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Ressler.\n \n This manual is for sketch, version 0.3 (build 7),\n-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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-Tuesday, February 18, 2025, a program that converts descriptions of simple\n+Tuesday, January 16, 2024, 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": "@@ -11,15 +11,15 @@\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), Tuesday, February 18, 2025, a\n+This manual is for sketch, version 0.3 (build 7), Tuesday, January 16, 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 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"}]}, {"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": "@@ -1,15 +1,15 @@\n Sketch\n Simple 3D sketching\n-Version 0.3 (build 7), Tuesday, February 18, 2025\n+Version 0.3 (build 7), Tuesday, January 16, 2024\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), Tuesday, February 18, 2025, a program that\n+This manual is for sketch, version 0.3 (build 7), Tuesday, January 16, 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 Sketch is free software. 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If not, see\n+000003e0: 0a68 7474 703a 2f2f 7777 772e 676e 752e  .http://www.gnu.\n+000003f0: 6f72 672f 636f 7079 6c65 6674 2e0a 0a49  org/copyleft...I\n+00000400: 4e46 4f2d 4449 522d 5345 4354 494f 4e20  NFO-DIR-SECTION \n+00000410: 5465 580a 5354 4152 542d 494e 464f 2d44  TeX.START-INFO-D\n+00000420: 4952 2d45 4e54 5259 0a2a 2053 6b65 7463  IR-ENTRY.* Sketc\n+00000430: 683a 2028 736b 6574 6368 292e 2020 2020  h: (sketch).    \n+00000440: 2020 2020 2020 2020 2053 696d 706c 6520           Simple \n+00000450: 3344 2073 6b65 7463 6869 6e67 2066 6f72  3D sketching for\n+00000460: 2054 6558 0a45 4e44 2d49 4e46 4f2d 4449   TeX.END-INFO-DI\n+00000470: 522d 454e 5452 590a 0a1f 0a46 696c 653a  R-ENTRY....File:\n+00000480: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n+00000490: 6f64 653a 2054 6f70 2c20 204e 6578 743a  ode: Top,  Next:\n+000004a0: 2041 626f 7574 2073 6b65 7463 682c 2020   About sketch,  \n+000004b0: 5072 6576 3a20 2864 6972 292c 2020 5570  Prev: (dir),  Up\n+000004c0: 3a20 2864 6972 290a 0a53 6b65 7463 680a  : (dir)..Sketch.\n+000004d0: 2a2a 2a2a 2a2a 0a0a 436f 7079 7269 6768  ******..Copyrigh\n+000004e0: 7420 2843 2920 3230 3035 2074 6f20 3230  t (C) 2005 to 20\n+000004f0: 3132 2045 7567 656e 6520 4b2e 2052 6573  12 Eugene K. Res\n+00000500: 736c 6572 2e0a 0a20 2020 5468 6973 206d  sler...   This m\n+00000510: 616e 7561 6c20 6973 2066 6f72 2027 736b  anual is for 'sk\n+00000520: 6574 6368 272c 2076 6572 7369 6f6e 2030  etch', version 0\n+00000530: 2e33 2028 6275 696c 6420 3729 2c20 5475  .3 (build 7), Tu\n+00000540: 6573 6461 792c 204a 616e 7561 7279 0a31  esday, January.1\n+00000550: 362c 2032 3032 342c 2061 2070 726f 6772  6, 2024, a progr\n+00000560: 616d 2074 6861 7420 636f 6e76 6572 7473  am that converts\n+00000570: 2064 6573 6372 6970 7469 6f6e 7320 6f66   descriptions of\n+00000580: 2073 696d 706c 650a 7468 7265 652d 6469   simple.three-di\n+00000590: 6d65 6e73 696f 6e61 6c20 7363 656e 6573  mensional scenes\n+000005a0: 2069 6e74 6f20 6c69 6e65 2064 7261 7769   into line drawi\n+000005b0: 6e67 732e 2020 5468 6973 2076 6572 7369  ngs.  This versi\n+000005c0: 6f6e 2067 656e 6572 6174 6573 0a27 5053  on generates.'PS\n+000005d0: 5472 6963 6b73 2720 6f72 2027 5047 462f  Tricks' or 'PGF/\n+000005e0: 5469 6b5a 2720 636f 6465 2073 7569 7461  TikZ' code suita\n+000005f0: 626c 6520 666f 7220 7573 6520 7769 7468  ble for use with\n+00000600: 2074 6865 2054 6558 2064 6f63 756d 656e   the TeX documen\n+00000610: 740a 7072 6f63 6573 7369 6e67 2073 7973  t.processing sys\n+00000620: 7465 6d2e 0a0a 2020 2027 536b 6574 6368  tem...   'Sketch\n+00000630: 2720 6973 2066 7265 6520 736f 6674 7761  ' is free softwa\n+00000640: 7265 2e20 2059 6f75 2063 616e 2072 6564  re.  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If not, see.\n+00000870: 6874 7470 3a2f 2f77 7777 2e67 6e75 2e6f  http://www.gnu.o\n+00000880: 7267 2f63 6f70 796c 6566 742e 0a0a 2a20  rg/copyleft...* \n+00000890: 4d65 6e75 3a0a 0a2a 2041 626f 7574 2073  Menu:..* About s\n+000008a0: 6b65 7463 683a 3a20 2020 2020 2020 2020  ketch::         \n+000008b0: 2020 2020 2020 2057 6879 2073 6b65 7463         Why sketc\n+000008c0: 6820 6578 6973 7473 2061 6e64 2077 6861  h exists and wha\n+000008d0: 7420 6974 2064 6f65 732e 0a2a 2049 6e74  t it does..* Int\n+000008e0: 726f 6475 6374 696f 6e20 6279 2065 7861  roduction by exa\n+000008f0: 6d70 6c65 3a3a 2020 2020 204d 6f73 7420  mple::     Most \n+00000900: 6665 6174 7572 6573 2073 686f 776e 2061  features shown a\n+00000910: 7320 776f 726b 696e 6720 636f 6465 2e0a  s working code..\n+00000920: 2a20 496e 7075 7420 6c61 6e67 7561 6765  * Input language\n+00000930: 3a3a 2020 2020 2020 2020 2020 2020 2020  ::              \n+00000940: 5379 6e74 6178 2061 6e64 2073 656d 616e  Syntax and 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733a 3a20 2020 2020 2020 2020 204d  als::          M\n-00001160: 6174 7269 7820 666f 726d 2e0a 0a41 7269  atrix form...Ari\n-00001170: 7468 6d65 7469 6320 6578 7072 6573 7369  thmetic expressi\n-00001180: 6f6e 730a 0a2a 2054 776f 2d6f 7065 7261  ons..* Two-opera\n-00001190: 6e64 2028 6269 6e61 7279 2920 666f 726d  nd (binary) form\n-000011a0: 733a 3a20 2041 206f 7020 420a 2a20 556e  s::  A op B.* Un\n-000011b0: 6172 7920 666f 726d 733a 3a20 2020 2020  ary forms::     \n-000011c0: 2020 2020 2020 2020 2020 2020 6f70 2041              op A\n-000011d0: 2028 616e 6420 6f74 6865 7273 290a 0a4f   (and others)..O\n-000011e0: 7074 696f 6e73 0a0a 2a20 5053 5472 6963  ptions..* PSTric\n-000011f0: 6b73 206f 7074 696f 6e73 3a3a 2020 2020  ks options::    \n-00001200: 2020 2020 2020 2020 4f70 7469 6f6e 7320          Options \n-00001210: 696e 6865 7269 7465 6420 6672 6f6d 2027  inherited from '\n-00001220: 5053 5472 6963 6b73 272e 0a2a 2054 696b  PSTricks'..* Tik\n-00001230: 5a2f 5047 4620 6f70 7469 6f6e 733a 3a20  Z/PGF options:: \n-00001240: 2020 2020 2020 2020 2020 204f 7074 696f             Optio\n-00001250: 6e73 2069 6e68 6572 6974 6564 2066 726f  ns inherited fro\n-00001260: 6d20 2754 696b 5a2f 5047 4627 2e0a 2a20  m 'TikZ/PGF'..* \n-00001270: 446f 7473 2069 6e20 5469 6b5a 2f50 4746  Dots in TikZ/PGF\n-00001280: 3a3a 2020 2020 2020 2020 2020 2020 536b  ::            Sk\n-00001290: 6574 6368 2075 7365 7320 2754 696b 5a2f  etch uses 'TikZ/\n-000012a0: 5047 4627 2063 6972 636c 6573 2066 6f72  PGF' circles for\n-000012b0: 2064 6f74 732e 0a2a 2054 696b 5a2f 5047   dots..* TikZ/PG\n-000012c0: 4620 7573 6572 2d64 6566 696e 6564 2073  F user-defined s\n-000012d0: 7479 6c65 733a 3a20 2053 7570 706f 7274  tyles::  Support\n-000012e0: 2066 6f72 2027 5469 6b5a 2f50 4746 2720   for 'TikZ/PGF' \n-000012f0: 6e61 6d65 642c 2075 7365 722d 6465 6669  named, user-defi\n-00001300: 6e65 6420 7374 796c 6573 2e0a 2a20 5472  ned styles..* Tr\n-00001310: 616e 7370 6172 656e 6379 3a3a 2020 2020  ansparency::    \n-00001320: 2020 2020 2020 2020 2020 2020 5365 652d              See-\n-00001330: 7468 726f 7567 6820 706f 6c79 676f 6e73  through polygons\n-00001340: 2e0a 2a20 496e 7465 726e 616c 206f 7074  ..* Internal opt\n-00001350: 696f 6e73 3a3a 2020 2020 2020 2020 2020  ions::          \n-00001360: 2020 4f70 7469 6f6e 7320 7573 6564 2062    Options used b\n-00001370: 7920 2773 6b65 7463 6827 2e0a 0a50 6f69  y 'sketch'...Poi\n-00001380: 6e74 206c 6973 7473 0a0a 2a20 4472 6177  nt lists..* Draw\n-00001390: 6162 6c65 733a 3a20 2020 2020 2020 2020  ables::         \n-000013a0: 2020 2020 2020 2020 2020 5468 696e 6773            Things\n-000013b0: 2074 6861 7420 6172 6520 6472 6177 6e2e   that are drawn.\n-000013c0: 0a2a 2044 6566 696e 6974 696f 6e73 3a3a  .* Definitions::\n-000013d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000013e0: 2054 6869 6e67 7320 7769 7468 206e 616d   Things with nam\n-000013f0: 6573 2e0a 0a44 7261 7761 626c 6573 0a0a  es...Drawables..\n-00001400: 2a20 446f 7473 3a3a 2020 2020 2020 2020  * Dots::        \n-00001410: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00001420: 4472 6177 2064 6f74 732e 0a2a 204c 696e  Draw dots..* Lin\n-00001430: 6573 3a3a 2020 2020 2020 2020 2020 2020  es::            \n-00001440: 2020 2020 2020 2020 2020 2044 7261 7720             Draw \n-00001450: 706f 6c79 6c69 6e65 732e 0a2a 2043 7572  polylines..* Cur\n-00001460: 7665 733a 3a20 2020 2020 2020 2020 2020  ves::           \n-00001470: 2020 2020 2020 2020 2020 2044 7261 7720             Draw \n-00001480: 6375 7276 6573 2e0a 2a20 506f 6c79 676f  curves..* Polygo\n-00001490: 6e73 3a3a 2020 2020 2020 2020 2020 2020  ns::            \n-000014a0: 2020 2020 2020 2020 4472 6177 2070 6f6c          Draw pol\n-000014b0: 7967 6f6e 732e 0a2a 2053 7065 6369 616c  ygons..* Special\n-000014c0: 733a 3a20 2020 2020 2020 2020 2020 2020  s::             \n-000014d0: 2020 2020 2020 2045 6d62 6564 2072 6177         Embed raw\n-000014e0: 204c 6154 6558 2061 6e64 2027 5053 5472   LaTeX and 'PSTr\n-000014f0: 6963 6b73 272e 0a2a 2053 7765 6570 733a  icks'..* Sweeps:\n-00001500: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00001510: 2020 2020 2020 2044 7261 7720 7377 6565         Draw swee\n-00001520: 7073 206f 6620 646f 7473 2061 6e64 2070  ps of dots and p\n-00001530: 6f6c 796c 696e 6573 2e0a 2a20 426c 6f63  olylines..* Bloc\n-00001540: 6b73 3a3a 2020 2020 2020 2020 2020 2020  ks::            \n-00001550: 2020 2020 2020 2020 2020 4772 6f75 7020            Group \n-00001560: 6f74 6865 7220 6472 6177 6162 6c65 732e  other drawables.\n-00001570: 0a2a 2052 6570 6561 7473 3a3a 2020 2020  .* Repeats::    \n-00001580: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00001590: 2044 7261 7720 7472 616e 7366 6f72 6d65   Draw transforme\n-000015a0: 6420 636f 7069 6573 206f 6620 6f62 6a65  d copies of obje\n-000015b0: 6374 732e 0a2a 2050 7574 733a 3a20 2020  cts..* Puts::   \n+00001040: 2043 6f6e 7374 616e 7473 2061 6e64 2063   Constants and c\n+00001050: 6f6e 7374 7275 6374 6f72 732e 0a2a 2041  onstructors..* A\n+00001060: 7269 7468 6d65 7469 633a 3a20 2020 2020  rithmetic::     \n+00001070: 2020 2020 2020 2020 2020 2020 2052 756c               Rul\n+00001080: 6573 2066 6f72 2065 7870 7265 7373 696f  es for expressio\n+00001090: 6e73 2e0a 2a20 4f70 7469 6f6e 733a 3a20  ns..* Options:: \n+000010a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000010b0: 2020 2020 4d6f 6469 6679 696e 6720 6f62      Modifying ob\n+000010c0: 6a65 6374 2061 7070 6561 7261 6e63 652e  ject appearance.\n+000010d0: 0a0a 4c69 7465 7261 6c73 0a0a 2a20 5363  ..Literals..* Sc\n+000010e0: 616c 6172 206c 6974 6572 616c 733a 3a20  alar literals:: \n+000010f0: 2020 2020 2020 2020 2020 2020 4a75 7374              Just\n+00001100: 2074 6865 206e 756d 6265 7273 2e0a 2a20   the numbers..* \n+00001110: 506f 696e 7420 616e 6420 7665 6374 6f72  Point and vector\n+00001120: 206c 6974 6572 616c 733a 3a20 2020 3364   literals::   3d\n+00001130: 2071 7561 6e74 6974 6965 732e 0a2a 2054   quantities..* T\n+00001140: 7261 6e73 666f 726d 206c 6974 6572 616c  ransform literal\n+00001150: 733a 3a20 2020 2020 2020 2020 204d 6174  s::          Mat\n+00001160: 7269 7820 666f 726d 2e0a 0a41 7269 7468  rix form...Arith\n+00001170: 6d65 7469 6320 6578 7072 6573 7369 6f6e  metic expression\n+00001180: 730a 0a2a 2054 776f 2d6f 7065 7261 6e64  s..* Two-operand\n+00001190: 2028 6269 6e61 7279 2920 666f 726d 733a   (binary) forms:\n+000011a0: 3a20 2041 206f 7020 420a 2a20 556e 6172  :  A op B.* Unar\n+000011b0: 7920 666f 726d 733a 3a20 2020 2020 2020  y forms::       \n+000011c0: 2020 2020 2020 2020 2020 6f70 2041 2028            op A (\n+000011d0: 616e 6420 6f74 6865 7273 290a 0a4f 7074  and others)..Opt\n+000011e0: 696f 6e73 0a0a 2a20 5053 5472 6963 6b73  ions..* PSTricks\n+000011f0: 206f 7074 696f 6e73 3a3a 2020 2020 2020   options::      \n+00001200: 2020 2020 2020 4f70 7469 6f6e 7320 696e        Options in\n+00001210: 6865 7269 7465 6420 6672 6f6d 2027 5053  herited from 'PS\n+00001220: 5472 6963 6b73 272e 0a2a 2054 696b 5a2f  Tricks'..* TikZ/\n+00001230: 5047 4620 6f70 7469 6f6e 733a 3a20 2020  PGF options::   \n+00001240: 2020 2020 2020 2020 204f 7074 696f 6e73           Options\n+00001250: 2069 6e68 6572 6974 6564 2066 726f 6d20   inherited from \n+00001260: 2754 696b 5a2f 5047 4627 2e0a 2a20 446f  'TikZ/PGF'..* Do\n+00001270: 7473 2069 6e20 5469 6b5a 2f50 4746 3a3a  ts in TikZ/PGF::\n+00001280: 2020 2020 2020 2020 2020 2020 536b 6574              Sket\n+00001290: 6368 2075 7365 7320 2754 696b 5a2f 5047  ch uses 'TikZ/PG\n+000012a0: 4627 2063 6972 636c 6573 2066 6f72 2064  F' circles for d\n+000012b0: 6f74 732e 0a2a 2054 696b 5a2f 5047 4620  ots..* TikZ/PGF \n+000012c0: 7573 6572 2d64 6566 696e 6564 2073 7479  user-defined sty\n+000012d0: 6c65 733a 3a20 2053 7570 706f 7274 2066  les::  Support f\n+000012e0: 6f72 2027 5469 6b5a 2f50 4746 2720 6e61  or 'TikZ/PGF' na\n+000012f0: 6d65 642c 2075 7365 722d 6465 6669 6e65  med, user-define\n+00001300: 6420 7374 796c 6573 2e0a 2a20 5472 616e  d styles..* Tran\n+00001310: 7370 6172 656e 6379 3a3a 2020 2020 2020  sparency::      \n+00001320: 2020 2020 2020 2020 2020 5365 652d 7468            See-th\n+00001330: 726f 7567 6820 706f 6c79 676f 6e73 2e0a  rough polygons..\n+00001340: 2a20 496e 7465 726e 616c 206f 7074 696f  * Internal optio\n+00001350: 6e73 3a3a 2020 2020 2020 2020 2020 2020  ns::            \n+00001360: 4f70 7469 6f6e 7320 7573 6564 2062 7920  Options used by \n+00001370: 2773 6b65 7463 6827 2e0a 0a50 6f69 6e74  'sketch'...Point\n+00001380: 206c 6973 7473 0a0a 2a20 4472 6177 6162   lists..* Drawab\n+00001390: 6c65 733a 3a20 2020 2020 2020 2020 2020  les::           \n+000013a0: 2020 2020 2020 2020 5468 696e 6773 2074          Things t\n+000013b0: 6861 7420 6172 6520 6472 6177 6e2e 0a2a  hat are drawn..*\n+000013c0: 2044 6566 696e 6974 696f 6e73 3a3a 2020   Definitions::  \n+000013d0: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n+000013e0: 6869 6e67 7320 7769 7468 206e 616d 6573  hings with names\n+000013f0: 2e0a 0a44 7261 7761 626c 6573 0a0a 2a20  ...Drawables..* \n+00001400: 446f 7473 3a3a 2020 2020 2020 2020 2020  Dots::          \n+00001410: 2020 2020 2020 2020 2020 2020 2020 4472                Dr\n+00001420: 6177 2064 6f74 732e 0a2a 204c 696e 6573  aw dots..* Lines\n+00001430: 3a3a 2020 2020 2020 2020 2020 2020 2020  ::              \n+00001440: 2020 2020 2020 2020 2044 7261 7720 706f           Draw po\n+00001450: 6c79 6c69 6e65 732e 0a2a 2043 7572 7665  lylines..* Curve\n+00001460: 733a 3a20 2020 2020 2020 2020 2020 2020  s::             \n+00001470: 2020 2020 2020 2020 2044 7261 7720 6375           Draw cu\n+00001480: 7276 6573 2e0a 2a20 506f 6c79 676f 6e73  rves..* Polygons\n+00001490: 3a3a 2020 2020 2020 2020 2020 2020 2020  ::              \n+000014a0: 2020 2020 2020 4472 6177 2070 6f6c 7967        Draw polyg\n+000014b0: 6f6e 732e 0a2a 2053 7065 6369 616c 733a  ons..* Specials:\n+000014c0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000014d0: 2020 2020 2045 6d62 6564 2072 6177 204c       Embed raw L\n+000014e0: 6154 6558 2061 6e64 2027 5053 5472 6963  aTeX and 'PSTric\n+000014f0: 6b73 272e 0a2a 2053 7765 6570 733a 3a20  ks'..* Sweeps:: \n+00001500: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00001510: 2020 2020 2044 7261 7720 7377 6565 7073       Draw sweeps\n+00001520: 206f 6620 646f 7473 2061 6e64 2070 6f6c   of dots and pol\n+00001530: 796c 696e 6573 2e0a 2a20 426c 6f63 6b73  ylines..* Blocks\n+00001540: 3a3a 2020 2020 2020 2020 2020 2020 2020  ::              \n+00001550: 2020 2020 2020 2020 4772 6f75 7020 6f74          Group ot\n+00001560: 6865 7220 6472 6177 6162 6c65 732e 0a2a  her drawables..*\n+00001570: 2052 6570 6561 7473 3a3a 2020 2020 2020   Repeats::      \n+00001580: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n+00001590: 7261 7720 7472 616e 7366 6f72 6d65 6420  raw transformed \n+000015a0: 636f 7069 6573 206f 6620 6f62 6a65 6374  copies of object\n+000015b0: 732e 0a2a 2050 7574 733a 3a20 2020 2020  s..* Puts::     \n 000015c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000015d0: 2020 2020 2044 7261 7720 6f6e 6520 6f62       Draw one ob\n-000015e0: 6a65 6374 2074 7261 6e73 666f 726d 6564  ject transformed\n-000015f0: 2e0a 0a53 7765 6570 730a 0a2a 2053 7765  ...Sweeps..* Swe\n-00001600: 7074 2070 6f69 6e74 733a 3a20 2020 2020  pt points::     \n-00001610: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-00001620: 2070 6f69 6e74 7320 6d61 6b65 206c 696e   points make lin\n-00001630: 6573 206f 7220 706f 6c79 676f 6e73 2e0a  es or polygons..\n-00001640: 2a20 5377 6570 7420 6c69 6e65 733a 3a20  * Swept lines:: \n-00001650: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00001660: 5377 6570 7420 6c69 6e65 7320 6d61 6b65  Swept lines make\n-00001670: 206f 7065 6e20 6f72 2063 6c6f 7365 6420   open or closed \n-00001680: 7375 7266 6163 6573 2e0a 2a20 5377 6570  surfaces..* Swep\n-00001690: 7420 706f 6c79 676f 6e73 3a3a 2020 2020  t polygons::    \n-000016a0: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n-000016b0: 706f 6c79 676f 6e73 206d 616b 6520 636c  polygons make cl\n-000016c0: 6f73 6564 2073 7572 6661 6365 732e 0a2a  osed surfaces..*\n-000016d0: 2053 7765 7074 2062 6c6f 636b 733a 3a20   Swept blocks:: \n-000016e0: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n-000016f0: 7765 7074 2062 6c6f 636b 203d 3d20 626c  wept block == bl\n-00001700: 6f63 6b20 6f66 2073 7765 6570 732e 0a2a  ock of sweeps..*\n-00001710: 2053 7765 6570 2066 6163 6520 7370 6c69   Sweep face spli\n-00001720: 7474 696e 673a 3a20 2020 2020 2020 2046  tting::        F\n-00001730: 6978 696e 6720 7761 7270 6564 2066 6163  ixing warped fac\n-00001740: 6573 2077 6974 6820 7472 6961 6e67 6c65  es with triangle\n-00001750: 732e 0a0a 4465 6669 6e69 7469 6f6e 730a  s...Definitions.\n-00001760: 0a2a 2046 6f72 6d73 206f 6620 6465 6669  .* Forms of defi\n-00001770: 6e69 7469 6f6e 733a 3a20 2020 2020 2020  nitions::       \n-00001780: 2044 6966 6665 7265 6e74 2064 6566 7320   Different defs \n-00001790: 666f 7220 6469 6666 6572 656e 7420 7075  for different pu\n-000017a0: 7270 6f73 6573 2e0a 2a20 466f 726d 7320  rposes..* Forms \n-000017b0: 6f66 2072 6566 6572 656e 6365 733a 3a20  of references:: \n-000017c0: 2020 2020 2020 2020 486f 7720 7265 6665          How refe\n-000017d0: 7265 6e63 6573 2064 656e 6f74 6520 7479  rences denote ty\n-000017e0: 7065 732e 0a0a 476c 6f62 616c 2065 6e76  pes...Global env\n-000017f0: 6972 6f6e 6d65 6e74 0a0a 2a20 476c 6f62  ironment..* Glob\n-00001800: 616c 206f 7074 696f 6e73 3a3a 2020 2020  al options::    \n-00001810: 2020 2020 2020 2020 2020 4174 7472 6962            Attrib\n-00001820: 7574 6573 206f 6620 7468 6520 656e 7469  utes of the enti\n-00001830: 7265 2064 7261 7769 6e67 2e0a 2a20 4361  re drawing..* Ca\n-00001840: 6d65 7261 3a3a 2020 2020 2020 2020 2020  mera::          \n-00001850: 2020 2020 2020 2020 2020 2020 4120 6669              A fi\n-00001860: 6e61 6c20 6361 6d65 7261 2074 7261 6e73  nal camera trans\n-00001870: 666f 726d 6174 696f 6e20 6f66 2074 6865  formation of the\n-00001880: 2073 6365 6e65 2e0a 2a20 5069 6374 7572   scene..* Pictur\n-00001890: 6520 626f 783a 3a20 2020 2020 2020 2020  e box::         \n-000018a0: 2020 2020 2020 2020 5365 7474 696e 6720          Setting \n-000018b0: 7468 6520 626f 756e 6469 6e67 2062 6f78  the bounding box\n-000018c0: 2061 6e64 2032 6420 636c 6970 7069 6e67   and 2d clipping\n-000018d0: 2e0a 2a20 4672 616d 653a 3a20 2020 2020  ..* Frame::     \n+000015d0: 2020 2044 7261 7720 6f6e 6520 6f62 6a65     Draw one obje\n+000015e0: 6374 2074 7261 6e73 666f 726d 6564 2e0a  ct transformed..\n+000015f0: 0a53 7765 6570 730a 0a2a 2053 7765 7074  .Sweeps..* Swept\n+00001600: 2070 6f69 6e74 733a 3a20 2020 2020 2020   points::       \n+00001610: 2020 2020 2020 2020 2053 7765 7074 2070           Swept p\n+00001620: 6f69 6e74 7320 6d61 6b65 206c 696e 6573  oints make lines\n+00001630: 206f 7220 706f 6c79 676f 6e73 2e0a 2a20   or polygons..* \n+00001640: 5377 6570 7420 6c69 6e65 733a 3a20 2020  Swept lines::   \n+00001650: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n+00001660: 6570 7420 6c69 6e65 7320 6d61 6b65 206f  ept lines make o\n+00001670: 7065 6e20 6f72 2063 6c6f 7365 6420 7375  pen or closed su\n+00001680: 7266 6163 6573 2e0a 2a20 5377 6570 7420  rfaces..* Swept \n+00001690: 706f 6c79 676f 6e73 3a3a 2020 2020 2020  polygons::      \n+000016a0: 2020 2020 2020 2020 5377 6570 7420 706f          Swept po\n+000016b0: 6c79 676f 6e73 206d 616b 6520 636c 6f73  lygons make clos\n+000016c0: 6564 2073 7572 6661 6365 732e 0a2a 2053  ed surfaces..* S\n+000016d0: 7765 7074 2062 6c6f 636b 733a 3a20 2020  wept blocks::   \n+000016e0: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n+000016f0: 7074 2062 6c6f 636b 203d 3d20 626c 6f63  pt block == bloc\n+00001700: 6b20 6f66 2073 7765 6570 732e 0a2a 2053  k of sweeps..* S\n+00001710: 7765 6570 2066 6163 6520 7370 6c69 7474  weep face splitt\n+00001720: 696e 673a 3a20 2020 2020 2020 2046 6978  ing::        Fix\n+00001730: 696e 6720 7761 7270 6564 2066 6163 6573  ing warped faces\n+00001740: 2077 6974 6820 7472 6961 6e67 6c65 732e   with triangles.\n+00001750: 0a0a 4465 6669 6e69 7469 6f6e 730a 0a2a  ..Definitions..*\n+00001760: 2046 6f72 6d73 206f 6620 6465 6669 6e69   Forms of defini\n+00001770: 7469 6f6e 733a 3a20 2020 2020 2020 2044  tions::        D\n+00001780: 6966 6665 7265 6e74 2064 6566 7320 666f  ifferent defs fo\n+00001790: 7220 6469 6666 6572 656e 7420 7075 7270  r different purp\n+000017a0: 6f73 6573 2e0a 2a20 466f 726d 7320 6f66  oses..* Forms of\n+000017b0: 2072 6566 6572 656e 6365 733a 3a20 2020   references::   \n+000017c0: 2020 2020 2020 486f 7720 7265 6665 7265        How refere\n+000017d0: 6e63 6573 2064 656e 6f74 6520 7479 7065  nces denote type\n+000017e0: 732e 0a0a 476c 6f62 616c 2065 6e76 6972  s...Global envir\n+000017f0: 6f6e 6d65 6e74 0a0a 2a20 476c 6f62 616c  onment..* Global\n+00001800: 206f 7074 696f 6e73 3a3a 2020 2020 2020   options::      \n+00001810: 2020 2020 2020 2020 4174 7472 6962 7574          Attribut\n+00001820: 6573 206f 6620 7468 6520 656e 7469 7265  es of the entire\n+00001830: 2064 7261 7769 6e67 2e0a 2a20 4361 6d65   drawing..* Came\n+00001840: 7261 3a3a 2020 2020 2020 2020 2020 2020  ra::            \n+00001850: 2020 2020 2020 2020 2020 4120 6669 6e61            A fina\n+00001860: 6c20 6361 6d65 7261 2074 7261 6e73 666f  l camera transfo\n+00001870: 726d 6174 696f 6e20 6f66 2074 6865 2073  rmation of the s\n+00001880: 6365 6e65 2e0a 2a20 5069 6374 7572 6520  cene..* Picture \n+00001890: 626f 783a 3a20 2020 2020 2020 2020 2020  box::           \n+000018a0: 2020 2020 2020 5365 7474 696e 6720 7468        Setting th\n+000018b0: 6520 626f 756e 6469 6e67 2062 6f78 2061  e bounding box a\n+000018c0: 6e64 2032 6420 636c 6970 7069 6e67 2e0a  nd 2d clipping..\n+000018d0: 2a20 4672 616d 653a 3a20 2020 2020 2020  * Frame::       \n 000018e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000018f0: 2020 4164 6469 6e67 2061 2062 6f78 2061    Adding a box a\n-00001900: 726f 756e 6420 7468 6520 6472 6177 696e  round the drawin\n-00001910: 672e 0a2a 204c 616e 6775 6167 653a 3a20  g..* Language:: \n+000018f0: 4164 6469 6e67 2061 2062 6f78 2061 726f  Adding a box aro\n+00001900: 756e 6420 7468 6520 6472 6177 696e 672e  und the drawing.\n+00001910: 0a2a 204c 616e 6775 6167 653a 3a20 2020  .* Language::   \n 00001920: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00001930: 2020 2053 6574 7469 6e67 2074 6865 206f     Setting the o\n-00001940: 7574 7075 7420 6c61 6e67 7561 6765 2e0a  utput language..\n-00001950: 0a42 7569 6c64 696e 6720 6120 6472 6177  .Building a draw\n-00001960: 696e 670a 0a2a 204f 7665 7276 6965 773a  ing..* Overview:\n-00001970: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00001980: 2020 2020 2042 7569 6c64 696e 6720 6120       Building a \n-00001990: 7375 6273 7461 6e74 6961 6c20 6472 6177  substantial draw\n-000019a0: 696e 672e 0a2a 2041 2074 6563 686e 6963  ing..* A technic\n-000019b0: 616c 2064 7261 7769 6e67 3a3a 2020 2020  al drawing::    \n-000019c0: 2020 2020 2041 6e20 6578 616d 706c 6520       An example \n-000019d0: 7769 7468 2066 696e 6520 706c 6163 656d  with fine placem\n-000019e0: 656e 742e 0a2a 2041 2068 6965 7261 7263  ent..* A hierarc\n-000019f0: 6869 6361 6c20 6d6f 6465 6c3a 3a20 2020  hical model::   \n-00001a00: 2020 2020 2041 6e20 6578 616d 706c 6520       An example \n-00001a10: 7769 7468 2073 7765 6570 7320 616e 6420  with sweeps and \n-00001a20: 7075 7473 2e0a 2a20 4361 7665 6174 733a  puts..* Caveats:\n-00001a30: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00001a40: 2020 2020 2020 5768 6572 6520 7472 6f75        Where trou\n-00001a50: 626c 6520 6361 6e20 6f63 6375 722e 0a0a  ble can 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0a31 2041 626f 7574  Up: Top..1 About\n-00001c30: 2073 6b65 7463 680a 2a2a 2a2a 2a2a 2a2a   sketch.********\n-00001c40: 2a2a 2a2a 2a2a 0a0a 2a20 4d65 6e75 3a0a  ******..* Menu:.\n-00001c50: 0a2a 2052 6570 6f72 7469 6e67 2062 7567  .* Reporting bug\n-00001c60: 733a 3a20 2020 2020 2020 2020 2020 2020  s::             \n-00001c70: 204c 6574 2075 7365 206b 6e6f 7720 7768   Let use know wh\n-00001c80: 6174 2773 2077 726f 6e67 210a 2a20 436f  at's wrong!.* Co\n-00001c90: 6e74 7269 6275 7469 6f6e 733a 3a20 2020  ntributions::   \n-00001ca0: 2020 2020 2020 2020 2020 2020 486f 7720              How \n-00001cb0: 796f 7520 6361 6e20 6865 6c70 2e2e 2e2e  you can help....\n-00001cc0: 0a0a 2753 6b65 7463 6827 2069 7320 6120  ..'Sketch' is a \n-00001cd0: 736d 616c 6c2c 2073 696d 706c 6520 7379  small, simple sy\n-00001ce0: 7374 656d 2066 6f72 2070 726f 6475 6369  stem for produci\n-00001cf0: 6e67 206c 696e 6520 6472 6177 696e 6773  ng line drawings\n-00001d00: 206f 6620 7477 6f2d 0a6f 7220 7468 7265  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We want\n-00001e00: 6564 2074 6f20 7072 6f64 7563 6520 6669  ed to produce fi\n-00001e10: 6e65 6c79 0a77 726f 7567 6874 2c20 6d61  nely.wrought, ma\n-00001e20: 7468 656d 6174 6963 616c 6c79 2d62 6173  thematically-bas\n-00001e30: 6564 2069 6c6c 7573 7472 6174 696f 6e73  ed illustrations\n-00001e40: 2077 6974 6820 6e6f 2065 7874 7261 6e65   with no extrane\n-00001e50: 6f75 7320 6465 7461 696c 2e0a 0a20 2020  ous detail...   \n-00001e60: 2753 6b65 7463 6827 2061 6363 6570 7473  'Sketch' accepts\n-00001e70: 2061 2074 696e 7920 7363 656e 6520 6465   a tiny scene de\n-00001e80: 7363 7269 7074 696f 6e20 6c61 6e67 7561  scription langua\n-00001e90: 6765 2061 6e64 2067 656e 6572 6174 6573  ge and generates\n-00001ea0: 0a27 5053 5472 6963 6b73 2720 6f72 2027  .'PSTricks' or '\n-00001eb0: 5469 6b5a 2f50 4746 2720 636f 6465 2066  TikZ/PGF' code f\n-00001ec0: 6f72 204c 6154 6558 2e20 2054 6865 2027  or LaTeX.  The '\n-00001ed0: 736b 6574 6368 2720 6c61 6e67 7561 6765  sketch' language\n-00001ee0: 2069 730a 7369 6d69 6c61 7220 746f 2027   is.similar to '\n-00001ef0: 5053 5472 6963 6b73 272c 206d 616b 696e  PSTricks', makin\n-00001f00: 6720 6974 2065 6173 7920 746f 206c 6561  g it easy to lea\n-00001f10: 726e 2066 6f72 2063 7572 7265 6e74 2027  rn for current '\n-00001f20: 5053 5472 6963 6b73 270a 7573 6572 732e  PSTricks'.users.\n-00001f30: 2020 5365 6520 7777 772e 7073 7472 6963    See www.pstric\n-00001f40: 6b73 2e64 6520 666f 7220 696e 666f 726d  ks.de for inform\n-00001f50: 6174 696f 6e20 6f6e 2027 5053 5472 6963  ation on 'PSTric\n-00001f60: 6b73 272e 2020 2754 696b 5a2f 5047 4627  ks'.  'TikZ/PGF'\n-00001f70: 0a69 7320 7369 6d69 6c61 722e 2020 5365  .is similar.  Se\n-00001f80: 6520 6874 7470 3a2f 2f73 6f75 7263 6566  e http://sourcef\n-00001f90: 6f72 6765 2e6e 6574 2f70 726f 6a65 6374  orge.net/project\n-00001fa0: 732f 7067 662e 2020 4f6e 6520 6361 6e20  s/pgf.  One can \n-00001fb0: 6561 7369 6c79 0a69 6e63 6c75 6465 2061  easily.include a\n-00001fc0: 7262 6974 7261 7279 2027 5053 5472 6963  rbitrary 'PSTric\n-00001fd0: 6b73 2720 6f72 2027 5469 6b5a 2f50 4746  ks' or 'TikZ/PGF\n-00001fe0: 2720 6472 6177 696e 6773 2061 6e64 2074  ' drawings and t\n-00001ff0: 6578 7420 6f76 6572 2c20 696e 2c0a 6f72  ext over, in,.or\n-00002000: 2075 6e64 6572 2027 736b 6574 6368 2720   under 'sketch' \n-00002010: 6472 6177 696e 6773 2c20 7072 6f76 6964  drawings, provid\n-00002020: 696e 6720 6163 6365 7373 2074 6f20 7468  ing access to th\n-00002030: 6520 6675 6c6c 2070 6f77 6572 206f 6620  e full power of \n-00002040: 4c61 5465 580a 7465 7874 2061 6e64 206d  LaTeX.text and m\n-00002050: 6174 6865 6d61 7469 6373 2066 6f72 6d61  athematics forma\n-00002060: 7474 696e 6720 696e 2061 2074 6872 6565  tting in a three\n-00002070: 2d64 696d 656e 7369 6f6e 616c 2073 6574  -dimensional set\n-00002080: 7469 6e67 2e0a 0a1f 0a46 696c 653a 2073  ting.....File: s\n-00002090: 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e can occur...Ca\n+00001a60: 7665 6174 730a 0a2a 204c 696d 6974 7320  veats..* Limits \n+00001a70: 6f6e 2065 7272 6f72 2064 6574 6563 7469  on error detecti\n+00001a80: 6f6e 3a3a 2020 2057 6861 7420 736b 6574  on::   What sket\n+00001a90: 6368 2064 6f65 736e 2774 2064 6f2e 0a2a  ch doesn't do..*\n+00001aa0: 2043 6c69 7070 696e 673a 3a20 2020 2020   Clipping::     \n+00001ab0: 2020 2020 2020 2020 2020 2020 2020 204e                 N\n+00001ac0: 6f20 636c 6970 7069 6e67 2061 7420 7072  o clipping at pr\n+00001ad0: 6573 656e 742e 0a2a 2048 6964 6465 6e20  esent..* Hidden \n+00001ae0: 7375 7266 6163 6520 7265 6d6f 7661 6c3a  surface removal:\n+00001af0: 3a20 2020 2020 2049 6d70 6572 6665 6374  :      Imperfect\n+00001b00: 696f 6e73 2074 6f20 6669 782e 0a0a 4869  ions to fix...Hi\n+00001b10: 6464 656e 2073 7572 6661 6365 2072 656d  dden surface rem\n+00001b20: 6f76 616c 2061 6e64 2070 6f6c 7967 6f6e  oval and polygon\n+00001b30: 2073 706c 6974 7469 6e67 0a0a 2a20 5374   splitting..* 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We wanted\n+00001e00: 2074 6f20 7072 6f64 7563 6520 6669 6e65   to produce fine\n+00001e10: 6c79 0a77 726f 7567 6874 2c20 6d61 7468  ly.wrought, math\n+00001e20: 656d 6174 6963 616c 6c79 2d62 6173 6564  ematically-based\n+00001e30: 2069 6c6c 7573 7472 6174 696f 6e73 2077   illustrations w\n+00001e40: 6974 6820 6e6f 2065 7874 7261 6e65 6f75  ith no extraneou\n+00001e50: 7320 6465 7461 696c 2e0a 0a20 2020 2753  s detail...   'S\n+00001e60: 6b65 7463 6827 2061 6363 6570 7473 2061  ketch' accepts a\n+00001e70: 2074 696e 7920 7363 656e 6520 6465 7363   tiny scene desc\n+00001e80: 7269 7074 696f 6e20 6c61 6e67 7561 6765  ription language\n+00001e90: 2061 6e64 2067 656e 6572 6174 6573 0a27   and generates.'\n+00001ea0: 5053 5472 6963 6b73 2720 6f72 2027 5469  PSTricks' or 'Ti\n+00001eb0: 6b5a 2f50 4746 2720 636f 6465 2066 6f72  kZ/PGF' code for\n+00001ec0: 204c 6154 6558 2e20 2054 6865 2027 736b   LaTeX.  The 'sk\n+00001ed0: 6574 6368 2720 6c61 6e67 7561 6765 2069  etch' language i\n+00001ee0: 730a 7369 6d69 6c61 7220 746f 2027 5053  s.similar to 'PS\n+00001ef0: 5472 6963 6b73 272c 206d 616b 696e 6720  Tricks', making \n+00001f00: 6974 2065 6173 7920 746f 206c 6561 726e  it easy to learn\n+00001f10: 2066 6f72 2063 7572 7265 6e74 2027 5053   for current 'PS\n+00001f20: 5472 6963 6b73 270a 7573 6572 732e 2020  Tricks'.users.  \n+00001f30: 5365 6520 7777 772e 7073 7472 6963 6b73  See www.pstricks\n+00001f40: 2e64 6520 666f 7220 696e 666f 726d 6174  .de for informat\n+00001f50: 696f 6e20 6f6e 2027 5053 5472 6963 6b73  ion on 'PSTricks\n+00001f60: 272e 2020 2754 696b 5a2f 5047 4627 0a69  '.  'TikZ/PGF'.i\n+00001f70: 7320 7369 6d69 6c61 722e 2020 5365 6520  s similar.  See \n+00001f80: 6874 7470 3a2f 2f73 6f75 7263 6566 6f72  http://sourcefor\n+00001f90: 6765 2e6e 6574 2f70 726f 6a65 6374 732f  ge.net/projects/\n+00001fa0: 7067 662e 2020 4f6e 6520 6361 6e20 6561  pgf.  One can ea\n+00001fb0: 7369 6c79 0a69 6e63 6c75 6465 2061 7262  sily.include arb\n+00001fc0: 6974 7261 7279 2027 5053 5472 6963 6b73  itrary 'PSTricks\n+00001fd0: 2720 6f72 2027 5469 6b5a 2f50 4746 2720  ' or 'TikZ/PGF' \n+00001fe0: 6472 6177 696e 6773 2061 6e64 2074 6578  drawings and tex\n+00001ff0: 7420 6f76 6572 2c20 696e 2c0a 6f72 2075  t over, in,.or u\n+00002000: 6e64 6572 2027 736b 6574 6368 2720 6472  nder 'sketch' dr\n+00002010: 6177 696e 6773 2c20 7072 6f76 6964 696e  awings, providin\n+00002020: 6720 6163 6365 7373 2074 6f20 7468 6520  g access to the \n+00002030: 6675 6c6c 2070 6f77 6572 206f 6620 4c61  full power of La\n+00002040: 5465 580a 7465 7874 2061 6e64 206d 6174  TeX.text and mat\n+00002050: 6865 6d61 7469 6373 2066 6f72 6d61 7474  hematics formatt\n+00002060: 696e 6720 696e 2061 2074 6872 6565 2d64  ing in a three-d\n+00002070: 696d 656e 7369 6f6e 616c 2073 6574 7469  imensional setti\n+00002080: 6e67 2e0a 0a1f 0a46 696c 653a 2073 6b65  ng.....File: ske\n+00002090: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n+000020a0: 2052 6570 6f72 7469 6e67 2062 7567 732c   Reporting bugs,\n+000020b0: 2020 4e65 7874 3a20 436f 6e74 7269 6275    Next: Contribu\n+000020c0: 7469 6f6e 732c 2020 5072 6576 3a20 4162  tions,  Prev: Ab\n+000020d0: 6f75 7420 736b 6574 6368 2c20 2055 703a  out sketch,  Up:\n+000020e0: 2041 626f 7574 2073 6b65 7463 680a 0a31   About sketch..1\n+000020f0: 2e31 2052 6570 6f72 7469 6e67 2062 7567  .1 Reporting bug\n+00002100: 7320 616e 6420 7265 636f 6d6d 656e 6469  s and recommendi\n+00002110: 6e67 2069 6d70 726f 7665 6d65 6e74 732e  ng improvements.\n+00002120: 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  .===============\n 00002130: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n 00002140: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n-00002150: 3d3d 3d3d 0a0a 5468 6520 6772 6f75 7020  ====..The group \n-00002160: 6874 7470 3a2f 2f67 726f 7570 732e 676f  http://groups.go\n-00002170: 6f67 6c65 2e63 6f6d 2f67 726f 7570 2f73  ogle.com/group/s\n-00002180: 6b65 7463 682d 7573 6572 7320 6973 2074  ketch-users is t\n-00002190: 6865 2062 6573 7420 706c 6163 650a 746f  he best place.to\n-000021a0: 2072 6570 6f72 7420 6275 6773 2061 6e64   report bugs and\n-000021b0: 206d 616b 6520 696d 7072 6f76 656d 656e   make improvemen\n-000021c0: 7473 2e20 2041 2073 6563 6f6e 6420 6d65  ts.  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It would ha\n-00003210: 7665 2062 6565 6e0a 2263 756c 6c65 6422  ve been.\"culled\"\n-00003220: 2066 726f 6d20 7468 6520 7363 656e 652e   from the scene.\n-00003230: 2020 5468 6973 2063 756c 6c69 6e67 2062    This culling b\n-00003240: 6568 6176 696f 7220 6d61 7920 7365 656d  ehavior may seem\n-00003250: 2073 7472 616e 6765 2c20 6275 740a 7374   strange, but.st\n-00003260: 6179 2074 756e 6564 2e0a 0a20 2020 2d2d  ay tuned...   --\n-00003270: 2d2d 2d2d 2d2d 2d2d 2046 6f6f 746e 6f74  -------- Footnot\n-00003280: 6573 202d 2d2d 2d2d 2d2d 2d2d 2d0a 0a20  es ----------.. \n-00003290: 2020 2831 2920 4f72 2066 6f72 2045 7572    (1) Or for Eur\n-000032a0: 6f70 6561 6e20 7573 6572 7320 6f66 2041  opean users of A\n-000032b0: 3420 7369 7a65 2070 6170 6572 2c20 272d  4 size paper, '-\n-000032c0: 5465 272e 0a0a 1f0a 4669 6c65 3a20 736b  Te'.....File: sk\n-000032d0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n-000032e0: 3a20 4472 6177 696e 6720 6f70 7469 6f6e  : Drawing option\n-000032f0: 732c 2020 4e65 7874 3a20 4472 6177 696e  s,  Next: Drawin\n-00003300: 6720 6120 736f 6c69 642c 2020 5072 6576  g a solid,  Prev\n-00003310: 3a20 4865 6c6c 6f20 776f 726c 642c 2020  : Hello world,  \n-00003320: 5570 3a20 496e 7472 6f64 7563 7469 6f6e  Up: Introduction\n-00003330: 2062 7920 6578 616d 706c 650a 0a32 2e32   by example..2.2\n-00003340: 204f 7074 696f 6e73 0a3d 3d3d 3d3d 3d3d   Options.=======\n-00003350: 3d3d 3d3d 0a0a 4d61 6e79 2027 5053 5472  ====..Many 'PSTr\n-00003360: 6963 6b73 2720 616e 6420 2754 696b 5a2f  icks' and 'TikZ/\n-00003370: 5047 4627 206f 7074 696f 6e73 2077 6f72  PGF' options wor\n-00003380: 6b20 6a75 7374 2066 696e 6520 696e 2027  k just fine in '\n-00003390: 736b 6574 6368 272e 2020 4966 0a67 656e  sketch'.  If.gen\n-000033a0: 6572 6174 696e 6720 2750 5354 7269 636b  erating 'PSTrick\n-000033b0: 7327 2c20 7468 6520 636f 6465 0a20 2070  s', the code.  p\n-000033c0: 6f6c 7967 6f6e 5b66 696c 6c63 6f6c 6f72  olygon[fillcolor\n-000033d0: 3d6c 6967 6874 6772 6179 2c6c 696e 6577  =lightgray,linew\n-000033e0: 6964 7468 3d33 7074 5d28 302c 302c 3129  idth=3pt](0,0,1)\n-000033f0: 2831 2c30 2c30 2928 302c 312c 3029 0a20  (1,0,0)(0,1,0). \n-00003400: 206c 696e 655b 6c69 6e65 7374 796c 653d   line[linestyle=\n-00003410: 646f 7474 6564 5d28 2d31 2c2d 312c 2d31  dotted](-1,-1,-1\n-00003420: 2928 322c 322c 3229 0a70 726f 6475 6365  )(2,2,2).produce\n-00003430: 730a 0a00 085b 696d 6167 6520 7372 633d  s....[image src=\n-00003440: 2265 7830 3330 2e70 6e67 2220 7465 7874  \"ex030.png\" text\n-00003450: 3d22 496d 6167 6520 6578 3033 3020 6f6d  =\"Image ex030 om\n-00003460: 6974 7465 6420 696e 2074 6578 7420 7665  itted in text ve\n-00003470: 7273 696f 6e20 6f66 2074 6869 7320 646f  rsion of this do\n-00003480: 6375 6d65 6e74 2e22 0008 5d0a 0a20 2020  cument.\"..]..   \n-00003490: 546f 2070 726f 6475 6365 2027 5469 6b5a  To produce 'TikZ\n-000034a0: 2f50 4746 272c 2074 6865 2063 6f72 7265  /PGF', the corre\n-000034b0: 7370 6f6e 6469 6e67 2063 6f64 6520 6973  sponding code is\n-000034c0: 0a20 2070 6f6c 7967 6f6e 5b66 696c 6c3d  .  polygon[fill=\n-000034d0: 6c69 6768 7467 7261 792c 6c69 6e65 2077  lightgray,line w\n-000034e0: 6964 7468 3d33 7074 5d28 302c 302c 3129  idth=3pt](0,0,1)\n-000034f0: 2831 2c30 2c30 2928 302c 312c 3029 0a20  (1,0,0)(0,1,0). \n-00003500: 206c 696e 655b 7374 796c 653d 646f 7474   line[style=dott\n-00003510: 6564 5d28 2d31 2c2d 312c 2d31 2928 322c  ed](-1,-1,-1)(2,\n-00003520: 322c 3229 0a20 2067 6c6f 6261 6c20 7b20  2,2).  global { \n-00003530: 6c61 6e67 7561 6765 2074 696b 7a20 7d0a  language tikz }.\n-00003540: 5468 6520 6669 6e61 6c20 2767 6c6f 6261  The final 'globa\n-00003550: 6c27 2069 6e73 7472 7563 7473 2027 736b  l' instructs 'sk\n-00003560: 6574 6368 2720 746f 2070 726f 6475 6365  etch' to produce\n-00003570: 2027 5469 6b5a 2f50 4746 2720 636f 6465   'TikZ/PGF' code\n-00003580: 2061 730a 6f75 7470 7574 2072 6174 6865   as.output rathe\n-00003590: 7220 7468 616e 2074 6865 2064 6566 6175  r than the defau\n-000035a0: 6c74 2c20 2750 5354 7269 636b 7327 2e20  lt, 'PSTricks'. \n-000035b0: 204e 6f74 6520 7468 6174 2027 706f 6c79   Note that 'poly\n-000035c0: 676f 6e27 2066 696c 6c0a 636f 6c6f 7220  gon' fill.color \n-000035d0: 616e 6420 276c 696e 6527 2073 7479 6c65  and 'line' style\n-000035e0: 206f 7074 696f 6e73 2062 6f74 6820 636f   options both co\n-000035f0: 6e66 6f72 6d20 746f 2027 5469 6b5a 2720  nform to 'TikZ' \n-00003600: 7379 6e74 6178 2072 756c 6573 2e20 2054  syntax rules.  T\n-00003610: 6865 0a72 6573 756c 7469 6e67 2027 5469  he.resulting 'Ti\n-00003620: 6b5a 2f50 4746 2720 6f75 7470 7574 2069  kZ/PGF' output i\n-00003630: 730a 2020 5c62 6567 696e 7b74 696b 7a70  s.  \\begin{tikzp\n-00003640: 6963 7475 7265 7d5b 6a6f 696e 3d72 6f75  icture}[join=rou\n-00003650: 6e64 5d0a 2020 5c64 7261 775b 646f 7474  nd].  \\draw[dott\n-00003660: 6564 5d28 2d31 2c2d 3129 2d2d 282e 3333  ed](-1,-1)--(.33\n-00003670: 332c 2e33 3333 293b 0a20 205c 6669 6c6c  3,.333);.  \\fill\n-00003680: 6472 6177 5b66 696c 6c3d 6c69 6768 7467  draw[fill=lightg\n-00003690: 7261 792c 6c69 6e65 2077 6964 7468 3d33  ray,line width=3\n-000036a0: 7074 5d28 302c 3029 2d2d 2831 2c30 292d  pt](0,0)--(1,0)-\n-000036b0: 2d28 302c 3129 2d2d 6379 636c 653b 0a20  -(0,1)--cycle;. \n-000036c0: 205c 6472 6177 5b64 6f74 7465 645d 282e   \\draw[dotted](.\n-000036d0: 3333 332c 2e33 3333 292d 2d28 322c 3229  333,.333)--(2,2)\n-000036e0: 3b0a 2020 5c65 6e64 7b74 696b 7a70 6963  ;.  \\end{tikzpic\n-000036f0: 7475 7265 7d0a 5468 6520 7265 6d61 696e  ture}.The remain\n-00003700: 696e 6720 6578 616d 706c 6573 206f 6620  ing examples of \n-00003710: 7468 6973 206d 616e 7561 6c20 6172 6520  this manual are \n-00003720: 696e 2050 5354 7269 636b 7320 7374 796c  in PSTricks styl\n-00003730: 652e 0a0a 1f0a 4669 6c65 3a20 736b 6574  e.....File: sket\n-00003740: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n-00003750: 4472 6177 696e 6720 6120 736f 6c69 642c  Drawing a solid,\n-00003760: 2020 4e65 7874 3a20 5370 6563 6961 6c20    Next: Special \n-00003770: 6f62 6a65 6374 732c 2020 5072 6576 3a20  objects,  Prev: \n-00003780: 4472 6177 696e 6720 6f70 7469 6f6e 732c  Drawing options,\n-00003790: 2020 5570 3a20 496e 7472 6f64 7563 7469    Up: Introducti\n-000037a0: 6f6e 2062 7920 6578 616d 706c 650a 0a32  on by example..2\n-000037b0: 2e33 2044 7261 7769 6e67 2061 2073 6f6c  .3 Drawing a sol\n-000037c0: 6964 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  id.=============\n-000037d0: 3d3d 3d3d 3d3d 0a0a 4c65 7427 7320 7472  ======..Let's tr\n-000037e0: 7920 736f 6d65 7468 696e 6720 6d6f 7265  y something more\n-000037f0: 2065 7863 6974 696e 672e 2020 2753 6b65   exciting.  'Ske\n-00003800: 7463 6827 2068 6173 206e 6f20 6e6f 7469  tch' has no noti\n-00003810: 6f6e 206f 6620 6120 736f 6c69 642c 0a62  on of a solid,.b\n-00003820: 7574 2070 6f6c 7967 6f6e 616c 2022 6661  ut polygonal \"fa\n-00003830: 6365 7322 2063 616e 2062 6520 7573 6564  ces\" can be used\n-00003840: 2074 6f20 7265 7072 6573 656e 7420 7468   to represent th\n-00003850: 6520 626f 756e 6461 7279 206f 6620 6120  e boundary of a \n-00003860: 736f 6c69 642e 0a54 6f20 7468 6520 7072  solid..To the pr\n-00003870: 6576 696f 7573 2065 7861 6d70 6c65 2c20  evious example, \n-00003880: 6c65 7427 7320 6164 6420 7468 7265 6520  let's add three \n-00003890: 6d6f 7265 2074 7269 616e 6775 6c61 7220  more triangular \n-000038a0: 706f 6c79 676f 6e73 2074 6f0a 6d61 6b65  polygons to.make\n-000038b0: 2074 6865 2066 6163 6573 206f 6620 616e   the faces of an\n-000038c0: 2069 7272 6567 756c 6172 2074 6574 7261   irregular tetra\n-000038d0: 6865 6472 6f6e 2e0a 2020 2520 7665 7274  hedron..  % vert\n-000038e0: 6963 6573 206f 6620 7468 6520 7465 7472  ices of the tetr\n-000038f0: 6168 6564 726f 6e0a 2020 6465 6620 7031  ahedron.  def p1\n-00003900: 2028 302c 302c 3129 2064 6566 2070 3220   (0,0,1) def p2 \n-00003910: 2831 2c30 2c30 290a 2020 6465 6620 7033  (1,0,0).  def p3\n-00003920: 2028 302c 312c 3029 2064 6566 2070 3420   (0,1,0) def p4 \n-00003930: 282d 2e33 2c2d 2e35 2c2d 2e38 290a 0a20  (-.3,-.5,-.8).. \n-00003940: 2025 2066 6163 6573 206f 6620 7468 6520   % faces of the \n-00003950: 7465 7472 6168 6564 726f 6e2e 0a20 2070  tetrahedron..  p\n-00003960: 6f6c 7967 6f6e 2870 3129 2870 3229 2870  olygon(p1)(p2)(p\n-00003970: 3329 2025 206f 7269 6769 6e61 6c20 6672  3) % original fr\n-00003980: 6f6e 7420 706f 6c79 676f 6e0a 2020 706f  ont polygon.  po\n-00003990: 6c79 676f 6e28 7031 2928 7034 2928 7032  lygon(p1)(p4)(p2\n-000039a0: 2920 2520 626f 7474 6f6d 0a20 2070 6f6c  ) % bottom.  pol\n-000039b0: 7967 6f6e 2870 3129 2870 3329 2870 3429  ygon(p1)(p3)(p4)\n-000039c0: 2025 206c 6566 740a 2020 706f 6c79 676f   % left.  polygo\n-000039d0: 6e28 7033 2928 7032 2928 7034 2920 2520  n(p3)(p2)(p4) % \n-000039e0: 7265 6172 0a0a 2020 2520 6c69 6e65 2074  rear..  % line t\n-000039f0: 6f20 7069 6572 6365 2074 6865 2074 6574  o pierce the tet\n-00003a00: 7261 6865 6472 6f6e 0a20 206c 696e 655b  rahedron.  line[\n-00003a10: 6c69 6e65 636f 6c6f 723d 7265 645d 282d  linecolor=red](-\n-00003a20: 312c 2d31 2c2d 3129 2832 2c32 2c32 290a  1,-1,-1)(2,2,2).\n-00003a30: 5468 6973 2065 7861 6d70 6c65 2075 7365  This example use\n-00003a40: 7320 2264 6566 696e 6974 696f 6e73 222c  s \"definitions\",\n-00003a50: 2077 6869 6368 2062 6567 696e 2077 6974   which begin wit\n-00003a60: 6820 2764 6566 272e 2020 5468 6573 6520  h 'def'.  These \n-00003a70: 2264 6566 696e 6522 0a6f 7220 6769 7665  \"define\".or give\n-00003a80: 206e 616d 6573 2074 6f20 706f 696e 7473   names to points\n-00003a90: 2c20 7768 6963 6820 6172 6520 7468 656e  , which are then\n-00003aa0: 2061 7661 696c 6162 6c65 2061 7320 2272   available as \"r\n-00003ab0: 6566 6572 656e 6365 7322 2062 790a 656e  eferences\" by.en\n-00003ac0: 636c 6f73 696e 6720 7468 6520 6e61 6d65  closing the name\n-00003ad0: 7320 696e 2070 6172 656e 7468 6573 6573  s in parentheses\n-00003ae0: 2c20 652e 672e 2028 666f 6f29 2e20 2054  , e.g. (foo).  T\n-00003af0: 6865 2070 6172 656e 7468 6573 6573 2064  he parentheses d\n-00003b00: 656e 6f74 650a 7468 6174 2074 6865 206e  enote.that the n\n-00003b10: 616d 6573 2072 6566 6572 2074 6f20 706f  ames refer to po\n-00003b20: 696e 7473 3b20 7468 6579 2061 7265 2072  ints; they are r\n-00003b30: 6571 7569 7265 642e 2020 5468 6572 6520  equired.  There \n-00003b40: 6361 6e20 6265 206e 6f0a 7768 6974 6520  can be no.white \n-00003b50: 7370 6163 6520 6265 7477 6565 6e20 7468  space between th\n-00003b60: 656d 2061 6e64 2074 6865 206e 616d 652e  em and the name.\n-00003b70: 0a0a 2020 2041 7320 796f 7520 6361 6e20  ..   As you can \n-00003b80: 7365 652c 2063 6f6d 6d65 6e74 7320 7374  see, comments st\n-00003b90: 6172 7420 7769 7468 2025 2061 7320 696e  art with % as in\n-00003ba0: 2054 6558 2061 6e64 2065 7874 656e 6420   TeX and extend \n-00003bb0: 746f 2074 6865 2065 6e64 0a6f 6620 7468  to the end.of th\n-00003bc0: 6520 6c69 6e65 2028 7468 6f75 6768 2023  e line (though #\n-00003bd0: 2077 696c 6c20 776f 726b 2061 7320 7765   will work as we\n-00003be0: 6c6c 292e 2020 5768 6974 6520 7370 6163  ll).  White spac\n-00003bf0: 652c 2069 6e63 6c75 6469 6e67 0a73 7061  e, including.spa\n-00003c00: 6365 732c 2074 6162 7320 616e 6420 626c  ces, tabs and bl\n-00003c10: 616e 6b20 6c69 6e65 732c 2068 6173 206e  ank lines, has n\n-00003c20: 6f20 6566 6665 6374 2069 6e20 7468 6520  o effect in the \n-00003c30: 2773 6b65 7463 6827 206c 616e 6775 6167  'sketch' languag\n-00003c40: 652e 0a0a 0008 5b69 6d61 6765 2073 7263  e.....[image src\n-00003c50: 3d22 6578 3034 302e 706e 6722 2074 6578  =\"ex040.png\" tex\n-00003c60: 743d 2249 6d61 6765 2065 7830 3430 206f  t=\"Image ex040 o\n-00003c70: 6d69 7474 6564 2069 6e20 7465 7874 2076  mitted in text v\n-00003c80: 6572 7369 6f6e 206f 6620 7468 6973 2064  ersion of this d\n-00003c90: 6f63 756d 656e 742e 2200 085d 0a0a 4966  ocument.\"..]..If\n-00003ca0: 2077 6520 6c6f 6f6b 2069 6e73 6964 6520   we look inside \n-00003cb0: 7468 6520 5465 5820 6669 6c65 2070 726f  the TeX file pro\n-00003cc0: 6475 6365 6420 6279 2027 736b 6574 6368  duced by 'sketch\n-00003cd0: 272c 2074 6865 7265 2077 696c 6c20 6265  ', there will be\n-00003ce0: 206f 6e6c 790a 7468 7265 6520 706f 6c79   only.three poly\n-00003cf0: 676f 6e73 2e20 2054 6865 2066 6f75 7274  gons.  The fourt\n-00003d00: 6820 6861 7320 6265 656e 2063 756c 6c65  h has been culle\n-00003d10: 6420 6265 6361 7573 6520 6974 2069 7320  d because it is \n-00003d20: 6120 2262 6163 6b20 6661 6365 220a 6f66  a \"back face\".of\n-00003d30: 2074 6865 2074 6574 7261 6865 6472 6f6e   the tetrahedron\n-00003d40: 2c20 696e 7669 7369 626c 6520 746f 206f  , invisible to o\n-00003d50: 7572 2076 6965 772e 2020 4974 2069 7320  ur view.  It is \n-00003d60: 756e 6e65 6365 7373 6172 792c 2061 6e64  unnecessary, and\n-00003d70: 2073 6f20 6974 0a69 7320 7265 6d6f 7665   so it.is remove\n-00003d80: 642e 0a0a 2020 2049 6e20 736f 6d65 2064  d...   In some d\n-00003d90: 7261 7769 6e67 732c 2070 6f6c 7967 6f6e  rawings, polygon\n-00003da0: 7320 6163 7420 6173 207a 6572 6f2d 7468  s act as zero-th\n-00003db0: 6963 6b6e 6573 7320 736f 6c69 6420 7375  ickness solid su\n-00003dc0: 7266 6163 6573 2077 6974 680a 626f 7468  rfaces with.both\n-00003dd0: 2073 6964 6573 2076 6973 6962 6c65 2072   sides visible r\n-00003de0: 6174 6865 7220 7468 616e 2061 7320 7468  ather than as th\n-00003df0: 6520 6661 6365 7320 6f66 2073 6f6c 6964  e faces of solid\n-00003e00: 206f 626a 6563 7473 2c20 7768 6572 6520   objects, where \n-00003e10: 6261 636b 0a66 6163 6573 2063 616e 2062  back.faces can b\n-00003e20: 6520 6375 6c6c 6564 2e20 2046 6f72 207a  e culled.  For z\n-00003e30: 6572 6f2d 7468 6963 6b6e 6573 7320 736f  ero-thickness so\n-00003e40: 6c69 6473 2c20 6375 6c6c 696e 6720 6973  lids, culling is\n-00003e50: 2061 2070 726f 626c 656d 2e0a 4f6e 6520   a problem..One \n-00003e60: 736f 6c75 7469 6f6e 2069 7320 746f 2075  solution is to u\n-00003e70: 7365 2061 2070 6169 7220 6f66 2027 736b  se a pair of 'sk\n-00003e80: 6574 6368 2720 706f 6c79 676f 6e73 2066  etch' polygons f\n-00003e90: 6f72 2065 6163 680a 7a65 726f 2d74 6869  or each.zero-thi\n-00003ea0: 636b 6e65 7373 2066 6163 652c 2069 6465  ckness face, ide\n-00003eb0: 6e74 6963 616c 2065 7863 6570 7420 7769  ntical except wi\n-00003ec0: 7468 206f 7070 6f73 6974 6520 7665 7274  th opposite vert\n-00003ed0: 6578 206f 7264 6572 732e 2020 5468 6973  ex orders.  This\n-00003ee0: 0a69 7320 756e 7769 656c 6479 2061 6e64  .is unwieldy and\n-00003ef0: 2065 7870 656e 7369 7665 2e20 2041 2062   expensive.  A b\n-00003f00: 6574 7465 7220 7761 7920 6973 2074 6f20  etter way is to \n-00003f10: 7365 7420 7468 6520 2773 6b65 7463 6827  set the 'sketch'\n-00003f20: 2069 6e74 6572 6e61 6c0a 6f70 7469 6f6e   internal.option\n-00003f30: 2027 6375 6c6c 2720 746f 2027 6661 6c73   'cull' to 'fals\n-00003f40: 6527 2069 6e20 7468 6520 7573 7561 6c20  e' in the usual \n-00003f50: 2750 5354 7269 636b 7327 206d 616e 6e65  'PSTricks' manne\n-00003f60: 722e 0a20 2070 6f6c 7967 6f6e 5b63 756c  r..  polygon[cul\n-00003f70: 6c3d 6661 6c73 655d 2870 3129 2870 3229  l=false](p1)(p2)\n-00003f80: 2870 3329 0a54 6865 2066 6f6c 6c6f 7769  (p3).The followi\n-00003f90: 6e67 2073 686f 7773 2074 6865 2073 616d  ng shows the sam\n-00003fa0: 6520 6865 6c69 7820 7368 6170 6520 6472  e helix shape dr\n-00003fb0: 6177 6e20 6669 7273 7420 7769 7468 2063  awn first with c\n-00003fc0: 756c 6c3d 7472 7565 2028 7468 650a 6465  ull=true (the.de\n-00003fd0: 6661 756c 7429 2061 6e64 2074 6865 6e20  fault) and then \n-00003fe0: 6375 6c6c 3d66 616c 7365 2e0a 0a00 085b  cull=false.....[\n-00003ff0: 696d 6167 6520 7372 633d 2265 7830 3435  image src=\"ex045\n-00004000: 2e70 6e67 2220 7465 7874 3d22 496d 6167  .png\" text=\"Imag\n-00004010: 6520 6578 3034 3520 6f6d 6974 7465 6420  e ex045 omitted \n-00004020: 696e 2074 6578 7420 7665 7273 696f 6e20  in text version \n-00004030: 6f66 2074 6869 7320 646f 6375 6d65 6e74  of this document\n-00004040: 2e22 0008 5d0a 0a57 6527 6c6c 2073 6f6f  .\"..]..We'll soo\n-00004050: 6e20 7365 6520 686f 7720 746f 2070 726f  n see how to pro\n-00004060: 6475 6365 2074 6865 7365 2068 656c 6978  duce these helix\n-00004070: 6573 2077 6974 6820 6120 6665 7720 6c69  es with a few li\n-00004080: 6e65 7320 6f66 2027 736b 6574 6368 270a  nes of 'sketch'.\n-00004090: 6c61 6e67 7561 6765 2063 6f64 652e 0a0a  language code...\n-000040a0: 2020 2049 7420 6d61 7920 6265 2074 656d     It may be tem\n-000040b0: 7074 696e 6720 746f 2074 7572 6e20 6375  pting to turn cu\n-000040c0: 6c6c 696e 6720 6f66 6620 6772 6174 7569  lling off gratui\n-000040d0: 746f 7573 6c79 2073 6f20 7468 6174 2076  tously so that v\n-000040e0: 6572 7465 780a 6f72 6465 7220 6361 6e20  ertex.order can \n-000040f0: 6265 2069 676e 6f72 6564 2e20 2054 6869  be ignored.  Thi\n-00004100: 7320 6973 206e 6f74 2061 2067 6f6f 6420  s is not a good \n-00004110: 6964 6561 2062 6563 6175 7365 206f 7574  idea because out\n-00004120: 7075 7420 6669 6c65 2073 697a 650a 616e  put file size.an\n-00004130: 6420 5465 5820 616e 6420 506f 7374 7363  d TeX and Postsc\n-00004140: 7269 7074 2070 726f 6365 7373 696e 6720  ript processing \n-00004150: 7469 6d65 2062 6f74 6820 6465 7065 6e64  time both depend\n-00004160: 206f 6e20 7468 6520 6e75 6d62 6572 206f   on the number o\n-00004170: 660a 6f75 7470 7574 2070 6f6c 7967 6f6e  f.output polygon\n-00004180: 732e 2020 4375 6c6c 696e 6720 7573 7561  s.  Culling usua\n-00004190: 6c6c 7920 696d 7072 6f76 6573 2070 6572  lly improves per\n-000041a0: 666f 726d 616e 6365 2062 7920 6120 6661  formance by a fa\n-000041b0: 6374 6f72 206f 660a 7477 6f2e 2020 4f6e  ctor of.two.  On\n-000041c0: 2074 6865 206f 7468 6572 2068 616e 642c   the other hand,\n-000041d0: 2067 6c6f 6261 6c6c 7920 7365 7474 696e   globally settin\n-000041e0: 6720 2763 756c 6c3d 6661 6c73 6527 2069  g 'cull=false' i\n-000041f0: 7320 7265 6173 6f6e 6162 6c65 0a77 6869  s reasonable.whi\n-00004200: 6c65 2064 6562 7567 6769 6e67 2e20 2053  le debugging.  S\n-00004210: 6565 202a 6e6f 7465 2047 6c6f 6261 6c20  ee *note Global \n-00004220: 6f70 7469 6f6e 733a 3a20 616e 6420 2a6e  options:: and *n\n-00004230: 6f74 6520 4c69 6d69 7473 206f 6e20 6572  ote Limits on er\n-00004240: 726f 720a 6465 7465 6374 696f 6e3a 3a2e  ror.detection::.\n-00004250: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n-00004260: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5370  .info,  Node: Sp\n-00004270: 6563 6961 6c20 6f62 6a65 6374 732c 2020  ecial objects,  \n-00004280: 4e65 7874 3a20 4f62 6a65 6374 2074 7261  Next: Object tra\n-00004290: 6e73 666f 726d 732c 2020 5072 6576 3a20  nsforms,  Prev: \n-000042a0: 4472 6177 696e 6720 6120 736f 6c69 642c  Drawing a solid,\n-000042b0: 2020 5570 3a20 496e 7472 6f64 7563 7469    Up: Introducti\n-000042c0: 6f6e 2062 7920 6578 616d 706c 650a 0a32  on by example..2\n-000042d0: 2e34 2053 7065 6369 616c 206f 626a 6563  .4 Special objec\n-000042e0: 7473 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ts.=============\n-000042f0: 3d3d 3d3d 3d3d 0a0a 5765 2063 616e 2061  ======..We can a\n-00004300: 6464 206c 6162 656c 7320 746f 2061 2064  dd labels to a d\n-00004310: 7261 7769 6e67 2062 7920 7573 696e 6720  rawing by using \n-00004320: 7370 6563 6961 6c20 6f62 6a65 6374 732c  special objects,\n-00004330: 2077 6869 6368 2070 726f 7669 6465 2061   which provide a\n-00004340: 0a77 6179 2074 6f20 656d 6265 6420 7261  .way to embed ra\n-00004350: 7720 4c61 5465 5820 616e 6420 2750 5354  w LaTeX and 'PST\n-00004360: 7269 636b 7327 2063 6f64 652e 2020 4164  ricks' code.  Ad\n-00004370: 6469 6e67 2074 6869 7320 746f 2074 6865  ding this to the\n-00004380: 0a74 6574 7261 6865 6472 6f6e 2064 6f65  .tetrahedron doe\n-00004390: 7320 7468 6520 7472 6963 6b2e 0a20 2073  s the trick..  s\n-000043a0: 7065 6369 616c 207c 5c66 6f6f 746e 6f74  pecial |\\footnot\n-000043b0: 6573 697a 650a 2020 2020 2020 2020 2020  esize.          \n-000043c0: 205c 7570 7574 7b32 7074 7d5b 7572 5d23   \\uput{2pt}[ur]#\n-000043d0: 317b 2450 3124 7d0a 2020 2020 2020 2020  1{$P1$}.        \n-000043e0: 2020 205c 7570 7574 5b72 5d23 327b 2450     \\uput[r]#2{$P\n-000043f0: 3224 7d0a 2020 2020 2020 2020 2020 205c  2$}.           \\\n-00004400: 7570 7574 5b75 5d23 337b 2450 3324 7d0a  uput[u]#3{$P3$}.\n-00004410: 2020 2020 2020 2020 2020 205c 7570 7574             \\uput\n-00004420: 5b64 5d23 347b 2450 3424 7d7c 0a20 2020  [d]#4{$P4$}|.   \n-00004430: 2028 7031 2928 7032 2928 7033 2928 7034   (p1)(p2)(p3)(p4\n-00004440: 290a 4865 7265 2069 7320 7468 6520 7265  ).Here is the re\n-00004450: 7375 6c74 2e0a 0a00 085b 696d 6167 6520  sult.....[image \n-00004460: 7372 633d 2265 7830 3432 2e70 6e67 2220  src=\"ex042.png\" \n-00004470: 7465 7874 3d22 496d 6167 6520 6578 3034  text=\"Image ex04\n-00004480: 3220 6f6d 6974 7465 6420 696e 2074 6578  2 omitted in tex\n-00004490: 7420 7665 7273 696f 6e20 6f66 2074 6869  t version of thi\n-000044a0: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a  s document.\"..].\n-000044b0: 0a20 2020 5468 6572 6520 6172 6520 7365  .   There are se\n-000044c0: 7665 7261 6c20 6465 7461 696c 7320 746f  veral details to\n-000044d0: 206e 6f74 6520 6865 7265 2e20 2046 6972   note here.  Fir\n-000044e0: 7374 2c20 7468 6520 7175 6f74 696e 670a  st, the quoting.\n-000044f0: 636f 6e76 656e 7469 6f6e 2066 6f72 2074  convention for t\n-00004500: 6865 2072 6177 2063 6f64 6520 6973 2073  he raw code is s\n-00004510: 696d 696c 6172 2074 6f20 7468 6520 4c61  imilar to the La\n-00004520: 5465 5820 5c76 6572 6220 636f 6d6d 616e  TeX \\verb comman\n-00004530: 642e 2020 5468 650a 6669 7273 7420 6e6f  d.  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Se\n-000045e0: 636f 6e64 2c20 7468 6520 6172 6775 6d65  cond, the argume\n-000045f0: 6e74 2072 6566 6572 656e 6365 7320 2331  nt references #1\n-00004600: 2c20 2332 2c20 2333 2c20 616e 6420 2334  , #2, #3, and #4\n-00004610: 2072 6566 6572 2074 6f20 706f 696e 742c   refer to point,\n-00004620: 0a76 6563 746f 722c 206f 7220 7363 616c  .vector, or scal\n-00004630: 6172 2076 616c 7565 7320 696e 2074 6865  ar values in the\n-00004640: 206c 6973 7420 7468 6174 2066 6f6c 6c6f   list that follo\n-00004650: 772e 2020 5468 6973 2069 7320 7369 6d69  w.  This is simi\n-00004660: 6c61 7220 746f 0a54 6558 206d 6163 726f  lar to.TeX macro\n-00004670: 2073 796e 7461 782e 2020 5468 6520 7472   syntax.  The tr\n-00004680: 616e 7366 6f72 6d65 6420 616e 6420 7477  ansformed and tw\n-00004690: 6f2d 6469 6d65 6e73 696f 6e61 6c20 7072  o-dimensional pr\n-000046a0: 6f6a 6563 7469 6f6e 7320 6f66 0a74 6865  ojections of.the\n-000046b0: 7365 2074 6872 6565 2d64 696d 656e 7369  se three-dimensi\n-000046c0: 6f6e 616c 2070 6f69 6e74 7320 6172 6520  onal points are \n-000046d0: 7375 6273 7469 7475 7465 6420 696e 2074  substituted in t\n-000046e0: 6865 2066 696e 616c 206f 7574 7075 742e  he final output.\n-000046f0: 2020 416e 0a61 7267 756d 656e 7420 7265    An.argument re\n-00004700: 6665 7265 6e63 6520 6f66 2074 6865 2066  ference of the f\n-00004710: 6f72 6d20 2331 2d32 2069 7320 7265 706c  orm #1-2 is repl\n-00004720: 6163 6564 2077 6974 6820 7468 6520 616e  aced with the an\n-00004730: 676c 6520 696e 0a64 6567 7265 6573 206f  gle in.degrees o\n-00004740: 6620 7468 6520 7477 6f2d 6469 6d65 6e73  f the two-dimens\n-00004750: 696f 6e61 6c20 7665 6374 6f72 2074 6861  ional vector tha\n-00004760: 7420 636f 6e6e 6563 7473 2074 6865 2070  t connects the p\n-00004770: 726f 6a65 6374 696f 6e73 206f 660a 7468  rojections of.th\n-00004780: 6520 7477 6f20 7265 7370 6563 7469 7665  e two respective\n-00004790: 2061 7267 756d 656e 7420 706f 696e 7473   argument points\n-000047a0: 2c20 6865 7265 2023 3120 616e 6420 2332  , here #1 and #2\n-000047b0: 2e20 2054 6865 2073 7562 7374 6974 7574  .  