177 696e 672e 0a0a 2020 2054  e drawing...   T\n-00010c70: 6865 2069 6e74 656e 7420 6f66 2064 6566  he intent of def\n-00010c80: 696e 6974 696f 6e73 2069 7320 746f 206d  initions is to m\n-00010c90: 616b 6520 2773 6b65 7463 6827 2063 6f64  ake 'sketch' cod\n-00010ca0: 6520 6d6f 7265 2063 6f6e 6369 7365 2061  e more concise a\n-00010cb0: 6e64 0a72 6561 6461 626c 652e 2020 5468  nd.readable.  Th\n-00010cc0: 6572 6520 6973 206e 6f20 696e 7075 7420  ere is no input \n-00010cd0: 6669 6c65 2065 6d70 6c6f 7969 6e67 2064  file employing d\n-00010ce0: 6566 696e 6974 696f 6e73 2074 6861 7420  efinitions that \n-00010cf0: 636f 756c 6420 6e6f 740a 6265 2072 652d  could not.be re-\n-00010d00: 7772 6974 7465 6e20 7769 7468 6f75 7420  written without \n-00010d10: 7468 656d 2e0a 0a20 2020 4465 6669 6e61  them...   Defina\n-00010d20: 626c 6520 6f62 6a65 6374 7320 696e 636c  ble objects incl\n-00010d30: 7564 6520 616e 7920 7265 7375 6c74 206f  ude any result o\n-00010d40: 6620 616e 2061 6666 696e 6520 6172 6974  f an affine arit\n-00010d50: 686d 6574 6963 0a65 7870 7265 7373 696f  hmetic.expressio\n-00010d60: 6e20 2873 6361 6c61 722c 2070 6f69 6e74  n (scalar, point\n-00010d70: 2c20 7665 6374 6f72 2c20 6f72 2074 7261  , vector, or tra\n-00010d80: 6e73 666f 726d 292c 2061 6e79 2064 7261  nsform), any dra\n-00010d90: 7761 626c 6520 6f62 6a65 6374 0a28 646f  wable object.(do\n-00010da0: 7473 2c20 6c69 6e65 2c20 6375 7276 652c  ts, line, curve,\n-00010db0: 2070 6f6c 7967 6f6e 2c20 626c 6f63 6b2c   polygon, block,\n-00010dc0: 2073 7765 6570 2c20 7075 742c 2072 6570   sweep, put, rep\n-00010dd0: 6561 742c 206f 7220 7370 6563 6961 6c29  eat, or special)\n-00010de0: 2c20 616e 640a 6f70 7469 6f6e 2073 7472  , and.option str\n-00010df0: 696e 6773 2e20 2049 6e20 6164 6469 7469  ings.  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If \n+0000fc60: 7468 6572 6520 6172 6520 6d20 706f 696e  there are m poin\n+0000fc70: 7473 2069 6e20 7468 6520 6f72 6967 696e  ts in the origin\n+0000fc80: 616c 2070 6f6c 7967 6f6e 2c20 7468 656e  al polygon, then\n+0000fc90: 206d 4e0a 626f 6479 2070 6f6c 7967 6f6e   mN.body polygon\n+0000fca0: 7320 6172 6520 666f 726d 6564 2062 7920  s are formed by \n+0000fcb0: 7468 6973 2073 7765 6570 2e20 2054 6865  this sweep.  The\n+0000fcc0: 2062 6f64 7920 706f 6c79 676f 6e73 2066   body polygons f\n+0000fcd0: 6f72 6d20 616e 0a22 6578 7472 7573 696f  orm an.\"extrusio\n+0000fce0: 6e22 206f 6620 7468 6520 626f 756e 6461  n\" of the bounda\n+0000fcf0: 7279 206f 6620 7468 6520 6f72 6967 696e  ry of the origin\n+0000fd00: 616c 2070 6f6c 7967 6f6e 2077 6974 6820  al polygon with \n+0000fd10: 7477 6f20 686f 6c65 7320 6174 0a74 6865  two holes at.the\n+0000fd20: 206f 7065 6e20 656e 6473 2e0a 0a20 2020   open ends...   \n+0000fd30: 4669 6e61 6c6c 792c 2074 6865 2073 7765  Finally, the swe\n+0000fd40: 6570 2061 6464 7320 7477 6f20 636f 7069  ep adds two copi\n+0000fd50: 6573 206f 6620 7468 6520 6f72 6967 696e  es of the origin\n+0000fd60: 616c 2070 6f6c 7967 6f6e 2074 6f20 636f  al polygon to co\n+0000fd70: 7665 720a 7468 6520 686f 6c65 732e 2020  ver.the holes.  \n+0000fd80: 5765 2063 616c 6c20 7468 6573 6520 686f  We call these ho\n+0000fd90: 6c65 2d66 696c 6c69 6e67 2070 6f6c 7967  le-filling polyg\n+0000fda0: 6f6e 7320 2265 6e64 7322 2e20 2049 6e20  ons \"ends\".  In \n+0000fdb0: 7468 6973 206d 616e 6e65 722c 0a27 7377  this manner,.'sw\n+0000fdc0: 6565 7027 2066 6f72 6d73 2074 6865 2062  eep' forms the b\n+0000fdd0: 6f75 6e64 6172 7920 6f66 2061 2074 6872  oundary of a thr\n+0000fde0: 6565 2d64 696d 656e 7369 6f6e 616c 206f  ee-dimensional o\n+0000fdf0: 626a 6563 7420 6672 6f6d 2061 0a74 776f  bject from a.two\n+0000fe00: 2d64 696d 656e 7369 6f6e 616c 2070 6f6c  -dimensional pol\n+0000fe10: 7967 6f6e 2e0a 0a20 2020 5468 6520 6f72  ygon...   The or\n+0000fe20: 6465 7220 6f66 2076 6572 7469 6365 7320  der of vertices \n+0000fe30: 6f66 2065 6e64 2070 6f6c 7967 6f6e 7320  of end polygons \n+0000fe40: 6973 2069 6d70 6f72 7461 6e74 2066 6f72  is important for\n+0000fe50: 2063 6f72 7265 6374 0a63 756c 6c69 6e67   correct.culling\n+0000fe60: 2061 7320 6465 7363 7269 6265 6420 6162   as described ab\n+0000fe70: 6f76 652e 2020 416e 2065 7861 6374 2063  ove.  An exact c\n+0000fe80: 6f70 7920 6f66 2074 6865 206f 7269 6769  opy of the origi\n+0000fe90: 6e61 6c20 706f 6c79 676f 6e20 7769 7468  nal polygon with\n+0000fea0: 0a76 6572 7465 7820 6f72 6465 7220 696e  .vertex order in\n+0000feb0: 7461 6374 2066 6f72 6d73 2074 6865 2066  tact forms the f\n+0000fec0: 6972 7374 2065 6e64 2070 6f6c 7967 6f6e  irst end polygon\n+0000fed0: 2e20 2054 6865 206f 7468 6572 2065 6e64  .  The other end\n+0000fee0: 2070 6f6c 7967 6f6e 0a72 6573 756c 7473   polygon.results\n+0000fef0: 2066 726f 6d20 7472 616e 7366 6f72 6d69   from transformi\n+0000ff00: 6e67 2061 6e64 2074 6865 2072 6576 6572  ng and the rever\n+0000ff10: 7369 6e67 2074 6865 206f 7264 6572 206f  sing the order o\n+0000ff20: 6620 7665 7274 6963 6573 2069 6e20 7468  f vertices in th\n+0000ff30: 650a 6f72 6967 696e 616c 2e20 2054 6865  e.original.  The\n+0000ff40: 2074 7261 6e73 666f 726d 2070 6c61 6365   transform place\n+0000ff50: 7320 7468 6520 6f72 6967 696e 616c 2070  s the original p\n+0000ff60: 6f6c 7967 6f6e 2061 7420 7468 6520 756e  olygon at the un\n+0000ff70: 636f 7665 7265 640a 686f 6c65 3b20 6974  covered.hole; it\n+0000ff80: 2069 730a 2020 2020 2054 5f31 5e6e 2074   is.     T_1^n t\n+0000ff90: 6865 6e20 545f 325e 6e20 7468 656e 202e  hen T_2^n then .\n+0000ffa0: 2e2e 2074 6865 6e20 545f 525e 6e2e 0a49  .. then T_R^n..I\n+0000ffb0: 6620 7468 6572 6520 6172 6520 6e6f 206f  f there are no o\n+0000ffc0: 7074 696f 6e73 206f 6e20 7468 6520 7377  ptions on the sw\n+0000ffd0: 6570 7420 706f 6c79 676f 6e2c 2074 6865  ept polygon, the\n+0000ffe0: 6e20 7468 6520 2773 7765 6570 2720 6f70  n the 'sweep' op\n+0000fff0: 7469 6f6e 730a 6172 6520 636f 7069 6564  tions.are copied\n+00010000: 2074 6f20 6561 6368 206f 7574 7075 7420   to each output \n+00010010: 706f 6c79 676f 6e2e 2020 4966 2074 6865  polygon.  If the\n+00010020: 2073 7765 7074 2070 6f6c 7967 6f6e 2064   swept polygon d\n+00010030: 6f65 7320 6861 7665 0a6f 7074 696f 6e73  oes have.options\n+00010040: 2c20 7468 6573 6520 6172 6520 636f 7069  , these are copi\n+00010050: 6564 2074 6f20 7468 6520 656e 6473 3b20  ed to the ends; \n+00010060: 7468 6520 7377 6565 7020 6f70 7469 6f6e  the sweep option\n+00010070: 7320 6172 6520 636f 7069 6564 2074 6f0a  s are copied to.\n+00010080: 7468 6520 626f 6479 2070 6f6c 7967 6f6e  the body polygon\n+00010090: 732e 2020 496e 2074 6869 7320 6d61 6e6e  s.  In this mann\n+000100a0: 6572 2c20 626f 6479 2061 6e64 2065 6e64  er, body and end\n+000100b0: 7320 6d61 7920 6265 2064 7261 776e 2077  s may be drawn w\n+000100c0: 6974 680a 6469 6666 6572 656e 7420 6368  ith.different ch\n+000100d0: 6172 6163 7465 7269 7374 6963 7320 7375  aracteristics su\n+000100e0: 6368 2061 7320 2766 696c 6c63 6f6c 6f72  ch as 'fillcolor\n+000100f0: 272e 0a0a 1f0a 4669 6c65 3a20 736b 6574  '.....File: sket\n+00010100: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n+00010110: 5377 6570 7420 626c 6f63 6b73 2c20 204e  Swept blocks,  N\n+00010120: 6578 743a 2053 7765 6570 2066 6163 6520  ext: Sweep face \n+00010130: 7370 6c69 7474 696e 672c 2020 5072 6576  splitting,  Prev\n+00010140: 3a20 5377 6570 7420 706f 6c79 676f 6e73  : Swept polygons\n+00010150: 2c20 2055 703a 2053 7765 6570 730a 0a33  ,  Up: Sweeps..3\n+00010160: 2e32 2e36 2e34 2053 7765 7074 2062 6c6f  .2.6.4 Swept blo\n+00010170: 636b 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  cks.............\n+00010180: 2e2e 2e2e 2e2e 2e2e 0a0a 5468 6520 7377  ..........The sw\n+00010190: 6570 7420 6f62 6a65 6374 2053 5745 5054  ept object SWEPT\n+000101a0: 5f4f 424a 4543 5420 6d61 7920 616c 736f  _OBJECT may also\n+000101b0: 2062 6520 616e 7920 636f 6c6c 6563 7469   be any collecti\n+000101c0: 6f6e 206f 6620 706f 6c79 6c69 6e65 730a  on of polylines.\n+000101d0: 616e 6420 706f 6c79 676f 6e73 2e20 2054  and polygons.  T\n+000101e0: 6869 7320 6d61 7920 6265 2061 2062 6c6f  his may be a blo\n+000101f0: 636b 2063 6f6d 706f 7365 6420 6f66 2027  ck composed of '\n+00010200: 6c69 6e65 2720 616e 642f 6f72 2027 706f  line' and/or 'po\n+00010210: 6c79 676f 6e27 0a63 6f6d 6d61 6e64 7320  lygon'.commands \n+00010220: 696e 2062 7261 6365 7320 277b 207d 272c  in braces '{ }',\n+00010230: 206f 7220 6974 206d 6179 2062 6520 7468   or it may be th\n+00010240: 6520 7265 7375 6c74 206f 6620 6120 2772  e result of a 'r\n+00010250: 6570 6561 7427 2c20 616e 6f74 6865 720a  epeat', another.\n+00010260: 2773 7765 6570 272c 2065 7463 2e20 2054  'sweep', etc.  T\n+00010270: 6865 2073 7765 6570 2061 6374 7320 696e  he sweep acts in\n+00010280: 6465 7065 6e64 656e 746c 7920 6f6e 2065  dependently on e\n+00010290: 6163 6820 6f62 6a65 6374 2069 6e20 7468  ach object in th\n+000102a0: 6520 626c 6f63 6b0a 6578 6163 746c 7920  e block.exactly \n+000102b0: 6173 2069 6620 6974 2077 6572 6520 6120  as if it were a \n+000102c0: 7369 6e67 6c65 2073 7765 7074 206f 626a  single swept obj\n+000102d0: 6563 7420 6465 7363 7269 6265 6420 6162  ect described ab\n+000102e0: 6f76 6520 696e 202a 6e6f 7465 0a53 7765  ove in *note.Swe\n+000102f0: 7074 206c 696e 6573 3a3a 2061 6e64 202a  pt lines:: and *\n+00010300: 6e6f 7465 2053 7765 7074 2070 6f6c 7967  note Swept polyg\n+00010310: 6f6e 733a 3a2e 0a0a 1f0a 4669 6c65 3a20  ons::.....File: \n+00010320: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n+00010330: 6465 3a20 5377 6565 7020 6661 6365 2073  de: Sweep face s\n+00010340: 706c 6974 7469 6e67 2c20 2050 7265 763a  plitting,  Prev:\n+00010350: 2053 7765 7074 2062 6c6f 636b 732c 2020   Swept blocks,  \n+00010360: 5570 3a20 5377 6565 7073 0a0a 332e 322e  Up: Sweeps..3.2.\n+00010370: 362e 3520 5377 6565 7020 6661 6365 2073  6.5 Sweep face s\n+00010380: 706c 6974 7469 6e67 0a2e 2e2e 2e2e 2e2e  plitting........\n+00010390: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+000103a0: 2e2e 2e2e 2e0a 0a42 6566 6f72 6520 7365  .......Before se\n+000103b0: 6e64 696e 6720 6561 6368 2066 6f75 722d  nding each four-\n+000103c0: 7369 6465 6420 626f 6479 2070 6f6c 7967  sided body polyg\n+000103d0: 6f6e 206f 6620 6120 2773 7765 6570 2720  on of a 'sweep' \n+000103e0: 746f 2074 6865 206f 7574 7075 742c 0a27  to the output,.'\n+000103f0: 736b 6574 6368 2720 7465 7374 7320 746f  sketch' tests to\n+00010400: 2073 6565 2069 6620 6974 2069 7320 726f   see if it is ro\n+00010410: 7567 686c 7920 706c 616e 6172 2e20 2053  ughly planar.  S\n+00010420: 696e 6365 2070 6c61 6e61 7269 7479 2069  ince planarity i\n+00010430: 730a 6e65 6365 7373 6172 7920 666f 7220  s.necessary for \n+00010440: 7072 6f70 6572 2066 756e 6374 696f 6e69  proper functioni\n+00010450: 6e67 206f 6620 7468 6520 6869 6464 656e  ng of the hidden\n+00010460: 2073 7572 6661 6365 2061 6c67 6f72 6974   surface algorit\n+00010470: 686d 2c0a 2277 6172 7065 6422 2070 6f6c  hm,.\"warped\" pol\n+00010480: 7967 6f6e 7320 6172 6520 6175 746f 6d61  ygons are automa\n+00010490: 7469 6361 6c6c 7920 7370 6c69 7420 696e  tically split in\n+000104a0: 746f 2074 776f 2074 7269 616e 676c 6573  to two triangles\n+000104b0: 2e0a 0a20 2020 486f 6c65 2d66 696c 6c69  ...   Hole-filli\n+000104c0: 6e67 2070 6f6c 7967 6f6e 7320 7072 6f64  ng polygons prod\n+000104d0: 7563 6564 2062 7920 636c 6f73 7572 652d  uced by closure-\n+000104e0: 7461 6767 6564 206c 696e 6520 7377 6565  tagged line swee\n+000104f0: 7073 2061 7265 206e 6f74 0a73 706c 6974  ps are not.split\n+00010500: 2e20 204e 6f72 2061 7265 206f 7269 6769  .  Nor are origi\n+00010510: 6e61 6c20 706f 6c79 676f 6e73 2069 6e20  nal polygons in \n+00010520: 706f 6c79 676f 6e20 7377 6565 7073 2e20  polygon sweeps. \n+00010530: 2049 7420 6973 2074 6865 2075 7365 7227   It is the user'\n+00010540: 730a 7265 7370 6f6e 7369 6269 6c69 7479  s.responsibility\n+00010550: 2074 6f20 656e 7375 7265 2074 6865 7365   to ensure these\n+00010560: 2061 7265 2070 6c61 6e61 722e 0a0a 1f0a   are planar.....\n+00010570: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n+00010580: 6f2c 2020 4e6f 6465 3a20 426c 6f63 6b73  o,  Node: Blocks\n+00010590: 2c20 204e 6578 743a 2052 6570 6561 7473  ,  Next: Repeats\n+000105a0: 2c20 2050 7265 763a 2053 7765 6570 732c  ,  Prev: Sweeps,\n+000105b0: 2020 5570 3a20 4472 6177 6162 6c65 730a    Up: Drawables.\n+000105c0: 0a33 2e32 2e37 2042 6c6f 636b 730a 2d2d  .3.2.7 Blocks.--\n+000105d0: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 416e 7920  ----------..Any \n+000105e0: 7365 7175 656e 6365 206f 6620 6472 6177  sequence of draw\n+000105f0: 6162 6c65 7320 6d61 7920 6265 2067 726f  ables may be gro\n+00010600: 7570 6564 2069 6e20 6120 2262 6c6f 636b  uped in a \"block\n+00010610: 2220 6d65 7265 6c79 2062 790a 656e 636c  \" merely by.encl\n+00010620: 6f73 696e 6720 7468 656d 2069 6e20 6272  osing them in br\n+00010630: 6163 6573 2027 7b20 7d27 2e20 2041 2062  aces '{ }'.  A b\n+00010640: 6c6f 636b 2069 7320 6974 7365 6c66 2064  lock is itself d\n+00010650: 7261 7761 626c 652e 2020 4120 6b65 7920  rawable.  A key \n+00010660: 7573 650a 6f66 2062 6c6f 636b 7320 6973  use.of blocks is\n+00010670: 2074 6f20 6578 7465 6e64 2074 6865 2065   to extend the e\n+00010680: 6666 6563 7420 6f66 2061 2073 696e 676c  ffect of a singl\n+00010690: 6520 2764 6566 272c 202a 6e6f 7465 0a44  e 'def', *note.D\n+000106a0: 6566 696e 6974 696f 6e73 3a3a 2c20 2770  efinitions::, 'p\n+000106b0: 7574 2720 2a6e 6f74 6520 5075 7473 3a3a  ut' *note Puts::\n+000106c0: 2c20 2773 7765 6570 2720 2a6e 6f74 6520  , 'sweep' *note \n+000106d0: 5377 6565 7073 3a3a 2c20 6f72 2027 7265  Sweeps::, or 're\n+000106e0: 7065 6174 270a 2a6e 6f74 6520 5265 7065  peat'.*note Repe\n+000106f0: 6174 733a 3a20 746f 2069 6e63 6c75 6465  ats:: to include\n+00010700: 2073 6576 6572 616c 206f 626a 6563 7473   several objects\n+00010710: 2072 6174 6865 7220 7468 616e 206f 6e65   rather than one\n+00010720: 2e0a 0a20 2020 4465 6669 6e69 7469 6f6e  ...   Definition\n+00010730: 7320 282a 4e6f 7465 2044 6566 696e 6974  s (*Note Definit\n+00010740: 696f 6e73 3a3a 2e29 2020 696e 7369 6465  ions::.)  inside\n+00010750: 2061 2062 6c6f 636b 2068 6176 6520 226c   a block have \"l\n+00010760: 6578 6963 616c 0a73 636f 7065 2220 6578  exical.scope\" ex\n+00010770: 7465 6e64 696e 6720 6672 6f6d 2074 6865  tending from the\n+00010780: 2070 6c61 6365 206f 6620 6465 6669 6e69   place of defini\n+00010790: 7469 6f6e 2074 6f20 7468 6520 656e 6420  tion to the end \n+000107a0: 6f66 2074 6865 2062 6c6f 636b 2e0a 0a1f  of the block....\n+000107b0: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n+000107c0: 666f 2c20 204e 6f64 653a 2052 6570 6561  fo,  Node: Repea\n+000107d0: 7473 2c20 204e 6578 743a 2050 7574 732c  ts,  Next: Puts,\n+000107e0: 2020 5072 6576 3a20 426c 6f63 6b73 2c20    Prev: Blocks, \n+000107f0: 2055 703a 2044 7261 7761 626c 6573 0a0a   Up: Drawables..\n+00010800: 332e 322e 3820 5265 7065 6174 730a 2d2d  3.2.8 Repeats.--\n+00010810: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a 5379  -----------..*Sy\n+00010820: 6e74 6178 3a2a 0a20 2020 2020 7265 7065  ntax:*.     repe\n+00010830: 6174 207b 204e 2c20 545f 312c 2054 5f32  at { N, T_1, T_2\n+00010840: 2c20 2e2e 2e2c 2054 5f52 207d 2052 4550  , ..., T_R } REP\n+00010850: 4541 5445 445f 4f42 4a45 4354 0a54 6865  EATED_OBJECT.The\n+00010860: 2072 6570 6561 7420 6d61 6b65 7320 4e20   repeat makes N \n+00010870: 7472 616e 7366 6f72 6d65 6420 636f 7069  transformed copi\n+00010880: 6573 206f 6620 5245 5045 4154 4544 5f4f  es of REPEATED_O\n+00010890: 424a 4543 5420 2869 6e63 6c75 6469 6e67  BJECT (including\n+000108a0: 2074 6865 0a6f 7269 6769 6e61 6c29 2e20   the.original). \n+000108b0: 2054 6865 2054 5f49 2061 7265 2074 7261   The T_I are tra\n+000108c0: 6e73 666f 726d 732e 2020 5468 6520 6b27  nsforms.  The k'\n+000108d0: 7468 2063 6f70 7920 6f66 2074 6865 0a52  th copy of the.R\n+000108e0: 4550 4541 5445 445f 4f42 4a45 4354 2028  EPEATED_OBJECT (\n+000108f0: 666f 7220 6b3d 302c 312c 2e2e 2e2c 6e2d  for k=0,1,...,n-\n+00010900: 3129 2069 7320 7072 6f64 7563 6564 2069  1) is produced i\n+00010910: 6e20 7468 6520 7361 6d65 206d 616e 6e65  n the same manne\n+00010920: 7220 6173 0a66 6f72 2027 7377 6565 7027  r as.for 'sweep'\n+00010930: 7320 6465 7363 7269 6265 6420 696e 202a  s described in *\n+00010940: 6e6f 7465 2053 7765 6570 733a 3a2e 2020  note Sweeps::.  \n+00010950: 5468 6973 2069 7320 7265 7065 6174 6564  This is repeated\n+00010960: 2068 6572 6520 286e 6f20 7075 6e0a 696e   here (no pun.in\n+00010970: 7465 6e64 6564 2920 666f 7220 636f 6e76  tended) for conv\n+00010980: 656e 6965 6e63 652e 2020 546f 206d 616b  enience.  To mak\n+00010990: 6520 7468 6520 6b27 7468 2063 6f70 792c  e the k'th copy,\n+000109a0: 2074 6865 2066 6f6c 6c6f 7769 6e67 0a74   the following.t\n+000109b0: 7261 6e73 666f 726d 2069 7320 6170 706c  ransform is appl\n+000109c0: 6965 6420 746f 2074 6865 206f 7269 6769  ied to the origi\n+000109d0: 6e61 6c20 6f62 6a65 6374 2e0a 2020 2020  nal object..    \n+000109e0: 2054 5f31 5e6b 2074 6865 6e20 545f 325e   T_1^k then T_2^\n+000109f0: 6b20 7468 656e 202e 2e2e 2074 6865 6e20  k then ... then \n+00010a00: 545f 525e 6b0a 4865 7265 2054 5e6b 206d  T_R^k.Here T^k m\n+00010a10: 6561 6e73 2022 7472 616e 7366 6f72 6d20  eans \"transform \n+00010a20: 5420 6170 706c 6965 6420 6b20 7469 6d65  T applied k time\n+00010a30: 732e 220a 0a1f 0a46 696c 653a 2073 6b65  s.\"....File: ske\n+00010a40: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n+00010a50: 2050 7574 732c 2020 5072 6576 3a20 5265   Puts,  Prev: Re\n+00010a60: 7065 6174 732c 2020 5570 3a20 4472 6177  peats,  Up: Draw\n+00010a70: 6162 6c65 730a 0a33 2e32 2e39 2050 7574  ables..3.2.9 Put\n+00010a80: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53  s.----------..*S\n+00010a90: 796e 7461 783a 2a0a 2020 2020 2070 7574  yntax:*.     put\n+00010aa0: 207b 2054 207d 2050 5554 5f4f 424a 4543   { T } PUT_OBJEC\n+00010ab0: 540a 5075 7420 6d65 7265 6c79 2061 7070  T.Put merely app\n+00010ac0: 6c69 6573 2074 7261 6e73 666f 726d 2054  lies transform T\n+00010ad0: 2074 6f20 7468 6520 6472 6177 6162 6c65   to the drawable\n+00010ae0: 2050 5554 5f4f 424a 4543 542e 0a0a 1f0a   PUT_OBJECT.....\n+00010af0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n+00010b00: 6f2c 2020 4e6f 6465 3a20 4465 6669 6e69  o,  Node: Defini\n+00010b10: 7469 6f6e 732c 2020 4e65 7874 3a20 476c  tions,  Next: Gl\n+00010b20: 6f62 616c 2065 6e76 6972 6f6e 6d65 6e74  obal environment\n+00010b30: 2c20 2050 7265 763a 2044 7261 7761 626c  ,  Prev: Drawabl\n+00010b40: 6573 2c20 2055 703a 2049 6e70 7574 206c  es,  Up: Input l\n+00010b50: 616e 6775 6167 650a 0a33 2e33 2044 6566  anguage..3.3 Def\n+00010b60: 696e 6974 696f 6e73 0a3d 3d3d 3d3d 3d3d  initions.=======\n+00010b70: 3d3d 3d3d 3d3d 3d3d 0a0a 4465 6669 6e69  ========..Defini\n+00010b80: 7469 6f6e 7320 6769 7665 206e 616d 6573  tions give names\n+00010b90: 2074 6f20 2773 6b65 7463 6827 206f 626a   to 'sketch' obj\n+00010ba0: 6563 7473 2e20 2044 6566 696e 6974 696f  ects.  Definitio\n+00010bb0: 6e73 2061 6c6f 6e65 2061 7265 0a62 656e  ns alone are.ben\n+00010bc0: 6967 6e2e 2020 4120 2773 6b65 7463 6827  ign.  A 'sketch'\n+00010bd0: 2069 6e70 7574 2066 696c 6520 636f 6e73   input file cons\n+00010be0: 6973 7469 6e67 2065 6e74 6972 656c 7920  isting entirely \n+00010bf0: 6f66 2064 6566 696e 6974 696f 6e73 2077  of definitions w\n+00010c00: 696c 6c0a 6765 6e65 7261 7465 206e 6f20  ill.generate no \n+00010c10: 6472 6177 696e 672e 2020 4f6e 6c79 2077  drawing.  Only w\n+00010c20: 6865 6e20 6465 6669 6e69 7469 6f6e 7320  hen definitions \n+00010c30: 6172 6520 2272 6566 6572 656e 6365 6422  are \"referenced\"\n+00010c40: 2064 6f20 7468 6579 0a70 6f74 656e 7469   do they.potenti\n+00010c50: 616c 6c79 206c 6561 6420 746f 2069 6e6b  ally lead to ink\n+00010c60: 206f 6e20 7468 6520 6472 6177 696e 672e   on the drawing.\n+00010c70: 0a0a 2020 2054 6865 2069 6e74 656e 7420  ..   The intent \n+00010c80: 6f66 2064 6566 696e 6974 696f 6e73 2069  of definitions i\n+00010c90: 7320 746f 206d 616b 6520 2773 6b65 7463  s to make 'sketc\n+00010ca0: 6827 2063 6f64 6520 6d6f 7265 2063 6f6e  h' code more con\n+00010cb0: 6369 7365 2061 6e64 0a72 6561 6461 626c  cise and.readabl\n+00010cc0: 652e 2020 5468 6572 6520 6973 206e 6f20  e.  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In \n+00010e00: 6164 6469 7469 6f6e 2c20 2274 6167 2064  addition, \"tag d\n+00010e10: 6566 696e 6974 696f 6e73 222c 2077 6869  efinitions\", whi\n+00010e20: 6368 2068 6176 6520 6e6f 0a61 7373 6f63  ch have no.assoc\n+00010e30: 6961 7465 6420 6f62 6a65 6374 2061 7420  iated object at \n+00010e40: 616c 6c2c 2061 6c6c 6f77 2074 6865 206d  all, allow the m\n+00010e50: 6561 6e69 6e67 206f 6620 6f74 6865 7220  eaning of other \n+00010e60: 6465 6669 6e69 7469 6f6e 7320 746f 2062  definitions to b\n+00010e70: 650a 7365 6c65 6374 6564 2066 726f 6d20  e.selected from \n+00010e80: 6120 7365 7420 6f66 2061 6c74 6572 6e61  a set of alterna\n+00010e90: 7469 7665 732e 2020 5369 6e63 6520 7461  tives.  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The i\n+000114e0: 6e74 656e 7420 6f66 2074 6869 7320 6d65  ntent of this me\n+000114f0: 6368 616e 6973 6d0a 6973 2c20 6167 6169  chanism.is, agai\n+00011500: 6e2c 2074 6f20 6d61 6b65 2027 736b 6574  n, to make 'sket\n+00011510: 6368 2720 696e 7075 7420 6669 6c65 7320  ch' input files \n+00011520: 6d6f 7265 2072 6561 6461 626c 652e 0a54  more readable..T\n+00011530: 7970 6520 2020 2020 2020 2052 6566 6572  ype        Refer\n+00011540: 656e 6365 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d  ence.-----------\n 00011550: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-00011560: 2d2d 2d2d 2d2d 2d2d 2d0a 7363 616c 6172  ---------.scalar\n-00011570: 2020 2020 2020 2749 4427 0a70 6f69 6e74        'ID'.point\n-00011580: 2020 2020 2020 2027 2849 4429 270a 7665         '(ID)'.ve\n-00011590: 6374 6f72 2020 2020 2020 275b 4944 5d27  ctor      '[ID]'\n-000115a0: 0a74 7261 6e73 666f 726d 2020 2027 5b5b  .transform   '[[\n-000115b0: 4944 5d5d 270a 6472 6177 6162 6c65 2020  ID]]'.drawable  \n-000115c0: 2020 277b 4944 7d27 0a6f 7074 696f 6e73    '{ID}'.options\n-000115d0: 2020 2020 2027 5b49 445d 2720 6f72 2027       '[ID]' or '\n-000115e0: 5b49 4431 2c2e 2e2e 2c49 444e 5d27 0a74  [ID1,...,IDN]'.t\n-000115f0: 6167 2020 2020 2020 2020 2027 3c49 443e  ag         '<ID>\n-00011600: 270a 0a4e 6f74 6520 7468 6174 2073 7175  '..Note that squ\n-00011610: 6172 6520 6272 6163 6b65 7473 2027 5b20  are brackets '[ \n-00011620: 5d27 2061 7265 2075 7365 6420 626f 7468  ]' are used both\n-00011630: 2066 6f72 2076 6563 746f 7220 616e 6420   for vector and \n-00011640: 666f 7220 6f70 7469 6f6e 730a 7265 6665  for options.refe\n-00011650: 7265 6e63 6573 2e20 2044 6574 6169 6c73  rences.  Details\n-00011660: 206f 6620 2773 6b65 7463 6827 2073 796e   of 'sketch' syn\n-00011670: 7461 7820 6d61 6b65 2069 7420 696d 706f  tax make it impo\n-00011680: 7373 6962 6c65 2066 6f72 2074 6865 7365  ssible for these\n-00011690: 2074 776f 0a72 6566 6572 656e 6365 2074   two.reference t\n-000116a0: 7970 6573 2074 6f20 6265 2063 6f6e 6675  ypes to be confu\n-000116b0: 7365 642e 2020 5468 6520 7370 6563 6961  sed.  The specia\n-000116c0: 6c20 6d75 6c74 6970 6c65 2072 6566 6572  l multiple refer\n-000116d0: 656e 6365 0a27 5b49 4431 2c49 4432 2c2e  ence.'[ID1,ID2,.\n-000116e0: 2e2e 2c49 444e 5d27 2061 6374 7320 6173  ..,IDN]' acts as\n-000116f0: 2069 6620 7468 6520 7265 7370 6563 7469   if the respecti\n-00011700: 7665 206c 6973 7473 206f 6620 6f70 7469  ve lists of opti\n-00011710: 6f6e 7320 7765 7265 0a63 6f6e 6361 7465  ons were.concate\n-00011720: 6e61 7465 642e 0a0a 1f0a 4669 6c65 3a20  nated.....File: \n-00011730: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n-00011740: 6465 3a20 476c 6f62 616c 2065 6e76 6972  de: Global envir\n-00011750: 6f6e 6d65 6e74 2c20 2050 7265 763a 2044  onment,  Prev: D\n-00011760: 6566 696e 6974 696f 6e73 2c20 2055 703a  efinitions,  Up:\n-00011770: 2049 6e70 7574 206c 616e 6775 6167 650a   Input language.\n-00011780: 0a33 2e34 2047 6c6f 6261 6c20 656e 7669  .3.4 Global envi\n-00011790: 726f 6e6d 656e 740a 3d3d 3d3d 3d3d 3d3d  ronment.========\n-000117a0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a  ==============..\n-000117b0: 416e 206f 7074 696f 6e61 6c20 676c 6f62  An optional glob\n-000117c0: 616c 2065 6e76 6972 6f6e 6d65 6e74 2062  al environment b\n-000117d0: 6c6f 636b 2070 726f 7669 6465 7320 6120  lock provides a \n-000117e0: 6665 7720 7761 7973 2074 6f20 6166 6665  few ways to affe\n-000117f0: 6374 2074 6865 0a65 6e74 6972 6520 7363  ct the.entire sc\n-00011800: 656e 652e 2020 5468 6520 626c 6f63 6b20  ene.  The block \n-00011810: 6d75 7374 2061 7070 6561 7220 6173 2074  must appear as t\n-00011820: 6865 206c 6173 7420 7465 7874 2069 6e20  he last text in \n-00011830: 7468 6520 2773 6b65 7463 6827 0a69 6e70  the 'sketch'.inp\n-00011840: 7574 2066 696c 652e 2020 4974 206d 6179  ut file.  It may\n-00011850: 2069 6e63 6c75 6465 2064 6566 696e 6974   include definit\n-00011860: 696f 6e73 2c20 6275 7420 6e6f 7465 2074  ions, but note t\n-00011870: 6861 7420 7072 6576 696f 7573 0a64 6566  hat previous.def\n-00011880: 696e 6974 696f 6e73 2061 7420 7468 6520  initions at the \n-00011890: 746f 7020 6c65 7665 6c20 286e 6f74 206e  top level (not n\n-000118a0: 6573 7465 6420 696e 7369 6465 2062 6c6f  ested inside blo\n-000118b0: 636b 7329 2061 7265 2061 6c73 6f0a 6176  cks) are also.av\n-000118c0: 6169 6c61 626c 652e 0a0a 2a53 796e 7461  ailable...*Synta\n-000118d0: 783a 2a0a 2020 2020 2067 6c6f 6261 6c20  x:*.     global \n-000118e0: 7b20 454e 5649 524f 4e4d 454e 545f 5345  { ENVIRONMENT_SE\n-000118f0: 5454 494e 4753 207d 0a54 6865 2063 6f6e  TTINGS }.The con\n-00011900: 7465 6e74 7320 6f66 2045 4e56 4952 4f4e  tents of ENVIRON\n-00011910: 4d45 4e54 5f53 4554 5449 4e47 5320 6172  MENT_SETTINGS ar\n-00011920: 6520 6469 7363 7573 7365 6420 696e 2074  e discussed in t\n-00011930: 6865 2073 6563 7469 6f6e 7320 7468 6174  he sections that\n-00011940: 0a66 6f6c 6c6f 772e 0a0a 2a20 4d65 6e75  .follow...* Menu\n-00011950: 3a0a 0a2a 2047 6c6f 6261 6c20 6f70 7469  :..* Global opti\n-00011960: 6f6e 733a 3a20 2020 2020 2020 2020 2020  ons::           \n-00011970: 2020 2041 7474 7269 6275 7465 7320 6f66     Attributes of\n-00011980: 2074 6865 2065 6e74 6972 6520 6472 6177   the entire draw\n-00011990: 696e 672e 0a2a 2043 616d 6572 613a 3a20  ing..* Camera:: \n-000119a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000119b0: 2020 2020 2041 2066 696e 616c 2063 616d       A final cam\n-000119c0: 6572 6120 7472 616e 7366 6f72 6d61 7469  era transformati\n-000119d0: 6f6e 206f 6620 7468 6520 7363 656e 652e  on of the scene.\n-000119e0: 0a2a 2050 6963 7475 7265 2062 6f78 3a3a  .* Picture box::\n-000119f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00011a00: 2053 6574 7469 6e67 2074 6865 2062 6f75   Setting the bou\n-00011a10: 6e64 696e 6720 626f 7820 616e 6420 3264  nding box and 2d\n-00011a20: 2063 6c69 7070 696e 672e 0a2a 2046 7261   clipping..* Fra\n-00011a30: 6d65 3a3a 2020 2020 2020 2020 2020 2020  me::            \n-00011a40: 2020 2020 2020 2020 2020 2041 6464 696e             Addin\n-00011a50: 6720 6120 626f 7820 6172 6f75 6e64 2074  g a box around t\n-00011a60: 6865 2064 7261 7769 6e67 2e0a 2a20 4c61  he drawing..* La\n-00011a70: 6e67 7561 6765 3a3a 2020 2020 2020 2020  nguage::        \n-00011a80: 2020 2020 2020 2020 2020 2020 5365 7474              Sett\n-00011a90: 696e 6720 7468 6520 6f75 7470 7574 206c  ing the output l\n-00011aa0: 616e 6775 6167 652e 0a0a 1f0a 4669 6c65  anguage.....File\n-00011ab0: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n-00011ac0: 4e6f 6465 3a20 476c 6f62 616c 206f 7074  Node: Global opt\n-00011ad0: 696f 6e73 2c20 204e 6578 743a 2043 616d  ions,  Next: Cam\n-00011ae0: 6572 612c 2020 5072 6576 3a20 476c 6f62  era,  Prev: Glob\n-00011af0: 616c 2065 6e76 6972 6f6e 6d65 6e74 2c20  al environment, \n-00011b00: 2055 703a 2047 6c6f 6261 6c20 656e 7669   Up: Global envi\n-00011b10: 726f 6e6d 656e 740a 0a33 2e34 2e31 2047  ronment..3.4.1 G\n-00011b20: 6c6f 6261 6c20 6f70 7469 6f6e 730a 2d2d  lobal options.--\n-00011b30: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-00011b40: 2d2d 0a0a 2a53 796e 7461 783a 2a0a 2020  --..*Syntax:*.  \n-00011b50: 2020 2073 6574 205b 204f 5054 494f 4e53     set [ OPTIONS\n-00011b60: 205d 0a54 6865 2063 6f6e 7465 6e74 7320   ].The contents \n-00011b70: 6f66 204f 5054 494f 4e53 2c20 6578 6365  of OPTIONS, exce\n-00011b80: 7074 2066 6f72 2027 736b 6574 6368 2720  pt for 'sketch' \n-00011b90: 696e 7465 726e 616c 206f 7074 696f 6e73  internal options\n-00011ba0: 2c20 6172 650a 636f 7069 6564 2061 732d  , are.copied as-\n-00011bb0: 6973 2074 6f20 6120 5c70 7373 6574 2074  is to a \\psset t\n-00011bc0: 6861 7420 6170 7065 6172 7320 6265 666f  hat appears befo\n-00011bd0: 7265 2061 6e79 7468 696e 6720 656c 7365  re anything else\n-00011be0: 2069 6e20 7468 6520 6f75 7470 7574 0a66   in the output.f\n-00011bf0: 696c 652e 2020 5468 6973 2069 7320 6120  ile.  This is a \n-00011c00: 676f 6f64 2070 6c61 6365 2074 6f20 7365  good place to se\n-00011c10: 7420 2775 6e69 7427 2c20 6120 6465 6661  t 'unit', a defa\n-00011c20: 756c 7420 276c 696e 6577 6964 7468 272c  ult 'linewidth',\n-00011c30: 2065 7463 2e0a 0a20 2020 496e 7465 726e   etc...   Intern\n-00011c40: 616c 206f 7074 696f 6e73 2077 6f72 6b20  al options work \n-00011c50: 6f6e 2061 6c6c 206f 626a 6563 7473 2077  on all objects w\n-00011c60: 6865 7265 2074 6865 7920 6d61 6b65 2073  here they make s\n-00011c70: 656e 7365 2e20 2054 6869 730a 696e 636c  ense.  This.incl\n-00011c80: 7564 6573 2027 6375 6c6c 2720 616e 6420  udes 'cull' and \n-00011c90: 2773 706c 6974 2720 2862 7574 206e 6f74  'split' (but not\n-00011ca0: 2027 6c61 7927 292e 2020 2a4e 6f74 6520   'lay').  *Note \n-00011cb0: 496e 7465 726e 616c 206f 7074 696f 6e73  Internal options\n-00011cc0: 3a3a 2e0a 0a1f 0a46 696c 653a 2073 6b65  ::.....File: ske\n-00011cd0: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n-00011ce0: 2043 616d 6572 612c 2020 4e65 7874 3a20   Camera,  Next: \n-00011cf0: 5069 6374 7572 6520 626f 782c 2020 5072  Picture box,  Pr\n-00011d00: 6576 3a20 476c 6f62 616c 206f 7074 696f  ev: Global optio\n-00011d10: 6e73 2c20 2055 703a 2047 6c6f 6261 6c20  ns,  Up: Global \n-00011d20: 656e 7669 726f 6e6d 656e 740a 0a33 2e34  environment..3.4\n-00011d30: 2e32 2043 616d 6572 610a 2d2d 2d2d 2d2d  .2 Camera.------\n-00011d40: 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 783a  ------..*Syntax:\n-00011d50: 2a0a 2020 2020 2063 616d 6572 6120 5452  *.     camera TR\n-00011d60: 414e 5346 4f52 4d5f 4558 5052 4553 5349  ANSFORM_EXPRESSI\n-00011d70: 4f4e 0a20 2020 5468 6520 5452 414e 5346  ON.   The TRANSF\n-00011d80: 4f52 4d5f 4558 5052 4553 5349 4f4e 2069  ORM_EXPRESSION i\n-00011d90: 7320 6170 706c 6965 6420 6166 7465 7220  s applied after \n-00011da0: 616c 6c20 6f74 6865 7220 7472 616e 7366  all other transf\n-00011db0: 6f72 6d61 7469 6f6e 730a 6f66 2074 6865  ormations.of the\n-00011dc0: 2073 6365 6e65 2e20 2054 6869 7320 6973   scene.  This is\n-00011dd0: 2063 7572 7265 6e74 6c79 206f 6e6c 7920   currently only \n-00011de0: 7573 6566 756c 2066 6f72 2074 7261 6e73  useful for trans\n-00011df0: 666f 726d 696e 6720 7468 650a 626f 756e  forming the.boun\n-00011e00: 6469 6e67 2062 6f78 2e20 202a 4e6f 7465  ding box.  *Note\n-00011e10: 2050 6963 7475 7265 2062 6f78 3a3a 2e20   Picture box::. \n-00011e20: 2049 7420 7769 6c6c 2070 6c61 7920 6120   It will play a \n-00011e30: 726f 6c65 2069 6e20 616e 7920 6675 7475  role in any futu\n-00011e40: 7265 0a69 6d70 6c65 6d65 6e74 6174 696f  re.implementatio\n-00011e50: 6e20 6f66 2063 6c69 7070 696e 672e 0a0a  n of clipping...\n-00011e60: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n-00011e70: 6e66 6f2c 2020 4e6f 6465 3a20 5069 6374  nfo,  Node: Pict\n-00011e80: 7572 6520 626f 782c 2020 4e65 7874 3a20  ure box,  Next: \n-00011e90: 4672 616d 652c 2020 5072 6576 3a20 4361  Frame,  Prev: Ca\n-00011ea0: 6d65 7261 2c20 2055 703a 2047 6c6f 6261  mera,  Up: Globa\n-00011eb0: 6c20 656e 7669 726f 6e6d 656e 740a 0a33  l environment..3\n-00011ec0: 2e34 2e33 2050 6963 7475 7265 2062 6f78  .4.3 Picture box\n-00011ed0: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  .---------------\n-00011ee0: 2d2d 0a0a 2a53 796e 7461 783a 2a0a 2020  --..*Syntax:*.  \n-00011ef0: 2020 2070 6963 7475 7265 626f 785b 4241     picturebox[BA\n-00011f00: 5345 4c49 4e45 5d0a 2020 2020 2070 6963  SELINE].     pic\n-00011f10: 7475 7265 626f 785b 4241 5345 4c49 4e45  turebox[BASELINE\n-00011f20: 5d20 2850 3129 2850 3229 0a54 6865 2066  ] (P1)(P2).The f\n-00011f30: 6972 7374 2066 6f72 6d20 6f66 2027 7069  irst form of 'pi\n-00011f40: 6374 7572 6562 6f78 2720 6361 7573 6573  cturebox' causes\n-00011f50: 2061 2073 6361 6c61 7220 4241 5345 4c49   a scalar BASELI\n-00011f60: 4e45 2066 7261 6374 696f 6e20 746f 2062  NE fraction to b\n-00011f70: 650a 656d 6974 7465 6420 696e 2074 6865  e.emitted in the\n-00011f80: 2027 7073 7069 6374 7572 6527 2065 6e76   'pspicture' env\n-00011f90: 6972 6f6e 6d65 6e74 206f 6620 7468 6520  ironment of the \n-00011fa0: 6f75 7470 7574 2e20 2053 6565 2027 5053  output.  See 'PS\n-00011fb0: 5472 6963 6b73 270a 646f 6375 6d65 6e74  Tricks'.document\n-00011fc0: 6174 696f 6e20 666f 7220 2770 7370 6963  ation for 'pspic\n-00011fd0: 7475 7265 272e 0a0a 2020 2049 6e20 7468  ture'...   In th\n-00011fe0: 6520 7365 636f 6e64 2066 6f72 6d2c 2074  e second form, t\n-00011ff0: 6865 2042 4153 454c 494e 4520 6672 6163  he BASELINE frac\n-00012000: 7469 6f6e 2069 7320 6f70 7469 6f6e 616c  tion is optional\n-00012010: 2c20 616e 6420 7468 6520 7477 6f0a 706f  , and the two.po\n-00012020: 696e 7473 2074 6861 7420 666f 6c6c 6f77  ints that follow\n-00012030: 2064 6566 696e 6520 7468 6520 6469 6167   define the diag\n-00012040: 6f6e 616c 206f 6620 6120 7468 7265 652d  onal of a three-\n-00012050: 6469 6d65 6e73 696f 6e61 6c20 626f 756e  dimensional boun\n-00012060: 6469 6e67 0a62 6f78 2066 6f72 2074 6865  ding.box for the\n-00012070: 2063 6f6d 706c 6574 6564 2073 6365 6e65   completed scene\n-00012080: 2e20 2054 6865 2070 6172 616c 6c65 6c20  .  The parallel \n-00012090: 7072 6f6a 6563 7469 6f6e 206f 6620 7468  projection of th\n-000120a0: 6520 626f 756e 6469 6e67 0a62 6f78 2064  e bounding.box d\n-000120b0: 6574 6572 6d69 6e65 7320 7468 6520 636f  etermines the co\n-000120c0: 726e 6572 7320 6f66 2074 6865 2064 7261  rners of the dra\n-000120d0: 7769 6e67 2773 2027 7073 7069 6374 7572  wing's 'pspictur\n-000120e0: 652a 2720 656e 7669 726f 6e6d 656e 742c  e*' environment,\n-000120f0: 0a77 6869 6368 2069 7320 7573 6564 2069  .which is used i\n-00012100: 6e20 706c 6163 6520 6f66 2027 7073 7069  n place of 'pspi\n-00012110: 6374 7572 6527 2e20 2054 6869 7320 6361  cture'.  This ca\n-00012120: 7573 6573 2050 6f73 7453 6372 6970 7420  uses PostScript \n-00012130: 746f 2063 6c69 700a 7468 6520 6669 6e61  to clip.the fina\n-00012140: 6c20 6472 6177 696e 6720 746f 2074 6865  l drawing to the\n-00012150: 2062 6f75 6e64 696e 6720 626f 7820 696e   bounding box in\n-00012160: 2032 642e 2020 4966 2074 6865 7265 2069   2d.  If there i\n-00012170: 7320 6120 2763 616d 6572 6127 0a73 7065  s a 'camera'.spe\n-00012180: 6369 6669 6564 2c20 7468 6520 6361 6d65  cified, the came\n-00012190: 7261 2074 7261 6e66 6f72 6d61 7469 6f6e  ra tranformation\n-000121a0: 2069 7320 6170 706c 6965 6420 746f 2074   is applied to t\n-000121b0: 6865 2062 6f75 6e64 696e 6720 626f 782c  he bounding box,\n-000121c0: 2061 6e64 0a74 6865 2027 7073 7069 6374   and.the 'pspict\n-000121d0: 7572 6527 2069 7320 7365 7420 6a75 7374  ure' is set just\n-000121e0: 206c 6172 6765 2065 6e6f 7567 6820 746f   large enough to\n-000121f0: 2069 6e63 6c75 6465 2074 6865 2074 7261   include the tra\n-00012200: 6e73 666f 726d 6564 2062 6f78 2e0a 0a20  nsformed box... \n-00012210: 2020 5768 656e 206e 6f20 626f 756e 6469    When no boundi\n-00012220: 6e67 2062 6f78 2069 7320 6769 7665 6e2c  ng box is given,\n-00012230: 2027 736b 6574 6368 2720 636f 6d70 7574   'sketch' comput\n-00012240: 6573 206f 6e65 2061 7574 6f6d 6174 6963  es one automatic\n-00012250: 616c 6c79 2e0a 0a1f 0a46 696c 653a 2073  ally.....File: s\n-00012260: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n-00012270: 653a 2046 7261 6d65 2c20 204e 6578 743a  e: Frame,  Next:\n-00012280: 204c 616e 6775 6167 652c 2020 5072 6576   Language,  Prev\n-00012290: 3a20 5069 6374 7572 6520 626f 782c 2020  : Picture box,  \n-000122a0: 5570 3a20 476c 6f62 616c 2065 6e76 6972  Up: Global envir\n-000122b0: 6f6e 6d65 6e74 0a0a 332e 342e 3420 4672  onment..3.4.4 Fr\n-000122c0: 616d 650a 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a  ame.-----------.\n-000122d0: 0a2a 5379 6e74 6178 3a2a 0a20 2020 2020  .*Syntax:*.     \n-000122e0: 6672 616d 6520 5b4f 5054 494f 4e53 5d0a  frame [OPTIONS].\n-000122f0: 4361 7573 6573 2061 205c 7073 6672 616d  Causes a \\psfram\n-00012300: 6562 6f78 2074 6f20 7375 7272 6f75 6e64  ebox to surround\n-00012310: 2074 6865 2027 7073 7069 6374 7572 6527   the 'pspicture'\n-00012320: 2065 6e76 6972 6f6e 6d65 6e74 2069 6e20   environment in \n-00012330: 7468 650a 6f75 7470 7574 2e20 2049 6620  the.output.  If \n-00012340: 4f50 5449 4f4e 5320 6172 6520 7072 6573  OPTIONS are pres\n-00012350: 656e 742c 2074 6865 7920 6172 6520 636f  ent, they are co\n-00012360: 7069 6564 2061 732d 6973 2e20 204e 6f72  pied as-is.  Nor\n-00012370: 6d61 6c6c 7920 6f6e 650a 776f 756c 6420  mally one.would \n-00012380: 7761 6e74 2074 6f20 7365 7420 276c 696e  want to set 'lin\n-00012390: 6577 6964 7468 272c 2027 6c69 6e65 7374  ewidth', 'linest\n-000123a0: 796c 6527 2c20 276c 696e 6563 6f6c 6f72  yle', 'linecolor\n-000123b0: 272c 2065 7463 2e20 2049 660a 6f6d 6974  ', etc.  If.omit\n-000123c0: 7465 642c 2074 6865 6e20 2766 7261 6d65  ted, then 'frame\n-000123d0: 7365 703d 3070 7427 2069 7320 6164 6465  sep=0pt' is adde\n-000123e0: 6420 736f 2074 6861 7420 7468 6520 6672  d so that the fr\n-000123f0: 616d 6520 7469 6768 746c 7920 6875 6773  ame tightly hugs\n-00012400: 2074 6865 0a27 7073 7069 6374 7572 6527   the.'pspicture'\n-00012410: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463  .....File: sketc\n-00012420: 682e 696e 666f 2c20 204e 6f64 653a 204c  h.info,  Node: L\n-00012430: 616e 6775 6167 652c 2020 5072 6576 3a20  anguage,  Prev: \n-00012440: 4672 616d 652c 2020 5570 3a20 476c 6f62  Frame,  Up: Glob\n-00012450: 616c 2065 6e76 6972 6f6e 6d65 6e74 0a0a  al environment..\n-00012460: 332e 342e 3520 4c61 6e67 7561 6765 0a2d  3.4.5 Language.-\n-00012470: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a20  -------------.. \n-00012480: 2020 2020 6c61 6e67 7561 6765 2074 696b      language tik\n-00012490: 7a0a 2020 2020 206c 616e 6775 6167 6520  z.     language \n-000124a0: 7469 6b7a 2c20 636f 6e74 6578 740a 2020  tikz, context.  \n-000124b0: 2020 206c 616e 6775 6167 6520 7073 7472     language pstr\n-000124c0: 6963 6b73 0a20 2020 2020 6c61 6e67 7561  icks.     langua\n-000124d0: 6765 2070 7374 7269 636b 732c 206c 6174  ge pstricks, lat\n-000124e0: 6578 0a53 6574 7320 7468 6520 6f75 7470  ex.Sets the outp\n-000124f0: 7574 206c 616e 6775 6167 6520 6765 6e65  ut language gene\n-00012500: 7261 7465 6420 6279 2027 736b 6574 6368  rated by 'sketch\n-00012510: 272e 2020 5468 6520 7365 7420 6f66 206f  '.  The set of o\n-00012520: 7074 696f 6e73 0a75 6e64 6572 7374 6f6f  ptions.understoo\n-00012530: 6420 6279 2073 6b65 7463 6820 616c 736f  d by sketch also\n-00012540: 2063 6861 6e67 6573 2e20 2046 6f72 2065   changes.  For e\n-00012550: 7861 6d70 6c65 2c20 7468 6520 2750 5354  xample, the 'PST\n-00012560: 7269 636b 7327 206f 7074 696f 6e0a 276c  ricks' option.'l\n-00012570: 696e 6577 6964 7468 2720 7769 6c6c 206e  inewidth' will n\n-00012580: 6f74 2062 6520 7072 6f70 6572 6c79 2068  ot be properly h\n-00012590: 616e 646c 6564 2069 6620 276c 616e 6775  andled if 'langu\n-000125a0: 6167 6527 2069 7320 7365 7420 746f 2027  age' is set to '\n-000125b0: 7469 6b7a 272e 0a53 696d 696c 6172 6c79  tikz'..Similarly\n-000125c0: 2c20 7468 6520 2754 696b 5a27 206f 7074  , the 'TikZ' opt\n-000125d0: 696f 6e20 276c 696e 6520 7374 796c 6527  ion 'line style'\n-000125e0: 2028 6e6f 7465 2074 6865 2073 7061 6365   (note the space\n-000125f0: 2920 7769 6c6c 206e 6f74 2062 650a 7072  ) will not be.pr\n-00012600: 6f70 6572 6c79 2068 616e 646c 6564 2069  operly handled i\n-00012610: 6620 276c 616e 6775 6167 6527 2069 7320  f 'language' is \n-00012620: 7365 7420 746f 2027 7073 7472 6963 6b73  set to 'pstricks\n-00012630: 272e 2020 4966 206e 6f20 6c61 6e67 7561  '.  If no langua\n-00012640: 6765 2069 730a 7370 6563 6966 6965 642c  ge is.specified,\n-00012650: 2074 6865 2064 6566 6175 6c74 2027 7073   the default 'ps\n-00012660: 7472 6963 6b73 2720 6973 2075 7365 642e  tricks' is used.\n-00012670: 0a0a 2020 2041 6e20 6f70 7469 6f6e 616c  ..   An optional\n-00012680: 2063 6f6d 6d61 2066 6f6c 6c6f 7765 6420   comma followed \n-00012690: 6279 2027 6c61 7465 7827 206f 7220 2763  by 'latex' or 'c\n-000126a0: 6f6e 7465 7874 2720 7370 6563 6966 6965  ontext' specifie\n-000126b0: 7320 7468 650a 6d61 6372 6f20 7061 636b  s the.macro pack\n-000126c0: 6167 6520 7468 6174 2074 6865 206f 7574  age that the out\n-000126d0: 7075 7420 7368 6f75 6c64 2061 7373 756d  put should assum\n-000126e0: 652e 2020 5468 6973 2061 6666 6563 7473  e.  This affects\n-000126f0: 2074 6865 2027 7069 6374 7572 6527 0a65   the 'picture'.e\n-00012700: 6e76 6972 6f6e 6d65 6e74 2063 6f6d 6d61  nvironment comma\n-00012710: 6e64 7320 656d 6974 7465 6420 616e 6420  nds emitted and \n-00012720: 7468 6520 646f 6375 6d65 6e74 2074 656d  the document tem\n-00012730: 706c 6174 6520 7573 6564 2077 6974 6820  plate used with \n-00012740: 7468 650a 272d 5427 206f 7074 696f 6e2e  the.'-T' option.\n-00012750: 2020 2a4e 6f74 6520 436f 6d6d 616e 6420    *Note Command \n-00012760: 6c69 6e65 3a3a 2e20 204e 6f74 6520 7468  line::.  Note th\n-00012770: 6174 2061 7420 7468 6520 7469 6d65 2074  at at the time t\n-00012780: 6869 7320 6d61 6e75 616c 0a77 6173 2067  his manual.was g\n-00012790: 656e 6572 6174 6564 2c20 2750 5354 7269  enerated, 'PSTri\n-000127a0: 636b 7327 2077 6173 206e 6f74 2073 7570  cks' was not sup\n-000127b0: 706f 7274 6564 2062 7920 4c61 5465 5820  ported by LaTeX \n-000127c0: 6f72 2062 7920 2743 6f6e 5465 5874 272e  or by 'ConTeXt'.\n-000127d0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n-000127e0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4275  .info,  Node: Bu\n-000127f0: 696c 6469 6e67 2061 2064 7261 7769 6e67  ilding a drawing\n-00012800: 2c20 204e 6578 743a 2043 6f6d 6d61 6e64  ,  Next: Command\n-00012810: 206c 696e 652c 2020 5072 6576 3a20 496e   line,  Prev: In\n-00012820: 7075 7420 6c61 6e67 7561 6765 2c20 2055  put language,  U\n-00012830: 703a 2054 6f70 0a0a 3420 4275 696c 6469  p: Top..4 Buildi\n-00012840: 6e67 2061 2064 7261 7769 6e67 0a2a 2a2a  ng a drawing.***\n-00012850: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  ****************\n-00012860: 2a0a 0a53 7563 6365 7373 6675 6c20 6472  *..Successful dr\n-00012870: 6177 696e 6773 2077 6974 6820 2773 6b65  awings with 'ske\n-00012880: 7463 6827 2061 6e64 2077 6974 6820 616e  tch' and with an\n-00012890: 7920 7363 656e 6520 6465 7363 7269 7074  y scene descript\n-000128a0: 696f 6e0a 6c61 6e67 7561 6765 2072 6571  ion.language req\n-000128b0: 7569 7265 2074 6861 7420 7468 6520 7573  uire that the us\n-000128c0: 6572 2064 6576 656c 6f70 2061 6e20 6163  er develop an ac\n-000128d0: 6375 7261 7465 206d 656e 7461 6c20 7069  curate mental pi\n-000128e0: 6374 7572 6520 6f66 2068 6572 0a63 6f64  cture of her.cod\n-000128f0: 6520 616e 6420 6974 7320 6d65 616e 696e  e and its meanin\n-00012900: 672e 2020 5468 6973 2069 6d61 6765 2069  g.  This image i\n-00012910: 7320 6265 7374 2062 7569 6c74 2069 6e20  s best built in \n-00012920: 736d 616c 6c20 7069 6563 6573 2e0a 5468  small pieces..Th\n-00012930: 6572 6566 6f72 652c 2027 736b 6574 6368  erefore, 'sketch\n-00012940: 2720 696e 7075 7473 2061 7265 2062 6573  ' inputs are bes\n-00012950: 7420 6372 6561 7465 6420 696e 2073 6d61  t created in sma\n-00012960: 6c6c 2069 6e63 7265 6d65 6e74 7320 7769  ll increments wi\n-00012970: 7468 0a66 7265 7175 656e 7420 7061 7573  th.frequent paus\n-00012980: 6573 2074 6f20 636f 6d70 696c 6520 616e  es to compile an\n-00012990: 6420 7669 6577 2074 6865 2072 6573 756c  d view the resul\n-000129a0: 7473 2e20 2043 6172 6566 756c 2063 6f6d  ts.  Careful com\n-000129b0: 6d65 6e74 7320 696e 0a74 6865 2069 6e70  ments in.the inp\n-000129c0: 7574 206f 6674 656e 2068 656c 7020 6173  ut often help as\n-000129d0: 2061 2073 6365 6e65 2067 726f 7773 2069   a scene grows i\n-000129e0: 6e20 636f 6d70 6c65 7869 7479 2e0a 0a2a  n complexity...*\n-000129f0: 204d 656e 753a 0a0a 2a20 4f76 6572 7669   Menu:..* Overvi\n-00012a00: 6577 3a3a 2020 2020 2020 2020 2020 2020  ew::            \n-00012a10: 2020 2020 2020 2020 4275 696c 6469 6e67          Building\n-00012a20: 2061 2073 7562 7374 616e 7469 616c 2064   a substantial d\n-00012a30: 7261 7769 6e67 2e0a 2a20 4120 7465 6368  rawing..* A tech\n-00012a40: 6e69 6361 6c20 6472 6177 696e 673a 3a20  nical drawing:: \n-00012a50: 2020 2020 2020 2020 416e 2065 7861 6d70          An examp\n-00012a60: 6c65 2077 6974 6820 6669 6e65 2070 6c61  le with fine pla\n-00012a70: 6365 6d65 6e74 2e0a 2a20 4120 6869 6572  cement..* A hier\n-00012a80: 6172 6368 6963 616c 206d 6f64 656c 3a3a  archical model::\n-00012a90: 2020 2020 2020 2020 416e 2065 7861 6d70          An examp\n-00012aa0: 6c65 2077 6974 6820 7377 6565 7073 2061  le with sweeps a\n-00012ab0: 6e64 2070 7574 732e 0a2a 2043 6176 6561  nd puts..* Cavea\n-00012ac0: 7473 3a3a 2020 2020 2020 2020 2020 2020  ts::            \n-00012ad0: 2020 2020 2020 2020 2057 6865 7265 2074           Where t\n-00012ae0: 726f 7562 6c65 2063 616e 206f 6363 7572  rouble can occur\n-00012af0: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463  .....File: sketc\n-00012b00: 682e 696e 666f 2c20 204e 6f64 653a 204f  h.info,  Node: O\n-00012b10: 7665 7276 6965 772c 2020 4e65 7874 3a20  verview,  Next: \n-00012b20: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n-00012b30: 696e 672c 2020 5072 6576 3a20 4275 696c  ing,  Prev: Buil\n-00012b40: 6469 6e67 2061 2064 7261 7769 6e67 2c20  ding a drawing, \n-00012b50: 2055 703a 2042 7569 6c64 696e 6720 6120   Up: Building a \n-00012b60: 6472 6177 696e 670a 0a34 2e31 204f 7665  drawing..4.1 Ove\n-00012b70: 7276 6965 770a 3d3d 3d3d 3d3d 3d3d 3d3d  rview.==========\n-00012b80: 3d3d 0a0a 4173 2061 6e20 6f76 6572 7669  ==..As an overvi\n-00012b90: 6577 2c20 6c65 7427 7320 6465 7665 6c6f  ew, let's develo\n-00012ba0: 7020 6120 6469 6167 7261 6d20 7468 6174  p a diagram that\n-00012bb0: 2073 686f 7773 2068 6f77 2061 2070 6572   shows how a per\n-00012bc0: 7370 6563 7469 7665 0a70 726f 6a65 6374  spective.project\n-00012bd0: 696f 6e20 7472 616e 7366 6f72 6d20 776f  ion transform wo\n-00012be0: 726b 732e 2020 5765 276c 6c20 7374 6172  rks.  We'll star\n-00012bf0: 7420 7769 7468 2074 6865 2074 7261 6469  t with the tradi\n-00012c00: 7469 6f6e 616c 2072 6566 6572 656e 6365  tional reference\n-00012c10: 0a6f 626a 6563 7420 7573 6564 2069 6e20  .object used in \n-00012c20: 636f 6d70 7574 6572 2067 7261 7068 6963  computer graphic\n-00012c30: 7320 7465 7874 626f 6f6b 732c 2061 2068  s textbooks, a h\n-00012c40: 6f75 7365 2d73 6861 7065 6420 7072 6973  ouse-shaped pris\n-00012c50: 6d2e 2020 4265 6769 6e0a 6279 2064 6566  m.  Begin.by def\n-00012c60: 696e 696e 6720 7468 6520 706f 696e 7473  ining the points\n-00012c70: 206f 6620 7468 6520 686f 7573 652e 2020   of the house.  \n-00012c80: 5261 7468 6572 2074 6861 6e20 6465 6669  Rather than defi\n-00012c90: 6e69 6e67 2074 6865 2066 6163 6573 206f  ning the faces o\n-00012ca0: 660a 7468 6520 686f 7573 6520 6173 2070  f.the house as p\n-00012cb0: 6f6c 7967 6f6e 7320 616e 6420 7472 616e  olygons and tran\n-00012cc0: 7366 6f72 6d69 6e67 2074 686f 7365 2c20  sforming those, \n-00012cd0: 7765 2061 7265 2067 6f69 6e67 2074 6f20  we are going to \n-00012ce0: 7472 616e 7366 6f72 6d0a 7468 6520 706f  transform.the po\n-00012cf0: 696e 7473 2074 6865 6d73 656c 7665 7320  ints themselves \n-00012d00: 7769 7468 2027 736b 6574 6368 2720 6172  with 'sketch' ar\n-00012d10: 6974 686d 6574 6963 2073 6f20 7468 6174  ithmetic so that\n-00012d20: 2077 6520 6861 7665 206e 616d 6573 2066   we have names f\n-00012d30: 6f72 0a74 6865 2074 7261 6e73 666f 726d  or.the transform\n-00012d40: 6564 2070 6f69 6e74 7320 6c61 7465 722e  ed points later.\n-00012d50: 0a20 2025 2072 6967 6874 2073 6964 6520  .  % right side \n-00012d60: 286f 7574 7369 6465 2074 6f20 7269 6768  (outside to righ\n-00012d70: 7429 0a20 2064 6566 2052 3120 2831 2c31  t).  def R1 (1,1\n-00012d80: 2c31 2920 6465 6620 5232 2028 312c 2d31  ,1) def R2 (1,-1\n-00012d90: 2c31 2920 6465 6620 5233 2028 312c 2d31  ,1) def R3 (1,-1\n-00012da0: 2c2d 3129 2064 6566 2052 3420 2831 2c31  ,-1) def R4 (1,1\n-00012db0: 2c2d 3129 0a20 2064 6566 2052 3520 2831  ,-1).  def R5 (1\n-00012dc0: 2c31 2e35 2c30 290a 0a20 2025 206c 6566  ,1.5,0)..  % lef\n-00012dd0: 7420 7369 6465 2028 6f75 7473 6964 6520  t side (outside \n-00012de0: 746f 2072 6967 6874 2d2d 6261 636b 7761  to right--backwa\n-00012df0: 7264 290a 2020 6465 6620 5720 205b 322c  rd).  def W  [2,\n-00012e00: 302c 305d 0a20 2064 6566 204c 3120 2852  0,0].  def L1 (R\n-00012e10: 3129 2d5b 575d 2064 6566 204c 3220 2852  1)-[W] def L2 (R\n-00012e20: 3229 2d5b 575d 2064 6566 204c 3320 2852  2)-[W] def L3 (R\n-00012e30: 3329 2d5b 575d 2064 6566 204c 3420 2852  3)-[W] def L4 (R\n-00012e40: 3429 2d5b 575d 0a20 2064 6566 204c 3520  4)-[W].  def L5 \n-00012e50: 2852 3529 2d5b 575d 0a54 6f20 6164 6420  (R5)-[W].To add \n-00012e60: 6120 646f 6f72 2074 6f20 7468 6520 686f  a door to the ho\n-00012e70: 7573 652c 2077 6520 7573 6520 6120 706f  use, we use a po\n-00012e80: 6c79 676f 6e20 736c 6967 6874 6c79 2069  lygon slightly i\n-00012e90: 6e20 6672 6f6e 7420 6f66 2074 6865 0a66  n front of the.f\n-00012ea0: 6f72 656d 6f73 7420 6661 6365 206f 6620  oremost face of \n-00012eb0: 7468 6520 686f 7573 652e 0a20 2025 2064  the house..  % d\n-00012ec0: 6f6f 720a 2020 6465 6620 6520 2e30 310a  oor.  def e .01.\n-00012ed0: 2020 6465 6620 4431 2028 302c 2d31 2c31    def D1 (0,-1,1\n-00012ee0: 2b65 2920 6465 6620 4432 2028 2e35 2c2d  +e) def D2 (.5,-\n-00012ef0: 312c 312b 6529 2064 6566 2044 3320 282e  1,1+e) def D3 (.\n-00012f00: 352c 302c 312b 6529 2064 6566 2044 3420  5,0,1+e) def D4 \n-00012f10: 2830 2c30 2c31 2b65 290a 4e6f 7720 6c65  (0,0,1+e).Now le\n-00012f20: 7427 7320 6372 6561 7465 2061 206e 6577  t's create a new\n-00012f30: 2073 6574 206f 6620 706f 696e 7473 2074   set of points t\n-00012f40: 6861 7420 6172 6520 6120 746f 2d62 652d  hat are a to-be-\n-00012f50: 6465 7465 726d 696e 6564 0a74 7261 6e73  determined.trans\n-00012f60: 666f 726d 206f 6620 7468 6520 6f72 6967  form of the orig\n-00012f70: 696e 616c 732e 0a20 2064 6566 2068 7020  inals..  def hp \n-00012f80: 7363 616c 6528 3129 2025 2068 6f75 7365  scale(1) % house\n-00012f90: 2070 6f73 6974 696f 6e65 720a 2020 6465   positioner.  de\n-00012fa0: 6620 7052 3120 5b5b 6870 5d5d 2a28 5231  f pR1 [[hp]]*(R1\n-00012fb0: 2920 6465 6620 7052 3220 5b5b 6870 5d5d  ) def pR2 [[hp]]\n-00012fc0: 2a28 5232 2920 6465 6620 7052 3320 5b5b  *(R2) def pR3 [[\n-00012fd0: 6870 5d5d 2a28 5233 290a 2020 6465 6620  hp]]*(R3).  def \n-00012fe0: 7052 3420 5b5b 6870 5d5d 2a28 5234 2920  pR4 [[hp]]*(R4) \n-00012ff0: 6465 6620 7052 3520 5b5b 6870 5d5d 2a28  def pR5 [[hp]]*(\n-00013000: 5235 290a 2020 6465 6620 704c 3120 5b5b  R5).  def pL1 [[\n-00013010: 6870 5d5d 2a28 4c31 2920 6465 6620 704c  hp]]*(L1) def pL\n-00013020: 3220 5b5b 6870 5d5d 2a28 4c32 2920 6465  2 [[hp]]*(L2) de\n-00013030: 6620 704c 3320 5b5b 6870 5d5d 2a28 4c33  f pL3 [[hp]]*(L3\n-00013040: 290a 2020 6465 6620 704c 3420 5b5b 6870  ).  def pL4 [[hp\n-00013050: 5d5d 2a28 4c34 2920 6465 6620 704c 3520  ]]*(L4) def pL5 \n-00013060: 5b5b 6870 5d5d 2a28 4c35 290a 2020 6465  [[hp]]*(L5).  de\n-00013070: 6620 7044 3120 5b5b 6870 5d5d 2a28 4431  f pD1 [[hp]]*(D1\n-00013080: 2920 6465 6620 7044 3220 5b5b 6870 5d5d  ) def pD2 [[hp]]\n-00013090: 2a28 4432 2920 6465 6620 7044 3320 5b5b  *(D2) def pD3 [[\n-000130a0: 6870 5d5d 2a28 4433 290a 2020 6465 6620  hp]]*(D3).  def \n-000130b0: 7044 3420 5b5b 6870 5d5d 2a28 4434 2920  pD4 [[hp]]*(D4) \n-000130c0: 0a4e 6f74 6520 7468 6520 7573 6520 6f66  .Note the use of\n-000130d0: 2061 2022 7472 616e 7366 6f72 6d20 6465   a \"transform de\n-000130e0: 6669 6e69 7469 6f6e 2220 616e 6420 2274  finition\" and \"t\n-000130f0: 7261 6e73 666f 726d 2072 6566 6572 656e  ransform referen\n-00013100: 6365 7322 2e0a 4e6f 7720 6465 6669 6e65  ces\"..Now define\n-00013110: 2074 6865 2073 6576 656e 2070 6f6c 7967   the seven polyg\n-00013120: 6f6e 616c 2066 6163 6573 206f 6620 7468  onal faces of th\n-00013130: 6520 686f 7573 6520 616e 6420 7468 6520  e house and the \n-00013140: 646f 6f72 2075 7369 6e67 2074 6865 0a74  door using the.t\n-00013150: 7261 6e73 666f 726d 6564 2070 6f69 6e74  ransformed point\n-00013160: 7320 6173 2076 6572 7469 6365 732e 2020  s as vertices.  \n-00013170: 4265 2063 6172 6566 756c 2077 6974 6820  Be careful with \n-00013180: 7665 7274 6578 206f 7264 6572 210a 2020  vertex order!.  \n-00013190: 6465 6620 7267 7420 706f 6c79 676f 6e20  def rgt polygon \n-000131a0: 2870 5231 2928 7052 3229 2870 5233 2928  (pR1)(pR2)(pR3)(\n-000131b0: 7052 3429 2870 5235 290a 2020 6465 6620  pR4)(pR5).  def \n-000131c0: 6c66 7420 706f 6c79 676f 6e20 2870 4c35  lft polygon (pL5\n-000131d0: 2928 704c 3429 2870 4c33 2928 704c 3229  )(pL4)(pL3)(pL2)\n-000131e0: 2870 4c31 290a 2020 6465 6620 6672 7420  (pL1).  def frt \n-000131f0: 706f 6c79 676f 6e20 2870 5232 2928 7052  polygon (pR2)(pR\n-00013200: 3129 2870 4c31 2928 704c 3229 0a20 2064  1)(pL1)(pL2).  d\n-00013210: 6566 2062 636b 2070 6f6c 7967 6f6e 2028  ef bck polygon (\n-00013220: 7052 3429 2870 5233 2928 704c 3329 2870  pR4)(pR3)(pL3)(p\n-00013230: 4c34 290a 2020 6465 6620 7466 7220 706f  L4).  def tfr po\n-00013240: 6c79 676f 6e20 2870 5231 2928 7052 3529  lygon (pR1)(pR5)\n-00013250: 2870 4c35 2928 704c 3129 0a20 2064 6566  (pL5)(pL1).  def\n-00013260: 2074 626b 2070 6f6c 7967 6f6e 2028 7052   tbk polygon (pR\n-00013270: 3529 2870 5234 2928 704c 3429 2870 4c35  5)(pR4)(pL4)(pL5\n-00013280: 290a 2020 6465 6620 626f 7420 706f 6c79  ).  def bot poly\n-00013290: 676f 6e20 2870 5232 2928 704c 3229 2870  gon (pR2)(pL2)(p\n-000132a0: 4c33 2928 7052 3329 0a20 2064 6566 2064  L3)(pR3).  def d\n-000132b0: 6f6f 7220 706f 6c79 676f 6e5b 6669 6c6c  oor polygon[fill\n-000132c0: 636f 6c6f 723d 6272 6f77 6e5d 2028 7044  color=brown] (pD\n-000132d0: 3129 2870 4432 2928 7044 3329 2870 4434  1)(pD2)(pD3)(pD4\n-000132e0: 290a 2020 6465 6620 686f 7573 6520 7b20  ).  def house { \n-000132f0: 7b72 6774 7d7b 6c66 747d 7b66 7274 7d7b  {rgt}{lft}{frt}{\n-00013300: 6263 6b7d 7b74 6672 7d7b 7462 6b7d 7b62  bck}{tfr}{tbk}{b\n-00013310: 6f74 7d7b 646f 6f72 7d20 7d0a 2020 2054  ot}{door} }.   T\n-00013320: 696d 6520 666f 7220 6120 7361 6e69 7479  ime for a sanity\n-00013330: 2063 6865 636b 2e20 2041 6464 2074 6865   check.  Add the\n-00013340: 206c 696e 650a 2020 7b68 6f75 7365 7d0a   line.  {house}.\n-00013350: 616e 6420 7468 6973 2069 7320 7768 6174  and this is what\n-00013360: 2077 6520 6765 742e 0a0a 0008 5b69 6d61   we get.....[ima\n-00013370: 6765 2073 7263 3d22 6578 3133 302e 706e  ge src=\"ex130.pn\n-00013380: 6722 2074 6578 743d 2249 6d61 6765 2065  g\" text=\"Image e\n-00013390: 7831 3330 206f 6d69 7474 6564 2069 6e20  x130 omitted in \n-000133a0: 7465 7874 2076 6572 7369 6f6e 206f 6620  text version of \n-000133b0: 7468 6973 2064 6f63 756d 656e 742e 2200  this document.\".\n-000133c0: 085d 0a0a 5468 6973 2069 7320 636f 7272  .]..This is corr\n-000133d0: 6563 742c 2062 7574 2064 6f65 7320 6e6f  ect, but does no\n-000133e0: 7420 7265 7665 616c 2076 6572 7920 6d75  t reveal very mu\n-000133f0: 6368 2e20 2043 6f6d 6d6f 6e20 6572 726f  ch.  Common erro\n-00013400: 7273 2061 7265 0a6d 6973 706c 6163 6564  rs are.misplaced\n-00013410: 2076 6572 7469 6365 7320 616e 6420 706f   vertices and po\n-00013420: 6c79 676f 6e73 206d 6973 7369 6e67 2065  lygons missing e\n-00013430: 6e74 6972 656c 7920 6475 6520 746f 2069  ntirely due to i\n-00013440: 6e63 6f72 7265 6374 2076 6572 7465 780a  ncorrect vertex.\n-00013450: 6f72 6465 722e 2020 546f 2072 756c 6520  order.  To rule \n-00013460: 7468 6573 6520 6f75 742c 206c 6574 2773  these out, let's\n-00013470: 2069 6e73 7065 6374 2061 6c6c 2073 6964   inspect all sid\n-00013480: 6573 206f 6620 7468 6520 686f 7573 652e  es of the house.\n-00013490: 2020 5468 6973 0a69 7320 6e6f 7420 6861    This.is not ha\n-000134a0: 7264 2e20 204d 6572 656c 7920 7265 706c  rd.  Merely repl\n-000134b0: 6163 6520 7468 6520 7265 6665 7265 6e63  ace the referenc\n-000134c0: 6520 7b68 6f75 7365 7d20 7769 7468 2061  e {house} with a\n-000134d0: 2027 7265 7065 6174 272e 0a2a 4e6f 7465   'repeat'..*Note\n-000134e0: 2052 6570 6561 7473 3a3a 2e0a 2020 7265   Repeats::..  re\n-000134f0: 7065 6174 207b 2031 332c 2072 6f74 6174  peat { 13, rotat\n-00013500: 6528 3330 2c20 5b31 2c32 2c33 5d29 2c20  e(30, [1,2,3]), \n-00013510: 7472 616e 736c 6174 6528 5b33 2c30 2c30  translate([3,0,0\n-00013520: 5d29 207d 207b 686f 7573 657d 0a00 085b  ]) } {house}...[\n-00013530: 696d 6167 6520 7372 633d 2265 7831 3430  image src=\"ex140\n-00013540: 2e70 6e67 2220 7465 7874 3d22 496d 6167  .png\" text=\"Imag\n-00013550: 6520 6578 3134 3020 6f6d 6974 7465 6420  e ex140 omitted \n-00013560: 696e 2074 6578 7420 7665 7273 696f 6e20  in text version \n-00013570: 6f66 2074 6869 7320 646f 6375 6d65 6e74  of this document\n-00013580: 2e22 0008 5d0a 0a41 6761 696e 2074 6869  .\"..]..Again thi\n-00013590: 6e67 7320 6c6f 6f6b 2063 6f72 7265 6374  ngs look correct\n-000135a0: 2e20 204e 6f74 6520 7468 6174 2074 6865  .  Note that the\n-000135b0: 2068 6964 6465 6e20 7375 7266 6163 6520   hidden surface \n-000135c0: 616c 676f 7269 7468 6d0a 6861 6e64 6c65  algorithm.handle\n-000135d0: 7320 696e 7465 7273 6563 7469 6e67 2070  s intersecting p\n-000135e0: 6f6c 7967 6f6e 7320 636f 7272 6563 746c  olygons correctl\n-000135f0: 7920 7768 6572 6520 736f 6d65 2063 6f70  y where some cop\n-00013600: 6965 7320 6f66 2074 6865 2068 6f75 7365  ies of the house\n-00013610: 0a6f 7665 726c 6170 2e0a 0a20 2020 4c65  .overlap...   Le\n-00013620: 7427 7320 6c61 7920 6f75 7420 7468 6520  t's lay out the \n-00013630: 6765 6f6d 6574 7279 206f 6620 7065 7273  geometry of pers\n-00013640: 7065 6374 6976 6520 7072 6f6a 6563 7469  pective projecti\n-00013650: 6f6e 206f 6620 7468 6520 686f 7573 650a  on of the house.\n-00013660: 6f6e 746f 2061 2070 6c61 6e65 2077 6974  onto a plane wit\n-00013670: 6820 7261 7973 2070 6173 7369 6e67 2074  h rays passing t\n-00013680: 6872 6f75 6768 2074 6865 206f 7269 6769  hrough the origi\n-00013690: 6e2e 2020 4265 6769 6e20 6279 2070 6f73  n.  Begin by pos\n-000136a0: 6974 696f 6e69 6e67 0a74 6865 2068 6f75  itioning.the hou\n-000136b0: 7365 2074 7765 6c76 6520 756e 6974 7320  se twelve units \n-000136c0: 6261 636b 206f 6e20 7468 6520 6e65 6761  back on the nega\n-000136d0: 7469 7665 207a 2d61 7869 7320 616e 6420  tive z-axis and \n-000136e0: 6164 6469 6e67 2061 2073 6574 206f 660a  adding a set of.\n-000136f0: 636f 6f72 6469 6e61 7465 2061 7865 732e  coordinate axes.\n-00013700: 2020 546f 206d 6f76 6520 7468 6520 686f    To move the ho\n-00013710: 7573 6520 7765 206e 6565 6420 6f6e 6c79  use we need only\n-00013720: 2063 6861 6e67 6520 7468 6520 2268 6f75   change the \"hou\n-00013730: 7365 0a70 6f73 6974 696f 6e69 6e67 2220  se.positioning\" \n-00013740: 7472 616e 7366 6f72 6d20 6465 6669 6e65  transform define\n-00013750: 6420 6561 726c 6965 722e 0a20 2064 6566  d earlier..  def\n-00013760: 2068 7020 726f 7461 7465 282d 3430 2c20   hp rotate(-40, \n-00013770: 5b30 2c31 2c30 5d29 2074 6865 6e20 7472  [0,1,0]) then tr\n-00013780: 616e 736c 6174 6528 5b30 2c30 2c2d 3132  anslate([0,0,-12\n-00013790: 5d29 0a20 2064 6566 2061 7865 7320 7b0a  ]).  def axes {.\n-000137a0: 2020 2020 6465 6620 737a 2031 0a20 2020      def sz 1.   \n-000137b0: 206c 696e 6520 5b61 7272 6f77 733d 3c2d   line [arrows=<-\n-000137c0: 3e5d 2028 737a 2c30 2c30 2928 4f29 2830  >] (sz,0,0)(O)(0\n-000137d0: 2c73 7a2c 3029 0a20 2020 206c 696e 6520  ,sz,0).    line \n-000137e0: 5b61 7272 6f77 733d 2d3e 5d20 2028 4f29  [arrows=->]  (O)\n-000137f0: 2830 2c30 2c73 7a29 0a20 2020 206c 696e  (0,0,sz).    lin\n-00013800: 6520 5b6c 696e 6577 6964 7468 3d2e 3270  e [linewidth=.2p\n-00013810: 742c 6c69 6e65 636f 6c6f 723d 626c 7565  t,linecolor=blue\n-00013820: 2c6c 696e 6573 7479 6c65 3d64 6173 6865  ,linestyle=dashe\n-00013830: 645d 2028 4f29 2830 2c30 2c2d 3130 290a  d] (O)(0,0,-10).\n-00013840: 2020 2020 7370 6563 6961 6c20 7c5c 7570      special |\\up\n-00013850: 7574 5b72 5d23 317b 2478 247d 5c75 7075  ut[r]#1{$x$}\\upu\n-00013860: 745b 755d 2332 7b24 7924 7d5c 7570 7574  t[u]#2{$y$}\\uput\n-00013870: 5b6c 5d23 337b 247a 247d 7c0a 2020 2020  [l]#3{$z$}|.    \n-00013880: 2020 2873 7a2c 302c 3029 2830 2c73 7a2c    (sz,0,0)(0,sz,\n-00013890: 3029 2830 2c30 2c73 7a29 0a20 207d 0a0a  0)(0,0,sz).  }..\n-000138a0: 2020 2054 696d 6520 666f 7220 616e 6f74     Time for anot\n-000138b0: 6865 7220 7465 7374 2e20 204c 6574 2773  her test.  Let's\n-000138c0: 2062 7569 6c64 2061 2072 6561 6c20 7669   build a real vi\n-000138d0: 6577 2074 7261 6e73 666f 726d 2c20 6372  ew transform, cr\n-000138e0: 6561 7469 6e67 2061 0a22 7669 7274 7561  eating a.\"virtua\n-000138f0: 6c20 6361 6d65 7261 2220 746f 206c 6f6f  l camera\" to loo\n-00013900: 6b20 6174 2074 6865 2073 6365 6e65 2077  k at the scene w\n-00013910: 6520 6172 6520 636f 6e73 7472 7563 7469  e are constructi\n-00013920: 6e67 2e20 2052 6570 6c61 6365 2074 6865  ng.  Replace the\n-00013930: 0a27 7265 7065 6174 2720 7769 7468 0a20  .'repeat' with. \n-00013940: 2064 6566 2065 7965 2028 3130 2c34 2c31   def eye (10,4,1\n-00013950: 3029 0a20 2064 6566 206c 6f6f 6b5f 6174  0).  def look_at\n-00013960: 2028 302c 302c 2d35 290a 2020 7075 7420   (0,0,-5).  put \n-00013970: 7b20 7669 6577 2828 6579 6529 2c20 286c  { view((eye), (l\n-00013980: 6f6f 6b5f 6174 2929 207d 207b 207b 686f  ook_at)) } { {ho\n-00013990: 7573 657d 7b61 7865 737d 207d 0a20 2020  use}{axes} }.   \n-000139a0: 5468 6520 2276 6965 7720 7472 616e 7366  The \"view transf\n-000139b0: 6f72 6d22 2072 6570 6f73 6974 696f 6e73  orm\" repositions\n-000139c0: 2074 6865 2073 6365 6e65 2073 6f20 7468   the scene so th\n-000139d0: 6174 2074 6865 2070 6f69 6e74 2027 6579  at the point 'ey\n-000139e0: 6527 2069 730a 6174 2074 6865 206f 7269  e' is.at the ori\n-000139f0: 6769 6e20 616e 6420 7468 6520 6469 7265  gin and the dire\n-00013a00: 6374 696f 6e20 6672 6f6d 2027 6579 6527  ction from 'eye'\n-00013a10: 2074 6f20 276c 6f6f 6b5f 6174 2720 6973   to 'look_at' is\n-00013a20: 2074 6865 206e 6567 6174 6976 650a 7a2d   the negative.z-\n-00013a30: 6178 6973 2e20 2054 6869 7320 7265 7175  axis.  This requ\n-00013a40: 6972 6573 2061 2072 6f74 6174 696f 6e20  ires a rotation \n-00013a50: 616e 6420 6120 7472 616e 736c 6174 696f  and a translatio\n-00013a60: 6e20 7468 6174 2061 7265 2061 6c6c 2070  n that are all p\n-00013a70: 6163 6b65 640a 696e 746f 2074 6865 2063  acked.into the c\n-00013a80: 6f6e 7374 7275 6374 6f72 2027 7669 6577  onstructor 'view\n-00013a90: 272e 0a0a 0008 5b69 6d61 6765 2073 7263  '.....[image src\n-00013aa0: 3d22 6578 3135 302e 706e 6722 2074 6578  =\"ex150.png\" tex\n-00013ab0: 743d 2249 6d61 6765 2065 7831 3530 206f  t=\"Image ex150 o\n-00013ac0: 6d69 7474 6564 2069 6e20 7465 7874 2076  mitted in text v\n-00013ad0: 6572 7369 6f6e 206f 6620 7468 6973 2064  ersion of this d\n-00013ae0: 6f63 756d 656e 742e 2200 085d 0a0a 5468  ocument.\"..]..Th\n-00013af0: 6973 2069 7320 7374 6172 7469 6e67 2074  is is starting t\n-00013b00: 6f20 6c6f 6f6b 2067 6f6f 6421 2020 4164  o look good!  Ad\n-00013b10: 6420 7468 6520 7072 6f6a 6563 7469 6f6e  d the projection\n-00013b20: 2070 6c61 6e65 2068 616c 6620 7761 790a   plane half way.\n-00013b30: 6265 7477 6565 6e20 7468 6520 6f72 6967  between the orig\n-00013b40: 696e 2061 6e64 2074 6865 2068 6f75 7365  in and the house\n-00013b50: 2061 7420 7a3d 2d35 2e20 2057 6527 6c6c   at z=-5.  We'll\n-00013b60: 2074 7279 2074 6865 2061 6e67 6c65 2061   try the angle a\n-00013b70: 7267 756d 656e 740a 6665 6174 7572 6520  rgument.feature \n-00013b80: 6f66 2027 7370 6563 6961 6c27 2074 6f20  of 'special' to \n-00013b90: 706f 7369 7469 6f6e 2061 206c 6162 656c  position a label\n-00013ba0: 2e0a 2020 6465 6620 7020 3520 2520 7072  ..  def p 5 % pr\n-00013bb0: 6f6a 6563 7469 6f6e 2064 6973 7461 6e63  ojection distanc\n-00013bc0: 6520 2870 6c61 6e65 2061 7420 7a3d 2d70  e (plane at z=-p\n-00013bd0: 290a 2020 6465 6620 7072 6f6a 6563 7469  ).  def projecti\n-00013be0: 6f6e 5f70 6c61 6e65 207b 0a20 2020 2064  on_plane {.    d\n-00013bf0: 6566 2073 7a20 312e 350a 2020 2020 706f  ef sz 1.5.    po\n-00013c00: 6c79 676f 6e20 282d 737a 2c2d 737a 2c2d  lygon (-sz,-sz,-\n-00013c10: 7029 2873 7a2c 2d73 7a2c 2d70 2928 737a  p)(sz,-sz,-p)(sz\n-00013c20: 2c73 7a2c 2d70 2928 2d73 7a2c 737a 2c2d  ,sz,-p)(-sz,sz,-\n-00013c30: 7029 0a20 2020 2073 7065 6369 616c 207c  p).    special |\n-00013c40: 5c72 7075 745b 625d 2331 2d32 2333 7b5c  \\rput[b]#1-2#3{\\\n-00013c50: 666f 6f74 6e6f 7465 7369 7a65 5c73 6620  footnotesize\\sf \n-00013c60: 7072 6f6a 6563 7469 6f6e 2070 6c61 6e65  projection plane\n-00013c70: 7d7c 200a 2020 2020 2020 282d 737a 2c2d  }| .      (-sz,-\n-00013c80: 737a 2c2d 7029 2873 7a2c 2d73 7a2c 2d70  sz,-p)(sz,-sz,-p\n-00013c90: 2928 302c 2d73 7a2b 2e31 2c2d 7029 0a20  )(0,-sz+.1,-p). \n-00013ca0: 207d 0a41 6464 207b 7072 6f6a 6563 7469   }.Add {projecti\n-00013cb0: 6f6e 5f70 6c61 6e65 7d20 746f 2074 6865  on_plane} to the\n-00013cc0: 206c 6973 7420 6f66 206f 626a 6563 7473   list of objects\n-00013cd0: 2069 6e20 7468 6520 2770 7574 2720 6162   in the 'put' ab\n-00013ce0: 6f76 652e 0a0a 0008 5b69 6d61 6765 2073  ove.....[image s\n-00013cf0: 7263 3d22 6578 3136 302e 706e 6722 2074  rc=\"ex160.png\" t\n-00013d00: 6578 743d 2249 6d61 6765 2065 7831 3630  ext=\"Image ex160\n-00013d10: 206f 6d69 7474 6564 2069 6e20 7465 7874   omitted in text\n-00013d20: 2076 6572 7369 6f6e 206f 6620 7468 6973   version of this\n-00013d30: 2064 6f63 756d 656e 742e 2200 085d 0a0a   document.\"..]..\n-00013d40: 2020 2054 6865 2077 6179 2077 6520 636f     The way we co\n-00013d50: 6e73 7472 7563 7465 6420 7468 6520 706f  nstructed the po\n-00013d60: 696e 7473 206f 6620 7468 6520 686f 7573  ints of the hous\n-00013d70: 6520 6e6f 7720 6d61 6b65 7320 6974 2065  e now makes it e\n-00013d80: 6173 7920 746f 0a64 7261 7720 7261 7973  asy to.draw rays\n-00013d90: 206f 6620 7072 6f6a 6563 7469 6f6e 2e20   of projection. \n-00013da0: 2057 6527 6c6c 2063 6173 7420 6f6e 6520   We'll cast one \n-00013db0: 7261 7920 6672 6f6d 2065 7665 7279 2076  ray from every v\n-00013dc0: 6973 6962 6c65 2076 6572 7465 780a 6f66  isible vertex.of\n-00013dd0: 2074 6865 2068 6f75 7365 2061 6e64 2064   the house and d\n-00013de0: 6566 696e 6520 6f70 7469 6f6e 7320 736f  efine options so\n-00013df0: 2074 6865 2061 7070 6561 7261 6e63 6520   the appearance \n-00013e00: 6f66 2061 6c6c 2072 6179 7320 6361 6e20  of all rays can \n-00013e10: 6265 0a63 6861 6e67 6564 2061 7420 7468  be.changed at th\n-00013e20: 6520 7361 6d65 2074 696d 652e 0a20 2064  e same time..  d\n-00013e30: 6566 2070 726f 6a65 6374 696f 6e5f 7261  ef projection_ra\n-00013e40: 7973 207b 0a20 2020 2064 6566 2072 6179  ys {.    def ray\n-00013e50: 6f70 7420 5b6c 696e 6577 6964 7468 3d2e  opt [linewidth=.\n-00013e60: 3370 742c 6c69 6e65 636f 6c6f 723d 6c69  3pt,linecolor=li\n-00013e70: 6768 7467 7261 795d 0a20 2020 206c 696e  ghtgray].    lin\n-00013e80: 6520 5b72 6179 6f70 745d 284f 2928 7052  e [rayopt](O)(pR\n-00013e90: 3129 206c 696e 6520 5b72 6179 6f70 745d  1) line [rayopt]\n-00013ea0: 284f 2928 7052 3229 206c 696e 655b 7261  (O)(pR2) line[ra\n-00013eb0: 796f 7074 5d28 4f29 2870 5233 290a 2020  yopt](O)(pR3).  \n-00013ec0: 2020 6c69 6e65 205b 7261 796f 7074 5d28    line [rayopt](\n-00013ed0: 4f29 2870 5234 2920 6c69 6e65 205b 7261  O)(pR4) line [ra\n-00013ee0: 796f 7074 5d28 4f29 2870 5235 290a 2020  yopt](O)(pR5).  \n-00013ef0: 2020 6c69 6e65 205b 7261 796f 7074 5d28    line [rayopt](\n-00013f00: 4f29 2870 4c31 2920 6c69 6e65 205b 7261  O)(pL1) line [ra\n-00013f10: 796f 7074 5d28 4f29 2870 4c32 2920 6c69  yopt](O)(pL2) li\n-00013f20: 6e65 5b72 6179 6f70 745d 284f 2928 704c  ne[rayopt](O)(pL\n-00013f30: 3529 0a20 2020 206c 696e 6520 5b72 6179  5).    line [ray\n-00013f40: 6f70 745d 284f 2928 7044 3129 206c 696e  opt](O)(pD1) lin\n-00013f50: 6520 5b72 6179 6f70 745d 284f 2928 7044  e [rayopt](O)(pD\n-00013f60: 3229 200a 2020 2020 6c69 6e65 205b 7261  2) .    line [ra\n-00013f70: 796f 7074 5d28 4f29 2870 4433 2920 6c69  yopt](O)(pD3) li\n-00013f80: 6e65 205b 7261 796f 7074 5d28 4f29 2870  ne [rayopt](O)(p\n-00013f90: 4434 2920 0a20 207d 0a54 6865 2072 6573  D4) .  }.The res\n-00013fa0: 756c 7420 6973 2073 686f 776e 2068 6572  ult is shown her\n-00013fb0: 652e 0a0a 0008 5b69 6d61 6765 2073 7263  e.....[image src\n-00013fc0: 3d22 6578 3137 302e 706e 6722 2074 6578  =\"ex170.png\" tex\n-00013fd0: 743d 2249 6d61 6765 2065 7831 3730 206f  t=\"Image ex170 o\n-00013fe0: 6d69 7474 6564 2069 6e20 7465 7874 2076  mitted in text v\n-00013ff0: 6572 7369 6f6e 206f 6620 7468 6973 2064  ersion of this d\n-00014000: 6f63 756d 656e 742e 2200 085d 0a0a 5468  ocument.\"..]..Th\n-00014010: 6520 7261 7973 2070 6965 7263 6520 7468  e rays pierce th\n-00014020: 6520 7072 6f6a 6563 7469 6f6e 2070 6c61  e projection pla\n-00014030: 6e65 2061 7420 7468 6520 636f 7272 6573  ne at the corres\n-00014040: 706f 6e64 696e 6720 706f 696e 7473 206f  ponding points o\n-00014050: 6e20 7468 650a 7065 7273 7065 6374 6976  n the.perspectiv\n-00014060: 6520 696d 6167 6520 7765 2061 7265 2074  e image we are t\n-00014070: 7279 696e 6720 746f 2064 7261 772e 2020  rying to draw.  \n-00014080: 416c 6272 6563 6874 2044 c3bc 7265 7220  Albrecht D..rer \n-00014090: 616e 6420 6869 730a 5265 6e61 6973 7361  and his.Renaissa\n-000140a0: 6e63 6520 636f 6e74 656d 706f 7261 7269  nce contemporari\n-000140b0: 6573 2068 6164 2074 6865 2073 616d 6520  es had the same \n-000140c0: 6964 6561 2069 6e20 7468 6520 6561 726c  idea in the earl\n-000140d0: 7920 3135 3030 2773 2e0a 0a00 085b 696d  y 1500's.....[im\n-000140e0: 6167 6520 7372 633d 2264 7565 7265 722e  age src=\"duerer.\n-000140f0: 706e 6722 2074 6578 743d 2249 6d61 6765  png\" text=\"Image\n-00014100: 206f 6620 4475 6572 6572 2773 2070 6572   of Duerer's per\n-00014110: 7370 6563 7469 7665 2063 6f6d 7075 7465  spective compute\n-00014120: 7220 6f6d 6974 7465 6420 696e 2074 6578  r omitted in tex\n-00014130: 7420 7665 7273 696f 6e20 6f66 2074 6869  t version of thi\n-00014140: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a  s document.\"..].\n-00014150: 0a20 2020 416c 6c20 7468 6174 2773 206c  .   All that's l\n-00014160: 6566 7420 6973 2074 6f20 6669 6e64 2061  eft is to find a\n-00014170: 2077 6179 2074 6f20 636f 6e6e 6563 7420   way to connect \n-00014180: 7468 6520 706f 696e 7473 206f 6620 7468  the points of th\n-00014190: 6520 686f 7573 650a 6f6e 2074 6865 2070  e house.on the p\n-000141a0: 726f 6a65 6374 696f 6e20 706c 616e 652e  rojection plane.\n-000141b0: 2020 5765 2063 6f75 6c64 2070 756c 6c20    We could pull \n-000141c0: 6f75 7420 6120 676f 6f64 2063 6f6d 7075  out a good compu\n-000141d0: 7465 7220 6772 6170 6869 6373 0a74 6578  ter graphics.tex\n-000141e0: 742c 2066 696e 6420 7468 6520 6e65 6365  t, find the nece\n-000141f0: 7373 6172 7920 6d61 7472 6978 2c20 616e  ssary matrix, an\n-00014200: 6420 656e 7465 7220 6974 206f 7572 7365  d enter it ourse\n-00014210: 6c76 6573 2061 7320 6120 7472 616e 7366  lves as a transf\n-00014220: 6f72 6d0a 6c69 7465 7261 6c2e 2020 2a4e  orm.literal.  *N\n-00014230: 6f74 6520 5472 616e 7366 6f72 6d20 6c69  ote Transform li\n-00014240: 7465 7261 6c73 3a3a 2e20 2054 6861 7420  terals::.  That \n-00014250: 776f 726b 2069 7320 616c 7265 6164 7920  work is already \n-00014260: 646f 6e65 2c0a 686f 7765 7665 722e 2020  done,.however.  \n-00014270: 5765 2063 616e 2075 7365 2074 6865 2027  We can use the '\n-00014280: 7072 6f6a 6563 7428 7029 2720 636f 6e73  project(p)' cons\n-00014290: 7472 7563 746f 722e 0a0a 2020 2054 6865  tructor...   The\n-000142a0: 7265 2061 7265 2073 7469 6c6c 2073 6f6d  re are still som\n-000142b0: 6520 6465 7461 696c 7320 7468 6174 2072  e details that r\n-000142c0: 6571 7569 7265 2063 6172 652e 2020 5072  equire care.  Pr\n-000142d0: 6f6a 6563 7469 6f6e 2077 696c 6c0a 666c  ojection will.fl\n-000142e0: 6174 7465 6e20 7768 6174 6576 6572 2069  atten whatever i\n-000142f0: 7320 7472 616e 7366 6f72 6d65 6420 6f6e  s transformed on\n-00014300: 746f 2074 6865 2070 6c61 6e65 207a 3d2d  to the plane z=-\n-00014310: 702e 2020 5468 6572 6566 6f72 6520 616e  p.  Therefore an\n-00014320: 7920 7061 7274 0a6f 6620 7468 6520 686f  y part.of the ho\n-00014330: 7573 6520 636f 756c 6420 6469 7361 7070  use could disapp\n-00014340: 6561 7220 6265 6869 6e64 2074 6865 2070  ear behind the p\n-00014350: 726f 6a65 6374 696f 6e20 706c 616e 6520  rojection plane \n-00014360: 2874 6865 2068 6964 6465 6e0a 7375 7266  (the hidden.surf\n-00014370: 6163 6520 616c 676f 7269 7468 6d20 6f72  ace algorithm or\n-00014380: 6465 7273 206f 626a 6563 7473 2061 7420  ders objects at \n-00014390: 7468 6520 7361 6d65 2064 6570 7468 2061  the same depth a\n-000143a0: 7262 6974 7261 7269 6c79 292e 2020 5468  rbitrarily).  Th\n-000143b0: 650a 646f 6f72 206d 6179 2061 6c73 6f20  e.door may also \n-000143c0: 6469 7361 7070 6561 7220 6265 6869 6e64  disappear behind\n-000143d0: 2074 6865 2066 726f 6e74 206f 6620 7468   the front of th\n-000143e0: 6520 686f 7573 652e 2020 546f 206d 616b  e house.  To mak\n-000143f0: 6520 7375 7265 0a65 7665 7279 7468 696e  e sure.everythin\n-00014400: 6720 7265 6d61 696e 7320 7669 7369 626c  g remains visibl\n-00014410: 652c 2077 6527 6c6c 2070 6c61 6365 2074  e, we'll place t\n-00014420: 6865 2068 6f75 7365 2061 2074 696e 7920  he house a tiny \n-00014430: 6269 7420 696e 2066 726f 6e74 206f 660a  bit in front of.\n-00014440: 7468 6520 7072 6f6a 6563 7469 6f6e 2070  the projection p\n-00014450: 6c61 6e65 2061 6e64 2061 2073 6563 6f6e  lane and a secon\n-00014460: 6420 636f 7079 206f 6620 7468 6520 646f  d copy of the do\n-00014470: 6f72 2069 6e20 6672 6f6e 7420 6f66 2074  or in front of t\n-00014480: 6865 0a68 6f75 7365 2e0a 2020 6465 6620  he.house..  def \n-00014490: 7072 6f6a 6563 7469 6f6e 207b 0a20 2020  projection {.   \n-000144a0: 2025 2065 2069 7320 6120 736d 616c 6c20   % e is a small \n-000144b0: 6e75 6d62 6572 2064 6566 696e 6564 2061  number defined a\n-000144c0: 626f 7665 0a20 2020 2070 7574 207b 2070  bove.    put { p\n-000144d0: 726f 6a65 6374 2870 2920 7468 656e 2074  roject(p) then t\n-000144e0: 7261 6e73 6c61 7465 285b 302c 302c 312a  ranslate([0,0,1*\n-000144f0: 655d 2920 7d20 7b68 6f75 7365 7d0a 2020  e]) } {house}.  \n-00014500: 2020 7075 7420 7b20 7072 6f6a 6563 7428    put { project(\n-00014510: 7029 2074 6865 6e20 7472 616e 736c 6174  p) then translat\n-00014520: 6528 5b30 2c30 2c32 2a65 5d29 207d 207b  e([0,0,2*e]) } {\n-00014530: 646f 6f72 7d0a 2020 7d0a 0a00 085b 696d  door}.  }....[im\n-00014540: 6167 6520 7372 633d 2265 7831 3830 2e70  age src=\"ex180.p\n-00014550: 6e67 2220 7465 7874 3d22 496d 6167 6520  ng\" text=\"Image \n-00014560: 6578 3138 3020 6f6d 6974 7465 6420 696e  ex180 omitted in\n-00014570: 2074 6578 7420 7665 7273 696f 6e20 6f66   text version of\n-00014580: 2074 6869 7320 646f 6375 6d65 6e74 2e22   this document.\"\n-00014590: 0008 5d0a 0a20 2020 4966 2079 6f75 2068  ..]..   If you h\n-000145a0: 6176 6520 7374 7564 6965 6420 616e 6420  ave studied and \n-000145b0: 756e 6465 7273 7461 6e64 2061 6c6c 2074  understand all t\n-000145c0: 6869 732c 2079 6f75 2061 7265 2077 656c  his, you are wel\n-000145d0: 6c20 6f6e 2074 6865 2077 6179 0a74 6f20  l on the way.to \n-000145e0: 7375 6363 6573 7320 7769 7468 2027 736b  success with 'sk\n-000145f0: 6574 6368 272e 2020 4e6f 7420 7368 6f77  etch'.  Not show\n-00014600: 6e20 6172 6520 7468 6520 3230 206f 7220  n are the 20 or \n-00014610: 736f 2069 7465 7261 7469 6f6e 7320 7468  so iterations th\n-00014620: 6174 0a77 6572 6520 7265 7175 6972 6564  at.were required\n-00014630: 2074 6f20 6669 6e64 2061 2072 6561 736f   to find a reaso\n-00014640: 6e61 626c 6520 7669 6577 696e 6720 616e  nable viewing an\n-00014650: 676c 6520 616e 6420 686f 7573 6520 706f  gle and house po\n-00014660: 7369 7469 6f6e 2c0a 6574 632e 2020 4e6f  sition,.etc.  No\n-00014670: 6e65 7468 656c 6573 732c 2074 6869 7320  netheless, this \n-00014680: 6472 6177 696e 6720 7761 7320 636f 6d70  drawing was comp\n-00014690: 6c65 7465 6420 696e 2061 626f 7574 2061  leted in about a\n-000146a0: 6e20 686f 7572 2e20 2057 6869 6c65 2061  n hour.  While a\n-000146b0: 0a47 5549 2074 6f6f 6c20 6d61 7920 6861  .GUI tool may ha\n-000146c0: 7665 2062 6565 6e20 6120 6c69 7474 6c65  ve been a little\n-000146d0: 2066 6173 7465 722c 2069 7420 6973 2075   faster, it is u\n-000146e0: 6e6c 696b 656c 7920 7468 6174 2061 206e  nlikely that a n\n-000146f0: 6577 0a64 7261 7769 6e67 2c20 6974 7365  ew.drawing, itse\n-00014700: 6c66 2061 2070 6572 7370 6563 7469 7665  lf a perspective\n-00014710: 2070 726f 6a65 6374 696f 6e20 6f66 2074   projection of t\n-00014720: 6865 2073 6365 6e65 2c20 636f 756c 6420  he scene, could \n-00014730: 6265 0a67 656e 6572 6174 6564 2077 6974  be.generated wit\n-00014740: 6820 7477 6f20 6d6f 7265 206d 696e 7574  h two more minut\n-00014750: 6573 2720 776f 726b 2120 204a 7573 7420  es' work!  Just \n-00014760: 6368 616e 6765 2074 6865 2076 6965 7720  change the view \n-00014770: 7472 616e 7366 6f72 6d0a 746f 0a20 2070  transform.to.  p\n-00014780: 7574 207b 2076 6965 7728 2865 7965 292c  ut { view((eye),\n-00014790: 2028 6c6f 6f6b 5f61 7429 2920 7468 656e   (look_at)) then\n-000147a0: 2070 6572 7370 6563 7469 7665 2839 2920   perspective(9) \n-000147b0: 7d20 7b20 2e2e 2e0a 616e 6420 7072 6f64  } { ....and prod\n-000147c0: 7563 6520 7468 6973 2e0a 0a00 085b 696d  uce this.....[im\n-000147d0: 6167 6520 7372 633d 2265 7831 3930 2e70  age src=\"ex190.p\n-000147e0: 6e67 2220 7465 7874 3d22 496d 6167 6520  ng\" text=\"Image \n-000147f0: 6578 3139 3020 6f6d 6974 7465 6420 696e  ex190 omitted in\n-00014800: 2074 6578 7420 7665 7273 696f 6e20 6f66   text version of\n-00014810: 2074 6869 7320 646f 6375 6d65 6e74 2e22   this document.\"\n-00014820: 0008 5d0a 0a1f 0a46 696c 653a 2073 6b65  ..]....File: ske\n-00014830: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n-00014840: 2041 2074 6563 686e 6963 616c 2064 7261   A technical dra\n-00014850: 7769 6e67 2c20 204e 6578 743a 2041 2068  wing,  Next: A h\n-00014860: 6965 7261 7263 6869 6361 6c20 6d6f 6465  ierarchical mode\n-00014870: 6c2c 2020 5072 6576 3a20 4f76 6572 7669  l,  Prev: Overvi\n-00014880: 6577 2c20 2055 703a 2042 7569 6c64 696e  ew,  Up: Buildin\n-00014890: 6720 6120 6472 6177 696e 670a 0a34 2e32  g a drawing..4.2\n-000148a0: 2041 2074 6563 686e 6963 616c 2064 7261   A technical dra\n-000148b0: 7769 6e67 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d  wing.===========\n-000148c0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a 4c65  ============..Le\n-000148d0: 7427 7320 6c6f 6f6b 2061 7420 6120 6472  t's look at a dr\n-000148e0: 6177 696e 6720 7468 6174 2072 6570 7265  awing that repre\n-000148f0: 7365 6e74 7320 7468 6520 6b69 6e64 206f  sents the kind o\n-00014900: 6620 7072 6f62 6c65 6d20 2773 6b65 7463  f problem 'sketc\n-00014910: 6827 2077 6173 0a6d 6561 6e74 2074 6f20  h' was.meant to \n-00014920: 736f 6c76 652d 2d61 2070 6169 7220 6f66  solve--a pair of\n-00014930: 2074 6578 7462 6f6f 6b20 6669 6775 7265   textbook figure\n-00014940: 7320 7265 6761 7264 696e 6720 6120 706f  s regarding a po\n-00014950: 6c79 676f 6e61 6c0a 6170 7072 6f78 696d  lygonal.approxim\n-00014960: 6174 696f 6e20 6f66 2061 2074 7275 6e63  ation of a trunc\n-00014970: 6174 6564 2063 6f6e 652e 2020 4865 7265  ated cone.  Here\n-00014980: 2061 7265 2074 6865 2070 6963 7475 7265   are the picture\n-00014990: 7320 7765 2077 696c 6c0a 7072 6f64 7563  s we will.produc\n-000149a0: 652e 0a0a 0008 5b69 6d61 6765 2073 7263  e.....[image src\n-000149b0: 3d22 6578 3235 302e 706e 6722 2074 6578  =\"ex250.png\" tex\n-000149c0: 743d 2249 6d61 6765 2065 7832 3530 206f  t=\"Image ex250 o\n-000149d0: 6d69 7474 6564 2069 6e20 7465 7874 2076  mitted in text v\n-000149e0: 6572 7369 6f6e 206f 6620 7468 6973 2064  ersion of this d\n-000149f0: 6f63 756d 656e 742e 2200 085d 2020 2020  ocument.\"..]    \n-00014a00: 2000 085b 696d 6167 6520 7372 633d 2265   ..[image src=\"e\n-00014a10: 7832 3630 2e70 6e67 2220 7465 7874 3d22  x260.png\" text=\"\n-00014a20: 496d 6167 6520 6578 3236 3020 6f6d 6974  Image ex260 omit\n-00014a30: 7465 6420 696e 2074 6578 7420 7665 7273  ted in text vers\n-00014a40: 696f 6e20 6f66 2074 6869 7320 646f 6375  ion of this docu\n-00014a50: 6d65 6e74 2e22 0008 5d0a 0a20 2020 5468  ment.\"..]..   Th\n-00014a60: 6520 636f 6e65 2073 6861 7065 2069 7320  e cone shape is \n-00014a70: 6a75 7374 2061 2073 7765 7074 206c 696e  just a swept lin\n-00014a80: 6520 7769 7468 206e 6f20 636c 6f73 7572  e with no closur\n-00014a90: 6520 7461 6720 616e 6420 6375 6c6c 696e  e tag and cullin\n-00014aa0: 670a 7475 726e 6564 206f 6666 2e20 2042  g.turned off.  B\n-00014ab0: 6567 696e 2062 7920 7365 7474 696e 6720  egin by setting \n-00014ac0: 7570 2073 6f6d 6520 7573 6566 756c 2063  up some useful c\n-00014ad0: 6f6e 7374 616e 7473 2e0a 2020 6465 6620  onstants..  def \n-00014ae0: 4f20 2830 2c30 2c30 2920 6465 6620 4920  O (0,0,0) def I \n-00014af0: 5b31 2c30 2c30 5d20 6465 6620 4a20 5b30  [1,0,0] def J [0\n-00014b00: 2c31 2c30 5d20 6465 6620 4b20 5b30 2c30  ,1,0] def K [0,0\n-00014b10: 2c31 5d0a 2020 6465 6620 7030 2028 312c  ,1].  def p0 (1,\n-00014b20: 3229 2064 6566 2070 3120 2831 2e35 2c30  2) def p1 (1.5,0\n-00014b30: 2920 6465 6620 4e20 380a 2020 6465 6620  ) def N 8.  def \n-00014b40: 7365 675f 726f 7420 726f 7461 7465 2833  seg_rot rotate(3\n-00014b50: 3630 202f 204e 2c20 5b4a 5d29 0a54 6865  60 / N, [J]).The\n-00014b60: 2070 6f69 6e74 7320 2770 3027 2061 6e64   points 'p0' and\n-00014b70: 2027 7031 2720 6172 6520 7468 6520 656e   'p1' are the en\n-00014b80: 6420 706f 696e 7473 206f 6620 7468 6520  d points of the \n-00014b90: 6c69 6e65 2074 6f20 6265 2073 7765 7074  line to be swept\n-00014ba0: 2e0a 5468 6520 6465 6669 6e69 7469 6f6e  ..The definition\n-00014bb0: 2027 7365 675f 726f 7427 2069 7320 7468   'seg_rot' is th\n-00014bc0: 6520 7377 6565 7020 7472 616e 7366 6f72  e sweep transfor\n-00014bd0: 6d61 7469 6f6e 2e20 2057 6974 6820 7468  mation.  With th\n-00014be0: 6573 652c 2074 6865 0a63 6f6e 6520 6974  ese, the.cone it\n-00014bf0: 7365 6c66 2069 7320 7369 6d70 6c65 2e0a  self is simple..\n-00014c00: 2020 7377 6565 705b 6375 6c6c 3d66 616c    sweep[cull=fal\n-00014c10: 7365 5d20 7b20 4e2c 205b 5b73 6567 5f72  se] { N, [[seg_r\n-00014c20: 6f74 5d5d 207d 206c 696e 6528 7030 2928  ot]] } line(p0)(\n-00014c30: 7031 290a 0a20 2020 5468 6520 6178 6573  p1)..   The axes\n-00014c40: 2061 7265 206e 6578 7420 616e 6420 696e   are next and in\n-00014c50: 636c 7564 6520 616e 2069 6e74 6572 6573  clude an interes\n-00014c60: 696e 6720 7472 6963 6b20 7468 6174 2073  ing trick that s\n-00014c70: 686f 7773 2074 6865 0a68 6964 6465 6e20  hows the.hidden \n-00014c80: 7061 7274 7320 6173 2064 6f74 7465 6420  parts as dotted \n-00014c90: 6c69 6e65 732e 2020 5468 6520 7365 6372  lines.  