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R\n-000048f0: 6566 6572 656e 6365 7320 746f 2073 6361  eferences to sca\n-00004900: 6c61 7220 6172 6775 6d65 6e74 7320 6172  lar arguments ar\n-00004910: 650a 6d65 7265 6c79 2072 6570 6c61 6365  e.merely replace\n-00004920: 6420 7769 7468 2061 206e 756d 6265 7220  d with a number \n-00004930: 666f 726d 6174 7465 6420 6a75 7374 2061  formatted just a\n-00004940: 7320 616e 7920 706f 696e 7420 636f 6f72  s any point coor\n-00004950: 6469 6e61 7465 2e0a 5265 6665 7265 6e63  dinate..Referenc\n-00004960: 6573 2074 6f20 7665 6374 6f72 7320 6265  es to vectors be\n-00004970: 636f 6d65 2074 776f 2d64 696d 656e 7369  come two-dimensi\n-00004980: 6f6e 616c 2070 6f69 6e74 732e 2020 5468  onal points.  Th\n-00004990: 6520 7469 636b 206f 7065 7261 746f 720a  e tick operator.\n-000049a0: 7468 6174 2073 656c 6563 7473 2069 6e64  that selects ind\n-000049b0: 6976 6964 7561 6c20 636f 6d70 6f6e 656e  ividual componen\n-000049c0: 7473 206f 6620 706f 696e 7473 2061 6e64  ts of points and\n-000049d0: 2076 6563 746f 7273 2065 6c73 6577 6865   vectors elsewhe\n-000049e0: 7265 2069 6e0a 2773 6b65 7463 6827 2028  re in.'sketch' (\n-000049f0: 7365 6520 666f 7220 6578 616d 706c 6520  see for example \n-00004a00: 2a6e 6f74 6520 4166 6669 6e65 2061 7269  *note Affine ari\n-00004a10: 7468 6d65 7469 633a 3a29 2063 616e 2061  thmetic::) can a\n-00004a20: 6c73 6f20 6265 2061 7070 6c69 6564 0a74  lso be applied.t\n-00004a30: 6f20 706f 696e 7420 616e 6420 7665 6374  o point and vect\n-00004a40: 6f72 2061 7267 756d 656e 7420 7265 6665  or argument refe\n-00004a50: 7265 6e63 6573 2e20 2041 6c6c 2074 6872  rences.  All thr\n-00004a60: 6565 2064 696d 656e 7369 6f6e 7320 6f66  ee dimensions of\n-00004a70: 2061 0a74 7261 6e73 666f 726d 6564 2070   a.transformed p\n-00004a80: 6f69 6e74 206f 7220 7665 6374 6f72 2063  oint or vector c\n-00004a90: 616e 2061 6c73 6f20 6265 2073 7562 7374  an also be subst\n-00004aa0: 6974 7565 6420 7769 7468 2027 2733 272e  itued with ''3'.\n-00004ab0: 2020 5365 6520 2a6e 6f74 650a 5370 6563    See *note.Spec\n-00004ac0: 6961 6c73 3a3a 2066 6f72 2064 6574 6169  ials:: for detai\n-00004ad0: 6c73 2e0a 0a20 2020 4279 2064 6566 6175  ls...   By defau\n-00004ae0: 6c74 2c20 2773 7065 6369 616c 2720 6f62  lt, 'special' ob\n-00004af0: 6a65 6374 7320 6172 6520 7072 696e 7465  jects are printe\n-00004b00: 6420 6c61 7374 2c20 6f76 6572 6c61 7969  d last, overlayi\n-00004b10: 6e67 2061 6c6c 206f 7468 6572 0a6f 626a  ng all other.obj\n-00004b20: 6563 7473 2069 6e20 7468 6520 7363 656e  ects in the scen\n-00004b30: 652e 2020 4966 2079 6f75 2073 7065 6369  e.  If you speci\n-00004b40: 6679 2074 6865 2069 6e74 6572 6e61 6c20  fy the internal \n-00004b50: 6f70 7469 6f6e 2027 6c61 793d 696e 272c  option 'lay=in',\n-00004b60: 2074 6865 0a68 6964 6465 6e20 7375 7266   the.hidden surf\n-00004b70: 6163 6520 616c 676f 7269 7468 6d20 636f  ace algorithm co\n-00004b80: 6e73 6964 6572 7320 7468 6520 656e 7469  nsiders the enti\n-00004b90: 7265 2073 7065 6369 616c 206f 626a 6563  re special objec\n-00004ba0: 7420 746f 2062 6520 7468 650a 6669 7273  t to be the.firs\n-00004bb0: 7420 706f 696e 7420 2823 3129 2069 6e20  t point (#1) in \n-00004bc0: 7468 6520 6172 6775 6d65 6e74 206c 6973  the argument lis\n-00004bd0: 742e 2020 4966 2074 6861 7420 706f 696e  t.  If that poin\n-00004be0: 7420 6973 2062 6568 696e 6420 286f 660a  t is behind (of.\n-00004bf0: 736d 616c 6c65 7220 7a2d 636f 6d70 6f6e  smaller z-compon\n-00004c00: 656e 7420 7468 616e 2920 616e 7920 6472  ent than) any dr\n-00004c10: 6177 6162 6c65 2c20 7468 656e 2074 6865  awable, then the\n-00004c20: 2065 6e74 6972 6520 7370 6563 6961 6c20   entire special \n-00004c30: 6f62 6a65 6374 0a69 7320 6472 6177 6e20  object.is drawn \n-00004c40: 6265 666f 7265 2074 6861 7420 6472 6177  before that draw\n-00004c50: 6162 6c65 2c20 736f 2074 6865 2064 7261  able, so the dra\n-00004c60: 7761 626c 6520 6f62 7363 7572 6573 2070  wable obscures p\n-00004c70: 6172 7473 206f 6620 7468 650a 7370 6563  arts of the.spec\n-00004c80: 6961 6c20 6f62 6a65 6374 2074 6861 7420  ial object that \n-00004c90: 6f76 6572 6c61 7073 2069 742e 2020 496e  overlaps it.  In\n-00004ca0: 206f 7572 2065 7861 6d70 6c65 2c20 7031   our example, p1\n-00004cb0: 2069 7320 7468 6520 6672 6f6e 742d 6d6f   is the front-mo\n-00004cc0: 7374 0a70 6f69 6e74 2069 6e20 7468 6520  st.point in the \n-00004cd0: 7363 656e 6520 2868 6173 2074 6865 206c  scene (has the l\n-00004ce0: 6172 6765 7374 207a 2d63 6f6d 706f 6e65  argest z-compone\n-00004cf0: 6e74 292c 2073 6f20 6164 6469 6e67 2027  nt), so adding '\n-00004d00: 6c61 793d 696e 2720 6861 730a 6e6f 2065  lay=in' has.no e\n-00004d10: 6666 6563 742e 0a0a 2020 2057 6974 6820  ffect...   With \n-00004d20: 6f70 7469 6f6e 2027 6c61 793d 756e 6465  option 'lay=unde\n-00004d30: 7227 2c20 6120 7370 6563 6961 6c20 6973  r', a special is\n-00004d40: 2064 7261 776e 205f 6265 666f 7265 5f2c   drawn _before_,\n-00004d50: 2068 656e 6365 2061 7070 6561 7273 0a5f   hence appears._\n-00004d60: 756e 6465 725f 2061 6e79 206f 6620 7468  under_ any of th\n-00004d70: 6520 6f62 6a65 6374 7320 6861 6e64 6c65  e objects handle\n-00004d80: 6420 6279 2074 6865 2068 6964 6465 6e20  d by the hidden \n-00004d90: 7375 7266 6163 6520 616c 676f 7269 7468  surface algorith\n-00004da0: 6d2e 0a54 6869 7320 6973 2068 6f77 2074  m..This is how t\n-00004db0: 6865 206c 6967 6874 2067 7261 7920 6178  he light gray ax\n-00004dc0: 6573 2077 6572 6520 6164 6465 6420 746f  es were added to\n-00004dd0: 2074 6865 2022 6865 6c6c 6f20 776f 726c   the \"hello worl\n-00004de0: 6422 2065 7861 6d70 6c65 0a2a 6e6f 7465  d\" example.*note\n-00004df0: 2048 656c 6c6f 2077 6f72 6c64 3a3a 2e0a   Hello world::..\n-00004e00: 0a20 2020 5370 6563 6961 6c20 6f62 6a65  .   Special obje\n-00004e10: 6374 7320 6172 6520 706f 7765 7266 756c  cts are powerful\n-00004e20: 2c20 7769 7468 206d 616e 7920 706f 7373  , with many poss\n-00004e30: 6962 6c65 2075 7365 732e 0a0a 1f0a 4669  ible uses.....Fi\n-00004e40: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n-00004e50: 2020 4e6f 6465 3a20 4f62 6a65 6374 2074    Node: Object t\n-00004e60: 7261 6e73 666f 726d 732c 2020 4e65 7874  ransforms,  Next\n-00004e70: 3a20 5265 7065 6174 6564 206f 626a 6563  : Repeated objec\n-00004e80: 7473 2c20 2050 7265 763a 2053 7065 6369  ts,  Prev: Speci\n-00004e90: 616c 206f 626a 6563 7473 2c20 2055 703a  al objects,  Up:\n-00004ea0: 2049 6e74 726f 6475 6374 696f 6e20 6279   Introduction by\n-00004eb0: 2065 7861 6d70 6c65 0a0a 322e 3520 5472   example..2.5 Tr\n-00004ec0: 616e 7366 6f72 6d73 0a3d 3d3d 3d3d 3d3d  ansforms.=======\n-00004ed0: 3d3d 3d3d 3d3d 3d0a 0a4e 6f77 206c 6574  =======..Now let\n-00004ee0: 2773 2061 6464 2061 2073 6563 6f6e 6420  's add a second \n-00004ef0: 636f 7079 206f 6620 7468 6520 7069 6572  copy of the pier\n-00004f00: 6365 6420 7465 7472 6168 6564 726f 6e2e  ced tetrahedron.\n-00004f10: 2020 5765 276c 6c20 726f 7461 7465 0a74    We'll rotate.t\n-00004f20: 6865 2063 6f70 7920 3930 2064 6567 7265  he copy 90 degre\n-00004f30: 6573 2061 626f 7574 2074 6865 2078 2d61  es about the x-a\n-00004f40: 7869 7320 7769 7468 2074 6865 206f 7269  xis with the ori\n-00004f50: 6769 6e20 6173 2022 6365 6e74 6572 206f  gin as \"center o\n-00004f60: 660a 726f 7461 7469 6f6e 2220 736f 2077  f.rotation\" so w\n-00004f70: 6520 6361 6e20 7365 6520 7468 6520 6261  e can see the ba\n-00004f80: 636b 2c20 7468 656e 2074 7261 6e73 6c61  ck, then transla\n-00004f90: 7465 2069 7420 746f 2074 6865 2072 6967  te it to the rig\n-00004fa0: 6874 2d2d 696e 2074 6865 0a70 6f73 6974  ht--in the.posit\n-00004fb0: 6976 6520 782d 6469 7265 6374 696f 6e2d  ive x-direction-\n-00004fc0: 2d73 6f20 6974 2064 6f65 736e 2774 2063  -so it doesn't c\n-00004fd0: 6f6c 6c69 6465 2077 6974 6820 7468 6520  ollide with the \n-00004fe0: 6f72 6967 696e 616c 2e20 2054 6f20 6865  original.  To he\n-00004ff0: 6c70 0a75 7320 7365 6520 7768 6174 2773  lp.us see what's\n-00005000: 2067 6f69 6e67 206f 6e2c 206d 616b 6520   going on, make \n-00005010: 7468 6520 6261 636b 2073 6964 6520 6772  the back side gr\n-00005020: 6179 2e0a 2020 6465 6620 7069 6572 6365  ay..  def pierce\n-00005030: 645f 7465 7472 6168 6564 726f 6e20 7b0a  d_tetrahedron {.\n-00005040: 2020 2020 6465 6620 7031 2028 302c 302c      def p1 (0,0,\n-00005050: 3129 2064 6566 2070 3220 2831 2c30 2c30  1) def p2 (1,0,0\n-00005060: 290a 2020 2020 6465 6620 7033 2028 302c  ).    def p3 (0,\n-00005070: 312c 3029 2064 6566 2070 3420 282d 2e33  1,0) def p4 (-.3\n-00005080: 2c2d 2e35 2c2d 2e38 290a 2020 2020 706f  ,-.5,-.8).    po\n-00005090: 6c79 676f 6e28 7031 2928 7032 2928 7033  lygon(p1)(p2)(p3\n-000050a0: 2920 2020 2020 2020 2020 2020 2020 2020  )               \n-000050b0: 2020 2020 2020 2025 206f 7269 6769 6e61         % origina\n-000050c0: 6c0a 2020 2020 706f 6c79 676f 6e28 7031  l.    polygon(p1\n-000050d0: 2928 7034 2928 7032 2920 2020 2020 2020  )(p4)(p2)       \n-000050e0: 2020 2020 2020 2020 2020 2020 2020 2025                 %\n-000050f0: 2062 6f74 746f 6d0a 2020 2020 706f 6c79   bottom.    poly\n-00005100: 676f 6e28 7031 2928 7033 2928 7034 2920  gon(p1)(p3)(p4) \n+00002150: 3d3d 0a0a 5468 6520 6772 6f75 7020 6874  ==..The group ht\n+00002160: 7470 3a2f 2f67 726f 7570 732e 676f 6f67  tp://groups.goog\n+00002170: 6c65 2e63 6f6d 2f67 726f 7570 2f73 6b65  le.com/group/ske\n+00002180: 7463 682d 7573 6572 7320 6973 2074 6865  tch-users is the\n+00002190: 2062 6573 7420 706c 6163 650a 746f 2072   best place.to r\n+000021a0: 6570 6f72 7420 6275 6773 2061 6e64 206d  eport bugs and m\n+000021b0: 616b 6520 696d 7072 6f76 656d 656e 7473  ake improvements\n+000021c0: 2e20 2041 2073 6563 6f6e 6420 6d65 7468  .  A second meth\n+000021d0: 6f64 2074 6861 7420 7769 6c6c 0a70 726f  od that will.pro\n+000021e0: 6261 626c 7920 7072 6f64 7563 6520 6120  bably produce a \n+000021f0: 736c 6f77 6572 2072 6573 706f 6e73 6520  slower response \n+00002200: 6973 2065 6d61 696c 2074 6f20 736b 6574  is email to sket\n+00002210: 6368 4066 726f 6e74 6965 726e 6574 2e6e  ch@frontiernet.n\n+00002220: 6574 2e0a 5765 2077 696c 6c20 7472 7920  et..We will try \n+00002230: 746f 2072 6573 706f 6e64 2c20 6275 7420  to respond, but \n+00002240: 6361 6e27 7420 7072 6f6d 6973 652e 2020  can't promise.  \n+00002250: 496e 2061 6e79 2065 7665 6e74 2c20 646f  In any event, do\n+00002260: 6e27 7420 6265 0a6f 6666 656e 6465 6420  n't be.offended \n+00002270: 6966 2061 2072 6570 6c79 2069 7320 6e6f  if a reply is no\n+00002280: 7420 666f 7274 6863 6f6d 696e 672e 2020  t forthcoming.  \n+00002290: 5765 2772 6520 6a75 7374 2062 7573 7920  We're just busy \n+000022a0: 616e 6420 7769 6c6c 2067 6574 2074 6f0a  and will get to.\n+000022b0: 796f 7572 2073 7567 6765 7374 696f 6e20  your suggestion \n+000022c0: 6576 656e 7475 616c 6c79 2e0a 0a20 2020  eventually...   \n+000022d0: 466f 7220 6275 6773 2c20 6174 7461 6368  For bugs, attach\n+000022e0: 2061 2027 736b 6574 6368 2720 696e 7075   a 'sketch' inpu\n+000022f0: 7420 6669 6c65 2074 6861 7420 6361 7573  t file that caus\n+00002300: 6573 2074 6865 2062 6164 2062 6568 6176  es the bad behav\n+00002310: 696f 722e 0a45 6d62 6564 2063 6f6d 6d65  ior..Embed comme\n+00002320: 6e74 7320 7468 6174 2065 7870 6c61 696e  nts that explain\n+00002330: 2077 6861 7420 746f 206c 6f6f 6b20 666f   what to look fo\n+00002340: 7220 696e 2074 6865 2062 6568 6176 696f  r in the behavio\n+00002350: 7220 6f66 2027 736b 6574 6368 270a 6f72  r of 'sketch'.or\n+00002360: 2069 7473 206f 7574 7075 742e 0a0a 2020   its output...  \n+00002370: 2041 2072 6563 6f6d 6d65 6e64 6174 696f   A recommendatio\n+00002380: 6e20 666f 7220 696d 7072 6f76 656d 656e  n for improvemen\n+00002390: 7420 6672 6f6d 206f 6e65 2075 6e6b 6e6f  t from one unkno\n+000023a0: 776e 2070 6572 736f 6e20 636f 756e 7473  wn person counts\n+000023b0: 2061 730a 6f6e 6520 766f 7465 2e20 2057   as.one vote.  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If it is sav\n+00002b80: 6564 2069 6e20 7468 6520 6669 6c65 2027  ed in the file '\n+00002b90: 7369 6d70 6c65 2e73 6b27 2c20 7468 656e  simple.sk', then\n+00002ba0: 0a74 6865 2063 6f6d 6d61 6e64 0a20 2073  .the command.  s\n+00002bb0: 6b65 7463 6820 7369 6d70 6c65 2e73 6b20  ketch simple.sk \n+00002bc0: 2d6f 2073 696d 706c 652e 7465 780a 6372  -o simple.tex.cr\n+00002bd0: 6561 7465 7320 6120 6669 6c65 2027 7369  eates a file 'si\n+00002be0: 6d70 6c65 2e74 6578 2720 636f 6e74 6169  mple.tex' contai\n+00002bf0: 6e69 6e67 2027 5053 5472 6963 6b73 2720  ning 'PSTricks' \n+00002c00: 636f 6d6d 616e 6473 2074 6f20 6472 6177  commands to draw\n+00002c10: 2074 6865 7365 0a6f 626a 6563 7473 206f   these.objects o\n+00002c20: 6e20 7061 7065 722e 2020 5468 6520 636f  n paper.  The co\n+00002c30: 6e74 656e 7473 206f 6620 2773 696d 706c  ntents of 'simpl\n+00002c40: 652e 7465 7827 206c 6f6f 6b20 6c69 6b65  e.tex' look like\n+00002c50: 2074 6869 732e 0a20 205c 6265 6769 6e7b   this..  \\begin{\n+00002c60: 7073 7069 6374 7572 657d 282d 312c 2d31  pspicture}(-1,-1\n+00002c70: 2928 322c 3229 0a20 205c 7073 7456 6572  )(2,2).  \\pstVer\n+00002c80: 627b 3120 7365 746c 696e 656a 6f69 6e7d  b{1 setlinejoin}\n+00002c90: 0a20 205c 7073 6c69 6e65 282d 312c 2d31  .  \\psline(-1,-1\n+00002ca0: 2928 2e33 3333 2c2e 3333 3329 0a20 205c  )(.333,.333).  \\\n+00002cb0: 7073 706f 6c79 676f 6e5b 6669 6c6c 7374  pspolygon[fillst\n+00002cc0: 796c 653d 736f 6c69 642c 6669 6c6c 636f  yle=solid,fillco\n+00002cd0: 6c6f 723d 7768 6974 655d 2830 2c30 2928  lor=white](0,0)(\n+00002ce0: 312c 3029 2830 2c31 290a 2020 5c70 736c  1,0)(0,1).  \\psl\n+00002cf0: 696e 6528 2e33 3333 2c2e 3333 3329 2832  ine(.333,.333)(2\n+00002d00: 2c32 290a 2020 5c65 6e64 7b70 7370 6963  ,2).  \\end{pspic\n+00002d10: 7475 7265 7d0a 5468 6520 6869 6464 656e  ture}.The hidden\n+00002d20: 2073 7572 6661 6365 2061 6c67 6f72 6974   surface algorit\n+00002d30: 686d 206f 6620 2773 6b65 7463 6827 2068  hm of 'sketch' h\n+00002d40: 6173 2073 706c 6974 2074 6865 206c 696e  as split the lin\n+00002d50: 6520 696e 746f 2074 776f 0a70 6965 6365  e into two.piece\n+00002d60: 7320 616e 6420 6f72 6465 7265 6420 7468  s and ordered th\n+00002d70: 6520 7468 7265 6520 7265 7375 6c74 696e  e three resultin\n+00002d80: 6720 6f62 6a65 6374 7320 736f 2074 6861  g objects so tha\n+00002d90: 7420 7468 6520 636f 7272 6563 740a 706f  t the correct.po\n+00002da0: 7274 696f 6e20 6f66 2074 6865 206c 696e  rtion of the lin\n+00002db0: 6520 6973 2068 6964 6465 6e2e 0a0a 2020  e is hidden...  \n+00002dc0: 2049 6620 796f 7527 7665 206e 6f74 6963   If you've notic\n+00002dd0: 6564 2074 6861 7420 7468 6520 7072 6f6a  ed that the proj\n+00002de0: 6563 7469 6f6e 2077 6520 6172 6520 7573  ection we are us\n+00002df0: 696e 6720 7365 656d 7320 6571 7569 7661  ing seems equiva\n+00002e00: 6c65 6e74 0a74 6f20 6572 6173 696e 6720  lent.to erasing \n+00002e10: 7468 6520 7a2d 636f 6f72 6469 6e61 7465  the z-coordinate\n+00002e20: 206f 6620 7468 6520 7468 7265 652d 6469   of the three-di\n+00002e30: 6d65 6e73 696f 6e61 6c20 696e 7075 7420  mensional input \n+00002e40: 706f 696e 7473 2c20 7061 740a 796f 7572  points, pat.your\n+00002e50: 7365 6c66 206f 6e20 7468 6520 6261 636b  self on the back\n+00002e60: 2e20 2059 6f75 2061 7265 2063 6f72 7265  .  You are corre\n+00002e70: 6374 2e20 2054 6869 7320 6973 2063 616c  ct.  This is cal\n+00002e80: 6c65 6420 6120 2270 6172 616c 6c65 6c0a  led a \"parallel.\n+00002e90: 7072 6f6a 6563 7469 6f6e 222e 2020 5468  projection\".  Th\n+00002ea0: 6520 7a2d 636f 6f72 6469 6e61 7465 2061  e z-coordinate a\n+00002eb0: 7869 7320 6973 2070 6f69 6e74 696e 6720  xis is pointing \n+00002ec0: 7374 7261 6967 6874 206f 7574 206f 6620  straight out of \n+00002ed0: 7468 650a 7061 7065 7220 6174 2075 732c  the.paper at us,\n+00002ee0: 2077 6869 6c65 2074 6865 2078 2d20 616e   while the x- an\n+00002ef0: 6420 792d 6178 6573 2070 6f69 6e74 2074  d y-axes point t\n+00002f00: 6f20 7468 6520 7269 6768 7420 616e 6420  o the right and \n+00002f10: 7570 2061 7320 7573 7561 6c2e 0a0a 2020  up as usual...  \n+00002f20: 2054 6865 2072 6573 756c 7469 6e67 2070   The resulting p\n+00002f30: 6963 7475 7265 2066 696c 6520 6361 6e20  icture file can \n+00002f40: 6265 2069 6e63 6c75 6465 6420 696e 2061  be included in a\n+00002f50: 204c 6154 6558 2064 6f63 756d 656e 7420   LaTeX document \n+00002f60: 7769 7468 0a5c 696e 7075 747b 7369 6d70  with.\\input{simp\n+00002f70: 6c65 7d2e 2020 416c 7465 726e 6174 656c  le}.  Alternatel\n+00002f80: 792c 2061 6464 696e 6720 7468 6520 636f  y, adding the co\n+00002f90: 6d6d 616e 6420 6c69 6e65 206f 7074 696f  mmand line optio\n+00002fa0: 6e20 272d 5427 2831 290a 6361 7573 6573  n '-T'(1).causes\n+00002fb0: 2074 6865 2027 7073 7069 6374 7572 6527   the 'pspicture'\n+00002fc0: 2074 6f20 6265 2077 7261 7070 6564 2069   to be wrapped i\n+00002fd0: 6e20 6120 7368 6f72 7420 6275 7420 636f  n a short but co\n+00002fe0: 6d70 6c65 7465 2064 6f63 756d 656e 742c  mplete document,\n+00002ff0: 0a72 6561 6479 2074 6f20 7275 6e20 7468  .ready to run th\n+00003000: 6f75 6768 204c 6154 6558 2e20 2049 6e20  ough LaTeX.  In \n+00003010: 6120 6669 6e69 7368 6564 2c20 7479 7065  a finished, type\n+00003020: 7365 7420 646f 6375 6d65 6e74 2c20 7468  set document, th\n+00003030: 6520 7069 6374 7572 650a 6c6f 6f6b 7320  e picture.looks \n+00003040: 6c69 6b65 2074 6869 732e 2020 2854 6865  like this.  (The\n+00003050: 2061 7865 7320 6861 7665 2062 6565 6e20   axes have been \n+00003060: 6164 6465 6420 696e 206c 6967 6874 2067  added in light g\n+00003070: 7261 792e 290a 0a00 085b 696d 6167 6520  ray.)....[image \n+00003080: 7372 633d 2265 7830 3230 2e70 6e67 2220  src=\"ex020.png\" \n+00003090: 7465 7874 3d22 496d 6167 6520 6578 3032  text=\"Image ex02\n+000030a0: 3020 6f6d 6974 7465 6420 696e 2074 6578  0 omitted in tex\n+000030b0: 7420 7665 7273 696f 6e20 6f66 2074 6869  t version of thi\n+000030c0: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a  s document.\"..].\n+000030d0: 0a49 7420 6973 2069 6d70 6f72 7461 6e74  .It is important\n+000030e0: 2074 6f20 6b6e 6f77 2074 6861 7420 6f6e   to know that on\n+000030f0: 6c79 2074 6865 2022 6f75 7473 6964 6522  ly the \"outside\"\n+00003100: 206f 6620 6120 706f 6c79 676f 6e20 6973   of a polygon is\n+00003110: 206e 6f72 6d61 6c6c 790a 6472 6177 6e2e   normally.drawn.\n+00003120: 2020 5468 6520 226f 7574 7369 6465 2220    The \"outside\" \n+00003130: 6973 2077 6865 7265 2074 6865 2076 6572  is where the ver\n+00003140: 7469 6365 7320 6769 7665 6e20 696e 2074  tices given in t\n+00003150: 6865 2027 706f 6c79 676f 6e27 0a63 6f6d  he 'polygon'.com\n+00003160: 6d61 6e64 2061 7070 6561 7220 696e 205f  mand appear in _\n+00003170: 636f 756e 7465 722d 636c 6f63 6b77 6973  counter-clockwis\n+00003180: 655f 206f 7264 6572 2e20 2054 6875 732c  e_ order.  Thus,\n+00003190: 2069 6620 7468 6520 636f 6d6d 616e 6420   if the command \n+000031a0: 6162 6f76 650a 6861 6420 6265 656e 0a20  above.had been. \n+000031b0: 2070 6f6c 7967 6f6e 2830 2c31 2c30 2928   polygon(0,1,0)(\n+000031c0: 312c 302c 3029 2830 2c30 2c31 290a 7468  1,0,0)(0,0,1).th\n+000031d0: 6520 706f 6c79 676f 6e20 776f 756c 6420  e polygon would \n+000031e0: 6e6f 7420 6170 7065 6172 2069 6e20 7468  not appear in th\n+000031f0: 6520 7069 6374 7572 6520 6174 2061 6c6c  e picture at all\n+00003200: 2e20 2049 7420 776f 756c 6420 6861 7665  .  It would have\n+00003210: 2062 6565 6e0a 2263 756c 6c65 6422 2066   been.\"culled\" f\n+00003220: 726f 6d20 7468 6520 7363 656e 652e 2020  rom the scene.  \n+00003230: 5468 6973 2063 756c 6c69 6e67 2062 6568  This culling beh\n+00003240: 6176 696f 7220 6d61 7920 7365 656d 2073  avior may seem s\n+00003250: 7472 616e 6765 2c20 6275 740a 7374 6179  trange, but.stay\n+00003260: 2074 756e 6564 2e0a 0a20 2020 2d2d 2d2d   tuned...   ----\n+00003270: 2d2d 2d2d 2d2d 2046 6f6f 746e 6f74 6573  ------ Footnotes\n+00003280: 202d 2d2d 2d2d 2d2d 2d2d 2d0a 0a20 2020   ----------..   \n+00003290: 2831 2920 4f72 2066 6f72 2045 7572 6f70  (1) Or for Europ\n+000032a0: 6561 6e20 7573 6572 7320 6f66 2041 3420  ean users of A4 \n+000032b0: 7369 7a65 2070 6170 6572 2c20 272d 5465  size paper, '-Te\n+000032c0: 272e 0a0a 1f0a 4669 6c65 3a20 736b 6574  '.....File: sket\n+000032d0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n+000032e0: 4472 6177 696e 6720 6f70 7469 6f6e 732c  Drawing options,\n+000032f0: 2020 4e65 7874 3a20 4472 6177 696e 6720    Next: Drawing \n+00003300: 6120 736f 6c69 642c 2020 5072 6576 3a20  a solid,  Prev: \n+00003310: 4865 6c6c 6f20 776f 726c 642c 2020 5570  Hello world,  Up\n+00003320: 3a20 496e 7472 6f64 7563 7469 6f6e 2062  : Introduction b\n+00003330: 7920 6578 616d 706c 650a 0a32 2e32 204f  y example..2.2 O\n+00003340: 7074 696f 6e73 0a3d 3d3d 3d3d 3d3d 3d3d  ptions.=========\n+00003350: 3d3d 0a0a 4d61 6e79 2027 5053 5472 6963  ==..Many 'PSTric\n+00003360: 6b73 2720 616e 6420 2754 696b 5a2f 5047  ks' and 'TikZ/PG\n+00003370: 4627 206f 7074 696f 6e73 2077 6f72 6b20  F' options work \n+00003380: 6a75 7374 2066 696e 6520 696e 2027 736b  just fine in 'sk\n+00003390: 6574 6368 272e 2020 4966 0a67 656e 6572  etch'.  If.gener\n+000033a0: 6174 696e 6720 2750 5354 7269 636b 7327  ating 'PSTricks'\n+000033b0: 2c20 7468 6520 636f 6465 0a20 2070 6f6c  , the code.  pol\n+000033c0: 7967 6f6e 5b66 696c 6c63 6f6c 6f72 3d6c  ygon[fillcolor=l\n+000033d0: 6967 6874 6772 6179 2c6c 696e 6577 6964  ightgray,linewid\n+000033e0: 7468 3d33 7074 5d28 302c 302c 3129 2831  th=3pt](0,0,1)(1\n+000033f0: 2c30 2c30 2928 302c 312c 3029 0a20 206c  ,0,0)(0,1,0).  l\n+00003400: 696e 655b 6c69 6e65 7374 796c 653d 646f  ine[linestyle=do\n+00003410: 7474 6564 5d28 2d31 2c2d 312c 2d31 2928  tted](-1,-1,-1)(\n+00003420: 322c 322c 3229 0a70 726f 6475 6365 730a  2,2,2).produces.\n+00003430: 0a00 085b 696d 6167 6520 7372 633d 2265  ...[image src=\"e\n+00003440: 7830 3330 2e70 6e67 2220 7465 7874 3d22  x030.png\" text=\"\n+00003450: 496d 6167 6520 6578 3033 3020 6f6d 6974  Image ex030 omit\n+00003460: 7465 6420 696e 2074 6578 7420 7665 7273  ted in text vers\n+00003470: 696f 6e20 6f66 2074 6869 7320 646f 6375  ion of this docu\n+00003480: 6d65 6e74 2e22 0008 5d0a 0a20 2020 546f  ment.\"..]..   To\n+00003490: 2070 726f 6475 6365 2027 5469 6b5a 2f50   produce 'TikZ/P\n+000034a0: 4746 272c 2074 6865 2063 6f72 7265 7370  GF', the corresp\n+000034b0: 6f6e 6469 6e67 2063 6f64 6520 6973 0a20  onding code is. \n+000034c0: 2070 6f6c 7967 6f6e 5b66 696c 6c3d 6c69   polygon[fill=li\n+000034d0: 6768 7467 7261 792c 6c69 6e65 2077 6964  ghtgray,line wid\n+000034e0: 7468 3d33 7074 5d28 302c 302c 3129 2831  th=3pt](0,0,1)(1\n+000034f0: 2c30 2c30 2928 302c 312c 3029 0a20 206c  ,0,0)(0,1,0).  l\n+00003500: 696e 655b 7374 796c 653d 646f 7474 6564  ine[style=dotted\n+00003510: 5d28 2d31 2c2d 312c 2d31 2928 322c 322c  ](-1,-1,-1)(2,2,\n+00003520: 3229 0a20 2067 6c6f 6261 6c20 7b20 6c61  2).  global { la\n+00003530: 6e67 7561 6765 2074 696b 7a20 7d0a 5468  nguage tikz }.Th\n+00003540: 6520 6669 6e61 6c20 2767 6c6f 6261 6c27  e final 'global'\n+00003550: 2069 6e73 7472 7563 7473 2027 736b 6574   instructs 'sket\n+00003560: 6368 2720 746f 2070 726f 6475 6365 2027  ch' to produce '\n+00003570: 5469 6b5a 2f50 4746 2720 636f 6465 2061  TikZ/PGF' code a\n+00003580: 730a 6f75 7470 7574 2072 6174 6865 7220  s.output rather \n+00003590: 7468 616e 2074 6865 2064 6566 6175 6c74  than the default\n+000035a0: 2c20 2750 5354 7269 636b 7327 2e20 204e  , 'PSTricks'.  N\n+000035b0: 6f74 6520 7468 6174 2027 706f 6c79 676f  ote that 'polygo\n+000035c0: 6e27 2066 696c 6c0a 636f 6c6f 7220 616e  n' fill.color an\n+000035d0: 6420 276c 696e 6527 2073 7479 6c65 206f  d 'line' style o\n+000035e0: 7074 696f 6e73 2062 6f74 6820 636f 6e66  ptions both conf\n+000035f0: 6f72 6d20 746f 2027 5469 6b5a 2720 7379  orm to 'TikZ' sy\n+00003600: 6e74 6178 2072 756c 6573 2e20 2054 6865  ntax rules.  The\n+00003610: 0a72 6573 756c 7469 6e67 2027 5469 6b5a  .resulting 'TikZ\n+00003620: 2f50 4746 2720 6f75 7470 7574 2069 730a  /PGF' output is.\n+00003630: 2020 5c62 6567 696e 7b74 696b 7a70 6963    \\begin{tikzpic\n+00003640: 7475 7265 7d5b 6a6f 696e 3d72 6f75 6e64  ture}[join=round\n+00003650: 5d0a 2020 5c64 7261 775b 646f 7474 6564  ].  \\draw[dotted\n+00003660: 5d28 2d31 2c2d 3129 2d2d 282e 3333 332c  ](-1,-1)--(.333,\n+00003670: 2e33 3333 293b 0a20 205c 6669 6c6c 6472  .333);.  \\filldr\n+00003680: 6177 5b66 696c 6c3d 6c69 6768 7467 7261  aw[fill=lightgra\n+00003690: 792c 6c69 6e65 2077 6964 7468 3d33 7074  y,line width=3pt\n+000036a0: 5d28 302c 3029 2d2d 2831 2c30 292d 2d28  ](0,0)--(1,0)--(\n+000036b0: 302c 3129 2d2d 6379 636c 653b 0a20 205c  0,1)--cycle;.  \\\n+000036c0: 6472 6177 5b64 6f74 7465 645d 282e 3333  draw[dotted](.33\n+000036d0: 332c 2e33 3333 292d 2d28 322c 3229 3b0a  3,.333)--(2,2);.\n+000036e0: 2020 5c65 6e64 7b74 696b 7a70 6963 7475    \\end{tikzpictu\n+000036f0: 7265 7d0a 5468 6520 7265 6d61 696e 696e  re}.The remainin\n+00003700: 6720 6578 616d 706c 6573 206f 6620 7468  g examples of th\n+00003710: 6973 206d 616e 7561 6c20 6172 6520 696e  is manual are in\n+00003720: 2050 5354 7269 636b 7320 7374 796c 652e   PSTricks style.\n+00003730: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n+00003740: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4472  .info,  Node: Dr\n+00003750: 6177 696e 6720 6120 736f 6c69 642c 2020  awing a solid,  \n+00003760: 4e65 7874 3a20 5370 6563 6961 6c20 6f62  Next: Special ob\n+00003770: 6a65 6374 732c 2020 5072 6576 3a20 4472  jects,  Prev: Dr\n+00003780: 6177 696e 6720 6f70 7469 6f6e 732c 2020  awing options,  \n+00003790: 5570 3a20 496e 7472 6f64 7563 7469 6f6e  Up: Introduction\n+000037a0: 2062 7920 6578 616d 706c 650a 0a32 2e33   by example..2.3\n+000037b0: 2044 7261 7769 6e67 2061 2073 6f6c 6964   Drawing a solid\n+000037c0: 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  .===============\n+000037d0: 3d3d 3d3d 0a0a 4c65 7427 7320 7472 7920  ====..Let's try \n+000037e0: 736f 6d65 7468 696e 6720 6d6f 7265 2065  something more e\n+000037f0: 7863 6974 696e 672e 2020 2753 6b65 7463  xciting.  'Sketc\n+00003800: 6827 2068 6173 206e 6f20 6e6f 7469 6f6e  h' has no notion\n+00003810: 206f 6620 6120 736f 6c69 642c 0a62 7574   of a solid,.but\n+00003820: 2070 6f6c 7967 6f6e 616c 2022 6661 6365   polygonal \"face\n+00003830: 7322 2063 616e 2062 6520 7573 6564 2074  s\" can be used t\n+00003840: 6f20 7265 7072 6573 656e 7420 7468 6520  o represent the \n+00003850: 626f 756e 6461 7279 206f 6620 6120 736f  boundary of a so\n+00003860: 6c69 642e 0a54 6f20 7468 6520 7072 6576  lid..To the prev\n+00003870: 696f 7573 2065 7861 6d70 6c65 2c20 6c65  ious example, le\n+00003880: 7427 7320 6164 6420 7468 7265 6520 6d6f  t's add three mo\n+00003890: 7265 2074 7269 616e 6775 6c61 7220 706f  re triangular po\n+000038a0: 6c79 676f 6e73 2074 6f0a 6d61 6b65 2074  lygons to.make t\n+000038b0: 6865 2066 6163 6573 206f 6620 616e 2069  he faces of an i\n+000038c0: 7272 6567 756c 6172 2074 6574 7261 6865  rregular tetrahe\n+000038d0: 6472 6f6e 2e0a 2020 2520 7665 7274 6963  dron..  % vertic\n+000038e0: 6573 206f 6620 7468 6520 7465 7472 6168  es of the tetrah\n+000038f0: 6564 726f 6e0a 2020 6465 6620 7031 2028  edron.  def p1 (\n+00003900: 302c 302c 3129 2064 6566 2070 3220 2831  0,0,1) def p2 (1\n+00003910: 2c30 2c30 290a 2020 6465 6620 7033 2028  ,0,0).  def p3 (\n+00003920: 302c 312c 3029 2064 6566 2070 3420 282d  0,1,0) def p4 (-\n+00003930: 2e33 2c2d 2e35 2c2d 2e38 290a 0a20 2025  .3,-.5,-.8)..  %\n+00003940: 2066 6163 6573 206f 6620 7468 6520 7465   faces of the te\n+00003950: 7472 6168 6564 726f 6e2e 0a20 2070 6f6c  trahedron..  pol\n+00003960: 7967 6f6e 2870 3129 2870 3229 2870 3329  ygon(p1)(p2)(p3)\n+00003970: 2025 206f 7269 6769 6e61 6c20 6672 6f6e   % original fron\n+00003980: 7420 706f 6c79 676f 6e0a 2020 706f 6c79  t polygon.  poly\n+00003990: 676f 6e28 7031 2928 7034 2928 7032 2920  gon(p1)(p4)(p2) \n+000039a0: 2520 626f 7474 6f6d 0a20 2070 6f6c 7967  % bottom.  polyg\n+000039b0: 6f6e 2870 3129 2870 3329 2870 3429 2025  on(p1)(p3)(p4) %\n+000039c0: 206c 6566 740a 2020 706f 6c79 676f 6e28   left.  polygon(\n+000039d0: 7033 2928 7032 2928 7034 2920 2520 7265  p3)(p2)(p4) % re\n+000039e0: 6172 0a0a 2020 2520 6c69 6e65 2074 6f20  ar..  % line to \n+000039f0: 7069 6572 6365 2074 6865 2074 6574 7261  pierce the tetra\n+00003a00: 6865 6472 6f6e 0a20 206c 696e 655b 6c69  hedron.  line[li\n+00003a10: 6e65 636f 6c6f 723d 7265 645d 282d 312c  necolor=red](-1,\n+00003a20: 2d31 2c2d 3129 2832 2c32 2c32 290a 5468  -1,-1)(2,2,2).Th\n+00003a30: 6973 2065 7861 6d70 6c65 2075 7365 7320  is example uses \n+00003a40: 2264 6566 696e 6974 696f 6e73 222c 2077  \"definitions\", w\n+00003a50: 6869 6368 2062 6567 696e 2077 6974 6820  hich begin with \n+00003a60: 2764 6566 272e 2020 5468 6573 6520 2264  'def'.  These \"d\n+00003a70: 6566 696e 6522 0a6f 7220 6769 7665 206e  efine\".or give n\n+00003a80: 616d 6573 2074 6f20 706f 696e 7473 2c20  ames to points, \n+00003a90: 7768 6963 6820 6172 6520 7468 656e 2061  which are then a\n+00003aa0: 7661 696c 6162 6c65 2061 7320 2272 6566  vailable as \"ref\n+00003ab0: 6572 656e 6365 7322 2062 790a 656e 636c  erences\" by.encl\n+00003ac0: 6f73 696e 6720 7468 6520 6e61 6d65 7320  osing the names \n+00003ad0: 696e 2070 6172 656e 7468 6573 6573 2c20  in parentheses, \n+00003ae0: 652e 672e 2028 666f 6f29 2e20 2054 6865  e.g. (foo).  The\n+00003af0: 2070 6172 656e 7468 6573 6573 2064 656e   parentheses den\n+00003b00: 6f74 650a 7468 6174 2074 6865 206e 616d  ote.that the nam\n+00003b10: 6573 2072 6566 6572 2074 6f20 706f 696e  es refer to poin\n+00003b20: 7473 3b20 7468 6579 2061 7265 2072 6571  ts; they are req\n+00003b30: 7569 7265 642e 2020 5468 6572 6520 6361  uired.  There ca\n+00003b40: 6e20 6265 206e 6f0a 7768 6974 6520 7370  n be no.white sp\n+00003b50: 6163 6520 6265 7477 6565 6e20 7468 656d  ace between them\n+00003b60: 2061 6e64 2074 6865 206e 616d 652e 0a0a   and the name...\n+00003b70: 2020 2041 7320 796f 7520 6361 6e20 7365     As you can se\n+00003b80: 652c 2063 6f6d 6d65 6e74 7320 7374 6172  e, comments star\n+00003b90: 7420 7769 7468 2025 2061 7320 696e 2054  t with % as in T\n+00003ba0: 6558 2061 6e64 2065 7874 656e 6420 746f  eX and extend to\n+00003bb0: 2074 6865 2065 6e64 0a6f 6620 7468 6520   the end.of the \n+00003bc0: 6c69 6e65 2028 7468 6f75 6768 2023 2077  line (though # w\n+00003bd0: 696c 6c20 776f 726b 2061 7320 7765 6c6c  ill work as well\n+00003be0: 292e 2020 5768 6974 6520 7370 6163 652c  ).  White space,\n+00003bf0: 2069 6e63 6c75 6469 6e67 0a73 7061 6365   including.space\n+00003c00: 732c 2074 6162 7320 616e 6420 626c 616e  s, tabs and blan\n+00003c10: 6b20 6c69 6e65 732c 2068 6173 206e 6f20  k lines, has no \n+00003c20: 6566 6665 6374 2069 6e20 7468 6520 2773  effect in the 's\n+00003c30: 6b65 7463 6827 206c 616e 6775 6167 652e  ketch' language.\n+00003c40: 0a0a 0008 5b69 6d61 6765 2073 7263 3d22  ....[image src=\"\n+00003c50: 6578 3034 302e 706e 6722 2074 6578 743d  ex040.png\" text=\n+00003c60: 2249 6d61 6765 2065 7830 3430 206f 6d69  \"Image ex040 omi\n+00003c70: 7474 6564 2069 6e20 7465 7874 2076 6572  tted in text ver\n+00003c80: 7369 6f6e 206f 6620 7468 6973 2064 6f63  sion of this doc\n+00003c90: 756d 656e 742e 2200 085d 0a0a 4966 2077  ument.\"..]..If w\n+00003ca0: 6520 6c6f 6f6b 2069 6e73 6964 6520 7468  e look inside th\n+00003cb0: 6520 5465 5820 6669 6c65 2070 726f 6475  e TeX file produ\n+00003cc0: 6365 6420 6279 2027 736b 6574 6368 272c  ced by 'sketch',\n+00003cd0: 2074 6865 7265 2077 696c 6c20 6265 206f   there will be o\n+00003ce0: 6e6c 790a 7468 7265 6520 706f 6c79 676f  nly.three polygo\n+00003cf0: 6e73 2e20 2054 6865 2066 6f75 7274 6820  ns.  The fourth \n+00003d00: 6861 7320 6265 656e 2063 756c 6c65 6420  has been culled \n+00003d10: 6265 6361 7573 6520 6974 2069 7320 6120  because it is a \n+00003d20: 2262 6163 6b20 6661 6365 220a 6f66 2074  \"back face\".of t\n+00003d30: 6865 2074 6574 7261 6865 6472 6f6e 2c20  he tetrahedron, \n+00003d40: 696e 7669 7369 626c 6520 746f 206f 7572  invisible to our\n+00003d50: 2076 6965 772e 2020 4974 2069 7320 756e   view.  It is un\n+00003d60: 6e65 6365 7373 6172 792c 2061 6e64 2073  necessary, and s\n+00003d70: 6f20 6974 0a69 7320 7265 6d6f 7665 642e  o it.is removed.\n+00003d80: 0a0a 2020 2049 6e20 736f 6d65 2064 7261  ..   In some dra\n+00003d90: 7769 6e67 732c 2070 6f6c 7967 6f6e 7320  wings, polygons \n+00003da0: 6163 7420 6173 207a 6572 6f2d 7468 6963  act as zero-thic\n+00003db0: 6b6e 6573 7320 736f 6c69 6420 7375 7266  kness solid surf\n+00003dc0: 6163 6573 2077 6974 680a 626f 7468 2073  aces with.both s\n+00003dd0: 6964 6573 2076 6973 6962 6c65 2072 6174  ides visible rat\n+00003de0: 6865 7220 7468 616e 2061 7320 7468 6520  her than as the \n+00003df0: 6661 6365 7320 6f66 2073 6f6c 6964 206f  faces of solid o\n+00003e00: 626a 6563 7473 2c20 7768 6572 6520 6261  bjects, where ba\n+00003e10: 636b 0a66 6163 6573 2063 616e 2062 6520  ck.faces can be \n+00003e20: 6375 6c6c 6564 2e20 2046 6f72 207a 6572  culled.  For zer\n+00003e30: 6f2d 7468 6963 6b6e 6573 7320 736f 6c69  o-thickness soli\n+00003e40: 6473 2c20 6375 6c6c 696e 6720 6973 2061  ds, culling is a\n+00003e50: 2070 726f 626c 656d 2e0a 4f6e 6520 736f   problem..One so\n+00003e60: 6c75 7469 6f6e 2069 7320 746f 2075 7365  lution is to use\n+00003e70: 2061 2070 6169 7220 6f66 2027 736b 6574   a pair of 'sket\n+00003e80: 6368 2720 706f 6c79 676f 6e73 2066 6f72  ch' polygons for\n+00003e90: 2065 6163 680a 7a65 726f 2d74 6869 636b   each.zero-thick\n+00003ea0: 6e65 7373 2066 6163 652c 2069 6465 6e74  ness face, ident\n+00003eb0: 6963 616c 2065 7863 6570 7420 7769 7468  ical except with\n+00003ec0: 206f 7070 6f73 6974 6520 7665 7274 6578   opposite vertex\n+00003ed0: 206f 7264 6572 732e 2020 5468 6973 0a69   orders.  This.i\n+00003ee0: 7320 756e 7769 656c 6479 2061 6e64 2065  s unwieldy and e\n+00003ef0: 7870 656e 7369 7665 2e20 2041 2062 6574  xpensive.  A bet\n+00003f00: 7465 7220 7761 7920 6973 2074 6f20 7365  ter way is to se\n+00003f10: 7420 7468 6520 2773 6b65 7463 6827 2069  t the 'sketch' i\n+00003f20: 6e74 6572 6e61 6c0a 6f70 7469 6f6e 2027  nternal.option '\n+00003f30: 6375 6c6c 2720 746f 2027 6661 6c73 6527  cull' to 'false'\n+00003f40: 2069 6e20 7468 6520 7573 7561 6c20 2750   in the usual 'P\n+00003f50: 5354 7269 636b 7327 206d 616e 6e65 722e  STricks' manner.\n+00003f60: 0a20 2070 6f6c 7967 6f6e 5b63 756c 6c3d  .  polygon[cull=\n+00003f70: 6661 6c73 655d 2870 3129 2870 3229 2870  false](p1)(p2)(p\n+00003f80: 3329 0a54 6865 2066 6f6c 6c6f 7769 6e67  3).The following\n+00003f90: 2073 686f 7773 2074 6865 2073 616d 6520   shows the same \n+00003fa0: 6865 6c69 7820 7368 6170 6520 6472 6177  helix shape draw\n+00003fb0: 6e20 6669 7273 7420 7769 7468 2063 756c  n first with cul\n+00003fc0: 6c3d 7472 7565 2028 7468 650a 6465 6661  l=true (the.defa\n+00003fd0: 756c 7429 2061 6e64 2074 6865 6e20 6375  ult) and then cu\n+00003fe0: 6c6c 3d66 616c 7365 2e0a 0a00 085b 696d  ll=false.....[im\n+00003ff0: 6167 6520 7372 633d 2265 7830 3435 2e70  age src=\"ex045.p\n+00004000: 6e67 2220 7465 7874 3d22 496d 6167 6520  ng\" text=\"Image \n+00004010: 6578 3034 3520 6f6d 6974 7465 6420 696e  ex045 omitted in\n+00004020: 2074 6578 7420 7665 7273 696f 6e20 6f66   text version of\n+00004030: 2074 6869 7320 646f 6375 6d65 6e74 2e22   this document.\"\n+00004040: 0008 5d0a 0a57 6527 6c6c 2073 6f6f 6e20  ..]..We'll soon \n+00004050: 7365 6520 686f 7720 746f 2070 726f 6475  see how to produ\n+00004060: 6365 2074 6865 7365 2068 656c 6978 6573  ce these helixes\n+00004070: 2077 6974 6820 6120 6665 7720 6c69 6e65   with a few line\n+00004080: 7320 6f66 2027 736b 6574 6368 270a 6c61  s of 'sketch'.la\n+00004090: 6e67 7561 6765 2063 6f64 652e 0a0a 2020  nguage code...  \n+000040a0: 2049 7420 6d61 7920 6265 2074 656d 7074   It may be tempt\n+000040b0: 696e 6720 746f 2074 7572 6e20 6375 6c6c  ing to turn cull\n+000040c0: 696e 6720 6f66 6620 6772 6174 7569 746f  ing off gratuito\n+000040d0: 7573 6c79 2073 6f20 7468 6174 2076 6572  usly so that ver\n+000040e0: 7465 780a 6f72 6465 7220 6361 6e20 6265  tex.order can be\n+000040f0: 2069 676e 6f72 6564 2e20 2054 6869 7320   ignored.  This \n+00004100: 6973 206e 6f74 2061 2067 6f6f 6420 6964  is not a good id\n+00004110: 6561 2062 6563 6175 7365 206f 7574 7075  ea because outpu\n+00004120: 7420 6669 6c65 2073 697a 650a 616e 6420  t file size.and \n+00004130: 5465 5820 616e 6420 506f 7374 7363 7269  TeX and Postscri\n+00004140: 7074 2070 726f 6365 7373 696e 6720 7469  pt processing ti\n+00004150: 6d65 2062 6f74 6820 6465 7065 6e64 206f  me both depend o\n+00004160: 6e20 7468 6520 6e75 6d62 6572 206f 660a  n the number of.\n+00004170: 6f75 7470 7574 2070 6f6c 7967 6f6e 732e  output polygons.\n+00004180: 2020 4375 6c6c 696e 6720 7573 7561 6c6c    Culling usuall\n+00004190: 7920 696d 7072 6f76 6573 2070 6572 666f  y improves perfo\n+000041a0: 726d 616e 6365 2062 7920 6120 6661 6374  rmance by a fact\n+000041b0: 6f72 206f 660a 7477 6f2e 2020 4f6e 2074  or of.two.  On t\n+000041c0: 6865 206f 7468 6572 2068 616e 642c 2067  he other hand, g\n+000041d0: 6c6f 6261 6c6c 7920 7365 7474 696e 6720  lobally setting \n+000041e0: 2763 756c 6c3d 6661 6c73 6527 2069 7320  'cull=false' is \n+000041f0: 7265 6173 6f6e 6162 6c65 0a77 6869 6c65  reasonable.while\n+00004200: 2064 6562 7567 6769 6e67 2e20 2053 6565   debugging.  See\n+00004210: 202a 6e6f 7465 2047 6c6f 6261 6c20 6f70   *note Global op\n+00004220: 7469 6f6e 733a 3a20 616e 6420 2a6e 6f74  tions:: and *not\n+00004230: 6520 4c69 6d69 7473 206f 6e20 6572 726f  e Limits on erro\n+00004240: 720a 6465 7465 6374 696f 6e3a 3a2e 0a0a  r.detection::...\n+00004250: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n+00004260: 6e66 6f2c 2020 4e6f 6465 3a20 5370 6563  nfo,  Node: Spec\n+00004270: 6961 6c20 6f62 6a65 6374 732c 2020 4e65  ial objects,  Ne\n+00004280: 7874 3a20 4f62 6a65 6374 2074 7261 6e73  xt: Object trans\n+00004290: 666f 726d 732c 2020 5072 6576 3a20 4472  forms,  Prev: Dr\n+000042a0: 6177 696e 6720 6120 736f 6c69 642c 2020  awing a solid,  \n+000042b0: 5570 3a20 496e 7472 6f64 7563 7469 6f6e  Up: Introduction\n+000042c0: 2062 7920 6578 616d 706c 650a 0a32 2e34   by example..2.4\n+000042d0: 2053 7065 6369 616c 206f 626a 6563 7473   Special objects\n+000042e0: 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  .===============\n+000042f0: 3d3d 3d3d 0a0a 5765 2063 616e 2061 6464  ====..We can add\n+00004300: 206c 6162 656c 7320 746f 2061 2064 7261   labels to a dra\n+00004310: 7769 6e67 2062 7920 7573 696e 6720 7370  wing by using sp\n+00004320: 6563 6961 6c20 6f62 6a65 6374 732c 2077  ecial objects, w\n+00004330: 6869 6368 2070 726f 7669 6465 2061 0a77  hich provide a.w\n+00004340: 6179 2074 6f20 656d 6265 6420 7261 7720  ay to embed raw \n+00004350: 4c61 5465 5820 616e 6420 2750 5354 7269  LaTeX and 'PSTri\n+00004360: 636b 7327 2063 6f64 652e 2020 4164 6469  cks' code.  Addi\n+00004370: 6e67 2074 6869 7320 746f 2074 6865 0a74  ng this to the.t\n+00004380: 6574 7261 6865 6472 6f6e 2064 6f65 7320  etrahedron does \n+00004390: 7468 6520 7472 6963 6b2e 0a20 2073 7065  the trick..  spe\n+000043a0: 6369 616c 207c 5c66 6f6f 746e 6f74 6573  cial |\\footnotes\n+000043b0: 697a 650a 2020 2020 2020 2020 2020 205c  ize.           \\\n+000043c0: 7570 7574 7b32 7074 7d5b 7572 5d23 317b  uput{2pt}[ur]#1{\n+000043d0: 2450 3124 7d0a 2020 2020 2020 2020 2020  $P1$}.          \n+000043e0: 205c 7570 7574 5b72 5d23 327b 2450 3224   \\uput[r]#2{$P2$\n+000043f0: 7d0a 2020 2020 2020 2020 2020 205c 7570  }.           \\up\n+00004400: 7574 5b75 5d23 337b 2450 3324 7d0a 2020  ut[u]#3{$P3$}.  \n+00004410: 2020 2020 2020 2020 205c 7570 7574 5b64           \\uput[d\n+00004420: 5d23 347b 2450 3424 7d7c 0a20 2020 2028  ]#4{$P4$}|.    (\n+00004430: 7031 2928 7032 2928 7033 2928 7034 290a  p1)(p2)(p3)(p4).\n+00004440: 4865 7265 2069 7320 7468 6520 7265 7375  Here is the resu\n+00004450: 6c74 2e0a 0a00 085b 696d 6167 6520 7372  lt.....[image sr\n+00004460: 633d 2265 7830 3432 2e70 6e67 2220 7465  c=\"ex042.png\" te\n+00004470: 7874 3d22 496d 6167 6520 6578 3034 3220  xt=\"Image ex042 \n+00004480: 6f6d 6974 7465 6420 696e 2074 6578 7420  omitted in text \n+00004490: 7665 7273 696f 6e20 6f66 2074 6869 7320  version of this \n+000044a0: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a20  document.\"..].. \n+000044b0: 2020 5468 6572 6520 6172 6520 7365 7665    There are seve\n+000044c0: 7261 6c20 6465 7461 696c 7320 746f 206e  ral details to n\n+000044d0: 6f74 6520 6865 7265 2e20 2046 6972 7374  ote here.  First\n+000044e0: 2c20 7468 6520 7175 6f74 696e 670a 636f  , the quoting.co\n+000044f0: 6e76 656e 7469 6f6e 2066 6f72 2074 6865  nvention for the\n+00004500: 2072 6177 2063 6f64 6520 6973 2073 696d   raw code is sim\n+00004510: 696c 6172 2074 6f20 7468 6520 4c61 5465  ilar to the LaTe\n+00004520: 5820 5c76 6572 6220 636f 6d6d 616e 642e  X \\verb command.\n+00004530: 2020 5468 650a 6669 7273 7420 6e6f 6e2d    The.first non-\n+00004540: 7768 6974 6520 7370 6163 6520 6368 6172  white space char\n+00004550: 6163 7465 7220 666f 6c6c 6f77 696e 6720  acter following \n+00004560: 7370 6563 6961 6c20 6973 2075 6e64 6572  special is under\n+00004570: 7374 6f6f 6420 746f 2062 650a 7468 6520  stood to be.the \n+00004580: 7175 6f74 6520 6368 6172 6163 7465 722c  quote character,\n+00004590: 2069 6e20 7468 6973 2063 6173 6520 277c   in this case '|\n+000045a0: 272e 2020 5468 6520 7261 7720 7465 7874  '.  The raw text\n+000045b0: 2063 6f6e 7469 6e75 6573 2075 6e74 696c   continues until\n+000045c0: 0a74 6869 7320 6368 6172 6163 7465 7220  .this character \n+000045d0: 7265 6375 7273 2e0a 0a20 2020 5365 636f  recurs...   Seco\n+000045e0: 6e64 2c20 7468 6520 6172 6775 6d65 6e74  nd, the argument\n+000045f0: 2072 6566 6572 656e 6365 7320 2331 2c20   references #1, \n+00004600: 2332 2c20 2333 2c20 616e 6420 2334 2072  #2, #3, and #4 r\n+00004610: 6566 6572 2074 6f20 706f 696e 742c 0a76  efer to point,.v\n+00004620: 6563 746f 722c 206f 7220 7363 616c 6172  ector, or scalar\n+00004630: 2076 616c 7565 7320 696e 2074 6865 206c   values in the l\n+00004640: 6973 7420 7468 6174 2066 6f6c 6c6f 772e  ist that follow.\n+00004650: 2020 5468 6973 2069 7320 7369 6d69 6c61    This is simila\n+00004660: 7220 746f 0a54 6558 206d 6163 726f 2073  r to.TeX macro s\n+00004670: 796e 7461 782e 2020 5468 6520 7472 616e  yntax.  The tran\n+00004680: 7366 6f72 6d65 6420 616e 6420 7477 6f2d  sformed and two-\n+00004690: 6469 6d65 6e73 696f 6e61 6c20 7072 6f6a  dimensional proj\n+000046a0: 6563 7469 6f6e 7320 6f66 0a74 6865 7365  ections of.these\n+000046b0: 2074 6872 6565 2d64 696d 656e 7369 6f6e   three-dimension\n+000046c0: 616c 2070 6f69 6e74 7320 6172 6520 7375  al points are su\n+000046d0: 6273 7469 7475 7465 6420 696e 2074 6865  bstituted in the\n+000046e0: 2066 696e 616c 206f 7574 7075 742e 2020   final output.  \n+000046f0: 416e 0a61 7267 756d 656e 7420 7265 6665  An.argument refe\n+00004700: 7265 6e63 6520 6f66 2074 6865 2066 6f72  rence of the for\n+00004710: 6d20 2331 2d32 2069 7320 7265 706c 6163  m #1-2 is replac\n+00004720: 6564 2077 6974 6820 7468 6520 616e 676c  ed with the angl\n+00004730: 6520 696e 0a64 6567 7265 6573 206f 6620  e in.degrees of \n+00004740: 7468 6520 7477 6f2d 6469 6d65 6e73 696f  the two-dimensio\n+00004750: 6e61 6c20 7665 6374 6f72 2074 6861 7420  nal vector that \n+00004760: 636f 6e6e 6563 7473 2074 6865 2070 726f  connects the pro\n+00004770: 6a65 6374 696f 6e73 206f 660a 7468 6520  jections of.the \n+00004780: 7477 6f20 7265 7370 6563 7469 7665 2061  two respective a\n+00004790: 7267 756d 656e 7420 706f 696e 7473 2c20  rgument points, \n+000047a0: 6865 7265 2023 3120 616e 6420 2332 2e20  here #1 and #2. \n+000047b0: 2054 6865 2073 7562 7374 6974 7574 6564   The substituted\n+000047c0: 0a61 6e67 6c65 2069 7320 656e 636c 6f73  .angle is enclos\n+000047d0: 6564 2069 6e20 6375 726c 7920 6272 6163  ed in curly brac\n+000047e0: 6573 2027 7b20 7d27 2e20 2057 6865 6e20  es '{ }'.  When \n+000047f0: 2754 696b 5a2f 5047 4627 206f 7574 7075  'TikZ/PGF' outpu\n+00004800: 7420 6973 0a62 6569 6e67 2067 656e 6572  t is.being gener\n+00004810: 6174 6564 2c20 7468 6520 616e 676c 6520  ated, the angle \n+00004820: 6973 2072 6f75 6e64 6564 2074 6f20 7468  is rounded to th\n+00004830: 6520 6e65 6172 6573 7420 6465 6772 6565  e nearest degree\n+00004840: 2062 6563 6175 7365 0a6e 6f6e 2d69 6e74   because.non-int\n+00004850: 6567 6572 2061 6e67 6c65 7320 6172 6520  eger angles are \n+00004860: 6e6f 7420 616c 6c6f 7765 6420 6279 2027  not allowed by '\n+00004870: 5469 6b5a 2f50 4746 2720 7072 696d 6974  TikZ/PGF' primit\n+00004880: 6976 6573 2e0a 0a20 2020 4173 206f 6620  ives...   As of \n+00004890: 5665 7273 696f 6e20 302e 3320 6f66 2027  Version 0.3 of '\n+000048a0: 736b 6574 6368 272c 2073 7065 6369 616c  sketch', special\n+000048b0: 2061 7267 756d 656e 7473 206d 6179 2062   arguments may b\n+000048c0: 6520 7363 616c 6172 7320 6f72 0a76 6563  e scalars or.vec\n+000048d0: 746f 7273 2069 6e20 6164 6469 7469 6f6e  tors in addition\n+000048e0: 2074 6f20 706f 696e 7473 2e20 2052 6566   to points.  Ref\n+000048f0: 6572 656e 6365 7320 746f 2073 6361 6c61  erences to scala\n+00004900: 7220 6172 6775 6d65 6e74 7320 6172 650a  r arguments are.\n+00004910: 6d65 7265 6c79 2072 6570 6c61 6365 6420  merely replaced \n+00004920: 7769 7468 2061 206e 756d 6265 7220 666f  with a number fo\n+00004930: 726d 6174 7465 6420 6a75 7374 2061 7320  rmatted just as \n+00004940: 616e 7920 706f 696e 7420 636f 6f72 6469  any point coordi\n+00004950: 6e61 7465 2e0a 5265 6665 7265 6e63 6573  nate..References\n+00004960: 2074 6f20 7665 6374 6f72 7320 6265 636f   to vectors beco\n+00004970: 6d65 2074 776f 2d64 696d 656e 7369 6f6e  me two-dimension\n+00004980: 616c 2070 6f69 6e74 732e 2020 5468 6520  al points.  The \n+00004990: 7469 636b 206f 7065 7261 746f 720a 7468  tick operator.th\n+000049a0: 6174 2073 656c 6563 7473 2069 6e64 6976  at selects indiv\n+000049b0: 6964 7561 6c20 636f 6d70 6f6e 656e 7473  idual components\n+000049c0: 206f 6620 706f 696e 7473 2061 6e64 2076   of points and v\n+000049d0: 6563 746f 7273 2065 6c73 6577 6865 7265  ectors elsewhere\n+000049e0: 2069 6e0a 2773 6b65 7463 6827 2028 7365   in.'sketch' (se\n+000049f0: 6520 666f 7220 6578 616d 706c 6520 2a6e  e for example *n\n+00004a00: 6f74 6520 4166 6669 6e65 2061 7269 7468  ote Affine arith\n+00004a10: 6d65 7469 633a 3a29 2063 616e 2061 6c73  metic::) can als\n+00004a20: 6f20 6265 2061 7070 6c69 6564 0a74 6f20  o be applied.to \n+00004a30: 706f 696e 7420 616e 6420 7665 6374 6f72  point and vector\n+00004a40: 2061 7267 756d 656e 7420 7265 6665 7265   argument refere\n+00004a50: 6e63 6573 2e20 2041 6c6c 2074 6872 6565  nces.  All three\n+00004a60: 2064 696d 656e 7369 6f6e 7320 6f66 2061   dimensions of a\n+00004a70: 0a74 7261 6e73 666f 726d 6564 2070 6f69  .transformed poi\n+00004a80: 6e74 206f 7220 7665 6374 6f72 2063 616e  nt or vector can\n+00004a90: 2061 6c73 6f20 6265 2073 7562 7374 6974   also be substit\n+00004aa0: 7565 6420 7769 7468 2027 2733 272e 2020  ued with ''3'.  \n+00004ab0: 5365 6520 2a6e 6f74 650a 5370 6563 6961  See *note.Specia\n+00004ac0: 6c73 3a3a 2066 6f72 2064 6574 6169 6c73  ls:: for details\n+00004ad0: 2e0a 0a20 2020 4279 2064 6566 6175 6c74  ...   By default\n+00004ae0: 2c20 2773 7065 6369 616c 2720 6f62 6a65  , 'special' obje\n+00004af0: 6374 7320 6172 6520 7072 696e 7465 6420  cts are printed \n+00004b00: 6c61 7374 2c20 6f76 6572 6c61 7969 6e67  last, overlaying\n+00004b10: 2061 6c6c 206f 7468 6572 0a6f 626a 6563   all other.objec\n+00004b20: 7473 2069 6e20 7468 6520 7363 656e 652e  ts in the scene.\n+00004b30: 2020 4966 2079 6f75 2073 7065 6369 6679    If you specify\n+00004b40: 2074 6865 2069 6e74 6572 6e61 6c20 6f70   the internal op\n+00004b50: 7469 6f6e 2027 6c61 793d 696e 272c 2074  tion 'lay=in', t\n+00004b60: 6865 0a68 6964 6465 6e20 7375 7266 6163  he.hidden surfac\n+00004b70: 6520 616c 676f 7269 7468 6d20 636f 6e73  e algorithm cons\n+00004b80: 6964 6572 7320 7468 6520 656e 7469 7265  iders the entire\n+00004b90: 2073 7065 6369 616c 206f 626a 6563 7420   special object \n+00004ba0: 746f 2062 6520 7468 650a 6669 7273 7420  to be the.first \n+00004bb0: 706f 696e 7420 2823 3129 2069 6e20 7468  point (#1) in th\n+00004bc0: 6520 6172 6775 6d65 6e74 206c 6973 742e  e argument list.\n+00004bd0: 2020 4966 2074 6861 7420 706f 696e 7420    If that point \n+00004be0: 6973 2062 6568 696e 6420 286f 660a 736d  is behind (of.sm\n+00004bf0: 616c 6c65 7220 7a2d 636f 6d70 6f6e 656e  aller z-componen\n+00004c00: 7420 7468 616e 2920 616e 7920 6472 6177  t than) any draw\n+00004c10: 6162 6c65 2c20 7468 656e 2074 6865 2065  able, then the e\n+00004c20: 6e74 6972 6520 7370 6563 6961 6c20 6f62  ntire special ob\n+00004c30: 6a65 6374 0a69 7320 6472 6177 6e20 6265  ject.is drawn be\n+00004c40: 666f 7265 2074 6861 7420 6472 6177 6162  fore that drawab\n+00004c50: 6c65 2c20 736f 2074 6865 2064 7261 7761  le, so the drawa\n+00004c60: 626c 6520 6f62 7363 7572 6573 2070 6172  ble obscures par\n+00004c70: 7473 206f 6620 7468 650a 7370 6563 6961  ts of the.specia\n+00004c80: 6c20 6f62 6a65 6374 2074 6861 7420 6f76  l object that ov\n+00004c90: 6572 6c61 7073 2069 742e 2020 496e 206f  erlaps it.  In o\n+00004ca0: 7572 2065 7861 6d70 6c65 2c20 7031 2069  ur example, p1 i\n+00004cb0: 7320 7468 6520 6672 6f6e 742d 6d6f 7374  s the front-most\n+00004cc0: 0a70 6f69 6e74 2069 6e20 7468 6520 7363  .point in the sc\n+00004cd0: 656e 6520 2868 6173 2074 6865 206c 6172  ene (has the lar\n+00004ce0: 6765 7374 207a 2d63 6f6d 706f 6e65 6e74  gest z-component\n+00004cf0: 292c 2073 6f20 6164 6469 6e67 2027 6c61  ), so adding 'la\n+00004d00: 793d 696e 2720 6861 730a 6e6f 2065 6666  y=in' has.no eff\n+00004d10: 6563 742e 0a0a 2020 2057 6974 6820 6f70  ect...   With op\n+00004d20: 7469 6f6e 2027 6c61 793d 756e 6465 7227  tion 'lay=under'\n+00004d30: 2c20 6120 7370 6563 6961 6c20 6973 2064  , a special is d\n+00004d40: 7261 776e 205f 6265 666f 7265 5f2c 2068  rawn _before_, h\n+00004d50: 656e 6365 2061 7070 6561 7273 0a5f 756e  ence appears._un\n+00004d60: 6465 725f 2061 6e79 206f 6620 7468 6520  der_ any of the \n+00004d70: 6f62 6a65 6374 7320 6861 6e64 6c65 6420  objects handled \n+00004d80: 6279 2074 6865 2068 6964 6465 6e20 7375  by the hidden su\n+00004d90: 7266 6163 6520 616c 676f 7269 7468 6d2e  rface algorithm.\n+00004da0: 0a54 6869 7320 6973 2068 6f77 2074 6865  .This is how the\n+00004db0: 206c 6967 6874 2067 7261 7920 6178 6573   light gray axes\n+00004dc0: 2077 6572 6520 6164 6465 6420 746f 2074   were added to t\n+00004dd0: 6865 2022 6865 6c6c 6f20 776f 726c 6422  he \"hello world\"\n+00004de0: 2065 7861 6d70 6c65 0a2a 6e6f 7465 2048   example.*note H\n+00004df0: 656c 6c6f 2077 6f72 6c64 3a3a 2e0a 0a20  ello world::... \n+00004e00: 2020 5370 6563 6961 6c20 6f62 6a65 6374    Special object\n+00004e10: 7320 6172 6520 706f 7765 7266 756c 2c20  s are powerful, \n+00004e20: 7769 7468 206d 616e 7920 706f 7373 6962  with many possib\n+00004e30: 6c65 2075 7365 732e 0a0a 1f0a 4669 6c65  le uses.....File\n+00004e40: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n+00004e50: 4e6f 6465 3a20 4f62 6a65 6374 2074 7261  Node: Object tra\n+00004e60: 6e73 666f 726d 732c 2020 4e65 7874 3a20  nsforms,  Next: \n+00004e70: 5265 7065 6174 6564 206f 626a 6563 7473  Repeated objects\n+00004e80: 2c20 2050 7265 763a 2053 7065 6369 616c  ,  Prev: Special\n+00004e90: 206f 626a 6563 7473 2c20 2055 703a 2049   objects,  Up: I\n+00004ea0: 6e74 726f 6475 6374 696f 6e20 6279 2065  ntroduction by e\n+00004eb0: 7861 6d70 6c65 0a0a 322e 3520 5472 616e  xample..2.5 Tran\n+00004ec0: 7366 6f72 6d73 0a3d 3d3d 3d3d 3d3d 3d3d  sforms.=========\n+00004ed0: 3d3d 3d3d 3d0a 0a4e 6f77 206c 6574 2773  =====..Now let's\n+00004ee0: 2061 6464 2061 2073 6563 6f6e 6420 636f   add a second co\n+00004ef0: 7079 206f 6620 7468 6520 7069 6572 6365  py of the pierce\n+00004f00: 6420 7465 7472 6168 6564 726f 6e2e 2020  d tetrahedron.  \n+00004f10: 5765 276c 6c20 726f 7461 7465 0a74 6865  We'll rotate.the\n+00004f20: 2063 6f70 7920 3930 2064 6567 7265 6573   copy 90 degrees\n+00004f30: 2061 626f 7574 2074 6865 2078 2d61 7869   about the x-axi\n+00004f40: 7320 7769 7468 2074 6865 206f 7269 6769  s with the origi\n+00004f50: 6e20 6173 2022 6365 6e74 6572 206f 660a  n as \"center of.\n+00004f60: 726f 7461 7469 6f6e 2220 736f 2077 6520  rotation\" so we \n+00004f70: 6361 6e20 7365 6520 7468 6520 6261 636b  can see the back\n+00004f80: 2c20 7468 656e 2074 7261 6e73 6c61 7465  , then translate\n+00004f90: 2069 7420 746f 2074 6865 2072 6967 6874   it to the right\n+00004fa0: 2d2d 696e 2074 6865 0a70 6f73 6974 6976  --in the.positiv\n+00004fb0: 6520 782d 6469 7265 6374 696f 6e2d 2d73  e x-direction--s\n+00004fc0: 6f20 6974 2064 6f65 736e 2774 2063 6f6c  o it doesn't col\n+00004fd0: 6c69 6465 2077 6974 6820 7468 6520 6f72  lide with the or\n+00004fe0: 6967 696e 616c 2e20 2054 6f20 6865 6c70  iginal.  To help\n+00004ff0: 0a75 7320 7365 6520 7768 6174 2773 2067  .us see what's g\n+00005000: 6f69 6e67 206f 6e2c 206d 616b 6520 7468  oing on, make th\n+00005010: 6520 6261 636b 2073 6964 6520 6772 6179  e back side gray\n+00005020: 2e0a 2020 6465 6620 7069 6572 6365 645f  ..  def pierced_\n+00005030: 7465 7472 6168 6564 726f 6e20 7b0a 2020  tetrahedron {.  \n+00005040: 2020 6465 6620 7031 2028 302c 302c 3129    def p1 (0,0,1)\n+00005050: 2064 6566 2070 3220 2831 2c30 2c30 290a   def p2 (1,0,0).\n+00005060: 2020 2020 6465 6620 7033 2028 302c 312c      def p3 (0,1,\n+00005070: 3029 2064 6566 2070 3420 282d 2e33 2c2d  0) def p4 (-.3,-\n+00005080: 2e35 2c2d 2e38 290a 2020 2020 706f 6c79  .5,-.8).    poly\n+00005090: 676f 6e28 7031 2928 7032 2928 7033 2920  gon(p1)(p2)(p3) \n+000050a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000050b0: 2020 2020 2025 206f 7269 6769 6e61 6c0a       % original.\n+000050c0: 2020 2020 706f 6c79 676f 6e28 7031 2928      polygon(p1)(\n+000050d0: 7034 2928 7032 2920 2020 2020 2020 2020  p4)(p2)         \n+000050e0: 2020 2020 2020 2020 2020 2020 2025 2062               % b\n+000050f0: 6f74 746f 6d0a 2020 2020 706f 6c79 676f  ottom.    polygo\n+00005100: 6e28 7031 2928 7033 2928 7034 2920 2020  n(p1)(p3)(p4)   \n 00005110: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00005120: 2020 2020 2025 206c 6566 740a 2020 2020       % left.    \n-00005130: 706f 6c79 676f 6e5b 6669 6c6c 636f 6c6f  polygon[fillcolo\n-00005140: 723d 6c69 6768 7467 7261 795d 2870 3329  r=lightgray](p3)\n-00005150: 2870 3229 2870 3429 2025 2072 6561 720a  (p2)(p4) % rear.\n-00005160: 2020 2020 6c69 6e65 5b6c 696e 6563 6f6c      line[linecol\n-00005170: 6f72 3d72 6564 5d28 2d31 2c2d 312c 2d31  or=red](-1,-1,-1\n-00005180: 2928 322c 322c 3229 0a20 207d 0a20 207b  )(2,2,2).  }.  {\n-00005190: 7069 6572 6365 645f 7465 7472 6168 6564  pierced_tetrahed\n-000051a0: 726f 6e7d 2020 2520 7465 7472 6168 6564  ron}  % tetrahed\n-000051b0: 726f 6e20 696e 206f 7269 6769 6e61 6c20  ron in original \n-000051c0: 706f 7369 7469 6f6e 0a20 2070 7574 207b  position.  put {\n-000051d0: 2072 6f74 6174 6528 3930 2c20 2830 2c30   rotate(90, (0,0\n-000051e0: 2c30 292c 205b 312c 302c 305d 2920 2520  ,0), [1,0,0]) % \n-000051f0: 636f 7079 2069 6e20 6e65 7720 706f 7369  copy in new posi\n-00005200: 7469 6f6e 0a20 2020 2020 2020 2074 6865  tion.        the\n-00005210: 6e20 7472 616e 736c 6174 6528 5b32 2e35  n translate([2.5\n-00005220: 2c30 2c30 5d29 207d 207b 7069 6572 6365  ,0,0]) } {pierce\n-00005230: 645f 7465 7472 6168 6564 726f 6e7d 0a48  d_tetrahedron}.H\n-00005240: 6572 6520 7468 6520 656e 7469 7265 2063  ere the entire c\n-00005250: 6f64 6520 6f66 2074 6865 2070 7265 7669  ode of the previ\n-00005260: 6f75 7320 6578 616d 706c 6520 6861 7320  ous example has \n-00005270: 6265 656e 2077 7261 7070 6564 2069 6e20  been wrapped in \n-00005280: 610a 6465 6669 6e69 7469 6f6e 2062 7920  a.definition by \n-00005290: 666f 726d 696e 6720 6120 2262 6c6f 636b  forming a \"block\n-000052a0: 2220 7769 7468 2062 7261 6365 7320 2861  \" with braces (a\n-000052b0: 2073 696e 676c 6520 6974 656d 2077 6f75   single item wou\n-000052c0: 6c64 206e 6f74 0a6e 6565 6420 7468 656d  ld not.need them\n-000052d0: 292e 2020 5468 6520 706f 696e 7420 6465  ).  The point de\n-000052e0: 6669 6e69 7469 6f6e 7320 6e65 7374 6564  finitions nested\n-000052f0: 2069 6e73 6964 6520 7468 6520 6272 6163   inside the brac\n-00005300: 6573 2061 7265 0a22 6c65 7869 6361 6c6c  es are.\"lexicall\n-00005310: 7920 7363 6f70 6564 222e 2020 5468 6569  y scoped\".  Thei\n-00005320: 7220 6d65 616e 696e 6720 6578 7465 6e64  r meaning extend\n-00005330: 7320 6f6e 6c79 2074 6f20 7468 6520 656e  s only to the en\n-00005340: 6420 6f66 2074 6865 2062 6c6f 636b 2e0a  d of the block..\n-00005350: 5468 6520 6f75 7465 7220 6465 6620 6973  The outer def is\n-00005360: 2063 616c 6c65 6420 6120 2264 7261 7761   called a \"drawa\n-00005370: 626c 6522 2064 6566 696e 6974 696f 6e20  ble\" definition \n-00005380: 6265 6361 7573 6520 6974 2064 6573 6372  because it descr\n-00005390: 6962 6573 0a73 6f6d 6574 6869 6e67 2074  ibes.something t\n-000053a0: 6861 7420 6361 6e20 6265 2064 7261 776e  hat can be drawn\n-000053b0: 2e0a 0a20 2020 4120 6472 6177 6162 6c65  ...   A drawable\n-000053c0: 2064 6566 696e 6974 696f 6e20 6279 2069   definition by i\n-000053d0: 7473 656c 6620 6361 7573 6573 206e 6f74  tself causes not\n-000053e0: 6869 6e67 2074 6f20 6861 7070 656e 2075  hing to happen u\n-000053f0: 6e74 696c 2069 7473 0a6e 616d 6520 6973  ntil its.name is\n-00005400: 2072 6566 6572 656e 6365 642e 2020 4472   referenced.  Dr\n-00005410: 6177 6162 6c65 2072 6566 6572 656e 6365  awable reference\n-00005420: 7320 6d75 7374 2062 6520 656e 636c 6f73  s must be enclos\n-00005430: 6564 2069 6e20 6375 726c 790a 6272 6163  ed in curly.brac\n-00005440: 6573 2c20 652e 672e 207b 666f 6f7d 2c20  es, e.g. {foo}, \n-00005450: 7769 7468 206e 6f20 696e 7465 7276 656e  with no interven\n-00005460: 696e 6720 7768 6974 6520 7370 6163 652e  ing white space.\n-00005470: 2020 496e 2074 6865 2063 6f64 6520 6162    In the code ab\n-00005480: 6f76 652c 0a74 6865 2066 6972 7374 2072  ove,.the first r\n-00005490: 6566 6572 656e 6365 207b 7069 6572 6365  eference {pierce\n-000054a0: 645f 7465 7472 6168 6564 726f 6e7d 2069  d_tetrahedron} i\n-000054b0: 7320 6120 706c 6169 6e20 6f6e 652e 2020  s a plain one.  \n-000054c0: 4974 7320 6566 6665 6374 2069 730a 6d65  Its effect is.me\n-000054d0: 7265 6c79 2074 6f20 6475 706c 6963 6174  rely to duplicat\n-000054e0: 6520 7468 6520 6561 726c 6965 7220 6472  e the earlier dr\n-000054f0: 6177 696e 672e 2020 416c 6d6f 7374 2061  awing.  Almost a\n-00005500: 6e79 2073 6572 6965 7320 6f66 2027 736b  ny series of 'sk\n-00005510: 6574 6368 270a 636f 6d6d 616e 6473 2073  etch'.commands s\n-00005520: 7475 6666 206d 6179 2062 6520 7265 706c  tuff may be repl\n-00005530: 6163 6564 2077 6974 6820 6465 6620 666f  aced with def fo\n-00005540: 6f20 7b20 7374 7566 6620 7d20 7b66 6f6f  o { stuff } {foo\n-00005550: 7d20 7769 7468 6f75 740a 6368 616e 6769  } without.changi\n-00005560: 6e67 2069 7473 206d 6561 6e69 6e67 2e0a  ng its meaning..\n-00005570: 0a20 2020 5468 6520 7075 7420 636f 6d6d  .   The put comm\n-00005580: 616e 6420 7375 7070 6c69 6573 2061 2073  and supplies a s\n-00005590: 6563 6f6e 6420 7265 6665 7265 6e63 652c  econd reference,\n-000055a0: 2074 6869 7320 7469 6d65 2077 6974 6820   this time with \n-000055b0: 610a 2274 7261 6e73 666f 726d 2220 6170  a.\"transform\" ap\n-000055c0: 706c 6965 6420 6669 7273 742e 2020 5468  plied first.  Th\n-000055d0: 6520 726f 7461 7465 2074 7261 6e73 666f  e rotate transfo\n-000055e0: 726d 2074 7572 6e73 2074 6865 2074 6574  rm turns the tet\n-000055f0: 7261 6865 6472 6f6e 0a39 3020 6465 6772  rahedron.90 degr\n-00005600: 6565 7320 6162 6f75 7420 7468 6520 6f72  ees about the or\n-00005610: 6967 696e 2e20 2054 6865 2061 7869 7320  igin.  The axis \n-00005620: 6f66 2072 6f74 6174 696f 6e20 6973 2074  of rotation is t\n-00005630: 6865 2076 6563 746f 720a 5b31 2c30 2c30  he vector.[1,0,0\n-00005640: 5d2e 2020 4279 2074 6865 2022 7269 6768  ].  By the \"righ\n-00005650: 7420 6861 6e64 2072 756c 6522 2c20 7468  t hand rule\", th\n-00005660: 6973 2063 6175 7365 7320 7468 6520 746f  is causes the to\n-00005670: 7020 6f66 2074 6865 0a74 6574 7261 6865  p of the.tetrahe\n-00005680: 6472 6f6e 2074 6f20 726f 7461 7465 2074  dron to rotate t\n-00005690: 6f77 6172 6420 7468 6520 7669 6577 6572  oward the viewer\n-000056a0: 2061 6e64 2074 6865 2062 6f74 746f 6d20   and the bottom \n-000056b0: 6177 6179 2e20 2054 6865 2072 756c 650a  away.  The rule.\n-000056c0: 7265 6365 6976 6573 2069 7473 206e 616d  receives its nam\n-000056d0: 6520 6672 6f6d 2074 6865 2066 6f6c 6c6f  e from the follo\n-000056e0: 7769 6e67 2064 6566 696e 6974 696f 6e3a  wing definition:\n-000056f0: 0a20 2020 2020 2a52 6967 6874 2068 616e  .     *Right han\n-00005700: 6420 7275 6c65 2e2a 2020 4966 2074 6865  d rule.*  If the\n-00005710: 2072 6967 6874 2068 616e 6420 6973 2077   right hand is w\n-00005720: 7261 7070 6564 2061 726f 756e 6420 616e  rapped around an\n-00005730: 7920 6178 6973 0a20 2020 2020 7769 7468  y axis.     with\n-00005740: 2074 6865 2074 6875 6d62 2070 6f69 6e74   the thumb point\n-00005750: 696e 6720 696e 2074 6865 2061 7869 7320  ing in the axis \n-00005760: 6469 7265 6374 696f 6e2c 2074 6865 6e20  direction, then \n-00005770: 7468 6520 6669 6e67 6572 730a 2020 2020  the fingers.    \n-00005780: 2063 7572 6c20 696e 2074 6865 2064 6972   curl in the dir\n-00005790: 6563 7469 6f6e 206f 6620 706f 7369 7469  ection of positi\n-000057a0: 7665 2072 6f74 6174 696f 6e20 6162 6f75  ve rotation abou\n-000057b0: 7420 7468 6174 2061 7869 732e 0a20 2020  t that axis..   \n-000057c0: 5468 6520 7472 616e 736c 6174 6520 7472  The translate tr\n-000057d0: 616e 7366 6f72 6d20 6d6f 7665 7320 7468  ansform moves th\n-000057e0: 6520 7079 7261 6d69 6420 6c61 7465 7261  e pyramid latera\n-000057f0: 6c6c 7920 746f 2074 6865 2072 6967 6874  lly to the right\n-00005800: 2062 790a 6164 6469 6e67 2074 6865 2076   by.adding the v\n-00005810: 6563 746f 7220 5b32 2e35 2c30 2c30 5d20  ector [2.5,0,0] \n-00005820: 746f 2065 6163 6820 7665 7274 6578 2063  to each vertex c\n-00005830: 6f6f 7264 696e 6174 652e 2020 5468 6520  oordinate.  The \n-00005840: 7265 7375 6c74 2069 730a 7368 6f77 6e20  result is.shown \n-00005850: 6865 7265 2e0a 0a00 085b 696d 6167 6520  here.....[image \n-00005860: 7372 633d 2265 7830 3530 2e70 6e67 2220  src=\"ex050.png\" \n-00005870: 7465 7874 3d22 496d 6167 6520 6578 3035  text=\"Image ex05\n-00005880: 3020 6f6d 6974 7465 6420 696e 2074 6578  0 omitted in tex\n-00005890: 7420 7665 7273 696f 6e20 6f66 2074 6869  t version of thi\n-000058a0: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a  s document.\"..].\n-000058b0: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n-000058c0: 696e 666f 2c20 204e 6f64 653a 2052 6570  info,  Node: Rep\n-000058d0: 6561 7465 6420 6f62 6a65 6374 732c 2020  eated objects,  \n-000058e0: 4e65 7874 3a20 5377 6570 7420 6f62 6a65  Next: Swept obje\n-000058f0: 6374 732c 2020 5072 6576 3a20 4f62 6a65  cts,  Prev: Obje\n-00005900: 6374 2074 7261 6e73 666f 726d 732c 2020  ct transforms,  \n-00005910: 5570 3a20 496e 7472 6f64 7563 7469 6f6e  Up: Introduction\n-00005920: 2062 7920 6578 616d 706c 650a 0a32 2e36   by example..2.6\n-00005930: 2052 6570 6561 7465 6420 6f62 6a65 6374   Repeated object\n-00005940: 730a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  s.==============\n-00005950: 3d3d 3d3d 3d3d 0a0a 546f 2064 7261 7720  ======..To draw \n-00005960: 7365 7665 6e20 696e 7374 616e 6365 7320  seven instances \n-00005970: 6f66 2074 6865 2074 6574 7261 6865 6472  of the tetrahedr\n-00005980: 6f6e 2c20 6561 6368 2064 6966 6665 7269  on, each differi\n-00005990: 6e67 2066 726f 6d20 7468 6520 6c61 7374  ng from the last\n-000059a0: 0a62 7920 7468 6520 7361 6d65 2074 7261  .by the same tra\n-000059b0: 6e73 666f 726d 2c20 7265 706c 6163 6520  nsform, replace \n-000059c0: 7468 6520 6c61 7374 2074 776f 2063 6f6d  the last two com\n-000059d0: 6d61 6e64 7320 6f66 2074 6865 2070 7265  mands of the pre\n-000059e0: 7669 6f75 730a 6578 616d 706c 6520 7769  vious.example wi\n-000059f0: 7468 0a20 2072 6570 6561 7420 7b20 372c  th.  repeat { 7,\n-00005a00: 2072 6f74 6174 6528 3135 2c20 2830 2c30   rotate(15, (0,0\n-00005a10: 2c30 292c 205b 312c 302c 305d 2920 2520  ,0), [1,0,0]) % \n-00005a20: 636f 7079 2069 6e20 6e65 7720 706f 7369  copy in new posi\n-00005a30: 7469 6f6e 0a20 2020 2020 2020 2020 2020  tion.           \n-00005a40: 2020 2074 6865 6e20 7472 616e 736c 6174     then translat\n-00005a50: 6528 5b32 2c30 2c30 5d29 207d 207b 7069  e([2,0,0]) } {pi\n-00005a60: 6572 6365 645f 7465 7472 6168 6564 726f  erced_tetrahedro\n-00005a70: 6e7d 0a41 6e64 2074 6865 2072 6573 756c  n}.And the resul\n-00005a80: 742e 2e2e 0a0a 0008 5b69 6d61 6765 2073  t.......[image s\n-00005a90: 7263 3d22 6578 3036 302e 706e 6722 2074  rc=\"ex060.png\" t\n-00005aa0: 6578 743d 2249 6d61 6765 2065 7830 3630  ext=\"Image ex060\n-00005ab0: 206f 6d69 7474 6564 2069 6e20 7465 7874   omitted in text\n-00005ac0: 2076 6572 7369 6f6e 206f 6620 7468 6973   version of this\n-00005ad0: 2064 6f63 756d 656e 742e 2200 085d 0a0a   document.\"..]..\n-00005ae0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n-00005af0: 6e66 6f2c 2020 4e6f 6465 3a20 5377 6570  nfo,  Node: Swep\n-00005b00: 7420 6f62 6a65 6374 732c 2020 5072 6576  t objects,  Prev\n-00005b10: 3a20 5265 7065 6174 6564 206f 626a 6563  : Repeated objec\n-00005b20: 7473 2c20 2055 703a 2049 6e74 726f 6475  ts,  Up: Introdu\n-00005b30: 6374 696f 6e20 6279 2065 7861 6d70 6c65  ction by example\n-00005b40: 0a0a 322e 3720 5377 6570 7420 6f62 6a65  ..2.7 Swept obje\n-00005b50: 6374 730a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  cts.============\n-00005b60: 3d3d 3d3d 3d0a 0a4d 616e 7920 6661 6d69  =====..Many fami\n-00005b70: 6c69 6172 2073 6861 7065 7320 6361 6e20  liar shapes can \n-00005b80: 6265 2067 656e 6572 6174 6564 2062 7920  be generated by \n-00005b90: 7377 6565 7069 6e67 2073 696d 706c 6572  sweeping simpler\n-00005ba0: 206f 6e65 7320 7468 726f 7567 680a 7370   ones through.sp\n-00005bb0: 6163 6520 616e 6420 636f 6e73 6964 6572  ace and consider\n-00005bc0: 696e 6720 7468 6520 7265 7375 6c74 696e  ing the resultin\n-00005bd0: 6720 7061 7468 2c20 7375 7266 6163 652c  g path, surface,\n-00005be0: 206f 7220 766f 6c75 6d65 2e20 2027 536b   or volume.  'Sk\n-00005bf0: 6574 6368 270a 696d 706c 656d 656e 7473  etch'.implements\n-00005c00: 2074 6869 7320 6964 6561 2069 6e20 7468   this idea in th\n-00005c10: 6520 7377 6565 7020 636f 6d6d 616e 642e  e sweep command.\n-00005c20: 0a20 2064 6566 206e 5f73 6567 7320 380a  .  def n_segs 8.\n-00005c30: 2020 7377 6565 7020 7b20 6e5f 7365 6773    sweep { n_segs\n-00005c40: 2c20 726f 7461 7465 2831 3830 202f 206e  , rotate(180 / n\n-00005c50: 5f73 6567 732c 2028 302c 302c 3029 2c20  _segs, (0,0,0), \n-00005c60: 5b30 2c30 2c31 5d29 207d 2028 312c 302c  [0,0,1]) } (1,0,\n-00005c70: 3029 0a54 6869 7320 636f 6465 2073 7765  0).This code swe\n-00005c80: 6570 7320 7468 6520 706f 696e 7420 2831  eps the point (1\n-00005c90: 2c30 2c30 2920 6569 6768 7420 7469 6d65  ,0,0) eight time\n-00005ca0: 7320 6279 2072 6f74 6174 696e 6720 6974  s by rotating it\n-00005cb0: 2031 3830 2f38 203d 0a32 322e 3520 6465   180/8 =.22.5 de\n-00005cc0: 6772 6565 7320 6561 6368 2074 696d 6520  grees each time \n-00005cd0: 616e 6420 636f 6e6e 6563 7469 6e67 2074  and connecting t\n-00005ce0: 6865 2072 6573 756c 7469 6e67 2070 6f69  he resulting poi\n-00005cf0: 6e74 7320 7769 7468 206c 696e 650a 7365  nts with line.se\n-00005d00: 676d 656e 7473 2e20 2054 6865 2064 6566  gments.  The def\n-00005d10: 2075 7365 6420 6865 7265 2069 7320 6120   used here is a \n-00005d20: 2273 6361 6c61 7222 2064 6566 696e 6974  \"scalar\" definit\n-00005d30: 696f 6e2e 2020 5265 6665 7265 6e63 6573  ion.  References\n-00005d40: 2074 6f0a 7363 616c 6172 7320 6861 7665   to.scalars have\n-00005d50: 206e 6f20 656e 636c 6f73 696e 6720 6272   no enclosing br\n-00005d60: 6163 6b65 7473 2061 7420 616c 6c2e 0a0a  ackets at all...\n-00005d70: 2a20 4d65 6e75 3a0a 0a2a 2050 6f69 6e74  * Menu:..* Point\n-00005d80: 2073 7765 6570 733a 3a20 2020 2020 2020   sweeps::       \n-00005d90: 2020 2020 2020 2020 2053 7765 7074 2070           Swept p\n-00005da0: 6f69 6e74 7320 6d61 6b65 206c 696e 6573  oints make lines\n-00005db0: 2061 6e64 2070 6f6c 7967 6f6e 732e 0a2a   and polygons..*\n-00005dc0: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n-00005dd0: 3a3a 2020 2020 2020 2020 2020 2020 2053  ::             S\n-00005de0: 7765 7074 206c 696e 6573 206d 616b 6520  wept lines make \n-00005df0: 7375 7266 6163 6573 2e0a 2a20 4e65 7374  surfaces..* Nest\n-00005e00: 6564 2073 7765 6570 733a 3a20 2020 2020  ed sweeps::     \n-00005e10: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n-00005e20: 7377 6565 7073 2061 7265 2075 7365 6675  sweeps are usefu\n-00005e30: 6c21 0a2a 2050 6f6c 7967 6f6e 2073 7765  l!.* Polygon swe\n-00005e40: 6570 733a 3a20 2020 2020 2020 2020 2020  eps::           \n-00005e50: 2020 2053 7765 7074 2070 6f6c 7967 6f6e     Swept polygon\n-00005e60: 7320 6d61 6b65 2073 6f6c 6964 732e 2e2e  s make solids...\n-00005e70: 0a2a 2050 6f6c 796c 696e 6520 7377 6565  .* Polyline swee\n-00005e80: 7073 2077 6974 6820 636c 6f73 7572 653a  ps with closure:\n-00005e90: 3a20 2061 6e64 2073 6f20 646f 2063 6c6f  :  and so do clo\n-00005ea0: 7365 6420 706f 6c79 6c69 6e65 2073 7765  sed polyline swe\n-00005eb0: 6570 732e 0a2a 2041 6666 696e 6520 6172  eps..* Affine ar\n-00005ec0: 6974 686d 6574 6963 3a3a 2020 2020 2020  ithmetic::      \n-00005ed0: 2020 2020 2053 6b65 7463 6820 7573 6566       Sketch usef\n-00005ee0: 756c 206d 6174 6820 6578 7072 6573 7369  ul math expressi\n-00005ef0: 6f6e 2e0a 2a20 4d6f 7265 2074 6f20 6c65  on..* More to le\n-00005f00: 6172 6e3a 3a20 2020 2020 2020 2020 2020  arn::           \n-00005f10: 2020 2020 4368 6563 6b20 6f75 7420 7468      Check out th\n-00005f20: 6520 4d6f 6269 7573 2073 7472 6970 210a  e Mobius strip!.\n-00005f30: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n-00005f40: 696e 666f 2c20 204e 6f64 653a 2050 6f69  info,  Node: Poi\n-00005f50: 6e74 2073 7765 6570 732c 2020 4e65 7874  nt sweeps,  Next\n-00005f60: 3a20 506f 6c79 6c69 6e65 2073 7765 6570  : Polyline sweep\n-00005f70: 732c 2020 5072 6576 3a20 5377 6570 7420  s,  Prev: Swept \n-00005f80: 6f62 6a65 6374 732c 2020 5570 3a20 5377  objects,  Up: Sw\n-00005f90: 6570 7420 6f62 6a65 6374 730a 0a32 2e37  ept objects..2.7\n-00005fa0: 2e31 2050 6f69 6e74 2073 7765 6570 730a  .1 Point sweeps.\n+00005120: 2020 2025 206c 6566 740a 2020 2020 706f     % left.    po\n+00005130: 6c79 676f 6e5b 6669 6c6c 636f 6c6f 723d  lygon[fillcolor=\n+00005140: 6c69 6768 7467 7261 795d 2870 3329 2870  lightgray](p3)(p\n+00005150: 3229 2870 3429 2025 2072 6561 720a 2020  2)(p4) % rear.  \n+00005160: 2020 6c69 6e65 5b6c 696e 6563 6f6c 6f72    line[linecolor\n+00005170: 3d72 6564 5d28 2d31 2c2d 312c 2d31 2928  =red](-1,-1,-1)(\n+00005180: 322c 322c 3229 0a20 207d 0a20 207b 7069  2,2,2).  }.  {pi\n+00005190: 6572 6365 645f 7465 7472 6168 6564 726f  erced_tetrahedro\n+000051a0: 6e7d 2020 2520 7465 7472 6168 6564 726f  n}  % tetrahedro\n+000051b0: 6e20 696e 206f 7269 6769 6e61 6c20 706f  n in original po\n+000051c0: 7369 7469 6f6e 0a20 2070 7574 207b 2072  sition.  put { r\n+000051d0: 6f74 6174 6528 3930 2c20 2830 2c30 2c30  otate(90, (0,0,0\n+000051e0: 292c 205b 312c 302c 305d 2920 2520 636f  ), [1,0,0]) % co\n+000051f0: 7079 2069 6e20 6e65 7720 706f 7369 7469  py in new positi\n+00005200: 6f6e 0a20 2020 2020 2020 2074 6865 6e20  on.        then \n+00005210: 7472 616e 736c 6174 6528 5b32 2e35 2c30  translate([2.5,0\n+00005220: 2c30 5d29 207d 207b 7069 6572 6365 645f  ,0]) } {pierced_\n+00005230: 7465 7472 6168 6564 726f 6e7d 0a48 6572  tetrahedron}.Her\n+00005240: 6520 7468 6520 656e 7469 7265 2063 6f64  e the entire cod\n+00005250: 6520 6f66 2074 6865 2070 7265 7669 6f75  e of the previou\n+00005260: 7320 6578 616d 706c 6520 6861 7320 6265  s example has be\n+00005270: 656e 2077 7261 7070 6564 2069 6e20 610a  en wrapped in a.\n+00005280: 6465 6669 6e69 7469 6f6e 2062 7920 666f  definition by fo\n+00005290: 726d 696e 6720 6120 2262 6c6f 636b 2220  rming a \"block\" \n+000052a0: 7769 7468 2062 7261 6365 7320 2861 2073  with braces (a s\n+000052b0: 696e 676c 6520 6974 656d 2077 6f75 6c64  ingle item would\n+000052c0: 206e 6f74 0a6e 6565 6420 7468 656d 292e   not.need them).\n+000052d0: 2020 5468 6520 706f 696e 7420 6465 6669    The point defi\n+000052e0: 6e69 7469 6f6e 7320 6e65 7374 6564 2069  nitions nested i\n+000052f0: 6e73 6964 6520 7468 6520 6272 6163 6573  nside the braces\n+00005300: 2061 7265 0a22 6c65 7869 6361 6c6c 7920   are.\"lexically \n+00005310: 7363 6f70 6564 222e 2020 5468 6569 7220  scoped\".  Their \n+00005320: 6d65 616e 696e 6720 6578 7465 6e64 7320  meaning extends \n+00005330: 6f6e 6c79 2074 6f20 7468 6520 656e 6420  only to the end \n+00005340: 6f66 2074 6865 2062 6c6f 636b 2e0a 5468  of the block..Th\n+00005350: 6520 6f75 7465 7220 6465 6620 6973 2063  e outer def is c\n+00005360: 616c 6c65 6420 6120 2264 7261 7761 626c  alled a \"drawabl\n+00005370: 6522 2064 6566 696e 6974 696f 6e20 6265  e\" definition be\n+00005380: 6361 7573 6520 6974 2064 6573 6372 6962  cause it describ\n+00005390: 6573 0a73 6f6d 6574 6869 6e67 2074 6861  es.something tha\n+000053a0: 7420 6361 6e20 6265 2064 7261 776e 2e0a  t can be drawn..\n+000053b0: 0a20 2020 4120 6472 6177 6162 6c65 2064  .   A drawable d\n+000053c0: 6566 696e 6974 696f 6e20 6279 2069 7473  efinition by its\n+000053d0: 656c 6620 6361 7573 6573 206e 6f74 6869  elf causes nothi\n+000053e0: 6e67 2074 6f20 6861 7070 656e 2075 6e74  ng to happen unt\n+000053f0: 696c 2069 7473 0a6e 616d 6520 6973 2072  il its.name is r\n+00005400: 6566 6572 656e 6365 642e 2020 4472 6177  eferenced.  Draw\n+00005410: 6162 6c65 2072 6566 6572 656e 6365 7320  able references \n+00005420: 6d75 7374 2062 6520 656e 636c 6f73 6564  must be enclosed\n+00005430: 2069 6e20 6375 726c 790a 6272 6163 6573   in curly.braces\n+00005440: 2c20 652e 672e 207b 666f 6f7d 2c20 7769  , e.g. {foo}, wi\n+00005450: 7468 206e 6f20 696e 7465 7276 656e 696e  th no intervenin\n+00005460: 6720 7768 6974 6520 7370 6163 652e 2020  g white space.  \n+00005470: 496e 2074 6865 2063 6f64 6520 6162 6f76  In the code abov\n+00005480: 652c 0a74 6865 2066 6972 7374 2072 6566  e,.the first ref\n+00005490: 6572 656e 6365 207b 7069 6572 6365 645f  erence {pierced_\n+000054a0: 7465 7472 6168 6564 726f 6e7d 2069 7320  tetrahedron} is \n+000054b0: 6120 706c 6169 6e20 6f6e 652e 2020 4974  a plain one.  It\n+000054c0: 7320 6566 6665 6374 2069 730a 6d65 7265  s effect is.mere\n+000054d0: 6c79 2074 6f20 6475 706c 6963 6174 6520  ly to duplicate \n+000054e0: 7468 6520 6561 726c 6965 7220 6472 6177  the earlier draw\n+000054f0: 696e 672e 2020 416c 6d6f 7374 2061 6e79  ing.  Almost any\n+00005500: 2073 6572 6965 7320 6f66 2027 736b 6574   series of 'sket\n+00005510: 6368 270a 636f 6d6d 616e 6473 2073 7475  ch'.commands stu\n+00005520: 6666 206d 6179 2062 6520 7265 706c 6163  ff may be replac\n+00005530: 6564 2077 6974 6820 6465 6620 666f 6f20  ed with def foo \n+00005540: 7b20 7374 7566 6620 7d20 7b66 6f6f 7d20  { stuff } {foo} \n+00005550: 7769 7468 6f75 740a 6368 616e 6769 6e67  without.changing\n+00005560: 2069 7473 206d 6561 6e69 6e67 2e0a 0a20   its meaning... \n+00005570: 2020 5468 6520 7075 7420 636f 6d6d 616e    The put comman\n+00005580: 6420 7375 7070 6c69 6573 2061 2073 6563  d supplies a sec\n+00005590: 6f6e 6420 7265 6665 7265 6e63 652c 2074  ond reference, t\n+000055a0: 6869 7320 7469 6d65 2077 6974 6820 610a  his time with a.\n+000055b0: 2274 7261 6e73 666f 726d 2220 6170 706c  \"transform\" appl\n+000055c0: 6965 6420 6669 7273 742e 2020 5468 6520  ied first.  The \n+000055d0: 726f 7461 7465 2074 7261 6e73 666f 726d  rotate transform\n+000055e0: 2074 7572 6e73 2074 6865 2074 6574 7261   turns the tetra\n+000055f0: 6865 6472 6f6e 0a39 3020 6465 6772 6565  hedron.90 degree\n+00005600: 7320 6162 6f75 7420 7468 6520 6f72 6967  s about the orig\n+00005610: 696e 2e20 2054 6865 2061 7869 7320 6f66  in.  The axis of\n+00005620: 2072 6f74 6174 696f 6e20 6973 2074 6865   rotation is the\n+00005630: 2076 6563 746f 720a 5b31 2c30 2c30 5d2e   vector.[1,0,0].\n+00005640: 2020 4279 2074 6865 2022 7269 6768 7420    By the \"right \n+00005650: 6861 6e64 2072 756c 6522 2c20 7468 6973  hand rule\", this\n+00005660: 2063 6175 7365 7320 7468 6520 746f 7020   causes the top \n+00005670: 6f66 2074 6865 0a74 6574 7261 6865 6472  of the.tetrahedr\n+00005680: 6f6e 2074 6f20 726f 7461 7465 2074 6f77  on to rotate tow\n+00005690: 6172 6420 7468 6520 7669 6577 6572 2061  ard the viewer a\n+000056a0: 6e64 2074 6865 2062 6f74 746f 6d20 6177  nd the bottom aw\n+000056b0: 6179 2e20 2054 6865 2072 756c 650a 7265  ay.  The rule.re\n+000056c0: 6365 6976 6573 2069 7473 206e 616d 6520  ceives its name \n+000056d0: 6672 6f6d 2074 6865 2066 6f6c 6c6f 7769  from the followi\n+000056e0: 6e67 2064 6566 696e 6974 696f 6e3a 0a20  ng definition:. \n+000056f0: 2020 2020 2a52 6967 6874 2068 616e 6420      *Right hand \n+00005700: 7275 6c65 2e2a 2020 4966 2074 6865 2072  rule.*  If the r\n+00005710: 6967 6874 2068 616e 6420 6973 2077 7261  ight hand is wra\n+00005720: 7070 6564 2061 726f 756e 6420 616e 7920  pped around any \n+00005730: 6178 6973 0a20 2020 2020 7769 7468 2074  axis.     with t\n+00005740: 6865 2074 6875 6d62 2070 6f69 6e74 696e  he thumb pointin\n+00005750: 6720 696e 2074 6865 2061 7869 7320 6469  g in the axis di\n+00005760: 7265 6374 696f 6e2c 2074 6865 6e20 7468  rection, then th\n+00005770: 6520 6669 6e67 6572 730a 2020 2020 2063  e fingers.     c\n+00005780: 7572 6c20 696e 2074 6865 2064 6972 6563  url in the direc\n+00005790: 7469 6f6e 206f 6620 706f 7369 7469 7665  tion of positive\n+000057a0: 2072 6f74 6174 696f 6e20 6162 6f75 7420   rotation about \n+000057b0: 7468 6174 2061 7869 732e 0a20 2020 5468  that axis..   Th\n+000057c0: 6520 7472 616e 736c 6174 6520 7472 616e  e translate tran\n+000057d0: 7366 6f72 6d20 6d6f 7665 7320 7468 6520  sform moves the \n+000057e0: 7079 7261 6d69 6420 6c61 7465 7261 6c6c  pyramid laterall\n+000057f0: 7920 746f 2074 6865 2072 6967 6874 2062  y to the right b\n+00005800: 790a 6164 6469 6e67 2074 6865 2076 6563  y.adding the vec\n+00005810: 746f 7220 5b32 2e35 2c30 2c30 5d20 746f  tor [2.5,0,0] to\n+00005820: 2065 6163 6820 7665 7274 6578 2063 6f6f   each vertex coo\n+00005830: 7264 696e 6174 652e 2020 5468 6520 7265  rdinate.  The re\n+00005840: 7375 6c74 2069 730a 7368 6f77 6e20 6865  sult is.shown he\n+00005850: 7265 2e0a 0a00 085b 696d 6167 6520 7372  re.....[image sr\n+00005860: 633d 2265 7830 3530 2e70 6e67 2220 7465  c=\"ex050.png\" te\n+00005870: 7874 3d22 496d 6167 6520 6578 3035 3020  xt=\"Image ex050 \n+00005880: 6f6d 6974 7465 6420 696e 2074 6578 7420  omitted in text \n+00005890: 7665 7273 696f 6e20 6f66 2074 6869 7320  version of this \n+000058a0: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a1f  document.\"..]...\n+000058b0: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n+000058c0: 666f 2c20 204e 6f64 653a 2052 6570 6561  fo,  Node: Repea\n+000058d0: 7465 6420 6f62 6a65 6374 732c 2020 4e65  ted objects,  Ne\n+000058e0: 7874 3a20 5377 6570 7420 6f62 6a65 6374  xt: Swept object\n+000058f0: 732c 2020 5072 6576 3a20 4f62 6a65 6374  s,  Prev: Object\n+00005900: 2074 7261 6e73 666f 726d 732c 2020 5570   transforms,  Up\n+00005910: 3a20 496e 7472 6f64 7563 7469 6f6e 2062  : Introduction b\n+00005920: 7920 6578 616d 706c 650a 0a32 2e36 2052  y example..2.6 R\n+00005930: 6570 6561 7465 6420 6f62 6a65 6374 730a  epeated objects.\n+00005940: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n+00005950: 3d3d 3d3d 0a0a 546f 2064 7261 7720 7365  ====..To draw se\n+00005960: 7665 6e20 696e 7374 616e 6365 7320 6f66  ven instances of\n+00005970: 2074 6865 2074 6574 7261 6865 6472 6f6e   the tetrahedron\n+00005980: 2c20 6561 6368 2064 6966 6665 7269 6e67  , each differing\n+00005990: 2066 726f 6d20 7468 6520 6c61 7374 0a62   from the last.b\n+000059a0: 7920 7468 6520 7361 6d65 2074 7261 6e73  y the same trans\n+000059b0: 666f 726d 2c20 7265 706c 6163 6520 7468  form, replace th\n+000059c0: 6520 6c61 7374 2074 776f 2063 6f6d 6d61  e last two comma\n+000059d0: 6e64 7320 6f66 2074 6865 2070 7265 7669  nds of the previ\n+000059e0: 6f75 730a 6578 616d 706c 6520 7769 7468  ous.example with\n+000059f0: 0a20 2072 6570 6561 7420 7b20 372c 2072  .  repeat { 7, r\n+00005a00: 6f74 6174 6528 3135 2c20 2830 2c30 2c30  otate(15, (0,0,0\n+00005a10: 292c 205b 312c 302c 305d 2920 2520 636f  ), [1,0,0]) % co\n+00005a20: 7079 2069 6e20 6e65 7720 706f 7369 7469  py in new positi\n+00005a30: 6f6e 0a20 2020 2020 2020 2020 2020 2020  on.             \n+00005a40: 2074 6865 6e20 7472 616e 736c 6174 6528   then translate(\n+00005a50: 5b32 2c30 2c30 5d29 207d 207b 7069 6572  [2,0,0]) } {pier\n+00005a60: 6365 645f 7465 7472 6168 6564 726f 6e7d  ced_tetrahedron}\n+00005a70: 0a41 6e64 2074 6865 2072 6573 756c 742e  .And the result.\n+00005a80: 2e2e 0a0a 0008 5b69 6d61 6765 2073 7263  ......[image src\n+00005a90: 3d22 6578 3036 302e 706e 6722 2074 6578  =\"ex060.png\" tex\n+00005aa0: 743d 2249 6d61 6765 2065 7830 3630 206f  t=\"Image ex060 o\n+00005ab0: 6d69 7474 6564 2069 6e20 7465 7874 2076  mitted in text v\n+00005ac0: 6572 7369 6f6e 206f 6620 7468 6973 2064  ersion of this d\n+00005ad0: 6f63 756d 656e 742e 2200 085d 0a0a 1f0a  ocument.\"..]....\n+00005ae0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n+00005af0: 6f2c 2020 4e6f 6465 3a20 5377 6570 7420  o,  Node: Swept \n+00005b00: 6f62 6a65 6374 732c 2020 5072 6576 3a20  objects,  Prev: \n+00005b10: 5265 7065 6174 6564 206f 626a 6563 7473  Repeated objects\n+00005b20: 2c20 2055 703a 2049 6e74 726f 6475 6374  ,  Up: Introduct\n+00005b30: 696f 6e20 6279 2065 7861 6d70 6c65 0a0a  ion by example..\n+00005b40: 322e 3720 5377 6570 7420 6f62 6a65 6374  2.7 Swept object\n+00005b50: 730a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  s.==============\n+00005b60: 3d3d 3d0a 0a4d 616e 7920 6661 6d69 6c69  ===..Many famili\n+00005b70: 6172 2073 6861 7065 7320 6361 6e20 6265  ar shapes can be\n+00005b80: 2067 656e 6572 6174 6564 2062 7920 7377   generated by sw\n+00005b90: 6565 7069 6e67 2073 696d 706c 6572 206f  eeping simpler o\n+00005ba0: 6e65 7320 7468 726f 7567 680a 7370 6163  nes through.spac\n+00005bb0: 6520 616e 6420 636f 6e73 6964 6572 696e  e and considerin\n+00005bc0: 6720 7468 6520 7265 7375 6c74 696e 6720  g the resulting \n+00005bd0: 7061 7468 2c20 7375 7266 6163 652c 206f  path, surface, o\n+00005be0: 7220 766f 6c75 6d65 2e20 2027 536b 6574  r volume.  'Sket\n+00005bf0: 6368 270a 696d 706c 656d 656e 7473 2074  ch'.implements t\n+00005c00: 6869 7320 6964 6561 2069 6e20 7468 6520  his idea in the \n+00005c10: 7377 6565 7020 636f 6d6d 616e 642e 0a20  sweep command.. \n+00005c20: 2064 6566 206e 5f73 6567 7320 380a 2020   def n_segs 8.  \n+00005c30: 7377 6565 7020 7b20 6e5f 7365 6773 2c20  sweep { n_segs, \n+00005c40: 726f 7461 7465 2831 3830 202f 206e 5f73  rotate(180 / n_s\n+00005c50: 6567 732c 2028 302c 302c 3029 2c20 5b30  egs, (0,0,0), [0\n+00005c60: 2c30 2c31 5d29 207d 2028 312c 302c 3029  ,0,1]) } (1,0,0)\n+00005c70: 0a54 6869 7320 636f 6465 2073 7765 6570  .This code sweep\n+00005c80: 7320 7468 6520 706f 696e 7420 2831 2c30  s the point (1,0\n+00005c90: 2c30 2920 6569 6768 7420 7469 6d65 7320  ,0) eight times \n+00005ca0: 6279 2072 6f74 6174 696e 6720 6974 2031  by rotating it 1\n+00005cb0: 3830 2f38 203d 0a32 322e 3520 6465 6772  80/8 =.22.5 degr\n+00005cc0: 6565 7320 6561 6368 2074 696d 6520 616e  ees each time an\n+00005cd0: 6420 636f 6e6e 6563 7469 6e67 2074 6865  d connecting the\n+00005ce0: 2072 6573 756c 7469 6e67 2070 6f69 6e74   resulting point\n+00005cf0: 7320 7769 7468 206c 696e 650a 7365 676d  s with line.segm\n+00005d00: 656e 7473 2e20 2054 6865 2064 6566 2075  ents.  The def u\n+00005d10: 7365 6420 6865 7265 2069 7320 6120 2273  sed here is a \"s\n+00005d20: 6361 6c61 7222 2064 6566 696e 6974 696f  calar\" definitio\n+00005d30: 6e2e 2020 5265 6665 7265 6e63 6573 2074  n.  References t\n+00005d40: 6f0a 7363 616c 6172 7320 6861 7665 206e  o.scalars have n\n+00005d50: 6f20 656e 636c 6f73 696e 6720 6272 6163  o enclosing brac\n+00005d60: 6b65 7473 2061 7420 616c 6c2e 0a0a 2a20  kets at all...* \n+00005d70: 4d65 6e75 3a0a 0a2a 2050 6f69 6e74 2073  Menu:..* Point s\n+00005d80: 7765 6570 733a 3a20 2020 2020 2020 2020  weeps::         \n+00005d90: 2020 2020 2020 2053 7765 7074 2070 6f69         Swept poi\n+00005da0: 6e74 7320 6d61 6b65 206c 696e 6573 2061  nts make lines a\n+00005db0: 6e64 2070 6f6c 7967 6f6e 732e 0a2a 2050  nd polygons..* P\n+00005dc0: 6f6c 796c 696e 6520 7377 6565 7073 3a3a  olyline sweeps::\n+00005dd0: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n+00005de0: 7074 206c 696e 6573 206d 616b 6520 7375  pt lines make su\n+00005df0: 7266 6163 6573 2e0a 2a20 4e65 7374 6564  rfaces..* Nested\n+00005e00: 2073 7765 6570 733a 3a20 2020 2020 2020   sweeps::       \n+00005e10: 2020 2020 2020 2020 5377 6570 7420 7377          Swept sw\n+00005e20: 6565 7073 2061 7265 2075 7365 6675 6c21  eeps are useful!\n+00005e30: 0a2a 2050 6f6c 7967 6f6e 2073 7765 6570  .* Polygon sweep\n+00005e40: 733a 3a20 2020 2020 2020 2020 2020 2020  s::             \n+00005e50: 2053 7765 7074 2070 6f6c 7967 6f6e 7320   Swept polygons \n+00005e60: 6d61 6b65 2073 6f6c 6964 732e 2e2e 0a2a  make solids....*\n+00005e70: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n+00005e80: 2077 6974 6820 636c 6f73 7572 653a 3a20   with closure:: \n+00005e90: 2061 6e64 2073 6f20 646f 2063 6c6f 7365   and so do close\n+00005ea0: 6420 706f 6c79 6c69 6e65 2073 7765 6570  d polyline sweep\n+00005eb0: 732e 0a2a 2041 6666 696e 6520 6172 6974  s..* Affine arit\n+00005ec0: 686d 6574 6963 3a3a 2020 2020 2020 2020  hmetic::        \n+00005ed0: 2020 2053 6b65 7463 6820 7573 6566 756c     Sketch useful\n+00005ee0: 206d 6174 6820 6578 7072 6573 7369 6f6e   math expression\n+00005ef0: 2e0a 2a20 4d6f 7265 2074 6f20 6c65 6172  ..* More to lear\n+00005f00: 6e3a 3a20 2020 2020 2020 2020 2020 2020  n::             \n+00005f10: 2020 4368 6563 6b20 6f75 7420 7468 6520    Check out the \n+00005f20: 4d6f 6269 7573 2073 7472 6970 210a 0a1f  Mobius strip!...\n+00005f30: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n+00005f40: 666f 2c20 204e 6f64 653a 2050 6f69 6e74  fo,  Node: Point\n+00005f50: 2073 7765 6570 732c 2020 4e65 7874 3a20   sweeps,  Next: \n+00005f60: 506f 6c79 6c69 6e65 2073 7765 6570 732c  Polyline sweeps,\n+00005f70: 2020 5072 6576 3a20 5377 6570 7420 6f62    Prev: Swept ob\n+00005f80: 6a65 6374 732c 2020 5570 3a20 5377 6570  jects,  Up: Swep\n+00005f90: 7420 6f62 6a65 6374 730a 0a32 2e37 2e31  t objects..2.7.1\n+00005fa0: 2050 6f69 6e74 2073 7765 6570 730a 2d2d   Point sweeps.--\n 00005fb0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-00005fc0: 2d2d 0a0a 5377 6565 7069 6e67 2061 2070  --..Sweeping a p\n-00005fd0: 6f69 6e74 206d 616b 6573 2061 206f 6e65  oint makes a one\n-00005fe0: 2d64 696d 656e 7369 6f6e 616c 2070 6174  -dimensional pat\n-00005ff0: 682c 2077 6869 6368 2069 7320 6120 706f  h, which is a po\n-00006000: 6c79 6c69 6e65 2e0a 5369 6e63 6520 7765  lyline..Since we\n-00006010: 2068 6176 6520 7377 6570 7420 7769 7468   have swept with\n-00006020: 2061 2072 6f74 6174 696f 6e2c 2074 6865   a rotation, the\n-00006030: 2072 6573 756c 7420 6973 2061 2063 6972   result is a cir\n-00006040: 6375 6c61 7220 6172 632e 2020 4865 7265  cular arc.  Here\n-00006050: 0a69 7320 7768 6174 2069 7420 6c6f 6f6b  .is what it look\n-00006060: 7320 6c69 6b65 2e0a 0a00 085b 696d 6167  s like.....[imag\n-00006070: 6520 7372 633d 2265 7830 3730 2e70 6e67  e src=\"ex070.png\n-00006080: 2220 7465 7874 3d22 496d 6167 6520 6578  \" text=\"Image ex\n-00006090: 3037 3020 6f6d 6974 7465 6420 696e 2074  070 omitted in t\n-000060a0: 6578 7420 7665 7273 696f 6e20 6f66 2074  ext version of t\n-000060b0: 6869 7320 646f 6375 6d65 6e74 2e22 0008  his document.\"..\n-000060c0: 5d0a 0a20 2020 5468 6973 2069 7320 7468  ]..   This is th\n-000060d0: 6520 6669 7273 7420 6578 616d 706c 6520  e first example \n-000060e0: 7765 2068 6176 6520 7365 656e 206f 6620  we have seen of \n-000060f0: 2773 6b65 7463 6827 2061 7269 7468 6d65  'sketch' arithme\n-00006100: 7469 632e 2020 5468 650a 6578 7072 6573  tic.  The.expres\n-00006110: 7369 6f6e 2031 3830 202f 206e 5f73 6567  sion 180 / n_seg\n-00006120: 7320 6361 7573 6573 2074 6865 2065 6967  s causes the eig\n-00006130: 6874 2072 6f74 6174 696f 6e73 2074 6f20  ht rotations to \n-00006140: 6164 6420 746f 2031 3830 2e20 2049 660a  add to 180.  If.\n-00006150: 796f 7527 7265 2070 6179 696e 6720 6174  you're paying at\n-00006160: 7465 6e74 696f 6e2c 2079 6f75 276c 6c20  tention, you'll \n-00006170: 6861 7665 2061 6c72 6561 6479 206e 6f74  have already not\n-00006180: 6564 2074 6861 7420 7468 6572 6520 6172  ed that there ar\n-00006190: 6520 5f6e 696e 655f 0a70 6f69 6e74 732c  e _nine_.points,\n-000061a0: 2070 726f 6475 6369 6e67 2065 6967 6874   producing eight\n-000061b0: 206c 696e 6520 7365 676d 656e 7473 2e0a   line segments..\n-000061c0: 0a20 2020 596f 7520 6361 6e20 6361 7573  .   You can caus\n-000061d0: 6520 7468 6520 7377 6570 7420 706f 696e  e the swept poin\n-000061e0: 7420 746f 2067 656e 6572 6174 6520 6120  t to generate a \n-000061f0: 7369 6e67 6c65 2070 6f6c 7967 6f6e 2072  single polygon r\n-00006200: 6174 6865 720a 7468 616e 2061 2070 6f6c  ather.than a pol\n-00006210: 796c 696e 6520 6279 2075 7369 6e67 2074  yline by using t\n-00006220: 6865 2022 636c 6f73 7572 6520 7461 6722  he \"closure tag\"\n-00006230: 203c 3e20 6166 7465 7220 7468 6520 6e75   <> after the nu\n-00006240: 6d62 6572 206f 6620 7377 6570 740a 6f62  mber of swept.ob\n-00006250: 6a65 6374 732e 2020 436f 6465 2061 6e64  jects.  Code and\n-00006260: 2072 6573 756c 7420 666f 6c6c 6f77 0a20   result follow. \n-00006270: 2064 6566 206e 5f73 6567 7320 380a 2020   def n_segs 8.  \n-00006280: 7377 6565 7020 7b20 6e5f 7365 6773 3c3e  sweep { n_segs<>\n-00006290: 2c20 726f 7461 7465 2831 3830 202f 206e  , rotate(180 / n\n-000062a0: 5f73 6567 732c 2028 302c 302c 3029 2c20  _segs, (0,0,0), \n-000062b0: 5b30 2c30 2c31 5d29 207d 2028 312c 302c  [0,0,1]) } (1,0,\n-000062c0: 3029 0a00 085b 696d 6167 6520 7372 633d  0)...[image src=\n-000062d0: 2265 7830 3830 2e70 6e67 2220 7465 7874  \"ex080.png\" text\n-000062e0: 3d22 496d 6167 6520 6578 3038 3020 6f6d  =\"Image ex080 om\n-000062f0: 6974 7465 6420 696e 2074 6578 7420 7665  itted in text ve\n-00006300: 7273 696f 6e20 6f66 2074 6869 7320 646f  rsion of this do\n-00006310: 6375 6d65 6e74 2e22 0008 5d0a 0a1f 0a46  cument.\"..]....F\n-00006320: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n-00006330: 2c20 204e 6f64 653a 2050 6f6c 796c 696e  ,  Node: Polylin\n-00006340: 6520 7377 6565 7073 2c20 204e 6578 743a  e sweeps,  Next:\n-00006350: 204e 6573 7465 6420 7377 6565 7073 2c20   Nested sweeps, \n-00006360: 2050 7265 763a 2050 6f69 6e74 2073 7765   Prev: Point swe\n-00006370: 6570 732c 2020 5570 3a20 5377 6570 7420  eps,  Up: Swept \n-00006380: 6f62 6a65 6374 730a 0a32 2e37 2e32 2050  objects..2.7.2 P\n-00006390: 6f6c 796c 696e 6520 7377 6565 7073 0a2d  olyline sweeps.-\n+00005fc0: 0a0a 5377 6565 7069 6e67 2061 2070 6f69  ..Sweeping a poi\n+00005fd0: 6e74 206d 616b 6573 2061 206f 6e65 2d64  nt makes a one-d\n+00005fe0: 696d 656e 7369 6f6e 616c 2070 6174 682c  imensional path,\n+00005ff0: 2077 6869 6368 2069 7320 6120 706f 6c79   which is a poly\n+00006000: 6c69 6e65 2e0a 5369 6e63 6520 7765 2068  line..Since we h\n+00006010: 6176 6520 7377 6570 7420 7769 7468 2061  ave swept with a\n+00006020: 2072 6f74 6174 696f 6e2c 2074 6865 2072   rotation, the r\n+00006030: 6573 756c 7420 6973 2061 2063 6972 6375  esult is a circu\n+00006040: 6c61 7220 6172 632e 2020 4865 7265 0a69  lar arc.  Here.i\n+00006050: 7320 7768 6174 2069 7420 6c6f 6f6b 7320  s what it looks \n+00006060: 6c69 6b65 2e0a 0a00 085b 696d 6167 6520  like.....[image \n+00006070: 7372 633d 2265 7830 3730 2e70 6e67 2220  src=\"ex070.png\" \n+00006080: 7465 7874 3d22 496d 6167 6520 6578 3037  text=\"Image ex07\n+00006090: 3020 6f6d 6974 7465 6420 696e 2074 6578  0 omitted in tex\n+000060a0: 7420 7665 7273 696f 6e20 6f66 2074 6869  t version of thi\n+000060b0: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a  s document.\"..].\n+000060c0: 0a20 2020 5468 6973 2069 7320 7468 6520  .   This is the \n+000060d0: 6669 7273 7420 6578 616d 706c 6520 7765  first example we\n+000060e0: 2068 6176 6520 7365 656e 206f 6620 2773   have seen of 's\n+000060f0: 6b65 7463 6827 2061 7269 7468 6d65 7469  ketch' arithmeti\n+00006100: 632e 2020 5468 650a 6578 7072 6573 7369  c.  The.expressi\n+00006110: 6f6e 2031 3830 202f 206e 5f73 6567 7320  on 180 / n_segs \n+00006120: 6361 7573 6573 2074 6865 2065 6967 6874  causes the eight\n+00006130: 2072 6f74 6174 696f 6e73 2074 6f20 6164   rotations to ad\n+00006140: 6420 746f 2031 3830 2e20 2049 660a 796f  d to 180.  If.yo\n+00006150: 7527 7265 2070 6179 696e 6720 6174 7465  u're paying atte\n+00006160: 6e74 696f 6e2c 2079 6f75 276c 6c20 6861  ntion, you'll ha\n+00006170: 7665 2061 6c72 6561 6479 206e 6f74 6564  ve already noted\n+00006180: 2074 6861 7420 7468 6572 6520 6172 6520   that there are \n+00006190: 5f6e 696e 655f 0a70 6f69 6e74 732c 2070  _nine_.points, p\n+000061a0: 726f 6475 6369 6e67 2065 6967 6874 206c  roducing eight l\n+000061b0: 696e 6520 7365 676d 656e 7473 2e0a 0a20  ine segments... \n+000061c0: 2020 596f 7520 6361 6e20 6361 7573 6520    You can cause \n+000061d0: 7468 6520 7377 6570 7420 706f 696e 7420  the swept point \n+000061e0: 746f 2067 656e 6572 6174 6520 6120 7369  to generate a si\n+000061f0: 6e67 6c65 2070 6f6c 7967 6f6e 2072 6174  ngle polygon rat\n+00006200: 6865 720a 7468 616e 2061 2070 6f6c 796c  her.than a polyl\n+00006210: 696e 6520 6279 2075 7369 6e67 2074 6865  ine by using the\n+00006220: 2022 636c 6f73 7572 6520 7461 6722 203c   \"closure tag\" <\n+00006230: 3e20 6166 7465 7220 7468 6520 6e75 6d62  > after the numb\n+00006240: 6572 206f 6620 7377 6570 740a 6f62 6a65  er of swept.obje\n+00006250: 6374 732e 2020 436f 6465 2061 6e64 2072  cts.  Code and r\n+00006260: 6573 756c 7420 666f 6c6c 6f77 0a20 2064  esult follow.  d\n+00006270: 6566 206e 5f73 6567 7320 380a 2020 7377  ef n_segs 8.  sw\n+00006280: 6565 7020 7b20 6e5f 7365 6773 3c3e 2c20  eep { n_segs<>, \n+00006290: 726f 7461 7465 2831 3830 202f 206e 5f73  rotate(180 / n_s\n+000062a0: 6567 732c 2028 302c 302c 3029 2c20 5b30  egs, (0,0,0), [0\n+000062b0: 2c30 2c31 5d29 207d 2028 312c 302c 3029  ,0,1]) } (1,0,0)\n+000062c0: 0a00 085b 696d 6167 6520 7372 633d 2265  ...[image src=\"e\n+000062d0: 7830 3830 2e70 6e67 2220 7465 7874 3d22  x080.png\" text=\"\n+000062e0: 496d 6167 6520 6578 3038 3020 6f6d 6974  Image ex080 omit\n+000062f0: 7465 6420 696e 2074 6578 7420 7665 7273  ted in text vers\n+00006300: 696f 6e20 6f66 2074 6869 7320 646f 6375  ion of this docu\n+00006310: 6d65 6e74 2e22 0008 5d0a 0a1f 0a46 696c  ment.\"..]....Fil\n+00006320: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n+00006330: 204e 6f64 653a 2050 6f6c 796c 696e 6520   Node: Polyline \n+00006340: 7377 6565 7073 2c20 204e 6578 743a 204e  sweeps,  Next: N\n+00006350: 6573 7465 6420 7377 6565 7073 2c20 2050  ested sweeps,  P\n+00006360: 7265 763a 2050 6f69 6e74 2073 7765 6570  rev: Point sweep\n+00006370: 732c 2020 5570 3a20 5377 6570 7420 6f62  s,  Up: Swept ob\n+00006380: 6a65 6374 730a 0a32 2e37 2e32 2050 6f6c  jects..2.7.2 Pol\n+00006390: 796c 696e 6520 7377 6565 7073 0a2d 2d2d  yline sweeps.---\n 000063a0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-000063b0: 2d2d 2d2d 0a0a 5377 6565 7069 6e67 2061  ----..Sweeping a\n-000063c0: 2070 6f6c 796c 696e 6520 7072 6f64 7563   polyline produc\n-000063d0: 6573 2061 2073 7572 6661 6365 2063 6f6d  es a surface com\n-000063e0: 706f 7365 6420 6f66 206d 616e 7920 6661  posed of many fa\n-000063f0: 6365 732e 2020 5468 650a 756e 6272 6f6b  ces.  The.unbrok\n-00006400: 656e 2068 656c 6978 2069 6e20 7468 6520  en helix in the \n-00006410: 6578 616d 706c 6520 2a6e 6f74 6520 4865  example *note He\n-00006420: 6c69 7820 7769 7468 2063 756c 6c20 7365  lix with cull se\n-00006430: 7420 6661 6c73 6520 7468 656e 0a74 7275  t false then.tru\n-00006440: 653a 3a20 6973 2070 726f 6475 6365 6420  e:: is produced \n-00006450: 6279 2074 6869 7320 636f 6465 2028 706c  by this code (pl\n-00006460: 7573 2061 2073 7572 726f 756e 6469 6e67  us a surrounding\n-00006470: 2070 7574 2072 6f74 6174 696f 6e20 746f   put rotation to\n-00006480: 206d 616b 650a 616e 2069 6e74 6572 6573   make.an interes\n-00006490: 7469 6e67 2076 6965 773b 2074 6869 7320  ting view; this \n-000064a0: 6861 7320 6265 656e 206f 6d69 7474 6564  has been omitted\n-000064b0: 292e 0a20 2064 6566 204b 205b 302c 302c  )..  def K [0,0,\n-000064c0: 315d 0a20 2073 7765 6570 5b63 756c 6c3d  1].  sweep[cull=\n-000064d0: 6661 6c73 655d 207b 0a20 2020 2036 302c  false] {.    60,\n-000064e0: 200a 2020 2020 726f 7461 7465 2831 302c   .    rotate(10,\n-000064f0: 2028 302c 302c 3029 2c20 5b4b 5d29 2074   (0,0,0), [K]) t\n-00006500: 6865 6e20 7472 616e 736c 6174 6528 312f  hen translate(1/\n-00006510: 3620 2a20 5b4b 5d29 200a 2020 7d20 6c69  6 * [K]) .  } li\n-00006520: 6e65 5b6c 696e 6577 6964 7468 3d32 7074  ne[linewidth=2pt\n-00006530: 5d28 2d31 2c30 2928 312c 3029 0a41 6761  ](-1,0)(1,0).Aga\n-00006540: 696e 2c20 3630 2073 6567 6d65 6e74 7320  in, 60 segments \n-00006550: 6f66 2074 6865 2068 656c 6978 2061 7265  of the helix are\n-00006560: 2070 726f 6475 6365 6420 6279 2063 6f6e   produced by con\n-00006570: 6e65 6374 696e 6720 3631 2069 6e73 7461  necting 61 insta\n-00006580: 6e63 6573 0a6f 6620 7468 6520 7377 6570  nces.of the swep\n-00006590: 7420 6c69 6e65 2e20 204f 7074 696f 6e73  t line.  Options\n-000065a0: 2061 7070 6c69 6564 2074 6f20 7468 6520   applied to the \n-000065b0: 7377 6565 702c 2068 6572 6520 6375 6c6c  sweep, here cull\n-000065c0: 3d66 616c 7365 2c20 6172 650a 7472 6561  =false, are.trea\n-000065d0: 7465 6420 6173 206f 7074 696f 6e73 2066  ted as options f\n-000065e0: 6f72 2074 6865 2067 656e 6572 6174 6564  or the generated\n-000065f0: 2070 6f6c 7967 6f6e 206f 7220 706f 6c79   polygon or poly\n-00006600: 6c69 6e65 2e20 204f 7074 696f 6e73 206f  line.  Options o\n-00006610: 660a 7468 6520 7377 6570 7420 6c69 6e65  f.the swept line\n-00006620: 2069 7473 656c 662c 2068 6572 6520 6c69   itself, here li\n-00006630: 6e65 7769 6474 683d 3270 742c 2061 7265  newidth=2pt, are\n-00006640: 2069 676e 6f72 6564 2c20 7468 6f75 6768   ignored, though\n-00006650: 2077 6974 6820 610a 7761 726e 696e 672e   with a.warning.\n-00006660: 2020 5468 6973 2064 6566 2069 7320 6120    This def is a \n-00006670: 2276 6563 746f 7222 2064 6566 696e 6974  \"vector\" definit\n-00006680: 696f 6e2c 2077 6869 6368 206d 7573 7420  ion, which must \n-00006690: 6265 2072 6566 6572 656e 6365 640a 7769  be referenced.wi\n-000066a0: 7468 2073 7175 6172 6520 6272 6163 6b65  th square bracke\n-000066b0: 7473 2c20 652e 672e 205b 666f 6f5d 2e0a  ts, e.g. [foo]..\n-000066c0: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n-000066d0: 696e 666f 2c20 204e 6f64 653a 204e 6573  info,  Node: Nes\n-000066e0: 7465 6420 7377 6565 7073 2c20 204e 6578  ted sweeps,  Nex\n-000066f0: 743a 2050 6f6c 7967 6f6e 2073 7765 6570  t: Polygon sweep\n-00006700: 732c 2020 5072 6576 3a20 506f 6c79 6c69  s,  Prev: Polyli\n-00006710: 6e65 2073 7765 6570 732c 2020 5570 3a20  ne sweeps,  Up: \n-00006720: 5377 6570 7420 6f62 6a65 6374 730a 0a32  Swept objects..2\n-00006730: 2e37 2e33 204e 6573 7465 6420 7377 6565  .7.3 Nested swee\n-00006740: 7073 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ps.-------------\n-00006750: 2d2d 2d2d 2d2d 0a0a 5768 656e 2074 6865  ------..When the\n-00006760: 2063 656e 7465 7220 706f 696e 7420 6f66   center point of\n-00006770: 2072 6f74 6174 696f 6e20 6973 206f 6d69   rotation is omi\n-00006780: 7474 6564 2c20 7468 6520 6f72 6967 696e  tted, the origin\n-00006790: 2069 7320 6173 7375 6d65 642e 0a57 6865   is assumed..Whe\n-000067a0: 6e20 6120 706f 696e 7420 6861 7320 6f6e  n a point has on\n-000067b0: 6c79 2074 776f 2063 6f6f 7264 696e 6174  ly two coordinat\n-000067c0: 6573 2c20 7468 6579 2061 7265 2074 616b  es, they are tak\n-000067d0: 656e 2061 7320 7820 616e 6420 792c 2077  en as x and y, w\n-000067e0: 6974 680a 7a3d 3020 6173 7375 6d65 642e  ith.z=0 assumed.\n-000067f0: 2020 4120 746f 726f 6964 2069 7320 7468    A toroid is th\n-00006800: 6572 6566 6f72 6520 6f62 7461 696e 6564  erefore obtained\n-00006810: 2077 6974 6820 7468 6973 2063 6f64 652e   with this code.\n-00006820: 0a20 2064 6566 206e 5f74 6f72 6f69 645f  .  def n_toroid_\n-00006830: 7365 6773 2032 3020 2020 6465 6620 6e5f  segs 20   def n_\n-00006840: 6369 7263 6c65 5f73 6567 7320 3136 0a20  circle_segs 16. \n-00006850: 2064 6566 2072 5f6d 696e 6f72 2031 2020   def r_minor 1  \n-00006860: 2020 2020 2020 2020 6465 6620 725f 6d61          def r_ma\n-00006870: 6a6f 7220 312e 350a 2020 7377 6565 7020  jor 1.5.  sweep \n-00006880: 7b20 6e5f 746f 726f 6964 5f73 6567 732c  { n_toroid_segs,\n-00006890: 2072 6f74 6174 6528 3336 3020 2f20 6e5f   rotate(360 / n_\n-000068a0: 746f 726f 6964 5f73 6567 732c 205b 302c  toroid_segs, [0,\n-000068b0: 312c 305d 2920 7d0a 2020 2020 7377 6565  1,0]) }.    swee\n-000068c0: 7020 7b20 6e5f 6369 7263 6c65 5f73 6567  p { n_circle_seg\n-000068d0: 732c 2072 6f74 6174 6528 3336 3020 2f20  s, rotate(360 / \n-000068e0: 6e5f 6369 7263 6c65 5f73 6567 732c 2028  n_circle_segs, (\n-000068f0: 725f 6d61 6a6f 722c 302c 3029 2920 7d20  r_major,0,0)) } \n-00006900: 0a20 2020 2020 2028 725f 6d61 6a6f 7220  .      (r_major \n-00006910: 2b20 725f 6d69 6e6f 722c 2030 290a 2020  + r_minor, 0).  \n-00006920: 2046 6f72 2069 6e74 7569 7469 6f6e 2c20   For intuition, \n-00006930: 7468 6520 6964 6561 206f 6620 7468 6520  the idea of the \n-00006940: 636f 6465 2069 7320 746f 2073 6b65 7463  code is to sketc\n-00006950: 6820 6120 6369 7263 6c65 2074 6f20 7468  h a circle to th\n-00006960: 650a 7269 6768 7420 6f66 2074 6865 206f  e.right of the o\n-00006970: 7269 6769 6e20 696e 2074 6865 2078 792d  rigin in the xy-\n-00006980: 706c 616e 652c 2074 6865 6e20 726f 7461  plane, then rota\n-00006990: 7465 2074 6861 7420 6369 7263 6c65 2022  te that circle \"\n-000069a0: 6f75 7420 6f66 2074 6865 0a70 6c61 6e65  out of the.plane\n-000069b0: 2220 6162 6f75 7420 7468 6520 792d 6178  \" about the y-ax\n-000069c0: 6973 2074 6f20 6d61 6b65 2074 6865 2066  is to make the f\n-000069d0: 696e 616c 2066 6967 7572 652e 2020 5468  inal figure.  Th\n-000069e0: 6973 2070 726f 6475 6365 7320 7468 650a  is produces the.\n-000069f0: 666f 6c6c 6f77 696e 672e 2020 2841 2076  following.  (A v\n-00006a00: 6965 7720 726f 7461 7469 6f6e 2061 6e64  iew rotation and\n-00006a10: 2073 6f6d 6520 6178 6573 2068 6176 6520   some axes have \n-00006a20: 6265 656e 2061 6464 6564 2e29 0a0a 0008  been added.)....\n-00006a30: 5b69 6d61 6765 2073 7263 3d22 6578 3039  [image src=\"ex09\n-00006a40: 302e 706e 6722 2074 6578 743d 2249 6d61  0.png\" text=\"Ima\n-00006a50: 6765 2065 7830 3930 206f 6d69 7474 6564  ge ex090 omitted\n-00006a60: 2069 6e20 7465 7874 2076 6572 7369 6f6e   in text version\n-00006a70: 206f 6620 7468 6973 2064 6f63 756d 656e   of this documen\n-00006a80: 742e 2200 085d 0a0a 2020 2054 6869 7320  t.\"..]..   This \n-00006a90: 6578 616d 706c 6520 616c 736f 2073 686f  example also sho\n-00006aa0: 7773 2074 6861 7420 7468 6520 7377 6570  ws that the swep\n-00006ab0: 7420 6f62 6a65 6374 206d 6179 2069 7473  t object may its\n-00006ac0: 656c 6620 6265 2061 6e6f 7468 6572 0a27  elf be another.'\n-00006ad0: 7377 6565 7027 2e20 2049 6e20 6661 6374  sweep'.  In fact\n-00006ae0: 2c20 6974 206d 6179 2062 6520 5f61 6e79  , it may be _any\n-00006af0: 5f20 2773 6b65 7463 6827 2065 7870 7265  _ 'sketch' expre\n-00006b00: 7373 696f 6e20 7468 6174 2072 6573 756c  ssion that resul\n-00006b10: 7473 2069 6e20 610a 6c69 7374 206f 6620  ts in a.list of \n-00006b20: 6f6e 6520 6f72 206d 6f72 6520 706f 696e  one or more poin\n-00006b30: 7473 206f 722c 2061 6c74 6572 6e61 7465  ts or, alternate\n-00006b40: 6c79 2c20 6120 6c69 7374 206f 6620 6f6e  ly, a list of on\n-00006b50: 6520 6f72 206d 6f72 650a 706f 6c79 6c69  e or more.polyli\n-00006b60: 6e65 7320 616e 6420 706f 6c79 676f 6e73  nes and polygons\n-00006b70: 2e20 2054 6865 206c 6174 7465 7220 6b69  .  The latter ki\n-00006b80: 6e64 206f 6620 6c69 7374 2063 616e 2062  nd of list can b\n-00006b90: 6520 6372 6561 7465 6420 7769 7468 2061  e created with a\n-00006ba0: 0a7b 207d 2d65 6e63 6c6f 7365 6420 626c  .{ }-enclosed bl\n-00006bb0: 6f63 6b2c 2070 6572 6861 7073 2066 6f6c  ock, perhaps fol\n-00006bc0: 6c6f 7769 6e67 2061 2070 7574 206f 7220  lowing a put or \n-00006bd0: 7265 7065 6174 2e0a 0a1f 0a46 696c 653a  repeat.....File:\n-00006be0: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n-00006bf0: 6f64 653a 2050 6f6c 7967 6f6e 2073 7765  ode: Polygon swe\n-00006c00: 6570 732c 2020 4e65 7874 3a20 506f 6c79  eps,  Next: Poly\n-00006c10: 6c69 6e65 2073 7765 6570 7320 7769 7468  line sweeps with\n-00006c20: 2063 6c6f 7375 7265 2c20 2050 7265 763a   closure,  Prev:\n-00006c30: 204e 6573 7465 6420 7377 6565 7073 2c20   Nested sweeps, \n-00006c40: 2055 703a 2053 7765 7074 206f 626a 6563   Up: Swept objec\n-00006c50: 7473 0a0a 322e 372e 3420 506f 6c79 676f  ts..2.7.4 Polygo\n-00006c60: 6e20 7377 6565 7073 0a2d 2d2d 2d2d 2d2d  n sweeps.-------\n-00006c70: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a53  -------------..S\n-00006c80: 7765 6570 696e 6720 6120 706f 6c79 676f  weeping a polygo\n-00006c90: 6e20 6372 6561 7465 7320 6120 636c 6f73  n creates a clos\n-00006ca0: 6564 2073 7572 6661 6365 2077 6974 6820  ed surface with \n-00006cb0: 706f 6c79 676f 6e73 2061 7420 7468 6520  polygons at the \n-00006cc0: 656e 6473 2c0a 7768 6963 6820 6172 6520  ends,.which are \n-00006cd0: 6a75 7374 2063 6f70 6965 7320 6f66 2074  just copies of t\n-00006ce0: 6865 206f 7269 6769 6e61 6c2c 2061 7070  he original, app\n-00006cf0: 726f 7072 6961 7465 6c79 2070 6f73 6974  ropriately posit\n-00006d00: 696f 6e65 642e 2020 2a4e 6f74 650a 536f  ioned.  *Note.So\n-00006d10: 6c69 6420 636f 696c 2065 7861 6d70 6c65  lid coil example\n-00006d20: 3a3a 2e20 204f 7074 696f 6e73 206f 6e20  ::.  Options on \n-00006d30: 7468 6520 7377 6570 7420 706f 6c79 676f  the swept polygo\n-00006d40: 6e2c 2069 6620 7468 6579 2065 7869 7374  n, if they exist\n-00006d50: 2c20 6172 650a 6170 706c 6965 6420 746f  , are.applied to\n-00006d60: 2074 6865 2065 6e64 732e 2020 4f74 6865   the ends.  Othe\n-00006d70: 7277 6973 6520 7468 6520 7377 6565 7020  rwise the sweep \n-00006d80: 6f70 7469 6f6e 7320 6172 6520 7573 6564  options are used\n-00006d90: 2074 6872 6f75 6768 6f75 742e 0a0a 1f0a   throughout.....\n-00006da0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n-00006db0: 6f2c 2020 4e6f 6465 3a20 506f 6c79 6c69  o,  Node: Polyli\n-00006dc0: 6e65 2073 7765 6570 7320 7769 7468 2063  ne sweeps with c\n-00006dd0: 6c6f 7375 7265 2c20 204e 6578 743a 2041  losure,  Next: A\n-00006de0: 6666 696e 6520 6172 6974 686d 6574 6963  ffine arithmetic\n-00006df0: 2c20 2050 7265 763a 2050 6f6c 7967 6f6e  ,  Prev: Polygon\n-00006e00: 2073 7765 6570 732c 2020 5570 3a20 5377   sweeps,  Up: Sw\n-00006e10: 6570 7420 6f62 6a65 6374 730a 0a32 2e37  ept objects..2.7\n-00006e20: 2e35 2050 6f6c 796c 696e 6520 7377 6565  .5 Polyline swee\n-00006e30: 7073 2077 6974 6820 636c 6f73 7572 650a  ps with closure.\n+000063b0: 2d2d 0a0a 5377 6565 7069 6e67 2061 2070  --..Sweeping a p\n+000063c0: 6f6c 796c 696e 6520 7072 6f64 7563 6573  olyline produces\n+000063d0: 2061 2073 7572 6661 6365 2063 6f6d 706f   a surface compo\n+000063e0: 7365 6420 6f66 206d 616e 7920 6661 6365  sed of many face\n+000063f0: 732e 2020 5468 650a 756e 6272 6f6b 656e  s.  The.unbroken\n+00006400: 2068 656c 6978 2069 6e20 7468 6520 6578   helix in the ex\n+00006410: 616d 706c 6520 2a6e 6f74 6520 4865 6c69  ample *note Heli\n+00006420: 7820 7769 7468 2063 756c 6c20 7365 7420  x with cull set \n+00006430: 6661 6c73 6520 7468 656e 0a74 7275 653a  false then.true:\n+00006440: 3a20 6973 2070 726f 6475 6365 6420 6279  : is produced by\n+00006450: 2074 6869 7320 636f 6465 2028 706c 7573   this code (plus\n+00006460: 2061 2073 7572 726f 756e 6469 6e67 2070   a surrounding p\n+00006470: 7574 2072 6f74 6174 696f 6e20 746f 206d  ut rotation to m\n+00006480: 616b 650a 616e 2069 6e74 6572 6573 7469  ake.an interesti\n+00006490: 6e67 2076 6965 773b 2074 6869 7320 6861  ng view; this ha\n+000064a0: 7320 6265 656e 206f 6d69 7474 6564 292e  s been omitted).\n+000064b0: 0a20 2064 6566 204b 205b 302c 302c 315d  .  def K [0,0,1]\n+000064c0: 0a20 2073 7765 6570 5b63 756c 6c3d 6661  .  sweep[cull=fa\n+000064d0: 6c73 655d 207b 0a20 2020 2036 302c 200a  lse] {.    60, .\n+000064e0: 2020 2020 726f 7461 7465 2831 302c 2028      rotate(10, (\n+000064f0: 302c 302c 3029 2c20 5b4b 5d29 2074 6865  0,0,0), [K]) the\n+00006500: 6e20 7472 616e 736c 6174 6528 312f 3620  n translate(1/6 \n+00006510: 2a20 5b4b 5d29 200a 2020 7d20 6c69 6e65  * [K]) .  } line\n+00006520: 5b6c 696e 6577 6964 7468 3d32 7074 5d28  [linewidth=2pt](\n+00006530: 2d31 2c30 2928 312c 3029 0a41 6761 696e  -1,0)(1,0).Again\n+00006540: 2c20 3630 2073 6567 6d65 6e74 7320 6f66  , 60 segments of\n+00006550: 2074 6865 2068 656c 6978 2061 7265 2070   the helix are p\n+00006560: 726f 6475 6365 6420 6279 2063 6f6e 6e65  roduced by conne\n+00006570: 6374 696e 6720 3631 2069 6e73 7461 6e63  cting 61 instanc\n+00006580: 6573 0a6f 6620 7468 6520 7377 6570 7420  es.of the swept \n+00006590: 6c69 6e65 2e20 204f 7074 696f 6e73 2061  line.  Options a\n+000065a0: 7070 6c69 6564 2074 6f20 7468 6520 7377  pplied to the sw\n+000065b0: 6565 702c 2068 6572 6520 6375 6c6c 3d66  eep, here cull=f\n+000065c0: 616c 7365 2c20 6172 650a 7472 6561 7465  alse, are.treate\n+000065d0: 6420 6173 206f 7074 696f 6e73 2066 6f72  d as options for\n+000065e0: 2074 6865 2067 656e 6572 6174 6564 2070   the generated p\n+000065f0: 6f6c 7967 6f6e 206f 7220 706f 6c79 6c69  olygon or polyli\n+00006600: 6e65 2e20 204f 7074 696f 6e73 206f 660a  ne.  Options of.\n+00006610: 7468 6520 7377 6570 7420 6c69 6e65 2069  the swept line i\n+00006620: 7473 656c 662c 2068 6572 6520 6c69 6e65  tself, here line\n+00006630: 7769 6474 683d 3270 742c 2061 7265 2069  width=2pt, are i\n+00006640: 676e 6f72 6564 2c20 7468 6f75 6768 2077  gnored, though w\n+00006650: 6974 6820 610a 7761 726e 696e 672e 2020  ith a.warning.  \n+00006660: 5468 6973 2064 6566 2069 7320 6120 2276  This def is a \"v\n+00006670: 6563 746f 7222 2064 6566 696e 6974 696f  ector\" definitio\n+00006680: 6e2c 2077 6869 6368 206d 7573 7420 6265  n, which must be\n+00006690: 2072 6566 6572 656e 6365 640a 7769 7468   referenced.with\n+000066a0: 2073 7175 6172 6520 6272 6163 6b65 7473   square brackets\n+000066b0: 2c20 652e 672e 205b 666f 6f5d 2e0a 0a1f  , e.g. [foo]....\n+000066c0: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n+000066d0: 666f 2c20 204e 6f64 653a 204e 6573 7465  fo,  Node: Neste\n+000066e0: 6420 7377 6565 7073 2c20 204e 6578 743a  d sweeps,  Next:\n+000066f0: 2050 6f6c 7967 6f6e 2073 7765 6570 732c   Polygon sweeps,\n+00006700: 2020 5072 6576 3a20 506f 6c79 6c69 6e65    Prev: Polyline\n+00006710: 2073 7765 6570 732c 2020 5570 3a20 5377   sweeps,  Up: Sw\n+00006720: 6570 7420 6f62 6a65 6374 730a 0a32 2e37  ept objects..2.7\n+00006730: 2e33 204e 6573 7465 6420 7377 6565 7073  .3 Nested sweeps\n+00006740: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  .---------------\n+00006750: 2d2d 2d2d 0a0a 5768 656e 2074 6865 2063  ----..When the c\n+00006760: 656e 7465 7220 706f 696e 7420 6f66 2072  enter point of r\n+00006770: 6f74 6174 696f 6e20 6973 206f 6d69 7474  otation is omitt\n+00006780: 6564 2c20 7468 6520 6f72 6967 696e 2069  ed, the origin i\n+00006790: 7320 6173 7375 6d65 642e 0a57 6865 6e20  s assumed..When \n+000067a0: 6120 706f 696e 7420 6861 7320 6f6e 6c79  a point has only\n+000067b0: 2074 776f 2063 6f6f 7264 696e 6174 6573   two coordinates\n+000067c0: 2c20 7468 6579 2061 7265 2074 616b 656e  , they are taken\n+000067d0: 2061 7320 7820 616e 6420 792c 2077 6974   as x and y, wit\n+000067e0: 680a 7a3d 3020 6173 7375 6d65 642e 2020  h.z=0 assumed.  \n+000067f0: 4120 746f 726f 6964 2069 7320 7468 6572  A toroid is ther\n+00006800: 6566 6f72 6520 6f62 7461 696e 6564 2077  efore obtained w\n+00006810: 6974 6820 7468 6973 2063 6f64 652e 0a20  ith this code.. \n+00006820: 2064 6566 206e 5f74 6f72 6f69 645f 7365   def n_toroid_se\n+00006830: 6773 2032 3020 2020 6465 6620 6e5f 6369  gs 20   def n_ci\n+00006840: 7263 6c65 5f73 6567 7320 3136 0a20 2064  rcle_segs 16.  d\n+00006850: 6566 2072 5f6d 696e 6f72 2031 2020 2020  ef r_minor 1    \n+00006860: 2020 2020 2020 6465 6620 725f 6d61 6a6f        def r_majo\n+00006870: 7220 312e 350a 2020 7377 6565 7020 7b20  r 1.5.  sweep { \n+00006880: 6e5f 746f 726f 6964 5f73 6567 732c 2072  n_toroid_segs, r\n+00006890: 6f74 6174 6528 3336 3020 2f20 6e5f 746f  otate(360 / n_to\n+000068a0: 726f 6964 5f73 6567 732c 205b 302c 312c  roid_segs, [0,1,\n+000068b0: 305d 2920 7d0a 2020 2020 7377 6565 7020  0]) }.    sweep \n+000068c0: 7b20 6e5f 6369 7263 6c65 5f73 6567 732c  { n_circle_segs,\n+000068d0: 2072 6f74 6174 6528 3336 3020 2f20 6e5f   rotate(360 / n_\n+000068e0: 6369 7263 6c65 5f73 6567 732c 2028 725f  circle_segs, (r_\n+000068f0: 6d61 6a6f 722c 302c 3029 2920 7d20 0a20  major,0,0)) } . \n+00006900: 2020 2020 2028 725f 6d61 6a6f 7220 2b20       (r_major + \n+00006910: 725f 6d69 6e6f 722c 2030 290a 2020 2046  r_minor, 0).   F\n+00006920: 6f72 2069 6e74 7569 7469 6f6e 2c20 7468  or intuition, th\n+00006930: 6520 6964 6561 206f 6620 7468 6520 636f  e idea of the co\n+00006940: 6465 2069 7320 746f 2073 6b65 7463 6820  de is to sketch \n+00006950: 6120 6369 7263 6c65 2074 6f20 7468 650a  a circle to the.\n+00006960: 7269 6768 7420 6f66 2074 6865 206f 7269  right of the ori\n+00006970: 6769 6e20 696e 2074 6865 2078 792d 706c  gin in the xy-pl\n+00006980: 616e 652c 2074 6865 6e20 726f 7461 7465  ane, then rotate\n+00006990: 2074 6861 7420 6369 7263 6c65 2022 6f75   that circle \"ou\n+000069a0: 7420 6f66 2074 6865 0a70 6c61 6e65 2220  t of the.plane\" \n+000069b0: 6162 6f75 7420 7468 6520 792d 6178 6973  about the y-axis\n+000069c0: 2074 6f20 6d61 6b65 2074 6865 2066 696e   to make the fin\n+000069d0: 616c 2066 6967 7572 652e 2020 5468 6973  al figure.  This\n+000069e0: 2070 726f 6475 6365 7320 7468 650a 666f   produces the.fo\n+000069f0: 6c6c 6f77 696e 672e 2020 2841 2076 6965  llowing.  (A vie\n+00006a00: 7720 726f 7461 7469 6f6e 2061 6e64 2073  w rotation and s\n+00006a10: 6f6d 6520 6178 6573 2068 6176 6520 6265  ome axes have be\n+00006a20: 656e 2061 6464 6564 2e29 0a0a 0008 5b69  en added.)....[i\n+00006a30: 6d61 6765 2073 7263 3d22 6578 3039 302e  mage src=\"ex090.\n+00006a40: 706e 6722 2074 6578 743d 2249 6d61 6765  png\" text=\"Image\n+00006a50: 2065 7830 3930 206f 6d69 7474 6564 2069   ex090 omitted i\n+00006a60: 6e20 7465 7874 2076 6572 7369 6f6e 206f  n text version o\n+00006a70: 6620 7468 6973 2064 6f63 756d 656e 742e  f this document.\n+00006a80: 2200 085d 0a0a 2020 2054 6869 7320 6578  \"..]..   