The secr\n-00014ca0: 6574 2069 7320 6472 6177 2074 6865 2061  et is draw the a\n-00014cb0: 7865 7320 7477 6963 652d 2d73 6f6c 6964  xes twice--solid\n-00014cc0: 0a6c 696e 6573 2077 6974 6820 7468 6520  .lines with the \n-00014cd0: 6e6f 726d 616c 2068 6964 6465 6e20 7375  normal hidden su\n-00014ce0: 7266 6163 6520 616c 676f 7269 7468 6d20  rface algorithm \n-00014cf0: 696e 2065 6666 6563 742c 2061 6e64 2074  in effect, and t\n-00014d00: 6865 6e0a 646f 7474 6564 2077 6974 6820  hen.dotted with \n-00014d10: 7468 6520 6f70 7469 6f6e 2027 6c61 793d  the option 'lay=\n-00014d20: 6f76 6572 2720 736f 2074 6861 7420 6e6f  over' so that no\n-00014d30: 2070 6f6c 7967 6f6e 7320 6361 6e20 6869   polygons can hi\n-00014d40: 6465 2074 6865 6d2e 0a20 2064 6566 2061  de them..  def a\n-00014d50: 7820 2864 782c 302c 3029 2025 2074 6970  x (dx,0,0) % tip\n-00014d60: 7320 6f66 2074 6865 2061 7865 730a 2020  s of the axes.  \n-00014d70: 6465 6620 6179 2028 302c 6479 2c30 290a  def ay (0,dy,0).\n-00014d80: 2020 6465 6620 617a 2028 302c 302c 647a    def az (0,0,dz\n-00014d90: 290a 2020 6c69 6e65 5b61 7272 6f77 733d  ).  line[arrows=\n-00014da0: 3c2d 3e2c 6c69 6e65 7769 6474 683d 2e34  <->,linewidth=.4\n-00014db0: 7074 5d28 6178 2928 4f29 2861 7929 0a20  pt](ax)(O)(ay). \n-00014dc0: 206c 696e 655b 6172 726f 7773 3d2d 3e2c   line[arrows=->,\n-00014dd0: 6c69 6e65 7769 6474 683d 2e34 7074 5d28  linewidth=.4pt](\n-00014de0: 4f29 2861 7a29 0a20 2025 2072 6570 6561  O)(az).  % repea\n-00014df0: 7420 646f 7474 6564 2061 7320 616e 206f  t dotted as an o\n-00014e00: 7665 726c 6179 2074 6f20 6869 6e74 2061  verlay to hint a\n-00014e10: 7420 7468 6520 6869 6464 656e 206c 696e  t the hidden lin\n-00014e20: 6573 0a20 206c 696e 655b 6c61 793d 6f76  es.  line[lay=ov\n-00014e30: 6572 2c6c 696e 6573 7479 6c65 3d64 6f74  er,linestyle=dot\n-00014e40: 7465 642c 6c69 6e65 7769 6474 683d 2e34  ted,linewidth=.4\n-00014e50: 7074 5d28 6178 2928 4f29 2861 7929 0a20  pt](ax)(O)(ay). \n-00014e60: 206c 696e 655b 6c61 793d 6f76 6572 2c6c   line[lay=over,l\n-00014e70: 696e 6573 7479 6c65 3d64 6f74 7465 642c  inestyle=dotted,\n-00014e80: 6c69 6e65 7769 6474 683d 2e34 7074 5d28  linewidth=.4pt](\n-00014e90: 4f29 2861 7a29 0a20 2073 7065 6369 616c  O)(az).  special\n-00014ea0: 7c5c 666f 6f74 6e6f 7465 7369 7a65 0a20  |\\footnotesize. \n-00014eb0: 2020 2020 2020 2020 205c 7570 7574 5b64           \\uput[d\n-00014ec0: 5d23 317b 2478 247d 5c75 7075 745b 755d  ]#1{$x$}\\uput[u]\n-00014ed0: 2332 7b24 7924 7d5c 7570 7574 5b6c 5d23  #2{$y$}\\uput[l]#\n-00014ee0: 337b 247a 247d 7c0a 2020 2020 2861 7829  3{$z$}|.    (ax)\n-00014ef0: 2861 7929 2861 7a29 0a54 6865 206c 6162  (ay)(az).The lab\n-00014f00: 656c 7320 6172 6520 6170 706c 6965 6420  els are applied \n-00014f10: 7769 7468 2027 5053 5472 6963 6b73 2720  with 'PSTricks' \n-00014f20: 7370 6563 6961 6c20 6f62 6a65 6374 7320  special objects \n-00014f30: 6173 2075 7375 616c 2e0a 0a20 2020 466f  as usual...   Fo\n-00014f40: 7220 7468 6520 6865 6967 6874 2064 696d  r the height dim\n-00014f50: 656e 7369 6f6e 206d 6172 6b2c 2074 6865  ension mark, the\n-00014f60: 2070 6f77 6572 206f 6620 6166 6669 6e65   power of affine\n-00014f70: 2061 7269 7468 6574 6963 2069 7320 7665   arithetic is ve\n-00014f80: 7279 0a68 656c 7066 756c 2e0a 2020 6465  ry.helpful..  de\n-00014f90: 6620 6864 696d 5f72 6566 2075 6e69 7428  f hdim_ref unit(\n-00014fa0: 2870 3129 202d 2028 4f29 2920 7468 656e  (p1) - (O)) then\n-00014fb0: 205b 5b73 6567 5f72 6f74 5d5d 5e32 0a20   [[seg_rot]]^2. \n-00014fc0: 2064 6566 2063 3020 2870 3029 2074 6865   def c0 (p0) the\n-00014fd0: 6e20 7363 616c 6528 5b4a 5d29 0a20 2064  n scale([J]).  d\n-00014fe0: 6566 2068 3030 2028 6330 2920 2b20 312e  ef h00 (c0) + 1.\n-00014ff0: 3120 2a20 5b68 6469 6d5f 7265 665d 0a20  1 * [hdim_ref]. \n-00015000: 2064 6566 2068 3031 2028 6330 2920 2b20   def h01 (c0) + \n-00015010: 312e 3920 2a20 5b68 6469 6d5f 7265 665d  1.9 * [hdim_ref]\n-00015020: 0a20 2064 6566 2068 3032 2028 6330 2920  .  def h02 (c0) \n-00015030: 2b20 312e 3820 2a20 5b68 6469 6d5f 7265  + 1.8 * [hdim_re\n-00015040: 665d 0a20 206c 696e 6528 6830 3029 2868  f].  line(h00)(h\n-00015050: 3031 290a 2020 6465 6620 6831 3020 284f  01).  def h10 (O\n-00015060: 2920 2b20 312e 3620 2a20 5b68 6469 6d5f  ) + 1.6 * [hdim_\n-00015070: 7265 665d 0a20 2064 6566 2068 3131 2028  ref].  def h11 (\n-00015080: 4f29 202b 2031 2e39 202a 205b 6864 696d  O) + 1.9 * [hdim\n-00015090: 5f72 6566 5d0a 2020 6465 6620 6831 3220  _ref].  def h12 \n-000150a0: 284f 2920 2b20 312e 3820 2a20 5b68 6469  (O) + 1.8 * [hdi\n-000150b0: 6d5f 7265 665d 0a20 206c 696e 6528 6831  m_ref].  line(h1\n-000150c0: 3029 2868 3131 290a 2020 6c69 6e65 5b61  0)(h11).  line[a\n-000150d0: 7272 6f77 733d 3c2d 3e5d 2868 3032 2928  rrows=<->](h02)(\n-000150e0: 6831 3229 0a20 2064 6566 2068 6d32 2028  h12).  def hm2 (\n-000150f0: 2868 3032 2920 2d20 284f 2920 2b20 2868  (h02) - (O) + (h\n-00015100: 3132 2920 2d20 284f 2929 202f 2032 202b  12) - (O)) / 2 +\n-00015110: 2028 4f29 0a20 2073 7065 6369 616c 7c5c   (O).  special|\\\n-00015120: 666f 6f74 6e6f 7465 7369 7a65 5c72 7075  footnotesize\\rpu\n-00015130: 742a 2331 7b24 6824 7d7c 2868 6d32 290a  t*#1{$h$}|(hm2).\n-00015140: 2020 2054 6865 2067 656e 6572 616c 2069     The general i\n-00015150: 6465 6120 656d 706c 6f79 6564 2068 6572  dea employed her\n-00015160: 6520 6973 2074 6f20 636f 6d70 7574 6520  e is to compute \n-00015170: 6120 756e 6974 2022 7265 6665 7265 6e63  a unit \"referenc\n-00015180: 650a 7665 6374 6f72 2220 7061 7261 6c6c  e.vector\" parall\n-00015190: 656c 2074 6f20 7468 6520 787a 2d70 6c61  el to the xz-pla\n-000151a0: 6e65 2069 6e20 7468 6520 6465 7369 7265  ne in the desire\n-000151b0: 6420 6469 7265 6374 696f 6e20 6f66 2074  d direction of t\n-000151c0: 6865 0a64 696d 656e 7369 6f6e 2066 726f  he.dimension fro\n-000151d0: 6d20 7468 6520 6f72 6967 696e 2e20 2054  m the origin.  T\n-000151e0: 6865 2074 7261 6e73 666f 726d 6174 696f  he transformatio\n-000151f0: 6e20 275b 5b73 6567 5f72 6f74 5d5d 5e32  n '[[seg_rot]]^2\n-00015200: 2720 726f 7461 7465 730a 7477 6f20 7365  ' rotates.two se\n-00015210: 676d 656e 7473 2061 626f 7574 2074 6865  gments about the\n-00015220: 2079 2d61 7869 732e 2020 5768 656e 2061   y-axis.  When a\n-00015230: 7070 6c69 6564 2074 6f20 2728 7031 2920  pplied to '(p1) \n-00015240: 2d20 284f 2927 2c20 7468 650a 7265 7375  - (O)', the.resu\n-00015250: 6c74 696e 6720 7665 6374 6f72 2070 6f69  lting vector poi\n-00015260: 6e74 7320 746f 2074 6865 2072 6967 6874  nts to the right\n-00015270: 2061 7320 7368 6f77 6e2e 2020 496e 2074   as shown.  In t\n-00015280: 6869 7320 6d61 6e6e 6572 2c20 7765 2063  his manner, we c\n-00015290: 616e 0a70 6963 6b20 616e 7920 7665 7274  an.pick any vert\n-000152a0: 6578 2061 7320 7468 6520 6c6f 6361 7469  ex as the locati\n-000152b0: 6f6e 206f 6620 7468 6520 6865 6967 6874  on of the height\n-000152c0: 2064 696d 656e 7369 6f6e 206c 696e 6573   dimension lines\n-000152d0: 2062 7920 7661 7279 696e 670a 7468 6520   by varying.the \n-000152e0: 6578 706f 6e65 6e74 206f 6620 275b 5b73  exponent of '[[s\n-000152f0: 6567 5f72 6f74 5d5d 272e 2020 5468 6973  eg_rot]]'.  This\n-00015300: 2069 7320 6f6e 6c79 206f 6e65 206f 6620   is only one of \n-00015310: 6d61 6e79 2070 6f73 7369 626c 650a 7374  many possible.st\n-00015320: 7261 7465 6769 6573 2e0a 0a20 2020 5468  rategies...   Th\n-00015330: 6520 636f 6d70 7574 6174 696f 6e20 6f66  e computation of\n-00015340: 2027 686d 3227 2069 7320 6120 7573 6566   'hm2' is a usef\n-00015350: 756c 2069 6469 6f6d 2066 6f72 2066 696e  ul idiom for fin\n-00015360: 6469 6e67 2074 6865 2063 656e 7472 6f69  ding the centroi\n-00015370: 640a 6f66 2061 2073 6574 206f 6620 706f  d.of a set of po\n-00015380: 696e 7473 2e0a 0a20 2020 5468 6520 7477  ints...   The tw\n-00015390: 6f20 7261 6469 7573 206d 6172 6b73 2061  o radius marks a\n-000153a0: 7265 2064 6f6e 6520 7369 6d69 6c61 726c  re done similarl\n-000153b0: 792c 2073 6f20 7765 2070 7265 7365 6e74  y, so we present\n-000153c0: 2074 6865 2063 6f64 650a 7769 7468 6f75   the code.withou\n-000153d0: 7420 636f 6d6d 656e 742e 0a20 2025 2072  t comment..  % r\n-000153e0: 6164 6975 7320 6d65 6173 7572 656d 656e  adius measuremen\n-000153f0: 7420 6d61 726b 730a 2020 6465 6620 6761  t marks.  def ga\n-00015400: 7020 5b30 2c2e 322c 305d 2020 2520 7573  p [0,.2,0]  % us\n-00015410: 6564 2074 6f20 6372 6561 7465 2073 6d61  ed to create sma\n-00015420: 6c6c 2076 6572 7469 6361 6c20 6761 7073  ll vertical gaps\n-00015430: 0a0a 2020 2520 6669 7273 7420 7231 0a20  ..  % first r1. \n-00015440: 2064 6566 2075 7031 205b 302c 332e 312c   def up1 [0,3.1,\n-00015450: 305d 2025 2074 6963 6b20 7269 7365 7320  0] % tick rises \n-00015460: 6162 6f76 6520 6469 6d65 6e73 696f 6e20  above dimension \n-00015470: 6120 6c69 7474 6c65 0a20 2064 6566 2072  a little.  def r\n-00015480: 3120 2828 7031 2920 7468 656e 205b 5b73  1 ((p1) then [[s\n-00015490: 6567 5f72 6f74 5d5d 5e2d 3229 202b 205b  eg_rot]]^-2) + [\n-000154a0: 7570 315d 0a20 2064 6566 2072 3163 2028  up1].  def r1c (\n-000154b0: 7231 2920 7468 656e 2073 6361 6c65 285b  r1) then scale([\n-000154c0: 4a5d 290a 2020 6465 6620 7231 7420 2872  J]).  def r1t (r\n-000154d0: 3129 202b 205b 6761 705d 0a20 2064 6566  1) + [gap].  def\n-000154e0: 2072 3162 2028 2872 3174 2920 7468 656e   r1b ((r1t) then\n-000154f0: 2073 6361 6c65 285b 312c 302c 315d 2929   scale([1,0,1]))\n-00015500: 202b 205b 6761 705d 0a20 206c 696e 655b   + [gap].  line[\n-00015510: 6172 726f 7773 3d3c 2d3e 5d28 7231 6329  arrows=<->](r1c)\n-00015520: 2872 3129 2020 2520 6469 6d65 6e73 696f  (r1)  % dimensio\n-00015530: 6e20 6c69 6e65 0a20 206c 696e 6528 7231  n line.  line(r1\n-00015540: 6229 2872 3174 2920 2020 2020 2020 2020  b)(r1t)         \n-00015550: 2020 2020 2520 7469 636b 0a20 2064 6566      % tick.  def\n-00015560: 2072 316d 2028 2872 3129 202d 2028 4f29   r1m ((r1) - (O)\n-00015570: 202b 2028 7231 6329 202d 2028 4f29 2920   + (r1c) - (O)) \n-00015580: 2f20 3220 2b20 284f 2920 2520 6c61 6265  / 2 + (O) % labe\n-00015590: 6c20 706f 7369 7469 6f6e 0a20 2073 7065  l position.  spe\n-000155a0: 6369 616c 207c 5c66 6f6f 746e 6f74 6573  cial |\\footnotes\n-000155b0: 697a 655c 7270 7574 2a23 317b 2472 5f31  ize\\rput*#1{$r_1\n-000155c0: 247d 7c28 7231 6d29 2020 2520 6c61 6265  $}|(r1m)  % labe\n-000155d0: 6c0a 0a20 2025 2073 616d 6520 6472 696c  l..  % same dril\n-000155e0: 6c20 666f 7220 7230 2c20 6275 7420 6d75  l for r0, but mu\n-000155f0: 7374 2070 726f 6a65 6374 2064 6f77 6e20  st project down \n-00015600: 6669 7273 740a 2020 6465 6620 7570 3020  first.  def up0 \n-00015610: 5b30 2c32 2e37 2c30 5d0a 2020 6465 6620  [0,2.7,0].  def \n-00015620: 7230 2028 2870 3029 2074 6865 6e20 7363  r0 ((p0) then sc\n-00015630: 616c 6528 5b31 2c30 2c31 5d29 2074 6865  ale([1,0,1]) the\n-00015640: 6e20 5b5b 7365 675f 726f 745d 5d5e 2d32  n [[seg_rot]]^-2\n-00015650: 2920 2b20 5b75 7030 5d0a 2020 6465 6620  ) + [up0].  def \n-00015660: 7230 6320 2872 3029 2074 6865 6e20 7363  r0c (r0) then sc\n-00015670: 616c 6528 5b4a 5d29 0a20 2064 6566 2072  ale([J]).  def r\n-00015680: 3074 2028 7230 2920 2b20 5b67 6170 5d0a  0t (r0) + [gap].\n-00015690: 2020 6465 6620 7230 6220 2828 7030 2920    def r0b ((p0) \n-000156a0: 7468 656e 205b 5b73 6567 5f72 6f74 5d5d  then [[seg_rot]]\n-000156b0: 5e2d 3229 202b 205b 6761 705d 0a20 206c  ^-2) + [gap].  l\n-000156c0: 696e 655b 6172 726f 7773 3d3c 2d3e 5d28  ine[arrows=<->](\n-000156d0: 7230 6329 2872 3029 0a20 206c 696e 6528  r0c)(r0).  line(\n-000156e0: 7230 6229 2872 3074 290a 2020 6465 6620  r0b)(r0t).  def \n-000156f0: 7230 6d20 2828 7230 2920 2d20 284f 2920  r0m ((r0) - (O) \n-00015700: 2b20 2872 3063 2920 2d20 284f 2929 202f  + (r0c) - (O)) /\n-00015710: 2032 202b 2028 4f29 0a20 2073 7065 6369   2 + (O).  speci\n-00015720: 616c 207c 5c66 6f6f 746e 6f74 6573 697a  al |\\footnotesiz\n-00015730: 655c 7270 7574 2a23 317b 2472 5f30 247d  e\\rput*#1{$r_0$}\n-00015740: 7c28 7230 6d29 0a0a 2020 2054 6865 2073  |(r0m)..   The s\n-00015750: 6563 6f6e 6420 6472 6177 696e 6720 7573  econd drawing us\n-00015760: 6573 2074 6865 2073 616d 6520 7465 6368  es the same tech\n-00015770: 6e69 7175 6573 2e20 204f 6e6c 7920 7468  niques.  Only th\n-00015780: 6520 6d65 7468 6f64 2066 6f72 0a64 7261  e method for.dra\n-00015790: 7769 6e67 2074 6865 2065 6c6c 6970 7469  wing the ellipti\n-000157a0: 6361 6c20 6172 6320 6973 206e 6577 2e20  cal arc is new. \n-000157b0: 2048 6572 6520 6973 2074 6865 2063 6f64   Here is the cod\n-000157c0: 652e 0a20 2064 6566 206d 6964 2028 2870  e..  def mid ((p\n-000157d0: 3030 292d 284f 292b 2870 3130 292d 284f  00)-(O)+(p10)-(O\n-000157e0: 292b 2870 3131 292d 284f 292b 2870 3031  )+(p11)-(O)+(p01\n-000157f0: 292d 284f 2929 2f34 2b28 4f29 0a20 2073  )-(O))/4+(O).  s\n-00015800: 7065 6369 616c 7c5c 7270 7574 2331 7b5c  pecial|\\rput#1{\\\n-00015810: 7073 6375 7374 6f6d 7b0a 2020 2020 5c73  pscustom{.    \\s\n-00015820: 6361 6c65 7b31 2031 2e33 7d0a 2020 2020  cale{1 1.3}.    \n-00015830: 5c70 7361 7263 5b61 7272 6f77 6c65 6e67  \\psarc[arrowleng\n-00015840: 7468 3d2e 355d 7b2d 3e7d 7b2e 3235 7d7b  th=.5]{->}{.25}{\n-00015850: 2d36 307d 7b32 3430 7d7d 7d7c 0a20 2020  -60}{240}}}|.   \n-00015860: 205b 6c61 793d 6f76 6572 5d28 6d69 6429   [lay=over](mid)\n-00015870: 0a57 6520 636f 756c 6420 6861 7665 2073  .We could have s\n-00015880: 7765 7074 2061 2070 6f69 6e74 2074 6f20  wept a point to \n-00015890: 6d61 6b65 2074 6865 2061 7263 2077 6974  make the arc wit\n-000158a0: 6820 2773 6b65 7463 6827 2c20 6275 7420  h 'sketch', but \n-000158b0: 7573 696e 6720 610a 2750 5354 7269 636b  using a.'PSTrick\n-000158c0: 7327 2063 7573 746f 6d20 6772 6170 6869  s' custom graphi\n-000158d0: 6320 7761 7320 7369 6d70 6c65 722e 2020  c was simpler.  \n-000158e0: 4167 6169 6e20 7765 2063 6f6d 7075 7465  Again we compute\n-000158f0: 6420 7468 6520 6365 6e74 726f 6964 0a6f  d the centroid.o\n-00015900: 6620 7468 6520 7175 6164 7269 6c61 7465  f the quadrilate\n-00015910: 7261 6c20 6279 2061 7665 7261 6769 6e67  ral by averaging\n-00015920: 2070 6f69 6e74 732e 2020 4e6f 7465 2074   points.  Note t\n-00015930: 6861 7420 7363 616c 696e 6720 696e 0a50  hat scaling in.P\n-00015940: 6f73 7473 6372 6970 7420 6469 7374 6f72  ostscript distor\n-00015950: 7473 2074 6865 2061 7272 6f77 6865 6164  ts the arrowhead\n-00015960: 2c20 6275 7420 696e 2074 6869 7320 6361  , but in this ca\n-00015970: 7365 2074 6865 2064 6973 746f 7274 696f  se the distortio\n-00015980: 6e0a 6163 7475 616c 6c79 206c 6f6f 6b73  n.actually looks\n-00015990: 2062 6574 7465 7220 696e 2074 6865 2070   better in the p\n-000159a0: 726f 6a65 6374 696f 6e20 6f66 2074 6865  rojection of the\n-000159b0: 2073 6c61 6e74 6564 2066 6163 652e 2020   slanted face.  \n-000159c0: 4120 2773 6b65 7463 6827 0a61 7272 6f77  A 'sketch'.arrow\n-000159d0: 6865 6164 2077 6f75 6c64 206e 6f74 2068  head would not h\n-000159e0: 6176 6520 6265 656e 2064 6973 746f 7274  ave been distort\n-000159f0: 6564 2e0a 0a20 2020 5468 6520 636f 6d70  ed...   The comp\n-00015a00: 6c65 7465 2063 6f64 6520 666f 7220 7468  lete code for th\n-00015a10: 6973 2065 7861 6d70 6c65 2c20 7768 6963  is example, whic\n-00015a20: 6820 6472 6177 7320 6569 7468 6572 2066  h draws either f\n-00015a30: 6967 7572 650a 6465 7065 6e64 696e 6720  igure.depending \n-00015a40: 6f6e 2074 6865 2064 6566 696e 6974 696f  on the definitio\n-00015a50: 6e20 6f66 2074 6865 2074 6167 2027 3c6c  n of the tag '<l\n-00015a60: 6162 656c 6564 3e27 2c20 6973 2069 6e63  abeled>', is inc\n-00015a70: 6c75 6465 6420 696e 2074 6865 0a27 736b  luded in the.'sk\n-00015a80: 6574 6368 2720 6469 7374 7269 6275 7469  etch' distributi\n-00015a90: 6f6e 2069 6e20 7468 6520 6669 6c65 2027  on in the file '\n-00015aa0: 7472 756e 6361 7465 6463 6f6e 652e 736b  truncatedcone.sk\n-00015ab0: 272e 0a0a 1f0a 4669 6c65 3a20 736b 6574  '.....File: sket\n-00015ac0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n-00015ad0: 4120 6869 6572 6172 6368 6963 616c 206d  A hierarchical m\n-00015ae0: 6f64 656c 2c20 204e 6578 743a 2043 6176  odel,  Next: Cav\n-00015af0: 6561 7473 2c20 2050 7265 763a 2041 2074  eats,  Prev: A t\n-00015b00: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n-00015b10: 2c20 2055 703a 2042 7569 6c64 696e 6720  ,  Up: Building \n-00015b20: 6120 6472 6177 696e 670a 0a34 2e33 2041  a drawing..4.3 A\n-00015b30: 2068 6965 7261 7263 6869 6361 6c20 6d6f   hierarchical mo\n-00015b40: 6465 6c0a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  del.============\n-00015b50: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a 5768  ============..Wh\n-00015b60: 696c 6520 2773 6b65 7463 6827 2077 6173  ile 'sketch' was\n-00015b70: 206e 6576 6572 206d 6561 6e74 2074 6f20   never meant to \n-00015b80: 6265 2061 2067 656f 6d65 7472 6963 206d  be a geometric m\n-00015b90: 6f64 656c 696e 6720 6c61 6e67 7561 6765  odeling language\n-00015ba0: 2c20 6974 0a63 6f6d 6573 2066 6169 726c  , it.comes fairl\n-00015bb0: 7920 636c 6f73 652e 2020 5468 6520 666f  y close.  The fo\n-00015bc0: 6c6c 6f77 696e 6720 6578 616d 706c 6520  llowing example \n-00015bd0: 7075 7473 2061 6c6c 2077 6520 6861 7665  puts all we have\n-00015be0: 2073 6565 6e20 746f 2077 6f72 6b0a 696e   seen to work.in\n-00015bf0: 2061 2076 6572 7920 7369 6d70 6c65 206d   a very simple m\n-00015c00: 6f64 656c 206f 6620 7468 6520 6875 6d61  odel of the huma\n-00015c10: 6e20 6861 6e64 2e20 2053 7461 7274 2062  n hand.  Start b\n-00015c20: 7920 7377 6565 7069 6e67 2061 206c 696e  y sweeping a lin\n-00015c30: 6520 746f 0a6d 616b 6520 6120 7472 756e  e to.make a trun\n-00015c40: 6361 7465 6420 636f 6e65 2c20 7768 6963  cated cone, whic\n-00015c50: 6820 7769 6c6c 2062 6520 636f 7069 6564  h will be copied\n-00015c60: 206f 7665 7220 616e 6420 6f76 6572 2061   over and over a\n-00015c70: 6761 696e 2074 6f20 6d61 6b65 0a74 6865  gain to make.the\n-00015c80: 2073 6567 6d65 6e74 7320 6f66 2066 696e   segments of fin\n-00015c90: 6765 7273 2e0a 2020 6465 6620 4f20 2830  gers..  def O (0\n-00015ca0: 2c30 2c30 2920 2520 6f72 6967 696e 0a20  ,0,0) % origin. \n-00015cb0: 2064 6566 2049 205b 312c 302c 305d 2064   def I [1,0,0] d\n-00015cc0: 6566 204a 205b 302c 312c 305d 2064 6566  ef J [0,1,0] def\n-00015cd0: 204b 205b 302c 302c 315d 2025 2063 616e   K [0,0,1] % can\n-00015ce0: 6f6e 6963 616c 2075 6e69 7420 7665 6374  onical unit vect\n-00015cf0: 6f72 730a 2020 6465 6620 7365 676d 656e  ors.  def segmen\n-00015d00: 7420 7b0a 2020 2020 6465 6620 6e5f 6661  t {.    def n_fa\n-00015d10: 6365 7320 380a 2020 2020 7377 6565 7020  ces 8.    sweep \n-00015d20: 7b20 6e5f 6661 6365 733c 3e2c 2072 6f74  { n_faces<>, rot\n-00015d30: 6174 6528 3336 3020 2f20 6e5f 6661 6365  ate(360 / n_face\n-00015d40: 732c 205b 4a5d 2920 7d20 0a20 2020 2020  s, [J]) } .     \n-00015d50: 206c 696e 6528 7072 6f78 696d 616c 5f72   line(proximal_r\n-00015d60: 6164 2c20 3029 2864 6973 7461 6c5f 7261  ad, 0)(distal_ra\n-00015d70: 642c 2064 6973 7461 6c5f 6c65 6e29 0a20  d, distal_len). \n-00015d80: 207d 0a49 6e20 6861 6e64 2061 6e61 746f   }.In hand anato\n-00015d90: 6d79 2c20 5f64 6973 7461 6c5f 2069 7320  my, _distal_ is \n-00015da0: 2261 7420 7468 6520 7469 7022 2061 6e64  \"at the tip\" and\n-00015db0: 205f 7072 6f78 696d 616c 5f20 6973 2022   _proximal_ is \"\n-00015dc0: 696e 2074 6865 2061 7265 610a 6f66 2074  in the area.of t\n-00015dd0: 6865 2070 616c 6d2e 2220 2057 6520 6861  he palm.\"  We ha\n-00015de0: 7665 206f 6d69 7474 6564 2061 6c6c 2074  ve omitted all t\n-00015df0: 6865 2073 6361 6c61 7220 636f 6e73 7461  he scalar consta\n-00015e00: 6e74 732e 2020 596f 7520 6361 6e20 6669  nts.  You can fi\n-00015e10: 6e64 0a74 6865 6d20 696e 2027 6861 6e64  nd.them in 'hand\n-00015e20: 2e73 6b27 2c20 7768 6963 6820 6973 2070  .sk', which is p\n-00015e30: 726f 7669 6465 6420 696e 2074 6865 2027  rovided in the '\n-00015e40: 736b 6574 6368 2720 6469 7374 7269 6275  sketch' distribu\n-00015e50: 7469 6f6e 2e0a 0a20 2020 5765 2061 6c73  tion...   We als\n-00015e60: 6f20 6e65 6564 2061 2070 726f 746f 7479  o need a prototy\n-00015e70: 7069 6361 6c20 7370 6865 7265 2074 6f20  pical sphere to \n-00015e80: 7573 6520 666f 7220 7468 6520 6a6f 696e  use for the join\n-00015e90: 7473 2074 6865 6d73 656c 7665 732e 0a20  ts themselves.. \n-00015ea0: 2064 6566 206a 6f69 6e74 5f73 7068 6572   def joint_spher\n-00015eb0: 6520 7b0a 2020 2020 6465 6620 6e5f 6a6f  e {.    def n_jo\n-00015ec0: 696e 745f 6661 6365 7320 380a 2020 2020  int_faces 8.    \n-00015ed0: 7377 6565 7020 5b66 696c 6c63 6f6c 6f72  sweep [fillcolor\n-00015ee0: 3d72 6564 5d20 7b20 6e5f 6a6f 696e 745f  =red] { n_joint_\n-00015ef0: 6661 6365 732c 2072 6f74 6174 6528 3336  faces, rotate(36\n-00015f00: 3020 2f20 6e5f 6a6f 696e 745f 6661 6365  0 / n_joint_face\n-00015f10: 732c 205b 4a5d 2920 7d0a 2020 2020 2020  s, [J]) }.      \n-00015f20: 7377 6565 7020 7b20 6e5f 6a6f 696e 745f  sweep { n_joint_\n-00015f30: 6661 6365 732c 2072 6f74 6174 6528 3138  faces, rotate(18\n-00015f40: 3020 2f20 6e5f 6a6f 696e 745f 6661 6365  0 / n_joint_face\n-00015f50: 7329 207d 200a 2020 2020 2020 2020 2830  s) } .        (0\n-00015f60: 2c20 2d6a 6f69 6e74 5f72 6164 290a 2020  , -joint_rad).  \n-00015f70: 7d0a 0a20 2020 5765 276c 6c20 6e6f 7720  }..   We'll now \n-00015f80: 6465 7369 676e 2074 6865 2069 6e64 6578  design the index\n-00015f90: 2066 696e 6765 7220 286e 756d 6265 7220   finger (number \n-00015fa0: 3120 696e 206f 7572 206e 6f74 6174 696f  1 in our notatio\n-00015fb0: 6e61 6c0a 636f 6e76 656e 7469 6f6e 3b20  nal.convention; \n-00015fc0: 6669 6e67 6572 2030 2069 7320 7468 6520  finger 0 is the \n-00015fd0: 7468 756d 6229 2e20 2054 6865 2064 6973  thumb).  The dis\n-00015fe0: 7461 6c20 726f 7461 7469 6f6e 2066 6f72  tal rotation for\n-00015ff0: 2074 6865 2066 696e 6765 720a 6170 706c   the finger.appl\n-00016000: 6965 7320 6f6e 6c79 2074 6f20 7468 6520  ies only to the \n-00016010: 7469 702c 2073 6f20 7765 2064 6566 696e  tip, so we defin\n-00016020: 6520 7468 6520 666f 6c6c 6f77 696e 672e  e the following.\n-00016030: 0a20 2064 6566 2064 6973 7461 6c5f 3120  .  def distal_1 \n-00016040: 7b0a 2020 2020 7075 7420 7b20 7472 616e  {.    put { tran\n-00016050: 736c 6174 6528 6a6f 696e 745f 6761 7020  slate(joint_gap \n-00016060: 2a20 6a6f 696e 745f 7261 6420 2a20 5b4a  * joint_rad * [J\n-00016070: 5d29 200a 2020 2020 2020 2020 2020 7468  ]) .          th\n-00016080: 656e 2072 6f74 6174 6528 6469 7374 616c  en rotate(distal\n-00016090: 5f31 5f72 6f74 2c20 5b49 5d29 200a 2020  _1_rot, [I]) .  \n-000160a0: 2020 2020 2020 2020 7468 656e 2074 7261          then tra\n-000160b0: 6e73 6c61 7465 2828 6469 7374 616c 5f6c  nslate((distal_l\n-000160c0: 656e 202b 206a 6f69 6e74 5f67 6170 202a  en + joint_gap *\n-000160d0: 206a 6f69 6e74 5f72 6164 2920 2a20 5b4a   joint_rad) * [J\n-000160e0: 5d29 207d 0a20 2020 2020 207b 7365 676d  ]) }.      {segm\n-000160f0: 656e 747d 0a20 2020 2070 7574 207b 2072  ent}.    put { r\n-00016100: 6f74 6174 6528 6469 7374 616c 5f31 5f72  otate(distal_1_r\n-00016110: 6f74 202f 2032 2c20 5b49 5d29 0a20 2020  ot / 2, [I]).   \n-00016120: 2020 2020 2020 2074 6865 6e20 7472 616e         then tran\n-00016130: 736c 6174 6528 2864 6973 7461 6c5f 6c65  slate((distal_le\n-00016140: 6e20 2b20 6a6f 696e 745f 6761 7020 2a20  n + joint_gap * \n-00016150: 6a6f 696e 745f 7261 6429 202a 205b 4a5d  joint_rad) * [J]\n-00016160: 2920 7d20 0a20 2020 2020 207b 6a6f 696e  ) } .      {join\n-00016170: 745f 7370 6865 7265 7d0a 2020 2020 7075  t_sphere}.    pu\n-00016180: 7420 7b20 7363 616c 6528 205b 4a5d 202b  t { scale( [J] +\n-00016190: 2070 726f 7869 6d61 6c5f 6469 7374 616c   proximal_distal\n-000161a0: 5f72 6174 696f 202a 2028 5b49 5d2b 5b4b  _ratio * ([I]+[K\n-000161b0: 5d29 2029 207d 0a20 2020 2020 207b 7365  ]) ) }.      {se\n-000161c0: 676d 656e 747d 0a20 207d 2020 0a54 6865  gment}.  }  .The\n-000161d0: 2069 6465 6e74 6966 6965 7273 2068 6572   identifiers her\n-000161e0: 6520 6172 6520 666f 7220 7369 7a65 2061  e are for size a\n-000161f0: 6e64 206c 6f63 6174 696f 6e20 636f 6e73  nd location cons\n-00016200: 7461 6e74 732e 2020 5468 6520 6578 6365  tants.  The exce\n-00016210: 7074 696f 6e0a 6973 2027 6469 7374 616c  ption.is 'distal\n-00016220: 5f72 6f74 5f31 272e 2020 5468 6973 2072  _rot_1'.  This r\n-00016230: 6f74 6174 696f 6e20 7061 7261 6d65 7465  otation paramete\n-00016240: 7220 6d6f 6465 6c73 2074 6865 2066 6c65  r models the fle\n-00016250: 7869 6e67 206f 6620 7468 650a 6669 6e67  xing of the.fing\n-00016260: 6572 2074 6970 2e20 2054 6865 2066 6972  er tip.  The fir\n-00016270: 7374 2027 7075 7427 206d 616b 6573 2061  st 'put' makes a\n-00016280: 2063 6f70 7920 6f66 2074 6865 2066 696e   copy of the fin\n-00016290: 6765 7220 7365 676d 656e 7420 7468 6174  ger segment that\n-000162a0: 2069 730a 7472 616e 736c 6174 6564 2075   is.translated u\n-000162b0: 7077 6172 6420 6a75 7374 2066 6172 2065  pward just far e\n-000162c0: 6e6f 7567 6820 746f 206d 616b 6520 726f  nough to make ro\n-000162d0: 6f6d 2066 6f72 2074 6865 2073 7068 6572  om for the spher\n-000162e0: 6963 616c 206a 6f69 6e74 2e0a 5468 656e  ical joint..Then\n-000162f0: 2069 7420 6170 706c 6965 7320 7468 6520   it applies the \n-00016300: 6469 7374 616c 2072 6f74 6174 696f 6e2e  distal rotation.\n-00016310: 2020 4669 6e61 6c6c 7920 6974 2074 7261    Finally it tra\n-00016320: 6e73 6c61 7465 7320 7468 6520 7768 6f6c  nslates the whol\n-00016330: 650a 6173 7365 6d62 6c79 2075 7077 6172  e.assembly upwar\n-00016340: 6420 6167 6169 6e20 746f 206d 616b 6520  d again to make \n-00016350: 726f 6f6d 2066 6f72 2074 6865 206d 6964  room for the mid\n-00016360: 646c 6520 7068 6c61 6e67 6573 2028 7468  dle phlanges (th\n-00016370: 6520 6e65 7874 0a62 6f6e 6520 746f 7761  e next.bone towa\n-00016380: 7264 2074 6865 2070 616c 6d29 2e20 2054  rd the palm).  T\n-00016390: 6865 2073 6563 6f6e 6420 2770 7574 2720  he second 'put' \n-000163a0: 706f 7369 7469 6f6e 7320 7468 6520 7370  positions the sp\n-000163b0: 6865 7265 2e20 2054 6865 7265 2069 730a  here.  There is.\n-000163c0: 6120 726f 7461 7469 6f6e 2074 6f20 706c  a rotation to pl\n-000163d0: 6163 6520 7468 6520 6772 6964 206f 6e20  ace the grid on \n-000163e0: 7468 6520 7370 6865 7265 2073 7572 6661  the sphere surfa\n-000163f0: 6365 2061 7420 616e 206e 6963 6520 616e  ce at an nice an\n-00016400: 676c 652c 0a74 6865 6e20 6120 7472 616e  gle,.then a tran\n-00016410: 736c 6174 696f 6e20 746f 2074 6865 2062  slation to the b\n-00016420: 6173 6520 6f66 2074 6865 2064 6973 7461  ase of the dista\n-00016430: 6c20 7068 6c61 6e67 6573 2c20 7768 6963  l phlanges, whic\n-00016440: 6820 6973 2061 6c73 6f0a 6365 6e74 6572  h is also.center\n-00016450: 206f 6620 6974 7320 726f 7461 7469 6f6e   of its rotation\n-00016460: 2e20 2046 696e 616c 6c79 2c20 7468 6520  .  Finally, the \n-00016470: 6c61 7374 2027 7075 7427 2070 6f73 6974  last 'put' posit\n-00016480: 696f 6e73 2074 6865 206d 6964 646c 650a  ions the middle.\n-00016490: 7365 676d 656e 7420 6974 7365 6c66 2e0a  segment itself..\n-000164a0: 0a20 2020 5468 6520 6d69 6464 6c65 206a  .   The middle j\n-000164b0: 6f69 6e74 2069 7320 7468 6520 6e65 7874  oint is the next\n-000164c0: 206f 6e65 2064 6f77 6e2c 2077 6974 6820   one down, with \n-000164d0: 726f 7461 7469 6f6e 2061 6e67 6c65 0a27  rotation angle.'\n-000164e0: 6d69 6464 6c65 5f72 6f74 5f31 272e 2020  middle_rot_1'.  \n-000164f0: 5768 656e 2074 6869 7320 616e 676c 6520  When this angle \n-00016500: 6368 616e 6765 732c 2077 6520 6e65 6564  changes, we need\n-00016510: 2061 6c6c 2074 6865 206f 626a 6563 7473   all the objects\n-00016520: 2069 6e0a 2764 6973 7461 6c5f 3127 2074   in.'distal_1' t\n-00016530: 6f20 726f 7461 7465 2061 7320 6120 756e  o rotate as a un\n-00016540: 6974 2e20 2054 6869 7320 6973 2074 6865  it.  This is the\n-00016550: 2072 6561 736f 6e69 6e67 2062 6568 696e   reasoning behin\n-00016560: 6420 7468 6520 6e65 7874 0a64 6566 696e  d the next.defin\n-00016570: 6974 696f 6e2e 0a20 2064 6566 2066 696e  ition..  def fin\n-00016580: 6765 725f 3120 7b0a 2020 2020 7075 7420  ger_1 {.    put \n-00016590: 7b20 7472 616e 736c 6174 6528 6a6f 696e  { translate(join\n-000165a0: 745f 6761 7020 2a20 6a6f 696e 745f 7261  t_gap * joint_ra\n-000165b0: 6420 2a20 5b4a 5d29 0a20 2020 2020 2020  d * [J]).       \n-000165c0: 2020 2074 6865 6e20 726f 7461 7465 286d     then rotate(m\n-000165d0: 6964 646c 655f 315f 726f 742c 205b 495d  iddle_1_rot, [I]\n-000165e0: 290a 2020 2020 2020 2020 2020 7468 656e  ).          then\n-000165f0: 2074 7261 6e73 6c61 7465 2828 6d69 6464   translate((midd\n-00016600: 6c65 5f72 6174 696f 202a 2064 6973 7461  le_ratio * dista\n-00016610: 6c5f 6c65 6e20 2b20 0a20 2020 2020 2020  l_len + .       \n+00011560: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a  ---------------.\n+00011570: 7363 616c 6172 2020 2020 2020 2749 4427  scalar      'ID'\n+00011580: 0a70 6f69 6e74 2020 2020 2020 2027 2849  .point       '(I\n+00011590: 4429 270a 7665 6374 6f72 2020 2020 2020  D)'.vector      \n+000115a0: 275b 4944 5d27 0a74 7261 6e73 666f 726d  '[ID]'.transform\n+000115b0: 2020 2027 5b5b 4944 5d5d 270a 6472 6177     '[[ID]]'.draw\n+000115c0: 6162 6c65 2020 2020 277b 4944 7d27 0a6f  able    '{ID}'.o\n+000115d0: 7074 696f 6e73 2020 2020 2027 5b49 445d  ptions     '[ID]\n+000115e0: 2720 6f72 2027 5b49 4431 2c2e 2e2e 2c49  ' or '[ID1,...,I\n+000115f0: 444e 5d27 0a74 6167 2020 2020 2020 2020  DN]'.tag        \n+00011600: 2027 3c49 443e 270a 0a4e 6f74 6520 7468   '<ID>'..Note th\n+00011610: 6174 2073 7175 6172 6520 6272 6163 6b65  at square bracke\n+00011620: 7473 2027 5b20 5d27 2061 7265 2075 7365  ts '[ ]' are use\n+00011630: 6420 626f 7468 2066 6f72 2076 6563 746f  d both for vecto\n+00011640: 7220 616e 6420 666f 7220 6f70 7469 6f6e  r and for option\n+00011650: 730a 7265 6665 7265 6e63 6573 2e20 2044  s.references.  D\n+00011660: 6574 6169 6c73 206f 6620 2773 6b65 7463  etails of 'sketc\n+00011670: 6827 2073 796e 7461 7820 6d61 6b65 2069  h' syntax make i\n+00011680: 7420 696d 706f 7373 6962 6c65 2066 6f72  t impossible for\n+00011690: 2074 6865 7365 2074 776f 0a72 6566 6572   these two.refer\n+000116a0: 656e 6365 2074 7970 6573 2074 6f20 6265  ence types to be\n+000116b0: 2063 6f6e 6675 7365 642e 2020 5468 6520   confused.  The \n+000116c0: 7370 6563 6961 6c20 6d75 6c74 6970 6c65  special multiple\n+000116d0: 2072 6566 6572 656e 6365 0a27 5b49 4431   reference.'[ID1\n+000116e0: 2c49 4432 2c2e 2e2e 2c49 444e 5d27 2061  ,ID2,...,IDN]' a\n+000116f0: 6374 7320 6173 2069 6620 7468 6520 7265  cts as if the re\n+00011700: 7370 6563 7469 7665 206c 6973 7473 206f  spective lists o\n+00011710: 6620 6f70 7469 6f6e 7320 7765 7265 0a63  f options were.c\n+00011720: 6f6e 6361 7465 6e61 7465 642e 0a0a 1f0a  oncatenated.....\n+00011730: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n+00011740: 6f2c 2020 4e6f 6465 3a20 476c 6f62 616c  o,  Node: Global\n+00011750: 2065 6e76 6972 6f6e 6d65 6e74 2c20 2050   environment,  P\n+00011760: 7265 763a 2044 6566 696e 6974 696f 6e73  rev: Definitions\n+00011770: 2c20 2055 703a 2049 6e70 7574 206c 616e  ,  Up: Input lan\n+00011780: 6775 6167 650a 0a33 2e34 2047 6c6f 6261  guage..3.4 Globa\n+00011790: 6c20 656e 7669 726f 6e6d 656e 740a 3d3d  l environment.==\n+000117a0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n+000117b0: 3d3d 3d3d 0a0a 416e 206f 7074 696f 6e61  ====..An optiona\n+000117c0: 6c20 676c 6f62 616c 2065 6e76 6972 6f6e  l global environ\n+000117d0: 6d65 6e74 2062 6c6f 636b 2070 726f 7669  ment block provi\n+000117e0: 6465 7320 6120 6665 7720 7761 7973 2074  des a few ways t\n+000117f0: 6f20 6166 6665 6374 2074 6865 0a65 6e74  o affect the.ent\n+00011800: 6972 6520 7363 656e 652e 2020 5468 6520  ire scene.  The \n+00011810: 626c 6f63 6b20 6d75 7374 2061 7070 6561  block must appea\n+00011820: 7220 6173 2074 6865 206c 6173 7420 7465  r as the last te\n+00011830: 7874 2069 6e20 7468 6520 2773 6b65 7463  xt in the 'sketc\n+00011840: 6827 0a69 6e70 7574 2066 696c 652e 2020  h'.input file.  \n+00011850: 4974 206d 6179 2069 6e63 6c75 6465 2064  It may include d\n+00011860: 6566 696e 6974 696f 6e73 2c20 6275 7420  efinitions, but \n+00011870: 6e6f 7465 2074 6861 7420 7072 6576 696f  note that previo\n+00011880: 7573 0a64 6566 696e 6974 696f 6e73 2061  us.definitions a\n+00011890: 7420 7468 6520 746f 7020 6c65 7665 6c20  t the top level \n+000118a0: 286e 6f74 206e 6573 7465 6420 696e 7369  (not nested insi\n+000118b0: 6465 2062 6c6f 636b 7329 2061 7265 2061  de blocks) are a\n+000118c0: 6c73 6f0a 6176 6169 6c61 626c 652e 0a0a  lso.available...\n+000118d0: 2a53 796e 7461 783a 2a0a 2020 2020 2067  *Syntax:*.     g\n+000118e0: 6c6f 6261 6c20 7b20 454e 5649 524f 4e4d  lobal { ENVIRONM\n+000118f0: 454e 545f 5345 5454 494e 4753 207d 0a54  ENT_SETTINGS }.T\n+00011900: 6865 2063 6f6e 7465 6e74 7320 6f66 2045  he contents of E\n+00011910: 4e56 4952 4f4e 4d45 4e54 5f53 4554 5449  NVIRONMENT_SETTI\n+00011920: 4e47 5320 6172 6520 6469 7363 7573 7365  NGS are discusse\n+00011930: 6420 696e 2074 6865 2073 6563 7469 6f6e  d in the section\n+00011940: 7320 7468 6174 0a66 6f6c 6c6f 772e 0a0a  s that.follow...\n+00011950: 2a20 4d65 6e75 3a0a 0a2a 2047 6c6f 6261  * Menu:..* Globa\n+00011960: 6c20 6f70 7469 6f6e 733a 3a20 2020 2020  l options::     \n+00011970: 2020 2020 2020 2020 2041 7474 7269 6275           Attribu\n+00011980: 7465 7320 6f66 2074 6865 2065 6e74 6972  tes of the entir\n+00011990: 6520 6472 6177 696e 672e 0a2a 2043 616d  e drawing..* Cam\n+000119a0: 6572 613a 3a20 2020 2020 2020 2020 2020  era::           \n+000119b0: 2020 2020 2020 2020 2020 2041 2066 696e             A fin\n+000119c0: 616c 2063 616d 6572 6120 7472 616e 7366  al camera transf\n+000119d0: 6f72 6d61 7469 6f6e 206f 6620 7468 6520  ormation of the \n+000119e0: 7363 656e 652e 0a2a 2050 6963 7475 7265  scene..* Picture\n+000119f0: 2062 6f78 3a3a 2020 2020 2020 2020 2020   box::          \n+00011a00: 2020 2020 2020 2053 6574 7469 6e67 2074         Setting t\n+00011a10: 6865 2062 6f75 6e64 696e 6720 626f 7820  he bounding box \n+00011a20: 616e 6420 3264 2063 6c69 7070 696e 672e  and 2d clipping.\n+00011a30: 0a2a 2046 7261 6d65 3a3a 2020 2020 2020  .* Frame::      \n+00011a40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00011a50: 2041 6464 696e 6720 6120 626f 7820 6172   Adding a box ar\n+00011a60: 6f75 6e64 2074 6865 2064 7261 7769 6e67  ound the drawing\n+00011a70: 2e0a 2a20 4c61 6e67 7561 6765 3a3a 2020  ..* Language::  \n+00011a80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00011a90: 2020 5365 7474 696e 6720 7468 6520 6f75    Setting the ou\n+00011aa0: 7470 7574 206c 616e 6775 6167 652e 0a0a  tput language...\n+00011ab0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n+00011ac0: 6e66 6f2c 2020 4e6f 6465 3a20 476c 6f62  nfo,  Node: Glob\n+00011ad0: 616c 206f 7074 696f 6e73 2c20 204e 6578  al options,  Nex\n+00011ae0: 743a 2043 616d 6572 612c 2020 5072 6576  t: Camera,  Prev\n+00011af0: 3a20 476c 6f62 616c 2065 6e76 6972 6f6e  : Global environ\n+00011b00: 6d65 6e74 2c20 2055 703a 2047 6c6f 6261  ment,  Up: Globa\n+00011b10: 6c20 656e 7669 726f 6e6d 656e 740a 0a33  l environment..3\n+00011b20: 2e34 2e31 2047 6c6f 6261 6c20 6f70 7469  .4.1 Global opti\n+00011b30: 6f6e 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ons.------------\n+00011b40: 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461  --------..*Synta\n+00011b50: 783a 2a0a 2020 2020 2073 6574 205b 204f  x:*.     set [ O\n+00011b60: 5054 494f 4e53 205d 0a54 6865 2063 6f6e  PTIONS ].The con\n+00011b70: 7465 6e74 7320 6f66 204f 5054 494f 4e53  tents of OPTIONS\n+00011b80: 2c20 6578 6365 7074 2066 6f72 2027 736b  , except for 'sk\n+00011b90: 6574 6368 2720 696e 7465 726e 616c 206f  etch' internal o\n+00011ba0: 7074 696f 6e73 2c20 6172 650a 636f 7069  ptions, are.copi\n+00011bb0: 6564 2061 732d 6973 2074 6f20 6120 5c70  ed as-is to a \\p\n+00011bc0: 7373 6574 2074 6861 7420 6170 7065 6172  sset that appear\n+00011bd0: 7320 6265 666f 7265 2061 6e79 7468 696e  s before anythin\n+00011be0: 6720 656c 7365 2069 6e20 7468 6520 6f75  g else in the ou\n+00011bf0: 7470 7574 0a66 696c 652e 2020 5468 6973  tput.file.  This\n+00011c00: 2069 7320 6120 676f 6f64 2070 6c61 6365   is a good place\n+00011c10: 2074 6f20 7365 7420 2775 6e69 7427 2c20   to set 'unit', \n+00011c20: 6120 6465 6661 756c 7420 276c 696e 6577  a default 'linew\n+00011c30: 6964 7468 272c 2065 7463 2e0a 0a20 2020  idth', etc...   \n+00011c40: 496e 7465 726e 616c 206f 7074 696f 6e73  Internal options\n+00011c50: 2077 6f72 6b20 6f6e 2061 6c6c 206f 626a   work on all obj\n+00011c60: 6563 7473 2077 6865 7265 2074 6865 7920  ects where they \n+00011c70: 6d61 6b65 2073 656e 7365 2e20 2054 6869  make sense.  Thi\n+00011c80: 730a 696e 636c 7564 6573 2027 6375 6c6c  s.includes 'cull\n+00011c90: 2720 616e 6420 2773 706c 6974 2720 2862  ' and 'split' (b\n+00011ca0: 7574 206e 6f74 2027 6c61 7927 292e 2020  ut not 'lay').  \n+00011cb0: 2a4e 6f74 6520 496e 7465 726e 616c 206f  *Note Internal o\n+00011cc0: 7074 696f 6e73 3a3a 2e0a 0a1f 0a46 696c  ptions::.....Fil\n+00011cd0: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n+00011ce0: 204e 6f64 653a 2043 616d 6572 612c 2020   Node: Camera,  \n+00011cf0: 4e65 7874 3a20 5069 6374 7572 6520 626f  Next: Picture bo\n+00011d00: 782c 2020 5072 6576 3a20 476c 6f62 616c  x,  Prev: Global\n+00011d10: 206f 7074 696f 6e73 2c20 2055 703a 2047   options,  Up: G\n+00011d20: 6c6f 6261 6c20 656e 7669 726f 6e6d 656e  lobal environmen\n+00011d30: 740a 0a33 2e34 2e32 2043 616d 6572 610a  t..3.4.2 Camera.\n+00011d40: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53  ------------..*S\n+00011d50: 796e 7461 783a 2a0a 2020 2020 2063 616d  yntax:*.     cam\n+00011d60: 6572 6120 5452 414e 5346 4f52 4d5f 4558  era TRANSFORM_EX\n+00011d70: 5052 4553 5349 4f4e 0a20 2020 5468 6520  PRESSION.   The \n+00011d80: 5452 414e 5346 4f52 4d5f 4558 5052 4553  TRANSFORM_EXPRES\n+00011d90: 5349 4f4e 2069 7320 6170 706c 6965 6420  SION is applied \n+00011da0: 6166 7465 7220 616c 6c20 6f74 6865 7220  after all other \n+00011db0: 7472 616e 7366 6f72 6d61 7469 6f6e 730a  transformations.\n+00011dc0: 6f66 2074 6865 2073 6365 6e65 2e20 2054  of the scene.  T\n+00011dd0: 6869 7320 6973 2063 7572 7265 6e74 6c79  his is currently\n+00011de0: 206f 6e6c 7920 7573 6566 756c 2066 6f72   only useful for\n+00011df0: 2074 7261 6e73 666f 726d 696e 6720 7468   transforming th\n+00011e00: 650a 626f 756e 6469 6e67 2062 6f78 2e20  e.bounding box. \n+00011e10: 202a 4e6f 7465 2050 6963 7475 7265 2062   *Note Picture b\n+00011e20: 6f78 3a3a 2e20 2049 7420 7769 6c6c 2070  ox::.  It will p\n+00011e30: 6c61 7920 6120 726f 6c65 2069 6e20 616e  lay a role in an\n+00011e40: 7920 6675 7475 7265 0a69 6d70 6c65 6d65  y future.impleme\n+00011e50: 6e74 6174 696f 6e20 6f66 2063 6c69 7070  ntation of clipp\n+00011e60: 696e 672e 0a0a 1f0a 4669 6c65 3a20 736b  ing.....File: sk\n+00011e70: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n+00011e80: 3a20 5069 6374 7572 6520 626f 782c 2020  : Picture box,  \n+00011e90: 4e65 7874 3a20 4672 616d 652c 2020 5072  Next: Frame,  Pr\n+00011ea0: 6576 3a20 4361 6d65 7261 2c20 2055 703a  ev: Camera,  Up:\n+00011eb0: 2047 6c6f 6261 6c20 656e 7669 726f 6e6d   Global environm\n+00011ec0: 656e 740a 0a33 2e34 2e33 2050 6963 7475  ent..3.4.3 Pictu\n+00011ed0: 7265 2062 6f78 0a2d 2d2d 2d2d 2d2d 2d2d  re box.---------\n+00011ee0: 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461  --------..*Synta\n+00011ef0: 783a 2a0a 2020 2020 2070 6963 7475 7265  x:*.     picture\n+00011f00: 626f 785b 4241 5345 4c49 4e45 5d0a 2020  box[BASELINE].  \n+00011f10: 2020 2070 6963 7475 7265 626f 785b 4241     picturebox[BA\n+00011f20: 5345 4c49 4e45 5d20 2850 3129 2850 3229  SELINE] (P1)(P2)\n+00011f30: 0a54 6865 2066 6972 7374 2066 6f72 6d20  .The first form \n+00011f40: 6f66 2027 7069 6374 7572 6562 6f78 2720  of 'picturebox' \n+00011f50: 6361 7573 6573 2061 2073 6361 6c61 7220  causes a scalar \n+00011f60: 4241 5345 4c49 4e45 2066 7261 6374 696f  BASELINE fractio\n+00011f70: 6e20 746f 2062 650a 656d 6974 7465 6420  n to be.emitted \n+00011f80: 696e 2074 6865 2027 7073 7069 6374 7572  in the 'pspictur\n+00011f90: 6527 2065 6e76 6972 6f6e 6d65 6e74 206f  e' environment o\n+00011fa0: 6620 7468 6520 6f75 7470 7574 2e20 2053  f the output.  S\n+00011fb0: 6565 2027 5053 5472 6963 6b73 270a 646f  ee 'PSTricks'.do\n+00011fc0: 6375 6d65 6e74 6174 696f 6e20 666f 7220  cumentation for \n+00011fd0: 2770 7370 6963 7475 7265 272e 0a0a 2020  'pspicture'...  \n+00011fe0: 2049 6e20 7468 6520 7365 636f 6e64 2066   In the second f\n+00011ff0: 6f72 6d2c 2074 6865 2042 4153 454c 494e  orm, the BASELIN\n+00012000: 4520 6672 6163 7469 6f6e 2069 7320 6f70  E fraction is op\n+00012010: 7469 6f6e 616c 2c20 616e 6420 7468 6520  tional, and the \n+00012020: 7477 6f0a 706f 696e 7473 2074 6861 7420  two.points that \n+00012030: 666f 6c6c 6f77 2064 6566 696e 6520 7468  follow define th\n+00012040: 6520 6469 6167 6f6e 616c 206f 6620 6120  e diagonal of a \n+00012050: 7468 7265 652d 6469 6d65 6e73 696f 6e61  three-dimensiona\n+00012060: 6c20 626f 756e 6469 6e67 0a62 6f78 2066  l bounding.box f\n+00012070: 6f72 2074 6865 2063 6f6d 706c 6574 6564  or the completed\n+00012080: 2073 6365 6e65 2e20 2054 6865 2070 6172   scene.  The par\n+00012090: 616c 6c65 6c20 7072 6f6a 6563 7469 6f6e  allel projection\n+000120a0: 206f 6620 7468 6520 626f 756e 6469 6e67   of the bounding\n+000120b0: 0a62 6f78 2064 6574 6572 6d69 6e65 7320  .box determines \n+000120c0: 7468 6520 636f 726e 6572 7320 6f66 2074  the corners of t\n+000120d0: 6865 2064 7261 7769 6e67 2773 2027 7073  he drawing's 'ps\n+000120e0: 7069 6374 7572 652a 2720 656e 7669 726f  picture*' enviro\n+000120f0: 6e6d 656e 742c 0a77 6869 6368 2069 7320  nment,.which is \n+00012100: 7573 6564 2069 6e20 706c 6163 6520 6f66  used in place of\n+00012110: 2027 7073 7069 6374 7572 6527 2e20 2054   'pspicture'.  T\n+00012120: 6869 7320 6361 7573 6573 2050 6f73 7453  his causes PostS\n+00012130: 6372 6970 7420 746f 2063 6c69 700a 7468  cript to clip.th\n+00012140: 6520 6669 6e61 6c20 6472 6177 696e 6720  e final drawing \n+00012150: 746f 2074 6865 2062 6f75 6e64 696e 6720  to the bounding \n+00012160: 626f 7820 696e 2032 642e 2020 4966 2074  box in 2d.  If t\n+00012170: 6865 7265 2069 7320 6120 2763 616d 6572  here is a 'camer\n+00012180: 6127 0a73 7065 6369 6669 6564 2c20 7468  a'.specified, th\n+00012190: 6520 6361 6d65 7261 2074 7261 6e66 6f72  e camera tranfor\n+000121a0: 6d61 7469 6f6e 2069 7320 6170 706c 6965  mation is applie\n+000121b0: 6420 746f 2074 6865 2062 6f75 6e64 696e  d to the boundin\n+000121c0: 6720 626f 782c 2061 6e64 0a74 6865 2027  g box, and.the '\n+000121d0: 7073 7069 6374 7572 6527 2069 7320 7365  pspicture' is se\n+000121e0: 7420 6a75 7374 206c 6172 6765 2065 6e6f  t just large eno\n+000121f0: 7567 6820 746f 2069 6e63 6c75 6465 2074  ugh to include t\n+00012200: 6865 2074 7261 6e73 666f 726d 6564 2062  he transformed b\n+00012210: 6f78 2e0a 0a20 2020 5768 656e 206e 6f20  ox...   When no \n+00012220: 626f 756e 6469 6e67 2062 6f78 2069 7320  bounding box is \n+00012230: 6769 7665 6e2c 2027 736b 6574 6368 2720  given, 'sketch' \n+00012240: 636f 6d70 7574 6573 206f 6e65 2061 7574  computes one aut\n+00012250: 6f6d 6174 6963 616c 6c79 2e0a 0a1f 0a46  omatically.....F\n+00012260: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n+00012270: 2c20 204e 6f64 653a 2046 7261 6d65 2c20  ,  Node: Frame, \n+00012280: 204e 6578 743a 204c 616e 6775 6167 652c   Next: Language,\n+00012290: 2020 5072 6576 3a20 5069 6374 7572 6520    Prev: Picture \n+000122a0: 626f 782c 2020 5570 3a20 476c 6f62 616c  box,  Up: Global\n+000122b0: 2065 6e76 6972 6f6e 6d65 6e74 0a0a 332e   environment..3.\n+000122c0: 342e 3420 4672 616d 650a 2d2d 2d2d 2d2d  4.4 Frame.------\n+000122d0: 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a  -----..*Syntax:*\n+000122e0: 0a20 2020 2020 6672 616d 6520 5b4f 5054  .     frame [OPT\n+000122f0: 494f 4e53 5d0a 4361 7573 6573 2061 205c  IONS].Causes a \\\n+00012300: 7073 6672 616d 6562 6f78 2074 6f20 7375  psframebox to su\n+00012310: 7272 6f75 6e64 2074 6865 2027 7073 7069  rround the 'pspi\n+00012320: 6374 7572 6527 2065 6e76 6972 6f6e 6d65  cture' environme\n+00012330: 6e74 2069 6e20 7468 650a 6f75 7470 7574  nt in the.output\n+00012340: 2e20 2049 6620 4f50 5449 4f4e 5320 6172  .  If OPTIONS ar\n+00012350: 6520 7072 6573 656e 742c 2074 6865 7920  e present, they \n+00012360: 6172 6520 636f 7069 6564 2061 732d 6973  are copied as-is\n+00012370: 2e20 204e 6f72 6d61 6c6c 7920 6f6e 650a  .  Normally one.\n+00012380: 776f 756c 6420 7761 6e74 2074 6f20 7365  would want to se\n+00012390: 7420 276c 696e 6577 6964 7468 272c 2027  t 'linewidth', '\n+000123a0: 6c69 6e65 7374 796c 6527 2c20 276c 696e  linestyle', 'lin\n+000123b0: 6563 6f6c 6f72 272c 2065 7463 2e20 2049  ecolor', etc.  I\n+000123c0: 660a 6f6d 6974 7465 642c 2074 6865 6e20  f.omitted, then \n+000123d0: 2766 7261 6d65 7365 703d 3070 7427 2069  'framesep=0pt' i\n+000123e0: 7320 6164 6465 6420 736f 2074 6861 7420  s added so that \n+000123f0: 7468 6520 6672 616d 6520 7469 6768 746c  the frame tightl\n+00012400: 7920 6875 6773 2074 6865 0a27 7073 7069  y hugs the.'pspi\n+00012410: 6374 7572 6527 2e0a 0a1f 0a46 696c 653a  cture'.....File:\n+00012420: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n+00012430: 6f64 653a 204c 616e 6775 6167 652c 2020  ode: Language,  \n+00012440: 5072 6576 3a20 4672 616d 652c 2020 5570  Prev: Frame,  Up\n+00012450: 3a20 476c 6f62 616c 2065 6e76 6972 6f6e  : Global environ\n+00012460: 6d65 6e74 0a0a 332e 342e 3520 4c61 6e67  ment..3.4.5 Lang\n+00012470: 7561 6765 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d  uage.-----------\n+00012480: 2d2d 2d0a 0a20 2020 2020 6c61 6e67 7561  ---..     langua\n+00012490: 6765 2074 696b 7a0a 2020 2020 206c 616e  ge tikz.     lan\n+000124a0: 6775 6167 6520 7469 6b7a 2c20 636f 6e74  guage tikz, cont\n+000124b0: 6578 740a 2020 2020 206c 616e 6775 6167  ext.     languag\n+000124c0: 6520 7073 7472 6963 6b73 0a20 2020 2020  e pstricks.     \n+000124d0: 6c61 6e67 7561 6765 2070 7374 7269 636b  language pstrick\n+000124e0: 732c 206c 6174 6578 0a53 6574 7320 7468  s, latex.Sets th\n+000124f0: 6520 6f75 7470 7574 206c 616e 6775 6167  e output languag\n+00012500: 6520 6765 6e65 7261 7465 6420 6279 2027  e generated by '\n+00012510: 736b 6574 6368 272e 2020 5468 6520 7365  sketch'.  The se\n+00012520: 7420 6f66 206f 7074 696f 6e73 0a75 6e64  t of options.und\n+00012530: 6572 7374 6f6f 6420 6279 2073 6b65 7463  erstood by sketc\n+00012540: 6820 616c 736f 2063 6861 6e67 6573 2e20  h also changes. \n+00012550: 2046 6f72 2065 7861 6d70 6c65 2c20 7468   For example, th\n+00012560: 6520 2750 5354 7269 636b 7327 206f 7074  e 'PSTricks' opt\n+00012570: 696f 6e0a 276c 696e 6577 6964 7468 2720  ion.'linewidth' \n+00012580: 7769 6c6c 206e 6f74 2062 6520 7072 6f70  will not be prop\n+00012590: 6572 6c79 2068 616e 646c 6564 2069 6620  erly handled if \n+000125a0: 276c 616e 6775 6167 6527 2069 7320 7365  'language' is se\n+000125b0: 7420 746f 2027 7469 6b7a 272e 0a53 696d  t to 'tikz'..Sim\n+000125c0: 696c 6172 6c79 2c20 7468 6520 2754 696b  ilarly, the 'Tik\n+000125d0: 5a27 206f 7074 696f 6e20 276c 696e 6520  Z' option 'line \n+000125e0: 7374 796c 6527 2028 6e6f 7465 2074 6865  style' (note the\n+000125f0: 2073 7061 6365 2920 7769 6c6c 206e 6f74   space) will not\n+00012600: 2062 650a 7072 6f70 6572 6c79 2068 616e   be.properly han\n+00012610: 646c 6564 2069 6620 276c 616e 6775 6167  dled if 'languag\n+00012620: 6527 2069 7320 7365 7420 746f 2027 7073  e' is set to 'ps\n+00012630: 7472 6963 6b73 272e 2020 4966 206e 6f20  tricks'.  If no \n+00012640: 6c61 6e67 7561 6765 2069 730a 7370 6563  language is.spec\n+00012650: 6966 6965 642c 2074 6865 2064 6566 6175  ified, the defau\n+00012660: 6c74 2027 7073 7472 6963 6b73 2720 6973  lt 'pstricks' is\n+00012670: 2075 7365 642e 0a0a 2020 2041 6e20 6f70   used...   An op\n+00012680: 7469 6f6e 616c 2063 6f6d 6d61 2066 6f6c  tional comma fol\n+00012690: 6c6f 7765 6420 6279 2027 6c61 7465 7827  lowed by 'latex'\n+000126a0: 206f 7220 2763 6f6e 7465 7874 2720 7370   or 'context' sp\n+000126b0: 6563 6966 6965 7320 7468 650a 6d61 6372  ecifies the.macr\n+000126c0: 6f20 7061 636b 6167 6520 7468 6174 2074  o package that t\n+000126d0: 6865 206f 7574 7075 7420 7368 6f75 6c64  he output should\n+000126e0: 2061 7373 756d 652e 2020 5468 6973 2061   assume.  This a\n+000126f0: 6666 6563 7473 2074 6865 2027 7069 6374  ffects the 'pict\n+00012700: 7572 6527 0a65 6e76 6972 6f6e 6d65 6e74  ure'.environment\n+00012710: 2063 6f6d 6d61 6e64 7320 656d 6974 7465   commands emitte\n+00012720: 6420 616e 6420 7468 6520 646f 6375 6d65  d and the docume\n+00012730: 6e74 2074 656d 706c 6174 6520 7573 6564  nt template used\n+00012740: 2077 6974 6820 7468 650a 272d 5427 206f   with the.'-T' o\n+00012750: 7074 696f 6e2e 2020 2a4e 6f74 6520 436f  ption.  *Note Co\n+00012760: 6d6d 616e 6420 6c69 6e65 3a3a 2e20 204e  mmand line::.  N\n+00012770: 6f74 6520 7468 6174 2061 7420 7468 6520  ote that at the \n+00012780: 7469 6d65 2074 6869 7320 6d61 6e75 616c  time this manual\n+00012790: 0a77 6173 2067 656e 6572 6174 6564 2c20  .was generated, \n+000127a0: 2750 5354 7269 636b 7327 2077 6173 206e  'PSTricks' was n\n+000127b0: 6f74 2073 7570 706f 7274 6564 2062 7920  ot supported by \n+000127c0: 4c61 5465 5820 6f72 2062 7920 2743 6f6e  LaTeX or by 'Con\n+000127d0: 5465 5874 272e 0a0a 1f0a 4669 6c65 3a20  TeXt'.....File: \n+000127e0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n+000127f0: 6465 3a20 4275 696c 6469 6e67 2061 2064  de: Building a d\n+00012800: 7261 7769 6e67 2c20 204e 6578 743a 2043  rawing,  Next: C\n+00012810: 6f6d 6d61 6e64 206c 696e 652c 2020 5072  ommand line,  Pr\n+00012820: 6576 3a20 496e 7075 7420 6c61 6e67 7561  ev: Input langua\n+00012830: 6765 2c20 2055 703a 2054 6f70 0a0a 3420  ge,  Up: Top..4 \n+00012840: 4275 696c 6469 6e67 2061 2064 7261 7769  Building a drawi\n+00012850: 6e67 0a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  ng.*************\n+00012860: 2a2a 2a2a 2a2a 2a0a 0a53 7563 6365 7373  *******..Success\n+00012870: 6675 6c20 6472 6177 696e 6773 2077 6974  ful drawings wit\n+00012880: 6820 2773 6b65 7463 6827 2061 6e64 2077  h 'sketch' and w\n+00012890: 6974 6820 616e 7920 7363 656e 6520 6465  ith any scene de\n+000128a0: 7363 7269 7074 696f 6e0a 6c61 6e67 7561  scription.langua\n+000128b0: 6765 2072 6571 7569 7265 2074 6861 7420  ge require that \n+000128c0: 7468 6520 7573 6572 2064 6576 656c 6f70  the user develop\n+000128d0: 2061 6e20 6163 6375 7261 7465 206d 656e   an accurate men\n+000128e0: 7461 6c20 7069 6374 7572 6520 6f66 2068  tal picture of h\n+000128f0: 6572 0a63 6f64 6520 616e 6420 6974 7320  er.code and its \n+00012900: 6d65 616e 696e 672e 2020 5468 6973 2069  meaning.  This i\n+00012910: 6d61 6765 2069 7320 6265 7374 2062 7569  mage is best bui\n+00012920: 6c74 2069 6e20 736d 616c 6c20 7069 6563  lt in small piec\n+00012930: 6573 2e0a 5468 6572 6566 6f72 652c 2027  es..Therefore, '\n+00012940: 736b 6574 6368 2720 696e 7075 7473 2061  sketch' inputs a\n+00012950: 7265 2062 6573 7420 6372 6561 7465 6420  re best created \n+00012960: 696e 2073 6d61 6c6c 2069 6e63 7265 6d65  in small increme\n+00012970: 6e74 7320 7769 7468 0a66 7265 7175 656e  nts with.frequen\n+00012980: 7420 7061 7573 6573 2074 6f20 636f 6d70  t pauses to comp\n+00012990: 696c 6520 616e 6420 7669 6577 2074 6865  ile and view the\n+000129a0: 2072 6573 756c 7473 2e20 2043 6172 6566   results.  Caref\n+000129b0: 756c 2063 6f6d 6d65 6e74 7320 696e 0a74  ul comments in.t\n+000129c0: 6865 2069 6e70 7574 206f 6674 656e 2068  he input often h\n+000129d0: 656c 7020 6173 2061 2073 6365 6e65 2067  elp as a scene g\n+000129e0: 726f 7773 2069 6e20 636f 6d70 6c65 7869  rows in complexi\n+000129f0: 7479 2e0a 0a2a 204d 656e 753a 0a0a 2a20  ty...* Menu:..* \n+00012a00: 4f76 6572 7669 6577 3a3a 2020 2020 2020  Overview::      \n+00012a10: 2020 2020 2020 2020 2020 2020 2020 4275                Bu\n+00012a20: 696c 6469 6e67 2061 2073 7562 7374 616e  ilding a substan\n+00012a30: 7469 616c 2064 7261 7769 6e67 2e0a 2a20  tial drawing..* \n+00012a40: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n+00012a50: 696e 673a 3a20 2020 2020 2020 2020 416e  ing::         An\n+00012a60: 2065 7861 6d70 6c65 2077 6974 6820 6669   example with fi\n+00012a70: 6e65 2070 6c61 6365 6d65 6e74 2e0a 2a20  ne placement..* \n+00012a80: 4120 6869 6572 6172 6368 6963 616c 206d  A hierarchical m\n+00012a90: 6f64 656c 3a3a 2020 2020 2020 2020 416e  odel::        An\n+00012aa0: 2065 7861 6d70 6c65 2077 6974 6820 7377   example with sw\n+00012ab0: 6565 7073 2061 6e64 2070 7574 732e 0a2a  eeps and puts..*\n+00012ac0: 2043 6176 6561 7473 3a3a 2020 2020 2020   Caveats::      \n+00012ad0: 2020 2020 2020 2020 2020 2020 2020 2057                 W\n+00012ae0: 6865 7265 2074 726f 7562 6c65 2063 616e  here trouble can\n+00012af0: 206f 6363 7572 2e0a 0a1f 0a46 696c 653a   occur.....File:\n+00012b00: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n+00012b10: 6f64 653a 204f 7665 7276 6965 772c 2020  ode: Overview,  \n+00012b20: 4e65 7874 3a20 4120 7465 6368 6e69 6361  Next: A technica\n+00012b30: 6c20 6472 6177 696e 672c 2020 5072 6576  l drawing,  Prev\n+00012b40: 3a20 4275 696c 6469 6e67 2061 2064 7261  : Building a dra\n+00012b50: 7769 6e67 2c20 2055 703a 2042 7569 6c64  wing,  Up: Build\n+00012b60: 696e 6720 6120 6472 6177 696e 670a 0a34  ing a drawing..4\n+00012b70: 2e31 204f 7665 7276 6965 770a 3d3d 3d3d  .1 Overview.====\n+00012b80: 3d3d 3d3d 3d3d 3d3d 0a0a 4173 2061 6e20  ========..As an \n+00012b90: 6f76 6572 7669 6577 2c20 6c65 7427 7320  overview, let's \n+00012ba0: 6465 7665 6c6f 7020 6120 6469 6167 7261  develop a diagra\n+00012bb0: 6d20 7468 6174 2073 686f 7773 2068 6f77  m that shows how\n+00012bc0: 2061 2070 6572 7370 6563 7469 7665 0a70   a perspective.p\n+00012bd0: 726f 6a65 6374 696f 6e20 7472 616e 7366  rojection transf\n+00012be0: 6f72 6d20 776f 726b 732e 2020 5765 276c  orm works.  We'l\n+00012bf0: 6c20 7374 6172 7420 7769 7468 2074 6865  l start with the\n+00012c00: 2074 7261 6469 7469 6f6e 616c 2072 6566   traditional ref\n+00012c10: 6572 656e 6365 0a6f 626a 6563 7420 7573  erence.object us\n+00012c20: 6564 2069 6e20 636f 6d70 7574 6572 2067  ed in computer g\n+00012c30: 7261 7068 6963 7320 7465 7874 626f 6f6b  raphics textbook\n+00012c40: 732c 2061 2068 6f75 7365 2d73 6861 7065  s, a house-shape\n+00012c50: 6420 7072 6973 6d2e 2020 4265 6769 6e0a  d prism.  Begin.\n+00012c60: 6279 2064 6566 696e 696e 6720 7468 6520  by defining the \n+00012c70: 706f 696e 7473 206f 6620 7468 6520 686f  points of the ho\n+00012c80: 7573 652e 2020 5261 7468 6572 2074 6861  use.  Rather tha\n+00012c90: 6e20 6465 6669 6e69 6e67 2074 6865 2066  n defining the f\n+00012ca0: 6163 6573 206f 660a 7468 6520 686f 7573  aces of.the hous\n+00012cb0: 6520 6173 2070 6f6c 7967 6f6e 7320 616e  e as polygons an\n+00012cc0: 6420 7472 616e 7366 6f72 6d69 6e67 2074  d transforming t\n+00012cd0: 686f 7365 2c20 7765 2061 7265 2067 6f69  hose, we are goi\n+00012ce0: 6e67 2074 6f20 7472 616e 7366 6f72 6d0a  ng to transform.\n+00012cf0: 7468 6520 706f 696e 7473 2074 6865 6d73  the points thems\n+00012d00: 656c 7665 7320 7769 7468 2027 736b 6574  elves with 'sket\n+00012d10: 6368 2720 6172 6974 686d 6574 6963 2073  ch' arithmetic s\n+00012d20: 6f20 7468 6174 2077 6520 6861 7665 206e  o that we have n\n+00012d30: 616d 6573 2066 6f72 0a74 6865 2074 7261  ames for.the tra\n+00012d40: 6e73 666f 726d 6564 2070 6f69 6e74 7320  nsformed points \n+00012d50: 6c61 7465 722e 0a20 2025 2072 6967 6874  later..  % right\n+00012d60: 2073 6964 6520 286f 7574 7369 6465 2074   side (outside t\n+00012d70: 6f20 7269 6768 7429 0a20 2064 6566 2052  o right).  def R\n+00012d80: 3120 2831 2c31 2c31 2920 6465 6620 5232  1 (1,1,1) def R2\n+00012d90: 2028 312c 2d31 2c31 2920 6465 6620 5233   (1,-1,1) def R3\n+00012da0: 2028 312c 2d31 2c2d 3129 2064 6566 2052   (1,-1,-1) def R\n+00012db0: 3420 2831 2c31 2c2d 3129 0a20 2064 6566  4 (1,1,-1).  def\n+00012dc0: 2052 3520 2831 2c31 2e35 2c30 290a 0a20   R5 (1,1.5,0).. \n+00012dd0: 2025 206c 6566 7420 7369 6465 2028 6f75   % left side (ou\n+00012de0: 7473 6964 6520 746f 2072 6967 6874 2d2d  tside to right--\n+00012df0: 6261 636b 7761 7264 290a 2020 6465 6620  backward).  def \n+00012e00: 5720 205b 322c 302c 305d 0a20 2064 6566  W  [2,0,0].  def\n+00012e10: 204c 3120 2852 3129 2d5b 575d 2064 6566   L1 (R1)-[W] def\n+00012e20: 204c 3220 2852 3229 2d5b 575d 2064 6566   L2 (R2)-[W] def\n+00012e30: 204c 3320 2852 3329 2d5b 575d 2064 6566   L3 (R3)-[W] def\n+00012e40: 204c 3420 2852 3429 2d5b 575d 0a20 2064   L4 (R4)-[W].  d\n+00012e50: 6566 204c 3520 2852 3529 2d5b 575d 0a54  ef L5 (R5)-[W].T\n+00012e60: 6f20 6164 6420 6120 646f 6f72 2074 6f20  o add a door to \n+00012e70: 7468 6520 686f 7573 652c 2077 6520 7573  the house, we us\n+00012e80: 6520 6120 706f 6c79 676f 6e20 736c 6967  e a polygon slig\n+00012e90: 6874 6c79 2069 6e20 6672 6f6e 7420 6f66  htly in front of\n+00012ea0: 2074 6865 0a66 6f72 656d 6f73 7420 6661   the.foremost fa\n+00012eb0: 6365 206f 6620 7468 6520 686f 7573 652e  ce of the house.\n+00012ec0: 0a20 2025 2064 6f6f 720a 2020 6465 6620  .  % door.  def \n+00012ed0: 6520 2e30 310a 2020 6465 6620 4431 2028  e .01.  def D1 (\n+00012ee0: 302c 2d31 2c31 2b65 2920 6465 6620 4432  0,-1,1+e) def D2\n+00012ef0: 2028 2e35 2c2d 312c 312b 6529 2064 6566   (.5,-1,1+e) def\n+00012f00: 2044 3320 282e 352c 302c 312b 6529 2064   D3 (.5,0,1+e) d\n+00012f10: 6566 2044 3420 2830 2c30 2c31 2b65 290a  ef D4 (0,0,1+e).\n+00012f20: 4e6f 7720 6c65 7427 7320 6372 6561 7465  Now let's create\n+00012f30: 2061 206e 6577 2073 6574 206f 6620 706f   a new set of po\n+00012f40: 696e 7473 2074 6861 7420 6172 6520 6120  ints that are a \n+00012f50: 746f 2d62 652d 6465 7465 726d 696e 6564  to-be-determined\n+00012f60: 0a74 7261 6e73 666f 726d 206f 6620 7468  .transform of th\n+00012f70: 6520 6f72 6967 696e 616c 732e 0a20 2064  e originals..  d\n+00012f80: 6566 2068 7020 7363 616c 6528 3129 2025  ef hp scale(1) %\n+00012f90: 2068 6f75 7365 2070 6f73 6974 696f 6e65   house positione\n+00012fa0: 720a 2020 6465 6620 7052 3120 5b5b 6870  r.  def pR1 [[hp\n+00012fb0: 5d5d 2a28 5231 2920 6465 6620 7052 3220  ]]*(R1) def pR2 \n+00012fc0: 5b5b 6870 5d5d 2a28 5232 2920 6465 6620  [[hp]]*(R2) def \n+00012fd0: 7052 3320 5b5b 6870 5d5d 2a28 5233 290a  pR3 [[hp]]*(R3).\n+00012fe0: 2020 6465 6620 7052 3420 5b5b 6870 5d5d    def pR4 [[hp]]\n+00012ff0: 2a28 5234 2920 6465 6620 7052 3520 5b5b  *(R4) def pR5 [[\n+00013000: 6870 5d5d 2a28 5235 290a 2020 6465 6620  hp]]*(R5).  def \n+00013010: 704c 3120 5b5b 6870 5d5d 2a28 4c31 2920  pL1 [[hp]]*(L1) \n+00013020: 6465 6620 704c 3220 5b5b 6870 5d5d 2a28  def pL2 [[hp]]*(\n+00013030: 4c32 2920 6465 6620 704c 3320 5b5b 6870  L2) def pL3 [[hp\n+00013040: 5d5d 2a28 4c33 290a 2020 6465 6620 704c  ]]*(L3).  def pL\n+00013050: 3420 5b5b 6870 5d5d 2a28 4c34 2920 6465  4 [[hp]]*(L4) de\n+00013060: 6620 704c 3520 5b5b 6870 5d5d 2a28 4c35  f pL5 [[hp]]*(L5\n+00013070: 290a 2020 6465 6620 7044 3120 5b5b 6870  ).  def pD1 [[hp\n+00013080: 5d5d 2a28 4431 2920 6465 6620 7044 3220  ]]*(D1) def pD2 \n+00013090: 5b5b 6870 5d5d 2a28 4432 2920 6465 6620  [[hp]]*(D2) def \n+000130a0: 7044 3320 5b5b 6870 5d5d 2a28 4433 290a  pD3 [[hp]]*(D3).\n+000130b0: 2020 6465 6620 7044 3420 5b5b 6870 5d5d    def pD4 [[hp]]\n+000130c0: 2a28 4434 2920 0a4e 6f74 6520 7468 6520  *(D4) .Note the \n+000130d0: 7573 6520 6f66 2061 2022 7472 616e 7366  use of a \"transf\n+000130e0: 6f72 6d20 6465 6669 6e69 7469 6f6e 2220  orm definition\" \n+000130f0: 616e 6420 2274 7261 6e73 666f 726d 2072  and \"transform r\n+00013100: 6566 6572 656e 6365 7322 2e0a 4e6f 7720  eferences\"..Now \n+00013110: 6465 6669 6e65 2074 6865 2073 6576 656e  define the seven\n+00013120: 2070 6f6c 7967 6f6e 616c 2066 6163 6573   polygonal faces\n+00013130: 206f 6620 7468 6520 686f 7573 6520 616e   of the house an\n+00013140: 6420 7468 6520 646f 6f72 2075 7369 6e67  d the door using\n+00013150: 2074 6865 0a74 7261 6e73 666f 726d 6564   the.transformed\n+00013160: 2070 6f69 6e74 7320 6173 2076 6572 7469   points as verti\n+00013170: 6365 732e 2020 4265 2063 6172 6566 756c  ces.  Be careful\n+00013180: 2077 6974 6820 7665 7274 6578 206f 7264   with vertex ord\n+00013190: 6572 210a 2020 6465 6620 7267 7420 706f  er!.  def rgt po\n+000131a0: 6c79 676f 6e20 2870 5231 2928 7052 3229  lygon (pR1)(pR2)\n+000131b0: 2870 5233 2928 7052 3429 2870 5235 290a  (pR3)(pR4)(pR5).\n+000131c0: 2020 6465 6620 6c66 7420 706f 6c79 676f    def lft polygo\n+000131d0: 6e20 2870 4c35 2928 704c 3429 2870 4c33  n (pL5)(pL4)(pL3\n+000131e0: 2928 704c 3229 2870 4c31 290a 2020 6465  )(pL2)(pL1).  de\n+000131f0: 6620 6672 7420 706f 6c79 676f 6e20 2870  f frt polygon (p\n+00013200: 5232 2928 7052 3129 2870 4c31 2928 704c  R2)(pR1)(pL1)(pL\n+00013210: 3229 0a20 2064 6566 2062 636b 2070 6f6c  2).  def bck pol\n+00013220: 7967 6f6e 2028 7052 3429 2870 5233 2928  ygon (pR4)(pR3)(\n+00013230: 704c 3329 2870 4c34 290a 2020 6465 6620  pL3)(pL4).  def \n+00013240: 7466 7220 706f 6c79 676f 6e20 2870 5231  tfr polygon (pR1\n+00013250: 2928 7052 3529 2870 4c35 2928 704c 3129  )(pR5)(pL5)(pL1)\n+00013260: 0a20 2064 6566 2074 626b 2070 6f6c 7967  .  def tbk polyg\n+00013270: 6f6e 2028 7052 3529 2870 5234 2928 704c  on (pR5)(pR4)(pL\n+00013280: 3429 2870 4c35 290a 2020 6465 6620 626f  4)(pL5).  def bo\n+00013290: 7420 706f 6c79 676f 6e20 2870 5232 2928  t polygon (pR2)(\n+000132a0: 704c 3229 2870 4c33 2928 7052 3329 0a20  pL2)(pL3)(pR3). \n+000132b0: 2064 6566 2064 6f6f 7220 706f 6c79 676f   def door polygo\n+000132c0: 6e5b 6669 6c6c 636f 6c6f 723d 6272 6f77  n[fillcolor=brow\n+000132d0: 6e5d 2028 7044 3129 2870 4432 2928 7044  n] (pD1)(pD2)(pD\n+000132e0: 3329 2870 4434 290a 2020 6465 6620 686f  3)(pD4).  def ho\n+000132f0: 7573 6520 7b20 7b72 6774 7d7b 6c66 747d  use { {rgt}{lft}\n+00013300: 7b66 7274 7d7b 6263 6b7d 7b74 6672 7d7b  {frt}{bck}{tfr}{\n+00013310: 7462 6b7d 7b62 6f74 7d7b 646f 6f72 7d20  tbk}{bot}{door} \n+00013320: 7d0a 2020 2054 696d 6520 666f 7220 6120  }.   Time for a \n+00013330: 7361 6e69 7479 2063 6865 636b 2e20 2041  sanity check.  A\n+00013340: 6464 2074 6865 206c 696e 650a 2020 7b68  dd the line.  {h\n+00013350: 6f75 7365 7d0a 616e 6420 7468 6973 2069  ouse}.and this i\n+00013360: 7320 7768 6174 2077 6520 6765 742e 0a0a  s what we get...\n+00013370: 0008 5b69 6d61 6765 2073 7263 3d22 6578  ..[image src=\"ex\n+00013380: 3133 302e 706e 6722 2074 6578 743d 2249  130.png\" text=\"I\n+00013390: 6d61 6765 2065 7831 3330 206f 6d69 7474  mage ex130 omitt\n+000133a0: 6564 2069 6e20 7465 7874 2076 6572 7369  ed in text versi\n+000133b0: 6f6e 206f 6620 7468 6973 2064 6f63 756d  on of this docum\n+000133c0: 656e 742e 2200 085d 0a0a 5468 6973 2069  ent.\"..]..This i\n+000133d0: 7320 636f 7272 6563 742c 2062 7574 2064  s correct, but d\n+000133e0: 6f65 7320 6e6f 7420 7265 7665 616c 2076  oes not reveal v\n+000133f0: 6572 7920 6d75 6368 2e20 2043 6f6d 6d6f  ery much.  Commo\n+00013400: 6e20 6572 726f 7273 2061 7265 0a6d 6973  n errors are.mis\n+00013410: 706c 6163 6564 2076 6572 7469 6365 7320  placed vertices \n+00013420: 616e 6420 706f 6c79 676f 6e73 206d 6973  and polygons mis\n+00013430: 7369 6e67 2065 6e74 6972 656c 7920 6475  sing entirely du\n+00013440: 6520 746f 2069 6e63 6f72 7265 6374 2076  e to incorrect v\n+00013450: 6572 7465 780a 6f72 6465 722e 2020 546f  ertex.order.  To\n+00013460: 2072 756c 6520 7468 6573 6520 6f75 742c   rule these out,\n+00013470: 206c 6574 2773 2069 6e73 7065 6374 2061   let's inspect a\n+00013480: 6c6c 2073 6964 6573 206f 6620 7468 6520  ll sides of the \n+00013490: 686f 7573 652e 2020 5468 6973 0a69 7320  house.  This.is \n+000134a0: 6e6f 7420 6861 7264 2e20 204d 6572 656c  not hard.  Merel\n+000134b0: 7920 7265 706c 6163 6520 7468 6520 7265  y replace the re\n+000134c0: 6665 7265 6e63 6520 7b68 6f75 7365 7d20  ference {house} \n+000134d0: 7769 7468 2061 2027 7265 7065 6174 272e  with a 'repeat'.\n+000134e0: 0a2a 4e6f 7465 2052 6570 6561 7473 3a3a  .*Note Repeats::\n+000134f0: 2e0a 2020 7265 7065 6174 207b 2031 332c  ..  repeat { 13,\n+00013500: 2072 6f74 6174 6528 3330 2c20 5b31 2c32   rotate(30, [1,2\n+00013510: 2c33 5d29 2c20 7472 616e 736c 6174 6528  ,3]), translate(\n+00013520: 5b33 2c30 2c30 5d29 207d 207b 686f 7573  [3,0,0]) } {hous\n+00013530: 657d 0a00 085b 696d 6167 6520 7372 633d  e}...[image src=\n+00013540: 2265 7831 3430 2e70 6e67 2220 7465 7874  \"ex140.png\" text\n+00013550: 3d22 496d 6167 6520 6578 3134 3020 6f6d  =\"Image ex140 om\n+00013560: 6974 7465 6420 696e 2074 6578 7420 7665  itted in text ve\n+00013570: 7273 696f 6e20 6f66 2074 6869 7320 646f  rsion of this do\n+00013580: 6375 6d65 6e74 2e22 0008 5d0a 0a41 6761  cument.\"..]..Aga\n+00013590: 696e 2074 6869 6e67 7320 6c6f 6f6b 2063  in things look c\n+000135a0: 6f72 7265 6374 2e20 204e 6f74 6520 7468  orrect.  Note th\n+000135b0: 6174 2074 6865 2068 6964 6465 6e20 7375  at the hidden su\n+000135c0: 7266 6163 6520 616c 676f 7269 7468 6d0a  rface algorithm.\n+000135d0: 6861 6e64 6c65 7320 696e 7465 7273 6563  handles intersec\n+000135e0: 7469 6e67 2070 6f6c 7967 6f6e 7320 636f  ting polygons co\n+000135f0: 7272 6563 746c 7920 7768 6572 6520 736f  rrectly where so\n+00013600: 6d65 2063 6f70 6965 7320 6f66 2074 6865  me copies of the\n+00013610: 2068 6f75 7365 0a6f 7665 726c 6170 2e0a   house.overlap..\n+00013620: 0a20 2020 4c65 7427 7320 6c61 7920 6f75  .   Let's lay ou\n+00013630: 7420 7468 6520 6765 6f6d 6574 7279 206f  t the geometry o\n+00013640: 6620 7065 7273 7065 6374 6976 6520 7072  f perspective pr\n+00013650: 6f6a 6563 7469 6f6e 206f 6620 7468 6520  ojection of the \n+00013660: 686f 7573 650a 6f6e 746f 2061 2070 6c61  house.onto a pla\n+00013670: 6e65 2077 6974 6820 7261 7973 2070 6173  ne with rays pas\n+00013680: 7369 6e67 2074 6872 6f75 6768 2074 6865  sing through the\n+00013690: 206f 7269 6769 6e2e 2020 4265 6769 6e20   origin.  Begin \n+000136a0: 6279 2070 6f73 6974 696f 6e69 6e67 0a74  by positioning.t\n+000136b0: 6865 2068 6f75 7365 2074 7765 6c76 6520  he house twelve \n+000136c0: 756e 6974 7320 6261 636b 206f 6e20 7468  units back on th\n+000136d0: 6520 6e65 6761 7469 7665 207a 2d61 7869  e negative z-axi\n+000136e0: 7320 616e 6420 6164 6469 6e67 2061 2073  s and adding a s\n+000136f0: 6574 206f 660a 636f 6f72 6469 6e61 7465  et of.coordinate\n+00013700: 2061 7865 732e 2020 546f 206d 6f76 6520   axes.  To move \n+00013710: 7468 6520 686f 7573 6520 7765 206e 6565  the house we nee\n+00013720: 6420 6f6e 6c79 2063 6861 6e67 6520 7468  d only change th\n+00013730: 6520 2268 6f75 7365 0a70 6f73 6974 696f  e \"house.positio\n+00013740: 6e69 6e67 2220 7472 616e 7366 6f72 6d20  ning\" transform \n+00013750: 6465 6669 6e65 6420 6561 726c 6965 722e  defined earlier.\n+00013760: 0a20 2064 6566 2068 7020 726f 7461 7465  .  def hp rotate\n+00013770: 282d 3430 2c20 5b30 2c31 2c30 5d29 2074  (-40, [0,1,0]) t\n+00013780: 6865 6e20 7472 616e 736c 6174 6528 5b30  hen translate([0\n+00013790: 2c30 2c2d 3132 5d29 0a20 2064 6566 2061  ,0,-12]).  def a\n+000137a0: 7865 7320 7b0a 2020 2020 6465 6620 737a  xes {.    def sz\n+000137b0: 2031 0a20 2020 206c 696e 6520 5b61 7272   1.    line [arr\n+000137c0: 6f77 733d 3c2d 3e5d 2028 737a 2c30 2c30  ows=<->] (sz,0,0\n+000137d0: 2928 4f29 2830 2c73 7a2c 3029 0a20 2020  )(O)(0,sz,0).   \n+000137e0: 206c 696e 6520 5b61 7272 6f77 733d 2d3e   line [arrows=->\n+000137f0: 5d20 2028 4f29 2830 2c30 2c73 7a29 0a20  ]  (O)(0,0,sz). \n+00013800: 2020 206c 696e 6520 5b6c 696e 6577 6964     line [linewid\n+00013810: 7468 3d2e 3270 742c 6c69 6e65 636f 6c6f  th=.2pt,linecolo\n+00013820: 723d 626c 7565 2c6c 696e 6573 7479 6c65  r=blue,linestyle\n+00013830: 3d64 6173 6865 645d 2028 4f29 2830 2c30  =dashed] (O)(0,0\n+00013840: 2c2d 3130 290a 2020 2020 7370 6563 6961  ,-10).    specia\n+00013850: 6c20 7c5c 7570 7574 5b72 5d23 317b 2478  l |\\uput[r]#1{$x\n+00013860: 247d 5c75 7075 745b 755d 2332 7b24 7924  $}\\uput[u]#2{$y$\n+00013870: 7d5c 7570 7574 5b6c 5d23 337b 247a 247d  }\\uput[l]#3{$z$}\n+00013880: 7c0a 2020 2020 2020 2873 7a2c 302c 3029  |.      (sz,0,0)\n+00013890: 2830 2c73 7a2c 3029 2830 2c30 2c73 7a29  (0,sz,0)(0,0,sz)\n+000138a0: 0a20 207d 0a0a 2020 2054 696d 6520 666f  .  }..   Time fo\n+000138b0: 7220 616e 6f74 6865 7220 7465 7374 2e20  r another test. \n+000138c0: 204c 6574 2773 2062 7569 6c64 2061 2072   Let's build a r\n+000138d0: 6561 6c20 7669 6577 2074 7261 6e73 666f  eal view transfo\n+000138e0: 726d 2c20 6372 6561 7469 6e67 2061 0a22  rm, creating a.\"\n+000138f0: 7669 7274 7561 6c20 6361 6d65 7261 2220  virtual camera\" \n+00013900: 746f 206c 6f6f 6b20 6174 2074 6865 2073  to look at the s\n+00013910: 6365 6e65 2077 6520 6172 6520 636f 6e73  cene we are cons\n+00013920: 7472 7563 7469 6e67 2e20 2052 6570 6c61  tructing.  Repla\n+00013930: 6365 2074 6865 0a27 7265 7065 6174 2720  ce the.'repeat' \n+00013940: 7769 7468 0a20 2064 6566 2065 7965 2028  with.  def eye (\n+00013950: 3130 2c34 2c31 3029 0a20 2064 6566 206c  10,4,10).  def l\n+00013960: 6f6f 6b5f 6174 2028 302c 302c 2d35 290a  ook_at (0,0,-5).\n+00013970: 2020 7075 7420 7b20 7669 6577 2828 6579    put { view((ey\n+00013980: 6529 2c20 286c 6f6f 6b5f 6174 2929 207d  e), (look_at)) }\n+00013990: 207b 207b 686f 7573 657d 7b61 7865 737d   { {house}{axes}\n+000139a0: 207d 0a20 2020 5468 6520 2276 6965 7720   }.   The \"view \n+000139b0: 7472 616e 7366 6f72 6d22 2072 6570 6f73  transform\" repos\n+000139c0: 6974 696f 6e73 2074 6865 2073 6365 6e65  itions the scene\n+000139d0: 2073 6f20 7468 6174 2074 6865 2070 6f69   so that the poi\n+000139e0: 6e74 2027 6579 6527 2069 730a 6174 2074  nt 'eye' is.at t\n+000139f0: 6865 206f 7269 6769 6e20 616e 6420 7468  he origin and th\n+00013a00: 6520 6469 7265 6374 696f 6e20 6672 6f6d  e direction from\n+00013a10: 2027 6579 6527 2074 6f20 276c 6f6f 6b5f   'eye' to 'look_\n+00013a20: 6174 2720 6973 2074 6865 206e 6567 6174  at' is the negat\n+00013a30: 6976 650a 7a2d 6178 6973 2e20 2054 6869  ive.z-axis.  Thi\n+00013a40: 7320 7265 7175 6972 6573 2061 2072 6f74  s requires a rot\n+00013a50: 6174 696f 6e20 616e 6420 6120 7472 616e  ation and a tran\n+00013a60: 736c 6174 696f 6e20 7468 6174 2061 7265  slation that are\n+00013a70: 2061 6c6c 2070 6163 6b65 640a 696e 746f   all packed.into\n+00013a80: 2074 6865 2063 6f6e 7374 7275 6374 6f72   the constructor\n+00013a90: 2027 7669 6577 272e 0a0a 0008 5b69 6d61   'view'.....[ima\n+00013aa0: 6765 2073 7263 3d22 6578 3135 302e 706e  ge src=\"ex150.pn\n+00013ab0: 6722 2074 6578 743d 2249 6d61 6765 2065  g\" text=\"Image e\n+00013ac0: 7831 3530 206f 6d69 7474 6564 2069 6e20  x150 omitted in \n+00013ad0: 7465 7874 2076 6572 7369 6f6e 206f 6620  text version of \n+00013ae0: 7468 6973 2064 6f63 756d 656e 742e 2200  this document.\".\n+00013af0: 085d 0a0a 5468 6973 2069 7320 7374 6172  .]..This is star\n+00013b00: 7469 6e67 2074 6f20 6c6f 6f6b 2067 6f6f  ting to look goo\n+00013b10: 6421 2020 4164 6420 7468 6520 7072 6f6a  d!  Add the proj\n+00013b20: 6563 7469 6f6e 2070 6c61 6e65 2068 616c  ection plane hal\n+00013b30: 6620 7761 790a 6265 7477 6565 6e20 7468  f way.between th\n+00013b40: 6520 6f72 6967 696e 2061 6e64 2074 6865  e origin and the\n+00013b50: 2068 6f75 7365 2061 7420 7a3d 2d35 2e20   house at z=-5. \n+00013b60: 2057 6527 6c6c 2074 7279 2074 6865 2061   We'll try the a\n+00013b70: 6e67 6c65 2061 7267 756d 656e 740a 6665  ngle argument.fe\n+00013b80: 6174 7572 6520 6f66 2027 7370 6563 6961  ature of 'specia\n+00013b90: 6c27 2074 6f20 706f 7369 7469 6f6e 2061  l' to position a\n+00013ba0: 206c 6162 656c 2e0a 2020 6465 6620 7020   label..  def p \n+00013bb0: 3520 2520 7072 6f6a 6563 7469 6f6e 2064  5 % projection d\n+00013bc0: 6973 7461 6e63 6520 2870 6c61 6e65 2061  istance (plane a\n+00013bd0: 7420 7a3d 2d70 290a 2020 6465 6620 7072  t z=-p).  def pr\n+00013be0: 6f6a 6563 7469 6f6e 5f70 6c61 6e65 207b  ojection_plane {\n+00013bf0: 0a20 2020 2064 6566 2073 7a20 312e 350a  .    def sz 1.5.\n+00013c00: 2020 2020 706f 6c79 676f 6e20 282d 737a      polygon (-sz\n+00013c10: 2c2d 737a 2c2d 7029 2873 7a2c 2d73 7a2c  ,-sz,-p)(sz,-sz,\n+00013c20: 2d70 2928 737a 2c73 7a2c 2d70 2928 2d73  -p)(sz,sz,-p)(-s\n+00013c30: 7a2c 737a 2c2d 7029 0a20 2020 2073 7065  z,sz,-p).    spe\n+00013c40: 6369 616c 207c 5c72 7075 745b 625d 2331  cial |\\rput[b]#1\n+00013c50: 2d32 2333 7b5c 666f 6f74 6e6f 7465 7369  -2#3{\\footnotesi\n+00013c60: 7a65 5c73 6620 7072 6f6a 6563 7469 6f6e  ze\\sf projection\n+00013c70: 2070 6c61 6e65 7d7c 200a 2020 2020 2020   plane}| .      \n+00013c80: 282d 737a 2c2d 737a 2c2d 7029 2873 7a2c  (-sz,-sz,-p)(sz,\n+00013c90: 2d73 7a2c 2d70 2928 302c 2d73 7a2b 2e31  -sz,-p)(0,-sz+.1\n+00013ca0: 2c2d 7029 0a20 207d 0a41 6464 207b 7072  ,-p).  }.Add {pr\n+00013cb0: 6f6a 6563 7469 6f6e 5f70 6c61 6e65 7d20  ojection_plane} \n+00013cc0: 746f 2074 6865 206c 6973 7420 6f66 206f  to the list of o\n+00013cd0: 626a 6563 7473 2069 6e20 7468 6520 2770  bjects in the 'p\n+00013ce0: 7574 2720 6162 6f76 652e 0a0a 0008 5b69  ut' above.....[i\n+00013cf0: 6d61 6765 2073 7263 3d22 6578 3136 302e  mage src=\"ex160.\n+00013d00: 706e 6722 2074 6578 743d 2249 6d61 6765  png\" text=\"Image\n+00013d10: 2065 7831 3630 206f 6d69 7474 6564 2069   ex160 omitted i\n+00013d20: 6e20 7465 7874 2076 6572 7369 6f6e 206f  n text version o\n+00013d30: 6620 7468 6973 2064 6f63 756d 656e 742e  f this document.\n+00013d40: 2200 085d 0a0a 2020 2054 6865 2077 6179  \"..]..   The way\n+00013d50: 2077 6520 636f 6e73 7472 7563 7465 6420   we constructed \n+00013d60: 7468 6520 706f 696e 7473 206f 6620 7468  the points of th\n+00013d70: 6520 686f 7573 6520 6e6f 7720 6d61 6b65  e house now make\n+00013d80: 7320 6974 2065 6173 7920 746f 0a64 7261  s it easy to.dra\n+00013d90: 7720 7261 7973 206f 6620 7072 6f6a 6563  w rays of projec\n+00013da0: 7469 6f6e 2e20 2057 6527 6c6c 2063 6173  tion.  We'll cas\n+00013db0: 7420 6f6e 6520 7261 7920 6672 6f6d 2065  t one ray from e\n+00013dc0: 7665 7279 2076 6973 6962 6c65 2076 6572  very visible ver\n+00013dd0: 7465 780a 6f66 2074 6865 2068 6f75 7365  tex.of the house\n+00013de0: 2061 6e64 2064 6566 696e 6520 6f70 7469   and define opti\n+00013df0: 6f6e 7320 736f 2074 6865 2061 7070 6561  ons so the appea\n+00013e00: 7261 6e63 6520 6f66 2061 6c6c 2072 6179  rance of all ray\n+00013e10: 7320 6361 6e20 6265 0a63 6861 6e67 6564  s can be.changed\n+00013e20: 2061 7420 7468 6520 7361 6d65 2074 696d   at the same tim\n+00013e30: 652e 0a20 2064 6566 2070 726f 6a65 6374  e..  def project\n+00013e40: 696f 6e5f 7261 7973 207b 0a20 2020 2064  ion_rays {.    d\n+00013e50: 6566 2072 6179 6f70 7420 5b6c 696e 6577  ef rayopt [linew\n+00013e60: 6964 7468 3d2e 3370 742c 6c69 6e65 636f  idth=.3pt,lineco\n+00013e70: 6c6f 723d 6c69 6768 7467 7261 795d 0a20  lor=lightgray]. \n+00013e80: 2020 206c 696e 6520 5b72 6179 6f70 745d     line [rayopt]\n+00013e90: 284f 2928 7052 3129 206c 696e 6520 5b72  (O)(pR1) line [r\n+00013ea0: 6179 6f70 745d 284f 2928 7052 3229 206c  ayopt](O)(pR2) l\n+00013eb0: 696e 655b 7261 796f 7074 5d28 4f29 2870  ine[rayopt](O)(p\n+00013ec0: 5233 290a 2020 2020 6c69 6e65 205b 7261  R3).    line [ra\n+00013ed0: 796f 7074 5d28 4f29 2870 5234 2920 6c69  yopt](O)(pR4) li\n+00013ee0: 6e65 205b 7261 796f 7074 5d28 4f29 2870  ne [rayopt](O)(p\n+00013ef0: 5235 290a 2020 2020 6c69 6e65 205b 7261  R5).    line [ra\n+00013f00: 796f 7074 5d28 4f29 2870 4c31 2920 6c69  yopt](O)(pL1) li\n+00013f10: 6e65 205b 7261 796f 7074 5d28 4f29 2870  ne [rayopt](O)(p\n+00013f20: 4c32 2920 6c69 6e65 5b72 6179 6f70 745d  L2) line[rayopt]\n+00013f30: 284f 2928 704c 3529 0a20 2020 206c 696e  (O)(pL5).    lin\n+00013f40: 6520 5b72 6179 6f70 745d 284f 2928 7044  e [rayopt](O)(pD\n+00013f50: 3129 206c 696e 6520 5b72 6179 6f70 745d  1) line [rayopt]\n+00013f60: 284f 2928 7044 3229 200a 2020 2020 6c69  (O)(pD2) .    li\n+00013f70: 6e65 205b 7261 796f 7074 5d28 4f29 2870  ne [rayopt](O)(p\n+00013f80: 4433 2920 6c69 6e65 205b 7261 796f 7074  D3) line [rayopt\n+00013f90: 5d28 4f29 2870 4434 2920 0a20 207d 0a54  ](O)(pD4) .  }.T\n+00013fa0: 6865 2072 6573 756c 7420 6973 2073 686f  he result is sho\n+00013fb0: 776e 2068 6572 652e 0a0a 0008 5b69 6d61  wn here.....[ima\n+00013fc0: 6765 2073 7263 3d22 6578 3137 302e 706e  ge src=\"ex170.pn\n+00013fd0: 6722 2074 6578 743d 2249 6d61 6765 2065  g\" text=\"Image e\n+00013fe0: 7831 3730 206f 6d69 7474 6564 2069 6e20  x170 omitted in \n+00013ff0: 7465 7874 2076 6572 7369 6f6e 206f 6620  text version of \n+00014000: 7468 6973 2064 6f63 756d 656e 742e 2200  this document.\".\n+00014010: 085d 0a0a 5468 6520 7261 7973 2070 6965  .]..The rays pie\n+00014020: 7263 6520 7468 6520 7072 6f6a 6563 7469  rce the projecti\n+00014030: 6f6e 2070 6c61 6e65 2061 7420 7468 6520  on plane at the \n+00014040: 636f 7272 6573 706f 6e64 696e 6720 706f  corresponding po\n+00014050: 696e 7473 206f 6e20 7468 650a 7065 7273  ints on the.pers\n+00014060: 7065 6374 6976 6520 696d 6167 6520 7765  pective image we\n+00014070: 2061 7265 2074 7279 696e 6720 746f 2064   are trying to d\n+00014080: 7261 772e 2020 416c 6272 6563 6874 2044  raw.  Albrecht D\n+00014090: c3bc 7265 7220 616e 6420 6869 730a 5265  ..rer and his.Re\n+000140a0: 6e61 6973 7361 6e63 6520 636f 6e74 656d  naissance contem\n+000140b0: 706f 7261 7269 6573 2068 6164 2074 6865  poraries had the\n+000140c0: 2073 616d 6520 6964 6561 2069 6e20 7468   same idea in th\n+000140d0: 6520 6561 726c 7920 3135 3030 2773 2e0a  e early 1500's..\n+000140e0: 0a00 085b 696d 6167 6520 7372 633d 2264  ...[image src=\"d\n+000140f0: 7565 7265 722e 706e 6722 2074 6578 743d  uerer.png\" text=\n+00014100: 2249 6d61 6765 206f 6620 4475 6572 6572  \"Image of Duerer\n+00014110: 2773 2070 6572 7370 6563 7469 7665 2063  's perspective c\n+00014120: 6f6d 7075 7465 7220 6f6d 6974 7465 6420  omputer omitted \n+00014130: 696e 2074 6578 7420 7665 7273 696f 6e20  in text version \n+00014140: 6f66 2074 6869 7320 646f 6375 6d65 6e74  of this document\n+00014150: 2e22 0008 5d0a 0a20 2020 416c 6c20 7468  .\"..]..   All th\n+00014160: 6174 2773 206c 6566 7420 6973 2074 6f20  at's left is to \n+00014170: 6669 6e64 2061 2077 6179 2074 6f20 636f  find a way to co\n+00014180: 6e6e 6563 7420 7468 6520 706f 696e 7473  nnect the points\n+00014190: 206f 6620 7468 6520 686f 7573 650a 6f6e   of the house.on\n+000141a0: 2074 6865 2070 726f 6a65 6374 696f 6e20   the projection \n+000141b0: 706c 616e 652e 2020 5765 2063 6f75 6c64  plane.  We could\n+000141c0: 2070 756c 6c20 6f75 7420 6120 676f 6f64   pull out a good\n+000141d0: 2063 6f6d 7075 7465 7220 6772 6170 6869   computer graphi\n+000141e0: 6373 0a74 6578 742c 2066 696e 6420 7468  cs.text, find th\n+000141f0: 6520 6e65 6365 7373 6172 7920 6d61 7472  e necessary matr\n+00014200: 6978 2c20 616e 6420 656e 7465 7220 6974  ix, and enter it\n+00014210: 206f 7572 7365 6c76 6573 2061 7320 6120   ourselves as a \n+00014220: 7472 616e 7366 6f72 6d0a 6c69 7465 7261  transform.litera\n+00014230: 6c2e 2020 2a4e 6f74 6520 5472 616e 7366  l.  *Note Transf\n+00014240: 6f72 6d20 6c69 7465 7261 6c73 3a3a 2e20  orm literals::. \n+00014250: 2054 6861 7420 776f 726b 2069 7320 616c   That work is al\n+00014260: 7265 6164 7920 646f 6e65 2c0a 686f 7765  ready done,.howe\n+00014270: 7665 722e 2020 5765 2063 616e 2075 7365  ver.  We can use\n+00014280: 2074 6865 2027 7072 6f6a 6563 7428 7029   the 'project(p)\n+00014290: 2720 636f 6e73 7472 7563 746f 722e 0a0a  ' constructor...\n+000142a0: 2020 2054 6865 7265 2061 7265 2073 7469     There are sti\n+000142b0: 6c6c 2073 6f6d 6520 6465 7461 696c 7320  ll some details \n+000142c0: 7468 6174 2072 6571 7569 7265 2063 6172  that require car\n+000142d0: 652e 2020 5072 6f6a 6563 7469 6f6e 2077  e.  Projection w\n+000142e0: 696c 6c0a 666c 6174 7465 6e20 7768 6174  ill.flatten what\n+000142f0: 6576 6572 2069 7320 7472 616e 7366 6f72  ever is transfor\n+00014300: 6d65 6420 6f6e 746f 2074 6865 2070 6c61  med onto the pla\n+00014310: 6e65 207a 3d2d 702e 2020 5468 6572 6566  ne z=-p.  Theref\n+00014320: 6f72 6520 616e 7920 7061 7274 0a6f 6620  ore any part.of \n+00014330: 7468 6520 686f 7573 6520 636f 756c 6420  the house could \n+00014340: 6469 7361 7070 6561 7220 6265 6869 6e64  disappear behind\n+00014350: 2074 6865 2070 726f 6a65 6374 696f 6e20   the projection \n+00014360: 706c 616e 6520 2874 6865 2068 6964 6465  plane (the hidde\n+00014370: 6e0a 7375 7266 6163 6520 616c 676f 7269  n.surface algori\n+00014380: 7468 6d20 6f72 6465 7273 206f 626a 6563  thm orders objec\n+00014390: 7473 2061 7420 7468 6520 7361 6d65 2064  ts at the same d\n+000143a0: 6570 7468 2061 7262 6974 7261 7269 6c79  epth arbitrarily\n+000143b0: 292e 2020 5468 650a 646f 6f72 206d 6179  ).  The.door may\n+000143c0: 2061 6c73 6f20 6469 7361 7070 6561 7220   also disappear \n+000143d0: 6265 6869 6e64 2074 6865 2066 726f 6e74  behind the front\n+000143e0: 206f 6620 7468 6520 686f 7573 652e 2020   of the house.  \n+000143f0: 546f 206d 616b 6520 7375 7265 0a65 7665  To make sure.eve\n+00014400: 7279 7468 696e 6720 7265 6d61 696e 7320  rything remains \n+00014410: 7669 7369 626c 652c 2077 6527 6c6c 2070  visible, we'll p\n+00014420: 6c61 6365 2074 6865 2068 6f75 7365 2061  lace the house a\n+00014430: 2074 696e 7920 6269 7420 696e 2066 726f   tiny bit in fro\n+00014440: 6e74 206f 660a 7468 6520 7072 6f6a 6563  nt of.the projec\n+00014450: 7469 6f6e 2070 6c61 6e65 2061 6e64 2061  tion plane and a\n+00014460: 2073 6563 6f6e 6420 636f 7079 206f 6620   second copy of \n+00014470: 7468 6520 646f 6f72 2069 6e20 6672 6f6e  the door in fron\n+00014480: 7420 6f66 2074 6865 0a68 6f75 7365 2e0a  t of the.house..\n+00014490: 2020 6465 6620 7072 6f6a 6563 7469 6f6e    def projection\n+000144a0: 207b 0a20 2020 2025 2065 2069 7320 6120   {.    % e is a \n+000144b0: 736d 616c 6c20 6e75 6d62 6572 2064 6566  small number def\n+000144c0: 696e 6564 2061 626f 7665 0a20 2020 2070  ined above.    p\n+000144d0: 7574 207b 2070 726f 6a65 6374 2870 2920  ut { project(p) \n+000144e0: 7468 656e 2074 7261 6e73 6c61 7465 285b  then translate([\n+000144f0: 302c 302c 312a 655d 2920 7d20 7b68 6f75  0,0,1*e]) } {hou\n+00014500: 7365 7d0a 2020 2020 7075 7420 7b20 7072  se}.    put { pr\n+00014510: 6f6a 6563 7428 7029 2074 6865 6e20 7472  oject(p) then tr\n+00014520: 616e 736c 6174 6528 5b30 2c30 2c32 2a65  anslate([0,0,2*e\n+00014530: 5d29 207d 207b 646f 6f72 7d0a 2020 7d0a  ]) } {door}.  }.\n+00014540: 0a00 085b 696d 6167 6520 7372 633d 2265  ...[image src=\"e\n+00014550: 7831 3830 2e70 6e67 2220 7465 7874 3d22  x180.png\" text=\"\n+00014560: 496d 6167 6520 6578 3138 3020 6f6d 6974  Image ex180 omit\n+00014570: 7465 6420 696e 2074 6578 7420 7665 7273  ted in text vers\n+00014580: 696f 6e20 6f66 2074 6869 7320 646f 6375  ion of this docu\n+00014590: 6d65 6e74 2e22 0008 5d0a 0a20 2020 4966  ment.\"..]..   If\n+000145a0: 2079 6f75 2068 6176 6520 7374 7564 6965   you have studie\n+000145b0: 6420 616e 6420 756e 6465 7273 7461 6e64  d and understand\n+000145c0: 2061 6c6c 2074 6869 732c 2079 6f75 2061   all this, you a\n+000145d0: 7265 2077 656c 6c20 6f6e 2074 6865 2077  re well on the w\n+000145e0: 6179 0a74 6f20 7375 6363 6573 7320 7769  ay.to success wi\n+000145f0: 7468 2027 736b 6574 6368 272e 2020 4e6f  th 'sketch'.  No\n+00014600: 7420 7368 6f77 6e20 6172 6520 7468 6520  t shown are the \n+00014610: 3230 206f 7220 736f 2069 7465 7261 7469  20 or so iterati\n+00014620: 6f6e 7320 7468 6174 0a77 6572 6520 7265  ons that.were re\n+00014630: 7175 6972 6564 2074 6f20 6669 6e64 2061  quired to find a\n+00014640: 2072 6561 736f 6e61 626c 6520 7669 6577   reasonable view\n+00014650: 696e 6720 616e 676c 6520 616e 6420 686f  ing angle and ho\n+00014660: 7573 6520 706f 7369 7469 6f6e 2c0a 6574  use position,.et\n+00014670: 632e 2020 4e6f 6e65 7468 656c 6573 732c  c.  Nonetheless,\n+00014680: 2074 6869 7320 6472 6177 696e 6720 7761   this drawing wa\n+00014690: 7320 636f 6d70 6c65 7465 6420 696e 2061  s completed in a\n+000146a0: 626f 7574 2061 6e20 686f 7572 2e20 2057  bout an hour.  W\n+000146b0: 6869 6c65 2061 0a47 5549 2074 6f6f 6c20  hile a.GUI tool \n+000146c0: 6d61 7920 6861 7665 2062 6565 6e20 6120  may have been a \n+000146d0: 6c69 7474 6c65 2066 6173 7465 722c 2069  little faster, i\n+000146e0: 7420 6973 2075 6e6c 696b 656c 7920 7468  t is unlikely th\n+000146f0: 6174 2061 206e 6577 0a64 7261 7769 6e67  at a new.drawing\n+00014700: 2c20 6974 7365 6c66 2061 2070 6572 7370  , itself a persp\n+00014710: 6563 7469 7665 2070 726f 6a65 6374 696f  ective projectio\n+00014720: 6e20 6f66 2074 6865 2073 6365 6e65 2c20  n of the scene, \n+00014730: 636f 756c 6420 6265 0a67 656e 6572 6174  could be.generat\n+00014740: 6564 2077 6974 6820 7477 6f20 6d6f 7265  ed with two more\n+00014750: 206d 696e 7574 6573 2720 776f 726b 2120   minutes' work! \n+00014760: 204a 7573 7420 6368 616e 6765 2074 6865   Just change the\n+00014770: 2076 6965 7720 7472 616e 7366 6f72 6d0a   view transform.