This ex\n+00006a90: 616d 706c 6520 616c 736f 2073 686f 7773  ample also shows\n+00006aa0: 2074 6861 7420 7468 6520 7377 6570 7420   that the swept \n+00006ab0: 6f62 6a65 6374 206d 6179 2069 7473 656c  object may itsel\n+00006ac0: 6620 6265 2061 6e6f 7468 6572 0a27 7377  f be another.'sw\n+00006ad0: 6565 7027 2e20 2049 6e20 6661 6374 2c20  eep'.  In fact, \n+00006ae0: 6974 206d 6179 2062 6520 5f61 6e79 5f20  it may be _any_ \n+00006af0: 2773 6b65 7463 6827 2065 7870 7265 7373  'sketch' express\n+00006b00: 696f 6e20 7468 6174 2072 6573 756c 7473  ion that results\n+00006b10: 2069 6e20 610a 6c69 7374 206f 6620 6f6e   in a.list of on\n+00006b20: 6520 6f72 206d 6f72 6520 706f 696e 7473  e or more points\n+00006b30: 206f 722c 2061 6c74 6572 6e61 7465 6c79   or, alternately\n+00006b40: 2c20 6120 6c69 7374 206f 6620 6f6e 6520  , a list of one \n+00006b50: 6f72 206d 6f72 650a 706f 6c79 6c69 6e65  or more.polyline\n+00006b60: 7320 616e 6420 706f 6c79 676f 6e73 2e20  s and polygons. \n+00006b70: 2054 6865 206c 6174 7465 7220 6b69 6e64   The latter kind\n+00006b80: 206f 6620 6c69 7374 2063 616e 2062 6520   of list can be \n+00006b90: 6372 6561 7465 6420 7769 7468 2061 0a7b  created with a.{\n+00006ba0: 207d 2d65 6e63 6c6f 7365 6420 626c 6f63   }-enclosed bloc\n+00006bb0: 6b2c 2070 6572 6861 7073 2066 6f6c 6c6f  k, perhaps follo\n+00006bc0: 7769 6e67 2061 2070 7574 206f 7220 7265  wing a put or re\n+00006bd0: 7065 6174 2e0a 0a1f 0a46 696c 653a 2073  peat.....File: s\n+00006be0: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n+00006bf0: 653a 2050 6f6c 7967 6f6e 2073 7765 6570  e: Polygon sweep\n+00006c00: 732c 2020 4e65 7874 3a20 506f 6c79 6c69  s,  Next: Polyli\n+00006c10: 6e65 2073 7765 6570 7320 7769 7468 2063  ne sweeps with c\n+00006c20: 6c6f 7375 7265 2c20 2050 7265 763a 204e  losure,  Prev: N\n+00006c30: 6573 7465 6420 7377 6565 7073 2c20 2055  ested sweeps,  U\n+00006c40: 703a 2053 7765 7074 206f 626a 6563 7473  p: Swept objects\n+00006c50: 0a0a 322e 372e 3420 506f 6c79 676f 6e20  ..2.7.4 Polygon \n+00006c60: 7377 6565 7073 0a2d 2d2d 2d2d 2d2d 2d2d  sweeps.---------\n+00006c70: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a53 7765  -----------..Swe\n+00006c80: 6570 696e 6720 6120 706f 6c79 676f 6e20  eping a polygon \n+00006c90: 6372 6561 7465 7320 6120 636c 6f73 6564  creates a closed\n+00006ca0: 2073 7572 6661 6365 2077 6974 6820 706f   surface with po\n+00006cb0: 6c79 676f 6e73 2061 7420 7468 6520 656e  lygons at the en\n+00006cc0: 6473 2c0a 7768 6963 6820 6172 6520 6a75  ds,.which are ju\n+00006cd0: 7374 2063 6f70 6965 7320 6f66 2074 6865  st copies of the\n+00006ce0: 206f 7269 6769 6e61 6c2c 2061 7070 726f   original, appro\n+00006cf0: 7072 6961 7465 6c79 2070 6f73 6974 696f  priately positio\n+00006d00: 6e65 642e 2020 2a4e 6f74 650a 536f 6c69  ned.  *Note.Soli\n+00006d10: 6420 636f 696c 2065 7861 6d70 6c65 3a3a  d coil example::\n+00006d20: 2e20 204f 7074 696f 6e73 206f 6e20 7468  .  Options on th\n+00006d30: 6520 7377 6570 7420 706f 6c79 676f 6e2c  e swept polygon,\n+00006d40: 2069 6620 7468 6579 2065 7869 7374 2c20   if they exist, \n+00006d50: 6172 650a 6170 706c 6965 6420 746f 2074  are.applied to t\n+00006d60: 6865 2065 6e64 732e 2020 4f74 6865 7277  he ends.  Otherw\n+00006d70: 6973 6520 7468 6520 7377 6565 7020 6f70  ise the sweep op\n+00006d80: 7469 6f6e 7320 6172 6520 7573 6564 2074  tions are used t\n+00006d90: 6872 6f75 6768 6f75 742e 0a0a 1f0a 4669  hroughout.....Fi\n+00006da0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n+00006db0: 2020 4e6f 6465 3a20 506f 6c79 6c69 6e65    Node: Polyline\n+00006dc0: 2073 7765 6570 7320 7769 7468 2063 6c6f   sweeps with clo\n+00006dd0: 7375 7265 2c20 204e 6578 743a 2041 6666  sure,  Next: Aff\n+00006de0: 696e 6520 6172 6974 686d 6574 6963 2c20  ine arithmetic, \n+00006df0: 2050 7265 763a 2050 6f6c 7967 6f6e 2073   Prev: Polygon s\n+00006e00: 7765 6570 732c 2020 5570 3a20 5377 6570  weeps,  Up: Swep\n+00006e10: 7420 6f62 6a65 6374 730a 0a32 2e37 2e35  t objects..2.7.5\n+00006e20: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n+00006e30: 2077 6974 6820 636c 6f73 7572 650a 2d2d   with closure.--\n 00006e40: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 00006e50: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-00006e60: 2d2d 0a0a 4120 706f 6c79 6c69 6e65 2073  --..A polyline s\n-00006e70: 7765 6570 2077 6974 6820 6120 636c 6f73  weep with a clos\n-00006e80: 7572 6520 7461 6720 6372 6561 7465 7320  ure tag creates \n-00006e90: 616e 6f74 6865 7220 6b69 6e64 206f 6620  another kind of \n-00006ea0: 636c 6f73 6564 0a73 7572 6661 6365 2e20  closed.surface. \n-00006eb0: 2046 6972 7374 2c20 7468 6520 706f 6c79   First, the poly\n-00006ec0: 6c69 6e65 2073 6567 6d65 6e74 7320 6172  line segments ar\n-00006ed0: 6520 636f 6e6e 6563 7465 6420 6279 2066  e connected by f\n-00006ee0: 6163 6573 2c20 6a75 7374 2061 730a 7769  aces, just as.wi\n-00006ef0: 7468 6f75 7420 7468 6520 636c 6f73 7572  thout the closur\n-00006f00: 6520 7461 672e 2020 5468 656e 2c20 6561  e tag.  Then, ea\n-00006f10: 6368 2073 6574 206f 6620 656e 6420 706f  ch set of end po\n-00006f20: 696e 7473 2069 7320 6a6f 696e 6564 2074  ints is joined t\n-00006f30: 6f20 6d61 6b65 0a61 2070 6f6c 7967 6f6e  o make.a polygon\n-00006f40: 2c20 6f6e 6520 666f 7220 6561 6368 2065  , one for each e\n-00006f50: 6e64 2e20 2041 2063 6f64 6520 666f 7220  nd.  A code for \n-00006f60: 7365 7665 7261 6c20 7669 6577 7320 6f66  several views of\n-00006f70: 2061 2063 796c 696e 6472 6963 616c 0a70   a cylindrical.p\n-00006f80: 7269 736d 2066 6f6c 6c6f 7773 2e0a 2020  rism follows..  \n-00006f90: 6465 6620 6e5f 6379 6c5f 7365 6773 2032  def n_cyl_segs 2\n-00006fa0: 3020 2064 6566 206e 5f76 6965 7773 2035  0  def n_views 5\n-00006fb0: 2020 6465 6620 4920 5b31 2c30 2c30 5d0a    def I [1,0,0].\n-00006fc0: 2020 6465 6620 656e 646f 7074 7320 5b66    def endopts [f\n-00006fd0: 696c 6c63 6f6c 6f72 3d6c 6967 6874 6772  illcolor=lightgr\n-00006fe0: 6179 5d0a 2020 7265 7065 6174 207b 206e  ay].  repeat { n\n-00006ff0: 5f76 6965 7773 2c20 726f 7461 7465 2831  _views, rotate(1\n-00007000: 3830 2f6e 5f76 6965 7773 2c20 5b49 5d29  80/n_views, [I])\n-00007010: 2074 6865 6e20 7472 616e 736c 6174 6528   then translate(\n-00007020: 5b49 5d20 2a20 322e 3129 207d 200a 2020  [I] * 2.1) } .  \n-00007030: 2020 7377 6565 705b 656e 646f 7074 735d    sweep[endopts]\n-00007040: 7b20 6e5f 6379 6c5f 7365 6773 3c3e 2c20  { n_cyl_segs<>, \n-00007050: 726f 7461 7465 2833 3630 2f6e 5f63 796c  rotate(360/n_cyl\n-00007060: 5f73 6567 732c 205b 302c 312c 305d 2920  _segs, [0,1,0]) \n-00007070: 7d20 0a20 2020 2020 206c 696e 655b 6669  } .      line[fi\n-00007080: 6c6c 636f 6c6f 723d 7768 6974 655d 2831  llcolor=white](1\n-00007090: 2c2d 3129 2831 2c31 290a 4974 2070 726f  ,-1)(1,1).It pro\n-000070a0: 6475 6365 7320 7468 6973 2064 7261 7769  duces this drawi\n-000070b0: 6e67 2e0a 0a00 085b 696d 6167 6520 7372  ng.....[image sr\n-000070c0: 633d 2265 7831 3130 2e70 6e67 2220 7465  c=\"ex110.png\" te\n-000070d0: 7874 3d22 496d 6167 6520 6578 3131 3020  xt=\"Image ex110 \n-000070e0: 6f6d 6974 7465 6420 696e 2074 6578 7420  omitted in text \n-000070f0: 7665 7273 696f 6e20 6f66 2074 6869 7320  version of this \n-00007100: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a54  document.\"..]..T\n-00007110: 6865 206f 7074 696f 6e73 206f 6620 7468  he options of th\n-00007120: 6520 7377 6570 7420 6c69 6e65 2c20 6966  e swept line, if\n-00007130: 2061 6e79 2c20 6172 6520 6170 706c 6965   any, are applie\n-00007140: 6420 746f 2074 6865 2066 6163 6573 2070  d to the faces p\n-00007150: 726f 6475 6365 640a 6279 2073 7765 6570  roduced.by sweep\n-00007160: 696e 6720 7468 6520 6c69 6e65 2c20 6275  ing the line, bu\n-00007170: 7420 6e6f 7420 7468 6520 656e 6420 706f  t not the end po\n-00007180: 6c79 676f 6e73 2e20 204f 7468 6572 7769  lygons.  Otherwi\n-00007190: 7365 2c20 7468 6520 7377 6565 700a 6f70  se, the sweep.op\n-000071a0: 7469 6f6e 7320 6172 6520 6170 706c 6965  tions are applie\n-000071b0: 6420 7468 726f 7567 686f 7574 2e20 2054  d throughout.  T\n-000071c0: 6865 2064 6566 2069 6e20 7468 6973 2065  he def in this e\n-000071d0: 7861 6d70 6c65 2069 7320 616e 2022 6f70  xample is an \"op\n-000071e0: 7469 6f6e 220a 6465 6669 6e69 7469 6f6e  tion\".definition\n-000071f0: 2e20 2052 6566 6572 656e 6365 7320 746f  .  References to\n-00007200: 206f 7074 696f 6e73 206d 7573 7420 6265   options must be\n-00007210: 2065 6e63 6c6f 7365 6420 696e 2073 7175   enclosed in squ\n-00007220: 6172 6520 6272 6163 6b65 7473 2c0a 652e  are brackets,.e.\n-00007230: 672e 2020 205b 666f 6f5d 2e20 2059 6f75  g.   [foo].  You\n-00007240: 2063 616e 2063 6f6e 6361 7465 6e61 7465   can concatenate\n-00007250: 2073 6576 6572 616c 2073 6574 7320 6f66   several sets of\n-00007260: 206f 7074 696f 6e73 2077 6974 6820 6120   options with a \n-00007270: 7369 6e67 6c65 0a72 6566 6572 656e 6365  single.reference\n-00007280: 2c20 652e 672e 2020 205b 636f 6c6f 722c  , e.g.   [color,\n-00007290: 2073 697a 652c 2073 7479 6c65 5d20 776f   size, style] wo\n-000072a0: 756c 6420 6361 7573 6520 7468 6520 6f70  uld cause the op\n-000072b0: 7469 6f6e 0a64 6566 696e 6974 696f 6e73  tion.definitions\n-000072c0: 2066 6f72 2027 636f 6c6f 7227 2c20 2773   for 'color', 's\n-000072d0: 697a 6527 2c20 616e 6420 2773 7479 6c65  ize', and 'style\n-000072e0: 2720 746f 2061 7070 6561 7220 696e 2073  ' to appear in s\n-000072f0: 6571 7565 6e63 6520 696e 0a74 6865 206f  equence in.the o\n-00007300: 7574 7075 7420 6372 6561 7465 6420 6279  utput created by\n-00007310: 2074 6865 2027 736b 6574 6368 2720 636f   the 'sketch' co\n-00007320: 6d6d 616e 6420 636f 6e74 6169 6e69 6e67  mmand containing\n-00007330: 2074 6865 2072 6566 6572 656e 6365 2e0a   the reference..\n-00007340: 4861 7070 696c 792c 2074 6865 2073 796e  Happily, the syn\n-00007350: 7461 7820 6f66 2027 736b 6574 6368 2720  tax of 'sketch' \n-00007360: 6973 2073 7563 6820 7468 6174 206f 7074  is such that opt\n-00007370: 696f 6e73 2072 6566 6572 656e 6365 7320  ions references \n-00007380: 6361 6e0a 6e65 7665 7220 6265 2063 6f6e  can.never be con\n-00007390: 6675 7365 6420 7769 7468 2076 6563 746f  fused with vecto\n-000073a0: 7220 7265 6665 7265 6e63 6573 2e20 2057  r references.  W\n-000073b0: 6869 6c65 206e 6f74 2061 7070 6172 656e  hile not apparen\n-000073c0: 7420 696e 2074 6869 730a 6578 616d 706c  t in this.exampl\n-000073d0: 652c 206f 7074 696f 6e73 2072 6566 6572  e, options refer\n-000073e0: 656e 6365 7320 6172 6520 7573 6566 756c  ences are useful\n-000073f0: 2077 6865 6e20 6465 6669 6e69 6e67 206d   when defining m\n-00007400: 616e 7920 6f62 6a65 6374 7320 7769 7468  any objects with\n-00007410: 2061 0a73 696d 696c 6172 2061 7070 6561   a.similar appea\n-00007420: 7261 6e63 652e 0a0a 1f0a 4669 6c65 3a20  rance.....File: \n-00007430: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n-00007440: 6465 3a20 4166 6669 6e65 2061 7269 7468  de: Affine arith\n-00007450: 6d65 7469 632c 2020 4e65 7874 3a20 4d6f  metic,  Next: Mo\n-00007460: 7265 2074 6f20 6c65 6172 6e2c 2020 5072  re to learn,  Pr\n-00007470: 6576 3a20 506f 6c79 6c69 6e65 2073 7765  ev: Polyline swe\n-00007480: 6570 7320 7769 7468 2063 6c6f 7375 7265  eps with closure\n-00007490: 2c20 2055 703a 2053 7765 7074 206f 626a  ,  Up: Swept obj\n-000074a0: 6563 7473 0a0a 322e 372e 3620 4166 6669  ects..2.7.6 Affi\n-000074b0: 6e65 2061 7269 7468 6d65 7469 630a 2d2d  ne arithmetic.--\n+00006e60: 0a0a 4120 706f 6c79 6c69 6e65 2073 7765  ..A polyline swe\n+00006e70: 6570 2077 6974 6820 6120 636c 6f73 7572  ep with a closur\n+00006e80: 6520 7461 6720 6372 6561 7465 7320 616e  e tag creates an\n+00006e90: 6f74 6865 7220 6b69 6e64 206f 6620 636c  other kind of cl\n+00006ea0: 6f73 6564 0a73 7572 6661 6365 2e20 2046  osed.surface.  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Otherwise\n+00007190: 2c20 7468 6520 7377 6565 700a 6f70 7469  , the sweep.opti\n+000071a0: 6f6e 7320 6172 6520 6170 706c 6965 6420  ons are applied \n+000071b0: 7468 726f 7567 686f 7574 2e20 2054 6865  throughout.  The\n+000071c0: 2064 6566 2069 6e20 7468 6973 2065 7861   def in this exa\n+000071d0: 6d70 6c65 2069 7320 616e 2022 6f70 7469  mple is an \"opti\n+000071e0: 6f6e 220a 6465 6669 6e69 7469 6f6e 2e20  on\".definition. \n+000071f0: 2052 6566 6572 656e 6365 7320 746f 206f   References to o\n+00007200: 7074 696f 6e73 206d 7573 7420 6265 2065  ptions must be e\n+00007210: 6e63 6c6f 7365 6420 696e 2073 7175 6172  nclosed in squar\n+00007220: 6520 6272 6163 6b65 7473 2c0a 652e 672e  e brackets,.e.g.\n+00007230: 2020 205b 666f 6f5d 2e20 2059 6f75 2063     [foo].  You c\n+00007240: 616e 2063 6f6e 6361 7465 6e61 7465 2073  an concatenate s\n+00007250: 6576 6572 616c 2073 6574 7320 6f66 206f  everal sets of o\n+00007260: 7074 696f 6e73 2077 6974 6820 6120 7369  ptions with a si\n+00007270: 6e67 6c65 0a72 6566 6572 656e 6365 2c20  ngle.reference, \n+00007280: 652e 672e 2020 205b 636f 6c6f 722c 2073  e.g.   [color, s\n+00007290: 697a 652c 2073 7479 6c65 5d20 776f 756c  ize, style] woul\n+000072a0: 6420 6361 7573 6520 7468 6520 6f70 7469  d cause the opti\n+000072b0: 6f6e 0a64 6566 696e 6974 696f 6e73 2066  on.definitions f\n+000072c0: 6f72 2027 636f 6c6f 7227 2c20 2773 697a  or 'color', 'siz\n+000072d0: 6527 2c20 616e 6420 2773 7479 6c65 2720  e', and 'style' \n+000072e0: 746f 2061 7070 6561 7220 696e 2073 6571  to appear in seq\n+000072f0: 7565 6e63 6520 696e 0a74 6865 206f 7574  uence in.the out\n+00007300: 7075 7420 6372 6561 7465 6420 6279 2074  put created by t\n+00007310: 6865 2027 736b 6574 6368 2720 636f 6d6d  he 'sketch' comm\n+00007320: 616e 6420 636f 6e74 6169 6e69 6e67 2074  and containing t\n+00007330: 6865 2072 6566 6572 656e 6365 2e0a 4861  he reference..Ha\n+00007340: 7070 696c 792c 2074 6865 2073 796e 7461  ppily, the synta\n+00007350: 7820 6f66 2027 736b 6574 6368 2720 6973  x of 'sketch' is\n+00007360: 2073 7563 6820 7468 6174 206f 7074 696f   such that optio\n+00007370: 6e73 2072 6566 6572 656e 6365 7320 6361  ns references ca\n+00007380: 6e0a 6e65 7665 7220 6265 2063 6f6e 6675  n.never be confu\n+00007390: 7365 6420 7769 7468 2076 6563 746f 7220  sed with vector \n+000073a0: 7265 6665 7265 6e63 6573 2e20 2057 6869  references.  Whi\n+000073b0: 6c65 206e 6f74 2061 7070 6172 656e 7420  le not apparent \n+000073c0: 696e 2074 6869 730a 6578 616d 706c 652c  in this.example,\n+000073d0: 206f 7074 696f 6e73 2072 6566 6572 656e   options referen\n+000073e0: 6365 7320 6172 6520 7573 6566 756c 2077  ces are useful w\n+000073f0: 6865 6e20 6465 6669 6e69 6e67 206d 616e  hen defining man\n+00007400: 7920 6f62 6a65 6374 7320 7769 7468 2061  y objects with a\n+00007410: 0a73 696d 696c 6172 2061 7070 6561 7261  .similar appeara\n+00007420: 6e63 652e 0a0a 1f0a 4669 6c65 3a20 736b  nce.....File: sk\n+00007430: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n+00007440: 3a20 4166 6669 6e65 2061 7269 7468 6d65  : Affine arithme\n+00007450: 7469 632c 2020 4e65 7874 3a20 4d6f 7265  tic,  Next: More\n+00007460: 2074 6f20 6c65 6172 6e2c 2020 5072 6576   to learn,  Prev\n+00007470: 3a20 506f 6c79 6c69 6e65 2073 7765 6570  : Polyline sweep\n+00007480: 7320 7769 7468 2063 6c6f 7375 7265 2c20  s with closure, \n+00007490: 2055 703a 2053 7765 7074 206f 626a 6563   Up: Swept objec\n+000074a0: 7473 0a0a 322e 372e 3620 4166 6669 6e65  ts..2.7.6 Affine\n+000074b0: 2061 7269 7468 6d65 7469 630a 2d2d 2d2d   arithmetic.----\n 000074c0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-000074d0: 2d2d 2d2d 2d0a 0a54 6865 2061 7269 7468  -----..The arith\n-000074e0: 6d65 7469 6320 5b49 5d20 2a20 322e 3120  metic [I] * 2.1 \n-000074f0: 6162 6f76 6520 6869 6e74 7320 6174 2061  above hints at a\n-00007500: 206c 6172 6765 7220 7472 7574 682e 2020   larger truth.  \n-00007510: 2753 6b65 7463 6827 0a6f 7065 7261 746f  'Sketch'.operato\n-00007520: 7273 2077 6f72 6b20 6f6e 2073 6361 6c61  rs work on scala\n-00007530: 7273 2c20 7665 6374 6f72 732c 2070 6f69  rs, vectors, poi\n-00007540: 6e74 732c 2061 6e64 2074 7261 6e73 666f  nts, and transfo\n-00007550: 726d 7320 6163 636f 7264 696e 6720 746f  rms according to\n-00007560: 0a74 6865 2067 656e 6572 616c 2072 756c  .the general rul\n-00007570: 6573 206f 6620 2261 6666 696e 6520 616c  es of \"affine al\n-00007580: 6765 6272 6122 2e20 2054 6869 7320 6361  gebra\".  This ca\n-00007590: 6e20 6265 2068 656c 7066 756c 2066 6f72  n be helpful for\n-000075a0: 2073 6574 7469 6e67 0a75 7020 6469 6167   setting.up diag\n-000075b0: 7261 6d73 2077 6974 6820 636f 6d70 7574  rams with comput\n-000075c0: 6564 2067 656f 6d65 7472 792e 2020 466f  ed geometry.  Fo\n-000075d0: 7220 6578 616d 706c 652c 2069 6620 796f  r example, if yo\n-000075e0: 7520 6861 7665 2074 7269 616e 676c 650a  u have triangle.\n-000075f0: 7665 7274 6963 6573 2028 7031 2920 7468  vertices (p1) th\n-00007600: 726f 7567 6820 2870 3329 2061 6e64 206e  rough (p3) and n\n-00007610: 6565 6420 746f 2064 7261 7720 6120 756e  eed to draw a un\n-00007620: 6974 206e 6f72 6d61 6c20 7665 6374 6f72  it normal vector\n-00007630: 0a70 6f69 6e74 696e 6720 6f75 7420 6f66  .pointing out of\n-00007640: 2074 6865 2063 656e 7465 7220 6f66 2074   the center of t\n-00007650: 6865 2074 7269 616e 676c 652c 2074 6869  he triangle, thi\n-00007660: 7320 636f 6465 2064 6f65 7320 7468 6520  s code does the \n-00007670: 7472 6963 6b2e 0a20 2064 6566 2070 3120  trick..  def p1 \n-00007680: 2831 2c30 2c30 2920 2064 6566 2070 3220  (1,0,0)  def p2 \n-00007690: 2830 2c30 2e35 2c30 2920 2064 6566 2070  (0,0.5,0)  def p\n-000076a0: 3320 282d 302e 352c 2d31 2c32 290a 2020  3 (-0.5,-1,2).  \n-000076b0: 6465 6620 4f20 2830 2c30 2c30 290a 2020  def O (0,0,0).  \n-000076c0: 6465 6620 4e20 756e 6974 2820 2828 7033  def N unit( ((p3\n-000076d0: 2920 2d20 2870 3229 2920 2a20 2828 7031  ) - (p2)) * ((p1\n-000076e0: 2920 2d20 2870 3229 2920 290a 2020 6465  ) - (p2)) ).  de\n-000076f0: 6620 6e31 2028 2870 3129 2d28 4f29 202b  f n1 ((p1)-(O) +\n-00007700: 2028 7032 292d 284f 2920 2b20 2870 3329   (p2)-(O) + (p3)\n-00007710: 2d28 4f29 2920 2f20 3320 2b20 284f 290a  -(O)) / 3 + (O).\n-00007720: 2020 6465 6620 6e32 2028 6e31 292b 5b4e    def n2 (n1)+[N\n-00007730: 5d0a 2020 706f 6c79 676f 6e28 7031 2928  ].  polygon(p1)(\n-00007740: 7032 2928 7033 290a 2020 6c69 6e65 5b61  p2)(p3).  line[a\n-00007750: 7272 6f77 733d 2a2d 3e5d 286e 3129 286e  rrows=*->](n1)(n\n-00007760: 3229 0a54 6865 2066 6972 7374 206c 696e  2).The first lin\n-00007770: 6520 636f 6d70 7574 6573 2074 6865 2063  e computes the c\n-00007780: 726f 7373 2070 726f 6475 6374 206f 6620  ross product of \n-00007790: 7477 6f20 6564 6765 2076 6563 746f 7273  two edge vectors\n-000077a0: 206f 6620 7468 650a 7472 6961 6e67 6c65   of the.triangle\n-000077b0: 2061 6e64 2073 6361 6c65 7320 6974 2074   and scales it t\n-000077c0: 6f20 756e 6974 206c 656e 6774 682e 2020  o unit length.  \n-000077d0: 5468 6520 7365 636f 6e64 2063 6f6d 7075  The second compu\n-000077e0: 7465 7320 7468 6520 6176 6572 6167 650a  tes the average.\n-000077f0: 6f66 2074 6865 2076 6572 7469 6365 732e  of the vertices.\n-00007800: 2020 4e6f 7465 2074 6861 7420 7375 6274    Note that subt\n-00007810: 7261 6374 696f 6e20 616e 6420 6164 6469  raction and addi\n-00007820: 7469 6f6e 206f 6620 7468 6520 6f72 6967  tion of the orig\n-00007830: 696e 0a65 6666 6563 7469 7665 6c79 2063  in.effectively c\n-00007840: 6f6e 7665 7274 2076 6563 746f 7273 2074  onvert vectors t\n-00007850: 6f20 706f 696e 7473 2061 6e64 205f 7669  o points and _vi\n-00007860: 6365 2076 6572 7361 5f2e 2020 5468 6520  ce versa_.  The \n-00007870: 6c69 6e65 0a63 6f6d 6d61 6e64 2064 7261  line.command dra\n-00007880: 7773 2074 6865 206e 6f72 6d61 6c20 6174  ws the normal at\n-00007890: 2074 6865 2063 6f72 7265 6374 2073 706f   the correct spo\n-000078a0: 742e 0a0a 0008 5b69 6d61 6765 2073 7263  t.....[image src\n-000078b0: 3d22 6578 3130 302e 706e 6722 2074 6578  =\"ex100.png\" tex\n-000078c0: 743d 2249 6d61 6765 2065 7831 3030 206f  t=\"Image ex100 o\n-000078d0: 6d69 7474 6564 2069 6e20 7465 7874 2076  mitted in text v\n-000078e0: 6572 7369 6f6e 206f 6620 7468 6973 2064  ersion of this d\n-000078f0: 6f63 756d 656e 742e 2200 085d 0a0a 2020  ocument.\"..]..  \n-00007900: 2054 776f 2063 6176 6561 7473 2072 6567   Two caveats reg\n-00007910: 6172 6469 6e67 2074 6869 7320 6578 616d  arding this exam\n-00007920: 706c 6520 7265 6d61 696e 2e20 2046 6972  ple remain.  Fir\n-00007930: 7374 2c20 7468 6520 6f6e 6c79 2077 6179  st, the only way\n-00007940: 2074 6f0a 7573 6520 2750 5354 7269 636b   to.use 'PSTrick\n-00007950: 7327 2d73 7479 6c65 2061 7272 6f77 7320  s'-style arrows \n-00007960: 6973 2077 6974 6820 6172 726f 7773 3d2e  is with arrows=.\n-00007970: 2020 5468 6520 616c 7465 726e 6174 6976    The alternativ\n-00007980: 6520 7379 6e74 6178 2066 6f72 0a27 5053  e syntax for.'PS\n-00007990: 5472 6963 6b73 2720 6172 726f 7773 2069  Tricks' arrows i\n-000079a0: 7320 6e6f 7420 616c 6c6f 7765 6420 696e  s not allowed in\n-000079b0: 2073 6b65 7463 682e 2020 5365 636f 6e64   sketch.  Second\n-000079c0: 2c20 796f 7520 6d69 6768 7420 6c69 6b65  , you might like\n-000079d0: 2074 6f0a 656c 696d 696e 6174 6520 7468   to.eliminate th\n-000079e0: 6520 7468 6972 6420 6465 6620 616e 6420  e third def and \n-000079f0: 7772 6974 6520 696e 7374 6561 6420 7468  write instead th\n-00007a00: 6520 666f 6c6c 6f77 696e 672e 0a20 206c  e following..  l\n-00007a10: 696e 655b 6172 726f 7773 3d2a 2d3e 5d28  ine[arrows=*->](\n-00007a20: 6e31 2920 286e 3129 2b5b 4e5d 0a54 6869  n1) (n1)+[N].Thi\n-00007a30: 7320 6973 206e 6f74 2061 6c6c 6f77 6564  s is not allowed\n-00007a40: 2e20 2054 6865 2070 6f69 6e74 206c 6973  .  The point lis\n-00007a50: 7473 2069 6e20 6472 6177 6162 6c65 7320  ts in drawables \n-00007a60: 6d61 7920 636f 6e73 6973 7420 6f6e 6c79  may consist only\n-00007a70: 206f 660a 6578 706c 6963 6974 2070 6f69   of.explicit poi\n-00007a80: 6e74 7320 6f72 2070 6f69 6e74 2072 6566  nts or point ref\n-00007a90: 6572 656e 6365 732e 2020 596f 7520 6d61  erences.  You ma\n-00007aa0: 792c 2068 6f77 6576 6572 2c20 7573 6520  y, however, use \n-00007ab0: 6172 6974 686d 6574 6963 0a74 6f20 6361  arithmetic.to ca\n-00007ac0: 6c63 756c 6174 6520 706f 696e 7420 636f  lculate point co\n-00007ad0: 6d70 6f6e 656e 7473 2e20 2054 6865 2066  mponents.  The f\n-00007ae0: 6f6c 6c6f 7769 6e67 2077 6f72 6b73 2c20  ollowing works, \n-00007af0: 7468 6f75 6768 2069 7427 7320 610a 6c69  though it's a.li\n-00007b00: 7474 6c65 2063 756d 6265 7273 6f6d 652e  ttle cumbersome.\n-00007b10: 0a20 206c 696e 655b 6172 726f 7773 3d2a  .  line[arrows=*\n-00007b20: 2d3e 5d28 6e31 2928 286e 3129 2778 2b28  ->](n1)((n1)'x+(\n-00007b30: 4e29 2778 2c20 286e 3129 2779 2b28 4e29  N)'x, (n1)'y+(N)\n-00007b40: 2779 2c20 286e 3129 277a 2b28 4e29 277a  'y, (n1)'z+(N)'z\n-00007b50: 290a 4f62 7669 6f75 736c 792c 2074 6865  ).Obviously, the\n-00007b60: 2022 7469 636b 206f 7065 7261 746f 7222   \"tick operator\"\n-00007b70: 2027 2778 2720 6578 7472 6163 7473 2063   ''x' extracts c\n-00007b80: 6f6d 706f 6e65 6e74 7320 6f66 2070 6f69  omponents of poi\n-00007b90: 6e74 7320 616e 640a 7665 6374 6f72 732e  nts and.vectors.\n-00007ba0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n-00007bb0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4d6f  .info,  Node: Mo\n-00007bc0: 7265 2074 6f20 6c65 6172 6e2c 2020 5072  re to learn,  Pr\n-00007bd0: 6576 3a20 4166 6669 6e65 2061 7269 7468  ev: Affine arith\n-00007be0: 6d65 7469 632c 2020 5570 3a20 5377 6570  metic,  Up: Swep\n-00007bf0: 7420 6f62 6a65 6374 730a 0a32 2e37 2e37  t objects..2.7.7\n-00007c00: 204d 6f72 6520 746f 206c 6561 726e 0a2d   More to learn.-\n+000074d0: 2d2d 2d0a 0a54 6865 2061 7269 7468 6d65  ---..The arithme\n+000074e0: 7469 6320 5b49 5d20 2a20 322e 3120 6162  tic [I] * 2.1 ab\n+000074f0: 6f76 6520 6869 6e74 7320 6174 2061 206c  ove hints at a l\n+00007500: 6172 6765 7220 7472 7574 682e 2020 2753  arger truth.  'S\n+00007510: 6b65 7463 6827 0a6f 7065 7261 746f 7273  ketch'.operators\n+00007520: 2077 6f72 6b20 6f6e 2073 6361 6c61 7273   work on scalars\n+00007530: 2c20 7665 6374 6f72 732c 2070 6f69 6e74  , vectors, point\n+00007540: 732c 2061 6e64 2074 7261 6e73 666f 726d  s, and transform\n+00007550: 7320 6163 636f 7264 696e 6720 746f 0a74  s according to.t\n+00007560: 6865 2067 656e 6572 616c 2072 756c 6573  he general rules\n+00007570: 206f 6620 2261 6666 696e 6520 616c 6765   of \"affine alge\n+00007580: 6272 6122 2e20 2054 6869 7320 6361 6e20  bra\".  This can \n+00007590: 6265 2068 656c 7066 756c 2066 6f72 2073  be helpful for s\n+000075a0: 6574 7469 6e67 0a75 7020 6469 6167 7261  etting.up diagra\n+000075b0: 6d73 2077 6974 6820 636f 6d70 7574 6564  ms with computed\n+000075c0: 2067 656f 6d65 7472 792e 2020 466f 7220   geometry.  For \n+000075d0: 6578 616d 706c 652c 2069 6620 796f 7520  example, if you \n+000075e0: 6861 7665 2074 7269 616e 676c 650a 7665  have triangle.ve\n+000075f0: 7274 6963 6573 2028 7031 2920 7468 726f  rtices (p1) thro\n+00007600: 7567 6820 2870 3329 2061 6e64 206e 6565  ugh (p3) and nee\n+00007610: 6420 746f 2064 7261 7720 6120 756e 6974  d to draw a unit\n+00007620: 206e 6f72 6d61 6c20 7665 6374 6f72 0a70   normal vector.p\n+00007630: 6f69 6e74 696e 6720 6f75 7420 6f66 2074  ointing out of t\n+00007640: 6865 2063 656e 7465 7220 6f66 2074 6865  he center of the\n+00007650: 2074 7269 616e 676c 652c 2074 6869 7320   triangle, this \n+00007660: 636f 6465 2064 6f65 7320 7468 6520 7472  code does the tr\n+00007670: 6963 6b2e 0a20 2064 6566 2070 3120 2831  ick..  def p1 (1\n+00007680: 2c30 2c30 2920 2064 6566 2070 3220 2830  ,0,0)  def p2 (0\n+00007690: 2c30 2e35 2c30 2920 2064 6566 2070 3320  ,0.5,0)  def p3 \n+000076a0: 282d 302e 352c 2d31 2c32 290a 2020 6465  (-0.5,-1,2).  de\n+000076b0: 6620 4f20 2830 2c30 2c30 290a 2020 6465  f O (0,0,0).  de\n+000076c0: 6620 4e20 756e 6974 2820 2828 7033 2920  f N unit( ((p3) \n+000076d0: 2d20 2870 3229 2920 2a20 2828 7031 2920  - (p2)) * ((p1) \n+000076e0: 2d20 2870 3229 2920 290a 2020 6465 6620  - (p2)) ).  def \n+000076f0: 6e31 2028 2870 3129 2d28 4f29 202b 2028  n1 ((p1)-(O) + (\n+00007700: 7032 292d 284f 2920 2b20 2870 3329 2d28  p2)-(O) + (p3)-(\n+00007710: 4f29 2920 2f20 3320 2b20 284f 290a 2020  O)) / 3 + (O).  \n+00007720: 6465 6620 6e32 2028 6e31 292b 5b4e 5d0a  def n2 (n1)+[N].\n+00007730: 2020 706f 6c79 676f 6e28 7031 2928 7032    polygon(p1)(p2\n+00007740: 2928 7033 290a 2020 6c69 6e65 5b61 7272  )(p3).  line[arr\n+00007750: 6f77 733d 2a2d 3e5d 286e 3129 286e 3229  ows=*->](n1)(n2)\n+00007760: 0a54 6865 2066 6972 7374 206c 696e 6520  .The first line \n+00007770: 636f 6d70 7574 6573 2074 6865 2063 726f  computes the cro\n+00007780: 7373 2070 726f 6475 6374 206f 6620 7477  ss product of tw\n+00007790: 6f20 6564 6765 2076 6563 746f 7273 206f  o edge vectors o\n+000077a0: 6620 7468 650a 7472 6961 6e67 6c65 2061  f the.triangle a\n+000077b0: 6e64 2073 6361 6c65 7320 6974 2074 6f20  nd scales it to \n+000077c0: 756e 6974 206c 656e 6774 682e 2020 5468  unit length.  Th\n+000077d0: 6520 7365 636f 6e64 2063 6f6d 7075 7465  e second compute\n+000077e0: 7320 7468 6520 6176 6572 6167 650a 6f66  s the average.of\n+000077f0: 2074 6865 2076 6572 7469 6365 732e 2020   the vertices.  \n+00007800: 4e6f 7465 2074 6861 7420 7375 6274 7261  Note that subtra\n+00007810: 6374 696f 6e20 616e 6420 6164 6469 7469  ction and additi\n+00007820: 6f6e 206f 6620 7468 6520 6f72 6967 696e  on of the origin\n+00007830: 0a65 6666 6563 7469 7665 6c79 2063 6f6e  .effectively con\n+00007840: 7665 7274 2076 6563 746f 7273 2074 6f20  vert vectors to \n+00007850: 706f 696e 7473 2061 6e64 205f 7669 6365  points and _vice\n+00007860: 2076 6572 7361 5f2e 2020 5468 6520 6c69   versa_.  The li\n+00007870: 6e65 0a63 6f6d 6d61 6e64 2064 7261 7773  ne.command draws\n+00007880: 2074 6865 206e 6f72 6d61 6c20 6174 2074   the normal at t\n+00007890: 6865 2063 6f72 7265 6374 2073 706f 742e  he correct spot.\n+000078a0: 0a0a 0008 5b69 6d61 6765 2073 7263 3d22  ....[image src=\"\n+000078b0: 6578 3130 302e 706e 6722 2074 6578 743d  ex100.png\" text=\n+000078c0: 2249 6d61 6765 2065 7831 3030 206f 6d69  \"Image ex100 omi\n+000078d0: 7474 6564 2069 6e20 7465 7874 2076 6572  tted in text ver\n+000078e0: 7369 6f6e 206f 6620 7468 6973 2064 6f63  sion of this doc\n+000078f0: 756d 656e 742e 2200 085d 0a0a 2020 2054  ument.\"..]..   T\n+00007900: 776f 2063 6176 6561 7473 2072 6567 6172  wo caveats regar\n+00007910: 6469 6e67 2074 6869 7320 6578 616d 706c  ding this exampl\n+00007920: 6520 7265 6d61 696e 2e20 2046 6972 7374  e remain.  First\n+00007930: 2c20 7468 6520 6f6e 6c79 2077 6179 2074  , the only way t\n+00007940: 6f0a 7573 6520 2750 5354 7269 636b 7327  o.use 'PSTricks'\n+00007950: 2d73 7479 6c65 2061 7272 6f77 7320 6973  -style arrows is\n+00007960: 2077 6974 6820 6172 726f 7773 3d2e 2020   with arrows=.  \n+00007970: 5468 6520 616c 7465 726e 6174 6976 6520  The alternative \n+00007980: 7379 6e74 6178 2066 6f72 0a27 5053 5472  syntax for.'PSTr\n+00007990: 6963 6b73 2720 6172 726f 7773 2069 7320  icks' arrows is \n+000079a0: 6e6f 7420 616c 6c6f 7765 6420 696e 2073  not allowed in s\n+000079b0: 6b65 7463 682e 2020 5365 636f 6e64 2c20  ketch.  Second, \n+000079c0: 796f 7520 6d69 6768 7420 6c69 6b65 2074  you might like t\n+000079d0: 6f0a 656c 696d 696e 6174 6520 7468 6520  o.eliminate the \n+000079e0: 7468 6972 6420 6465 6620 616e 6420 7772  third def and wr\n+000079f0: 6974 6520 696e 7374 6561 6420 7468 6520  ite instead the \n+00007a00: 666f 6c6c 6f77 696e 672e 0a20 206c 696e  following..  lin\n+00007a10: 655b 6172 726f 7773 3d2a 2d3e 5d28 6e31  e[arrows=*->](n1\n+00007a20: 2920 286e 3129 2b5b 4e5d 0a54 6869 7320  ) (n1)+[N].This \n+00007a30: 6973 206e 6f74 2061 6c6c 6f77 6564 2e20  is not allowed. \n+00007a40: 2054 6865 2070 6f69 6e74 206c 6973 7473   The point lists\n+00007a50: 2069 6e20 6472 6177 6162 6c65 7320 6d61   in drawables ma\n+00007a60: 7920 636f 6e73 6973 7420 6f6e 6c79 206f  y consist only o\n+00007a70: 660a 6578 706c 6963 6974 2070 6f69 6e74  f.explicit point\n+00007a80: 7320 6f72 2070 6f69 6e74 2072 6566 6572  s or point refer\n+00007a90: 656e 6365 732e 2020 596f 7520 6d61 792c  ences.  You may,\n+00007aa0: 2068 6f77 6576 6572 2c20 7573 6520 6172   however, use ar\n+00007ab0: 6974 686d 6574 6963 0a74 6f20 6361 6c63  ithmetic.to calc\n+00007ac0: 756c 6174 6520 706f 696e 7420 636f 6d70  ulate point comp\n+00007ad0: 6f6e 656e 7473 2e20 2054 6865 2066 6f6c  onents.  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It.de\n+00007fc0: 7363 7269 6265 7320 6120 2273 6365 6e65  scribes a \"scene\n+00007fd0: 222c 2073 6f20 7468 6520 736b 6574 6368  \", so the sketch\n+00007fe0: 206c 616e 6775 6167 6520 6973 2061 2022   language is a \"\n+00007ff0: 7363 656e 6520 6465 7363 7269 7074 696f  scene descriptio\n+00008000: 6e0a 6c61 6e67 7561 6765 222e 2020 2753  n.language\".  'S\n+00008010: 6b65 7463 6827 2069 6e70 7574 2069 7320  ketch' input is \n+00008020: 616c 736f 2022 6465 636c 6172 6174 6976  also \"declarativ\n+00008030: 6522 2e20 2049 7420 6d65 7265 6c79 2064  e\".  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There is a \n+00008290: 7369 6d70 6c65 2022 696e 636c 7564 650a  simple \"include.\n+000082a0: 6669 6c65 2220 6d65 6368 616e 6973 6d2e  file\" mechanism.\n+000082b0: 2020 5468 6520 636f 6d6d 616e 640a 2020    The command.  \n+000082c0: 696e 7075 747b 6f74 6865 7266 696c 652e  input{otherfile.\n+000082d0: 736b 7d0a 6361 7573 6573 2074 6865 2063  sk}.causes the c\n+000082e0: 6f6e 7465 6e74 7320 6f66 2027 6f74 6865  ontents of 'othe\n+000082f0: 7266 696c 652e 736b 2720 746f 2062 6520  rfile.sk' to be \n+00008300: 696e 7365 7274 6564 2061 7320 7468 6f75  inserted as thou\n+00008310: 6768 2074 6865 7920 7765 7265 0a70 6172  gh they were.par\n+00008320: 7420 6f66 2074 6865 2063 7572 7265 6e74  t of the current\n+00008330: 2066 696c 652e 0a0a 2a20 4d65 6e75 3a0a   file...* Menu:.\n+00008340: 0a2a 2049 6465 6e74 6966 6965 7273 3a3a  .* Identifiers::\n+00008350: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00008360: 204e 616d 6573 2066 6f72 2074 6869 6e67   Names for thing\n+00008370: 732e 0a2a 204b 6579 2061 6e64 2072 6573  s..* Key and res\n+00008380: 6572 7665 6420 776f 7264 733a 3a20 2020  erved words::   \n+00008390: 2020 204e 616d 6573 2079 6f75 2073 686f     Names you sho\n+000083a0: 756c 646e 2774 2075 7365 2e0a 2a20 4c69  uldn't use..* Li\n+000083b0: 7465 7261 6c73 3a3a 2020 2020 2020 2020  terals::        \n+000083c0: 2020 2020 2020 2020 2020 2020 436f 6e73              Cons\n+000083d0: 7461 6e74 7320 616e 6420 636f 6e73 7472  tants and constr\n+000083e0: 7563 746f 7273 2e0a 2a20 4172 6974 686d  uctors..* Arithm\n+000083f0: 6574 6963 3a3a 2020 2020 2020 2020 2020  etic::          \n+00008400: 2020 2020 2020 2020 5275 6c65 7320 666f          Rules fo\n+00008410: 7220 6578 7072 6573 7369 6f6e 732e 0a2a  r expressions..*\n+00008420: 204f 7074 696f 6e73 3a3a 2020 2020 2020   Options::      \n+00008430: 2020 2020 2020 2020 2020 2020 2020 204d                 M\n+00008440: 6f64 6966 7969 6e67 206f 626a 6563 7420  odifying object \n+00008450: 6170 7065 6172 616e 6365 2e0a 0a1f 0a46  appearance.....F\n+00008460: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n+00008470: 2c20 204e 6f64 653a 2049 6465 6e74 6966  ,  Node: Identif\n+00008480: 6965 7273 2c20 204e 6578 743a 204b 6579  iers,  Next: Key\n+00008490: 2061 6e64 2072 6573 6572 7665 6420 776f   and reserved wo\n+000084a0: 7264 732c 2020 5072 6576 3a20 4c61 6e67  rds,  Prev: Lang\n+000084b0: 7561 6765 2062 6173 6963 732c 2020 5570  uage basics,  Up\n+000084c0: 3a20 4c61 6e67 7561 6765 2062 6173 6963  : Language basic\n+000084d0: 730a 0a33 2e31 2e31 2049 6465 6e74 6966  s..3.1.1 Identif\n+000084e0: 6965 7273 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d  iers.-----------\n+000084f0: 2d2d 2d2d 2d2d 0a0a 4964 656e 7469 6669  ------..Identifi\n+00008500: 6572 7320 696e 2027 736b 6574 6368 2720  ers in 'sketch' \n+00008510: 6172 6520 7265 6665 7265 6e63 6573 2074  are references t\n+00008520: 6f20 6561 726c 6965 722d 6465 6669 6e65  o earlier-define\n+00008530: 6420 6f70 7469 6f6e 732c 0a73 6361 6c61  d options,.scala\n+00008540: 7273 2c20 706f 696e 7473 2c20 7665 6374  rs, points, vect\n+00008550: 6f72 732c 2074 7261 6e73 666f 726d 732c  ors, transforms,\n+00008560: 2064 7261 7761 626c 6573 2c20 616e 6420   drawables, and \n+00008570: 7461 6773 2e20 2044 6566 696e 6974 696f  tags.  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The last \n+00008610: 6368 6172 6163 7465 7220 6d61 7920 5f6e  character may _n\n+00008620: 6f74 5f20 6265 2061 6e20 756e 6465 7273  ot_ be an unders\n+00008630: 636f 7265 2e0a 4b65 7977 6f72 6473 2063  core..Keywords c\n+00008640: 616e 6e6f 7420 6265 2075 7365 6420 6173  annot be used as\n+00008650: 2069 6465 6e74 6966 6965 7273 2c20 616e   identifiers, an\n+00008660: 6420 7265 7365 7276 6564 2077 6f72 6473  d reserved words\n+00008670: 206f 7567 6874 2074 6f20 6265 0a61 766f   ought to be.avo\n+00008680: 6964 6564 2e20 202a 4e6f 7465 204b 6579  ided.  *Note Key\n+00008690: 2061 6e64 2072 6573 6572 7665 6420 776f   and reserved wo\n+000086a0: 7264 733a 3a2e 0a0a 1f0a 4669 6c65 3a20  rds::.....File: \n+000086b0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n+000086c0: 6465 3a20 4b65 7920 616e 6420 7265 7365  de: Key and rese\n+000086d0: 7276 6564 2077 6f72 6473 2c20 204e 6578  rved words,  Nex\n+000086e0: 743a 204c 6974 6572 616c 732c 2020 5072  t: Literals,  Pr\n+000086f0: 6576 3a20 4964 656e 7469 6669 6572 732c  ev: Identifiers,\n+00008700: 2020 5570 3a20 4c61 6e67 7561 6765 2062    Up: Language b\n+00008710: 6173 6963 730a 0a33 2e31 2e32 204b 6579  asics..3.1.2 Key\n+00008720: 2061 6e64 2072 6573 6572 7665 6420 776f   and reserved wo\n+00008730: 7264 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  rds.------------\n 00008740: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-00008750: 2d2d 0a0a 5468 6520 6b65 7977 6f72 6473  --..The keywords\n-00008760: 206f 6620 2773 6b65 7463 6827 2061 7265   of 'sketch' are\n-00008770: 2027 7069 6374 7572 6562 6f78 2720 2763   'picturebox' 'c\n-00008780: 7572 7665 2720 2764 6566 2720 2764 6f74  urve' 'def' 'dot\n-00008790: 7327 2027 6672 616d 6527 0a27 676c 6f62  s' 'frame'.'glob\n-000087a0: 616c 2720 2769 6e70 7574 2720 276c 696e  al' 'input' 'lin\n-000087b0: 6527 2027 706f 6c79 676f 6e27 2027 7075  e' 'polygon' 'pu\n-000087c0: 7427 2027 7265 7065 6174 2720 2773 6574  t' 'repeat' 'set\n-000087d0: 2720 2773 7765 6570 2720 616e 640a 2774  ' 'sweep' and.'t\n-000087e0: 6865 6e27 2e20 2054 6865 2027 736b 6574  hen'.  The 'sket\n-000087f0: 6368 2720 7061 7273 6572 2077 696c 6c20  ch' parser will \n-00008800: 6e6f 7465 2061 2073 796e 7461 7820 6572  note a syntax er\n-00008810: 726f 7220 6966 2061 6e79 206f 6620 7468  ror if any of th\n-00008820: 6573 650a 6172 6520 7573 6564 2069 6e20  ese.are used in \n-00008830: 706c 6163 6520 6f66 2061 2070 726f 7065  place of a prope\n-00008840: 7220 6964 656e 7469 6669 6572 2e0a 0a20  r identifier... \n-00008850: 2020 496e 2061 6464 6974 696f 6e2c 2074    In addition, t\n-00008860: 6865 7265 2061 7265 2072 6573 6572 7665  here are reserve\n-00008870: 6420 776f 7264 7320 7468 6174 2063 616e  d words that can\n-00008880: 2063 7572 7265 6e74 6c79 2062 6520 6465   currently be de\n-00008890: 6669 6e65 640a 6279 2074 6865 2075 7365  fined.by the use\n-000088a0: 722c 2062 7574 2077 6974 6820 7468 6520  r, but with the \n-000088b0: 7269 736b 2074 6861 7420 6675 7475 7265  risk that future\n-000088c0: 2076 6572 7369 6f6e 7320 6f66 2027 736b   versions of 'sk\n-000088d0: 6574 6368 2720 7769 6c6c 0a72 656a 6563  etch' will.rejec\n-000088e0: 7420 7468 6f73 6520 6465 6669 6e69 7469  t those definiti\n-000088f0: 6f6e 732e 2020 5468 6520 7265 7365 7276  ons.  The reserv\n-00008900: 6564 2077 6f72 6473 2061 7265 2027 6163  ed words are 'ac\n-00008910: 6f73 2720 2761 7369 6e27 2027 6174 616e  os' 'asin' 'atan\n-00008920: 3227 0a27 636f 7327 2027 696e 7665 7273  2'.'cos' 'invers\n-00008930: 6527 2027 7065 7273 7065 6374 6976 6527  e' 'perspective'\n-00008940: 2027 7072 6f6a 6563 7427 2027 726f 7461   'project' 'rota\n-00008950: 7465 2720 2773 6361 6c65 2720 2773 696e  te' 'scale' 'sin\n-00008960: 2720 2773 7065 6369 616c 270a 2773 7172  ' 'special'.'sqr\n-00008970: 7427 2027 7472 616e 736c 6174 6527 2027  t' 'translate' '\n-00008980: 756e 6974 2720 616e 6420 2776 6965 7727  unit' and 'view'\n-00008990: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463  .....File: sketc\n-000089a0: 682e 696e 666f 2c20 204e 6f64 653a 204c  h.info,  Node: L\n-000089b0: 6974 6572 616c 732c 2020 4e65 7874 3a20  iterals,  Next: \n-000089c0: 4172 6974 686d 6574 6963 2c20 2050 7265  Arithmetic,  Pre\n-000089d0: 763a 204b 6579 2061 6e64 2072 6573 6572  v: Key and reser\n-000089e0: 7665 6420 776f 7264 732c 2020 5570 3a20  ved words,  Up: \n-000089f0: 4c61 6e67 7561 6765 2062 6173 6963 730a  Language basics.\n-00008a00: 0a33 2e31 2e33 204c 6974 6572 616c 730a  .3.1.3 Literals.\n-00008a10: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a  --------------..\n-00008a20: 4c69 7465 7261 6c73 2069 6e20 2773 6b65  Literals in 'ske\n-00008a30: 7463 6827 2069 6e63 6c75 6465 2073 6361  tch' include sca\n-00008a40: 6c61 7273 2c20 706f 696e 7473 2c20 7665  lars, points, ve\n-00008a50: 6374 6f72 732c 2061 6e64 2074 7261 6e73  ctors, and trans\n-00008a60: 666f 726d 732e 0a4c 6974 6572 616c 732c  forms..Literals,\n-00008a70: 2061 6c6f 6e67 2077 6974 6820 6465 6669   along with defi\n-00008a80: 6e65 6420 6f62 6a65 6374 2072 6566 6572  ned object refer\n-00008a90: 656e 6365 732c 2061 7265 2075 7365 6420  ences, are used \n-00008aa0: 696e 2061 7269 7468 6d65 7469 630a 6578  in arithmetic.ex\n-00008ab0: 7072 6573 7369 6f6e 732e 2020 2a4e 6f74  pressions.  *Not\n-00008ac0: 6520 4172 6974 686d 6574 6963 3a3a 2e0a  e Arithmetic::..\n-00008ad0: 0a2a 204d 656e 753a 0a0a 2a20 5363 616c  .* Menu:..* Scal\n-00008ae0: 6172 206c 6974 6572 616c 733a 3a20 2020  ar literals::   \n-00008af0: 2020 2020 2020 2020 2020 4a75 7374 2074            Just t\n-00008b00: 6865 206e 756d 6265 7273 2e0a 2a20 506f  he numbers..* Po\n-00008b10: 696e 7420 616e 6420 7665 6374 6f72 206c  int and vector l\n-00008b20: 6974 6572 616c 733a 3a20 2020 3364 2071  iterals::   3d q\n-00008b30: 7561 6e74 6974 6965 732e 0a2a 2054 7261  uantities..* Tra\n-00008b40: 6e73 666f 726d 206c 6974 6572 616c 733a  nsform literals:\n-00008b50: 3a20 2020 2020 2020 2020 204d 6174 7269  :          Matri\n-00008b60: 7820 666f 726d 2e0a 0a1f 0a46 696c 653a  x form.....File:\n-00008b70: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n-00008b80: 6f64 653a 2053 6361 6c61 7220 6c69 7465  ode: Scalar lite\n-00008b90: 7261 6c73 2c20 204e 6578 743a 2050 6f69  rals,  Next: Poi\n-00008ba0: 6e74 2061 6e64 2076 6563 746f 7220 6c69  nt and vector li\n-00008bb0: 7465 7261 6c73 2c20 2050 7265 763a 204c  terals,  Prev: L\n-00008bc0: 6974 6572 616c 732c 2020 5570 3a20 4c69  iterals,  Up: Li\n-00008bd0: 7465 7261 6c73 0a0a 332e 312e 332e 3120  terals..3.1.3.1 \n-00008be0: 5363 616c 6172 206c 6974 6572 616c 730a  Scalar literals.\n+00008750: 0a0a 5468 6520 6b65 7977 6f72 6473 206f  ..The keywords o\n+00008760: 6620 2773 6b65 7463 6827 2061 7265 2027  f 'sketch' are '\n+00008770: 7069 6374 7572 6562 6f78 2720 2763 7572  picturebox' 'cur\n+00008780: 7665 2720 2764 6566 2720 2764 6f74 7327  ve' 'def' 'dots'\n+00008790: 2027 6672 616d 6527 0a27 676c 6f62 616c   'frame'.'global\n+000087a0: 2720 2769 6e70 7574 2720 276c 696e 6527  ' 'input' 'line'\n+000087b0: 2027 706f 6c79 676f 6e27 2027 7075 7427   'polygon' 'put'\n+000087c0: 2027 7265 7065 6174 2720 2773 6574 2720   'repeat' 'set' \n+000087d0: 2773 7765 6570 2720 616e 640a 2774 6865  'sweep' and.'the\n+000087e0: 6e27 2e20 2054 6865 2027 736b 6574 6368  n'.  The 'sketch\n+000087f0: 2720 7061 7273 6572 2077 696c 6c20 6e6f  ' parser will no\n+00008800: 7465 2061 2073 796e 7461 7820 6572 726f  te a syntax erro\n+00008810: 7220 6966 2061 6e79 206f 6620 7468 6573  r if any of thes\n+00008820: 650a 6172 6520 7573 6564 2069 6e20 706c  e.are used in pl\n+00008830: 6163 6520 6f66 2061 2070 726f 7065 7220  ace of a proper \n+00008840: 6964 656e 7469 6669 6572 2e0a 0a20 2020  identifier...   \n+00008850: 496e 2061 6464 6974 696f 6e2c 2074 6865  In addition, the\n+00008860: 7265 2061 7265 2072 6573 6572 7665 6420  re are reserved \n+00008870: 776f 7264 7320 7468 6174 2063 616e 2063  words that can c\n+00008880: 7572 7265 6e74 6c79 2062 6520 6465 6669  urrently be defi\n+00008890: 6e65 640a 6279 2074 6865 2075 7365 722c  ned.by the user,\n+000088a0: 2062 7574 2077 6974 6820 7468 6520 7269   but with the ri\n+000088b0: 736b 2074 6861 7420 6675 7475 7265 2076  sk that future v\n+000088c0: 6572 7369 6f6e 7320 6f66 2027 736b 6574  ersions of 'sket\n+000088d0: 6368 2720 7769 6c6c 0a72 656a 6563 7420  ch' will.reject \n+000088e0: 7468 6f73 6520 6465 6669 6e69 7469 6f6e  those definition\n+000088f0: 732e 2020 5468 6520 7265 7365 7276 6564  s.  The reserved\n+00008900: 2077 6f72 6473 2061 7265 2027 6163 6f73   words are 'acos\n+00008910: 2720 2761 7369 6e27 2027 6174 616e 3227  ' 'asin' 'atan2'\n+00008920: 0a27 636f 7327 2027 696e 7665 7273 6527  .'cos' 'inverse'\n+00008930: 2027 7065 7273 7065 6374 6976 6527 2027   'perspective' '\n+00008940: 7072 6f6a 6563 7427 2027 726f 7461 7465  project' 'rotate\n+00008950: 2720 2773 6361 6c65 2720 2773 696e 2720  ' 'scale' 'sin' \n+00008960: 2773 7065 6369 616c 270a 2773 7172 7427  'special'.'sqrt'\n+00008970: 2027 7472 616e 736c 6174 6527 2027 756e   'translate' 'un\n+00008980: 6974 2720 616e 6420 2776 6965 7727 2e0a  it' and 'view'..\n+00008990: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n+000089a0: 696e 666f 2c20 204e 6f64 653a 204c 6974  info,  Node: Lit\n+000089b0: 6572 616c 732c 2020 4e65 7874 3a20 4172  erals,  Next: Ar\n+000089c0: 6974 686d 6574 6963 2c20 2050 7265 763a  ithmetic,  Prev:\n+000089d0: 204b 6579 2061 6e64 2072 6573 6572 7665   Key and reserve\n+000089e0: 6420 776f 7264 732c 2020 5570 3a20 4c61  d words,  Up: La\n+000089f0: 6e67 7561 6765 2062 6173 6963 730a 0a33  nguage basics..3\n+00008a00: 2e31 2e33 204c 6974 6572 616c 730a 2d2d  .1.3 Literals.--\n+00008a10: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 4c69  ------------..Li\n+00008a20: 7465 7261 6c73 2069 6e20 2773 6b65 7463  terals in 'sketc\n+00008a30: 6827 2069 6e63 6c75 6465 2073 6361 6c61  h' include scala\n+00008a40: 7273 2c20 706f 696e 7473 2c20 7665 6374  rs, points, vect\n+00008a50: 6f72 732c 2061 6e64 2074 7261 6e73 666f  ors, and transfo\n+00008a60: 726d 732e 0a4c 6974 6572 616c 732c 2061  rms..Literals, a\n+00008a70: 6c6f 6e67 2077 6974 6820 6465 6669 6e65  long with define\n+00008a80: 6420 6f62 6a65 6374 2072 6566 6572 656e  d object referen\n+00008a90: 6365 732c 2061 7265 2075 7365 6420 696e  ces, are used in\n+00008aa0: 2061 7269 7468 6d65 7469 630a 6578 7072   arithmetic.expr\n+00008ab0: 6573 7369 6f6e 732e 2020 2a4e 6f74 6520  essions.  *Note \n+00008ac0: 4172 6974 686d 6574 6963 3a3a 2e0a 0a2a  Arithmetic::...*\n+00008ad0: 204d 656e 753a 0a0a 2a20 5363 616c 6172   Menu:..* Scalar\n+00008ae0: 206c 6974 6572 616c 733a 3a20 2020 2020   literals::     \n+00008af0: 2020 2020 2020 2020 4a75 7374 2074 6865          Just the\n+00008b00: 206e 756d 6265 7273 2e0a 2a20 506f 696e   numbers..* Poin\n+00008b10: 7420 616e 6420 7665 6374 6f72 206c 6974  t and vector lit\n+00008b20: 6572 616c 733a 3a20 2020 3364 2071 7561  erals::   3d qua\n+00008b30: 6e74 6974 6965 732e 0a2a 2054 7261 6e73  ntities..* Trans\n+00008b40: 666f 726d 206c 6974 6572 616c 733a 3a20  form literals:: \n+00008b50: 2020 2020 2020 2020 204d 6174 7269 7820           Matrix \n+00008b60: 666f 726d 2e0a 0a1f 0a46 696c 653a 2073  form.....File: s\n+00008b70: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n+00008b80: 653a 2053 6361 6c61 7220 6c69 7465 7261  e: Scalar litera\n+00008b90: 6c73 2c20 204e 6578 743a 2050 6f69 6e74  ls,  Next: Point\n+00008ba0: 2061 6e64 2076 6563 746f 7220 6c69 7465   and vector lite\n+00008bb0: 7261 6c73 2c20 2050 7265 763a 204c 6974  rals,  Prev: Lit\n+00008bc0: 6572 616c 732c 2020 5570 3a20 4c69 7465  erals,  Up: Lite\n+00008bd0: 7261 6c73 0a0a 332e 312e 332e 3120 5363  rals..3.1.3.1 Sc\n+00008be0: 616c 6172 206c 6974 6572 616c 730a 2e2e  alar literals...\n 00008bf0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-00008c00: 2e2e 2e2e 2e2e 2e0a 0a53 6361 6c61 7220  .........Scalar \n-00008c10: 6c69 7465 7261 6c73 2061 7265 2070 6f73  literals are pos\n-00008c20: 6974 6976 6520 666c 6f61 7469 6e67 2070  itive floating p\n-00008c30: 6f69 6e74 206e 756d 6265 7273 2077 6974  oint numbers wit\n-00008c40: 6820 7379 6e74 6178 0a61 6363 6f72 6469  h syntax.accordi\n-00008c50: 6e67 2074 6f20 4320 636f 6e76 656e 7469  ng to C conventi\n-00008c60: 6f6e 732e 2020 5468 6520 666f 6c6c 6f77  ons.  The follow\n-00008c70: 696e 6720 6172 6520 736f 6d65 2065 7861  ing are some exa\n-00008c80: 6d70 6c65 732e 0a20 2020 2020 3020 3130  mples..     0 10\n-00008c90: 3034 202e 3030 3120 382e 3331 3433 2033  04 .001 8.3143 3\n-00008ca0: 2e20 312e 3630 452d 3139 2036 2e30 3265  . 1.60E-19 6.02e\n-00008cb0: 2b32 330a 5363 616c 6172 206c 6974 6572  +23.Scalar liter\n-00008cc0: 616c 7320 6d61 7920 6e6f 7420 636f 6e74  als may not cont\n-00008cd0: 6169 6e20 656d 6265 6464 6564 2073 7061  ain embedded spa\n-00008ce0: 6365 732e 0a0a 1f0a 4669 6c65 3a20 736b  ces.....File: sk\n-00008cf0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n-00008d00: 3a20 506f 696e 7420 616e 6420 7665 6374  : Point and vect\n-00008d10: 6f72 206c 6974 6572 616c 732c 2020 4e65  or literals,  Ne\n-00008d20: 7874 3a20 5472 616e 7366 6f72 6d20 6c69  xt: Transform li\n-00008d30: 7465 7261 6c73 2c20 2050 7265 763a 2053  terals,  Prev: S\n-00008d40: 6361 6c61 7220 6c69 7465 7261 6c73 2c20  calar literals, \n-00008d50: 2055 703a 204c 6974 6572 616c 730a 0a33   Up: Literals..3\n-00008d60: 2e31 2e33 2e32 2050 6f69 6e74 2061 6e64  .1.3.2 Point and\n-00008d70: 2076 6563 746f 7220 6c69 7465 7261 6c73   vector literals\n-00008d80: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+00008c00: 2e2e 2e2e 2e0a 0a53 6361 6c61 7220 6c69  .......Scalar li\n+00008c10: 7465 7261 6c73 2061 7265 2070 6f73 6974  terals are posit\n+00008c20: 6976 6520 666c 6f61 7469 6e67 2070 6f69  ive floating poi\n+00008c30: 6e74 206e 756d 6265 7273 2077 6974 6820  nt numbers with \n+00008c40: 7379 6e74 6178 0a61 6363 6f72 6469 6e67  syntax.according\n+00008c50: 2074 6f20 4320 636f 6e76 656e 7469 6f6e   to C convention\n+00008c60: 732e 2020 5468 6520 666f 6c6c 6f77 696e  s.  The followin\n+00008c70: 6720 6172 6520 736f 6d65 2065 7861 6d70  g are some examp\n+00008c80: 6c65 732e 0a20 2020 2020 3020 3130 3034  les..     0 1004\n+00008c90: 202e 3030 3120 382e 3331 3433 2033 2e20   .001 8.3143 3. \n+00008ca0: 312e 3630 452d 3139 2036 2e30 3265 2b32  1.60E-19 6.02e+2\n+00008cb0: 330a 5363 616c 6172 206c 6974 6572 616c  3.Scalar literal\n+00008cc0: 7320 6d61 7920 6e6f 7420 636f 6e74 6169  s may not contai\n+00008cd0: 6e20 656d 6265 6464 6564 2073 7061 6365  n embedded space\n+00008ce0: 732e 0a0a 1f0a 4669 6c65 3a20 736b 6574  s.....File: sket\n+00008cf0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n+00008d00: 506f 696e 7420 616e 6420 7665 6374 6f72  Point and vector\n+00008d10: 206c 6974 6572 616c 732c 2020 4e65 7874   literals,  Next\n+00008d20: 3a20 5472 616e 7366 6f72 6d20 6c69 7465  : Transform lite\n+00008d30: 7261 6c73 2c20 2050 7265 763a 2053 6361  rals,  Prev: Sca\n+00008d40: 6c61 7220 6c69 7465 7261 6c73 2c20 2055  lar literals,  U\n+00008d50: 703a 204c 6974 6572 616c 730a 0a33 2e31  p: Literals..3.1\n+00008d60: 2e33 2e32 2050 6f69 6e74 2061 6e64 2076  .3.2 Point and v\n+00008d70: 6563 746f 7220 6c69 7465 7261 6c73 0a2e  ector literals..\n+00008d80: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n 00008d90: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-00008da0: 2e2e 0a0a 506f 696e 7473 2061 6e64 2076  ....Points and v\n-00008db0: 6563 746f 7220 6c69 7465 7261 6c73 2068  ector literals h\n-00008dc0: 6176 6520 7468 6573 6520 666f 726d 7320  ave these forms \n-00008dd0: 7265 7370 6563 7469 7665 6c79 2e0a 2020  respectively..  \n-00008de0: 2020 2028 582c 592c 5a29 2020 5b58 2c59     (X,Y,Z)  [X,Y\n-00008df0: 2c5a 5d0a 4561 6368 206f 6620 7468 6520  ,Z].Each of the \n-00008e00: 636f 6d70 6f6e 656e 7473 2069 7320 6974  components is it\n-00008e10: 7365 6c66 2061 2073 6361 6c61 7220 6578  self a scalar ex\n-00008e20: 7072 6573 7369 6f6e 2e20 2054 6865 207a  pression.  The z\n-00008e30: 2d63 6f6d 706f 6e65 6e74 730a 6172 6520  -components.are \n-00008e40: 6f70 7469 6f6e 616c 2061 6e64 2064 6566  optional and def\n-00008e50: 6175 6c74 2074 6f20 7a65 726f 2e0a 0a1f  ault to zero....\n-00008e60: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n-00008e70: 666f 2c20 204e 6f64 653a 2054 7261 6e73  fo,  Node: Trans\n-00008e80: 666f 726d 206c 6974 6572 616c 732c 2020  form literals,  \n-00008e90: 5072 6576 3a20 506f 696e 7420 616e 6420  Prev: Point and \n-00008ea0: 7665 6374 6f72 206c 6974 6572 616c 732c  vector literals,\n-00008eb0: 2020 5570 3a20 4c69 7465 7261 6c73 0a0a    Up: Literals..\n-00008ec0: 332e 312e 332e 3320 5472 616e 7366 6f72  3.1.3.3 Transfor\n-00008ed0: 6d20 6c69 7465 7261 6c73 0a2e 2e2e 2e2e  m literals......\n+00008da0: 0a0a 506f 696e 7473 2061 6e64 2076 6563  ..Points and vec\n+00008db0: 746f 7220 6c69 7465 7261 6c73 2068 6176  tor literals hav\n+00008dc0: 6520 7468 6573 6520 666f 726d 7320 7265  e these forms re\n+00008dd0: 7370 6563 7469 7665 6c79 2e0a 2020 2020  spectively..    \n+00008de0: 2028 582c 592c 5a29 2020 5b58 2c59 2c5a   (X,Y,Z)  [X,Y,Z\n+00008df0: 5d0a 4561 6368 206f 6620 7468 6520 636f  ].Each of the co\n+00008e00: 6d70 6f6e 656e 7473 2069 7320 6974 7365  mponents is itse\n+00008e10: 6c66 2061 2073 6361 6c61 7220 6578 7072  lf a scalar expr\n+00008e20: 6573 7369 6f6e 2e20 2054 6865 207a 2d63  ession.  The z-c\n+00008e30: 6f6d 706f 6e65 6e74 730a 6172 6520 6f70  omponents.are op\n+00008e40: 7469 6f6e 616c 2061 6e64 2064 6566 6175  tional and defau\n+00008e50: 6c74 2074 6f20 7a65 726f 2e0a 0a1f 0a46  lt to zero.....F\n+00008e60: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n+00008e70: 2c20 204e 6f64 653a 2054 7261 6e73 666f  ,  Node: Transfo\n+00008e80: 726d 206c 6974 6572 616c 732c 2020 5072  rm literals,  Pr\n+00008e90: 6576 3a20 506f 696e 7420 616e 6420 7665  ev: Point and ve\n+00008ea0: 6374 6f72 206c 6974 6572 616c 732c 2020  ctor literals,  \n+00008eb0: 5570 3a20 4c69 7465 7261 6c73 0a0a 332e  Up: Literals..3.\n+00008ec0: 312e 332e 3320 5472 616e 7366 6f72 6d20  1.3.3 Transform \n+00008ed0: 6c69 7465 7261 6c73 0a2e 2e2e 2e2e 2e2e  literals........\n 00008ee0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-00008ef0: 2e2e 2e2e 2e0a 0a4d 6f73 7420 7472 616e  .......Most tran\n-00008f00: 7366 6f72 6d20 6c69 7465 7261 6c73 2061  sform literals a\n-00008f10: 7265 2066 6f72 6d65 6420 6279 2022 636f  re formed by \"co\n-00008f20: 6e73 7472 7563 746f 7273 222e 2020 5468  nstructors\".  Th\n-00008f30: 6573 6520 6172 650a 7375 6d6d 6172 697a  ese are.summariz\n-00008f40: 6564 2069 6e20 7468 6520 666f 6c6c 6f77  ed in the follow\n-00008f50: 696e 6720 7461 626c 652e 0a43 6f6e 7374  ing table..Const\n-00008f60: 7275 6374 6f72 2020 2020 2020 2020 2020  ructor          \n-00008f70: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n-00008f80: 6172 616d 2074 7970 6573 2020 2020 2020  aram types      \n-00008f90: 2020 2020 2044 6573 6372 6970 7469 6f6e       Description\n-00008fa0: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  .---------------\n+00008ef0: 2e2e 2e0a 0a4d 6f73 7420 7472 616e 7366  .....Most transf\n+00008f00: 6f72 6d20 6c69 7465 7261 6c73 2061 7265  orm literals are\n+00008f10: 2066 6f72 6d65 6420 6279 2022 636f 6e73   formed by \"cons\n+00008f20: 7472 7563 746f 7273 222e 2020 5468 6573  tructors\".  Thes\n+00008f30: 6520 6172 650a 7375 6d6d 6172 697a 6564  e are.summarized\n+00008f40: 2069 6e20 7468 6520 666f 6c6c 6f77 696e   in the followin\n+00008f50: 6720 7461 626c 652e 0a43 6f6e 7374 7275  g table..Constru\n+00008f60: 6374 6f72 2020 2020 2020 2020 2020 2020  ctor            \n+00008f70: 2020 2020 2020 2020 2020 2020 2050 6172               Par\n+00008f80: 616d 2074 7970 6573 2020 2020 2020 2020  am types        \n+00008f90: 2020 2044 6573 6372 6970 7469 6f6e 0a2d     Description.-\n+00008fa0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\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 2d2d 2d2d 0a27 726f  ------------.'ro\n-00009010: 7461 7465 2841 2c50 2c58 2927 2020 2020  tate(A,P,X)'    \n-00009020: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009030: 2073 6361 6c61 722c 706f 696e 742c 7665   scalar,point,ve\n-00009040: 6374 6f72 2020 2052 6f74 6174 6520 2741  ctor   Rotate 'A\n-00009050: 2720 6465 6772 6565 7320 6162 6f75 7420  ' degrees about \n-00009060: 706f 696e 7420 2750 2720 7769 7468 2061  point 'P' with a\n-00009070: 7869 730a 2020 2020 2020 2020 2020 2020  xis.            \n+00009000: 2d2d 2d2d 2d2d 2d2d 2d2d 0a27 726f 7461  ----------.'rota\n+00009010: 7465 2841 2c50 2c58 2927 2020 2020 2020  te(A,P,X)'      \n+00009020: 2020 2020 2020 2020 2020 2020 2020 2073                 s\n+00009030: 6361 6c61 722c 706f 696e 742c 7665 6374  calar,point,vect\n+00009040: 6f72 2020 2052 6f74 6174 6520 2741 2720  or   Rotate 'A' \n+00009050: 6465 6772 6565 7320 6162 6f75 7420 706f  degrees about po\n+00009060: 696e 7420 2750 2720 7769 7468 2061 7869  int 'P' with axi\n+00009070: 730a 2020 2020 2020 2020 2020 2020 2020  s.              \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 2020 2020 2758                'X\n-000090b0: 2720 6163 636f 7264 696e 6720 746f 2074  ' according to t\n-000090c0: 6865 2072 6967 6874 2068 616e 6420 7275  he right hand ru\n-000090d0: 6c65 2e0a 2020 2020 2020 2020 2020 2020  le..            \n+000090a0: 2020 2020 2020 2020 2020 2020 2758 2720              'X' \n+000090b0: 6163 636f 7264 696e 6720 746f 2074 6865  according to the\n+000090c0: 2072 6967 6874 2068 616e 6420 7275 6c65   right hand rule\n+000090d0: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020 2020 2a4e                *N\n-00009110: 6f74 6520 5269 6768 7420 6861 6e64 2072  ote Right hand r\n-00009120: 756c 653a 3a2e 2020 2750 2720 616e 6420  ule::.  'P' and \n-00009130: 2758 2720 6172 6520 626f 7468 0a20 2020  'X' are both.   \n+00009100: 2020 2020 2020 2020 2020 2020 2a4e 6f74              *Not\n+00009110: 6520 5269 6768 7420 6861 6e64 2072 756c  e Right hand rul\n+00009120: 653a 3a2e 2020 2750 2720 616e 6420 2758  e::.  'P' and 'X\n+00009130: 2720 6172 6520 626f 7468 0a20 2020 2020  ' 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 2020 2020 206f 7074 696f 6e61 6c20         optional \n-00009180: 616e 6420 6465 6661 756c 7420 746f 2074  and default to t\n-00009190: 6865 206f 7269 6769 6e20 616e 6420 7468  he origin and th\n-000091a0: 650a 2020 2020 2020 2020 2020 2020 2020  e.              \n+00009170: 2020 2020 206f 7074 696f 6e61 6c20 616e       optional an\n+00009180: 6420 6465 6661 756c 7420 746f 2074 6865  d default to the\n+00009190: 206f 7269 6769 6e20 616e 6420 7468 650a   origin and the.\n+000091a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020 7a2d 6178              z-ax\n-000091e0: 6973 2072 6573 7065 6374 6976 656c 792e  is respectively.\n-000091f0: 0a27 7472 616e 736c 6174 6528 5829 2720  .'translate(X)' \n+000091d0: 2020 2020 2020 2020 2020 7a2d 6178 6973            z-axis\n+000091e0: 2072 6573 7065 6374 6976 656c 792e 0a27   respectively..'\n+000091f0: 7472 616e 736c 6174 6528 5829 2720 2020  translate(X)'   \n 00009200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009210: 2020 2020 2076 6563 746f 7220 2020 2020       vector     \n-00009220: 2020 2020 2020 2020 2020 2054 7261 6e73             Trans\n-00009230: 6c61 7465 2062 7920 2758 272e 0a27 7363  late by 'X'..'sc\n-00009240: 616c 6528 5329 2720 2020 2020 2020 2020  ale(S)'         \n-00009250: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009260: 2073 6361 6c61 7220 2020 2020 2020 2020   scalar         \n-00009270: 2020 2020 2020 2053 6361 6c65 2075 6e69         Scale uni\n-00009280: 666f 726d 6c79 2062 7920 6661 6374 6f72  formly by factor\n-00009290: 2027 5327 2e0a 2773 6361 6c65 2856 2927   'S'..'scale(V)'\n+00009210: 2020 2076 6563 746f 7220 2020 2020 2020     vector       \n+00009220: 2020 2020 2020 2020 2054 7261 6e73 6c61           Transla\n+00009230: 7465 2062 7920 2758 272e 0a27 7363 616c  te by 'X'..'scal\n+00009240: 6528 5329 2720 2020 2020 2020 2020 2020  e(S)'           \n+00009250: 2020 2020 2020 2020 2020 2020 2020 2073                 s\n+00009260: 6361 6c61 7220 2020 2020 2020 2020 2020  calar           \n+00009270: 2020 2020 2053 6361 6c65 2075 6e69 666f       Scale unifo\n+00009280: 726d 6c79 2062 7920 6661 6374 6f72 2027  rmly by factor '\n+00009290: 5327 2e0a 2773 6361 6c65 2856 2927 2020  S'..'scale(V)'  \n 000092a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000092b0: 2020 2020 2020 2020 2020 7665 6374 6f72            vector\n-000092c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000092d0: 5363 616c 6520 616c 6f6e 6720 6561 6368  Scale along each\n-000092e0: 2061 7869 7320 6279 2063 6f6d 706f 6e65   axis by compone\n-000092f0: 6e74 7320 6f66 2027 5627 2e0a 2770 726f  nts of 'V'..'pro\n-00009300: 6a65 6374 2829 2720 2020 2020 2020 2020  ject()'         \n-00009310: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009320: 2d2d 2020 2020 2020 2020 2020 2020 2020  --              \n-00009330: 2020 2020 2020 5361 6d65 2061 7320 2773        Same as 's\n-00009340: 6361 6c65 285b 312c 312c 305d 2927 2e0a  cale([1,1,0])'..\n-00009350: 2770 726f 6a65 6374 2853 2927 2020 2020  'project(S)'    \n+000092b0: 2020 2020 2020 2020 7665 6374 6f72 2020          vector  \n+000092c0: 2020 2020 2020 2020 2020 2020 2020 5363                Sc\n+000092d0: 616c 6520 616c 6f6e 6720 6561 6368 2061  ale along each a\n+000092e0: 7869 7320 6279 2063 6f6d 706f 6e65 6e74  xis by component\n+000092f0: 7320 6f66 2027 5627 2e0a 2770 726f 6a65  s of 'V'..'proje\n+00009300: 6374 2829 2720 2020 2020 2020 2020 2020  ct()'           \n+00009310: 2020 2020 2020 2020 2020 2020 2020 2d2d                --\n+00009320: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00009330: 2020 2020 5361 6d65 2061 7320 2773 6361      Same as 'sca\n+00009340: 6c65 285b 312c 312c 305d 2927 2e0a 2770  le([1,1,0])'..'p\n+00009350: 726f 6a65 6374 2853 2927 2020 2020 2020  roject(S)'      \n 00009360: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009370: 2020 2020 7363 616c 6172 2020 2020 2020      scalar      \n-00009380: 2020 2020 2020 2020 2020 5065 7273 7065            Perspe\n-00009390: 6374 6976 6520 7072 6f6a 6563 7469 6f6e  ctive projection\n-000093a0: 2077 6974 6820 7669 6577 2063 656e 7465   with view cente\n-000093b0: 7220 6174 0a20 2020 2020 2020 2020 2020  r at.           \n+00009370: 2020 7363 616c 6172 2020 2020 2020 2020    scalar        \n+00009380: 2020 2020 2020 2020 5065 7273 7065 6374          Perspect\n+00009390: 6976 6520 7072 6f6a 6563 7469 6f6e 2077  ive projection w\n+000093a0: 6974 6820 7669 6577 2063 656e 7465 7220  ith view center \n+000093b0: 6174 0a20 2020 2020 2020 2020 2020 2020  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 2020 2020 206f                 o\n-000093f0: 7269 6769 6e20 616e 6420 7072 6f6a 6563  rigin and projec\n-00009400: 7469 6f6e 2070 6c61 6e65 207a 3d2d 2753  tion plane z=-'S\n-00009410: 272e 0a27 7065 7273 7065 6374 6976 6528  '..'perspective(\n-00009420: 5329 2720 2020 2020 2020 2020 2020 2020  S)'             \n-00009430: 2020 2020 2020 2073 6361 6c61 7220 2020         scalar   \n-00009440: 2020 2020 2020 2020 2020 2020 2050 6572               Per\n-00009450: 7370 6563 7469 7665 205f 7472 616e 7366  spective _transf\n-00009460: 6f72 6d5f 2069 6465 6e74 6963 616c 2074  orm_ identical t\n-00009470: 6f0a 2020 2020 2020 2020 2020 2020 2020  o.              \n+000093e0: 2020 2020 2020 2020 2020 2020 206f 7269               ori\n+000093f0: 6769 6e20 616e 6420 7072 6f6a 6563 7469  gin and projecti\n+00009400: 6f6e 2070 6c61 6e65 207a 3d2d 2753 272e  on plane z=-'S'.\n+00009410: 0a27 7065 7273 7065 6374 6976 6528 5329  .'perspective(S)\n+00009420: 2720 2020 2020 2020 2020 2020 2020 2020  '               \n+00009430: 2020 2020 2073 6361 6c61 7220 2020 2020       scalar     \n+00009440: 2020 2020 2020 2020 2020 2050 6572 7370             Persp\n+00009450: 6563 7469 7665 205f 7472 616e 7366 6f72  ective _transfor\n+00009460: 6d5f 2069 6465 6e74 6963 616c 2074 6f0a  m_ identical to.\n+00009470: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020 2770 726f              'pro\n-000094b0: 6a65 6374 2853 2927 2065 7863 6570 7420  ject(S)' except \n-000094c0: 7468 6174 2074 6865 207a 2d63 6f6f 7264  that the z-coord\n-000094d0: 696e 6174 6520 6f66 0a20 2020 2020 2020  inate of.       \n+000094a0: 2020 2020 2020 2020 2020 2770 726f 6a65            'proje\n+000094b0: 6374 2853 2927 2065 7863 6570 7420 7468  ct(S)' except th\n+000094c0: 6174 2074 6865 207a 2d63 6f6f 7264 696e  at the z-coordin\n+000094d0: 6174 6520 6f66 0a20 2020 2020 2020 2020  ate 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 2020                  \n-00009510: 2020 2074 6865 2074 7261 6e73 666f 726d     the transform\n-00009520: 6564 2072 6573 756c 7420 6973 2022 7073  ed result is \"ps\n-00009530: 6575 646f 6465 7074 6822 2c0a 2020 2020  eudodepth\",.    \n+00009510: 2074 6865 2074 7261 6e73 666f 726d 6564   the transformed\n+00009520: 2072 6573 756c 7420 6973 2022 7073 6575   result is \"pseu\n+00009530: 646f 6465 7074 6822 2c0a 2020 2020 2020  dodepth\",.      \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 2020 2020 7573 6162 6c65 2062 7920        usable by \n-00009580: 7468 6520 6869 6464 656e 2073 7572 6661  the hidden surfa\n-00009590: 6365 2061 6c67 6f72 6974 686d 2e0a 2776  ce algorithm..'v\n-000095a0: 6965 7728 452c 442c 5529 2720 2020 2020  iew(E,D,U)'     \n+00009570: 2020 2020 7573 6162 6c65 2062 7920 7468      usable by th\n+00009580: 6520 6869 6464 656e 2073 7572 6661 6365  e hidden surface\n+00009590: 2061 6c67 6f72 6974 686d 2e0a 2776 6965   algorithm..'vie\n+000095a0: 7728 452c 442c 5529 2720 2020 2020 2020  w(E,D,U)'       \n 000095b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000095c0: 2020 706f 696e 742c 7665 6374 6f72 2c76    point,vector,v\n-000095d0: 6563 746f 7220 2020 5669 6577 2074 7261  ector   View tra\n-000095e0: 6e73 666f 726d 2073 696d 696c 6172 2074  nsform similar t\n-000095f0: 6f20 7468 6174 206f 6620 274f 7065 6e47  o that of 'OpenG\n-00009600: 4c27 2773 2e0a 2020 2020 2020 2020 2020  L''s..          \n+000095c0: 706f 696e 742c 7665 6374 6f72 2c76 6563  point,vector,vec\n+000095d0: 746f 7220 2020 5669 6577 2074 7261 6e73  tor   View trans\n+000095e0: 666f 726d 2073 696d 696c 6172 2074 6f20  form similar to \n+000095f0: 7468 6174 206f 6620 274f 7065 6e47 4c27  that of 'OpenGL'\n+00009600: 2773 2e0a 2020 2020 2020 2020 2020 2020  '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 2020 2020                  \n-00009640: 5468 6520 5f65 7965 2070 6f69 6e74 5f20  The _eye point_ \n-00009650: 2745 2720 6973 2074 7261 6e73 6c61 7465  'E' is translate\n-00009660: 6420 746f 2074 6865 0a20 2020 2020 2020  d to the.       \n+00009630: 2020 2020 2020 2020 2020 2020 2020 5468                Th\n+00009640: 6520 5f65 7965 2070 6f69 6e74 5f20 2745  e _eye point_ 'E\n+00009650: 2720 6973 2074 7261 6e73 6c61 7465 6420  ' is translated \n+00009660: 746f 2074 6865 0a20 2020 2020 2020 2020  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 2020                  \n-000096a0: 2020 206f 7269 6769 6e20 7768 696c 6520     origin while \n-000096b0: 6120 726f 7461 7469 6f6e 2069 7320 616c  a rotation is al\n-000096c0: 736f 2061 7070 6c69 6564 2074 6861 740a  so applied that.\n+000096a0: 206f 7269 6769 6e20 7768 696c 6520 6120   origin while a \n+000096b0: 726f 7461 7469 6f6e 2069 7320 616c 736f  rotation is also\n+000096c0: 2061 7070 6c69 6564 2074 6861 740a 2020   applied that.  \n 000096d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020 6d61 6b65 7320            makes \n-00009710: 7468 6520 5f76 6965 7720 6469 7265 6374  the _view direct\n-00009720: 696f 6e20 7665 6374 6f72 5f20 2744 2720  ion vector_ 'D' \n-00009730: 616e 6420 7468 650a 2020 2020 2020 2020  and the.        \n+00009700: 2020 2020 2020 2020 6d61 6b65 7320 7468          makes th\n+00009710: 6520 5f76 6965 7720 6469 7265 6374 696f  e _view directio\n+00009720: 6e20 7665 6374 6f72 5f20 2744 2720 616e  n vector_ 'D' an\n+00009730: 6420 7468 650a 2020 2020 2020 2020 2020  d 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 2020                  \n-00009770: 2020 5f76 6965 7720 2275 7022 2076 6563    _view \"up\" vec\n-00009780: 746f 725f 2027 5527 2070 6f69 6e74 2069  tor_ 'U' point i\n-00009790: 6e20 7468 6520 6e65 6761 7469 7665 0a20  n the negative. \n+00009770: 5f76 6965 7720 2275 7022 2076 6563 746f  _view \"up\" vecto\n+00009780: 725f 2027 5527 2070 6f69 6e74 2069 6e20  r_ 'U' point in \n+00009790: 7468 6520 6e65 6761 7469 7665 0a20 2020  the negative.   \n 000097a0: 2020 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 2020 2020 207a 2d20 616e 6420           z- and \n-000097e0: 7468 6520 792d 6469 7265 6374 696f 6e73  the y-directions\n-000097f0: 2072 6573 7065 6374 6976 656c 792e 2020   respectively.  \n-00009800: 4966 2027 5527 0a20 2020 2020 2020 2020  If 'U'.         \n+000097d0: 2020 2020 2020 207a 2d20 616e 6420 7468         z- and th\n+000097e0: 6520 792d 6469 7265 6374 696f 6e73 2072  e y-directions r\n+000097f0: 6573 7065 6374 6976 656c 792e 2020 4966  espectively.  If\n+00009800: 2027 5527 0a20 2020 2020 2020 2020 2020   '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 2020 2020                  \n-00009840: 2069 7320 6f6d 6974 7465 642c 2069 7420   is omitted, it \n-00009850: 6465 6661 756c 7473 2074 6f20 5b30 2c31  defaults to [0,1\n-00009860: 2c30 5d2e 2020 5768 656e 2027 5527 0a20  ,0].  When 'U'. \n+00009830: 2020 2020 2020 2020 2020 2020 2020 2069                 i\n+00009840: 7320 6f6d 6974 7465 642c 2069 7420 6465  s omitted, it de\n+00009850: 6661 756c 7473 2074 6f20 5b30 2c31 2c30  faults to [0,1,0\n+00009860: 5d2e 2020 5768 656e 2027 5527 0a20 2020  ].  When 'U'.   \n 00009870: 2020 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 2020 2020 2069 7320 6f6d 6974           is omit\n-000098b0: 7465 642c 2027 4427 206d 6179 2062 6520  ted, 'D' may be \n-000098c0: 616c 736f 3b20 6974 2064 6566 6175 6c74  also; it default\n-000098d0: 7320 746f 0a20 2020 2020 2020 2020 2020  s to.           \n+000098a0: 2020 2020 2020 2069 7320 6f6d 6974 7465         is omitte\n+000098b0: 642c 2027 4427 206d 6179 2062 6520 616c  d, 'D' may be al\n+000098c0: 736f 3b20 6974 2064 6566 6175 6c74 7320  so; it defaults \n+000098d0: 746f 0a20 2020 2020 2020 2020 2020 2020  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 2020 2020 2027                 '\n-00009910: 2830 2c30 2c30 292d 2845 2927 2c20 6120  (0,0,0)-(E)', a \n-00009920: 7665 6374 6f72 2070 6f69 6e74 696e 6720  vector pointing \n-00009930: 6672 6f6d 2074 6865 2065 7965 0a20 2020  from the eye.   \n+00009900: 2020 2020 2020 2020 2020 2020 2027 2830               '(0\n+00009910: 2c30 2c30 292d 2845 2927 2c20 6120 7665  ,0,0)-(E)', a ve\n+00009920: 6374 6f72 2070 6f69 6e74 696e 6720 6672  ctor pointing fr\n+00009930: 6f6d 2074 6865 2065 7965 0a20 2020 2020  om 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 2020 2020 2074 6f77 6172 6420 7468         toward th\n-00009980: 6520 6f72 6967 696e 2e0a 2776 6965 7728  e origin..'view(\n-00009990: 452c 4c2c 5529 2720 2020 2020 2020 2020  E,L,U)'         \n-000099a0: 2020 2020 2020 2020 2020 2020 2020 706f                po\n-000099b0: 696e 742c 706f 696e 742c 7665 6374 6f72  int,point,vector\n-000099c0: 2020 2020 416e 2061 6c74 6572 6e61 7465      An alternate\n-000099d0: 2066 6f72 6d20 6f66 2027 7669 6577 2845   form of 'view(E\n-000099e0: 2c44 2c55 2927 2061 626f 7665 2077 6865  ,D,U)' above whe\n-000099f0: 7265 0a20 2020 2020 2020 2020 2020 2020  re.             \n+00009970: 2020 2020 2074 6f77 6172 6420 7468 6520       toward the \n+00009980: 6f72 6967 696e 2e0a 2776 6965 7728 452c  origin..'view(E,\n+00009990: 4c2c 5529 2720 2020 2020 2020 2020 2020  L,U)'           \n+000099a0: 2020 2020 2020 2020 2020 2020 706f 696e              poin\n+000099b0: 742c 706f 696e 742c 7665 6374 6f72 2020  t,point,vector  \n+000099c0: 2020 416e 2061 6c74 6572 6e61 7465 2066    An alternate f\n+000099d0: 6f72 6d20 6f66 2027 7669 6577 2845 2c44  orm of 'view(E,D\n+000099e0: 2c55 2927 2061 626f 7665 2077 6865 7265  ,U)' above where\n+000099f0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \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 2020 2020 2074 6865               the\n-00009a30: 2076 6965 7720 6469 7265 6374 696f 6e20   view direction \n-00009a40: 7061 7261 6d65 7465 7220 2744 2720 6973  parameter 'D' is\n-00009a50: 2072 6570 6c61 6365 640a 2020 2020 2020   replaced.      \n+00009a20: 2020 2020 2020 2020 2020 2074 6865 2076             the v\n+00009a30: 6965 7720 6469 7265 6374 696f 6e20 7061  iew direction pa\n+00009a40: 7261 6d65 7465 7220 2744 2720 6973 2072  rameter 'D' is r\n+00009a50: 6570 6c61 6365 640a 2020 2020 2020 2020  eplaced.        \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: 2020 2020 7769 7468 2061 2022 6c6f 6f6b      with a \"look\n-00009aa0: 2061 7422 2070 6f69 6e74 2027 4c27 2c20   at\" point 'L', \n-00009ab0: 692e 652e 2c20 6120 706f 696e 740a 2020  i.e., a point.  \n+00009a90: 2020 7769 7468 2061 2022 6c6f 6f6b 2061    with a \"look a\n+00009aa0: 7422 2070 6f69 6e74 2027 4c27 2c20 692e  t\" point 'L', i.\n+00009ab0: 652e 2c20 6120 706f 696e 740a 2020 2020  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 2020 2020 7768 6572 6520 7468          where th\n-00009b00: 6520 7669 6577 6572 2069 7320 666f 6375  e viewer is focu\n-00009b10: 7369 6e67 2068 6572 2061 7474 656e 7469  sing her attenti\n-00009b20: 6f6e 2e0a 2020 2020 2020 2020 2020 2020  on..            \n+00009af0: 2020 2020 2020 7768 6572 6520 7468 6520        where the \n+00009b00: 7669 6577 6572 2069 7320 666f 6375 7369  viewer is focusi\n+00009b10: 6e67 2068 6572 2061 7474 656e 7469 6f6e  ng her attention\n+00009b20: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020 2020 5468                Th\n-00009b60: 6973 2066 6f72 6d20 6f66 2076 6965 7720  is form of view \n-00009b70: 6973 2065 7175 6976 616c 656e 7420 746f  is equivalent to\n-00009b80: 2027 7669 6577 2845 2c0a 2020 2020 2020   'view(E,.      \n+00009b50: 2020 2020 2020 2020 2020 2020 5468 6973              This\n+00009b60: 2066 6f72 6d20 6f66 2076 6965 7720 6973   form of view is\n+00009b70: 2065 7175 6976 616c 656e 7420 746f 2027   equivalent to '\n+00009b80: 7669 6577 2845 2c0a 2020 2020 2020 2020  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: 2020 2020 284c 292d 2845 292c 2055 2927      (L)-(E), U)'\n-00009bd0: 2c20 7768 6572 6520 2728 4c29 2d28 4529  , where '(L)-(E)\n-00009be0: 2720 6973 2061 2064 6972 6563 7469 6f6e  ' is a direction\n-00009bf0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+00009bc0: 2020 284c 292d 2845 292c 2055 2927 2c20    (L)-(E), U)', \n+00009bd0: 7768 6572 6520 2728 4c29 2d28 4529 2720  where '(L)-(E)' \n+00009be0: 6973 2061 2064 6972 6563 7469 6f6e 0a20  is a direction. \n+00009bf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020 2076 6563 746f             vecto\n-00009c30: 722e 2020 2755 2720 6973 206f 7074 696f  r.  'U' is optio\n-00009c40: 6e61 6c20 616e 6420 6465 6661 756c 7473  nal and defaults\n-00009c50: 2074 6f0a 2020 2020 2020 2020 2020 2020   to.            \n+00009c20: 2020 2020 2020 2020 2076 6563 746f 722e           vector.\n+00009c30: 2020 2755 2720 6973 206f 7074 696f 6e61    'U' is optiona\n+00009c40: 6c20 616e 6420 6465 6661 756c 7473 2074  l and defaults t\n+00009c50: 6f0a 2020 2020 2020 2020 2020 2020 2020  o.              \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 2020 2020 5b30                [0\n-00009c90: 2c31 2c30 5d2e 0a27 5b5b 615f 7b31 317d  ,1,0]..'[[a_{11}\n-00009ca0: 2c61 5f7b 3132 7d2c 615f 7b31 337d 2c61  ,a_{12},a_{13},a\n-00009cb0: 5f7b 3134 7d5d 2720 2020 2031 3620 7363  _{14}]'    16 sc\n-00009cc0: 616c 6172 7320 2020 2020 2020 2020 2020  alars           \n-00009cd0: 2044 6972 6563 7420 7472 616e 7366 6f72   Direct transfor\n-00009ce0: 6d20 6d61 7472 6978 2064 6566 696e 6974  m matrix definit\n-00009cf0: 696f 6e2e 2020 4561 6368 206f 660a 2720  ion.  Each of.' \n-00009d00: 5b61 5f7b 3231 7d2c 615f 7b32 327d 2c61  [a_{21},a_{22},a\n-00009d10: 5f7b 3233 7d2c 615f 7b32 347d 5d27 2020  _{23},a_{24}]'  \n+00009c80: 2020 2020 2020 2020 2020 2020 5b30 2c31              [0,1\n+00009c90: 2c30 5d2e 0a27 5b5b 615f 7b31 317d 2c61  ,0]..'[[a_{11},a\n+00009ca0: 5f7b 3132 7d2c 615f 7b31 337d 2c61 5f7b  _{12},a_{13},a_{\n+00009cb0: 3134 7d5d 2720 2020 2031 3620 7363 616c  14}]'    16 scal\n+00009cc0: 6172 7320 2020 2020 2020 2020 2020 2044  ars            D\n+00009cd0: 6972 6563 7420 7472 616e 7366 6f72 6d20  irect transform \n+00009ce0: 6d61 7472 6978 2064 6566 696e 6974 696f  matrix definitio\n+00009cf0: 6e2e 2020 4561 6368 206f 660a 2720 5b61  n.  Each of.' [a\n+00009d00: 5f7b 3231 7d2c 615f 7b32 327d 2c61 5f7b  _{21},a_{22},a_{\n+00009d10: 3233 7d2c 615f 7b32 347d 5d27 2020 2020  23},a_{24}]'    \n 00009d20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00009d30: 2020 2020 2020 2020 7468 6520 615f 7b69          the a_{i\n-00009d40: 6a7d 2069 7320 6120 7363 616c 6172 2065  j} is a scalar e\n-00009d50: 7870 7265 7373 696f 6e2e 2020 5365 6520  xpression.  See \n-00009d60: 7465 7874 0a27 205b 615f 7b33 317d 2c61  text.' [a_{31},a\n-00009d70: 5f7b 3332 7d2c 615f 7b33 337d 2c61 5f7b  _{32},a_{33},a_{\n-00009d80: 3334 7d5d 2720 2020 2020 2020 2020 2020  34}]'           \n-00009d90: 2020 2020 2020 2020 2020 2020 2020 2066                 f\n-00009da0: 6f72 2064 6574 6169 6c73 2e0a 2720 5b61  or details..' [a\n-00009db0: 5f7b 3431 7d2c 615f 7b34 327d 2c61 5f7b  _{41},a_{42},a_{\n-00009dc0: 3433 7d2c 615f 7b34 347d 5d5d 270a 5468  43},a_{44}]]'.Th\n-00009dd0: 6520 2770 726f 6a65 6374 2720 636f 6e73  e 'project' cons\n-00009de0: 7472 7563 746f 7220 6973 206e 6f74 2067  tructor is not g\n-00009df0: 656e 6572 616c 6c79 2075 7365 6675 6c20  enerally useful \n-00009e00: 6265 6361 7573 6520 6974 2064 6566 6561  because it defea\n-00009e10: 7473 0a68 6964 6465 6e20 7375 7266 6163  ts.hidden surfac\n-00009e20: 6520 7265 6d6f 7661 6c20 6279 2063 6f6c  e removal by col\n-00009e30: 6c61 7073 696e 6720 7468 6520 7363 656e  lapsing the scen\n-00009e40: 6520 6f6e 746f 2061 2073 696e 676c 6520  e onto a single \n-00009e50: 706c 616e 652e 2020 4974 0a69 7320 6120  plane.  It.is a \n-00009e60: 7370 6563 6961 6c20 7075 7270 6f73 6520  special purpose \n-00009e70: 7472 616e 7366 6f72 6d20 666f 7220 6472  transform for dr\n-00009e80: 6177 696e 6720 7069 6374 7572 6573 206f  awing pictures o\n-00009e90: 6620 7363 656e 6573 2077 6865 7265 0a74  f scenes where.t\n-00009ea0: 6872 6565 2d64 696d 656e 7369 6f6e 616c  hree-dimensional\n-00009eb0: 206f 626a 6563 7473 2061 7265 2062 6569   objects are bei\n-00009ec0: 6e67 2070 726f 6a65 6374 6564 206f 6e74  ng projected ont\n-00009ed0: 6f20 706c 616e 6573 2e20 2053 6565 2c20  o planes.  See, \n-00009ee0: 666f 720a 6578 616d 706c 652c 202a 6e6f  for.example, *no\n-00009ef0: 7465 204f 7665 7276 6965 773a 3a2e 0a0a  te Overview::...\n-00009f00: 2020 2054 6865 2064 6972 6563 7420 7472     The direct tr\n-00009f10: 616e 7366 6f72 6d20 636f 6e73 7472 7563  ansform construc\n-00009f20: 746f 7220 616c 6c6f 7773 2064 6972 6563  tor allows direc\n-00009f30: 7420 656e 7472 7920 6f66 2061 2034 7834  t entry of a 4x4\n-00009f40: 0a74 7261 6e73 666f 726d 6174 696f 6e20  .transformation \n-00009f50: 6d61 7472 6978 2e20 204d 6f73 7420 3364  matrix.  Most 3d\n-00009f60: 2067 7261 7068 6963 7320 7379 7374 656d   graphics system\n-00009f70: 732c 2069 6e63 6c75 6469 6e67 2027 736b  s, including 'sk\n-00009f80: 6574 6368 272c 0a75 7365 2034 2d64 696d  etch',.use 4-dim\n-00009f90: 656e 7369 6f6e 616c 2068 6f6d 6f67 656e  ensional homogen\n-00009fa0: 656f 7573 2063 6f6f 7264 696e 6174 6573  eous coordinates\n-00009fb0: 2069 6e74 6572 6e61 6c6c 792e 2020 5468   internally.  Th\n-00009fc0: 6573 6520 6172 650a 7472 616e 7366 6f72  ese are.transfor\n-00009fd0: 6d65 6420 6279 206d 756c 7469 706c 6963  med by multiplic\n-00009fe0: 6174 696f 6e20 7769 7468 2034 7834 206d  ation with 4x4 m\n-00009ff0: 6174 7269 6365 732e 2020 5468 6520 6275  atrices.  The bu\n-0000a000: 696c 742d 696e 0a63 6f6e 7374 7275 6374  ilt-in.construct\n-0000a010: 6f72 7320 2827 726f 7461 7465 272c 2027  ors ('rotate', '\n-0000a020: 7363 616c 6527 2c20 6574 632e 2920 2061  scale', etc.)  a\n-0000a030: 7265 2061 6c6c 2074 7261 6e73 6c61 7465  re all translate\n-0000a040: 6420 696e 7465 726e 616c 6c79 2074 6f0a  d internally to.\n-0000a050: 7375 6368 2034 7834 206d 6174 7269 6365  such 4x4 matrice\n-0000a060: 732e 2020 466f 7220 6d6f 7265 2069 6e66  s.  For more inf\n-0000a070: 6f72 6d61 7469 6f6e 206f 6e20 686f 6d6f  ormation on homo\n-0000a080: 6765 6e65 6f75 7320 636f 6f72 6469 6e61  geneous coordina\n-0000a090: 7465 0a74 7261 6e73 666f 726d 6174 696f  te.transformatio\n-0000a0a0: 6e73 2c20 7365 6520 616e 7920 676f 6f64  ns, see any good\n-0000a0b0: 2063 6f6d 7075 7465 7220 6772 6170 6869   computer graphi\n-0000a0c0: 6373 2074 6578 7462 6f6f 6b2e 2020 5468  cs textbook.  Th\n-0000a0d0: 6520 6469 7265 6374 0a74 7261 6e73 666f  e direct.transfo\n-0000a0e0: 726d 2066 6561 7475 7265 206f 6620 2773  rm feature of 's\n-0000a0f0: 6b65 7463 6827 2061 6c6c 6f77 7320 796f  ketch' allows yo\n-0000a100: 7520 746f 2065 6e74 6572 2061 206d 6174  u to enter a mat\n-0000a110: 7269 7820 6f66 2079 6f75 7220 6f77 6e0a  rix of your own.\n-0000a120: 6368 6f69 6365 2e20 2054 6865 7265 2061  choice.  There a\n-0000a130: 7265 206e 6f74 206d 616e 7920 6361 7365  re not many case\n-0000a140: 7320 7768 6572 6520 7468 6973 2069 7320  s where this is \n-0000a150: 7573 6566 756c 2c20 6275 7420 6966 2079  useful, but if y\n-0000a160: 6f75 2064 6f0a 6e65 6564 2069 742c 2079  ou do.need it, y\n-0000a170: 6f75 206e 6565 6420 6974 2062 6164 6c79  ou need it badly\n-0000a180: 210a 0a1f 0a46 696c 653a 2073 6b65 7463  !....File: sketc\n-0000a190: 682e 696e 666f 2c20 204e 6f64 653a 2041  h.info,  Node: A\n-0000a1a0: 7269 7468 6d65 7469 632c 2020 4e65 7874  rithmetic,  Next\n-0000a1b0: 3a20 4f70 7469 6f6e 732c 2020 5072 6576  : Options,  Prev\n-0000a1c0: 3a20 4c69 7465 7261 6c73 2c20 2055 703a  : Literals,  Up:\n-0000a1d0: 204c 616e 6775 6167 6520 6261 7369 6373   Language basics\n-0000a1e0: 0a0a 332e 312e 3420 4172 6974 686d 6574  ..3.1.4 Arithmet\n-0000a1f0: 6963 2065 7870 7265 7373 696f 6e73 0a2d  ic expressions.-\n+00009d30: 2020 2020 2020 7468 6520 615f 7b69 6a7d        the a_{ij}\n+00009d40: 2069 7320 6120 7363 616c 6172 2065 7870   is a scalar exp\n+00009d50: 7265 7373 696f 6e2e 2020 5365 6520 7465  ression.  See te\n+00009d60: 7874 0a27 205b 615f 7b33 317d 2c61 5f7b  xt.' [a_{31},a_{\n+00009d70: 3332 7d2c 615f 7b33 337d 2c61 5f7b 3334  32},a_{33},a_{34\n+00009d80: 7d5d 2720 2020 2020 2020 2020 2020 2020  }]'             \n+00009d90: 2020 2020 2020 2020 2020 2020 2066 6f72               for\n+00009da0: 2064 6574 6169 6c73 2e0a 2720 5b61 5f7b   details..' [a_{\n+00009db0: 3431 7d2c 615f 7b34 327d 2c61 5f7b 3433  41},a_{42},a_{43\n+00009dc0: 7d2c 615f 7b34 347d 5d5d 270a 5468 6520  },a_{44}]]'.The \n+00009dd0: 2770 726f 6a65 6374 2720 636f 6e73 7472  'project' constr\n+00009de0: 7563 746f 7220 6973 206e 6f74 2067 656e  uctor is not gen\n+00009df0: 6572 616c 6c79 2075 7365 6675 6c20 6265  erally useful be\n+00009e00: 6361 7573 6520 6974 2064 6566 6561 7473  cause it defeats\n+00009e10: 0a68 6964 6465 6e20 7375 7266 6163 6520  .hidden surface \n+00009e20: 7265 6d6f 7661 6c20 6279 2063 6f6c 6c61  removal by colla\n+00009e30: 7073 696e 6720 7468 6520 7363 656e 6520  psing the scene \n+00009e40: 6f6e 746f 2061 2073 696e 676c 6520 706c  onto a single pl\n+00009e50: 616e 652e 2020 4974 0a69 7320 6120 7370  ane.  It.is a sp\n+00009e60: 6563 6961 6c20 7075 7270 6f73 6520 7472  ecial purpose tr\n+00009e70: 616e 7366 6f72 6d20 666f 7220 6472 6177  ansform for draw\n+00009e80: 696e 6720 7069 6374 7572 6573 206f 6620  ing pictures of \n+00009e90: 7363 656e 6573 2077 6865 7265 0a74 6872  scenes where.thr\n+00009ea0: 6565 2d64 696d 656e 7369 6f6e 616c 206f  ee-dimensional o\n+00009eb0: 626a 6563 7473 2061 7265 2062 6569 6e67  bjects are being\n+00009ec0: 2070 726f 6a65 6374 6564 206f 6e74 6f20   projected onto \n+00009ed0: 706c 616e 6573 2e20 2053 6565 2c20 666f  planes.  See, fo\n+00009ee0: 720a 6578 616d 706c 652c 202a 6e6f 7465  r.example, *note\n+00009ef0: 204f 7665 7276 6965 773a 3a2e 0a0a 2020   Overview::...  \n+00009f00: 2054 6865 2064 6972 6563 7420 7472 616e   The direct tran\n+00009f10: 7366 6f72 6d20 636f 6e73 7472 7563 746f  sform constructo\n+00009f20: 7220 616c 6c6f 7773 2064 6972 6563 7420  r allows direct \n+00009f30: 656e 7472 7920 6f66 2061 2034 7834 0a74  entry of a 4x4.t\n+00009f40: 7261 6e73 666f 726d 6174 696f 6e20 6d61  ransformation ma\n+00009f50: 7472 6978 2e20 204d 6f73 7420 3364 2067  trix.  Most 3d g\n+00009f60: 7261 7068 6963 7320 7379 7374 656d 732c  raphics systems,\n+00009f70: 2069 6e63 6c75 6469 6e67 2027 736b 6574   including 'sket\n+00009f80: 6368 272c 0a75 7365 2034 2d64 696d 656e  ch',.use 4-dimen\n+00009f90: 7369 6f6e 616c 2068 6f6d 6f67 656e 656f  sional homogeneo\n+00009fa0: 7573 2063 6f6f 7264 696e 6174 6573 2069  us coordinates i\n+00009fb0: 6e74 6572 6e61 6c6c 792e 2020 5468 6573  nternally.  Thes\n+00009fc0: 6520 6172 650a 7472 616e 7366 6f72 6d65  e are.transforme\n+00009fd0: 6420 6279 206d 756c 7469 706c 6963 6174  d by multiplicat\n+00009fe0: 696f 6e20 7769 7468 2034 7834 206d 6174  ion with 4x4 mat\n+00009ff0: 7269 6365 732e 2020 5468 6520 6275 696c  rices.  The buil\n+0000a000: 742d 696e 0a63 6f6e 7374 7275 6374 6f72  t-in.constructor\n+0000a010: 7320 2827 726f 7461 7465 272c 2027 7363  s ('rotate', 'sc\n+0000a020: 616c 6527 2c20 6574 632e 2920 2061 7265  ale', etc.)  are\n+0000a030: 2061 6c6c 2074 7261 6e73 6c61 7465 6420   all translated \n+0000a040: 696e 7465 726e 616c 6c79 2074 6f0a 7375  internally to.su\n+0000a050: 6368 2034 7834 206d 6174 7269 6365 732e  ch 4x4 matrices.\n+0000a060: 2020 466f 7220 6d6f 7265 2069 6e66 6f72    For more infor\n+0000a070: 6d61 7469 6f6e 206f 6e20 686f 6d6f 6765  mation on homoge\n+0000a080: 6e65 6f75 7320 636f 6f72 6469 6e61 7465  neous coordinate\n+0000a090: 0a74 7261 6e73 666f 726d 6174 696f 6e73  .transformations\n+0000a0a0: 2c20 7365 6520 616e 7920 676f 6f64 2063  , see any good c\n+0000a0b0: 6f6d 7075 7465 7220 6772 6170 6869 6373  omputer graphics\n+0000a0c0: 2074 6578 7462 6f6f 6b2e 2020 5468 6520   textbook.  The \n+0000a0d0: 6469 7265 6374 0a74 7261 6e73 666f 726d  direct.transform\n+0000a0e0: 2066 6561 7475 7265 206f 6620 2773 6b65   feature of 'ske\n+0000a0f0: 7463 6827 2061 6c6c 6f77 7320 796f 7520  tch' allows you \n+0000a100: 746f 2065 6e74 6572 2061 206d 6174 7269  to enter a matri\n+0000a110: 7820 6f66 2079 6f75 7220 6f77 6e0a 6368  x of your own.ch\n+0000a120: 6f69 6365 2e20 2054 6865 7265 2061 7265  oice.  There are\n+0000a130: 206e 6f74 206d 616e 7920 6361 7365 7320   not many cases \n+0000a140: 7768 6572 6520 7468 6973 2069 7320 7573  where this is us\n+0000a150: 6566 756c 2c20 6275 7420 6966 2079 6f75  eful, but if you\n+0000a160: 2064 6f0a 6e65 6564 2069 742c 2079 6f75   do.need it, you\n+0000a170: 206e 6565 6420 6974 2062 6164 6c79 210a   need it badly!.\n+0000a180: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n+0000a190: 696e 666f 2c20 204e 6f64 653a 2041 7269  info,  Node: Ari\n+0000a1a0: 7468 6d65 7469 632c 2020 4e65 7874 3a20  thmetic,  Next: \n+0000a1b0: 4f70 7469 6f6e 732c 2020 5072 6576 3a20  Options,  Prev: \n+0000a1c0: 4c69 7465 7261 6c73 2c20 2055 703a 204c  Literals,  Up: L\n+0000a1d0: 616e 6775 6167 6520 6261 7369 6373 0a0a  anguage basics..\n+0000a1e0: 332e 312e 3420 4172 6974 686d 6574 6963  3.1.4 Arithmetic\n+0000a1f0: 2065 7870 7265 7373 696f 6e73 0a2d 2d2d   expressions.---\n 0000a200: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-0000a210: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a41 7269  -----------..Ari\n-0000a220: 7468 6d65 7469 6320 6578 7072 6573 7369  thmetic expressi\n-0000a230: 6f6e 7320 6f76 6572 2027 736b 6574 6368  ons over 'sketch\n-0000a240: 2720 6c69 7465 7261 6c73 2061 6e64 2064  ' literals and d\n-0000a250: 6566 696e 6564 2069 6465 6e74 6966 6965  efined identifie\n-0000a260: 7273 0a61 7265 2073 756d 6d61 7269 7a65  rs.are summarize\n-0000a270: 6420 696e 2074 6865 2066 6f6c 6c6f 7769  d in the followi\n-0000a280: 6e67 2074 6162 6c65 732e 0a0a 2a20 4d65  ng tables...* Me\n-0000a290: 6e75 3a0a 0a2a 2054 776f 2d6f 7065 7261  nu:..* Two-opera\n-0000a2a0: 6e64 2028 6269 6e61 7279 2920 666f 726d  nd (binary) form\n-0000a2b0: 733a 3a20 2041 206f 7020 420a 2a20 556e  s::  A op B.* Un\n-0000a2c0: 6172 7920 666f 726d 733a 3a20 2020 2020  ary forms::     \n-0000a2d0: 2020 2020 2020 2020 2020 2020 6f70 2041              op A\n-0000a2e0: 2028 616e 6420 6f74 6865 7273 290a 0a1f   (and others)...\n-0000a2f0: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n-0000a300: 666f 2c20 204e 6f64 653a 2054 776f 2d6f  fo,  Node: Two-o\n-0000a310: 7065 7261 6e64 2028 6269 6e61 7279 2920  perand (binary) \n-0000a320: 666f 726d 732c 2020 4e65 7874 3a20 556e  forms,  Next: Un\n-0000a330: 6172 7920 666f 726d 732c 2020 5072 6576  ary forms,  Prev\n-0000a340: 3a20 4172 6974 686d 6574 6963 2c20 2055  : Arithmetic,  U\n-0000a350: 703a 2041 7269 7468 6d65 7469 630a 0a33  p: Arithmetic..3\n-0000a360: 2e31 2e34 2e31 2054 776f 2d6f 7065 7261  .1.4.1 Two-opera\n-0000a370: 6e64 2028 6269 6e61 7279 2920 666f 726d  nd (binary) form\n-0000a380: 7320 616e 6420 7072 6563 6564 656e 6365  s and precedence\n-0000a390: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+0000a210: 2d2d 2d2d 2d2d 2d2d 2d0a 0a41 7269 7468  ---------..Arith\n+0000a220: 6d65 7469 6320 6578 7072 6573 7369 6f6e  metic expression\n+0000a230: 7320 6f76 6572 2027 736b 6574 6368 2720  s over 'sketch' \n+0000a240: 6c69 7465 7261 6c73 2061 6e64 2064 6566  literals and def\n+0000a250: 696e 6564 2069 6465 6e74 6966 6965 7273  ined identifiers\n+0000a260: 0a61 7265 2073 756d 6d61 7269 7a65 6420  .are summarized \n+0000a270: 696e 2074 6865 2066 6f6c 6c6f 7769 6e67  in the following\n+0000a280: 2074 6162 6c65 732e 0a0a 2a20 4d65 6e75   tables...* Menu\n+0000a290: 3a0a 0a2a 2054 776f 2d6f 7065 7261 6e64  :..* Two-operand\n+0000a2a0: 2028 6269 6e61 7279 2920 666f 726d 733a   (binary) forms:\n+0000a2b0: 3a20 2041 206f 7020 420a 2a20 556e 6172  :  A op B.* Unar\n+0000a2c0: 7920 666f 726d 733a 3a20 2020 2020 2020  y forms::       \n+0000a2d0: 2020 2020 2020 2020 2020 6f70 2041 2028            op A (\n+0000a2e0: 616e 6420 6f74 6865 7273 290a 0a1f 0a46  and others)....F\n+0000a2f0: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n+0000a300: 2c20 204e 6f64 653a 2054 776f 2d6f 7065  ,  Node: Two-ope\n+0000a310: 7261 6e64 2028 6269 6e61 7279 2920 666f  rand (binary) fo\n+0000a320: 726d 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An exh\n+0000a420: 6175 7374 6976 6520 7375 6d6d 6172 7920  austive summary \n+0000a430: 6f66 2074 6865 2070 6f73 7369 6269 6c69  of the possibili\n+0000a440: 7469 6573 2069 7320 6769 7665 6e20 696e  ties is given in\n+0000a450: 0a74 6865 2066 6f6c 6c6f 7769 6e67 2074  .the following t\n+0000a460: 6162 6c65 2e0a 4c65 6674 2020 2020 2020  able..Left      \n+0000a470: 2020 4f70 2020 2020 2020 2052 6967 6874    Op       Right\n+0000a480: 2020 2020 2020 2052 6573 756c 7420 2020         Result   \n+0000a490: 2020 2044 6573 6372 6970 7469 6f6e 0a2d     Description.-\n+0000a4a0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\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: 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6e74 2020 2020 2020       point      \n-0000a5f0: 2022 2020 2020 2020 2020 2020 2022 0a73   \"           \".s\n-0000a600: 6361 6c61 7220 2020 2020 2027 2d27 2020  calar      '-'  \n-0000a610: 2020 2020 7363 616c 6172 2020 2020 2020      scalar      \n-0000a620: 7363 616c 6172 2020 2020 2020 5363 616c  scalar      Scal\n-0000a630: 6172 2064 6966 6665 7265 6e63 652e 0a76  ar difference..v\n-0000a640: 6563 746f 7220 2020 2020 2027 2d27 2020  ector      '-'  \n-0000a650: 2020 2020 7665 6374 6f72 2020 2020 2020      vector      \n-0000a660: 7665 6374 6f72 2020 2020 2020 5665 6374  vector      Vect\n-0000a670: 6f72 2064 6966 6665 7265 6e63 652e 0a70  or difference..p\n-0000a680: 6f69 6e74 2020 2020 2020 2027 2d27 2020  oint       '-'  \n-0000a690: 2020 2020 706f 696e 7420 2020 2020 2020      point       \n-0000a6a0: 7665 6374 6f72 2020 2020 2020 506f 696e  vector      Poin\n-0000a6b0: 742d 706f 696e 7420 6166 6669 6e65 2064  t-point affine d\n-0000a6c0: 6966 6665 7265 6e63 652e 0a70 6f69 6e74  ifference..point\n-0000a6d0: 2020 2020 2020 2027 2d27 2020 2020 2020         '-'      \n-0000a6e0: 7665 6374 6f72 2020 2020 2020 706f 696e  vector      poin\n-0000a6f0: 7420 2020 2020 2020 506f 696e 742d 7665  t       Point-ve\n-0000a700: 6374 6f72 2061 6666 696e 6520 6469 6666  ctor affine diff\n-0000a710: 6572 656e 6365 2e0a 7363 616c 6172 2020  erence..scalar  \n-0000a720: 2020 2020 272a 2720 6f72 2020 2073 6361      '*' or   sca\n-0000a730: 6c61 7220 2020 2020 2073 6361 6c61 7220  lar      scalar \n-0000a740: 2020 2020 2053 6361 6c61 7220 7072 6f64       Scalar prod\n-0000a750: 7563 742e 0a20 2020 2020 2020 2020 2020  uct..           \n-0000a760: 2027 2e27 0a73 6361 6c61 7220 2020 2020   '.'.scalar     \n-0000a770: 2027 2a27 206f 7220 2020 7665 6374 6f72   '*' or   vector\n-0000a780: 2020 2020 2020 7665 6374 6f72 2020 2020        vector    \n-0000a790: 2020 5363 616c 6172 2d76 6563 746f 7220    Scalar-vector \n-0000a7a0: 7072 6f64 7563 742e 0a20 2020 2020 2020  product..       \n-0000a7b0: 2020 2020 2027 2e27 0a76 6563 746f 7220       '.'.vector \n-0000a7c0: 2020 2020 2027 2a27 206f 7220 2020 7363       '*' or   sc\n-0000a7d0: 616c 6172 2020 2020 2020 2220 2020 2020  alar      \"     \n-0000a7e0: 2020 2020 2020 220a 2020 2020 2020 2020        \".        \n-0000a7f0: 2020 2020 272e 270a 7665 6374 6f72 2020      '.'.vector  \n-0000a800: 2020 2020 272a 2720 2020 2020 2076 6563      '*'      vec\n-0000a810: 746f 7220 2020 2020 2076 6563 746f 7220  tor      vector \n-0000a820: 2020 2020 2056 6563 746f 7220 6372 6f73       Vector cros\n-0000a830: 732d 7072 6f64 7563 742e 0a76 6563 746f  s-product..vecto\n-0000a840: 7220 2020 2020 2027 2e27 2020 2020 2020  r      '.'      \n-0000a850: 7665 6374 6f72 2020 2020 2020 7363 616c  vector      scal\n-0000a860: 6172 2020 2020 2020 5665 6374 6f72 2064  ar      Vector d\n-0000a870: 6f74 2070 726f 6475 6374 2e0a 7363 616c  ot product..scal\n-0000a880: 6172 2020 2020 2020 275e 2720 2020 2020  ar      '^'     \n-0000a890: 2073 6361 6c61 7220 2020 2020 2073 6361   scalar      sca\n-0000a8a0: 6c61 7220 2020 2020 2052 6169 7365 2073  lar      Raise s\n-0000a8b0: 6361 6c61 7220 746f 2073 6361 6c61 7220  calar to scalar \n-0000a8c0: 706f 7765 722e 0a74 7261 6e73 666f 726d  power..transform\n-0000a8d0: 2020 2027 5e27 2020 2020 2020 696e 7465     '^'      inte\n-0000a8e0: 6765 7220 2020 2020 7472 616e 7366 6f72  ger     transfor\n-0000a8f0: 6d20 2020 5261 6973 6520 7472 616e 7366  m   Raise transf\n-0000a900: 6f72 6d20 746f 2069 6e74 6567 6572 2070  orm to integer p\n-0000a910: 6f77 6572 2e0a 7472 616e 7366 6f72 6d20  ower..transform \n-0000a920: 2020 272a 2720 6f72 2020 2070 6f69 6e74    '*' or   point\n-0000a930: 2020 2020 2020 2070 6f69 6e74 2020 2020         point    \n-0000a940: 2020 2041 6666 696e 6520 706f 696e 7420     Affine point \n-0000a950: 7472 616e 7366 6f72 6d20 2872 6967 6874  transform (right\n-0000a960: 2d74 6f2d 6c65 6674 292e 0a20 2020 2020  -to-left)..     \n-0000a970: 2020 2020 2020 2027 2e27 0a74 7261 6e73         '.'.trans\n-0000a980: 666f 726d 2020 2027 2a27 206f 7220 2020  form   '*' or   \n-0000a990: 7665 6374 6f72 2020 2020 2020 7665 6374  vector      vect\n-0000a9a0: 6f72 2020 2020 2020 4166 6669 6e65 2076  or      Affine v\n-0000a9b0: 6563 746f 7220 7472 616e 7366 6f72 6d20  ector transform \n-0000a9c0: 2872 6967 6874 2d74 6f2d 6c65 6674 292e  (right-to-left).\n-0000a9d0: 0a20 2020 2020 2020 2020 2020 2027 2e27  .            '.'\n-0000a9e0: 0a74 7261 6e73 666f 726d 2020 2027 2a27  .transform   '*'\n-0000a9f0: 206f 7220 2020 7472 616e 7366 6f72 6d20   or   transform \n-0000aa00: 2020 7472 616e 7366 6f72 6d20 2020 5472    transform   Tr\n-0000aa10: 616e 7366 6f72 6d20 636f 6d70 6f73 6974  ansform composit\n-0000aa20: 696f 6e20 2872 6967 6874 2d74 6f2d 6c65  ion (right-to-le\n-0000aa30: 6674 292e 0a20 2020 2020 2020 2020 2020  ft)..           \n-0000aa40: 2027 2e27 0a70 6f69 6e74 2020 2020 2020   '.'.point      \n-0000aa50: 2027 7468 656e 2720 2020 7472 616e 7366   'then'   transf\n-0000aa60: 6f72 6d20 2020 706f 696e 7420 2020 2020  orm   point     \n-0000aa70: 2020 4166 6669 6e65 2070 6f69 6e74 2074    Affine point t\n-0000aa80: 7261 6e73 666f 726d 2028 6c65 6674 2d74  ransform (left-t\n-0000aa90: 6f2d 7269 6768 7429 2e0a 7665 6374 6f72  o-right)..vector\n-0000aaa0: 2020 2020 2020 2774 6865 6e27 2020 2074        'then'   t\n-0000aab0: 7261 6e73 666f 726d 2020 2076 6563 746f  ransform   vecto\n-0000aac0: 7220 2020 2020 2041 6666 696e 6520 7665  r      Affine ve\n-0000aad0: 6374 6f72 2074 7261 6e73 666f 726d 2028  ctor transform (\n-0000aae0: 6c65 6674 2d74 6f2d 7269 6768 7429 2e0a  left-to-right)..\n-0000aaf0: 7472 616e 7366 6f72 6d20 2020 2774 6865  transform   'the\n-0000ab00: 6e27 2020 2074 7261 6e73 666f 726d 2020  n'   transform  \n-0000ab10: 2074 7261 6e73 666f 726d 2020 2054 7261   transform   Tra\n-0000ab20: 6e73 666f 726d 2063 6f6d 706f 7369 7469  nsform compositi\n-0000ab30: 6f6e 2028 6c65 6674 2d74 6f2d 7269 6768  on (left-to-righ\n-0000ab40: 7429 2e0a 7363 616c 6172 2020 2020 2020  t)..scalar      \n-0000ab50: 272f 2720 2020 2020 2073 6361 6c61 7220  '/'      scalar \n-0000ab60: 2020 2020 2073 6361 6c61 7220 2020 2020       scalar     \n-0000ab70: 2053 6361 6c61 7220 6469 7669 7369 6f6e   Scalar division\n-0000ab80: 2e0a 7665 6374 6f72 2020 2020 2020 272f  ..vector      '/\n-0000ab90: 2720 2020 2020 2073 6361 6c61 7220 2020  '      scalar   \n-0000aba0: 2020 2076 6563 746f 7220 2020 2020 2056     vector      V\n-0000abb0: 6563 746f 7220 636f 6d70 6f6e 656e 742d  ector component-\n-0000abc0: 7769 7365 2064 6976 6973 696f 6e20 6279  wise division by\n-0000abd0: 2073 6361 6c61 722e 0a70 6f69 6e74 2020   scalar..point  \n-0000abe0: 2020 2020 2027 2727 2020 2020 2020 2778       '''      'x\n-0000abf0: 272c 2027 7927 2c20 2020 7363 616c 6172  ', 'y',   scalar\n-0000ac00: 2020 2020 2020 506f 696e 7420 636f 6d70        Point comp\n-0000ac10: 6f6e 656e 7420 6578 7472 6163 7469 6f6e  onent extraction\n-0000ac20: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n-0000ac30: 2020 2020 2020 206f 7220 277a 270a 7665         or 'z'.ve\n-0000ac40: 6374 6f72 2020 2020 2020 2727 2720 2020  ctor      '''   \n-0000ac50: 2020 2027 7827 2c20 2779 272c 2020 2073     'x', 'y',   s\n-0000ac60: 6361 6c61 7220 2020 2020 2056 6563 746f  calar      Vecto\n-0000ac70: 7220 636f 6d70 6f6e 656e 7420 6578 7472  r component extr\n-0000ac80: 6163 7469 6f6e 2e0a 2020 2020 2020 2020  action..        \n-0000ac90: 2020 2020 2020 2020 2020 2020 206f 7220               or \n-0000aca0: 277a 270a 0a4f 7065 7261 746f 7220 7072  'z'..Operator pr\n-0000acb0: 6563 6564 656e 6365 2069 7320 7368 6f77  ecedence is show\n-0000acc0: 6e20 696e 2074 6869 7320 7461 626c 652e  n in this table.\n-0000acd0: 0a4f 7020 2020 2020 2020 5072 6563 6564  .Op       Preced\n-0000ace0: 656e 6365 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d  ence.-----------\n+0000a510: 2d2d 2d2d 2d0a 7363 616c 6172 2020 2020  -----.scalar    \n+0000a520: 2020 272b 2720 2020 2020 2073 6361 6c61    '+'      scala\n+0000a530: 7220 2020 2020 2073 6361 6c61 7220 2020  r      scalar   \n+0000a540: 2020 2053 6361 6c61 7220 7375 6d2e 0a76     Scalar sum..v\n+0000a550: 6563 746f 7220 2020 2020 2027 2b27 2020  ector      '+'  \n+0000a560: 2020 2020 7665 6374 6f72 2020 2020 2020      vector      \n+0000a570: 7665 6374 6f72 2020 2020 2020 5665 6374  vector      Vect\n+0000a580: 6f72 2073 756d 2e0a 706f 696e 7420 2020  or sum..point   \n+0000a590: 2020 2020 272b 2720 2020 2020 2076 6563      '+'      vec\n+0000a5a0: 746f 7220 2020 2020 2070 6f69 6e74 2020  tor      point  \n+0000a5b0: 2020 2020 2050 6f69 6e74 2d76 6563 746f       Point-vecto\n+0000a5c0: 7220 6166 6669 6e65 2073 756d 2e0a 7665  r affine sum..ve\n+0000a5d0: 6374 6f72 2020 2020 2020 272b 2720 2020  ctor      '+'   \n+0000a5e0: 2020 2070 6f69 6e74 2020 2020 2020 2022     point       \"\n+0000a5f0: 2020 2020 2020 2020 2020 2022 0a73 6361             \".sca\n+0000a600: 6c61 7220 2020 2020 2027 2d27 2020 2020  lar      '-'    \n+0000a610: 2020 7363 616c 6172 2020 2020 2020 7363    scalar      sc\n+0000a620: 616c 6172 2020 2020 2020 5363 616c 6172  alar      Scalar\n+0000a630: 2064 6966 6665 7265 6e63 652e 0a76 6563   difference..vec\n+0000a640: 746f 7220 2020 2020 2027 2d27 2020 2020  tor      '-'    \n+0000a650: 2020 7665 6374 6f72 2020 2020 2020 7665    vector      ve\n+0000a660: 6374 6f72 2020 2020 2020 5665 6374 6f72  ctor      Vector\n+0000a670: 2064 6966 6665 7265 6e63 652e 0a70 6f69   difference..poi\n+0000a680: 6e74 2020 2020 2020 2027 2d27 2020 2020  nt       '-'    \n+0000a690: 2020 706f 696e 7420 2020 2020 2020 7665    point       ve\n+0000a6a0: 6374 6f72 2020 2020 2020 506f 696e 742d  ctor      Point-\n+0000a6b0: 706f 696e 7420 6166 6669 6e65 2064 6966  point affine dif\n+0000a6c0: 6665 7265 6e63 652e 0a70 6f69 6e74 2020  ference..point  \n+0000a6d0: 2020 2020 2027 2d27 2020 2020 2020 7665       '-'      ve\n+0000a6e0: 6374 6f72 2020 2020 2020 706f 696e 7420  ctor      point \n+0000a6f0: 2020 2020 2020 506f 696e 742d 7665 6374        Point-vect\n+0000a700: 6f72 2061 6666 696e 6520 6469 6666 6572  or affine differ\n+0000a710: 656e 6365 2e0a 7363 616c 6172 2020 2020  ence..scalar    \n+0000a720: 2020 272a 2720 6f72 2020 2073 6361 6c61    '*' or   scala\n+0000a730: 7220 2020 2020 2073 6361 6c61 7220 2020  r      scalar   \n+0000a740: 2020 2053 6361 6c61 7220 7072 6f64 7563     Scalar produc\n+0000a750: 742e 0a20 2020 2020 2020 2020 2020 2027  t..            '\n+0000a760: 2e27 0a73 6361 6c61 7220 2020 2020 2027  .'.scalar      '\n+0000a770: 2a27 206f 7220 2020 7665 6374 6f72 2020  *' or   vector  \n+0000a780: 2020 2020 7665 6374 6f72 2020 2020 2020      vector      \n+0000a790: 5363 616c 6172 2d76 6563 746f 7220 7072  Scalar-vector pr\n+0000a7a0: 6f64 7563 742e 0a20 2020 2020 2020 2020  oduct..         \n+0000a7b0: 2020 2027 2e27 0a76 6563 746f 7220 2020     '.'.vector   \n+0000a7c0: 2020 2027 2a27 206f 7220 2020 7363 616c     '*' or   scal\n+0000a7d0: 6172 2020 2020 2020 2220 2020 2020 2020  ar      \"       \n+0000a7e0: 2020 2020 220a 2020 2020 2020 2020 2020      \".          \n+0000a7f0: 2020 272e 270a 7665 6374 6f72 2020 2020    '.'.vector    \n+0000a800: 2020 272a 2720 2020 2020 2076 6563 746f    '*'      vecto\n+0000a810: 7220 2020 2020 2076 6563 746f 7220 2020  r      vector   \n+0000a820: 2020 2056 6563 746f 7220 6372 6f73 732d     Vector cross-\n+0000a830: 7072 6f64 7563 742e 0a76 6563 746f 7220  product..vector \n+0000a840: 2020 2020 2027 2e27 2020 2020 2020 7665       '.'      ve\n+0000a850: 6374 6f72 2020 2020 2020 7363 616c 6172  ctor      scalar\n+0000a860: 2020 2020 2020 5665 6374 6f72 2064 6f74        Vector dot\n+0000a870: 2070 726f 6475 6374 2e0a 7363 616c 6172   product..scalar\n+0000a880: 2020 2020 2020 275e 2720 2020 2020 2073        '^'      s\n+0000a890: 6361 6c61 7220 2020 2020 2073 6361 6c61  calar      scala\n+0000a8a0: 7220 2020 2020 2052 6169 7365 2073 6361  r      Raise sca\n+0000a8b0: 6c61 7220 746f 2073 6361 6c61 7220 706f  lar to scalar po\n+0000a8c0: 7765 722e 0a74 7261 6e73 666f 726d 2020  wer..transform  \n+0000a8d0: 2027 5e27 2020 2020 2020 696e 7465 6765   '^'      intege\n+0000a8e0: 7220 2020 2020 7472 616e 7366 6f72 6d20  r     transform \n+0000a8f0: 2020 5261 6973 6520 7472 616e 7366 6f72    Raise transfor\n+0000a900: 6d20 746f 2069 6e74 6567 6572 2070 6f77  m to integer pow\n+0000a910: 6572 2e0a 7472 616e 7366 6f72 6d20 2020  er..transform   \n+0000a920: 272a 2720 6f72 2020 2070 6f69 6e74 2020  '*' or   point  \n+0000a930: 2020 2020 2070 6f69 6e74 2020 2020 2020       point      \n+0000a940: 2041 6666 696e 6520 706f 696e 7420 7472   Affine point tr\n+0000a950: 616e 7366 6f72 6d20 2872 6967 6874 2d74  ansform (right-t\n+0000a960: 6f2d 6c65 6674 292e 0a20 2020 2020 2020  o-left)..       \n+0000a970: 2020 2020 2027 2e27 0a74 7261 6e73 666f       '.'.transfo\n+0000a980: 726d 2020 2027 2a27 206f 7220 2020 7665  rm   '*' or   ve\n+0000a990: 6374 6f72 2020 2020 2020 7665 6374 6f72  ctor      vector\n+0000a9a0: 2020 2020 2020 4166 6669 6e65 2076 6563        Affine vec\n+0000a9b0: 746f 7220 7472 616e 7366 6f72 6d20 2872  tor transform (r\n+0000a9c0: 6967 6874 2d74 6f2d 6c65 6674 292e 0a20  ight-to-left).. \n+0000a9d0: 2020 2020 2020 2020 2020 2027 2e27 0a74             '.'.t\n+0000a9e0: 7261 6e73 666f 726d 2020 2027 2a27 206f  ransform   '*' o\n+0000a9f0: 7220 2020 7472 616e 7366 6f72 6d20 2020  r   transform   \n+0000aa00: 7472 616e 7366 6f72 6d20 2020 5472 616e  transform   Tran\n+0000aa10: 7366 6f72 6d20 636f 6d70 6f73 6974 696f  sform compositio\n+0000aa20: 6e20 2872 6967 6874 2d74 6f2d 6c65 6674  n (right-to-left\n+0000aa30: 292e 0a20 2020 2020 2020 2020 2020 2027  )..            '\n+0000aa40: 2e27 0a70 6f69 6e74 2020 2020 2020 2027  .'.point       '\n+0000aa50: 7468 656e 2720 2020 7472 616e 7366 6f72  then'   transfor\n+0000aa60: 6d20 2020 706f 696e 7420 2020 2020 2020  m   point       \n+0000aa70: 4166 6669 6e65 2070 6f69 6e74 2074 7261  Affine point tra\n+0000aa80: 6e73 666f 726d 2028 6c65 6674 2d74 6f2d  nsform (left-to-\n+0000aa90: 7269 6768 7429 2e0a 7665 6374 6f72 2020  right)..vector  \n+0000aaa0: 2020 2020 2774 6865 6e27 2020 2074 7261      'then'   tra\n+0000aab0: 6e73 666f 726d 2020 2076 6563 746f 7220  nsform   vector \n+0000aac0: 2020 2020 2041 6666 696e 6520 7665 6374       Affine vect\n+0000aad0: 6f72 2074 7261 6e73 666f 726d 2028 6c65  or transform (le\n+0000aae0: 6674 2d74 6f2d 7269 6768 7429 2e0a 7472  ft-to-right)..tr\n+0000aaf0: 616e 7366 6f72 6d20 2020 2774 6865 6e27  ansform   'then'\n+0000ab00: 2020 2074 7261 6e73 666f 726d 2020 2074     transform   t\n+0000ab10: 7261 6e73 666f 726d 2020 2054 7261 6e73  ransform   Trans\n+0000ab20: 666f 726d 2063 6f6d 706f 7369 7469 6f6e  form composition\n+0000ab30: 2028 6c65 6674 2d74 6f2d 7269 6768 7429   (left-to-right)\n+0000ab40: 2e0a 7363 616c 6172 2020 2020 2020 272f  ..scalar      '/\n+0000ab50: 2720 2020 2020 2073 6361 6c61 7220 2020  '      scalar   \n+0000ab60: 2020 2073 6361 6c61 7220 2020 2020 2053     scalar      S\n+0000ab70: 6361 6c61 7220 6469 7669 7369 6f6e 2e0a  calar division..\n+0000ab80: 7665 6374 6f72 2020 2020 2020 272f 2720  vector      '/' \n+0000ab90: 2020 2020 2073 6361 6c61 7220 2020 2020       scalar     \n+0000aba0: 2076 6563 746f 7220 2020 2020 2056 6563   vector      Vec\n+0000abb0: 746f 7220 636f 6d70 6f6e 656e 742d 7769  tor component-wi\n+0000abc0: 7365 2064 6976 6973 696f 6e20 6279 2073  se division by s\n+0000abd0: 6361 6c61 722e 0a70 6f69 6e74 2020 2020  calar..point    \n+0000abe0: 2020 2027 2727 2020 2020 2020 2778 272c     '''      'x',\n+0000abf0: 2027 7927 2c20 2020 7363 616c 6172 2020   'y',   scalar  \n+0000ac00: 2020 2020 506f 696e 7420 636f 6d70 6f6e      Point compon\n+0000ac10: 656e 7420 6578 7472 6163 7469 6f6e 2e0a  ent extraction..\n+0000ac20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000ac30: 2020 2020 206f 7220 277a 270a 7665 6374       or 'z'.vect\n+0000ac40: 6f72 2020 2020 2020 2727 2720 2020 2020  or      '''     \n+0000ac50: 2027 7827 2c20 2779 272c 2020 2073 6361   'x', 'y',   sca\n+0000ac60: 6c61 7220 2020 2020 2056 6563 746f 7220  lar      Vector \n+0000ac70: 636f 6d70 6f6e 656e 7420 6578 7472 6163  component extrac\n+0000ac80: 7469 6f6e 2e0a 2020 2020 2020 2020 2020  tion..          \n+0000ac90: 2020 2020 2020 2020 2020 206f 7220 277a             or 'z\n+0000aca0: 270a 0a4f 7065 7261 746f 7220 7072 6563  '..Operator prec\n+0000acb0: 6564 656e 6365 2069 7320 7368 6f77 6e20  edence is shown \n+0000acc0: 696e 2074 6869 7320 7461 626c 652e 0a4f  in this table..O\n+0000acd0: 7020 2020 2020 2020 5072 6563 6564 656e  p       Preceden\n+0000ace0: 6365 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ce.-------------\n 0000acf0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-0000ad00: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a  ---------------.\n-0000ad10: 2727 2720 2020 2020 2068 6967 6865 7374  '''      highest\n-0000ad20: 2028 6d6f 7374 2074 6967 6874 6c79 2062   (most tightly b\n-0000ad30: 696e 6469 6e67 290a 275e 270a 272d 2720  inding).'^'.'-' \n-0000ad40: 2020 2020 2028 756e 6172 7920 6e65 6761       (unary nega\n-0000ad50: 7469 6f6e 290a 272a 270a 272e 270a 272f  tion).'*'.'.'.'/\n-0000ad60: 270a 272b 270a 272d 270a 2774 6865 6e27  '.'+'.'-'.'then'\n-0000ad70: 2020 206c 6f77 6573 7420 286c 6561 7374     lowest (least\n-0000ad80: 2074 6967 6874 6c79 2062 696e 6469 6e67   tightly binding\n-0000ad90: 290a 0a41 6c6c 206f 7065 7261 7469 6f6e  )..All operation\n-0000ada0: 7320 6172 6520 6c65 6674 2d61 7373 6f63  s are left-assoc\n-0000adb0: 6961 7469 7665 2065 7863 6570 7420 666f  iative except fo\n-0000adc0: 7220 275e 272e 2020 5061 7265 6e74 6865  r '^'.  Parenthe\n-0000add0: 7365 7320 2728 2029 270a 6172 6520 7573  ses '( )'.are us\n-0000ade0: 6564 2066 6f72 2067 726f 7570 696e 6720  ed for grouping \n-0000adf0: 746f 206f 7665 7272 6964 6520 7072 6563  to override prec\n-0000ae00: 6564 656e 6365 2069 6e20 7468 6520 7573  edence in the us\n-0000ae10: 7561 6c20 7761 792e 0a0a 2020 2041 7320  ual way...   As \n-0000ae20: 796f 7520 6361 6e20 7365 652c 2074 6865  you can see, the\n-0000ae30: 2064 6f74 206f 7065 7261 746f 7220 272e   dot operator '.\n-0000ae40: 2720 6973 2075 7375 616c 6c79 2061 2073  ' is usually a s\n-0000ae50: 796e 6f6e 796d 2066 6f72 0a72 756e 2d6f  ynonym for.run-o\n-0000ae60: 662d 7468 652d 6d69 6c6c 206d 756c 7469  f-the-mill multi\n-0000ae70: 706c 6963 6174 696f 6e2c 2027 2a27 2e20  plication, '*'. \n-0000ae80: 2054 6865 206d 6561 6e69 6e67 7320 6469   The meanings di\n-0000ae90: 6666 6572 206f 6e6c 7920 666f 720a 7665  ffer only for.ve\n-0000aea0: 6374 6f72 206f 7065 7261 6e64 732e 2020  ctor operands.  \n-0000aeb0: 5468 6520 2774 6865 6e27 206f 7065 7261  The 'then' opera\n-0000aec0: 746f 7220 6d65 7265 6c79 2072 6576 6572  tor merely rever\n-0000aed0: 7365 7320 7468 6520 6f70 6572 616e 6420  ses the operand \n-0000aee0: 6f72 6465 720a 7769 7468 2072 6573 7065  order.with respe\n-0000aef0: 6374 2074 6f20 6e6f 726d 616c 206d 756c  ct to normal mul\n-0000af00: 7469 706c 6963 6174 696f 6e20 272a 272e  tiplication '*'.\n-0000af10: 2020 5468 6520 696e 7465 6e74 2068 6572    The intent her\n-0000af20: 6520 6973 2074 6f20 6d61 6b65 0a63 6f6d  e is to make.com\n-0000af30: 706f 7369 7469 6f6e 7320 7265 6164 206d  positions read m\n-0000af40: 6f72 6520 6e61 7475 7261 6c6c 792e 2020  ore naturally.  \n-0000af50: 5468 6520 636f 6465 0a20 2020 2020 2831  The code.     (1\n-0000af60: 2c32 2c33 2920 7468 656e 2073 6361 6c65  ,2,3) then scale\n-0000af70: 2832 2920 7468 656e 2072 6f74 6174 6528  (2) then rotate(\n-0000af80: 3330 2920 7468 656e 2074 7261 6e73 6c61  30) then transla\n-0000af90: 7465 285b 312c 332c 305d 290a 6578 7072  te([1,3,0]).expr\n-0000afa0: 6573 7365 7320 6120 7365 7269 6573 206f  esses a series o\n-0000afb0: 6620 7375 6363 6573 7369 7665 206d 6f64  f successive mod\n-0000afc0: 6966 6963 6174 696f 6e73 2074 6f20 7468  ifications to th\n-0000afd0: 6520 706f 696e 742c 2077 6865 7265 6173  e point, whereas\n-0000afe0: 2074 6865 0a65 7175 6976 616c 656e 7420   the.equivalent \n-0000aff0: 666f 726d 0a20 2020 2020 7472 616e 736c  form.     transl\n-0000b000: 6174 6528 5b31 2c33 2c30 5d29 202a 2072  ate([1,3,0]) * r\n-0000b010: 6f74 6174 6528 3330 2920 2a20 7363 616c  otate(30) * scal\n-0000b020: 6528 3229 202a 2028 312c 322c 3329 0a77  e(2) * (1,2,3).w\n-0000b030: 696c 6c20 6265 2069 6e74 7569 7469 7665  ill be intuitive\n-0000b040: 206f 6e6c 7920 746f 206d 6174 6865 6d61   only to mathema\n-0000b050: 7469 6369 616e 7320 2861 6e64 2070 6572  ticians (and per\n-0000b060: 6861 7073 2041 7261 6269 6320 6c61 6e67  haps Arabic lang\n-0000b070: 7561 6765 0a72 6561 6465 7273 292e 0a0a  uage.readers)...\n-0000b080: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n-0000b090: 6e66 6f2c 2020 4e6f 6465 3a20 556e 6172  nfo,  Node: Unar\n-0000b0a0: 7920 666f 726d 732c 2020 5072 6576 3a20  y forms,  Prev: \n-0000b0b0: 5477 6f2d 6f70 6572 616e 6420 2862 696e  Two-operand (bin\n-0000b0c0: 6172 7929 2066 6f72 6d73 2c20 2055 703a  ary) forms,  Up:\n-0000b0d0: 2041 7269 7468 6d65 7469 630a 0a33 2e31   Arithmetic..3.1\n-0000b0e0: 2e34 2e32 2055 6e61 7279 2066 6f72 6d73  .4.2 Unary forms\n-0000b0f0: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000b100: 2e2e 2e2e 0a0a 556e 6172 7920 6f72 206f  ......Unary or o\n-0000b110: 6e65 2d6f 7065 7261 6e64 2066 6f72 6d73  ne-operand forms\n-0000b120: 2061 7265 2073 756d 6d61 7269 7a65 6420   are summarized \n-0000b130: 696e 2074 6865 2066 6f6c 6c6f 7769 6e67  in the following\n-0000b140: 2074 6162 6c65 2c20 7768 6572 650a 2758   table, where.'X\n-0000b150: 2720 7374 616e 6473 2066 6f72 2074 6865  ' stands for the\n-0000b160: 206f 7065 7261 6e64 2e0a 4f70 2020 2020   operand..Op    \n-0000b170: 2020 2020 2020 2020 204f 7065 7261 6e64           Operand\n-0000b180: 2020 2020 2052 6573 756c 7420 2020 2020       Result     \n-0000b190: 2044 6573 6372 6970 7469 6f6e 0a2d 2d2d   Description.---\n+0000ad00: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 2727  -------------.''\n+0000ad10: 2720 2020 2020 2068 6967 6865 7374 2028  '      highest (\n+0000ad20: 6d6f 7374 2074 6967 6874 6c79 2062 696e  most tightly bin\n+0000ad30: 6469 6e67 290a 275e 270a 272d 2720 2020  ding).'^'.'-'   \n+0000ad40: 2020 2028 756e 6172 7920 6e65 6761 7469     (unary negati\n+0000ad50: 6f6e 290a 272a 270a 272e 270a 272f 270a  on).'*'.'.'.'/'.\n+0000ad60: 272b 270a 272d 270a 2774 6865 6e27 2020  '+'.'-'.'then'  \n+0000ad70: 206c 6f77 6573 7420 286c 6561 7374 2074   lowest (least t\n+0000ad80: 6967 6874 6c79 2062 696e 6469 6e67 290a  ightly binding).\n+0000ad90: 0a41 6c6c 206f 7065 7261 7469 6f6e 7320  .All operations \n+0000ada0: 6172 6520 6c65 6674 2d61 7373 6f63 6961  are left-associa\n+0000adb0: 7469 7665 2065 7863 6570 7420 666f 7220  tive except for \n+0000adc0: 275e 272e 2020 5061 7265 6e74 6865 7365  '^'.  Parenthese\n+0000add0: 7320 2728 2029 270a 6172 6520 7573 6564  s '( )'.are used\n+0000ade0: 2066 6f72 2067 726f 7570 696e 6720 746f   for grouping to\n+0000adf0: 206f 7665 7272 6964 6520 7072 6563 6564   override preced\n+0000ae00: 656e 6365 2069 6e20 7468 6520 7573 7561  ence in the usua\n+0000ae10: 6c20 7761 792e 0a0a 2020 2041 7320 796f  l way...   As yo\n+0000ae20: 7520 6361 6e20 7365 652c 2074 6865 2064  u can see, the d\n+0000ae30: 6f74 206f 7065 7261 746f 7220 272e 2720  ot operator '.' \n+0000ae40: 6973 2075 7375 616c 6c79 2061 2073 796e  is usually a syn\n+0000ae50: 6f6e 796d 2066 6f72 0a72 756e 2d6f 662d  onym for.run-of-\n+0000ae60: 7468 652d 6d69 6c6c 206d 756c 7469 706c  the-mill multipl\n+0000ae70: 6963 6174 696f 6e2c 2027 2a27 2e20 2054  ication, '*'.  T\n+0000ae80: 6865 206d 6561 6e69 6e67 7320 6469 6666  he meanings diff\n+0000ae90: 6572 206f 6e6c 7920 666f 720a 7665 6374  er only for.vect\n+0000aea0: 6f72 206f 7065 7261 6e64 732e 2020 5468  or operands.  Th\n+0000aeb0: 6520 2774 6865 6e27 206f 7065 7261 746f  e 'then' operato\n+0000aec0: 7220 6d65 7265 6c79 2072 6576 6572 7365  r merely reverse\n+0000aed0: 7320 7468 6520 6f70 6572 616e 6420 6f72  s the operand or\n+0000aee0: 6465 720a 7769 7468 2072 6573 7065 6374  der.with respect\n+0000aef0: 2074 6f20 6e6f 726d 616c 206d 756c 7469   to normal multi\n+0000af00: 706c 6963 6174 696f 6e20 272a 272e 2020  plication '*'.  \n+0000af10: 5468 6520 696e 7465 6e74 2068 6572 6520  The intent here \n+0000af20: 6973 2074 6f20 6d61 6b65 0a63 6f6d 706f  is to make.compo\n+0000af30: 7369 7469 6f6e 7320 7265 6164 206d 6f72  sitions read mor\n+0000af40: 6520 6e61 7475 7261 6c6c 792e 2020 5468  e naturally.  Th\n+0000af50: 6520 636f 6465 0a20 2020 2020 2831 2c32  e code.     (1,2\n+0000af60: 2c33 2920 7468 656e 2073 6361 6c65 2832  ,3) then scale(2\n+0000af70: 2920 7468 656e 2072 6f74 6174 6528 3330  ) then rotate(30\n+0000af80: 2920 7468 656e 2074 7261 6e73 6c61 7465  ) then translate\n+0000af90: 285b 312c 332c 305d 290a 6578 7072 6573  ([1,3,0]).expres\n+0000afa0: 7365 7320 6120 7365 7269 6573 206f 6620  ses a series of \n+0000afb0: 7375 6363 6573 7369 7665 206d 6f64 6966  successive modif\n+0000afc0: 6963 6174 696f 6e73 2074 6f20 7468 6520  ications to the \n+0000afd0: 706f 696e 742c 2077 6865 7265 6173 2074  point, whereas t\n+0000afe0: 6865 0a65 7175 6976 616c 656e 7420 666f  he.equivalent fo\n+0000aff0: 726d 0a20 2020 2020 7472 616e 736c 6174  rm.     translat\n+0000b000: 6528 5b31 2c33 2c30 5d29 202a 2072 6f74  e([1,3,0]) * rot\n+0000b010: 6174 6528 3330 2920 2a20 7363 616c 6528  ate(30) * scale(\n+0000b020: 3229 202a 2028 312c 322c 3329 0a77 696c  2) * (1,2,3).wil\n+0000b030: 6c20 6265 2069 6e74 7569 7469 7665 206f  l be intuitive o\n+0000b040: 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7269 7a65 6420 696e  re summarized in\n+0000b130: 2074 6865 2066 6f6c 6c6f 7769 6e67 2074   the following t\n+0000b140: 6162 6c65 2c20 7768 6572 650a 2758 2720  able, where.'X' \n+0000b150: 7374 616e 6473 2066 6f72 2074 6865 206f  stands for the o\n+0000b160: 7065 7261 6e64 2e0a 4f70 2020 2020 2020  perand..Op      \n+0000b170: 2020 2020 2020 204f 7065 7261 6e64 2020         Operand  \n+0000b180: 2020 2052 6573 756c 7420 2020 2020 2044     Result      D\n+0000b190: 6573 6372 6970 7469 6f6e 0a2d 2d2d 2d2d  escription.