\n+00014780: 746f 0a20 2070 7574 207b 2076 6965 7728  to.  put { view(\n+00014790: 2865 7965 292c 2028 6c6f 6f6b 5f61 7429  (eye), (look_at)\n+000147a0: 2920 7468 656e 2070 6572 7370 6563 7469  ) then perspecti\n+000147b0: 7665 2839 2920 7d20 7b20 2e2e 2e0a 616e  ve(9) } { ....an\n+000147c0: 6420 7072 6f64 7563 6520 7468 6973 2e0a  d produce this..\n+000147d0: 0a00 085b 696d 6167 6520 7372 633d 2265  ...[image src=\"e\n+000147e0: 7831 3930 2e70 6e67 2220 7465 7874 3d22  x190.png\" text=\"\n+000147f0: 496d 6167 6520 6578 3139 3020 6f6d 6974  Image ex190 omit\n+00014800: 7465 6420 696e 2074 6578 7420 7665 7273  ted in text vers\n+00014810: 696f 6e20 6f66 2074 6869 7320 646f 6375  ion of this docu\n+00014820: 6d65 6e74 2e22 0008 5d0a 0a1f 0a46 696c  ment.\"..]....Fil\n+00014830: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n+00014840: 204e 6f64 653a 2041 2074 6563 686e 6963   Node: A technic\n+00014850: 616c 2064 7261 7769 6e67 2c20 204e 6578  al drawing,  Nex\n+00014860: 743a 2041 2068 6965 7261 7263 6869 6361  t: A hierarchica\n+00014870: 6c20 6d6f 6465 6c2c 2020 5072 6576 3a20  l model,  Prev: \n+00014880: 4f76 6572 7669 6577 2c20 2055 703a 2042  Overview,  Up: B\n+00014890: 7569 6c64 696e 6720 6120 6472 6177 696e  uilding a drawin\n+000148a0: 670a 0a34 2e32 2041 2074 6563 686e 6963  g..4.2 A technic\n+000148b0: 616c 2064 7261 7769 6e67 0a3d 3d3d 3d3d  al drawing.=====\n+000148c0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n+000148d0: 3d3d 0a0a 4c65 7427 7320 6c6f 6f6b 2061  ==..Let's look a\n+000148e0: 7420 6120 6472 6177 696e 6720 7468 6174  t a drawing that\n+000148f0: 2072 6570 7265 7365 6e74 7320 7468 6520   represents the \n+00014900: 6b69 6e64 206f 6620 7072 6f62 6c65 6d20  kind of problem \n+00014910: 2773 6b65 7463 6827 2077 6173 0a6d 6561  'sketch' was.mea\n+00014920: 6e74 2074 6f20 736f 6c76 652d 2d61 2070  nt to solve--a p\n+00014930: 6169 7220 6f66 2074 6578 7462 6f6f 6b20  air of textbook \n+00014940: 6669 6775 7265 7320 7265 6761 7264 696e  figures regardin\n+00014950: 6720 6120 706f 6c79 676f 6e61 6c0a 6170  g a polygonal.ap\n+00014960: 7072 6f78 696d 6174 696f 6e20 6f66 2061  proximation of a\n+00014970: 2074 7275 6e63 6174 6564 2063 6f6e 652e   truncated cone.\n+00014980: 2020 4865 7265 2061 7265 2074 6865 2070    Here are the p\n+00014990: 6963 7475 7265 7320 7765 2077 696c 6c0a  ictures we will.\n+000149a0: 7072 6f64 7563 652e 0a0a 0008 5b69 6d61  produce.....[ima\n+000149b0: 6765 2073 7263 3d22 6578 3235 302e 706e  ge src=\"ex250.pn\n+000149c0: 6722 2074 6578 743d 2249 6d61 6765 2065  g\" text=\"Image e\n+000149d0: 7832 3530 206f 6d69 7474 6564 2069 6e20  x250 omitted in \n+000149e0: 7465 7874 2076 6572 7369 6f6e 206f 6620  text version of \n+000149f0: 7468 6973 2064 6f63 756d 656e 742e 2200  this document.\".\n+00014a00: 085d 2020 2020 2000 085b 696d 6167 6520  .]     ..[image \n+00014a10: 7372 633d 2265 7832 3630 2e70 6e67 2220  src=\"ex260.png\" \n+00014a20: 7465 7874 3d22 496d 6167 6520 6578 3236  text=\"Image ex26\n+00014a30: 3020 6f6d 6974 7465 6420 696e 2074 6578  0 omitted in tex\n+00014a40: 7420 7665 7273 696f 6e20 6f66 2074 6869  t version of thi\n+00014a50: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a  s document.\"..].\n+00014a60: 0a20 2020 5468 6520 636f 6e65 2073 6861  .   The cone sha\n+00014a70: 7065 2069 7320 6a75 7374 2061 2073 7765  pe is just a swe\n+00014a80: 7074 206c 696e 6520 7769 7468 206e 6f20  pt line with no \n+00014a90: 636c 6f73 7572 6520 7461 6720 616e 6420  closure tag and \n+00014aa0: 6375 6c6c 696e 670a 7475 726e 6564 206f  culling.turned o\n+00014ab0: 6666 2e20 2042 6567 696e 2062 7920 7365  ff.  Begin by se\n+00014ac0: 7474 696e 6720 7570 2073 6f6d 6520 7573  tting up some us\n+00014ad0: 6566 756c 2063 6f6e 7374 616e 7473 2e0a  eful constants..\n+00014ae0: 2020 6465 6620 4f20 2830 2c30 2c30 2920    def O (0,0,0) \n+00014af0: 6465 6620 4920 5b31 2c30 2c30 5d20 6465  def I [1,0,0] de\n+00014b00: 6620 4a20 5b30 2c31 2c30 5d20 6465 6620  f J [0,1,0] def \n+00014b10: 4b20 5b30 2c30 2c31 5d0a 2020 6465 6620  K [0,0,1].  def \n+00014b20: 7030 2028 312c 3229 2064 6566 2070 3120  p0 (1,2) def p1 \n+00014b30: 2831 2e35 2c30 2920 6465 6620 4e20 380a  (1.5,0) def N 8.\n+00014b40: 2020 6465 6620 7365 675f 726f 7420 726f    def seg_rot ro\n+00014b50: 7461 7465 2833 3630 202f 204e 2c20 5b4a  tate(360 / N, [J\n+00014b60: 5d29 0a54 6865 2070 6f69 6e74 7320 2770  ]).The points 'p\n+00014b70: 3027 2061 6e64 2027 7031 2720 6172 6520  0' and 'p1' are \n+00014b80: 7468 6520 656e 6420 706f 696e 7473 206f  the end points o\n+00014b90: 6620 7468 6520 6c69 6e65 2074 6f20 6265  f the line to be\n+00014ba0: 2073 7765 7074 2e0a 5468 6520 6465 6669   swept..The defi\n+00014bb0: 6e69 7469 6f6e 2027 7365 675f 726f 7427  nition 'seg_rot'\n+00014bc0: 2069 7320 7468 6520 7377 6565 7020 7472   is the sweep tr\n+00014bd0: 616e 7366 6f72 6d61 7469 6f6e 2e20 2057  ansformation.  W\n+00014be0: 6974 6820 7468 6573 652c 2074 6865 0a63  ith these, the.c\n+00014bf0: 6f6e 6520 6974 7365 6c66 2069 7320 7369  one itself is si\n+00014c00: 6d70 6c65 2e0a 2020 7377 6565 705b 6375  mple..  sweep[cu\n+00014c10: 6c6c 3d66 616c 7365 5d20 7b20 4e2c 205b  ll=false] { N, [\n+00014c20: 5b73 6567 5f72 6f74 5d5d 207d 206c 696e  [seg_rot]] } lin\n+00014c30: 6528 7030 2928 7031 290a 0a20 2020 5468  e(p0)(p1)..   Th\n+00014c40: 6520 6178 6573 2061 7265 206e 6578 7420  e axes are next \n+00014c50: 616e 6420 696e 636c 7564 6520 616e 2069  and include an i\n+00014c60: 6e74 6572 6573 696e 6720 7472 6963 6b20  nteresing trick \n+00014c70: 7468 6174 2073 686f 7773 2074 6865 0a68  that shows the.h\n+00014c80: 6964 6465 6e20 7061 7274 7320 6173 2064  idden parts as d\n+00014c90: 6f74 7465 6420 6c69 6e65 732e 2020 5468  otted lines.  Th\n+00014ca0: 6520 7365 6372 6574 2069 7320 6472 6177  e secret is draw\n+00014cb0: 2074 6865 2061 7865 7320 7477 6963 652d   the axes twice-\n+00014cc0: 2d73 6f6c 6964 0a6c 696e 6573 2077 6974  -solid.lines wit\n+00014cd0: 6820 7468 6520 6e6f 726d 616c 2068 6964  h the normal hid\n+00014ce0: 6465 6e20 7375 7266 6163 6520 616c 676f  den surface algo\n+00014cf0: 7269 7468 6d20 696e 2065 6666 6563 742c  rithm in effect,\n+00014d00: 2061 6e64 2074 6865 6e0a 646f 7474 6564   and then.dotted\n+00014d10: 2077 6974 6820 7468 6520 6f70 7469 6f6e   with the option\n+00014d20: 2027 6c61 793d 6f76 6572 2720 736f 2074   'lay=over' so t\n+00014d30: 6861 7420 6e6f 2070 6f6c 7967 6f6e 7320  hat no polygons \n+00014d40: 6361 6e20 6869 6465 2074 6865 6d2e 0a20  can hide them.. \n+00014d50: 2064 6566 2061 7820 2864 782c 302c 3029   def ax (dx,0,0)\n+00014d60: 2025 2074 6970 7320 6f66 2074 6865 2061   % tips of the a\n+00014d70: 7865 730a 2020 6465 6620 6179 2028 302c  xes.  def ay (0,\n+00014d80: 6479 2c30 290a 2020 6465 6620 617a 2028  dy,0).  def az (\n+00014d90: 302c 302c 647a 290a 2020 6c69 6e65 5b61  0,0,dz).  line[a\n+00014da0: 7272 6f77 733d 3c2d 3e2c 6c69 6e65 7769  rrows=<->,linewi\n+00014db0: 6474 683d 2e34 7074 5d28 6178 2928 4f29  dth=.4pt](ax)(O)\n+00014dc0: 2861 7929 0a20 206c 696e 655b 6172 726f  (ay).  line[arro\n+00014dd0: 7773 3d2d 3e2c 6c69 6e65 7769 6474 683d  ws=->,linewidth=\n+00014de0: 2e34 7074 5d28 4f29 2861 7a29 0a20 2025  .4pt](O)(az).  %\n+00014df0: 2072 6570 6561 7420 646f 7474 6564 2061   repeat dotted a\n+00014e00: 7320 616e 206f 7665 726c 6179 2074 6f20  s an overlay to \n+00014e10: 6869 6e74 2061 7420 7468 6520 6869 6464  hint at the hidd\n+00014e20: 656e 206c 696e 6573 0a20 206c 696e 655b  en lines.  line[\n+00014e30: 6c61 793d 6f76 6572 2c6c 696e 6573 7479  lay=over,linesty\n+00014e40: 6c65 3d64 6f74 7465 642c 6c69 6e65 7769  le=dotted,linewi\n+00014e50: 6474 683d 2e34 7074 5d28 6178 2928 4f29  dth=.4pt](ax)(O)\n+00014e60: 2861 7929 0a20 206c 696e 655b 6c61 793d  (ay).  line[lay=\n+00014e70: 6f76 6572 2c6c 696e 6573 7479 6c65 3d64  over,linestyle=d\n+00014e80: 6f74 7465 642c 6c69 6e65 7769 6474 683d  otted,linewidth=\n+00014e90: 2e34 7074 5d28 4f29 2861 7a29 0a20 2073  .4pt](O)(az).  s\n+00014ea0: 7065 6369 616c 7c5c 666f 6f74 6e6f 7465  pecial|\\footnote\n+00014eb0: 7369 7a65 0a20 2020 2020 2020 2020 205c  size.          \\\n+00014ec0: 7570 7574 5b64 5d23 317b 2478 247d 5c75  uput[d]#1{$x$}\\u\n+00014ed0: 7075 745b 755d 2332 7b24 7924 7d5c 7570  put[u]#2{$y$}\\up\n+00014ee0: 7574 5b6c 5d23 337b 247a 247d 7c0a 2020  ut[l]#3{$z$}|.  \n+00014ef0: 2020 2861 7829 2861 7929 2861 7a29 0a54    (ax)(ay)(az).T\n+00014f00: 6865 206c 6162 656c 7320 6172 6520 6170  he labels are ap\n+00014f10: 706c 6965 6420 7769 7468 2027 5053 5472  plied with 'PSTr\n+00014f20: 6963 6b73 2720 7370 6563 6961 6c20 6f62  icks' special ob\n+00014f30: 6a65 6374 7320 6173 2075 7375 616c 2e0a  jects as usual..\n+00014f40: 0a20 2020 466f 7220 7468 6520 6865 6967  .   For the heig\n+00014f50: 6874 2064 696d 656e 7369 6f6e 206d 6172  ht dimension mar\n+00014f60: 6b2c 2074 6865 2070 6f77 6572 206f 6620  k, the power of \n+00014f70: 6166 6669 6e65 2061 7269 7468 6574 6963  affine arithetic\n+00014f80: 2069 7320 7665 7279 0a68 656c 7066 756c   is very.helpful\n+00014f90: 2e0a 2020 6465 6620 6864 696d 5f72 6566  ..  def hdim_ref\n+00014fa0: 2075 6e69 7428 2870 3129 202d 2028 4f29   unit((p1) - (O)\n+00014fb0: 2920 7468 656e 205b 5b73 6567 5f72 6f74  ) then [[seg_rot\n+00014fc0: 5d5d 5e32 0a20 2064 6566 2063 3020 2870  ]]^2.  def c0 (p\n+00014fd0: 3029 2074 6865 6e20 7363 616c 6528 5b4a  0) then scale([J\n+00014fe0: 5d29 0a20 2064 6566 2068 3030 2028 6330  ]).  def h00 (c0\n+00014ff0: 2920 2b20 312e 3120 2a20 5b68 6469 6d5f  ) + 1.1 * [hdim_\n+00015000: 7265 665d 0a20 2064 6566 2068 3031 2028  ref].  def h01 (\n+00015010: 6330 2920 2b20 312e 3920 2a20 5b68 6469  c0) + 1.9 * [hdi\n+00015020: 6d5f 7265 665d 0a20 2064 6566 2068 3032  m_ref].  def h02\n+00015030: 2028 6330 2920 2b20 312e 3820 2a20 5b68   (c0) + 1.8 * [h\n+00015040: 6469 6d5f 7265 665d 0a20 206c 696e 6528  dim_ref].  line(\n+00015050: 6830 3029 2868 3031 290a 2020 6465 6620  h00)(h01).  def \n+00015060: 6831 3020 284f 2920 2b20 312e 3620 2a20  h10 (O) + 1.6 * \n+00015070: 5b68 6469 6d5f 7265 665d 0a20 2064 6566  [hdim_ref].  def\n+00015080: 2068 3131 2028 4f29 202b 2031 2e39 202a   h11 (O) + 1.9 *\n+00015090: 205b 6864 696d 5f72 6566 5d0a 2020 6465   [hdim_ref].  de\n+000150a0: 6620 6831 3220 284f 2920 2b20 312e 3820  f h12 (O) + 1.8 \n+000150b0: 2a20 5b68 6469 6d5f 7265 665d 0a20 206c  * [hdim_ref].  l\n+000150c0: 696e 6528 6831 3029 2868 3131 290a 2020  ine(h10)(h11).  \n+000150d0: 6c69 6e65 5b61 7272 6f77 733d 3c2d 3e5d  line[arrows=<->]\n+000150e0: 2868 3032 2928 6831 3229 0a20 2064 6566  (h02)(h12).  def\n+000150f0: 2068 6d32 2028 2868 3032 2920 2d20 284f   hm2 ((h02) - (O\n+00015100: 2920 2b20 2868 3132 2920 2d20 284f 2929  ) + (h12) - (O))\n+00015110: 202f 2032 202b 2028 4f29 0a20 2073 7065   / 2 + (O).  spe\n+00015120: 6369 616c 7c5c 666f 6f74 6e6f 7465 7369  cial|\\footnotesi\n+00015130: 7a65 5c72 7075 742a 2331 7b24 6824 7d7c  ze\\rput*#1{$h$}|\n+00015140: 2868 6d32 290a 2020 2054 6865 2067 656e  (hm2).   The gen\n+00015150: 6572 616c 2069 6465 6120 656d 706c 6f79  eral idea employ\n+00015160: 6564 2068 6572 6520 6973 2074 6f20 636f  ed here is to co\n+00015170: 6d70 7574 6520 6120 756e 6974 2022 7265  mpute a unit \"re\n+00015180: 6665 7265 6e63 650a 7665 6374 6f72 2220  ference.vector\" \n+00015190: 7061 7261 6c6c 656c 2074 6f20 7468 6520  parallel to the \n+000151a0: 787a 2d70 6c61 6e65 2069 6e20 7468 6520  xz-plane in the \n+000151b0: 6465 7369 7265 6420 6469 7265 6374 696f  desired directio\n+000151c0: 6e20 6f66 2074 6865 0a64 696d 656e 7369  n of the.dimensi\n+000151d0: 6f6e 2066 726f 6d20 7468 6520 6f72 6967  on from the orig\n+000151e0: 696e 2e20 2054 6865 2074 7261 6e73 666f  in.  The transfo\n+000151f0: 726d 6174 696f 6e20 275b 5b73 6567 5f72  rmation '[[seg_r\n+00015200: 6f74 5d5d 5e32 2720 726f 7461 7465 730a  ot]]^2' rotates.\n+00015210: 7477 6f20 7365 676d 656e 7473 2061 626f  two segments abo\n+00015220: 7574 2074 6865 2079 2d61 7869 732e 2020  ut the y-axis.  \n+00015230: 5768 656e 2061 7070 6c69 6564 2074 6f20  When applied to \n+00015240: 2728 7031 2920 2d20 284f 2927 2c20 7468  '(p1) - (O)', th\n+00015250: 650a 7265 7375 6c74 696e 6720 7665 6374  e.resulting vect\n+00015260: 6f72 2070 6f69 6e74 7320 746f 2074 6865  or points to the\n+00015270: 2072 6967 6874 2061 7320 7368 6f77 6e2e   right as shown.\n+00015280: 2020 496e 2074 6869 7320 6d61 6e6e 6572    In this manner\n+00015290: 2c20 7765 2063 616e 0a70 6963 6b20 616e  , we can.pick an\n+000152a0: 7920 7665 7274 6578 2061 7320 7468 6520  y vertex as the \n+000152b0: 6c6f 6361 7469 6f6e 206f 6620 7468 6520  location of the \n+000152c0: 6865 6967 6874 2064 696d 656e 7369 6f6e  height dimension\n+000152d0: 206c 696e 6573 2062 7920 7661 7279 696e   lines by varyin\n+000152e0: 670a 7468 6520 6578 706f 6e65 6e74 206f  g.the exponent o\n+000152f0: 6620 275b 5b73 6567 5f72 6f74 5d5d 272e  f '[[seg_rot]]'.\n+00015300: 2020 5468 6973 2069 7320 6f6e 6c79 206f    This is only o\n+00015310: 6e65 206f 6620 6d61 6e79 2070 6f73 7369  ne of many possi\n+00015320: 626c 650a 7374 7261 7465 6769 6573 2e0a  ble.strategies..\n+00015330: 0a20 2020 5468 6520 636f 6d70 7574 6174  .   The computat\n+00015340: 696f 6e20 6f66 2027 686d 3227 2069 7320  ion of 'hm2' is \n+00015350: 6120 7573 6566 756c 2069 6469 6f6d 2066  a useful idiom f\n+00015360: 6f72 2066 696e 6469 6e67 2074 6865 2063  or finding the c\n+00015370: 656e 7472 6f69 640a 6f66 2061 2073 6574  entroid.of a set\n+00015380: 206f 6620 706f 696e 7473 2e0a 0a20 2020   of points...   \n+00015390: 5468 6520 7477 6f20 7261 6469 7573 206d  The two radius m\n+000153a0: 6172 6b73 2061 7265 2064 6f6e 6520 7369  arks are done si\n+000153b0: 6d69 6c61 726c 792c 2073 6f20 7765 2070  milarly, so we p\n+000153c0: 7265 7365 6e74 2074 6865 2063 6f64 650a  resent the code.\n+000153d0: 7769 7468 6f75 7420 636f 6d6d 656e 742e  without comment.\n+000153e0: 0a20 2025 2072 6164 6975 7320 6d65 6173  .  % radius meas\n+000153f0: 7572 656d 656e 7420 6d61 726b 730a 2020  urement marks.  \n+00015400: 6465 6620 6761 7020 5b30 2c2e 322c 305d  def gap [0,.2,0]\n+00015410: 2020 2520 7573 6564 2074 6f20 6372 6561    % used to crea\n+00015420: 7465 2073 6d61 6c6c 2076 6572 7469 6361  te small vertica\n+00015430: 6c20 6761 7073 0a0a 2020 2520 6669 7273  l gaps..  % firs\n+00015440: 7420 7231 0a20 2064 6566 2075 7031 205b  t r1.  def up1 [\n+00015450: 302c 332e 312c 305d 2025 2074 6963 6b20  0,3.1,0] % tick \n+00015460: 7269 7365 7320 6162 6f76 6520 6469 6d65  rises above dime\n+00015470: 6e73 696f 6e20 6120 6c69 7474 6c65 0a20  nsion a little. \n+00015480: 2064 6566 2072 3120 2828 7031 2920 7468   def r1 ((p1) th\n+00015490: 656e 205b 5b73 6567 5f72 6f74 5d5d 5e2d  en [[seg_rot]]^-\n+000154a0: 3229 202b 205b 7570 315d 0a20 2064 6566  2) + [up1].  def\n+000154b0: 2072 3163 2028 7231 2920 7468 656e 2073   r1c (r1) then s\n+000154c0: 6361 6c65 285b 4a5d 290a 2020 6465 6620  cale([J]).  def \n+000154d0: 7231 7420 2872 3129 202b 205b 6761 705d  r1t (r1) + [gap]\n+000154e0: 0a20 2064 6566 2072 3162 2028 2872 3174  .  def r1b ((r1t\n+000154f0: 2920 7468 656e 2073 6361 6c65 285b 312c  ) then scale([1,\n+00015500: 302c 315d 2929 202b 205b 6761 705d 0a20  0,1])) + [gap]. \n+00015510: 206c 696e 655b 6172 726f 7773 3d3c 2d3e   line[arrows=<->\n+00015520: 5d28 7231 6329 2872 3129 2020 2520 6469  ](r1c)(r1)  % di\n+00015530: 6d65 6e73 696f 6e20 6c69 6e65 0a20 206c  mension line.  l\n+00015540: 696e 6528 7231 6229 2872 3174 2920 2020  ine(r1b)(r1t)   \n+00015550: 2020 2020 2020 2020 2020 2520 7469 636b            % tick\n+00015560: 0a20 2064 6566 2072 316d 2028 2872 3129  .  def r1m ((r1)\n+00015570: 202d 2028 4f29 202b 2028 7231 6329 202d   - (O) + (r1c) -\n+00015580: 2028 4f29 2920 2f20 3220 2b20 284f 2920   (O)) / 2 + (O) \n+00015590: 2520 6c61 6265 6c20 706f 7369 7469 6f6e  % label position\n+000155a0: 0a20 2073 7065 6369 616c 207c 5c66 6f6f  .  special |\\foo\n+000155b0: 746e 6f74 6573 697a 655c 7270 7574 2a23  tnotesize\\rput*#\n+000155c0: 317b 2472 5f31 247d 7c28 7231 6d29 2020  1{$r_1$}|(r1m)  \n+000155d0: 2520 6c61 6265 6c0a 0a20 2025 2073 616d  % label..  % sam\n+000155e0: 6520 6472 696c 6c20 666f 7220 7230 2c20  e drill for r0, \n+000155f0: 6275 7420 6d75 7374 2070 726f 6a65 6374  but must project\n+00015600: 2064 6f77 6e20 6669 7273 740a 2020 6465   down first.  de\n+00015610: 6620 7570 3020 5b30 2c32 2e37 2c30 5d0a  f up0 [0,2.7,0].\n+00015620: 2020 6465 6620 7230 2028 2870 3029 2074    def r0 ((p0) t\n+00015630: 6865 6e20 7363 616c 6528 5b31 2c30 2c31  hen scale([1,0,1\n+00015640: 5d29 2074 6865 6e20 5b5b 7365 675f 726f  ]) then [[seg_ro\n+00015650: 745d 5d5e 2d32 2920 2b20 5b75 7030 5d0a  t]]^-2) + [up0].\n+00015660: 2020 6465 6620 7230 6320 2872 3029 2074    def r0c (r0) t\n+00015670: 6865 6e20 7363 616c 6528 5b4a 5d29 0a20  hen scale([J]). \n+00015680: 2064 6566 2072 3074 2028 7230 2920 2b20   def r0t (r0) + \n+00015690: 5b67 6170 5d0a 2020 6465 6620 7230 6220  [gap].  def r0b \n+000156a0: 2828 7030 2920 7468 656e 205b 5b73 6567  ((p0) then [[seg\n+000156b0: 5f72 6f74 5d5d 5e2d 3229 202b 205b 6761  _rot]]^-2) + [ga\n+000156c0: 705d 0a20 206c 696e 655b 6172 726f 7773  p].  line[arrows\n+000156d0: 3d3c 2d3e 5d28 7230 6329 2872 3029 0a20  =<->](r0c)(r0). \n+000156e0: 206c 696e 6528 7230 6229 2872 3074 290a   line(r0b)(r0t).\n+000156f0: 2020 6465 6620 7230 6d20 2828 7230 2920    def r0m ((r0) \n+00015700: 2d20 284f 2920 2b20 2872 3063 2920 2d20  - (O) + (r0c) - \n+00015710: 284f 2929 202f 2032 202b 2028 4f29 0a20  (O)) / 2 + (O). \n+00015720: 2073 7065 6369 616c 207c 5c66 6f6f 746e   special |\\footn\n+00015730: 6f74 6573 697a 655c 7270 7574 2a23 317b  otesize\\rput*#1{\n+00015740: 2472 5f30 247d 7c28 7230 6d29 0a0a 2020  $r_0$}|(r0m)..  \n+00015750: 2054 6865 2073 6563 6f6e 6420 6472 6177   The second draw\n+00015760: 696e 6720 7573 6573 2074 6865 2073 616d  ing uses the sam\n+00015770: 6520 7465 6368 6e69 7175 6573 2e20 204f  e techniques.  O\n+00015780: 6e6c 7920 7468 6520 6d65 7468 6f64 2066  nly the method f\n+00015790: 6f72 0a64 7261 7769 6e67 2074 6865 2065  or.drawing the e\n+000157a0: 6c6c 6970 7469 6361 6c20 6172 6320 6973  lliptical arc is\n+000157b0: 206e 6577 2e20 2048 6572 6520 6973 2074   new.  Here is t\n+000157c0: 6865 2063 6f64 652e 0a20 2064 6566 206d  he code..  def m\n+000157d0: 6964 2028 2870 3030 292d 284f 292b 2870  id ((p00)-(O)+(p\n+000157e0: 3130 292d 284f 292b 2870 3131 292d 284f  10)-(O)+(p11)-(O\n+000157f0: 292b 2870 3031 292d 284f 2929 2f34 2b28  )+(p01)-(O))/4+(\n+00015800: 4f29 0a20 2073 7065 6369 616c 7c5c 7270  O).  special|\\rp\n+00015810: 7574 2331 7b5c 7073 6375 7374 6f6d 7b0a  ut#1{\\pscustom{.\n+00015820: 2020 2020 5c73 6361 6c65 7b31 2031 2e33      \\scale{1 1.3\n+00015830: 7d0a 2020 2020 5c70 7361 7263 5b61 7272  }.    \\psarc[arr\n+00015840: 6f77 6c65 6e67 7468 3d2e 355d 7b2d 3e7d  owlength=.5]{->}\n+00015850: 7b2e 3235 7d7b 2d36 307d 7b32 3430 7d7d  {.25}{-60}{240}}\n+00015860: 7d7c 0a20 2020 205b 6c61 793d 6f76 6572  }|.    [lay=over\n+00015870: 5d28 6d69 6429 0a57 6520 636f 756c 6420  ](mid).We could \n+00015880: 6861 7665 2073 7765 7074 2061 2070 6f69  have swept a poi\n+00015890: 6e74 2074 6f20 6d61 6b65 2074 6865 2061  nt to make the a\n+000158a0: 7263 2077 6974 6820 2773 6b65 7463 6827  rc with 'sketch'\n+000158b0: 2c20 6275 7420 7573 696e 6720 610a 2750  , but using a.'P\n+000158c0: 5354 7269 636b 7327 2063 7573 746f 6d20  STricks' custom \n+000158d0: 6772 6170 6869 6320 7761 7320 7369 6d70  graphic was simp\n+000158e0: 6c65 722e 2020 4167 6169 6e20 7765 2063  ler.  Again we c\n+000158f0: 6f6d 7075 7465 6420 7468 6520 6365 6e74  omputed the cent\n+00015900: 726f 6964 0a6f 6620 7468 6520 7175 6164  roid.of the quad\n+00015910: 7269 6c61 7465 7261 6c20 6279 2061 7665  rilateral by ave\n+00015920: 7261 6769 6e67 2070 6f69 6e74 732e 2020  raging points.  \n+00015930: 4e6f 7465 2074 6861 7420 7363 616c 696e  Note that scalin\n+00015940: 6720 696e 0a50 6f73 7473 6372 6970 7420  g in.Postscript \n+00015950: 6469 7374 6f72 7473 2074 6865 2061 7272  distorts the arr\n+00015960: 6f77 6865 6164 2c20 6275 7420 696e 2074  owhead, but in t\n+00015970: 6869 7320 6361 7365 2074 6865 2064 6973  his case the dis\n+00015980: 746f 7274 696f 6e0a 6163 7475 616c 6c79  tortion.actually\n+00015990: 206c 6f6f 6b73 2062 6574 7465 7220 696e   looks better in\n+000159a0: 2074 6865 2070 726f 6a65 6374 696f 6e20   the projection \n+000159b0: 6f66 2074 6865 2073 6c61 6e74 6564 2066  of the slanted f\n+000159c0: 6163 652e 2020 4120 2773 6b65 7463 6827  ace.  A 'sketch'\n+000159d0: 0a61 7272 6f77 6865 6164 2077 6f75 6c64  .arrowhead would\n+000159e0: 206e 6f74 2068 6176 6520 6265 656e 2064   not have been d\n+000159f0: 6973 746f 7274 6564 2e0a 0a20 2020 5468  istorted...   Th\n+00015a00: 6520 636f 6d70 6c65 7465 2063 6f64 6520  e complete code \n+00015a10: 666f 7220 7468 6973 2065 7861 6d70 6c65  for this example\n+00015a20: 2c20 7768 6963 6820 6472 6177 7320 6569  , which draws ei\n+00015a30: 7468 6572 2066 6967 7572 650a 6465 7065  ther figure.depe\n+00015a40: 6e64 696e 6720 6f6e 2074 6865 2064 6566  nding on the def\n+00015a50: 696e 6974 696f 6e20 6f66 2074 6865 2074  inition of the t\n+00015a60: 6167 2027 3c6c 6162 656c 6564 3e27 2c20  ag '<labeled>', \n+00015a70: 6973 2069 6e63 6c75 6465 6420 696e 2074  is included in t\n+00015a80: 6865 0a27 736b 6574 6368 2720 6469 7374  he.'sketch' dist\n+00015a90: 7269 6275 7469 6f6e 2069 6e20 7468 6520  ribution in the \n+00015aa0: 6669 6c65 2027 7472 756e 6361 7465 6463  file 'truncatedc\n+00015ab0: 6f6e 652e 736b 272e 0a0a 1f0a 4669 6c65  one.sk'.....File\n+00015ac0: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n+00015ad0: 4e6f 6465 3a20 4120 6869 6572 6172 6368  Node: A hierarch\n+00015ae0: 6963 616c 206d 6f64 656c 2c20 204e 6578  ical model,  Nex\n+00015af0: 743a 2043 6176 6561 7473 2c20 2050 7265  t: Caveats,  Pre\n+00015b00: 763a 2041 2074 6563 686e 6963 616c 2064  v: A technical d\n+00015b10: 7261 7769 6e67 2c20 2055 703a 2042 7569  rawing,  Up: Bui\n+00015b20: 6c64 696e 6720 6120 6472 6177 696e 670a  lding a drawing.\n+00015b30: 0a34 2e33 2041 2068 6965 7261 7263 6869  .4.3 A hierarchi\n+00015b40: 6361 6c20 6d6f 6465 6c0a 3d3d 3d3d 3d3d  cal model.======\n+00015b50: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n+00015b60: 3d3d 0a0a 5768 696c 6520 2773 6b65 7463  ==..While 'sketc\n+00015b70: 6827 2077 6173 206e 6576 6572 206d 6561  h' was never mea\n+00015b80: 6e74 2074 6f20 6265 2061 2067 656f 6d65  nt to be a geome\n+00015b90: 7472 6963 206d 6f64 656c 696e 6720 6c61  tric modeling la\n+00015ba0: 6e67 7561 6765 2c20 6974 0a63 6f6d 6573  nguage, it.comes\n+00015bb0: 2066 6169 726c 7920 636c 6f73 652e 2020   fairly close.  \n+00015bc0: 5468 6520 666f 6c6c 6f77 696e 6720 6578  The following ex\n+00015bd0: 616d 706c 6520 7075 7473 2061 6c6c 2077  ample puts all w\n+00015be0: 6520 6861 7665 2073 6565 6e20 746f 2077  e have seen to w\n+00015bf0: 6f72 6b0a 696e 2061 2076 6572 7920 7369  ork.in a very si\n+00015c00: 6d70 6c65 206d 6f64 656c 206f 6620 7468  mple model of th\n+00015c10: 6520 6875 6d61 6e20 6861 6e64 2e20 2053  e human hand.  S\n+00015c20: 7461 7274 2062 7920 7377 6565 7069 6e67  tart by sweeping\n+00015c30: 2061 206c 696e 6520 746f 0a6d 616b 6520   a line to.make \n+00015c40: 6120 7472 756e 6361 7465 6420 636f 6e65  a truncated cone\n+00015c50: 2c20 7768 6963 6820 7769 6c6c 2062 6520  , which will be \n+00015c60: 636f 7069 6564 206f 7665 7220 616e 6420  copied over and \n+00015c70: 6f76 6572 2061 6761 696e 2074 6f20 6d61  over again to ma\n+00015c80: 6b65 0a74 6865 2073 6567 6d65 6e74 7320  ke.the segments \n+00015c90: 6f66 2066 696e 6765 7273 2e0a 2020 6465  of fingers..  de\n+00015ca0: 6620 4f20 2830 2c30 2c30 2920 2520 6f72  f O (0,0,0) % or\n+00015cb0: 6967 696e 0a20 2064 6566 2049 205b 312c  igin.  def I [1,\n+00015cc0: 302c 305d 2064 6566 204a 205b 302c 312c  0,0] def J [0,1,\n+00015cd0: 305d 2064 6566 204b 205b 302c 302c 315d  0] def K [0,0,1]\n+00015ce0: 2025 2063 616e 6f6e 6963 616c 2075 6e69   % canonical uni\n+00015cf0: 7420 7665 6374 6f72 730a 2020 6465 6620  t vectors.  def \n+00015d00: 7365 676d 656e 7420 7b0a 2020 2020 6465  segment {.    de\n+00015d10: 6620 6e5f 6661 6365 7320 380a 2020 2020  f n_faces 8.    \n+00015d20: 7377 6565 7020 7b20 6e5f 6661 6365 733c  sweep { n_faces<\n+00015d30: 3e2c 2072 6f74 6174 6528 3336 3020 2f20  >, rotate(360 / \n+00015d40: 6e5f 6661 6365 732c 205b 4a5d 2920 7d20  n_faces, [J]) } \n+00015d50: 0a20 2020 2020 206c 696e 6528 7072 6f78  .      line(prox\n+00015d60: 696d 616c 5f72 6164 2c20 3029 2864 6973  imal_rad, 0)(dis\n+00015d70: 7461 6c5f 7261 642c 2064 6973 7461 6c5f  tal_rad, distal_\n+00015d80: 6c65 6e29 0a20 207d 0a49 6e20 6861 6e64  len).  }.In hand\n+00015d90: 2061 6e61 746f 6d79 2c20 5f64 6973 7461   anatomy, _dista\n+00015da0: 6c5f 2069 7320 2261 7420 7468 6520 7469  l_ is \"at the ti\n+00015db0: 7022 2061 6e64 205f 7072 6f78 696d 616c  p\" and _proximal\n+00015dc0: 5f20 6973 2022 696e 2074 6865 2061 7265  _ is \"in the are\n+00015dd0: 610a 6f66 2074 6865 2070 616c 6d2e 2220  a.of the palm.\" \n+00015de0: 2057 6520 6861 7665 206f 6d69 7474 6564   We have omitted\n+00015df0: 2061 6c6c 2074 6865 2073 6361 6c61 7220   all the scalar \n+00015e00: 636f 6e73 7461 6e74 732e 2020 596f 7520  constants.  You \n+00015e10: 6361 6e20 6669 6e64 0a74 6865 6d20 696e  can find.them in\n+00015e20: 2027 6861 6e64 2e73 6b27 2c20 7768 6963   'hand.sk', whic\n+00015e30: 6820 6973 2070 726f 7669 6465 6420 696e  h is provided in\n+00015e40: 2074 6865 2027 736b 6574 6368 2720 6469   the 'sketch' di\n+00015e50: 7374 7269 6275 7469 6f6e 2e0a 0a20 2020  stribution...   \n+00015e60: 5765 2061 6c73 6f20 6e65 6564 2061 2070  We also need a p\n+00015e70: 726f 746f 7479 7069 6361 6c20 7370 6865  rototypical sphe\n+00015e80: 7265 2074 6f20 7573 6520 666f 7220 7468  re to use for th\n+00015e90: 6520 6a6f 696e 7473 2074 6865 6d73 656c  e joints themsel\n+00015ea0: 7665 732e 0a20 2064 6566 206a 6f69 6e74  ves..  def joint\n+00015eb0: 5f73 7068 6572 6520 7b0a 2020 2020 6465  _sphere {.    de\n+00015ec0: 6620 6e5f 6a6f 696e 745f 6661 6365 7320  f n_joint_faces \n+00015ed0: 380a 2020 2020 7377 6565 7020 5b66 696c  8.    sweep [fil\n+00015ee0: 6c63 6f6c 6f72 3d72 6564 5d20 7b20 6e5f  lcolor=red] { n_\n+00015ef0: 6a6f 696e 745f 6661 6365 732c 2072 6f74  joint_faces, rot\n+00015f00: 6174 6528 3336 3020 2f20 6e5f 6a6f 696e  ate(360 / n_join\n+00015f10: 745f 6661 6365 732c 205b 4a5d 2920 7d0a  t_faces, [J]) }.\n+00015f20: 2020 2020 2020 7377 6565 7020 7b20 6e5f        sweep { n_\n+00015f30: 6a6f 696e 745f 6661 6365 732c 2072 6f74  joint_faces, rot\n+00015f40: 6174 6528 3138 3020 2f20 6e5f 6a6f 696e  ate(180 / n_join\n+00015f50: 745f 6661 6365 7329 207d 200a 2020 2020  t_faces) } .    \n+00015f60: 2020 2020 2830 2c20 2d6a 6f69 6e74 5f72      (0, -joint_r\n+00015f70: 6164 290a 2020 7d0a 0a20 2020 5765 276c  ad).  }..   We'l\n+00015f80: 6c20 6e6f 7720 6465 7369 676e 2074 6865  l now design the\n+00015f90: 2069 6e64 6578 2066 696e 6765 7220 286e   index finger (n\n+00015fa0: 756d 6265 7220 3120 696e 206f 7572 206e  umber 1 in our n\n+00015fb0: 6f74 6174 696f 6e61 6c0a 636f 6e76 656e  otational.conven\n+00015fc0: 7469 6f6e 3b20 6669 6e67 6572 2030 2069  tion; finger 0 i\n+00015fd0: 7320 7468 6520 7468 756d 6229 2e20 2054  s the thumb).  T\n+00015fe0: 6865 2064 6973 7461 6c20 726f 7461 7469  he distal rotati\n+00015ff0: 6f6e 2066 6f72 2074 6865 2066 696e 6765  on for the finge\n+00016000: 720a 6170 706c 6965 7320 6f6e 6c79 2074  r.applies only t\n+00016010: 6f20 7468 6520 7469 702c 2073 6f20 7765  o the tip, so we\n+00016020: 2064 6566 696e 6520 7468 6520 666f 6c6c   define the foll\n+00016030: 6f77 696e 672e 0a20 2064 6566 2064 6973  owing..  def dis\n+00016040: 7461 6c5f 3120 7b0a 2020 2020 7075 7420  tal_1 {.    put \n+00016050: 7b20 7472 616e 736c 6174 6528 6a6f 696e  { translate(join\n+00016060: 745f 6761 7020 2a20 6a6f 696e 745f 7261  t_gap * joint_ra\n+00016070: 6420 2a20 5b4a 5d29 200a 2020 2020 2020  d * [J]) .      \n+00016080: 2020 2020 7468 656e 2072 6f74 6174 6528      then rotate(\n+00016090: 6469 7374 616c 5f31 5f72 6f74 2c20 5b49  distal_1_rot, [I\n+000160a0: 5d29 200a 2020 2020 2020 2020 2020 7468  ]) .          th\n+000160b0: 656e 2074 7261 6e73 6c61 7465 2828 6469  en translate((di\n+000160c0: 7374 616c 5f6c 656e 202b 206a 6f69 6e74  stal_len + joint\n+000160d0: 5f67 6170 202a 206a 6f69 6e74 5f72 6164  _gap * joint_rad\n+000160e0: 2920 2a20 5b4a 5d29 207d 0a20 2020 2020  ) * [J]) }.     \n+000160f0: 207b 7365 676d 656e 747d 0a20 2020 2070   {segment}.    p\n+00016100: 7574 207b 2072 6f74 6174 6528 6469 7374  ut { rotate(dist\n+00016110: 616c 5f31 5f72 6f74 202f 2032 2c20 5b49  al_1_rot / 2, [I\n+00016120: 5d29 0a20 2020 2020 2020 2020 2074 6865  ]).          the\n+00016130: 6e20 7472 616e 736c 6174 6528 2864 6973  n translate((dis\n+00016140: 7461 6c5f 6c65 6e20 2b20 6a6f 696e 745f  tal_len + joint_\n+00016150: 6761 7020 2a20 6a6f 696e 745f 7261 6429  gap * joint_rad)\n+00016160: 202a 205b 4a5d 2920 7d20 0a20 2020 2020   * [J]) } .     \n+00016170: 207b 6a6f 696e 745f 7370 6865 7265 7d0a   {joint_sphere}.\n+00016180: 2020 2020 7075 7420 7b20 7363 616c 6528      put { scale(\n+00016190: 205b 4a5d 202b 2070 726f 7869 6d61 6c5f   [J] + proximal_\n+000161a0: 6469 7374 616c 5f72 6174 696f 202a 2028  distal_ratio * (\n+000161b0: 5b49 5d2b 5b4b 5d29 2029 207d 0a20 2020  [I]+[K]) ) }.   \n+000161c0: 2020 207b 7365 676d 656e 747d 0a20 207d     {segment}.  }\n+000161d0: 2020 0a54 6865 2069 6465 6e74 6966 6965    .The identifie\n+000161e0: 7273 2068 6572 6520 6172 6520 666f 7220  rs here are for \n+000161f0: 7369 7a65 2061 6e64 206c 6f63 6174 696f  size and locatio\n+00016200: 6e20 636f 6e73 7461 6e74 732e 2020 5468  n constants.  Th\n+00016210: 6520 6578 6365 7074 696f 6e0a 6973 2027  e exception.is '\n+00016220: 6469 7374 616c 5f72 6f74 5f31 272e 2020  distal_rot_1'.  \n+00016230: 5468 6973 2072 6f74 6174 696f 6e20 7061  This rotation pa\n+00016240: 7261 6d65 7465 7220 6d6f 6465 6c73 2074  rameter models t\n+00016250: 6865 2066 6c65 7869 6e67 206f 6620 7468  he flexing of th\n+00016260: 650a 6669 6e67 6572 2074 6970 2e20 2054  e.finger tip.  T\n+00016270: 6865 2066 6972 7374 2027 7075 7427 206d  he first 'put' m\n+00016280: 616b 6573 2061 2063 6f70 7920 6f66 2074  akes a copy of t\n+00016290: 6865 2066 696e 6765 7220 7365 676d 656e  he finger segmen\n+000162a0: 7420 7468 6174 2069 730a 7472 616e 736c  t that is.transl\n+000162b0: 6174 6564 2075 7077 6172 6420 6a75 7374  ated upward just\n+000162c0: 2066 6172 2065 6e6f 7567 6820 746f 206d   far enough to m\n+000162d0: 616b 6520 726f 6f6d 2066 6f72 2074 6865  ake room for the\n+000162e0: 2073 7068 6572 6963 616c 206a 6f69 6e74   spherical joint\n+000162f0: 2e0a 5468 656e 2069 7420 6170 706c 6965  ..Then it applie\n+00016300: 7320 7468 6520 6469 7374 616c 2072 6f74  s the distal rot\n+00016310: 6174 696f 6e2e 2020 4669 6e61 6c6c 7920  ation.  Finally \n+00016320: 6974 2074 7261 6e73 6c61 7465 7320 7468  it translates th\n+00016330: 6520 7768 6f6c 650a 6173 7365 6d62 6c79  e whole.assembly\n+00016340: 2075 7077 6172 6420 6167 6169 6e20 746f   upward again to\n+00016350: 206d 616b 6520 726f 6f6d 2066 6f72 2074   make room for t\n+00016360: 6865 206d 6964 646c 6520 7068 6c61 6e67  he middle phlang\n+00016370: 6573 2028 7468 6520 6e65 7874 0a62 6f6e  es (the next.bon\n+00016380: 6520 746f 7761 7264 2074 6865 2070 616c  e toward the pal\n+00016390: 6d29 2e20 2054 6865 2073 6563 6f6e 6420  m).  The second \n+000163a0: 2770 7574 2720 706f 7369 7469 6f6e 7320  'put' positions \n+000163b0: 7468 6520 7370 6865 7265 2e20 2054 6865  the sphere.  The\n+000163c0: 7265 2069 730a 6120 726f 7461 7469 6f6e  re is.a rotation\n+000163d0: 2074 6f20 706c 6163 6520 7468 6520 6772   to place the gr\n+000163e0: 6964 206f 6e20 7468 6520 7370 6865 7265  id on the sphere\n+000163f0: 2073 7572 6661 6365 2061 7420 616e 206e   surface at an n\n+00016400: 6963 6520 616e 676c 652c 0a74 6865 6e20  ice angle,.then \n+00016410: 6120 7472 616e 736c 6174 696f 6e20 746f  a translation to\n+00016420: 2074 6865 2062 6173 6520 6f66 2074 6865   the base of the\n+00016430: 2064 6973 7461 6c20 7068 6c61 6e67 6573   distal phlanges\n+00016440: 2c20 7768 6963 6820 6973 2061 6c73 6f0a  , which is also.\n+00016450: 6365 6e74 6572 206f 6620 6974 7320 726f  center of its ro\n+00016460: 7461 7469 6f6e 2e20 2046 696e 616c 6c79  tation.  Finally\n+00016470: 2c20 7468 6520 6c61 7374 2027 7075 7427  , the last 'put'\n+00016480: 2070 6f73 6974 696f 6e73 2074 6865 206d   positions the m\n+00016490: 6964 646c 650a 7365 676d 656e 7420 6974  iddle.segment it\n+000164a0: 7365 6c66 2e0a 0a20 2020 5468 6520 6d69  self...   The mi\n+000164b0: 6464 6c65 206a 6f69 6e74 2069 7320 7468  ddle joint is th\n+000164c0: 6520 6e65 7874 206f 6e65 2064 6f77 6e2c  e next one down,\n+000164d0: 2077 6974 6820 726f 7461 7469 6f6e 2061   with rotation a\n+000164e0: 6e67 6c65 0a27 6d69 6464 6c65 5f72 6f74  ngle.'middle_rot\n+000164f0: 5f31 272e 2020 5768 656e 2074 6869 7320  _1'.  When this \n+00016500: 616e 676c 6520 6368 616e 6765 732c 2077  angle changes, w\n+00016510: 6520 6e65 6564 2061 6c6c 2074 6865 206f  e need all the o\n+00016520: 626a 6563 7473 2069 6e0a 2764 6973 7461  bjects in.'dista\n+00016530: 6c5f 3127 2074 6f20 726f 7461 7465 2061  l_1' to rotate a\n+00016540: 7320 6120 756e 6974 2e20 2054 6869 7320  s a unit.  This \n+00016550: 6973 2074 6865 2072 6561 736f 6e69 6e67  is the reasoning\n+00016560: 2062 6568 696e 6420 7468 6520 6e65 7874   behind the next\n+00016570: 0a64 6566 696e 6974 696f 6e2e 0a20 2064  .definition..  d\n+00016580: 6566 2066 696e 6765 725f 3120 7b0a 2020  ef finger_1 {.  \n+00016590: 2020 7075 7420 7b20 7472 616e 736c 6174    put { translat\n+000165a0: 6528 6a6f 696e 745f 6761 7020 2a20 6a6f  e(joint_gap * jo\n+000165b0: 696e 745f 7261 6420 2a20 5b4a 5d29 0a20  int_rad * [J]). \n+000165c0: 2020 2020 2020 2020 2074 6865 6e20 726f           then ro\n+000165d0: 7461 7465 286d 6964 646c 655f 315f 726f  tate(middle_1_ro\n+000165e0: 742c 205b 495d 290a 2020 2020 2020 2020  t, [I]).        \n+000165f0: 2020 7468 656e 2074 7261 6e73 6c61 7465    then translate\n+00016600: 2828 6d69 6464 6c65 5f72 6174 696f 202a  ((middle_ratio *\n+00016610: 2064 6973 7461 6c5f 6c65 6e20 2b20 0a20   distal_len + . \n 00016620: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00016630: 2020 206a 6f69 6e74 5f67 6170 202a 206a     joint_gap * j\n-00016640: 6f69 6e74 5f72 6164 2920 2a20 5b4a 5d29  oint_rad) * [J])\n-00016650: 207d 0a20 2020 2020 207b 6469 7374 616c   }.      {distal\n-00016660: 5f31 7d0a 2020 2020 7075 7420 7b20 7363  _1}.    put { sc\n-00016670: 616c 6528 7072 6f78 696d 616c 5f64 6973  ale(proximal_dis\n-00016680: 7461 6c5f 7261 7469 6f29 0a20 2020 2020  tal_ratio).     \n-00016690: 2020 2020 2074 6865 6e20 726f 7461 7465       then rotate\n-000166a0: 286d 6964 646c 655f 315f 726f 7420 2f20  (middle_1_rot / \n-000166b0: 322c 205b 495d 290a 2020 2020 2020 2020  2, [I]).        \n-000166c0: 2020 7468 656e 2074 7261 6e73 6c61 7465    then translate\n-000166d0: 2828 6d69 6464 6c65 5f72 6174 696f 202a  ((middle_ratio *\n-000166e0: 2064 6973 7461 6c5f 6c65 6e20 2b20 0a20   distal_len + . \n-000166f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00016700: 2020 2020 2020 2020 206a 6f69 6e74 5f67           joint_g\n-00016710: 6170 202a 206a 6f69 6e74 5f72 6164 2920  ap * joint_rad) \n-00016720: 2a20 5b4a 5d29 207d 200a 2020 2020 2020  * [J]) } .      \n-00016730: 7b6a 6f69 6e74 5f73 7068 6572 657d 0a20  {joint_sphere}. \n-00016740: 2020 2070 7574 207b 2073 6361 6c65 2820     put { scale( \n-00016750: 6d69 6464 6c65 5f72 6174 696f 202a 205b  middle_ratio * [\n-00016760: 4a5d 202b 200a 2020 2020 2020 2020 2020  J] + .          \n-00016770: 2020 2020 2020 2070 726f 7869 6d61 6c5f         proximal_\n-00016780: 6469 7374 616c 5f72 6174 696f 5e32 202a  distal_ratio^2 *\n-00016790: 2028 5b49 5d2b 5b4b 5d29 2029 207d 0a20   ([I]+[K]) ) }. \n-000167a0: 2020 2020 207b 7365 676d 656e 747d 0a20       {segment}. \n-000167b0: 207d 0a54 6869 7320 6c6f 6f6b 7320 7665   }.This looks ve\n-000167c0: 7279 2073 696d 696c 6172 2074 6f20 7468  ry similar to th\n-000167d0: 6520 7072 6576 696f 7573 2064 6566 696e  e previous defin\n-000167e0: 6974 696f 6e2c 2061 6e64 2069 7420 6973  ition, and it is\n-000167f0: 2e20 2054 6865 0a69 6d70 6f72 7461 6e74  .  The.important\n-00016800: 2064 6966 6665 7265 6e63 6520 6973 2074   difference is t\n-00016810: 6861 7420 7261 7468 6572 2074 6861 6e20  hat rather than \n-00016820: 706f 7369 7469 6f6e 696e 6720 616e 6420  positioning and \n-00016830: 726f 7461 7469 6e67 2061 0a73 696e 676c  rotating a.singl\n-00016840: 6520 7365 676d 656e 742c 2077 6520 706f  e segment, we po\n-00016850: 7369 7469 6f6e 2061 6e64 2072 6f74 6174  sition and rotat\n-00016860: 6520 7468 6520 656e 7469 7265 2022 6173  e the entire \"as\n-00016870: 7365 6d62 6c79 2220 6465 6669 6e65 6420  sembly\" defined \n-00016880: 6173 0a27 6469 7374 616c 5f31 272e 2020  as.'distal_1'.  \n-00016890: 5468 6520 7265 7374 2069 7320 6a75 7374  The rest is just\n-000168a0: 2061 7269 7468 6d65 7469 6320 746f 2063   arithmetic to c\n-000168b0: 6f6d 7075 7465 2073 697a 6573 2061 6e64  ompute sizes and\n-000168c0: 2070 6f73 6974 696f 6e73 0a74 6861 7420   positions.that \n-000168d0: 6c6f 6f6b 206e 6963 652e 2020 5468 6520  look nice.  The \n-000168e0: 6c61 7374 2027 7075 7427 2070 6c61 6365  last 'put' place\n-000168f0: 7320 616e 2061 7070 726f 7072 6961 7465  s an appropriate\n-00016900: 6c79 2073 6861 7065 6420 7365 676d 656e  ly shaped segmen\n-00016910: 740a 7468 6174 2069 7320 7468 6520 5f70  t.that is the _p\n-00016920: 726f 7869 6d61 6c20 7068 6c61 6e67 6573  roximal phlanges\n-00016930: 5f2c 2074 6865 2062 6f6e 6520 7468 6174  _, the bone that\n-00016940: 206a 6f69 6e73 2074 6865 2070 616c 6d20   joins the palm \n-00016950: 6f66 2074 6865 0a68 616e 642e 2020 5468  of the.hand.  Th\n-00016960: 6973 2063 6f6d 706c 6574 6573 2074 6865  is completes the\n-00016970: 2066 696e 6765 7220 6974 7365 6c66 2e0a   finger itself..\n-00016980: 0a20 2020 416c 6c20 7468 6520 6f74 6865  .   All the othe\n-00016990: 7220 6669 6e67 6572 7320 6172 6520 6465  r fingers are de\n-000169a0: 7363 7269 6265 6420 6964 656e 7469 6361  scribed identica\n-000169b0: 6c6c 7920 746f 2074 6869 7320 6f6e 652e  lly to this one.\n-000169c0: 2020 5765 0a61 6363 6f75 6e74 2066 6f72    We.account for\n-000169d0: 2074 6865 2066 6163 7420 7468 6174 2072   the fact that r\n-000169e0: 6561 6c20 6669 6e67 6572 7320 6172 6520  eal fingers are \n-000169f0: 6469 6666 6572 656e 7420 7369 7a65 7320  different sizes \n-00016a00: 696e 2074 6865 206e 6578 740a 7374 6570  in the next.step\n-00016a10: 2c20 7768 6963 6820 6973 2074 6f20 6275  , which is to bu\n-00016a20: 696c 6420 7468 6520 656e 7469 7265 2068  ild the entire h\n-00016a30: 616e 642e 0a0a 2020 2054 6865 2027 6861  and...   The 'ha\n-00016a40: 6e64 2720 6465 6669 6e69 7469 6f6e 2074  nd' definition t\n-00016a50: 6861 7420 666f 6c6c 6f77 7320 696e 636c  hat follows incl\n-00016a60: 7564 6573 2061 2073 6563 7469 6f6e 2066  udes a section f\n-00016a70: 6f72 2065 6163 680a 6669 6e67 6572 2e20  or each.finger. \n-00016a80: 2057 6527 6c6c 2063 6f6e 7469 6e75 6520   We'll continue \n-00016a90: 7769 7468 2066 696e 6765 7220 3120 616e  with finger 1 an\n-00016aa0: 6420 6f6d 6974 2061 6c6c 2074 6865 206f  d omit all the o\n-00016ab0: 7468 6572 732e 2020 284f 6620 6e6f 7465  thers.  (Of note\n-00016ac0: 0a69 7320 7468 6174 2074 6865 2074 6875  .is that the thu\n-00016ad0: 6d62 206e 6565 6473 2073 6c69 6768 746c  mb needs slightl\n-00016ae0: 7920 7370 6563 6961 6c20 7472 6561 746d  y special treatm\n-00016af0: 656e 742d 2d61 6e20 6578 7472 6120 726f  ent--an extra ro\n-00016b00: 7461 7469 6f6e 2074 6f0a 6163 636f 756e  tation to.accoun\n-00016b10: 7420 666f 7220 6974 7320 6f70 706f 7369  t for its opposi\n-00016b20: 6e67 2061 6e67 6c65 2e20 2054 6869 7320  ng angle.  This \n-00016b30: 6973 2063 6c65 6172 2069 6e20 7468 6520  is clear in the \n-00016b40: 6675 6c6c 2073 6f75 7263 6520 636f 6465  full source code\n-00016b50: 2e29 0a4e 6f74 2073 7572 7072 6973 696e  .).Not surprisin\n-00016b60: 676c 792c 2074 6865 2027 6861 6e64 2720  gly, the 'hand' \n-00016b70: 6465 6669 6e69 7469 6f6e 206c 6f6f 6b73  definition looks\n-00016b80: 2076 6572 7920 6d75 6368 206c 696b 6520   very much like \n-00016b90: 7468 650a 7072 6576 696f 7573 2074 776f  the.previous two\n-00016ba0: 2e20 2049 7420 7368 6f75 6c64 2062 6520  .  It should be \n-00016bb0: 6e6f 2073 7572 7072 6973 6520 7468 6174  no surprise that\n-00016bc0: 2077 6865 6e20 7468 6520 726f 7461 7469   when the rotati\n-00016bd0: 6f6e 2070 6172 616d 6574 6572 0a27 6d65  on parameter.'me\n-00016be0: 7461 5f31 5f72 6f74 2720 6368 616e 6765  ta_1_rot' change\n-00016bf0: 732c 2074 6865 2065 6e74 6972 6520 6669  s, the entire fi\n-00016c00: 6e67 6572 2072 6f74 6174 6573 2120 2054  nger rotates!  T\n-00016c10: 6865 7265 2069 7320 616e 2061 6464 6974  here is an addit\n-00016c20: 696f 6e61 6c0a 726f 7461 7469 6f6e 2074  ional.rotation t\n-00016c30: 6861 7420 616c 6c6f 7773 2074 6865 2066  hat allows the f\n-00016c40: 696e 6765 7273 2074 6f20 7370 7265 6164  ingers to spread\n-00016c50: 206c 6174 6572 616c 6c79 2e20 2057 6520   laterally.  We \n-00016c60: 7361 7920 7468 6573 650a 6a6f 696e 7473  say these.joints\n-00016c70: 206f 6620 7468 6520 7072 6f78 696d 616c   of the proximal\n-00016c80: 2070 686c 616e 6765 7320 6861 7665 2074   phlanges have t\n-00016c90: 776f 205f 6465 6772 6565 7320 6f66 2066  wo _degrees of f\n-00016ca0: 7265 6564 6f6d 5f2e 2020 5468 650a 6a6f  reedom_.  The.jo\n-00016cb0: 696e 7473 2068 6967 6865 7220 6f6e 2074  ints higher on t\n-00016cc0: 6865 2066 696e 6765 7220 6861 7665 206f  he finger have o\n-00016cd0: 6e6c 7920 6f6e 652e 2020 4669 6e61 6c6c  nly one.  Finall\n-00016ce0: 792c 2065 6163 6820 6669 6e67 6572 2069  y, each finger i\n-00016cf0: 730a 7363 616c 6564 2062 7920 6120 6661  s.scaled by a fa\n-00016d00: 6374 6f72 2074 6f20 6c65 6e64 2069 7420  ctor to lend it \n-00016d10: 7072 6f70 6f72 7469 6f6e 2e0a 2020 6465  proportion..  de\n-00016d20: 6620 6861 6e64 207b 0a20 2020 2025 2066  f hand {.    % f\n-00016d30: 696e 6765 7220 3120 5b61 6c6c 206f 7468  inger 1 [all oth\n-00016d40: 6572 2066 696e 6765 7273 206f 6d69 7474  er fingers omitt\n-00016d50: 6564 5d0a 2020 2020 6465 6620 7363 616c  ed].    def scal\n-00016d60: 655f 3120 2e38 350a 2020 2020 7075 7420  e_1 .85.    put \n-00016d70: 7b20 7363 616c 6528 7363 616c 655f 3129  { scale(scale_1)\n-00016d80: 200a 2020 2020 2020 2020 2020 7468 656e   .          then\n-00016d90: 2074 7261 6e73 6c61 7465 2828 6a6f 696e   translate((join\n-00016da0: 745f 6761 7020 2a20 6a6f 696e 745f 7261  t_gap * joint_ra\n-00016db0: 6429 202a 205b 4a5d 290a 0920 2074 6865  d) * [J])..  the\n-00016dc0: 6e20 726f 7461 7465 286d 6574 615f 315f  n rotate(meta_1_\n-00016dd0: 726f 742c 205b 495d 290a 2020 2020 2020  rot, [I]).      \n-00016de0: 2020 2020 7468 656e 2072 6f74 6174 6528      then rotate(\n-00016df0: 2d73 7072 6561 645f 726f 742c 205b 4b5d  -spread_rot, [K]\n-00016e00: 290a 2020 2020 2020 2020 2020 7468 656e  ).          then\n-00016e10: 2074 7261 6e73 6c61 7465 2828 7072 6f78   translate((prox\n-00016e20: 696d 616c 5f31 5f6c 6f63 2920 2d20 284f  imal_1_loc) - (O\n-00016e30: 2929 207d 200a 2020 2020 2020 7b66 696e  )) } .      {fin\n-00016e40: 6765 725f 317d 0a20 2020 2070 7574 207b  ger_1}.    put {\n-00016e50: 2073 6361 6c65 2873 6361 6c65 5f31 202a   scale(scale_1 *\n-00016e60: 2070 726f 7869 6d61 6c5f 6469 7374 616c   proximal_distal\n-00016e70: 5f72 6174 696f 5e32 290a 2020 2020 2020  _ratio^2).      \n-00016e80: 2020 2020 7468 656e 2072 6f74 6174 6528      then rotate(\n-00016e90: 6d65 7461 5f31 5f72 6f74 202f 2032 2c20  meta_1_rot / 2, \n-00016ea0: 5b49 5d29 0a20 2020 2020 2020 2020 2074  [I]).          t\n-00016eb0: 6865 6e20 726f 7461 7465 282d 7370 7265  hen rotate(-spre\n-00016ec0: 6164 5f72 6f74 2c20 5b4b 5d29 0a20 2020  ad_rot, [K]).   \n-00016ed0: 2020 2020 2020 2074 6865 6e20 7472 616e         then tran\n-00016ee0: 736c 6174 6528 2870 726f 7869 6d61 6c5f  slate((proximal_\n-00016ef0: 315f 6c6f 6329 202d 2028 4f29 2920 7d20  1_loc) - (O)) } \n-00016f00: 0a20 2020 2020 207b 6a6f 696e 745f 7370  .      {joint_sp\n-00016f10: 6865 7265 7d0a 0a20 2020 2025 2070 616c  here}..    % pal\n-00016f20: 6d0a 2020 2020 7377 6565 7020 7b20 312c  m.    sweep { 1,\n-00016f30: 2072 6f74 6174 6528 362c 2028 302c 3135   rotate(6, (0,15\n-00016f40: 2c30 292c 205b 495d 2920 7d0a 2020 2020  ,0), [I]) }.    \n-00016f50: 2020 7075 7420 7b20 726f 7461 7465 282d    put { rotate(-\n-00016f60: 332c 2028 302c 3135 2c30 292c 205b 495d  3, (0,15,0), [I]\n-00016f70: 2920 7d20 7b0a 2020 2020 2020 2020 706f  ) } {.        po\n-00016f80: 6c79 676f 6e28 7072 6f78 696d 616c 5f31  lygon(proximal_1\n-00016f90: 5f6c 6f63 2928 7072 6f78 696d 616c 5f32  _loc)(proximal_2\n-00016fa0: 5f6c 6f63 290a 2020 2020 2020 2020 2020  _loc).          \n-00016fb0: 2020 2020 2028 7072 6f78 696d 616c 5f33       (proximal_3\n-00016fc0: 5f6c 6f63 2928 7072 6f78 696d 616c 5f34  _loc)(proximal_4\n-00016fd0: 5f6c 6f63 290a 2020 2020 2020 2020 2020  _loc).          \n-00016fe0: 2020 2020 2028 6835 2928 6836 2928 6836       (h5)(h6)(h6\n-00016ff0: 6129 2868 3929 2868 3130 290a 2020 2020  a)(h9)(h10).    \n-00017000: 2020 2020 706f 6c79 676f 6e28 6836 6129      polygon(h6a)\n-00017010: 2868 3729 2868 3829 2868 3929 0a20 2020  (h7)(h8)(h9).   \n-00017020: 7d20 207d 0a54 6865 206c 6173 7420 7365  }  }.The last se\n-00017030: 6374 696f 6e20 6f66 2074 6865 2064 6566  ction of the def\n-00017040: 696e 6974 696f 6e20 6372 6561 7465 7320  inition creates \n-00017050: 7468 6520 706f 6c79 746f 7065 2066 6f72  the polytope for\n-00017060: 2074 6865 2070 616c 6d20 6f66 0a74 6865   the palm of.the\n-00017070: 2068 616e 6420 6279 2027 7377 6565 7027   hand by 'sweep'\n-00017080: 696e 6720 6120 3130 2d73 6964 6564 2070  ing a 10-sided p\n-00017090: 6f6c 7967 6f6e 2074 6872 6f75 6768 2061  olygon through a\n-000170a0: 2076 6572 7920 7368 6f72 7420 6172 630a   very short arc.\n-000170b0: 2839 2064 6567 7265 6573 292e 2020 5468  (9 degrees).  Th\n-000170c0: 6973 2070 726f 7669 6465 7320 6120 7765  is provides a we\n-000170d0: 6467 652d 7368 6170 6564 2070 726f 6669  dge-shaped profi\n-000170e0: 6c65 2077 6865 6e20 7669 6577 6564 2066  le when viewed f\n-000170f0: 726f 6d20 7468 650a 7369 6465 2e20 2054  rom the.side.  T\n-00017100: 6865 2074 6869 636b 2065 6e64 206f 6620  he thick end of \n-00017110: 7468 6520 7765 6467 6520 6973 2074 6865  the wedge is the\n-00017120: 2077 7269 7374 2e20 2042 6563 6175 7365   wrist.  Because\n-00017130: 2074 6865 2070 6f6c 7967 6f6e 2069 730a   the polygon is.\n-00017140: 636f 6e63 6176 652c 2069 7420 6973 2073  concave, it is s\n-00017150: 706c 6974 2069 6e74 6f20 696e 746f 2074  plit into into t\n-00017160: 776f 2063 6f6e 7665 7820 7368 6170 6573  wo convex shapes\n-00017170: 2077 6974 6820 6e69 6e65 2061 6e64 2066   with nine and f\n-00017180: 6f75 720a 7665 7274 6963 6573 2e0a 0a20  our.vertices... \n-00017190: 2020 5765 2063 616e 206e 6f77 2068 6176    We can now hav\n-000171a0: 6520 6675 6e20 706f 7369 7469 6f6e 696e  e fun positionin\n-000171b0: 6720 7468 6520 6861 6e64 2062 7920 6164  g the hand by ad\n-000171c0: 6a75 7374 696e 6720 7468 6520 7661 7269  justing the vari\n-000171d0: 6f75 730a 726f 7461 7469 6f6e 2061 6e67  ous.rotation ang\n-000171e0: 6c65 732e 2020 5468 6520 636f 6d70 6c65  les.  The comple\n-000171f0: 7465 2073 6f75 7263 6520 696e 636c 7564  te source includ\n-00017200: 6573 2064 6566 696e 6974 696f 6e73 2077  es definitions w\n-00017210: 6974 680a 616c 7465 726e 6174 6976 6573  ith.alternatives\n-00017220: 2074 6861 7420 696e 636c 7564 6520 7468   that include th\n-00017230: 6520 666f 6c6c 6f77 696e 6720 7669 6577  e following view\n-00017240: 7320 616e 6420 6d6f 7265 2e0a 0a00 085b  s and more.....[\n-00017250: 696d 6167 6520 7372 633d 2265 7832 3130  image src=\"ex210\n-00017260: 2e70 6e67 2220 7465 7874 3d22 496d 6167  .png\" text=\"Imag\n-00017270: 6520 6578 3231 3020 6f6d 6974 7465 6420  e ex210 omitted \n-00017280: 696e 2074 6578 7420 7665 7273 696f 6e20  in text version \n-00017290: 6f66 2074 6869 7320 646f 6375 6d65 6e74  of this document\n-000172a0: 2e22 0008 5d00 085b 696d 6167 6520 7372  .\"..]..[image sr\n-000172b0: 633d 2265 7832 3230 2e70 6e67 2220 7465  c=\"ex220.png\" te\n-000172c0: 7874 3d22 496d 6167 6520 6578 3232 3020  xt=\"Image ex220 \n-000172d0: 6f6d 6974 7465 6420 696e 2074 6578 7420  omitted in text \n-000172e0: 7665 7273 696f 6e20 6f66 2074 6869 7320  version of this \n-000172f0: 646f 6375 6d65 6e74 2e22 0008 5d00 085b  document.\"..]..[\n-00017300: 696d 6167 6520 7372 633d 2265 7832 3330  image src=\"ex230\n-00017310: 2e70 6e67 2220 7465 7874 3d22 496d 6167  .png\" text=\"Imag\n-00017320: 6520 6578 3233 3020 6f6d 6974 7465 6420  e ex230 omitted \n-00017330: 696e 2074 6578 7420 7665 7273 696f 6e20  in text version \n-00017340: 6f66 2074 6869 7320 646f 6375 6d65 6e74  of this document\n-00017350: 2e22 0008 5d00 085b 696d 6167 6520 7372  .\"..]..[image sr\n-00017360: 633d 2265 7832 3430 2e70 6e67 2220 7465  c=\"ex240.png\" te\n-00017370: 7874 3d22 496d 6167 6520 6578 3234 3020  xt=\"Image ex240 \n-00017380: 6f6d 6974 7465 6420 696e 2074 6578 7420  omitted in text \n-00017390: 7665 7273 696f 6e20 6f66 2074 6869 7320  version of this \n-000173a0: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a1f  document.\"..]...\n-000173b0: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n-000173c0: 666f 2c20 204e 6f64 653a 2043 6176 6561  fo,  Node: Cavea\n-000173d0: 7473 2c20 2050 7265 763a 2041 2068 6965  ts,  Prev: A hie\n-000173e0: 7261 7263 6869 6361 6c20 6d6f 6465 6c2c  rarchical model,\n-000173f0: 2020 5570 3a20 4275 696c 6469 6e67 2061    Up: Building a\n-00017400: 2064 7261 7769 6e67 0a0a 342e 3420 4361   drawing..4.4 Ca\n-00017410: 7665 6174 730a 3d3d 3d3d 3d3d 3d3d 3d3d  veats.==========\n-00017420: 3d0a 0a27 536b 6574 6368 2720 6973 2061  =..'Sketch' is a\n-00017430: 2066 6169 726c 7920 706f 7765 7266 756c   fairly powerful\n-00017440: 2074 6f6f 6c20 666f 7220 6472 6177 696e   tool for drawin\n-00017450: 672c 2062 7574 2c20 6a75 7374 2061 7320  g, but, just as \n-00017460: 7769 7468 2054 6558 2c0a 7468 6520 706f  with TeX,.the po\n-00017470: 7765 7220 746f 2063 7265 6174 6520 6265  wer to create be\n-00017480: 6175 7469 6675 6c20 7265 7375 6c74 7320  autiful results \n-00017490: 636f 6d65 7320 616c 6f6e 6720 7769 7468  comes along with\n-000174a0: 2074 6865 2070 6f77 6572 2074 6f20 6d61   the power to ma\n-000174b0: 6b65 0a6d 6973 7461 6b65 732e 2020 5468  ke.mistakes.  Th\n-000174c0: 6520 666f 6c6c 6f77 696e 6720 6172 6520  e following are \n-000174d0: 736f 6d65 2070 6f69 6e74 7320 7768 6572  some points wher\n-000174e0: 6520 6361 7265 2069 7320 6e65 6365 7373  e care is necess\n-000174f0: 6172 7920 616e 640a 7768 6572 6520 7468  ary and.where th\n-00017500: 6520 6375 7272 656e 7420 7665 7273 696f  e current versio\n-00017510: 6e20 6f66 2027 736b 6574 6368 2720 6973  n of 'sketch' is\n-00017520: 206c 696d 6974 6564 206f 7220 6861 7320   limited or has \n-00017530: 6b6e 6f77 6e20 6275 6773 2e0a 0a2a 204d  known bugs...* M\n-00017540: 656e 753a 0a0a 2a20 4c69 6d69 7473 206f  enu:..* Limits o\n-00017550: 6e20 6572 726f 7220 6465 7465 6374 696f  n error detectio\n-00017560: 6e3a 3a20 2020 5768 6174 2073 6b65 7463  n::   What sketc\n-00017570: 6820 646f 6573 6e27 7420 646f 2e0a 2a20  h doesn't do..* \n-00017580: 436c 6970 7069 6e67 3a3a 2020 2020 2020  Clipping::      \n-00017590: 2020 2020 2020 2020 2020 2020 2020 4e6f                No\n-000175a0: 2063 6c69 7070 696e 6720 6174 2070 7265   clipping at pre\n-000175b0: 7365 6e74 2e0a 2a20 4869 6464 656e 2073  sent..* Hidden s\n-000175c0: 7572 6661 6365 2072 656d 6f76 616c 3a3a  urface removal::\n-000175d0: 2020 2020 2020 496d 7065 7266 6563 7469        Imperfecti\n-000175e0: 6f6e 7320 746f 2066 6978 2e0a 0a1f 0a46  ons to fix.....F\n-000175f0: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n-00017600: 2c20 204e 6f64 653a 204c 696d 6974 7320  ,  Node: Limits \n-00017610: 6f6e 2065 7272 6f72 2064 6574 6563 7469  on error detecti\n-00017620: 6f6e 2c20 204e 6578 743a 2043 6c69 7070  on,  Next: Clipp\n-00017630: 696e 672c 2020 5072 6576 3a20 4361 7665  ing,  Prev: Cave\n-00017640: 6174 732c 2020 5570 3a20 4361 7665 6174  ats,  Up: Caveat\n-00017650: 730a 0a34 2e34 2e31 204c 696d 6974 7320  s..4.4.1 Limits \n-00017660: 6f6e 2027 736b 6574 6368 2720 6572 726f  on 'sketch' erro\n-00017670: 7220 6465 7465 6374 696f 6e0a 2d2d 2d2d  r detection.----\n-00017680: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n+00016630: 2020 2020 2020 2020 206a 6f69 6e74 5f67           joint_g\n+00016640: 6170 202a 206a 6f69 6e74 5f72 6164 2920  ap * joint_rad) \n+00016650: 2a20 5b4a 5d29 207d 0a20 2020 2020 207b  * [J]) }.      {\n+00016660: 6469 7374 616c 5f31 7d0a 2020 2020 7075  distal_1}.    pu\n+00016670: 7420 7b20 7363 616c 6528 7072 6f78 696d  t { scale(proxim\n+00016680: 616c 5f64 6973 7461 6c5f 7261 7469 6f29  al_distal_ratio)\n+00016690: 0a20 2020 2020 2020 2020 2074 6865 6e20  .          then \n+000166a0: 726f 7461 7465 286d 6964 646c 655f 315f  rotate(middle_1_\n+000166b0: 726f 7420 2f20 322c 205b 495d 290a 2020  rot / 2, [I]).  \n+000166c0: 2020 2020 2020 2020 7468 656e 2074 7261          then tra\n+000166d0: 6e73 6c61 7465 2828 6d69 6464 6c65 5f72  nslate((middle_r\n+000166e0: 6174 696f 202a 2064 6973 7461 6c5f 6c65  atio * distal_le\n+000166f0: 6e20 2b20 0a20 2020 2020 2020 2020 2020  n + .           \n+00016700: 2020 2020 2020 2020 2020 2020 2020 206a                 j\n+00016710: 6f69 6e74 5f67 6170 202a 206a 6f69 6e74  oint_gap * joint\n+00016720: 5f72 6164 2920 2a20 5b4a 5d29 207d 200a  _rad) * [J]) } .\n+00016730: 2020 2020 2020 7b6a 6f69 6e74 5f73 7068        {joint_sph\n+00016740: 6572 657d 0a20 2020 2070 7574 207b 2073  ere}.    put { s\n+00016750: 6361 6c65 2820 6d69 6464 6c65 5f72 6174  cale( middle_rat\n+00016760: 696f 202a 205b 4a5d 202b 200a 2020 2020  io * [J] + .    \n+00016770: 2020 2020 2020 2020 2020 2020 2070 726f               pro\n+00016780: 7869 6d61 6c5f 6469 7374 616c 5f72 6174  ximal_distal_rat\n+00016790: 696f 5e32 202a 2028 5b49 5d2b 5b4b 5d29  io^2 * ([I]+[K])\n+000167a0: 2029 207d 0a20 2020 2020 207b 7365 676d   ) }.      {segm\n+000167b0: 656e 747d 0a20 207d 0a54 6869 7320 6c6f  ent}.  }.This lo\n+000167c0: 6f6b 7320 7665 7279 2073 696d 696c 6172  oks very similar\n+000167d0: 2074 6f20 7468 6520 7072 6576 696f 7573   to the previous\n+000167e0: 2064 6566 696e 6974 696f 6e2c 2061 6e64   definition, and\n+000167f0: 2069 7420 6973 2e20 2054 6865 0a69 6d70   it is.  The.imp\n+00016800: 6f72 7461 6e74 2064 6966 6665 7265 6e63  ortant differenc\n+00016810: 6520 6973 2074 6861 7420 7261 7468 6572  e is that rather\n+00016820: 2074 6861 6e20 706f 7369 7469 6f6e 696e   than positionin\n+00016830: 6720 616e 6420 726f 7461 7469 6e67 2061  g and rotating a\n+00016840: 0a73 696e 676c 6520 7365 676d 656e 742c  .single segment,\n+00016850: 2077 6520 706f 7369 7469 6f6e 2061 6e64   we position and\n+00016860: 2072 6f74 6174 6520 7468 6520 656e 7469   rotate the enti\n+00016870: 7265 2022 6173 7365 6d62 6c79 2220 6465  re \"assembly\" de\n+00016880: 6669 6e65 6420 6173 0a27 6469 7374 616c  fined as.'distal\n+00016890: 5f31 272e 2020 5468 6520 7265 7374 2069  _1'.  The rest i\n+000168a0: 7320 6a75 7374 2061 7269 7468 6d65 7469  s just arithmeti\n+000168b0: 6320 746f 2063 6f6d 7075 7465 2073 697a  c to compute siz\n+000168c0: 6573 2061 6e64 2070 6f73 6974 696f 6e73  es and positions\n+000168d0: 0a74 6861 7420 6c6f 6f6b 206e 6963 652e  .that look nice.\n+000168e0: 2020 5468 6520 6c61 7374 2027 7075 7427    The last 'put'\n+000168f0: 2070 6c61 6365 7320 616e 2061 7070 726f   places an appro\n+00016900: 7072 6961 7465 6c79 2073 6861 7065 6420  priately shaped \n+00016910: 7365 676d 656e 740a 7468 6174 2069 7320  segment.that is \n+00016920: 7468 6520 5f70 726f 7869 6d61 6c20 7068  the _proximal ph\n+00016930: 6c61 6e67 6573 5f2c 2074 6865 2062 6f6e  langes_, the bon\n+00016940: 6520 7468 6174 206a 6f69 6e73 2074 6865  e that joins the\n+00016950: 2070 616c 6d20 6f66 2074 6865 0a68 616e   palm of the.han\n+00016960: 642e 2020 5468 6973 2063 6f6d 706c 6574  d.  This complet\n+00016970: 6573 2074 6865 2066 696e 6765 7220 6974  es the finger it\n+00016980: 7365 6c66 2e0a 0a20 2020 416c 6c20 7468  self...   All th\n+00016990: 6520 6f74 6865 7220 6669 6e67 6572 7320  e other fingers \n+000169a0: 6172 6520 6465 7363 7269 6265 6420 6964  are described id\n+000169b0: 656e 7469 6361 6c6c 7920 746f 2074 6869  entically to thi\n+000169c0: 7320 6f6e 652e 2020 5765 0a61 6363 6f75  s one.  We.accou\n+000169d0: 6e74 2066 6f72 2074 6865 2066 6163 7420  nt for the fact \n+000169e0: 7468 6174 2072 6561 6c20 6669 6e67 6572  that real finger\n+000169f0: 7320 6172 6520 6469 6666 6572 656e 7420  s are different \n+00016a00: 7369 7a65 7320 696e 2074 6865 206e 6578  sizes in the nex\n+00016a10: 740a 7374 6570 2c20 7768 6963 6820 6973  t.step, which is\n+00016a20: 2074 6f20 6275 696c 6420 7468 6520 656e   to build the en\n+00016a30: 7469 7265 2068 616e 642e 0a0a 2020 2054  tire hand...   T\n+00016a40: 6865 2027 6861 6e64 2720 6465 6669 6e69  he 'hand' defini\n+00016a50: 7469 6f6e 2074 6861 7420 666f 6c6c 6f77  tion that follow\n+00016a60: 7320 696e 636c 7564 6573 2061 2073 6563  s includes a sec\n+00016a70: 7469 6f6e 2066 6f72 2065 6163 680a 6669  tion for each.fi\n+00016a80: 6e67 6572 2e20 2057 6527 6c6c 2063 6f6e  nger.  We'll con\n+00016a90: 7469 6e75 6520 7769 7468 2066 696e 6765  tinue with finge\n+00016aa0: 7220 3120 616e 6420 6f6d 6974 2061 6c6c  r 1 and omit all\n+00016ab0: 2074 6865 206f 7468 6572 732e 2020 284f   the others.  (O\n+00016ac0: 6620 6e6f 7465 0a69 7320 7468 6174 2074  f note.is that t\n+00016ad0: 6865 2074 6875 6d62 206e 6565 6473 2073  he thumb needs s\n+00016ae0: 6c69 6768 746c 7920 7370 6563 6961 6c20  lightly special \n+00016af0: 7472 6561 746d 656e 742d 2d61 6e20 6578  treatment--an ex\n+00016b00: 7472 6120 726f 7461 7469 6f6e 2074 6f0a  tra rotation to.\n+00016b10: 6163 636f 756e 7420 666f 7220 6974 7320  account for its \n+00016b20: 6f70 706f 7369 6e67 2061 6e67 6c65 2e20  opposing angle. \n+00016b30: 2054 6869 7320 6973 2063 6c65 6172 2069   This is clear i\n+00016b40: 6e20 7468 6520 6675 6c6c 2073 6f75 7263  n the full sourc\n+00016b50: 6520 636f 6465 2e29 0a4e 6f74 2073 7572  e code.).Not sur\n+00016b60: 7072 6973 696e 676c 792c 2074 6865 2027  prisingly, the '\n+00016b70: 6861 6e64 2720 6465 6669 6e69 7469 6f6e  hand' definition\n+00016b80: 206c 6f6f 6b73 2076 6572 7920 6d75 6368   looks very much\n+00016b90: 206c 696b 6520 7468 650a 7072 6576 696f   like the.previo\n+00016ba0: 7573 2074 776f 2e20 2049 7420 7368 6f75  us two.  It shou\n+00016bb0: 6c64 2062 6520 6e6f 2073 7572 7072 6973  ld be no surpris\n+00016bc0: 6520 7468 6174 2077 6865 6e20 7468 6520  e that when the \n+00016bd0: 726f 7461 7469 6f6e 2070 6172 616d 6574  rotation paramet\n+00016be0: 6572 0a27 6d65 7461 5f31 5f72 6f74 2720  er.'meta_1_rot' \n+00016bf0: 6368 616e 6765 732c 2074 6865 2065 6e74  changes, the ent\n+00016c00: 6972 6520 6669 6e67 6572 2072 6f74 6174  ire finger rotat\n+00016c10: 6573 2120 2054 6865 7265 2069 7320 616e  es!  There is an\n+00016c20: 2061 6464 6974 696f 6e61 6c0a 726f 7461   additional.rota\n+00016c30: 7469 6f6e 2074 6861 7420 616c 6c6f 7773  tion that allows\n+00016c40: 2074 6865 2066 696e 6765 7273 2074 6f20   the fingers to \n+00016c50: 7370 7265 6164 206c 6174 6572 616c 6c79  spread laterally\n+00016c60: 2e20 2057 6520 7361 7920 7468 6573 650a  .  We say these.\n+00016c70: 6a6f 696e 7473 206f 6620 7468 6520 7072  joints of the pr\n+00016c80: 6f78 696d 616c 2070 686c 616e 6765 7320  oximal phlanges \n+00016c90: 6861 7665 2074 776f 205f 6465 6772 6565  have two _degree\n+00016ca0: 7320 6f66 2066 7265 6564 6f6d 5f2e 2020  s of freedom_.  \n+00016cb0: 5468 650a 6a6f 696e 7473 2068 6967 6865  The.joints highe\n+00016cc0: 7220 6f6e 2074 6865 2066 696e 6765 7220  r on the finger \n+00016cd0: 6861 7665 206f 6e6c 7920 6f6e 652e 2020  have only one.  \n+00016ce0: 4669 6e61 6c6c 792c 2065 6163 6820 6669  Finally, each fi\n+00016cf0: 6e67 6572 2069 730a 7363 616c 6564 2062  nger is.scaled b\n+00016d00: 7920 6120 6661 6374 6f72 2074 6f20 6c65  y a factor to le\n+00016d10: 6e64 2069 7420 7072 6f70 6f72 7469 6f6e  nd it proportion\n+00016d20: 2e0a 2020 6465 6620 6861 6e64 207b 0a20  ..  def hand {. \n+00016d30: 2020 2025 2066 696e 6765 7220 3120 5b61     % finger 1 [a\n+00016d40: 6c6c 206f 7468 6572 2066 696e 6765 7273  ll other fingers\n+00016d50: 206f 6d69 7474 6564 5d0a 2020 2020 6465   omitted].    de\n+00016d60: 6620 7363 616c 655f 3120 2e38 350a 2020  f scale_1 .85.  \n+00016d70: 2020 7075 7420 7b20 7363 616c 6528 7363    put { scale(sc\n+00016d80: 616c 655f 3129 200a 2020 2020 2020 2020  ale_1) .        \n+00016d90: 2020 7468 656e 2074 7261 6e73 6c61 7465    then translate\n+00016da0: 2828 6a6f 696e 745f 6761 7020 2a20 6a6f  ((joint_gap * jo\n+00016db0: 696e 745f 7261 6429 202a 205b 4a5d 290a  int_rad) * [J]).\n+00016dc0: 0920 2074 6865 6e20 726f 7461 7465 286d  .  then rotate(m\n+00016dd0: 6574 615f 315f 726f 742c 205b 495d 290a  eta_1_rot, [I]).\n+00016de0: 2020 2020 2020 2020 2020 7468 656e 2072            then r\n+00016df0: 6f74 6174 6528 2d73 7072 6561 645f 726f  otate(-spread_ro\n+00016e00: 742c 205b 4b5d 290a 2020 2020 2020 2020  t, [K]).        \n+00016e10: 2020 7468 656e 2074 7261 6e73 6c61 7465    then translate\n+00016e20: 2828 7072 6f78 696d 616c 5f31 5f6c 6f63  ((proximal_1_loc\n+00016e30: 2920 2d20 284f 2929 207d 200a 2020 2020  ) - (O)) } .    \n+00016e40: 2020 7b66 696e 6765 725f 317d 0a20 2020    {finger_1}.   \n+00016e50: 2070 7574 207b 2073 6361 6c65 2873 6361   put { scale(sca\n+00016e60: 6c65 5f31 202a 2070 726f 7869 6d61 6c5f  le_1 * proximal_\n+00016e70: 6469 7374 616c 5f72 6174 696f 5e32 290a  distal_ratio^2).\n+00016e80: 2020 2020 2020 2020 2020 7468 656e 2072            then r\n+00016e90: 6f74 6174 6528 6d65 7461 5f31 5f72 6f74  otate(meta_1_rot\n+00016ea0: 202f 2032 2c20 5b49 5d29 0a20 2020 2020   / 2, [I]).     \n+00016eb0: 2020 2020 2074 6865 6e20 726f 7461 7465       then rotate\n+00016ec0: 282d 7370 7265 6164 5f72 6f74 2c20 5b4b  (-spread_rot, [K\n+00016ed0: 5d29 0a20 2020 2020 2020 2020 2074 6865  ]).          the\n+00016ee0: 6e20 7472 616e 736c 6174 6528 2870 726f  n translate((pro\n+00016ef0: 7869 6d61 6c5f 315f 6c6f 6329 202d 2028  ximal_1_loc) - (\n+00016f00: 4f29 2920 7d20 0a20 2020 2020 207b 6a6f  O)) } .      {jo\n+00016f10: 696e 745f 7370 6865 7265 7d0a 0a20 2020  int_sphere}..   \n+00016f20: 2025 2070 616c 6d0a 2020 2020 7377 6565   % palm.    swee\n+00016f30: 7020 7b20 312c 2072 6f74 6174 6528 362c  p { 1, rotate(6,\n+00016f40: 2028 302c 3135 2c30 292c 205b 495d 2920   (0,15,0), [I]) \n+00016f50: 7d0a 2020 2020 2020 7075 7420 7b20 726f  }.      put { ro\n+00016f60: 7461 7465 282d 332c 2028 302c 3135 2c30  tate(-3, (0,15,0\n+00016f70: 292c 205b 495d 2920 7d20 7b0a 2020 2020  ), [I]) } {.    \n+00016f80: 2020 2020 706f 6c79 676f 6e28 7072 6f78      polygon(prox\n+00016f90: 696d 616c 5f31 5f6c 6f63 2928 7072 6f78  imal_1_loc)(prox\n+00016fa0: 696d 616c 5f32 5f6c 6f63 290a 2020 2020  imal_2_loc).    \n+00016fb0: 2020 2020 2020 2020 2020 2028 7072 6f78             (prox\n+00016fc0: 696d 616c 5f33 5f6c 6f63 2928 7072 6f78  imal_3_loc)(prox\n+00016fd0: 696d 616c 5f34 5f6c 6f63 290a 2020 2020  imal_4_loc).    \n+00016fe0: 2020 2020 2020 2020 2020 2028 6835 2928             (h5)(\n+00016ff0: 6836 2928 6836 6129 2868 3929 2868 3130  h6)(h6a)(h9)(h10\n+00017000: 290a 2020 2020 2020 2020 706f 6c79 676f  ).        polygo\n+00017010: 6e28 6836 6129 2868 3729 2868 3829 2868  n(h6a)(h7)(h8)(h\n+00017020: 3929 0a20 2020 7d20 207d 0a54 6865 206c  9).   }  }.The l\n+00017030: 6173 7420 7365 6374 696f 6e20 6f66 2074  ast section of t\n+00017040: 6865 2064 6566 696e 6974 696f 6e20 6372  he definition cr\n+00017050: 6561 7465 7320 7468 6520 706f 6c79 746f  eates the polyto\n+00017060: 7065 2066 6f72 2074 6865 2070 616c 6d20  pe for the palm \n+00017070: 6f66 0a74 6865 2068 616e 6420 6279 2027  of.the hand by '\n+00017080: 7377 6565 7027 696e 6720 6120 3130 2d73  sweep'ing a 10-s\n+00017090: 6964 6564 2070 6f6c 7967 6f6e 2074 6872  ided polygon thr\n+000170a0: 6f75 6768 2061 2076 6572 7920 7368 6f72  ough a very shor\n+000170b0: 7420 6172 630a 2839 2064 6567 7265 6573  t arc.(9 degrees\n+000170c0: 292e 2020 5468 6973 2070 726f 7669 6465  ).  This provide\n+000170d0: 7320 6120 7765 6467 652d 7368 6170 6564  s a wedge-shaped\n+000170e0: 2070 726f 6669 6c65 2077 6865 6e20 7669   profile when vi\n+000170f0: 6577 6564 2066 726f 6d20 7468 650a 7369  ewed from the.si\n+00017100: 6465 2e20 2054 6865 2074 6869 636b 2065  de.  The thick e\n+00017110: 6e64 206f 6620 7468 6520 7765 6467 6520  nd of the wedge \n+00017120: 6973 2074 6865 2077 7269 7374 2e20 2042  is the wrist.  B\n+00017130: 6563 6175 7365 2074 6865 2070 6f6c 7967  ecause the polyg\n+00017140: 6f6e 2069 730a 636f 6e63 6176 652c 2069  on is.concave, i\n+00017150: 7420 6973 2073 706c 6974 2069 6e74 6f20  t is split into \n+00017160: 696e 746f 2074 776f 2063 6f6e 7665 7820  into two convex \n+00017170: 7368 6170 6573 2077 6974 6820 6e69 6e65  shapes with nine\n+00017180: 2061 6e64 2066 6f75 720a 7665 7274 6963   and four.vertic\n+00017190: 6573 2e0a 0a20 2020 5765 2063 616e 206e  es...   We can n\n+000171a0: 6f77 2068 6176 6520 6675 6e20 706f 7369  ow have fun posi\n+000171b0: 7469 6f6e 696e 6720 7468 6520 6861 6e64  tioning the hand\n+000171c0: 2062 7920 6164 6a75 7374 696e 6720 7468   by adjusting th\n+000171d0: 6520 7661 7269 6f75 730a 726f 7461 7469  e various.rotati\n+000171e0: 6f6e 2061 6e67 6c65 732e 2020 5468 6520  on angles.  The \n+000171f0: 636f 6d70 6c65 7465 2073 6f75 7263 6520  complete source \n+00017200: 696e 636c 7564 6573 2064 6566 696e 6974  includes definit\n+00017210: 696f 6e73 2077 6974 680a 616c 7465 726e  ions with.altern\n+00017220: 6174 6976 6573 2074 6861 7420 696e 636c  atives that incl\n+00017230: 7564 6520 7468 6520 666f 6c6c 6f77 696e  ude the followin\n+00017240: 6720 7669 6577 7320 616e 6420 6d6f 7265  g views and more\n+00017250: 2e0a 0a00 085b 696d 6167 6520 7372 633d  .....[image src=\n+00017260: 2265 7832 3130 2e70 6e67 2220 7465 7874  \"ex210.png\" text\n+00017270: 3d22 496d 6167 6520 6578 3231 3020 6f6d  =\"Image ex210 om\n+00017280: 6974 7465 6420 696e 2074 6578 7420 7665  itted in text ve\n+00017290: 7273 696f 6e20 6f66 2074 6869 7320 646f  rsion of this do\n+000172a0: 6375 6d65 6e74 2e22 0008 5d00 085b 696d  cument.\"..]..[im\n+000172b0: 6167 6520 7372 633d 2265 7832 3230 2e70  age src=\"ex220.p\n+000172c0: 6e67 2220 7465 7874 3d22 496d 6167 6520  ng\" text=\"Image \n+000172d0: 6578 3232 3020 6f6d 6974 7465 6420 696e  ex220 omitted in\n+000172e0: 2074 6578 7420 7665 7273 696f 6e20 6f66   text version of\n+000172f0: 2074 6869 7320 646f 6375 6d65 6e74 2e22   this document.\"\n+00017300: 0008 5d00 085b 696d 6167 6520 7372 633d  ..]..[image src=\n+00017310: 2265 7832 3330 2e70 6e67 2220 7465 7874  \"ex230.png\" text\n+00017320: 3d22 496d 6167 6520 6578 3233 3020 6f6d  =\"Image ex230 om\n+00017330: 6974 7465 6420 696e 2074 6578 7420 7665  itted in text ve\n+00017340: 7273 696f 6e20 6f66 2074 6869 7320 646f  rsion of this do\n+00017350: 6375 6d65 6e74 2e22 0008 5d00 085b 696d  cument.\"..]..[im\n+00017360: 6167 6520 7372 633d 2265 7832 3430 2e70  age src=\"ex240.p\n+00017370: 6e67 2220 7465 7874 3d22 496d 6167 6520  ng\" text=\"Image \n+00017380: 6578 3234 3020 6f6d 6974 7465 6420 696e  ex240 omitted in\n+00017390: 2074 6578 7420 7665 7273 696f 6e20 6f66   text version of\n+000173a0: 2074 6869 7320 646f 6375 6d65 6e74 2e22   this document.\"\n+000173b0: 0008 5d0a 0a1f 0a46 696c 653a 2073 6b65  ..]....File: ske\n+000173c0: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n+000173d0: 2043 6176 6561 7473 2c20 2050 7265 763a   Caveats,  Prev:\n+000173e0: 2041 2068 6965 7261 7263 6869 6361 6c20   A hierarchical \n+000173f0: 6d6f 6465 6c2c 2020 5570 3a20 4275 696c  model,  Up: Buil\n+00017400: 6469 6e67 2061 2064 7261 7769 6e67 0a0a  ding a drawing..\n+00017410: 342e 3420 4361 7665 6174 730a 3d3d 3d3d  4.4 Caveats.====\n+00017420: 3d3d 3d3d 3d3d 3d0a 0a27 536b 6574 6368  =======..'Sketch\n+00017430: 2720 6973 2061 2066 6169 726c 7920 706f  ' is a fairly po\n+00017440: 7765 7266 756c 2074 6f6f 6c20 666f 7220  werful tool for \n+00017450: 6472 6177 696e 672c 2062 7574 2c20 6a75  drawing, but, ju\n+00017460: 7374 2061 7320 7769 7468 2054 6558 2c0a  st as with TeX,.\n+00017470: 7468 6520 706f 7765 7220 746f 2063 7265  the power to cre\n+00017480: 6174 6520 6265 6175 7469 6675 6c20 7265  ate beautiful re\n+00017490: 7375 6c74 7320 636f 6d65 7320 616c 6f6e  sults comes alon\n+000174a0: 6720 7769 7468 2074 6865 2070 6f77 6572  g with the power\n+000174b0: 2074 6f20 6d61 6b65 0a6d 6973 7461 6b65   to make.mistake\n+000174c0: 732e 2020 5468 6520 666f 6c6c 6f77 696e  s.  The followin\n+000174d0: 6720 6172 6520 736f 6d65 2070 6f69 6e74  g are some point\n+000174e0: 7320 7768 6572 6520 6361 7265 2069 7320  s where care is \n+000174f0: 6e65 6365 7373 6172 7920 616e 640a 7768  necessary and.wh\n+00017500: 6572 6520 7468 6520 6375 7272 656e 7420  ere the current \n+00017510: 7665 7273 696f 6e20 6f66 2027 736b 6574  version of 'sket\n+00017520: 6368 2720 6973 206c 696d 6974 6564 206f  ch' is limited o\n+00017530: 7220 6861 7320 6b6e 6f77 6e20 6275 6773  r has known bugs\n+00017540: 2e0a 0a2a 204d 656e 753a 0a0a 2a20 4c69  ...* Menu:..* Li\n+00017550: 6d69 7473 206f 6e20 6572 726f 7220 6465  mits on error de\n+00017560: 7465 6374 696f 6e3a 3a20 2020 5768 6174  tection::   What\n+00017570: 2073 6b65 7463 6820 646f 6573 6e27 7420   sketch doesn't \n+00017580: 646f 2e0a 2a20 436c 6970 7069 6e67 3a3a  do..* Clipping::\n+00017590: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000175a0: 2020 2020 4e6f 2063 6c69 7070 696e 6720      No clipping \n+000175b0: 6174 2070 7265 7365 6e74 2e0a 2a20 4869  at present..* Hi\n+000175c0: 6464 656e 2073 7572 6661 6365 2072 656d  dden surface rem\n+000175d0: 6f76 616c 3a3a 2020 2020 2020 496d 7065  oval::      Impe\n+000175e0: 7266 6563 7469 6f6e 7320 746f 2066 6978  rfections to fix\n+000175f0: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463  .....File: sketc\n+00017600: 682e 696e 666f 2c20 204e 6f64 653a 204c  h.info,  Node: L\n+00017610: 696d 6974 7320 6f6e 2065 7272 6f72 2064  imits on error d\n+00017620: 6574 6563 7469 6f6e 2c20 204e 6578 743a  etection,  Next:\n+00017630: 2043 6c69 7070 696e 672c 2020 5072 6576   Clipping,  Prev\n+00017640: 3a20 4361 7665 6174 732c 2020 5570 3a20  : Caveats,  Up: \n+00017650: 4361 7665 6174 730a 0a34 2e34 2e31 204c  Caveats..4.4.1 L\n+00017660: 696d 6974 7320 6f6e 2027 736b 6574 6368  imits on 'sketch\n+00017670: 2720 6572 726f 7220 6465 7465 6374 696f  ' error detectio\n+00017680: 6e0a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  n.--------------\n 00017690: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-000176a0: 2d2d 2d2d 0a0a 2753 6b65 7463 6827 2063  ----..'Sketch' c\n-000176b0: 6174 6368 6573 206d 616e 7920 6b69 6e64  atches many kind\n-000176c0: 7320 6f66 2065 7272 6f72 732c 2062 7574  s of errors, but\n-000176d0: 206e 6f74 2061 6c6c 2e20 2046 6f72 2065   not all.  For e\n-000176e0: 7861 6d70 6c65 2c0a 6f70 7469 6f6e 7320  xample,.options \n-000176f0: 7468 6174 2073 6b65 7463 6820 646f 6573  that sketch does\n-00017700: 206e 6f74 2072 6563 6f67 6e69 7a65 2c20   not recognize, \n-00017710: 6576 656e 2069 6e63 6f72 7265 6374 206f  even incorrect o\n-00017720: 6e65 732c 2061 7265 2071 7569 6574 6c79  nes, are quietly\n-00017730: 0a63 6f70 6965 6420 746f 2027 5053 5472  .copied to 'PSTr\n-00017740: 6963 6b73 2720 636f 6d6d 616e 6473 2069  icks' commands i\n-00017750: 6e20 7468 6520 6f75 7470 7574 2e20 2049  n the output.  I\n-00017760: 7420 6973 2061 6c73 6f20 756e 666f 7274  t is also unfort\n-00017770: 756e 6174 656c 790a 6561 7379 2074 6f20  unately.easy to \n-00017780: 7072 6f64 7563 6520 2773 6b65 7463 6827  produce 'sketch'\n-00017790: 2069 6e70 7574 7320 7468 6174 206c 6561   inputs that lea\n-000177a0: 6420 746f 206e 6f20 7069 6374 7572 6520  d to no picture \n-000177b0: 6174 2061 6c6c 2028 696d 7072 6f70 6572  at all (improper\n-000177c0: 0a76 6572 7465 7820 6f72 6465 7269 6e67  .vertex ordering\n-000177d0: 2063 6175 7365 7320 6576 6572 7974 6869   causes everythi\n-000177e0: 6e67 2074 6f20 6265 2063 756c 6c65 6429  ng to be culled)\n-000177f0: 2c20 746f 2070 6963 7475 7265 7320 7468  , to pictures th\n-00017800: 6174 2061 7265 0a74 6f6f 2062 6967 206f  at are.too big o\n-00017810: 7220 746f 6f20 736d 616c 6c20 666f 7220  r too small for \n-00017820: 2750 5354 7269 636b 7327 2074 6f20 6472  'PSTricks' to dr\n-00017830: 6177 2028 6475 6520 746f 206c 696d 6974  aw (due to limit\n-00017840: 7320 6f66 2054 6558 206d 6174 6829 2c0a  s of TeX math),.\n-00017850: 616e 6420 7069 6374 7572 6573 2074 6861  and pictures tha\n-00017860: 7420 6c6f 6f6b 206e 6f74 6869 6e67 206c  t look nothing l\n-00017870: 696b 6520 7768 6174 2077 6173 2069 6e74  ike what was int\n-00017880: 656e 6465 642e 2020 4120 7069 6374 7572  ended.  A pictur\n-00017890: 6520 7769 7468 0a6f 6e65 206f 6620 7468  e with.one of th\n-000178a0: 6573 6520 7072 6f62 6c65 6d73 2063 616e  ese problems can\n-000178b0: 2062 6520 6469 6666 6963 756c 7420 746f   be difficult to\n-000178c0: 2022 6465 6275 672e 2220 2057 6520 6f66   \"debug.\"  We of\n-000178d0: 6665 7220 7468 650a 666f 6c6c 6f77 696e  fer the.followin\n-000178e0: 6720 7375 6767 6573 7469 6f6e 732e 0a20  g suggestions.. \n-000178f0: 2020 2a20 466f 6c6c 6f77 2074 6865 2073    * Follow the s\n-00017900: 7567 6765 7374 6564 2069 6e63 7265 6d65  uggested increme\n-00017910: 6e74 616c 2064 6576 656c 6f70 6d65 6e74  ntal development\n-00017920: 206d 6574 686f 6420 6465 7363 7269 6265   method describe\n-00017930: 6420 696e 0a20 2020 2020 2a6e 6f74 6520  d in.     *note \n-00017940: 4f76 6572 7669 6577 3a3a 2e0a 2020 202a  Overview::..   *\n-00017950: 2041 6c77 6179 7320 6d61 696e 7461 696e   Always maintain\n-00017960: 206f 6e65 206f 7220 7477 6f20 6261 636b   one or two back\n-00017970: 2d76 6572 7369 6f6e 7320 6f66 2061 2064  -versions of a d\n-00017980: 7261 7769 6e67 2073 6f20 7468 6174 2069  rawing so that i\n-00017990: 7420 6973 0a20 2020 2020 6561 7379 2074  t is.     easy t\n-000179a0: 6f20 6661 6c6c 2062 6163 6b20 746f 2061  o fall back to a\n-000179b0: 206b 6e6f 776e 2d67 6f6f 6420 696e 6372   known-good incr\n-000179c0: 656d 656e 742e 0a20 2020 2a20 5768 656e  ement..   * When\n-000179d0: 2075 7369 6e67 2027 7065 7273 7065 6374   using 'perspect\n-000179e0: 6976 6527 2c20 656e 7375 7265 2061 6c6c  ive', ensure all\n-000179f0: 2066 696e 616c 6c79 2074 7261 6e73 666f   finally transfo\n-00017a00: 726d 6564 206f 626a 6563 7473 0a20 2020  rmed objects.   \n-00017a10: 2020 7361 7469 7366 7920 7a3c 3020 616e    satisfy z<0 an\n-00017a20: 642c 2069 6e20 6661 6374 2c20 646f 206e  d, in fact, do n\n-00017a30: 6f74 2063 6f6d 6520 7665 7279 2063 6c6f  ot come very clo\n-00017a40: 7365 2074 6f20 7468 6520 6f72 6967 696e  se to the origin\n-00017a50: 2061 740a 2020 2020 2061 6c6c 2e0a 2020   at.     all..  \n-00017a60: 202a 2054 656d 706f 7261 7269 6c79 2075   * Temporarily u\n-00017a70: 7365 2027 6375 6c6c 3d66 616c 7365 2720  se 'cull=false' \n-00017a80: 746f 2073 6565 2077 6865 7265 2076 6572  to see where ver\n-00017a90: 7465 7820 6f72 6465 7269 6e67 2070 726f  tex ordering pro\n-00017aa0: 626c 656d 730a 2020 2020 206c 6965 2e0a  blems.     lie..\n-00017ab0: 2020 202a 2055 7365 2074 656d 706f 7261     * Use tempora\n-00017ac0: 7279 2063 6861 6e67 6573 206f 6620 636f  ry changes of co\n-00017ad0: 6c6f 7220 6f66 206f 6e65 206f 7220 6d6f  lor of one or mo\n-00017ae0: 7265 206f 626a 6563 7473 2074 6f20 656e  re objects to en\n-00017af0: 7375 7265 0a20 2020 2020 7468 6174 2079  sure.     that y\n-00017b00: 6f75 7220 756e 6465 7273 7461 6e64 696e  our understandin\n-00017b10: 6720 6f66 2074 6865 2073 6365 6e65 2067  g of the scene g\n-00017b20: 656f 6d65 7472 7920 6973 2063 6f72 7265  eometry is corre\n-00017b30: 6374 2e0a 2020 202a 2049 6620 2750 5354  ct..   * If 'PST\n-00017b40: 7269 636b 7327 2063 6f6d 706c 6169 6e73  ricks' complains\n-00017b50: 2061 626f 7574 2073 6f6d 6574 6869 6e67   about something\n-00017b60: 2c20 696e 7370 6563 7420 7468 6520 6f75  , inspect the ou\n-00017b70: 7470 7574 0a20 2020 2020 6469 7265 6374  tput.     direct\n-00017b80: 6c79 2066 6f72 2063 6c75 6573 2e0a 0a1f  ly for clues....\n-00017b90: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n-00017ba0: 666f 2c20 204e 6f64 653a 2043 6c69 7070  fo,  Node: Clipp\n-00017bb0: 696e 672c 2020 4e65 7874 3a20 4869 6464  ing,  Next: Hidd\n-00017bc0: 656e 2073 7572 6661 6365 2072 656d 6f76  en surface remov\n-00017bd0: 616c 2c20 2050 7265 763a 204c 696d 6974  al,  Prev: Limit\n-00017be0: 7320 6f6e 2065 7272 6f72 2064 6574 6563  s on error detec\n-00017bf0: 7469 6f6e 2c20 2055 703a 2043 6176 6561  tion,  Up: Cavea\n-00017c00: 7473 0a0a 342e 342e 3220 436c 6970 7069  ts..4.4.2 Clippi\n-00017c10: 6e67 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ng.-------------\n-00017c20: 2d0a 0a54 6865 2063 7572 7265 6e74 2076  -..The current v\n-00017c30: 6572 7369 6f6e 206f 6620 2773 6b65 7463  ersion of 'sketc\n-00017c40: 6827 2068 6173 206e 6f20 636c 6970 7069  h' has no clippi\n-00017c50: 6e67 206f 7065 7261 7469 6f6e 732e 2020  ng operations.  \n-00017c60: 5468 6520 656e 7469 7265 0a73 6365 6e65  The entire.scene\n-00017c70: 2069 7320 616c 7761 7973 2064 7261 776e   is always drawn\n-00017c80: 2e20 2054 6869 7320 6d65 616e 7320 7468  .  This means th\n-00017c90: 6174 2077 6865 6e20 6120 7065 7273 7065  at when a perspe\n-00017ca0: 6374 6976 6520 7472 616e 7366 6f72 6d20  ctive transform \n-00017cb0: 6973 0a65 6d70 6c6f 7965 642c 2069 7420  is.employed, it \n-00017cc0: 6973 2074 6865 2075 7365 7227 7320 7265  is the user's re\n-00017cd0: 7370 6f6e 7369 6269 6c69 7479 2074 6f20  sponsibility to \n-00017ce0: 6d61 6b65 2073 7572 6520 7468 6520 656e  make sure the en\n-00017cf0: 7469 7265 2073 6365 6e65 0a72 656d 6169  tire scene.remai\n-00017d00: 6e73 2069 6e20 6672 6f6e 7420 6f66 2074  ns in front of t\n-00017d10: 6865 2076 6965 7765 722c 2074 6865 2072  he viewer, the r\n-00017d20: 6567 696f 6e20 7a3c 302e 0a0a 1f0a 4669  egion z<0.....Fi\n-00017d30: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n-00017d40: 2020 4e6f 6465 3a20 4869 6464 656e 2073    Node: Hidden s\n-00017d50: 7572 6661 6365 2072 656d 6f76 616c 2c20  urface removal, \n-00017d60: 2050 7265 763a 2043 6c69 7070 696e 672c   Prev: Clipping,\n-00017d70: 2020 5570 3a20 4361 7665 6174 730a 0a34    Up: Caveats..4\n-00017d80: 2e34 2e33 2048 6964 6465 6e20 7375 7266  .4.3 Hidden surf\n-00017d90: 6163 6520 7265 6d6f 7661 6c20 616e 6420  ace removal and \n-00017da0: 706f 6c79 676f 6e20 7370 6c69 7474 696e  polygon splittin\n-00017db0: 670a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  g.--------------\n+000176a0: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2753 6b65  ----------..'Ske\n+000176b0: 7463 6827 2063 6174 6368 6573 206d 616e  tch' catches man\n+000176c0: 7920 6b69 6e64 7320 6f66 2065 7272 6f72  y kinds of error\n+000176d0: 732c 2062 7574 206e 6f74 2061 6c6c 2e20  s, but not all. \n+000176e0: 2046 6f72 2065 7861 6d70 6c65 2c0a 6f70   For example,.op\n+000176f0: 7469 6f6e 7320 7468 6174 2073 6b65 7463  tions that sketc\n+00017700: 6820 646f 6573 206e 6f74 2072 6563 6f67  h does not recog\n+00017710: 6e69 7a65 2c20 6576 656e 2069 6e63 6f72  nize, even incor\n+00017720: 7265 6374 206f 6e65 732c 2061 7265 2071  rect ones, are q\n+00017730: 7569 6574 6c79 0a63 6f70 6965 6420 746f  uietly.copied to\n+00017740: 2027 5053 5472 6963 6b73 2720 636f 6d6d   'PSTricks' comm\n+00017750: 616e 6473 2069 6e20 7468 6520 6f75 7470  ands in the outp\n+00017760: 7574 2e20 2049 7420 6973 2061 6c73 6f20  ut.  It is also \n+00017770: 756e 666f 7274 756e 6174 656c 790a 6561  unfortunately.ea\n+00017780: 7379 2074 6f20 7072 6f64 7563 6520 2773  sy to produce 's\n+00017790: 6b65 7463 6827 2069 6e70 7574 7320 7468  ketch' inputs th\n+000177a0: 6174 206c 6561 6420 746f 206e 6f20 7069  at lead to no pi\n+000177b0: 6374 7572 6520 6174 2061 6c6c 2028 696d  cture at all (im\n+000177c0: 7072 6f70 6572 0a76 6572 7465 7820 6f72  proper.vertex or\n+000177d0: 6465 7269 6e67 2063 6175 7365 7320 6576  dering causes ev\n+000177e0: 6572 7974 6869 6e67 2074 6f20 6265 2063  erything to be c\n+000177f0: 756c 6c65 6429 2c20 746f 2070 6963 7475  ulled), to pictu\n+00017800: 7265 7320 7468 6174 2061 7265 0a74 6f6f  res that are.too\n+00017810: 2062 6967 206f 7220 746f 6f20 736d 616c   big or too smal\n+00017820: 6c20 666f 7220 2750 5354 7269 636b 7327  l for 'PSTricks'\n+00017830: 2074 6f20 6472 6177 2028 6475 6520 746f   to draw (due to\n+00017840: 206c 696d 6974 7320 6f66 2054 6558 206d   limits of TeX m\n+00017850: 6174 6829 2c0a 616e 6420 7069 6374 7572  ath),.and pictur\n+00017860: 6573 2074 6861 7420 6c6f 6f6b 206e 6f74  es that look not\n+00017870: 6869 6e67 206c 696b 6520 7768 6174 2077  hing like what w\n+00017880: 6173 2069 6e74 656e 6465 642e 2020 4120  as intended.  A \n+00017890: 7069 6374 7572 6520 7769 7468 0a6f 6e65  picture with.one\n+000178a0: 206f 6620 7468 6573 6520 7072 6f62 6c65   of these proble\n+000178b0: 6d73 2063 616e 2062 6520 6469 6666 6963  ms can be diffic\n+000178c0: 756c 7420 746f 2022 6465 6275 672e 2220  ult to \"debug.\" \n+000178d0: 2057 6520 6f66 6665 7220 7468 650a 666f   We offer the.fo\n+000178e0: 6c6c 6f77 696e 6720 7375 6767 6573 7469  llowing suggesti\n+000178f0: 6f6e 732e 0a20 2020 2a20 466f 6c6c 6f77  ons..   * Follow\n+00017900: 2074 6865 2073 7567 6765 7374 6564 2069   the suggested i\n+00017910: 6e63 7265 6d65 6e74 616c 2064 6576 656c  ncremental devel\n+00017920: 6f70 6d65 6e74 206d 6574 686f 6420 6465  opment method de\n+00017930: 7363 7269 6265 6420 696e 0a20 2020 2020  scribed in.     \n+00017940: 2a6e 6f74 6520 4f76 6572 7669 6577 3a3a  *note Overview::\n+00017950: 2e0a 2020 202a 2041 6c77 6179 7320 6d61  ..   * Always ma\n+00017960: 696e 7461 696e 206f 6e65 206f 7220 7477  intain one or tw\n+00017970: 6f20 6261 636b 2d76 6572 7369 6f6e 7320  o back-versions \n+00017980: 6f66 2061 2064 7261 7769 6e67 2073 6f20  of a drawing so \n+00017990: 7468 6174 2069 7420 6973 0a20 2020 2020  that it is.     \n+000179a0: 6561 7379 2074 6f20 6661 6c6c 2062 6163  easy to fall bac\n+000179b0: 6b20 746f 2061 206b 6e6f 776e 2d67 6f6f  k to a known-goo\n+000179c0: 6420 696e 6372 656d 656e 742e 0a20 2020  d increment..   \n+000179d0: 2a20 5768 656e 2075 7369 6e67 2027 7065  * When using 'pe\n+000179e0: 7273 7065 6374 6976 6527 2c20 656e 7375  rspective', ensu\n+000179f0: 7265 2061 6c6c 2066 696e 616c 6c79 2074  re all finally t\n+00017a00: 7261 6e73 666f 726d 6564 206f 626a 6563  ransformed objec\n+00017a10: 7473 0a20 2020 2020 7361 7469 7366 7920  ts.     satisfy \n+00017a20: 7a3c 3020 616e 642c 2069 6e20 6661 6374  z<0 and, in fact\n+00017a30: 2c20 646f 206e 6f74 2063 6f6d 6520 7665  , do not come ve\n+00017a40: 7279 2063 6c6f 7365 2074 6f20 7468 6520  ry close to the \n+00017a50: 6f72 6967 696e 2061 740a 2020 2020 2061  origin at.     a\n+00017a60: 6c6c 2e0a 2020 202a 2054 656d 706f 7261  ll..   * Tempora\n+00017a70: 7269 6c79 2075 7365 2027 6375 6c6c 3d66  rily use 'cull=f\n+00017a80: 616c 7365 2720 746f 2073 6565 2077 6865  alse' to see whe\n+00017a90: 7265 2076 6572 7465 7820 6f72 6465 7269  re vertex orderi\n+00017aa0: 6e67 2070 726f 626c 656d 730a 2020 2020  ng problems.    \n+00017ab0: 206c 6965 2e0a 2020 202a 2055 7365 2074   lie..   * Use t\n+00017ac0: 656d 706f 7261 7279 2063 6861 6e67 6573  emporary changes\n+00017ad0: 206f 6620 636f 6c6f 7220 6f66 206f 6e65   of color of one\n+00017ae0: 206f 7220 6d6f 7265 206f 626a 6563 7473   or more objects\n+00017af0: 2074 6f20 656e 7375 7265 0a20 2020 2020   to ensure.     \n+00017b00: 7468 6174 2079 6f75 7220 756e 6465 7273  that your unders\n+00017b10: 7461 6e64 696e 6720 6f66 2074 6865 2073  tanding of the s\n+00017b20: 6365 6e65 2067 656f 6d65 7472 7920 6973  cene geometry is\n+00017b30: 2063 6f72 7265 6374 2e0a 2020 202a 2049   correct..   * I\n+00017b40: 6620 2750 5354 7269 636b 7327 2063 6f6d  f 'PSTricks' com\n+00017b50: 706c 6169 6e73 2061 626f 7574 2073 6f6d  plains about som\n+00017b60: 6574 6869 6e67 2c20 696e 7370 6563 7420  ething, inspect \n+00017b70: 7468 6520 6f75 7470 7574 0a20 2020 2020  the output.     \n+00017b80: 6469 7265 6374 6c79 2066 6f72 2063 6c75  directly for clu\n+00017b90: 6573 2e0a 0a1f 0a46 696c 653a 2073 6b65  es.....File: ske\n+00017ba0: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n+00017bb0: 2043 6c69 7070 696e 672c 2020 4e65 7874   Clipping,  Next\n+00017bc0: 3a20 4869 6464 656e 2073 7572 6661 6365  : Hidden surface\n+00017bd0: 2072 656d 6f76 616c 2c20 2050 7265 763a   removal,  Prev:\n+00017be0: 204c 696d 6974 7320 6f6e 2065 7272 6f72   Limits on error\n+00017bf0: 2064 6574 6563 7469 6f6e 2c20 2055 703a   detection,  Up:\n+00017c00: 2043 6176 6561 7473 0a0a 342e 342e 3220   Caveats..4.4.2 \n+00017c10: 436c 6970 7069 6e67 0a2d 2d2d 2d2d 2d2d  Clipping.-------\n+00017c20: 2d2d 2d2d 2d2d 2d0a 0a54 6865 2063 7572  -------..The cur\n+00017c30: 7265 6e74 2076 6572 7369 6f6e 206f 6620  rent version of \n+00017c40: 2773 6b65 7463 6827 2068 6173 206e 6f20  'sketch' has no \n+00017c50: 636c 6970 7069 6e67 206f 7065 7261 7469  clipping operati\n+00017c60: 6f6e 732e 2020 5468 6520 656e 7469 7265  ons.  The entire\n+00017c70: 0a73 6365 6e65 2069 7320 616c 7761 7973  .scene is always\n+00017c80: 2064 7261 776e 2e20 2054 6869 7320 6d65   drawn.  This me\n+00017c90: 616e 7320 7468 6174 2077 6865 6e20 6120  ans that when a \n+00017ca0: 7065 7273 7065 6374 6976 6520 7472 616e  perspective tran\n+00017cb0: 7366 6f72 6d20 6973 0a65 6d70 6c6f 7965  sform is.employe\n+00017cc0: 642c 2069 7420 6973 2074 6865 2075 7365  d, it is the use\n+00017cd0: 7227 7320 7265 7370 6f6e 7369 6269 6c69  r's responsibili\n+00017ce0: 7479 2074 6f20 6d61 6b65 2073 7572 6520  ty to make sure \n+00017cf0: 7468 6520 656e 7469 7265 2073 6365 6e65  the entire scene\n+00017d00: 0a72 656d 6169 6e73 2069 6e20 6672 6f6e  .remains in fron\n+00017d10: 7420 6f66 2074 6865 2076 6965 7765 722c  t of the viewer,\n+00017d20: 2074 6865 2072 6567 696f 6e20 7a3c 302e   the region z<0.\n+00017d30: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n+00017d40: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4869  .info,  Node: Hi\n+00017d50: 6464 656e 2073 7572 6661 6365 2072 656d  dden surface rem\n+00017d60: 6f76 616c 2c20 2050 7265 763a 2043 6c69  oval,  Prev: Cli\n+00017d70: 7070 696e 672c 2020 5570 3a20 4361 7665  pping,  Up: Cave\n+00017d80: 6174 730a 0a34 2e34 2e33 2048 6964 6465  ats..4.4.3 Hidde\n+00017d90: 6e20 7375 7266 6163 6520 7265 6d6f 7661  n surface remova\n+00017da0: 6c20 616e 6420 706f 6c79 676f 6e20 7370  l and polygon sp\n+00017db0: 6c69 7474 696e 670a 2d2d 2d2d 2d2d 2d2d  litting.--------\n 00017dc0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 00017dd0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-00017de0: 2d2d 2d2d 0a0a 2753 6b65 7463 6827 2075  ----..'Sketch' u\n-00017df0: 7365 7320 7468 6520 2264 6570 7468 2073  ses the \"depth s\n-00017e00: 6f72 7420 616c 676f 7269 7468 6d22 2066  ort algorithm\" f\n-00017e10: 6f72 2068 6964 6465 6e20 7375 7266 6163  or hidden surfac\n-00017e20: 6520 7265 6d6f 7661 6c2e 0a54 6869 7320  e removal..This \n-00017e30: 6973 2061 2076 6572 7920 6f6c 6420 7465  is a very old te\n-00017e40: 6368 6e69 7175 6520 6475 6520 746f 204e  chnique due to N\n-00017e50: 6577 656c 6c2e 2831 2920 2049 7420 6973  ewell.(1)  It is\n-00017e60: 2067 656e 6572 616c 6c79 2072 6567 6172   generally regar\n-00017e70: 6465 640a 6173 2074 6f6f 2073 6c6f 7720  ded.as too slow \n-00017e80: 666f 7220 7265 616c 2074 696d 6520 6772  for real time gr\n-00017e90: 6170 6869 6373 2c20 6275 7420 6974 2069  aphics, but it i\n-00017ea0: 7320 6964 6561 6c20 666f 7220 6f75 7220  s ideal for our \n-00017eb0: 7075 7270 6f73 650a 7768 6572 6520 7370  purpose.where sp\n-00017ec0: 6565 6420 6973 206e 6f74 2076 6572 7920  eed is not very \n-00017ed0: 696d 706f 7274 616e 742e 2832 290a 0a20  important.(2).. \n-00017ee0: 2020 5468 6520 6465 7074 6820 736f 7274    The depth sort\n-00017ef0: 2061 6c67 6f72 6974 686d 206d 6572 656c   algorithm merel\n-00017f00: 7920 736f 7274 7320 6f62 6a65 6374 7320  y sorts objects \n-00017f10: 6f6e 2061 206b 6579 206f 6620 696e 6372  on a key of incr\n-00017f20: 6561 7369 6e67 0a7a 2d63 6f6f 7264 696e  easing.z-coordin\n-00017f30: 6174 652c 2065 7175 6976 616c 656e 7420  ate, equivalent \n-00017f40: 746f 2064 6563 7265 6173 696e 6720 6465  to decreasing de\n-00017f50: 7074 682e 2020 4f62 6a65 6374 7320 6172  pth.  Objects ar\n-00017f60: 6520 7468 656e 2064 7261 776e 2069 6e0a  e then drawn in.\n-00017f70: 7468 6520 736f 7274 6564 2073 6571 7565  the sorted seque\n-00017f80: 6e63 6520 736f 2074 6861 7420 7468 6f73  nce so that thos\n-00017f90: 6520 6174 2074 6865 2072 6561 7220 6f66  e at the rear of\n-00017fa0: 2074 6865 2073 6365 6e65 2061 7265 0a6f   the scene are.o\n-00017fb0: 7665 7277 7269 7474 656e 2062 7920 7468  verwritten by th\n-00017fc0: 6f73 6520 636c 6f73 6572 2074 6f20 7468  ose closer to th\n-00017fd0: 6520 7669 6577 6572 2e20 2053 696e 6365  e viewer.  Since\n-00017fe0: 2074 6869 7320 6973 2061 6c73 6f20 686f   this is also ho\n-00017ff0: 7720 6f69 6c0a 7061 696e 7465 7273 2070  w oil.painters p\n-00018000: 7261 6374 6963 6520 7468 6569 7220 6172  ractice their ar\n-00018010: 742c 2064 6570 7468 2073 6f72 7420 6973  t, depth sort is\n-00018020: 2073 6f6d 6574 696d 6573 2063 616c 6c65   sometimes calle\n-00018030: 6420 2274 6865 0a70 6169 6e74 6572 2773  d \"the.painter's\n-00018040: 2061 6c67 6f72 6974 686d 2e22 0a0a 2020   algorithm.\"..  \n-00018050: 2049 6e20 736f 6d65 2063 6173 6573 2069   In some cases i\n-00018060: 7420 6973 2069 6d70 6f73 7369 626c 6520  t is impossible \n-00018070: 746f 2073 7472 6963 746c 7920 6f72 6465  to strictly orde\n-00018080: 7220 706f 6c79 676f 6e73 2061 6363 6f72  r polygons accor\n-00018090: 6469 6e67 0a74 6f20 6465 7074 682e 2020  ding.to depth.  \n-000180a0: 4d6f 7265 6f76 6572 2c20 6576 656e 2069  Moreover, even i\n-000180b0: 6620 6120 636f 7272 6563 7420 6465 7074  f a correct dept\n-000180c0: 6820 6f72 6465 7269 6e67 2065 7869 7374  h ordering exist\n-000180d0: 732c 2074 6865 0a63 6f6d 7075 7461 7469  s, the.computati\n-000180e0: 6f6e 206e 6565 6465 6420 746f 2066 696e  on needed to fin\n-000180f0: 6420 6974 206d 6179 2062 6520 746f 6f20  d it may be too \n-00018100: 636f 6d70 6c65 7820 616e 6420 736c 6f77  complex and slow\n-00018110: 2e20 2049 6e20 7468 6573 650a 6361 7365  .  In these.case\n-00018120: 732c 2027 736b 6574 6368 2720 7370 6c69  s, 'sketch' spli\n-00018130: 7473 206f 6e65 206f 7220 6d6f 7265 2070  ts one or more p\n-00018140: 6f6c 7967 6f6e 7320 696e 746f 2070 6965  olygons into pie\n-00018150: 6365 732e 2020 5468 650a 6578 7065 6374  ces.  The.expect\n-00018160: 6174 696f 6e20 6973 2074 6861 7420 7468  ation is that th\n-00018170: 6520 6e65 772c 2073 6d61 6c6c 6572 2070  e new, smaller p\n-00018180: 6f6c 7967 6f6e 7320 7769 6c6c 2062 6520  olygons will be \n-00018190: 7369 6d70 6c65 7220 746f 206f 7264 6572  simpler to order\n-000181a0: 2e0a 2753 6b65 7463 6827 2075 7365 7320  ..'Sketch' uses \n-000181b0: 6120 4253 5020 2862 696e 6172 7920 7370  a BSP (binary sp\n-000181c0: 6163 6520 7061 7274 6974 696f 6e29 2074  ace partition) t\n-000181d0: 6f20 6861 6e64 6c65 2074 6865 2073 706c  o handle the spl\n-000181e0: 6974 7469 6e67 0a6f 7065 7261 7469 6f6e  itting.operation\n-000181f0: 2e0a 0a2a 204d 656e 753a 0a0a 2a20 5374  ...* Menu:..* St\n-00018200: 6174 6973 7469 6373 3a3a 2020 2020 2020  atistics::      \n-00018210: 2020 2020 2020 2020 2020 2020 5065 7266              Perf\n-00018220: 6f72 6d61 6e63 6520 6e75 6d62 6572 7320  ormance numbers \n-00018230: 6f6e 2064 6570 7468 2073 6f72 742e 0a2a  on depth sort..*\n-00018240: 2042 7567 7320 616e 6420 616e 6f6d 616c   Bugs and anomal\n-00018250: 6965 733a 3a20 2020 2020 2020 2020 2049  ies::          I\n-00018260: 6d70 6572 6665 6374 696f 6e73 2069 6e20  mperfections in \n-00018270: 7468 6973 2069 6d70 6c65 6d65 6e74 6174  this implementat\n-00018280: 696f 6e2e 0a0a 2020 202d 2d2d 2d2d 2d2d  ion...   -------\n-00018290: 2d2d 2d20 466f 6f74 6e6f 7465 7320 2d2d  --- Footnotes --\n-000182a0: 2d2d 2d2d 2d2d 2d2d 0a0a 2020 2028 3129  --------..   (1)\n-000182b0: 204e 6577 656c 6c2c 204d 2e45 2e2c 2052   Newell, M.E., R\n-000182c0: 2e47 2e20 4e65 7765 6c6c 2c20 616e 6420  .G. Newell, and \n-000182d0: 542e 4c2e 2053 616e 6368 612c 2041 2073  T.L. Sancha, A s\n-000182e0: 6f6c 7574 696f 6e20 746f 2074 6865 0a68  olution to the.h\n-000182f0: 6964 6465 6e20 7375 7266 6163 6520 7072  idden surface pr\n-00018300: 6f62 6c65 6d2e 2020 5072 6f63 6565 6469  oblem.  Proceedi\n-00018310: 6e67 7320 6f66 2074 6865 2041 434d 2061  ngs of the ACM a\n-00018320: 6e6e 7561 6c20 636f 6e66 6572 656e 6365  nnual conference\n-00018330: 202d 0a56 6f6c 756d 6520 312c 2070 6167   -.Volume 1, pag\n-00018340: 6520 3434 332d 3435 302c 2041 434d 2050  e 443-450, ACM P\n-00018350: 7265 7373 2c20 3139 3732 2e0a 0a20 2020  ress, 1972...   \n-00018360: 2832 2920 5765 2068 6176 6520 7275 6e20  (2) We have run \n-00018370: 2773 6b65 7463 6827 206f 6e20 7468 6520  'sketch' on the \n-00018380: 6661 6d6f 7573 2053 7461 6e66 6f72 6420  famous Stanford \n-00018390: 4275 6e6e 792c 2077 6869 6368 2063 6f6e  Bunny, which con\n-000183a0: 7369 7374 730a 6f66 206e 6561 726c 7920  sists.of nearly \n-000183b0: 3730 2c30 3030 2074 7269 616e 676c 6573  70,000 triangles\n-000183c0: 2e20 2052 756e 2074 696d 6520 7761 7320  .  Run time was \n-000183d0: 6162 6f75 7420 3620 7365 636f 6e64 732e  about 6 seconds.\n-000183e0: 2020 4d6f 7374 206f 6620 7468 6973 0a77    Most of this.w\n-000183f0: 6173 2073 7065 6e74 2077 7269 7469 6e67  as spent writing\n-00018400: 2074 6865 206f 7574 7075 7420 6669 6c65   the output file\n-00018410: 2072 6174 6865 7220 7468 616e 2069 6e20   rather than in \n-00018420: 7468 6520 6869 6464 656e 2073 7572 6661  the hidden surfa\n-00018430: 6365 0a61 6c67 6f72 6974 686d 2e20 204c  ce.algorithm.  L\n-00018440: 6154 6558 2074 6f6f 6b20 6d75 6368 206c  aTeX took much l\n-00018450: 6f6e 6765 7220 746f 2070 726f 6365 7373  onger to process\n-00018460: 2074 6865 2072 6573 756c 7469 6e67 2027   the resulting '\n-00018470: 5053 5472 6963 6b73 270a 636f 6465 2e20  PSTricks'.code. \n-00018480: 2054 6865 206f 6276 696f 7573 2063 6f6e   The obvious con\n-00018490: 636c 7573 696f 6e20 6973 2074 6861 7420  clusion is that \n-000184a0: 7468 6520 7370 6565 6420 6f66 2074 6865  the speed of the\n-000184b0: 2064 6570 7468 2073 6f72 740a 616c 676f   depth sort.algo\n-000184c0: 7269 7468 6d20 6973 206e 6f74 2061 2077  rithm is not a w\n-000184d0: 6f72 7279 2e0a 0a1f 0a46 696c 653a 2073  orry.....File: s\n-000184e0: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n-000184f0: 653a 2053 7461 7469 7374 6963 732c 2020  e: Statistics,  \n-00018500: 4e65 7874 3a20 4275 6773 2061 6e64 2061  Next: Bugs and a\n-00018510: 6e6f 6d61 6c69 6573 2c20 2050 7265 763a  nomalies,  Prev:\n-00018520: 2048 6964 6465 6e20 7375 7266 6163 6520   Hidden surface \n-00018530: 7265 6d6f 7661 6c2c 2020 5570 3a20 4869  removal,  Up: Hi\n-00018540: 6464 656e 2073 7572 6661 6365 2072 656d  dden surface rem\n-00018550: 6f76 616c 0a0a 342e 342e 332e 3120 5374  oval..4.4.3.1 St\n-00018560: 6174 6973 7469 6373 0a2e 2e2e 2e2e 2e2e  atistics........\n-00018570: 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a46 6f72  .............For\n-00018580: 2074 6865 2063 7572 696f 7573 2c20 2773   the curious, 's\n-00018590: 6b65 7463 6827 2077 7269 7465 7320 6f6e  ketch' writes on\n-000185a0: 6520 6c69 6e65 206f 6620 6465 7074 6820  e line of depth \n-000185b0: 736f 7274 2073 7461 7469 7374 6963 732e  sort statistics.\n-000185c0: 0a48 6572 6520 6973 2061 6e20 6578 616d  .Here is an exam\n-000185d0: 706c 6520 666f 7220 6120 6c61 7267 6520  ple for a large \n-000185e0: 636f 6c6c 6563 7469 6f6e 206f 6620 7472  collection of tr\n-000185f0: 6961 6e67 6c65 732e 0a20 2072 656d 6172  iangles..  remar\n-00018600: 6b2c 206e 6f64 653d 3334 3832 3420 7072  k, node=34824 pr\n-00018610: 6f62 653d 3538 312e 3920 7377 6170 3d35  obe=581.9 swap=5\n-00018620: 2073 706c 6974 3d32 2028 696e 3d34 206f   split=2 (in=4 o\n-00018630: 7574 3d36 2920 6f6c 733d 3234 3835 312f  ut=6) ols=24851/\n-00018640: 300a 4974 206d 6561 6e73 2074 6861 7420  0.It means that \n-00018650: 3334 2c38 3234 206f 626a 6563 7473 2077  34,824 objects w\n-00018660: 6572 6520 6465 7074 6820 736f 7274 6564  ere depth sorted\n-00018670: 2061 6674 6572 2063 756c 6c69 6e67 2e20   after culling. \n-00018680: 2046 6f72 2065 6163 682c 0a61 6e20 6176   For each,.an av\n-00018690: 6572 6167 6520 6f66 2035 3831 2e39 206f  erage of 581.9 o\n-000186a0: 7468 6572 7320 6861 6420 746f 2062 6520  thers had to be \n-000186b0: 6368 6563 6b65 6420 746f 2065 6e73 7572  checked to ensur\n-000186c0: 6520 7468 6174 2074 6865 2069 6e69 7469  e that the initi\n-000186d0: 616c 2c0a 6170 7072 6f78 696d 6174 6520  al,.approximate \n-000186e0: 6f72 6465 7269 6e67 2077 6173 2063 6f72  ordering was cor\n-000186f0: 7265 6374 2e20 2041 6d6f 6e67 2061 6c6c  rect.  Among all\n-00018700: 2074 6865 7365 2063 6865 636b 732c 206f   these checks, o\n-00018710: 6e6c 7920 350a 7265 7375 6c74 6564 2069  nly 5.resulted i\n-00018720: 6e20 7377 6170 7320 746f 2072 656f 7264  n swaps to reord\n-00018730: 6572 2074 6865 2069 6e69 7469 616c 2073  er the initial s\n-00018740: 6f72 742e 2020 496e 2074 776f 2063 6173  ort.  In two cas\n-00018750: 6573 2c20 6120 636f 7272 6563 740a 6f72  es, a correct.or\n-00018760: 6465 7269 6e67 2063 6f75 6c64 206e 6f74  dering could not\n-00018770: 2062 6520 6465 7465 726d 696e 6564 2c20   be determined, \n-00018780: 736f 2062 696e 6172 7920 7370 6163 6520  so binary space \n-00018790: 7061 7274 6974 696f 6e73 2077 6572 650a  partitions were.\n-000187a0: 636f 6e73 7472 7563 7465 6420 666f 7220  constructed for \n-000187b0: 7370 6c69 7474 696e 672e 2020 4120 746f  splitting.  A to\n-000187c0: 7461 6c20 6f66 2034 206f 626a 6563 7473  tal of 4 objects\n-000187d0: 2028 7472 6961 6e67 6c65 7320 696e 2074   (triangles in t\n-000187e0: 6869 730a 6361 7365 2920 7765 7265 2069  his.case) were i\n-000187f0: 6e73 6572 7465 6420 696e 2074 6865 2070  nserted in the p\n-00018800: 6172 7469 7469 6f6e 732c 2061 6e64 2036  artitions, and 6\n-00018810: 2070 6f6c 7967 6f6e 7320 7765 7265 2070   polygons were p\n-00018820: 726f 6475 6365 642e 0a46 696e 616c 6c79  roduced..Finally\n-00018830: 2c20 3234 2c38 3531 2022 6c61 7374 2072  , 24,851 \"last r\n-00018840: 6573 6f72 7422 2070 6f6c 7967 6f6e 206f  esort\" polygon o\n-00018850: 7665 726c 6170 2063 6865 636b 7320 7765  verlap checks we\n-00018860: 7265 2070 6572 666f 726d 6564 0a61 6674  re performed.aft\n-00018870: 6572 2073 696d 706c 6572 2c20 6661 7374  er simpler, fast\n-00018880: 6572 2063 6865 636b 7320 6661 696c 6564  er checks failed\n-00018890: 2074 6f20 7969 656c 6420 636f 6e63 6c75   to yield conclu\n-000188a0: 7369 7665 2072 6573 756c 7473 2e20 2054  sive results.  T\n-000188b0: 6865 0a66 696e 616c 202f 3020 6973 2066  he.final /0 is f\n-000188c0: 6f72 206c 696e 652d 706f 6c79 676f 6e20  or line-polygon \n-000188d0: 6f76 6572 6c61 7020 6368 6563 6b73 2e20  overlap checks. \n-000188e0: 2046 6f72 2063 6f6d 7061 7269 736f 6e2c   For comparison,\n-000188f0: 2074 6865 0a73 7461 7469 7374 6963 7320   the.statistics \n-00018900: 666f 7220 7468 6520 6c61 7374 2066 6967  for the last fig\n-00018910: 7572 6520 696e 202a 6e6f 7465 204f 7665  ure in *note Ove\n-00018920: 7276 6965 773a 3a20 666f 6c6c 6f77 2e0a  rview:: follow..\n-00018930: 2020 7265 6d61 726b 2c20 6e6f 6465 3d32    remark, node=2\n-00018940: 3720 7072 6f62 653d 3134 2e36 2073 7761  7 probe=14.6 swa\n-00018950: 703d 3336 2073 706c 6974 3d31 3520 2869  p=36 split=15 (i\n-00018960: 6e3d 3330 206f 7574 3d34 3529 206f 6c73  n=30 out=45) ols\n-00018970: 3d30 2f36 390a 4e6f 7465 2074 6861 7420  =0/69.Note that \n-00018980: 7468 6572 6520 7761 7320 7072 6f70 6f72  there was propor\n-00018990: 7469 6f6e 616c 6c79 206d 7563 6820 6d6f  tionally much mo\n-000189a0: 7265 2073 7761 7070 696e 6720 616e 6420  re swapping and \n-000189b0: 7370 6c69 7474 696e 670a 6163 7469 7669  splitting.activi\n-000189c0: 7479 2069 6e20 7468 6973 2068 6967 686c  ty in this highl\n-000189d0: 7920 636f 6e6e 6563 7465 6420 7363 656e  y connected scen\n-000189e0: 652e 0a0a 1f0a 4669 6c65 3a20 736b 6574  e.....File: sket\n-000189f0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n-00018a00: 4275 6773 2061 6e64 2061 6e6f 6d61 6c69  Bugs and anomali\n-00018a10: 6573 2c20 2050 7265 763a 2053 7461 7469  es,  Prev: Stati\n-00018a20: 7374 6963 732c 2020 5570 3a20 4869 6464  stics,  Up: Hidd\n-00018a30: 656e 2073 7572 6661 6365 2072 656d 6f76  en surface remov\n-00018a40: 616c 0a0a 342e 342e 332e 3220 4275 6773  al..4.4.3.2 Bugs\n-00018a50: 2061 6e64 2061 6e6f 6d61 6c69 6573 0a2e   and anomalies..\n-00018a60: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-00018a70: 2e2e 2e2e 2e2e 2e2e 2e0a 0a50 6f6c 7967  ...........Polyg\n-00018a80: 6f6e 2061 6e64 206c 696e 6520 7370 6c69  on and line spli\n-00018a90: 7474 696e 6720 6361 6e20 626f 7468 2063  tting can both c\n-00018aa0: 6175 7365 2061 6e6f 6d61 6c69 6573 2069  ause anomalies i\n-00018ab0: 6e20 7468 6520 6f75 7470 7574 2e0a 2750  n the output..'P\n-00018ac0: 5354 7269 636b 7327 2064 6173 6820 7061  STricks' dash pa\n-00018ad0: 7474 6572 6e73 2c20 7370 6563 6966 6965  tterns, specifie\n-00018ae0: 6420 7769 7468 2027 6c69 6e65 7374 796c  d with 'linestyl\n-00018af0: 653d 6461 7368 6564 272c 2063 616e 2062  e=dashed', can b\n-00018b00: 650a 6469 7372 7570 7465 6420 6279 2073  e.disrupted by s\n-00018b10: 706c 6974 7469 6e67 2e20 2054 6869 7320  plitting.  This \n-00018b20: 6f63 6375 7273 2077 6865 6e20 7468 6520  occurs when the \n-00018b30: 6465 7074 6820 736f 7274 2067 6976 6573  depth sort gives\n-00018b40: 2075 7020 746f 6f0a 6561 726c 7920 616e   up too.early an\n-00018b50: 6420 7370 6c69 7473 2061 206c 696e 6520  d splits a line \n-00018b60: 7768 6572 6520 6974 2069 7320 6e6f 7420  where it is not \n-00018b70: 7265 616c 6c79 206e 6563 6573 7361 7279  really necessary\n-00018b80: 2e20 2041 2077 6f72 6b61 726f 756e 640a  .  A workaround.\n-00018b90: 6973 2074 6f20 7573 6520 6772 6179 206f  is to use gray o\n-00018ba0: 7220 6669 6e65 6c79 2064 6f74 7465 6420  r finely dotted \n-00018bb0: 6c69 6e65 7320 696e 7374 6561 642e 2020  lines instead.  \n-00018bc0: 4966 2079 6f75 7220 6472 6177 696e 6720  If your drawing \n-00018bd0: 6973 0a73 6d61 6c6c 2c20 796f 7520 6361  is.small, you ca\n-00018be0: 6e20 616c 736f 2065 6469 7420 7468 6520  n also edit the \n-00018bf0: 2773 6b65 7463 6827 206f 7574 7075 7420  'sketch' output \n-00018c00: 6279 2068 616e 6420 746f 206d 6572 6765  by hand to merge\n-00018c10: 2074 6865 2070 6965 6365 730a 6f66 2074   the pieces.of t\n-00018c20: 6865 206f 6666 656e 6469 6e67 206c 696e  he offending lin\n-00018c30: 652e 0a0a 2020 2041 6e6f 7468 6572 2061  e...   Another a\n-00018c40: 6e6f 6d61 6c79 2069 7320 7469 6e79 2028  nomaly is tiny (\n-00018c50: 6f72 2069 6e20 6465 6765 6e65 7261 7465  or in degenerate\n-00018c60: 2063 6173 6573 206e 6f74 2d73 6f2d 7469   cases not-so-ti\n-00018c70: 6e79 2920 6e6f 7463 6865 730a 696e 2074  ny) notches.in t\n-00018c80: 6865 206c 696e 6573 2074 6861 7420 626f  he lines that bo\n-00018c90: 7264 6572 2073 706c 6974 2070 6f6c 7967  rder split polyg\n-00018ca0: 6f6e 732e 2020 5468 6573 6520 6465 7269  ons.  These deri\n-00018cb0: 7665 2066 726f 6d20 7468 6520 7761 7920  ve from the way \n-00018cc0: 6561 6368 0a70 6f6c 7967 6f6e 2069 7320  each.polygon is \n-00018cd0: 7061 696e 7465 643a 2066 6972 7374 2c20  painted: first, \n-00018ce0: 616c 6c20 7069 7865 6c73 2077 6974 6869  all pixels withi\n-00018cf0: 6e20 7468 6520 626f 756e 6461 7279 2061  n the boundary a\n-00018d00: 7265 2022 6669 6c6c 6564 220a 7769 7468  re \"filled\".with\n-00018d10: 2063 6f6c 6f72 2028 7065 7268 6170 7320   color (perhaps \n-00018d20: 7768 6974 6529 2c20 7468 656e 2074 6865  white), then the\n-00018d30: 2073 616d 6520 626f 756e 6461 7279 2069   same boundary i\n-00018d40: 7320 2273 7472 6f6b 6564 2220 2861 0a50  s \"stroked\" (a.P\n-00018d50: 6f73 7473 6372 6970 7420 7465 726d 2920  ostscript term) \n-00018d60: 7769 7468 2061 206c 696e 652e 2020 5468  with a line.  Th\n-00018d70: 6520 7265 7375 6c74 2069 7320 7468 6174  e result is that\n-00018d80: 2068 616c 6620 7468 6520 6c69 6e65 206c   half the line l\n-00018d90: 6965 730a 696e 7369 6465 2074 6865 2062  ies.inside the b\n-00018da0: 6f75 6e64 6172 7920 616e 6420 6861 6c66  oundary and half\n-00018db0: 206f 7574 7369 6465 2c20 7768 696c 6520   outside, while \n-00018dc0: 7468 6520 5061 696e 7465 7227 7320 616c  the Painter's al\n-00018dd0: 676f 7269 7468 6d0a 6173 7375 6d65 7320  gorithm.assumes \n-00018de0: 7468 6520 706f 6c79 676f 6e20 6c69 6573  the polygon lies\n-00018df0: 2065 6e74 6972 656c 7920 7769 7468 696e   entirely within\n-00018e00: 2069 7473 2062 6f75 6e64 6172 792e 2020   its boundary.  \n-00018e10: 5468 6520 6e6f 7463 6865 7320 6172 650a  The notches are.\n-00018e20: 6475 6520 746f 206f 6e65 2070 6f6c 7967  due to one polyg\n-00018e30: 6f6e 2066 696c 6c20 6f70 6572 6174 696f  on fill operatio\n-00018e40: 6e20 6f76 6572 7772 6974 696e 6720 7468  n overwriting th\n-00018e50: 6520 616c 7265 6164 792d 6472 6177 6e20  e already-drawn \n-00018e60: 696e 7369 6465 0a6f 6620 7468 6520 626f  inside.of the bo\n-00018e70: 7264 6572 206f 6620 616e 6f74 6865 7220  rder of another \n-00018e80: 706f 6c79 676f 6e2e 2831 2920 204f 6e65  polygon.(1)  One\n-00018e90: 2077 6f72 6b61 726f 756e 6420 6973 2074   workaround is t\n-00018ea0: 6f20 6d61 6b65 2062 6f72 6465 720a 6c69  o make border.li\n-00018eb0: 6e65 7320 7665 7279 2074 6869 6e2e 2020  nes very thin.  \n-00018ec0: 496e 2066 6163 7420 276c 696e 6577 6964  In fact 'linewid\n-00018ed0: 7468 3d30 7074 2720 6973 2067 7561 7261  th=0pt' is guara\n-00018ee0: 6e74 6565 6420 746f 2065 6c69 6d69 6e61  nteed to elimina\n-00018ef0: 7465 0a74 6869 7320 7072 6f62 6c65 6d2c  te.this problem,\n-00018f00: 2074 686f 7567 6820 7468 6973 2072 6573   though this res\n-00018f10: 756c 7473 2069 6e20 7468 6520 7468 696e  ults in the thin\n-00018f20: 6e65 7374 206c 696e 6520 796f 7572 206f  nest line your o\n-00018f30: 7574 7075 740a 6465 7669 6365 2063 616e  utput.device can\n-00018f40: 2064 7261 772c 2077 6869 6368 2069 7320   draw, which is \n-00018f50: 7573 7561 6c6c 7920 746f 6f20 7468 696e  usually too thin\n-00018f60: 2e20 2059 6f75 206d 6967 6874 2067 6574  .  You might get\n-00018f70: 206c 7563 6b79 2062 790a 6d65 7265 6c79   lucky by.merely\n-00018f80: 2072 656f 7264 6572 696e 6720 7468 696e   reordering thin\n-00018f90: 6773 2069 6e20 7468 6520 696e 7075 7420  gs in the input \n-00018fa0: 6669 6c65 2c20 7768 6963 6820 6973 206c  file, which is l\n-00018fb0: 696b 656c 7920 746f 206d 6f76 6520 7468  ikely to move th\n-00018fc0: 650a 7370 6c69 7473 2074 6f20 6469 6666  e.splits to diff\n-00018fd0: 6572 656e 7420 706c 6163 6573 2e20 2054  erent places.  T\n-00018fe0: 6865 206f 6e6c 7920 7375 7265 2d66 6972  he only sure-fir\n-00018ff0: 6520 736f 6c75 7469 6f6e 2069 7320 7072  e solution is pr\n-00019000: 6574 7479 0a74 6572 7269 626c 653a 2063  etty.terrible: c\n-00019010: 7573 746f 6d20 6669 7420 2773 7065 6369  ustom fit 'speci\n-00019020: 616c 2720 6f76 6572 6c61 7920 6c69 6e65  al' overlay line\n-00019030: 7320 2877 6974 6820 275c 7073 6c69 6e65  s (with '\\psline\n-00019040: 2729 2074 6f20 636f 7665 720a 7468 6520  ') to cover.the \n-00019050: 6e6f 7463 6865 732e 0a0a 2020 2050 6f6c  notches...   Pol\n-00019060: 7967 6f6e 2073 706c 6974 7469 6e67 2061  ygon splitting a\n-00019070: 6c73 6f20 6272 6561 6b73 2027 5053 5472  lso breaks 'PSTr\n-00019080: 6963 6b73 2720 6861 7463 6820 7061 7474  icks' hatch patt\n-00019090: 6572 6e73 2e20 2054 6865 206f 6e6c 790a  erns.  The only.\n-000190a0: 6b6e 6f77 6e20 776f 726b 6172 6f75 6e64  known workaround\n-000190b0: 2069 7320 746f 2073 7562 7374 6974 7574   is to substitut\n-000190c0: 6520 6120 736f 6c69 6420 6669 6c6c 2066  e a solid fill f\n-000190d0: 6f72 2074 6865 2068 6174 6368 2e0a 0a20  or the hatch... \n-000190e0: 2020 2d2d 2d2d 2d2d 2d2d 2d2d 2046 6f6f    ---------- Foo\n-000190f0: 746e 6f74 6573 202d 2d2d 2d2d 2d2d 2d2d  tnotes ---------\n-00019100: 2d0a 0a20 2020 2831 2920 4920 6b6e 6f77  -..   (1) I know\n-00019110: 2068 6f77 2074 6f20 6669 7820 7468 6973   how to fix this\n-00019120: 2070 726f 626c 656d 2c20 6275 7420 4920   problem, but I \n-00019130: 646f 6e27 7420 6c69 6b65 206d 7920 736f  don't like my so\n-00019140: 6c75 7469 6f6e 2c20 616e 640a 4927 6d20  lution, and.I'm \n-00019150: 696e 7465 7265 7374 6564 2069 6e20 796f  interested in yo\n-00019160: 7572 732e 0a0a 1f0a 4669 6c65 3a20 736b  urs.....File: sk\n-00019170: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n-00019180: 3a20 436f 6d6d 616e 6420 6c69 6e65 2c20  : Command line, \n-00019190: 204e 6578 743a 2049 6e73 7461 6c6c 696e   Next: Installin\n-000191a0: 6720 736b 6574 6368 2c20 2050 7265 763a  g sketch,  Prev:\n-000191b0: 2042 7569 6c64 696e 6720 6120 6472 6177   Building a draw\n-000191c0: 696e 672c 2020 5570 3a20 546f 700a 0a35  ing,  Up: Top..5\n-000191d0: 2043 6f6d 6d61 6e64 206c 696e 650a 2a2a   Command line.**\n-000191e0: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 0a0a 2a53  ************..*S\n-000191f0: 796e 6f70 7369 733a 2a0a 2020 2020 2073  ynopsis:*.     s\n-00019200: 6b65 7463 6820 5b2d 685d 5b2d 5620 782e  ketch [-h][-V x.\n-00019210: 795d 5b2d 765d 5b2d 625d 5b2d 645d 5b74  y][-v][-b][-d][t\n-00019220: 2064 6f63 746d 705d 5b2d 545b 757c 655d   doctmp][-T[u|e]\n-00019230: 5b70 5b50 7c54 5d5b 4c7c 435d 5d5d 5b2d  [p[P|T][L|C]]][-\n-00019240: 6f20 6f75 7470 7574 2e74 6578 5d0a 2020  o output.tex].  \n-00019250: 2020 2020 205b 2d44 2054 4147 202e 2e2e       [-D TAG ...\n-00019260: 5d20 696e 7075 7431 2e73 6b20 5b2d 5520  ] input1.sk [-U \n-00019270: 5441 4720 2e2e 2e5d 2069 6e70 7574 322e  TAG ...] input2.\n-00019280: 736b 202e 2e2e 0a0a 2a44 6573 6372 6970  sk .....*Descrip\n-00019290: 7469 6f6e 2a20 5072 6f63 6573 7365 7320  tion* Processes \n-000192a0: 7468 6520 2773 6b65 7463 6827 2069 6e70  the 'sketch' inp\n-000192b0: 7574 2066 696c 6573 2069 6e20 6f72 6465  ut files in orde\n-000192c0: 7220 746f 2070 726f 6475 6365 0a27 5053  r to produce.'PS\n-000192d0: 5472 6963 6b73 2720 6f75 7470 7574 2063  Tricks' output c\n-000192e0: 6f64 6520 7375 6974 6162 6c65 2066 6f72  ode suitable for\n-000192f0: 2069 6e63 6c75 7369 6f6e 2069 6e20 6120   inclusion in a \n-00019300: 5465 5820 6f72 204c 6154 6558 0a64 6f63  TeX or LaTeX.doc\n-00019310: 756d 656e 742e 0a0a 2a4f 7074 696f 6e73  ument...*Options\n-00019320: 3a2a 0a27 2d68 270a 2020 2020 2050 7269  :*.'-h'.     Pri\n-00019330: 6e74 2061 2073 686f 7274 2063 6174 616c  nt a short catal\n-00019340: 6f67 206f 6620 6f70 7469 6f6e 732e 0a27  og of options..'\n-00019350: 2d56 270a 2020 2020 2053 6574 2074 6865  -V'.     Set the\n-00019360: 2027 5053 5472 6963 6b73 2720 7665 7273   'PSTricks' vers\n-00019370: 696f 6e20 6173 7375 6d65 6420 666f 7220  ion assumed for \n-00019380: 6f75 7470 7574 2070 7572 706f 7365 7320  output purposes \n-00019390: 746f 2027 782e 7927 2c0a 2020 2020 2066  to 'x.y',.     f\n-000193a0: 6f72 2065 7861 6d70 6c65 2031 2e31 392e  or example 1.19.\n-000193b0: 2020 5573 7561 6c6c 7920 6e65 6564 6564    Usually needed\n-000193c0: 206f 6e6c 7920 6966 2079 6f75 7220 2750   only if your 'P\n-000193d0: 5354 7269 636b 7327 2069 7320 6f6c 640a  STricks' is old.\n-000193e0: 2020 2020 2063 6f6d 7061 7265 6420 746f       compared to\n-000193f0: 2079 6f75 7220 2773 6b65 7463 6827 2e20   your 'sketch'. \n-00019400: 2055 7365 2027 2d76 2720 746f 2073 6565   Use '-v' to see\n-00019410: 2077 6861 7420 2773 6b65 7463 6827 2061   what 'sketch' a\n-00019420: 7373 756d 6573 0a20 2020 2020 6279 2064  ssumes.     by d\n-00019430: 6566 6175 6c74 2e0a 272d 7627 0a20 2020  efault..'-v'.   \n-00019440: 2020 5072 696e 7420 7665 7273 696f 6e20    Print version \n-00019450: 696e 666f 726d 6174 696f 6e20 746f 2073  information to s\n-00019460: 7461 6e64 6172 6420 6f75 7470 7574 2c20  tandard output, \n-00019470: 696e 636c 7564 696e 6720 7468 6520 7665  including the ve\n-00019480: 7273 696f 6e0a 2020 2020 206f 6620 2750  rsion.     of 'P\n-00019490: 5354 7269 636b 7327 2061 7373 756d 6564  STricks' assumed\n-000194a0: 2066 6f72 206f 7574 7075 7420 2863 616e   for output (can\n-000194b0: 2062 6520 6368 616e 6765 6420 7769 7468   be changed with\n-000194c0: 2027 2d56 2720 6162 6f76 6529 2e0a 272d   '-V' above)..'-\n-000194d0: 6227 0a20 2020 2020 5573 6520 6120 4253  b'.     Use a BS\n-000194e0: 5020 282a 4e6f 7465 2048 6964 6465 6e20  P (*Note Hidden \n-000194f0: 7375 7266 6163 6520 7265 6d6f 7661 6c3a  surface removal:\n-00019500: 3a2e 2920 2066 6f72 205f 616c 6c5f 2068  :.)  for _all_ h\n-00019510: 6964 6465 6e0a 2020 2020 2073 7572 6661  idden.     surfa\n-00019520: 6365 2072 656d 6f76 616c 2072 6174 6865  ce removal rathe\n-00019530: 7220 7468 616e 2074 6865 2064 6566 6175  r than the defau\n-00019540: 6c74 2c20 7768 6963 6820 6973 2074 6865  lt, which is the\n-00019550: 2064 6570 7468 2073 6f72 740a 2020 2020   depth sort.    \n-00019560: 2061 6c67 6f72 6974 686d 2077 6974 6820   algorithm with \n-00019570: 4253 5073 2075 7365 6420 6f6e 6c79 2066  BSPs used only f\n-00019580: 6f72 2063 7963 6c65 2072 6573 6f6c 7574  or cycle resolut\n-00019590: 696f 6e2e 2020 5468 6973 206d 6179 0a20  ion.  This may. \n-000195a0: 2020 2020 7072 6f64 7563 6520 636f 7272      produce corr\n-000195b0: 6563 7420 6f75 7470 7574 2069 6e20 6365  ect output in ce\n-000195c0: 7274 6169 6e20 6465 6765 6e65 7261 7465  rtain degenerate\n-000195d0: 2063 6173 6573 2077 6865 7265 2074 6865   cases where the\n-000195e0: 2064 6570 7468 0a20 2020 2020 736f 7274   depth.     sort\n-000195f0: 2063 616e 6e6f 742c 2062 7574 2069 7420   cannot, but it \n-00019600: 616c 736f 206c 6561 6473 2074 6f20 6d61  also leads to ma\n-00019610: 6e79 2067 7261 7475 6974 6f75 7320 7370  ny gratuitous sp\n-00019620: 6c69 7473 2c20 6865 6e63 650a 2020 2020  lits, hence.    \n-00019630: 206d 6f72 6520 616e 6f6d 616c 6965 7320   more anomalies \n-00019640: 2a6e 6f74 6520 4275 6773 2061 6e64 2061  *note Bugs and a\n-00019650: 6e6f 6d61 6c69 6573 3a3a 2061 6e64 2062  nomalies:: and b\n-00019660: 6967 206f 7574 7075 7420 6669 6c65 732e  ig output files.\n-00019670: 0a27 2d64 270a 2020 2020 2052 756e 2027  .'-d'.     Run '\n-00019680: 736b 6574 6368 2727 7320 7061 7273 6572  sketch''s parser\n-00019690: 2069 6e20 6465 6275 6767 696e 6720 6d6f   in debugging mo\n-000196a0: 6465 2e20 2054 6869 7320 6973 2070 7269  de.  This is pri\n-000196b0: 6d61 7269 6c79 2066 6f72 0a20 2020 2020  marily for.     \n-000196c0: 6465 7665 6c6f 706d 656e 742e 0a27 2d74  development..'-t\n-000196d0: 270a 2020 2020 2055 7365 2063 6f6e 7465  '.     Use conte\n-000196e0: 6e74 7320 6f66 2066 696c 6520 2764 6f63  nts of file 'doc\n-000196f0: 746d 7027 2061 7320 6120 646f 6375 6d65  tmp' as a docume\n-00019700: 6e74 2074 656d 706c 6174 6520 696e 2077  nt template in w\n-00019710: 6869 6368 2074 6f0a 2020 2020 2065 6e63  hich to.     enc\n-00019720: 6c6f 7365 2027 5053 5472 6963 6b73 2720  lose 'PSTricks' \n-00019730: 6f75 7470 7574 2063 6f64 652e 2020 5468  output code.  Th\n-00019740: 6520 636f 6465 2069 7320 696e 7365 7274  e code is insert\n-00019750: 6564 2069 6e20 706c 6163 6520 6f66 0a20  ed in place of. \n-00019760: 2020 2020 7468 6520 6669 7273 7420 696e      the first in\n-00019770: 7374 616e 6365 206f 6620 7468 6520 6573  stance of the es\n-00019780: 6361 7065 2073 7472 696e 6720 2525 534b  cape string %%SK\n-00019790: 4554 4348 5f4f 5554 5055 5425 252e 0a27  ETCH_OUTPUT%%..'\n-000197a0: 2d54 270a 2020 2020 2043 6175 7365 7320  -T'.     Causes \n-000197b0: 2750 5354 7269 636b 7327 206f 7574 7075  'PSTricks' outpu\n-000197c0: 7420 746f 2062 6520 656e 636c 6f73 6564  t to be enclosed\n-000197d0: 2069 6e20 6465 6661 756c 7420 5553 2064   in default US d\n-000197e0: 6f63 756d 656e 740a 2020 2020 2074 656d  ocument.     tem\n-000197f0: 706c 6174 6520 7465 7874 2e20 204f 7074  plate text.  Opt\n-00019800: 696f 6e20 272d 5475 2720 6973 2061 2073  ion '-Tu' is a s\n-00019810: 796e 6f6e 796d 2e20 204f 7074 696f 6e20  ynonym.  Option \n-00019820: 272d 5465 2720 6361 7573 6573 2074 6865  '-Te' causes the\n-00019830: 0a20 2020 2020 4575 726f 2073 7461 6e64  .     Euro stand\n-00019840: 6172 6420 646f 6375 6d65 6e74 2074 656d  ard document tem\n-00019850: 706c 6174 6520 746f 2062 6520 7573 6564  plate to be used\n-00019860: 2e20 2041 2027 7027 2061 7070 656e 6465  .  A 'p' appende\n-00019870: 6420 746f 2061 6e79 0a20 2020 2020 6f66  d to any.     of\n-00019880: 2074 6865 7365 206f 7074 696f 6e73 2063   these options c\n-00019890: 6175 7365 7320 7468 6520 7265 7370 6563  auses the respec\n-000198a0: 7469 7665 2064 6566 6175 6c74 2027 5053  tive default 'PS\n-000198b0: 5472 6963 6b73 2720 646f 6375 6d65 6e74  Tricks' document\n-000198c0: 0a20 2020 2020 7465 6d70 6c61 7465 2074  .     template t\n-000198d0: 6f20 6265 2070 7269 6e74 6564 2074 6f20  o be printed to \n-000198e0: 7374 616e 6461 7264 206f 7574 7075 742e  standard output.\n-000198f0: 2020 416e 2061 7070 656e 6465 6420 2750    An appended 'P\n-00019900: 2720 6973 2061 0a20 2020 2020 7379 6e6f  ' is a.     syno\n-00019910: 6e79 6d2e 2020 416e 2061 7070 656e 6465  nym.  An appende\n-00019920: 6420 2754 2720 6361 7573 6573 2074 6865  d 'T' causes the\n-00019930: 2074 6865 2027 5469 6b5a 2f50 4746 2720   the 'TikZ/PGF' \n-00019940: 7465 6d70 6c61 7465 2074 6f20 6265 0a20  template to be. \n-00019950: 2020 2020 7072 696e 7465 642e 2020 416e      printed.  An\n-00019960: 2061 7070 656e 6465 6420 274c 2720 7072   appended 'L' pr\n-00019970: 696e 7473 2074 6865 204c 6154 6558 2076  ints the LaTeX v\n-00019980: 6572 7369 6f6e 206f 6620 7468 6520 646f  ersion of the do\n-00019990: 6375 6d65 6e74 0a20 2020 2020 7465 6d70  cument.     temp\n-000199a0: 6c61 7465 2c20 6120 7379 6e6f 6e79 6d20  late, a synonym \n-000199b0: 666f 7220 7468 6520 6465 6661 756c 742e  for the default.\n-000199c0: 2020 4120 2743 2720 7072 696e 7473 2074    A 'C' prints t\n-000199d0: 6865 2027 436f 6e54 6558 7427 0a20 2020  he 'ConTeXt'.   \n-000199e0: 2020 7465 6d70 6c61 7465 2e0a 272d 6f27    template..'-o'\n-000199f0: 0a20 2020 2020 5573 6520 276f 7574 7075  .     Use 'outpu\n-00019a00: 742e 7465 7827 2061 7320 7468 6520 6f75  t.tex' as the ou\n-00019a10: 7470 7574 2066 696c 652e 2020 5468 6520  tput file.  The \n-00019a20: 6465 6661 756c 7420 6973 2073 7461 6e64  default is stand\n-00019a30: 6172 640a 2020 2020 206f 7574 7075 742e  ard.     output.\n-00019a40: 0a27 2d44 270a 2020 2020 2044 6566 696e  .'-D'.     Defin\n-00019a50: 6520 6120 7461 6720 666f 7220 7075 7270  e a tag for purp\n-00019a60: 6f73 6573 206f 6620 7365 6c65 6374 696e  oses of selectin\n-00019a70: 6720 6465 6669 6e69 7469 6f6e 2061 6c74  g definition alt\n-00019a80: 6572 6e61 7469 7665 732e 0a20 2020 2020  ernatives..     \n-00019a90: 2a4e 6f74 6520 4465 6669 6e69 7469 6f6e  *Note Definition\n-00019aa0: 733a 3a2e 2020 5468 6520 6465 6669 6e69  s::.  The defini\n-00019ab0: 7469 6f6e 2061 7070 6c69 6573 2066 6f72  tion applies for\n-00019ac0: 2061 6c6c 2069 6e70 7574 2066 696c 6573   all input files\n-00019ad0: 0a20 2020 2020 7468 6174 2066 6f6c 6c6f  .     that follo\n-00019ae0: 7720 756e 6c65 7373 2074 6865 2074 6167  w unless the tag\n-00019af0: 2069 7320 756e 6465 6669 6e65 6420 7769   is undefined wi\n-00019b00: 7468 2027 2d55 272e 0a27 696e 7075 7469  th '-U'..'inputi\n-00019b10: 2e73 6b27 0a20 2020 2020 496e 7075 7420  .sk'.     Input \n-00019b20: 6669 6c65 732c 2072 6561 6420 696e 2074  files, read in t\n-00019b30: 6865 2073 6571 7565 6e63 6520 7468 6579  he sequence they\n-00019b40: 2061 7265 2067 6976 656e 2e0a 272d 5527   are given..'-U'\n-00019b50: 0a20 2020 2020 556e 2d64 6566 696e 6520  .     Un-define \n-00019b60: 6120 7461 6720 666f 7220 7075 7270 6f73  a tag for purpos\n-00019b70: 6573 206f 6620 7365 6c65 6374 696e 6720  es of selecting \n-00019b80: 6465 6669 6e69 7469 6f6e 2061 6c74 6572  definition alter\n-00019b90: 6e61 7469 7665 732e 0a0a 1f0a 4669 6c65  natives.....File\n-00019ba0: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n-00019bb0: 4e6f 6465 3a20 496e 7374 616c 6c69 6e67  Node: Installing\n-00019bc0: 2073 6b65 7463 682c 2020 4e65 7874 3a20   sketch,  Next: \n-00019bd0: 496e 6465 7820 6f66 2073 796e 7461 782c  Index of syntax,\n-00019be0: 2020 5072 6576 3a20 436f 6d6d 616e 6420    Prev: Command \n-00019bf0: 6c69 6e65 2c20 2055 703a 2054 6f70 0a0a  line,  Up: Top..\n-00019c00: 3620 4275 696c 6469 6e67 2061 6e64 2069  6 Building and i\n-00019c10: 6e73 7461 6c6c 696e 6720 2773 6b65 7463  nstalling 'sketc\n-00019c20: 6827 0a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  h'.*************\n+00017de0: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2753 6b65  ----------..'Ske\n+00017df0: 7463 6827 2075 7365 7320 7468 6520 2264  tch' uses the \"d\n+00017e00: 6570 7468 2073 6f72 7420 616c 676f 7269  epth sort algori\n+00017e10: 7468 6d22 2066 6f72 2068 6964 6465 6e20  thm\" for hidden \n+00017e20: 7375 7266 6163 6520 7265 6d6f 7661 6c2e  surface removal.\n+00017e30: 0a54 6869 7320 6973 2061 2076 6572 7920  .This is a very \n+00017e40: 6f6c 6420 7465 6368 6e69 7175 6520 6475  old technique du\n+00017e50: 6520 746f 204e 6577 656c 6c2e 2831 2920  e to Newell.(1) \n+00017e60: 2049 7420 6973 2067 656e 6572 616c 6c79   It is generally\n+00017e70: 2072 6567 6172 6465 640a 6173 2074 6f6f   regarded.as too\n+00017e80: 2073 6c6f 7720 666f 7220 7265 616c 2074   slow for real t\n+00017e90: 696d 6520 6772 6170 6869 6373 2c20 6275  ime graphics, bu\n+00017ea0: 7420 6974 2069 7320 6964 6561 6c20 666f  t it is ideal fo\n+00017eb0: 7220 6f75 7220 7075 7270 6f73 650a 7768  r our purpose.wh\n+00017ec0: 6572 6520 7370 6565 6420 6973 206e 6f74  ere speed is not\n+00017ed0: 2076 6572 7920 696d 706f 7274 616e 742e   very important.\n+00017ee0: 2832 290a 0a20 2020 5468 6520 6465 7074  (2)..   The dept\n+00017ef0: 6820 736f 7274 2061 6c67 6f72 6974 686d  h sort algorithm\n+00017f00: 206d 6572 656c 7920 736f 7274 7320 6f62   merely sorts ob\n+00017f10: 6a65 6374 7320 6f6e 2061 206b 6579 206f  jects on a key o\n+00017f20: 6620 696e 6372 6561 7369 6e67 0a7a 2d63  f increasing.z-c\n+00017f30: 6f6f 7264 696e 6174 652c 2065 7175 6976  oordinate, equiv\n+00017f40: 616c 656e 7420 746f 2064 6563 7265 6173  alent to decreas\n+00017f50: 696e 6720 6465 7074 682e 2020 4f62 6a65  ing depth.  Obje\n+00017f60: 6374 7320 6172 6520 7468 656e 2064 7261  cts are then dra\n+00017f70: 776e 2069 6e0a 7468 6520 736f 7274 6564  wn in.the sorted\n+00017f80: 2073 6571 7565 6e63 6520 736f 2074 6861   sequence so tha\n+00017f90: 7420 7468 6f73 6520 6174 2074 6865 2072  t those at the r\n+00017fa0: 6561 7220 6f66 2074 6865 2073 6365 6e65  ear of the scene\n+00017fb0: 2061 7265 0a6f 7665 7277 7269 7474 656e   are.overwritten\n+00017fc0: 2062 7920 7468 6f73 6520 636c 6f73 6572   by those closer\n+00017fd0: 2074 6f20 7468 6520 7669 6577 6572 2e20   to the viewer. \n+00017fe0: 2053 696e 6365 2074 6869 7320 6973 2061   Since this is a\n+00017ff0: 6c73 6f20 686f 7720 6f69 6c0a 7061 696e  lso how oil.pain\n+00018000: 7465 7273 2070 7261 6374 6963 6520 7468  ters practice th\n+00018010: 6569 7220 6172 742c 2064 6570 7468 2073  eir art, depth s\n+00018020: 6f72 7420 6973 2073 6f6d 6574 696d 6573  ort is sometimes\n+00018030: 2063 616c 6c65 6420 2274 6865 0a70 6169   called \"the.pai\n+00018040: 6e74 6572 2773 2061 6c67 6f72 6974 686d  nter's algorithm\n+00018050: 2e22 0a0a 2020 2049 6e20 736f 6d65 2063  .\"..   In some c\n+00018060: 6173 6573 2069 7420 6973 2069 6d70 6f73  ases it is impos\n+00018070: 7369 626c 6520 746f 2073 7472 6963 746c  sible to strictl\n+00018080: 7920 6f72 6465 7220 706f 6c79 676f 6e73  y order polygons\n+00018090: 2061 6363 6f72 6469 6e67 0a74 6f20 6465   according.to de\n+000180a0: 7074 682e 2020 4d6f 7265 6f76 6572 2c20  pth.  Moreover, \n+000180b0: 6576 656e 2069 6620 6120 636f 7272 6563  even if a correc\n+000180c0: 7420 6465 7074 6820 6f72 6465 7269 6e67  t depth ordering\n+000180d0: 2065 7869 7374 732c 2074 6865 0a63 6f6d   exists, the.com\n+000180e0: 7075 7461 7469 6f6e 206e 6565 6465 6420  putation needed \n+000180f0: 746f 2066 696e 6420 6974 206d 6179 2062  to find it may b\n+00018100: 6520 746f 6f20 636f 6d70 6c65 7820 616e  e too complex an\n+00018110: 6420 736c 6f77 2e20 2049 6e20 7468 6573  d slow.  In thes\n+00018120: 650a 6361 7365 732c 2027 736b 6574 6368  e.cases, 'sketch\n+00018130: 2720 7370 6c69 7473 206f 6e65 206f 7220  ' splits one or \n+00018140: 6d6f 7265 2070 6f6c 7967 6f6e 7320 696e  more polygons in\n+00018150: 746f 2070 6965 6365 732e 2020 5468 650a  to pieces.  The.\n+00018160: 6578 7065 6374 6174 696f 6e20 6973 2074  expectation is t\n+00018170: 6861 7420 7468 6520 6e65 772c 2073 6d61  hat the new, sma\n+00018180: 6c6c 6572 2070 6f6c 7967 6f6e 7320 7769  ller polygons wi\n+00018190: 6c6c 2062 6520 7369 6d70 6c65 7220 746f  ll be simpler to\n+000181a0: 206f 7264 6572 2e0a 2753 6b65 7463 6827   order..'Sketch'\n+000181b0: 2075 7365 7320 6120 4253 5020 2862 696e   uses a BSP (bin\n+000181c0: 6172 7920 7370 6163 6520 7061 7274 6974  ary space partit\n+000181d0: 696f 6e29 2074 6f20 6861 6e64 6c65 2074  ion) to handle t\n+000181e0: 6865 2073 706c 6974 7469 6e67 0a6f 7065  he splitting.ope\n+000181f0: 7261 7469 6f6e 2e0a 0a2a 204d 656e 753a  ration...* Menu:\n+00018200: 0a0a 2a20 5374 6174 6973 7469 6373 3a3a  ..* Statistics::\n+00018210: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00018220: 2020 5065 7266 6f72 6d61 6e63 6520 6e75    Performance nu\n+00018230: 6d62 6572 7320 6f6e 2064 6570 7468 2073  mbers on depth s\n+00018240: 6f72 742e 0a2a 2042 7567 7320 616e 6420  ort..* Bugs and \n+00018250: 616e 6f6d 616c 6965 733a 3a20 2020 2020  anomalies::     \n+00018260: 2020 2020 2049 6d70 6572 6665 6374 696f       Imperfectio\n+00018270: 6e73 2069 6e20 7468 6973 2069 6d70 6c65  ns in this imple\n+00018280: 6d65 6e74 6174 696f 6e2e 0a0a 2020 202d  mentation...   -\n+00018290: 2d2d 2d2d 2d2d 2d2d 2d20 466f 6f74 6e6f  --------- Footno\n+000182a0: 7465 7320 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a  tes ----------..\n+000182b0: 2020 2028 3129 204e 6577 656c 6c2c 204d     (1) Newell, M\n+000182c0: 2e45 2e2c 2052 2e47 2e20 4e65 7765 6c6c  .E., R.G. Newell\n+000182d0: 2c20 616e 6420 542e 4c2e 2053 616e 6368  , and T.L. Sanch\n+000182e0: 612c 2041 2073 6f6c 7574 696f 6e20 746f  a, A solution to\n+000182f0: 2074 6865 0a68 6964 6465 6e20 7375 7266   the.hidden surf\n+00018300: 6163 6520 7072 6f62 6c65 6d2e 2020 5072  ace problem.  Pr\n+00018310: 6f63 6565 6469 6e67 7320 6f66 2074 6865  oceedings of the\n+00018320: 2041 434d 2061 6e6e 7561 6c20 636f 6e66   ACM annual conf\n+00018330: 6572 656e 6365 202d 0a56 6f6c 756d 6520  erence -.Volume \n+00018340: 312c 2070 6167 6520 3434 332d 3435 302c  1, page 443-450,\n+00018350: 2041 434d 2050 7265 7373 2c20 3139 3732   ACM Press, 1972\n+00018360: 2e0a 0a20 2020 2832 2920 5765 2068 6176  ...   (2) We hav\n+00018370: 6520 7275 6e20 2773 6b65 7463 6827 206f  e run 'sketch' o\n+00018380: 6e20 7468 6520 6661 6d6f 7573 2053 7461  n the famous Sta\n+00018390: 6e66 6f72 6420 4275 6e6e 792c 2077 6869  nford Bunny, whi\n+000183a0: 6368 2063 6f6e 7369 7374 730a 6f66 206e  ch consists.of n\n+000183b0: 6561 726c 7920 3730 2c30 3030 2074 7269  early 70,000 tri\n+000183c0: 616e 676c 6573 2e20 2052 756e 2074 696d  angles.  Run tim\n+000183d0: 6520 7761 7320 6162 6f75 7420 3620 7365  e was about 6 se\n+000183e0: 636f 6e64 732e 2020 4d6f 7374 206f 6620  conds.  Most of \n+000183f0: 7468 6973 0a77 6173 2073 7065 6e74 2077  this.was spent w\n+00018400: 7269 7469 6e67 2074 6865 206f 7574 7075  riting the outpu\n+00018410: 7420 6669 6c65 2072 6174 6865 7220 7468  t file rather th\n+00018420: 616e 2069 6e20 7468 6520 6869 6464 656e  an in the hidden\n+00018430: 2073 7572 6661 6365 0a61 6c67 6f72 6974   surface.algorit\n+00018440: 686d 2e20 204c 6154 6558 2074 6f6f 6b20  hm.  LaTeX took \n+00018450: 6d75 6368 206c 6f6e 6765 7220 746f 2070  much longer to p\n+00018460: 726f 6365 7373 2074 6865 2072 6573 756c  rocess the resul\n+00018470: 7469 6e67 2027 5053 5472 6963 6b73 270a  ting 'PSTricks'.\n+00018480: 636f 6465 2e20 2054 6865 206f 6276 696f  code.  The obvio\n+00018490: 7573 2063 6f6e 636c 7573 696f 6e20 6973  us conclusion is\n+000184a0: 2074 6861 7420 7468 6520 7370 6565 6420   that the speed \n+000184b0: 6f66 2074 6865 2064 6570 7468 2073 6f72  of the depth sor\n+000184c0: 740a 616c 676f 7269 7468 6d20 6973 206e  t.algorithm is n\n+000184d0: 6f74 2061 2077 6f72 7279 2e0a 0a1f 0a46  ot a worry.....F\n+000184e0: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n+000184f0: 2c20 204e 6f64 653a 2053 7461 7469 7374  ,  Node: Statist\n+00018500: 6963 732c 2020 4e65 7874 3a20 4275 6773  ics,  Next: Bugs\n+00018510: 2061 6e64 2061 6e6f 6d61 6c69 6573 2c20   and anomalies, \n+00018520: 2050 7265 763a 2048 6964 6465 6e20 7375   Prev: Hidden su\n+00018530: 7266 6163 6520 7265 6d6f 7661 6c2c 2020  rface removal,  \n+00018540: 5570 3a20 4869 6464 656e 2073 7572 6661  Up: Hidden surfa\n+00018550: 6365 2072 656d 6f76 616c 0a0a 342e 342e  ce removal..4.4.\n+00018560: 332e 3120 5374 6174 6973 7469 6373 0a2e  3.1 Statistics..\n+00018570: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+00018580: 2e0a 0a46 6f72 2074 6865 2063 7572 696f  ...For the curio\n+00018590: 7573 2c20 2773 6b65 7463 6827 2077 7269  us, 'sketch' wri\n+000185a0: 7465 7320 6f6e 6520 6c69 6e65 206f 6620  tes one line of \n+000185b0: 6465 7074 6820 736f 7274 2073 7461 7469  depth sort stati\n+000185c0: 7374 6963 732e 0a48 6572 6520 6973 2061  stics..Here is a\n+000185d0: 6e20 6578 616d 706c 6520 666f 7220 6120  n example for a \n+000185e0: 6c61 7267 6520 636f 6c6c 6563 7469 6f6e  large collection\n+000185f0: 206f 6620 7472 6961 6e67 6c65 732e 0a20   of triangles.. \n+00018600: 2072 656d 6172 6b2c 206e 6f64 653d 3334   remark, node=34\n+00018610: 3832 3420 7072 6f62 653d 3538 312e 3920  824 probe=581.9 \n+00018620: 7377 6170 3d35 2073 706c 6974 3d32 2028  swap=5 split=2 (\n+00018630: 696e 3d34 206f 7574 3d36 2920 6f6c 733d  in=4 out=6) ols=\n+00018640: 3234 3835 312f 300a 4974 206d 6561 6e73  24851/0.It means\n+00018650: 2074 6861 7420 3334 2c38 3234 206f 626a   that 34,824 obj\n+00018660: 6563 7473 2077 6572 6520 6465 7074 6820  ects were depth \n+00018670: 736f 7274 6564 2061 6674 6572 2063 756c  sorted after cul\n+00018680: 6c69 6e67 2e20 2046 6f72 2065 6163 682c  ling.  For each,\n+00018690: 0a61 6e20 6176 6572 6167 6520 6f66 2035  .an average of 5\n+000186a0: 3831 2e39 206f 7468 6572 7320 6861 6420  81.9 others had \n+000186b0: 746f 2062 6520 6368 6563 6b65 6420 746f  to be checked to\n+000186c0: 2065 6e73 7572 6520 7468 6174 2074 6865   ensure that the\n+000186d0: 2069 6e69 7469 616c 2c0a 6170 7072 6f78   initial,.approx\n+000186e0: 696d 6174 6520 6f72 6465 7269 6e67 2077  imate ordering w\n+000186f0: 6173 2063 6f72 7265 6374 2e20 2041 6d6f  as correct.  Amo\n+00018700: 6e67 2061 6c6c 2074 6865 7365 2063 6865  ng all these che\n+00018710: 636b 732c 206f 6e6c 7920 350a 7265 7375  cks, only 5.resu\n+00018720: 6c74 6564 2069 6e20 7377 6170 7320 746f  lted in swaps to\n+00018730: 2072 656f 7264 6572 2074 6865 2069 6e69   reorder the ini\n+00018740: 7469 616c 2073 6f72 742e 2020 496e 2074  tial sort.  In t\n+00018750: 776f 2063 6173 6573 2c20 6120 636f 7272  wo cases, a corr\n+00018760: 6563 740a 6f72 6465 7269 6e67 2063 6f75  ect.ordering cou\n+00018770: 6c64 206e 6f74 2062 6520 6465 7465 726d  ld not be determ\n+00018780: 696e 6564 2c20 736f 2062 696e 6172 7920  ined, so binary \n+00018790: 7370 6163 6520 7061 7274 6974 696f 6e73  space partitions\n+000187a0: 2077 6572 650a 636f 6e73 7472 7563 7465   were.constructe\n+000187b0: 6420 666f 7220 7370 6c69 7474 696e 672e  d for splitting.\n+000187c0: 2020 4120 746f 7461 6c20 6f66 2034 206f    A total of 4 o\n+000187d0: 626a 6563 7473 2028 7472 6961 6e67 6c65  bjects (triangle\n+000187e0: 7320 696e 2074 6869 730a 6361 7365 2920  s in this.case) \n+000187f0: 7765 7265 2069 6e73 6572 7465 6420 696e  were inserted in\n+00018800: 2074 6865 2070 6172 7469 7469 6f6e 732c   the partitions,\n+00018810: 2061 6e64 2036 2070 6f6c 7967 6f6e 7320   and 6 polygons \n+00018820: 7765 7265 2070 726f 6475 6365 642e 0a46  were produced..F\n+00018830: 696e 616c 6c79 2c20 3234 2c38 3531 2022  inally, 24,851 \"\n+00018840: 6c61 7374 2072 6573 6f72 7422 2070 6f6c  last resort\" pol\n+00018850: 7967 6f6e 206f 7665 726c 6170 2063 6865  ygon overlap che\n+00018860: 636b 7320 7765 7265 2070 6572 666f 726d  cks were perform\n+00018870: 6564 0a61 6674 6572 2073 696d 706c 6572  ed.after simpler\n+00018880: 2c20 6661 7374 6572 2063 6865 636b 7320  , faster checks \n+00018890: 6661 696c 6564 2074 6f20 7969 656c 6420  failed to yield \n+000188a0: 636f 6e63 6c75 7369 7665 2072 6573 756c  conclusive resul\n+000188b0: 7473 2e20 2054 6865 0a66 696e 616c 202f  ts.  The.final /\n+000188c0: 3020 6973 2066 6f72 206c 696e 652d 706f  0 is for line-po\n+000188d0: 6c79 676f 6e20 6f76 6572 6c61 7020 6368  lygon overlap ch\n+000188e0: 6563 6b73 2e20 2046 6f72 2063 6f6d 7061  ecks.  For compa\n+000188f0: 7269 736f 6e2c 2074 6865 0a73 7461 7469  rison, the.stati\n+00018900: 7374 6963 7320 666f 7220 7468 6520 6c61  stics for the la\n+00018910: 7374 2066 6967 7572 6520 696e 202a 6e6f  st figure in *no\n+00018920: 7465 204f 7665 7276 6965 773a 3a20 666f  te Overview:: fo\n+00018930: 6c6c 6f77 2e0a 2020 7265 6d61 726b 2c20  llow..  remark, \n+00018940: 6e6f 6465 3d32 3720 7072 6f62 653d 3134  node=27 probe=14\n+00018950: 2e36 2073 7761 703d 3336 2073 706c 6974  .6 swap=36 split\n+00018960: 3d31 3520 2869 6e3d 3330 206f 7574 3d34  =15 (in=30 out=4\n+00018970: 3529 206f 6c73 3d30 2f36 390a 4e6f 7465  5) ols=0/69.Note\n+00018980: 2074 6861 7420 7468 6572 6520 7761 7320   that there was \n+00018990: 7072 6f70 6f72 7469 6f6e 616c 6c79 206d  proportionally m\n+000189a0: 7563 6820 6d6f 7265 2073 7761 7070 696e  uch more swappin\n+000189b0: 6720 616e 6420 7370 6c69 7474 696e 670a  g and splitting.\n+000189c0: 6163 7469 7669 7479 2069 6e20 7468 6973  activity in this\n+000189d0: 2068 6967 686c 7920 636f 6e6e 6563 7465   highly connecte\n+000189e0: 6420 7363 656e 652e 0a0a 1f0a 4669 6c65  d scene.....File\n+000189f0: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n+00018a00: 4e6f 6465 3a20 4275 6773 2061 6e64 2061  Node: Bugs and a\n+00018a10: 6e6f 6d61 6c69 6573 2c20 2050 7265 763a  nomalies,  Prev:\n+00018a20: 2053 7461 7469 7374 6963 732c 2020 5570   Statistics,  Up\n+00018a30: 3a20 4869 6464 656e 2073 7572 6661 6365  : Hidden surface\n+00018a40: 2072 656d 6f76 616c 0a0a 342e 342e 332e   removal..4.4.3.\n+00018a50: 3220 4275 6773 2061 6e64 2061 6e6f 6d61  2 Bugs and anoma\n+00018a60: 6c69 6573 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e  lies............\n+00018a70: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a  ................\n+00018a80: 0a50 6f6c 7967 6f6e 2061 6e64 206c 696e  .Polygon and lin\n+00018a90: 6520 7370 6c69 7474 696e 6720 6361 6e20  e splitting can \n+00018aa0: 626f 7468 2063 6175 7365 2061 6e6f 6d61  both cause anoma\n+00018ab0: 6c69 6573 2069 6e20 7468 6520 6f75 7470  lies in the outp\n+00018ac0: 7574 2e0a 2750 5354 7269 636b 7327 2064  ut..'PSTricks' d\n+00018ad0: 6173 6820 7061 7474 6572 6e73 2c20 7370  ash patterns, sp\n+00018ae0: 6563 6966 6965 6420 7769 7468 2027 6c69  ecified with 'li\n+00018af0: 6e65 7374 796c 653d 6461 7368 6564 272c  nestyle=dashed',\n+00018b00: 2063 616e 2062 650a 6469 7372 7570 7465   can be.disrupte\n+00018b10: 6420 6279 2073 706c 6974 7469 6e67 2e20  d by splitting. \n+00018b20: 2054 6869 7320 6f63 6375 7273 2077 6865   This occurs whe\n+00018b30: 6e20 7468 6520 6465 7074 6820 736f 7274  n the depth sort\n+00018b40: 2067 6976 6573 2075 7020 746f 6f0a 6561   gives up too.ea\n+00018b50: 726c 7920 616e 6420 7370 6c69 7473 2061  rly and splits a\n+00018b60: 206c 696e 6520 7768 6572 6520 6974 2069   line where it i\n+00018b70: 7320 6e6f 7420 7265 616c 6c79 206e 6563  s not really nec\n+00018b80: 6573 7361 7279 2e20 2041 2077 6f72 6b61  essary.  A worka\n+00018b90: 726f 756e 640a 6973 2074 6f20 7573 6520  round.is to use \n+00018ba0: 6772 6179 206f 7220 6669 6e65 6c79 2064  gray or finely d\n+00018bb0: 6f74 7465 6420 6c69 6e65 7320 696e 7374  otted lines inst\n+00018bc0: 6561 642e 2020 4966 2079 6f75 7220 6472  ead.  If your dr\n+00018bd0: 6177 696e 6720 6973 0a73 6d61 6c6c 2c20  awing is.small, \n+00018be0: 796f 7520 6361 6e20 616c 736f 2065 6469  you can also edi\n+00018bf0: 7420 7468 6520 2773 6b65 7463 6827 206f  t the 'sketch' o\n+00018c00: 7574 7075 7420 6279 2068 616e 6420 746f  utput by hand to\n+00018c10: 206d 6572 6765 2074 6865 2070 6965 6365   merge the piece\n+00018c20: 730a 6f66 2074 6865 206f 6666 656e 6469  s.of the offendi\n+00018c30: 6e67 206c 696e 652e 0a0a 2020 2041 6e6f  ng line...   Ano\n+00018c40: 7468 6572 2061 6e6f 6d61 6c79 2069 7320  ther anomaly is \n+00018c50: 7469 6e79 2028 6f72 2069 6e20 6465 6765  tiny (or in dege\n+00018c60: 6e65 7261 7465 2063 6173 6573 206e 6f74  nerate cases not\n+00018c70: 2d73 6f2d 7469 6e79 2920 6e6f 7463 6865  -so-tiny) notche\n+00018c80: 730a 696e 2074 6865 206c 696e 6573 2074  s.in the lines t\n+00018c90: 6861 7420 626f 7264 6572 2073 706c 6974  hat border split\n+00018ca0: 2070 6f6c 7967 6f6e 732e 2020 5468 6573   polygons.  Thes\n+00018cb0: 6520 6465 7269 7665 2066 726f 6d20 7468  e derive from th\n+00018cc0: 6520 7761 7920 6561 6368 0a70 6f6c 7967  e way each.polyg\n+00018cd0: 6f6e 2069 7320 7061 696e 7465 643a 2066  on is painted: f\n+00018ce0: 6972 7374 2c20 616c 6c20 7069 7865 6c73  irst, all pixels\n+00018cf0: 2077 6974 6869 6e20 7468 6520 626f 756e   within the boun\n+00018d00: 6461 7279 2061 7265 2022 6669 6c6c 6564  dary are \"filled\n+00018d10: 220a 7769 7468 2063 6f6c 6f72 2028 7065  \".with color (pe\n+00018d20: 7268 6170 7320 7768 6974 6529 2c20 7468  rhaps white), th\n+00018d30: 656e 2074 6865 2073 616d 6520 626f 756e  en the same boun\n+00018d40: 6461 7279 2069 7320 2273 7472 6f6b 6564  dary is \"stroked\n+00018d50: 2220 2861 0a50 6f73 7473 6372 6970 7420  \" (a.Postscript \n+00018d60: 7465 726d 2920 7769 7468 2061 206c 696e  term) with a lin\n+00018d70: 652e 2020 5468 6520 7265 7375 6c74 2069  e.  The result i\n+00018d80: 7320 7468 6174 2068 616c 6620 7468 6520  s that half the \n+00018d90: 6c69 6e65 206c 6965 730a 696e 7369 6465  line lies.inside\n+00018da0: 2074 6865 2062 6f75 6e64 6172 7920 616e   the boundary an\n+00018db0: 6420 6861 6c66 206f 7574 7369 6465 2c20  d half outside, \n+00018dc0: 7768 696c 6520 7468 6520 5061 696e 7465  while the Painte\n+00018dd0: 7227 7320 616c 676f 7269 7468 6d0a 6173  r's algorithm.as\n+00018de0: 7375 6d65 7320 7468 6520 706f 6c79 676f  sumes the polygo\n+00018df0: 6e20 6c69 6573 2065 6e74 6972 656c 7920  n lies entirely \n+00018e00: 7769 7468 696e 2069 7473 2062 6f75 6e64  within its bound\n+00018e10: 6172 792e 2020 5468 6520 6e6f 7463 6865  ary.  The notche\n+00018e20: 7320 6172 650a 6475 6520 746f 206f 6e65  s are.due to one\n+00018e30: 2070 6f6c 7967 6f6e 2066 696c 6c20 6f70   polygon fill op\n+00018e40: 6572 6174 696f 6e20 6f76 6572 7772 6974  eration overwrit\n+00018e50: 696e 6720 7468 6520 616c 7265 6164 792d  ing the already-\n+00018e60: 6472 6177 6e20 696e 7369 6465 0a6f 6620  drawn inside.of \n+00018e70: 7468 6520 626f 7264 6572 206f 6620 616e  the border of an\n+00018e80: 6f74 6865 7220 706f 6c79 676f 6e2e 2831  other polygon.(1\n+00018e90: 2920 204f 6e65 2077 6f72 6b61 726f 756e  )  One workaroun\n+00018ea0: 6420 6973 2074 6f20 6d61 6b65 2062 6f72  d is to make bor\n+00018eb0: 6465 720a 6c69 6e65 7320 7665 7279 2074  der.lines very t\n+00018ec0: 6869 6e2e 2020 496e 2066 6163 7420 276c  hin.  In fact 'l\n+00018ed0: 696e 6577 6964 7468 3d30 7074 2720 6973  inewidth=0pt' is\n+00018ee0: 2067 7561 7261 6e74 6565 6420 746f 2065   guaranteed to e\n+00018ef0: 6c69 6d69 6e61 7465 0a74 6869 7320 7072  liminate.this pr\n+00018f00: 6f62 6c65 6d2c 2074 686f 7567 6820 7468  oblem, though th\n+00018f10: 6973 2072 6573 756c 7473 2069 6e20 7468  is results in th\n+00018f20: 6520 7468 696e 6e65 7374 206c 696e 6520  e thinnest line \n+00018f30: 796f 7572 206f 7574 7075 740a 6465 7669  your output.devi\n+00018f40: 6365 2063 616e 2064 7261 772c 2077 6869  ce can draw, whi\n+00018f50: 6368 2069 7320 7573 7561 6c6c 7920 746f  ch is usually to\n+00018f60: 6f20 7468 696e 2e20 2059 6f75 206d 6967  o thin.  You mig\n+00018f70: 6874 2067 6574 206c 7563 6b79 2062 790a  ht get lucky by.\n+00018f80: 6d65 7265 6c79 2072 656f 7264 6572 696e  merely reorderin\n+00018f90: 6720 7468 696e 6773 2069 6e20 7468 6520  g things in the \n+00018fa0: 696e 7075 7420 6669 6c65 2c20 7768 6963  input file, whic\n+00018fb0: 6820 6973 206c 696b 656c 7920 746f 206d  h is likely to m\n+00018fc0: 6f76 6520 7468 650a 7370 6c69 7473 2074  ove the.splits t\n+00018fd0: 6f20 6469 6666 6572 656e 7420 706c 6163  o different plac\n+00018fe0: 6573 2e20 2054 6865 206f 6e6c 7920 7375  es.  The only su\n+00018ff0: 7265 2d66 6972 6520 736f 6c75 7469 6f6e  re-fire solution\n+00019000: 2069 7320 7072 6574 7479 0a74 6572 7269   is pretty.terri\n+00019010: 626c 653a 2063 7573 746f 6d20 6669 7420  ble: custom fit \n+00019020: 2773 7065 6369 616c 2720 6f76 6572 6c61  'special' overla\n+00019030: 7920 6c69 6e65 7320 2877 6974 6820 275c  y lines (with '\\\n+00019040: 7073 6c69 6e65 2729 2074 6f20 636f 7665  psline') to cove\n+00019050: 720a 7468 6520 6e6f 7463 6865 732e 0a0a  r.the notches...\n+00019060: 2020 2050 6f6c 7967 6f6e 2073 706c 6974     Polygon split\n+00019070: 7469 6e67 2061 6c73 6f20 6272 6561 6b73  ting also breaks\n+00019080: 2027 5053 5472 6963 6b73 2720 6861 7463   'PSTricks' hatc\n+00019090: 6820 7061 7474 6572 6e73 2e20 2054 6865  h patterns.  The\n+000190a0: 206f 6e6c 790a 6b6e 6f77 6e20 776f 726b   only.known work\n+000190b0: 6172 6f75 6e64 2069 7320 746f 2073 7562  around is to sub\n+000190c0: 7374 6974 7574 6520 6120 736f 6c69 6420  stitute a solid \n+000190d0: 6669 6c6c 2066 6f72 2074 6865 2068 6174  fill for the hat\n+000190e0: 6368 2e0a 0a20 2020 2d2d 2d2d 2d2d 2d2d  ch...   --------\n+000190f0: 2d2d 2046 6f6f 746e 6f74 6573 202d 2d2d  -- Footnotes ---\n+00019100: 2d2d 2d2d 2d2d 2d0a 0a20 2020 2831 2920  -------..   (1) \n+00019110: 4920 6b6e 6f77 2068 6f77 2074 6f20 6669  I know how to fi\n+00019120: 7820 7468 6973 2070 726f 626c 656d 2c20  x this problem, \n+00019130: 6275 7420 4920 646f 6e27 7420 6c69 6b65  but I don't like\n+00019140: 206d 7920 736f 6c75 7469 6f6e 2c20 616e   my solution, an\n+00019150: 640a 4927 6d20 696e 7465 7265 7374 6564  d.I'm interested\n+00019160: 2069 6e20 796f 7572 732e 0a0a 1f0a 4669   in yours.....Fi\n+00019170: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n+00019180: 2020 4e6f 6465 3a20 436f 6d6d 616e 6420    Node: Command \n+00019190: 6c69 6e65 2c20 204e 6578 743a 2049 6e73  line,  Next: Ins\n+000191a0: 7461 6c6c 696e 6720 736b 6574 6368 2c20  talling sketch, \n+000191b0: 2050 7265 763a 2042 7569 6c64 696e 6720   Prev: Building \n+000191c0: 6120 6472 6177 696e 672c 2020 5570 3a20  a drawing,  Up: \n+000191d0: 546f 700a 0a35 2043 6f6d 6d61 6e64 206c  Top..5 Command l\n+000191e0: 696e 650a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  ine.************\n+000191f0: 2a2a 0a0a 2a53 796e 6f70 7369 733a 2a0a  **..*Synopsis:*.\n+00019200: 2020 2020 2073 6b65 7463 6820 5b2d 685d       sketch [-h]\n+00019210: 5b2d 5620 782e 795d 5b2d 765d 5b2d 625d  [-V x.y][-v][-b]\n+00019220: 5b2d 645d 5b74 2064 6f63 746d 705d 5b2d  [-d][t doctmp][-\n+00019230: 545b 757c 655d 5b70 5b50 7c54 5d5b 4c7c  T[u|e][p[P|T][L|\n+00019240: 435d 5d5d 5b2d 6f20 6f75 7470 7574 2e74  C]]][-o output.t\n+00019250: 6578 5d0a 2020 2020 2020 205b 2d44 2054  ex].       [-D T\n+00019260: 4147 202e 2e2e 5d20 696e 7075 7431 2e73  AG ...] input1.s\n+00019270: 6b20 5b2d 5520 5441 4720 2e2e 2e5d 2069  k [-U TAG ...] i\n+00019280: 6e70 7574 322e 736b 202e 2e2e 0a0a 2a44  nput2.sk .....*D\n+00019290: 6573 6372 6970 7469 6f6e 2a20 5072 6f63  escription* Proc\n+000192a0: 6573 7365 7320 7468 6520 2773 6b65 7463  esses the 'sketc\n+000192b0: 6827 2069 6e70 7574 2066 696c 6573 2069  h' input files i\n+000192c0: 6e20 6f72 6465 7220 746f 2070 726f 6475  n order to produ\n+000192d0: 6365 0a27 5053 5472 6963 6b73 2720 6f75  ce.'PSTricks' ou\n+000192e0: 7470 7574 2063 6f64 6520 7375 6974 6162  tput code suitab\n+000192f0: 6c65 2066 6f72 2069 6e63 6c75 7369 6f6e  le for inclusion\n+00019300: 2069 6e20 6120 5465 5820 6f72 204c 6154   in a TeX or LaT\n+00019310: 6558 0a64 6f63 756d 656e 742e 0a0a 2a4f  eX.document...*O\n+00019320: 7074 696f 6e73 3a2a 0a27 2d68 270a 2020  ptions:*.'-h'.  \n+00019330: 2020 2050 7269 6e74 2061 2073 686f 7274     Print a short\n+00019340: 2063 6174 616c 6f67 206f 6620 6f70 7469   catalog of opti\n+00019350: 6f6e 732e 0a27 2d56 270a 2020 2020 2053  ons..'-V'.     S\n+00019360: 6574 2074 6865 2027 5053 5472 6963 6b73  et the 'PSTricks\n+00019370: 2720 7665 7273 696f 6e20 6173 7375 6d65  ' version assume\n+00019380: 6420 666f 7220 6f75 7470 7574 2070 7572  d for output pur\n+00019390: 706f 7365 7320 746f 2027 782e 7927 2c0a  poses to 'x.y',.\n+000193a0: 2020 2020 2066 6f72 2065 7861 6d70 6c65       for example\n+000193b0: 2031 2e31 392e 2020 5573 7561 6c6c 7920   1.19.  Usually \n+000193c0: 6e65 6564 6564 206f 6e6c 7920 6966 2079  needed only if y\n+000193d0: 6f75 7220 2750 5354 7269 636b 7327 2069  our 'PSTricks' i\n+000193e0: 7320 6f6c 640a 2020 2020 2063 6f6d 7061  s old.     compa\n+000193f0: 7265 6420 746f 2079 6f75 7220 2773 6b65  red to your 'ske\n+00019400: 7463 6827 2e20 2055 7365 2027 2d76 2720  tch'.  Use '-v' \n+00019410: 746f 2073 6565 2077 6861 7420 2773 6b65  to see what 'ske\n+00019420: 7463 6827 2061 7373 756d 6573 0a20 2020  tch' assumes.   \n+00019430: 2020 6279 2064 6566 6175 6c74 2e0a 272d    by default..'-\n+00019440: 7627 0a20 2020 2020 5072 696e 7420 7665  v'.     Print ve\n+00019450: 7273 696f 6e20 696e 666f 726d 6174 696f  rsion informatio\n+00019460: 6e20 746f 2073 7461 6e64 6172 6420 6f75  n to standard ou\n+00019470: 7470 7574 2c20 696e 636c 7564 696e 6720  tput, including \n+00019480: 7468 6520 7665 7273 696f 6e0a 2020 2020  the version.    \n+00019490: 206f 6620 2750 5354 7269 636b 7327 2061   of 'PSTricks' a\n+000194a0: 7373 756d 6564 2066 6f72 206f 7574 7075  ssumed for outpu\n+000194b0: 7420 2863 616e 2062 6520 6368 616e 6765  t (can be change\n+000194c0: 6420 7769 7468 2027 2d56 2720 6162 6f76  d with '-V' abov\n+000194d0: 6529 2e0a 272d 6227 0a20 2020 2020 5573  e)..'-b'.     Us\n+000194e0: 6520 6120 4253 5020 282a 4e6f 7465 2048  e a BSP (*Note H\n+000194f0: 6964 6465 6e20 7375 7266 6163 6520 7265  idden surface re\n+00019500: 6d6f 7661 6c3a 3a2e 2920 2066 6f72 205f  moval::.)  for _\n+00019510: 616c 6c5f 2068 6964 6465 6e0a 2020 2020  all_ hidden.    \n+00019520: 2073 7572 6661 6365 2072 656d 6f76 616c   surface removal\n+00019530: 2072 6174 6865 7220 7468 616e 2074 6865   rather than the\n+00019540: 2064 6566 6175 6c74 2c20 7768 6963 6820   default, which \n+00019550: 6973 2074 6865 2064 6570 7468 2073 6f72  is the depth sor\n+00019560: 740a 2020 2020 2061 6c67 6f72 6974 686d  t.     algorithm\n+00019570: 2077 6974 6820 4253 5073 2075 7365 6420   with BSPs used \n+00019580: 6f6e 6c79 2066 6f72 2063 7963 6c65 2072  only for cycle r\n+00019590: 6573 6f6c 7574 696f 6e2e 2020 5468 6973  esolution.  This\n+000195a0: 206d 6179 0a20 2020 2020 7072 6f64 7563   may.     produc\n+000195b0: 6520 636f 7272 6563 7420 6f75 7470 7574  e correct output\n+000195c0: 2069 6e20 6365 7274 6169 6e20 6465 6765   in certain dege\n+000195d0: 6e65 7261 7465 2063 6173 6573 2077 6865  nerate cases whe\n+000195e0: 7265 2074 6865 2064 6570 7468 0a20 2020  re the depth.   \n+000195f0: 2020 736f 7274 2063 616e 6e6f 742c 2062    sort cannot, b\n+00019600: 7574 2069 7420 616c 736f 206c 6561 6473  ut it also leads\n+00019610: 2074 6f20 6d61 6e79 2067 7261 7475 6974   to many gratuit\n+00019620: 6f75 7320 7370 6c69 7473 2c20 6865 6e63  ous splits, henc\n+00019630: 650a 2020 2020 206d 6f72 6520 616e 6f6d  e.     more anom\n+00019640: 616c 6965 7320 2a6e 6f74 6520 4275 6773  alies *note Bugs\n+00019650: 2061 6e64 2061 6e6f 6d61 6c69 6573 3a3a   and anomalies::\n+00019660: 2061 6e64 2062 6967 206f 7574 7075 7420   and big output \n+00019670: 6669 6c65 732e 0a27 2d64 270a 2020 2020  files..'-d'.    \n+00019680: 2052 756e 2027 736b 6574 6368 2727 7320   Run 'sketch''s \n+00019690: 7061 7273 6572 2069 6e20 6465 6275 6767  parser in debugg\n+000196a0: 696e 6720 6d6f 6465 2e20 2054 6869 7320  ing mode.  This \n+000196b0: 6973 2070 7269 6d61 7269 6c79 2066 6f72  is primarily for\n+000196c0: 0a20 2020 2020 6465 7665 6c6f 706d 656e  .     developmen\n+000196d0: 742e 0a27 2d74 270a 2020 2020 2055 7365  t..'-t'.     Use\n+000196e0: 2063 6f6e 7465 6e74 7320 6f66 2066 696c   contents of fil\n+000196f0: 6520 2764 6f63 746d 7027 2061 7320 6120  e 'doctmp' as a \n+00019700: 646f 6375 6d65 6e74 2074 656d 706c 6174  document templat\n+00019710: 6520 696e 2077 6869 6368 2074 6f0a 2020  e in which to.  \n+00019720: 2020 2065 6e63 6c6f 7365 2027 5053 5472     enclose 'PSTr\n+00019730: 6963 6b73 2720 6f75 7470 7574 2063 6f64  icks' output cod\n+00019740: 652e 2020 5468 6520 636f 6465 2069 7320  e.  The code is \n+00019750: 696e 7365 7274 6564 2069 6e20 706c 6163  inserted in plac\n+00019760: 6520 6f66 0a20 2020 2020 7468 6520 6669  e of.     the fi\n+00019770: 7273 7420 696e 7374 616e 6365 206f 6620  rst instance of \n+00019780: 7468 6520 6573 6361 7065 2073 7472 696e  the escape strin\n+00019790: 6720 2525 534b 4554 4348 5f4f 5554 5055  g %%SKETCH_OUTPU\n+000197a0: 5425 252e 0a27 2d54 270a 2020 2020 2043  T%%..'-T'.     C\n+000197b0: 6175 7365 7320 2750 5354 7269 636b 7327  auses 'PSTricks'\n+000197c0: 206f 7574 7075 7420 746f 2062 6520 656e   output to be en\n+000197d0: 636c 6f73 6564 2069 6e20 6465 6661 756c  closed in defaul\n+000197e0: 7420 5553 2064 6f63 756d 656e 740a 2020  t US document.  \n+000197f0: 2020 2074 656d 706c 6174 6520 7465 7874     template text\n+00019800: 2e20 204f 7074 696f 6e20 272d 5475 2720  .  Option '-Tu' \n+00019810: 6973 2061 2073 796e 6f6e 796d 2e20 204f  is a synonym.  O\n+00019820: 7074 696f 6e20 272d 5465 2720 6361 7573  ption '-Te' caus\n+00019830: 6573 2074 6865 0a20 2020 2020 4575 726f  es the.     Euro\n+00019840: 2073 7461 6e64 6172 6420 646f 6375 6d65   standard docume\n+00019850: 6e74 2074 656d 706c 6174 6520 746f 2062  nt template to b\n+00019860: 6520 7573 6564 2e20 2041 2027 7027 2061  e used.  A 'p' a\n+00019870: 7070 656e 6465 6420 746f 2061 6e79 0a20  ppended to any. \n+00019880: 2020 2020 6f66 2074 6865 7365 206f 7074      of these opt\n+00019890: 696f 6e73 2063 6175 7365 7320 7468 6520  ions causes the \n+000198a0: 7265 7370 6563 7469 7665 2064 6566 6175  respective defau\n+000198b0: 6c74 2027 5053 5472 6963 6b73 2720 646f  lt 'PSTricks' do\n+000198c0: 6375 6d65 6e74 0a20 2020 2020 7465 6d70  cument.     temp\n+000198d0: 6c61 7465 2074 6f20 6265 2070 7269 6e74  late to be print\n+000198e0: 6564 2074 6f20 7374 616e 6461 7264 206f  ed to standard o\n+000198f0: 7574 7075 742e 2020 416e 2061 7070 656e  utput.  An appen\n+00019900: 6465 6420 2750 2720 6973 2061 0a20 2020  ded 'P' is a.   \n+00019910: 2020 7379 6e6f 6e79 6d2e 2020 416e 2061    synonym.  An a\n+00019920: 7070 656e 6465 6420 2754 2720 6361 7573  ppended 'T' caus\n+00019930: 6573 2074 6865 2074 6865 2027 5469 6b5a  es the the 'TikZ\n+00019940: 2f50 4746 2720 7465 6d70 6c61 7465 2074  /PGF' template t\n+00019950: 6f20 6265 0a20 2020 2020 7072 696e 7465  o be.     printe\n+00019960: 642e 2020 416e 2061 7070 656e 6465 6420  d.  An appended \n+00019970: 274c 2720 7072 696e 7473 2074 6865 204c  'L' prints the L\n+00019980: 6154 6558 2076 6572 7369 6f6e 206f 6620  aTeX version of \n+00019990: 7468 6520 646f 6375 6d65 6e74 0a20 2020  the document.   \n+000199a0: 2020 7465 6d70 6c61 7465 2c20 6120 7379    template, a sy\n+000199b0: 6e6f 6e79 6d20 666f 7220 7468 6520 6465  nonym for the de\n+000199c0: 6661 756c 742e 2020 4120 2743 2720 7072  fault.  A 'C' pr\n+000199d0: 696e 7473 2074 6865 2027 436f 6e54 6558  ints the 'ConTeX\n+000199e0: 7427 0a20 2020 2020 7465 6d70 6c61 7465  t'.     template\n+000199f0: 2e0a 272d 6f27 0a20 2020 2020 5573 6520  ..'-o'.     Use \n+00019a00: 276f 7574 7075 742e 7465 7827 2061 7320  'output.tex' as \n+00019a10: 7468 6520 6f75 7470 7574 2066 696c 652e  the output file.\n+00019a20: 2020 5468 6520 6465 6661 756c 7420 6973    The default is\n+00019a30: 2073 7461 6e64 6172 640a 2020 2020 206f   standard.     o\n+00019a40: 7574 7075 742e 0a27 2d44 270a 2020 2020  utput..'-D'.    \n+00019a50: 2044 6566 696e 6520 6120 7461 6720 666f   Define a tag fo\n+00019a60: 7220 7075 7270 6f73 6573 206f 6620 7365  r purposes of se\n+00019a70: 6c65 6374 696e 6720 6465 6669 6e69 7469  lecting definiti\n+00019a80: 6f6e 2061 6c74 6572 6e61 7469 7665 732e  on alternatives.\n+00019a90: 0a20 2020 2020 2a4e 6f74 6520 4465 6669  .     *Note Defi\n+00019aa0: 6e69 7469 6f6e 733a 3a2e 2020 5468 6520  nitions::.  The \n+00019ab0: 6465 6669 6e69 7469 6f6e 2061 7070 6c69  definition appli\n+00019ac0: 6573 2066 6f72 2061 6c6c 2069 6e70 7574  es for all input\n+00019ad0: 2066 696c 6573 0a20 2020 2020 7468 6174   files.     that\n+00019ae0: 2066 6f6c 6c6f 7720 756e 6c65 7373 2074   follow unless t\n+00019af0: 6865 2074 6167 2069 7320 756e 6465 6669  he tag is undefi\n+00019b00: 6e65 6420 7769 7468 2027 2d55 272e 0a27  ned with '-U'..'\n+00019b10: 696e 7075 7469 2e73 6b27 0a20 2020 2020  inputi.sk'.     \n+00019b20: 496e 7075 7420 6669 6c65 732c 2072 6561  Input files, rea\n+00019b30: 6420 696e 2074 6865 2073 6571 7565 6e63  d in the sequenc\n+00019b40: 6520 7468 6579 2061 7265 2067 6976 656e  e they are given\n+00019b50: 2e0a 272d 5527 0a20 2020 2020 556e 2d64  ..'-U'.     Un-d\n+00019b60: 6566 696e 6520 6120 7461 6720 666f 7220  efine a tag for \n+00019b70: 7075 7270 6f73 6573 206f 6620 7365 6c65  purposes of sele\n+00019b80: 6374 696e 6720 6465 6669 6e69 7469 6f6e  cting definition\n+00019b90: 2061 6c74 6572 6e61 7469 7665 732e 0a0a   alternatives...\n+00019ba0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n+00019bb0: 6e66 6f2c 2020 4e6f 6465 3a20 496e 7374  nfo,  Node: Inst\n+00019bc0: 616c 6c69 6e67 2073 6b65 7463 682c 2020  alling sketch,  \n+00019bd0: 4e65 7874 3a20 496e 6465 7820 6f66 2073  Next: Index of s\n+00019be0: 796e 7461 782c 2020 5072 6576 3a20 436f  yntax,  Prev: Co\n+00019bf0: 6d6d 616e 6420 6c69 6e65 2c20 2055 703a  mmand line,  Up:\n+00019c00: 2054 6f70 0a0a 3620 4275 696c 6469 6e67   Top..6 Building\n+00019c10: 2061 6e64 2069 6e73 7461 6c6c 696e 6720   and installing \n+00019c20: 2773 6b65 7463 6827 0a2a 2a2a 2a2a 2a2a  'sketch'.*******\n 00019c30: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  ****************\n-00019c40: 2a2a 2a2a 2a0a 0a27 536b 6574 6368 2720  *****..'Sketch' \n-00019c50: 6973 2073 6f20 736d 616c 6c20 7468 6174  is so small that\n-00019c60: 2063 6f6d 7069 6c69 6e67 2062 7920 6272   compiling by br\n-00019c70: 7574 6520 666f 7263 6520 6973 2070 726f  ute force is pro\n-00019c80: 6261 626c 7920 6265 7374 2e0a 5468 6520  bably best..The \n-00019c90: 666f 6c6c 6f77 696e 6720 636f 6d6d 616e  following comman\n-00019ca0: 6420 6f75 6768 7420 746f 2064 6f20 7468  d ought to do th\n-00019cb0: 6520 7472 6963 6b20 6f6e 2061 6e79 2073  e trick on any s\n-00019cc0: 7973 7465 6d73 2077 6865 7265 2027 6763  ystems where 'gc\n-00019cd0: 6327 0a69 7320 696e 7374 616c 6c65 642e  c'.is installed.\n-00019ce0: 2020 4d61 6b65 2073 7572 6520 746f 2066    Make sure to f\n-00019cf0: 6972 7374 2063 6861 6e67 6520 6375 7272  irst change curr\n-00019d00: 656e 7420 6469 7265 6374 6f72 6965 7320  ent directories \n-00019d10: 746f 2074 6865 0a70 6c61 6365 2077 6865  to the.place whe\n-00019d20: 7265 2079 6f75 2068 6176 6520 756e 7061  re you have unpa\n-00019d30: 636b 6564 2074 6865 2073 6f75 7263 6573  cked the sources\n-00019d40: 2e0a 2020 2020 2067 6363 202a 2e63 202d  ..     gcc *.c -\n-00019d50: 6f20 736b 6574 6368 2e65 7865 202d 6c6d  o sketch.exe -lm\n-00019d60: 0a54 6865 2027 2e65 7865 2720 6174 2074  .The '.exe' at t\n-00019d70: 6865 2065 6e64 2069 7320 6e65 6365 7373  he end is necess\n-00019d80: 6172 7920 666f 7220 5769 6e64 6f77 7320  ary for Windows \n-00019d90: 7379 7374 656d 732e 2020 4472 6f70 2069  systems.  Drop i\n-00019da0: 7420 6966 2079 6f75 720a 7379 7374 656d  t if your.system\n-00019db0: 2069 7320 736f 6d65 2076 6572 7369 6f6e   is some version\n-00019dc0: 206f 6620 556e 6978 2e20 204f 7468 6572   of Unix.  Other\n-00019dd0: 2043 2063 6f6d 7069 6c65 7273 206f 7567   C compilers oug\n-00019de0: 6874 2074 6f20 776f 726b 2061 7320 6a75  ht to work as ju\n-00019df0: 7374 0a61 7320 7765 6c6c 2e20 2046 6f72  st.as well.  For\n-00019e00: 2065 7861 6d70 6c65 2c0a 2020 2020 2063   example,.     c\n-00019e10: 6c20 2a2e 6320 2d6f 2073 6b65 7463 682e  l *.c -o sketch.\n-00019e20: 6578 650a 6973 2074 6865 2063 6f72 7265  exe.is the corre\n-00019e30: 6374 2063 6f6d 6d61 6e64 2066 6f72 206d  ct command for m\n-00019e40: 616e 7920 7665 7273 696f 6e73 206f 6620  any versions of \n-00019e50: 4d53 2056 6973 7561 6c20 432e 2049 6e20  MS Visual C. In \n-00019e60: 7468 6520 6c61 7465 7374 0a76 6572 7369  the latest.versi\n-00019e70: 6f6e 732c 204d 6963 726f 736f 6674 2068  ons, Microsoft h\n-00019e80: 6173 2064 6570 7265 6361 7465 6420 7468  as deprecated th\n-00019e90: 6520 272d 6f27 206f 7074 696f 6e20 616e  e '-o' option an\n-00019ea0: 642c 2062 7920 6465 6661 756c 742c 2064  d, by default, d\n-00019eb0: 6f65 730a 6e6f 7420 6465 6669 6e65 2074  oes.not define t\n-00019ec0: 6865 2027 5f5f 5354 4443 5f5f 2720 6d61  he '__STDC__' ma\n-00019ed0: 6372 6f2e 2020 5468 6973 2063 6175 7365  cro.  This cause\n-00019ee0: 7320 7072 6f62 6c65 6d73 2077 6974 6820  s problems with \n-00019ef0: 736f 6d65 0a76 6572 7369 6f6e 7320 6f66  some.versions of\n-00019f00: 2027 666c 6578 272c 2027 6269 736f 6e27   'flex', 'bison'\n-00019f10: 2c20 276c 6578 272c 2061 6e64 2027 7961  , 'lex', and 'ya\n-00019f20: 6363 272c 2077 6869 6368 2061 7265 2075  cc', which are u\n-00019f30: 7365 6420 746f 2063 7265 6174 650a 7468  sed to create.th\n-00019f40: 6520 2773 6b65 7463 6827 2073 6361 6e6e  e 'sketch' scann\n-00019f50: 6572 2061 6e64 2070 6172 7365 722e 2020  er and parser.  \n-00019f60: 4974 2773 206e 6561 726c 7920 616c 7761  It's nearly alwa\n-00019f70: 7973 2070 6f73 7369 626c 6520 746f 2066  ys possible to f\n-00019f80: 696e 6420 610a 7365 7420 6f66 206f 7074  ind a.set of opt\n-00019f90: 696f 6e73 2074 6861 7420 636f 6d70 696c  ions that compil\n-00019fa0: 6573 2077 6974 6820 6e6f 2065 7272 6f72  es with no error\n-00019fb0: 7320 6f72 2077 6172 6e69 6e67 732c 2061  s or warnings, a\n-00019fc0: 6e64 2074 6869 7320 6d65 616e 730a 2773  nd this means.'s\n-00019fd0: 6b65 7463 6827 2069 7320 5f76 6572 795f  ketch' is _very_\n-00019fe0: 206c 696b 656c 7920 746f 2077 6f72 6b20   likely to work \n-00019ff0: 636f 7272 6563 746c 792e 2020 466f 7220  correctly.  For \n-0001a000: 6578 616d 706c 652c 2074 6865 2056 6973  example, the Vis\n-0001a010: 7561 6c0a 432b 2b20 3230 3035 2045 7870  ual.C++ 2005 Exp\n-0001a020: 7265 7373 2045 6469 7469 6f6e 2063 6f6d  ress Edition com\n-0001a030: 7069 6c65 7220 2861 7661 696c 6162 6c65  piler (available\n-0001a040: 2066 7265 6520 6f66 2063 6861 7267 6520   free of charge \n-0001a050: 6672 6f6d 2074 6865 0a4d 6963 726f 736f  from the.Microso\n-0001a060: 6674 2077 6562 2073 6974 6529 2c20 2766  ft web site), 'f\n-0001a070: 6c65 7827 2076 6572 7369 6f6e 2032 2e35  lex' version 2.5\n-0001a080: 2e34 2c20 616e 6420 2762 6973 6f6e 2720  .4, and 'bison' \n-0001a090: 7665 7273 696f 6e20 322e 3120 6275 696c  version 2.1 buil\n-0001a0a0: 640a 6572 726f 722d 6672 6565 2077 6974  d.error-free wit\n-0001a0b0: 680a 2020 2020 2063 6c20 2d44 5959 5f4e  h.     cl -DYY_N\n-0001a0c0: 4556 4552 5f49 4e54 4552 4143 5449 5645  EVER_INTERACTIVE\n-0001a0d0: 3d31 202d 5a61 202d 4f78 202d 4665 736b  =1 -Za -Ox -Fesk\n-0001a0e0: 6574 6368 2e65 7865 202a 2e63 0a0a 2020  etch.exe *.c..  \n-0001a0f0: 2046 6f72 2070 7572 6973 7473 2c20 7468   For purists, th\n-0001a100: 6572 6520 6973 2061 6c73 6f20 6120 276d  ere is also a 'm\n-0001a110: 616b 6566 696c 6527 2063 6f6d 7061 7469  akefile' compati\n-0001a120: 626c 6520 7769 7468 2047 4e55 2027 6d61  ble with GNU 'ma\n-0001a130: 6b65 270a 616e 6420 2767 6363 272e 2020  ke'.and 'gcc'.  \n-0001a140: 5468 6520 636f 6d6d 616e 640a 2020 2020  The command.    \n-0001a150: 206d 616b 650a 7769 6c6c 2062 7569 6c64   make.will build\n-0001a160: 2074 6865 2065 7865 6375 7461 626c 652c   the executable,\n-0001a170: 2069 6e63 6c75 6469 6e67 2074 6865 2072   including the r\n-0001a180: 6562 7569 6c64 696e 6720 6f66 2074 6865  ebuilding of the\n-0001a190: 2073 6361 6e6e 6572 2061 6e64 0a70 6172   scanner and.par\n-0001a1a0: 7365 7220 7769 7468 2027 666c 6578 2720  ser with 'flex' \n-0001a1b0: 616e 6420 2762 6973 6f6e 2720 6966 2079  and 'bison' if y\n-0001a1c0: 6f75 2068 6176 6520 6368 616e 6765 6420  ou have changed \n-0001a1d0: 2773 6b65 7463 682e 6c27 206f 720a 2773  'sketch.l' or.'s\n-0001a1e0: 6b65 7463 682e 7927 2072 6573 7065 6374  ketch.y' respect\n-0001a1f0: 6976 656c 792e 0a0a 2020 2057 6869 6c65  ively...   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To buil\n-0001a260: 6420 7468 6973 2064 6f63 756d 656e 7420  d this document \n-0001a270: 696e 2061 6c6c 2069 7473 206d 7972 6961  in all its myria\n-0001a280: 6420 666f 726d 730a 2861 7373 756d 696e  d forms.(assumin\n-0001a290: 6720 796f 7520 6861 7665 2074 6865 206e  g you have the n\n-0001a2a0: 6563 6573 7361 7279 2063 6f6e 7665 7273  ecessary convers\n-0001a2b0: 696f 6e20 7072 6f67 7261 6d73 206f 6e20  ion programs on \n-0001a2c0: 796f 7572 2073 7973 7465 6d29 2c0a 7573  your system),.us\n-0001a2d0: 650a 2020 2020 206d 616b 6520 646f 6373  e.     make docs\n-0001a2e0: 0a54 6865 2070 6f73 7369 6269 6c69 7469  .The possibiliti\n-0001a2f0: 6573 2061 7265 206c 6973 7465 6420 696e  es are listed in\n-0001a300: 2074 6869 7320 666f 6c6c 6f77 696e 6720   this following \n-0001a310: 7461 626c 652e 0a46 6f72 6d61 7420 2020  table..Format   \n-0001a320: 2020 2020 2020 2020 2020 2020 2043 6f6e               Con\n-0001a330: 7665 7274 6572 2020 2020 2020 2020 5069  verter        Pi\n-0001a340: 6374 7572 6573 2020 2044 6573 6372 6970  ctures   Descrip\n-0001a350: 7469 6f6e 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d  tion.-----------\n+00019c40: 2a2a 2a2a 2a2a 2a2a 2a2a 2a0a 0a27 536b  ***********..'Sk\n+00019c50: 6574 6368 2720 6973 2073 6f20 736d 616c  etch' is so smal\n+00019c60: 6c20 7468 6174 2063 6f6d 7069 6c69 6e67  l that compiling\n+00019c70: 2062 7920 6272 7574 6520 666f 7263 6520   by brute force \n+00019c80: 6973 2070 726f 6261 626c 7920 6265 7374  is probably best\n+00019c90: 2e0a 5468 6520 666f 6c6c 6f77 696e 6720  ..The following \n+00019ca0: 636f 6d6d 616e 6420 6f75 6768 7420 746f  command ought to\n+00019cb0: 2064 6f20 7468 6520 7472 6963 6b20 6f6e   do the trick on\n+00019cc0: 2061 6e79 2073 7973 7465 6d73 2077 6865   any systems whe\n+00019cd0: 7265 2027 6763 6327 0a69 7320 696e 7374  re 'gcc'.is inst\n+00019ce0: 616c 6c65 642e 2020 4d61 6b65 2073 7572  alled.  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     Unary \n-0001ac10: 666f 726d 732e 2020 2020 2020 2020 2020  forms.          \n-0001ac20: 286c 696e 6520 3130 290a 2a20 2e2c 2064  (line 10).* ., d\n-0001ac30: 6f74 206f 7065 7261 746f 723a 2020 2020  ot operator:    \n-0001ac40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ac50: 2020 2054 776f 2d6f 7065 7261 6e64 2028     Two-operand (\n-0001ac60: 6269 6e61 7279 2920 666f 726d 732e 0a20  binary) forms.. \n-0001ac70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001abd0: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n+0001abe0: 6e65 2031 3529 0a2a 202d 2c20 756e 6172  ne 15).* -, unar\n+0001abf0: 7920 6d69 6e75 7320 6f70 6572 6174 6f72  y minus operator\n+0001ac00: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001ac10: 556e 6172 7920 666f 726d 732e 2020 2020  Unary forms.    \n+0001ac20: 2020 2020 2020 286c 696e 6520 3130 290a        (line 10).\n+0001ac30: 2a20 2e2c 2064 6f74 206f 7065 7261 746f  * ., dot operato\n+0001ac40: 723a 2020 2020 2020 2020 2020 2020 2020  r:              \n+0001ac50: 2020 2020 2020 2020 2054 776f 2d6f 7065           Two-ope\n+0001ac60: 7261 6e64 2028 6269 6e61 7279 2920 666f  rand (binary) fo\n+0001ac70: 726d 732e 0a20 2020 2020 2020 2020 2020  rms..           \n 0001ac80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ac90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001aca0: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-0001acb0: 696e 6520 3139 290a 2a20 2e2c 2064 6f74  ine 19).* ., dot\n-0001acc0: 206f 7065 7261 746f 7220 3c31 3e3a 2020   operator <1>:  \n-0001acd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ace0: 2054 776f 2d6f 7065 7261 6e64 2028 6269   Two-operand (bi\n-0001acf0: 6e61 7279 2920 666f 726d 732e 0a20 2020  nary) forms..   \n-0001ad00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001aca0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001acb0: 2020 2020 286c 696e 6520 3139 290a 2a20      (line 19).* \n+0001acc0: 2e2c 2064 6f74 206f 7065 7261 746f 7220  ., dot operator \n+0001acd0: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n+0001ace0: 2020 2020 2020 2054 776f 2d6f 7065 7261         Two-opera\n+0001acf0: 6e64 2028 6269 6e61 7279 2920 666f 726d  nd (binary) form\n+0001ad00: 732e 0a20 2020 2020 2020 2020 2020 2020  s..             \n 0001ad10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ad20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ad30: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-0001ad40: 6520 3631 290a 2a20 2f2c 2064 6976 6973  e 61).* /, divis\n-0001ad50: 696f 6e20 6f70 6572 6174 6f72 3a20 2020  ion operator:   \n-0001ad60: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n-0001ad70: 776f 2d6f 7065 7261 6e64 2028 6269 6e61  wo-operand (bina\n-0001ad80: 7279 2920 666f 726d 732e 0a20 2020 2020  ry) forms..     \n-0001ad90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ad30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ad40: 2020 286c 696e 6520 3631 290a 2a20 2f2c    (line 61).* /,\n+0001ad50: 2064 6976 6973 696f 6e20 6f70 6572 6174   division operat\n+0001ad60: 6f72 3a20 2020 2020 2020 2020 2020 2020  or:             \n+0001ad70: 2020 2020 2054 776f 2d6f 7065 7261 6e64       Two-operand\n+0001ad80: 2028 6269 6e61 7279 2920 666f 726d 732e   (binary) forms.\n+0001ad90: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n 0001ada0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001adb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001adc0: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-0001add0: 3338 290a 2a20 3c3e 2c20 636c 6f73 7572  38).* <>, closur\n-0001ade0: 6520 7461 673a 2020 2020 2020 2020 2020  e tag:          \n-0001adf0: 2020 2020 2020 2020 2020 2020 2050 6f69               Poi\n-0001ae00: 6e74 2073 7765 6570 732e 2020 2020 2020  nt sweeps.      \n-0001ae10: 2020 2028 6c69 6e65 2031 3829 0a2a 203c     (line 18).