-----\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 2d2d 2d2d  ----------------\n-0000b1f0: 2d0a 272d 5827 2020 2020 2020 2020 2020  -.'-X'          \n-0000b200: 2073 6361 6c61 7220 2020 2020 2073 6361   scalar      sca\n-0000b210: 6c61 7220 2020 2020 2055 6e61 7279 2073  lar      Unary s\n-0000b220: 6361 6c61 7220 6e65 6761 7469 6f6e 2e0a  calar negation..\n-0000b230: 272d 5827 2020 2020 2020 2020 2020 2076  '-X'           v\n-0000b240: 6563 746f 7220 2020 2020 2076 6563 746f  ector      vecto\n-0000b250: 7220 2020 2020 2055 6e61 7279 2076 6563  r      Unary vec\n-0000b260: 746f 7220 6e65 6761 7469 6f6e 2e0a 277c  tor negation..'|\n-0000b270: 587c 2720 2020 2020 2020 2020 2076 6563  X|'          vec\n-0000b280: 746f 7220 2020 2020 2073 6361 6c61 7220  tor      scalar \n-0000b290: 2020 2020 2056 6563 746f 7220 6c65 6e67       Vector leng\n-0000b2a0: 7468 2e0a 2775 6e69 7428 5829 2720 2020  th..'unit(X)'   \n-0000b2b0: 2020 2076 6563 746f 7220 2020 2020 2076     vector      v\n-0000b2c0: 6563 746f 7220 2020 2020 2055 6e69 7420  ector      Unit \n-0000b2d0: 7665 6374 6f72 2077 6974 6820 7361 6d65  vector with same\n-0000b2e0: 2064 6972 6563 7469 6f6e 2e0a 2773 7172   direction..'sqr\n-0000b2f0: 7428 5829 2720 2020 2020 2073 6361 6c61  t(X)'      scala\n-0000b300: 7220 2020 2020 2073 6361 6c61 7220 2020  r      scalar   \n-0000b310: 2020 2053 6361 6c61 7220 7371 7561 7265     Scalar square\n-0000b320: 2072 6f6f 742e 0a27 7369 6e28 5829 2720   root..'sin(X)' \n-0000b330: 2020 2020 2020 7363 616c 6172 2020 2020        scalar    \n-0000b340: 2020 7363 616c 6172 2020 2020 2020 5472    scalar      Tr\n-0000b350: 6967 6f6e 6f6d 6574 7269 6320 7369 6e65  igonometric sine\n-0000b360: 2028 2758 2720 696e 2064 6567 7265 6573   ('X' in degrees\n-0000b370: 292e 0a27 636f 7328 5829 2720 2020 2020  )..'cos(X)'     \n-0000b380: 2020 7363 616c 6172 2020 2020 2020 7363    scalar      sc\n-0000b390: 616c 6172 2020 2020 2020 5472 6967 6f6e  alar      Trigon\n-0000b3a0: 6f6d 6574 7269 6320 636f 7369 6e65 2028  ometric cosine (\n-0000b3b0: 2758 2720 696e 2064 6567 7265 6573 292e  'X' in degrees).\n-0000b3c0: 0a27 6173 696e 2858 2927 2020 2020 2020  .'asin(X)'      \n-0000b3d0: 7363 616c 6172 2020 2020 2020 7363 616c  scalar      scal\n-0000b3e0: 6172 2020 2020 2020 496e 7665 7273 6520  ar      Inverse \n-0000b3f0: 7369 6e65 2028 2758 2720 696e 2064 6567  sine ('X' in deg\n-0000b400: 7265 6573 292e 0a27 6163 6f73 2858 2927  rees)..'acos(X)'\n-0000b410: 2020 2020 2020 7363 616c 6172 2020 2020        scalar    \n-0000b420: 2020 7363 616c 6172 2020 2020 2020 496e    scalar      In\n-0000b430: 7665 7273 6520 636f 7369 6e65 2028 2758  verse cosine ('X\n-0000b440: 2720 696e 2064 6567 7265 6573 292e 0a27  ' in degrees)..'\n-0000b450: 6174 616e 3228 582c 5929 2720 2020 7363  atan2(X,Y)'   sc\n-0000b460: 616c 6172 2020 2020 2020 7363 616c 6172  alar      scalar\n-0000b470: 2020 2020 2020 506f 6c61 7220 616e 676c        Polar angl\n-0000b480: 6520 696e 2064 6567 7265 6573 206f 6620  e in degrees of \n-0000b490: 7665 6374 6f72 205b 582c 595d 2e0a 2769  vector [X,Y]..'i\n-0000b4a0: 6e76 6572 7365 2858 2927 2020 2074 7261  nverse(X)'   tra\n-0000b4b0: 6e73 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key-value pai\n-0000b680: 7273 2e0a 0a2a 204d 656e 753a 0a0a 2a20  rs...* Menu:..* \n-0000b690: 5053 5472 6963 6b73 206f 7074 696f 6e73  PSTricks options\n-0000b6a0: 3a3a 2020 2020 2020 2020 2020 2020 4f70  ::            Op\n-0000b6b0: 7469 6f6e 7320 696e 6865 7269 7465 6420  tions inherited \n-0000b6c0: 6672 6f6d 2027 5053 5472 6963 6b73 272e  from 'PSTricks'.\n-0000b6d0: 0a2a 2054 696b 5a2f 5047 4620 6f70 7469  .* TikZ/PGF opti\n-0000b6e0: 6f6e 733a 3a20 2020 2020 2020 2020 2020  ons::           \n-0000b6f0: 204f 7074 696f 6e73 2069 6e68 6572 6974   Options inherit\n-0000b700: 6564 2066 726f 6d20 2754 696b 5a2f 5047  ed from 'TikZ/PG\n-0000b710: 4627 2e0a 2a20 446f 7473 2069 6e20 5469  F'..* Dots in Ti\n-0000b720: 6b5a 2f50 4746 3a3a 2020 2020 2020 2020  kZ/PGF::        \n-0000b730: 2020 2020 536b 6574 6368 2075 7365 7320      Sketch uses \n-0000b740: 2754 696b 5a2f 5047 4627 2063 6972 636c  'TikZ/PGF' circl\n-0000b750: 6573 2066 6f72 2064 6f74 732e 0a2a 2054  es for dots..* T\n-0000b760: 696b 5a2f 5047 4620 7573 6572 2d64 6566  ikZ/PGF user-def\n-0000b770: 696e 6564 2073 7479 6c65 733a 3a20 2053  ined styles::  S\n-0000b780: 7570 706f 7274 2066 6f72 2027 5469 6b5a  upport for 'TikZ\n-0000b790: 2f50 4746 2720 6e61 6d65 642c 2075 7365  /PGF' named, use\n-0000b7a0: 722d 6465 6669 6e65 6420 7374 796c 6573  r-defined styles\n-0000b7b0: 2e0a 2a20 5472 616e 7370 6172 656e 6379  ..* Transparency\n-0000b7c0: 3a3a 2020 2020 2020 2020 2020 2020 2020  ::              \n-0000b7d0: 2020 5365 652d 7468 726f 7567 6820 706f    See-through po\n-0000b7e0: 6c79 676f 6e73 2e0a 2a20 496e 7465 726e  lygons..* Intern\n-0000b7f0: 616c 206f 7074 696f 6e73 3a3a 2020 2020  al options::    \n-0000b800: 2020 2020 2020 2020 4f70 7469 6f6e 7320          Options \n-0000b810: 7573 6564 2062 7920 2773 6b65 7463 6827  used by 'sketch'\n-0000b820: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463  .....File: sketc\n-0000b830: 682e 696e 666f 2c20 204e 6f64 653a 2050  h.info,  Node: P\n-0000b840: 5354 7269 636b 7320 6f70 7469 6f6e 732c  STricks options,\n-0000b850: 2020 4e65 7874 3a20 5469 6b5a 2f50 4746    Next: TikZ/PGF\n-0000b860: 206f 7074 696f 6e73 2c20 2050 7265 763a   options,  Prev:\n-0000b870: 204f 7074 696f 6e73 2c20 2055 703a 204f   Options,  Up: O\n-0000b880: 7074 696f 6e73 0a0a 332e 312e 352e 3120  ptions..3.1.5.1 \n-0000b890: 2750 5354 7269 636b 7327 206f 7074 696f  'PSTricks' optio\n-0000b8a0: 6e73 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ns..............\n-0000b8b0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a57  ...............W\n-0000b8c0: 6865 6e20 276c 616e 6775 6167 6520 7073  hen 'language ps\n-0000b8d0: 7472 6963 6b73 2720 6973 2073 656c 6563  tricks' is selec\n-0000b8e0: 7465 6420 2874 6865 2064 6566 6175 6c74  ted (the default\n-0000b8f0: 292c 2070 6572 6d69 7373 6962 6c65 0a6b  ), permissible.k\n-0000b900: 6579 2d76 616c 7565 2070 6169 7273 2069  ey-value pairs i\n-0000b910: 6e63 6c75 6465 2061 6c6c 2074 686f 7365  nclude all those\n-0000b920: 2066 6f72 2073 696d 696c 6172 2027 5053   for similar 'PS\n-0000b930: 5472 6963 6b73 2720 6f62 6a65 6374 732e  Tricks' objects.\n-0000b940: 2020 466f 720a 6578 616d 706c 652c 2061    For.example, a\n-0000b950: 2070 6f6c 7967 6f6e 206d 6967 6874 2068   polygon might h\n-0000b960: 6176 6520 7468 6520 6f70 7469 6f6e 730a  ave the options.\n-0000b970: 2020 5b6c 696e 6577 6964 7468 3d31 7074    [linewidth=1pt\n-0000b980: 2c6c 696e 6563 6f6c 6f72 3d62 6c75 652c  ,linecolor=blue,\n-0000b990: 6669 6c6c 636f 6c6f 723d 6379 616e 5d0a  fillcolor=cyan].\n-0000b9a0: 2753 6b65 7463 6827 206d 6572 656c 7920  'Sketch' merely \n-0000b9b0: 7061 7373 6573 2074 6865 7365 206f 6e20  passes these on \n-0000b9c0: 746f 2027 5053 5472 6963 6b73 2720 7769  to 'PSTricks' wi\n-0000b9d0: 7468 6f75 7420 6368 6563 6b69 6e67 206f  thout checking o\n-0000b9e0: 720a 6d6f 6469 6669 6361 7469 6f6e 2e20  r.modification. \n-0000b9f0: 204f 7074 696f 6e20 6c69 7374 7320 6172   Option lists ar\n-0000ba00: 6520 616c 7761 7973 206f 7074 696f 6e61  e always optiona\n-0000ba10: 6c2e 2020 4120 6d69 7373 696e 6720 6f70  l.  A missing op\n-0000ba20: 7469 6f6e 7320 6c69 7374 0a69 7320 6571  tions list.is eq\n-0000ba30: 7569 7661 6c65 6e74 2074 6f20 616e 2065  uivalent to an e\n-0000ba40: 6d70 7479 206f 6e65 2027 5b5d 272e 0a0a  mpty one '[]'...\n-0000ba50: 2020 2057 6865 6e20 6120 2770 6f6c 7967     When a 'polyg\n-0000ba60: 6f6e 2720 6861 7320 6f70 7469 6f6e 7320  on' has options \n-0000ba70: 666f 7220 626f 7468 2069 7473 2066 6163  for both its fac\n-0000ba80: 6520 616e 6420 6974 7320 6564 6765 732c  e and its edges,\n-0000ba90: 2061 6e64 2074 6865 0a70 6f6c 7967 6f6e   and the.polygon\n-0000baa0: 2069 7320 7370 6c69 7420 6279 2074 6865   is split by the\n-0000bab0: 2068 6964 6465 6e20 7375 7266 6163 6520   hidden surface \n-0000bac0: 616c 676f 7269 7468 6d2c 2027 736b 6574  algorithm, 'sket\n-0000bad0: 6368 2720 6d75 7374 2063 6f70 7920 7468  ch' must copy th\n-0000bae0: 650a 6564 6765 206f 7074 696f 6e73 2074  e.edge options t\n-0000baf0: 6f20 2770 736c 696e 6527 7320 666f 7220  o 'psline's for \n-0000bb00: 7468 6520 6564 6765 2073 6567 6d65 6e74  the edge segment\n-0000bb10: 7320 616e 6420 7468 6520 6661 6365 206f  s and the face o\n-0000bb20: 7074 696f 6e73 2074 6f0a 2770 7370 6f6c  ptions to.'pspol\n-0000bb30: 7967 6f6e 2773 2e20 204f 7074 696f 6e73  ygon's.  Options\n-0000bb40: 206b 6e6f 776e 2074 6f20 2773 6b65 7463   known to 'sketc\n-0000bb50: 6827 2066 6f72 2070 7572 706f 7365 7320  h' for purposes \n-0000bb60: 6f66 2074 6869 7320 7370 6c69 7474 696e  of this splittin\n-0000bb70: 670a 6f70 6572 6174 696f 6e20 696e 636c  g.operation incl\n-0000bb80: 7564 6520 2761 7272 6f77 7327 2c20 2764  ude 'arrows', 'd\n-0000bb90: 6173 6827 2c20 2764 6f74 7365 7027 2c20  ash', 'dotsep', \n-0000bba0: 2766 696c 6c63 6f6c 6f72 272c 2027 6669  'fillcolor', 'fi\n-0000bbb0: 6c6c 7374 796c 6527 2c0a 276c 696e 6563  llstyle',.'linec\n-0000bbc0: 6f6c 6f72 272c 2027 6c69 6e65 7374 796c  olor', 'linestyl\n-0000bbd0: 6527 2c20 276c 696e 6577 6964 7468 272c  e', 'linewidth',\n-0000bbe0: 2027 6f70 6163 6974 7927 2c20 2773 686f   'opacity', 'sho\n-0000bbf0: 7770 6f69 6e74 7327 2c0a 2773 7472 6f6b  wpoints',.'strok\n-0000bc00: 656f 7061 6369 7479 272c 2061 6e64 2027  eopacity', and '\n-0000bc10: 7472 616e 7370 616c 7068 6127 2e0a 0a1f  transpalpha'....\n-0000bc20: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n-0000bc30: 666f 2c20 204e 6f64 653a 2054 696b 5a2f  fo,  Node: TikZ/\n-0000bc40: 5047 4620 6f70 7469 6f6e 732c 2020 4e65  PGF options,  Ne\n-0000bc50: 7874 3a20 446f 7473 2069 6e20 5469 6b5a  xt: Dots in TikZ\n-0000bc60: 2f50 4746 2c20 2050 7265 763a 2050 5354  /PGF,  Prev: PST\n-0000bc70: 7269 636b 7320 6f70 7469 6f6e 732c 2020  ricks options,  \n-0000bc80: 5570 3a20 4f70 7469 6f6e 730a 0a33 2e31  Up: Options..3.1\n-0000bc90: 2e35 2e32 2027 5469 6b5a 2f50 4746 2720  .5.2 'TikZ/PGF' \n-0000bca0: 6f70 7469 6f6e 730a 2e2e 2e2e 2e2e 2e2e  options.........\n+0000b1e0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a  ---------------.\n+0000b1f0: 272d 5827 2020 2020 2020 2020 2020 2073  '-X'           s\n+0000b200: 6361 6c61 7220 2020 2020 2073 6361 6c61  calar      scala\n+0000b210: 7220 2020 2020 2055 6e61 7279 2073 6361  r      Unary sca\n+0000b220: 6c61 7220 6e65 6761 7469 6f6e 2e0a 272d  lar negation..'-\n+0000b230: 5827 2020 2020 2020 2020 2020 2076 6563  X'           vec\n+0000b240: 746f 7220 2020 2020 2076 6563 746f 7220  tor      vector \n+0000b250: 2020 2020 2055 6e61 7279 2076 6563 746f       Unary vecto\n+0000b260: 7220 6e65 6761 7469 6f6e 2e0a 277c 587c  r negation..'|X|\n+0000b270: 2720 2020 2020 2020 2020 2076 6563 746f  '          vecto\n+0000b280: 7220 2020 2020 2073 6361 6c61 7220 2020  r      scalar   \n+0000b290: 2020 2056 6563 746f 7220 6c65 6e67 7468     Vector length\n+0000b2a0: 2e0a 2775 6e69 7428 5829 2720 2020 2020  ..'unit(X)'     \n+0000b2b0: 2076 6563 746f 7220 2020 2020 2076 6563   vector      vec\n+0000b2c0: 746f 7220 2020 2020 2055 6e69 7420 7665  tor      Unit ve\n+0000b2d0: 6374 6f72 2077 6974 6820 7361 6d65 2064  ctor with same d\n+0000b2e0: 6972 6563 7469 6f6e 2e0a 2773 7172 7428  irection..'sqrt(\n+0000b2f0: 5829 2720 2020 2020 2073 6361 6c61 7220  X)'      scalar \n+0000b300: 2020 2020 2073 6361 6c61 7220 2020 2020       scalar     \n+0000b310: 2053 6361 6c61 7220 7371 7561 7265 2072   Scalar square r\n+0000b320: 6f6f 742e 0a27 7369 6e28 5829 2720 2020  oot..'sin(X)'   \n+0000b330: 2020 2020 7363 616c 6172 2020 2020 2020      scalar      \n+0000b340: 7363 616c 6172 2020 2020 2020 5472 6967  scalar      Trig\n+0000b350: 6f6e 6f6d 6574 7269 6320 7369 6e65 2028  onometric sine (\n+0000b360: 2758 2720 696e 2064 6567 7265 6573 292e  'X' in degrees).\n+0000b370: 0a27 636f 7328 5829 2720 2020 2020 2020  .'cos(X)'       \n+0000b380: 7363 616c 6172 2020 2020 2020 7363 616c  scalar      scal\n+0000b390: 6172 2020 2020 2020 5472 6967 6f6e 6f6d  ar      Trigonom\n+0000b3a0: 6574 7269 6320 636f 7369 6e65 2028 2758  etric cosine ('X\n+0000b3b0: 2720 696e 2064 6567 7265 6573 292e 0a27  ' in degrees)..'\n+0000b3c0: 6173 696e 2858 2927 2020 2020 2020 7363  asin(X)'      sc\n+0000b3d0: 616c 6172 2020 2020 2020 7363 616c 6172  alar      scalar\n+0000b3e0: 2020 2020 2020 496e 7665 7273 6520 7369        Inverse si\n+0000b3f0: 6e65 2028 2758 2720 696e 2064 6567 7265  ne ('X' in degre\n+0000b400: 6573 292e 0a27 6163 6f73 2858 2927 2020  es)..'acos(X)'  \n+0000b410: 2020 2020 7363 616c 6172 2020 2020 2020      scalar      \n+0000b420: 7363 616c 6172 2020 2020 2020 496e 7665  scalar      Inve\n+0000b430: 7273 6520 636f 7369 6e65 2028 2758 2720  rse cosine ('X' \n+0000b440: 696e 2064 6567 7265 6573 292e 0a27 6174  in degrees)..'at\n+0000b450: 616e 3228 582c 5929 2720 2020 7363 616c  an2(X,Y)'   scal\n+0000b460: 6172 2020 2020 2020 7363 616c 6172 2020  ar      scalar  \n+0000b470: 2020 2020 506f 6c61 7220 616e 676c 6520      Polar angle \n+0000b480: 696e 2064 6567 7265 6573 206f 6620 7665  in degrees of ve\n+0000b490: 6374 6f72 205b 582c 595d 2e0a 2769 6e76  ctor [X,Y]..'inv\n+0000b4a0: 6572 7365 2858 2927 2020 2074 7261 6e73  erse(X)'   trans\n+0000b4b0: 666f 726d 2020 2074 7261 6e73 666f 726d  form   transform\n+0000b4c0: 2020 2049 6e76 6572 7365 2074 7261 6e73     Inverse trans\n+0000b4d0: 666f 726d 2e0a 0a45 7272 6f72 7320 6172  form...Errors ar\n+0000b4e0: 6520 7265 706f 7274 6564 2077 6865 6e20  e reported when \n+0000b4f0: 277c 587c 272c 2027 756e 6974 272c 2027  '|X|', 'unit', '\n+0000b500: 6173 696e 272c 2027 6163 6f73 272c 2027  asin', 'acos', '\n+0000b510: 7371 7274 272c 2027 6174 616e 3227 2c0a  sqrt', 'atan2',.\n+0000b520: 616e 6420 2769 6e76 6572 7365 2720 6661  and 'inverse' fa\n+0000b530: 696c 2064 7565 2074 6f20 6f70 6572 616e  il due to operan\n+0000b540: 6473 206f 7574 7369 6465 2074 6865 6972  ds outside their\n+0000b550: 2072 6573 7065 6374 6976 6520 646f 6d61   respective doma\n+0000b560: 696e 732e 0a0a 1f0a 4669 6c65 3a20 736b  ins.....File: sk\n+0000b570: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n+0000b580: 3a20 4f70 7469 6f6e 732c 2020 5072 6576  : Options,  Prev\n+0000b590: 3a20 4172 6974 686d 6574 6963 2c20 2055  : Arithmetic,  U\n+0000b5a0: 703a 204c 616e 6775 6167 6520 6261 7369  p: Language basi\n+0000b5b0: 6373 0a0a 332e 312e 3520 4f70 7469 6f6e  cs..3.1.5 Option\n+0000b5c0: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a  s.-------------.\n+0000b5d0: 0a2a 5379 6e74 6178 3a2a 0a20 2020 2020  .*Syntax:*.     \n+0000b5e0: 5b4b 4559 313d 5641 4c31 2c4b 4559 323d  [KEY1=VAL1,KEY2=\n+0000b5f0: 5641 4c32 2c2e 2e2e 5d0a 4f70 7469 6f6e  VAL2,...].Option\n+0000b600: 7320 6172 6520 7573 6564 2074 6f20 7370  s are used to sp\n+0000b610: 6563 6966 7920 6465 7461 696c 7320 6f66  ecify details of\n+0000b620: 2074 6865 2061 7070 6561 7261 6e63 6520   the appearance \n+0000b630: 6f66 2064 7261 7761 626c 6573 2e20 2041  of drawables.  A\n+0000b640: 730a 7368 6f77 6e20 6162 6f76 652c 2074  s.shown above, t\n+0000b650: 6865 7920 6172 6520 6769 7665 6e20 6173  hey are given as\n+0000b660: 2063 6f6d 6d61 2d73 6570 6172 6174 6564   comma-separated\n+0000b670: 206b 6579 2d76 616c 7565 2070 6169 7273   key-value pairs\n+0000b680: 2e0a 0a2a 204d 656e 753a 0a0a 2a20 5053  ...* Menu:..* PS\n+0000b690: 5472 6963 6b73 206f 7074 696f 6e73 3a3a  Tricks options::\n+0000b6a0: 2020 2020 2020 2020 2020 2020 4f70 7469              Opti\n+0000b6b0: 6f6e 7320 696e 6865 7269 7465 6420 6672  ons inherited fr\n+0000b6c0: 6f6d 2027 5053 5472 6963 6b73 272e 0a2a  om 'PSTricks'..*\n+0000b6d0: 2054 696b 5a2f 5047 4620 6f70 7469 6f6e   TikZ/PGF option\n+0000b6e0: 733a 3a20 2020 2020 2020 2020 2020 204f  s::            O\n+0000b6f0: 7074 696f 6e73 2069 6e68 6572 6974 6564  ptions inherited\n+0000b700: 2066 726f 6d20 2754 696b 5a2f 5047 4627   from 'TikZ/PGF'\n+0000b710: 2e0a 2a20 446f 7473 2069 6e20 5469 6b5a  ..* Dots in TikZ\n+0000b720: 2f50 4746 3a3a 2020 2020 2020 2020 2020  /PGF::          \n+0000b730: 2020 536b 6574 6368 2075 7365 7320 2754    Sketch uses 'T\n+0000b740: 696b 5a2f 5047 4627 2063 6972 636c 6573  ikZ/PGF' circles\n+0000b750: 2066 6f72 2064 6f74 732e 0a2a 2054 696b   for dots..* Tik\n+0000b760: 5a2f 5047 4620 7573 6572 2d64 6566 696e  Z/PGF user-defin\n+0000b770: 6564 2073 7479 6c65 733a 3a20 2053 7570  ed styles::  Sup\n+0000b780: 706f 7274 2066 6f72 2027 5469 6b5a 2f50  port for 'TikZ/P\n+0000b790: 4746 2720 6e61 6d65 642c 2075 7365 722d  GF' named, user-\n+0000b7a0: 6465 6669 6e65 6420 7374 796c 6573 2e0a  defined styles..\n+0000b7b0: 2a20 5472 616e 7370 6172 656e 6379 3a3a  * Transparency::\n+0000b7c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000b7d0: 5365 652d 7468 726f 7567 6820 706f 6c79  See-through poly\n+0000b7e0: 676f 6e73 2e0a 2a20 496e 7465 726e 616c  gons..* Internal\n+0000b7f0: 206f 7074 696f 6e73 3a3a 2020 2020 2020   options::      \n+0000b800: 2020 2020 2020 4f70 7469 6f6e 7320 7573        Options us\n+0000b810: 6564 2062 7920 2773 6b65 7463 6827 2e0a  ed by 'sketch'..\n+0000b820: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n+0000b830: 696e 666f 2c20 204e 6f64 653a 2050 5354  info,  Node: PST\n+0000b840: 7269 636b 7320 6f70 7469 6f6e 732c 2020  ricks options,  \n+0000b850: 4e65 7874 3a20 5469 6b5a 2f50 4746 206f  Next: TikZ/PGF o\n+0000b860: 7074 696f 6e73 2c20 2050 7265 763a 204f  ptions,  Prev: O\n+0000b870: 7074 696f 6e73 2c20 2055 703a 204f 7074  ptions,  Up: Opt\n+0000b880: 696f 6e73 0a0a 332e 312e 352e 3120 2750  ions..3.1.5.1 'P\n+0000b890: 5354 7269 636b 7327 206f 7074 696f 6e73  STricks' options\n+0000b8a0: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+0000b8b0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a57 6865  .............Whe\n+0000b8c0: 6e20 276c 616e 6775 6167 6520 7073 7472  n 'language pstr\n+0000b8d0: 6963 6b73 2720 6973 2073 656c 6563 7465  icks' is selecte\n+0000b8e0: 6420 2874 6865 2064 6566 6175 6c74 292c  d (the default),\n+0000b8f0: 2070 6572 6d69 7373 6962 6c65 0a6b 6579   permissible.key\n+0000b900: 2d76 616c 7565 2070 6169 7273 2069 6e63  -value pairs inc\n+0000b910: 6c75 6465 2061 6c6c 2074 686f 7365 2066  lude all those f\n+0000b920: 6f72 2073 696d 696c 6172 2027 5053 5472  or similar 'PSTr\n+0000b930: 6963 6b73 2720 6f62 6a65 6374 732e 2020  icks' objects.  \n+0000b940: 466f 720a 6578 616d 706c 652c 2061 2070  For.example, a p\n+0000b950: 6f6c 7967 6f6e 206d 6967 6874 2068 6176  olygon might hav\n+0000b960: 6520 7468 6520 6f70 7469 6f6e 730a 2020  e the options.  \n+0000b970: 5b6c 696e 6577 6964 7468 3d31 7074 2c6c  [linewidth=1pt,l\n+0000b980: 696e 6563 6f6c 6f72 3d62 6c75 652c 6669  inecolor=blue,fi\n+0000b990: 6c6c 636f 6c6f 723d 6379 616e 5d0a 2753  llcolor=cyan].'S\n+0000b9a0: 6b65 7463 6827 206d 6572 656c 7920 7061  ketch' merely pa\n+0000b9b0: 7373 6573 2074 6865 7365 206f 6e20 746f  sses these on to\n+0000b9c0: 2027 5053 5472 6963 6b73 2720 7769 7468   'PSTricks' with\n+0000b9d0: 6f75 7420 6368 6563 6b69 6e67 206f 720a  out checking or.\n+0000b9e0: 6d6f 6469 6669 6361 7469 6f6e 2e20 204f  modification.  O\n+0000b9f0: 7074 696f 6e20 6c69 7374 7320 6172 6520  ption lists are \n+0000ba00: 616c 7761 7973 206f 7074 696f 6e61 6c2e  always optional.\n+0000ba10: 2020 4120 6d69 7373 696e 6720 6f70 7469    A missing opti\n+0000ba20: 6f6e 7320 6c69 7374 0a69 7320 6571 7569  ons list.is equi\n+0000ba30: 7661 6c65 6e74 2074 6f20 616e 2065 6d70  valent to an emp\n+0000ba40: 7479 206f 6e65 2027 5b5d 272e 0a0a 2020  ty one '[]'...  \n+0000ba50: 2057 6865 6e20 6120 2770 6f6c 7967 6f6e   When a 'polygon\n+0000ba60: 2720 6861 7320 6f70 7469 6f6e 7320 666f  ' has options fo\n+0000ba70: 7220 626f 7468 2069 7473 2066 6163 6520  r both its face \n+0000ba80: 616e 6420 6974 7320 6564 6765 732c 2061  and its edges, a\n+0000ba90: 6e64 2074 6865 0a70 6f6c 7967 6f6e 2069  nd the.polygon i\n+0000baa0: 7320 7370 6c69 7420 6279 2074 6865 2068  s split by the h\n+0000bab0: 6964 6465 6e20 7375 7266 6163 6520 616c  idden surface al\n+0000bac0: 676f 7269 7468 6d2c 2027 736b 6574 6368  gorithm, 'sketch\n+0000bad0: 2720 6d75 7374 2063 6f70 7920 7468 650a  ' must copy the.\n+0000bae0: 6564 6765 206f 7074 696f 6e73 2074 6f20  edge options to \n+0000baf0: 2770 736c 696e 6527 7320 666f 7220 7468  'psline's for th\n+0000bb00: 6520 6564 6765 2073 6567 6d65 6e74 7320  e edge segments \n+0000bb10: 616e 6420 7468 6520 6661 6365 206f 7074  and the face opt\n+0000bb20: 696f 6e73 2074 6f0a 2770 7370 6f6c 7967  ions to.'pspolyg\n+0000bb30: 6f6e 2773 2e20 204f 7074 696f 6e73 206b  on's.  Options k\n+0000bb40: 6e6f 776e 2074 6f20 2773 6b65 7463 6827  nown to 'sketch'\n+0000bb50: 2066 6f72 2070 7572 706f 7365 7320 6f66   for purposes of\n+0000bb60: 2074 6869 7320 7370 6c69 7474 696e 670a   this splitting.\n+0000bb70: 6f70 6572 6174 696f 6e20 696e 636c 7564  operation includ\n+0000bb80: 6520 2761 7272 6f77 7327 2c20 2764 6173  e 'arrows', 'das\n+0000bb90: 6827 2c20 2764 6f74 7365 7027 2c20 2766  h', 'dotsep', 'f\n+0000bba0: 696c 6c63 6f6c 6f72 272c 2027 6669 6c6c  illcolor', 'fill\n+0000bbb0: 7374 796c 6527 2c0a 276c 696e 6563 6f6c  style',.'linecol\n+0000bbc0: 6f72 272c 2027 6c69 6e65 7374 796c 6527  or', 'linestyle'\n+0000bbd0: 2c20 276c 696e 6577 6964 7468 272c 2027  , 'linewidth', '\n+0000bbe0: 6f70 6163 6974 7927 2c20 2773 686f 7770  opacity', 'showp\n+0000bbf0: 6f69 6e74 7327 2c0a 2773 7472 6f6b 656f  oints',.'strokeo\n+0000bc00: 7061 6369 7479 272c 2061 6e64 2027 7472  pacity', and 'tr\n+0000bc10: 616e 7370 616c 7068 6127 2e0a 0a1f 0a46  anspalpha'.....F\n+0000bc20: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n+0000bc30: 2c20 204e 6f64 653a 2054 696b 5a2f 5047  ,  Node: TikZ/PG\n+0000bc40: 4620 6f70 7469 6f6e 732c 2020 4e65 7874  F options,  Next\n+0000bc50: 3a20 446f 7473 2069 6e20 5469 6b5a 2f50  : Dots in TikZ/P\n+0000bc60: 4746 2c20 2050 7265 763a 2050 5354 7269  GF,  Prev: PSTri\n+0000bc70: 636b 7320 6f70 7469 6f6e 732c 2020 5570  cks options,  Up\n+0000bc80: 3a20 4f70 7469 6f6e 730a 0a33 2e31 2e35  : Options..3.1.5\n+0000bc90: 2e32 2027 5469 6b5a 2f50 4746 2720 6f70  .2 'TikZ/PGF' op\n+0000bca0: 7469 6f6e 730a 2e2e 2e2e 2e2e 2e2e 2e2e  tions...........\n 0000bcb0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000bcc0: 2e2e 0a0a 2754 696b 5a2f 5047 4627 206f  ....'TikZ/PGF' o\n-0000bcd0: 7074 696f 6e73 2061 7265 2068 616e 646c  ptions are handl\n-0000bce0: 6564 206d 7563 6820 6173 2066 6f72 2027  ed much as for '\n-0000bcf0: 5053 5472 6963 6b73 272e 2020 5468 6f75  PSTricks'.  Thou\n-0000bd00: 6768 0a27 5469 6b5a 2f50 4746 2720 6f66  gh.'TikZ/PGF' of\n-0000bd10: 7465 6e20 616c 6c6f 7773 2063 6f6c 6f72  ten allows color\n-0000bd20: 7320 616e 6420 7374 796c 6573 2074 6f20  s and styles to \n-0000bd30: 6265 2067 6976 656e 2077 6974 686f 7574  be given without\n-0000bd40: 0a63 6f72 7265 7370 6f6e 6469 6e67 206b  .corresponding k\n-0000bd50: 6579 732c 2066 6f72 2065 7861 6d70 6c65  eys, for example\n-0000bd60: 2c0a 2020 5c64 7261 775b 7265 642c 756c  ,.  \\draw[red,ul\n-0000bd70: 7472 6120 7468 6963 6b5d 2830 2c30 292d  tra thick](0,0)-\n-0000bd80: 2d28 312c 3129 3b0a 7468 6973 2069 7320  -(1,1);.this is \n-0000bd90: 6e6f 7420 7065 726d 6974 7465 6420 696e  not permitted in\n-0000bda0: 2027 736b 6574 6368 272e 2020 546f 2064   'sketch'.  To d\n-0000bdb0: 7261 7720 6120 7265 642c 2075 6c74 7261  raw a red, ultra\n-0000bdc0: 2d74 6869 636b 206c 696e 6520 696e 0a27  -thick line in.'\n-0000bdd0: 736b 6574 6368 272c 2074 6865 2066 6f72  sketch', the for\n-0000bde0: 6d20 6973 0a20 206c 696e 655b 6472 6177  m is.  line[draw\n-0000bdf0: 3d72 6564 2c73 7479 6c65 3d75 6c74 7261  =red,style=ultra\n-0000be00: 2074 6869 636b 5d28 302c 3029 2831 2c31   thick](0,0)(1,1\n-0000be10: 290a 0a20 2020 4a75 7374 2061 7320 666f  )..   Just as fo\n-0000be20: 7220 2750 5354 7269 636b 7327 2c20 7768  r 'PSTricks', wh\n-0000be30: 656e 2061 2027 706f 6c79 676f 6e27 2068  en a 'polygon' h\n-0000be40: 6173 206f 7074 696f 6e73 2066 6f72 2062  as options for b\n-0000be50: 6f74 6820 6974 730a 6661 6365 2061 6e64  oth its.face and\n-0000be60: 2069 7473 2065 6467 6573 2c20 616e 6420   its edges, and \n-0000be70: 7468 6520 706f 6c79 676f 6e20 6973 2073  the polygon is s\n-0000be80: 706c 6974 2062 7920 7468 6520 6869 6464  plit by the hidd\n-0000be90: 656e 2073 7572 6661 6365 0a61 6c67 6f72  en surface.algor\n-0000bea0: 6974 686d 2c20 2773 6b65 7463 6827 206d  ithm, 'sketch' m\n-0000beb0: 7573 7420 636f 7079 2074 6865 2065 6467  ust copy the edg\n-0000bec0: 6520 6f70 7469 6f6e 7320 746f 2027 7073  e options to 'ps\n-0000bed0: 6c69 6e65 2773 2066 6f72 2074 6865 2065  line's for the e\n-0000bee0: 6467 650a 7365 676d 656e 7473 2061 6e64  dge.segments and\n-0000bef0: 2074 6865 2066 6163 6520 6f70 7469 6f6e   the face option\n-0000bf00: 7320 746f 2027 7073 706f 6c79 676f 6e27  s to 'pspolygon'\n-0000bf10: 732e 2020 2754 696b 5a2f 5047 4627 206f  s.  'TikZ/PGF' o\n-0000bf20: 7074 696f 6e73 206b 6e6f 776e 0a74 6f20  ptions known.to \n-0000bf30: 2773 6b65 7463 6827 2066 6f72 2070 7572  'sketch' for pur\n-0000bf40: 706f 7365 7320 6f66 2074 6869 7320 7370  poses of this sp\n-0000bf50: 6c69 7474 696e 6720 6f70 6572 6174 696f  litting operatio\n-0000bf60: 6e20 696e 636c 7564 6520 2761 7272 6f77  n include 'arrow\n-0000bf70: 7327 2c0a 2763 6170 272c 2027 636f 6c6f  s',.'cap', 'colo\n-0000bf80: 7227 2c20 2764 6173 6820 7061 7474 6572  r', 'dash patter\n-0000bf90: 6e27 2c20 2764 6173 6820 7068 6173 6527  n', 'dash phase'\n-0000bfa0: 2c20 2764 6f75 626c 6527 2c20 2764 6f75  , 'double', 'dou\n-0000bfb0: 626c 650a 6469 7374 616e 6365 272c 2027  ble.distance', '\n-0000bfc0: 6472 6177 272c 2027 6472 6177 206f 7061  draw', 'draw opa\n-0000bfd0: 6369 7479 272c 2027 6669 6c6c 272c 2027  city', 'fill', '\n-0000bfe0: 6669 6c6c 206f 7061 6369 7479 272c 2027  fill opacity', '\n-0000bff0: 6a6f 696e 272c 2027 6c69 6e65 0a77 6964  join', 'line.wid\n-0000c000: 7468 272c 2027 6d69 7465 7220 6c69 6d69  th', 'miter limi\n-0000c010: 7427 2c20 2770 6174 7465 726e 272c 2027  t', 'pattern', '\n-0000c020: 7061 7474 6572 6e20 636f 6c6f 7227 2c20  pattern color', \n-0000c030: 616e 6420 2773 7479 6c65 272e 0a0a 2020  and 'style'...  \n-0000c040: 2054 6865 2027 7374 796c 6527 206f 7074   The 'style' opt\n-0000c050: 696f 6e20 6361 6e20 636f 6e74 6169 6e20  ion can contain \n-0000c060: 626f 7468 2066 6163 6520 616e 6420 6564  both face and ed\n-0000c070: 6765 2069 6e66 6f72 6d61 7469 6f6e 2c20  ge information, \n-0000c080: 736f 0a27 736b 6574 6368 2720 6d75 7374  so.'sketch' must\n-0000c090: 2063 6865 636b 2074 6865 2073 7479 6c65   check the style\n-0000c0a0: 2076 616c 7565 2e20 2056 616c 7565 7320   value.  Values \n-0000c0b0: 6b6e 6f77 6e20 746f 2027 736b 6574 6368  known to 'sketch\n-0000c0c0: 2720 696e 636c 7564 650a 2764 6173 6865  ' include.'dashe\n-0000c0d0: 6427 2c20 2764 656e 7365 6c79 2064 6173  d', 'densely das\n-0000c0e0: 6865 6427 2c20 2764 656e 7365 6c79 2064  hed', 'densely d\n-0000c0f0: 6f74 7465 6427 2c20 2764 6f74 7465 6427  otted', 'dotted'\n-0000c100: 2c20 2764 6f75 626c 6527 2c0a 276c 6f6f  , 'double',.'loo\n-0000c110: 7365 6c79 2064 6173 6865 6427 2c20 276c  sely dashed', 'l\n-0000c120: 6f6f 7365 6c79 2064 6f74 7465 6427 2c20  oosely dotted', \n-0000c130: 276e 6561 726c 7920 6f70 6171 7565 272c  'nearly opaque',\n-0000c140: 2027 6e65 6172 6c79 0a74 7261 6e73 7061   'nearly.transpa\n-0000c150: 7265 6e74 272c 2027 7365 6d69 7468 6963  rent', 'semithic\n-0000c160: 6b27 2c20 2773 656d 6974 7261 6e73 7061  k', 'semitranspa\n-0000c170: 7265 6e74 272c 2027 736f 6c69 6427 2c20  rent', 'solid', \n-0000c180: 2774 6869 636b 272c 2027 7468 696e 272c  'thick', 'thin',\n-0000c190: 0a27 7472 616e 7370 6172 656e 7427 2c20  .'transparent', \n-0000c1a0: 2775 6c74 7261 206e 6561 726c 7920 7472  'ultra nearly tr\n-0000c1b0: 616e 7370 6172 656e 7427 2c20 2775 6c74  ansparent', 'ult\n-0000c1c0: 7261 2074 6869 636b 272c 2027 756c 7472  ra thick', 'ultr\n-0000c1d0: 6120 7468 696e 272c 0a27 7665 7279 206e  a thin',.'very n\n-0000c1e0: 6561 726c 7920 7472 616e 7370 6172 656e  early transparen\n-0000c1f0: 7427 2c20 2776 6572 7920 7468 6963 6b27  t', 'very thick'\n-0000c200: 2c20 616e 6420 2776 6572 7920 7468 696e  , and 'very thin\n-0000c210: 272e 0a0a 1f0a 4669 6c65 3a20 736b 6574  '.....File: sket\n-0000c220: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n-0000c230: 446f 7473 2069 6e20 5469 6b5a 2f50 4746  Dots in TikZ/PGF\n-0000c240: 2c20 204e 6578 743a 2054 696b 5a2f 5047  ,  Next: TikZ/PG\n-0000c250: 4620 7573 6572 2d64 6566 696e 6564 2073  F user-defined s\n-0000c260: 7479 6c65 732c 2020 5072 6576 3a20 5469  tyles,  Prev: Ti\n-0000c270: 6b5a 2f50 4746 206f 7074 696f 6e73 2c20  kZ/PGF options, \n-0000c280: 2055 703a 204f 7074 696f 6e73 0a0a 332e   Up: Options..3.\n-0000c290: 312e 352e 3320 446f 7473 2069 6e20 2754  1.5.3 Dots in 'T\n-0000c2a0: 696b 5a2f 5047 4627 0a2e 2e2e 2e2e 2e2e  ikZ/PGF'........\n+0000bcc0: 0a0a 2754 696b 5a2f 5047 4627 206f 7074  ..'TikZ/PGF' opt\n+0000bcd0: 696f 6e73 2061 7265 2068 616e 646c 6564  ions are handled\n+0000bce0: 206d 7563 6820 6173 2066 6f72 2027 5053   much as for 'PS\n+0000bcf0: 5472 6963 6b73 272e 2020 5468 6f75 6768  Tricks'.  Though\n+0000bd00: 0a27 5469 6b5a 2f50 4746 2720 6f66 7465  .'TikZ/PGF' ofte\n+0000bd10: 6e20 616c 6c6f 7773 2063 6f6c 6f72 7320  n allows colors \n+0000bd20: 616e 6420 7374 796c 6573 2074 6f20 6265  and styles to be\n+0000bd30: 2067 6976 656e 2077 6974 686f 7574 0a63   given without.c\n+0000bd40: 6f72 7265 7370 6f6e 6469 6e67 206b 6579  orresponding key\n+0000bd50: 732c 2066 6f72 2065 7861 6d70 6c65 2c0a  s, for example,.\n+0000bd60: 2020 5c64 7261 775b 7265 642c 756c 7472    \\draw[red,ultr\n+0000bd70: 6120 7468 6963 6b5d 2830 2c30 292d 2d28  a thick](0,0)--(\n+0000bd80: 312c 3129 3b0a 7468 6973 2069 7320 6e6f  1,1);.this is no\n+0000bd90: 7420 7065 726d 6974 7465 6420 696e 2027  t permitted in '\n+0000bda0: 736b 6574 6368 272e 2020 546f 2064 7261  sketch'.  To dra\n+0000bdb0: 7720 6120 7265 642c 2075 6c74 7261 2d74  w a red, ultra-t\n+0000bdc0: 6869 636b 206c 696e 6520 696e 0a27 736b  hick line in.'sk\n+0000bdd0: 6574 6368 272c 2074 6865 2066 6f72 6d20  etch', the form \n+0000bde0: 6973 0a20 206c 696e 655b 6472 6177 3d72  is.  line[draw=r\n+0000bdf0: 6564 2c73 7479 6c65 3d75 6c74 7261 2074  ed,style=ultra t\n+0000be00: 6869 636b 5d28 302c 3029 2831 2c31 290a  hick](0,0)(1,1).\n+0000be10: 0a20 2020 4a75 7374 2061 7320 666f 7220  .   Just as for \n+0000be20: 2750 5354 7269 636b 7327 2c20 7768 656e  'PSTricks', when\n+0000be30: 2061 2027 706f 6c79 676f 6e27 2068 6173   a 'polygon' has\n+0000be40: 206f 7074 696f 6e73 2066 6f72 2062 6f74   options for bot\n+0000be50: 6820 6974 730a 6661 6365 2061 6e64 2069  h its.face and i\n+0000be60: 7473 2065 6467 6573 2c20 616e 6420 7468  ts edges, and th\n+0000be70: 6520 706f 6c79 676f 6e20 6973 2073 706c  e polygon is spl\n+0000be80: 6974 2062 7920 7468 6520 6869 6464 656e  it by the hidden\n+0000be90: 2073 7572 6661 6365 0a61 6c67 6f72 6974   surface.algorit\n+0000bea0: 686d 2c20 2773 6b65 7463 6827 206d 7573  hm, 'sketch' mus\n+0000beb0: 7420 636f 7079 2074 6865 2065 6467 6520  t copy the edge \n+0000bec0: 6f70 7469 6f6e 7320 746f 2027 7073 6c69  options to 'psli\n+0000bed0: 6e65 2773 2066 6f72 2074 6865 2065 6467  ne's for the edg\n+0000bee0: 650a 7365 676d 656e 7473 2061 6e64 2074  e.segments and t\n+0000bef0: 6865 2066 6163 6520 6f70 7469 6f6e 7320  he face options \n+0000bf00: 746f 2027 7073 706f 6c79 676f 6e27 732e  to 'pspolygon's.\n+0000bf10: 2020 2754 696b 5a2f 5047 4627 206f 7074    'TikZ/PGF' opt\n+0000bf20: 696f 6e73 206b 6e6f 776e 0a74 6f20 2773  ions known.to 's\n+0000bf30: 6b65 7463 6827 2066 6f72 2070 7572 706f  ketch' for purpo\n+0000bf40: 7365 7320 6f66 2074 6869 7320 7370 6c69  ses of this spli\n+0000bf50: 7474 696e 6720 6f70 6572 6174 696f 6e20  tting operation \n+0000bf60: 696e 636c 7564 6520 2761 7272 6f77 7327  include 'arrows'\n+0000bf70: 2c0a 2763 6170 272c 2027 636f 6c6f 7227  ,.'cap', 'color'\n+0000bf80: 2c20 2764 6173 6820 7061 7474 6572 6e27  , 'dash pattern'\n+0000bf90: 2c20 2764 6173 6820 7068 6173 6527 2c20  , 'dash phase', \n+0000bfa0: 2764 6f75 626c 6527 2c20 2764 6f75 626c  'double', 'doubl\n+0000bfb0: 650a 6469 7374 616e 6365 272c 2027 6472  e.distance', 'dr\n+0000bfc0: 6177 272c 2027 6472 6177 206f 7061 6369  aw', 'draw opaci\n+0000bfd0: 7479 272c 2027 6669 6c6c 272c 2027 6669  ty', 'fill', 'fi\n+0000bfe0: 6c6c 206f 7061 6369 7479 272c 2027 6a6f  ll opacity', 'jo\n+0000bff0: 696e 272c 2027 6c69 6e65 0a77 6964 7468  in', 'line.width\n+0000c000: 272c 2027 6d69 7465 7220 6c69 6d69 7427  ', 'miter limit'\n+0000c010: 2c20 2770 6174 7465 726e 272c 2027 7061  , 'pattern', 'pa\n+0000c020: 7474 6572 6e20 636f 6c6f 7227 2c20 616e  ttern color', an\n+0000c030: 6420 2773 7479 6c65 272e 0a0a 2020 2054  d 'style'...   T\n+0000c040: 6865 2027 7374 796c 6527 206f 7074 696f  he 'style' optio\n+0000c050: 6e20 6361 6e20 636f 6e74 6169 6e20 626f  n can contain bo\n+0000c060: 7468 2066 6163 6520 616e 6420 6564 6765  th face and edge\n+0000c070: 2069 6e66 6f72 6d61 7469 6f6e 2c20 736f   information, so\n+0000c080: 0a27 736b 6574 6368 2720 6d75 7374 2063  .'sketch' must c\n+0000c090: 6865 636b 2074 6865 2073 7479 6c65 2076  heck the style v\n+0000c0a0: 616c 7565 2e20 2056 616c 7565 7320 6b6e  alue.  Values kn\n+0000c0b0: 6f77 6e20 746f 2027 736b 6574 6368 2720  own to 'sketch' \n+0000c0c0: 696e 636c 7564 650a 2764 6173 6865 6427  include.'dashed'\n+0000c0d0: 2c20 2764 656e 7365 6c79 2064 6173 6865  , 'densely dashe\n+0000c0e0: 6427 2c20 2764 656e 7365 6c79 2064 6f74  d', 'densely dot\n+0000c0f0: 7465 6427 2c20 2764 6f74 7465 6427 2c20  ted', 'dotted', \n+0000c100: 2764 6f75 626c 6527 2c0a 276c 6f6f 7365  'double',.'loose\n+0000c110: 6c79 2064 6173 6865 6427 2c20 276c 6f6f  ly dashed', 'loo\n+0000c120: 7365 6c79 2064 6f74 7465 6427 2c20 276e  sely dotted', 'n\n+0000c130: 6561 726c 7920 6f70 6171 7565 272c 2027  early opaque', '\n+0000c140: 6e65 6172 6c79 0a74 7261 6e73 7061 7265  nearly.transpare\n+0000c150: 6e74 272c 2027 7365 6d69 7468 6963 6b27  nt', 'semithick'\n+0000c160: 2c20 2773 656d 6974 7261 6e73 7061 7265  , 'semitranspare\n+0000c170: 6e74 272c 2027 736f 6c69 6427 2c20 2774  nt', 'solid', 't\n+0000c180: 6869 636b 272c 2027 7468 696e 272c 0a27  hick', 'thin',.'\n+0000c190: 7472 616e 7370 6172 656e 7427 2c20 2775  transparent', 'u\n+0000c1a0: 6c74 7261 206e 6561 726c 7920 7472 616e  ltra nearly tran\n+0000c1b0: 7370 6172 656e 7427 2c20 2775 6c74 7261  sparent', 'ultra\n+0000c1c0: 2074 6869 636b 272c 2027 756c 7472 6120   thick', 'ultra \n+0000c1d0: 7468 696e 272c 0a27 7665 7279 206e 6561  thin',.'very nea\n+0000c1e0: 726c 7920 7472 616e 7370 6172 656e 7427  rly transparent'\n+0000c1f0: 2c20 2776 6572 7920 7468 6963 6b27 2c20  , 'very thick', \n+0000c200: 616e 6420 2776 6572 7920 7468 696e 272e  and 'very thin'.\n+0000c210: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n+0000c220: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 446f  .info,  Node: Do\n+0000c230: 7473 2069 6e20 5469 6b5a 2f50 4746 2c20  ts in TikZ/PGF, \n+0000c240: 204e 6578 743a 2054 696b 5a2f 5047 4620   Next: TikZ/PGF \n+0000c250: 7573 6572 2d64 6566 696e 6564 2073 7479  user-defined sty\n+0000c260: 6c65 732c 2020 5072 6576 3a20 5469 6b5a  les,  Prev: TikZ\n+0000c270: 2f50 4746 206f 7074 696f 6e73 2c20 2055  /PGF options,  U\n+0000c280: 703a 204f 7074 696f 6e73 0a0a 332e 312e  p: Options..3.1.\n+0000c290: 352e 3320 446f 7473 2069 6e20 2754 696b  5.3 Dots in 'Tik\n+0000c2a0: 5a2f 5047 4627 0a2e 2e2e 2e2e 2e2e 2e2e  Z/PGF'..........\n 0000c2b0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000c2c0: 2e2e 2e0a 0a27 5469 6b5a 2f50 4746 2720  .....'TikZ/PGF' \n-0000c2d0: 646f 6573 206e 6f74 2068 6176 6520 6120  does not have a \n-0000c2e0: 2764 6f74 7327 2063 6f6d 6d61 6e64 2061  'dots' command a\n-0000c2f0: 7320 646f 6573 2050 5354 7269 636b 732e  s does PSTricks.\n-0000c300: 2020 496e 7374 6561 642c 0a27 536b 6574    Instead,.'Sket\n-0000c310: 6368 2720 656d 6974 7320 646f 7473 2061  ch' emits dots a\n-0000c320: 7320 2766 696c 6c64 7261 7727 2063 6972  s 'filldraw' cir\n-0000c330: 636c 6573 2e20 2054 6865 2064 6961 6d65  cles.  The diame\n-0000c340: 7465 7220 6d61 7920 6265 2073 6574 0a75  ter may be set.u\n-0000c350: 7369 6e67 2074 6865 206f 7074 696f 6e20  sing the option \n-0000c360: 2764 6f74 7369 7a65 2720 626f 7272 6f77  'dotsize' borrow\n-0000c370: 6564 2066 726f 6d20 5053 5472 6963 6b73  ed from PSTricks\n-0000c380: 2e20 2054 6865 2027 646f 7473 697a 6527  .  The 'dotsize'\n-0000c390: 206f 7074 696f 6e0a 7769 6c6c 2062 6520   option.will be \n-0000c3a0: 7265 6d6f 7665 6420 6672 6f6d 2074 6865  removed from the\n-0000c3b0: 206f 7074 696f 6e20 6c69 7374 2069 6e20   option list in \n-0000c3c0: 7468 6520 6f75 7470 7574 2027 6669 6c6c  the output 'fill\n-0000c3d0: 6472 6177 2720 636f 6d6d 616e 642e 0a4f  draw' command..O\n-0000c3e0: 7468 6572 206f 7074 696f 6e73 2077 6f72  ther options wor\n-0000c3f0: 6b20 696e 2074 6865 2065 7870 6563 7465  k in the expecte\n-0000c400: 6420 7761 792e 2020 466f 7220 6578 616d  d way.  For exam\n-0000c410: 706c 652c 2027 6669 6c6c 2720 7365 7473  ple, 'fill' sets\n-0000c420: 2066 696c 6c0a 636f 6c6f 7220 616e 6420   fill.color and \n-0000c430: 2763 6f6c 6f72 2720 7365 7473 206c 696e  'color' sets lin\n-0000c440: 6520 636f 6c6f 7220 6f66 2074 6865 2063  e color of the c\n-0000c450: 6972 636c 6573 2e0a 0a1f 0a46 696c 653a  ircles.....File:\n-0000c460: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n-0000c470: 6f64 653a 2054 696b 5a2f 5047 4620 7573  ode: TikZ/PGF us\n-0000c480: 6572 2d64 6566 696e 6564 2073 7479 6c65  er-defined style\n-0000c490: 732c 2020 4e65 7874 3a20 5472 616e 7370  s,  Next: Transp\n-0000c4a0: 6172 656e 6379 2c20 2050 7265 763a 2044  arency,  Prev: D\n-0000c4b0: 6f74 7320 696e 2054 696b 5a2f 5047 462c  ots in TikZ/PGF,\n-0000c4c0: 2020 5570 3a20 4f70 7469 6f6e 730a 0a33    Up: Options..3\n-0000c4d0: 2e31 2e35 2e34 2027 5469 6b5a 2f50 4746  .1.5.4 'TikZ/PGF\n-0000c4e0: 2720 7573 6572 2d64 6566 696e 6564 2073  ' user-defined s\n-0000c4f0: 7479 6c65 730a 2e2e 2e2e 2e2e 2e2e 2e2e  tyles...........\n+0000c2c0: 2e0a 0a27 5469 6b5a 2f50 4746 2720 646f  ...'TikZ/PGF' do\n+0000c2d0: 6573 206e 6f74 2068 6176 6520 6120 2764  es not have a 'd\n+0000c2e0: 6f74 7327 2063 6f6d 6d61 6e64 2061 7320  ots' command as \n+0000c2f0: 646f 6573 2050 5354 7269 636b 732e 2020  does PSTricks.  \n+0000c300: 496e 7374 6561 642c 0a27 536b 6574 6368  Instead,.'Sketch\n+0000c310: 2720 656d 6974 7320 646f 7473 2061 7320  ' emits dots as \n+0000c320: 2766 696c 6c64 7261 7727 2063 6972 636c  'filldraw' circl\n+0000c330: 6573 2e20 2054 6865 2064 6961 6d65 7465  es.  The diamete\n+0000c340: 7220 6d61 7920 6265 2073 6574 0a75 7369  r may be set.usi\n+0000c350: 6e67 2074 6865 206f 7074 696f 6e20 2764  ng the option 'd\n+0000c360: 6f74 7369 7a65 2720 626f 7272 6f77 6564  otsize' borrowed\n+0000c370: 2066 726f 6d20 5053 5472 6963 6b73 2e20   from PSTricks. \n+0000c380: 2054 6865 2027 646f 7473 697a 6527 206f   The 'dotsize' o\n+0000c390: 7074 696f 6e0a 7769 6c6c 2062 6520 7265  ption.will be re\n+0000c3a0: 6d6f 7665 6420 6672 6f6d 2074 6865 206f  moved from the o\n+0000c3b0: 7074 696f 6e20 6c69 7374 2069 6e20 7468  ption list in th\n+0000c3c0: 6520 6f75 7470 7574 2027 6669 6c6c 6472  e output 'filldr\n+0000c3d0: 6177 2720 636f 6d6d 616e 642e 0a4f 7468  aw' command..Oth\n+0000c3e0: 6572 206f 7074 696f 6e73 2077 6f72 6b20  er options work \n+0000c3f0: 696e 2074 6865 2065 7870 6563 7465 6420  in the expected \n+0000c400: 7761 792e 2020 466f 7220 6578 616d 706c  way.  For exampl\n+0000c410: 652c 2027 6669 6c6c 2720 7365 7473 2066  e, 'fill' sets f\n+0000c420: 696c 6c0a 636f 6c6f 7220 616e 6420 2763  ill.color and 'c\n+0000c430: 6f6c 6f72 2720 7365 7473 206c 696e 6520  olor' sets line \n+0000c440: 636f 6c6f 7220 6f66 2074 6865 2063 6972  color of the cir\n+0000c450: 636c 6573 2e0a 0a1f 0a46 696c 653a 2073  cles.....File: s\n+0000c460: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n+0000c470: 653a 2054 696b 5a2f 5047 4620 7573 6572  e: TikZ/PGF user\n+0000c480: 2d64 6566 696e 6564 2073 7479 6c65 732c  -defined styles,\n+0000c490: 2020 4e65 7874 3a20 5472 616e 7370 6172    Next: Transpar\n+0000c4a0: 656e 6379 2c20 2050 7265 763a 2044 6f74  ency,  Prev: Dot\n+0000c4b0: 7320 696e 2054 696b 5a2f 5047 462c 2020  s in TikZ/PGF,  \n+0000c4c0: 5570 3a20 4f70 7469 6f6e 730a 0a33 2e31  Up: Options..3.1\n+0000c4d0: 2e35 2e34 2027 5469 6b5a 2f50 4746 2720  .5.4 'TikZ/PGF' \n+0000c4e0: 7573 6572 2d64 6566 696e 6564 2073 7479  user-defined sty\n+0000c4f0: 6c65 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  les.............\n 0000c500: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000c510: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 2754  ..............'T\n-0000c520: 696b 5a2f 5047 4627 2061 6c6c 6f77 7320  ikZ/PGF' allows \n-0000c530: 6e61 6d65 6420 7374 796c 6573 2064 6566  named styles def\n-0000c540: 696e 6564 2062 7920 7468 6520 7573 6572  ined by the user\n-0000c550: 2c20 666f 7220 6578 616d 706c 650a 2020  , for example.  \n-0000c560: 5c74 696b 7a73 7479 6c65 7b6d 7970 6f6c  \\tikzstyle{mypol\n-0000c570: 7967 6f6e 7374 796c 657d 203d 205b 6669  ygonstyle} = [fi\n-0000c580: 6c6c 3d62 6c75 6521 3230 2c66 696c 6c20  ll=blue!20,fill \n-0000c590: 6f70 6163 6974 793d 302e 385d 2020 0a20  opacity=0.8]  . \n-0000c5a0: 205c 7469 6b7a 7374 796c 657b 6d79 6c69   \\tikzstyle{myli\n-0000c5b0: 6e65 7374 796c 657d 203d 205b 7265 6421  nestyle} = [red!\n-0000c5c0: 3230 2c64 6173 6865 645d 0a53 696e 6365  20,dashed].Since\n-0000c5d0: 2027 736b 6574 6368 2720 6861 7320 6e6f   'sketch' has no\n-0000c5e0: 2069 6e66 6f72 6d61 7469 6f6e 206f 6e20   information on \n-0000c5f0: 7468 6520 636f 6e74 656e 7473 206f 6620  the contents of \n-0000c600: 7375 6368 2073 7479 6c65 732c 2069 740a  such styles, it.\n-0000c610: 6f6d 6974 7320 7468 656d 2065 6e74 6972  omits them entir\n-0000c620: 656c 7920 6672 6f6d 206c 696e 6573 2c20  ely from lines, \n-0000c630: 706f 6c79 676f 6e73 2c20 616e 6420 7468  polygons, and th\n-0000c640: 6569 7220 6564 6765 7320 6475 7269 6e67  eir edges during\n-0000c650: 206f 7074 696f 6e0a 7370 6c69 7474 696e   option.splittin\n-0000c660: 672e 2020 466f 7220 6578 616d 706c 652c  g.  For example,\n-0000c670: 0a20 2070 6f6c 7967 6f6e 5b73 7479 6c65  .  polygon[style\n-0000c680: 3d6d 7970 6f6c 7967 6f6e 7374 796c 652c  =mypolygonstyle,\n-0000c690: 7374 796c 653d 7468 6963 6b5d 2830 2c30  style=thick](0,0\n-0000c6a0: 2c31 2928 312c 302c 3029 2830 2c31 2c30  ,1)(1,0,0)(0,1,0\n-0000c6b0: 290a 2020 6c69 6e65 5b73 7479 6c65 3d6d  ).  line[style=m\n-0000c6c0: 796c 696e 6573 7479 6c65 5d28 2d31 2c2d  ylinestyle](-1,-\n-0000c6d0: 312c 2d31 2928 322c 322c 3229 0a70 726f  1,-1)(2,2,2).pro\n-0000c6e0: 6475 6365 7320 7468 6520 2754 696b 5a27  duces the 'TikZ'\n-0000c6f0: 206f 7574 7075 740a 2020 5c64 7261 7728   output.  \\draw(\n-0000c700: 2d31 2c2d 3129 2d2d 282e 3333 332c 2e33  -1,-1)--(.333,.3\n-0000c710: 3333 293b 0a20 205c 6669 6c6c 6472 6177  33);.  \\filldraw\n-0000c720: 5b74 6869 636b 2c66 696c 6c3d 7768 6974  [thick,fill=whit\n-0000c730: 655d 2830 2c30 292d 2d28 312c 3029 2d2d  e](0,0)--(1,0)--\n-0000c740: 2830 2c31 292d 2d63 7963 6c65 3b0a 2020  (0,1)--cycle;.  \n-0000c750: 5c64 7261 7728 2e33 3333 2c2e 3333 3329  \\draw(.333,.333)\n-0000c760: 2d2d 2832 2c32 293b 0a4e 6f74 6520 7468  --(2,2);.Note th\n-0000c770: 6174 2074 6865 2075 7365 722d 6465 6669  at the user-defi\n-0000c780: 6e65 6420 7374 796c 6573 2061 7265 206e  ned styles are n\n-0000c790: 6f74 2070 7265 7365 6e74 2e20 2053 6b65  ot present.  Ske\n-0000c7a0: 7463 6820 616c 736f 2069 7373 7565 730a  tch also issues.\n-0000c7b0: 7761 726e 696e 6773 3a0a 2020 7761 726e  warnings:.  warn\n-0000c7c0: 696e 672c 2075 6e6b 6e6f 776e 2070 6f6c  ing, unknown pol\n-0000c7d0: 7967 6f6e 206f 7074 696f 6e20 7374 796c  ygon option styl\n-0000c7e0: 653d 6d79 706f 6c79 676f 6e73 7479 6c65  e=mypolygonstyle\n-0000c7f0: 2077 696c 6c20 6265 2069 676e 6f72 6564   will be ignored\n-0000c800: 0a20 2077 6172 6e69 6e67 2c20 756e 6b6e  .  warning, unkn\n-0000c810: 6f77 6e20 6c69 6e65 206f 7074 696f 6e20  own line option \n-0000c820: 7374 796c 653d 6d79 6c69 6e65 7374 796c  style=mylinestyl\n-0000c830: 6520 7769 6c6c 2062 6520 6967 6e6f 7265  e will be ignore\n-0000c840: 640a 0a20 2020 5468 6520 7265 6d65 6479  d..   The remedy\n-0000c850: 2069 7320 746f 2073 7461 7465 2065 7870   is to state exp\n-0000c860: 6c69 6369 746c 7920 7768 6574 6865 7220  licitly whether \n-0000c870: 6120 7573 6572 2d64 6566 696e 6564 2073  a user-defined s\n-0000c880: 7479 6c65 2073 686f 756c 640a 6265 2061  tyle should.be a\n-0000c890: 7474 6368 6564 2074 6f20 706f 6c79 676f  ttched to polygo\n-0000c8a0: 6e73 206f 7220 6c69 6e65 7320 696e 2074  ns or lines in t\n-0000c8b0: 6865 2027 5469 6b5a 2720 6f75 7470 7574  he 'TikZ' output\n-0000c8c0: 2075 7369 6e67 0a5f 7073 6575 646f 2d6f   using._pseudo-o\n-0000c8d0: 7074 696f 6e73 5f20 2766 696c 6c20 7374  ptions_ 'fill st\n-0000c8e0: 796c 6527 2061 6e64 2027 6c69 6e65 2073  yle' and 'line s\n-0000c8f0: 7479 6c65 272c 0a20 2070 6f6c 7967 6f6e  tyle',.  polygon\n-0000c900: 5b66 696c 6c20 7374 796c 653d 6d79 706f  [fill style=mypo\n-0000c910: 6c79 676f 6e73 7479 6c65 2c73 7479 6c65  lygonstyle,style\n-0000c920: 3d74 6869 636b 5d28 302c 302c 3129 2831  =thick](0,0,1)(1\n-0000c930: 2c30 2c30 2928 302c 312c 3029 0a20 206c  ,0,0)(0,1,0).  l\n-0000c940: 696e 655b 6c69 6e65 2073 7479 6c65 3d6d  ine[line style=m\n-0000c950: 796c 696e 6573 7479 6c65 5d28 2d31 2c2d  ylinestyle](-1,-\n-0000c960: 312c 2d31 2928 322c 322c 3229 0a4e 6f77  1,-1)(2,2,2).Now\n-0000c970: 2c20 7468 6520 6f75 7470 7574 2069 730a  , the output is.\n-0000c980: 2020 5c64 7261 775b 6d79 6c69 6e65 7374    \\draw[mylinest\n-0000c990: 796c 655d 282d 312c 2d31 292d 2d28 2e33  yle](-1,-1)--(.3\n-0000c9a0: 3333 2c2e 3333 3329 3b0a 2020 5c66 696c  33,.333);.  \\fil\n-0000c9b0: 6c64 7261 775b 6d79 706f 6c79 676f 6e73  ldraw[mypolygons\n-0000c9c0: 7479 6c65 2c74 6869 636b 5d28 302c 3029  tyle,thick](0,0)\n-0000c9d0: 2d2d 2831 2c30 292d 2d28 302c 3129 2d2d  --(1,0)--(0,1)--\n-0000c9e0: 6379 636c 653b 0a20 205c 6472 6177 5b6d  cycle;.  \\draw[m\n-0000c9f0: 796c 696e 6573 7479 6c65 5d28 2e33 3333  ylinestyle](.333\n-0000ca00: 2c2e 3333 3329 2d2d 2832 2c32 293b 0a0a  ,.333)--(2,2);..\n-0000ca10: 2020 2041 2075 7365 6675 6c20 7465 6368     A useful tech\n-0000ca20: 6e69 7175 6520 6973 2074 6f20 696e 636c  nique is to incl\n-0000ca30: 7564 6520 7573 6572 2d64 6566 696e 6564  ude user-defined\n-0000ca40: 2073 7479 6c65 2064 6566 696e 6974 696f   style definitio\n-0000ca50: 6e73 2069 6e0a 2773 6b65 7463 6827 2063  ns in.'sketch' c\n-0000ca60: 6f64 6520 6173 2027 7370 6563 6961 6c27  ode as 'special'\n-0000ca70: 7320 7769 7468 206f 7074 696f 6e20 275b  s with option '[\n-0000ca80: 6c61 793d 756e 6465 725d 2720 746f 2065  lay=under]' to e\n-0000ca90: 6e73 7572 6520 7468 6174 2074 6865 0a73  nsure that the.s\n-0000caa0: 7479 6c65 7320 6172 6520 656d 6974 7465  tyles are emitte\n-0000cab0: 6420 6669 7273 7420 696e 2074 6865 206f  d first in the o\n-0000cac0: 7574 7075 742c 2062 6566 6f72 6520 616e  utput, before an\n-0000cad0: 7920 7573 6573 206f 6620 7468 6520 7374  y uses of the st\n-0000cae0: 796c 650a 6e61 6d65 732e 2020 2831 2920  yle.names.  (1) \n-0000caf0: 2046 6f72 2065 7861 6d70 6c65 2c0a 2020   For example,.  \n-0000cb00: 7370 6563 6961 6c7c 5c74 696b 7a73 7479  special|\\tikzsty\n-0000cb10: 6c65 7b6d 7970 6f6c 7967 6f6e 7374 796c  le{mypolygonstyl\n-0000cb20: 657d 203d 205b 6669 6c6c 3d62 6c75 6521  e} = [fill=blue!\n-0000cb30: 3230 2c66 696c 6c20 6f70 6163 6974 793d  20,fill opacity=\n-0000cb40: 302e 385d 7c5b 6c61 793d 756e 6465 725d  0.8]|[lay=under]\n-0000cb50: 0a20 2073 7065 6369 616c 7c5c 7469 6b7a  .  special|\\tikz\n-0000cb60: 7374 796c 657b 6d79 6c69 6e65 7374 796c  style{mylinestyl\n-0000cb70: 657d 203d 205b 7265 6421 3230 2c64 6173  e} = [red!20,das\n-0000cb80: 6865 645d 7c5b 6c61 793d 756e 6465 725d  hed]|[lay=under]\n-0000cb90: 0a54 6865 2061 7574 686f 7220 6973 2072  .The author is r\n-0000cba0: 6573 706f 6e73 6962 6c65 2066 6f72 2075  esponsible for u\n-0000cbb0: 7369 6e67 2074 6865 206b 6579 2c20 276c  sing the key, 'l\n-0000cbc0: 696e 6520 7374 796c 6527 206f 7220 2766  ine style' or 'f\n-0000cbd0: 696c 6c0a 7374 796c 6527 2c20 7468 6174  ill.style', that\n-0000cbe0: 206d 6174 6368 6573 2074 6865 2063 6f6e   matches the con\n-0000cbf0: 7465 6e74 206f 6620 7468 6520 7374 796c  tent of the styl\n-0000cc00: 6520 6465 6669 6e69 7469 6f6e 2e0a 0a20  e definition... \n-0000cc10: 2020 2d2d 2d2d 2d2d 2d2d 2d2d 2046 6f6f    ---------- Foo\n-0000cc20: 746e 6f74 6573 202d 2d2d 2d2d 2d2d 2d2d  tnotes ---------\n-0000cc30: 2d0a 0a20 2020 2831 2920 5468 6973 2063  -..   (1) This c\n-0000cc40: 6c65 7665 7220 7472 6963 6b20 6973 2064  lever trick is d\n-0000cc50: 7565 2074 6f20 4b6a 656c 6c20 4d61 676e  ue to Kjell Magn\n-0000cc60: 6520 4661 7573 6b65 2e0a 0a1f 0a46 696c  e Fauske.....Fil\n-0000cc70: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n-0000cc80: 204e 6f64 653a 2054 7261 6e73 7061 7265   Node: Transpare\n-0000cc90: 6e63 792c 2020 4e65 7874 3a20 496e 7465  ncy,  Next: Inte\n-0000cca0: 726e 616c 206f 7074 696f 6e73 2c20 2050  rnal options,  P\n-0000ccb0: 7265 763a 2054 696b 5a2f 5047 4620 7573  rev: TikZ/PGF us\n-0000ccc0: 6572 2d64 6566 696e 6564 2073 7479 6c65  er-defined style\n-0000ccd0: 732c 2020 5570 3a20 4f70 7469 6f6e 730a  s,  Up: Options.\n-0000cce0: 0a33 2e31 2e35 2e35 2054 7261 6e73 7061  .3.1.5.5 Transpa\n-0000ccf0: 7265 6e63 790a 2e2e 2e2e 2e2e 2e2e 2e2e  rency...........\n-0000cd00: 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 426f 7468  ............Both\n-0000cd10: 2027 5053 5472 6963 6b73 2720 616e 6420   'PSTricks' and \n-0000cd20: 2754 696b 5a2f 5047 4627 2073 7570 706f  'TikZ/PGF' suppo\n-0000cd30: 7274 2070 6f6c 7967 6f6e 206f 7074 696f  rt polygon optio\n-0000cd40: 6e73 2074 6861 7420 6861 7665 2074 6865  ns that have the\n-0000cd50: 0a65 6666 6563 7420 6f66 206d 616b 696e  .effect of makin\n-0000cd60: 6720 7468 6520 706f 6c79 676f 6e20 6170  g the polygon ap\n-0000cd70: 7065 6172 2074 7261 6e73 7061 7265 6e74  pear transparent\n-0000cd80: 2e20 2046 6f72 2027 5053 5472 6963 6b73  .  For 'PSTricks\n-0000cd90: 272c 0a6b 6579 776f 7264 2027 7472 616e  ',.keyword 'tran\n-0000cda0: 7370 616c 7068 6127 2077 6173 2075 7365  spalpha' was use\n-0000cdb0: 6420 6475 7269 6e67 2069 6e69 7469 616c  d during initial\n-0000cdc0: 2064 6576 656c 6f70 6d65 6e74 206f 660a   development of.\n-0000cdd0: 7472 616e 7370 6172 656e 6379 2066 6561  transparency fea\n-0000cde0: 7475 7265 732c 2061 6e64 2027 6f70 6163  tures, and 'opac\n-0000cdf0: 6974 7927 2077 6173 2061 646f 7074 6564  ity' was adopted\n-0000ce00: 206c 6174 6572 2e20 2027 536b 6574 6368   later.  'Sketch\n-0000ce10: 2720 686f 6e6f 7273 0a62 6f74 682e 2020  ' honors.both.  \n-0000ce20: 2754 696b 5a2f 5047 4627 2075 7365 7320  'TikZ/PGF' uses \n-0000ce30: 276f 7061 6369 7479 2720 6f6e 6c79 2e20  'opacity' only. \n-0000ce40: 2057 6865 6e20 7472 616e 7370 6172 656e   When transparen\n-0000ce50: 7420 706f 6c79 676f 6e73 2061 7265 2069  t polygons are i\n-0000ce60: 6e0a 7468 6520 666f 7265 6772 6f75 6e64  n.the foreground\n-0000ce70: 2c20 6f62 6a65 6374 7320 6265 6869 6e64  , objects behind\n-0000ce80: 2074 6865 6d20 2864 7261 776e 2065 6172   them (drawn ear\n-0000ce90: 6c69 6572 2920 6172 6520 7669 7369 626c  lier) are visibl\n-0000cea0: 6520 7769 7468 0a63 6f6c 6f72 2073 7562  e with.color sub\n-0000ceb0: 6475 6564 2061 6e64 2074 696e 7465 642e  dued and tinted.\n-0000cec0: 2020 5468 6520 6869 6464 656e 2073 7572    The hidden sur\n-0000ced0: 6661 6365 2061 6c67 6f72 6974 686d 206f  face algorithm o\n-0000cee0: 6620 2773 6b65 7463 6827 0a77 6f72 6b73  f 'sketch'.works\n-0000cef0: 2077 656c 6c20 7769 7468 2073 7563 6820   well with such \n-0000cf00: 7472 616e 7370 6172 656e 7420 706f 6c79  transparent poly\n-0000cf10: 676f 6e73 2e0a 0a20 2020 4e6f 7465 2074  gons...   Note t\n-0000cf20: 6861 7420 6375 6c6c 3d66 616c 7365 206d  hat cull=false m\n-0000cf30: 7573 7420 6265 2075 7365 6420 666f 7220  ust be used for \n-0000cf40: 7265 6172 2d66 6163 696e 6720 706f 6c79  rear-facing poly\n-0000cf50: 676f 6e73 2074 6f20 6265 0a76 6973 6962  gons to be.visib\n-0000cf60: 6c65 2077 6865 6e20 706f 7369 7469 6f6e  le when position\n-0000cf70: 6564 2062 6568 696e 6420 6f74 6865 7220  ed behind other \n-0000cf80: 7472 616e 7370 6172 656e 7420 7375 7266  transparent surf\n-0000cf90: 6163 6573 2e0a 0a1f 0a46 696c 653a 2073  aces.....File: s\n-0000cfa0: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n-0000cfb0: 653a 2049 6e74 6572 6e61 6c20 6f70 7469  e: Internal opti\n-0000cfc0: 6f6e 732c 2020 5072 6576 3a20 5472 616e  ons,  Prev: Tran\n-0000cfd0: 7370 6172 656e 6379 2c20 2055 703a 204f  sparency,  Up: O\n-0000cfe0: 7074 696f 6e73 0a0a 332e 312e 352e 3620  ptions..3.1.5.6 \n-0000cff0: 496e 7465 726e 616c 206f 7074 696f 6e73  Internal options\n-0000d000: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000d010: 2e2e 2e2e 2e2e 2e2e 2e0a 0a54 6865 7265  ...........There\n-0000d020: 2061 7265 2061 6c73 6f20 5f69 6e74 6572   are also _inter\n-0000d030: 6e61 6c5f 206f 7074 696f 6e73 2075 7365  nal_ options use\n-0000d040: 6420 6f6e 6c79 2062 7920 2773 6b65 7463  d only by 'sketc\n-0000d050: 6827 2061 6e64 206e 6f74 2070 6173 7365  h' and not passe\n-0000d060: 640a 6f6e 2074 6f20 2750 5354 7269 636b  d.on to 'PSTrick\n-0000d070: 7327 2e20 2054 6865 7365 2061 7265 2073  s'.  These are s\n-0000d080: 756d 6d61 7269 7a65 6420 696e 2074 6865  ummarized in the\n-0000d090: 2066 6f6c 6c6f 7769 6e67 2074 6162 6c65   following table\n-0000d0a0: 2e0a 4b65 7920 2020 2020 2020 506f 7373  ..Key       Poss\n-0000d0b0: 6962 6c65 2076 616c 7565 7320 2020 2020  ible values     \n-0000d0c0: 2020 2020 4465 7363 7269 7074 696f 6e0a      Description.\n+0000c510: 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 2754 696b  ............'Tik\n+0000c520: 5a2f 5047 4627 2061 6c6c 6f77 7320 6e61  Z/PGF' allows na\n+0000c530: 6d65 6420 7374 796c 6573 2064 6566 696e  med styles defin\n+0000c540: 6564 2062 7920 7468 6520 7573 6572 2c20  ed by the user, \n+0000c550: 666f 7220 6578 616d 706c 650a 2020 5c74  for example.  \\t\n+0000c560: 696b 7a73 7479 6c65 7b6d 7970 6f6c 7967  ikzstyle{mypolyg\n+0000c570: 6f6e 7374 796c 657d 203d 205b 6669 6c6c  onstyle} = [fill\n+0000c580: 3d62 6c75 6521 3230 2c66 696c 6c20 6f70  =blue!20,fill op\n+0000c590: 6163 6974 793d 302e 385d 2020 0a20 205c  acity=0.8]  .  \\\n+0000c5a0: 7469 6b7a 7374 796c 657b 6d79 6c69 6e65  tikzstyle{myline\n+0000c5b0: 7374 796c 657d 203d 205b 7265 6421 3230  style} = [red!20\n+0000c5c0: 2c64 6173 6865 645d 0a53 696e 6365 2027  ,dashed].Since '\n+0000c5d0: 736b 6574 6368 2720 6861 7320 6e6f 2069  sketch' has no i\n+0000c5e0: 6e66 6f72 6d61 7469 6f6e 206f 6e20 7468  nformation on th\n+0000c5f0: 6520 636f 6e74 656e 7473 206f 6620 7375  e contents of su\n+0000c600: 6368 2073 7479 6c65 732c 2069 740a 6f6d  ch styles, it.om\n+0000c610: 6974 7320 7468 656d 2065 6e74 6972 656c  its them entirel\n+0000c620: 7920 6672 6f6d 206c 696e 6573 2c20 706f  y from lines, po\n+0000c630: 6c79 676f 6e73 2c20 616e 6420 7468 6569  lygons, and thei\n+0000c640: 7220 6564 6765 7320 6475 7269 6e67 206f  r edges during o\n+0000c650: 7074 696f 6e0a 7370 6c69 7474 696e 672e  ption.splitting.\n+0000c660: 2020 466f 7220 6578 616d 706c 652c 0a20    For example,. \n+0000c670: 2070 6f6c 7967 6f6e 5b73 7479 6c65 3d6d   polygon[style=m\n+0000c680: 7970 6f6c 7967 6f6e 7374 796c 652c 7374  ypolygonstyle,st\n+0000c690: 796c 653d 7468 6963 6b5d 2830 2c30 2c31  yle=thick](0,0,1\n+0000c6a0: 2928 312c 302c 3029 2830 2c31 2c30 290a  )(1,0,0)(0,1,0).\n+0000c6b0: 2020 6c69 6e65 5b73 7479 6c65 3d6d 796c    line[style=myl\n+0000c6c0: 696e 6573 7479 6c65 5d28 2d31 2c2d 312c  inestyle](-1,-1,\n+0000c6d0: 2d31 2928 322c 322c 3229 0a70 726f 6475  -1)(2,2,2).produ\n+0000c6e0: 6365 7320 7468 6520 2754 696b 5a27 206f  ces the 'TikZ' o\n+0000c6f0: 7574 7075 740a 2020 5c64 7261 7728 2d31  utput.  \\draw(-1\n+0000c700: 2c2d 3129 2d2d 282e 3333 332c 2e33 3333  ,-1)--(.333,.333\n+0000c710: 293b 0a20 205c 6669 6c6c 6472 6177 5b74  );.  \\filldraw[t\n+0000c720: 6869 636b 2c66 696c 6c3d 7768 6974 655d  hick,fill=white]\n+0000c730: 2830 2c30 292d 2d28 312c 3029 2d2d 2830  (0,0)--(1,0)--(0\n+0000c740: 2c31 292d 2d63 7963 6c65 3b0a 2020 5c64  ,1)--cycle;.  \\d\n+0000c750: 7261 7728 2e33 3333 2c2e 3333 3329 2d2d  raw(.333,.333)--\n+0000c760: 2832 2c32 293b 0a4e 6f74 6520 7468 6174  (2,2);.Note that\n+0000c770: 2074 6865 2075 7365 722d 6465 6669 6e65   the user-define\n+0000c780: 6420 7374 796c 6573 2061 7265 206e 6f74  d styles are not\n+0000c790: 2070 7265 7365 6e74 2e20 2053 6b65 7463   present.  Sketc\n+0000c7a0: 6820 616c 736f 2069 7373 7565 730a 7761  h also issues.wa\n+0000c7b0: 726e 696e 6773 3a0a 2020 7761 726e 696e  rnings:.  