* <\n-0001ae20: 3e2c 2063 6c6f 7375 7265 2074 6167 203c  >, closure tag <\n-0001ae30: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-0001ae40: 2020 2020 2020 506f 6c79 6c69 6e65 2073        Polyline s\n-0001ae50: 7765 6570 7320 7769 7468 2063 6c6f 7375  weeps with closu\n-0001ae60: 7265 2e0a 2020 2020 2020 2020 2020 2020  re..            \n+0001adc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001add0: 286c 696e 6520 3338 290a 2a20 3c3e 2c20  (line 38).* <>, \n+0001ade0: 636c 6f73 7572 6520 7461 673a 2020 2020  closure tag:    \n+0001adf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ae00: 2020 2050 6f69 6e74 2073 7765 6570 732e     Point sweeps.\n+0001ae10: 2020 2020 2020 2020 2028 6c69 6e65 2031           (line 1\n+0001ae20: 3829 0a2a 203c 3e2c 2063 6c6f 7375 7265  8).* <>, closure\n+0001ae30: 2074 6167 203c 313e 3a20 2020 2020 2020   tag <1>:       \n+0001ae40: 2020 2020 2020 2020 2020 2020 506f 6c79              Poly\n+0001ae50: 6c69 6e65 2073 7765 6570 7320 7769 7468  line sweeps with\n+0001ae60: 2063 6c6f 7375 7265 2e0a 2020 2020 2020   closure..      \n 0001ae70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ae80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ae90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001aea0: 2020 2028 6c69 6e65 2020 3629 0a2a 203c     (line  6).* <\n-0001aeb0: 3e2c 2063 6c6f 7375 7265 2074 6167 203c  >, closure tag <\n-0001aec0: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n-0001aed0: 2020 2020 2020 5377 6565 7073 2e20 2020        Sweeps.   \n-0001aee0: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-0001aef0: 6520 3139 290a 2a20 3c3e 2c20 636c 6f73  e 19).* <>, clos\n-0001af00: 7572 6520 7461 6720 3c33 3e3a 2020 2020  ure tag <3>:    \n-0001af10: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n-0001af20: 7765 7074 2070 6f69 6e74 732e 2020 2020  wept points.    \n-0001af30: 2020 2020 2028 6c69 6e65 2020 3629 0a2a       (line  6).*\n-0001af40: 203c 3e2c 2063 6c6f 7375 7265 2074 6167   <>, closure tag\n-0001af50: 203c 343e 3a20 2020 2020 2020 2020 2020   <4>:           \n-0001af60: 2020 2020 2020 2020 5377 6570 7420 706f          Swept po\n-0001af70: 696e 7473 2e20 2020 2020 2020 2020 286c  ints.         (l\n-0001af80: 696e 6520 3133 290a 2a20 3c3e 2c20 636c  ine 13).* <>, cl\n-0001af90: 6f73 7572 6520 7461 6720 3c35 3e3a 2020  osure tag <5>:  \n-0001afa0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001afb0: 2053 7765 7074 206c 696e 6573 2e20 2020   Swept lines.   \n-0001afc0: 2020 2020 2020 2028 6c69 6e65 2020 3629         (line  6)\n-0001afd0: 0a2a 203c 3e2c 2063 6c6f 7375 7265 2074  .* <>, closure t\n-0001afe0: 6167 203c 363e 3a20 2020 2020 2020 2020  ag <6>:         \n-0001aff0: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n-0001b000: 6c69 6e65 732e 2020 2020 2020 2020 2020  lines.          \n-0001b010: 286c 696e 6520 3238 290a 2a20 3c3e 2c20  (line 28).* <>, \n-0001b020: 636c 6f73 7572 6520 7461 6720 3c37 3e3a  closure tag <7>:\n-0001b030: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b040: 2020 2053 7765 6570 2066 6163 6520 7370     Sweep face sp\n-0001b050: 6c69 7474 696e 672e 2028 6c69 6e65 2031  litting. (line 1\n-0001b060: 3129 0a2a 203c 666f 6f3e 2c20 7461 6720  1).* <foo>, tag \n-0001b070: 7265 6665 7265 6e63 653a 2020 2020 2020  reference:      \n-0001b080: 2020 2020 2020 2020 2020 2020 466f 726d              Form\n-0001b090: 7320 6f66 2064 6566 696e 6974 696f 6e73  s of definitions\n-0001b0a0: 2e20 286c 696e 6520 3230 290a 2a20 3c66  . (line 20).* <f\n-0001b0b0: 6f6f 3e2c 2074 6167 2072 6566 6572 656e  oo>, tag referen\n-0001b0c0: 6365 203c 313e 3a20 2020 2020 2020 2020  ce <1>:         \n-0001b0d0: 2020 2020 2046 6f72 6d73 206f 6620 7265       Forms of re\n-0001b0e0: 6665 7265 6e63 6573 2e20 2028 6c69 6e65  ferences.  (line\n-0001b0f0: 2031 3929 0a2a 205b 666f 6f2c 2e2e 2e2c   19).* [foo,...,\n-0001b100: 6261 725d 2c20 6d75 6c74 6970 6c65 206f  bar], multiple o\n-0001b110: 7074 696f 6e73 2072 6566 6572 656e 6365  ptions reference\n-0001b120: 3a20 466f 726d 7320 6f66 2072 6566 6572  : Forms of refer\n-0001b130: 656e 6365 732e 0a20 2020 2020 2020 2020  ences..         \n+0001aea0: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+0001aeb0: 3629 0a2a 203c 3e2c 2063 6c6f 7375 7265  6).* <>, closure\n+0001aec0: 2074 6167 203c 323e 3a20 2020 2020 2020   tag <2>:       \n+0001aed0: 2020 2020 2020 2020 2020 2020 5377 6565              Swee\n+0001aee0: 7073 2e20 2020 2020 2020 2020 2020 2020  ps.             \n+0001aef0: 2020 286c 696e 6520 3139 290a 2a20 3c3e    (line 19).* <>\n+0001af00: 2c20 636c 6f73 7572 6520 7461 6720 3c33  , closure tag <3\n+0001af10: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001af20: 2020 2020 2053 7765 7074 2070 6f69 6e74       Swept point\n+0001af30: 732e 2020 2020 2020 2020 2028 6c69 6e65  s.         (line\n+0001af40: 2020 3629 0a2a 203c 3e2c 2063 6c6f 7375    6).* <>, closu\n+0001af50: 7265 2074 6167 203c 343e 3a20 2020 2020  re tag <4>:     \n+0001af60: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n+0001af70: 6570 7420 706f 696e 7473 2e20 2020 2020  ept points.     \n+0001af80: 2020 2020 286c 696e 6520 3133 290a 2a20      (line 13).* \n+0001af90: 3c3e 2c20 636c 6f73 7572 6520 7461 6720  <>, closure tag \n+0001afa0: 3c35 3e3a 2020 2020 2020 2020 2020 2020  <5>:            \n+0001afb0: 2020 2020 2020 2053 7765 7074 206c 696e         Swept lin\n+0001afc0: 6573 2e20 2020 2020 2020 2020 2028 6c69  es.          (li\n+0001afd0: 6e65 2020 3629 0a2a 203c 3e2c 2063 6c6f  ne  6).* <>, clo\n+0001afe0: 7375 7265 2074 6167 203c 363e 3a20 2020  sure tag <6>:   \n+0001aff0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001b000: 5377 6570 7420 6c69 6e65 732e 2020 2020  Swept lines.    \n+0001b010: 2020 2020 2020 286c 696e 6520 3238 290a        (line 28).\n+0001b020: 2a20 3c3e 2c20 636c 6f73 7572 6520 7461  * <>, closure ta\n+0001b030: 6720 3c37 3e3a 2020 2020 2020 2020 2020  g <7>:          \n+0001b040: 2020 2020 2020 2020 2053 7765 6570 2066           Sweep f\n+0001b050: 6163 6520 7370 6c69 7474 696e 672e 2028  ace splitting. (\n+0001b060: 6c69 6e65 2031 3129 0a2a 203c 666f 6f3e  line 11).* <foo>\n+0001b070: 2c20 7461 6720 7265 6665 7265 6e63 653a  , tag reference:\n+0001b080: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001b090: 2020 466f 726d 7320 6f66 2064 6566 696e    Forms of defin\n+0001b0a0: 6974 696f 6e73 2e20 286c 696e 6520 3230  itions. (line 20\n+0001b0b0: 290a 2a20 3c66 6f6f 3e2c 2074 6167 2072  ).* <foo>, tag r\n+0001b0c0: 6566 6572 656e 6365 203c 313e 3a20 2020  eference <1>:   \n+0001b0d0: 2020 2020 2020 2020 2020 2046 6f72 6d73             Forms\n+0001b0e0: 206f 6620 7265 6665 7265 6e63 6573 2e20   of references. \n+0001b0f0: 2028 6c69 6e65 2031 3929 0a2a 205b 666f   (line 19).* [fo\n+0001b100: 6f2c 2e2e 2e2c 6261 725d 2c20 6d75 6c74  o,...,bar], mult\n+0001b110: 6970 6c65 206f 7074 696f 6e73 2072 6566  iple options ref\n+0001b120: 6572 656e 6365 3a20 466f 726d 7320 6f66  erence: Forms of\n+0001b130: 2072 6566 6572 656e 6365 732e 0a20 2020   references..   \n 0001b140: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001b150: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001b160: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b170: 2020 2020 2020 286c 696e 6520 3138 290a        (line 18).\n-0001b180: 2a20 5b66 6f6f 5d2c 206f 7074 696f 6e73  * [foo], options\n-0001b190: 2072 6566 6572 656e 6365 3a20 2020 2020   reference:     \n-0001b1a0: 2020 2020 2020 2020 2050 6f6c 796c 696e           Polylin\n-0001b1b0: 6520 7377 6565 7073 2077 6974 6820 636c  e sweeps with cl\n-0001b1c0: 6f73 7572 652e 0a20 2020 2020 2020 2020  osure..         \n+0001b170: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+0001b180: 6520 3138 290a 2a20 5b66 6f6f 5d2c 206f  e 18).* [foo], o\n+0001b190: 7074 696f 6e73 2072 6566 6572 656e 6365  ptions reference\n+0001b1a0: 3a20 2020 2020 2020 2020 2020 2020 2050  :              P\n+0001b1b0: 6f6c 796c 696e 6520 7377 6565 7073 2077  olyline sweeps w\n+0001b1c0: 6974 6820 636c 6f73 7572 652e 0a20 2020  ith closure..   \n 0001b1d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001b1e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001b1f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b200: 2020 2020 2020 286c 696e 6520 3234 290a        (line 24).\n-0001b210: 2a20 5b66 6f6f 5d2c 206f 7074 696f 6e73  * [foo], options\n-0001b220: 2072 6566 6572 656e 6365 203c 313e 3a20   reference <1>: \n-0001b230: 2020 2020 2020 2020 2046 6f72 6d73 206f           Forms o\n-0001b240: 6620 7265 6665 7265 6e63 6573 2e20 2028  f references.  (\n-0001b250: 6c69 6e65 2031 3829 0a2a 205b 666f 6f5d  line 18).* [foo]\n-0001b260: 2c20 7665 6374 6f72 2072 6566 6572 656e  , vector referen\n-0001b270: 6365 3a20 2020 2020 2020 2020 2020 2020  ce:             \n-0001b280: 2020 506f 6c79 6c69 6e65 2073 7765 6570    Polyline sweep\n-0001b290: 732e 2020 2020 2020 286c 696e 6520 3230  s.      (line 20\n-0001b2a0: 290a 2a20 5b66 6f6f 5d2c 2076 6563 746f  ).* [foo], vecto\n-0001b2b0: 7220 7265 6665 7265 6e63 6520 3c31 3e3a  r reference <1>:\n-0001b2c0: 2020 2020 2020 2020 2020 2046 6f72 6d73             Forms\n-0001b2d0: 206f 6620 7265 6665 7265 6e63 6573 2e20   of references. \n-0001b2e0: 2028 6c69 6e65 2031 3529 0a2a 205b 5b20   (line 15).* [[ \n-0001b2f0: 5d5b 205d 5b20 5d5b 205d 5d2c 2074 7261  ][ ][ ][ ]], tra\n-0001b300: 6e73 666f 726d 206c 6974 6572 616c 3a20  nsform literal: \n-0001b310: 2020 2020 5472 616e 7366 6f72 6d20 6c69      Transform li\n-0001b320: 7465 7261 6c73 2e20 2020 286c 696e 6520  terals.   (line \n-0001b330: 3437 290a 2a20 5b5b 205d 5b20 5d5b 205d  47).* [[ ][ ][ ]\n-0001b340: 5b20 5d5d 2c20 7472 616e 7366 6f72 6d20  [ ]], transform \n-0001b350: 6c69 7465 7261 6c20 3c31 3e3a 2054 7261  literal <1>: Tra\n-0001b360: 6e73 666f 726d 206c 6974 6572 616c 732e  nsform literals.\n-0001b370: 2020 2028 6c69 6e65 2035 3329 0a2a 205b     (line 53).* [\n-0001b380: 5b66 6f6f 5d5d 2c20 7472 616e 7366 6f72  [foo]], transfor\n-0001b390: 6d20 7265 6665 7265 6e63 653a 2020 2020  m reference:    \n-0001b3a0: 2020 2020 2020 466f 726d 7320 6f66 2072        Forms of r\n-0001b3b0: 6566 6572 656e 6365 732e 2020 286c 696e  eferences.  (lin\n-0001b3c0: 6520 3136 290a 2a20 5b5b 666f 6f5d 5d2c  e 16).* [[foo]],\n-0001b3d0: 2074 7261 6e73 666f 726d 2072 6566 6572   transform refer\n-0001b3e0: 656e 6365 203c 313e 3a20 2020 2020 204f  ence <1>:      O\n-0001b3f0: 7665 7276 6965 772e 2020 2020 2020 2020  verview.        \n-0001b400: 2020 2020 2028 6c69 6e65 2033 3529 0a2a       (line 35).*\n-0001b410: 205b 5b66 6f6f 5d5d 2c20 7472 616e 7366   [[foo]], transf\n-0001b420: 6f72 6d20 7265 6665 7265 6e63 6520 3c32  orm reference <2\n-0001b430: 3e3a 2020 2020 2020 4f76 6572 7669 6577  >:      Overview\n-0001b440: 2e20 2020 2020 2020 2020 2020 2020 286c  .             (l\n-0001b450: 696e 6520 3335 290a 2a20 5e2c 2065 7870  ine 35).* ^, exp\n-0001b460: 6f6e 656e 7469 6174 696f 6e20 6f70 6572  onentiation oper\n-0001b470: 6174 6f72 3a20 2020 2020 2020 2020 2020  ator:           \n-0001b480: 2054 776f 2d6f 7065 7261 6e64 2028 6269   Two-operand (bi\n-0001b490: 6e61 7279 2920 666f 726d 732e 0a20 2020  nary) forms..   \n-0001b4a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001b200: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+0001b210: 6520 3234 290a 2a20 5b66 6f6f 5d2c 206f  e 24).* [foo], o\n+0001b220: 7074 696f 6e73 2072 6566 6572 656e 6365  ptions reference\n+0001b230: 203c 313e 3a20 2020 2020 2020 2020 2046   <1>:          F\n+0001b240: 6f72 6d73 206f 6620 7265 6665 7265 6e63  orms of referenc\n+0001b250: 6573 2e20 2028 6c69 6e65 2031 3829 0a2a  es.  (line 18).*\n+0001b260: 205b 666f 6f5d 2c20 7665 6374 6f72 2072   [foo], vector r\n+0001b270: 6566 6572 656e 6365 3a20 2020 2020 2020  eference:       \n+0001b280: 2020 2020 2020 2020 506f 6c79 6c69 6e65          Polyline\n+0001b290: 2073 7765 6570 732e 2020 2020 2020 286c   sweeps.      (l\n+0001b2a0: 696e 6520 3230 290a 2a20 5b66 6f6f 5d2c  ine 20).* [foo],\n+0001b2b0: 2076 6563 746f 7220 7265 6665 7265 6e63   vector referenc\n+0001b2c0: 6520 3c31 3e3a 2020 2020 2020 2020 2020  e <1>:          \n+0001b2d0: 2046 6f72 6d73 206f 6620 7265 6665 7265   Forms of refere\n+0001b2e0: 6e63 6573 2e20 2028 6c69 6e65 2031 3529  nces.  (line 15)\n+0001b2f0: 0a2a 205b 5b20 5d5b 205d 5b20 5d5b 205d  .* [[ ][ ][ ][ ]\n+0001b300: 5d2c 2074 7261 6e73 666f 726d 206c 6974  ], transform lit\n+0001b310: 6572 616c 3a20 2020 2020 5472 616e 7366  eral:     Transf\n+0001b320: 6f72 6d20 6c69 7465 7261 6c73 2e20 2020  orm literals.   \n+0001b330: 286c 696e 6520 3437 290a 2a20 5b5b 205d  (line 47).* [[ ]\n+0001b340: 5b20 5d5b 205d 5b20 5d5d 2c20 7472 616e  [ ][ ][ ]], tran\n+0001b350: 7366 6f72 6d20 6c69 7465 7261 6c20 3c31  sform literal <1\n+0001b360: 3e3a 2054 7261 6e73 666f 726d 206c 6974  >: Transform lit\n+0001b370: 6572 616c 732e 2020 2028 6c69 6e65 2035  erals.   (line 5\n+0001b380: 3329 0a2a 205b 5b66 6f6f 5d5d 2c20 7472  3).* [[foo]], tr\n+0001b390: 616e 7366 6f72 6d20 7265 6665 7265 6e63  ansform referenc\n+0001b3a0: 653a 2020 2020 2020 2020 2020 466f 726d  e:          Form\n+0001b3b0: 7320 6f66 2072 6566 6572 656e 6365 732e  s of references.\n+0001b3c0: 2020 286c 696e 6520 3136 290a 2a20 5b5b    (line 16).* [[\n+0001b3d0: 666f 6f5d 5d2c 2074 7261 6e73 666f 726d  foo]], transform\n+0001b3e0: 2072 6566 6572 656e 6365 203c 313e 3a20   reference <1>: \n+0001b3f0: 2020 2020 204f 7665 7276 6965 772e 2020       Overview.  \n+0001b400: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001b410: 2033 3529 0a2a 205b 5b66 6f6f 5d5d 2c20   35).* [[foo]], \n+0001b420: 7472 616e 7366 6f72 6d20 7265 6665 7265  transform refere\n+0001b430: 6e63 6520 3c32 3e3a 2020 2020 2020 4f76  nce <2>:      Ov\n+0001b440: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n+0001b450: 2020 2020 286c 696e 6520 3335 290a 2a20      (line 35).* \n+0001b460: 5e2c 2065 7870 6f6e 656e 7469 6174 696f  ^, exponentiatio\n+0001b470: 6e20 6f70 6572 6174 6f72 3a20 2020 2020  n operator:     \n+0001b480: 2020 2020 2020 2054 776f 2d6f 7065 7261         Two-opera\n+0001b490: 6e64 2028 6269 6e61 7279 2920 666f 726d  nd (binary) form\n+0001b4a0: 732e 0a20 2020 2020 2020 2020 2020 2020  s..             \n 0001b4b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001b4c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b4d0: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-0001b4e0: 6520 3237 290a 2a20 7b20 7d2c 2062 6c6f  e 27).* { }, blo\n-0001b4f0: 636b 2064 7261 7761 626c 653a 2020 2020  ck drawable:    \n-0001b500: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n-0001b510: 626a 6563 7420 7472 616e 7366 6f72 6d73  bject transforms\n-0001b520: 2e20 2020 2028 6c69 6e65 2032 3429 0a2a  .    (line 24).*\n-0001b530: 207b 207d 2c20 626c 6f63 6b20 6472 6177   { }, block draw\n-0001b540: 6162 6c65 203c 313e 3a20 2020 2020 2020  able <1>:       \n-0001b550: 2020 2020 2020 2020 4e65 7374 6564 2073          Nested s\n-0001b560: 7765 6570 732e 2020 2020 2020 2020 286c  weeps.        (l\n-0001b570: 696e 6520 3235 290a 2a20 7b20 7d2c 2062  ine 25).* { }, b\n-0001b580: 6c6f 636b 2064 7261 7761 626c 6520 3c32  lock drawable <2\n-0001b590: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001b5a0: 2053 7765 7074 2062 6c6f 636b 732e 2020   Swept blocks.  \n-0001b5b0: 2020 2020 2020 2028 6c69 6e65 2020 3729         (line  7)\n-0001b5c0: 0a2a 207b 207d 2c20 626c 6f63 6b20 6472  .* { }, block dr\n-0001b5d0: 6177 6162 6c65 203c 333e 3a20 2020 2020  awable <3>:     \n-0001b5e0: 2020 2020 2020 2020 2020 426c 6f63 6b73            Blocks\n-0001b5f0: 2e20 2020 2020 2020 2020 2020 2020 2020  .               \n-0001b600: 286c 696e 6520 2036 290a 2a20 7b20 7d2c  (line  6).* { },\n-0001b610: 2062 6c6f 636b 2064 7261 7761 626c 6520   block drawable \n-0001b620: 3c34 3e3a 2020 2020 2020 2020 2020 2020  <4>:            \n-0001b630: 2020 204f 7665 7276 6965 772e 2020 2020     Overview.    \n-0001b640: 2020 2020 2020 2020 2028 6c69 6e65 2033           (line 3\n-0001b650: 3729 0a2a 207b 666f 6f7d 2c20 6472 6177  7).* {foo}, draw\n-0001b660: 6162 6c65 2072 6566 6572 656e 6365 3a20  able reference: \n-0001b670: 2020 2020 2020 2020 2020 2020 4f62 6a65              Obje\n-0001b680: 6374 2074 7261 6e73 666f 726d 732e 2020  ct transforms.  \n-0001b690: 2020 286c 696e 6520 3333 290a 2a20 7b66    (line 33).* {f\n-0001b6a0: 6f6f 7d2c 2064 7261 7761 626c 6520 7265  oo}, drawable re\n-0001b6b0: 6665 7265 6e63 6520 3c31 3e3a 2020 2020  ference <1>:    \n-0001b6c0: 2020 2020 2046 6f72 6d73 206f 6620 7265       Forms of re\n-0001b6d0: 6665 7265 6e63 6573 2e20 2028 6c69 6e65  ferences.  (line\n-0001b6e0: 2031 3729 0a2a 207b 666f 6f7d 2c20 6472   17).* {foo}, dr\n-0001b6f0: 6177 6162 6c65 2072 6566 6572 656e 6365  awable reference\n-0001b700: 203c 323e 3a20 2020 2020 2020 2020 4f76   <2>:         Ov\n-0001b710: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n-0001b720: 2020 2020 286c 696e 6520 3437 290a 2a20      (line 47).* \n-0001b730: 7b66 6f6f 7d2c 2064 7261 7761 626c 6520  {foo}, drawable \n-0001b740: 7265 6665 7265 6e63 6520 3c33 3e3a 2020  reference <3>:  \n-0001b750: 2020 2020 2020 204f 7665 7276 6965 772e         Overview.\n-0001b760: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n-0001b770: 6e65 2035 3729 0a2a 207c 587c 2c20 6d61  ne 57).* |X|, ma\n-0001b780: 676e 6974 7564 6520 6f70 6572 6174 6f72  gnitude operator\n-0001b790: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001b7a0: 556e 6172 7920 666f 726d 732e 2020 2020  Unary forms.    \n-0001b7b0: 2020 2020 2020 286c 696e 6520 3132 290a        (line 12).\n-0001b7c0: 2a20 6163 6f73 3a20 2020 2020 2020 2020  * acos:         \n+0001b4d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001b4e0: 2020 286c 696e 6520 3237 290a 2a20 7b20    (line 27).* { \n+0001b4f0: 7d2c 2062 6c6f 636b 2064 7261 7761 626c  }, block drawabl\n+0001b500: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n+0001b510: 2020 2020 204f 626a 6563 7420 7472 616e       Object tran\n+0001b520: 7366 6f72 6d73 2e20 2020 2028 6c69 6e65  sforms.    (line\n+0001b530: 2032 3429 0a2a 207b 207d 2c20 626c 6f63   24).* { }, bloc\n+0001b540: 6b20 6472 6177 6162 6c65 203c 313e 3a20  k drawable <1>: \n+0001b550: 2020 2020 2020 2020 2020 2020 2020 4e65                Ne\n+0001b560: 7374 6564 2073 7765 6570 732e 2020 2020  sted sweeps.    \n+0001b570: 2020 2020 286c 696e 6520 3235 290a 2a20      (line 25).* \n+0001b580: 7b20 7d2c 2062 6c6f 636b 2064 7261 7761  { }, block drawa\n+0001b590: 626c 6520 3c32 3e3a 2020 2020 2020 2020  ble <2>:        \n+0001b5a0: 2020 2020 2020 2053 7765 7074 2062 6c6f         Swept blo\n+0001b5b0: 636b 732e 2020 2020 2020 2020 2028 6c69  cks.         (li\n+0001b5c0: 6e65 2020 3729 0a2a 207b 207d 2c20 626c  ne  7).* { }, bl\n+0001b5d0: 6f63 6b20 6472 6177 6162 6c65 203c 333e  ock drawable <3>\n+0001b5e0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001b5f0: 426c 6f63 6b73 2e20 2020 2020 2020 2020  Blocks.         \n+0001b600: 2020 2020 2020 286c 696e 6520 2036 290a        (line  6).\n+0001b610: 2a20 7b20 7d2c 2062 6c6f 636b 2064 7261  * { }, block dra\n+0001b620: 7761 626c 6520 3c34 3e3a 2020 2020 2020  wable <4>:      \n+0001b630: 2020 2020 2020 2020 204f 7665 7276 6965           Overvie\n+0001b640: 772e 2020 2020 2020 2020 2020 2020 2028  w.             (\n+0001b650: 6c69 6e65 2033 3729 0a2a 207b 666f 6f7d  line 37).* {foo}\n+0001b660: 2c20 6472 6177 6162 6c65 2072 6566 6572  , drawable refer\n+0001b670: 656e 6365 3a20 2020 2020 2020 2020 2020  ence:           \n+0001b680: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n+0001b690: 726d 732e 2020 2020 286c 696e 6520 3333  rms.    (line 33\n+0001b6a0: 290a 2a20 7b66 6f6f 7d2c 2064 7261 7761  ).* {foo}, drawa\n+0001b6b0: 626c 6520 7265 6665 7265 6e63 6520 3c31  ble reference <1\n+0001b6c0: 3e3a 2020 2020 2020 2020 2046 6f72 6d73  >:         Forms\n+0001b6d0: 206f 6620 7265 6665 7265 6e63 6573 2e20   of references. \n+0001b6e0: 2028 6c69 6e65 2031 3729 0a2a 207b 666f   (line 17).* {fo\n+0001b6f0: 6f7d 2c20 6472 6177 6162 6c65 2072 6566  o}, drawable ref\n+0001b700: 6572 656e 6365 203c 323e 3a20 2020 2020  erence <2>:     \n+0001b710: 2020 2020 4f76 6572 7669 6577 2e20 2020      Overview.   \n+0001b720: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+0001b730: 3437 290a 2a20 7b66 6f6f 7d2c 2064 7261  47).* {foo}, dra\n+0001b740: 7761 626c 6520 7265 6665 7265 6e63 6520  wable reference \n+0001b750: 3c33 3e3a 2020 2020 2020 2020 204f 7665  <3>:         Ove\n+0001b760: 7276 6965 772e 2020 2020 2020 2020 2020  rview.          \n+0001b770: 2020 2028 6c69 6e65 2035 3729 0a2a 207c     (line 57).* |\n+0001b780: 587c 2c20 6d61 676e 6974 7564 6520 6f70  X|, magnitude op\n+0001b790: 6572 6174 6f72 3a20 2020 2020 2020 2020  erator:         \n+0001b7a0: 2020 2020 2020 556e 6172 7920 666f 726d        Unary form\n+0001b7b0: 732e 2020 2020 2020 2020 2020 286c 696e  s.          (lin\n+0001b7c0: 6520 3132 290a 2a20 6163 6f73 3a20 2020  e 12).* acos:   \n 0001b7d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b7e0: 2020 2020 2020 2020 2055 6e61 7279 2066           Unary f\n-0001b7f0: 6f72 6d73 2e20 2020 2020 2020 2020 2028  orms.          (\n-0001b800: 6c69 6e65 2031 3829 0a2a 2061 7272 6f77  line 18).* arrow\n-0001b810: 733a 2020 2020 2020 2020 2020 2020 2020  s:              \n+0001b7e0: 2020 2020 2020 2020 2020 2020 2020 2055                 U\n+0001b7f0: 6e61 7279 2066 6f72 6d73 2e20 2020 2020  nary forms.     \n+0001b800: 2020 2020 2028 6c69 6e65 2031 3829 0a2a       (line 18).*\n+0001b810: 2061 7272 6f77 733a 2020 2020 2020 2020   arrows:        \n 0001b820: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b830: 2020 4166 6669 6e65 2061 7269 7468 6d65    Affine arithme\n-0001b840: 7469 632e 2020 2020 286c 696e 6520 3131  tic.    (line 11\n-0001b850: 290a 2a20 6172 726f 7773 203c 313e 3a20  ).* arrows <1>: \n-0001b860: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b870: 2020 2020 2020 2020 2020 2041 6666 696e             Affin\n-0001b880: 6520 6172 6974 686d 6574 6963 2e20 2020  e arithmetic.   \n-0001b890: 2028 6c69 6e65 2032 3829 0a2a 2061 7272   (line 28).* arr\n-0001b8a0: 6f77 7320 3c32 3e3a 2020 2020 2020 2020  ows <2>:        \n+0001b830: 2020 2020 2020 2020 4166 6669 6e65 2061          Affine a\n+0001b840: 7269 7468 6d65 7469 632e 2020 2020 286c  rithmetic.    (l\n+0001b850: 696e 6520 3131 290a 2a20 6172 726f 7773  ine 11).* arrows\n+0001b860: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+0001b870: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001b880: 2041 6666 696e 6520 6172 6974 686d 6574   Affine arithmet\n+0001b890: 6963 2e20 2020 2028 6c69 6e65 2032 3829  ic.    (line 28)\n+0001b8a0: 0a2a 2061 7272 6f77 7320 3c32 3e3a 2020  .* arrows <2>:  \n 0001b8b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b8c0: 2020 2020 4f76 6572 7669 6577 2e20 2020      Overview.   \n-0001b8d0: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-0001b8e0: 3639 290a 2a20 6172 726f 7773 203c 333e  69).* arrows <3>\n-0001b8f0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001b900: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n-0001b910: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n-0001b920: 2e20 2028 6c69 6e65 2032 3629 0a2a 2061  .  (line 26).* a\n-0001b930: 7272 6f77 7320 3c34 3e3a 2020 2020 2020  rrows <4>:      \n+0001b8c0: 2020 2020 2020 2020 2020 4f76 6572 7669            Overvi\n+0001b8d0: 6577 2e20 2020 2020 2020 2020 2020 2020  ew.             \n+0001b8e0: 286c 696e 6520 3639 290a 2a20 6172 726f  (line 69).* arro\n+0001b8f0: 7773 203c 333e 3a20 2020 2020 2020 2020  ws <3>:         \n+0001b900: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001b910: 2020 2041 2074 6563 686e 6963 616c 2064     A technical d\n+0001b920: 7261 7769 6e67 2e20 2028 6c69 6e65 2032  rawing.  (line 2\n+0001b930: 3629 0a2a 2061 7272 6f77 7320 3c34 3e3a  6).* arrows <4>:\n 0001b940: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b950: 2020 2020 2020 4120 7465 6368 6e69 6361        A technica\n-0001b960: 6c20 6472 6177 696e 672e 2020 286c 696e  l drawing.  (lin\n-0001b970: 6520 3638 290a 2a20 6173 696e 3a20 2020  e 68).* asin:   \n-0001b980: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b990: 2020 2020 2020 2020 2020 2020 2020 2055                 U\n-0001b9a0: 6e61 7279 2066 6f72 6d73 2e20 2020 2020  nary forms.     \n-0001b9b0: 2020 2020 2028 6c69 6e65 2031 3729 0a2a       (line 17).*\n-0001b9c0: 2061 7461 6e32 3a20 2020 2020 2020 2020   atan2:         \n+0001b950: 2020 2020 2020 2020 2020 2020 4120 7465              A te\n+0001b960: 6368 6e69 6361 6c20 6472 6177 696e 672e  chnical drawing.\n+0001b970: 2020 286c 696e 6520 3638 290a 2a20 6173    (line 68).* as\n+0001b980: 696e 3a20 2020 2020 2020 2020 2020 2020  in:             \n+0001b990: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001b9a0: 2020 2020 2055 6e61 7279 2066 6f72 6d73       Unary forms\n+0001b9b0: 2e20 2020 2020 2020 2020 2028 6c69 6e65  .          (line\n+0001b9c0: 2031 3729 0a2a 2061 7461 6e32 3a20 2020   17).* atan2:   \n 0001b9d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b9e0: 2020 2020 2020 2020 556e 6172 7920 666f          Unary fo\n-0001b9f0: 726d 732e 2020 2020 2020 2020 2020 286c  rms.          (l\n-0001ba00: 696e 6520 3139 290a 2a20 6361 6d65 7261  ine 19).* camera\n-0001ba10: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001b9e0: 2020 2020 2020 2020 2020 2020 2020 556e                Un\n+0001b9f0: 6172 7920 666f 726d 732e 2020 2020 2020  ary forms.      \n+0001ba00: 2020 2020 286c 696e 6520 3139 290a 2a20      (line 19).* \n+0001ba10: 6361 6d65 7261 3a20 2020 2020 2020 2020  camera:         \n 0001ba20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ba30: 2043 616d 6572 612e 2020 2020 2020 2020   Camera.        \n-0001ba40: 2020 2020 2020 2028 6c69 6e65 2020 3629         (line  6)\n-0001ba50: 0a2a 2063 6f6e 7465 7874 3a20 2020 2020  .* context:     \n-0001ba60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ba70: 2020 2020 2020 2020 2020 4c61 6e67 7561            Langua\n-0001ba80: 6765 2e20 2020 2020 2020 2020 2020 2020  ge.             \n-0001ba90: 286c 696e 6520 3137 290a 2a20 636f 733a  (line 17).* cos:\n-0001baa0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ba30: 2020 2020 2020 2043 616d 6572 612e 2020         Camera.  \n+0001ba40: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n+0001ba50: 6e65 2020 3629 0a2a 2063 6f6e 7465 7874  ne  6).* context\n+0001ba60: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001ba70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ba80: 4c61 6e67 7561 6765 2e20 2020 2020 2020  Language.       \n+0001ba90: 2020 2020 2020 286c 696e 6520 3137 290a        (line 17).\n+0001baa0: 2a20 636f 733a 2020 2020 2020 2020 2020  * cos:          \n 0001bab0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bac0: 2020 2055 6e61 7279 2066 6f72 6d73 2e20     Unary forms. \n-0001bad0: 2020 2020 2020 2020 2028 6c69 6e65 2031           (line 1\n-0001bae0: 3629 0a2a 2063 756c 6c3a 2020 2020 2020  6).* cull:      \n+0001bac0: 2020 2020 2020 2020 2055 6e61 7279 2066           Unary f\n+0001bad0: 6f72 6d73 2e20 2020 2020 2020 2020 2028  orms.          (\n+0001bae0: 6c69 6e65 2031 3629 0a2a 2063 756c 6c3a  line 16).* cull:\n 0001baf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bb00: 2020 2020 2020 2020 2020 2020 4472 6177              Draw\n-0001bb10: 696e 6720 6120 736f 6c69 642e 2020 2020  ing a solid.    \n-0001bb20: 2020 286c 696e 6520 3435 290a 2a20 6375    (line 45).* cu\n-0001bb30: 6c6c 203c 313e 3a20 2020 2020 2020 2020  ll <1>:         \n+0001bb00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001bb10: 2020 4472 6177 696e 6720 6120 736f 6c69    Drawing a soli\n+0001bb20: 642e 2020 2020 2020 286c 696e 6520 3435  d.      (line 45\n+0001bb30: 290a 2a20 6375 6c6c 203c 313e 3a20 2020  ).* cull <1>:   \n 0001bb40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bb50: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n-0001bb60: 6565 7073 2e20 2020 2020 2028 6c69 6e65  eeps.      (line\n-0001bb70: 2020 3929 0a2a 2063 756c 6c20 3c32 3e3a    9).* cull <2>:\n-0001bb80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bb90: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n-0001bba0: 616e 7370 6172 656e 6379 2e20 2020 2020  ansparency.     \n-0001bbb0: 2020 2020 286c 696e 6520 3135 290a 2a20      (line 15).* \n-0001bbc0: 6375 6c6c 203c 333e 3a20 2020 2020 2020  cull <3>:       \n+0001bb50: 2020 2020 2020 2020 2020 2050 6f6c 796c             Polyl\n+0001bb60: 696e 6520 7377 6565 7073 2e20 2020 2020  ine sweeps.     \n+0001bb70: 2028 6c69 6e65 2020 3929 0a2a 2063 756c   (line  9).* cul\n+0001bb80: 6c20 3c32 3e3a 2020 2020 2020 2020 2020  l <2>:          \n+0001bb90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001bba0: 2020 2020 5472 616e 7370 6172 656e 6379      Transparency\n+0001bbb0: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n+0001bbc0: 3135 290a 2a20 6375 6c6c 203c 333e 3a20  15).* cull <3>: \n 0001bbd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bbe0: 2020 2020 2020 2041 2074 6563 686e 6963         A technic\n-0001bbf0: 616c 2064 7261 7769 6e67 2e20 2028 6c69  al drawing.  (li\n-0001bc00: 6e65 2032 3029 0a2a 2063 756c 6c20 3c34  ne 20).* cull <4\n-0001bc10: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001bbe0: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n+0001bbf0: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n+0001bc00: 2e20 2028 6c69 6e65 2032 3029 0a2a 2063  .  (line 20).* c\n+0001bc10: 756c 6c20 3c34 3e3a 2020 2020 2020 2020  ull <4>:        \n 0001bc20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bc30: 496e 7465 726e 616c 206f 7074 696f 6e73  Internal options\n-0001bc40: 2e20 2020 2020 286c 696e 6520 2037 290a  .     (line  7).\n-0001bc50: 2a20 6375 6c6c 203c 353e 3a20 2020 2020  * cull <5>:     \n-0001bc60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bc70: 2020 2020 2020 2020 2047 6c6f 6261 6c20           Global \n-0001bc80: 6f70 7469 6f6e 732e 2020 2020 2020 2028  options.       (\n-0001bc90: 6c69 6e65 2031 3329 0a2a 2063 7572 7665  line 13).* curve\n-0001bca0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001bc30: 2020 2020 2020 496e 7465 726e 616c 206f        Internal o\n+0001bc40: 7074 696f 6e73 2e20 2020 2020 286c 696e  ptions.     (lin\n+0001bc50: 6520 2037 290a 2a20 6375 6c6c 203c 353e  e  7).* cull <5>\n+0001bc60: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001bc70: 2020 2020 2020 2020 2020 2020 2020 2047                 G\n+0001bc80: 6c6f 6261 6c20 6f70 7469 6f6e 732e 2020  lobal options.  \n+0001bc90: 2020 2020 2028 6c69 6e65 2031 3329 0a2a       (line 13).*\n+0001bca0: 2063 7572 7665 3a20 2020 2020 2020 2020   curve:         \n 0001bcb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bcc0: 2020 4375 7276 6573 2e20 2020 2020 2020    Curves.       \n-0001bcd0: 2020 2020 2020 2020 286c 696e 6520 2036          (line  6\n-0001bce0: 290a 2a20 6465 663a 2020 2020 2020 2020  ).* def:        \n+0001bcc0: 2020 2020 2020 2020 4375 7276 6573 2e20          Curves. \n+0001bcd0: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+0001bce0: 696e 6520 2036 290a 2a20 6465 663a 2020  ine  6).* def:  \n 0001bcf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bd00: 2020 2020 2020 2020 2020 2044 7261 7769             Drawi\n-0001bd10: 6e67 2061 2073 6f6c 6964 2e20 2020 2020  ng a solid.     \n-0001bd20: 2028 6c69 6e65 2020 3929 0a2a 2064 6566   (line  9).* def\n-0001bd30: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+0001bd00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001bd10: 2044 7261 7769 6e67 2061 2073 6f6c 6964   Drawing a solid\n+0001bd20: 2e20 2020 2020 2028 6c69 6e65 2020 3929  .      (line  9)\n+0001bd30: 0a2a 2064 6566 203c 313e 3a20 2020 2020  .* def <1>:     \n 0001bd40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bd50: 2020 2020 4472 6177 696e 6720 6120 736f      Drawing a so\n-0001bd60: 6c69 642e 2020 2020 2020 286c 696e 6520  lid.      (line \n-0001bd70: 3232 290a 2a20 6465 6620 3c32 3e3a 2020  22).* def <2>:  \n-0001bd80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bd90: 2020 2020 2020 2020 2020 2020 204f 626a               Obj\n-0001bda0: 6563 7420 7472 616e 7366 6f72 6d73 2e20  ect transforms. \n-0001bdb0: 2020 2028 6c69 6e65 2031 3029 0a2a 2064     (line 10).* d\n-0001bdc0: 6566 203c 333e 3a20 2020 2020 2020 2020  ef <3>:         \n+0001bd50: 2020 2020 2020 2020 2020 4472 6177 696e            Drawin\n+0001bd60: 6720 6120 736f 6c69 642e 2020 2020 2020  g a solid.      \n+0001bd70: 286c 696e 6520 3232 290a 2a20 6465 6620  (line 22).* def \n+0001bd80: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n+0001bd90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001bda0: 2020 204f 626a 6563 7420 7472 616e 7366     Object transf\n+0001bdb0: 6f72 6d73 2e20 2020 2028 6c69 6e65 2031  orms.    (line 1\n+0001bdc0: 3029 0a2a 2064 6566 203c 333e 3a20 2020  0).* def <3>:   \n 0001bdd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bde0: 2020 2020 2020 506f 696e 7420 7377 6565        Point swee\n-0001bdf0: 7073 2e20 2020 2020 2020 2020 286c 696e  ps.         (lin\n-0001be00: 6520 3139 290a 2a20 6465 6620 3c34 3e3a  e 19).* def <4>:\n-0001be10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001be20: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n-0001be30: 6f6c 796c 696e 6520 7377 6565 7073 2e20  olyline sweeps. \n-0001be40: 2020 2020 2028 6c69 6e65 2020 3929 0a2a       (line  9).*\n-0001be50: 2064 6566 203c 353e 3a20 2020 2020 2020   def <5>:       \n+0001bde0: 2020 2020 2020 2020 2020 2020 506f 696e              Poin\n+0001bdf0: 7420 7377 6565 7073 2e20 2020 2020 2020  t sweeps.       \n+0001be00: 2020 286c 696e 6520 3139 290a 2a20 6465    (line 19).* de\n+0001be10: 6620 3c34 3e3a 2020 2020 2020 2020 2020  f <4>:          \n+0001be20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001be30: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n+0001be40: 6565 7073 2e20 2020 2020 2028 6c69 6e65  eeps.      (line\n+0001be50: 2020 3929 0a2a 2064 6566 203c 353e 3a20    9).* def <5>: \n 0001be60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001be70: 2020 2020 2020 2020 4e65 7374 6564 2073          Nested s\n-0001be80: 7765 6570 732e 2020 2020 2020 2020 286c  weeps.        (l\n-0001be90: 696e 6520 2038 290a 2a20 6465 6620 3c36  ine  8).* def <6\n-0001bea0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001be70: 2020 2020 2020 2020 2020 2020 2020 4e65                Ne\n+0001be80: 7374 6564 2073 7765 6570 732e 2020 2020  sted sweeps.    \n+0001be90: 2020 2020 286c 696e 6520 2038 290a 2a20      (line  8).* \n+0001bea0: 6465 6620 3c36 3e3a 2020 2020 2020 2020  def <6>:        \n 0001beb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bec0: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n-0001bed0: 2077 6974 6820 636c 6f73 7572 652e 0a20   with closure.. \n-0001bee0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001bec0: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n+0001bed0: 7377 6565 7073 2077 6974 6820 636c 6f73  sweeps with clos\n+0001bee0: 7572 652e 0a20 2020 2020 2020 2020 2020  ure..           \n 0001bef0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001bf00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bf10: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-0001bf20: 696e 6520 3130 290a 2a20 6465 6620 3c37  ine 10).* def <7\n-0001bf30: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001bf10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001bf20: 2020 2020 286c 696e 6520 3130 290a 2a20      (line 10).* \n+0001bf30: 6465 6620 3c37 3e3a 2020 2020 2020 2020  def <7>:        \n 0001bf40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bf50: 2041 6666 696e 6520 6172 6974 686d 6574   Affine arithmet\n-0001bf60: 6963 2e20 2020 2028 6c69 6e65 2031 3129  ic.    (line 11)\n-0001bf70: 0a2a 2064 6566 203c 383e 3a20 2020 2020  .* def <8>:     \n-0001bf80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bf90: 2020 2020 2020 2020 2020 4f76 6572 7669            Overvi\n-0001bfa0: 6577 2e20 2020 2020 2020 2020 2020 2020  ew.             \n-0001bfb0: 286c 696e 6520 3132 290a 2a20 6465 6620  (line 12).* def \n-0001bfc0: 3c39 3e3a 2020 2020 2020 2020 2020 2020  <9>:            \n+0001bf50: 2020 2020 2020 2041 6666 696e 6520 6172         Affine ar\n+0001bf60: 6974 686d 6574 6963 2e20 2020 2028 6c69  ithmetic.    (li\n+0001bf70: 6e65 2031 3129 0a2a 2064 6566 203c 383e  ne 11).* def <8>\n+0001bf80: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001bf90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001bfa0: 4f76 6572 7669 6577 2e20 2020 2020 2020  Overview.       \n+0001bfb0: 2020 2020 2020 286c 696e 6520 3132 290a        (line 12).\n+0001bfc0: 2a20 6465 6620 3c39 3e3a 2020 2020 2020  * def <9>:      \n 0001bfd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bfe0: 2020 204f 7665 7276 6965 772e 2020 2020     Overview.    \n-0001bff0: 2020 2020 2020 2020 2028 6c69 6e65 2033           (line 3\n-0001c000: 3729 0a2a 2064 6566 203c 3130 3e3a 2020  7).* def <10>:  \n-0001c010: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c020: 2020 2020 2020 2020 2020 2020 4f76 6572              Over\n-0001c030: 7669 6577 2e20 2020 2020 2020 2020 2020  view.           \n-0001c040: 2020 286c 696e 6520 3639 290a 2a20 6465    (line 69).* de\n-0001c050: 6620 3c31 313e 3a20 2020 2020 2020 2020  f <11>:         \n+0001bfe0: 2020 2020 2020 2020 204f 7665 7276 6965           Overvie\n+0001bff0: 772e 2020 2020 2020 2020 2020 2020 2028  w.             (\n+0001c000: 6c69 6e65 2033 3729 0a2a 2064 6566 203c  line 37).* def <\n+0001c010: 3130 3e3a 2020 2020 2020 2020 2020 2020  10>:            \n+0001c020: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c030: 2020 4f76 6572 7669 6577 2e20 2020 2020    Overview.     \n+0001c040: 2020 2020 2020 2020 286c 696e 6520 3639          (line 69\n+0001c050: 290a 2a20 6465 6620 3c31 313e 3a20 2020  ).* def <11>:   \n 0001c060: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c070: 2020 2020 2041 2074 6563 686e 6963 616c       A technical\n-0001c080: 2064 7261 7769 6e67 2e20 2028 6c69 6e65   drawing.  (line\n-0001c090: 2031 3429 0a2a 2064 6566 203c 3132 3e3a   14).* def <12>:\n-0001c0a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c0b0: 2020 2020 2020 2020 2020 2020 2020 4120                A \n-0001c0c0: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n-0001c0d0: 672e 2020 286c 696e 6520 3236 290a 2a20  g.  (line 26).* \n-0001c0e0: 6465 6620 3c31 333e 3a20 2020 2020 2020  def <13>:       \n+0001c070: 2020 2020 2020 2020 2020 2041 2074 6563             A tec\n+0001c080: 686e 6963 616c 2064 7261 7769 6e67 2e20  hnical drawing. \n+0001c090: 2028 6c69 6e65 2031 3429 0a2a 2064 6566   (line 14).* def\n+0001c0a0: 203c 3132 3e3a 2020 2020 2020 2020 2020   <12>:          \n+0001c0b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c0c0: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n+0001c0d0: 6472 6177 696e 672e 2020 286c 696e 6520  drawing.  (line \n+0001c0e0: 3236 290a 2a20 6465 6620 3c31 333e 3a20  26).* def <13>: \n 0001c0f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c100: 2020 2020 2020 2041 2074 6563 686e 6963         A technic\n-0001c110: 616c 2064 7261 7769 6e67 2e20 2028 6c69  al drawing.  (li\n-0001c120: 6e65 2034 3129 0a2a 2064 6566 203c 3134  ne 41).* def <14\n-0001c130: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001c100: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n+0001c110: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n+0001c120: 2e20 2028 6c69 6e65 2034 3129 0a2a 2064  .  (line 41).* d\n+0001c130: 6566 203c 3134 3e3a 2020 2020 2020 2020  ef <14>:        \n 0001c140: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c150: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n-0001c160: 696e 672e 2020 286c 696e 6520 3638 290a  ing.  (line 68).\n-0001c170: 2a20 6465 6620 3c31 353e 3a20 2020 2020  * def <15>:     \n-0001c180: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c190: 2020 2020 2020 2020 2041 2074 6563 686e           A techn\n-0001c1a0: 6963 616c 2064 7261 7769 6e67 2e20 2028  ical drawing.  (\n-0001c1b0: 6c69 6e65 2039 3529 0a2a 2064 6566 203c  line 95).* def <\n-0001c1c0: 3136 3e3a 2020 2020 2020 2020 2020 2020  16>:            \n+0001c150: 2020 2020 2020 4120 7465 6368 6e69 6361        A technica\n+0001c160: 6c20 6472 6177 696e 672e 2020 286c 696e  l drawing.  (lin\n+0001c170: 6520 3638 290a 2a20 6465 6620 3c31 353e  e 68).* def <15>\n+0001c180: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001c190: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+0001c1a0: 2074 6563 686e 6963 616c 2064 7261 7769   technical drawi\n+0001c1b0: 6e67 2e20 2028 6c69 6e65 2039 3529 0a2a  ng.  (line 95).*\n+0001c1c0: 2064 6566 203c 3136 3e3a 2020 2020 2020   def <16>:      \n 0001c1d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c1e0: 2020 4120 6869 6572 6172 6368 6963 616c    A hierarchical\n-0001c1f0: 206d 6f64 656c 2e20 286c 696e 6520 3130   model. (line 10\n-0001c200: 290a 2a20 6465 6620 3c31 373e 3a20 2020  ).* def <17>:   \n-0001c210: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c220: 2020 2020 2020 2020 2020 2041 2068 6965             A hie\n-0001c230: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e  rarchical model.\n-0001c240: 2028 6c69 6e65 2032 3329 0a2a 2064 6566   (line 23).* def\n-0001c250: 203c 3138 3e3a 2020 2020 2020 2020 2020   <18>:          \n+0001c1e0: 2020 2020 2020 2020 4120 6869 6572 6172          A hierar\n+0001c1f0: 6368 6963 616c 206d 6f64 656c 2e20 286c  chical model. (l\n+0001c200: 696e 6520 3130 290a 2a20 6465 6620 3c31  ine 10).* def <1\n+0001c210: 373e 3a20 2020 2020 2020 2020 2020 2020  7>:             \n+0001c220: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c230: 2041 2068 6965 7261 7263 6869 6361 6c20   A hierarchical \n+0001c240: 6d6f 6465 6c2e 2028 6c69 6e65 2032 3329  model. (line 23)\n+0001c250: 0a2a 2064 6566 203c 3138 3e3a 2020 2020  .* def <18>:    \n 0001c260: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c270: 2020 2020 4120 6869 6572 6172 6368 6963      A hierarchic\n-0001c280: 616c 206d 6f64 656c 2e20 286c 696e 6520  al model. (line \n-0001c290: 3332 290a 2a20 646f 7473 3a20 2020 2020  32).* dots:     \n-0001c2a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c2b0: 2020 2020 2020 2020 2020 2020 2044 6f74               Dot\n-0001c2c0: 732e 2020 2020 2020 2020 2020 2020 2020  s.              \n-0001c2d0: 2020 2028 6c69 6e65 2020 3629 0a2a 2066     (line  6).* f\n-0001c2e0: 696c 6c20 6f70 6163 6974 793a 2020 2020  ill opacity:    \n-0001c2f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c300: 2020 2020 2020 5472 616e 7370 6172 656e        Transparen\n-0001c310: 6379 2e20 2020 2020 2020 2020 286c 696e  cy.         (lin\n-0001c320: 6520 3130 290a 2a20 6669 6c6c 2073 7479  e 10).* fill sty\n-0001c330: 6c65 3a20 2020 2020 2020 2020 2020 2020  le:             \n-0001c340: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n-0001c350: 696b 5a2f 5047 4620 7573 6572 2d64 6566  ikZ/PGF user-def\n-0001c360: 696e 6564 2073 7479 6c65 732e 0a20 2020  ined styles..   \n-0001c370: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c270: 2020 2020 2020 2020 2020 4120 6869 6572            A hier\n+0001c280: 6172 6368 6963 616c 206d 6f64 656c 2e20  archical model. \n+0001c290: 286c 696e 6520 3332 290a 2a20 646f 7473  (line 32).* dots\n+0001c2a0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001c2b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c2c0: 2020 2044 6f74 732e 2020 2020 2020 2020     Dots.        \n+0001c2d0: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+0001c2e0: 3629 0a2a 2066 696c 6c20 6f70 6163 6974  6).* fill opacit\n+0001c2f0: 793a 2020 2020 2020 2020 2020 2020 2020  y:              \n+0001c300: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n+0001c310: 7370 6172 656e 6379 2e20 2020 2020 2020  sparency.       \n+0001c320: 2020 286c 696e 6520 3130 290a 2a20 6669    (line 10).* fi\n+0001c330: 6c6c 2073 7479 6c65 3a20 2020 2020 2020  ll style:       \n+0001c340: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c350: 2020 2020 2054 696b 5a2f 5047 4620 7573       TikZ/PGF us\n+0001c360: 6572 2d64 6566 696e 6564 2073 7479 6c65  er-defined style\n+0001c370: 732e 0a20 2020 2020 2020 2020 2020 2020  s..             \n 0001c380: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001c390: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c3a0: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-0001c3b0: 6520 3235 290a 2a20 6669 6c6c 636f 6c6f  e 25).* fillcolo\n-0001c3c0: 723a 2020 2020 2020 2020 2020 2020 2020  r:              \n-0001c3d0: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n-0001c3e0: 626a 6563 7420 7472 616e 7366 6f72 6d73  bject transforms\n-0001c3f0: 2e20 2020 2028 6c69 6e65 2031 3029 0a2a  .    (line 10).*\n-0001c400: 2066 696c 6c63 6f6c 6f72 203c 313e 3a20   fillcolor <1>: \n-0001c410: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c420: 2020 2020 2020 2020 506f 6c79 6c69 6e65          Polyline\n-0001c430: 2073 7765 6570 7320 7769 7468 2063 6c6f   sweeps with clo\n-0001c440: 7375 7265 2e0a 2020 2020 2020 2020 2020  sure..          \n+0001c3a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c3b0: 2020 286c 696e 6520 3235 290a 2a20 6669    (line 25).* fi\n+0001c3c0: 6c6c 636f 6c6f 723a 2020 2020 2020 2020  llcolor:        \n+0001c3d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c3e0: 2020 2020 204f 626a 6563 7420 7472 616e       Object tran\n+0001c3f0: 7366 6f72 6d73 2e20 2020 2028 6c69 6e65  sforms.    (line\n+0001c400: 2031 3029 0a2a 2066 696c 6c63 6f6c 6f72   10).* fillcolor\n+0001c410: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+0001c420: 2020 2020 2020 2020 2020 2020 2020 506f                Po\n+0001c430: 6c79 6c69 6e65 2073 7765 6570 7320 7769  lyline sweeps wi\n+0001c440: 7468 2063 6c6f 7375 7265 2e0a 2020 2020  th closure..    \n 0001c450: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001c460: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001c470: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c480: 2020 2020 2028 6c69 6e65 2031 3029 0a2a       (line 10).*\n-0001c490: 2066 696c 6c63 6f6c 6f72 203c 323e 3a20   fillcolor <2>: \n-0001c4a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c4b0: 2020 2020 2020 2020 4f76 6572 7669 6577          Overview\n-0001c4c0: 2e20 2020 2020 2020 2020 2020 2020 286c  .             (l\n-0001c4d0: 696e 6520 3337 290a 2a20 6672 616d 653a  ine 37).* frame:\n-0001c4e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c480: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001c490: 2031 3029 0a2a 2066 696c 6c63 6f6c 6f72   10).* fillcolor\n+0001c4a0: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n+0001c4b0: 2020 2020 2020 2020 2020 2020 2020 4f76                Ov\n+0001c4c0: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n+0001c4d0: 2020 2020 286c 696e 6520 3337 290a 2a20      (line 37).* \n+0001c4e0: 6672 616d 653a 2020 2020 2020 2020 2020  frame:          \n 0001c4f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c500: 2046 7261 6d65 2e20 2020 2020 2020 2020   Frame.         \n-0001c510: 2020 2020 2020 2028 6c69 6e65 2020 3629         (line  6)\n-0001c520: 0a2a 2066 7261 6d65 7365 703a 2020 2020  .* framesep:    \n-0001c530: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c540: 2020 2020 2020 2020 2020 4672 616d 652e            Frame.\n-0001c550: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c560: 286c 696e 6520 3131 290a 2a20 676c 6f62  (line 11).* glob\n-0001c570: 616c 3a20 2020 2020 2020 2020 2020 2020  al:             \n+0001c500: 2020 2020 2020 2046 7261 6d65 2e20 2020         Frame.   \n+0001c510: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n+0001c520: 6e65 2020 3629 0a2a 2066 7261 6d65 7365  ne  6).* framese\n+0001c530: 703a 2020 2020 2020 2020 2020 2020 2020  p:              \n+0001c540: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c550: 4672 616d 652e 2020 2020 2020 2020 2020  Frame.          \n+0001c560: 2020 2020 2020 286c 696e 6520 3131 290a        (line 11).\n+0001c570: 2a20 676c 6f62 616c 3a20 2020 2020 2020  * global:       \n 0001c580: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c590: 2020 2047 6c6f 6261 6c20 656e 7669 726f     Global enviro\n-0001c5a0: 6e6d 656e 742e 2020 2028 6c69 6e65 2031  nment.   (line 1\n-0001c5b0: 3229 0a2a 2069 6e70 7574 3a20 2020 2020  2).* input:     \n-0001c5c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c5d0: 2020 2020 2020 2020 2020 2020 4c61 6e67              Lang\n-0001c5e0: 7561 6765 2062 6173 6963 732e 2020 2020  uage basics.    \n-0001c5f0: 2020 286c 696e 6520 3139 290a 2a20 696e    (line 19).* in\n-0001c600: 7665 7273 653a 2020 2020 2020 2020 2020  verse:          \n+0001c590: 2020 2020 2020 2020 2047 6c6f 6261 6c20           Global \n+0001c5a0: 656e 7669 726f 6e6d 656e 742e 2020 2028  environment.   (\n+0001c5b0: 6c69 6e65 2031 3229 0a2a 2069 6e70 7574  line 12).* input\n+0001c5c0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001c5d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c5e0: 2020 4c61 6e67 7561 6765 2062 6173 6963    Language basic\n+0001c5f0: 732e 2020 2020 2020 286c 696e 6520 3139  s.      (line 19\n+0001c600: 290a 2a20 696e 7665 7273 653a 2020 2020  ).* inverse:    \n 0001c610: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c620: 2020 2020 2055 6e61 7279 2066 6f72 6d73       Unary forms\n-0001c630: 2e20 2020 2020 2020 2020 2028 6c69 6e65  .          (line\n-0001c640: 2032 3129 0a2a 206c 616e 6775 6167 653a   21).* language:\n-0001c650: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c660: 2020 2020 2020 2020 2020 2020 2020 4c61                La\n-0001c670: 6e67 7561 6765 2e20 2020 2020 2020 2020  nguage.         \n-0001c680: 2020 2020 286c 696e 6520 2036 290a 2a20      (line  6).* \n-0001c690: 6c61 7465 783a 2020 2020 2020 2020 2020  latex:          \n+0001c620: 2020 2020 2020 2020 2020 2055 6e61 7279             Unary\n+0001c630: 2066 6f72 6d73 2e20 2020 2020 2020 2020   forms.         \n+0001c640: 2028 6c69 6e65 2032 3129 0a2a 206c 616e   (line 21).* lan\n+0001c650: 6775 6167 653a 2020 2020 2020 2020 2020  guage:          \n+0001c660: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c670: 2020 2020 4c61 6e67 7561 6765 2e20 2020      Language.   \n+0001c680: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+0001c690: 2036 290a 2a20 6c61 7465 783a 2020 2020   6).* latex:    \n 0001c6a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c6b0: 2020 2020 2020 204c 616e 6775 6167 652e         Language.\n-0001c6c0: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n-0001c6d0: 6e65 2031 3729 0a2a 206c 6179 3a20 2020  ne 17).* lay:   \n-0001c6e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c6b0: 2020 2020 2020 2020 2020 2020 204c 616e               Lan\n+0001c6c0: 6775 6167 652e 2020 2020 2020 2020 2020  guage.          \n+0001c6d0: 2020 2028 6c69 6e65 2031 3729 0a2a 206c     (line 17).* l\n+0001c6e0: 6179 3a20 2020 2020 2020 2020 2020 2020  ay:             \n 0001c6f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c700: 5370 6563 6961 6c20 6f62 6a65 6374 732e  Special objects.\n-0001c710: 2020 2020 2020 286c 696e 6520 3438 290a        (line 48).\n-0001c720: 2a20 6c61 7920 3c31 3e3a 2020 2020 2020  * lay <1>:      \n+0001c700: 2020 2020 2020 5370 6563 6961 6c20 6f62        Special ob\n+0001c710: 6a65 6374 732e 2020 2020 2020 286c 696e  jects.      (lin\n+0001c720: 6520 3438 290a 2a20 6c61 7920 3c31 3e3a  e 48).* lay <1>:\n 0001c730: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c740: 2020 2020 2020 2020 2054 696b 5a2f 5047           TikZ/PG\n-0001c750: 4620 7573 6572 2d64 6566 696e 6564 2073  F user-defined s\n-0001c760: 7479 6c65 732e 0a20 2020 2020 2020 2020  tyles..         \n+0001c740: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n+0001c750: 696b 5a2f 5047 4620 7573 6572 2d64 6566  ikZ/PGF user-def\n+0001c760: 696e 6564 2073 7479 6c65 732e 0a20 2020  ined styles..   \n 0001c770: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001c780: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001c790: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c7a0: 2020 2020 2020 286c 696e 6520 3336 290a        (line 36).\n-0001c7b0: 2a20 6c61 7920 3c32 3e3a 2020 2020 2020  * lay <2>:      \n+0001c7a0: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+0001c7b0: 6520 3336 290a 2a20 6c61 7920 3c32 3e3a  e 36).* lay <2>:\n 0001c7c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c7d0: 2020 2020 2020 2020 2041 2074 6563 686e           A techn\n-0001c7e0: 6963 616c 2064 7261 7769 6e67 2e20 2028  ical drawing.  (\n-0001c7f0: 6c69 6e65 2032 3629 0a2a 206c 6179 203c  line 26).* lay <\n-0001c800: 333e 3a20 2020 2020 2020 2020 2020 2020  3>:             \n+0001c7d0: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+0001c7e0: 2074 6563 686e 6963 616c 2064 7261 7769   technical drawi\n+0001c7f0: 6e67 2e20 2028 6c69 6e65 2032 3629 0a2a  ng.  (line 26).*\n+0001c800: 206c 6179 203c 333e 3a20 2020 2020 2020   lay <3>:       \n 0001c810: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c820: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n-0001c830: 6177 696e 672e 2020 286c 696e 6520 3236  awing.  (line 26\n-0001c840: 290a 2a20 6c61 7920 3c34 3e3a 2020 2020  ).* lay <4>:    \n-0001c850: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c860: 2020 2020 2020 2020 2020 2041 2074 6563             A tec\n-0001c870: 686e 6963 616c 2064 7261 7769 6e67 2e20  hnical drawing. \n-0001c880: 2028 6c69 6e65 2039 3529 0a2a 206c 6179   (line 95).* lay\n-0001c890: 203c 353e 3a20 2020 2020 2020 2020 2020   <5>:           \n+0001c820: 2020 2020 2020 2020 4120 7465 6368 6e69          A techni\n+0001c830: 6361 6c20 6472 6177 696e 672e 2020 286c  cal drawing.  (l\n+0001c840: 696e 6520 3236 290a 2a20 6c61 7920 3c34  ine 26).* lay <4\n+0001c850: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001c860: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c870: 2041 2074 6563 686e 6963 616c 2064 7261   A technical dra\n+0001c880: 7769 6e67 2e20 2028 6c69 6e65 2039 3529  wing.  (line 95)\n+0001c890: 0a2a 206c 6179 203c 353e 3a20 2020 2020  .* lay <5>:     \n 0001c8a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c8b0: 2020 2020 496e 7465 726e 616c 206f 7074      Internal opt\n-0001c8c0: 696f 6e73 2e20 2020 2020 286c 696e 6520  ions.     (line \n-0001c8d0: 2037 290a 2a20 6c61 7920 3c36 3e3a 2020   7).* lay <6>:  \n-0001c8e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c8f0: 2020 2020 2020 2020 2020 2020 2053 7065               Spe\n-0001c900: 6369 616c 732e 2020 2020 2020 2020 2020  cials.          \n-0001c910: 2020 2028 6c69 6e65 2034 3229 0a2a 206c     (line 42).* l\n-0001c920: 6179 203c 373e 3a20 2020 2020 2020 2020  ay <7>:         \n+0001c8b0: 2020 2020 2020 2020 2020 496e 7465 726e            Intern\n+0001c8c0: 616c 206f 7074 696f 6e73 2e20 2020 2020  al options.     \n+0001c8d0: 286c 696e 6520 2037 290a 2a20 6c61 7920  (line  7).* lay \n+0001c8e0: 3c36 3e3a 2020 2020 2020 2020 2020 2020  <6>:            \n+0001c8f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c900: 2020 2053 7065 6369 616c 732e 2020 2020     Specials.    \n+0001c910: 2020 2020 2020 2020 2028 6c69 6e65 2034           (line 4\n+0001c920: 3229 0a2a 206c 6179 203c 373e 3a20 2020  2).* lay <7>:   \n 0001c930: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c940: 2020 2020 2020 476c 6f62 616c 206f 7074        Global opt\n-0001c950: 696f 6e73 2e20 2020 2020 2020 286c 696e  ions.       (lin\n-0001c960: 6520 3133 290a 2a20 6c69 6e65 3a20 2020  e 13).* line:   \n-0001c970: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c980: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n-0001c990: 7261 7769 6e67 206f 7074 696f 6e73 2e20  rawing options. \n-0001c9a0: 2020 2020 2028 6c69 6e65 2020 3729 0a2a       (line  7).*\n-0001c9b0: 206c 696e 6520 3c31 3e3a 2020 2020 2020   line <1>:      \n+0001c940: 2020 2020 2020 2020 2020 2020 476c 6f62              Glob\n+0001c950: 616c 206f 7074 696f 6e73 2e20 2020 2020  al options.     \n+0001c960: 2020 286c 696e 6520 3133 290a 2a20 6c69    (line 13).* li\n+0001c970: 6e65 3a20 2020 2020 2020 2020 2020 2020  ne:             \n+0001c980: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c990: 2020 2020 2044 7261 7769 6e67 206f 7074       Drawing opt\n+0001c9a0: 696f 6e73 2e20 2020 2020 2028 6c69 6e65  ions.      (line\n+0001c9b0: 2020 3729 0a2a 206c 696e 6520 3c31 3e3a    7).* line <1>:\n 0001c9c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c9d0: 2020 2020 2020 2020 4f62 6a65 6374 2074          Object t\n-0001c9e0: 7261 6e73 666f 726d 732e 2020 2020 286c  ransforms.    (l\n-0001c9f0: 696e 6520 3130 290a 2a20 6c69 6e65 203c  ine 10).* line <\n-0001ca00: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n+0001c9d0: 2020 2020 2020 2020 2020 2020 2020 4f62                Ob\n+0001c9e0: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n+0001c9f0: 2020 2020 286c 696e 6520 3130 290a 2a20      (line 10).* \n+0001ca00: 6c69 6e65 203c 323e 3a20 2020 2020 2020  line <2>:       \n 0001ca10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ca20: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n-0001ca30: 2077 6974 6820 636c 6f73 7572 652e 0a20   with closure.. \n-0001ca40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ca20: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n+0001ca30: 7377 6565 7073 2077 6974 6820 636c 6f73  sweeps with clos\n+0001ca40: 7572 652e 0a20 2020 2020 2020 2020 2020  ure..           \n 0001ca50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ca60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ca70: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-0001ca80: 696e 6520 3130 290a 2a20 6c69 6e65 203c  ine 10).* line <\n-0001ca90: 333e 3a20 2020 2020 2020 2020 2020 2020  3>:             \n+0001ca70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ca80: 2020 2020 286c 696e 6520 3130 290a 2a20      (line 10).* \n+0001ca90: 6c69 6e65 203c 333e 3a20 2020 2020 2020  line <3>:       \n 0001caa0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cab0: 2041 6666 696e 6520 6172 6974 686d 6574   Affine arithmet\n-0001cac0: 6963 2e20 2020 2028 6c69 6e65 2031 3129  ic.    (line 11)\n-0001cad0: 0a2a 206c 696e 6520 3c34 3e3a 2020 2020  .* line <4>:    \n-0001cae0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001caf0: 2020 2020 2020 2020 2020 4c69 6e65 732e            Lines.\n-0001cb00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cb10: 286c 696e 6520 2036 290a 2a20 6c69 6e65  (line  6).* line\n-0001cb20: 203c 353e 3a20 2020 2020 2020 2020 2020   <5>:           \n+0001cab0: 2020 2020 2020 2041 6666 696e 6520 6172         Affine ar\n+0001cac0: 6974 686d 6574 6963 2e20 2020 2028 6c69  ithmetic.    (li\n+0001cad0: 6e65 2031 3129 0a2a 206c 696e 6520 3c34  ne 11).* line <4\n+0001cae0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001caf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001cb00: 4c69 6e65 732e 2020 2020 2020 2020 2020  Lines.          \n+0001cb10: 2020 2020 2020 286c 696e 6520 2036 290a        (line  6).\n+0001cb20: 2a20 6c69 6e65 203c 353e 3a20 2020 2020  * line <5>:     \n 0001cb30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cb40: 2020 2053 7765 7074 2062 6c6f 636b 732e     Swept blocks.\n-0001cb50: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-0001cb60: 3729 0a2a 206c 696e 6520 3c36 3e3a 2020  7).* line <6>:  \n-0001cb70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cb80: 2020 2020 2020 2020 2020 2020 4f76 6572              Over\n-0001cb90: 7669 6577 2e20 2020 2020 2020 2020 2020  view.           \n-0001cba0: 2020 286c 696e 6520 3639 290a 2a20 6c69    (line 69).* li\n-0001cbb0: 6e65 203c 373e 3a20 2020 2020 2020 2020  ne <7>:         \n+0001cb40: 2020 2020 2020 2020 2053 7765 7074 2062           Swept b\n+0001cb50: 6c6f 636b 732e 2020 2020 2020 2020 2028  locks.         (\n+0001cb60: 6c69 6e65 2020 3729 0a2a 206c 696e 6520  line  7).* line \n+0001cb70: 3c36 3e3a 2020 2020 2020 2020 2020 2020  <6>:            \n+0001cb80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001cb90: 2020 4f76 6572 7669 6577 2e20 2020 2020    Overview.     \n+0001cba0: 2020 2020 2020 2020 286c 696e 6520 3639          (line 69\n+0001cbb0: 290a 2a20 6c69 6e65 203c 373e 3a20 2020  ).* line <7>:   \n 0001cbc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cbd0: 2020 2020 2041 2074 6563 686e 6963 616c       A technical\n-0001cbe0: 2064 7261 7769 6e67 2e20 2028 6c69 6e65   drawing.  (line\n-0001cbf0: 2032 3029 0a2a 206c 696e 6520 3c38 3e3a   20).* line <8>:\n-0001cc00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cc10: 2020 2020 2020 2020 2020 2020 2020 4120                A \n-0001cc20: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n-0001cc30: 672e 2020 286c 696e 6520 3236 290a 2a20  g.  (line 26).* \n-0001cc40: 6c69 6e65 203c 393e 3a20 2020 2020 2020  line <9>:       \n+0001cbd0: 2020 2020 2020 2020 2020 2041 2074 6563             A tec\n+0001cbe0: 686e 6963 616c 2064 7261 7769 6e67 2e20  hnical drawing. \n+0001cbf0: 2028 6c69 6e65 2032 3029 0a2a 206c 696e   (line 20).* lin\n+0001cc00: 6520 3c38 3e3a 2020 2020 2020 2020 2020  e <8>:          \n+0001cc10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001cc20: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n+0001cc30: 6472 6177 696e 672e 2020 286c 696e 6520  drawing.  (line \n+0001cc40: 3236 290a 2a20 6c69 6e65 203c 393e 3a20  26).* line <9>: \n 0001cc50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cc60: 2020 2020 2020 2041 2074 6563 686e 6963         A technic\n-0001cc70: 616c 2064 7261 7769 6e67 2e20 2028 6c69  al drawing.  (li\n-0001cc80: 6e65 2034 3129 0a2a 206c 696e 6520 3c31  ne 41).* line <1\n-0001cc90: 303e 3a20 2020 2020 2020 2020 2020 2020  0>:             \n+0001cc60: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n+0001cc70: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n+0001cc80: 2e20 2028 6c69 6e65 2034 3129 0a2a 206c  .  (line 41).* l\n+0001cc90: 696e 6520 3c31 303e 3a20 2020 2020 2020  ine <10>:       \n 0001cca0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ccb0: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n-0001ccc0: 696e 672e 2020 286c 696e 6520 3638 290a  ing.  (line 68).\n-0001ccd0: 2a20 6c69 6e65 203c 3131 3e3a 2020 2020  * line <11>:    \n-0001cce0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ccf0: 2020 2020 2020 2020 2041 2068 6965 7261           A hiera\n-0001cd00: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028  rchical model. (\n-0001cd10: 6c69 6e65 2031 3029 0a2a 206c 696e 6520  line 10).* line \n-0001cd20: 7374 796c 653a 2020 2020 2020 2020 2020  style:          \n+0001ccb0: 2020 2020 2020 4120 7465 6368 6e69 6361        A technica\n+0001ccc0: 6c20 6472 6177 696e 672e 2020 286c 696e  l drawing.  (lin\n+0001ccd0: 6520 3638 290a 2a20 6c69 6e65 203c 3131  e 68).* line <11\n+0001cce0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001ccf0: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+0001cd00: 2068 6965 7261 7263 6869 6361 6c20 6d6f   hierarchical mo\n+0001cd10: 6465 6c2e 2028 6c69 6e65 2031 3029 0a2a  del. (line 10).*\n+0001cd20: 206c 696e 6520 7374 796c 653a 2020 2020   line style:    \n 0001cd30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cd40: 2020 5469 6b5a 2f50 4746 2075 7365 722d    TikZ/PGF user-\n-0001cd50: 6465 6669 6e65 6420 7374 796c 6573 2e0a  defined styles..\n-0001cd60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001cd40: 2020 2020 2020 2020 5469 6b5a 2f50 4746          TikZ/PGF\n+0001cd50: 2075 7365 722d 6465 6669 6e65 6420 7374   user-defined st\n+0001cd60: 796c 6573 2e0a 2020 2020 2020 2020 2020  yles..          \n 0001cd70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001cd80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cd90: 2020 2020 2020 2020 2020 2020 2020 2028                 (\n-0001cda0: 6c69 6e65 2032 3529 0a2a 206c 696e 6563  line 25).* linec\n-0001cdb0: 6f6c 6f72 3a20 2020 2020 2020 2020 2020  olor:           \n+0001cd90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001cda0: 2020 2020 2028 6c69 6e65 2032 3529 0a2a       (line 25).*\n+0001cdb0: 206c 696e 6563 6f6c 6f72 3a20 2020 2020   linecolor:     \n 0001cdc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cdd0: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n-0001cde0: 726d 732e 2020 2020 286c 696e 6520 3130  rms.    (line 10\n-0001cdf0: 290a 2a20 6c69 6e65 636f 6c6f 7220 3c31  ).* linecolor <1\n-0001ce00: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001ce10: 2020 2020 2020 2020 2020 2046 7261 6d65             Frame\n-0001ce20: 2e20 2020 2020 2020 2020 2020 2020 2020  .               \n-0001ce30: 2028 6c69 6e65 2031 3029 0a2a 206c 696e   (line 10).* lin\n-0001ce40: 6563 6f6c 6f72 203c 323e 3a20 2020 2020  ecolor <2>:     \n-0001ce50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ce60: 2020 2020 4f76 6572 7669 6577 2e20 2020      Overview.   \n-0001ce70: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-0001ce80: 3639 290a 2a20 6c69 6e65 7374 796c 653a  69).* linestyle:\n-0001ce90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cea0: 2020 2020 2020 2020 2020 2020 2046 7261               Fra\n-0001ceb0: 6d65 2e20 2020 2020 2020 2020 2020 2020  me.             \n-0001cec0: 2020 2028 6c69 6e65 2031 3029 0a2a 206c     (line 10).* l\n-0001ced0: 696e 6573 7479 6c65 203c 313e 3a20 2020  inestyle <1>:   \n-0001cee0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cef0: 2020 2020 2020 4f76 6572 7669 6577 2e20        Overview. \n-0001cf00: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-0001cf10: 6520 3639 290a 2a20 6c69 6e65 7374 796c  e 69).* linestyl\n-0001cf20: 6520 3c32 3e3a 2020 2020 2020 2020 2020  e <2>:          \n-0001cf30: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n-0001cf40: 2074 6563 686e 6963 616c 2064 7261 7769   technical drawi\n-0001cf50: 6e67 2e20 2028 6c69 6e65 2032 3629 0a2a  ng.  (line 26).*\n-0001cf60: 206c 696e 6573 7479 6c65 203c 333e 3a20   linestyle <3>: \n-0001cf70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cf80: 2020 2020 2020 2020 4275 6773 2061 6e64          Bugs and\n-0001cf90: 2061 6e6f 6d61 6c69 6573 2e20 2020 286c   anomalies.   (l\n-0001cfa0: 696e 6520 2037 290a 2a20 6c69 6e65 7769  ine  7).* linewi\n-0001cfb0: 6474 683a 2020 2020 2020 2020 2020 2020  dth:            \n+0001cdd0: 2020 2020 2020 2020 4f62 6a65 6374 2074          Object t\n+0001cde0: 7261 6e73 666f 726d 732e 2020 2020 286c  ransforms.    (l\n+0001cdf0: 696e 6520 3130 290a 2a20 6c69 6e65 636f  ine 10).* lineco\n+0001ce00: 6c6f 7220 3c31 3e3a 2020 2020 2020 2020  lor <1>:        \n+0001ce10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ce20: 2046 7261 6d65 2e20 2020 2020 2020 2020   Frame.         \n+0001ce30: 2020 2020 2020 2028 6c69 6e65 2031 3029         (line 10)\n+0001ce40: 0a2a 206c 696e 6563 6f6c 6f72 203c 323e  .* linecolor <2>\n+0001ce50: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001ce60: 2020 2020 2020 2020 2020 4f76 6572 7669            Overvi\n+0001ce70: 6577 2e20 2020 2020 2020 2020 2020 2020  ew.             \n+0001ce80: 286c 696e 6520 3639 290a 2a20 6c69 6e65  (line 69).* line\n+0001ce90: 7374 796c 653a 2020 2020 2020 2020 2020  style:          \n+0001cea0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ceb0: 2020 2046 7261 6d65 2e20 2020 2020 2020     Frame.       \n+0001cec0: 2020 2020 2020 2020 2028 6c69 6e65 2031           (line 1\n+0001ced0: 3029 0a2a 206c 696e 6573 7479 6c65 203c  0).* linestyle <\n+0001cee0: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+0001cef0: 2020 2020 2020 2020 2020 2020 4f76 6572              Over\n+0001cf00: 7669 6577 2e20 2020 2020 2020 2020 2020  view.           \n+0001cf10: 2020 286c 696e 6520 3639 290a 2a20 6c69    (line 69).* li\n+0001cf20: 6e65 7374 796c 6520 3c32 3e3a 2020 2020  nestyle <2>:    \n+0001cf30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001cf40: 2020 2020 2041 2074 6563 686e 6963 616c       A technical\n+0001cf50: 2064 7261 7769 6e67 2e20 2028 6c69 6e65   drawing.  (line\n+0001cf60: 2032 3629 0a2a 206c 696e 6573 7479 6c65   26).* linestyle\n+0001cf70: 203c 333e 3a20 2020 2020 2020 2020 2020   <3>:           \n+0001cf80: 2020 2020 2020 2020 2020 2020 2020 4275                Bu\n+0001cf90: 6773 2061 6e64 2061 6e6f 6d61 6c69 6573  gs and anomalies\n+0001cfa0: 2e20 2020 286c 696e 6520 2037 290a 2a20  .   (line  7).* \n+0001cfb0: 6c69 6e65 7769 6474 683a 2020 2020 2020  linewidth:      \n 0001cfc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cfd0: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n-0001cfe0: 2e20 2020 2020 2028 6c69 6e65 2020 3929  .      (line  9)\n-0001cff0: 0a2a 206c 696e 6577 6964 7468 203c 313e  .* linewidth <1>\n-0001d000: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001d010: 2020 2020 2020 2020 2020 4672 616d 652e            Frame.\n-0001d020: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d030: 286c 696e 6520 3130 290a 2a20 6c69 6e65  (line 10).* line\n-0001d040: 7769 6474 6820 3c32 3e3a 2020 2020 2020  width <2>:      \n+0001cfd0: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n+0001cfe0: 7377 6565 7073 2e20 2020 2020 2028 6c69  sweeps.      (li\n+0001cff0: 6e65 2020 3929 0a2a 206c 696e 6577 6964  ne  9).* linewid\n+0001d000: 7468 203c 313e 3a20 2020 2020 2020 2020  th <1>:         \n+0001d010: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d020: 4672 616d 652e 2020 2020 2020 2020 2020  Frame.          \n+0001d030: 2020 2020 2020 286c 696e 6520 3130 290a        (line 10).\n+0001d040: 2a20 6c69 6e65 7769 6474 6820 3c32 3e3a  * linewidth <2>:\n 0001d050: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d060: 2020 204f 7665 7276 6965 772e 2020 2020     Overview.    \n-0001d070: 2020 2020 2020 2020 2028 6c69 6e65 2036           (line 6\n-0001d080: 3929 0a2a 206c 696e 6577 6964 7468 203c  9).* linewidth <\n-0001d090: 333e 3a20 2020 2020 2020 2020 2020 2020  3>:             \n-0001d0a0: 2020 2020 2020 2020 2020 2020 4120 7465              A te\n-0001d0b0: 6368 6e69 6361 6c20 6472 6177 696e 672e  chnical drawing.\n-0001d0c0: 2020 286c 696e 6520 3236 290a 2a20 6f70    (line 26).* op\n-0001d0d0: 6163 6974 793a 2020 2020 2020 2020 2020  acity:          \n+0001d060: 2020 2020 2020 2020 204f 7665 7276 6965           Overvie\n+0001d070: 772e 2020 2020 2020 2020 2020 2020 2028  w.             (\n+0001d080: 6c69 6e65 2036 3929 0a2a 206c 696e 6577  line 69).* linew\n+0001d090: 6964 7468 203c 333e 3a20 2020 2020 2020  idth <3>:       \n+0001d0a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d0b0: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n+0001d0c0: 6177 696e 672e 2020 286c 696e 6520 3236  awing.  (line 26\n+0001d0d0: 290a 2a20 6f70 6163 6974 793a 2020 2020  ).* opacity:    \n 0001d0e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d0f0: 2020 2020 2054 7261 6e73 7061 7265 6e63       Transparenc\n-0001d100: 792e 2020 2020 2020 2020 2028 6c69 6e65  y.         (line\n-0001d110: 2031 3029 0a2a 2070 6572 7370 6563 7469   10).* perspecti\n-0001d120: 7665 3a20 2020 2020 2020 2020 2020 2020  ve:             \n-0001d130: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n-0001d140: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n-0001d150: 2e20 2020 286c 696e 6520 3231 290a 2a20  .   (line 21).* \n-0001d160: 7069 6374 7572 6562 6f78 3a20 2020 2020  picturebox:     \n-0001d170: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d180: 2020 2020 2020 2050 6963 7475 7265 2062         Picture b\n-0001d190: 6f78 2e20 2020 2020 2020 2020 2028 6c69  ox.          (li\n-0001d1a0: 6e65 2020 3629 0a2a 2070 6f69 6e74 206c  ne  6).* point l\n-0001d1b0: 6973 743a 2020 2020 2020 2020 2020 2020  ist:            \n+0001d0f0: 2020 2020 2020 2020 2020 2054 7261 6e73             Trans\n+0001d100: 7061 7265 6e63 792e 2020 2020 2020 2020  parency.        \n+0001d110: 2028 6c69 6e65 2031 3029 0a2a 2070 6572   (line 10).* per\n+0001d120: 7370 6563 7469 7665 3a20 2020 2020 2020  spective:       \n+0001d130: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d140: 2020 2020 5472 616e 7366 6f72 6d20 6c69      Transform li\n+0001d150: 7465 7261 6c73 2e20 2020 286c 696e 6520  terals.   (line \n+0001d160: 3231 290a 2a20 7069 6374 7572 6562 6f78  21).* picturebox\n+0001d170: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001d180: 2020 2020 2020 2020 2020 2020 2050 6963               Pic\n+0001d190: 7475 7265 2062 6f78 2e20 2020 2020 2020  ture box.       \n+0001d1a0: 2020 2028 6c69 6e65 2020 3629 0a2a 2070     (line  6).* p\n+0001d1b0: 6f69 6e74 206c 6973 743a 2020 2020 2020  oint list:      \n 0001d1c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d1d0: 496e 7465 726e 616c 206f 7074 696f 6e73  Internal options\n-0001d1e0: 2e20 2020 2020 286c 696e 6520 3234 290a  .     (line 24).\n-0001d1f0: 2a20 706f 6c79 676f 6e3a 2020 2020 2020  * polygon:      \n+0001d1d0: 2020 2020 2020 496e 7465 726e 616c 206f        Internal o\n+0001d1e0: 7074 696f 6e73 2e20 2020 2020 286c 696e  ptions.     (lin\n+0001d1f0: 6520 3234 290a 2a20 706f 6c79 676f 6e3a  e 24).* polygon:\n 0001d200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d210: 2020 2020 2020 2020 2048 656c 6c6f 2077           Hello w\n-0001d220: 6f72 6c64 2e20 2020 2020 2020 2020 2028  orld.          (\n-0001d230: 6c69 6e65 2033 3829 0a2a 2070 6f6c 7967  line 38).* polyg\n-0001d240: 6f6e 203c 313e 3a20 2020 2020 2020 2020  on <1>:         \n+0001d210: 2020 2020 2020 2020 2020 2020 2020 2048                 H\n+0001d220: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020  ello world.     \n+0001d230: 2020 2020 2028 6c69 6e65 2033 3829 0a2a       (line 38).*\n+0001d240: 2070 6f6c 7967 6f6e 203c 313e 3a20 2020   polygon <1>:   \n 0001d250: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d260: 2020 4472 6177 696e 6720 6120 736f 6c69    Drawing a soli\n-0001d270: 642e 2020 2020 2020 286c 696e 6520 2039  d.      (line  9\n-0001d280: 290a 2a20 706f 6c79 676f 6e20 3c32 3e3a  ).* polygon <2>:\n-0001d290: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d2a0: 2020 2020 2020 2020 2020 204f 626a 6563             Objec\n-0001d2b0: 7420 7472 616e 7366 6f72 6d73 2e20 2020  t transforms.   \n-0001d2c0: 2028 6c69 6e65 2031 3029 0a2a 2070 6f6c   (line 10).* pol\n-0001d2d0: 7967 6f6e 203c 333e 3a20 2020 2020 2020  ygon <3>:       \n+0001d260: 2020 2020 2020 2020 4472 6177 696e 6720          Drawing \n+0001d270: 6120 736f 6c69 642e 2020 2020 2020 286c  a solid.      (l\n+0001d280: 696e 6520 2039 290a 2a20 706f 6c79 676f  ine  9).* polygo\n+0001d290: 6e20 3c32 3e3a 2020 2020 2020 2020 2020  n <2>:          \n+0001d2a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d2b0: 204f 626a 6563 7420 7472 616e 7366 6f72   Object transfor\n+0001d2c0: 6d73 2e20 2020 2028 6c69 6e65 2031 3029  ms.    (line 10)\n+0001d2d0: 0a2a 2070 6f6c 7967 6f6e 203c 333e 3a20  .* polygon <3>: \n 0001d2e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d2f0: 2020 2020 4166 6669 6e65 2061 7269 7468      Affine arith\n-0001d300: 6d65 7469 632e 2020 2020 286c 696e 6520  metic.    (line \n-0001d310: 3131 290a 2a20 706f 6c79 676f 6e20 3c34  11).* polygon <4\n-0001d320: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001d330: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n-0001d340: 7967 6f6e 732e 2020 2020 2020 2020 2020  ygons.          \n-0001d350: 2020 2028 6c69 6e65 2020 3629 0a2a 2070     (line  6).* p\n-0001d360: 6f6c 7967 6f6e 203c 353e 3a20 2020 2020  olygon <5>:     \n-0001d370: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d380: 2020 2020 2020 5377 6570 7420 626c 6f63        Swept bloc\n-0001d390: 6b73 2e20 2020 2020 2020 2020 286c 696e  ks.         (lin\n-0001d3a0: 6520 2037 290a 2a20 706f 6c79 676f 6e20  e  7).* polygon \n-0001d3b0: 3c36 3e3a 2020 2020 2020 2020 2020 2020  <6>:            \n-0001d3c0: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n-0001d3d0: 7665 7276 6965 772e 2020 2020 2020 2020  verview.        \n-0001d3e0: 2020 2020 2028 6c69 6e65 2033 3729 0a2a       (line 37).*\n-0001d3f0: 2070 726f 6a65 6374 3a20 2020 2020 2020   project:       \n+0001d2f0: 2020 2020 2020 2020 2020 4166 6669 6e65            Affine\n+0001d300: 2061 7269 7468 6d65 7469 632e 2020 2020   arithmetic.    \n+0001d310: 286c 696e 6520 3131 290a 2a20 706f 6c79  (line 11).* poly\n+0001d320: 676f 6e20 3c34 3e3a 2020 2020 2020 2020  gon <4>:        \n+0001d330: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d340: 2020 2050 6f6c 7967 6f6e 732e 2020 2020     Polygons.    \n+0001d350: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+0001d360: 3629 0a2a 2070 6f6c 7967 6f6e 203c 353e  6).* polygon <5>\n+0001d370: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001d380: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n+0001d390: 7420 626c 6f63 6b73 2e20 2020 2020 2020  t blocks.       \n+0001d3a0: 2020 286c 696e 6520 2037 290a 2a20 706f    (line  7).* po\n+0001d3b0: 6c79 676f 6e20 3c36 3e3a 2020 2020 2020  lygon <6>:      \n+0001d3c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d3d0: 2020 2020 204f 7665 7276 6965 772e 2020       Overview.  \n+0001d3e0: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001d3f0: 2033 3729 0a2a 2070 726f 6a65 6374 3a20   37).* project: \n 0001d400: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d410: 2020 2020 2020 2020 5472 616e 7366 6f72          Transfor\n-0001d420: 6d20 6c69 7465 7261 6c73 2e20 2020 286c  m literals.   (l\n-0001d430: 696e 6520 3138 290a 2a20 7072 6f6a 6563  ine 18).* projec\n-0001d440: 7420 3c31 3e3a 2020 2020 2020 2020 2020  t <1>:          \n+0001d410: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n+0001d420: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n+0001d430: 2e20 2020 286c 696e 6520 3138 290a 2a20  .   (line 18).* \n+0001d440: 7072 6f6a 6563 7420 3c31 3e3a 2020 2020  project <1>:    \n 0001d450: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d460: 2054 7261 6e73 666f 726d 206c 6974 6572   Transform liter\n-0001d470: 616c 732e 2020 2028 6c69 6e65 2031 3929  als.   (line 19)\n-0001d480: 0a2a 2070 726f 6a65 6374 203c 323e 3a20  .* project <2>: \n-0001d490: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d4a0: 2020 2020 2020 2020 2020 5472 616e 7366            Transf\n-0001d4b0: 6f72 6d20 6c69 7465 7261 6c73 2e20 2020  orm literals.   \n-0001d4c0: 286c 696e 6520 3437 290a 2a20 7073 7472  (line 47).* pstr\n-0001d4d0: 6963 6b73 3a20 2020 2020 2020 2020 2020  icks:           \n+0001d460: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n+0001d470: 206c 6974 6572 616c 732e 2020 2028 6c69   literals.   (li\n+0001d480: 6e65 2031 3929 0a2a 2070 726f 6a65 6374  ne 19).* project\n+0001d490: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n+0001d4a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d4b0: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n+0001d4c0: 6c73 2e20 2020 286c 696e 6520 3437 290a  ls.   (line 47).\n+0001d4d0: 2a20 7073 7472 6963 6b73 3a20 2020 2020  * pstricks:     \n 0001d4e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d4f0: 2020 204c 616e 6775 6167 652e 2020 2020     Language.    \n-0001d500: 2020 2020 2020 2020 2028 6c69 6e65 2031           (line 1\n-0001d510: 3029 0a2a 2070 7574 3a20 2020 2020 2020  0).* put:       \n+0001d4f0: 2020 2020 2020 2020 204c 616e 6775 6167           Languag\n+0001d500: 652e 2020 2020 2020 2020 2020 2020 2028  e.             (\n+0001d510: 6c69 6e65 2031 3029 0a2a 2070 7574 3a20  line 10).* put: \n 0001d520: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d530: 2020 2020 2020 2020 2020 2020 4f62 6a65              Obje\n-0001d540: 6374 2074 7261 6e73 666f 726d 732e 2020  ct transforms.  \n-0001d550: 2020 286c 696e 6520 3130 290a 2a20 7075    (line 10).* pu\n-0001d560: 7420 3c31 3e3a 2020 2020 2020 2020 2020  t <1>:          \n+0001d530: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d540: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n+0001d550: 726d 732e 2020 2020 286c 696e 6520 3130  rms.    (line 10\n+0001d560: 290a 2a20 7075 7420 3c31 3e3a 2020 2020  ).* put <1>:    \n 0001d570: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d580: 2020 2020 204e 6573 7465 6420 7377 6565       Nested swee\n-0001d590: 7073 2e20 2020 2020 2020 2028 6c69 6e65  ps.        (line\n-0001d5a0: 2032 3529 0a2a 2070 7574 203c 323e 3a20   25).* put <2>: \n-0001d5b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d5c0: 2020 2020 2020 2020 2020 2020 2020 5075                Pu\n-0001d5d0: 7473 2e20 2020 2020 2020 2020 2020 2020  ts.             \n-0001d5e0: 2020 2020 286c 696e 6520 2036 290a 2a20      (line  6).* \n-0001d5f0: 7075 7420 3c33 3e3a 2020 2020 2020 2020  put <3>:        \n+0001d580: 2020 2020 2020 2020 2020 204e 6573 7465             Neste\n+0001d590: 6420 7377 6565 7073 2e20 2020 2020 2020  d sweeps.       \n+0001d5a0: 2028 6c69 6e65 2032 3529 0a2a 2070 7574   (line 25).* put\n+0001d5b0: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n+0001d5c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d5d0: 2020 2020 5075 7473 2e20 2020 2020 2020      Puts.       \n+0001d5e0: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+0001d5f0: 2036 290a 2a20 7075 7420 3c33 3e3a 2020   6).* put <3>:  \n 0001d600: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d610: 2020 2020 2020 2041 2068 6965 7261 7263         A hierarc\n-0001d620: 6869 6361 6c20 6d6f 6465 6c2e 2028 6c69  hical model. (li\n-0001d630: 6e65 2033 3229 0a2a 2072 6570 6561 743a  ne 32).* repeat:\n-0001d640: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d610: 2020 2020 2020 2020 2020 2020 2041 2068               A h\n+0001d620: 6965 7261 7263 6869 6361 6c20 6d6f 6465  ierarchical mode\n+0001d630: 6c2e 2028 6c69 6e65 2033 3229 0a2a 2072  l. (line 32).* r\n+0001d640: 6570 6561 743a 2020 2020 2020 2020 2020  epeat:          \n 0001d650: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d660: 5265 7065 6174 6564 206f 626a 6563 7473  Repeated objects\n-0001d670: 2e20 2020 2020 286c 696e 6520 2038 290a  .     (line  8).\n-0001d680: 2a20 7265 7065 6174 203c 313e 3a20 2020  * repeat <1>:   \n-0001d690: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d6a0: 2020 2020 2020 2020 204e 6573 7465 6420           Nested \n-0001d6b0: 7377 6565 7073 2e20 2020 2020 2020 2028  sweeps.        (\n-0001d6c0: 6c69 6e65 2032 3529 0a2a 2072 6570 6561  line 25).* repea\n-0001d6d0: 7420 3c32 3e3a 2020 2020 2020 2020 2020  t <2>:          \n+0001d660: 2020 2020 2020 5265 7065 6174 6564 206f        Repeated o\n+0001d670: 626a 6563 7473 2e20 2020 2020 286c 696e  bjects.     (lin\n+0001d680: 6520 2038 290a 2a20 7265 7065 6174 203c  e  8).* repeat <\n+0001d690: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+0001d6a0: 2020 2020 2020 2020 2020 2020 2020 204e                 N\n+0001d6b0: 6573 7465 6420 7377 6565 7073 2e20 2020  ested sweeps.   \n+0001d6c0: 2020 2020 2028 6c69 6e65 2032 3529 0a2a       (line 25).*\n+0001d6d0: 2072 6570 6561 7420 3c32 3e3a 2020 2020   repeat <2>:    \n 0001d6e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d6f0: 2020 506f 6c79 6c69 6e65 2073 7765 6570    Polyline sweep\n-0001d700: 7320 7769 7468 2063 6c6f 7375 7265 2e0a  s with closure..\n-0001d710: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d6f0: 2020 2020 2020 2020 506f 6c79 6c69 6e65          Polyline\n+0001d700: 2073 7765 6570 7320 7769 7468 2063 6c6f   sweeps with clo\n+0001d710: 7375 7265 2e0a 2020 2020 2020 2020 2020  sure..          \n 0001d720: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001d730: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d740: 2020 2020 2020 2020 2020 2020 2020 2028                 (\n-0001d750: 6c69 6e65 2031 3029 0a2a 2072 6570 6561  line 10).* repea\n-0001d760: 7420 3c33 3e3a 2020 2020 2020 2020 2020  t <3>:          \n+0001d740: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d750: 2020 2020 2028 6c69 6e65 2031 3029 0a2a       (line 10).*\n+0001d760: 2072 6570 6561 7420 3c33 3e3a 2020 2020   repeat <3>:    \n 0001d770: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d780: 2020 5265 7065 6174 732e 2020 2020 2020    Repeats.      \n-0001d790: 2020 2020 2020 2020 286c 696e 6520 2036          (line  6\n-0001d7a0: 290a 2a20 7265 7065 6174 203c 343e 3a20  ).