warnin\n+0000c7c0: 672c 2075 6e6b 6e6f 776e 2070 6f6c 7967  g, unknown polyg\n+0000c7d0: 6f6e 206f 7074 696f 6e20 7374 796c 653d  on option style=\n+0000c7e0: 6d79 706f 6c79 676f 6e73 7479 6c65 2077  mypolygonstyle w\n+0000c7f0: 696c 6c20 6265 2069 676e 6f72 6564 0a20  ill be ignored. \n+0000c800: 2077 6172 6e69 6e67 2c20 756e 6b6e 6f77   warning, unknow\n+0000c810: 6e20 6c69 6e65 206f 7074 696f 6e20 7374  n line option st\n+0000c820: 796c 653d 6d79 6c69 6e65 7374 796c 6520  yle=mylinestyle \n+0000c830: 7769 6c6c 2062 6520 6967 6e6f 7265 640a  will be ignored.\n+0000c840: 0a20 2020 5468 6520 7265 6d65 6479 2069  .   The remedy i\n+0000c850: 7320 746f 2073 7461 7465 2065 7870 6c69  s to state expli\n+0000c860: 6369 746c 7920 7768 6574 6865 7220 6120  citly whether a \n+0000c870: 7573 6572 2d64 6566 696e 6564 2073 7479  user-defined sty\n+0000c880: 6c65 2073 686f 756c 640a 6265 2061 7474  le should.be att\n+0000c890: 6368 6564 2074 6f20 706f 6c79 676f 6e73  ched to polygons\n+0000c8a0: 206f 7220 6c69 6e65 7320 696e 2074 6865   or lines in the\n+0000c8b0: 2027 5469 6b5a 2720 6f75 7470 7574 2075   'TikZ' output u\n+0000c8c0: 7369 6e67 0a5f 7073 6575 646f 2d6f 7074  sing._pseudo-opt\n+0000c8d0: 696f 6e73 5f20 2766 696c 6c20 7374 796c  ions_ 'fill styl\n+0000c8e0: 6527 2061 6e64 2027 6c69 6e65 2073 7479  e' and 'line sty\n+0000c8f0: 6c65 272c 0a20 2070 6f6c 7967 6f6e 5b66  le',.  polygon[f\n+0000c900: 696c 6c20 7374 796c 653d 6d79 706f 6c79  ill style=mypoly\n+0000c910: 676f 6e73 7479 6c65 2c73 7479 6c65 3d74  gonstyle,style=t\n+0000c920: 6869 636b 5d28 302c 302c 3129 2831 2c30  hick](0,0,1)(1,0\n+0000c930: 2c30 2928 302c 312c 3029 0a20 206c 696e  ,0)(0,1,0).  lin\n+0000c940: 655b 6c69 6e65 2073 7479 6c65 3d6d 796c  e[line style=myl\n+0000c950: 696e 6573 7479 6c65 5d28 2d31 2c2d 312c  inestyle](-1,-1,\n+0000c960: 2d31 2928 322c 322c 3229 0a4e 6f77 2c20  -1)(2,2,2).Now, \n+0000c970: 7468 6520 6f75 7470 7574 2069 730a 2020  the output is.  \n+0000c980: 5c64 7261 775b 6d79 6c69 6e65 7374 796c  \\draw[mylinestyl\n+0000c990: 655d 282d 312c 2d31 292d 2d28 2e33 3333  e](-1,-1)--(.333\n+0000c9a0: 2c2e 3333 3329 3b0a 2020 5c66 696c 6c64  ,.333);.  \\filld\n+0000c9b0: 7261 775b 6d79 706f 6c79 676f 6e73 7479  raw[mypolygonsty\n+0000c9c0: 6c65 2c74 6869 636b 5d28 302c 3029 2d2d  le,thick](0,0)--\n+0000c9d0: 2831 2c30 292d 2d28 302c 3129 2d2d 6379  (1,0)--(0,1)--cy\n+0000c9e0: 636c 653b 0a20 205c 6472 6177 5b6d 796c  cle;.  \\draw[myl\n+0000c9f0: 696e 6573 7479 6c65 5d28 2e33 3333 2c2e  inestyle](.333,.\n+0000ca00: 3333 3329 2d2d 2832 2c32 293b 0a0a 2020  333)--(2,2);..  \n+0000ca10: 2041 2075 7365 6675 6c20 7465 6368 6e69   A useful techni\n+0000ca20: 7175 6520 6973 2074 6f20 696e 636c 7564  que is to includ\n+0000ca30: 6520 7573 6572 2d64 6566 696e 6564 2073  e user-defined s\n+0000ca40: 7479 6c65 2064 6566 696e 6974 696f 6e73  tyle definitions\n+0000ca50: 2069 6e0a 2773 6b65 7463 6827 2063 6f64   in.'sketch' cod\n+0000ca60: 6520 6173 2027 7370 6563 6961 6c27 7320  e as 'special's \n+0000ca70: 7769 7468 206f 7074 696f 6e20 275b 6c61  with option '[la\n+0000ca80: 793d 756e 6465 725d 2720 746f 2065 6e73  y=under]' to ens\n+0000ca90: 7572 6520 7468 6174 2074 6865 0a73 7479  ure that the.sty\n+0000caa0: 6c65 7320 6172 6520 656d 6974 7465 6420  les are emitted \n+0000cab0: 6669 7273 7420 696e 2074 6865 206f 7574  first in the out\n+0000cac0: 7075 742c 2062 6566 6f72 6520 616e 7920  put, before any \n+0000cad0: 7573 6573 206f 6620 7468 6520 7374 796c  uses of the styl\n+0000cae0: 650a 6e61 6d65 732e 2020 2831 2920 2046  e.names.  (1)  F\n+0000caf0: 6f72 2065 7861 6d70 6c65 2c0a 2020 7370  or example,.  sp\n+0000cb00: 6563 6961 6c7c 5c74 696b 7a73 7479 6c65  ecial|\\tikzstyle\n+0000cb10: 7b6d 7970 6f6c 7967 6f6e 7374 796c 657d  {mypolygonstyle}\n+0000cb20: 203d 205b 6669 6c6c 3d62 6c75 6521 3230   = [fill=blue!20\n+0000cb30: 2c66 696c 6c20 6f70 6163 6974 793d 302e  ,fill opacity=0.\n+0000cb40: 385d 7c5b 6c61 793d 756e 6465 725d 0a20  8]|[lay=under]. \n+0000cb50: 2073 7065 6369 616c 7c5c 7469 6b7a 7374   special|\\tikzst\n+0000cb60: 796c 657b 6d79 6c69 6e65 7374 796c 657d  yle{mylinestyle}\n+0000cb70: 203d 205b 7265 6421 3230 2c64 6173 6865   = [red!20,dashe\n+0000cb80: 645d 7c5b 6c61 793d 756e 6465 725d 0a54  d]|[lay=under].T\n+0000cb90: 6865 2061 7574 686f 7220 6973 2072 6573  he author is res\n+0000cba0: 706f 6e73 6962 6c65 2066 6f72 2075 7369  ponsible for usi\n+0000cbb0: 6e67 2074 6865 206b 6579 2c20 276c 696e  ng the key, 'lin\n+0000cbc0: 6520 7374 796c 6527 206f 7220 2766 696c  e style' or 'fil\n+0000cbd0: 6c0a 7374 796c 6527 2c20 7468 6174 206d  l.style', that m\n+0000cbe0: 6174 6368 6573 2074 6865 2063 6f6e 7465  atches the conte\n+0000cbf0: 6e74 206f 6620 7468 6520 7374 796c 6520  nt of the style \n+0000cc00: 6465 6669 6e69 7469 6f6e 2e0a 0a20 2020  definition...   \n+0000cc10: 2d2d 2d2d 2d2d 2d2d 2d2d 2046 6f6f 746e  ---------- Footn\n+0000cc20: 6f74 6573 202d 2d2d 2d2d 2d2d 2d2d 2d0a  otes ----------.\n+0000cc30: 0a20 2020 2831 2920 5468 6973 2063 6c65  .   (1) This cle\n+0000cc40: 7665 7220 7472 6963 6b20 6973 2064 7565  ver trick is due\n+0000cc50: 2074 6f20 4b6a 656c 6c20 4d61 676e 6520   to Kjell Magne \n+0000cc60: 4661 7573 6b65 2e0a 0a1f 0a46 696c 653a  Fauske.....File:\n+0000cc70: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n+0000cc80: 6f64 653a 2054 7261 6e73 7061 7265 6e63  ode: Transparenc\n+0000cc90: 792c 2020 4e65 7874 3a20 496e 7465 726e  y,  Next: Intern\n+0000cca0: 616c 206f 7074 696f 6e73 2c20 2050 7265  al options,  Pre\n+0000ccb0: 763a 2054 696b 5a2f 5047 4620 7573 6572  v: TikZ/PGF user\n+0000ccc0: 2d64 6566 696e 6564 2073 7479 6c65 732c  -defined styles,\n+0000ccd0: 2020 5570 3a20 4f70 7469 6f6e 730a 0a33    Up: Options..3\n+0000cce0: 2e31 2e35 2e35 2054 7261 6e73 7061 7265  .1.5.5 Transpare\n+0000ccf0: 6e63 790a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ncy.............\n+0000cd00: 2e2e 2e2e 2e2e 2e2e 0a0a 426f 7468 2027  ..........Both '\n+0000cd10: 5053 5472 6963 6b73 2720 616e 6420 2754  PSTricks' and 'T\n+0000cd20: 696b 5a2f 5047 4627 2073 7570 706f 7274  ikZ/PGF' support\n+0000cd30: 2070 6f6c 7967 6f6e 206f 7074 696f 6e73   polygon options\n+0000cd40: 2074 6861 7420 6861 7665 2074 6865 0a65   that have the.e\n+0000cd50: 6666 6563 7420 6f66 206d 616b 696e 6720  ffect of making \n+0000cd60: 7468 6520 706f 6c79 676f 6e20 6170 7065  the polygon appe\n+0000cd70: 6172 2074 7261 6e73 7061 7265 6e74 2e20  ar transparent. \n+0000cd80: 2046 6f72 2027 5053 5472 6963 6b73 272c   For 'PSTricks',\n+0000cd90: 0a6b 6579 776f 7264 2027 7472 616e 7370  .keyword 'transp\n+0000cda0: 616c 7068 6127 2077 6173 2075 7365 6420  alpha' was used \n+0000cdb0: 6475 7269 6e67 2069 6e69 7469 616c 2064  during initial d\n+0000cdc0: 6576 656c 6f70 6d65 6e74 206f 660a 7472  evelopment of.tr\n+0000cdd0: 616e 7370 6172 656e 6379 2066 6561 7475  ansparency featu\n+0000cde0: 7265 732c 2061 6e64 2027 6f70 6163 6974  res, and 'opacit\n+0000cdf0: 7927 2077 6173 2061 646f 7074 6564 206c  y' was adopted l\n+0000ce00: 6174 6572 2e20 2027 536b 6574 6368 2720  ater.  'Sketch' \n+0000ce10: 686f 6e6f 7273 0a62 6f74 682e 2020 2754  honors.both.  'T\n+0000ce20: 696b 5a2f 5047 4627 2075 7365 7320 276f  ikZ/PGF' uses 'o\n+0000ce30: 7061 6369 7479 2720 6f6e 6c79 2e20 2057  pacity' only.  W\n+0000ce40: 6865 6e20 7472 616e 7370 6172 656e 7420  hen transparent \n+0000ce50: 706f 6c79 676f 6e73 2061 7265 2069 6e0a  polygons are in.\n+0000ce60: 7468 6520 666f 7265 6772 6f75 6e64 2c20  the foreground, \n+0000ce70: 6f62 6a65 6374 7320 6265 6869 6e64 2074  objects behind t\n+0000ce80: 6865 6d20 2864 7261 776e 2065 6172 6c69  hem (drawn earli\n+0000ce90: 6572 2920 6172 6520 7669 7369 626c 6520  er) are visible \n+0000cea0: 7769 7468 0a63 6f6c 6f72 2073 7562 6475  with.color subdu\n+0000ceb0: 6564 2061 6e64 2074 696e 7465 642e 2020  ed and tinted.  \n+0000cec0: 5468 6520 6869 6464 656e 2073 7572 6661  The hidden surfa\n+0000ced0: 6365 2061 6c67 6f72 6974 686d 206f 6620  ce algorithm of \n+0000cee0: 2773 6b65 7463 6827 0a77 6f72 6b73 2077  'sketch'.works w\n+0000cef0: 656c 6c20 7769 7468 2073 7563 6820 7472  ell with such tr\n+0000cf00: 616e 7370 6172 656e 7420 706f 6c79 676f  ansparent polygo\n+0000cf10: 6e73 2e0a 0a20 2020 4e6f 7465 2074 6861  ns...   Note tha\n+0000cf20: 7420 6375 6c6c 3d66 616c 7365 206d 7573  t cull=false mus\n+0000cf30: 7420 6265 2075 7365 6420 666f 7220 7265  t be used for re\n+0000cf40: 6172 2d66 6163 696e 6720 706f 6c79 676f  ar-facing polygo\n+0000cf50: 6e73 2074 6f20 6265 0a76 6973 6962 6c65  ns to be.visible\n+0000cf60: 2077 6865 6e20 706f 7369 7469 6f6e 6564   when positioned\n+0000cf70: 2062 6568 696e 6420 6f74 6865 7220 7472   behind other tr\n+0000cf80: 616e 7370 6172 656e 7420 7375 7266 6163  ansparent surfac\n+0000cf90: 6573 2e0a 0a1f 0a46 696c 653a 2073 6b65  es.....File: ske\n+0000cfa0: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n+0000cfb0: 2049 6e74 6572 6e61 6c20 6f70 7469 6f6e   Internal option\n+0000cfc0: 732c 2020 5072 6576 3a20 5472 616e 7370  s,  Prev: Transp\n+0000cfd0: 6172 656e 6379 2c20 2055 703a 204f 7074  arency,  Up: Opt\n+0000cfe0: 696f 6e73 0a0a 332e 312e 352e 3620 496e  ions..3.1.5.6 In\n+0000cff0: 7465 726e 616c 206f 7074 696f 6e73 0a2e  ternal options..\n+0000d000: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+0000d010: 2e2e 2e2e 2e2e 2e0a 0a54 6865 7265 2061  .........There a\n+0000d020: 7265 2061 6c73 6f20 5f69 6e74 6572 6e61  re also _interna\n+0000d030: 6c5f 206f 7074 696f 6e73 2075 7365 6420  l_ options used \n+0000d040: 6f6e 6c79 2062 7920 2773 6b65 7463 6827  only by 'sketch'\n+0000d050: 2061 6e64 206e 6f74 2070 6173 7365 640a   and not passed.\n+0000d060: 6f6e 2074 6f20 2750 5354 7269 636b 7327  on to 'PSTricks'\n+0000d070: 2e20 2054 6865 7365 2061 7265 2073 756d  .  These are sum\n+0000d080: 6d61 7269 7a65 6420 696e 2074 6865 2066  marized in the f\n+0000d090: 6f6c 6c6f 7769 6e67 2074 6162 6c65 2e0a  ollowing table..\n+0000d0a0: 4b65 7920 2020 2020 2020 506f 7373 6962  Key       Possib\n+0000d0b0: 6c65 2076 616c 7565 7320 2020 2020 2020  le values       \n+0000d0c0: 2020 4465 7363 7269 7074 696f 6e0a 2d2d    Description.--\n 0000d0d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\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 2d2d 2d2d  ----------------\n-0000d130: 0a27 6375 6c6c 2720 2020 2027 7472 7565  .'cull'    'true\n-0000d140: 272c 2027 6661 6c73 6527 2020 2020 2020  ', 'false'      \n-0000d150: 2020 2054 7572 6e20 6375 6c6c 696e 6720     Turn culling \n-0000d160: 6f66 2062 6163 6b66 6163 6573 206f 6e20  of backfaces on \n-0000d170: 616e 6420 6f66 6620 7265 7370 6563 7469  and off respecti\n-0000d180: 7665 6c79 2066 6f72 2074 6869 730a 2020  vely for this.  \n+0000d120: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a27  --------------.'\n+0000d130: 6375 6c6c 2720 2020 2027 7472 7565 272c  cull'    'true',\n+0000d140: 2027 6661 6c73 6527 2020 2020 2020 2020   'false'        \n+0000d150: 2054 7572 6e20 6375 6c6c 696e 6720 6f66   Turn culling of\n+0000d160: 2062 6163 6b66 6163 6573 206f 6e20 616e   backfaces on an\n+0000d170: 6420 6f66 6620 7265 7370 6563 7469 7665  d off respective\n+0000d180: 6c79 2066 6f72 2074 6869 730a 2020 2020  ly for this.    \n 0000d190: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d1a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d1b0: 6f62 6a65 6374 2e20 2054 6865 2064 6566  object.  The def\n-0000d1c0: 6175 6c74 2076 616c 7565 2069 7320 2774  ault value is 't\n-0000d1d0: 7275 6527 2e0a 276c 6179 2720 2020 2020  rue'..'lay'     \n-0000d1e0: 276f 7665 7227 2c20 2769 6e27 2c20 2775  'over', 'in', 'u\n-0000d1f0: 6e64 6572 2720 2020 466f 7263 6520 7468  nder'   Force th\n-0000d200: 6973 206f 626a 6563 7420 746f 2062 6520  is object to be \n-0000d210: 2775 6e64 6572 2720 6f72 2027 6f76 6572  'under' or 'over\n-0000d220: 2720 616c 6c20 6f74 6865 7220 6f62 6a65  ' all other obje\n-0000d230: 6374 730a 2020 2020 2020 2020 2020 2020  cts.            \n+0000d1a0: 2020 2020 2020 2020 2020 2020 2020 6f62                ob\n+0000d1b0: 6a65 6374 2e20 2054 6865 2064 6566 6175  ject.  The defau\n+0000d1c0: 6c74 2076 616c 7565 2069 7320 2774 7275  lt value is 'tru\n+0000d1d0: 6527 2e0a 276c 6179 2720 2020 2020 276f  e'..'lay'     'o\n+0000d1e0: 7665 7227 2c20 2769 6e27 2c20 2775 6e64  ver', 'in', 'und\n+0000d1f0: 6572 2720 2020 466f 7263 6520 7468 6973  er'   Force this\n+0000d200: 206f 626a 6563 7420 746f 2062 6520 2775   object to be 'u\n+0000d210: 6e64 6572 2720 6f72 2027 6f76 6572 2720  nder' or 'over' \n+0000d220: 616c 6c20 6f74 6865 7220 6f62 6a65 6374  all other object\n+0000d230: 730a 2020 2020 2020 2020 2020 2020 2020  s.              \n 0000d240: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d250: 2020 2020 2020 696e 2074 6865 2064 6570        in the dep\n-0000d260: 7468 2073 6f72 7420 6f72 6465 7220 6372  th sort order cr\n-0000d270: 6561 7465 6420 6279 2074 6865 2068 6964  eated by the hid\n-0000d280: 6465 6e20 7375 7266 6163 650a 2020 2020  den surface.    \n+0000d250: 2020 2020 696e 2074 6865 2064 6570 7468      in the depth\n+0000d260: 2073 6f72 7420 6f72 6465 7220 6372 6561   sort order crea\n+0000d270: 7465 6420 6279 2074 6865 2068 6964 6465  ted by the hidde\n+0000d280: 6e20 7375 7266 6163 650a 2020 2020 2020  n surface.      \n 0000d290: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d2a0: 2020 2020 2020 2020 2020 2020 2020 616c                al\n-0000d2b0: 676f 7269 7468 6d2e 2020 5468 6520 6465  gorithm.  The de\n-0000d2c0: 6661 756c 7420 7661 6c75 6520 276f 7665  fault value 'ove\n-0000d2d0: 7227 2067 7561 7261 6e74 6565 7320 7468  r' guarantees th\n-0000d2e0: 6174 206f 7574 7075 740a 2020 2020 2020  at output.      \n+0000d2a0: 2020 2020 2020 2020 2020 2020 616c 676f              algo\n+0000d2b0: 7269 7468 6d2e 2020 5468 6520 6465 6661  rithm.  The defa\n+0000d2c0: 756c 7420 7661 6c75 6520 276f 7665 7227  ult value 'over'\n+0000d2d0: 2067 7561 7261 6e74 6565 7320 7468 6174   guarantees that\n+0000d2e0: 206f 7574 7075 740a 2020 2020 2020 2020   output.        \n 0000d2f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d300: 2020 2020 2020 2020 2020 2020 6475 6520              due \n-0000d310: 746f 2074 6865 2027 7370 6563 6961 6c27  to the 'special'\n-0000d320: 2077 696c 6c20 6265 2076 6973 6962 6c65   will be visible\n-0000d330: 2e0a 2773 706c 6974 2720 2020 2774 7275  ..'split'   'tru\n-0000d340: 6527 2c20 2766 616c 7365 2720 2020 2020  e', 'false'     \n-0000d350: 2020 2020 5475 726e 2073 706c 6974 7469      Turn splitti\n-0000d360: 6e67 206f 6620 7377 6565 702d 6765 6e65  ng of sweep-gene\n-0000d370: 7261 7465 6420 626f 6479 2070 6f6c 7967  rated body polyg\n-0000d380: 6f6e 7320 6f6e 2061 6e64 206f 6666 0a20  ons on and off. \n+0000d300: 2020 2020 2020 2020 2020 6475 6520 746f            due to\n+0000d310: 2074 6865 2027 7370 6563 6961 6c27 2077   the 'special' w\n+0000d320: 696c 6c20 6265 2076 6973 6962 6c65 2e0a  ill be visible..\n+0000d330: 2773 706c 6974 2720 2020 2774 7275 6527  'split'   'true'\n+0000d340: 2c20 2766 616c 7365 2720 2020 2020 2020  , 'false'       \n+0000d350: 2020 5475 726e 2073 706c 6974 7469 6e67    Turn splitting\n+0000d360: 206f 6620 7377 6565 702d 6765 6e65 7261   of sweep-genera\n+0000d370: 7465 6420 626f 6479 2070 6f6c 7967 6f6e  ted body polygon\n+0000d380: 7320 6f6e 2061 6e64 206f 6666 0a20 2020  s on and off.   \n 0000d390: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d3a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d3b0: 2072 6573 7065 6374 6976 656c 792e 2020   respectively.  \n-0000d3c0: 2a4e 6f74 6520 5377 6565 7073 3a3a 2e20  *Note Sweeps::. \n-0000d3d0: 2054 6865 2064 6566 6175 6c74 2076 616c   The default val\n-0000d3e0: 7565 2027 7472 7565 270a 2020 2020 2020  ue 'true'.      \n+0000d3a0: 2020 2020 2020 2020 2020 2020 2020 2072                 r\n+0000d3b0: 6573 7065 6374 6976 656c 792e 2020 2a4e  espectively.  *N\n+0000d3c0: 6f74 6520 5377 6565 7073 3a3a 2e20 2054  ote Sweeps::.  T\n+0000d3d0: 6865 2064 6566 6175 6c74 2076 616c 7565  he default value\n+0000d3e0: 2027 7472 7565 270a 2020 2020 2020 2020   'true'.        \n 0000d3f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d400: 2020 2020 2020 2020 2020 2020 6361 7573              caus\n-0000d410: 6573 2022 7761 7270 6564 2220 706f 6c79  es \"warped\" poly\n-0000d420: 676f 6e73 2074 6f20 6265 2073 706c 6974  gons to be split\n-0000d430: 2069 6e74 6f20 7472 6961 6e67 6c65 732c   into triangles,\n-0000d440: 2077 6869 6368 0a20 2020 2020 2020 2020   which.         \n+0000d400: 2020 2020 2020 2020 2020 6361 7573 6573            causes\n+0000d410: 2022 7761 7270 6564 2220 706f 6c79 676f   \"warped\" polygo\n+0000d420: 6e73 2074 6f20 6265 2073 706c 6974 2069  ns to be split i\n+0000d430: 6e74 6f20 7472 6961 6e67 6c65 732c 2077  nto triangles, w\n+0000d440: 6869 6368 0a20 2020 2020 2020 2020 2020  hich.           \n 0000d450: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d460: 2020 2020 2020 2020 2061 766f 6964 7320           avoids \n-0000d470: 6d69 7374 616b 6573 2062 7920 7468 6520  mistakes by the \n-0000d480: 6869 6464 656e 2073 7572 6661 6365 2061  hidden surface a\n-0000d490: 6c67 6f72 6974 686d 2e0a 0a33 2e31 2e36  lgorithm...3.1.6\n-0000d4a0: 2050 6f69 6e74 206c 6973 7473 0a2d 2d2d   Point lists.---\n-0000d4b0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a  --------------..\n-0000d4c0: 2a53 796e 7461 783a 2a0a 2020 2020 2028  *Syntax:*.     (\n-0000d4d0: 5831 2c59 312c 5a31 2928 5832 2c59 322c  X1,Y1,Z1)(X2,Y2,\n-0000d4e0: 5a32 292e 2e2e 0a41 2073 6571 7565 6e63  Z2)....A sequenc\n-0000d4f0: 6520 6f66 206f 6e65 206f 7220 6d6f 7265  e of one or more\n-0000d500: 2070 6f69 6e74 7320 6d61 6b65 7320 6120   points makes a \n-0000d510: 706f 696e 7420 6c69 7374 2c20 6120 6665  point list, a fe\n-0000d520: 6174 7572 6520 636f 6d6d 6f6e 2074 6f0a  ature common to.\n-0000d530: 616c 6c20 6472 6177 6162 6c65 732e 2020  all drawables.  \n-0000d540: 4561 6368 206f 6620 7468 6520 706f 696e  Each of the poin\n-0000d550: 7420 636f 6d70 6f6e 656e 7473 2069 7320  t components is \n-0000d560: 6120 7363 616c 6172 2061 7269 7468 6d65  a scalar arithme\n-0000d570: 7469 630a 6578 7072 6573 7369 6f6e 2e20  tic.expression. \n-0000d580: 2041 6e79 2070 6f69 6e74 206d 6179 2068   Any point may h\n-0000d590: 6176 6520 7468 6520 7a2d 636f 6d70 6f6e  ave the z-compon\n-0000d5a0: 656e 7420 6f6d 6974 7465 643b 2069 7420  ent omitted; it \n-0000d5b0: 7769 6c6c 2064 6566 6175 6c74 0a74 6f20  will default.to \n-0000d5c0: 7a3d 302e 0a0a 2a20 4d65 6e75 3a0a 0a2a  z=0...* Menu:..*\n-0000d5d0: 2044 7261 7761 626c 6573 3a3a 2020 2020   Drawables::    \n-0000d5e0: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n-0000d5f0: 6869 6e67 7320 7468 6174 2061 7265 2064  hings that are d\n-0000d600: 7261 776e 2e0a 2a20 4465 6669 6e69 7469  rawn..* Definiti\n-0000d610: 6f6e 733a 3a20 2020 2020 2020 2020 2020  ons::           \n-0000d620: 2020 2020 2020 5468 696e 6773 2077 6974        Things wit\n-0000d630: 6820 6e61 6d65 732e 0a0a 1f0a 4669 6c65  h names.....File\n-0000d640: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n-0000d650: 4e6f 6465 3a20 4472 6177 6162 6c65 732c  Node: Drawables,\n-0000d660: 2020 4e65 7874 3a20 4465 6669 6e69 7469    Next: Definiti\n-0000d670: 6f6e 732c 2020 5072 6576 3a20 4c61 6e67  ons,  Prev: Lang\n-0000d680: 7561 6765 2062 6173 6963 732c 2020 5570  uage basics,  Up\n-0000d690: 3a20 496e 7075 7420 6c61 6e67 7561 6765  : Input language\n-0000d6a0: 0a0a 332e 3220 4472 6177 6162 6c65 730a  ..3.2 Drawables.\n-0000d6b0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a 0a44  =============..D\n-0000d6c0: 7261 7761 626c 6573 2061 7265 2073 696d  rawables are sim\n-0000d6d0: 706c 7920 2773 6b65 7463 6827 206f 626a  ply 'sketch' obj\n-0000d6e0: 6563 7473 2074 6861 7420 6d69 6768 7420  ects that might \n-0000d6f0: 6170 7065 6172 2069 6e20 7468 6520 6472  appear in the dr\n-0000d700: 6177 696e 672e 0a54 6865 7920 696e 636c  awing..They incl\n-0000d710: 7564 6520 646f 7473 2c20 706f 6c79 6c69  ude dots, polyli\n-0000d720: 6e65 732c 2063 7572 7665 732c 2070 6f6c  nes, curves, pol\n-0000d730: 7967 6f6e 732c 2061 6e64 206d 6f72 6520  ygons, and more \n-0000d740: 636f 6d70 6c65 7820 6f62 6a65 6374 730a  complex objects.\n-0000d750: 7468 6174 2061 7265 2062 7569 6c74 2075  that are built u\n-0000d760: 7020 6672 6f6d 2073 696d 706c 6572 206f  p from simpler o\n-0000d770: 6e65 7320 696e 2076 6172 696f 7573 2077  nes in various w\n-0000d780: 6179 732e 2020 4669 6e61 6c6c 792c 2022  ays.  Finally, \"\n-0000d790: 7370 6563 6961 6c22 0a6f 626a 6563 7473  special\".objects\n-0000d7a0: 2061 7265 2074 686f 7365 2063 6f6d 706f   are those compo\n-0000d7b0: 7365 6420 6f66 204c 6154 6558 206f 7220  sed of LaTeX or \n-0000d7c0: 2750 5354 7269 636b 7327 2063 6f64 652c  'PSTricks' code,\n-0000d7d0: 2070 6572 6861 7073 0a69 6e63 6c75 6469   perhaps.includi\n-0000d7e0: 6e67 2063 6f6f 7264 696e 6174 6573 2061  ng coordinates a\n-0000d7f0: 6e64 2061 6e67 6c65 7320 636f 6d70 7574  nd angles comput\n-0000d800: 6564 2062 7920 2773 6b65 7463 6827 2e0a  ed by 'sketch'..\n-0000d810: 0a2a 204d 656e 753a 0a0a 2a20 446f 7473  .* Menu:..* Dots\n-0000d820: 3a3a 2020 2020 2020 2020 2020 2020 2020  ::              \n-0000d830: 2020 2020 2020 2020 2020 4472 6177 2064            Draw d\n-0000d840: 6f74 732e 0a2a 204c 696e 6573 3a3a 2020  ots..* Lines::  \n+0000d460: 2020 2020 2020 2061 766f 6964 7320 6d69         avoids mi\n+0000d470: 7374 616b 6573 2062 7920 7468 6520 6869  stakes by the hi\n+0000d480: 6464 656e 2073 7572 6661 6365 2061 6c67  dden surface alg\n+0000d490: 6f72 6974 686d 2e0a 0a33 2e31 2e36 2050  orithm...3.1.6 P\n+0000d4a0: 6f69 6e74 206c 6973 7473 0a2d 2d2d 2d2d  oint lists.-----\n+0000d4b0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53  ------------..*S\n+0000d4c0: 796e 7461 783a 2a0a 2020 2020 2028 5831  yntax:*.     (X1\n+0000d4d0: 2c59 312c 5a31 2928 5832 2c59 322c 5a32  ,Y1,Z1)(X2,Y2,Z2\n+0000d4e0: 292e 2e2e 0a41 2073 6571 7565 6e63 6520  )....A sequence \n+0000d4f0: 6f66 206f 6e65 206f 7220 6d6f 7265 2070  of one or more p\n+0000d500: 6f69 6e74 7320 6d61 6b65 7320 6120 706f  oints makes a po\n+0000d510: 696e 7420 6c69 7374 2c20 6120 6665 6174  int list, a feat\n+0000d520: 7572 6520 636f 6d6d 6f6e 2074 6f0a 616c  ure common to.al\n+0000d530: 6c20 6472 6177 6162 6c65 732e 2020 4561  l drawables.  Ea\n+0000d540: 6368 206f 6620 7468 6520 706f 696e 7420  ch of the point \n+0000d550: 636f 6d70 6f6e 656e 7473 2069 7320 6120  components is a \n+0000d560: 7363 616c 6172 2061 7269 7468 6d65 7469  scalar arithmeti\n+0000d570: 630a 6578 7072 6573 7369 6f6e 2e20 2041  c.expression.  A\n+0000d580: 6e79 2070 6f69 6e74 206d 6179 2068 6176  ny point may hav\n+0000d590: 6520 7468 6520 7a2d 636f 6d70 6f6e 656e  e the z-componen\n+0000d5a0: 7420 6f6d 6974 7465 643b 2069 7420 7769  t omitted; it wi\n+0000d5b0: 6c6c 2064 6566 6175 6c74 0a74 6f20 7a3d  ll default.to z=\n+0000d5c0: 302e 0a0a 2a20 4d65 6e75 3a0a 0a2a 2044  0...* Menu:..* D\n+0000d5d0: 7261 7761 626c 6573 3a3a 2020 2020 2020  rawables::      \n+0000d5e0: 2020 2020 2020 2020 2020 2020 2054 6869               Thi\n+0000d5f0: 6e67 7320 7468 6174 2061 7265 2064 7261  ngs that are dra\n+0000d600: 776e 2e0a 2a20 4465 6669 6e69 7469 6f6e  wn..* Definition\n+0000d610: 733a 3a20 2020 2020 2020 2020 2020 2020  s::             \n+0000d620: 2020 2020 5468 696e 6773 2077 6974 6820      Things with \n+0000d630: 6e61 6d65 732e 0a0a 1f0a 4669 6c65 3a20  names.....File: \n+0000d640: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n+0000d650: 6465 3a20 4472 6177 6162 6c65 732c 2020  de: Drawables,  \n+0000d660: 4e65 7874 3a20 4465 6669 6e69 7469 6f6e  Next: Definition\n+0000d670: 732c 2020 5072 6576 3a20 4c61 6e67 7561  s,  Prev: Langua\n+0000d680: 6765 2062 6173 6963 732c 2020 5570 3a20  ge basics,  Up: \n+0000d690: 496e 7075 7420 6c61 6e67 7561 6765 0a0a  Input language..\n+0000d6a0: 332e 3220 4472 6177 6162 6c65 730a 3d3d  3.2 Drawables.==\n+0000d6b0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a 0a44 7261  ===========..Dra\n+0000d6c0: 7761 626c 6573 2061 7265 2073 696d 706c  wables are simpl\n+0000d6d0: 7920 2773 6b65 7463 6827 206f 626a 6563  y 'sketch' objec\n+0000d6e0: 7473 2074 6861 7420 6d69 6768 7420 6170  ts that might ap\n+0000d6f0: 7065 6172 2069 6e20 7468 6520 6472 6177  pear in the draw\n+0000d700: 696e 672e 0a54 6865 7920 696e 636c 7564  ing..They includ\n+0000d710: 6520 646f 7473 2c20 706f 6c79 6c69 6e65  e dots, polyline\n+0000d720: 732c 2063 7572 7665 732c 2070 6f6c 7967  s, curves, polyg\n+0000d730: 6f6e 732c 2061 6e64 206d 6f72 6520 636f  ons, and more co\n+0000d740: 6d70 6c65 7820 6f62 6a65 6374 730a 7468  mplex objects.th\n+0000d750: 6174 2061 7265 2062 7569 6c74 2075 7020  at are built up \n+0000d760: 6672 6f6d 2073 696d 706c 6572 206f 6e65  from simpler one\n+0000d770: 7320 696e 2076 6172 696f 7573 2077 6179  s in various way\n+0000d780: 732e 2020 4669 6e61 6c6c 792c 2022 7370  s.  Finally, \"sp\n+0000d790: 6563 6961 6c22 0a6f 626a 6563 7473 2061  ecial\".objects a\n+0000d7a0: 7265 2074 686f 7365 2063 6f6d 706f 7365  re those compose\n+0000d7b0: 6420 6f66 204c 6154 6558 206f 7220 2750  d of LaTeX or 'P\n+0000d7c0: 5354 7269 636b 7327 2063 6f64 652c 2070  STricks' code, p\n+0000d7d0: 6572 6861 7073 0a69 6e63 6c75 6469 6e67  erhaps.including\n+0000d7e0: 2063 6f6f 7264 696e 6174 6573 2061 6e64   coordinates and\n+0000d7f0: 2061 6e67 6c65 7320 636f 6d70 7574 6564   angles computed\n+0000d800: 2062 7920 2773 6b65 7463 6827 2e0a 0a2a   by 'sketch'...*\n+0000d810: 204d 656e 753a 0a0a 2a20 446f 7473 3a3a   Menu:..* Dots::\n+0000d820: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0000d830: 2020 2020 2020 2020 4472 6177 2064 6f74          Draw dot\n+0000d840: 732e 0a2a 204c 696e 6573 3a3a 2020 2020  s..* Lines::    \n 0000d850: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d860: 2020 2020 2044 7261 7720 706f 6c79 6c69       Draw polyli\n-0000d870: 6e65 732e 0a2a 2043 7572 7665 733a 3a20  nes..* Curves:: \n+0000d860: 2020 2044 7261 7720 706f 6c79 6c69 6e65     Draw polyline\n+0000d870: 732e 0a2a 2043 7572 7665 733a 3a20 2020  s..* Curves::   \n 0000d880: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d890: 2020 2020 2044 7261 7720 6375 7276 6573       Draw curves\n-0000d8a0: 2e0a 2a20 506f 6c79 676f 6e73 3a3a 2020  ..* Polygons::  \n+0000d890: 2020 2044 7261 7720 6375 7276 6573 2e0a     Draw curves..\n+0000d8a0: 2a20 506f 6c79 676f 6e73 3a3a 2020 2020  * Polygons::    \n 0000d8b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d8c0: 2020 4472 6177 2070 6f6c 7967 6f6e 732e    Draw polygons.\n-0000d8d0: 0a2a 2053 7065 6369 616c 733a 3a20 2020  .* Specials::   \n-0000d8e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d8f0: 2045 6d62 6564 2072 6177 204c 6154 6558   Embed raw LaTeX\n-0000d900: 2061 6e64 2027 5053 5472 6963 6b73 272e   and 'PSTricks'.\n-0000d910: 0a2a 2053 7765 6570 733a 3a20 2020 2020  .* Sweeps::     \n-0000d920: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d930: 2044 7261 7720 7377 6565 7073 206f 6620   Draw sweeps of \n-0000d940: 646f 7473 2061 6e64 2070 6f6c 796c 696e  dots and polylin\n-0000d950: 6573 2e0a 2a20 426c 6f63 6b73 3a3a 2020  es..* Blocks::  \n+0000d8c0: 4472 6177 2070 6f6c 7967 6f6e 732e 0a2a  Draw polygons..*\n+0000d8d0: 2053 7065 6369 616c 733a 3a20 2020 2020   Specials::     \n+0000d8e0: 2020 2020 2020 2020 2020 2020 2020 2045                 E\n+0000d8f0: 6d62 6564 2072 6177 204c 6154 6558 2061  mbed raw LaTeX a\n+0000d900: 6e64 2027 5053 5472 6963 6b73 272e 0a2a  nd 'PSTricks'..*\n+0000d910: 2053 7765 6570 733a 3a20 2020 2020 2020   Sweeps::       \n+0000d920: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n+0000d930: 7261 7720 7377 6565 7073 206f 6620 646f  raw sweeps of do\n+0000d940: 7473 2061 6e64 2070 6f6c 796c 696e 6573  ts and polylines\n+0000d950: 2e0a 2a20 426c 6f63 6b73 3a3a 2020 2020  ..* Blocks::    \n 0000d960: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000d970: 2020 2020 4772 6f75 7020 6f74 6865 7220      Group other \n-0000d980: 6472 6177 6162 6c65 732e 0a2a 2052 6570  drawables..* Rep\n-0000d990: 6561 7473 3a3a 2020 2020 2020 2020 2020  eats::          \n-0000d9a0: 2020 2020 2020 2020 2020 2044 7261 7720             Draw \n-0000d9b0: 7472 616e 7366 6f72 6d65 6420 636f 7069  transformed copi\n-0000d9c0: 6573 206f 6620 6f62 6a65 6374 732e 0a2a  es of objects..*\n-0000d9d0: 2050 7574 733a 3a20 2020 2020 2020 2020   Puts::         \n-0000d9e0: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n-0000d9f0: 7261 7720 6f6e 6520 6f62 6a65 6374 2074  raw one object t\n-0000da00: 7261 6e73 666f 726d 6564 2e0a 0a1f 0a46  ransformed.....F\n-0000da10: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n-0000da20: 2c20 204e 6f64 653a 2044 6f74 732c 2020  ,  Node: Dots,  \n-0000da30: 4e65 7874 3a20 4c69 6e65 732c 2020 5072  Next: Lines,  Pr\n-0000da40: 6576 3a20 4472 6177 6162 6c65 732c 2020  ev: Drawables,  \n-0000da50: 5570 3a20 4472 6177 6162 6c65 730a 0a33  Up: Drawables..3\n-0000da60: 2e32 2e31 2044 6f74 730a 2d2d 2d2d 2d2d  .2.1 Dots.------\n-0000da70: 2d2d 2d2d 0a0a 2a53 796e 7461 783a 2a0a  ----..*Syntax:*.\n-0000da80: 2020 2020 2064 6f74 735b 4f50 5449 4f4e       dots[OPTION\n-0000da90: 535d 2050 4f49 4e54 5f4c 4953 540a 5468  S] POINT_LIST.Th\n-0000daa0: 6973 2063 6f6d 6d61 6e64 2069 7320 7468  is command is th\n-0000dab0: 6520 7468 7265 652d 6469 6d65 6e73 696f  e three-dimensio\n-0000dac0: 6e61 6c20 6571 7569 7661 6c65 6e74 206f  nal equivalent o\n-0000dad0: 6620 7468 6520 2750 5354 7269 636b 7327  f the 'PSTricks'\n-0000dae0: 0a63 6f6d 6d61 6e64 2027 5c70 7364 6f74  .command '\\psdot\n-0000daf0: 7327 2e0a 0a1f 0a46 696c 653a 2073 6b65  s'.....File: ske\n-0000db00: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n-0000db10: 204c 696e 6573 2c20 204e 6578 743a 2043   Lines,  Next: C\n-0000db20: 7572 7665 732c 2020 5072 6576 3a20 446f  urves,  Prev: Do\n-0000db30: 7473 2c20 2055 703a 2044 7261 7761 626c  ts,  Up: Drawabl\n-0000db40: 6573 0a0a 332e 322e 3220 4c69 6e65 730a  es..3.2.2 Lines.\n-0000db50: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a 5379  -----------..*Sy\n-0000db60: 6e74 6178 3a2a 0a20 2020 2020 6c69 6e65  ntax:*.     line\n-0000db70: 5b4f 5054 494f 4e53 5d20 504f 494e 545f  [OPTIONS] POINT_\n-0000db80: 4c49 5354 0a54 6869 7320 636f 6d6d 616e  LIST.This comman\n-0000db90: 6420 6973 2074 6865 2074 6872 6565 2d64  d is the three-d\n-0000dba0: 696d 656e 7369 6f6e 616c 2065 7175 6976  imensional equiv\n-0000dbb0: 616c 656e 7420 6f66 2074 6865 2027 5053  alent of the 'PS\n-0000dbc0: 5472 6963 6b73 270a 636f 6d6d 616e 6420  Tricks'.command \n-0000dbd0: 275c 7073 6c69 6e65 272e 0a0a 1f0a 4669  '\\psline'.....Fi\n-0000dbe0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n-0000dbf0: 2020 4e6f 6465 3a20 4375 7276 6573 2c20    Node: Curves, \n-0000dc00: 204e 6578 743a 2050 6f6c 7967 6f6e 732c   Next: Polygons,\n-0000dc10: 2020 5072 6576 3a20 4c69 6e65 732c 2020    Prev: Lines,  \n-0000dc20: 5570 3a20 4472 6177 6162 6c65 730a 0a33  Up: Drawables..3\n-0000dc30: 2e32 2e33 2043 7572 7665 730a 2d2d 2d2d  .2.3 Curves.----\n-0000dc40: 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461  --------..*Synta\n-0000dc50: 783a 2a0a 2020 2020 2063 7572 7665 5b4f  x:*.     curve[O\n-0000dc60: 5054 494f 4e53 5d20 504f 494e 545f 4c49  PTIONS] POINT_LI\n-0000dc70: 5354 0a54 6869 7320 636f 6d6d 616e 6420  ST.This command \n-0000dc80: 6973 2074 6865 2074 6872 6565 2d64 696d  is the three-dim\n-0000dc90: 656e 7369 6f6e 616c 2065 7175 6976 616c  ensional equival\n-0000dca0: 656e 7420 6f66 2074 6865 2027 5053 5472  ent of the 'PSTr\n-0000dcb0: 6963 6b73 270a 636f 6d6d 616e 6420 275c  icks'.command '\\\n-0000dcc0: 7073 6375 7276 6527 2e20 2049 7420 6973  pscurve'.  It is\n-0000dcd0: 206e 6f74 2069 6d70 6c65 6d65 6e74 6564   not implemented\n-0000dce0: 2069 6e20 7468 6520 6375 7272 656e 7420   in the current \n-0000dcf0: 7665 7273 696f 6e20 6f66 0a27 736b 6574  version of.'sket\n-0000dd00: 6368 272e 0a0a 1f0a 4669 6c65 3a20 736b  ch'.....File: sk\n-0000dd10: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n-0000dd20: 3a20 506f 6c79 676f 6e73 2c20 204e 6578  : Polygons,  Nex\n-0000dd30: 743a 2053 7065 6369 616c 732c 2020 5072  t: Specials,  Pr\n-0000dd40: 6576 3a20 4375 7276 6573 2c20 2055 703a  ev: Curves,  Up:\n-0000dd50: 2044 7261 7761 626c 6573 0a0a 332e 322e   Drawables..3.2.\n-0000dd60: 3420 506f 6c79 676f 6e73 0a2d 2d2d 2d2d  4 Polygons.-----\n-0000dd70: 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74  ---------..*Synt\n-0000dd80: 6178 3a2a 0a20 2020 2020 706f 6c79 676f  ax:*.     polygo\n-0000dd90: 6e5b 4f50 5449 4f4e 535d 2050 4f49 4e54  n[OPTIONS] POINT\n-0000dda0: 5f4c 4953 540a 5468 6973 2063 6f6d 6d61  _LIST.This comma\n-0000ddb0: 6e64 2069 7320 7468 6520 7468 7265 652d  nd is the three-\n-0000ddc0: 6469 6d65 6e73 696f 6e61 6c20 6571 7569  dimensional equi\n-0000ddd0: 7661 6c65 6e74 206f 6620 7468 6520 2750  valent of the 'P\n-0000dde0: 5354 7269 636b 7327 0a63 6f6d 6d61 6e64  STricks'.command\n-0000ddf0: 2027 5c70 7370 6f6c 7967 6f6e 272e 2020   '\\pspolygon'.  \n-0000de00: 5468 6520 2773 6b65 7463 6827 2068 6964  The 'sketch' hid\n-0000de10: 6465 6e20 7375 7266 6163 6520 616c 676f  den surface algo\n-0000de20: 7269 7468 6d20 6173 7375 6d65 730a 7468  rithm assumes.th\n-0000de30: 6174 2070 6f6c 7967 6f6e 7320 6172 6520  at polygons are \n-0000de40: 636f 6e76 6578 2061 6e64 2070 6c61 6e61  convex and plana\n-0000de50: 722e 2020 496e 2070 7261 6374 6963 652c  r.  In practice,\n-0000de60: 2064 7261 7769 6e67 7320 6d61 7920 7765   drawings may we\n-0000de70: 6c6c 0a74 7572 6e20 6f75 7420 636f 7272  ll.turn out corr\n-0000de80: 6563 746c 7920 6576 656e 2069 6620 7468  ectly even if th\n-0000de90: 6573 6520 6173 7375 6d70 7469 6f6e 7320  ese assumptions \n-0000dea0: 6172 6520 7669 6f6c 6174 6564 2e0a 0a1f  are violated....\n-0000deb0: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n-0000dec0: 666f 2c20 204e 6f64 653a 2053 7065 6369  fo,  Node: Speci\n-0000ded0: 616c 732c 2020 4e65 7874 3a20 5377 6565  als,  Next: Swee\n-0000dee0: 7073 2c20 2050 7265 763a 2050 6f6c 7967  ps,  Prev: Polyg\n-0000def0: 6f6e 732c 2020 5570 3a20 4472 6177 6162  ons,  Up: Drawab\n-0000df00: 6c65 730a 0a33 2e32 2e35 2053 7065 6369  les..3.2.5 Speci\n-0000df10: 616c 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  als.------------\n-0000df20: 2d2d 0a0a 2a53 796e 7461 783a 2a0a 2020  --..*Syntax:*.  \n-0000df30: 2020 2073 7065 6369 616c 2024 5241 575f     special $RAW_\n-0000df40: 5445 5854 245b 4f50 5449 4f4e 535d 2041  TEXT$[OPTIONS] A\n-0000df50: 5247 5f4c 4953 540a 4865 7265 2027 2427  RG_LIST.Here '$'\n-0000df60: 2063 616e 2062 6520 616e 7920 6368 6172   can be any char\n-0000df70: 6163 7465 7220 616e 6420 6973 2075 7365  acter and is use\n-0000df80: 6420 746f 2064 656c 696d 6974 2074 6865  d to delimit the\n-0000df90: 2073 7461 7274 2061 6e64 2065 6e64 0a6f   start and end.o\n-0000dfa0: 6620 5241 575f 5445 5854 2e20 2054 6865  f RAW_TEXT.  The\n-0000dfb0: 2063 6f6d 6d61 6e64 2065 6d62 6564 7320   command embeds \n-0000dfc0: 5241 575f 5445 5854 2069 6e20 7468 6520  RAW_TEXT in the \n-0000dfd0: 2773 6b65 7463 6827 206f 7574 7075 7420  'sketch' output \n-0000dfe0: 6166 7465 720a 7065 7266 6f72 6d69 6e67  after.performing\n-0000dff0: 2073 7562 7374 6974 7574 696f 6e73 2061   substitutions a\n-0000e000: 7320 666f 6c6c 6f77 732e 0a20 2020 2a20  s follows..   * \n-0000e010: 2723 4927 2077 6865 7265 2049 2069 7320  '#I' where I is \n-0000e020: 6120 706f 7369 7469 7665 2069 6e74 6567  a positive integ\n-0000e030: 6572 2069 7320 7265 706c 6163 6564 2062  er is replaced b\n-0000e040: 7920 7468 6520 4927 7468 2076 616c 7565  y the I'th value\n-0000e050: 2069 6e0a 2020 2020 2041 5247 5f4c 4953   in.     ARG_LIS\n-0000e060: 542e 2020 506f 696e 7420 616e 6420 7665  T.  Point and ve\n-0000e070: 6374 6f72 2061 7267 756d 656e 7473 2062  ctor arguments b\n-0000e080: 6563 6f6d 6520 7477 6f2d 6469 6d65 6e73  ecome two-dimens\n-0000e090: 696f 6e61 6c0a 2020 2020 2070 6f69 6e74  ional.     point\n-0000e0a0: 732c 2077 6869 6368 2061 7265 2074 6865  s, which are the\n-0000e0b0: 2074 7261 6e73 666f 726d 6564 2033 6420   transformed 3d \n-0000e0c0: 6172 6775 6d65 6e74 7320 7072 6f6a 6563  arguments projec\n-0000e0d0: 7465 6420 6f6e 746f 2074 6865 0a20 2020  ted onto the.   \n-0000e0e0: 2020 582d 5920 706c 616e 652e 2020 5468    X-Y plane.  Th\n-0000e0f0: 6973 2061 6c6c 6f77 7320 7477 6f2d 6469  is allows two-di\n-0000e100: 6d65 6e74 696f 6e61 6c20 6f75 7470 7574  mentional output\n-0000e110: 2065 6c65 6d65 6e74 7320 7375 6368 2061   elements such a\n-0000e120: 730a 2020 2020 206c 6162 656c 7320 746f  s.     labels to\n-0000e130: 2062 6520 6561 7369 6c79 2070 6f73 6974   be easily posit\n-0000e140: 696f 6e65 6420 7769 7468 2072 6573 7065  ioned with respe\n-0000e150: 6374 2074 6f20 7468 7265 652d 6469 6d65  ct to three-dime\n-0000e160: 6e73 696f 6e61 6c0a 2020 2020 2066 6561  nsional.     fea\n-0000e170: 7475 7265 7320 696e 2074 6865 2064 7261  tures in the dra\n-0000e180: 7769 6e67 2e20 2053 6361 6c61 7220 6172  wing.  Scalar ar\n-0000e190: 6775 6d65 6e74 7320 6172 6520 7375 6273  guments are subs\n-0000e1a0: 6974 7574 6564 2064 6972 6563 746c 792e  ituted directly.\n-0000e1b0: 0a20 2020 2020 4e6f 2074 7261 6e73 666f  .     No transfo\n-0000e1c0: 726d 6174 696f 6e20 6973 2061 7070 6c69  rmation is appli\n-0000e1d0: 6564 2e0a 2020 202a 2027 237b 497d 2720  ed..   * '#{I}' \n-0000e1e0: 6973 2061 6c73 6f20 7265 706c 6163 6564  is also replaced\n-0000e1f0: 2061 7320 6162 6f76 652e 0a20 2020 2a20   as above..   * \n-0000e200: 2723 4927 3227 2069 7320 7265 706c 6163  '#I'2' is replac\n-0000e210: 6564 2061 7320 6162 6f76 6520 666f 7220  ed as above for \n-0000e220: 706f 696e 7473 206f 7220 7665 6374 6f72  points or vector\n-0000e230: 732e 2020 4974 2069 7320 616e 2065 7272  s.  It is an err\n-0000e240: 6f72 0a20 2020 2020 666f 7220 7468 6520  or.     for the \n-0000e250: 4927 7468 2061 7267 756d 656e 7420 746f  I'th argument to\n-0000e260: 2062 6520 6120 7363 616c 6172 2e0a 2020   be a scalar..  \n-0000e270: 202a 2027 2349 2778 272c 2027 2349 2779   * '#I'x', '#I'y\n-0000e280: 272c 206f 7220 2723 4927 7a27 2069 7320  ', or '#I'z' is \n-0000e290: 7265 706c 6163 6564 2c20 7265 7370 6563  replaced, respec\n-0000e2a0: 7469 7665 6c79 2c20 6279 2074 6865 2073  tively, by the s\n-0000e2b0: 6361 6c61 720a 2020 2020 2058 2c20 592c  calar.     X, Y,\n-0000e2c0: 206f 7220 5a2d 636f 6f72 6469 6e61 7465   or Z-coordinate\n-0000e2d0: 206f 6620 7468 6520 6172 6775 6d65 6e74   of the argument\n-0000e2e0: 2070 6f69 6e74 206f 7220 7665 6374 6f72   point or vector\n-0000e2f0: 2e20 2049 7420 6973 2061 6e0a 2020 2020  .  It is an.    \n-0000e300: 2065 7272 6f72 2066 6f72 2074 6865 2049   error for the I\n-0000e310: 2774 6820 6172 6775 6d65 6e74 2074 6f20  'th argument to \n-0000e320: 6265 2061 2073 6361 6c61 722e 0a20 2020  be a scalar..   \n-0000e330: 2a20 2723 4927 3327 2069 7320 7265 706c  * '#I'3' is repl\n-0000e340: 6163 6564 2062 7920 7468 6520 7468 7265  aced by the thre\n-0000e350: 652d 6469 6d65 6e73 696f 6e61 6c20 7472  e-dimensional tr\n-0000e360: 616e 7366 6f72 6d65 6420 6172 6775 6d65  ansformed argume\n-0000e370: 6e74 2e0a 2020 2020 204e 6f74 6520 7468  nt..     Note th\n-0000e380: 6174 2069 6620 6120 7065 7273 7065 6374  at if a perspect\n-0000e390: 6976 6520 7472 616e 7366 6f72 6d61 7469  ive transformati\n-0000e3a0: 6f6e 2068 6173 2062 6565 6e20 6170 706c  on has been appl\n-0000e3b0: 6965 642c 2074 6865 0a20 2020 2020 5a2d  ied, the.     Z-\n-0000e3c0: 636f 6f72 6469 6e61 7465 2068 6173 206c  coordinate has l\n-0000e3d0: 6974 746c 6520 6765 6f6d 6574 7269 6320  ittle geometric \n-0000e3e0: 7369 676e 6966 6963 616e 6365 2c20 7468  significance, th\n-0000e3f0: 6f75 6768 2069 740a 2020 2020 2061 6363  ough it.     acc\n-0000e400: 7572 6174 656c 7920 696e 6469 6361 7465  urately indicate\n-0000e410: 7320 7265 6c61 7469 7665 2064 6570 7468  s relative depth\n-0000e420: 2e0a 2020 202a 2027 2349 2d4a 2720 7768  ..   * '#I-J' wh\n-0000e430: 6572 6520 4920 616e 6420 4a20 6172 6520  ere I and J are \n-0000e440: 706f 7369 7469 7665 2069 6e74 6567 6572  positive integer\n-0000e450: 7320 6973 2072 6570 6c61 6365 6420 6279  s is replaced by\n-0000e460: 2061 2073 7472 696e 670a 2020 2020 2027   a string.     '\n-0000e470: 7b41 4e47 4c45 7d27 2077 6865 7265 2041  {ANGLE}' where A\n-0000e480: 4e47 4c45 2069 7320 7468 6520 706f 6c61  NGLE is the pola\n-0000e490: 7220 616e 676c 6520 6f66 2061 2076 6563  r angle of a vec\n-0000e4a0: 746f 7220 6672 6f6d 2074 6865 2049 2774  tor from the I't\n-0000e4b0: 680a 2020 2020 2070 6f69 6e74 2069 6e20  h.     point in \n-0000e4c0: 504f 494e 545f 4c49 5354 2074 6f20 7468  POINT_LIST to th\n-0000e4d0: 6520 4a27 7468 2070 6f69 6e74 2070 726f  e J'th point pro\n-0000e4e0: 6a65 6374 6564 2069 6e74 6f20 7468 6520  jected into the \n-0000e4f0: 782d 7920 706c 616e 652e 0a20 2020 2020  x-y plane..     \n-0000e500: 4974 2069 7320 616e 2065 7272 6f72 2066  It is an error f\n-0000e510: 6f72 2074 6865 2049 2774 6820 6f72 204a  or the I'th or J\n-0000e520: 2774 6820 6172 6775 6d65 6e74 2074 6f20  'th argument to \n-0000e530: 6265 2061 2073 6361 6c61 7220 6f72 2061  be a scalar or a\n-0000e540: 0a20 2020 2020 7665 6374 6f72 2e0a 2020  .     vector..  \n-0000e550: 202a 2027 237b 492d 4a7d 2720 6973 2061   * '#{I-J}' is a\n-0000e560: 6c73 6f20 7265 706c 6163 6564 2061 7320  lso replaced as \n-0000e570: 6162 6f76 652e 0a20 2020 2a20 2723 2327  above..   * '##'\n-0000e580: 2069 7320 7265 706c 6163 6564 2077 6974   is replaced wit\n-0000e590: 6820 2723 272e 0a54 6865 2066 6f72 6d73  h '#'..The forms\n-0000e5a0: 2077 6974 6820 6272 6163 6573 2027 7b20   with braces '{ \n-0000e5b0: 7d27 2061 7265 2075 7365 6675 6c20 7768  }' are useful wh\n-0000e5c0: 656e 2074 6865 2061 7267 756d 656e 7420  en the argument \n-0000e5d0: 6973 2069 6d6d 6564 6961 7465 6c79 0a66  is immediately.f\n-0000e5e0: 6f6c 6c6f 7765 6420 6279 2061 2064 6967  ollowed by a dig\n-0000e5f0: 6974 206f 7220 6120 7469 636b 2063 6861  it or a tick cha\n-0000e600: 7261 6374 6572 2074 6861 7420 6973 2070  racter that is p\n-0000e610: 6172 7420 6f66 2074 6865 2054 6558 2063  art of the TeX c\n-0000e620: 6f64 652e 0a0a 2020 2054 6865 206f 6e6c  ode...   The onl\n-0000e630: 7920 7573 6566 756c 206f 7074 696f 6e20  y useful option \n-0000e640: 6f66 2027 7370 6563 6961 6c27 2069 7320  of 'special' is \n-0000e650: 276c 6179 272c 2077 6869 6368 2064 6574  'lay', which det\n-0000e660: 6572 6d69 6e65 7320 6966 2074 6865 0a73  ermines if the.s\n-0000e670: 7562 7374 6974 7565 6420 7261 7720 7465  ubstitued raw te\n-0000e680: 7874 2069 7320 656d 6974 7465 6420 6265  xt is emitted be\n-0000e690: 666f 7265 2c20 6166 7465 722c 206f 7220  fore, after, or \n-0000e6a0: 7573 696e 6720 7468 6520 6669 7273 7420  using the first \n-0000e6b0: 706f 696e 740a 696e 2050 4f49 4e54 5f4c  point.in POINT_L\n-0000e6c0: 4953 5420 6173 2061 6e20 696e 6469 6361  IST as an indica\n-0000e6d0: 746f 7220 6f66 2064 6570 7468 2e20 2054  tor of depth.  T\n-0000e6e0: 6865 7365 206f 6363 7572 2c20 7265 7370  hese occur, resp\n-0000e6f0: 6563 7469 7665 6c79 2c20 7769 7468 0a27  ectively, with.'\n-0000e700: 6c61 793d 756e 6465 7227 2c20 276c 6179  lay=under', 'lay\n-0000e710: 3d6f 7665 7227 2c20 616e 6420 276c 6179  =over', and 'lay\n-0000e720: 3d69 6e27 2e20 2053 6565 202a 6e6f 7465  =in'.  See *note\n-0000e730: 2053 7065 6369 616c 206f 626a 6563 7473   Special objects\n-0000e740: 3a3a 2061 6e64 0a2a 6e6f 7465 2054 696b  :: and.*note Tik\n-0000e750: 5a2f 5047 4620 7573 6572 2d64 6566 696e  Z/PGF user-defin\n-0000e760: 6564 2073 7479 6c65 733a 3a20 666f 7220  ed styles:: for \n-0000e770: 6578 616d 706c 6573 2e20 202a 4e6f 7465  examples.  *Note\n-0000e780: 2049 6e74 6572 6e61 6c0a 6f70 7469 6f6e   Internal.option\n-0000e790: 733a 3a2e 0a0a 1f0a 4669 6c65 3a20 736b  s::.....File: sk\n-0000e7a0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n-0000e7b0: 3a20 5377 6565 7073 2c20 204e 6578 743a  : Sweeps,  Next:\n-0000e7c0: 2042 6c6f 636b 732c 2020 5072 6576 3a20   Blocks,  Prev: \n-0000e7d0: 5370 6563 6961 6c73 2c20 2055 703a 2044  Specials,  Up: D\n-0000e7e0: 7261 7761 626c 6573 0a0a 332e 322e 3620  rawables..3.2.6 \n-0000e7f0: 5377 6565 7073 0a2d 2d2d 2d2d 2d2d 2d2d  Sweeps.---------\n-0000e800: 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a 0a20  ---..*Syntax:*. \n-0000e810: 2020 2020 7377 6565 7020 7b20 4e2c 2054      sweep { N, T\n-0000e820: 5f31 2c20 545f 322c 202e 2e2e 2c20 545f  _1, T_2, ..., T_\n-0000e830: 5220 7d5b 4f50 5449 4f4e 535d 2053 5745  R }[OPTIONS] SWE\n-0000e840: 5054 5f4f 424a 4543 540a 2020 2020 2073  PT_OBJECT.     s\n-0000e850: 7765 6570 207b 204e 3c3e 2c20 545f 312c  weep { N<>, T_1,\n-0000e860: 2054 5f32 2c20 2e2e 2e2c 2054 5f52 207d   T_2, ..., T_R }\n-0000e870: 5b4f 5054 494f 4e53 5d20 5357 4550 545f  [OPTIONS] SWEPT_\n-0000e880: 4f42 4a45 4354 0a54 6865 2073 7765 6570  OBJECT.The sweep\n-0000e890: 2063 6f6e 6e65 6374 7320 4e20 286f 7220   connects N (or \n-0000e8a0: 7065 7268 6170 7320 4e2b 3129 2063 6f70  perhaps N+1) cop\n-0000e8b0: 6965 7320 6f66 2053 5745 5054 5f4f 424a  ies of SWEPT_OBJ\n-0000e8c0: 4543 5420 696e 206f 7264 6572 2074 6f0a  ECT in order to.\n-0000e8d0: 6372 6561 7465 2061 206e 6577 206f 626a  create a new obj\n-0000e8e0: 6563 7420 6f66 2068 6967 6865 7220 6469  ect of higher di\n-0000e8f0: 6d65 6e73 696f 6e2e 2020 5468 6520 545f  mension.  The T_\n-0000e900: 4920 2866 6f72 2069 2062 6574 7765 656e  I (for i between\n-0000e910: 2031 2061 6e64 0a72 2920 6172 6520 7472   1 and.r) are tr\n-0000e920: 616e 7366 6f72 6d73 2e20 2054 6865 206b  ansforms.  The k\n-0000e930: 2774 6820 636f 7079 206f 6620 5357 4550  'th copy of SWEP\n-0000e940: 545f 4f42 4a45 4354 2069 7320 7072 6f64  T_OBJECT is prod\n-0000e950: 7563 6564 2062 790a 6170 706c 7969 6e67  uced by.applying\n-0000e960: 2074 6865 2066 6f6c 6c6f 7769 6e67 2074   the following t\n-0000e970: 7261 6e73 666f 726d 2074 6f20 7468 6520  ransform to the \n-0000e980: 6f72 6967 696e 616c 2e0a 2020 2020 2054  original..     T\n-0000e990: 5f31 5e6b 2074 6865 6e20 545f 325e 6b20  _1^k then T_2^k \n-0000e9a0: 7468 656e 202e 2e2e 2074 6865 6e20 545f  then ... then T_\n-0000e9b0: 525e 6b0a 4865 7265 2054 5e6b 206d 6561  R^k.Here T^k mea\n-0000e9c0: 6e73 2022 7472 616e 7366 6f72 6d20 5420  ns \"transform T \n-0000e9d0: 6170 706c 6965 6420 6b20 7469 6d65 732e  applied k times.\n-0000e9e0: 2220 2054 6865 206f 7269 6769 6e61 6c20  \"  The original \n-0000e9f0: 6f62 6a65 6374 2069 730a 7468 6520 7a65  object is.the ze\n-0000ea00: 726f 2774 6820 636f 7079 2c20 7769 7468  ro'th copy, with\n-0000ea10: 206b 3d30 2061 6e64 2065 6666 6563 7469   k=0 and effecti\n-0000ea20: 7665 6c79 206e 6f20 7472 616e 7366 6f72  vely no transfor\n-0000ea30: 6d20 6170 706c 6965 6420 2854 5e30 3d49  m applied (T^0=I\n-0000ea40: 2c0a 7468 6520 6964 656e 7469 7479 2074  ,.the identity t\n-0000ea50: 7261 6e73 666f 726d 292e 0a0a 2020 2054  ransform)...   T\n-0000ea60: 6865 206d 6574 686f 6420 6f66 2063 6f6e  he method of con\n-0000ea70: 6e65 6374 696e 6720 7468 6520 636f 7069  necting the copi\n-0000ea80: 6573 2064 6570 656e 6473 206f 6e20 7468  es depends on th\n-0000ea90: 6520 7479 7065 206f 660a 5357 4550 545f  e type of.SWEPT_\n-0000eaa0: 4f42 4a45 4354 2061 6e64 206f 6e20 7768  OBJECT and on wh\n-0000eab0: 6574 6865 7220 7468 6520 636c 6f73 7572  ether the closur\n-0000eac0: 6520 7461 6720 273c 3e27 2069 7320 7072  e tag '<>' is pr\n-0000ead0: 6573 656e 7420 6f72 206e 6f74 2e0a 0a20  esent or not... \n-0000eae0: 2020 416e 2065 7861 6d70 6c65 206f 6620    An example of \n-0000eaf0: 6120 7377 6565 7020 7768 6572 6520 723d  a sweep where r=\n-0000eb00: 3220 6973 2074 6865 204d 6f62 6975 7320  2 is the Mobius \n-0000eb10: 6669 6775 7265 2061 7420 2a6e 6f74 6520  figure at *note \n-0000eb20: 4d6f 7265 2074 6f0a 6c65 6172 6e3a 3a2e  More to.learn::.\n-0000eb30: 0a0a 2a20 4d65 6e75 3a0a 0a2a 2053 7765  ..* Menu:..* Swe\n-0000eb40: 7074 2070 6f69 6e74 733a 3a20 2020 2020  pt points::     \n-0000eb50: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-0000eb60: 2070 6f69 6e74 7320 6d61 6b65 206c 696e   points make lin\n-0000eb70: 6573 206f 7220 706f 6c79 676f 6e73 2e0a  es or polygons..\n-0000eb80: 2a20 5377 6570 7420 6c69 6e65 733a 3a20  * Swept lines:: \n-0000eb90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0000eba0: 5377 6570 7420 6c69 6e65 7320 6d61 6b65  Swept lines make\n-0000ebb0: 206f 7065 6e20 6f72 2063 6c6f 7365 6420   open or closed \n-0000ebc0: 7375 7266 6163 6573 2e0a 2a20 5377 6570  surfaces..* Swep\n-0000ebd0: 7420 706f 6c79 676f 6e73 3a3a 2020 2020  t polygons::    \n-0000ebe0: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n-0000ebf0: 706f 6c79 676f 6e73 206d 616b 6520 636c  polygons make cl\n-0000ec00: 6f73 6564 2073 7572 6661 6365 732e 0a2a  osed surfaces..*\n-0000ec10: 2053 7765 7074 2062 6c6f 636b 733a 3a20   Swept blocks:: \n-0000ec20: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n-0000ec30: 7765 7074 2062 6c6f 636b 203d 3d20 626c  wept block == bl\n-0000ec40: 6f63 6b20 6f66 2073 7765 6570 732e 0a2a  ock of sweeps..*\n-0000ec50: 2053 7765 6570 2066 6163 6520 7370 6c69   Sweep face spli\n-0000ec60: 7474 696e 673a 3a20 2020 2020 2020 2046  tting::        F\n-0000ec70: 6978 696e 6720 7761 7270 6564 2066 6163  ixing warped fac\n-0000ec80: 6573 2077 6974 6820 7472 6961 6e67 6c65  es with triangle\n-0000ec90: 732e 0a0a 1f0a 4669 6c65 3a20 736b 6574  s.....File: sket\n-0000eca0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n-0000ecb0: 5377 6570 7420 706f 696e 7473 2c20 204e  Swept points,  N\n-0000ecc0: 6578 743a 2053 7765 7074 206c 696e 6573  ext: Swept lines\n-0000ecd0: 2c20 2050 7265 763a 2053 7765 6570 732c  ,  Prev: Sweeps,\n-0000ece0: 2020 5570 3a20 5377 6565 7073 0a0a 332e    Up: Sweeps..3.\n-0000ecf0: 322e 362e 3120 5377 6570 7420 706f 696e  2.6.1 Swept poin\n-0000ed00: 7473 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ts..............\n-0000ed10: 2e2e 2e2e 2e2e 2e0a 0a49 6620 5357 4550  .........If SWEP\n-0000ed20: 545f 4f42 4a45 4354 2069 7320 6120 706f  T_OBJECT is a po\n-0000ed30: 696e 7420 6c69 7374 2061 6e64 2074 6865  int list and the\n-0000ed40: 7265 2069 7320 6e6f 2063 6c6f 7375 7265  re is no closure\n-0000ed50: 2074 6167 2c20 7468 656e 0a27 7377 6565   tag, then.'swee\n-0000ed60: 7027 2063 6f6e 6e65 6374 7320 4e2b 3120  p' connects N+1 \n-0000ed70: 7375 6363 6573 7369 7665 2063 6f70 6965  successive copie\n-0000ed80: 7320 6f66 2065 6163 6820 706f 696e 7420  s of each point \n-0000ed90: 2869 6e63 6c75 6469 6e67 2074 6865 0a6f  (including the.o\n-0000eda0: 7269 6769 6e61 6c29 2077 6974 6820 7374  riginal) with st\n-0000edb0: 7261 6967 6874 206c 696e 6520 7365 676d  raight line segm\n-0000edc0: 656e 7473 2074 6f20 666f 726d 2061 2070  ents to form a p\n-0000edd0: 6f6c 796c 696e 652e 2020 4966 2074 6865  olyline.  If the\n-0000ede0: 7265 2061 7265 0a6d 2070 6f69 6e74 7320  re are.m points \n-0000edf0: 696e 2074 6865 206f 7269 6769 6e61 6c20  in the original \n-0000ee00: 706f 696e 7420 6c69 7374 2c20 7468 656e  point list, then\n-0000ee10: 206d 2070 6f6c 796c 696e 6573 2077 6974   m polylines wit\n-0000ee20: 6820 4e20 7365 676d 656e 7473 0a65 6163  h N segments.eac\n-0000ee30: 6820 6172 6520 666f 726d 6564 2062 7920  h are formed by \n-0000ee40: 7468 6520 7377 6565 702e 2020 496e 2074  the sweep.  In t\n-0000ee50: 6869 7320 6d61 6e6e 6572 2c20 2773 7765  his manner, 'swe\n-0000ee60: 6570 2720 666f 726d 7320 6120 7365 7420  ep' forms a set \n-0000ee70: 6f66 0a6f 6e65 2d64 696d 656e 7369 6f6e  of.one-dimension\n-0000ee80: 616c 206f 626a 6563 7473 2028 706f 6c79  al objects (poly\n-0000ee90: 6c69 6e65 7329 2066 726f 6d20 7a65 726f  lines) from zero\n-0000eea0: 2d64 696d 656e 7369 6f6e 616c 206f 6e65  -dimensional one\n-0000eeb0: 7320 2870 6f69 6e74 7329 2e0a 0a20 2020  s (points)...   \n-0000eec0: 5768 656e 2074 6865 7265 205f 6973 5f20  When there _is_ \n-0000eed0: 6120 636c 6f73 7572 6520 7461 672c 2027  a closure tag, '\n-0000eee0: 7377 6565 7027 2063 6f6e 6e65 6374 7320  sweep' connects \n-0000eef0: 4e20 7375 6363 6573 7369 7665 2063 6f70  N successive cop\n-0000ef00: 6965 730a 6f66 2065 6163 6820 706f 696e  ies.of each poin\n-0000ef10: 7420 2869 6e63 6c75 6469 6e67 2074 6865  t (including the\n-0000ef20: 206f 7269 6769 6e61 6c29 2077 6974 6820   original) with \n-0000ef30: 7374 7261 6967 6874 206c 696e 6520 7365  straight line se\n-0000ef40: 676d 656e 7473 2061 6e64 0a66 696e 616c  gments and.final\n-0000ef50: 6c79 2063 6f6e 6e65 6374 7320 7468 6520  ly connects the \n-0000ef60: 6c61 7374 2063 6f70 7920 6261 636b 2074  last copy back t\n-0000ef70: 6f20 7468 6520 6f72 6967 696e 616c 2074  o the original t\n-0000ef80: 6f20 666f 726d 2061 2070 6f6c 7967 6f6e  o form a polygon\n-0000ef90: 0a77 6974 6820 4e20 7369 6465 732e 2020  .with N sides.  \n-0000efa0: 4966 2074 6865 7265 2061 7265 206d 2070  If there are m p\n-0000efb0: 6f69 6e74 7320 696e 2074 6865 206f 7269  oints in the ori\n-0000efc0: 6769 6e61 6c20 706f 696e 7420 6c69 7374  ginal point list\n-0000efd0: 2c20 7468 656e 206d 0a70 6f6c 7967 6f6e  , then m.polygon\n-0000efe0: 7320 7769 7468 204e 2073 6964 6573 2065  s with N sides e\n-0000eff0: 6163 6820 6172 6520 666f 726d 6564 2062  ach are formed b\n-0000f000: 7920 7468 6520 7377 6565 702e 2020 496e  y the sweep.  In\n-0000f010: 2074 6869 7320 6d61 6e6e 6572 2c0a 2773   this manner,.'s\n-0000f020: 7765 6570 2720 666f 726d 7320 6120 7365  weep' forms a se\n-0000f030: 7420 6f66 2074 776f 2d64 696d 656e 7369  t of two-dimensi\n-0000f040: 6f6e 616c 206f 626a 6563 7473 2028 706f  onal objects (po\n-0000f050: 6c79 676f 6e73 2920 6672 6f6d 0a7a 6572  lygons) from.zer\n-0000f060: 6f2d 6469 6d65 6e73 696f 6e61 6c20 6f6e  o-dimensional on\n-0000f070: 6573 2028 706f 696e 7473 292e 0a0a 2020  es (points)...  \n-0000f080: 204f 7074 696f 6e73 206f 6620 7468 6520   Options of the \n-0000f090: 2773 7765 6570 2720 6172 6520 636f 7069  'sweep' are copi\n-0000f0a0: 6564 2064 6972 6563 746c 7920 746f 2074  ed directly to t\n-0000f0b0: 6865 2072 6573 756c 7469 6e67 0a70 6f6c  he resulting.pol\n-0000f0c0: 796c 696e 6528 7329 2e0a 0a1f 0a46 696c  yline(s).....Fil\n-0000f0d0: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n-0000f0e0: 204e 6f64 653a 2053 7765 7074 206c 696e   Node: Swept lin\n-0000f0f0: 6573 2c20 204e 6578 743a 2053 7765 7074  es,  Next: Swept\n-0000f100: 2070 6f6c 7967 6f6e 732c 2020 5072 6576   polygons,  Prev\n-0000f110: 3a20 5377 6570 7420 706f 696e 7473 2c20  : Swept points, \n-0000f120: 2055 703a 2053 7765 6570 730a 0a33 2e32   Up: Sweeps..3.2\n-0000f130: 2e36 2e32 2053 7765 7074 206c 696e 6573  .6.2 Swept lines\n-0000f140: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000f150: 2e2e 2e2e 0a0a 4966 2053 5745 5054 5f4f  ......If SWEPT_O\n-0000f160: 424a 4543 5420 6973 2061 2070 6f6c 796c  BJECT is a polyl\n-0000f170: 696e 6520 616e 6420 7468 6572 6520 6973  ine and there is\n-0000f180: 206e 6f20 636c 6f73 7572 6520 7461 672c   no closure tag,\n-0000f190: 2074 6865 6e20 2773 7765 6570 270a 636f   then 'sweep'.co\n-0000f1a0: 6e6e 6563 7473 204e 2b31 2073 7563 6365  nnects N+1 succe\n-0000f1b0: 7373 6976 6520 636f 7069 6573 206f 6620  ssive copies of \n-0000f1c0: 7468 6520 706f 6c79 6c69 6e65 2028 696e  the polyline (in\n-0000f1d0: 636c 7564 696e 6720 7468 6520 6f72 6967  cluding the orig\n-0000f1e0: 696e 616c 290a 7769 7468 2066 6f75 722d  inal).with four-\n-0000f1f0: 7369 6465 6420 706f 6c79 676f 6e73 2c20  sided polygons, \n-0000f200: 6561 6368 2070 6169 7220 6f66 2063 6f70  each pair of cop\n-0000f210: 6965 7320 6769 7669 6e67 2072 6973 6520  ies giving rise \n-0000f220: 746f 2061 2022 706f 6c79 676f 6e0a 7374  to a \"polygon.st\n-0000f230: 7269 702e 2220 2049 6620 7468 6572 6520  rip.\"  If there \n-0000f240: 6172 6520 6d20 706f 696e 7473 2069 6e20  are m points in \n-0000f250: 7468 6520 6f72 6967 696e 616c 2070 6f6c  the original pol\n-0000f260: 796c 696e 652c 2074 6865 6e20 286d 2d31  yline, then (m-1\n-0000f270: 294e 0a70 6f6c 7967 6f6e 7320 6172 6520  )N.polygons are \n-0000f280: 666f 726d 6564 2062 7920 7468 6520 7377  formed by the sw\n-0000f290: 6565 702e 2020 5765 2063 616c 6c20 7468  eep.  We call th\n-0000f2a0: 6573 6520 2262 6f64 7920 706f 6c79 676f  ese \"body polygo\n-0000f2b0: 6e73 222e 2020 496e 0a74 6869 7320 6d61  ns\".  In.this ma\n-0000f2c0: 6e6e 6572 2c20 2773 7765 6570 2720 666f  nner, 'sweep' fo\n-0000f2d0: 726d 7320 6120 7477 6f2d 6469 6d65 6e73  rms a two-dimens\n-0000f2e0: 696f 6e61 6c20 7375 7266 6163 6520 6672  ional surface fr\n-0000f2f0: 6f6d 2066 726f 6d20 610a 6f6e 652d 6469  om from a.one-di\n-0000f300: 6d65 6e73 696f 6e61 6c20 706f 6c79 6c69  mensional polyli\n-0000f310: 6e65 2e0a 0a20 2020 5468 6520 6f72 6465  ne...   The orde\n-0000f320: 7220 6f66 2076 6572 7469 6365 7320 7072  r of vertices pr\n-0000f330: 6f64 7563 6564 2062 7920 2773 7765 6570  oduced by 'sweep\n-0000f340: 2720 6973 2069 6d70 6f72 7461 6e74 2e20  ' is important. \n-0000f350: 2049 6620 610a 706f 6c79 676f 6e27 7320   If a.polygon's \n-0000f360: 7665 7274 6963 6573 2064 6f20 6e6f 7420  vertices do not \n-0000f370: 6170 7065 6172 2069 6e20 636f 756e 7465  appear in counte\n-0000f380: 722d 636c 6f63 6b77 6973 6520 6f72 6465  r-clockwise orde\n-0000f390: 7220 696e 2074 6865 2066 696e 616c 0a69  r in the final.i\n-0000f3a0: 6d61 6765 2c20 7468 6520 706f 6c79 676f  mage, the polygo\n-0000f3b0: 6e20 7769 6c6c 2062 6520 6375 6c6c 6564  n will be culled\n-0000f3c0: 2028 756e 6c65 7373 2027 6375 6c6c 3d66   (unless 'cull=f\n-0000f3d0: 616c 7365 2720 6973 2073 6574 292e 2020  alse' is set).  \n-0000f3e0: 4966 2074 6865 0a70 6f69 6e74 7320 696e  If the.points in\n-0000f3f0: 2074 6865 206b 2774 6820 636f 7079 206f   the k'th copy o\n-0000f400: 6620 7468 6520 706f 6c79 6c69 6e65 2061  f the polyline a\n-0000f410: 7265 2050 5f31 2c20 505f 322c 202e 2e2e  re P_1, P_2, ...