* repeat <4>: \n-0001d7b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d7c0: 2020 2020 2020 2020 2020 204f 7665 7276             Overv\n-0001d7d0: 6965 772e 2020 2020 2020 2020 2020 2020  iew.            \n-0001d7e0: 2028 6c69 6e65 2035 3729 0a2a 2072 6f74   (line 57).* rot\n-0001d7f0: 6174 653a 2020 2020 2020 2020 2020 2020  ate:            \n+0001d780: 2020 2020 2020 2020 5265 7065 6174 732e          Repeats.\n+0001d790: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+0001d7a0: 696e 6520 2036 290a 2a20 7265 7065 6174  ine  6).* repeat\n+0001d7b0: 203c 343e 3a20 2020 2020 2020 2020 2020   <4>:           \n+0001d7c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d7d0: 204f 7665 7276 6965 772e 2020 2020 2020   Overview.      \n+0001d7e0: 2020 2020 2020 2028 6c69 6e65 2035 3729         (line 57)\n+0001d7f0: 0a2a 2072 6f74 6174 653a 2020 2020 2020  .* rotate:      \n 0001d800: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d810: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n-0001d820: 666f 726d 732e 2020 2020 286c 696e 6520  forms.    (line \n-0001d830: 3130 290a 2a20 726f 7461 7465 203c 313e  10).* rotate <1>\n-0001d840: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001d850: 2020 2020 2020 2020 2020 2020 204f 626a               Obj\n-0001d860: 6563 7420 7472 616e 7366 6f72 6d73 2e20  ect transforms. \n-0001d870: 2020 2028 6c69 6e65 2033 3929 0a2a 2072     (line 39).* r\n-0001d880: 6f74 6174 6520 3c32 3e3a 2020 2020 2020  otate <2>:      \n+0001d810: 2020 2020 2020 2020 2020 4f62 6a65 6374            Object\n+0001d820: 2074 7261 6e73 666f 726d 732e 2020 2020   transforms.    \n+0001d830: 286c 696e 6520 3130 290a 2a20 726f 7461  (line 10).* rota\n+0001d840: 7465 203c 313e 3a20 2020 2020 2020 2020  te <1>:         \n+0001d850: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d860: 2020 204f 626a 6563 7420 7472 616e 7366     Object transf\n+0001d870: 6f72 6d73 2e20 2020 2028 6c69 6e65 2033  orms.    (line 3\n+0001d880: 3929 0a2a 2072 6f74 6174 6520 3c32 3e3a  9).* rotate <2>:\n 0001d890: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d8a0: 2020 2020 2020 5265 7065 6174 6564 206f        Repeated o\n-0001d8b0: 626a 6563 7473 2e20 2020 2020 286c 696e  bjects.     (lin\n-0001d8c0: 6520 2038 290a 2a20 726f 7461 7465 203c  e  8).* rotate <\n-0001d8d0: 333e 3a20 2020 2020 2020 2020 2020 2020  3>:             \n-0001d8e0: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n-0001d8f0: 7765 7074 206f 626a 6563 7473 2e20 2020  wept objects.   \n-0001d900: 2020 2020 2028 6c69 6e65 2020 3829 0a2a       (line  8).*\n-0001d910: 2072 6f74 6174 6520 3c34 3e3a 2020 2020   rotate <4>:    \n-0001d920: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d930: 2020 2020 2020 2020 506f 696e 7420 7377          Point sw\n-0001d940: 6565 7073 2e20 2020 2020 2020 2020 286c  eeps.         (l\n-0001d950: 696e 6520 3139 290a 2a20 726f 7461 7465  ine 19).* rotate\n-0001d960: 203c 353e 3a20 2020 2020 2020 2020 2020   <5>:           \n+0001d8a0: 2020 2020 2020 2020 2020 2020 5265 7065              Repe\n+0001d8b0: 6174 6564 206f 626a 6563 7473 2e20 2020  ated objects.   \n+0001d8c0: 2020 286c 696e 6520 2038 290a 2a20 726f    (line  8).* ro\n+0001d8d0: 7461 7465 203c 333e 3a20 2020 2020 2020  tate <3>:       \n+0001d8e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d8f0: 2020 2020 2053 7765 7074 206f 626a 6563       Swept objec\n+0001d900: 7473 2e20 2020 2020 2020 2028 6c69 6e65  ts.        (line\n+0001d910: 2020 3829 0a2a 2072 6f74 6174 6520 3c34    8).* rotate <4\n+0001d920: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001d930: 2020 2020 2020 2020 2020 2020 2020 506f                Po\n+0001d940: 696e 7420 7377 6565 7073 2e20 2020 2020  int sweeps.     \n+0001d950: 2020 2020 286c 696e 6520 3139 290a 2a20      (line 19).* \n+0001d960: 726f 7461 7465 203c 353e 3a20 2020 2020  rotate <5>:     \n 0001d970: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d980: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n-0001d990: 2e20 2020 2020 2028 6c69 6e65 2020 3929  .      (line  9)\n-0001d9a0: 0a2a 2072 6f74 6174 6520 3c36 3e3a 2020  .* rotate <6>:  \n-0001d9b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d9c0: 2020 2020 2020 2020 2020 4e65 7374 6564            Nested\n-0001d9d0: 2073 7765 6570 732e 2020 2020 2020 2020   sweeps.        \n-0001d9e0: 286c 696e 6520 2038 290a 2a20 726f 7461  (line  8).* rota\n-0001d9f0: 7465 203c 373e 3a20 2020 2020 2020 2020  te <7>:         \n+0001d980: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n+0001d990: 7377 6565 7073 2e20 2020 2020 2028 6c69  sweeps.      (li\n+0001d9a0: 6e65 2020 3929 0a2a 2072 6f74 6174 6520  ne  9).* rotate \n+0001d9b0: 3c36 3e3a 2020 2020 2020 2020 2020 2020  <6>:            \n+0001d9c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d9d0: 4e65 7374 6564 2073 7765 6570 732e 2020  Nested sweeps.  \n+0001d9e0: 2020 2020 2020 286c 696e 6520 2038 290a        (line  8).\n+0001d9f0: 2a20 726f 7461 7465 203c 373e 3a20 2020  * rotate <7>:   \n 0001da00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001da10: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n-0001da20: 7073 2077 6974 6820 636c 6f73 7572 652e  ps with closure.\n-0001da30: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+0001da10: 2020 2020 2020 2020 2050 6f6c 796c 696e           Polylin\n+0001da20: 6520 7377 6565 7073 2077 6974 6820 636c  e sweeps with cl\n+0001da30: 6f73 7572 652e 0a20 2020 2020 2020 2020  osure..         \n 0001da40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001da50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001da60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001da70: 286c 696e 6520 3130 290a 2a20 726f 7461  (line 10).* rota\n-0001da80: 7465 203c 383e 3a20 2020 2020 2020 2020  te <8>:         \n+0001da70: 2020 2020 2020 286c 696e 6520 3130 290a        (line 10).\n+0001da80: 2a20 726f 7461 7465 203c 383e 3a20 2020  * rotate <8>:   \n 0001da90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001daa0: 2020 2054 7261 6e73 666f 726d 206c 6974     Transform lit\n-0001dab0: 6572 616c 732e 2020 2028 6c69 6e65 2031  erals.   (line 1\n-0001dac0: 3029 0a2a 2072 6f74 6174 6520 3c39 3e3a  0).* rotate <9>:\n-0001dad0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dae0: 2020 2020 2020 2020 2020 2020 4f76 6572              Over\n-0001daf0: 7669 6577 2e20 2020 2020 2020 2020 2020  view.           \n-0001db00: 2020 286c 696e 6520 3537 290a 2a20 726f    (line 57).* ro\n-0001db10: 7461 7465 203c 3130 3e3a 2020 2020 2020  tate <10>:      \n+0001daa0: 2020 2020 2020 2020 2054 7261 6e73 666f           Transfo\n+0001dab0: 726d 206c 6974 6572 616c 732e 2020 2028  rm literals.   (\n+0001dac0: 6c69 6e65 2031 3029 0a2a 2072 6f74 6174  line 10).* rotat\n+0001dad0: 6520 3c39 3e3a 2020 2020 2020 2020 2020  e <9>:          \n+0001dae0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001daf0: 2020 4f76 6572 7669 6577 2e20 2020 2020    Overview.     \n+0001db00: 2020 2020 2020 2020 286c 696e 6520 3537          (line 57\n+0001db10: 290a 2a20 726f 7461 7465 203c 3130 3e3a  ).* rotate <10>:\n 0001db20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001db30: 2020 2020 204f 7665 7276 6965 772e 2020       Overview.  \n-0001db40: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-0001db50: 2036 3929 0a2a 2072 6f74 6174 6520 3c31   69).* rotate <1\n-0001db60: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-0001db70: 2020 2020 2020 2020 2020 2020 2020 4120                A \n-0001db80: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n-0001db90: 672e 2020 286c 696e 6520 3134 290a 2a20  g.  (line 14).* \n-0001dba0: 726f 7461 7465 203c 3132 3e3a 2020 2020  rotate <12>:    \n-0001dbb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dbc0: 2020 2020 2020 2041 2068 6965 7261 7263         A hierarc\n-0001dbd0: 6869 6361 6c20 6d6f 6465 6c2e 2028 6c69  hical model. (li\n-0001dbe0: 6e65 2031 3029 0a2a 2072 6f74 6174 6520  ne 10).* rotate \n-0001dbf0: 3c31 333e 3a20 2020 2020 2020 2020 2020  <13>:           \n+0001db30: 2020 2020 2020 2020 2020 204f 7665 7276             Overv\n+0001db40: 6965 772e 2020 2020 2020 2020 2020 2020  iew.            \n+0001db50: 2028 6c69 6e65 2036 3929 0a2a 2072 6f74   (line 69).* rot\n+0001db60: 6174 6520 3c31 313e 3a20 2020 2020 2020  ate <11>:       \n+0001db70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001db80: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n+0001db90: 6472 6177 696e 672e 2020 286c 696e 6520  drawing.  (line \n+0001dba0: 3134 290a 2a20 726f 7461 7465 203c 3132  14).* rotate <12\n+0001dbb0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001dbc0: 2020 2020 2020 2020 2020 2020 2041 2068               A h\n+0001dbd0: 6965 7261 7263 6869 6361 6c20 6d6f 6465  ierarchical mode\n+0001dbe0: 6c2e 2028 6c69 6e65 2031 3029 0a2a 2072  l. (line 10).* r\n+0001dbf0: 6f74 6174 6520 3c31 333e 3a20 2020 2020  otate <13>:     \n 0001dc00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dc10: 4120 6869 6572 6172 6368 6963 616c 206d  A hierarchical m\n-0001dc20: 6f64 656c 2e20 286c 696e 6520 3233 290a  odel. (line 23).\n-0001dc30: 2a20 726f 7461 7465 203c 3134 3e3a 2020  * rotate <14>:  \n-0001dc40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dc50: 2020 2020 2020 2020 2041 2068 6965 7261           A hiera\n-0001dc60: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028  rchical model. (\n-0001dc70: 6c69 6e65 2033 3229 0a2a 2073 6361 6c65  line 32).* scale\n-0001dc80: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001dc10: 2020 2020 2020 4120 6869 6572 6172 6368        A hierarch\n+0001dc20: 6963 616c 206d 6f64 656c 2e20 286c 696e  ical model. (lin\n+0001dc30: 6520 3233 290a 2a20 726f 7461 7465 203c  e 23).* rotate <\n+0001dc40: 3134 3e3a 2020 2020 2020 2020 2020 2020  14>:            \n+0001dc50: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+0001dc60: 2068 6965 7261 7263 6869 6361 6c20 6d6f   hierarchical mo\n+0001dc70: 6465 6c2e 2028 6c69 6e65 2033 3229 0a2a  del. (line 32).*\n+0001dc80: 2073 6361 6c65 3a20 2020 2020 2020 2020   scale:         \n 0001dc90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dca0: 2020 5472 616e 7366 6f72 6d20 6c69 7465    Transform lite\n-0001dcb0: 7261 6c73 2e20 2020 286c 696e 6520 3136  rals.   (line 16\n-0001dcc0: 290a 2a20 7363 616c 6520 3c31 3e3a 2020  ).* scale <1>:  \n-0001dcd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dce0: 2020 2020 2020 2020 2020 2054 7261 6e73             Trans\n-0001dcf0: 666f 726d 206c 6974 6572 616c 732e 2020  form literals.  \n-0001dd00: 2028 6c69 6e65 2031 3729 0a2a 2073 6361   (line 17).* sca\n-0001dd10: 6c65 203c 323e 3a20 2020 2020 2020 2020  le <2>:         \n+0001dca0: 2020 2020 2020 2020 5472 616e 7366 6f72          Transfor\n+0001dcb0: 6d20 6c69 7465 7261 6c73 2e20 2020 286c  m literals.   (l\n+0001dcc0: 696e 6520 3136 290a 2a20 7363 616c 6520  ine 16).* scale \n+0001dcd0: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n+0001dce0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001dcf0: 2054 7261 6e73 666f 726d 206c 6974 6572   Transform liter\n+0001dd00: 616c 732e 2020 2028 6c69 6e65 2031 3729  als.   (line 17)\n+0001dd10: 0a2a 2073 6361 6c65 203c 323e 3a20 2020  .* scale <2>:   \n 0001dd20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dd30: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n-0001dd40: 6472 6177 696e 672e 2020 286c 696e 6520  drawing.  (line \n-0001dd50: 3431 290a 2a20 7363 616c 6520 3c33 3e3a  41).* scale <3>:\n-0001dd60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dd70: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n-0001dd80: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n-0001dd90: 2e20 2028 6c69 6e65 2036 3829 0a2a 2073  .  (line 68).* s\n-0001dda0: 6361 6c65 203c 343e 3a20 2020 2020 2020  cale <4>:       \n+0001dd30: 2020 2020 2020 2020 2020 4120 7465 6368            A tech\n+0001dd40: 6e69 6361 6c20 6472 6177 696e 672e 2020  nical drawing.  \n+0001dd50: 286c 696e 6520 3431 290a 2a20 7363 616c  (line 41).* scal\n+0001dd60: 6520 3c33 3e3a 2020 2020 2020 2020 2020  e <3>:          \n+0001dd70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001dd80: 2020 2041 2074 6563 686e 6963 616c 2064     A technical d\n+0001dd90: 7261 7769 6e67 2e20 2028 6c69 6e65 2036  rawing.  (line 6\n+0001dda0: 3829 0a2a 2073 6361 6c65 203c 343e 3a20  8).* scale <4>: \n 0001ddb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ddc0: 2020 2020 2020 4120 6869 6572 6172 6368        A hierarch\n-0001ddd0: 6963 616c 206d 6f64 656c 2e20 286c 696e  ical model. (lin\n-0001dde0: 6520 3332 290a 2a20 7365 743a 2020 2020  e 32).* set:    \n-0001ddf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001de00: 2020 2020 2020 2020 2020 2020 2020 2047                 G\n-0001de10: 6c6f 6261 6c20 6f70 7469 6f6e 732e 2020  lobal options.  \n-0001de20: 2020 2020 2028 6c69 6e65 2020 3629 0a2a       (line  6).*\n-0001de30: 2073 696e 3a20 2020 2020 2020 2020 2020   sin:           \n+0001ddc0: 2020 2020 2020 2020 2020 2020 4120 6869              A hi\n+0001ddd0: 6572 6172 6368 6963 616c 206d 6f64 656c  erarchical model\n+0001dde0: 2e20 286c 696e 6520 3332 290a 2a20 7365  . (line 32).* se\n+0001ddf0: 743a 2020 2020 2020 2020 2020 2020 2020  t:              \n+0001de00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001de10: 2020 2020 2047 6c6f 6261 6c20 6f70 7469       Global opti\n+0001de20: 6f6e 732e 2020 2020 2020 2028 6c69 6e65  ons.       (line\n+0001de30: 2020 3629 0a2a 2073 696e 3a20 2020 2020    6).* sin:     \n 0001de40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001de50: 2020 2020 2020 2020 556e 6172 7920 666f          Unary fo\n-0001de60: 726d 732e 2020 2020 2020 2020 2020 286c  rms.          (l\n-0001de70: 696e 6520 3135 290a 2a20 7370 6563 6961  ine 15).* specia\n-0001de80: 6c3a 2020 2020 2020 2020 2020 2020 2020  l:              \n+0001de50: 2020 2020 2020 2020 2020 2020 2020 556e                Un\n+0001de60: 6172 7920 666f 726d 732e 2020 2020 2020  ary forms.      \n+0001de70: 2020 2020 286c 696e 6520 3135 290a 2a20      (line 15).* \n+0001de80: 7370 6563 6961 6c3a 2020 2020 2020 2020  special:        \n 0001de90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dea0: 2053 7065 6369 616c 206f 626a 6563 7473   Special objects\n-0001deb0: 2e20 2020 2020 2028 6c69 6e65 2020 3629  .      (line  6)\n-0001dec0: 0a2a 2073 7065 6369 616c 203c 313e 3a20  .* special <1>: \n-0001ded0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dee0: 2020 2020 2020 2020 2020 5370 6563 6961            Specia\n-0001def0: 6c73 2e20 2020 2020 2020 2020 2020 2020  ls.             \n-0001df00: 286c 696e 6520 2036 290a 2a20 7370 6563  (line  6).* spec\n-0001df10: 6961 6c20 3c32 3e3a 2020 2020 2020 2020  ial <2>:        \n+0001dea0: 2020 2020 2020 2053 7065 6369 616c 206f         Special o\n+0001deb0: 626a 6563 7473 2e20 2020 2020 2028 6c69  bjects.      (li\n+0001dec0: 6e65 2020 3629 0a2a 2073 7065 6369 616c  ne  6).* special\n+0001ded0: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+0001dee0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001def0: 5370 6563 6961 6c73 2e20 2020 2020 2020  Specials.       \n+0001df00: 2020 2020 2020 286c 696e 6520 2036 290a        (line  6).\n+0001df10: 2a20 7370 6563 6961 6c20 3c32 3e3a 2020  * special <2>:  \n 0001df20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001df30: 2020 204f 7665 7276 6965 772e 2020 2020     Overview.    \n-0001df40: 2020 2020 2020 2020 2028 6c69 6e65 2036           (line 6\n-0001df50: 3929 0a2a 2073 7065 6369 616c 203c 333e  9).* special <3>\n-0001df60: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001df70: 2020 2020 2020 2020 2020 2020 4120 7465              A te\n-0001df80: 6368 6e69 6361 6c20 6472 6177 696e 672e  chnical drawing.\n-0001df90: 2020 286c 696e 6520 3236 290a 2a20 7370    (line 26).* sp\n-0001dfa0: 6563 6961 6c20 3c34 3e3a 2020 2020 2020  ecial <4>:      \n+0001df30: 2020 2020 2020 2020 204f 7665 7276 6965           Overvie\n+0001df40: 772e 2020 2020 2020 2020 2020 2020 2028  w.             (\n+0001df50: 6c69 6e65 2036 3929 0a2a 2073 7065 6369  line 69).* speci\n+0001df60: 616c 203c 333e 3a20 2020 2020 2020 2020  al <3>:         \n+0001df70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001df80: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n+0001df90: 6177 696e 672e 2020 286c 696e 6520 3236  awing.  (line 26\n+0001dfa0: 290a 2a20 7370 6563 6961 6c20 3c34 3e3a  ).* special <4>:\n 0001dfb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dfc0: 2020 2020 2041 2074 6563 686e 6963 616c       A technical\n-0001dfd0: 2064 7261 7769 6e67 2e20 2028 6c69 6e65   drawing.  (line\n-0001dfe0: 2034 3129 0a2a 2073 7065 6369 616c 203c   41).* special <\n-0001dff0: 353e 3a20 2020 2020 2020 2020 2020 2020  5>:             \n-0001e000: 2020 2020 2020 2020 2020 2020 2020 4120                A \n-0001e010: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n-0001e020: 672e 2020 286c 696e 6520 3638 290a 2a20  g.  (line 68).* \n-0001e030: 7370 6563 6961 6c20 3c36 3e3a 2020 2020  special <6>:    \n-0001e040: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e050: 2020 2020 2020 2041 2074 6563 686e 6963         A technic\n-0001e060: 616c 2064 7261 7769 6e67 2e20 2028 6c69  al drawing.  (li\n-0001e070: 6e65 2039 3529 0a2a 2073 706c 6974 3a20  ne 95).* split: \n-0001e080: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001dfc0: 2020 2020 2020 2020 2020 2041 2074 6563             A tec\n+0001dfd0: 686e 6963 616c 2064 7261 7769 6e67 2e20  hnical drawing. \n+0001dfe0: 2028 6c69 6e65 2034 3129 0a2a 2073 7065   (line 41).* spe\n+0001dff0: 6369 616c 203c 353e 3a20 2020 2020 2020  cial <5>:       \n+0001e000: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e010: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n+0001e020: 6472 6177 696e 672e 2020 286c 696e 6520  drawing.  (line \n+0001e030: 3638 290a 2a20 7370 6563 6961 6c20 3c36  68).* special <6\n+0001e040: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001e050: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n+0001e060: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n+0001e070: 2e20 2028 6c69 6e65 2039 3529 0a2a 2073  .  (line 95).* s\n+0001e080: 706c 6974 3a20 2020 2020 2020 2020 2020  plit:           \n 0001e090: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e0a0: 496e 7465 726e 616c 206f 7074 696f 6e73  Internal options\n-0001e0b0: 2e20 2020 2020 286c 696e 6520 2037 290a  .     (line  7).\n-0001e0c0: 2a20 7370 6c69 7420 3c31 3e3a 2020 2020  * split <1>:    \n-0001e0d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e0e0: 2020 2020 2020 2020 2047 6c6f 6261 6c20           Global \n-0001e0f0: 6f70 7469 6f6e 732e 2020 2020 2020 2028  options.       (\n-0001e100: 6c69 6e65 2031 3329 0a2a 2073 7172 743a  line 13).* sqrt:\n-0001e110: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e0a0: 2020 2020 2020 496e 7465 726e 616c 206f        Internal o\n+0001e0b0: 7074 696f 6e73 2e20 2020 2020 286c 696e  ptions.     (lin\n+0001e0c0: 6520 2037 290a 2a20 7370 6c69 7420 3c31  e  7).* split <1\n+0001e0d0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001e0e0: 2020 2020 2020 2020 2020 2020 2020 2047                 G\n+0001e0f0: 6c6f 6261 6c20 6f70 7469 6f6e 732e 2020  lobal options.  \n+0001e100: 2020 2020 2028 6c69 6e65 2031 3329 0a2a       (line 13).*\n+0001e110: 2073 7172 743a 2020 2020 2020 2020 2020   sqrt:          \n 0001e120: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e130: 2020 556e 6172 7920 666f 726d 732e 2020    Unary forms.  \n-0001e140: 2020 2020 2020 2020 286c 696e 6520 3134          (line 14\n-0001e150: 290a 2a20 7377 6565 703a 2020 2020 2020  ).* sweep:      \n+0001e130: 2020 2020 2020 2020 556e 6172 7920 666f          Unary fo\n+0001e140: 726d 732e 2020 2020 2020 2020 2020 286c  rms.          (l\n+0001e150: 696e 6520 3134 290a 2a20 7377 6565 703a  ine 14).* sweep:\n 0001e160: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e170: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-0001e180: 206f 626a 6563 7473 2e20 2020 2020 2020   objects.       \n-0001e190: 2028 6c69 6e65 2020 3829 0a2a 2073 7765   (line  8).* swe\n-0001e1a0: 6570 203c 313e 3a20 2020 2020 2020 2020  ep <1>:         \n+0001e170: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e180: 2053 7765 7074 206f 626a 6563 7473 2e20   Swept objects. \n+0001e190: 2020 2020 2020 2028 6c69 6e65 2020 3829         (line  8)\n+0001e1a0: 0a2a 2073 7765 6570 203c 313e 3a20 2020  .* sweep <1>:   \n 0001e1b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e1c0: 2020 2020 506f 696e 7420 7377 6565 7073      Point sweeps\n-0001e1d0: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n-0001e1e0: 3139 290a 2a20 7377 6565 7020 3c32 3e3a  19).* sweep <2>:\n-0001e1f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e200: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n-0001e210: 796c 696e 6520 7377 6565 7073 2e20 2020  yline sweeps.   \n-0001e220: 2020 2028 6c69 6e65 2020 3929 0a2a 2073     (line  9).* s\n-0001e230: 7765 6570 203c 333e 3a20 2020 2020 2020  weep <3>:       \n+0001e1c0: 2020 2020 2020 2020 2020 506f 696e 7420            Point \n+0001e1d0: 7377 6565 7073 2e20 2020 2020 2020 2020  sweeps.         \n+0001e1e0: 286c 696e 6520 3139 290a 2a20 7377 6565  (line 19).* swee\n+0001e1f0: 7020 3c32 3e3a 2020 2020 2020 2020 2020  p <2>:          \n+0001e200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e210: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n+0001e220: 7073 2e20 2020 2020 2028 6c69 6e65 2020  ps.      (line  \n+0001e230: 3929 0a2a 2073 7765 6570 203c 333e 3a20  9).* sweep <3>: \n 0001e240: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e250: 2020 2020 2020 4e65 7374 6564 2073 7765        Nested swe\n-0001e260: 6570 732e 2020 2020 2020 2020 286c 696e  eps.        (lin\n-0001e270: 6520 2038 290a 2a20 7377 6565 7020 3c34  e  8).* sweep <4\n-0001e280: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001e290: 2020 2020 2020 2020 2020 2020 2020 204e                 N\n-0001e2a0: 6573 7465 6420 7377 6565 7073 2e20 2020  ested sweeps.   \n-0001e2b0: 2020 2020 2028 6c69 6e65 2032 3229 0a2a       (line 22).*\n-0001e2c0: 2073 7765 6570 203c 353e 3a20 2020 2020   sweep <5>:     \n-0001e2d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e2e0: 2020 2020 2020 2020 506f 6c79 6c69 6e65          Polyline\n-0001e2f0: 2073 7765 6570 7320 7769 7468 2063 6c6f   sweeps with clo\n-0001e300: 7375 7265 2e0a 2020 2020 2020 2020 2020  sure..          \n+0001e250: 2020 2020 2020 2020 2020 2020 4e65 7374              Nest\n+0001e260: 6564 2073 7765 6570 732e 2020 2020 2020  ed sweeps.      \n+0001e270: 2020 286c 696e 6520 2038 290a 2a20 7377    (line  8).* sw\n+0001e280: 6565 7020 3c34 3e3a 2020 2020 2020 2020  eep <4>:        \n+0001e290: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e2a0: 2020 2020 204e 6573 7465 6420 7377 6565       Nested swee\n+0001e2b0: 7073 2e20 2020 2020 2020 2028 6c69 6e65  ps.        (line\n+0001e2c0: 2032 3229 0a2a 2073 7765 6570 203c 353e   22).* sweep <5>\n+0001e2d0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001e2e0: 2020 2020 2020 2020 2020 2020 2020 506f                Po\n+0001e2f0: 6c79 6c69 6e65 2073 7765 6570 7320 7769  lyline sweeps wi\n+0001e300: 7468 2063 6c6f 7375 7265 2e0a 2020 2020  th closure..    \n 0001e310: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001e320: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001e330: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e340: 2020 2020 2028 6c69 6e65 2031 3029 0a2a       (line 10).*\n-0001e350: 2073 7765 6570 203c 363e 3a20 2020 2020   sweep <6>:     \n-0001e360: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e370: 2020 2020 2020 2020 5377 6565 7073 2e20          Sweeps. \n-0001e380: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-0001e390: 696e 6520 2036 290a 2a20 7377 6565 7020  ine  6).* sweep \n-0001e3a0: 3c37 3e3a 2020 2020 2020 2020 2020 2020  <7>:            \n+0001e340: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001e350: 2031 3029 0a2a 2073 7765 6570 203c 363e   10).* sweep <6>\n+0001e360: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001e370: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n+0001e380: 6565 7073 2e20 2020 2020 2020 2020 2020  eeps.           \n+0001e390: 2020 2020 286c 696e 6520 2036 290a 2a20      (line  6).* \n+0001e3a0: 7377 6565 7020 3c37 3e3a 2020 2020 2020  sweep <7>:      \n 0001e3b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e3c0: 2041 2074 6563 686e 6963 616c 2064 7261   A technical dra\n-0001e3d0: 7769 6e67 2e20 2028 6c69 6e65 2032 3029  wing.  (line 20)\n-0001e3e0: 0a2a 2073 7765 6570 203c 383e 3a20 2020  .* sweep <8>:   \n-0001e3f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e400: 2020 2020 2020 2020 2020 4120 6869 6572            A hier\n-0001e410: 6172 6368 6963 616c 206d 6f64 656c 2e20  archical model. \n-0001e420: 286c 696e 6520 3130 290a 2a20 7377 6565  (line 10).* swee\n-0001e430: 7020 3c39 3e3a 2020 2020 2020 2020 2020  p <9>:          \n+0001e3c0: 2020 2020 2020 2041 2074 6563 686e 6963         A technic\n+0001e3d0: 616c 2064 7261 7769 6e67 2e20 2028 6c69  al drawing.  (li\n+0001e3e0: 6e65 2032 3029 0a2a 2073 7765 6570 203c  ne 20).* sweep <\n+0001e3f0: 383e 3a20 2020 2020 2020 2020 2020 2020  8>:             \n+0001e400: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e410: 4120 6869 6572 6172 6368 6963 616c 206d  A hierarchical m\n+0001e420: 6f64 656c 2e20 286c 696e 6520 3130 290a  odel. (line 10).\n+0001e430: 2a20 7377 6565 7020 3c39 3e3a 2020 2020  * sweep <9>:    \n 0001e440: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e450: 2020 2041 2068 6965 7261 7263 6869 6361     A hierarchica\n-0001e460: 6c20 6d6f 6465 6c2e 2028 6c69 6e65 2032  l model. (line 2\n-0001e470: 3329 0a2a 2074 6865 6e3a 2020 2020 2020  3).* then:      \n+0001e450: 2020 2020 2020 2020 2041 2068 6965 7261           A hiera\n+0001e460: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028  rchical model. (\n+0001e470: 6c69 6e65 2032 3329 0a2a 2074 6865 6e3a  line 23).* then:\n 0001e480: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e490: 2020 2020 2020 2020 2020 2020 4f62 6a65              Obje\n-0001e4a0: 6374 2074 7261 6e73 666f 726d 732e 2020  ct transforms.  \n-0001e4b0: 2020 286c 696e 6520 3130 290a 2a20 7468    (line 10).* th\n-0001e4c0: 656e 203c 313e 3a20 2020 2020 2020 2020  en <1>:         \n+0001e490: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e4a0: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n+0001e4b0: 726d 732e 2020 2020 286c 696e 6520 3130  rms.    (line 10\n+0001e4c0: 290a 2a20 7468 656e 203c 313e 3a20 2020  ).* then <1>:   \n 0001e4d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e4e0: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n-0001e4f0: 6565 7073 2077 6974 6820 636c 6f73 7572  eeps with closur\n-0001e500: 652e 0a20 2020 2020 2020 2020 2020 2020  e..             \n+0001e4e0: 2020 2020 2020 2020 2020 2050 6f6c 796c             Polyl\n+0001e4f0: 696e 6520 7377 6565 7073 2077 6974 6820  ine sweeps with \n+0001e500: 636c 6f73 7572 652e 0a20 2020 2020 2020  closure..       \n 0001e510: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001e520: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001e530: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e540: 2020 286c 696e 6520 3130 290a 2a20 7468    (line 10).* th\n-0001e550: 656e 203c 323e 3a20 2020 2020 2020 2020  en <2>:         \n+0001e540: 2020 2020 2020 2020 286c 696e 6520 3130          (line 10\n+0001e550: 290a 2a20 7468 656e 203c 323e 3a20 2020  ).* then <2>:   \n 0001e560: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e570: 2020 2020 2054 776f 2d6f 7065 7261 6e64       Two-operand\n-0001e580: 2028 6269 6e61 7279 2920 666f 726d 732e   (binary) forms.\n-0001e590: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+0001e570: 2020 2020 2020 2020 2020 2054 776f 2d6f             Two-o\n+0001e580: 7065 7261 6e64 2028 6269 6e61 7279 2920  perand (binary) \n+0001e590: 666f 726d 732e 0a20 2020 2020 2020 2020  forms..         \n 0001e5a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001e5b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001e5c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e5d0: 286c 696e 6520 3336 290a 2a20 7468 656e  (line 36).* then\n-0001e5e0: 203c 333e 3a20 2020 2020 2020 2020 2020   <3>:           \n+0001e5d0: 2020 2020 2020 286c 696e 6520 3336 290a        (line 36).\n+0001e5e0: 2a20 7468 656e 203c 333e 3a20 2020 2020  * then <3>:     \n 0001e5f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e600: 2020 2054 776f 2d6f 7065 7261 6e64 2028     Two-operand (\n-0001e610: 6269 6e61 7279 2920 666f 726d 732e 0a20  binary) forms.. \n-0001e620: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e600: 2020 2020 2020 2020 2054 776f 2d6f 7065           Two-ope\n+0001e610: 7261 6e64 2028 6269 6e61 7279 2920 666f  rand (binary) fo\n+0001e620: 726d 732e 0a20 2020 2020 2020 2020 2020  rms..           \n 0001e630: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001e640: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e650: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-0001e660: 696e 6520 3633 290a 2a20 7469 6b7a 3a20  ine 63).* tikz: \n-0001e670: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e650: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e660: 2020 2020 286c 696e 6520 3633 290a 2a20      (line 63).* \n+0001e670: 7469 6b7a 3a20 2020 2020 2020 2020 2020  tikz:           \n 0001e680: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e690: 204c 616e 6775 6167 652e 2020 2020 2020   Language.      \n-0001e6a0: 2020 2020 2020 2028 6c69 6e65 2031 3029         (line 10)\n-0001e6b0: 0a2a 2074 7261 6e73 6c61 7465 3a20 2020  .* translate:   \n-0001e6c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e6d0: 2020 2020 2020 2020 2020 4f62 6a65 6374            Object\n-0001e6e0: 2074 7261 6e73 666f 726d 732e 2020 2020   transforms.    \n-0001e6f0: 286c 696e 6520 3130 290a 2a20 7472 616e  (line 10).* tran\n-0001e700: 736c 6174 6520 3c31 3e3a 2020 2020 2020  slate <1>:      \n+0001e690: 2020 2020 2020 204c 616e 6775 6167 652e         Language.\n+0001e6a0: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n+0001e6b0: 6e65 2031 3029 0a2a 2074 7261 6e73 6c61  ne 10).* transla\n+0001e6c0: 7465 3a20 2020 2020 2020 2020 2020 2020  te:             \n+0001e6d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e6e0: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n+0001e6f0: 732e 2020 2020 286c 696e 6520 3130 290a  s.    (line 10).\n+0001e700: 2a20 7472 616e 736c 6174 6520 3c31 3e3a  * translate <1>:\n 0001e710: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e720: 2020 204f 626a 6563 7420 7472 616e 7366     Object transf\n-0001e730: 6f72 6d73 2e20 2020 2028 6c69 6e65 2034  orms.    (line 4\n-0001e740: 3729 0a2a 2074 7261 6e73 6c61 7465 203c  7).* translate <\n-0001e750: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n-0001e760: 2020 2020 2020 2020 2020 2020 5265 7065              Repe\n-0001e770: 6174 6564 206f 626a 6563 7473 2e20 2020  ated objects.   \n-0001e780: 2020 286c 696e 6520 2038 290a 2a20 7472    (line  8).* tr\n-0001e790: 616e 736c 6174 6520 3c33 3e3a 2020 2020  anslate <3>:    \n-0001e7a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e7b0: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n-0001e7c0: 6565 7073 2e20 2020 2020 2028 6c69 6e65  eeps.      (line\n-0001e7d0: 2020 3929 0a2a 2074 7261 6e73 6c61 7465    9).* translate\n-0001e7e0: 203c 343e 3a20 2020 2020 2020 2020 2020   <4>:           \n-0001e7f0: 2020 2020 2020 2020 2020 2020 2020 506f                Po\n-0001e800: 6c79 6c69 6e65 2073 7765 6570 7320 7769  lyline sweeps wi\n-0001e810: 7468 2063 6c6f 7375 7265 2e0a 2020 2020  th closure..    \n-0001e820: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e720: 2020 2020 2020 2020 204f 626a 6563 7420           Object \n+0001e730: 7472 616e 7366 6f72 6d73 2e20 2020 2028  transforms.    (\n+0001e740: 6c69 6e65 2034 3729 0a2a 2074 7261 6e73  line 47).* trans\n+0001e750: 6c61 7465 203c 323e 3a20 2020 2020 2020  late <2>:       \n+0001e760: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e770: 2020 5265 7065 6174 6564 206f 626a 6563    Repeated objec\n+0001e780: 7473 2e20 2020 2020 286c 696e 6520 2038  ts.     (line  8\n+0001e790: 290a 2a20 7472 616e 736c 6174 6520 3c33  ).* translate <3\n+0001e7a0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001e7b0: 2020 2020 2020 2020 2020 2050 6f6c 796c             Polyl\n+0001e7c0: 696e 6520 7377 6565 7073 2e20 2020 2020  ine sweeps.     \n+0001e7d0: 2028 6c69 6e65 2020 3929 0a2a 2074 7261   (line  9).* tra\n+0001e7e0: 6e73 6c61 7465 203c 343e 3a20 2020 2020  nslate <4>:     \n+0001e7f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e800: 2020 2020 506f 6c79 6c69 6e65 2073 7765      Polyline swe\n+0001e810: 6570 7320 7769 7468 2063 6c6f 7375 7265  eps with closure\n+0001e820: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n 0001e830: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001e840: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e850: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-0001e860: 2031 3029 0a2a 2074 7261 6e73 6c61 7465   10).* translate\n-0001e870: 203c 353e 3a20 2020 2020 2020 2020 2020   <5>:           \n-0001e880: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n-0001e890: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n-0001e8a0: 2e20 2020 286c 696e 6520 3135 290a 2a20  .   (line 15).* \n-0001e8b0: 7472 616e 736c 6174 6520 3c36 3e3a 2020  translate <6>:  \n-0001e8c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e8d0: 2020 2020 2020 204f 7665 7276 6965 772e         Overview.\n-0001e8e0: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n-0001e8f0: 6e65 2035 3729 0a2a 2074 7261 6e73 6c61  ne 57).* transla\n-0001e900: 7465 203c 373e 3a20 2020 2020 2020 2020  te <7>:         \n+0001e850: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e860: 2028 6c69 6e65 2031 3029 0a2a 2074 7261   (line 10).* tra\n+0001e870: 6e73 6c61 7465 203c 353e 3a20 2020 2020  nslate <5>:     \n+0001e880: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e890: 2020 2020 5472 616e 7366 6f72 6d20 6c69      Transform li\n+0001e8a0: 7465 7261 6c73 2e20 2020 286c 696e 6520  terals.   (line \n+0001e8b0: 3135 290a 2a20 7472 616e 736c 6174 6520  15).* translate \n+0001e8c0: 3c36 3e3a 2020 2020 2020 2020 2020 2020  <6>:            \n+0001e8d0: 2020 2020 2020 2020 2020 2020 204f 7665               Ove\n+0001e8e0: 7276 6965 772e 2020 2020 2020 2020 2020  rview.          \n+0001e8f0: 2020 2028 6c69 6e65 2035 3729 0a2a 2074     (line 57).* t\n+0001e900: 7261 6e73 6c61 7465 203c 373e 3a20 2020  ranslate <7>:   \n 0001e910: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e920: 4f76 6572 7669 6577 2e20 2020 2020 2020  Overview.       \n-0001e930: 2020 2020 2020 286c 696e 6520 3639 290a        (line 69).\n-0001e940: 2a20 7472 616e 736c 6174 6520 3c38 3e3a  * translate <8>:\n-0001e950: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e960: 2020 2020 2020 2020 2041 2068 6965 7261           A hiera\n-0001e970: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028  rchical model. (\n-0001e980: 6c69 6e65 2033 3229 0a2a 2074 7261 6e73  line 32).* trans\n-0001e990: 7061 6c70 6861 3a20 2020 2020 2020 2020  palpha:         \n+0001e920: 2020 2020 2020 4f76 6572 7669 6577 2e20        Overview. \n+0001e930: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+0001e940: 6520 3639 290a 2a20 7472 616e 736c 6174  e 69).* translat\n+0001e950: 6520 3c38 3e3a 2020 2020 2020 2020 2020  e <8>:          \n+0001e960: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+0001e970: 2068 6965 7261 7263 6869 6361 6c20 6d6f   hierarchical mo\n+0001e980: 6465 6c2e 2028 6c69 6e65 2033 3229 0a2a  del. (line 32).*\n+0001e990: 2074 7261 6e73 7061 6c70 6861 3a20 2020   transpalpha:   \n 0001e9a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e9b0: 2020 5472 616e 7370 6172 656e 6379 2e20    Transparency. \n-0001e9c0: 2020 2020 2020 2020 286c 696e 6520 3130          (line 10\n-0001e9d0: 290a 2a20 756e 6974 3a20 2020 2020 2020  ).* unit:       \n+0001e9b0: 2020 2020 2020 2020 5472 616e 7370 6172          Transpar\n+0001e9c0: 656e 6379 2e20 2020 2020 2020 2020 286c  ency.         (l\n+0001e9d0: 696e 6520 3130 290a 2a20 756e 6974 3a20  ine 10).* unit: \n 0001e9e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e9f0: 2020 2020 2020 2020 2020 2055 6e61 7279             Unary\n-0001ea00: 2066 6f72 6d73 2e20 2020 2020 2020 2020   forms.         \n-0001ea10: 2028 6c69 6e65 2031 3329 0a2a 2075 6e69   (line 13).* uni\n-0001ea20: 7420 3c31 3e3a 2020 2020 2020 2020 2020  t <1>:          \n+0001e9f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ea00: 2055 6e61 7279 2066 6f72 6d73 2e20 2020   Unary forms.   \n+0001ea10: 2020 2020 2020 2028 6c69 6e65 2031 3329         (line 13)\n+0001ea20: 0a2a 2075 6e69 7420 3c31 3e3a 2020 2020  .* unit <1>:    \n 0001ea30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ea40: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n-0001ea50: 6472 6177 696e 672e 2020 286c 696e 6520  drawing.  (line \n-0001ea60: 3431 290a 2a20 7669 6577 3a20 2020 2020  41).* view:     \n-0001ea70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ea80: 2020 2020 2020 2020 2020 2020 2054 7261               Tra\n-0001ea90: 6e73 666f 726d 206c 6974 6572 616c 732e  nsform literals.\n-0001eaa0: 2020 2028 6c69 6e65 2032 3529 0a2a 2076     (line 25).* v\n-0001eab0: 6965 7720 3c31 3e3a 2020 2020 2020 2020  iew <1>:        \n+0001ea40: 2020 2020 2020 2020 2020 4120 7465 6368            A tech\n+0001ea50: 6e69 6361 6c20 6472 6177 696e 672e 2020  nical drawing.  \n+0001ea60: 286c 696e 6520 3431 290a 2a20 7669 6577  (line 41).* view\n+0001ea70: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001ea80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ea90: 2020 2054 7261 6e73 666f 726d 206c 6974     Transform lit\n+0001eaa0: 6572 616c 732e 2020 2028 6c69 6e65 2032  erals.   (line 2\n+0001eab0: 3529 0a2a 2076 6965 7720 3c31 3e3a 2020  5).* view <1>:  \n 0001eac0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ead0: 2020 2020 2020 5472 616e 7366 6f72 6d20        Transform \n-0001eae0: 6c69 7465 7261 6c73 2e20 2020 286c 696e  literals.   (lin\n-0001eaf0: 6520 3335 290a 0a1f 0a46 696c 653a 2073  e 35)....File: s\n-0001eb00: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n-0001eb10: 653a 2049 6e64 6578 2c20 2050 7265 763a  e: Index,  Prev:\n-0001eb20: 2049 6e64 6578 206f 6620 7379 6e74 6178   Index of syntax\n-0001eb30: 2c20 2055 703a 2054 6f70 0a0a 496e 6465  ,  Up: Top..Inde\n-0001eb40: 7820 6f66 2063 6f6e 6365 7074 730a 2a2a  x of concepts.**\n-0001eb50: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a0a  ***************.\n-0001eb60: 0a00 085b 696e 6465 7800 085d 0a2a 204d  ...[index..].* M\n-0001eb70: 656e 753a 0a0a 2a20 6166 6669 6e65 2061  enu:..* affine a\n-0001eb80: 7269 7468 6d65 7469 633a 2020 2020 2020  rithmetic:      \n-0001eb90: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n-0001eba0: 6666 696e 6520 6172 6974 686d 6574 6963  ffine arithmetic\n-0001ebb0: 2e20 2020 286c 696e 6520 2020 3829 0a2a  .   (line   8).*\n-0001ebc0: 2061 6666 696e 6520 6172 6974 686d 6574   affine arithmet\n-0001ebd0: 6963 203c 313e 3a20 2020 2020 2020 2020  ic <1>:         \n-0001ebe0: 2020 2020 2020 2020 4120 7465 6368 6e69          A techni\n-0001ebf0: 6361 6c20 6472 6177 696e 672e 2028 6c69  cal drawing. (li\n-0001ec00: 6e65 2020 3430 290a 2a20 616c 7465 726e  ne  40).* altern\n-0001ec10: 6174 6976 6573 2c20 6465 6669 6e69 7469  atives, definiti\n-0001ec20: 6f6e 3a20 2020 2020 2020 2020 2020 2020  on:             \n-0001ec30: 2046 6f72 6d73 206f 6620 6465 6669 6e69   Forms of defini\n-0001ec40: 7469 6f6e 732e 0a20 2020 2020 2020 2020  tions..         \n+0001ead0: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n+0001eae0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n+0001eaf0: 2020 286c 696e 6520 3335 290a 0a1f 0a46    (line 35)....F\n+0001eb00: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n+0001eb10: 2c20 204e 6f64 653a 2049 6e64 6578 2c20  ,  Node: Index, \n+0001eb20: 2050 7265 763a 2049 6e64 6578 206f 6620   Prev: Index of \n+0001eb30: 7379 6e74 6178 2c20 2055 703a 2054 6f70  syntax,  Up: Top\n+0001eb40: 0a0a 496e 6465 7820 6f66 2063 6f6e 6365  ..Index of conce\n+0001eb50: 7074 730a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  pts.************\n+0001eb60: 2a2a 2a2a 2a0a 0a00 085b 696e 6465 7800  *****....[index.\n+0001eb70: 085d 0a2a 204d 656e 753a 0a0a 2a20 6166  .].* Menu:..* af\n+0001eb80: 6669 6e65 2061 7269 7468 6d65 7469 633a  fine arithmetic:\n+0001eb90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001eba0: 2020 2020 2041 6666 696e 6520 6172 6974       Affine arit\n+0001ebb0: 686d 6574 6963 2e20 2020 286c 696e 6520  hmetic.   (line \n+0001ebc0: 2020 3829 0a2a 2061 6666 696e 6520 6172    8).* affine ar\n+0001ebd0: 6974 686d 6574 6963 203c 313e 3a20 2020  ithmetic <1>:   \n+0001ebe0: 2020 2020 2020 2020 2020 2020 2020 4120                A \n+0001ebf0: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n+0001ec00: 672e 2028 6c69 6e65 2020 3430 290a 2a20  g. (line  40).* \n+0001ec10: 616c 7465 726e 6174 6976 6573 2c20 6465  alternatives, de\n+0001ec20: 6669 6e69 7469 6f6e 3a20 2020 2020 2020  finition:       \n+0001ec30: 2020 2020 2020 2046 6f72 6d73 206f 6620         Forms of \n+0001ec40: 6465 6669 6e69 7469 6f6e 732e 0a20 2020  definitions..   \n 0001ec50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ec60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ec70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ec80: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n-0001ec90: 2a20 6172 6775 6d65 6e74 2c20 7370 6563  * argument, spec\n-0001eca0: 6961 6c3a 2020 2020 2020 2020 2020 2020  ial:            \n-0001ecb0: 2020 2020 2020 2020 2053 7065 6369 616c           Special\n-0001ecc0: 206f 626a 6563 7473 2e20 2020 2020 286c   objects.     (l\n-0001ecd0: 696e 6520 2032 3529 0a2a 2061 7267 756d  ine  25).* argum\n-0001ece0: 656e 742c 2073 7065 6369 616c 203c 313e  ent, special <1>\n-0001ecf0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001ed00: 2020 5370 6563 6961 6c73 2e20 2020 2020    Specials.     \n-0001ed10: 2020 2020 2020 2028 6c69 6e65 2020 3130         (line  10\n-0001ed20: 290a 2a20 6173 736f 6369 6174 6976 6974  ).* associativit\n-0001ed30: 792c 206f 7065 7261 746f 723a 2020 2020  y, operator:    \n-0001ed40: 2020 2020 2020 2020 2020 2054 776f 2d6f             Two-o\n-0001ed50: 7065 7261 6e64 2028 6269 6e61 7279 2920  perand (binary) \n-0001ed60: 666f 726d 732e 0a20 2020 2020 2020 2020  forms..         \n+0001ec80: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001ec90: 2020 2036 290a 2a20 6172 6775 6d65 6e74     6).* argument\n+0001eca0: 2c20 7370 6563 6961 6c3a 2020 2020 2020  , special:      \n+0001ecb0: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n+0001ecc0: 7065 6369 616c 206f 626a 6563 7473 2e20  pecial objects. \n+0001ecd0: 2020 2020 286c 696e 6520 2032 3529 0a2a      (line  25).*\n+0001ece0: 2061 7267 756d 656e 742c 2073 7065 6369   argument, speci\n+0001ecf0: 616c 203c 313e 3a20 2020 2020 2020 2020  al <1>:         \n+0001ed00: 2020 2020 2020 2020 5370 6563 6961 6c73          Specials\n+0001ed10: 2e20 2020 2020 2020 2020 2020 2028 6c69  .            (li\n+0001ed20: 6e65 2020 3130 290a 2a20 6173 736f 6369  ne  10).* associ\n+0001ed30: 6174 6976 6974 792c 206f 7065 7261 746f  ativity, operato\n+0001ed40: 723a 2020 2020 2020 2020 2020 2020 2020  r:              \n+0001ed50: 2054 776f 2d6f 7065 7261 6e64 2028 6269   Two-operand (bi\n+0001ed60: 6e61 7279 2920 666f 726d 732e 0a20 2020  nary) forms..   \n 0001ed70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ed80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ed90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001eda0: 2020 2020 2028 6c69 6e65 2020 3538 290a       (line  58).\n-0001edb0: 2a20 6178 6973 2c20 726f 7461 7469 6f6e  * axis, rotation\n-0001edc0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001edd0: 2020 2020 2020 2020 204f 626a 6563 7420           Object \n-0001ede0: 7472 616e 7366 6f72 6d73 2e20 2020 286c  transforms.   (l\n-0001edf0: 696e 6520 2034 3029 0a2a 2062 6163 6b20  ine  40).* back \n-0001ee00: 6661 6365 3a20 2020 2020 2020 2020 2020  face:           \n+0001eda0: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001edb0: 2020 3538 290a 2a20 6178 6973 2c20 726f    58).* axis, ro\n+0001edc0: 7461 7469 6f6e 3a20 2020 2020 2020 2020  tation:         \n+0001edd0: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n+0001ede0: 626a 6563 7420 7472 616e 7366 6f72 6d73  bject transforms\n+0001edf0: 2e20 2020 286c 696e 6520 2034 3029 0a2a  .   (line  40).*\n+0001ee00: 2062 6163 6b20 6661 6365 3a20 2020 2020   back face:     \n 0001ee10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ee20: 2020 4472 6177 696e 6720 6120 736f 6c69    Drawing a soli\n-0001ee30: 642e 2020 2020 2028 6c69 6e65 2020 3335  d.     (line  35\n-0001ee40: 290a 2a20 6261 7365 6c69 6e65 2066 7261  ).* baseline fra\n-0001ee50: 6374 696f 6e3a 2020 2020 2020 2020 2020  ction:          \n-0001ee60: 2020 2020 2020 2020 2020 2050 6963 7475             Pictu\n-0001ee70: 7265 2062 6f78 2e20 2020 2020 2020 2020  re box.         \n-0001ee80: 286c 696e 6520 2031 3029 0a2a 2062 696e  (line  10).* bin\n-0001ee90: 6172 7920 666f 726d 3a20 2020 2020 2020  ary form:       \n+0001ee20: 2020 2020 2020 2020 4472 6177 696e 6720          Drawing \n+0001ee30: 6120 736f 6c69 642e 2020 2020 2028 6c69  a solid.     (li\n+0001ee40: 6e65 2020 3335 290a 2a20 6261 7365 6c69  ne  35).* baseli\n+0001ee50: 6e65 2066 7261 6374 696f 6e3a 2020 2020  ne fraction:    \n+0001ee60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ee70: 2050 6963 7475 7265 2062 6f78 2e20 2020   Picture box.   \n+0001ee80: 2020 2020 2020 286c 696e 6520 2031 3029        (line  10)\n+0001ee90: 0a2a 2062 696e 6172 7920 666f 726d 3a20  .* binary form: \n 0001eea0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001eeb0: 2020 2020 5477 6f2d 6f70 6572 616e 6420      Two-operand \n-0001eec0: 2862 696e 6172 7929 2066 6f72 6d73 2e0a  (binary) forms..\n-0001eed0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001eeb0: 2020 2020 2020 2020 2020 5477 6f2d 6f70            Two-op\n+0001eec0: 6572 616e 6420 2862 696e 6172 7929 2066  erand (binary) f\n+0001eed0: 6f72 6d73 2e0a 2020 2020 2020 2020 2020  orms..          \n 0001eee0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001eef0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ef00: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-0001ef10: 696e 6520 2020 3629 0a2a 2062 696e 6172  ine   6).* binar\n-0001ef20: 7920 7370 6163 6520 7061 7274 6974 696f  y space partitio\n-0001ef30: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n-0001ef40: 2020 4869 6464 656e 2073 7572 6661 6365    Hidden surface\n-0001ef50: 2072 656d 6f76 616c 2e0a 2020 2020 2020   removal..      \n+0001ef00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ef10: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n+0001ef20: 2062 696e 6172 7920 7370 6163 6520 7061   binary space pa\n+0001ef30: 7274 6974 696f 6e3a 2020 2020 2020 2020  rtition:        \n+0001ef40: 2020 2020 2020 2020 4869 6464 656e 2073          Hidden s\n+0001ef50: 7572 6661 6365 2072 656d 6f76 616c 2e0a  urface removal..\n 0001ef60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ef70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ef80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ef90: 2020 2020 2020 2020 286c 696e 6520 2032          (line  2\n-0001efa0: 3329 0a2a 2062 696e 6172 7920 7370 6163  3).* binary spac\n-0001efb0: 6520 7061 7274 6974 696f 6e20 3c31 3e3a  e partition <1>:\n-0001efc0: 2020 2020 2020 2020 2020 2020 5374 6174              Stat\n-0001efd0: 6973 7469 6373 2e20 2020 2020 2020 2020  istics.         \n-0001efe0: 2028 6c69 6e65 2020 3133 290a 2a20 6269   (line  13).* bi\n-0001eff0: 6e61 7279 2073 7061 6365 2070 6172 7469  nary space parti\n-0001f000: 7469 6f6e 203c 323e 3a20 2020 2020 2020  tion <2>:       \n-0001f010: 2020 2020 2043 6f6d 6d61 6e64 206c 696e       Command lin\n-0001f020: 652e 2020 2020 2020 2020 286c 696e 6520  e.        (line \n-0001f030: 2032 3629 0a2a 2062 6c6f 636b 3a20 2020   26).* block:   \n-0001f040: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f050: 2020 2020 2020 2020 2020 2020 2020 4f62                Ob\n-0001f060: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n-0001f070: 2020 2028 6c69 6e65 2020 3234 290a 2a20     (line  24).* \n-0001f080: 626c 6f63 6b20 3c31 3e3a 2020 2020 2020  block <1>:      \n+0001ef90: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+0001efa0: 696e 6520 2032 3329 0a2a 2062 696e 6172  ine  23).* binar\n+0001efb0: 7920 7370 6163 6520 7061 7274 6974 696f  y space partitio\n+0001efc0: 6e20 3c31 3e3a 2020 2020 2020 2020 2020  n <1>:          \n+0001efd0: 2020 5374 6174 6973 7469 6373 2e20 2020    Statistics.   \n+0001efe0: 2020 2020 2020 2028 6c69 6e65 2020 3133         (line  13\n+0001eff0: 290a 2a20 6269 6e61 7279 2073 7061 6365  ).* binary space\n+0001f000: 2070 6172 7469 7469 6f6e 203c 323e 3a20   partition <2>: \n+0001f010: 2020 2020 2020 2020 2020 2043 6f6d 6d61             Comma\n+0001f020: 6e64 206c 696e 652e 2020 2020 2020 2020  nd line.        \n+0001f030: 286c 696e 6520 2032 3629 0a2a 2062 6c6f  (line  26).* blo\n+0001f040: 636b 3a20 2020 2020 2020 2020 2020 2020  ck:             \n+0001f050: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f060: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n+0001f070: 666f 726d 732e 2020 2028 6c69 6e65 2020  forms.   (line  \n+0001f080: 3234 290a 2a20 626c 6f63 6b20 3c31 3e3a  24).* block <1>:\n 0001f090: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f0a0: 2020 2020 2020 2053 7765 7074 2062 6c6f         Swept blo\n-0001f0b0: 636b 732e 2020 2020 2020 2020 286c 696e  cks.        (lin\n-0001f0c0: 6520 2020 3729 0a2a 2062 6c6f 636b 203c  e   7).* block <\n-0001f0d0: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n+0001f0a0: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n+0001f0b0: 7074 2062 6c6f 636b 732e 2020 2020 2020  pt blocks.      \n+0001f0c0: 2020 286c 696e 6520 2020 3729 0a2a 2062    (line   7).* b\n+0001f0d0: 6c6f 636b 203c 323e 3a20 2020 2020 2020  lock <2>:       \n 0001f0e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f0f0: 426c 6f63 6b73 2e20 2020 2020 2020 2020  Blocks.         \n-0001f100: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n-0001f110: 2a20 626c 6f63 6b20 7377 6565 703a 2020  * block sweep:  \n-0001f120: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f130: 2020 2020 2020 2020 2053 7765 7074 2062           Swept b\n-0001f140: 6c6f 636b 732e 2020 2020 2020 2020 286c  locks.        (l\n-0001f150: 696e 6520 2020 3629 0a2a 2062 6f64 7920  ine   6).* body \n-0001f160: 706f 6c79 676f 6e3a 2020 2020 2020 2020  polygon:        \n+0001f0f0: 2020 2020 2020 426c 6f63 6b73 2e20 2020        Blocks.   \n+0001f100: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001f110: 2020 2036 290a 2a20 626c 6f63 6b20 7377     6).* block sw\n+0001f120: 6565 703a 2020 2020 2020 2020 2020 2020  eep:            \n+0001f130: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n+0001f140: 7765 7074 2062 6c6f 636b 732e 2020 2020  wept blocks.    \n+0001f150: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n+0001f160: 2062 6f64 7920 706f 6c79 676f 6e3a 2020   body polygon:  \n 0001f170: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f180: 2020 496e 7465 726e 616c 206f 7074 696f    Internal optio\n-0001f190: 6e73 2e20 2020 2028 6c69 6e65 2020 3136  ns.    (line  16\n-0001f1a0: 290a 2a20 626f 6479 2070 6f6c 7967 6f6e  ).* body polygon\n-0001f1b0: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-0001f1c0: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-0001f1d0: 206c 696e 6573 2e20 2020 2020 2020 2020   lines.         \n-0001f1e0: 286c 696e 6520 2031 3029 0a2a 2062 6f64  (line  10).* bod\n-0001f1f0: 7920 706f 6c79 676f 6e20 3c32 3e3a 2020  y polygon <2>:  \n-0001f200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f210: 2020 2020 5377 6570 7420 706f 6c79 676f      Swept polygo\n-0001f220: 6e73 2e20 2020 2020 2028 6c69 6e65 2020  ns.      (line  \n-0001f230: 2039 290a 2a20 626f 756e 6469 6e67 2062   9).* bounding b\n-0001f240: 6f78 3a20 2020 2020 2020 2020 2020 2020  ox:             \n-0001f250: 2020 2020 2020 2020 2020 2020 2050 6963               Pic\n-0001f260: 7475 7265 2062 6f78 2e20 2020 2020 2020  ture box.       \n-0001f270: 2020 286c 696e 6520 2031 3529 0a2a 2042    (line  15).* B\n-0001f280: 5350 2c20 6269 6e61 7279 2073 7061 6365  SP, binary space\n-0001f290: 2070 6172 7469 7469 6f6e 3a20 2020 2020   partition:     \n-0001f2a0: 2020 2020 2020 4869 6464 656e 2073 7572        Hidden sur\n-0001f2b0: 6661 6365 2072 656d 6f76 616c 2e0a 2020  face removal..  \n-0001f2c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f180: 2020 2020 2020 2020 496e 7465 726e 616c          Internal\n+0001f190: 206f 7074 696f 6e73 2e20 2020 2028 6c69   options.    (li\n+0001f1a0: 6e65 2020 3136 290a 2a20 626f 6479 2070  ne  16).* body p\n+0001f1b0: 6f6c 7967 6f6e 203c 313e 3a20 2020 2020  olygon <1>:     \n+0001f1c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f1d0: 2053 7765 7074 206c 696e 6573 2e20 2020   Swept lines.   \n+0001f1e0: 2020 2020 2020 286c 696e 6520 2031 3029        (line  10)\n+0001f1f0: 0a2a 2062 6f64 7920 706f 6c79 676f 6e20  .* body polygon \n+0001f200: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n+0001f210: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n+0001f220: 706f 6c79 676f 6e73 2e20 2020 2020 2028  polygons.      (\n+0001f230: 6c69 6e65 2020 2039 290a 2a20 626f 756e  line   9).* boun\n+0001f240: 6469 6e67 2062 6f78 3a20 2020 2020 2020  ding box:       \n+0001f250: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f260: 2020 2050 6963 7475 7265 2062 6f78 2e20     Picture box. \n+0001f270: 2020 2020 2020 2020 286c 696e 6520 2031          (line  1\n+0001f280: 3529 0a2a 2042 5350 2c20 6269 6e61 7279  5).* BSP, binary\n+0001f290: 2073 7061 6365 2070 6172 7469 7469 6f6e   space partition\n+0001f2a0: 3a20 2020 2020 2020 2020 2020 4869 6464  :           Hidd\n+0001f2b0: 656e 2073 7572 6661 6365 2072 656d 6f76  en surface remov\n+0001f2c0: 616c 2e0a 2020 2020 2020 2020 2020 2020  al..            \n 0001f2d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001f2e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f2f0: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-0001f300: 6520 2032 3329 0a2a 2042 5350 2c20 6269  e  23).* BSP, bi\n-0001f310: 6e61 7279 2073 7061 6365 2070 6172 7469  nary space parti\n-0001f320: 7469 6f6e 203c 313e 3a20 2020 2020 2020  tion <1>:       \n-0001f330: 436f 6d6d 616e 6420 6c69 6e65 2e20 2020  Command line.   \n-0001f340: 2020 2020 2028 6c69 6e65 2020 3236 290a       (line  26).\n-0001f350: 2a20 6361 6d65 7261 3a20 2020 2020 2020  * camera:       \n+0001f2f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f300: 2020 286c 696e 6520 2032 3329 0a2a 2042    (line  23).* B\n+0001f310: 5350 2c20 6269 6e61 7279 2073 7061 6365  SP, binary space\n+0001f320: 2070 6172 7469 7469 6f6e 203c 313e 3a20   partition <1>: \n+0001f330: 2020 2020 2020 436f 6d6d 616e 6420 6c69        Command li\n+0001f340: 6e65 2e20 2020 2020 2020 2028 6c69 6e65  ne.        (line\n+0001f350: 2020 3236 290a 2a20 6361 6d65 7261 3a20    26).* camera: \n 0001f360: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f370: 2020 2020 2020 2020 2043 616d 6572 612e           Camera.\n-0001f380: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-0001f390: 696e 6520 2020 3629 0a2a 2063 656e 7465  ine   6).* cente\n-0001f3a0: 7220 6f66 2072 6f74 6174 696f 6e3a 2020  r of rotation:  \n-0001f3b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f3c0: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n-0001f3d0: 726d 732e 2020 2028 6c69 6e65 2020 2038  rms.   (line   8\n-0001f3e0: 290a 2a20 6365 6e74 6572 206f 6620 726f  ).* center of ro\n-0001f3f0: 7461 7469 6f6e 203c 313e 3a20 2020 2020  tation <1>:     \n-0001f400: 2020 2020 2020 2020 2020 204e 6573 7465             Neste\n-0001f410: 6420 7377 6565 7073 2e20 2020 2020 2020  d sweeps.       \n-0001f420: 286c 696e 6520 2020 3629 0a2a 2063 656e  (line   6).* cen\n-0001f430: 7472 6f69 643a 2020 2020 2020 2020 2020  troid:          \n+0001f370: 2020 2020 2020 2020 2020 2020 2020 2043                 C\n+0001f380: 616d 6572 612e 2020 2020 2020 2020 2020  amera.          \n+0001f390: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n+0001f3a0: 2063 656e 7465 7220 6f66 2072 6f74 6174   center of rotat\n+0001f3b0: 696f 6e3a 2020 2020 2020 2020 2020 2020  ion:            \n+0001f3c0: 2020 2020 2020 2020 4f62 6a65 6374 2074          Object t\n+0001f3d0: 7261 6e73 666f 726d 732e 2020 2028 6c69  ransforms.   (li\n+0001f3e0: 6e65 2020 2038 290a 2a20 6365 6e74 6572  ne   8).* center\n+0001f3f0: 206f 6620 726f 7461 7469 6f6e 203c 313e   of rotation <1>\n+0001f400: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001f410: 204e 6573 7465 6420 7377 6565 7073 2e20   Nested sweeps. \n+0001f420: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+0001f430: 0a2a 2063 656e 7472 6f69 643a 2020 2020  .* centroid:    \n 0001f440: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f450: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n-0001f460: 6472 6177 696e 672e 2028 6c69 6e65 2020  drawing. (line  \n-0001f470: 3634 290a 2a20 6365 6e74 726f 6964 203c  64).* centroid <\n-0001f480: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-0001f490: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n-0001f4a0: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n-0001f4b0: 2e20 286c 696e 6520 3130 3229 0a2a 2063  . (line 102).* c\n-0001f4c0: 6c69 7070 696e 673a 2020 2020 2020 2020  lipping:        \n+0001f450: 2020 2020 2020 2020 2020 4120 7465 6368            A tech\n+0001f460: 6e69 6361 6c20 6472 6177 696e 672e 2028  nical drawing. (\n+0001f470: 6c69 6e65 2020 3634 290a 2a20 6365 6e74  line  64).* cent\n+0001f480: 726f 6964 203c 313e 3a20 2020 2020 2020  roid <1>:       \n+0001f490: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f4a0: 2020 2041 2074 6563 686e 6963 616c 2064     A technical d\n+0001f4b0: 7261 7769 6e67 2e20 286c 696e 6520 3130  rawing. (line 10\n+0001f4c0: 3229 0a2a 2063 6c69 7070 696e 673a 2020  2).* clipping:  \n 0001f4d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f4e0: 2020 2020 2020 5069 6374 7572 6520 626f        Picture bo\n-0001f4f0: 782e 2020 2020 2020 2020 2028 6c69 6e65  x.         (line\n-0001f500: 2020 3137 290a 2a20 636c 6970 7069 6e67    17).* clipping\n-0001f510: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-0001f520: 2020 2020 2020 2020 2020 2020 2020 2043                 C\n-0001f530: 6c69 7070 696e 672e 2020 2020 2020 2020  lipping.        \n-0001f540: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-0001f550: 2063 6c6f 7375 7265 2074 6167 2c20 3c3e   closure tag, <>\n-0001f560: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001f570: 2020 2020 2020 2020 506f 696e 7420 7377          Point sw\n-0001f580: 6565 7073 2e20 2020 2020 2020 2028 6c69  eeps.        (li\n-0001f590: 6e65 2020 3138 290a 2a20 636c 6f73 7572  ne  18).* closur\n-0001f5a0: 6520 7461 672c 203c 3e20 3c31 3e3a 2020  e tag, <> <1>:  \n-0001f5b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f5c0: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n-0001f5d0: 2077 6974 6820 636c 6f73 7572 652e 0a20   with closure.. \n-0001f5e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f4e0: 2020 2020 2020 2020 2020 2020 5069 6374              Pict\n+0001f4f0: 7572 6520 626f 782e 2020 2020 2020 2020  ure box.        \n+0001f500: 2028 6c69 6e65 2020 3137 290a 2a20 636c   (line  17).* cl\n+0001f510: 6970 7069 6e67 203c 313e 3a20 2020 2020  ipping <1>:     \n+0001f520: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f530: 2020 2020 2043 6c69 7070 696e 672e 2020       Clipping.  \n+0001f540: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+0001f550: 2020 3629 0a2a 2063 6c6f 7375 7265 2074    6).* closure t\n+0001f560: 6167 2c20 3c3e 3a20 2020 2020 2020 2020  ag, <>:         \n+0001f570: 2020 2020 2020 2020 2020 2020 2020 506f                Po\n+0001f580: 696e 7420 7377 6565 7073 2e20 2020 2020  int sweeps.     \n+0001f590: 2020 2028 6c69 6e65 2020 3138 290a 2a20     (line  18).* \n+0001f5a0: 636c 6f73 7572 6520 7461 672c 203c 3e20  closure tag, <> \n+0001f5b0: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n+0001f5c0: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n+0001f5d0: 7377 6565 7073 2077 6974 6820 636c 6f73  sweeps with clos\n+0001f5e0: 7572 652e 0a20 2020 2020 2020 2020 2020  ure..           \n 0001f5f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001f600: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f610: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n-0001f620: 6e65 2020 2036 290a 2a20 636c 6f73 7572  ne   6).* closur\n-0001f630: 6520 7461 672c 203c 3e20 3c32 3e3a 2020  e tag, <> <2>:  \n-0001f640: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f650: 2053 7765 6570 732e 2020 2020 2020 2020   Sweeps.        \n-0001f660: 2020 2020 2020 286c 696e 6520 2031 3929        (line  19)\n-0001f670: 0a2a 2063 6c6f 7375 7265 2074 6167 2c20  .* closure tag, \n-0001f680: 3c3e 203c 333e 3a20 2020 2020 2020 2020  <> <3>:         \n-0001f690: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n-0001f6a0: 706f 696e 7473 2e20 2020 2020 2020 2028  points.        (\n-0001f6b0: 6c69 6e65 2020 2036 290a 2a20 636c 6f73  line   6).* clos\n-0001f6c0: 7572 6520 7461 672c 203c 3e20 3c34 3e3a  ure tag, <> <4>:\n-0001f6d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f6e0: 2020 2053 7765 7074 2070 6f69 6e74 732e     Swept points.\n-0001f6f0: 2020 2020 2020 2020 286c 696e 6520 2031          (line  1\n-0001f700: 3329 0a2a 2063 6c6f 7375 7265 2074 6167  3).* closure tag\n-0001f710: 2c20 3c3e 203c 353e 3a20 2020 2020 2020  , <> <5>:       \n-0001f720: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n-0001f730: 7420 6c69 6e65 732e 2020 2020 2020 2020  t lines.        \n-0001f740: 2028 6c69 6e65 2020 2036 290a 2a20 636c   (line   6).* cl\n-0001f750: 6f73 7572 6520 7461 672c 203c 3e20 3c36  osure tag, <> <6\n-0001f760: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001f770: 2020 2020 2053 7765 7074 206c 696e 6573       Swept lines\n-0001f780: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n-0001f790: 2032 3829 0a2a 2063 6c6f 7375 7265 2074   28).* closure t\n-0001f7a0: 6167 2c20 3c3e 203c 373e 3a20 2020 2020  ag, <> <7>:     \n-0001f7b0: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n-0001f7c0: 6565 7020 6661 6365 2073 706c 6974 7469  eep face splitti\n-0001f7d0: 6e67 2e0a 2020 2020 2020 2020 2020 2020  ng..            \n+0001f610: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f620: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n+0001f630: 636c 6f73 7572 6520 7461 672c 203c 3e20  closure tag, <> \n+0001f640: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n+0001f650: 2020 2020 2020 2053 7765 6570 732e 2020         Sweeps.  \n+0001f660: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+0001f670: 6520 2031 3929 0a2a 2063 6c6f 7375 7265  e  19).* closure\n+0001f680: 2074 6167 2c20 3c3e 203c 333e 3a20 2020   tag, <> <3>:   \n+0001f690: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f6a0: 5377 6570 7420 706f 696e 7473 2e20 2020  Swept points.   \n+0001f6b0: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n+0001f6c0: 2a20 636c 6f73 7572 6520 7461 672c 203c  * closure tag, <\n+0001f6d0: 3e20 3c34 3e3a 2020 2020 2020 2020 2020  > <4>:          \n+0001f6e0: 2020 2020 2020 2020 2053 7765 7074 2070           Swept p\n+0001f6f0: 6f69 6e74 732e 2020 2020 2020 2020 286c  oints.        (l\n+0001f700: 696e 6520 2031 3329 0a2a 2063 6c6f 7375  ine  13).* closu\n+0001f710: 7265 2074 6167 2c20 3c3e 203c 353e 3a20  re tag, <> <5>: \n+0001f720: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f730: 2020 5377 6570 7420 6c69 6e65 732e 2020    Swept lines.  \n+0001f740: 2020 2020 2020 2028 6c69 6e65 2020 2036         (line   6\n+0001f750: 290a 2a20 636c 6f73 7572 6520 7461 672c  ).* closure tag,\n+0001f760: 203c 3e20 3c36 3e3a 2020 2020 2020 2020   <> <6>:        \n+0001f770: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n+0001f780: 206c 696e 6573 2e20 2020 2020 2020 2020   lines.         \n+0001f790: 286c 696e 6520 2032 3829 0a2a 2063 6c6f  (line  28).* clo\n+0001f7a0: 7375 7265 2074 6167 2c20 3c3e 203c 373e  sure tag, <> <7>\n+0001f7b0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001f7c0: 2020 2020 5377 6565 7020 6661 6365 2073      Sweep face s\n+0001f7d0: 706c 6974 7469 6e67 2e0a 2020 2020 2020  plitting..      \n 0001f7e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001f7f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001f800: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f810: 2020 286c 696e 6520 2031 3129 0a2a 2063    (line  11).* c\n-0001f820: 6f6d 6d61 6e64 206c 696e 6520 6f70 7469  ommand line opti\n-0001f830: 6f6e 3a20 2020 2020 2020 2020 2020 2020  on:             \n-0001f840: 2020 2020 2020 4865 6c6c 6f20 776f 726c        Hello worl\n-0001f850: 642e 2020 2020 2020 2020 2028 6c69 6e65  d.         (line\n-0001f860: 2020 3330 290a 2a20 636f 6d6d 616e 6420    30).* command \n-0001f870: 6c69 6e65 206f 7074 696f 6e73 3a20 2020  line options:   \n-0001f880: 2020 2020 2020 2020 2020 2020 2020 2043                 C\n-0001f890: 6f6d 6d61 6e64 206c 696e 652e 2020 2020  ommand line.    \n-0001f8a0: 2020 2020 286c 696e 6520 2031 3429 0a2a      (line  14).*\n-0001f8b0: 2063 6f6d 6d61 6e64 206c 696e 652c 2073   command line, s\n-0001f8c0: 6b65 7463 683a 2020 2020 2020 2020 2020  ketch:          \n-0001f8d0: 2020 2020 2020 2020 4865 6c6c 6f20 776f          Hello wo\n-0001f8e0: 726c 642e 2020 2020 2020 2020 2028 6c69  rld.         (li\n-0001f8f0: 6e65 2020 2039 290a 2a20 636f 6d6d 616e  ne   9).* comman\n-0001f900: 6420 6c69 6e65 2c20 736b 6574 6368 203c  d line, sketch <\n-0001f910: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-0001f920: 2043 6f6d 6d61 6e64 206c 696e 652e 2020   Command line.  \n-0001f930: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n-0001f940: 0a2a 2063 6f6d 6d65 6e74 733a 2020 2020  .* comments:    \n-0001f950: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f960: 2020 2020 2020 2020 2020 4472 6177 696e            Drawin\n-0001f970: 6720 6120 736f 6c69 642e 2020 2020 2028  g a solid.     (\n-0001f980: 6c69 6e65 2020 3238 290a 2a20 636f 6d6d  line  28).* comm\n-0001f990: 656e 7473 203c 313e 3a20 2020 2020 2020  ents <1>:       \n+0001f810: 2020 2020 2020 2020 286c 696e 6520 2031          (line  1\n+0001f820: 3129 0a2a 2063 6f6d 6d61 6e64 206c 696e  1).* command lin\n+0001f830: 6520 6f70 7469 6f6e 3a20 2020 2020 2020  e option:       \n+0001f840: 2020 2020 2020 2020 2020 2020 4865 6c6c              Hell\n+0001f850: 6f20 776f 726c 642e 2020 2020 2020 2020  o world.        \n+0001f860: 2028 6c69 6e65 2020 3330 290a 2a20 636f   (line  30).* co\n+0001f870: 6d6d 616e 6420 6c69 6e65 206f 7074 696f  mmand line optio\n+0001f880: 6e73 3a20 2020 2020 2020 2020 2020 2020  ns:             \n+0001f890: 2020 2020 2043 6f6d 6d61 6e64 206c 696e       Command lin\n+0001f8a0: 652e 2020 2020 2020 2020 286c 696e 6520  e.        (line \n+0001f8b0: 2031 3429 0a2a 2063 6f6d 6d61 6e64 206c   14).* command l\n+0001f8c0: 696e 652c 2073 6b65 7463 683a 2020 2020  ine, sketch:    \n+0001f8d0: 2020 2020 2020 2020 2020 2020 2020 4865                He\n+0001f8e0: 6c6c 6f20 776f 726c 642e 2020 2020 2020  llo world.      \n+0001f8f0: 2020 2028 6c69 6e65 2020 2039 290a 2a20     (line   9).* \n+0001f900: 636f 6d6d 616e 6420 6c69 6e65 2c20 736b  command line, sk\n+0001f910: 6574 6368 203c 313e 3a20 2020 2020 2020  etch <1>:       \n+0001f920: 2020 2020 2020 2043 6f6d 6d61 6e64 206c         Command l\n+0001f930: 696e 652e 2020 2020 2020 2020 286c 696e  ine.        (lin\n+0001f940: 6520 2020 3629 0a2a 2063 6f6d 6d65 6e74  e   6).* comment\n+0001f950: 733a 2020 2020 2020 2020 2020 2020 2020  s:              \n+0001f960: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f970: 4472 6177 696e 6720 6120 736f 6c69 642e  Drawing a solid.\n+0001f980: 2020 2020 2028 6c69 6e65 2020 3238 290a       (line  28).\n+0001f990: 2a20 636f 6d6d 656e 7473 203c 313e 3a20  * comments <1>: \n 0001f9a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f9b0: 2020 204c 616e 6775 6167 6520 6261 7369     Language basi\n-0001f9c0: 6373 2e20 2020 2020 286c 696e 6520 2031  cs.     (line  1\n-0001f9d0: 3829 0a2a 2063 6f6e 7374 7275 6374 6f72  8).* constructor\n-0001f9e0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001f9f0: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n-0001fa00: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n-0001fa10: 2028 6c69 6e65 2020 2036 290a 2a20 636f   (line   6).* co\n-0001fa20: 6f72 6469 6e61 7465 2073 7973 7465 6d2c  ordinate system,\n-0001fa30: 2072 6967 6874 2d68 616e 6465 643a 2020   right-handed:  \n-0001fa40: 2020 2020 2049 6e74 726f 6475 6374 696f       Introductio\n-0001fa50: 6e20 6279 2065 7861 6d70 6c65 2e0a 2020  n by example..  \n-0001fa60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f9b0: 2020 2020 2020 2020 204c 616e 6775 6167           Languag\n+0001f9c0: 6520 6261 7369 6373 2e20 2020 2020 286c  e basics.     (l\n+0001f9d0: 696e 6520 2031 3829 0a2a 2063 6f6e 7374  ine  18).* const\n+0001f9e0: 7275 6374 6f72 3a20 2020 2020 2020 2020  ructor:         \n+0001f9f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001fa00: 2020 5472 616e 7366 6f72 6d20 6c69 7465    Transform lite\n+0001fa10: 7261 6c73 2e20 2028 6c69 6e65 2020 2036  rals.  (line   6\n+0001fa20: 290a 2a20 636f 6f72 6469 6e61 7465 2073  ).* coordinate s\n+0001fa30: 7973 7465 6d2c 2072 6967 6874 2d68 616e  ystem, right-han\n+0001fa40: 6465 643a 2020 2020 2020 2049 6e74 726f  ded:       Intro\n+0001fa50: 6475 6374 696f 6e20 6279 2065 7861 6d70  duction by examp\n+0001fa60: 6c65 2e0a 2020 2020 2020 2020 2020 2020  le..            \n 0001fa70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001fa80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fa90: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-0001faa0: 6520 2031 3129 0a2a 2063 6f75 6e74 6572  e  11).* counter\n-0001fab0: 2d63 6c6f 636b 7769 7365 2070 6f6c 7967  -clockwise polyg\n-0001fac0: 6f6e 2076 6572 7465 7820 6f72 6465 723a  on vertex order:\n-0001fad0: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020   Hello world.   \n-0001fae0: 2020 2020 2028 6c69 6e65 2020 3339 290a       (line  39).\n-0001faf0: 2a20 6375 6c6c 696e 673a 2020 2020 2020  * culling:      \n+0001fa90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001faa0: 2020 286c 696e 6520 2031 3129 0a2a 2063    (line  11).* c\n+0001fab0: 6f75 6e74 6572 2d63 6c6f 636b 7769 7365  ounter-clockwise\n+0001fac0: 2070 6f6c 7967 6f6e 2076 6572 7465 7820   polygon vertex \n+0001fad0: 6f72 6465 723a 2048 656c 6c6f 2077 6f72  order: Hello wor\n+0001fae0: 6c64 2e20 2020 2020 2020 2028 6c69 6e65  ld.        (line\n+0001faf0: 2020 3339 290a 2a20 6375 6c6c 696e 673a    39).* culling:\n 0001fb00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fb10: 2020 2020 2020 2020 2048 656c 6c6f 2077           Hello w\n-0001fb20: 6f72 6c64 2e20 2020 2020 2020 2020 286c  orld.         (l\n-0001fb30: 696e 6520 2034 3329 0a2a 2063 756c 6c69  ine  43).* culli\n-0001fb40: 6e67 203c 313e 3a20 2020 2020 2020 2020  ng <1>:         \n+0001fb10: 2020 2020 2020 2020 2020 2020 2020 2048                 H\n+0001fb20: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020  ello world.     \n+0001fb30: 2020 2020 286c 696e 6520 2034 3329 0a2a      (line  43).*\n+0001fb40: 2063 756c 6c69 6e67 203c 313e 3a20 2020   culling <1>:   \n 0001fb50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fb60: 2020 4472 6177 696e 6720 6120 736f 6c69    Drawing a soli\n-0001fb70: 642e 2020 2020 2028 6c69 6e65 2020 3335  d.     (line  35\n-0001fb80: 290a 2a20 6375 6c6c 696e 6720 3c32 3e3a  ).* culling <2>:\n-0001fb90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fba0: 2020 2020 2020 2020 2020 2044 7261 7769             Drawi\n-0001fbb0: 6e67 2061 2073 6f6c 6964 2e20 2020 2020  ng a solid.     \n-0001fbc0: 286c 696e 6520 2034 3129 0a2a 2063 756c  (line  41).* cul\n-0001fbd0: 6c69 6e67 203c 333e 3a20 2020 2020 2020  ling <3>:       \n+0001fb60: 2020 2020 2020 2020 4472 6177 696e 6720          Drawing \n+0001fb70: 6120 736f 6c69 642e 2020 2020 2028 6c69  a solid.     (li\n+0001fb80: 6e65 2020 3335 290a 2a20 6375 6c6c 696e  ne  35).* cullin\n+0001fb90: 6720 3c32 3e3a 2020 2020 2020 2020 2020  g <2>:          \n+0001fba0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001fbb0: 2044 7261 7769 6e67 2061 2073 6f6c 6964   Drawing a solid\n+0001fbc0: 2e20 2020 2020 286c 696e 6520 2034 3129  .     (line  41)\n+0001fbd0: 0a2a 2063 756c 6c69 6e67 203c 333e 3a20  .* culling <3>: \n 0001fbe0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fbf0: 2020 2020 5377 6570 7420 6c69 6e65 732e      Swept lines.\n-0001fc00: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-0001fc10: 3136 290a 2a20 6465 636c 6172 6174 6976  16).* declarativ\n-0001fc20: 6520 6c61 6e67 7561 6765 3a20 2020 2020  e language:     \n-0001fc30: 2020 2020 2020 2020 2020 2020 204c 616e               Lan\n-0001fc40: 6775 6167 6520 6261 7369 6373 2e20 2020  guage basics.   \n-0001fc50: 2020 286c 696e 6520 2020 3829 0a2a 2064    (line   8).* d\n-0001fc60: 6566 696e 6974 696f 6e3a 2020 2020 2020  efinition:      \n+0001fbf0: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n+0001fc00: 6c69 6e65 732e 2020 2020 2020 2020 2028  lines.         (\n+0001fc10: 6c69 6e65 2020 3136 290a 2a20 6465 636c  line  16).* decl\n+0001fc20: 6172 6174 6976 6520 6c61 6e67 7561 6765  arative language\n+0001fc30: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001fc40: 2020 204c 616e 6775 6167 6520 6261 7369     Language basi\n+0001fc50: 6373 2e20 2020 2020 286c 696e 6520 2020  cs.     (line   \n+0001fc60: 3829 0a2a 2064 6566 696e 6974 696f 6e3a  8).* definition:\n 0001fc70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fc80: 2020 2020 2020 4472 6177 696e 6720 6120        Drawing a \n-0001fc90: 736f 6c69 642e 2020 2020 2028 6c69 6e65  solid.     (line\n-0001fca0: 2020 3232 290a 2a20 6465 6669 6e69 7469    22).* definiti\n-0001fcb0: 6f6e 203c 313e 3a20 2020 2020 2020 2020  on <1>:         \n-0001fcc0: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n-0001fcd0: 6566 696e 6974 696f 6e73 2e20 2020 2020  efinitions.     \n-0001fce0: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-0001fcf0: 2064 6566 696e 6974 696f 6e20 7769 7468   definition with\n-0001fd00: 2061 6c74 6572 6e61 7469 7665 733a 2020   alternatives:  \n-0001fd10: 2020 2020 2020 2020 466f 726d 7320 6f66          Forms of\n-0001fd20: 2064 6566 696e 6974 696f 6e73 2e0a 2020   definitions..  \n-0001fd30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001fc80: 2020 2020 2020 2020 2020 2020 4472 6177              Draw\n+0001fc90: 696e 6720 6120 736f 6c69 642e 2020 2020  ing a solid.    \n+0001fca0: 2028 6c69 6e65 2020 3232 290a 2a20 6465   (line  22).* de\n+0001fcb0: 6669 6e69 7469 6f6e 203c 313e 3a20 2020  finition <1>:   \n+0001fcc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001fcd0: 2020 2020 2044 6566 696e 6974 696f 6e73       Definitions\n+0001fce0: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n+0001fcf0: 2020 3629 0a2a 2064 6566 696e 6974 696f    6).* definitio\n+0001fd00: 6e20 7769 7468 2061 6c74 6572 6e61 7469  n with alternati\n+0001fd10: 7665 733a 2020 2020 2020 2020 2020 466f  ves:          Fo\n+0001fd20: 726d 7320 6f66 2064 6566 696e 6974 696f  rms of definitio\n+0001fd30: 6e73 2e0a 2020 2020 2020 2020 2020 2020  ns..            \n 0001fd40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001fd50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fd60: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-0001fd70: 6520 2020 3629 0a2a 2064 6566 696e 6974  e   6).* definit\n-0001fd80: 696f 6e2c 2064 7261 7761 626c 653a 2020  ion, drawable:  \n-0001fd90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fda0: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n-0001fdb0: 732e 2020 2028 6c69 6e65 2020 3237 290a  s.   (line  27).\n-0001fdc0: 2a20 6465 6669 6e69 7469 6f6e 2c20 6f70  * definition, op\n-0001fdd0: 7469 6f6e 733a 2020 2020 2020 2020 2020  tions:          \n-0001fde0: 2020 2020 2020 2020 2050 6f6c 796c 696e           Polylin\n-0001fdf0: 6520 7377 6565 7073 2077 6974 6820 636c  e sweeps with cl\n-0001fe00: 6f73 7572 652e 0a20 2020 2020 2020 2020  osure..         \n+0001fd60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001fd70: 2020 286c 696e 6520 2020 3629 0a2a 2064    (line   6).* d\n+0001fd80: 6566 696e 6974 696f 6e2c 2064 7261 7761  efinition, drawa\n+0001fd90: 626c 653a 2020 2020 2020 2020 2020 2020  ble:            \n+0001fda0: 2020 2020 2020 4f62 6a65 6374 2074 7261        Object tra\n+0001fdb0: 6e73 666f 726d 732e 2020 2028 6c69 6e65  nsforms.   (line\n+0001fdc0: 2020 3237 290a 2a20 6465 6669 6e69 7469    27).* definiti\n+0001fdd0: 6f6e 2c20 6f70 7469 6f6e 733a 2020 2020  on, options:    \n+0001fde0: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n+0001fdf0: 6f6c 796c 696e 6520 7377 6565 7073 2077  olyline sweeps w\n+0001fe00: 6974 6820 636c 6f73 7572 652e 0a20 2020  ith closure..   \n 0001fe10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001fe20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001fe30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fe40: 2020 2020 2028 6c69 6e65 2020 3233 290a       (line  23).\n-0001fe50: 2a20 6465 6669 6e69 7469 6f6e 2c20 706f  * definition, po\n-0001fe60: 696e 743a 2020 2020 2020 2020 2020 2020  int:            \n-0001fe70: 2020 2020 2020 2020 2044 7261 7769 6e67           Drawing\n-0001fe80: 2061 2073 6f6c 6964 2e20 2020 2020 286c   a solid.     (l\n-0001fe90: 696e 6520 2032 3329 0a2a 2064 6566 696e  ine  23).* defin\n-0001fea0: 6974 696f 6e2c 2073 6361 6c61 723a 2020  ition, scalar:  \n-0001feb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fec0: 2020 5377 6570 7420 6f62 6a65 6374 732e    Swept objects.\n-0001fed0: 2020 2020 2020 2028 6c69 6e65 2020 3133         (line  13\n-0001fee0: 290a 2a20 6465 6669 6e69 7469 6f6e 2c20  ).* definition, \n-0001fef0: 7369 6d70 6c65 3a20 2020 2020 2020 2020  simple:         \n-0001ff00: 2020 2020 2020 2020 2020 2046 6f72 6d73             Forms\n-0001ff10: 206f 6620 6465 6669 6e69 7469 6f6e 732e   of definitions.\n-0001ff20: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+0001fe40: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001fe50: 2020 3233 290a 2a20 6465 6669 6e69 7469    23).* definiti\n+0001fe60: 6f6e 2c20 706f 696e 743a 2020 2020 2020  on, point:      \n+0001fe70: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n+0001fe80: 7261 7769 6e67 2061 2073 6f6c 6964 2e20  rawing a solid. \n+0001fe90: 2020 2020 286c 696e 6520 2032 3329 0a2a      (line  23).*\n+0001fea0: 2064 6566 696e 6974 696f 6e2c 2073 6361   definition, sca\n+0001feb0: 6c61 723a 2020 2020 2020 2020 2020 2020  lar:            \n+0001fec0: 2020 2020 2020 2020 5377 6570 7420 6f62          Swept ob\n+0001fed0: 6a65 6374 732e 2020 2020 2020 2028 6c69  jects.       (li\n+0001fee0: 6e65 2020 3133 290a 2a20 6465 6669 6e69  ne  13).* defini\n+0001fef0: 7469 6f6e 2c20 7369 6d70 6c65 3a20 2020  tion, simple:   \n+0001ff00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ff10: 2046 6f72 6d73 206f 6620 6465 6669 6e69   Forms of defini\n+0001ff20: 7469 6f6e 732e 0a20 2020 2020 2020 2020  tions..         \n 0001ff30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001ff40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ff50: 2020 2020 2020 2020 2020 2020 2020 2028                 (\n-0001ff60: 6c69 6e65 2020 2036 290a 2a20 6465 6669  line   6).* defi\n-0001ff70: 6e69 7469 6f6e 2c20 7461 673a 2020 2020  nition, tag:    \n-0001ff80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ff90: 2020 2044 6566 696e 6974 696f 6e73 2e20     Definitions. \n-0001ffa0: 2020 2020 2020 2020 286c 696e 6520 2031          (line  1\n-0001ffb0: 3829 0a2a 2064 6566 696e 6974 696f 6e2c  8).* definition,\n-0001ffc0: 2074 6167 203c 313e 3a20 2020 2020 2020   tag <1>:       \n-0001ffd0: 2020 2020 2020 2020 2020 2020 466f 726d              Form\n-0001ffe0: 7320 6f66 2064 6566 696e 6974 696f 6e73  s of definitions\n-0001fff0: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+0001ff50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ff60: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n+0001ff70: 2a20 6465 6669 6e69 7469 6f6e 2c20 7461  * definition, ta\n+0001ff80: 673a 2020 2020 2020 2020 2020 2020 2020  g:              \n+0001ff90: 2020 2020 2020 2020 2044 6566 696e 6974           Definit\n+0001ffa0: 696f 6e73 2e20 2020 2020 2020 2020 286c  ions.         (l\n+0001ffb0: 696e 6520 2031 3829 0a2a 2064 6566 696e  ine  18).* defin\n+0001ffc0: 6974 696f 6e2c 2074 6167 203c 313e 3a20  ition, tag <1>: \n+0001ffd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001ffe0: 2020 466f 726d 7320 6f66 2064 6566 696e    Forms of defin\n+0001fff0: 6974 696f 6e73 2e0a 2020 2020 2020 2020  itions..        \n 00020000: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00020010: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00020020: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020030: 286c 696e 6520 2020 3729 0a2a 2064 6566  (line   7).* def\n-00020040: 696e 6974 696f 6e2c 2074 6167 203c 323e  inition, tag <2>\n-00020050: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00020060: 2020 2020 436f 6d6d 616e 6420 6c69 6e65      Command line\n-00020070: 2e20 2020 2020 2020 2028 6c69 6e65 2020  .        (line  \n-00020080: 3533 290a 2a20 6465 6669 6e69 7469 6f6e  53).* definition\n-00020090: 2c20 7472 616e 7366 6f72 6d3a 2020 2020  , transform:    \n-000200a0: 2020 2020 2020 2020 2020 2020 204f 7665               Ove\n-000200b0: 7276 6965 772e 2020 2020 2020 2020 2020  rview.          \n-000200c0: 2020 286c 696e 6520 2033 3529 0a2a 2064    (line  35).* d\n-000200d0: 6566 696e 6974 696f 6e2c 2076 6563 746f  efinition, vecto\n-000200e0: 723a 2020 2020 2020 2020 2020 2020 2020  r:              \n-000200f0: 2020 2020 2020 506f 6c79 6c69 6e65 2073        Polyline s\n-00020100: 7765 6570 732e 2020 2020 2028 6c69 6e65  weeps.     (line\n-00020110: 2020 3139 290a 2a20 6465 7074 6820 736f    19).* depth so\n-00020120: 7274 3a20 2020 2020 2020 2020 2020 2020  rt:             \n-00020130: 2020 2020 2020 2020 2020 2020 2020 2049                 I\n-00020140: 6e74 6572 6e61 6c20 6f70 7469 6f6e 732e  nternal options.\n-00020150: 2020 2020 286c 696e 6520 2031 3329 0a2a      (line  13).*\n-00020160: 2064 6570 7468 2073 6f72 7420 3c31 3e3a   depth sort <1>:\n-00020170: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020180: 2020 2020 2020 2020 4869 6464 656e 2073          Hidden s\n-00020190: 7572 6661 6365 2072 656d 6f76 616c 2e0a  urface removal..\n-000201a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020030: 2020 2020 2020 286c 696e 6520 2020 3729        (line   7)\n+00020040: 0a2a 2064 6566 696e 6974 696f 6e2c 2074  .* definition, t\n+00020050: 6167 203c 323e 3a20 2020 2020 2020 2020  ag <2>:         \n+00020060: 2020 2020 2020 2020 2020 436f 6d6d 616e            Comman\n+00020070: 6420 6c69 6e65 2e20 2020 2020 2020 2028  d line.        (\n+00020080: 6c69 6e65 2020 3533 290a 2a20 6465 6669  line  53).* defi\n+00020090: 6e69 7469 6f6e 2c20 7472 616e 7366 6f72  nition, transfor\n+000200a0: 6d3a 2020 2020 2020 2020 2020 2020 2020  m:              \n+000200b0: 2020 204f 7665 7276 6965 772e 2020 2020     Overview.    \n+000200c0: 2020 2020 2020 2020 286c 696e 6520 2033          (line  3\n+000200d0: 3529 0a2a 2064 6566 696e 6974 696f 6e2c  5).* definition,\n+000200e0: 2076 6563 746f 723a 2020 2020 2020 2020   vector:        \n+000200f0: 2020 2020 2020 2020 2020 2020 506f 6c79              Poly\n+00020100: 6c69 6e65 2073 7765 6570 732e 2020 2020  line sweeps.    \n+00020110: 2028 6c69 6e65 2020 3139 290a 2a20 6465   (line  19).* de\n+00020120: 7074 6820 736f 7274 3a20 2020 2020 2020  pth sort:       \n+00020130: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020140: 2020 2020 2049 6e74 6572 6e61 6c20 6f70       Internal op\n+00020150: 7469 6f6e 732e 2020 2020 286c 696e 6520  tions.    (line \n+00020160: 2031 3329 0a2a 2064 6570 7468 2073 6f72   13).* depth sor\n+00020170: 7420 3c31 3e3a 2020 2020 2020 2020 2020  t <1>:          \n+00020180: 2020 2020 2020 2020 2020 2020 2020 4869                Hi\n+00020190: 6464 656e 2073 7572 6661 6365 2072 656d  dden surface rem\n+000201a0: 6f76 616c 2e0a 2020 2020 2020 2020 2020  oval..          \n 000201b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000201c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000201d0: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-000201e0: 696e 6520 2020 3629 0a2a 2064 6570 7468  ine   6).* depth\n-000201f0: 2073 6f72 7420 3c32 3e3a 2020 2020 2020   sort <2>:      \n+000201d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000201e0: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n+000201f0: 2064 6570 7468 2073 6f72 7420 3c32 3e3a   depth sort <2>:\n 00020200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020210: 2020 4275 6773 2061 6e64 2061 6e6f 6d61    Bugs and anoma\n-00020220: 6c69 6573 2e20 2028 6c69 6e65 2020 2038  lies.  (line   8\n-00020230: 290a 2a20 6469 7265 6374 2074 7261 6e73  ).* direct trans\n-00020240: 666f 726d 3a20 2020 2020 2020 2020 2020  form:           \n-00020250: 2020 2020 2020 2020 2020 2054 7261 6e73             Trans\n-00020260: 666f 726d 206c 6974 6572 616c 732e 2020  form literals.  \n-00020270: 286c 696e 6520 2034 3729 0a2a 2064 6972  (line  47).* dir\n-00020280: 6563 7420 7472 616e 7366 6f72 6d20 3c31  ect transform <1\n-00020290: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-000202a0: 2020 2020 5472 616e 7366 6f72 6d20 6c69      Transform li\n-000202b0: 7465 7261 6c73 2e20 2028 6c69 6e65 2020  terals.  (line  \n-000202c0: 3533 290a 2a20 646f 6375 6d65 6e74 2074  53).* document t\n-000202d0: 656d 706c 6174 653a 2020 2020 2020 2020  emplate:        \n-000202e0: 2020 2020 2020 2020 2020 2020 2048 656c               Hel\n-000202f0: 6c6f 2077 6f72 6c64 2e20 2020 2020 2020  lo world.       \n-00020300: 2020 286c 696e 6520 2033 3229 0a2a 2064    (line  32).* d\n-00020310: 6f63 756d 656e 7420 7465 6d70 6c61 7465  ocument template\n-00020320: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-00020330: 2020 2020 2020 436f 6d6d 616e 6420 6c69        Command li\n-00020340: 6e65 2e20 2020 2020 2020 2028 6c69 6e65  ne.        (line\n-00020350: 2020 3336 290a 2a20 6472 6177 6162 6c65    36).* drawable\n-00020360: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00020370: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n-00020380: 626a 6563 7420 7472 616e 7366 6f72 6d73  bject transforms\n-00020390: 2e20 2020 286c 696e 6520 2032 3729 0a2a  .   (line  27).*\n-000203a0: 2064 7261 7761 626c 6520 3c31 3e3a 2020   drawable <1>:  \n-000203b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000203c0: 2020 2020 2020 2020 4472 6177 6162 6c65          Drawable\n-000203d0: 732e 2020 2020 2020 2020 2020 2028 6c69  s.           (li\n-000203e0: 6e65 2020 2036 290a 2a20 6472 6177 6162  ne   6).* drawab\n-000203f0: 6c65 2064 6566 696e 6974 696f 6e3a 2020  le definition:  \n-00020400: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020410: 204f 626a 6563 7420 7472 616e 7366 6f72   Object transfor\n-00020420: 6d73 2e20 2020 286c 696e 6520 2032 3729  ms.   (line  27)\n-00020430: 0a2a 2064 7261 7761 626c 6520 7265 6665  .* drawable refe\n-00020440: 7265 6e63 653a 2020 2020 2020 2020 2020  rence:          \n-00020450: 2020 2020 2020 2020 2020 466f 726d 7320            Forms \n-00020460: 6f66 2072 6566 6572 656e 6365 732e 2028  of references. (\n-00020470: 6c69 6e65 2020 3137 290a 2a20 656e 6420  line  17).* end \n-00020480: 706f 6c79 676f 6e3a 2020 2020 2020 2020  polygon:        \n+00020210: 2020 2020 2020 2020 4275 6773 2061 6e64          Bugs and\n+00020220: 2061 6e6f 6d61 6c69 6573 2e20 2028 6c69   anomalies.  (li\n+00020230: 6e65 2020 2038 290a 2a20 6469 7265 6374  ne   8).* direct\n+00020240: 2074 7261 6e73 666f 726d 3a20 2020 2020   transform:     \n+00020250: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020260: 2054 7261 6e73 666f 726d 206c 6974 6572   Transform liter\n+00020270: 616c 732e 2020 286c 696e 6520 2034 3729  als.  (line  47)\n+00020280: 0a2a 2064 6972 6563 7420 7472 616e 7366  .* direct transf\n+00020290: 6f72 6d20 3c31 3e3a 2020 2020 2020 2020  orm <1>:        \n+000202a0: 2020 2020 2020 2020 2020 5472 616e 7366            Transf\n+000202b0: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028  orm literals.  (\n+000202c0: 6c69 6e65 2020 3533 290a 2a20 646f 6375  line  53).* docu\n+000202d0: 6d65 6e74 2074 656d 706c 6174 653a 2020  ment template:  \n+000202e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000202f0: 2020 2048 656c 6c6f 2077 6f72 6c64 2e20     Hello world. \n+00020300: 2020 2020 2020 2020 286c 696e 6520 2033          (line  3\n+00020310: 3229 0a2a 2064 6f63 756d 656e 7420 7465  2).* document te\n+00020320: 6d70 6c61 7465 203c 313e 3a20 2020 2020  mplate <1>:     \n+00020330: 2020 2020 2020 2020 2020 2020 436f 6d6d              Comm\n+00020340: 616e 6420 6c69 6e65 2e20 2020 2020 2020  and line.       \n+00020350: 2028 6c69 6e65 2020 3336 290a 2a20 6472   (line  36).* dr\n+00020360: 6177 6162 6c65 3a20 2020 2020 2020 2020  awable:         \n+00020370: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020380: 2020 2020 204f 626a 6563 7420 7472 616e       Object tran\n+00020390: 7366 6f72 6d73 2e20 2020 286c 696e 6520  sforms.   (line \n+000203a0: 2032 3729 0a2a 2064 7261 7761 626c 6520   27).* drawable \n+000203b0: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n+000203c0: 2020 2020 2020 2020 2020 2020 2020 4472                Dr\n+000203d0: 6177 6162 6c65 732e 2020 2020 2020 2020  awables.        \n+000203e0: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n+000203f0: 6472 6177 6162 6c65 2064 6566 696e 6974  drawable definit\n+00020400: 696f 6e3a 2020 2020 2020 2020 2020 2020  ion:            \n+00020410: 2020 2020 2020 204f 626a 6563 7420 7472         Object tr\n+00020420: 616e 7366 6f72 6d73 2e20 2020 286c 696e  ansforms.   (lin\n+00020430: 6520 2032 3729 0a2a 2064 7261 7761 626c  e  27).* drawabl\n+00020440: 6520 7265 6665 7265 6e63 653a 2020 2020  e reference:    \n+00020450: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020460: 466f 726d 7320 6f66 2072 6566 6572 656e  Forms of referen\n+00020470: 6365 732e 2028 6c69 6e65 2020 3137 290a  ces. (line  17).\n+00020480: 2a20 656e 6420 706f 6c79 676f 6e3a 2020  * end polygon:  \n 00020490: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000204a0: 2020 2053 7765 7074 206c 696e 6573 2e20     Swept lines. \n-000204b0: 2020 2020 2020 2020 286c 696e 6520 2033          (line  3\n-000204c0: 3829 0a2a 2065 6e64 2070 6f6c 7967 6f6e  8).* end polygon\n-000204d0: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-000204e0: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n-000204f0: 7420 706f 6c79 676f 6e73 2e20 2020 2020  t polygons.     \n-00020500: 2028 6c69 6e65 2020 3135 290a 2a20 6661   (line  15).* fa\n-00020510: 6365 733a 2020 2020 2020 2020 2020 2020  ces:            \n+000204a0: 2020 2020 2020 2020 2053 7765 7074 206c           Swept l\n+000204b0: 696e 6573 2e20 2020 2020 2020 2020 286c  ines.         (l\n+000204c0: 696e 6520 2033 3829 0a2a 2065 6e64 2070  ine  38).* end p\n+000204d0: 6f6c 7967 6f6e 203c 313e 3a20 2020 2020  olygon <1>:     \n+000204e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000204f0: 2020 5377 6570 7420 706f 6c79 676f 6e73    Swept polygons\n+00020500: 2e20 2020 2020 2028 6c69 6e65 2020 3135  .      (line  15\n+00020510: 290a 2a20 6661 6365 733a 2020 2020 2020  ).* faces:      \n 00020520: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020530: 2020 2020 2044 7261 7769 6e67 2061 2073       Drawing a s\n-00020540: 6f6c 6964 2e20 2020 2020 286c 696e 6520  olid.     (line \n-00020550: 2020 3729 0a2a 2066 6163 6573 203c 313e    7).* faces <1>\n-00020560: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00020570: 2020 2020 2020 2020 2020 2020 2020 506f                Po\n-00020580: 6c79 6c69 6e65 2073 7765 6570 732e 2020  lyline sweeps.  \n-00020590: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n-000205a0: 6669 6c65 2c20 696e 636c 7564 653a 2020  file, include:  \n-000205b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000205c0: 2020 2020 2020 204c 616e 6775 6167 6520         Language \n-000205d0: 6261 7369 6373 2e20 2020 2020 286c 696e  basics.     (lin\n-000205e0: 6520 2031 3929 0a2a 2066 696c 652c 2069  e  19).* file, i\n-000205f0: 6e70 7574 3a20 2020 2020 2020 2020 2020  nput:           \n+00020530: 2020 2020 2020 2020 2020 2044 7261 7769             Drawi\n+00020540: 6e67 2061 2073 6f6c 6964 2e20 2020 2020  ng a solid.     \n+00020550: 286c 696e 6520 2020 3729 0a2a 2066 6163  (line   7).* fac\n+00020560: 6573 203c 313e 3a20 2020 2020 2020 2020  es <1>:         \n+00020570: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020580: 2020 2020 506f 6c79 6c69 6e65 2073 7765      Polyline swe\n+00020590: 6570 732e 2020 2020 2028 6c69 6e65 2020  eps.     (line  \n+000205a0: 2036 290a 2a20 6669 6c65 2c20 696e 636c   6).* file, incl\n+000205b0: 7564 653a 2020 2020 2020 2020 2020 2020  ude:            \n+000205c0: 2020 2020 2020 2020 2020 2020 204c 616e               Lan\n+000205d0: 6775 6167 6520 6261 7369 6373 2e20 2020  guage basics.   \n+000205e0: 2020 286c 696e 6520 2031 3929 0a2a 2066    (line  19).* f\n+000205f0: 696c 652c 2069 6e70 7574 3a20 2020 2020  ile, input:     \n 00020600: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020610: 4c61 6e67 7561 6765 2062 6173 6963 732e  Language basics.\n-00020620: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n-00020630: 2a20 6672 616d 6520 626f 783a 2020 2020  * frame box:    \n-00020640: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020650: 2020 2020 2020 2020 2046 7261 6d65 2e20           Frame. \n-00020660: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-00020670: 696e 6520 2020 3629 0a2a 2067 6c6f 6261  ine   6).* globa\n-00020680: 6c20 6f70 7469 6f6e 733a 2020 2020 2020  l options:      \n+00020610: 2020 2020 2020 4c61 6e67 7561 6765 2062        Language b\n+00020620: 6173 6963 732e 2020 2020 2028 6c69 6e65  asics.     (line\n+00020630: 2020 2036 290a 2a20 6672 616d 6520 626f     6).* frame bo\n+00020640: 783a 2020 2020 2020 2020 2020 2020 2020  x:              \n+00020650: 2020 2020 2020 2020 2020 2020 2020 2046                 F\n+00020660: 7261 6d65 2e20 2020 2020 2020 2020 2020  rame.           \n+00020670: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n+00020680: 2067 6c6f 6261 6c20 6f70 7469 6f6e 733a   global options:\n 00020690: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000206a0: 2020 4472 6177 696e 6720 6f70 7469 6f6e    Drawing option\n-000206b0: 732e 2020 2020 2028 6c69 6e65 2020 3138  s.     (line  18\n-000206c0: 290a 2a20 676c 6f62 616c 206f 7074 696f  ).* global optio\n-000206d0: 6e73 203c 313e 3a20 2020 2020 2020 2020  ns <1>:         \n-000206e0: 2020 2020 2020 2020 2020 2047 6c6f 6261             Globa\n-000206f0: 6c20 6f70 7469 6f6e 732e 2020 2020 2020  l options.      \n-00020700: 286c 696e 6520 2020 3629 0a2a 2068 656c  (line   6).* hel\n-00020710: 6978 3a20 2020 2020 2020 2020 2020 2020  ix:             \n+000206a0: 2020 2020 2020 2020 4472 6177 696e 6720          Drawing \n+000206b0: 6f70 7469 6f6e 732e 2020 2020 2028 6c69  options.     (li\n+000206c0: 6e65 2020 3138 290a 2a20 676c 6f62 616c  ne  18).* global\n+000206d0: 206f 7074 696f 6e73 203c 313e 3a20 2020   options <1>:   \n+000206e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000206f0: 2047 6c6f 6261 6c20 6f70 7469 6f6e 732e   Global options.\n+00020700: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+00020710: 0a2a 2068 656c 6978 3a20 2020 2020 2020  .* helix:       \n 00020720: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020730: 2020 2020 4472 6177 696e 6720 6120 736f      Drawing a so\n-00020740: 6c69 642e 2020 2020 2028 6c69 6e65 2020  lid.     (line  \n-00020750: 3437 290a 2a20 6865 6c69 7820 3c31 3e3a  47).* helix <1>:\n-00020760: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020770: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n-00020780: 796c 696e 6520 7377 6565 7073 2e20 2020  yline sweeps.   \n-00020790: 2020 286c 696e 6520 2031 3529 0a2a 2068    (line  15).* h\n-000207a0: 656c 6c6f 2077 6f72 6c64 3a20 2020 2020  ello world:     \n-000207b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000207c0: 2020 2020 2020 4865 6c6c 6f20 776f 726c        Hello worl\n-000207d0: 642e 2020 2020 2020 2020 2028 6c69 6e65  d.         (line\n-000207e0: 2020 2037 290a 2a20 6869 6464 656e 2073     7).* hidden s\n-000207f0: 7572 6661 6365 2061 6c67 6f72 6974 686d  urface algorithm\n-00020800: 3a20 2020 2020 2020 2020 2020 2020 2048  :              H\n-00020810: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020  ello world.     \n-00020820: 2020 2020 286c 696e 6520 2031 3929 0a2a      (line  19).*\n-00020830: 2068 6964 6465 6e20 7375 7266 6163 6520   hidden surface \n-00020840: 616c 676f 7269 7468 6d20 3c31 3e3a 2020  algorithm <1>:  \n-00020850: 2020 2020 2020 2020 5370 6563 6961 6c20          Special \n-00020860: 6f62 6a65 6374 732e 2020 2020 2028 6c69  objects.     (li\n-00020870: 6e65 2020 3438 290a 2a20 6869 6464 656e  ne  48).* hidden\n-00020880: 2073 7572 6661 6365 2061 6c67 6f72 6974   surface algorit\n-00020890: 686d 203c 323e 3a20 2020 2020 2020 2020  hm <2>:         \n-000208a0: 2054 7261 6e73 666f 726d 206c 6974 6572   Transform liter\n-000208b0: 616c 732e 2020 286c 696e 6520 2032 3429  als.  (line  24)\n-000208c0: 0a2a 2068 6964 6465 6e20 7375 7266 6163  .* hidden surfac\n-000208d0: 6520 616c 676f 7269 7468 6d20 3c33 3e3a  e algorithm <3>:\n-000208e0: 2020 2020 2020 2020 2020 4120 7465 6368            A tech\n-000208f0: 6e69 6361 6c20 6472 6177 696e 672e 2028  nical drawing. (\n-00020900: 6c69 6e65 2020 3235 290a 2a20 6869 6464  line  25).* hidd\n-00020910: 656e 2073 7572 6661 6365 2061 6c67 6f72  en surface algor\n-00020920: 6974 686d 203c 343e 3a20 2020 2020 2020  ithm <4>:       \n-00020930: 2020 2048 6964 6465 6e20 7375 7266 6163     Hidden surfac\n-00020940: 6520 7265 6d6f 7661 6c2e 0a20 2020 2020  e removal..     \n-00020950: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020730: 2020 2020 2020 2020 2020 4472 6177 696e            Drawin\n+00020740: 6720 6120 736f 6c69 642e 2020 2020 2028  g a solid.     (\n+00020750: 6c69 6e65 2020 3437 290a 2a20 6865 6c69  line  47).* heli\n+00020760: 7820 3c31 3e3a 2020 2020 2020 2020 2020  x <1>:          \n+00020770: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020780: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n+00020790: 7073 2e20 2020 2020 286c 696e 6520 2031  ps.     (line  1\n+000207a0: 3529 0a2a 2068 656c 6c6f 2077 6f72 6c64  5).* hello world\n+000207b0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000207c0: 2020 2020 2020 2020 2020 2020 4865 6c6c              Hell\n+000207d0: 6f20 776f 726c 642e 2020 2020 2020 2020  o world.        \n+000207e0: 2028 6c69 6e65 2020 2037 290a 2a20 6869   (line   7).* hi\n+000207f0: 6464 656e 2073 7572 6661 6365 2061 6c67  dden surface alg\n+00020800: 6f72 6974 686d 3a20 2020 2020 2020 2020  orithm:         \n+00020810: 2020 2020 2048 656c 6c6f 2077 6f72 6c64       Hello world\n+00020820: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n+00020830: 2031 3929 0a2a 2068 6964 6465 6e20 7375   19).* hidden su\n+00020840: 7266 6163 6520 616c 676f 7269 7468 6d20  rface algorithm \n+00020850: 3c31 3e3a 2020 2020 2020 2020 2020 5370  <1>:          Sp\n+00020860: 6563 6961 6c20 6f62 6a65 6374 732e 2020  ecial objects.  \n+00020870: 2020 2028 6c69 6e65 2020 3438 290a 2a20     (line  48).* \n+00020880: 6869 6464 656e 2073 7572 6661 6365 2061  hidden surface a\n+00020890: 6c67 6f72 6974 686d 203c 323e 3a20 2020  lgorithm <2>:   \n+000208a0: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n+000208b0: 206c 6974 6572 616c 732e 2020 286c 696e   literals.  (lin\n+000208c0: 6520 2032 3429 0a2a 2068 6964 6465 6e20  e  24).* hidden \n+000208d0: 7375 7266 6163 6520 616c 676f 7269 7468  surface algorith\n+000208e0: 6d20 3c33 3e3a 2020 2020 2020 2020 2020  m <3>:          \n+000208f0: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n+00020900: 696e 672e 2028 6c69 6e65 2020 3235 290a  ing. (line  25).\n+00020910: 2a20 6869 6464 656e 2073 7572 6661 6365  * hidden surface\n+00020920: 2061 6c67 6f72 6974 686d 203c 343e 3a20   algorithm <4>: \n+00020930: 2020 2020 2020 2020 2048 6964 6465 6e20           Hidden \n+00020940: 7375 7266 6163 6520 7265 6d6f 7661 6c2e  surface removal.\n+00020950: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n 00020960: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00020970: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020980: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-00020990: 2036 290a 2a20 6869 6572 6172 6368 6963   6).* hierarchic\n-000209a0: 616c 206d 6f64 656c 3a20 2020 2020 2020  al model:       \n-000209b0: 2020 2020 2020 2020 2020 2020 2041 2068               A h\n-000209c0: 6965 7261 7263 6869 6361 6c20 6d6f 6465  ierarchical mode\n-000209d0: 6c2e 0a20 2020 2020 2020 2020 2020 2020  l..             \n+00020980: 2020 2020 2020 2020 2020 2020 2020 2028                 (\n+00020990: 6c69 6e65 2020 2036 290a 2a20 6869 6572  line   6).* hier\n+000209a0: 6172 6368 6963 616c 206d 6f64 656c 3a20  archical model: \n+000209b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000209c0: 2020 2041 2068 6965 7261 7263 6869 6361     A hierarchica\n+000209d0: 6c20 6d6f 6465 6c2e 0a20 2020 2020 2020  l model..       \n 000209e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000209f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00020a00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020a10: 2028 6c69 6e65 2020 2036 290a 2a20 6964   (line   6).* id\n-00020a20: 656e 7469 6669 6572 733a 2020 2020 2020  entifiers:      \n+00020a10: 2020 2020 2020 2028 6c69 6e65 2020 2036         (line   6\n+00020a20: 290a 2a20 6964 656e 7469 6669 6572 733a  ).* identifiers:\n 00020a30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020a40: 2020 2020 2049 6465 6e74 6966 6965 7273       Identifiers\n-00020a50: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n-00020a60: 2020 3729 0a2a 2069 6e63 6c75 6465 2066    7).* include f\n-00020a70: 696c 653a 2020 2020 2020 2020 2020 2020  ile:            \n-00020a80: 2020 2020 2020 2020 2020 2020 2020 4c61                La\n-00020a90: 6e67 7561 6765 2062 6173 6963 732e 2020  nguage basics.  \n-00020aa0: 2020 2028 6c69 6e65 2020 3139 290a 2a20     (line  19).* \n-00020ab0: 696e 7075 7420 6669 6c65 3a20 2020 2020  input file:     \n-00020ac0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020ad0: 2020 2020 2020 204c 616e 6775 6167 6520         Language \n-00020ae0: 6261 7369 6373 2e20 2020 2020 286c 696e  basics.     (lin\n-00020af0: 6520 2020 3629 0a2a 2069 6e74 6572 6e61  e   6).* interna\n-00020b00: 6c20 6f70 7469 6f6e 3a20 2020 2020 2020  l option:       \n+00020a40: 2020 2020 2020 2020 2020 2049 6465 6e74             Ident\n+00020a50: 6966 6965 7273 2e20 2020 2020 2020 2020  ifiers.         \n+00020a60: 286c 696e 6520 2020 3729 0a2a 2069 6e63  (line   7).* inc\n+00020a70: 6c75 6465 2066 696c 653a 2020 2020 2020  lude file:      \n+00020a80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020a90: 2020 2020 4c61 6e67 7561 6765 2062 6173      Language bas\n+00020aa0: 6963 732e 2020 2020 2028 6c69 6e65 2020  ics.     (line  \n+00020ab0: 3139 290a 2a20 696e 7075 7420 6669 6c65  19).* input file\n+00020ac0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00020ad0: 2020 2020 2020 2020 2020 2020 204c 616e               Lan\n+00020ae0: 6775 6167 6520 6261 7369 6373 2e20 2020  guage basics.   \n+00020af0: 2020 286c 696e 6520 2020 3629 0a2a 2069    (line   6).* i\n+00020b00: 6e74 6572 6e61 6c20 6f70 7469 6f6e 3a20  nternal option: \n 00020b10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020b20: 5370 6563 6961 6c20 6f62 6a65 6374 732e  Special objects.\n-00020b30: 2020 2020 2028 6c69 6e65 2020 3437 290a       (line  47).\n-00020b40: 2a20 696e 7465 726e 616c 206f 7074 696f  * internal optio\n-00020b50: 6e73 3a20 2020 2020 2020 2020 2020 2020  ns:             \n-00020b60: 2020 2020 2020 2020 2049 6e74 6572 6e61           Interna\n-00020b70: 6c20 6f70 7469 6f6e 732e 2020 2020 286c  l options.    (l\n-00020b80: 696e 6520 2020 3629 0a2a 2069 6e74 6572  ine   6).* inter\n-00020b90: 6e61 6c20 6f70 7469 6f6e 7320 3c31 3e3a  nal options <1>:\n-00020ba0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020bb0: 2020 476c 6f62 616c 206f 7074 696f 6e73    Global options\n-00020bc0: 2e20 2020 2020 2028 6c69 6e65 2020 3132  .      (line  12\n-00020bd0: 290a 2a20 6b65 7977 6f72 6473 3a20 2020  ).* keywords:   \n-00020be0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020bf0: 2020 2020 2020 2020 2020 204b 6579 2061             Key a\n-00020c00: 6e64 2072 6573 6572 7665 6420 776f 7264  nd reserved word\n-00020c10: 732e 0a20 2020 2020 2020 2020 2020 2020  s..             \n+00020b20: 2020 2020 2020 5370 6563 6961 6c20 6f62        Special ob\n+00020b30: 6a65 6374 732e 2020 2020 2028 6c69 6e65  jects.     (line\n+00020b40: 2020 3437 290a 2a20 696e 7465 726e 616c    47).* internal\n+00020b50: 206f 7074 696f 6e73 3a20 2020 2020 2020   options:       \n+00020b60: 2020 2020 2020 2020 2020 2020 2020 2049                 I\n+00020b70: 6e74 6572 6e61 6c20 6f70 7469 6f6e 732e  nternal options.\n+00020b80: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n+00020b90: 2069 6e74 6572 6e61 6c20 6f70 7469 6f6e   internal option\n+00020ba0: 7320 3c31 3e3a 2020 2020 2020 2020 2020  s <1>:          \n+00020bb0: 2020 2020 2020 2020 476c 6f62 616c 206f          Global o\n+00020bc0: 7074 696f 6e73 2e20 2020 2020 2028 6c69  ptions.      (li\n+00020bd0: 6e65 2020 3132 290a 2a20 6b65 7977 6f72  ne  12).* keywor\n+00020be0: 6473 3a20 2020 2020 2020 2020 2020 2020  ds:             \n+00020bf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020c00: 204b 6579 2061 6e64 2072 6573 6572 7665   Key and reserve\n+00020c10: 6420 776f 7264 732e 0a20 2020 2020 2020  d words..       \n 00020c20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00020c30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00020c40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020c50: 2028 6c69 6e65 2020 2036 290a 2a20 6c61   (line   6).* la\n-00020c60: 6265 6c73 3a20 2020 2020 2020 2020 2020  bels:           \n+00020c50: 2020 2020 2020 2028 6c69 6e65 2020 2036         (line   6\n+00020c60: 290a 2a20 6c61 6265 6c73 3a20 2020 2020  ).* labels:     \n 00020c70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020c80: 2020 2020 2053 7065 6369 616c 206f 626a       Special obj\n-00020c90: 6563 7473 2e20 2020 2020 286c 696e 6520  ects.     (line \n-00020ca0: 2020 3629 0a2a 206c 616e 6775 6167 652c    6).* language,\n-00020cb0: 2064 6563 6c61 7261 7469 7665 3a20 2020   declarative:   \n-00020cc0: 2020 2020 2020 2020 2020 2020 2020 4c61                La\n-00020cd0: 6e67 7561 6765 2062 6173 6963 732e 2020  nguage basics.  \n-00020ce0: 2020 2028 6c69 6e65 2020 2038 290a 2a20     (line   8).* \n-00020cf0: 6c61 6e67 7561 6765 2c20 6f75 7470 7574  language, output\n-00020d00: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00020d10: 2020 2020 2020 204c 616e 6775 6167 652e         Language.\n-00020d20: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-00020d30: 6520 2020 3629 0a2a 206c 616e 6775 6167  e   6).* languag\n-00020d40: 652c 2073 6365 6e65 2064 6573 6372 6970  e, scene descrip\n-00020d50: 7469 6f6e 3a20 2020 2020 2020 2020 2020  tion:           \n-00020d60: 4c61 6e67 7561 6765 2062 6173 6963 732e  Language basics.\n-00020d70: 2020 2020 2028 6c69 6e65 2020 2038 290a       (line   8).\n-00020d80: 2a20 6c65 7869 6361 6c20 7363 6f70 653a  * lexical scope:\n-00020d90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020da0: 2020 2020 2020 2020 204f 626a 6563 7420           Object \n-00020db0: 7472 616e 7366 6f72 6d73 2e20 2020 286c  transforms.   (l\n-00020dc0: 696e 6520 2032 3629 0a2a 206c 6578 6963  ine  26).* lexic\n-00020dd0: 616c 2073 636f 7065 203c 313e 3a20 2020  al scope <1>:   \n-00020de0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020df0: 2020 426c 6f63 6b73 2e20 2020 2020 2020    Blocks.       \n-00020e00: 2020 2020 2020 2028 6c69 6e65 2020 3133         (line  13\n-00020e10: 290a 2a20 6c69 6e65 2073 7765 6570 3a20  ).* line sweep: \n-00020e20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020e30: 2020 2020 2020 2020 2020 2050 6f6c 796c             Polyl\n-00020e40: 696e 6520 7377 6565 7073 2e20 2020 2020  ine sweeps.     \n-00020e50: 286c 696e 6520 2020 3629 0a2a 206c 696e  (line   6).* lin\n-00020e60: 6520 7377 6565 7020 3c31 3e3a 2020 2020  e sweep <1>:    \n-00020e70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020e80: 2020 2020 5377 6570 7420 6c69 6e65 732e      Swept lines.\n-00020e90: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-00020ea0: 2036 290a 2a20 6c69 6e65 2073 7765 6570   6).* line sweep\n-00020eb0: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n-00020ec0: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n-00020ed0: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n-00020ee0: 2e20 286c 696e 6520 2032 3029 0a2a 206c  . (line  20).* l\n-00020ef0: 6974 6572 616c 2c20 706f 696e 743a 2020  iteral, point:  \n-00020f00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020f10: 2020 2020 2020 506f 696e 7420 616e 6420        Point and \n-00020f20: 7665 6374 6f72 206c 6974 6572 616c 732e  vector literals.\n-00020f30: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+00020c80: 2020 2020 2020 2020 2020 2053 7065 6369             Speci\n+00020c90: 616c 206f 626a 6563 7473 2e20 2020 2020  al objects.     \n+00020ca0: 286c 696e 6520 2020 3629 0a2a 206c 616e  (line   6).* lan\n+00020cb0: 6775 6167 652c 2064 6563 6c61 7261 7469  guage, declarati\n+00020cc0: 7665 3a20 2020 2020 2020 2020 2020 2020  ve:             \n+00020cd0: 2020 2020 4c61 6e67 7561 6765 2062 6173      Language bas\n+00020ce0: 6963 732e 2020 2020 2028 6c69 6e65 2020  ics.     (line  \n+00020cf0: 2038 290a 2a20 6c61 6e67 7561 6765 2c20   8).* language, \n+00020d00: 6f75 7470 7574 3a20 2020 2020 2020 2020  output:         \n+00020d10: 2020 2020 2020 2020 2020 2020 204c 616e               Lan\n+00020d20: 6775 6167 652e 2020 2020 2020 2020 2020  guage.          \n+00020d30: 2020 286c 696e 6520 2020 3629 0a2a 206c    (line   6).* l\n+00020d40: 616e 6775 6167 652c 2073 6365 6e65 2064  anguage, scene d\n+00020d50: 6573 6372 6970 7469 6f6e 3a20 2020 2020  escription:     \n+00020d60: 2020 2020 2020 4c61 6e67 7561 6765 2062        Language b\n+00020d70: 6173 6963 732e 2020 2020 2028 6c69 6e65  asics.     (line\n+00020d80: 2020 2038 290a 2a20 6c65 7869 6361 6c20     8).* lexical \n+00020d90: 7363 6f70 653a 2020 2020 2020 2020 2020  scope:          \n+00020da0: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n+00020db0: 626a 6563 7420 7472 616e 7366 6f72 6d73  bject transforms\n+00020dc0: 2e20 2020 286c 696e 6520 2032 3629 0a2a  .   (line  26).*\n+00020dd0: 206c 6578 6963 616c 2073 636f 7065 203c   lexical scope <\n+00020de0: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+00020df0: 2020 2020 2020 2020 426c 6f63 6b73 2e20          Blocks. \n+00020e00: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n+00020e10: 6e65 2020 3133 290a 2a20 6c69 6e65 2073  ne  13).* line s\n+00020e20: 7765 6570 3a20 2020 2020 2020 2020 2020  weep:           \n+00020e30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020e40: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n+00020e50: 2e20 2020 2020 286c 696e 6520 2020 3629  .     (line   6)\n+00020e60: 0a2a 206c 696e 6520 7377 6565 7020 3c31  .* line sweep <1\n+00020e70: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+00020e80: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n+00020e90: 6c69 6e65 732e 2020 2020 2020 2020 2028  lines.         (\n+00020ea0: 6c69 6e65 2020 2036 290a 2a20 6c69 6e65  line   6).* line\n+00020eb0: 2073 7765 6570 203c 323e 3a20 2020 2020   sweep <2>:     \n+00020ec0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020ed0: 2020 2041 2074 6563 686e 6963 616c 2064     A technical d\n+00020ee0: 7261 7769 6e67 2e20 286c 696e 6520 2032  rawing. (line  2\n+00020ef0: 3029 0a2a 206c 6974 6572 616c 2c20 706f  0).* literal, po\n+00020f00: 696e 743a 2020 2020 2020 2020 2020 2020  int:            \n+00020f10: 2020 2020 2020 2020 2020 2020 506f 696e              Poin\n+00020f20: 7420 616e 6420 7665 6374 6f72 206c 6974  t and vector lit\n+00020f30: 6572 616c 732e 0a20 2020 2020 2020 2020  erals..         \n 00020f40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00020f50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020f60: 2020 2020 2020 2020 2020 2020 2020 2028                 (\n-00020f70: 6c69 6e65 2020 2036 290a 2a20 6c69 7465  line   6).* lite\n-00020f80: 7261 6c2c 2073 6361 6c61 723a 2020 2020  ral, scalar:    \n-00020f90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020fa0: 2020 2053 6361 6c61 7220 6c69 7465 7261     Scalar litera\n-00020fb0: 6c73 2e20 2020 2020 286c 696e 6520 2020  ls.     (line   \n-00020fc0: 3629 0a2a 206c 6974 6572 616c 2c20 7472  6).* literal, tr\n-00020fd0: 616e 7366 6f72 6d3a 2020 2020 2020 2020  ansform:        \n-00020fe0: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n-00020ff0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n-00021000: 2028 6c69 6e65 2020 2036 290a 2a20 6c69   (line   6).* li\n-00021010: 7465 7261 6c2c 2076 6563 746f 723a 2020  teral, vector:  \n-00021020: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021030: 2020 2020 2050 6f69 6e74 2061 6e64 2076       Point and v\n-00021040: 6563 746f 7220 6c69 7465 7261 6c73 2e0a  ector literals..\n-00021050: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020f60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020f70: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n+00020f80: 2a20 6c69 7465 7261 6c2c 2073 6361 6c61  * literal, scala\n+00020f90: 723a 2020 2020 2020 2020 2020 2020 2020  r:              \n+00020fa0: 2020 2020 2020 2020 2053 6361 6c61 7220           Scalar \n+00020fb0: 6c69 7465 7261 6c73 2e20 2020 2020 286c  literals.     (l\n+00020fc0: 696e 6520 2020 3629 0a2a 206c 6974 6572  ine   6).* liter\n+00020fd0: 616c 2c20 7472 616e 7366 6f72 6d3a 2020  al, transform:  \n+00020fe0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020ff0: 2020 5472 616e 7366 6f72 6d20 6c69 7465    Transform lite\n+00021000: 7261 6c73 2e20 2028 6c69 6e65 2020 2036  rals.  (line   6\n+00021010: 290a 2a20 6c69 7465 7261 6c2c 2076 6563  ).* literal, vec\n+00021020: 746f 723a 2020 2020 2020 2020 2020 2020  tor:            \n+00021030: 2020 2020 2020 2020 2020 2050 6f69 6e74             Point\n+00021040: 2061 6e64 2076 6563 746f 7220 6c69 7465   and vector lite\n+00021050: 7261 6c73 2e0a 2020 2020 2020 2020 2020  rals..          \n 00021060: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00021070: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021080: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-00021090: 696e 6520 2020 3629 0a2a 206e 6573 7469  ine   6).* nesti\n-000210a0: 6e67 2c20 7377 6570 7420 6f62 6a65 6374  ng, swept object\n-000210b0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-000210c0: 2020 4e65 7374 6564 2073 7765 6570 732e    Nested sweeps.\n-000210d0: 2020 2020 2020 2028 6c69 6e65 2020 3232         (line  22\n-000210e0: 290a 2a20 6f6e 652d 6f70 6572 616e 6420  ).* one-operand \n-000210f0: 666f 726d 3a20 2020 2020 2020 2020 2020  form:           \n-00021100: 2020 2020 2020 2020 2020 2055 6e61 7279             Unary\n-00021110: 2066 6f72 6d73 2e20 2020 2020 2020 2020   forms.         \n-00021120: 286c 696e 6520 2020 3629 0a2a 206f 7065  (line   6).* ope\n-00021130: 7261 746f 7220 6173 736f 6369 6174 6976  rator associativ\n-00021140: 6974 793a 2020 2020 2020 2020 2020 2020  ity:            \n-00021150: 2020 2020 5477 6f2d 6f70 6572 616e 6420      Two-operand \n-00021160: 2862 696e 6172 7929 2066 6f72 6d73 2e0a  (binary) forms..\n-00021170: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021080: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021090: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n+000210a0: 206e 6573 7469 6e67 2c20 7377 6570 7420   nesting, swept \n+000210b0: 6f62 6a65 6374 3a20 2020 2020 2020 2020  object:         \n+000210c0: 2020 2020 2020 2020 4e65 7374 6564 2073          Nested s\n+000210d0: 7765 6570 732e 2020 2020 2020 2028 6c69  weeps.       (li\n+000210e0: 6e65 2020 3232 290a 2a20 6f6e 652d 6f70  ne  22).* one-op\n+000210f0: 6572 616e 6420 666f 726d 3a20 2020 2020  erand form:     \n+00021100: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021110: 2055 6e61 7279 2066 6f72 6d73 2e20 2020   Unary forms.   \n+00021120: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+00021130: 0a2a 206f 7065 7261 746f 7220 6173 736f  .* operator asso\n+00021140: 6369 6174 6976 6974 793a 2020 2020 2020  ciativity:      \n+00021150: 2020 2020 2020 2020 2020 5477 6f2d 6f70            Two-op\n+00021160: 6572 616e 6420 2862 696e 6172 7929 2066  erand (binary) f\n+00021170: 6f72 6d73 2e0a 2020 2020 2020 2020 2020  orms..          \n 00021180: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00021190: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000211a0: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-000211b0: 696e 6520 2035 3829 0a2a 206f 7065 7261  ine  58).* opera\n-000211c0: 746f 7220 7072 6563 6564 656e 6365 3a20  tor precedence: \n-000211d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000211e0: 2020 5477 6f2d 6f70 6572 616e 6420 2862    Two-operand (b\n-000211f0: 696e 6172 7929 2066 6f72 6d73 2e0a 2020  inary) forms..  \n-00021200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000211a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000211b0: 2020 2020 286c 696e 6520 2035 3829 0a2a      (line  58).*\n+000211c0: 206f 7065 7261 746f 7220 7072 6563 6564   operator preced\n+000211d0: 656e 6365 3a20 2020 2020 2020 2020 2020  ence:           \n+000211e0: 2020 2020 2020 2020 5477 6f2d 6f70 6572          Two-oper\n+000211f0: 616e 6420 2862 696e 6172 7929 2066 6f72  and (binary) for\n+00021200: 6d73 2e0a 2020 2020 2020 2020 2020 2020  ms..            \n 00021210: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00021220: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021230: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-00021240: 6520 2034 3529 0a2a 206f 7074 696f 6e3a  e  45).* option:\n-00021250: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021230: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021240: 2020 286c 696e 6520 2034 3529 0a2a 206f    (line  45).* o\n+00021250: 7074 696f 6e3a 2020 2020 2020 2020 2020  ption:          \n 00021260: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021270: 4472 6177 696e 6720 6f70 7469 6f6e 732e  Drawing options.\n-00021280: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n-00021290: 2a20 6f70 7469 6f6e 2c20 636f 6d6d 616e  * option, comman\n-000212a0: 6420 6c69 6e65 3a20 2020 2020 2020 2020  d line:         \n-000212b0: 2020 2020 2020 2020 2048 656c 6c6f 2077           Hello w\n-000212c0: 6f72 6c64 2e20 2020 2020 2020 2020 286c  orld.         (l\n-000212d0: 696e 6520 2033 3029 0a2a 206f 7074 696f  ine  30).* optio\n-000212e0: 6e2c 2069 6e74 6572 6e61 6c3a 2020 2020  n, internal:    \n-000212f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021300: 2020 5370 6563 6961 6c20 6f62 6a65 6374    Special object\n-00021310: 732e 2020 2020 2028 6c69 6e65 2020 3437  s.     (line  47\n-00021320: 290a 2a20 6f70 7469 6f6e 733a 2020 2020  ).* options:    \n-00021330: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021340: 2020 2020 2020 2020 2020 204f 7074 696f             Optio\n-00021350: 6e73 2e20 2020 2020 2020 2020 2020 2020  ns.             \n-00021360: 286c 696e 6520 2020 3629 0a2a 206f 7074  (line   6).* opt\n-00021370: 696f 6e73 2064 6566 696e 6974 696f 6e3a  ions definition:\n-00021380: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021390: 2020 2020 506f 6c79 6c69 6e65 2073 7765      Polyline swe\n-000213a0: 6570 7320 7769 7468 2063 6c6f 7375 7265  eps with closure\n-000213b0: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+00021270: 2020 2020 2020 4472 6177 696e 6720 6f70        Drawing op\n+00021280: 7469 6f6e 732e 2020 2020 2028 6c69 6e65  tions.     (line\n+00021290: 2020 2036 290a 2a20 6f70 7469 6f6e 2c20     6).* option, \n+000212a0: 636f 6d6d 616e 6420 6c69 6e65 3a20 2020  command line:   \n+000212b0: 2020 2020 2020 2020 2020 2020 2020 2048                 H\n+000212c0: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020  ello world.     \n+000212d0: 2020 2020 286c 696e 6520 2033 3029 0a2a      (line  30).*\n+000212e0: 206f 7074 696f 6e2c 2069 6e74 6572 6e61   option, interna\n+000212f0: 6c3a 2020 2020 2020 2020 2020 2020 2020  l:              \n+00021300: 2020 2020 2020 2020 5370 6563 6961 6c20          Special \n+00021310: 6f62 6a65 6374 732e 2020 2020 2028 6c69  objects.     (li\n+00021320: 6e65 2020 3437 290a 2a20 6f70 7469 6f6e  ne  47).* option\n+00021330: 733a 2020 2020 2020 2020 2020 2020 2020  s:              \n+00021340: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021350: 204f 7074 696f 6e73 2e20 2020 2020 2020   Options.       \n+00021360: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+00021370: 0a2a 206f 7074 696f 6e73 2064 6566 696e  .* options defin\n+00021380: 6974 696f 6e3a 2020 2020 2020 2020 2020  ition:          \n+00021390: 2020 2020 2020 2020 2020 506f 6c79 6c69            Polyli\n+000213a0: 6e65 2073 7765 6570 7320 7769 7468 2063  ne sweeps with c\n+000213b0: 6c6f 7375 7265 2e0a 2020 2020 2020 2020  losure..        \n 000213c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000213d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000213e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000213f0: 286c 696e 6520 2032 3329 0a2a 206f 7074  (line  23).* opt\n-00021400: 696f 6e73 206d 756c 7469 706c 6520 7265  ions multiple re\n-00021410: 6665 7265 6e63 653a 2020 2020 2020 2020  ference:        \n-00021420: 2020 2020 466f 726d 7320 6f66 2072 6566      Forms of ref\n-00021430: 6572 656e 6365 732e 2028 6c69 6e65 2020  erences. (line  \n-00021440: 3138 290a 2a20 6f70 7469 6f6e 7320 7265  18).* options re\n-00021450: 6665 7265 6e63 653a 2020 2020 2020 2020  ference:        \n-00021460: 2020 2020 2020 2020 2020 2020 2046 6f72               For\n-00021470: 6d73 206f 6620 7265 6665 7265 6e63 6573  ms of references\n-00021480: 2e20 286c 696e 6520 2031 3829 0a2a 206f  . (line  18).* o\n-00021490: 7074 696f 6e73 2c20 636f 6d6d 616e 6420  ptions, command \n-000214a0: 6c69 6e65 3a20 2020 2020 2020 2020 2020  line:           \n-000214b0: 2020 2020 2020 436f 6d6d 616e 6420 6c69        Command li\n-000214c0: 6e65 2e20 2020 2020 2020 2028 6c69 6e65  ne.        (line\n-000214d0: 2020 3134 290a 2a20 6f70 7469 6f6e 732c    14).* options,\n-000214e0: 2067 6c6f 6261 6c3a 2020 2020 2020 2020   global:        \n-000214f0: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n-00021500: 7261 7769 6e67 206f 7074 696f 6e73 2e20  rawing options. \n-00021510: 2020 2020 286c 696e 6520 2031 3829 0a2a      (line  18).*\n-00021520: 206f 7074 696f 6e73 2c20 676c 6f62 616c   options, global\n-00021530: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-00021540: 2020 2020 2020 2020 476c 6f62 616c 206f          Global o\n-00021550: 7074 696f 6e73 2e20 2020 2020 2028 6c69  ptions.      (li\n-00021560: 6e65 2020 2036 290a 2a20 6f70 7469 6f6e  ne   6).* option\n-00021570: 732c 2069 6e74 6572 6e61 6c3a 2020 2020  s, internal:    \n-00021580: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021590: 2049 6e74 6572 6e61 6c20 6f70 7469 6f6e   Internal option\n-000215a0: 732e 2020 2020 286c 696e 6520 2020 3629  s.    (line   6)\n-000215b0: 0a2a 206f 7074 696f 6e73 2c20 696e 7465  .* options, inte\n-000215c0: 726e 616c 203c 313e 3a20 2020 2020 2020  rnal <1>:       \n-000215d0: 2020 2020 2020 2020 2020 476c 6f62 616c            Global\n-000215e0: 206f 7074 696f 6e73 2e20 2020 2020 2028   options.      (\n-000215f0: 6c69 6e65 2020 3132 290a 2a20 6f70 7469  line  12).* opti\n-00021600: 6f6e 732c 2073 7765 6570 3a20 2020 2020  ons, sweep:     \n-00021610: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021620: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n-00021630: 7073 2e20 2020 2020 286c 696e 6520 2031  ps.     (line  1\n-00021640: 3629 0a2a 206f 7074 696f 6e73 2c20 7377  6).* options, sw\n-00021650: 6565 7020 3c31 3e3a 2020 2020 2020 2020  eep <1>:        \n-00021660: 2020 2020 2020 2020 2020 2020 506f 6c79              Poly\n-00021670: 676f 6e20 7377 6565 7073 2e20 2020 2020  gon sweeps.     \n-00021680: 2028 6c69 6e65 2020 2039 290a 2a20 6f70   (line   9).* op\n-00021690: 7469 6f6e 732c 2073 7765 6570 203c 323e  tions, sweep <2>\n-000216a0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-000216b0: 2020 2020 2053 7765 7074 2070 6f69 6e74       Swept point\n-000216c0: 732e 2020 2020 2020 2020 286c 696e 6520  s.        (line \n-000216d0: 2032 3129 0a2a 206f 7074 696f 6e73 2c20   21).* options, \n-000216e0: 7377 6565 7020 3c33 3e3a 2020 2020 2020  sweep <3>:      \n-000216f0: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n-00021700: 6570 7420 6c69 6e65 732e 2020 2020 2020  ept lines.      \n-00021710: 2020 2028 6c69 6e65 2020 3235 290a 2a20     (line  25).* \n-00021720: 6f70 7469 6f6e 732c 2073 7765 6570 203c  options, sweep <\n-00021730: 343e 3a20 2020 2020 2020 2020 2020 2020  4>:             \n-00021740: 2020 2020 2020 2053 7765 7074 206c 696e         Swept lin\n-00021750: 6573 2e20 2020 2020 2020 2020 286c 696e  es.         (lin\n-00021760: 6520 2034 3829 0a2a 206f 7074 696f 6e73  e  48).* options\n-00021770: 2c20 7377 6570 7420 6f62 6a65 6374 3a20  , swept object: \n-00021780: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021790: 506f 6c79 676f 6e20 7377 6565 7073 2e20  Polygon sweeps. \n-000217a0: 2020 2020 2028 6c69 6e65 2020 2038 290a       (line   8).\n-000217b0: 2a20 6f70 7469 6f6e 732c 2073 7765 7074  * options, swept\n-000217c0: 206f 626a 6563 7420 3c31 3e3a 2020 2020   object <1>:    \n-000217d0: 2020 2020 2020 2020 2050 6f6c 796c 696e           Polylin\n-000217e0: 6520 7377 6565 7073 2077 6974 6820 636c  e sweeps with cl\n-000217f0: 6f73 7572 652e 0a20 2020 2020 2020 2020  osure..         \n+000213f0: 2020 2020 2020 286c 696e 6520 2032 3329        (line  23)\n+00021400: 0a2a 206f 7074 696f 6e73 206d 756c 7469  .* options multi\n+00021410: 706c 6520 7265 6665 7265 6e63 653a 2020  ple reference:  \n+00021420: 2020 2020 2020 2020 2020 466f 726d 7320            Forms \n+00021430: 6f66 2072 6566 6572 656e 6365 732e 2028  of references. (\n+00021440: 6c69 6e65 2020 3138 290a 2a20 6f70 7469  line  18).* opti\n+00021450: 6f6e 7320 7265 6665 7265 6e63 653a 2020  ons reference:  \n+00021460: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021470: 2020 2046 6f72 6d73 206f 6620 7265 6665     Forms of refe\n+00021480: 7265 6e63 6573 2e20 286c 696e 6520 2031  rences. (line  1\n+00021490: 3829 0a2a 206f 7074 696f 6e73 2c20 636f  8).* options, co\n+000214a0: 6d6d 616e 6420 6c69 6e65 3a20 2020 2020  mmand line:     \n+000214b0: 2020 2020 2020 2020 2020 2020 436f 6d6d              Comm\n+000214c0: 616e 6420 6c69 6e65 2e20 2020 2020 2020  and line.       \n+000214d0: 2028 6c69 6e65 2020 3134 290a 2a20 6f70   (line  14).* op\n+000214e0: 7469 6f6e 732c 2067 6c6f 6261 6c3a 2020  tions, global:  \n+000214f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021500: 2020 2020 2044 7261 7769 6e67 206f 7074       Drawing opt\n+00021510: 696f 6e73 2e20 2020 2020 286c 696e 6520  ions.     (line \n+00021520: 2031 3829 0a2a 206f 7074 696f 6e73 2c20   18).* options, \n+00021530: 676c 6f62 616c 203c 313e 3a20 2020 2020  global <1>:     \n+00021540: 2020 2020 2020 2020 2020 2020 2020 476c                Gl\n+00021550: 6f62 616c 206f 7074 696f 6e73 2e20 2020  obal options.   \n+00021560: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n+00021570: 6f70 7469 6f6e 732c 2069 6e74 6572 6e61  options, interna\n+00021580: 6c3a 2020 2020 2020 2020 2020 2020 2020  l:              \n+00021590: 2020 2020 2020 2049 6e74 6572 6e61 6c20         Internal \n+000215a0: 6f70 7469 6f6e 732e 2020 2020 286c 696e  options.    (lin\n+000215b0: 6520 2020 3629 0a2a 206f 7074 696f 6e73  e   6).* options\n+000215c0: 2c20 696e 7465 726e 616c 203c 313e 3a20  , internal <1>: \n+000215d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000215e0: 476c 6f62 616c 206f 7074 696f 6e73 2e20  Global options. \n+000215f0: 2020 2020 2028 6c69 6e65 2020 3132 290a       (line  12).\n+00021600: 2a20 6f70 7469 6f6e 732c 2073 7765 6570  * options, sweep\n+00021610: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00021620: 2020 2020 2020 2020 2050 6f6c 796c 696e           Polylin\n+00021630: 6520 7377 6565 7073 2e20 2020 2020 286c  e sweeps.     (l\n+00021640: 696e 6520 2031 3629 0a2a 206f 7074 696f  ine  16).* optio\n+00021650: 6e73 2c20 7377 6565 7020 3c31 3e3a 2020  ns, sweep <1>:  \n+00021660: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021670: 2020 506f 6c79 676f 6e20 7377 6565 7073    Polygon sweeps\n+00021680: 2e20 2020 2020 2028 6c69 6e65 2020 2039  .      (line   9\n+00021690: 290a 2a20 6f70 7469 6f6e 732c 2073 7765  ).* options, swe\n+000216a0: 6570 203c 323e 3a20 2020 2020 2020 2020  ep <2>:         \n+000216b0: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n+000216c0: 2070 6f69 6e74 732e 2020 2020 2020 2020   points.        \n+000216d0: 286c 696e 6520 2032 3129 0a2a 206f 7074  (line  21).* opt\n+000216e0: 696f 6e73 2c20 7377 6565 7020 3c33 3e3a  ions, sweep <3>:\n+000216f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021700: 2020 2020 5377 6570 7420 6c69 6e65 732e      Swept lines.\n+00021710: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+00021720: 3235 290a 2a20 6f70 7469 6f6e 732c 2073  25).* options, s\n+00021730: 7765 6570 203c 343e 3a20 2020 2020 2020  weep <4>:       \n+00021740: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n+00021750: 7074 206c 696e 6573 2e20 2020 2020 2020  pt lines.       \n+00021760: 2020 286c 696e 6520 2034 3829 0a2a 206f    (line  48).* o\n+00021770: 7074 696f 6e73 2c20 7377 6570 7420 6f62  ptions, swept ob\n+00021780: 6a65 6374 3a20 2020 2020 2020 2020 2020  ject:           \n+00021790: 2020 2020 2020 506f 6c79 676f 6e20 7377        Polygon sw\n+000217a0: 6565 7073 2e20 2020 2020 2028 6c69 6e65  eeps.      (line\n+000217b0: 2020 2038 290a 2a20 6f70 7469 6f6e 732c     8).* options,\n+000217c0: 2073 7765 7074 206f 626a 6563 7420 3c31   swept object <1\n+000217d0: 3e3a 2020 2020 2020 2020 2020 2020 2050  >:             P\n+000217e0: 6f6c 796c 696e 6520 7377 6565 7073 2077  olyline sweeps w\n+000217f0: 6974 6820 636c 6f73 7572 652e 0a20 2020  ith closure..   \n 00021800: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00021810: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00021820: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021830: 2020 2020 2028 6c69 6e65 2020 3232 290a       (line  22).\n-00021840: 2a20 6f70 7469 6f6e 732c 2073 7765 7074  * options, swept\n-00021850: 206f 626a 6563 7420 3c32 3e3a 2020 2020   object <2>:    \n-00021860: 2020 2020 2020 2020 2053 7765 7074 206c           Swept l\n-00021870: 696e 6573 2e20 2020 2020 2020 2020 286c  ines.         (l\n-00021880: 696e 6520 2032 3629 0a2a 206f 7074 696f  ine  26).* optio\n-00021890: 6e73 2c20 7377 6570 7420 6f62 6a65 6374  ns, swept object\n-000218a0: 203c 333e 3a20 2020 2020 2020 2020 2020   <3>:           \n-000218b0: 2020 5377 6570 7420 6c69 6e65 732e 2020    Swept lines.  \n-000218c0: 2020 2020 2020 2028 6c69 6e65 2020 3438         (line  48\n-000218d0: 290a 2a20 6f72 6465 722c 2070 6f6c 7967  ).* order, polyg\n-000218e0: 6f6e 2076 6572 7465 783a 2020 2020 2020  on vertex:      \n-000218f0: 2020 2020 2020 2020 2020 2048 656c 6c6f             Hello\n-00021900: 2077 6f72 6c64 2e20 2020 2020 2020 2020   world.         \n-00021910: 286c 696e 6520 2033 3929 0a2a 206f 7264  (line  39).* ord\n-00021920: 6572 2c20 706f 6c79 676f 6e20 7665 7274  er, polygon vert\n-00021930: 6578 203c 313e 3a20 2020 2020 2020 2020  ex <1>:         \n-00021940: 2020 2020 5377 6570 7420 6c69 6e65 732e      Swept lines.\n-00021950: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-00021960: 3134 290a 2a20 6f72 6465 722c 2070 6f6c  14).* order, pol\n-00021970: 7967 6f6e 2076 6572 7465 7820 3c32 3e3a  ygon vertex <2>:\n-00021980: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n-00021990: 7074 206c 696e 6573 2e20 2020 2020 2020  pt lines.       \n-000219a0: 2020 286c 696e 6520 2034 3029 0a2a 206f    (line  40).* o\n-000219b0: 7264 6572 2c20 706f 6c79 676f 6e20 7665  rder, polygon ve\n-000219c0: 7274 6578 203c 333e 3a20 2020 2020 2020  rtex <3>:       \n-000219d0: 2020 2020 2020 5377 6570 7420 706f 6c79        Swept poly\n-000219e0: 676f 6e73 2e20 2020 2020 2028 6c69 6e65  gons.      (line\n-000219f0: 2020 3139 290a 2a20 6f72 6465 722c 2070    19).* order, p\n-00021a00: 6f6c 7967 6f6e 2076 6572 7465 7820 3c34  olygon vertex <4\n-00021a10: 3e3a 2020 2020 2020 2020 2020 2020 204f  >:             O\n-00021a20: 7665 7276 6965 772e 2020 2020 2020 2020  verview.        \n-00021a30: 2020 2020 286c 696e 6520 2033 3729 0a2a      (line  37).*\n-00021a40: 206f 7264 6572 2c20 706f 6c79 676f 6e20   order, polygon \n-00021a50: 7665 7274 6578 203c 353e 3a20 2020 2020  vertex <5>:     \n-00021a60: 2020 2020 2020 2020 4f76 6572 7669 6577          Overview\n-00021a70: 2e20 2020 2020 2020 2020 2020 2028 6c69  .            (li\n-00021a80: 6e65 2020 3535 290a 2a20 6f75 7470 7574  ne  55).* output\n-00021a90: 206c 616e 6775 6167 653a 2020 2020 2020   language:      \n+00021830: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+00021840: 2020 3232 290a 2a20 6f70 7469 6f6e 732c    22).* options,\n+00021850: 2073 7765 7074 206f 626a 6563 7420 3c32   swept object <2\n+00021860: 3e3a 2020 2020 2020 2020 2020 2020 2053  >:             S\n+00021870: 7765 7074 206c 696e 6573 2e20 2020 2020  wept lines.     \n+00021880: 2020 2020 286c 696e 6520 2032 3629 0a2a      (line  26).*\n+00021890: 206f 7074 696f 6e73 2c20 7377 6570 7420   options, swept \n+000218a0: 6f62 6a65 6374 203c 333e 3a20 2020 2020  object <3>:     \n+000218b0: 2020 2020 2020 2020 5377 6570 7420 6c69          Swept li\n+000218c0: 6e65 732e 2020 2020 2020 2020 2028 6c69  nes.         (li\n+000218d0: 6e65 2020 3438 290a 2a20 6f72 6465 722c  ne  48).* order,\n+000218e0: 2070 6f6c 7967 6f6e 2076 6572 7465 783a   polygon vertex:\n+000218f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021900: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020   Hello world.   \n+00021910: 2020 2020 2020 286c 696e 6520 2033 3929        (line  39)\n+00021920: 0a2a 206f 7264 6572 2c20 706f 6c79 676f  .* order, polygo\n+00021930: 6e20 7665 7274 6578 203c 313e 3a20 2020  n vertex <1>:   \n+00021940: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n+00021950: 6c69 6e65 732e 2020 2020 2020 2020 2028  lines.         (\n+00021960: 6c69 6e65 2020 3134 290a 2a20 6f72 6465  line  14).* orde\n+00021970: 722c 2070 6f6c 7967 6f6e 2076 6572 7465  r, polygon verte\n+00021980: 7820 3c32 3e3a 2020 2020 2020 2020 2020  x <2>:          \n+00021990: 2020 2053 7765 7074 206c 696e 6573 2e20     Swept lines. \n+000219a0: 2020 2020 2020 2020 286c 696e 6520 2034          (line  4\n+000219b0: 3029 0a2a 206f 7264 6572 2c20 706f 6c79  0).* order, poly\n+000219c0: 676f 6e20 7665 7274 6578 203c 333e 3a20  gon vertex <3>: \n+000219d0: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n+000219e0: 7420 706f 6c79 676f 6e73 2e20 2020 2020  t polygons.     \n+000219f0: 2028 6c69 6e65 2020 3139 290a 2a20 6f72   (line  19).* or\n+00021a00: 6465 722c 2070 6f6c 7967 6f6e 2076 6572  der, polygon ver\n+00021a10: 7465 7820 3c34 3e3a 2020 2020 2020 2020  tex <4>:        \n+00021a20: 2020 2020 204f 7665 7276 6965 772e 2020       Overview.  \n+00021a30: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00021a40: 2033 3729 0a2a 206f 7264 6572 2c20 706f   37).* order, po\n+00021a50: 6c79 676f 6e20 7665 7274 6578 203c 353e  lygon vertex <5>\n+00021a60: 3a20 2020 2020 2020 2020 2020 2020 4f76  :             Ov\n+00021a70: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n+00021a80: 2020 2028 6c69 6e65 2020 3535 290a 2a20     (line  55).* \n+00021a90: 6f75 7470 7574 206c 616e 6775 6167 653a  output language:\n 00021aa0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021ab0: 204c 616e 6775 6167 652e 2020 2020 2020   Language.      \n-00021ac0: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n-00021ad0: 0a2a 206f 7574 7369 6465 206f 6620 6120  .* outside of a \n-00021ae0: 706f 6c79 676f 6e3a 2020 2020 2020 2020  polygon:        \n-00021af0: 2020 2020 2020 2020 2020 4865 6c6c 6f20            Hello \n-00021b00: 776f 726c 642e 2020 2020 2020 2020 2028  world.         (\n-00021b10: 6c69 6e65 2020 3337 290a 2a20 7061 7261  line  37).* para\n-00021b20: 6c6c 656c 2070 726f 6a65 6374 696f 6e3a  llel projection:\n-00021b30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021b40: 2020 2048 656c 6c6f 2077 6f72 6c64 2e20     Hello world. \n-00021b50: 2020 2020 2020 2020 286c 696e 6520 2032          (line  2\n-00021b60: 3629 0a2a 2070 6172 616c 6c65 6c20 7072  6).* parallel pr\n-00021b70: 6f6a 6563 7469 6f6e 203c 313e 3a20 2020  ojection <1>:   \n-00021b80: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n-00021b90: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n-00021ba0: 2028 6c69 6e65 2020 3138 290a 2a20 7061   (line  18).* pa\n-00021bb0: 7261 6c6c 656c 2070 726f 6a65 6374 696f  rallel projectio\n-00021bc0: 6e20 3c32 3e3a 2020 2020 2020 2020 2020  n <2>:          \n-00021bd0: 2020 2020 2050 6963 7475 7265 2062 6f78       Picture box\n-00021be0: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n-00021bf0: 2031 3529 0a2a 2070 6172 656e 7468 6573   15).* parenthes\n-00021c00: 6573 3a20 2020 2020 2020 2020 2020 2020  es:             \n-00021c10: 2020 2020 2020 2020 2020 2020 2020 5477                Tw\n-00021c20: 6f2d 6f70 6572 616e 6420 2862 696e 6172  o-operand (binar\n-00021c30: 7929 2066 6f72 6d73 2e0a 2020 2020 2020  y) forms..      \n+00021ab0: 2020 2020 2020 204c 616e 6775 6167 652e         Language.\n+00021ac0: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+00021ad0: 6520 2020 3629 0a2a 206f 7574 7369 6465  e   6).* outside\n+00021ae0: 206f 6620 6120 706f 6c79 676f 6e3a 2020   of a polygon:  \n+00021af0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021b00: 4865 6c6c 6f20 776f 726c 642e 2020 2020  Hello world.    \n+00021b10: 2020 2020 2028 6c69 6e65 2020 3337 290a       (line  37).\n+00021b20: 2a20 7061 7261 6c6c 656c 2070 726f 6a65  * parallel proje\n+00021b30: 6374 696f 6e3a 2020 2020 2020 2020 2020  ction:          \n+00021b40: 2020 2020 2020 2020 2048 656c 6c6f 2077           Hello w\n+00021b50: 6f72 6c64 2e20 2020 2020 2020 2020 286c  orld.         (l\n+00021b60: 696e 6520 2032 3629 0a2a 2070 6172 616c  ine  26).* paral\n+00021b70: 6c65 6c20 7072 6f6a 6563 7469 6f6e 203c  lel projection <\n+00021b80: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+00021b90: 2020 5472 616e 7366 6f72 6d20 6c69 7465    Transform lite\n+00021ba0: 7261 6c73 2e20 2028 6c69 6e65 2020 3138  rals.  (line  18\n+00021bb0: 290a 2a20 7061 7261 6c6c 656c 2070 726f  ).* parallel pro\n+00021bc0: 6a65 6374 696f 6e20 3c32 3e3a 2020 2020  jection <2>:    \n+00021bd0: 2020 2020 2020 2020 2020 2050 6963 7475             Pictu\n+00021be0: 7265 2062 6f78 2e20 2020 2020 2020 2020  re box.         \n+00021bf0: 286c 696e 6520 2031 3529 0a2a 2070 6172  (line  15).* par\n+00021c00: 656e 7468 6573 6573 3a20 2020 2020 2020  entheses:       \n+00021c10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021c20: 2020 2020 5477 6f2d 6f70 6572 616e 6420      Two-operand \n+00021c30: 2862 696e 6172 7929 2066 6f72 6d73 2e0a  (binary) forms..\n 00021c40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00021c50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00021c60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021c70: 2020 2020 2020 2020 286c 696e 6520 2035          (line  5\n-00021c80: 3829 0a2a 2070 6572 7370 6563 7469 7665  8).* perspective\n-00021c90: 2070 726f 6a65 6374 696f 6e3a 2020 2020   projection:    \n-00021ca0: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n-00021cb0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n-00021cc0: 2028 6c69 6e65 2020 3139 290a 2a20 7065   (line  19).* pe\n-00021cd0: 7273 7065 6374 6976 6520 7072 6f6a 6563  rspective projec\n-00021ce0: 7469 6f6e 203c 313e 3a20 2020 2020 2020  tion <1>:       \n-00021cf0: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n-00021d00: 6974 6572 616c 732e 2020 286c 696e 6520  iterals.  (line \n-00021d10: 2032 3129 0a2a 2070 6572 7370 6563 7469   21).* perspecti\n-00021d20: 7665 2070 726f 6a65 6374 696f 6e20 3c32  ve projection <2\n-00021d30: 3e3a 2020 2020 2020 2020 2020 2020 4f76  >:            Ov\n-00021d40: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n-00021d50: 2020 2028 6c69 6e65 2020 2037 290a 2a20     (line   7).* \n-00021d60: 7069 6374 7572 6520 626f 783a 2020 2020  picture box:    \n-00021d70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021d80: 2020 2020 2020 2050 6963 7475 7265 2062         Picture b\n-00021d90: 6f78 2e20 2020 2020 2020 2020 286c 696e  ox.         (lin\n-00021da0: 6520 2020 3629 0a2a 2070 6c61 6e61 7269  e   6).* planari\n-00021db0: 7479 206f 6620 706f 6c79 676f 6e73 3a20  ty of polygons: \n-00021dc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021dd0: 506f 6c79 676f 6e73 2e20 2020 2020 2020  Polygons.       \n-00021de0: 2020 2020 2028 6c69 6e65 2020 3130 290a       (line  10).\n-00021df0: 2a20 706c 616e 6172 6974 7920 6f66 2070  * planarity of p\n-00021e00: 6f6c 7967 6f6e 7320 3c31 3e3a 2020 2020  olygons <1>:    \n-00021e10: 2020 2020 2020 2020 2053 7765 6570 2066           Sweep f\n-00021e20: 6163 6520 7370 6c69 7474 696e 672e 0a20  ace splitting.. \n-00021e30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021c70: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+00021c80: 696e 6520 2035 3829 0a2a 2070 6572 7370  ine  58).* persp\n+00021c90: 6563 7469 7665 2070 726f 6a65 6374 696f  ective projectio\n+00021ca0: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n+00021cb0: 2020 5472 616e 7366 6f72 6d20 6c69 7465    Transform lite\n+00021cc0: 7261 6c73 2e20 2028 6c69 6e65 2020 3139  rals.  (line  19\n+00021cd0: 290a 2a20 7065 7273 7065 6374 6976 6520  ).* perspective \n+00021ce0: 7072 6f6a 6563 7469 6f6e 203c 313e 3a20  projection <1>: \n+00021cf0: 2020 2020 2020 2020 2020 2054 7261 6e73             Trans\n+00021d00: 666f 726d 206c 6974 6572 616c 732e 2020  form literals.  \n+00021d10: 286c 696e 6520 2032 3129 0a2a 2070 6572  (line  21).* per\n+00021d20: 7370 6563 7469 7665 2070 726f 6a65 6374  spective project\n+00021d30: 696f 6e20 3c32 3e3a 2020 2020 2020 2020  ion <2>:        \n+00021d40: 2020 2020 4f76 6572 7669 6577 2e20 2020      Overview.   \n+00021d50: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+00021d60: 2037 290a 2a20 7069 6374 7572 6520 626f   7).* picture bo\n+00021d70: 783a 2020 2020 2020 2020 2020 2020 2020  x:              \n+00021d80: 2020 2020 2020 2020 2020 2020 2050 6963               Pic\n+00021d90: 7475 7265 2062 6f78 2e20 2020 2020 2020  ture box.       \n+00021da0: 2020 286c 696e 6520 2020 3629 0a2a 2070    (line   6).* p\n+00021db0: 6c61 6e61 7269 7479 206f 6620 706f 6c79  lanarity of poly\n+00021dc0: 676f 6e73 3a20 2020 2020 2020 2020 2020  gons:           \n+00021dd0: 2020 2020 2020 506f 6c79 676f 6e73 2e20        Polygons. \n+00021de0: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+00021df0: 2020 3130 290a 2a20 706c 616e 6172 6974    10).* planarit\n+00021e00: 7920 6f66 2070 6f6c 7967 6f6e 7320 3c31  y of polygons <1\n+00021e10: 3e3a 2020 2020 2020 2020 2020 2020 2053  >:             S\n+00021e20: 7765 6570 2066 6163 6520 7370 6c69 7474  weep face splitt\n+00021e30: 696e 672e 0a20 2020 2020 2020 2020 2020  ing..           \n 00021e40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00021e50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021e60: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n-00021e70: 6e65 2020 2037 290a 2a20 706f 696e 7420  ne   7).* point \n-00021e80: 6465 6669 6e69 7469 6f6e 3a20 2020 2020  definition:     \n-00021e90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021ea0: 2044 7261 7769 6e67 2061 2073 6f6c 6964   Drawing a solid\n-00021eb0: 2e20 2020 2020 286c 696e 6520 2032 3329  .     (line  23)\n-00021ec0: 0a2a 2070 6f69 6e74 206c 6973 743a 2020  .* point list:  \n-00021ed0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021ee0: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n-00021ef0: 706f 696e 7473 2e20 2020 2020 2020 2028  points.        (\n-00021f00: 6c69 6e65 2020 2039 290a 2a20 706f 696e  line   9).* poin\n-00021f10: 7420 6c69 7465 7261 6c3a 2020 2020 2020  t literal:      \n+00021e60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021e70: 2020 2028 6c69 6e65 2020 2037 290a 2a20     (line   7).* \n+00021e80: 706f 696e 7420 6465 6669 6e69 7469 6f6e  point definition\n+00021e90: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00021ea0: 2020 2020 2020 2044 7261 7769 6e67 2061         Drawing a\n+00021eb0: 2073 6f6c 6964 2e20 2020 2020 286c 696e   solid.     (lin\n+00021ec0: 6520 2032 3329 0a2a 2070 6f69 6e74 206c  e  23).* point l\n+00021ed0: 6973 743a 2020 2020 2020 2020 2020 2020  ist:            \n+00021ee0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021ef0: 5377 6570 7420 706f 696e 7473 2e20 2020  Swept points.   \n+00021f00: 2020 2020 2028 6c69 6e65 2020 2039 290a       (line   9).\n+00021f10: 2a20 706f 696e 7420 6c69 7465 7261 6c3a  * point literal:\n 00021f20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021f30: 2020 2050 6f69 6e74 2061 6e64 2076 6563     Point and vec\n-00021f40: 746f 7220 6c69 7465 7261 6c73 2e0a 2020  tor literals..  \n-00021f50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021f30: 2020 2020 2020 2020 2050 6f69 6e74 2061           Point a\n+00021f40: 6e64 2076 6563 746f 7220 6c69 7465 7261  nd vector litera\n+00021f50: 6c73 2e0a 2020 2020 2020 2020 2020 2020  ls..            \n 00021f60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00021f70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021f80: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-00021f90: 6520 2020 3629 0a2a 2070 6f69 6e74 2072  e   6).* point r\n-00021fa0: 6566 6572 656e 6365 3a20 2020 2020 2020  eference:       \n+00021f80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021f90: 2020 286c 696e 6520 2020 3629 0a2a 2070    (line   6).* p\n+00021fa0: 6f69 6e74 2072 6566 6572 656e 6365 3a20  oint reference: \n 00021fb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021fc0: 466f 726d 7320 6f66 2072 6566 6572 656e  Forms of referen\n-00021fd0: 6365 732e 2028 6c69 6e65 2020 3134 290a  ces. (line  14).\n-00021fe0: 2a20 706f 696e 7420 7377 6565 703a 2020  * point sweep:  \n-00021ff0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022000: 2020 2020 2020 2020 2053 7765 7074 206f           Swept o\n-00022010: 626a 6563 7473 2e20 2020 2020 2020 286c  bjects.       (l\n-00022020: 696e 6520 2031 3129 0a2a 2070 6f69 6e74  ine  11).* point\n-00022030: 2073 7765 6570 203c 313e 3a20 2020 2020   sweep <1>:     \n-00022040: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022050: 2020 5377 6570 7420 706f 696e 7473 2e20    Swept points. \n-00022060: 2020 2020 2020 2028 6c69 6e65 2020 2036         (line   6\n-00022070: 290a 2a20 706f 6c79 676f 6e20 7377 6565  ).* polygon swee\n-00022080: 703a 2020 2020 2020 2020 2020 2020 2020  p:              \n-00022090: 2020 2020 2020 2020 2020 2050 6f6c 7967             Polyg\n-000220a0: 6f6e 2073 7765 6570 732e 2020 2020 2020  on sweeps.      \n-000220b0: 286c 696e 6520 2020 3629 0a2a 2070 6f6c  (line   6).* pol\n-000220c0: 7967 6f6e 2073 7765 6570 203c 313e 3a20  ygon sweep <1>: \n-000220d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000220e0: 2020 2020 5377 6570 7420 706f 6c79 676f      Swept polygo\n-000220f0: 6e73 2e20 2020 2020 2028 6c69 6e65 2020  ns.      (line  \n-00022100: 2036 290a 2a20 706f 6c79 676f 6e20 7377   6).* polygon sw\n-00022110: 6565 7020 3c32 3e3a 2020 2020 2020 2020  eep <2>:        \n-00022120: 2020 2020 2020 2020 2020 2020 2041 2068               A h\n-00022130: 6965 7261 7263 6869 6361 6c20 6d6f 6465  ierarchical mode\n-00022140: 6c2e 0a20 2020 2020 2020 2020 2020 2020  l..             \n+00021fc0: 2020 2020 2020 466f 726d 7320 6f66 2072        Forms of r\n+00021fd0: 6566 6572 656e 6365 732e 2028 6c69 6e65  eferences. (line\n+00021fe0: 2020 3134 290a 2a20 706f 696e 7420 7377    14).* point sw\n+00021ff0: 6565 703a 2020 2020 2020 2020 2020 2020  eep:            \n+00022000: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n+00022010: 7765 7074 206f 626a 6563 7473 2e20 2020  wept objects.   \n+00022020: 2020 2020 286c 696e 6520 2031 3129 0a2a      (line  11).*\n+00022030: 2070 6f69 6e74 2073 7765 6570 203c 313e   point sweep <1>\n+00022040: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00022050: 2020 2020 2020 2020 5377 6570 7420 706f          Swept po\n+00022060: 696e 7473 2e20 2020 2020 2020 2028 6c69  ints.        (li\n+00022070: 6e65 2020 2036 290a 2a20 706f 6c79 676f  ne   6).* polygo\n+00022080: 6e20 7377 6565 703a 2020 2020 2020 2020  n sweep:        \n+00022090: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000220a0: 2050 6f6c 7967 6f6e 2073 7765 6570 732e   Polygon sweeps.\n+000220b0: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+000220c0: 0a2a 2070 6f6c 7967 6f6e 2073 7765 6570  .* polygon sweep\n+000220d0: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+000220e0: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n+000220f0: 706f 6c79 676f 6e73 2e20 2020 2020 2028  polygons.      (\n+00022100: 6c69 6e65 2020 2036 290a 2a20 706f 6c79  line   6).* poly\n+00022110: 676f 6e20 7377 6565 7020 3c32 3e3a 2020  gon sweep <2>:  \n+00022120: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022130: 2020 2041 2068 6965 7261 7263 6869 6361     A hierarchica\n+00022140: 6c20 6d6f 6465 6c2e 0a20 2020 2020 2020  l model..       \n 00022150: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00022160: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00022170: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022180: 2028 6c69 6e65 2031 3232 290a 2a20 706f   (line 122).* po\n-00022190: 6c79 676f 6e20 7665 7274 6578 206f 7264  lygon vertex ord\n-000221a0: 6572 3a20 2020 2020 2020 2020 2020 2020  er:             \n-000221b0: 2020 2020 2048 656c 6c6f 2077 6f72 6c64       Hello world\n-000221c0: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n-000221d0: 2033 3929 0a2a 2070 6f6c 7967 6f6e 2076   39).* polygon v\n-000221e0: 6572 7465 7820 6f72 6465 7220 3c31 3e3a  ertex order <1>:\n-000221f0: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n-00022200: 6570 7420 6c69 6e65 732e 2020 2020 2020  ept lines.      \n-00022210: 2020 2028 6c69 6e65 2020 3134 290a 2a20     (line  14).* \n-00022220: 706f 6c79 676f 6e20 7665 7274 6578 206f  polygon vertex o\n-00022230: 7264 6572 203c 323e 3a20 2020 2020 2020  rder <2>:       \n-00022240: 2020 2020 2020 2053 7765 7074 206c 696e         Swept lin\n-00022250: 6573 2e20 2020 2020 2020 2020 286c 696e  es.         (lin\n-00022260: 6520 2034 3029 0a2a 2070 6f6c 7967 6f6e  e  40).* polygon\n-00022270: 2076 6572 7465 7820 6f72 6465 7220 3c33   vertex order <3\n-00022280: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-00022290: 5377 6570 7420 706f 6c79 676f 6e73 2e20  Swept polygons. \n-000222a0: 2020 2020 2028 6c69 6e65 2020 3139 290a       (line  19).\n-000222b0: 2a20 706f 6c79 676f 6e20 7665 7274 6578  * polygon vertex\n-000222c0: 206f 7264 6572 203c 343e 3a20 2020 2020   order <4>:     \n-000222d0: 2020 2020 2020 2020 204f 7665 7276 6965           Overvie\n-000222e0: 772e 2020 2020 2020 2020 2020 2020 286c  w.            (l\n-000222f0: 696e 6520 2033 3729 0a2a 2070 6f6c 7967  ine  37).* polyg\n-00022300: 6f6e 2076 6572 7465 7820 6f72 6465 7220  on vertex order \n-00022310: 3c35 3e3a 2020 2020 2020 2020 2020 2020  <5>:            \n-00022320: 2020 4f76 6572 7669 6577 2e20 2020 2020    Overview.     \n-00022330: 2020 2020 2020 2028 6c69 6e65 2020 3535         (line  55\n-00022340: 290a 2a20 706f 6c79 676f 6e2c 2062 6f64  ).* polygon, bod\n-00022350: 793a 2020 2020 2020 2020 2020 2020 2020  y:              \n-00022360: 2020 2020 2020 2020 2020 2049 6e74 6572             Inter\n-00022370: 6e61 6c20 6f70 7469 6f6e 732e 2020 2020  nal options.    \n-00022380: 286c 696e 6520 2031 3629 0a2a 2070 6f6c  (line  16).* pol\n-00022390: 7967 6f6e 2c20 626f 6479 203c 313e 3a20  ygon, body <1>: \n-000223a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000223b0: 2020 2020 5377 6570 7420 6c69 6e65 732e      Swept lines.\n-000223c0: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-000223d0: 3130 290a 2a20 706f 6c79 676f 6e2c 2062  10).* polygon, b\n-000223e0: 6f64 7920 3c32 3e3a 2020 2020 2020 2020  ody <2>:        \n-000223f0: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n-00022400: 7074 2070 6f6c 7967 6f6e 732e 2020 2020  pt polygons.    \n-00022410: 2020 286c 696e 6520 2020 3929 0a2a 2070    (line   9).* p\n-00022420: 6f6c 7967 6f6e 2c20 656e 643a 2020 2020  olygon, end:    \n-00022430: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022440: 2020 2020 2020 5377 6570 7420 6c69 6e65        Swept line\n-00022450: 732e 2020 2020 2020 2020 2028 6c69 6e65  s.         (line\n-00022460: 2020 3338 290a 2a20 706f 6c79 676f 6e2c    38).* polygon,\n-00022470: 2065 6e64 203c 313e 3a20 2020 2020 2020   end <1>:       \n-00022480: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n-00022490: 7765 7074 2070 6f6c 7967 6f6e 732e 2020  wept polygons.  \n-000224a0: 2020 2020 286c 696e 6520 2031 3529 0a2a      (line  15).*\n-000224b0: 2070 6f6c 7967 6f6e 2c20 6f75 7473 6964   polygon, outsid\n-000224c0: 6520 6f66 3a20 2020 2020 2020 2020 2020  e of:           \n-000224d0: 2020 2020 2020 2020 4865 6c6c 6f20 776f          Hello wo\n-000224e0: 726c 642e 2020 2020 2020 2020 2028 6c69  rld.         (li\n-000224f0: 6e65 2020 3337 290a 2a20 706f 6c79 676f  ne  37).* polygo\n-00022500: 6e2c 2070 6c61 6e61 723a 2020 2020 2020  n, planar:      \n+00022180: 2020 2020 2020 2028 6c69 6e65 2031 3232         (line 122\n+00022190: 290a 2a20 706f 6c79 676f 6e20 7665 7274  ).* polygon vert\n+000221a0: 6578 206f 7264 6572 3a20 2020 2020 2020  ex order:       \n+000221b0: 2020 2020 2020 2020 2020 2048 656c 6c6f             Hello\n+000221c0: 2077 6f72 6c64 2e20 2020 2020 2020 2020   world.         \n+000221d0: 286c 696e 6520 2033 3929 0a2a 2070 6f6c  (line  39).* pol\n+000221e0: 7967 6f6e 2076 6572 7465 7820 6f72 6465  ygon vertex orde\n+000221f0: 7220 3c31 3e3a 2020 2020 2020 2020 2020  r <1>:          \n+00022200: 2020 2020 5377 6570 7420 6c69 6e65 732e      Swept lines.\n+00022210: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+00022220: 3134 290a 2a20 706f 6c79 676f 6e20 7665  14).* polygon ve\n+00022230: 7274 6578 206f 7264 6572 203c 323e 3a20  rtex order <2>: \n+00022240: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n+00022250: 7074 206c 696e 6573 2e20 2020 2020 2020  pt lines.       \n+00022260: 2020 286c 696e 6520 2034 3029 0a2a 2070    (line  40).* p\n+00022270: 6f6c 7967 6f6e 2076 6572 7465 7820 6f72  olygon vertex or\n+00022280: 6465 7220 3c33 3e3a 2020 2020 2020 2020  der <3>:        \n+00022290: 2020 2020 2020 5377 6570 7420 706f 6c79        Swept poly\n+000222a0: 676f 6e73 2e20 2020 2020 2028 6c69 6e65  gons.      (line\n+000222b0: 2020 3139 290a 2a20 706f 6c79 676f 6e20    19).* polygon \n+000222c0: 7665 7274 6578 206f 7264 6572 203c 343e  vertex order <4>\n+000222d0: 3a20 2020 2020 2020 2020 2020 2020 204f  :              O\n+000222e0: 7665 7276 6965 772e 2020 2020 2020 2020  verview.        \n+000222f0: 2020 2020 286c 696e 6520 2033 3729 0a2a      (line  37).*\n+00022300: 2070 6f6c 7967 6f6e 2076 6572 7465 7820   polygon vertex \n+00022310: 6f72 6465 7220 3c35 3e3a 2020 2020 2020  order <5>:      \n+00022320: 2020 2020 2020 2020 4f76 6572 7669 6577          Overview\n+00022330: 2e20 2020 2020 2020 2020 2020 2028 6c69  .            (li\n+00022340: 6e65 2020 3535 290a 2a20 706f 6c79 676f  ne  55).* polygo\n+00022350: 6e2c 2062 6f64 793a 2020 2020 2020 2020  n, body:        \n+00022360: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022370: 2049 6e74 6572 6e61 6c20 6f70 7469 6f6e   Internal option\n+00022380: 732e 2020 2020 286c 696e 6520 2031 3629  s.    (line  16)\n+00022390: 0a2a 2070 6f6c 7967 6f6e 2c20 626f 6479  .* polygon, body\n+000223a0: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+000223b0: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n+000223c0: 6c69 6e65 732e 2020 2020 2020 2020 2028  lines.         (\n+000223d0: 6c69 6e65 2020 3130 290a 2a20 706f 6c79  line  10).* poly\n+000223e0: 676f 6e2c 2062 6f64 7920 3c32 3e3a 2020  gon, body <2>:  \n+000223f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022400: 2020 2053 7765 7074 2070 6f6c 7967 6f6e     Swept polygon\n+00022410: 732e 2020 2020 2020 286c 696e 6520 2020  s.      (line   \n+00022420: 3929 0a2a 2070 6f6c 7967 6f6e 2c20 656e  9).* polygon, en\n+00022430: 643a 2020 2020 2020 2020 2020 2020 2020  d:              \n+00022440: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n+00022450: 7420 6c69 6e65 732e 2020 2020 2020 2020  t lines.        \n+00022460: 2028 6c69 6e65 2020 3338 290a 2a20 706f   (line  38).* po\n+00022470: 6c79 676f 6e2c 2065 6e64 203c 313e 3a20  lygon, end <1>: \n+00022480: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022490: 2020 2020 2053 7765 7074 2070 6f6c 7967       Swept polyg\n+000224a0: 6f6e 732e 2020 2020 2020 286c 696e 6520  ons.      (line \n+000224b0: 2031 3529 0a2a 2070 6f6c 7967 6f6e 2c20   15).* polygon, \n+000224c0: 6f75 7473 6964 6520 6f66 3a20 2020 2020  outside of:     \n+000224d0: 2020 2020 2020 2020 2020 2020 2020 4865                He\n+000224e0: 6c6c 6f20 776f 726c 642e 2020 2020 2020  llo world.      \n+000224f0: 2020 2028 6c69 6e65 2020 3337 290a 2a20     (line  37).* \n+00022500: 706f 6c79 676f 6e2c 2070 6c61 6e61 723a  polygon, planar:\n 00022510: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022520: 2050 6f6c 7967 6f6e 732e 2020 2020 2020   Polygons.      \n-00022530: 2020 2020 2020 286c 696e 6520 2031 3029        (line  10)\n-00022540: 0a2a 2070 6f6c 7967 6f6e 2c20 706c 616e  .* polygon, plan\n-00022550: 6172 203c 313e 3a20 2020 2020 2020 2020  ar <1>:         \n-00022560: 2020 2020 2020 2020 2020 5377 6565 7020            Sweep \n-00022570: 6661 6365 2073 706c 6974 7469 6e67 2e0a  face splitting..\n-00022580: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022520: 2020 2020 2020 2050 6f6c 7967 6f6e 732e         Polygons.\n+00022530: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+00022540: 6520 2031 3029 0a2a 2070 6f6c 7967 6f6e  e  10).* polygon\n+00022550: 2c20 706c 616e 6172 203c 313e 3a20 2020  , planar <1>:   \n+00022560: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022570: 5377 6565 7020 6661 6365 2073 706c 6974  Sweep face split\n+00022580: 7469 6e67 2e0a 2020 2020 2020 2020 2020  ting..          \n 00022590: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000225a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000225b0: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-000225c0: 696e 6520 2020 3729 0a2a 2070 7265 6365  ine   7).* prece\n-000225d0: 6465 6e63 652c 206f 7065 7261 746f 723a  dence, operator:\n-000225e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000225f0: 2020 5477 6f2d 6f70 6572 616e 6420 2862    Two-operand (b\n-00022600: 696e 6172 7929 2066 6f72 6d73 2e0a 2020  inary) forms..  \n-00022610: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000225b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000225c0: 2020 2020 286c 696e 6520 2020 3729 0a2a      (line   7).*\n+000225d0: 2070 7265 6365 6465 6e63 652c 206f 7065   precedence, ope\n+000225e0: 7261 746f 723a 2020 2020 2020 2020 2020  rator:          \n+000225f0: 2020 2020 2020 2020 5477 6f2d 6f70 6572          Two-oper\n+00022600: 616e 6420 2862 696e 6172 7929 2066 6f72  and (binary) for\n+00022610: 6d73 2e0a 2020 2020 2020 2020 2020 2020  ms..            \n 00022620: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00022630: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022640: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-00022650: 6520 2034 3529 0a2a 2070 726f 6772 616d  e  45).* program\n-00022660: 2c20 6865 6c6c 6f20 776f 726c 643a 2020  , hello world:  \n-00022670: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022680: 4865 6c6c 6f20 776f 726c 642e 2020 2020  Hello world.    \n-00022690: 2020 2020 2028 6c69 6e65 2020 2037 290a       (line   7).\n-000226a0: 2a20 7072 6f6a 6563 7469 6f6e 2c20 7061  * projection, pa\n-000226b0: 7261 6c6c 656c 3a20 2020 2020 2020 2020  rallel:         \n-000226c0: 2020 2020 2020 2020 2048 656c 6c6f 2077           Hello w\n-000226d0: 6f72 6c64 2e20 2020 2020 2020 2020 286c  orld.         (l\n-000226e0: 696e 6520 2032 3629 0a2a 2070 726f 6a65  ine  26).* proje\n-000226f0: 6374 696f 6e2c 2070 6172 616c 6c65 6c20  ction, parallel \n-00022700: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n-00022710: 2020 5472 616e 7366 6f72 6d20 6c69 7465    Transform lite\n-00022720: 7261 6c73 2e20 2028 6c69 6e65 2020 3138  rals.  (line  18\n-00022730: 290a 2a20 7072 6f6a 6563 7469 6f6e 2c20  ).* projection, \n-00022740: 7061 7261 6c6c 656c 203c 323e 3a20 2020  parallel <2>:   \n-00022750: 2020 2020 2020 2020 2020 2050 6963 7475             Pictu\n-00022760: 7265 2062 6f78 2e20 2020 2020 2020 2020  re box.         \n-00022770: 286c 696e 6520 2031 3529 0a2a 2070 726f  (line  15).* pro\n-00022780: 6a65 6374 696f 6e2c 2070 6572 7370 6563  jection, perspec\n-00022790: 7469 7665 3a20 2020 2020 2020 2020 2020  tive:           \n-000227a0: 2020 2020 5472 616e 7366 6f72 6d20 6c69      Transform li\n-000227b0: 7465 7261 6c73 2e20 2028 6c69 6e65 2020  terals.  (line  \n-000227c0: 3139 290a 2a20 7072 6f6a 6563 7469 6f6e  19).* projection\n-000227d0: 2c20 7065 7273 7065 6374 6976 6520 3c31  , perspective <1\n-000227e0: 3e3a 2020 2020 2020 2020 2020 2054 7261  >:           Tra\n-000227f0: 6e73 666f 726d 206c 6974 6572 616c 732e  nsform literals.\n-00022800: 2020 286c 696e 6520 2032 3129 0a2a 2070    (line  21).* p\n-00022810: 726f 6a65 6374 696f 6e2c 2070 6572 7370  rojection, persp\n-00022820: 6563 7469 7665 203c 323e 3a20 2020 2020  ective <2>:     \n-00022830: 2020 2020 2020 4f76 6572 7669 6577 2e20        Overview. \n-00022840: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-00022850: 2020 2037 290a 2a20 7073 6575 646f 2d6f     7).* pseudo-o\n-00022860: 7074 696f 6e73 3a20 2020 2020 2020 2020  ptions:         \n-00022870: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n-00022880: 696b 5a2f 5047 4620 7573 6572 2d64 6566  ikZ/PGF user-def\n-00022890: 696e 6564 2073 7479 6c65 732e 0a20 2020  ined styles..   \n-000228a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022640: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022650: 2020 286c 696e 6520 2034 3529 0a2a 2070    (line  45).* p\n+00022660: 726f 6772 616d 2c20 6865 6c6c 6f20 776f  rogram, hello wo\n+00022670: 726c 643a 2020 2020 2020 2020 2020 2020  rld:            \n+00022680: 2020 2020 2020 4865 6c6c 6f20 776f 726c        Hello worl\n+00022690: 642e 2020 2020 2020 2020 2028 6c69 6e65  d.         (line\n+000226a0: 2020 2037 290a 2a20 7072 6f6a 6563 7469     7).* projecti\n+000226b0: 6f6e 2c20 7061 7261 6c6c 656c 3a20 2020  on, parallel:   \n+000226c0: 2020 2020 2020 2020 2020 2020 2020 2048                 H\n+000226d0: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020  ello world.     \n+000226e0: 2020 2020 286c 696e 6520 2032 3629 0a2a      (line  26).*\n+000226f0: 2070 726f 6a65 6374 696f 6e2c 2070 6172   projection, par\n+00022700: 616c 6c65 6c20 3c31 3e3a 2020 2020 2020  allel <1>:      \n+00022710: 2020 2020 2020 2020 5472 616e 7366 6f72          Transfor\n+00022720: 6d20 6c69 7465 7261 6c73 2e20 2028 6c69  m literals.  (li\n+00022730: 6e65 2020 3138 290a 2a20 7072 6f6a 6563  ne  18).* projec\n+00022740: 7469 6f6e 2c20 7061 7261 6c6c 656c 203c  tion, parallel <\n+00022750: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n+00022760: 2050 6963 7475 7265 2062 6f78 2e20 2020   Picture box.   \n+00022770: 2020 2020 2020 286c 696e 6520 2031 3529        (line  15)\n+00022780: 0a2a 2070 726f 6a65 6374 696f 6e2c 2070  .* projection, p\n+00022790: 6572 7370 6563 7469 7665 3a20 2020 2020  erspective:     \n+000227a0: 2020 2020 2020 2020 2020 5472 616e 7366            Transf\n+000227b0: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028  orm literals.  (\n+000227c0: 6c69 6e65 2020 3139 290a 2a20 7072 6f6a  line  19).* proj\n+000227d0: 6563 7469 6f6e 2c20 7065 7273 7065 6374  ection, perspect\n+000227e0: 6976 6520 3c31 3e3a 2020 2020 2020 2020  ive <1>:        \n+000227f0: 2020 2054 7261 6e73 666f 726d 206c 6974     Transform lit\n+00022800: 6572 616c 732e 2020 286c 696e 6520 2032  erals.  (line  2\n+00022810: 3129 0a2a 2070 726f 6a65 6374 696f 6e2c  1).* projection,\n+00022820: 2070 6572 7370 6563 7469 7665 203c 323e   perspective <2>\n+00022830: 3a20 2020 2020 2020 2020 2020 4f76 6572  :           Over\n+00022840: 7669 6577 2e20 2020 2020 2020 2020 2020  view.           \n+00022850: 2028 6c69 6e65 2020 2037 290a 2a20 7073   (line   7).* ps\n+00022860: 6575 646f 2d6f 7074 696f 6e73 3a20 2020  eudo-options:   \n+00022870: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022880: 2020 2020 2054 696b 5a2f 5047 4620 7573       TikZ/PGF us\n+00022890: 6572 2d64 6566 696e 6564 2073 7479 6c65  er-defined style\n+000228a0: 732e 0a20 2020 2020 2020 2020 2020 2020  s..             \n 000228b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000228c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000228d0: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-000228e0: 2020 3235 290a 2a20 7073 6672 616d 6562    25).* psframeb\n-000228f0: 6f78 3a20 2020 2020 2020 2020 2020 2020  ox:             \n-00022900: 2020 2020 2020 2020 2020 2020 2020 2046                 F\n-00022910: 7261 6d65 2e20 2020 2020 2020 2020 2020  rame.           \n-00022920: 2020 2020 286c 696e 6520 2020 3829 0a2a      (line   8).*\n-00022930: 2070 7370 6963 7475 7265 3a20 2020 2020   pspicture:     \n-00022940: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022950: 2020 2020 2020 2020 5069 6374 7572 6520          Picture \n-00022960: 626f 782e 2020 2020 2020 2020 2028 6c69  box.         (li\n-00022970: 6e65 2020 3130 290a 2a20 5053 5472 6963  ne  10).* PSTric\n-00022980: 6b73 3a20 2020 2020 2020 2020 2020 2020  ks:             \n+000228d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000228e0: 2028 6c69 6e65 2020 3235 290a 2a20 7073   (line  25).* ps\n+000228f0: 6672 616d 6562 6f78 3a20 2020 2020 2020  framebox:       \n+00022900: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022910: 2020 2020 2046 7261 6d65 2e20 2020 2020       Frame.     \n+00022920: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00022930: 2020 3829 0a2a 2070 7370 6963 7475 7265    8).* pspicture\n+00022940: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00022950: 2020 2020 2020 2020 2020 2020 2020 5069                Pi\n+00022960: 6374 7572 6520 626f 782e 2020 2020 2020  cture box.      \n+00022970: 2020 2028 6c69 6e65 2020 3130 290a 2a20     (line  10).* \n+00022980: 5053 5472 6963 6b73 3a20 2020 2020 2020  PSTricks:       \n 00022990: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000229a0: 2041 626f 7574 2073 6b65 7463 682e 2020   About sketch.  \n-000229b0: 2020 2020 2020 286c 696e 6520 2032 3129        (line  21)\n-000229c0: 0a2a 2071 756f 7469 6e67 2c20 7370 6563  .* quoting, spec\n-000229d0: 6961 6c3a 2020 2020 2020 2020 2020 2020  ial:            \n-000229e0: 2020 2020 2020 2020 2020 5370 6563 6961            Specia\n-000229f0: 6c20 6f62 6a65 6374 732e 2020 2020 2028  l objects.     (\n-00022a00: 6c69 6e65 2020 3230 290a 2a20 7175 6f74  line  20).* quot\n-00022a10: 696e 672c 2073 7065 6369 616c 203c 313e  ing, special <1>\n-00022a20: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00022a30: 2020 2053 7065 6369 616c 732e 2020 2020     Specials.    \n-00022a40: 2020 2020 2020 2020 286c 696e 6520 2020          (line   \n-00022a50: 3829 0a2a 2072 6566 6572 656e 6365 2c20  8).* reference, \n-00022a60: 6472 6177 6162 6c65 3a20 2020 2020 2020  drawable:       \n-00022a70: 2020 2020 2020 2020 2020 2020 4f62 6a65              Obje\n-00022a80: 6374 2074 7261 6e73 666f 726d 732e 2020  ct transforms.  \n-00022a90: 2028 6c69 6e65 2020 3333 290a 2a20 7265   (line  33).* re\n-00022aa0: 6665 7265 6e63 652c 2064 7261 7761 626c  ference, drawabl\n-00022ab0: 6520 3c31 3e3a 2020 2020 2020 2020 2020  e <1>:          \n-00022ac0: 2020 2020 2046 6f72 6d73 206f 6620 7265       Forms of re\n-00022ad0: 6665 7265 6e63 6573 2e20 286c 696e 6520  ferences. (line \n-00022ae0: 2031 3729 0a2a 2072 6566 6572 656e 6365   17).* reference\n-00022af0: 2c20 6472 6177 6162 6c65 203c 323e 3a20  , drawable <2>: \n-00022b00: 2020 2020 2020 2020 2020 2020 2020 4f76                Ov\n-00022b10: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n-00022b20: 2020 2028 6c69 6e65 2020 3437 290a 2a20     (line  47).* \n-00022b30: 7265 6665 7265 6e63 652c 2064 7261 7761  reference, drawa\n-00022b40: 626c 6520 3c33 3e3a 2020 2020 2020 2020  ble <3>:        \n-00022b50: 2020 2020 2020 204f 7665 7276 6965 772e         Overview.\n-00022b60: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-00022b70: 6520 2035 3729 0a2a 2072 6566 6572 656e  e  57).* referen\n-00022b80: 6365 2c20 6d75 6c74 6970 6c65 206f 7074  ce, multiple opt\n-00022b90: 696f 6e73 3a20 2020 2020 2020 2020 2020  ions:           \n-00022ba0: 466f 726d 7320 6f66 2072 6566 6572 656e  Forms of referen\n-00022bb0: 6365 732e 2028 6c69 6e65 2020 3138 290a  ces. (line  18).\n-00022bc0: 2a20 7265 6665 7265 6e63 652c 206f 7074  * reference, opt\n-00022bd0: 696f 6e73 3a20 2020 2020 2020 2020 2020  ions:           \n-00022be0: 2020 2020 2020 2020 2050 6f6c 796c 696e           Polylin\n-00022bf0: 6520 7377 6565 7073 2077 6974 6820 636c  e sweeps with cl\n-00022c00: 6f73 7572 652e 0a20 2020 2020 2020 2020  osure..         \n+000229a0: 2020 2020 2020 2041 626f 7574 2073 6b65         About ske\n+000229b0: 7463 682e 2020 2020 2020 2020 286c 696e  tch.        (lin\n+000229c0: 6520 2032 3129 0a2a 2071 756f 7469 6e67  e  21).* quoting\n+000229d0: 2c20 7370 6563 6961 6c3a 2020 2020 2020  , special:      \n+000229e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000229f0: 5370 6563 6961 6c20 6f62 6a65 6374 732e  Special objects.\n+00022a00: 2020 2020 2028 6c69 6e65 2020 3230 290a       (line  20).\n+00022a10: 2a20 7175 6f74 696e 672c 2073 7065 6369  * quoting, speci\n+00022a20: 616c 203c 313e 3a20 2020 2020 2020 2020  al <1>:         \n+00022a30: 2020 2020 2020 2020 2053 7065 6369 616c           Special\n+00022a40: 732e 2020 2020 2020 2020 2020 2020 286c  s.            (l\n+00022a50: 696e 6520 2020 3829 0a2a 2072 6566 6572  ine   8).* refer\n+00022a60: 656e 6365 2c20 6472 6177 6162 6c65 3a20  ence, drawable: \n+00022a70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022a80: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n+00022a90: 726d 732e 2020 2028 6c69 6e65 2020 3333  rms.   (line  33\n+00022aa0: 290a 2a20 7265 6665 7265 6e63 652c 2064  ).* reference, d\n+00022ab0: 7261 7761 626c 6520 3c31 3e3a 2020 2020  rawable <1>:    \n+00022ac0: 2020 2020 2020 2020 2020 2046 6f72 6d73             Forms\n+00022ad0: 206f 6620 7265 6665 7265 6e63 6573 2e20   of references. \n+00022ae0: 286c 696e 6520 2031 3729 0a2a 2072 6566  (line  17).* ref\n+00022af0: 6572 656e 6365 2c20 6472 6177 6162 6c65  erence, drawable\n+00022b00: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n+00022b10: 2020 2020 4f76 6572 7669 6577 2e20 2020      Overview.   \n+00022b20: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+00022b30: 3437 290a 2a20 7265 6665 7265 6e63 652c  47).* reference,\n+00022b40: 2064 7261 7761 626c 6520 3c33 3e3a 2020   drawable <3>:  \n+00022b50: 2020 2020 2020 2020 2020 2020 204f 7665               Ove\n+00022b60: 7276 6965 772e 2020 2020 2020 2020 2020  rview.          \n+00022b70: 2020 286c 696e 6520 2035 3729 0a2a 2072    (line  57).* r\n+00022b80: 6566 6572 656e 6365 2c20 6d75 6c74 6970  eference, multip\n+00022b90: 6c65 206f 7074 696f 6e73 3a20 2020 2020  le options:     \n+00022ba0: 2020 2020 2020 466f 726d 7320 6f66 2072        Forms of r\n+00022bb0: 6566 6572 656e 6365 732e 2028 6c69 6e65  eferences. (line\n+00022bc0: 2020 3138 290a 2a20 7265 6665 7265 6e63    18).* referenc\n+00022bd0: 652c 206f 7074 696f 6e73 3a20 2020 2020  e, options:     \n+00022be0: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n+00022bf0: 6f6c 796c 696e 6520 7377 6565 7073 2077  olyline sweeps w\n+00022c00: 6974 6820 636c 6f73 7572 652e 0a20 2020  ith closure..   \n 00022c10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00022c20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00022c30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022c40: 2020 2020 2028 6c69 6e65 2020 3234 290a       (line  24).\n-00022c50: 2a20 7265 6665 7265 6e63 652c 206f 7074  * reference, opt\n-00022c60: 696f 6e73 203c 313e 3a20 2020 2020 2020  ions <1>:       \n-00022c70: 2020 2020 2020 2020 2046 6f72 6d73 206f           Forms o\n-00022c80: 6620 7265 6665 7265 6e63 6573 2e20 286c  f references. (l\n-00022c90: 696e 6520 2031 3829 0a2a 2072 6566 6572  ine  18).* refer\n-00022ca0: 656e 6365 2c20 706f 696e 743a 2020 2020  ence, point:    \n-00022cb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022cc0: 2020 4472 6177 696e 6720 6120 736f 6c69    Drawing a soli\n-00022cd0: 642e 2020 2020 2028 6c69 6e65 2020 3233  d.     (line  23\n-00022ce0: 290a 2a20 7265 6665 7265 6e63 652c 2070  ).* reference, p\n-00022cf0: 6f69 6e74 203c 313e 3a20 2020 2020 2020  oint <1>:       \n-00022d00: 2020 2020 2020 2020 2020 2046 6f72 6d73             Forms\n-00022d10: 206f 6620 7265 6665 7265 6e63 6573 2e20   of references. \n-00022d20: 286c 696e 6520 2031 3429 0a2a 2072 6566  (line  14).* ref\n-00022d30: 6572 656e 6365 2c20 7363 616c 6172 3a20  erence, scalar: \n-00022d40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022d50: 2020 2020 5377 6570 7420 6f62 6a65 6374      Swept object\n-00022d60: 732e 2020 2020 2020 2028 6c69 6e65 2020  s.       (line  \n-00022d70: 3133 290a 2a20 7265 6665 7265 6e63 652c  13).* reference,\n-00022d80: 2073 6361 6c61 7220 3c31 3e3a 2020 2020   scalar <1>:    \n-00022d90: 2020 2020 2020 2020 2020 2020 2046 6f72               For\n-00022da0: 6d73 206f 6620 7265 6665 7265 6e63 6573  ms of references\n-00022db0: 2e20 286c 696e 6520 2031 3329 0a2a 2072  . (line  13).* r\n-00022dc0: 6566 6572 656e 6365 2c20 7461 673a 2020  eference, tag:  \n-00022dd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022de0: 2020 2020 2020 466f 726d 7320 6f66 2064        Forms of d\n-00022df0: 6566 696e 6974 696f 6e73 2e0a 2020 2020  efinitions..    \n-00022e00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022c40: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+00022c50: 2020 3234 290a 2a20 7265 6665 7265 6e63    24).* referenc\n+00022c60: 652c 206f 7074 696f 6e73 203c 313e 3a20  e, options <1>: \n+00022c70: 2020 2020 2020 2020 2020 2020 2020 2046                 F\n+00022c80: 6f72 6d73 206f 6620 7265 6665 7265 6e63  orms of referenc\n+00022c90: 6573 2e20 286c 696e 6520 2031 3829 0a2a  es. (line  18).*\n+00022ca0: 2072 6566 6572 656e 6365 2c20 706f 696e   reference, poin\n+00022cb0: 743a 2020 2020 2020 2020 2020 2020 2020  t:              \n+00022cc0: 2020 2020 2020 2020 4472 6177 696e 6720          Drawing \n+00022cd0: 6120 736f 6c69 642e 2020 2020 2028 6c69  a solid.     (li\n+00022ce0: 6e65 2020 3233 290a 2a20 7265 6665 7265  ne  23).* refere\n+00022cf0: 6e63 652c 2070 6f69 6e74 203c 313e 3a20  nce, point <1>: \n+00022d00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022d10: 2046 6f72 6d73 206f 6620 7265 6665 7265   Forms of refere\n+00022d20: 6e63 6573 2e20 286c 696e 6520 2031 3429  nces. (line  14)\n+00022d30: 0a2a 2072 6566 6572 656e 6365 2c20 7363  .* reference, sc\n+00022d40: 616c 6172 3a20 2020 2020 2020 2020 2020  alar:           \n+00022d50: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n+00022d60: 6f62 6a65 6374 732e 2020 2020 2020 2028  objects.       (\n+00022d70: 6c69 6e65 2020 3133 290a 2a20 7265 6665  line  13).* refe\n+00022d80: 7265 6e63 652c 2073 6361 6c61 7220 3c31  rence, scalar <1\n+00022d90: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+00022da0: 2020 2046 6f72 6d73 206f 6620 7265 6665     Forms of refe\n+00022db0: 7265 6e63 6573 2e20 286c 696e 6520 2031  rences. (line  1\n+00022dc0: 3329 0a2a 2072 6566 6572 656e 6365 2c20  3).* reference, \n+00022dd0: 7461 673a 2020 2020 2020 2020 2020 2020  tag:            \n+00022de0: 2020 2020 2020 2020 2020 2020 466f 726d              Form\n+00022df0: 7320 6f66 2064 6566 696e 6974 696f 6e73  s of definitions\n+00022e00: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n 00022e10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00022e20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022e30: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-00022e40: 2032 3029 0a2a 2072 6566 6572 656e 6365   20).* reference\n-00022e50: 2c20 7461 6720 3c31 3e3a 2020 2020 2020  , tag <1>:      \n-00022e60: 2020 2020 2020 2020 2020 2020 2020 466f                Fo\n-00022e70: 726d 7320 6f66 2072 6566 6572 656e 6365  rms of reference\n-00022e80: 732e 2028 6c69 6e65 2020 3139 290a 2a20  s. (line  19).* \n-00022e90: 7265 6665 7265 6e63 652c 2074 7261 6e73  reference, trans\n-00022ea0: 666f 726d 3a20 2020 2020 2020 2020 2020  form:           \n-00022eb0: 2020 2020 2020 2046 6f72 6d73 206f 6620         Forms of \n-00022ec0: 7265 6665 7265 6e63 6573 2e20 286c 696e  references. (lin\n-00022ed0: 6520 2031 3629 0a2a 2072 6566 6572 656e  e  16).* referen\n-00022ee0: 6365 2c20 7472 616e 7366 6f72 6d20 3c31  ce, transform <1\n-00022ef0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-00022f00: 4f76 6572 7669 6577 2e20 2020 2020 2020  Overview.       \n-00022f10: 2020 2020 2028 6c69 6e65 2020 3335 290a       (line  35).\n-00022f20: 2a20 7265 6665 7265 6e63 652c 2076 6563  * reference, vec\n-00022f30: 746f 723a 2020 2020 2020 2020 2020 2020  tor:            \n-00022f40: 2020 2020 2020 2020 2050 6f6c 796c 696e           Polylin\n-00022f50: 6520 7377 6565 7073 2e20 2020 2020 286c  e sweeps.     (l\n-00022f60: 696e 6520 2032 3029 0a2a 2072 6566 6572  ine  20).* refer\n-00022f70: 656e 6365 2c20 7665 6374 6f72 203c 313e  ence, vector <1>\n-00022f80: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00022f90: 2020 466f 726d 7320 6f66 2072 6566 6572    Forms of refer\n-00022fa0: 656e 6365 732e 2028 6c69 6e65 2020 3135  ences. (line  15\n-00022fb0: 290a 2a20 7265 7065 6174 6564 206f 626a  ).* repeated obj\n-00022fc0: 6563 743a 2020 2020 2020 2020 2020 2020  ect:            \n-00022fd0: 2020 2020 2020 2020 2020 2052 6570 6561             Repea\n-00022fe0: 7473 2e20 2020 2020 2020 2020 2020 2020  ts.             \n-00022ff0: 286c 696e 6520 2020 3629 0a2a 2072 6573  (line   6).* res\n-00023000: 6572 7665 6420 776f 7264 733a 2020 2020  erved words:    \n-00023010: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023020: 2020 2020 4b65 7920 616e 6420 7265 7365      Key and rese\n-00023030: 7276 6564 2077 6f72 6473 2e0a 2020 2020  rved words..    \n-00023040: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022e30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022e40: 286c 696e 6520 2032 3029 0a2a 2072 6566  (line  20).* ref\n+00022e50: 6572 656e 6365 2c20 7461 6720 3c31 3e3a  erence, tag <1>:\n+00022e60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022e70: 2020 2020 466f 726d 7320 6f66 2072 6566      Forms of ref\n+00022e80: 6572 656e 6365 732e 2028 6c69 6e65 2020  erences. (line  \n+00022e90: 3139 290a 2a20 7265 6665 7265 6e63 652c  19).* reference,\n+00022ea0: 2074 7261 6e73 666f 726d 3a20 2020 2020   transform:     \n+00022eb0: 2020 2020 2020 2020 2020 2020 2046 6f72               For\n+00022ec0: 6d73 206f 6620 7265 6665 7265 6e63 6573  ms of references\n+00022ed0: 2e20 286c 696e 6520 2031 3629 0a2a 2072  . (line  16).* r\n+00022ee0: 6566 6572 656e 6365 2c20 7472 616e 7366  eference, transf\n+00022ef0: 6f72 6d20 3c31 3e3a 2020 2020 2020 2020  orm <1>:        \n+00022f00: 2020 2020 2020 4f76 6572 7669 6577 2e20        Overview. \n+00022f10: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+00022f20: 2020 3335 290a 2a20 7265 6665 7265 6e63    35).* referenc\n+00022f30: 652c 2076 6563 746f 723a 2020 2020 2020  e, vector:      \n+00022f40: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n+00022f50: 6f6c 796c 696e 6520 7377 6565 7073 2e20  olyline sweeps. \n+00022f60: 2020 2020 286c 696e 6520 2032 3029 0a2a      (line  20).*\n+00022f70: 2072 6566 6572 656e 6365 2c20 7665 6374   reference, vect\n+00022f80: 6f72 203c 313e 3a20 2020 2020 2020 2020  or <1>:         \n+00022f90: 2020 2020 2020 2020 466f 726d 7320 6f66          Forms of\n+00022fa0: 2072 6566 6572 656e 6365 732e 2028 6c69   references. (li\n+00022fb0: 6e65 2020 3135 290a 2a20 7265 7065 6174  ne  15).* repeat\n+00022fc0: 6564 206f 626a 6563 743a 2020 2020 2020  ed object:      \n+00022fd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022fe0: 2052 6570 6561 7473 2e20 2020 2020 2020   Repeats.       \n+00022ff0: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+00023000: 0a2a 2072 6573 6572 7665 6420 776f 7264  .* reserved word\n+00023010: 733a 2020 2020 2020 2020 2020 2020 2020  s:              \n+00023020: 2020 2020 2020 2020 2020 4b65 7920 616e            Key an\n+00023030: 6420 7265 7365 7276 6564 2077 6f72 6473  d reserved words\n+00023040: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n 00023050: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023060: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023070: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-00023080: 2031 3129 0a2a 2072 6967 6874 2068 616e   11).* right han\n-00023090: 6420 7275 6c65 3a20 2020 2020 2020 2020  d rule:         \n-000230a0: 2020 2020 2020 2020 2020 2020 2020 4f62                Ob\n-000230b0: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n-000230c0: 2020 2028 6c69 6e65 2020 3431 290a 2a20     (line  41).* \n-000230d0: 7269 6768 742d 6861 6e64 2063 6f6f 7264  right-hand coord\n-000230e0: 696e 6174 6520 7379 7374 656d 3a20 2020  inate system:   \n-000230f0: 2020 2020 2020 2049 6e74 726f 6475 6374         Introduct\n-00023100: 696f 6e20 6279 2065 7861 6d70 6c65 2e0a  ion by example..\n-00023110: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023070: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023080: 286c 696e 6520 2031 3129 0a2a 2072 6967  (line  11).* rig\n+00023090: 6874 2068 616e 6420 7275 6c65 3a20 2020  ht hand rule:   \n+000230a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000230b0: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n+000230c0: 666f 726d 732e 2020 2028 6c69 6e65 2020  forms.   (line  \n+000230d0: 3431 290a 2a20 7269 6768 742d 6861 6e64  41).* right-hand\n+000230e0: 2063 6f6f 7264 696e 6174 6520 7379 7374   coordinate syst\n+000230f0: 656d 3a20 2020 2020 2020 2020 2049 6e74  em:          Int\n+00023100: 726f 6475 6374 696f 6e20 6279 2065 7861  roduction by exa\n+00023110: 6d70 6c65 2e0a 2020 2020 2020 2020 2020  mple..          \n 00023120: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023130: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023140: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-00023150: 696e 6520 2031 3129 0a2a 2072 6f74 6174  ine  11).* rotat\n-00023160: 696f 6e3a 2020 2020 2020 2020 2020 2020  ion:            \n+00023140: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023150: 2020 2020 286c 696e 6520 2031 3129 0a2a      (line  11).*\n+00023160: 2072 6f74 6174 696f 6e3a 2020 2020 2020   rotation:      \n 00023170: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023180: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n-00023190: 726d 732e 2020 2028 6c69 6e65 2020 3339  rms.   (line  39\n-000231a0: 290a 2a20 726f 7461 7469 6f6e 2074 7261  ).* rotation tra\n-000231b0: 6e73 666f 726d 3a20 2020 2020 2020 2020  nsform:         \n-000231c0: 2020 2020 2020 2020 2020 2054 7261 6e73             Trans\n-000231d0: 666f 726d 206c 6974 6572 616c 732e 2020  form literals.  \n-000231e0: 286c 696e 6520 2031 3029 0a2a 2072 6f74  (line  10).* rot\n-000231f0: 6174 696f 6e20 7472 616e 7366 6f72 6d20  ation transform \n-00023200: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n-00023210: 2020 2020 4120 6869 6572 6172 6368 6963      A hierarchic\n-00023220: 616c 206d 6f64 656c 2e0a 2020 2020 2020  al model..      \n+00023180: 2020 2020 2020 2020 4f62 6a65 6374 2074          Object t\n+00023190: 7261 6e73 666f 726d 732e 2020 2028 6c69  ransforms.   (li\n+000231a0: 6e65 2020 3339 290a 2a20 726f 7461 7469  ne  39).* rotati\n+000231b0: 6f6e 2074 7261 6e73 666f 726d 3a20 2020  on transform:   \n+000231c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000231d0: 2054 7261 6e73 666f 726d 206c 6974 6572   Transform liter\n+000231e0: 616c 732e 2020 286c 696e 6520 2031 3029  als.  (line  10)\n+000231f0: 0a2a 2072 6f74 6174 696f 6e20 7472 616e  .* rotation tran\n+00023200: 7366 6f72 6d20 3c31 3e3a 2020 2020 2020  sform <1>:      \n+00023210: 2020 2020 2020 2020 2020 4120 6869 6572            A hier\n+00023220: 6172 6368 6963 616c 206d 6f64 656c 2e0a  archical model..\n 00023230: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023240: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023250: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023260: 2020 2020 2020 2020 286c 696e 6520 2034          (line  4\n-00023270: 3829 0a2a 2072 6f74 6174 696f 6e20 7472  8).* rotation tr\n-00023280: 616e 7366 6f72 6d20 3c32 3e3a 2020 2020  ansform <2>:    \n-00023290: 2020 2020 2020 2020 2020 2020 4120 6869              A hi\n-000232a0: 6572 6172 6368 6963 616c 206d 6f64 656c  erarchical model\n-000232b0: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+00023260: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+00023270: 696e 6520 2034 3829 0a2a 2072 6f74 6174  ine  48).* rotat\n+00023280: 696f 6e20 7472 616e 7366 6f72 6d20 3c32  ion transform <2\n+00023290: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+000232a0: 2020 4120 6869 6572 6172 6368 6963 616c    A hierarchical\n+000232b0: 206d 6f64 656c 2e0a 2020 2020 2020 2020   model..        \n 000232c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000232d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000232e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000232f0: 286c 696e 6520 2035 3829 0a2a 2072 6f74  (line  58).* rot\n-00023300: 6174 696f 6e20 7472 616e 7366 6f72 6d20  ation transform \n-00023310: 3c33 3e3a 2020 2020 2020 2020 2020 2020  <3>:            \n-00023320: 2020 2020 4120 6869 6572 6172 6368 6963      A hierarchic\n-00023330: 616c 206d 6f64 656c 2e0a 2020 2020 2020  al model..      \n+000232f0: 2020 2020 2020 286c 696e 6520 2035 3829        (line  58)\n+00023300: 0a2a 2072 6f74 6174 696f 6e20 7472 616e  .* rotation tran\n+00023310: 7366 6f72 6d20 3c33 3e3a 2020 2020 2020  sform <3>:      \n+00023320: 2020 2020 2020 2020 2020 4120 6869 6572            A hier\n+00023330: 6172 6368 6963 616c 206d 6f64 656c 2e0a  archical model..\n 00023340: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023350: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023360: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023370: 2020 2020 2020 2020 286c 696e 6520 2037          (line  7\n-00023380: 3829 0a2a 2072 6f74 6174 696f 6e20 7472  8).* rotation tr\n-00023390: 616e 7366 6f72 6d20 3c34 3e3a 2020 2020  ansform <4>:    \n-000233a0: 2020 2020 2020 2020 2020 2020 4120 6869              A hi\n-000233b0: 6572 6172 6368 6963 616c 206d 6f64 656c  erarchical model\n-000233c0: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+00023370: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+00023380: 696e 6520 2037 3829 0a2a 2072 6f74 6174  ine  78).* rotat\n+00023390: 696f 6e20 7472 616e 7366 6f72 6d20 3c34  ion transform <4\n+000233a0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+000233b0: 2020 4120 6869 6572 6172 6368 6963 616c    A hierarchical\n+000233c0: 206d 6f64 656c 2e0a 2020 2020 2020 2020   model..        \n 000233d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000233e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000233f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023400: 286c 696e 6520 2039 3329 0a2a 2072 6f74  (line  93).* rot\n-00023410: 6174 696f 6e2c 2063 656e 7465 7220 6f66  ation, center of\n-00023420: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00023430: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n-00023440: 666f 726d 732e 2020 2028 6c69 6e65 2020  forms.   (line  \n-00023450: 2038 290a 2a20 726f 7461 7469 6f6e 2c20   8).* rotation, \n-00023460: 6365 6e74 6572 206f 6620 3c31 3e3a 2020  center of <1>:  \n-00023470: 2020 2020 2020 2020 2020 2020 204e 6573               Nes\n-00023480: 7465 6420 7377 6565 7073 2e20 2020 2020  ted sweeps.     \n-00023490: 2020 286c 696e 6520 2020 3629 0a2a 2072    (line   6).* r\n-000234a0: 756e 6e69 6e67 2073 6b65 7463 683a 2020  unning sketch:  \n-000234b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000234c0: 2020 2020 2020 4865 6c6c 6f20 776f 726c        Hello worl\n-000234d0: 642e 2020 2020 2020 2020 2028 6c69 6e65  d.         (line\n-000234e0: 2020 2039 290a 2a20 7363 616c 6172 2064     9).* scalar d\n-000234f0: 6566 696e 6974 696f 6e3a 2020 2020 2020  efinition:      \n-00023500: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n-00023510: 7765 7074 206f 626a 6563 7473 2e20 2020  wept objects.   \n-00023520: 2020 2020 286c 696e 6520 2031 3329 0a2a      (line  13).*\n-00023530: 2073 6361 6c61 7220 6c69 7465 7261 6c3a   scalar literal:\n-00023540: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023550: 2020 2020 2020 2020 5363 616c 6172 206c          Scalar l\n-00023560: 6974 6572 616c 732e 2020 2020 2028 6c69  iterals.     (li\n-00023570: 6e65 2020 2036 290a 2a20 7363 616c 6172  ne   6).* scalar\n-00023580: 2072 6566 6572 656e 6365 3a20 2020 2020   reference:     \n-00023590: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000235a0: 2046 6f72 6d73 206f 6620 7265 6665 7265   Forms of refere\n-000235b0: 6e63 6573 2e20 286c 696e 6520 2031 3329  nces. (line  13)\n-000235c0: 0a2a 2073 6361 6c65 2074 7261 6e73 666f  .* scale transfo\n-000235d0: 726d 3a20 2020 2020 2020 2020 2020 2020  rm:             \n-000235e0: 2020 2020 2020 2020 2020 5472 616e 7366            Transf\n-000235f0: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028  orm literals.  (\n-00023600: 6c69 6e65 2020 3136 290a 2a20 7363 616c  line  16).* scal\n-00023610: 6520 7472 616e 7366 6f72 6d20 3c31 3e3a  e transform <1>:\n-00023620: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023630: 2020 2054 7261 6e73 666f 726d 206c 6974     Transform lit\n-00023640: 6572 616c 732e 2020 286c 696e 6520 2031  erals.  (line  1\n-00023650: 3729 0a2a 2073 6365 6e65 2064 6573 6372  7).* scene descr\n-00023660: 6970 7469 6f6e 206c 616e 6775 6167 653a  iption language:\n-00023670: 2020 2020 2020 2020 2020 2020 4c61 6e67              Lang\n-00023680: 7561 6765 2062 6173 6963 732e 2020 2020  uage basics.    \n-00023690: 2028 6c69 6e65 2020 2038 290a 2a20 7363   (line   8).* sc\n-000236a0: 656e 6520 6465 7363 7269 7074 696f 6e20  ene description \n-000236b0: 6c61 6e67 7561 6765 203c 313e 3a20 2020  language <1>:   \n-000236c0: 2020 2020 2042 7569 6c64 696e 6720 6120       Building a \n-000236d0: 6472 6177 696e 672e 2020 286c 696e 6520  drawing.  (line \n-000236e0: 2020 3729 0a2a 2073 636f 7065 2c20 6964    7).* scope, id\n-000236f0: 656e 7469 6669 6572 3a20 2020 2020 2020  entifier:       \n-00023700: 2020 2020 2020 2020 2020 2020 2020 4f62                Ob\n-00023710: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n-00023720: 2020 2028 6c69 6e65 2020 3236 290a 2a20     (line  26).* \n-00023730: 7363 6f70 652c 2069 6465 6e74 6966 6965  scope, identifie\n-00023740: 7220 3c31 3e3a 2020 2020 2020 2020 2020  r <1>:          \n-00023750: 2020 2020 2020 2042 6c6f 636b 732e 2020         Blocks.  \n-00023760: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-00023770: 6520 2031 3329 0a2a 2073 696d 706c 6520  e  13).* simple \n-00023780: 6465 6669 6e69 7469 6f6e 3a20 2020 2020  definition:     \n-00023790: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000237a0: 466f 726d 7320 6f66 2064 6566 696e 6974  Forms of definit\n-000237b0: 696f 6e73 2e0a 2020 2020 2020 2020 2020  ions..          \n+00023400: 2020 2020 2020 286c 696e 6520 2039 3329        (line  93)\n+00023410: 0a2a 2072 6f74 6174 696f 6e2c 2063 656e  .* rotation, cen\n+00023420: 7465 7220 6f66 3a20 2020 2020 2020 2020  ter of:         \n+00023430: 2020 2020 2020 2020 2020 4f62 6a65 6374            Object\n+00023440: 2074 7261 6e73 666f 726d 732e 2020 2028   transforms.   (\n+00023450: 6c69 6e65 2020 2038 290a 2a20 726f 7461  line   8).* rota\n+00023460: 7469 6f6e 2c20 6365 6e74 6572 206f 6620  tion, center of \n+00023470: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n+00023480: 2020 204e 6573 7465 6420 7377 6565 7073     Nested sweeps\n+00023490: 2e20 2020 2020 2020 286c 696e 6520 2020  .       (line   \n+000234a0: 3629 0a2a 2072 756e 6e69 6e67 2073 6b65  6).* running ske\n+000234b0: 7463 683a 2020 2020 2020 2020 2020 2020  tch:            \n+000234c0: 2020 2020 2020 2020 2020 2020 4865 6c6c              Hell\n+000234d0: 6f20 776f 726c 642e 2020 2020 2020 2020  o world.        \n+000234e0: 2028 6c69 6e65 2020 2039 290a 2a20 7363   (line   9).* sc\n+000234f0: 616c 6172 2064 6566 696e 6974 696f 6e3a  alar definition:\n+00023500: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023510: 2020 2020 2053 7765 7074 206f 626a 6563       Swept objec\n+00023520: 7473 2e20 2020 2020 2020 286c 696e 6520  ts.       (line \n+00023530: 2031 3329 0a2a 2073 6361 6c61 7220 6c69   13).* scalar li\n+00023540: 7465 7261 6c3a 2020 2020 2020 2020 2020  teral:          \n+00023550: 2020 2020 2020 2020 2020 2020 2020 5363                Sc\n+00023560: 616c 6172 206c 6974 6572 616c 732e 2020  alar literals.  \n+00023570: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n+00023580: 7363 616c 6172 2072 6566 6572 656e 6365  scalar reference\n+00023590: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000235a0: 2020 2020 2020 2046 6f72 6d73 206f 6620         Forms of \n+000235b0: 7265 6665 7265 6e63 6573 2e20 286c 696e  references. (lin\n+000235c0: 6520 2031 3329 0a2a 2073 6361 6c65 2074  e  13).* scale t\n+000235d0: 7261 6e73 666f 726d 3a20 2020 2020 2020  ransform:       \n+000235e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000235f0: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n+00023600: 6c73 2e20 2028 6c69 6e65 2020 3136 290a  ls.  (line  16).\n+00023610: 2a20 7363 616c 6520 7472 616e 7366 6f72  * scale transfor\n+00023620: 6d20 3c31 3e3a 2020 2020 2020 2020 2020  m <1>:          \n+00023630: 2020 2020 2020 2020 2054 7261 6e73 666f           Transfo\n+00023640: 726d 206c 6974 6572 616c 732e 2020 286c  rm literals.  (l\n+00023650: 696e 6520 2031 3729 0a2a 2073 6365 6e65  ine  17).* scene\n+00023660: 2064 6573 6372 6970 7469 6f6e 206c 616e   description lan\n+00023670: 6775 6167 653a 2020 2020 2020 2020 2020  guage:          \n+00023680: 2020 4c61 6e67 7561 6765 2062 6173 6963    Language basic\n+00023690: 732e 2020 2020 2028 6c69 6e65 2020 2038  s.     (line   8\n+000236a0: 290a 2a20 7363 656e 6520 6465 7363 7269  ).* scene descri\n+000236b0: 7074 696f 6e20 6c61 6e67 7561 6765 203c  ption language <\n+000236c0: 313e 3a20 2020 2020 2020 2042 7569 6c64  1>:        Build\n+000236d0: 696e 6720 6120 6472 6177 696e 672e 2020  ing a drawing.  \n+000236e0: 286c 696e 6520 2020 3729 0a2a 2073 636f  (line   7).* sco\n+000236f0: 7065 2c20 6964 656e 7469 6669 6572 3a20  pe, identifier: \n+00023700: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023710: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n+00023720: 666f 726d 732e 2020 2028 6c69 6e65 2020  forms.   (line  \n+00023730: 3236 290a 2a20 7363 6f70 652c 2069 6465  26).* scope, ide\n+00023740: 6e74 6966 6965 7220 3c31 3e3a 2020 2020  ntifier <1>:    \n+00023750: 2020 2020 2020 2020 2020 2020 2042 6c6f               Blo\n+00023760: 636b 732e 2020 2020 2020 2020 2020 2020  cks.            \n+00023770: 2020 286c 696e 6520 2031 3329 0a2a 2073    (line  13).* s\n+00023780: 696d 706c 6520 6465 6669 6e69 7469 6f6e  imple definition\n+00023790: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000237a0: 2020 2020 2020 466f 726d 7320 6f66 2064        Forms of d\n+000237b0: 6566 696e 6974 696f 6e73 2e0a 2020 2020  efinitions..    \n 000237c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000237d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000237e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000237f0: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-00023800: 2073 6f6c 6964 3a20 2020 2020 2020 2020   solid:         \n+000237f0: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00023800: 2020 3629 0a2a 2073 6f6c 6964 3a20 2020    6).* solid:   \n 00023810: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023820: 2020 2020 2020 2020 4472 6177 696e 6720          Drawing \n-00023830: 6120 736f 6c69 642e 2020 2020 2028 6c69  a solid.     (li\n-00023840: 6e65 2020 2036 290a 2a20 7370 6563 6961  ne   6).* specia\n-00023850: 6c20 6172 6775 6d65 6e74 2073 7562 7374  l argument subst\n-00023860: 6974 7574 696f 6e3a 2020 2020 2020 2020  itution:        \n-00023870: 2053 7065 6369 616c 206f 626a 6563 7473   Special objects\n-00023880: 2e20 2020 2020 286c 696e 6520 2032 3829  .     (line  28)\n-00023890: 0a2a 2073 7065 6369 616c 2061 7267 756d  .* special argum\n-000238a0: 656e 7420 7375 6273 7469 7475 7469 6f6e  ent substitution\n-000238b0: 203c 313e 3a20 2020 2020 5370 6563 6961   <1>:     Specia\n-000238c0: 6c73 2e20 2020 2020 2020 2020 2020 2028  ls.            (\n-000238d0: 6c69 6e65 2020 3130 290a 2a20 7370 6563  line  10).* spec\n-000238e0: 6961 6c20 6f62 6a65 6374 3a20 2020 2020  ial object:     \n-000238f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023900: 2020 2053 7065 6369 616c 206f 626a 6563     Special objec\n-00023910: 7473 2e20 2020 2020 286c 696e 6520 2020  ts.     (line   \n-00023920: 3629 0a2a 2073 7065 6369 616c 206f 626a  6).* special obj\n-00023930: 6563 7473 3a20 2020 2020 2020 2020 2020  ects:           \n-00023940: 2020 2020 2020 2020 2020 2020 4120 7465              A te\n-00023950: 6368 6e69 6361 6c20 6472 6177 696e 672e  chnical drawing.\n-00023960: 2028 6c69 6e65 2020 3338 290a 2a20 7370   (line  38).* sp\n-00023970: 6c69 7474 696e 672c 206c 696e 6520 616e  litting, line an\n-00023980: 6420 7375 7266 6163 653a 2020 2020 2020  d surface:      \n-00023990: 2020 2020 2048 656c 6c6f 2077 6f72 6c64       Hello world\n-000239a0: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n-000239b0: 2031 3929 0a2a 2073 706c 6974 7469 6e67   19).* splitting\n-000239c0: 2c20 6c69 6e65 2061 6e64 2073 7572 6661  , line and surfa\n-000239d0: 6365 203c 313e 3a20 2020 2020 2020 4869  ce <1>:       Hi\n-000239e0: 6464 656e 2073 7572 6661 6365 2072 656d  dden surface rem\n-000239f0: 6f76 616c 2e0a 2020 2020 2020 2020 2020  oval..          \n+00023820: 2020 2020 2020 2020 2020 2020 2020 4472                Dr\n+00023830: 6177 696e 6720 6120 736f 6c69 642e 2020  awing a solid.  \n+00023840: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n+00023850: 7370 6563 6961 6c20 6172 6775 6d65 6e74  special argument\n+00023860: 2073 7562 7374 6974 7574 696f 6e3a 2020   substitution:  \n+00023870: 2020 2020 2020 2053 7065 6369 616c 206f         Special o\n+00023880: 626a 6563 7473 2e20 2020 2020 286c 696e  bjects.     (lin\n+00023890: 6520 2032 3829 0a2a 2073 7065 6369 616c  e  28).* special\n+000238a0: 2061 7267 756d 656e 7420 7375 6273 7469   argument substi\n+000238b0: 7475 7469 6f6e 203c 313e 3a20 2020 2020  tution <1>:     \n+000238c0: 5370 6563 6961 6c73 2e20 2020 2020 2020  Specials.       \n+000238d0: 2020 2020 2028 6c69 6e65 2020 3130 290a       (line  10).\n+000238e0: 2a20 7370 6563 6961 6c20 6f62 6a65 6374  * special object\n+000238f0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00023900: 2020 2020 2020 2020 2053 7065 6369 616c           Special\n+00023910: 206f 626a 6563 7473 2e20 2020 2020 286c   objects.     (l\n+00023920: 696e 6520 2020 3629 0a2a 2073 7065 6369  ine   6).* speci\n+00023930: 616c 206f 626a 6563 7473 3a20 2020 2020  al objects:     \n+00023940: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023950: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n+00023960: 6177 696e 672e 2028 6c69 6e65 2020 3338  awing. (line  38\n+00023970: 290a 2a20 7370 6c69 7474 696e 672c 206c  ).* splitting, l\n+00023980: 696e 6520 616e 6420 7375 7266 6163 653a  ine and surface:\n+00023990: 2020 2020 2020 2020 2020 2048 656c 6c6f             Hello\n+000239a0: 2077 6f72 6c64 2e20 2020 2020 2020 2020   world.         \n+000239b0: 286c 696e 6520 2031 3929 0a2a 2073 706c  (line  19).* spl\n+000239c0: 6974 7469 6e67 2c20 6c69 6e65 2061 6e64  itting, line and\n+000239d0: 2073 7572 6661 6365 203c 313e 3a20 2020   surface <1>:   \n+000239e0: 2020 2020 4869 6464 656e 2073 7572 6661      Hidden surfa\n+000239f0: 6365 2072 656d 6f76 616c 2e0a 2020 2020  ce removal..    \n 00023a00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023a10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023a20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023a30: 2020 2020 286c 696e 6520 2032 3129 0a2a      (line  21).*\n-00023a40: 2073 7562 7374 6974 7574 696f 6e2c 2073   substitution, s\n-00023a50: 7065 6369 616c 3a20 2020 2020 2020 2020  pecial:         \n-00023a60: 2020 2020 2020 2020 5370 6563 6961 6c20          Special \n-00023a70: 6f62 6a65 6374 732e 2020 2020 2028 6c69  objects.     (li\n-00023a80: 6e65 2020 3238 290a 2a20 7375 7266 6163  ne  28).* surfac\n-00023a90: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n+00023a30: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00023a40: 2032 3129 0a2a 2073 7562 7374 6974 7574   21).* substitut\n+00023a50: 696f 6e2c 2073 7065 6369 616c 3a20 2020  ion, special:   \n+00023a60: 2020 2020 2020 2020 2020 2020 2020 5370                Sp\n+00023a70: 6563 6961 6c20 6f62 6a65 6374 732e 2020  ecial objects.  \n+00023a80: 2020 2028 6c69 6e65 2020 3238 290a 2a20     (line  28).* \n+00023a90: 7375 7266 6163 653a 2020 2020 2020 2020  surface:        \n 00023aa0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023ab0: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n-00023ac0: 2e20 2020 2020 286c 696e 6520 2020 3629  .     (line   6)\n-00023ad0: 0a2a 2073 7765 6570 3a20 2020 2020 2020  .* sweep:       \n+00023ab0: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n+00023ac0: 7377 6565 7073 2e20 2020 2020 286c 696e  sweeps.     (lin\n+00023ad0: 6520 2020 3629 0a2a 2073 7765 6570 3a20  e   6).* sweep: \n 00023ae0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023af0: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n-00023b00: 6f62 6a65 6374 732e 2020 2020 2020 2028  objects.       (\n-00023b10: 6c69 6e65 2020 2036 290a 2a20 7377 6570  line   6).* swep\n-00023b20: 7420 626f 636b 3a20 2020 2020 2020 2020  t bock:         \n+00023af0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023b00: 5377 6570 7420 6f62 6a65 6374 732e 2020  Swept objects.  \n+00023b10: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n+00023b20: 2a20 7377 6570 7420 626f 636b 3a20 2020  * swept bock:   \n 00023b30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023b40: 2020 2053 7765 7074 2062 6c6f 636b 732e     Swept blocks.\n-00023b50: 2020 2020 2020 2020 286c 696e 6520 2020          (line   \n-00023b60: 3629 0a2a 2073 7765 7074 206c 696e 653a  6).* swept line:\n-00023b70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023b80: 2020 2020 2020 2020 2020 2020 506f 6c79              Poly\n-00023b90: 6c69 6e65 2073 7765 6570 732e 2020 2020  line sweeps.    \n-00023ba0: 2028 6c69 6e65 2020 2036 290a 2a20 7377   (line   6).* sw\n-00023bb0: 6570 7420 6c69 6e65 203c 313e 3a20 2020  ept line <1>:   \n-00023bc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023bd0: 2020 2020 2053 7765 7074 206c 696e 6573       Swept lines\n-00023be0: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n-00023bf0: 2020 3629 0a2a 2073 7765 7074 206c 696e    6).* swept lin\n-00023c00: 6520 3c32 3e3a 2020 2020 2020 2020 2020  e <2>:          \n-00023c10: 2020 2020 2020 2020 2020 2020 2020 4120                A \n-00023c20: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n-00023c30: 672e 2028 6c69 6e65 2020 3230 290a 2a20  g. (line  20).* \n-00023c40: 7377 6570 7420 6f62 6a65 6374 3a20 2020  swept object:   \n-00023c50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023c60: 2020 2020 2020 2053 7765 7074 206f 626a         Swept obj\n-00023c70: 6563 7473 2e20 2020 2020 2020 286c 696e  ects.       (lin\n-00023c80: 6520 2020 3629 0a2a 2073 7765 7074 206f  e   6).* swept o\n-00023c90: 626a 6563 7420 3c31 3e3a 2020 2020 2020  bject <1>:      \n+00023b40: 2020 2020 2020 2020 2053 7765 7074 2062           Swept b\n+00023b50: 6c6f 636b 732e 2020 2020 2020 2020 286c  locks.        (l\n+00023b60: 696e 6520 2020 3629 0a2a 2073 7765 7074  ine   6).* swept\n+00023b70: 206c 696e 653a 2020 2020 2020 2020 2020   line:          \n+00023b80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023b90: 2020 506f 6c79 6c69 6e65 2073 7765 6570    Polyline sweep\n+00023ba0: 732e 2020 2020 2028 6c69 6e65 2020 2036  s.     (line   6\n+00023bb0: 290a 2a20 7377 6570 7420 6c69 6e65 203c  ).* swept line <\n+00023bc0: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+00023bd0: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n+00023be0: 206c 696e 6573 2e20 2020 2020 2020 2020   lines.         \n+00023bf0: 286c 696e 6520 2020 3629 0a2a 2073 7765  (line   6).* swe\n+00023c00: 7074 206c 696e 6520 3c32 3e3a 2020 2020  pt line <2>:    \n+00023c10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023c20: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n+00023c30: 6472 6177 696e 672e 2028 6c69 6e65 2020  drawing. (line  \n+00023c40: 3230 290a 2a20 7377 6570 7420 6f62 6a65  20).* swept obje\n+00023c50: 6374 3a20 2020 2020 2020 2020 2020 2020  ct:             \n+00023c60: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n+00023c70: 7074 206f 626a 6563 7473 2e20 2020 2020  pt objects.     \n+00023c80: 2020 286c 696e 6520 2020 3629 0a2a 2073    (line   6).* s\n+00023c90: 7765 7074 206f 626a 6563 7420 3c31 3e3a  wept object <1>:\n 00023ca0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023cb0: 5377 6565 7073 2e20 2020 2020 2020 2020  Sweeps.         \n-00023cc0: 2020 2020 2028 6c69 6e65 2020 2039 290a       (line   9).\n-00023cd0: 2a20 7377 6570 7420 706f 696e 743a 2020  * swept point:  \n-00023ce0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023cf0: 2020 2020 2020 2020 2053 7765 7074 206f           Swept o\n-00023d00: 626a 6563 7473 2e20 2020 2020 2020 286c  bjects.       (l\n-00023d10: 696e 6520 2031 3129 0a2a 2073 7765 7074  ine  11).* swept\n-00023d20: 2070 6f69 6e74 203c 313e 3a20 2020 2020   point <1>:     \n-00023d30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023d40: 2020 5377 6570 7420 706f 696e 7473 2e20    Swept points. \n-00023d50: 2020 2020 2020 2028 6c69 6e65 2020 2036         (line   6\n-00023d60: 290a 2a20 7377 6570 7420 706f 6c79 676f  ).* swept polygo\n-00023d70: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n-00023d80: 2020 2020 2020 2020 2020 2050 6f6c 7967             Polyg\n-00023d90: 6f6e 2073 7765 6570 732e 2020 2020 2020  on sweeps.      \n-00023da0: 286c 696e 6520 2020 3629 0a2a 2073 7765  (line   6).* swe\n-00023db0: 7074 2070 6f6c 7967 6f6e 203c 313e 3a20  pt polygon <1>: \n-00023dc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023dd0: 2020 2020 4120 6869 6572 6172 6368 6963      A hierarchic\n-00023de0: 616c 206d 6f64 656c 2e0a 2020 2020 2020  al model..      \n+00023cb0: 2020 2020 2020 5377 6565 7073 2e20 2020        Sweeps.   \n+00023cc0: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+00023cd0: 2020 2039 290a 2a20 7377 6570 7420 706f     9).* swept po\n+00023ce0: 696e 743a 2020 2020 2020 2020 2020 2020  int:            \n+00023cf0: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n+00023d00: 7765 7074 206f 626a 6563 7473 2e20 2020  wept objects.   \n+00023d10: 2020 2020 286c 696e 6520 2031 3129 0a2a      (line  11).*\n+00023d20: 2073 7765 7074 2070 6f69 6e74 203c 313e   swept point <1>\n+00023d30: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00023d40: 2020 2020 2020 2020 5377 6570 7420 706f          Swept po\n+00023d50: 696e 7473 2e20 2020 2020 2020 2028 6c69  ints.        (li\n+00023d60: 6e65 2020 2036 290a 2a20 7377 6570 7420  ne   6).* swept \n+00023d70: 706f 6c79 676f 6e3a 2020 2020 2020 2020  polygon:        \n+00023d80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023d90: 2050 6f6c 7967 6f6e 2073 7765 6570 732e   Polygon sweeps.\n+00023da0: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+00023db0: 0a2a 2073 7765 7074 2070 6f6c 7967 6f6e  .* swept polygon\n+00023dc0: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+00023dd0: 2020 2020 2020 2020 2020 4120 6869 6572            A hier\n+00023de0: 6172 6368 6963 616c 206d 6f64 656c 2e0a  archical model..\n 00023df0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023e00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023e10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023e20: 2020 2020 2020 2020 286c 696e 6520 3132          (line 12\n-00023e30: 3229 0a2a 2074 6167 2064 6566 696e 6974  2).* tag definit\n-00023e40: 696f 6e3a 2020 2020 2020 2020 2020 2020  ion:            \n-00023e50: 2020 2020 2020 2020 2020 2020 4465 6669              Defi\n-00023e60: 6e69 7469 6f6e 732e 2020 2020 2020 2020  nitions.        \n-00023e70: 2028 6c69 6e65 2020 3138 290a 2a20 7461   (line  18).* ta\n-00023e80: 6720 6465 6669 6e69 7469 6f6e 203c 313e  g definition <1>\n-00023e90: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00023ea0: 2020 2020 2046 6f72 6d73 206f 6620 6465       Forms of de\n-00023eb0: 6669 6e69 7469 6f6e 732e 0a20 2020 2020  finitions..     \n-00023ec0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023e20: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+00023e30: 696e 6520 3132 3229 0a2a 2074 6167 2064  ine 122).* tag d\n+00023e40: 6566 696e 6974 696f 6e3a 2020 2020 2020  efinition:      \n+00023e50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023e60: 2020 4465 6669 6e69 7469 6f6e 732e 2020    Definitions.  \n+00023e70: 2020 2020 2020 2028 6c69 6e65 2020 3138         (line  18\n+00023e80: 290a 2a20 7461 6720 6465 6669 6e69 7469  ).* tag definiti\n+00023e90: 6f6e 203c 313e 3a20 2020 2020 2020 2020  on <1>:         \n+00023ea0: 2020 2020 2020 2020 2020 2046 6f72 6d73             Forms\n+00023eb0: 206f 6620 6465 6669 6e69 7469 6f6e 732e   of definitions.\n+00023ec0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n 00023ed0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023ee0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023ef0: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-00023f00: 2037 290a 2a20 7461 6720 6465 6669 6e69   7).* tag defini\n-00023f10: 7469 6f6e 203c 323e 3a20 2020 2020 2020  tion <2>:       \n-00023f20: 2020 2020 2020 2020 2020 2020 2043 6f6d               Com\n-00023f30: 6d61 6e64 206c 696e 652e 2020 2020 2020  mand line.      \n-00023f40: 2020 286c 696e 6520 2035 3329 0a2a 2074    (line  53).* t\n-00023f50: 6167 2072 6566 6572 656e 6365 3a20 2020  ag reference:   \n-00023f60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023f70: 2020 2020 2020 466f 726d 7320 6f66 2064        Forms of d\n-00023f80: 6566 696e 6974 696f 6e73 2e0a 2020 2020  efinitions..    \n-00023f90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023ef0: 2020 2020 2020 2020 2020 2020 2020 2028                 (\n+00023f00: 6c69 6e65 2020 2037 290a 2a20 7461 6720  line   7).* tag \n+00023f10: 6465 6669 6e69 7469 6f6e 203c 323e 3a20  definition <2>: \n+00023f20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023f30: 2020 2043 6f6d 6d61 6e64 206c 696e 652e     Command line.\n+00023f40: 2020 2020 2020 2020 286c 696e 6520 2035          (line  5\n+00023f50: 3329 0a2a 2074 6167 2072 6566 6572 656e  3).* tag referen\n+00023f60: 6365 3a20 2020 2020 2020 2020 2020 2020  ce:             \n+00023f70: 2020 2020 2020 2020 2020 2020 466f 726d              Form\n+00023f80: 7320 6f66 2064 6566 696e 6974 696f 6e73  s of definitions\n+00023f90: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n 00023fa0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00023fb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023fc0: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-00023fd0: 2032 3029 0a2a 2074 6167 2072 6566 6572   20).* tag refer\n-00023fe0: 656e 6365 203c 313e 3a20 2020 2020 2020  ence <1>:       \n-00023ff0: 2020 2020 2020 2020 2020 2020 2020 466f                Fo\n-00024000: 726d 7320 6f66 2072 6566 6572 656e 6365  rms of reference\n-00024010: 732e 2028 6c69 6e65 2020 3139 290a 2a20  s. (line  19).* \n-00024020: 7465 6d70 6c61 7465 2c20 646f 6375 6d65  template, docume\n-00024030: 6e74 3a20 2020 2020 2020 2020 2020 2020  nt:             \n-00024040: 2020 2020 2020 2048 656c 6c6f 2077 6f72         Hello wor\n-00024050: 6c64 2e20 2020 2020 2020 2020 286c 696e  ld.         (lin\n-00024060: 6520 2033 3229 0a2a 2074 656d 706c 6174  e  32).* templat\n-00024070: 652c 2064 6f63 756d 656e 7420 3c31 3e3a  e, document <1>:\n-00024080: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024090: 436f 6d6d 616e 6420 6c69 6e65 2e20 2020  Command line.   \n-000240a0: 2020 2020 2028 6c69 6e65 2020 3336 290a       (line  36).\n-000240b0: 2a20 7465 7472 6168 6564 726f 6e3a 2020  * tetrahedron:  \n-000240c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000240d0: 2020 2020 2020 2020 2044 7261 7769 6e67           Drawing\n-000240e0: 2061 2073 6f6c 6964 2e20 2020 2020 286c   a solid.     (l\n-000240f0: 696e 6520 2020 3929 0a2a 2074 6963 6b20  ine   9).* tick \n-00024100: 6f70 6572 6174 6f72 2028 2729 3a20 2020  operator ('):   \n-00024110: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024120: 2020 4166 6669 6e65 2061 7269 7468 6d65    Affine arithme\n-00024130: 7469 632e 2020 2028 6c69 6e65 2020 3337  tic.   (line  37\n-00024140: 290a 2a20 7469 636b 206f 7065 7261 746f  ).* tick operato\n-00024150: 7220 2827 2920 3c31 3e3a 2020 2020 2020  r (') <1>:      \n-00024160: 2020 2020 2020 2020 2020 2054 776f 2d6f             Two-o\n-00024170: 7065 7261 6e64 2028 6269 6e61 7279 2920  perand (binary) \n-00024180: 666f 726d 732e 0a20 2020 2020 2020 2020  forms..         \n+00023fc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023fd0: 286c 696e 6520 2032 3029 0a2a 2074 6167  (line  20).* tag\n+00023fe0: 2072 6566 6572 656e 6365 203c 313e 3a20   reference <1>: \n+00023ff0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024000: 2020 2020 466f 726d 7320 6f66 2072 6566      Forms of ref\n+00024010: 6572 656e 6365 732e 2028 6c69 6e65 2020  erences. (line  \n+00024020: 3139 290a 2a20 7465 6d70 6c61 7465 2c20  19).* template, \n+00024030: 646f 6375 6d65 6e74 3a20 2020 2020 2020  document:       \n+00024040: 2020 2020 2020 2020 2020 2020 2048 656c               Hel\n+00024050: 6c6f 2077 6f72 6c64 2e20 2020 2020 2020  lo world.       \n+00024060: 2020 286c 696e 6520 2033 3229 0a2a 2074    (line  32).* t\n+00024070: 656d 706c 6174 652c 2064 6f63 756d 656e  emplate, documen\n+00024080: 7420 3c31 3e3a 2020 2020 2020 2020 2020  t <1>:          \n+00024090: 2020 2020 2020 436f 6d6d 616e 6420 6c69        Command li\n+000240a0: 6e65 2e20 2020 2020 2020 2028 6c69 6e65  ne.        (line\n+000240b0: 2020 3336 290a 2a20 7465 7472 6168 6564    36).* tetrahed\n+000240c0: 726f 6e3a 2020 2020 2020 2020 2020 2020  ron:            \n+000240d0: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n+000240e0: 7261 7769 6e67 2061 2073 6f6c 6964 2e20  rawing a solid. \n+000240f0: 2020 2020 286c 696e 6520 2020 3929 0a2a      (line   9).*\n+00024100: 2074 6963 6b20 6f70 6572 6174 6f72 2028   tick operator (\n+00024110: 2729 3a20 2020 2020 2020 2020 2020 2020  '):             \n+00024120: 2020 2020 2020 2020 4166 6669 6e65 2061          Affine a\n+00024130: 7269 7468 6d65 7469 632e 2020 2028 6c69  rithmetic.   (li\n+00024140: 6e65 2020 3337 290a 2a20 7469 636b 206f  ne  37).* tick o\n+00024150: 7065 7261 746f 7220 2827 2920 3c31 3e3a  perator (') <1>:\n+00024160: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024170: 2054 776f 2d6f 7065 7261 6e64 2028 6269   Two-operand (bi\n+00024180: 6e61 7279 2920 666f 726d 732e 0a20 2020  nary) forms..   \n 00024190: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000241a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000241b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000241c0: 2020 2020 2028 6c69 6e65 2020 3431 290a       (line  41).\n-000241d0: 2a20 5469 6b5a 2f50 4746 3a20 2020 2020  * TikZ/PGF:     \n-000241e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000241f0: 2020 2020 2020 2020 2041 626f 7574 2073           About s\n-00024200: 6b65 7463 682e 2020 2020 2020 2020 286c  ketch.        (l\n-00024210: 696e 6520 2032 3229 0a2a 2074 6f72 6f69  ine  22).* toroi\n-00024220: 643a 2020 2020 2020 2020 2020 2020 2020  d:              \n+000241c0: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+000241d0: 2020 3431 290a 2a20 5469 6b5a 2f50 4746    41).* TikZ/PGF\n+000241e0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000241f0: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+00024200: 626f 7574 2073 6b65 7463 682e 2020 2020  bout sketch.    \n+00024210: 2020 2020 286c 696e 6520 2032 3229 0a2a      (line  22).*\n+00024220: 2074 6f72 6f69 643a 2020 2020 2020 2020   toroid:        \n 00024230: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024240: 2020 4e65 7374 6564 2073 7765 6570 732e    Nested sweeps.\n-00024250: 2020 2020 2020 2028 6c69 6e65 2020 2038         (line   8\n-00024260: 290a 2a20 7472 616e 7366 6f72 6d3a 2020  ).* transform:  \n-00024270: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024280: 2020 2020 2020 2020 2020 204f 626a 6563             Objec\n-00024290: 7420 7472 616e 7366 6f72 6d73 2e20 2020  t transforms.   \n-000242a0: 286c 696e 6520 2020 3629 0a2a 2074 7261  (line   6).* tra\n-000242b0: 6e73 666f 726d 203c 313e 3a20 2020 2020  nsform <1>:     \n-000242c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000242d0: 2020 2020 5477 6f2d 6f70 6572 616e 6420      Two-operand \n-000242e0: 2862 696e 6172 7929 2066 6f72 6d73 2e0a  (binary) forms..\n-000242f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024240: 2020 2020 2020 2020 4e65 7374 6564 2073          Nested s\n+00024250: 7765 6570 732e 2020 2020 2020 2028 6c69  weeps.       (li\n+00024260: 6e65 2020 2038 290a 2a20 7472 616e 7366  ne   8).* transf\n+00024270: 6f72 6d3a 2020 2020 2020 2020 2020 2020  orm:            \n+00024280: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024290: 204f 626a 6563 7420 7472 616e 7366 6f72   Object transfor\n+000242a0: 6d73 2e20 2020 286c 696e 6520 2020 3629  ms.   (line   6)\n+000242b0: 0a2a 2074 7261 6e73 666f 726d 203c 313e  .* transform <1>\n+000242c0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000242d0: 2020 2020 2020 2020 2020 5477 6f2d 6f70            Two-op\n+000242e0: 6572 616e 6420 2862 696e 6172 7929 2066  erand (binary) f\n+000242f0: 6f72 6d73 2e0a 2020 2020 2020 2020 2020  orms..          \n 00024300: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024310: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024320: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n-00024330: 696e 6520 2032 3829 0a2a 2074 7261 6e73  ine  28).* trans\n-00024340: 666f 726d 203c 323e 3a20 2020 2020 2020  form <2>:       \n+00024320: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024330: 2020 2020 286c 696e 6520 2032 3829 0a2a      (line  28).*\n+00024340: 2074 7261 6e73 666f 726d 203c 323e 3a20   transform <2>: \n 00024350: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024360: 2020 5377 6565 7073 2e20 2020 2020 2020    Sweeps.       \n-00024370: 2020 2020 2020 2028 6c69 6e65 2020 3131         (line  11\n-00024380: 290a 2a20 7472 616e 7366 6f72 6d20 3c33  ).* transform <3\n-00024390: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-000243a0: 2020 2020 2020 2020 2020 2052 6570 6561             Repea\n-000243b0: 7473 2e20 2020 2020 2020 2020 2020 2020  ts.             \n-000243c0: 286c 696e 6520 2020 3929 0a2a 2074 7261  (line   9).* tra\n-000243d0: 6e73 666f 726d 203c 343e 3a20 2020 2020  nsform <4>:     \n-000243e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000243f0: 2020 2020 4f76 6572 7669 6577 2e20 2020      Overview.   \n-00024400: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-00024410: 2037 290a 2a20 7472 616e 7366 6f72 6d20   7).* transform \n-00024420: 6465 6669 6e69 7469 6f6e 3a20 2020 2020  definition:     \n-00024430: 2020 2020 2020 2020 2020 2020 204f 7665               Ove\n-00024440: 7276 6965 772e 2020 2020 2020 2020 2020  rview.          \n-00024450: 2020 286c 696e 6520 2033 3529 0a2a 2074    (line  35).* t\n-00024460: 7261 6e73 666f 726d 206c 6974 6572 616c  ransform literal\n-00024470: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00024480: 2020 2020 2020 5472 616e 7366 6f72 6d20        Transform \n-00024490: 6c69 7465 7261 6c73 2e20 2028 6c69 6e65  literals.  (line\n-000244a0: 2020 2036 290a 2a20 7472 616e 7366 6f72     6).* transfor\n-000244b0: 6d20 7265 6665 7265 6e63 653a 2020 2020  m reference:    \n-000244c0: 2020 2020 2020 2020 2020 2020 2020 2046                 F\n-000244d0: 6f72 6d73 206f 6620 7265 6665 7265 6e63  orms of referenc\n-000244e0: 6573 2e20 286c 696e 6520 2031 3629 0a2a  es. (line  16).*\n-000244f0: 2074 7261 6e73 666f 726d 2072 6566 6572   transform refer\n-00024500: 656e 6365 203c 313e 3a20 2020 2020 2020  ence <1>:       \n-00024510: 2020 2020 2020 2020 4f76 6572 7669 6577          Overview\n-00024520: 2e20 2020 2020 2020 2020 2020 2028 6c69  .            (li\n-00024530: 6e65 2020 3335 290a 2a20 7472 616e 7366  ne  35).* transf\n-00024540: 6f72 6d2c 2064 6972 6563 743a 2020 2020  orm, direct:    \n-00024550: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024560: 2054 7261 6e73 666f 726d 206c 6974 6572   Transform liter\n-00024570: 616c 732e 2020 286c 696e 6520 2034 3729  als.  (line  47)\n-00024580: 0a2a 2074 7261 6e73 666f 726d 2c20 6469  .* transform, di\n-00024590: 7265 6374 203c 313e 3a20 2020 2020 2020  rect <1>:       \n-000245a0: 2020 2020 2020 2020 2020 5472 616e 7366            Transf\n-000245b0: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028  orm literals.  (\n-000245c0: 6c69 6e65 2020 3533 290a 2a20 7472 616e  line  53).* tran\n-000245d0: 7366 6f72 6d2c 2072 6f74 6174 696f 6e3a  sform, rotation:\n-000245e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000245f0: 2020 2054 7261 6e73 666f 726d 206c 6974     Transform lit\n-00024600: 6572 616c 732e 2020 286c 696e 6520 2031  erals.  (line  1\n-00024610: 3029 0a2a 2074 7261 6e73 666f 726d 2c20  0).* transform, \n-00024620: 726f 7461 7469 6f6e 203c 313e 3a20 2020  rotation <1>:   \n-00024630: 2020 2020 2020 2020 2020 2020 4120 6869              A hi\n-00024640: 6572 6172 6368 6963 616c 206d 6f64 656c  erarchical model\n-00024650: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+00024360: 2020 2020 2020 2020 5377 6565 7073 2e20          Sweeps. \n+00024370: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n+00024380: 6e65 2020 3131 290a 2a20 7472 616e 7366  ne  11).* transf\n+00024390: 6f72 6d20 3c33 3e3a 2020 2020 2020 2020  orm <3>:        \n+000243a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000243b0: 2052 6570 6561 7473 2e20 2020 2020 2020   Repeats.       \n+000243c0: 2020 2020 2020 286c 696e 6520 2020 3929        (line   9)\n+000243d0: 0a2a 2074 7261 6e73 666f 726d 203c 343e  .* transform <4>\n+000243e0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000243f0: 2020 2020 2020 2020 2020 4f76 6572 7669            Overvi\n+00024400: 6577 2e20 2020 2020 2020 2020 2020 2028  ew.            (\n+00024410: 6c69 6e65 2020 2037 290a 2a20 7472 616e  line   7).* tran\n+00024420: 7366 6f72 6d20 6465 6669 6e69 7469 6f6e  sform definition\n+00024430: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00024440: 2020 204f 7665 7276 6965 772e 2020 2020     Overview.    \n+00024450: 2020 2020 2020 2020 286c 696e 6520 2033          (line  3\n+00024460: 3529 0a2a 2074 7261 6e73 666f 726d 206c  5).* transform l\n+00024470: 6974 6572 616c 3a20 2020 2020 2020 2020  iteral:         \n+00024480: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n+00024490: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n+000244a0: 2028 6c69 6e65 2020 2036 290a 2a20 7472   (line   6).* tr\n+000244b0: 616e 7366 6f72 6d20 7265 6665 7265 6e63  ansform referenc\n+000244c0: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n+000244d0: 2020 2020 2046 6f72 6d73 206f 6620 7265       Forms of re\n+000244e0: 6665 7265 6e63 6573 2e20 286c 696e 6520  ferences. (line \n+000244f0: 2031 3629 0a2a 2074 7261 6e73 666f 726d   16).* transform\n+00024500: 2072 6566 6572 656e 6365 203c 313e 3a20   reference <1>: \n+00024510: 2020 2020 2020 2020 2020 2020 2020 4f76                Ov\n+00024520: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n+00024530: 2020 2028 6c69 6e65 2020 3335 290a 2a20     (line  35).* \n+00024540: 7472 616e 7366 6f72 6d2c 2064 6972 6563  transform, direc\n+00024550: 743a 2020 2020 2020 2020 2020 2020 2020  t:              \n+00024560: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n+00024570: 206c 6974 6572 616c 732e 2020 286c 696e   literals.  (lin\n+00024580: 6520 2034 3729 0a2a 2074 7261 6e73 666f  e  47).* transfo\n+00024590: 726d 2c20 6469 7265 6374 203c 313e 3a20  rm, direct <1>: \n+000245a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000245b0: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n+000245c0: 6c73 2e20 2028 6c69 6e65 2020 3533 290a  ls.  (line  53).\n+000245d0: 2a20 7472 616e 7366 6f72 6d2c 2072 6f74  * transform, rot\n+000245e0: 6174 696f 6e3a 2020 2020 2020 2020 2020  ation:          \n+000245f0: 2020 2020 2020 2020 2054 7261 6e73 666f           Transfo\n+00024600: 726d 206c 6974 6572 616c 732e 2020 286c  rm literals.  (l\n+00024610: 696e 6520 2031 3029 0a2a 2074 7261 6e73  ine  10).* trans\n+00024620: 666f 726d 2c20 726f 7461 7469 6f6e 203c  form, rotation <\n+00024630: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+00024640: 2020 4120 6869 6572 6172 6368 6963 616c    A hierarchical\n+00024650: 206d 6f64 656c 2e0a 2020 2020 2020 2020   model..        \n 00024660: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024670: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024680: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024690: 286c 696e 6520 2034 3829 0a2a 2074 7261  (line  48).* tra\n-000246a0: 6e73 666f 726d 2c20 726f 7461 7469 6f6e  nsform, rotation\n-000246b0: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n-000246c0: 2020 2020 4120 6869 6572 6172 6368 6963      A hierarchic\n-000246d0: 616c 206d 6f64 656c 2e0a 2020 2020 2020  al model..      \n+00024690: 2020 2020 2020 286c 696e 6520 2034 3829        (line  48)\n+000246a0: 0a2a 2074 7261 6e73 666f 726d 2c20 726f  .* transform, ro\n+000246b0: 7461 7469 6f6e 203c 323e 3a20 2020 2020  tation <2>:     \n+000246c0: 2020 2020 2020 2020 2020 4120 6869 6572            A hier\n+000246d0: 6172 6368 6963 616c 206d 6f64 656c 2e0a  archical model..\n 000246e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000246f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024700: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024710: 2020 2020 2020 2020 286c 696e 6520 2035          (line  5\n-00024720: 3829 0a2a 2074 7261 6e73 666f 726d 2c20  8).* transform, \n-00024730: 726f 7461 7469 6f6e 203c 333e 3a20 2020  rotation <3>:   \n-00024740: 2020 2020 2020 2020 2020 2020 4120 6869              A hi\n-00024750: 6572 6172 6368 6963 616c 206d 6f64 656c  erarchical model\n-00024760: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+00024710: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+00024720: 696e 6520 2035 3829 0a2a 2074 7261 6e73  ine  58).* trans\n+00024730: 666f 726d 2c20 726f 7461 7469 6f6e 203c  form, rotation <\n+00024740: 333e 3a20 2020 2020 2020 2020 2020 2020  3>:             \n+00024750: 2020 4120 6869 6572 6172 6368 6963 616c    A hierarchical\n+00024760: 206d 6f64 656c 2e0a 2020 2020 2020 2020   model..        \n 00024770: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024780: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024790: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000247a0: 286c 696e 6520 2037 3829 0a2a 2074 7261  (line  78).* tra\n-000247b0: 6e73 666f 726d 2c20 726f 7461 7469 6f6e  nsform, rotation\n-000247c0: 203c 343e 3a20 2020 2020 2020 2020 2020   <4>:           \n-000247d0: 2020 2020 4120 6869 6572 6172 6368 6963      A hierarchic\n-000247e0: 616c 206d 6f64 656c 2e0a 2020 2020 2020  al model..      \n+000247a0: 2020 2020 2020 286c 696e 6520 2037 3829        (line  78)\n+000247b0: 0a2a 2074 7261 6e73 666f 726d 2c20 726f  .* transform, ro\n+000247c0: 7461 7469 6f6e 203c 343e 3a20 2020 2020  tation <4>:     \n+000247d0: 2020 2020 2020 2020 2020 4120 6869 6572            A hier\n+000247e0: 6172 6368 6963 616c 206d 6f64 656c 2e0a  archical model..\n 000247f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024800: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024810: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024820: 2020 2020 2020 2020 286c 696e 6520 2039          (line  9\n-00024830: 3329 0a2a 2074 7261 6e73 666f 726d 2c20  3).* transform, \n-00024840: 7363 616c 653a 2020 2020 2020 2020 2020  scale:          \n-00024850: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n-00024860: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n-00024870: 2028 6c69 6e65 2020 3136 290a 2a20 7472   (line  16).* tr\n-00024880: 616e 7366 6f72 6d2c 2073 6361 6c65 203c  ansform, scale <\n-00024890: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-000248a0: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n-000248b0: 6974 6572 616c 732e 2020 286c 696e 6520  iterals.  (line \n-000248c0: 2031 3729 0a2a 2074 7261 6e73 666f 726d   17).* transform\n-000248d0: 2c20 7472 616e 736c 6174 696f 6e3a 2020  , translation:  \n-000248e0: 2020 2020 2020 2020 2020 2020 2020 4f62                Ob\n-000248f0: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n-00024900: 2020 2028 6c69 6e65 2020 3437 290a 2a20     (line  47).* \n-00024910: 7472 616e 7366 6f72 6d2c 2074 7261 6e73  transform, trans\n-00024920: 6c61 7469 6f6e 203c 313e 3a20 2020 2020  lation <1>:     \n-00024930: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n-00024940: 206c 6974 6572 616c 732e 2020 286c 696e   literals.  (lin\n-00024950: 6520 2031 3529 0a2a 2074 7261 6e73 666f  e  15).* transfo\n-00024960: 726d 2c20 7472 616e 736c 6174 696f 6e20  rm, translation \n-00024970: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n-00024980: 4120 6869 6572 6172 6368 6963 616c 206d  A hierarchical m\n-00024990: 6f64 656c 2e0a 2020 2020 2020 2020 2020  odel..          \n+00024820: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+00024830: 696e 6520 2039 3329 0a2a 2074 7261 6e73  ine  93).* trans\n+00024840: 666f 726d 2c20 7363 616c 653a 2020 2020  form, scale:    \n+00024850: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024860: 2020 5472 616e 7366 6f72 6d20 6c69 7465    Transform lite\n+00024870: 7261 6c73 2e20 2028 6c69 6e65 2020 3136  rals.  (line  16\n+00024880: 290a 2a20 7472 616e 7366 6f72 6d2c 2073  ).* transform, s\n+00024890: 6361 6c65 203c 313e 3a20 2020 2020 2020  cale <1>:       \n+000248a0: 2020 2020 2020 2020 2020 2054 7261 6e73             Trans\n+000248b0: 666f 726d 206c 6974 6572 616c 732e 2020  form literals.  \n+000248c0: 286c 696e 6520 2031 3729 0a2a 2074 7261  (line  17).* tra\n+000248d0: 6e73 666f 726d 2c20 7472 616e 736c 6174  nsform, translat\n+000248e0: 696f 6e3a 2020 2020 2020 2020 2020 2020  ion:            \n+000248f0: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n+00024900: 666f 726d 732e 2020 2028 6c69 6e65 2020  forms.   (line  \n+00024910: 3437 290a 2a20 7472 616e 7366 6f72 6d2c  47).* transform,\n+00024920: 2074 7261 6e73 6c61 7469 6f6e 203c 313e   translation <1>\n+00024930: 3a20 2020 2020 2020 2020 2020 2054 7261  :            Tra\n+00024940: 6e73 666f 726d 206c 6974 6572 616c 732e  nsform literals.\n+00024950: 2020 286c 696e 6520 2031 3529 0a2a 2074    (line  15).* t\n+00024960: 7261 6e73 666f 726d 2c20 7472 616e 736c  ransform, transl\n+00024970: 6174 696f 6e20 3c32 3e3a 2020 2020 2020  ation <2>:      \n+00024980: 2020 2020 2020 4120 6869 6572 6172 6368        A hierarch\n+00024990: 6963 616c 206d 6f64 656c 2e0a 2020 2020  ical model..    \n 000249a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000249b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 000249c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000249d0: 2020 2020 286c 696e 6520 2034 3729 0a2a      (line  47).*\n-000249e0: 2074 7261 6e73 666f 726d 2c20 7669 6577   transform, view\n-000249f0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00024a00: 2020 2020 2020 2020 5472 616e 7366 6f72          Transfor\n-00024a10: 6d20 6c69 7465 7261 6c73 2e20 2028 6c69  m literals.  (li\n-00024a20: 6e65 2020 3235 290a 2a20 7472 616e 7366  ne  25).* transf\n-00024a30: 6f72 6d2c 2076 6965 7720 3c31 3e3a 2020  orm, view <1>:  \n-00024a40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024a50: 2054 7261 6e73 666f 726d 206c 6974 6572   Transform liter\n-00024a60: 616c 732e 2020 286c 696e 6520 2033 3529  als.  (line  35)\n-00024a70: 0a2a 2074 7261 6e73 6c61 7469 6f6e 2074  .* translation t\n-00024a80: 7261 6e73 666f 726d 3a20 2020 2020 2020  ransform:       \n-00024a90: 2020 2020 2020 2020 2020 4f62 6a65 6374            Object\n-00024aa0: 2074 7261 6e73 666f 726d 732e 2020 2028   transforms.   (\n-00024ab0: 6c69 6e65 2020 3437 290a 2a20 7472 616e  line  47).* tran\n-00024ac0: 736c 6174 696f 6e20 7472 616e 7366 6f72  slation transfor\n-00024ad0: 6d20 3c31 3e3a 2020 2020 2020 2020 2020  m <1>:          \n-00024ae0: 2020 2054 7261 6e73 666f 726d 206c 6974     Transform lit\n-00024af0: 6572 616c 732e 2020 286c 696e 6520 2031  erals.  (line  1\n-00024b00: 3529 0a2a 2074 7261 6e73 6c61 7469 6f6e  5).* translation\n-00024b10: 2074 7261 6e73 666f 726d 203c 323e 3a20   transform <2>: \n-00024b20: 2020 2020 2020 2020 2020 2020 4120 6869              A hi\n-00024b30: 6572 6172 6368 6963 616c 206d 6f64 656c  erarchical model\n-00024b40: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+000249d0: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+000249e0: 2034 3729 0a2a 2074 7261 6e73 666f 726d   47).* transform\n+000249f0: 2c20 7669 6577 3a20 2020 2020 2020 2020  , view:         \n+00024a00: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n+00024a10: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n+00024a20: 2e20 2028 6c69 6e65 2020 3235 290a 2a20  .  (line  25).* \n+00024a30: 7472 616e 7366 6f72 6d2c 2076 6965 7720  transform, view \n+00024a40: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n+00024a50: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n+00024a60: 206c 6974 6572 616c 732e 2020 286c 696e   literals.  (lin\n+00024a70: 6520 2033 3529 0a2a 2074 7261 6e73 6c61  e  35).* transla\n+00024a80: 7469 6f6e 2074 7261 6e73 666f 726d 3a20  tion transform: \n+00024a90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024aa0: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n+00024ab0: 732e 2020 2028 6c69 6e65 2020 3437 290a  s.   (line  47).\n+00024ac0: 2a20 7472 616e 736c 6174 696f 6e20 7472  * translation tr\n+00024ad0: 616e 7366 6f72 6d20 3c31 3e3a 2020 2020  ansform <1>:    \n+00024ae0: 2020 2020 2020 2020 2054 7261 6e73 666f           Transfo\n+00024af0: 726d 206c 6974 6572 616c 732e 2020 286c  rm literals.  (l\n+00024b00: 696e 6520 2031 3529 0a2a 2074 7261 6e73  ine  15).* trans\n+00024b10: 6c61 7469 6f6e 2074 7261 6e73 666f 726d  lation transform\n+00024b20: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n+00024b30: 2020 4120 6869 6572 6172 6368 6963 616c    A hierarchical\n+00024b40: 206d 6f64 656c 2e0a 2020 2020 2020 2020   model..        \n 00024b50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024b60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024b70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024b80: 286c 696e 6520 2034 3729 0a2a 2074 7261  (line  47).* tra\n-00024b90: 6e73 7061 7265 6e63 793a 2020 2020 2020  nsparency:      \n+00024b80: 2020 2020 2020 286c 696e 6520 2034 3729        (line  47)\n+00024b90: 0a2a 2074 7261 6e73 7061 7265 6e63 793a  .* transparency:\n 00024ba0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024bb0: 2020 2020 5472 616e 7370 6172 656e 6379      Transparency\n-00024bc0: 2e20 2020 2020 2020 2028 6c69 6e65 2020  .        (line  \n-00024bd0: 2036 290a 2a20 7477 6f2d 6f70 6572 616e   6).* two-operan\n-00024be0: 6420 666f 726d 3a20 2020 2020 2020 2020  d form:         \n-00024bf0: 2020 2020 2020 2020 2020 2020 2054 776f               Two\n-00024c00: 2d6f 7065 7261 6e64 2028 6269 6e61 7279  -operand (binary\n-00024c10: 2920 666f 726d 732e 0a20 2020 2020 2020  ) forms..       \n+00024bb0: 2020 2020 2020 2020 2020 5472 616e 7370            Transp\n+00024bc0: 6172 656e 6379 2e20 2020 2020 2020 2028  arency.        (\n+00024bd0: 6c69 6e65 2020 2036 290a 2a20 7477 6f2d  line   6).* two-\n+00024be0: 6f70 6572 616e 6420 666f 726d 3a20 2020  operand form:   \n+00024bf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024c00: 2020 2054 776f 2d6f 7065 7261 6e64 2028     Two-operand (\n+00024c10: 6269 6e61 7279 2920 666f 726d 732e 0a20  binary) forms.. \n 00024c20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024c30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024c40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024c50: 2020 2020 2020 2028 6c69 6e65 2020 2036         (line   6\n-00024c60: 290a 2a20 756e 6172 7920 666f 726d 3a20  ).* unary form: \n-00024c70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024c80: 2020 2020 2020 2020 2020 2055 6e61 7279             Unary\n-00024c90: 2066 6f72 6d73 2e20 2020 2020 2020 2020   forms.         \n-00024ca0: 286c 696e 6520 2020 3629 0a2a 2076 6563  (line   6).* vec\n-00024cb0: 746f 723a 2020 2020 2020 2020 2020 2020  tor:            \n+00024c50: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n+00024c60: 6e65 2020 2036 290a 2a20 756e 6172 7920  ne   6).* unary \n+00024c70: 666f 726d 3a20 2020 2020 2020 2020 2020  form:           \n+00024c80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024c90: 2055 6e61 7279 2066 6f72 6d73 2e20 2020   Unary forms.   \n+00024ca0: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+00024cb0: 0a2a 2076 6563 746f 723a 2020 2020 2020  .* vector:      \n 00024cc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024cd0: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n-00024ce0: 666f 726d 732e 2020 2028 6c69 6e65 2020  forms.   (line  \n-00024cf0: 3438 290a 2a20 7665 6374 6f72 2064 6566  48).* vector def\n-00024d00: 696e 6974 696f 6e3a 2020 2020 2020 2020  inition:        \n-00024d10: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n-00024d20: 796c 696e 6520 7377 6565 7073 2e20 2020  yline sweeps.   \n-00024d30: 2020 286c 696e 6520 2031 3929 0a2a 2076    (line  19).* v\n-00024d40: 6563 746f 7220 6c69 7465 7261 6c3a 2020  ector literal:  \n-00024d50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024d60: 2020 2020 2020 506f 696e 7420 616e 6420        Point and \n-00024d70: 7665 6374 6f72 206c 6974 6572 616c 732e  vector literals.\n-00024d80: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+00024cd0: 2020 2020 2020 2020 2020 4f62 6a65 6374            Object\n+00024ce0: 2074 7261 6e73 666f 726d 732e 2020 2028   transforms.   (\n+00024cf0: 6c69 6e65 2020 3438 290a 2a20 7665 6374  line  48).* vect\n+00024d00: 6f72 2064 6566 696e 6974 696f 6e3a 2020  or definition:  \n+00024d10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024d20: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n+00024d30: 7073 2e20 2020 2020 286c 696e 6520 2031  ps.     (line  1\n+00024d40: 3929 0a2a 2076 6563 746f 7220 6c69 7465  9).* vector lite\n+00024d50: 7261 6c3a 2020 2020 2020 2020 2020 2020  ral:            \n+00024d60: 2020 2020 2020 2020 2020 2020 506f 696e              Poin\n+00024d70: 7420 616e 6420 7665 6374 6f72 206c 6974  t and vector lit\n+00024d80: 6572 616c 732e 0a20 2020 2020 2020 2020  erals..         \n 00024d90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 00024da0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024db0: 2020 2020 2020 2020 2020 2020 2020 2028                 (\n-00024dc0: 6c69 6e65 2020 2036 290a 2a20 7665 6374  line   6).* vect\n-00024dd0: 6f72 2072 6566 6572 656e 6365 3a20 2020  or reference:   \n-00024de0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024df0: 2020 2046 6f72 6d73 206f 6620 7265 6665     Forms of refe\n-00024e00: 7265 6e63 6573 2e20 286c 696e 6520 2031  rences. (line  1\n-00024e10: 3529 0a2a 2076 6965 7720 7472 616e 7366  5).* view transf\n-00024e20: 6f72 6d3a 2020 2020 2020 2020 2020 2020  orm:            \n-00024e30: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n-00024e40: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n-00024e50: 2028 6c69 6e65 2020 3235 290a 2a20 7669   (line  25).* vi\n-00024e60: 6577 2074 7261 6e73 666f 726d 203c 313e  ew transform <1>\n-00024e70: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00024e80: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n-00024e90: 6974 6572 616c 732e 2020 286c 696e 6520  iterals.  (line \n-00024ea0: 2033 3529 0a2a 2076 6972 7475 616c 2063   35).* virtual c\n-00024eb0: 616d 6572 613a 2020 2020 2020 2020 2020  amera:          \n-00024ec0: 2020 2020 2020 2020 2020 2020 2020 4f76                Ov\n-00024ed0: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n-00024ee0: 2020 2028 6c69 6e65 2020 3831 290a 2a20     (line  81).* \n-00024ef0: 7768 6974 6520 7370 6163 653a 2020 2020  white space:    \n-00024f00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024f10: 2020 2020 2020 2044 7261 7769 6e67 2061         Drawing a\n-00024f20: 2073 6f6c 6964 2e20 2020 2020 286c 696e   solid.     (lin\n-00024f30: 6520 2032 3529 0a2a 2077 6869 7465 2073  e  25).* white s\n-00024f40: 7061 6365 203c 313e 3a20 2020 2020 2020  pace <1>:       \n+00024db0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024dc0: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n+00024dd0: 2a20 7665 6374 6f72 2072 6566 6572 656e  * vector referen\n+00024de0: 6365 3a20 2020 2020 2020 2020 2020 2020  ce:             \n+00024df0: 2020 2020 2020 2020 2046 6f72 6d73 206f           Forms o\n+00024e00: 6620 7265 6665 7265 6e63 6573 2e20 286c  f references. (l\n+00024e10: 696e 6520 2031 3529 0a2a 2076 6965 7720  ine  15).* view \n+00024e20: 7472 616e 7366 6f72 6d3a 2020 2020 2020  transform:      \n+00024e30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024e40: 2020 5472 616e 7366 6f72 6d20 6c69 7465    Transform lite\n+00024e50: 7261 6c73 2e20 2028 6c69 6e65 2020 3235  rals.  (line  25\n+00024e60: 290a 2a20 7669 6577 2074 7261 6e73 666f  ).* view transfo\n+00024e70: 726d 203c 313e 3a20 2020 2020 2020 2020  rm <1>:         \n+00024e80: 2020 2020 2020 2020 2020 2054 7261 6e73             Trans\n+00024e90: 666f 726d 206c 6974 6572 616c 732e 2020  form literals.  \n+00024ea0: 286c 696e 6520 2033 3529 0a2a 2076 6972  (line  35).* vir\n+00024eb0: 7475 616c 2063 616d 6572 613a 2020 2020  tual camera:    \n+00024ec0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024ed0: 2020 2020 4f76 6572 7669 6577 2e20 2020      Overview.   \n+00024ee0: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+00024ef0: 3831 290a 2a20 7768 6974 6520 7370 6163  81).* white spac\n+00024f00: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n+00024f10: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n+00024f20: 7769 6e67 2061 2073 6f6c 6964 2e20 2020  wing a solid.   \n+00024f30: 2020 286c 696e 6520 2032 3529 0a2a 2077    (line  25).* w\n+00024f40: 6869 7465 2073 7061 6365 203c 313e 3a20  hite space <1>: \n 00024f50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024f60: 4472 6177 696e 6720 6120 736f 6c69 642e  Drawing a solid.\n-00024f70: 2020 2020 2028 6c69 6e65 2020 3239 290a       (line  29).\n-00024f80: 2a20 7768 6974 6520 7370 6163 6520 3c32  * white space <2\n-00024f90: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-00024fa0: 2020 2020 2020 2020 204f 626a 6563 7420           Object \n-00024fb0: 7472 616e 7366 6f72 6d73 2e20 2020 286c  transforms.   (l\n-00024fc0: 696e 6520 2033 3229 0a2a 2077 6869 7465  ine  32).* white\n-00024fd0: 2073 7061 6365 203c 333e 3a20 2020 2020   space <3>:     \n-00024fe0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024ff0: 2020 4c61 6e67 7561 6765 2062 6173 6963    Language basic\n-00025000: 732e 2020 2020 2028 6c69 6e65 2020 3136  s.     (line  16\n-00025010: 290a 0a0a 1f0a 5461 6720 5461 626c 653a  ).....Tag Table:\n-00025020: 0a4e 6f64 653a 2054 6f70 7f31 3134 340a  .Node: Top.1144.\n-00025030: 4e6f 6465 3a20 4162 6f75 7420 736b 6574  Node: About sket\n-00025040: 6368 7f37 3130 390a 4e6f 6465 3a20 5265  ch.7109.Node: Re\n-00025050: 706f 7274 696e 6720 6275 6773 7f38 3332  porting bugs.832\n-00025060: 330a 4e6f 6465 3a20 436f 6e74 7269 6275  3.Node: Contribu\n-00025070: 7469 6f6e 737f 3933 3534 0a52 6566 3a20  tions.9354.Ref: \n-00025080: 536f 6c69 6420 636f 696c 2065 7861 6d70  Solid coil examp\n-00025090: 6c65 7f39 3737 320a 4e6f 6465 3a20 496e  le.9772.Node: In\n-000250a0: 7472 6f64 7563 7469 6f6e 2062 7920 6578  troduction by ex\n-000250b0: 616d 706c 657f 3937 3733 0a4e 6f64 653a  ample.9773.Node:\n-000250c0: 2048 656c 6c6f 2077 6f72 6c64 7f31 3037   Hello world.107\n-000250d0: 3935 0a52 6566 3a20 4865 6c6c 6f20 776f  95.Ref: Hello wo\n-000250e0: 726c 642d 466f 6f74 6e6f 7465 2d31 7f31  rld-Footnote-1.1\n-000250f0: 3239 3339 0a4e 6f64 653a 2044 7261 7769  2939.Node: Drawi\n-00025100: 6e67 206f 7074 696f 6e73 7f31 3239 3934  ng options.12994\n-00025110: 0a4e 6f64 653a 2044 7261 7769 6e67 2061  .Node: Drawing a\n-00025120: 2073 6f6c 6964 7f31 3431 3238 0a52 6566   solid.14128.Ref\n-00025130: 3a20 4865 6c69 7820 7769 7468 2063 756c  : Helix with cul\n-00025140: 6c20 7365 7420 6661 6c73 6520 7468 656e  l set false then\n-00025150: 2074 7275 657f 3136 3434 390a 4e6f 6465   true.16449.Node\n-00025160: 3a20 5370 6563 6961 6c20 6f62 6a65 6374  : Special object\n-00025170: 737f 3136 3937 340a 4e6f 6465 3a20 4f62  s.16974.Node: Ob\n-00025180: 6a65 6374 2074 7261 6e73 666f 726d 737f  ject transforms.\n-00025190: 3230 3032 340a 5265 663a 2052 6967 6874  20024.Ref: Right\n-000251a0: 2068 616e 6420 7275 6c65 7f32 3232 3533   hand rule.22253\n-000251b0: 0a4e 6f64 653a 2052 6570 6561 7465 6420  .Node: Repeated \n-000251c0: 6f62 6a65 6374 737f 3232 3730 310a 4e6f  objects.22701.No\n-000251d0: 6465 3a20 5377 6570 7420 6f62 6a65 6374  de: Swept object\n-000251e0: 737f 3233 3236 300a 4e6f 6465 3a20 506f  s.23260.Node: Po\n-000251f0: 696e 7420 7377 6565 7073 7f32 3433 3635  int sweeps.24365\n-00025200: 0a4e 6f64 653a 2050 6f6c 796c 696e 6520  .Node: Polyline \n-00025210: 7377 6565 7073 7f32 3533 3639 0a4e 6f64  sweeps.25369.Nod\n-00025220: 653a 204e 6573 7465 6420 7377 6565 7073  e: Nested sweeps\n-00025230: 7f32 3633 3031 0a4e 6f64 653a 2050 6f6c  .26301.Node: Pol\n-00025240: 7967 6f6e 2073 7765 6570 737f 3237 3630  ygon sweeps.2760\n-00025250: 350a 4e6f 6465 3a20 506f 6c79 6c69 6e65  5.Node: Polyline\n-00025260: 2073 7765 6570 7320 7769 7468 2063 6c6f   sweeps with clo\n-00025270: 7375 7265 7f32 3830 3538 0a4e 6f64 653a  sure.28058.Node:\n-00025280: 2041 6666 696e 6520 6172 6974 686d 6574   Affine arithmet\n-00025290: 6963 7f32 3937 3332 0a4e 6f64 653a 204d  ic.29732.Node: M\n-000252a0: 6f72 6520 746f 206c 6561 726e 7f33 3136  ore to 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data.tar.xz\n+-rw-r--r--   0        0        0    61616 2020-11-07 02:36:18.000000 data.tar.xz\n"}, {"source1": "control.tar.xz", "source2": "control.tar.xz", "unified_diff": null, "details": [{"source1": "control.tar", "source2": "control.tar", "unified_diff": null, "details": [{"source1": "./md5sums", "source2": "./md5sums", "unified_diff": null, "details": [{"source1": "./md5sums", "source2": "./md5sums", "comments": ["Files differ"], "unified_diff": null}]}]}]}, {"source1": "data.tar.xz", "source2": "data.tar.xz", "unified_diff": null, "details": [{"source1": "data.tar", "source2": "data.tar", "unified_diff": null, "details": [{"source1": "./usr/bin/sketch", "source2": "./usr/bin/sketch", "comments": ["File has been modified after NT_GNU_BUILD_ID has been applied."], "unified_diff": null, "details": [{"source1": "readelf --wide --notes {}", "source2": "readelf --wide --notes {}", "unified_diff": "@@ -1,12 +1,12 @@\n \n Displaying notes found in: .note.gnu.property\n   Owner         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--hex-dump=.gnu_debuglink {}`:", "readelf: Error: Unable to find program interpreter name", "readelf: Error: no .dynamic section in the dynamic segment"], "unified_diff": "@@ -1,7 +1,7 @@\n \n Hex dump of section '.gnu_debuglink':\n-  0x00000000 30663331 37613636 39646630 34343561 0f317a669df0445a\n-  0x00000010 31616362 36333635 38343830 34363263 1acb63658480462c\n-  0x00000020 61656365 36322e64 65627567 00000000 aece62.debug....\n-  0x00000030 e8f3cc06                            ....\n+  0x00000000 37633763 66376433 32323531 61393362 7c7cf7d32251a93b\n+  0x00000010 33653061 39633831 37653937 63653734 3e0a9c817e97ce74\n+  0x00000020 34333532 38372e64 65627567 00000000 435287.debug....\n+  0x00000030 e8aa0f07                            ....\n \n"}]}]}]}]}, {"source1": "sketch-dbgsym_0.3.7-12_amd64.deb", "source2": "sketch-dbgsym_0.3.7-12_amd64.deb", "unified_diff": null, "details": [{"source1": "control.tar.xz", "source2": "control.tar.xz", "unified_diff": null, "details": [{"source1": "control.tar", "source2": "control.tar", "unified_diff": null, "details": [{"source1": "./control", "source2": "./control", "unified_diff": "@@ -5,8 +5,8 @@\n Architecture: amd64\n Maintainer: Debian Science Maintainers <debian-science-maintainers@lists.alioth.debian.org>\n Installed-Size: 224\n Depends: sketch (= 1:0.3.7-12)\n Section: debug\n Priority: optional\n Description: debug symbols for sketch\n-Build-Ids: bc0f317a669df0445a1acb63658480462caece62\n+Build-Ids: dc7c7cf7d32251a93b3e0a9c817e97ce74435287\n"}, {"source1": "./md5sums", "source2": "./md5sums", "unified_diff": null, "details": [{"source1": "./md5sums", "source2": "./md5sums", "comments": ["Files differ"], "unified_diff": null}, {"source1": "line order", "source2": "line order", "unified_diff": "@@ -1 +1 @@\n-usr/lib/debug/.build-id/bc/0f317a669df0445a1acb63658480462caece62.debug\n+usr/lib/debug/.build-id/dc/7c7cf7d32251a93b3e0a9c817e97ce74435287.debug\n"}]}]}]}, {"source1": "data.tar.xz", "source2": "data.tar.xz", 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