\n-0000f420: 2c20 505f 6d2c 2061 6e64 2074 6865 0a70  , P_m, and the.p\n-0000f430: 6f69 6e74 7320 696e 2074 6865 206e 6578  oints in the nex\n-0000f440: 7420 636f 7079 2c20 7468 6520 286b 2b31  t copy, the (k+1\n-0000f450: 2973 742c 2061 7265 2050 5f31 272c 2050  )st, are P_1', P\n-0000f460: 5f32 272c 202e 2e2e 2c20 505f 6d27 2c20  _2', ..., P_m', \n-0000f470: 7468 656e 0a74 6865 2076 6572 7465 7820  then.the vertex \n-0000f480: 6f72 6465 7220 6f66 2074 6865 2067 656e  order of the gen\n-0000f490: 6572 6174 6564 2070 6f6c 7967 6f6e 7320  erated polygons \n-0000f4a0: 6973 0a20 2020 2020 426f 6479 2070 6f6c  is.     Body pol\n-0000f4b0: 7967 6f6e 2031 3a20 505f 3220 505f 3120  ygon 1: P_2 P_1 \n-0000f4c0: 505f 3127 2050 5f32 270a 2020 2020 2042  P_1' P_2'.     B\n-0000f4d0: 6f64 7920 706f 6c79 676f 6e20 323a 2050  ody polygon 2: P\n-0000f4e0: 5f33 2050 5f32 2050 5f32 2720 505f 3327  _3 P_2 P_2' P_3'\n-0000f4f0: 0a20 2020 2020 2e2e 2e0a 2020 2020 2042  .     ....     B\n-0000f500: 6f64 7920 706f 6c79 676f 6e20 6d2d 313a  ody polygon m-1:\n-0000f510: 2050 5f6d 2050 5f7b 6d2d 317d 2050 5f7b   P_m P_{m-1} P_{\n-0000f520: 6d2d 317d 2720 505f 6d27 0a0a 2020 204f  m-1}' P_m'..   O\n-0000f530: 7074 696f 6e73 206f 6620 756e 636c 6f73  ptions of unclos\n-0000f540: 6564 206c 696e 6520 7377 6565 7073 2061  ed line sweeps a\n-0000f550: 7265 2063 6f70 6965 6420 746f 2065 6163  re copied to eac\n-0000f560: 6820 6f75 7470 7574 2070 6f6c 7967 6f6e  h output polygon\n-0000f570: 2e0a 4f70 7469 6f6e 7320 6f66 2074 6865  ..Options of the\n-0000f580: 2073 7765 7074 206c 696e 6520 6172 6520   swept line are \n-0000f590: 6967 6e6f 7265 642e 0a0a 2020 2057 6865  ignored...   Whe\n-0000f5a0: 6e20 7468 6572 6520 5f69 735f 2061 2063  n there _is_ a c\n-0000f5b0: 6c6f 7375 7265 2074 6167 2c20 7468 656e  losure tag, then\n-0000f5c0: 2027 7377 6565 7027 2063 6f6e 6e65 6374   'sweep' connect\n-0000f5d0: 7320 4e20 7375 6363 6573 7369 7665 0a63  s N successive.c\n-0000f5e0: 6f70 6965 7320 6f66 2074 6865 2070 6f6c  opies of the pol\n-0000f5f0: 796c 696e 6520 2869 6e63 6c75 6469 6e67  yline (including\n-0000f600: 2074 6865 206f 7269 6769 6e61 6c29 2077   the original) w\n-0000f610: 6974 6820 666f 7572 2d73 6964 6564 2062  ith four-sided b\n-0000f620: 6f64 790a 706f 6c79 676f 6e73 206a 7573  ody.polygons jus\n-0000f630: 7420 6173 2074 6865 2063 6173 6520 7769  t as the case wi\n-0000f640: 7468 206e 6f20 636c 6f73 7572 6520 7461  th no closure ta\n-0000f650: 672e 2020 4974 2074 6865 6e20 636f 6e6e  g.  It then conn\n-0000f660: 6563 7473 2074 6865 0a6c 6173 7420 636f  ects the.last co\n-0000f670: 7079 2062 6163 6b20 746f 2074 6865 206f  py back to the o\n-0000f680: 7269 6769 6e61 6c20 746f 2066 6f72 6d20  riginal to form \n-0000f690: 6120 7269 6262 6f6e 2d73 6861 7065 6420  a ribbon-shaped \n-0000f6a0: 7375 7266 6163 6520 7468 6174 0a63 6c6f  surface that.clo\n-0000f6b0: 7365 7320 6f6e 2069 7473 656c 6620 7769  ses on itself wi\n-0000f6c0: 7468 2074 776f 2068 6f6c 6573 2072 656d  th two holes rem\n-0000f6d0: 6169 6e69 6e67 2e0a 0a20 2020 4669 6e61  aining...   Fina\n-0000f6e0: 6c6c 792c 2074 6865 2073 7765 6570 2061  lly, the sweep a\n-0000f6f0: 6464 7320 7477 6f20 6d6f 7265 2070 6f6c  dds two more pol\n-0000f700: 7967 6f6e 7320 746f 2073 6561 6c20 7468  ygons to seal th\n-0000f710: 6520 686f 6c65 7320 616e 6420 666f 726d  e holes and form\n-0000f720: 0a61 2063 6c6f 7365 6420 7375 7266 6163  .a closed surfac\n-0000f730: 6520 7468 6174 2c20 6465 7065 6e64 696e  e that, dependin\n-0000f740: 6720 6f6e 2074 6865 2073 7765 6570 2074  g on the sweep t\n-0000f750: 7261 6e73 666f 726d 732c 206d 6179 2072  ransforms, may r\n-0000f760: 6570 7265 7365 6e74 0a74 6865 2062 6f75  epresent.the bou\n-0000f770: 6e64 6172 7920 6f66 2061 2073 6f6c 6964  ndary of a solid\n-0000f780: 2e20 2049 6e20 7468 6973 206d 616e 6e65  .  In this manne\n-0000f790: 722c 2027 7377 6565 7027 2066 6f72 6d73  r, 'sweep' forms\n-0000f7a0: 2074 6865 2062 6f75 6e64 6172 7920 6f66   the boundary of\n-0000f7b0: 0a61 2074 6872 6565 2d64 696d 656e 7369  .a three-dimensi\n-0000f7c0: 6f6e 616c 206f 626a 6563 7420 6672 6f6d  onal object from\n-0000f7d0: 2061 206f 6e65 2d64 696d 656e 7369 6f6e   a one-dimension\n-0000f7e0: 616c 2070 6f6c 796c 696e 652e 2020 5765  al polyline.  We\n-0000f7f0: 2063 616c 6c0a 7468 6573 6520 686f 6c65   call.these hole\n-0000f800: 2d66 696c 6c69 6e67 2070 6f6c 7967 6f6e  -filling polygon\n-0000f810: 7320 2265 6e64 7322 2e0a 0a20 2020 5468  s \"ends\"...   Th\n-0000f820: 6520 6f72 6465 7220 6f66 2076 6572 7469  e order of verti\n-0000f830: 6365 7320 6f66 2065 6e64 2070 6f6c 7967  ces of end polyg\n-0000f840: 6f6e 7320 6973 2069 6d70 6f72 7461 6e74  ons is important\n-0000f850: 2066 6f72 2063 6f72 7265 6374 0a63 756c   for correct.cul\n-0000f860: 6c69 6e67 2061 7320 6465 7363 7269 6265  ling as describe\n-0000f870: 6420 6162 6f76 652e 2020 4966 2050 5f31  d above.  If P_1\n-0000f880: 5e31 2c20 505f 315e 322c 202e 2e2e 2c20  ^1, P_1^2, ..., \n-0000f890: 505f 315e 6e20 6172 6520 7468 6520 4e0a  P_1^n are the N.\n-0000f8a0: 636f 7069 6573 206f 6620 7468 6520 6669  copies of the fi\n-0000f8b0: 7273 7420 706f 6c79 6c69 6e65 2070 6f69  rst polyline poi\n-0000f8c0: 6e74 2061 6e64 2050 5f6d 5e31 2c20 505f  nt and P_m^1, P_\n-0000f8d0: 6d5e 322c 202e 2e2e 202c 505f 6d5e 6e20  m^2, ... ,P_m^n \n-0000f8e0: 6172 6520 7468 650a 4e20 636f 7069 6573  are the.N copies\n-0000f8f0: 206f 6620 7468 6520 6c61 7374 2070 6f6c   of the last pol\n-0000f900: 796c 696e 6520 706f 696e 742c 2074 6865  yline point, the\n-0000f910: 6e20 7468 6520 656e 6420 706f 6c79 676f  n the end polygo\n-0000f920: 6e20 7665 7274 6578 206f 7264 6572 0a69  n vertex order.i\n-0000f930: 730a 2020 2020 2045 6e64 2070 6f6c 7967  s.     End polyg\n-0000f940: 6f6e 2031 3a20 505f 315e 6e2c 2050 5f31  on 1: P_1^n, P_1\n-0000f950: 5e7b 6e2d 317d 2c20 2e2e 2e20 2c50 5f31  ^{n-1}, ... ,P_1\n-0000f960: 5e31 0a20 2020 2020 456e 6420 706f 6c79  ^1.     End poly\n-0000f970: 676f 6e20 323a 2050 5f6d 5e31 2c20 505f  gon 2: P_m^1, P_\n-0000f980: 6d5e 322c 202e 2e2e 202c 505f 6d5e 6e0a  m^2, ... ,P_m^n.\n-0000f990: 0a20 2020 4966 2074 6865 7265 2061 7265  .   If there are\n-0000f9a0: 206e 6f20 6f70 7469 6f6e 7320 6f6e 2074   no options on t\n-0000f9b0: 6865 2073 7765 7074 206c 696e 652c 2074  he swept line, t\n-0000f9c0: 6865 6e20 7468 6520 2773 7765 6570 2720  hen the 'sweep' \n-0000f9d0: 6f70 7469 6f6e 730a 6172 6520 636f 7069  options.are copi\n-0000f9e0: 6564 2074 6f20 6561 6368 206f 7574 7075  ed to each outpu\n-0000f9f0: 7420 706f 6c79 676f 6e2e 2020 4966 2074  t polygon.  If t\n-0000fa00: 6865 2073 7765 7074 206c 696e 6520 646f  he swept line do\n-0000fa10: 6573 2068 6176 6520 6f70 7469 6f6e 732c  es have options,\n-0000fa20: 0a74 6865 7365 2061 7265 2063 6f70 6965  .these are copie\n-0000fa30: 6420 746f 2063 6f72 7265 7370 6f6e 6469  d to correspondi\n-0000fa40: 6e67 2062 6f64 7920 706f 6c79 676f 6e73  ng body polygons\n-0000fa50: 3b20 7468 6520 7377 6565 7020 6f70 7469  ; the sweep opti\n-0000fa60: 6f6e 7320 6172 650a 636f 7069 6564 2074  ons are.copied t\n-0000fa70: 6f20 7468 6520 656e 6420 706f 6c79 676f  o the end polygo\n-0000fa80: 6e73 2e20 2049 6e20 7468 6973 206d 616e  ns.  In this man\n-0000fa90: 6e65 722c 2062 6f64 7920 616e 6420 656e  ner, body and en\n-0000faa0: 6473 206d 6179 2062 6520 6472 6177 6e0a  ds may be drawn.\n-0000fab0: 7769 7468 2064 6966 6665 7265 6e74 2063  with different c\n-0000fac0: 6861 7261 6374 6572 6973 7469 6373 2073  haracteristics s\n-0000fad0: 7563 6820 6173 2027 6669 6c6c 636f 6c6f  uch as 'fillcolo\n-0000fae0: 7227 2e0a 0a1f 0a46 696c 653a 2073 6b65  r'.....File: ske\n-0000faf0: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n-0000fb00: 2053 7765 7074 2070 6f6c 7967 6f6e 732c   Swept polygons,\n-0000fb10: 2020 4e65 7874 3a20 5377 6570 7420 626c    Next: Swept bl\n-0000fb20: 6f63 6b73 2c20 2050 7265 763a 2053 7765  ocks,  Prev: Swe\n-0000fb30: 7074 206c 696e 6573 2c20 2055 703a 2053  pt lines,  Up: S\n-0000fb40: 7765 6570 730a 0a33 2e32 2e36 2e33 2053  weeps..3.2.6.3 S\n-0000fb50: 7765 7074 2070 6f6c 7967 6f6e 730a 2e2e  wept polygons...\n+0000d970: 2020 4772 6f75 7020 6f74 6865 7220 6472    Group other dr\n+0000d980: 6177 6162 6c65 732e 0a2a 2052 6570 6561  awables..* Repea\n+0000d990: 7473 3a3a 2020 2020 2020 2020 2020 2020  ts::            \n+0000d9a0: 2020 2020 2020 2020 2044 7261 7720 7472           Draw tr\n+0000d9b0: 616e 7366 6f72 6d65 6420 636f 7069 6573  ansformed copies\n+0000d9c0: 206f 6620 6f62 6a65 6374 732e 0a2a 2050   of objects..* P\n+0000d9d0: 7574 733a 3a20 2020 2020 2020 2020 2020  uts::           \n+0000d9e0: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n+0000d9f0: 7720 6f6e 6520 6f62 6a65 6374 2074 7261  w one object tra\n+0000da00: 6e73 666f 726d 6564 2e0a 0a1f 0a46 696c  nsformed.....Fil\n+0000da10: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n+0000da20: 204e 6f64 653a 2044 6f74 732c 2020 4e65   Node: Dots,  Ne\n+0000da30: 7874 3a20 4c69 6e65 732c 2020 5072 6576  xt: Lines,  Prev\n+0000da40: 3a20 4472 6177 6162 6c65 732c 2020 5570  : Drawables,  Up\n+0000da50: 3a20 4472 6177 6162 6c65 730a 0a33 2e32  : Drawables..3.2\n+0000da60: 2e31 2044 6f74 730a 2d2d 2d2d 2d2d 2d2d  .1 Dots.--------\n+0000da70: 2d2d 0a0a 2a53 796e 7461 783a 2a0a 2020  --..*Syntax:*.  \n+0000da80: 2020 2064 6f74 735b 4f50 5449 4f4e 535d     dots[OPTIONS]\n+0000da90: 2050 4f49 4e54 5f4c 4953 540a 5468 6973   POINT_LIST.This\n+0000daa0: 2063 6f6d 6d61 6e64 2069 7320 7468 6520   command is the \n+0000dab0: 7468 7265 652d 6469 6d65 6e73 696f 6e61  three-dimensiona\n+0000dac0: 6c20 6571 7569 7661 6c65 6e74 206f 6620  l equivalent of \n+0000dad0: 7468 6520 2750 5354 7269 636b 7327 0a63  the 'PSTricks'.c\n+0000dae0: 6f6d 6d61 6e64 2027 5c70 7364 6f74 7327  ommand '\\psdots'\n+0000daf0: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463  .....File: sketc\n+0000db00: 682e 696e 666f 2c20 204e 6f64 653a 204c  h.info,  Node: L\n+0000db10: 696e 6573 2c20 204e 6578 743a 2043 7572  ines,  Next: Cur\n+0000db20: 7665 732c 2020 5072 6576 3a20 446f 7473  ves,  Prev: Dots\n+0000db30: 2c20 2055 703a 2044 7261 7761 626c 6573  ,  Up: Drawables\n+0000db40: 0a0a 332e 322e 3220 4c69 6e65 730a 2d2d  ..3.2.2 Lines.--\n+0000db50: 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74  ---------..*Synt\n+0000db60: 6178 3a2a 0a20 2020 2020 6c69 6e65 5b4f  ax:*.     line[O\n+0000db70: 5054 494f 4e53 5d20 504f 494e 545f 4c49  PTIONS] POINT_LI\n+0000db80: 5354 0a54 6869 7320 636f 6d6d 616e 6420  ST.This command \n+0000db90: 6973 2074 6865 2074 6872 6565 2d64 696d  is the three-dim\n+0000dba0: 656e 7369 6f6e 616c 2065 7175 6976 616c  ensional equival\n+0000dbb0: 656e 7420 6f66 2074 6865 2027 5053 5472  ent of the 'PSTr\n+0000dbc0: 6963 6b73 270a 636f 6d6d 616e 6420 275c  icks'.command '\\\n+0000dbd0: 7073 6c69 6e65 272e 0a0a 1f0a 4669 6c65  psline'.....File\n+0000dbe0: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n+0000dbf0: 4e6f 6465 3a20 4375 7276 6573 2c20 204e  Node: Curves,  N\n+0000dc00: 6578 743a 2050 6f6c 7967 6f6e 732c 2020  ext: Polygons,  \n+0000dc10: 5072 6576 3a20 4c69 6e65 732c 2020 5570  Prev: Lines,  Up\n+0000dc20: 3a20 4472 6177 6162 6c65 730a 0a33 2e32  : Drawables..3.2\n+0000dc30: 2e33 2043 7572 7665 730a 2d2d 2d2d 2d2d  .3 Curves.------\n+0000dc40: 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 783a  ------..*Syntax:\n+0000dc50: 2a0a 2020 2020 2063 7572 7665 5b4f 5054  *.     curve[OPT\n+0000dc60: 494f 4e53 5d20 504f 494e 545f 4c49 5354  IONS] POINT_LIST\n+0000dc70: 0a54 6869 7320 636f 6d6d 616e 6420 6973  .This command is\n+0000dc80: 2074 6865 2074 6872 6565 2d64 696d 656e   the three-dimen\n+0000dc90: 7369 6f6e 616c 2065 7175 6976 616c 656e  sional equivalen\n+0000dca0: 7420 6f66 2074 6865 2027 5053 5472 6963  t of the 'PSTric\n+0000dcb0: 6b73 270a 636f 6d6d 616e 6420 275c 7073  ks'.command '\\ps\n+0000dcc0: 6375 7276 6527 2e20 2049 7420 6973 206e  curve'.  It is n\n+0000dcd0: 6f74 2069 6d70 6c65 6d65 6e74 6564 2069  ot implemented i\n+0000dce0: 6e20 7468 6520 6375 7272 656e 7420 7665  n the current ve\n+0000dcf0: 7273 696f 6e20 6f66 0a27 736b 6574 6368  rsion of.'sketch\n+0000dd00: 272e 0a0a 1f0a 4669 6c65 3a20 736b 6574  '.....File: sket\n+0000dd10: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n+0000dd20: 506f 6c79 676f 6e73 2c20 204e 6578 743a  Polygons,  Next:\n+0000dd30: 2053 7065 6369 616c 732c 2020 5072 6576   Specials,  Prev\n+0000dd40: 3a20 4375 7276 6573 2c20 2055 703a 2044  : Curves,  Up: D\n+0000dd50: 7261 7761 626c 6573 0a0a 332e 322e 3420  rawables..3.2.4 \n+0000dd60: 506f 6c79 676f 6e73 0a2d 2d2d 2d2d 2d2d  Polygons.-------\n+0000dd70: 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178  -------..*Syntax\n+0000dd80: 3a2a 0a20 2020 2020 706f 6c79 676f 6e5b  :*.     polygon[\n+0000dd90: 4f50 5449 4f4e 535d 2050 4f49 4e54 5f4c  OPTIONS] POINT_L\n+0000dda0: 4953 540a 5468 6973 2063 6f6d 6d61 6e64  IST.This command\n+0000ddb0: 2069 7320 7468 6520 7468 7265 652d 6469   is the three-di\n+0000ddc0: 6d65 6e73 696f 6e61 6c20 6571 7569 7661  mensional equiva\n+0000ddd0: 6c65 6e74 206f 6620 7468 6520 2750 5354  lent of the 'PST\n+0000dde0: 7269 636b 7327 0a63 6f6d 6d61 6e64 2027  ricks'.command '\n+0000ddf0: 5c70 7370 6f6c 7967 6f6e 272e 2020 5468  \\pspolygon'.  Th\n+0000de00: 6520 2773 6b65 7463 6827 2068 6964 6465  e 'sketch' hidde\n+0000de10: 6e20 7375 7266 6163 6520 616c 676f 7269  n surface algori\n+0000de20: 7468 6d20 6173 7375 6d65 730a 7468 6174  thm assumes.that\n+0000de30: 2070 6f6c 7967 6f6e 7320 6172 6520 636f   polygons are co\n+0000de40: 6e76 6578 2061 6e64 2070 6c61 6e61 722e  nvex and planar.\n+0000de50: 2020 496e 2070 7261 6374 6963 652c 2064    In practice, d\n+0000de60: 7261 7769 6e67 7320 6d61 7920 7765 6c6c  rawings may well\n+0000de70: 0a74 7572 6e20 6f75 7420 636f 7272 6563  .turn out correc\n+0000de80: 746c 7920 6576 656e 2069 6620 7468 6573  tly even if thes\n+0000de90: 6520 6173 7375 6d70 7469 6f6e 7320 6172  e assumptions ar\n+0000dea0: 6520 7669 6f6c 6174 6564 2e0a 0a1f 0a46  e violated.....F\n+0000deb0: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n+0000dec0: 2c20 204e 6f64 653a 2053 7065 6369 616c  ,  Node: Special\n+0000ded0: 732c 2020 4e65 7874 3a20 5377 6565 7073  s,  Next: Sweeps\n+0000dee0: 2c20 2050 7265 763a 2050 6f6c 7967 6f6e  ,  Prev: Polygon\n+0000def0: 732c 2020 5570 3a20 4472 6177 6162 6c65  s,  Up: Drawable\n+0000df00: 730a 0a33 2e32 2e35 2053 7065 6369 616c  s..3.2.5 Special\n+0000df10: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  s.--------------\n+0000df20: 0a0a 2a53 796e 7461 783a 2a0a 2020 2020  ..*Syntax:*.    \n+0000df30: 2073 7065 6369 616c 2024 5241 575f 5445   special $RAW_TE\n+0000df40: 5854 245b 4f50 5449 4f4e 535d 2041 5247  XT$[OPTIONS] ARG\n+0000df50: 5f4c 4953 540a 4865 7265 2027 2427 2063  _LIST.Here '$' c\n+0000df60: 616e 2062 6520 616e 7920 6368 6172 6163  an be any charac\n+0000df70: 7465 7220 616e 6420 6973 2075 7365 6420  ter and is used \n+0000df80: 746f 2064 656c 696d 6974 2074 6865 2073  to delimit the s\n+0000df90: 7461 7274 2061 6e64 2065 6e64 0a6f 6620  tart and end.of \n+0000dfa0: 5241 575f 5445 5854 2e20 2054 6865 2063  RAW_TEXT.  The c\n+0000dfb0: 6f6d 6d61 6e64 2065 6d62 6564 7320 5241  ommand embeds RA\n+0000dfc0: 575f 5445 5854 2069 6e20 7468 6520 2773  W_TEXT in the 's\n+0000dfd0: 6b65 7463 6827 206f 7574 7075 7420 6166  ketch' output af\n+0000dfe0: 7465 720a 7065 7266 6f72 6d69 6e67 2073  ter.performing s\n+0000dff0: 7562 7374 6974 7574 696f 6e73 2061 7320  ubstitutions as \n+0000e000: 666f 6c6c 6f77 732e 0a20 2020 2a20 2723  follows..   * '#\n+0000e010: 4927 2077 6865 7265 2049 2069 7320 6120  I' where I is a \n+0000e020: 706f 7369 7469 7665 2069 6e74 6567 6572  positive integer\n+0000e030: 2069 7320 7265 706c 6163 6564 2062 7920   is replaced by \n+0000e040: 7468 6520 4927 7468 2076 616c 7565 2069  the I'th value i\n+0000e050: 6e0a 2020 2020 2041 5247 5f4c 4953 542e  n.     ARG_LIST.\n+0000e060: 2020 506f 696e 7420 616e 6420 7665 6374    Point and vect\n+0000e070: 6f72 2061 7267 756d 656e 7473 2062 6563  or arguments bec\n+0000e080: 6f6d 6520 7477 6f2d 6469 6d65 6e73 696f  ome two-dimensio\n+0000e090: 6e61 6c0a 2020 2020 2070 6f69 6e74 732c  nal.     points,\n+0000e0a0: 2077 6869 6368 2061 7265 2074 6865 2074   which are the t\n+0000e0b0: 7261 6e73 666f 726d 6564 2033 6420 6172  ransformed 3d ar\n+0000e0c0: 6775 6d65 6e74 7320 7072 6f6a 6563 7465  guments projecte\n+0000e0d0: 6420 6f6e 746f 2074 6865 0a20 2020 2020  d onto the.     \n+0000e0e0: 582d 5920 706c 616e 652e 2020 5468 6973  X-Y plane.  This\n+0000e0f0: 2061 6c6c 6f77 7320 7477 6f2d 6469 6d65   allows two-dime\n+0000e100: 6e74 696f 6e61 6c20 6f75 7470 7574 2065  ntional output e\n+0000e110: 6c65 6d65 6e74 7320 7375 6368 2061 730a  lements such as.\n+0000e120: 2020 2020 206c 6162 656c 7320 746f 2062       labels to b\n+0000e130: 6520 6561 7369 6c79 2070 6f73 6974 696f  e easily positio\n+0000e140: 6e65 6420 7769 7468 2072 6573 7065 6374  ned with respect\n+0000e150: 2074 6f20 7468 7265 652d 6469 6d65 6e73   to three-dimens\n+0000e160: 696f 6e61 6c0a 2020 2020 2066 6561 7475  ional.     featu\n+0000e170: 7265 7320 696e 2074 6865 2064 7261 7769  res in the drawi\n+0000e180: 6e67 2e20 2053 6361 6c61 7220 6172 6775  ng.  Scalar argu\n+0000e190: 6d65 6e74 7320 6172 6520 7375 6273 6974  ments are subsit\n+0000e1a0: 7574 6564 2064 6972 6563 746c 792e 0a20  uted directly.. \n+0000e1b0: 2020 2020 4e6f 2074 7261 6e73 666f 726d      No transform\n+0000e1c0: 6174 696f 6e20 6973 2061 7070 6c69 6564  ation is applied\n+0000e1d0: 2e0a 2020 202a 2027 237b 497d 2720 6973  ..   * '#{I}' is\n+0000e1e0: 2061 6c73 6f20 7265 706c 6163 6564 2061   also replaced a\n+0000e1f0: 7320 6162 6f76 652e 0a20 2020 2a20 2723  s above..   * '#\n+0000e200: 4927 3227 2069 7320 7265 706c 6163 6564  I'2' is replaced\n+0000e210: 2061 7320 6162 6f76 6520 666f 7220 706f   as above for po\n+0000e220: 696e 7473 206f 7220 7665 6374 6f72 732e  ints or vectors.\n+0000e230: 2020 4974 2069 7320 616e 2065 7272 6f72    It is an error\n+0000e240: 0a20 2020 2020 666f 7220 7468 6520 4927  .     for the I'\n+0000e250: 7468 2061 7267 756d 656e 7420 746f 2062  th argument to b\n+0000e260: 6520 6120 7363 616c 6172 2e0a 2020 202a  e a scalar..   *\n+0000e270: 2027 2349 2778 272c 2027 2349 2779 272c   '#I'x', '#I'y',\n+0000e280: 206f 7220 2723 4927 7a27 2069 7320 7265   or '#I'z' is re\n+0000e290: 706c 6163 6564 2c20 7265 7370 6563 7469  placed, respecti\n+0000e2a0: 7665 6c79 2c20 6279 2074 6865 2073 6361  vely, by the sca\n+0000e2b0: 6c61 720a 2020 2020 2058 2c20 592c 206f  lar.     X, Y, o\n+0000e2c0: 7220 5a2d 636f 6f72 6469 6e61 7465 206f  r Z-coordinate o\n+0000e2d0: 6620 7468 6520 6172 6775 6d65 6e74 2070  f the argument p\n+0000e2e0: 6f69 6e74 206f 7220 7665 6374 6f72 2e20  oint or vector. \n+0000e2f0: 2049 7420 6973 2061 6e0a 2020 2020 2065   It is an.     e\n+0000e300: 7272 6f72 2066 6f72 2074 6865 2049 2774  rror for the I't\n+0000e310: 6820 6172 6775 6d65 6e74 2074 6f20 6265  h argument to be\n+0000e320: 2061 2073 6361 6c61 722e 0a20 2020 2a20   a scalar..   * \n+0000e330: 2723 4927 3327 2069 7320 7265 706c 6163  '#I'3' is replac\n+0000e340: 6564 2062 7920 7468 6520 7468 7265 652d  ed by the three-\n+0000e350: 6469 6d65 6e73 696f 6e61 6c20 7472 616e  dimensional tran\n+0000e360: 7366 6f72 6d65 6420 6172 6775 6d65 6e74  sformed argument\n+0000e370: 2e0a 2020 2020 204e 6f74 6520 7468 6174  ..     Note that\n+0000e380: 2069 6620 6120 7065 7273 7065 6374 6976   if a perspectiv\n+0000e390: 6520 7472 616e 7366 6f72 6d61 7469 6f6e  e transformation\n+0000e3a0: 2068 6173 2062 6565 6e20 6170 706c 6965   has been applie\n+0000e3b0: 642c 2074 6865 0a20 2020 2020 5a2d 636f  d, the.     Z-co\n+0000e3c0: 6f72 6469 6e61 7465 2068 6173 206c 6974  ordinate has lit\n+0000e3d0: 746c 6520 6765 6f6d 6574 7269 6320 7369  tle geometric si\n+0000e3e0: 676e 6966 6963 616e 6365 2c20 7468 6f75  gnificance, thou\n+0000e3f0: 6768 2069 740a 2020 2020 2061 6363 7572  gh it.     accur\n+0000e400: 6174 656c 7920 696e 6469 6361 7465 7320  ately indicates \n+0000e410: 7265 6c61 7469 7665 2064 6570 7468 2e0a  relative depth..\n+0000e420: 2020 202a 2027 2349 2d4a 2720 7768 6572     * '#I-J' wher\n+0000e430: 6520 4920 616e 6420 4a20 6172 6520 706f  e I and J are po\n+0000e440: 7369 7469 7665 2069 6e74 6567 6572 7320  sitive integers \n+0000e450: 6973 2072 6570 6c61 6365 6420 6279 2061  is replaced by a\n+0000e460: 2073 7472 696e 670a 2020 2020 2027 7b41   string.     '{A\n+0000e470: 4e47 4c45 7d27 2077 6865 7265 2041 4e47  NGLE}' where ANG\n+0000e480: 4c45 2069 7320 7468 6520 706f 6c61 7220  LE is the polar \n+0000e490: 616e 676c 6520 6f66 2061 2076 6563 746f  angle of a vecto\n+0000e4a0: 7220 6672 6f6d 2074 6865 2049 2774 680a  r from the I'th.\n+0000e4b0: 2020 2020 2070 6f69 6e74 2069 6e20 504f       point in PO\n+0000e4c0: 494e 545f 4c49 5354 2074 6f20 7468 6520  INT_LIST to the \n+0000e4d0: 4a27 7468 2070 6f69 6e74 2070 726f 6a65  J'th point proje\n+0000e4e0: 6374 6564 2069 6e74 6f20 7468 6520 782d  cted into the x-\n+0000e4f0: 7920 706c 616e 652e 0a20 2020 2020 4974  y plane..     It\n+0000e500: 2069 7320 616e 2065 7272 6f72 2066 6f72   is an error for\n+0000e510: 2074 6865 2049 2774 6820 6f72 204a 2774   the I'th or J't\n+0000e520: 6820 6172 6775 6d65 6e74 2074 6f20 6265  h argument to be\n+0000e530: 2061 2073 6361 6c61 7220 6f72 2061 0a20   a scalar or a. \n+0000e540: 2020 2020 7665 6374 6f72 2e0a 2020 202a      vector..   *\n+0000e550: 2027 237b 492d 4a7d 2720 6973 2061 6c73   '#{I-J}' is als\n+0000e560: 6f20 7265 706c 6163 6564 2061 7320 6162  o replaced as ab\n+0000e570: 6f76 652e 0a20 2020 2a20 2723 2327 2069  ove..   * '##' i\n+0000e580: 7320 7265 706c 6163 6564 2077 6974 6820  s replaced with \n+0000e590: 2723 272e 0a54 6865 2066 6f72 6d73 2077  '#'..The forms w\n+0000e5a0: 6974 6820 6272 6163 6573 2027 7b20 7d27  ith braces '{ }'\n+0000e5b0: 2061 7265 2075 7365 6675 6c20 7768 656e   are useful when\n+0000e5c0: 2074 6865 2061 7267 756d 656e 7420 6973   the argument is\n+0000e5d0: 2069 6d6d 6564 6961 7465 6c79 0a66 6f6c   immediately.fol\n+0000e5e0: 6c6f 7765 6420 6279 2061 2064 6967 6974  lowed by a digit\n+0000e5f0: 206f 7220 6120 7469 636b 2063 6861 7261   or a tick chara\n+0000e600: 6374 6572 2074 6861 7420 6973 2070 6172  cter that is par\n+0000e610: 7420 6f66 2074 6865 2054 6558 2063 6f64  t of the TeX cod\n+0000e620: 652e 0a0a 2020 2054 6865 206f 6e6c 7920  e...   The only \n+0000e630: 7573 6566 756c 206f 7074 696f 6e20 6f66  useful option of\n+0000e640: 2027 7370 6563 6961 6c27 2069 7320 276c   'special' is 'l\n+0000e650: 6179 272c 2077 6869 6368 2064 6574 6572  ay', which deter\n+0000e660: 6d69 6e65 7320 6966 2074 6865 0a73 7562  mines if the.sub\n+0000e670: 7374 6974 7565 6420 7261 7720 7465 7874  stitued raw text\n+0000e680: 2069 7320 656d 6974 7465 6420 6265 666f   is emitted befo\n+0000e690: 7265 2c20 6166 7465 722c 206f 7220 7573  re, after, or us\n+0000e6a0: 696e 6720 7468 6520 6669 7273 7420 706f  ing the first po\n+0000e6b0: 696e 740a 696e 2050 4f49 4e54 5f4c 4953  int.in POINT_LIS\n+0000e6c0: 5420 6173 2061 6e20 696e 6469 6361 746f  T as an indicato\n+0000e6d0: 7220 6f66 2064 6570 7468 2e20 2054 6865  r of depth.  The\n+0000e6e0: 7365 206f 6363 7572 2c20 7265 7370 6563  se occur, respec\n+0000e6f0: 7469 7665 6c79 2c20 7769 7468 0a27 6c61  tively, with.'la\n+0000e700: 793d 756e 6465 7227 2c20 276c 6179 3d6f  y=under', 'lay=o\n+0000e710: 7665 7227 2c20 616e 6420 276c 6179 3d69  ver', and 'lay=i\n+0000e720: 6e27 2e20 2053 6565 202a 6e6f 7465 2053  n'.  See *note S\n+0000e730: 7065 6369 616c 206f 626a 6563 7473 3a3a  pecial objects::\n+0000e740: 2061 6e64 0a2a 6e6f 7465 2054 696b 5a2f   and.*note TikZ/\n+0000e750: 5047 4620 7573 6572 2d64 6566 696e 6564  PGF user-defined\n+0000e760: 2073 7479 6c65 733a 3a20 666f 7220 6578   styles:: for ex\n+0000e770: 616d 706c 6573 2e20 202a 4e6f 7465 2049  amples.  *Note I\n+0000e780: 6e74 6572 6e61 6c0a 6f70 7469 6f6e 733a  nternal.options:\n+0000e790: 3a2e 0a0a 1f0a 4669 6c65 3a20 736b 6574  :.....File: sket\n+0000e7a0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n+0000e7b0: 5377 6565 7073 2c20 204e 6578 743a 2042  Sweeps,  Next: B\n+0000e7c0: 6c6f 636b 732c 2020 5072 6576 3a20 5370  locks,  Prev: Sp\n+0000e7d0: 6563 6961 6c73 2c20 2055 703a 2044 7261  ecials,  Up: Dra\n+0000e7e0: 7761 626c 6573 0a0a 332e 322e 3620 5377  wables..3.2.6 Sw\n+0000e7f0: 6565 7073 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d  eeps.-----------\n+0000e800: 2d0a 0a2a 5379 6e74 6178 3a2a 0a20 2020  -..*Syntax:*.   \n+0000e810: 2020 7377 6565 7020 7b20 4e2c 2054 5f31    sweep { N, T_1\n+0000e820: 2c20 545f 322c 202e 2e2e 2c20 545f 5220  , T_2, ..., T_R \n+0000e830: 7d5b 4f50 5449 4f4e 535d 2053 5745 5054  }[OPTIONS] SWEPT\n+0000e840: 5f4f 424a 4543 540a 2020 2020 2073 7765  _OBJECT.     swe\n+0000e850: 6570 207b 204e 3c3e 2c20 545f 312c 2054  ep { N<>, T_1, T\n+0000e860: 5f32 2c20 2e2e 2e2c 2054 5f52 207d 5b4f  _2, ..., T_R }[O\n+0000e870: 5054 494f 4e53 5d20 5357 4550 545f 4f42  PTIONS] SWEPT_OB\n+0000e880: 4a45 4354 0a54 6865 2073 7765 6570 2063  JECT.The sweep c\n+0000e890: 6f6e 6e65 6374 7320 4e20 286f 7220 7065  onnects N (or pe\n+0000e8a0: 7268 6170 7320 4e2b 3129 2063 6f70 6965  rhaps N+1) copie\n+0000e8b0: 7320 6f66 2053 5745 5054 5f4f 424a 4543  s of SWEPT_OBJEC\n+0000e8c0: 5420 696e 206f 7264 6572 2074 6f0a 6372  T in order to.cr\n+0000e8d0: 6561 7465 2061 206e 6577 206f 626a 6563  eate a new objec\n+0000e8e0: 7420 6f66 2068 6967 6865 7220 6469 6d65  t of higher dime\n+0000e8f0: 6e73 696f 6e2e 2020 5468 6520 545f 4920  nsion.  The T_I \n+0000e900: 2866 6f72 2069 2062 6574 7765 656e 2031  (for i between 1\n+0000e910: 2061 6e64 0a72 2920 6172 6520 7472 616e   and.r) are tran\n+0000e920: 7366 6f72 6d73 2e20 2054 6865 206b 2774  sforms.  The k't\n+0000e930: 6820 636f 7079 206f 6620 5357 4550 545f  h copy of SWEPT_\n+0000e940: 4f42 4a45 4354 2069 7320 7072 6f64 7563  OBJECT is produc\n+0000e950: 6564 2062 790a 6170 706c 7969 6e67 2074  ed by.applying t\n+0000e960: 6865 2066 6f6c 6c6f 7769 6e67 2074 7261  he following tra\n+0000e970: 6e73 666f 726d 2074 6f20 7468 6520 6f72  nsform to the or\n+0000e980: 6967 696e 616c 2e0a 2020 2020 2054 5f31  iginal..     T_1\n+0000e990: 5e6b 2074 6865 6e20 545f 325e 6b20 7468  ^k then T_2^k th\n+0000e9a0: 656e 202e 2e2e 2074 6865 6e20 545f 525e  en ... then T_R^\n+0000e9b0: 6b0a 4865 7265 2054 5e6b 206d 6561 6e73  k.Here T^k means\n+0000e9c0: 2022 7472 616e 7366 6f72 6d20 5420 6170   \"transform T ap\n+0000e9d0: 706c 6965 6420 6b20 7469 6d65 732e 2220  plied k times.\" \n+0000e9e0: 2054 6865 206f 7269 6769 6e61 6c20 6f62   The original ob\n+0000e9f0: 6a65 6374 2069 730a 7468 6520 7a65 726f  ject is.the zero\n+0000ea00: 2774 6820 636f 7079 2c20 7769 7468 206b  'th copy, with k\n+0000ea10: 3d30 2061 6e64 2065 6666 6563 7469 7665  =0 and effective\n+0000ea20: 6c79 206e 6f20 7472 616e 7366 6f72 6d20  ly no transform \n+0000ea30: 6170 706c 6965 6420 2854 5e30 3d49 2c0a  applied (T^0=I,.\n+0000ea40: 7468 6520 6964 656e 7469 7479 2074 7261  the identity tra\n+0000ea50: 6e73 666f 726d 292e 0a0a 2020 2054 6865  nsform)...   The\n+0000ea60: 206d 6574 686f 6420 6f66 2063 6f6e 6e65   method of conne\n+0000ea70: 6374 696e 6720 7468 6520 636f 7069 6573  cting the copies\n+0000ea80: 2064 6570 656e 6473 206f 6e20 7468 6520   depends on the \n+0000ea90: 7479 7065 206f 660a 5357 4550 545f 4f42  type of.SWEPT_OB\n+0000eaa0: 4a45 4354 2061 6e64 206f 6e20 7768 6574  JECT and on whet\n+0000eab0: 6865 7220 7468 6520 636c 6f73 7572 6520  her the closure \n+0000eac0: 7461 6720 273c 3e27 2069 7320 7072 6573  tag '<>' is pres\n+0000ead0: 656e 7420 6f72 206e 6f74 2e0a 0a20 2020  ent or not...   \n+0000eae0: 416e 2065 7861 6d70 6c65 206f 6620 6120  An example of a \n+0000eaf0: 7377 6565 7020 7768 6572 6520 723d 3220  sweep where r=2 \n+0000eb00: 6973 2074 6865 204d 6f62 6975 7320 6669  is the Mobius fi\n+0000eb10: 6775 7265 2061 7420 2a6e 6f74 6520 4d6f  gure at *note Mo\n+0000eb20: 7265 2074 6f0a 6c65 6172 6e3a 3a2e 0a0a  re to.learn::...\n+0000eb30: 2a20 4d65 6e75 3a0a 0a2a 2053 7765 7074  * Menu:..* Swept\n+0000eb40: 2070 6f69 6e74 733a 3a20 2020 2020 2020   points::       \n+0000eb50: 2020 2020 2020 2020 2053 7765 7074 2070           Swept p\n+0000eb60: 6f69 6e74 7320 6d61 6b65 206c 696e 6573  oints make lines\n+0000eb70: 206f 7220 706f 6c79 676f 6e73 2e0a 2a20   or polygons..* \n+0000eb80: 5377 6570 7420 6c69 6e65 733a 3a20 2020  Swept lines::   \n+0000eb90: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n+0000eba0: 6570 7420 6c69 6e65 7320 6d61 6b65 206f  ept lines make o\n+0000ebb0: 7065 6e20 6f72 2063 6c6f 7365 6420 7375  pen or closed su\n+0000ebc0: 7266 6163 6573 2e0a 2a20 5377 6570 7420  rfaces..* Swept \n+0000ebd0: 706f 6c79 676f 6e73 3a3a 2020 2020 2020  polygons::      \n+0000ebe0: 2020 2020 2020 2020 5377 6570 7420 706f          Swept po\n+0000ebf0: 6c79 676f 6e73 206d 616b 6520 636c 6f73  lygons make clos\n+0000ec00: 6564 2073 7572 6661 6365 732e 0a2a 2053  ed surfaces..* S\n+0000ec10: 7765 7074 2062 6c6f 636b 733a 3a20 2020  wept blocks::   \n+0000ec20: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n+0000ec30: 7074 2062 6c6f 636b 203d 3d20 626c 6f63  pt block == bloc\n+0000ec40: 6b20 6f66 2073 7765 6570 732e 0a2a 2053  k of sweeps..* S\n+0000ec50: 7765 6570 2066 6163 6520 7370 6c69 7474  weep face splitt\n+0000ec60: 696e 673a 3a20 2020 2020 2020 2046 6978  ing::        Fix\n+0000ec70: 696e 6720 7761 7270 6564 2066 6163 6573  ing warped faces\n+0000ec80: 2077 6974 6820 7472 6961 6e67 6c65 732e   with triangles.\n+0000ec90: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n+0000eca0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5377  .info,  Node: Sw\n+0000ecb0: 6570 7420 706f 696e 7473 2c20 204e 6578  ept points,  Nex\n+0000ecc0: 743a 2053 7765 7074 206c 696e 6573 2c20  t: Swept lines, \n+0000ecd0: 2050 7265 763a 2053 7765 6570 732c 2020   Prev: Sweeps,  \n+0000ece0: 5570 3a20 5377 6565 7073 0a0a 332e 322e  Up: Sweeps..3.2.\n+0000ecf0: 362e 3120 5377 6570 7420 706f 696e 7473  6.1 Swept points\n+0000ed00: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+0000ed10: 2e2e 2e2e 2e0a 0a49 6620 5357 4550 545f  .......If SWEPT_\n+0000ed20: 4f42 4a45 4354 2069 7320 6120 706f 696e  OBJECT is a poin\n+0000ed30: 7420 6c69 7374 2061 6e64 2074 6865 7265  t list and there\n+0000ed40: 2069 7320 6e6f 2063 6c6f 7375 7265 2074   is no closure t\n+0000ed50: 6167 2c20 7468 656e 0a27 7377 6565 7027  ag, then.'sweep'\n+0000ed60: 2063 6f6e 6e65 6374 7320 4e2b 3120 7375   connects N+1 su\n+0000ed70: 6363 6573 7369 7665 2063 6f70 6965 7320  ccessive copies \n+0000ed80: 6f66 2065 6163 6820 706f 696e 7420 2869  of each point (i\n+0000ed90: 6e63 6c75 6469 6e67 2074 6865 0a6f 7269  ncluding the.ori\n+0000eda0: 6769 6e61 6c29 2077 6974 6820 7374 7261  ginal) with stra\n+0000edb0: 6967 6874 206c 696e 6520 7365 676d 656e  ight line segmen\n+0000edc0: 7473 2074 6f20 666f 726d 2061 2070 6f6c  ts to form a pol\n+0000edd0: 796c 696e 652e 2020 4966 2074 6865 7265  yline.  If there\n+0000ede0: 2061 7265 0a6d 2070 6f69 6e74 7320 696e   are.m points in\n+0000edf0: 2074 6865 206f 7269 6769 6e61 6c20 706f   the original po\n+0000ee00: 696e 7420 6c69 7374 2c20 7468 656e 206d  int list, then m\n+0000ee10: 2070 6f6c 796c 696e 6573 2077 6974 6820   polylines with \n+0000ee20: 4e20 7365 676d 656e 7473 0a65 6163 6820  N segments.each \n+0000ee30: 6172 6520 666f 726d 6564 2062 7920 7468  are formed by th\n+0000ee40: 6520 7377 6565 702e 2020 496e 2074 6869  e sweep.  In thi\n+0000ee50: 7320 6d61 6e6e 6572 2c20 2773 7765 6570  s manner, 'sweep\n+0000ee60: 2720 666f 726d 7320 6120 7365 7420 6f66  ' forms a set of\n+0000ee70: 0a6f 6e65 2d64 696d 656e 7369 6f6e 616c  .one-dimensional\n+0000ee80: 206f 626a 6563 7473 2028 706f 6c79 6c69   objects (polyli\n+0000ee90: 6e65 7329 2066 726f 6d20 7a65 726f 2d64  nes) from zero-d\n+0000eea0: 696d 656e 7369 6f6e 616c 206f 6e65 7320  imensional ones \n+0000eeb0: 2870 6f69 6e74 7329 2e0a 0a20 2020 5768  (points)...   Wh\n+0000eec0: 656e 2074 6865 7265 205f 6973 5f20 6120  en there _is_ a \n+0000eed0: 636c 6f73 7572 6520 7461 672c 2027 7377  closure tag, 'sw\n+0000eee0: 6565 7027 2063 6f6e 6e65 6374 7320 4e20  eep' connects N \n+0000eef0: 7375 6363 6573 7369 7665 2063 6f70 6965  successive copie\n+0000ef00: 730a 6f66 2065 6163 6820 706f 696e 7420  s.of each point \n+0000ef10: 2869 6e63 6c75 6469 6e67 2074 6865 206f  (including the o\n+0000ef20: 7269 6769 6e61 6c29 2077 6974 6820 7374  riginal) with st\n+0000ef30: 7261 6967 6874 206c 696e 6520 7365 676d  raight line segm\n+0000ef40: 656e 7473 2061 6e64 0a66 696e 616c 6c79  ents and.finally\n+0000ef50: 2063 6f6e 6e65 6374 7320 7468 6520 6c61   connects the la\n+0000ef60: 7374 2063 6f70 7920 6261 636b 2074 6f20  st copy back to \n+0000ef70: 7468 6520 6f72 6967 696e 616c 2074 6f20  the original to \n+0000ef80: 666f 726d 2061 2070 6f6c 7967 6f6e 0a77  form a polygon.w\n+0000ef90: 6974 6820 4e20 7369 6465 732e 2020 4966  ith N sides.  If\n+0000efa0: 2074 6865 7265 2061 7265 206d 2070 6f69   there are m poi\n+0000efb0: 6e74 7320 696e 2074 6865 206f 7269 6769  nts in the origi\n+0000efc0: 6e61 6c20 706f 696e 7420 6c69 7374 2c20  nal point list, \n+0000efd0: 7468 656e 206d 0a70 6f6c 7967 6f6e 7320  then m.polygons \n+0000efe0: 7769 7468 204e 2073 6964 6573 2065 6163  with N sides eac\n+0000eff0: 6820 6172 6520 666f 726d 6564 2062 7920  h are formed by \n+0000f000: 7468 6520 7377 6565 702e 2020 496e 2074  the sweep.  In t\n+0000f010: 6869 7320 6d61 6e6e 6572 2c0a 2773 7765  his manner,.'swe\n+0000f020: 6570 2720 666f 726d 7320 6120 7365 7420  ep' forms a set \n+0000f030: 6f66 2074 776f 2d64 696d 656e 7369 6f6e  of two-dimension\n+0000f040: 616c 206f 626a 6563 7473 2028 706f 6c79  al objects (poly\n+0000f050: 676f 6e73 2920 6672 6f6d 0a7a 6572 6f2d  gons) from.zero-\n+0000f060: 6469 6d65 6e73 696f 6e61 6c20 6f6e 6573  dimensional ones\n+0000f070: 2028 706f 696e 7473 292e 0a0a 2020 204f   (points)...   O\n+0000f080: 7074 696f 6e73 206f 6620 7468 6520 2773  ptions of the 's\n+0000f090: 7765 6570 2720 6172 6520 636f 7069 6564  weep' are copied\n+0000f0a0: 2064 6972 6563 746c 7920 746f 2074 6865   directly to the\n+0000f0b0: 2072 6573 756c 7469 6e67 0a70 6f6c 796c   resulting.polyl\n+0000f0c0: 696e 6528 7329 2e0a 0a1f 0a46 696c 653a  ine(s).....File:\n+0000f0d0: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n+0000f0e0: 6f64 653a 2053 7765 7074 206c 696e 6573  ode: Swept lines\n+0000f0f0: 2c20 204e 6578 743a 2053 7765 7074 2070  ,  Next: Swept p\n+0000f100: 6f6c 7967 6f6e 732c 2020 5072 6576 3a20  olygons,  Prev: \n+0000f110: 5377 6570 7420 706f 696e 7473 2c20 2055  Swept points,  U\n+0000f120: 703a 2053 7765 6570 730a 0a33 2e32 2e36  p: Sweeps..3.2.6\n+0000f130: 2e32 2053 7765 7074 206c 696e 6573 0a2e  .2 Swept lines..\n+0000f140: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+0000f150: 2e2e 0a0a 4966 2053 5745 5054 5f4f 424a  ....If SWEPT_OBJ\n+0000f160: 4543 5420 6973 2061 2070 6f6c 796c 696e  ECT is a polylin\n+0000f170: 6520 616e 6420 7468 6572 6520 6973 206e  e and there is n\n+0000f180: 6f20 636c 6f73 7572 6520 7461 672c 2074  o closure tag, t\n+0000f190: 6865 6e20 2773 7765 6570 270a 636f 6e6e  hen 'sweep'.conn\n+0000f1a0: 6563 7473 204e 2b31 2073 7563 6365 7373  ects N+1 success\n+0000f1b0: 6976 6520 636f 7069 6573 206f 6620 7468  ive copies of th\n+0000f1c0: 6520 706f 6c79 6c69 6e65 2028 696e 636c  e polyline (incl\n+0000f1d0: 7564 696e 6720 7468 6520 6f72 6967 696e  uding the origin\n+0000f1e0: 616c 290a 7769 7468 2066 6f75 722d 7369  al).with four-si\n+0000f1f0: 6465 6420 706f 6c79 676f 6e73 2c20 6561  ded polygons, ea\n+0000f200: 6368 2070 6169 7220 6f66 2063 6f70 6965  ch pair of copie\n+0000f210: 7320 6769 7669 6e67 2072 6973 6520 746f  s giving rise to\n+0000f220: 2061 2022 706f 6c79 676f 6e0a 7374 7269   a \"polygon.stri\n+0000f230: 702e 2220 2049 6620 7468 6572 6520 6172  p.\"  If there ar\n+0000f240: 6520 6d20 706f 696e 7473 2069 6e20 7468  e m points in th\n+0000f250: 6520 6f72 6967 696e 616c 2070 6f6c 796c  e original polyl\n+0000f260: 696e 652c 2074 6865 6e20 286d 2d31 294e  ine, then (m-1)N\n+0000f270: 0a70 6f6c 7967 6f6e 7320 6172 6520 666f  .polygons are fo\n+0000f280: 726d 6564 2062 7920 7468 6520 7377 6565  rmed by the swee\n+0000f290: 702e 2020 5765 2063 616c 6c20 7468 6573  p.  We call thes\n+0000f2a0: 6520 2262 6f64 7920 706f 6c79 676f 6e73  e \"body polygons\n+0000f2b0: 222e 2020 496e 0a74 6869 7320 6d61 6e6e  \".  In.this mann\n+0000f2c0: 6572 2c20 2773 7765 6570 2720 666f 726d  er, 'sweep' form\n+0000f2d0: 7320 6120 7477 6f2d 6469 6d65 6e73 696f  s a two-dimensio\n+0000f2e0: 6e61 6c20 7375 7266 6163 6520 6672 6f6d  nal surface from\n+0000f2f0: 2066 726f 6d20 610a 6f6e 652d 6469 6d65   from a.one-dime\n+0000f300: 6e73 696f 6e61 6c20 706f 6c79 6c69 6e65  nsional polyline\n+0000f310: 2e0a 0a20 2020 5468 6520 6f72 6465 7220  ...   The order \n+0000f320: 6f66 2076 6572 7469 6365 7320 7072 6f64  of vertices prod\n+0000f330: 7563 6564 2062 7920 2773 7765 6570 2720  uced by 'sweep' \n+0000f340: 6973 2069 6d70 6f72 7461 6e74 2e20 2049  is important.  I\n+0000f350: 6620 610a 706f 6c79 676f 6e27 7320 7665  f a.polygon's ve\n+0000f360: 7274 6963 6573 2064 6f20 6e6f 7420 6170  rtices do not ap\n+0000f370: 7065 6172 2069 6e20 636f 756e 7465 722d  pear in counter-\n+0000f380: 636c 6f63 6b77 6973 6520 6f72 6465 7220  clockwise order \n+0000f390: 696e 2074 6865 2066 696e 616c 0a69 6d61  in the final.ima\n+0000f3a0: 6765 2c20 7468 6520 706f 6c79 676f 6e20  ge, the polygon \n+0000f3b0: 7769 6c6c 2062 6520 6375 6c6c 6564 2028  will be culled (\n+0000f3c0: 756e 6c65 7373 2027 6375 6c6c 3d66 616c  unless 'cull=fal\n+0000f3d0: 7365 2720 6973 2073 6574 292e 2020 4966  se' is set).  If\n+0000f3e0: 2074 6865 0a70 6f69 6e74 7320 696e 2074   the.points in t\n+0000f3f0: 6865 206b 2774 6820 636f 7079 206f 6620  he k'th copy of \n+0000f400: 7468 6520 706f 6c79 6c69 6e65 2061 7265  the polyline are\n+0000f410: 2050 5f31 2c20 505f 322c 202e 2e2e 2c20   P_1, P_2, ..., \n+0000f420: 505f 6d2c 2061 6e64 2074 6865 0a70 6f69  P_m, and the.poi\n+0000f430: 6e74 7320 696e 2074 6865 206e 6578 7420  nts in the next \n+0000f440: 636f 7079 2c20 7468 6520 286b 2b31 2973  copy, the (k+1)s\n+0000f450: 742c 2061 7265 2050 5f31 272c 2050 5f32  t, are P_1', P_2\n+0000f460: 272c 202e 2e2e 2c20 505f 6d27 2c20 7468  ', ..., P_m', th\n+0000f470: 656e 0a74 6865 2076 6572 7465 7820 6f72  en.the vertex or\n+0000f480: 6465 7220 6f66 2074 6865 2067 656e 6572  der of the gener\n+0000f490: 6174 6564 2070 6f6c 7967 6f6e 7320 6973  ated polygons is\n+0000f4a0: 0a20 2020 2020 426f 6479 2070 6f6c 7967  .     Body polyg\n+0000f4b0: 6f6e 2031 3a20 505f 3220 505f 3120 505f  on 1: P_2 P_1 P_\n+0000f4c0: 3127 2050 5f32 270a 2020 2020 2042 6f64  1' P_2'.     Bod\n+0000f4d0: 7920 706f 6c79 676f 6e20 323a 2050 5f33  y polygon 2: P_3\n+0000f4e0: 2050 5f32 2050 5f32 2720 505f 3327 0a20   P_2 P_2' P_3'. \n+0000f4f0: 2020 2020 2e2e 2e0a 2020 2020 2042 6f64      ....     Bod\n+0000f500: 7920 706f 6c79 676f 6e20 6d2d 313a 2050  y polygon m-1: P\n+0000f510: 5f6d 2050 5f7b 6d2d 317d 2050 5f7b 6d2d  _m P_{m-1} P_{m-\n+0000f520: 317d 2720 505f 6d27 0a0a 2020 204f 7074  1}' P_m'..   Opt\n+0000f530: 696f 6e73 206f 6620 756e 636c 6f73 6564  ions of unclosed\n+0000f540: 206c 696e 6520 7377 6565 7073 2061 7265   line sweeps are\n+0000f550: 2063 6f70 6965 6420 746f 2065 6163 6820   copied to each \n+0000f560: 6f75 7470 7574 2070 6f6c 7967 6f6e 2e0a  output polygon..\n+0000f570: 4f70 7469 6f6e 7320 6f66 2074 6865 2073  Options of the s\n+0000f580: 7765 7074 206c 696e 6520 6172 6520 6967  wept line are ig\n+0000f590: 6e6f 7265 642e 0a0a 2020 2057 6865 6e20  nored...   When \n+0000f5a0: 7468 6572 6520 5f69 735f 2061 2063 6c6f  there _is_ a clo\n+0000f5b0: 7375 7265 2074 6167 2c20 7468 656e 2027  sure tag, then '\n+0000f5c0: 7377 6565 7027 2063 6f6e 6e65 6374 7320  sweep' connects \n+0000f5d0: 4e20 7375 6363 6573 7369 7665 0a63 6f70  N successive.cop\n+0000f5e0: 6965 7320 6f66 2074 6865 2070 6f6c 796c  ies of the polyl\n+0000f5f0: 696e 6520 2869 6e63 6c75 6469 6e67 2074  ine (including t\n+0000f600: 6865 206f 7269 6769 6e61 6c29 2077 6974  he original) wit\n+0000f610: 6820 666f 7572 2d73 6964 6564 2062 6f64  h four-sided bod\n+0000f620: 790a 706f 6c79 676f 6e73 206a 7573 7420  y.polygons just \n+0000f630: 6173 2074 6865 2063 6173 6520 7769 7468  as the case with\n+0000f640: 206e 6f20 636c 6f73 7572 6520 7461 672e   no closure tag.\n+0000f650: 2020 4974 2074 6865 6e20 636f 6e6e 6563    It then connec\n+0000f660: 7473 2074 6865 0a6c 6173 7420 636f 7079  ts the.last copy\n+0000f670: 2062 6163 6b20 746f 2074 6865 206f 7269   back to the ori\n+0000f680: 6769 6e61 6c20 746f 2066 6f72 6d20 6120  ginal to form a \n+0000f690: 7269 6262 6f6e 2d73 6861 7065 6420 7375  ribbon-shaped su\n+0000f6a0: 7266 6163 6520 7468 6174 0a63 6c6f 7365  rface that.close\n+0000f6b0: 7320 6f6e 2069 7473 656c 6620 7769 7468  s on itself with\n+0000f6c0: 2074 776f 2068 6f6c 6573 2072 656d 6169   two holes remai\n+0000f6d0: 6e69 6e67 2e0a 0a20 2020 4669 6e61 6c6c  ning...   Finall\n+0000f6e0: 792c 2074 6865 2073 7765 6570 2061 6464  y, the sweep add\n+0000f6f0: 7320 7477 6f20 6d6f 7265 2070 6f6c 7967  s two more polyg\n+0000f700: 6f6e 7320 746f 2073 6561 6c20 7468 6520  ons to seal the \n+0000f710: 686f 6c65 7320 616e 6420 666f 726d 0a61  holes and form.a\n+0000f720: 2063 6c6f 7365 6420 7375 7266 6163 6520   closed surface \n+0000f730: 7468 6174 2c20 6465 7065 6e64 696e 6720  that, depending \n+0000f740: 6f6e 2074 6865 2073 7765 6570 2074 7261  on the sweep tra\n+0000f750: 6e73 666f 726d 732c 206d 6179 2072 6570  nsforms, may rep\n+0000f760: 7265 7365 6e74 0a74 6865 2062 6f75 6e64  resent.the bound\n+0000f770: 6172 7920 6f66 2061 2073 6f6c 6964 2e20  ary of a solid. \n+0000f780: 2049 6e20 7468 6973 206d 616e 6e65 722c   In this manner,\n+0000f790: 2027 7377 6565 7027 2066 6f72 6d73 2074   'sweep' forms t\n+0000f7a0: 6865 2062 6f75 6e64 6172 7920 6f66 0a61  he boundary of.a\n+0000f7b0: 2074 6872 6565 2d64 696d 656e 7369 6f6e   three-dimension\n+0000f7c0: 616c 206f 626a 6563 7420 6672 6f6d 2061  al object from a\n+0000f7d0: 206f 6e65 2d64 696d 656e 7369 6f6e 616c   one-dimensional\n+0000f7e0: 2070 6f6c 796c 696e 652e 2020 5765 2063   polyline.  We c\n+0000f7f0: 616c 6c0a 7468 6573 6520 686f 6c65 2d66  all.these hole-f\n+0000f800: 696c 6c69 6e67 2070 6f6c 7967 6f6e 7320  illing polygons \n+0000f810: 2265 6e64 7322 2e0a 0a20 2020 5468 6520  \"ends\"...   The \n+0000f820: 6f72 6465 7220 6f66 2076 6572 7469 6365  order of vertice\n+0000f830: 7320 6f66 2065 6e64 2070 6f6c 7967 6f6e  s of end polygon\n+0000f840: 7320 6973 2069 6d70 6f72 7461 6e74 2066  s is important f\n+0000f850: 6f72 2063 6f72 7265 6374 0a63 756c 6c69  or correct.culli\n+0000f860: 6e67 2061 7320 6465 7363 7269 6265 6420  ng as described \n+0000f870: 6162 6f76 652e 2020 4966 2050 5f31 5e31  above.  If P_1^1\n+0000f880: 2c20 505f 315e 322c 202e 2e2e 2c20 505f  , P_1^2, ..., P_\n+0000f890: 315e 6e20 6172 6520 7468 6520 4e0a 636f  1^n are the N.co\n+0000f8a0: 7069 6573 206f 6620 7468 6520 6669 7273  pies of the firs\n+0000f8b0: 7420 706f 6c79 6c69 6e65 2070 6f69 6e74  t polyline point\n+0000f8c0: 2061 6e64 2050 5f6d 5e31 2c20 505f 6d5e   and P_m^1, P_m^\n+0000f8d0: 322c 202e 2e2e 202c 505f 6d5e 6e20 6172  2, ... ,P_m^n ar\n+0000f8e0: 6520 7468 650a 4e20 636f 7069 6573 206f  e the.N copies o\n+0000f8f0: 6620 7468 6520 6c61 7374 2070 6f6c 796c  f the last polyl\n+0000f900: 696e 6520 706f 696e 742c 2074 6865 6e20  ine point, then \n+0000f910: 7468 6520 656e 6420 706f 6c79 676f 6e20  the end polygon \n+0000f920: 7665 7274 6578 206f 7264 6572 0a69 730a  vertex order.is.\n+0000f930: 2020 2020 2045 6e64 2070 6f6c 7967 6f6e       End polygon\n+0000f940: 2031 3a20 505f 315e 6e2c 2050 5f31 5e7b   1: P_1^n, P_1^{\n+0000f950: 6e2d 317d 2c20 2e2e 2e20 2c50 5f31 5e31  n-1}, ... ,P_1^1\n+0000f960: 0a20 2020 2020 456e 6420 706f 6c79 676f  .     End polygo\n+0000f970: 6e20 323a 2050 5f6d 5e31 2c20 505f 6d5e  n 2: P_m^1, P_m^\n+0000f980: 322c 202e 2e2e 202c 505f 6d5e 6e0a 0a20  2, ... ,P_m^n.. \n+0000f990: 2020 4966 2074 6865 7265 2061 7265 206e    If there are n\n+0000f9a0: 6f20 6f70 7469 6f6e 7320 6f6e 2074 6865  o options on the\n+0000f9b0: 2073 7765 7074 206c 696e 652c 2074 6865   swept line, the\n+0000f9c0: 6e20 7468 6520 2773 7765 6570 2720 6f70  n the 'sweep' op\n+0000f9d0: 7469 6f6e 730a 6172 6520 636f 7069 6564  tions.are copied\n+0000f9e0: 2074 6f20 6561 6368 206f 7574 7075 7420   to each output \n+0000f9f0: 706f 6c79 676f 6e2e 2020 4966 2074 6865  polygon.  If the\n+0000fa00: 2073 7765 7074 206c 696e 6520 646f 6573   swept line does\n+0000fa10: 2068 6176 6520 6f70 7469 6f6e 732c 0a74   have options,.t\n+0000fa20: 6865 7365 2061 7265 2063 6f70 6965 6420  hese are copied \n+0000fa30: 746f 2063 6f72 7265 7370 6f6e 6469 6e67  to corresponding\n+0000fa40: 2062 6f64 7920 706f 6c79 676f 6e73 3b20   body polygons; \n+0000fa50: 7468 6520 7377 6565 7020 6f70 7469 6f6e  the sweep option\n+0000fa60: 7320 6172 650a 636f 7069 6564 2074 6f20  s are.copied to \n+0000fa70: 7468 6520 656e 6420 706f 6c79 676f 6e73  the end polygons\n+0000fa80: 2e20 2049 6e20 7468 6973 206d 616e 6e65  .  In this manne\n+0000fa90: 722c 2062 6f64 7920 616e 6420 656e 6473  r, body and ends\n+0000faa0: 206d 6179 2062 6520 6472 6177 6e0a 7769   may be drawn.wi\n+0000fab0: 7468 2064 6966 6665 7265 6e74 2063 6861  th different cha\n+0000fac0: 7261 6374 6572 6973 7469 6373 2073 7563  racteristics suc\n+0000fad0: 6820 6173 2027 6669 6c6c 636f 6c6f 7227  h as 'fillcolor'\n+0000fae0: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463  .....File: sketc\n+0000faf0: 682e 696e 666f 2c20 204e 6f64 653a 2053  h.info,  Node: S\n+0000fb00: 7765 7074 2070 6f6c 7967 6f6e 732c 2020  wept polygons,  \n+0000fb10: 4e65 7874 3a20 5377 6570 7420 626c 6f63  Next: Swept bloc\n+0000fb20: 6b73 2c20 2050 7265 763a 2053 7765 7074  ks,  Prev: Swept\n+0000fb30: 206c 696e 6573 2c20 2055 703a 2053 7765   lines,  Up: Swe\n+0000fb40: 6570 730a 0a33 2e32 2e36 2e33 2053 7765  eps..3.2.6.3 Swe\n+0000fb50: 7074 2070 6f6c 7967 6f6e 730a 2e2e 2e2e  pt polygons.....\n 0000fb60: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-0000fb70: 2e2e 2e2e 0a0a 4966 2053 5745 5054 5f4f  ......If SWEPT_O\n-0000fb80: 424a 4543 5420 6973 2061 2070 6f6c 7967  BJECT is a polyg\n-0000fb90: 6f6e 2c20 7468 6520 2773 7765 6570 2720  on, the 'sweep' \n-0000fba0: 636f 6e6e 6563 7473 204e 2b31 2073 7563  connects N+1 suc\n-0000fbb0: 6365 7373 6976 6520 636f 7069 6573 0a6f  cessive copies.o\n-0000fbc0: 6620 7468 6520 636c 6f73 6564 2070 6f6c  f the closed pol\n-0000fbd0: 796c 696e 6520 626f 7264 6572 206f 6620  yline border of \n-0000fbe0: 7468 6520 706f 6c79 676f 6e20 746f 2066  the polygon to f\n-0000fbf0: 6f72 6d20 626f 6479 2070 6f6c 7967 6f6e  orm body polygon\n-0000fc00: 730a 6578 6163 746c 7920 6173 2074 686f  s.exactly as tho\n-0000fc10: 7567 6820 7468 6520 626f 7264 6572 2077  ugh the border w\n-0000fc20: 6572 6520 6120 7377 6570 7420 706f 6c79  ere a swept poly\n-0000fc30: 6c69 6e65 2061 7320 6465 7363 7269 6265  line as describe\n-0000fc40: 6420 696e 202a 6e6f 7465 0a53 7765 7074  d in *note.Swept\n-0000fc50: 206c 696e 6573 3a3a 2e20 2049 6620 7468   lines::.  If th\n-0000fc60: 6572 6520 6172 6520 6d20 706f 696e 7473  ere are m points\n-0000fc70: 2069 6e20 7468 6520 6f72 6967 696e 616c   in the original\n-0000fc80: 2070 6f6c 7967 6f6e 2c20 7468 656e 206d   polygon, then m\n-0000fc90: 4e0a 626f 6479 2070 6f6c 7967 6f6e 7320  N.body polygons \n-0000fca0: 6172 6520 666f 726d 6564 2062 7920 7468  are formed by th\n-0000fcb0: 6973 2073 7765 6570 2e20 2054 6865 2062  is sweep.  The b\n-0000fcc0: 6f64 7920 706f 6c79 676f 6e73 2066 6f72  ody polygons for\n-0000fcd0: 6d20 616e 0a22 6578 7472 7573 696f 6e22  m an.\"extrusion\"\n-0000fce0: 206f 6620 7468 6520 626f 756e 6461 7279   of the boundary\n-0000fcf0: 206f 6620 7468 6520 6f72 6967 696e 616c   of the original\n-0000fd00: 2070 6f6c 7967 6f6e 2077 6974 6820 7477   polygon with tw\n-0000fd10: 6f20 686f 6c65 7320 6174 0a74 6865 206f  o holes at.the o\n-0000fd20: 7065 6e20 656e 6473 2e0a 0a20 2020 4669  pen ends...   Fi\n-0000fd30: 6e61 6c6c 792c 2074 6865 2073 7765 6570  nally, the sweep\n-0000fd40: 2061 6464 7320 7477 6f20 636f 7069 6573   adds two copies\n-0000fd50: 206f 6620 7468 6520 6f72 6967 696e 616c   of the original\n-0000fd60: 2070 6f6c 7967 6f6e 2074 6f20 636f 7665   polygon to cove\n-0000fd70: 720a 7468 6520 686f 6c65 732e 2020 5765  r.the holes.  We\n-0000fd80: 2063 616c 6c20 7468 6573 6520 686f 6c65   call these hole\n-0000fd90: 2d66 696c 6c69 6e67 2070 6f6c 7967 6f6e  -filling polygon\n-0000fda0: 7320 2265 6e64 7322 2e20 2049 6e20 7468  s \"ends\".  In th\n-0000fdb0: 6973 206d 616e 6e65 722c 0a27 7377 6565  is manner,.'swee\n-0000fdc0: 7027 2066 6f72 6d73 2074 6865 2062 6f75  p' forms the bou\n-0000fdd0: 6e64 6172 7920 6f66 2061 2074 6872 6565  ndary of a three\n-0000fde0: 2d64 696d 656e 7369 6f6e 616c 206f 626a  -dimensional obj\n-0000fdf0: 6563 7420 6672 6f6d 2061 0a74 776f 2d64  ect from a.two-d\n-0000fe00: 696d 656e 7369 6f6e 616c 2070 6f6c 7967  imensional polyg\n-0000fe10: 6f6e 2e0a 0a20 2020 5468 6520 6f72 6465  on...   The orde\n-0000fe20: 7220 6f66 2076 6572 7469 6365 7320 6f66  r of vertices of\n-0000fe30: 2065 6e64 2070 6f6c 7967 6f6e 7320 6973   end polygons is\n-0000fe40: 2069 6d70 6f72 7461 6e74 2066 6f72 2063   important for c\n-0000fe50: 6f72 7265 6374 0a63 756c 6c69 6e67 2061  orrect.culling a\n-0000fe60: 7320 6465 7363 7269 6265 6420 6162 6f76  s described abov\n-0000fe70: 652e 2020 416e 2065 7861 6374 2063 6f70  e.  An exact cop\n-0000fe80: 7920 6f66 2074 6865 206f 7269 6769 6e61  y of the origina\n-0000fe90: 6c20 706f 6c79 676f 6e20 7769 7468 0a76  l polygon with.v\n-0000fea0: 6572 7465 7820 6f72 6465 7220 696e 7461  ertex order inta\n-0000feb0: 6374 2066 6f72 6d73 2074 6865 2066 6972  ct forms the fir\n-0000fec0: 7374 2065 6e64 2070 6f6c 7967 6f6e 2e20  st end polygon. \n-0000fed0: 2054 6865 206f 7468 6572 2065 6e64 2070   The other end p\n-0000fee0: 6f6c 7967 6f6e 0a72 6573 756c 7473 2066  olygon.results f\n-0000fef0: 726f 6d20 7472 616e 7366 6f72 6d69 6e67  rom transforming\n-0000ff00: 2061 6e64 2074 6865 2072 6576 6572 7369   and the reversi\n-0000ff10: 6e67 2074 6865 206f 7264 6572 206f 6620  ng the order of \n-0000ff20: 7665 7274 6963 6573 2069 6e20 7468 650a  vertices in the.\n-0000ff30: 6f72 6967 696e 616c 2e20 2054 6865 2074  original.  The t\n-0000ff40: 7261 6e73 666f 726d 2070 6c61 6365 7320  ransform places \n-0000ff50: 7468 6520 6f72 6967 696e 616c 2070 6f6c  the original pol\n-0000ff60: 7967 6f6e 2061 7420 7468 6520 756e 636f  ygon at the unco\n-0000ff70: 7665 7265 640a 686f 6c65 3b20 6974 2069  vered.hole; it i\n-0000ff80: 730a 2020 2020 2054 5f31 5e6e 2074 6865  s.     T_1^n the\n-0000ff90: 6e20 545f 325e 6e20 7468 656e 202e 2e2e  n T_2^n then ...\n-0000ffa0: 2074 6865 6e20 545f 525e 6e2e 0a49 6620   then T_R^n..If \n-0000ffb0: 7468 6572 6520 6172 6520 6e6f 206f 7074  there are no opt\n-0000ffc0: 696f 6e73 206f 6e20 7468 6520 7377 6570  ions on the swep\n-0000ffd0: 7420 706f 6c79 676f 6e2c 2074 6865 6e20  t polygon, then \n-0000ffe0: 7468 6520 2773 7765 6570 2720 6f70 7469  the 'sweep' opti\n-0000fff0: 6f6e 730a 6172 6520 636f 7069 6564 2074  ons.are copied t\n-00010000: 6f20 6561 6368 206f 7574 7075 7420 706f  o each output po\n-00010010: 6c79 676f 6e2e 2020 4966 2074 6865 2073  lygon.  If the s\n-00010020: 7765 7074 2070 6f6c 7967 6f6e 2064 6f65  wept polygon doe\n-00010030: 7320 6861 7665 0a6f 7074 696f 6e73 2c20  s have.options, \n-00010040: 7468 6573 6520 6172 6520 636f 7069 6564  these are copied\n-00010050: 2074 6f20 7468 6520 656e 6473 3b20 7468   to the ends; th\n-00010060: 6520 7377 6565 7020 6f70 7469 6f6e 7320  e sweep options \n-00010070: 6172 6520 636f 7069 6564 2074 6f0a 7468  are copied to.th\n-00010080: 6520 626f 6479 2070 6f6c 7967 6f6e 732e  e body polygons.\n-00010090: 2020 496e 2074 6869 7320 6d61 6e6e 6572    In this manner\n-000100a0: 2c20 626f 6479 2061 6e64 2065 6e64 7320  , body and ends \n-000100b0: 6d61 7920 6265 2064 7261 776e 2077 6974  may be drawn wit\n-000100c0: 680a 6469 6666 6572 656e 7420 6368 6172  h.different char\n-000100d0: 6163 7465 7269 7374 6963 7320 7375 6368  acteristics such\n-000100e0: 2061 7320 2766 696c 6c63 6f6c 6f72 272e   as 'fillcolor'.\n-000100f0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n-00010100: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5377  .info,  Node: Sw\n-00010110: 6570 7420 626c 6f63 6b73 2c20 204e 6578  ept blocks,  Nex\n-00010120: 743a 2053 7765 6570 2066 6163 6520 7370  t: Sweep face sp\n-00010130: 6c69 7474 696e 672c 2020 5072 6576 3a20  litting,  Prev: \n-00010140: 5377 6570 7420 706f 6c79 676f 6e73 2c20  Swept polygons, \n-00010150: 2055 703a 2053 7765 6570 730a 0a33 2e32   Up: Sweeps..3.2\n-00010160: 2e36 2e34 2053 7765 7074 2062 6c6f 636b  .6.4 Swept block\n-00010170: 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  s...............\n-00010180: 2e2e 2e2e 2e2e 0a0a 5468 6520 7377 6570  ........The swep\n-00010190: 7420 6f62 6a65 6374 2053 5745 5054 5f4f  t object SWEPT_O\n-000101a0: 424a 4543 5420 6d61 7920 616c 736f 2062  BJECT may also b\n-000101b0: 6520 616e 7920 636f 6c6c 6563 7469 6f6e  e any collection\n-000101c0: 206f 6620 706f 6c79 6c69 6e65 730a 616e   of polylines.an\n-000101d0: 6420 706f 6c79 676f 6e73 2e20 2054 6869  d polygons.  Thi\n-000101e0: 7320 6d61 7920 6265 2061 2062 6c6f 636b  s may be a block\n-000101f0: 2063 6f6d 706f 7365 6420 6f66 2027 6c69   composed of 'li\n-00010200: 6e65 2720 616e 642f 6f72 2027 706f 6c79  ne' and/or 'poly\n-00010210: 676f 6e27 0a63 6f6d 6d61 6e64 7320 696e  gon'.commands in\n-00010220: 2062 7261 6365 7320 277b 207d 272c 206f   braces '{ }', o\n-00010230: 7220 6974 206d 6179 2062 6520 7468 6520  r it may be the \n-00010240: 7265 7375 6c74 206f 6620 6120 2772 6570  result of a 'rep\n-00010250: 6561 7427 2c20 616e 6f74 6865 720a 2773  eat', another.'s\n-00010260: 7765 6570 272c 2065 7463 2e20 2054 6865  weep', etc.  The\n-00010270: 2073 7765 6570 2061 6374 7320 696e 6465   sweep acts inde\n-00010280: 7065 6e64 656e 746c 7920 6f6e 2065 6163  pendently on eac\n-00010290: 6820 6f62 6a65 6374 2069 6e20 7468 6520  h object in the \n-000102a0: 626c 6f63 6b0a 6578 6163 746c 7920 6173  block.exactly as\n-000102b0: 2069 6620 6974 2077 6572 6520 6120 7369   if it were a si\n-000102c0: 6e67 6c65 2073 7765 7074 206f 626a 6563  ngle swept objec\n-000102d0: 7420 6465 7363 7269 6265 6420 6162 6f76  t described abov\n-000102e0: 6520 696e 202a 6e6f 7465 0a53 7765 7074  e in *note.Swept\n-000102f0: 206c 696e 6573 3a3a 2061 6e64 202a 6e6f   lines:: and *no\n-00010300: 7465 2053 7765 7074 2070 6f6c 7967 6f6e  te Swept polygon\n-00010310: 733a 3a2e 0a0a 1f0a 4669 6c65 3a20 736b  s::.....File: sk\n-00010320: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n-00010330: 3a20 5377 6565 7020 6661 6365 2073 706c  : Sweep face spl\n-00010340: 6974 7469 6e67 2c20 2050 7265 763a 2053  itting,  Prev: S\n-00010350: 7765 7074 2062 6c6f 636b 732c 2020 5570  wept blocks,  Up\n-00010360: 3a20 5377 6565 7073 0a0a 332e 322e 362e  : Sweeps..3.2.6.\n-00010370: 3520 5377 6565 7020 6661 6365 2073 706c  5 Sweep face spl\n-00010380: 6974 7469 6e67 0a2e 2e2e 2e2e 2e2e 2e2e  itting..........\n+0000fb70: 2e2e 0a0a 4966 2053 5745 5054 5f4f 424a  ....If SWEPT_OBJ\n+0000fb80: 4543 5420 6973 2061 2070 6f6c 7967 6f6e  ECT is a polygon\n+0000fb90: 2c20 7468 6520 2773 7765 6570 2720 636f  , the 'sweep' co\n+0000fba0: 6e6e 6563 7473 204e 2b31 2073 7563 6365  nnects N+1 succe\n+0000fbb0: 7373 6976 6520 636f 7069 6573 0a6f 6620  ssive copies.of \n+0000fbc0: 7468 6520 636c 6f73 6564 2070 6f6c 796c  the closed polyl\n+0000fbd0: 696e 6520 626f 7264 6572 206f 6620 7468  ine border of th\n+0000fbe0: 6520 706f 6c79 676f 6e20 746f 2066 6f72  e polygon to for\n+0000fbf0: 6d20 626f 6479 2070 6f6c 7967 6f6e 730a  m body polygons.\n+0000fc00: 6578 6163 746c 7920 6173 2074 686f 7567  exactly as thoug\n+0000fc10: 6820 7468 6520 626f 7264 6572 2077 6572  h the border wer\n+0000fc20: 6520 6120 7377 6570 7420 706f 6c79 6c69  e a swept polyli\n+0000fc30: 6e65 2061 7320 6465 7363 7269 6265 6420  ne as described \n+0000fc40: 696e 202a 6e6f 7465 0a53 7765 7074 206c  in *note.Swept l\n+0000fc50: 696e 6573 3a3a 2e20 2049 6620 7468 6572  ines::.  If ther\n+0000fc60: 6520 6172 6520 6d20 706f 696e 7473 2069  e are m points i\n+0000fc70: 6e20 7468 6520 6f72 6967 696e 616c 2070  n the original p\n+0000fc80: 6f6c 7967 6f6e 2c20 7468 656e 206d 4e0a  olygon, then mN.\n+0000fc90: 626f 6479 2070 6f6c 7967 6f6e 7320 6172  body polygons ar\n+0000fca0: 6520 666f 726d 6564 2062 7920 7468 6973  e formed by this\n+0000fcb0: 2073 7765 6570 2e20 2054 6865 2062 6f64   sweep.  The bod\n+0000fcc0: 7920 706f 6c79 676f 6e73 2066 6f72 6d20  y polygons form \n+0000fcd0: 616e 0a22 6578 7472 7573 696f 6e22 206f  an.\"extrusion\" o\n+0000fce0: 6620 7468 6520 626f 756e 6461 7279 206f  f the boundary o\n+0000fcf0: 6620 7468 6520 6f72 6967 696e 616c 2070  f the original p\n+0000fd00: 6f6c 7967 6f6e 2077 6974 6820 7477 6f20  olygon with two \n+0000fd10: 686f 6c65 7320 6174 0a74 6865 206f 7065  holes at.the ope\n+0000fd20: 6e20 656e 6473 2e0a 0a20 2020 4669 6e61  n ends...   Fina\n+0000fd30: 6c6c 792c 2074 6865 2073 7765 6570 2061  lly, the sweep a\n+0000fd40: 6464 7320 7477 6f20 636f 7069 6573 206f  dds two copies o\n+0000fd50: 6620 7468 6520 6f72 6967 696e 616c 2070  f the original p\n+0000fd60: 6f6c 7967 6f6e 2074 6f20 636f 7665 720a  olygon to cover.\n+0000fd70: 7468 6520 686f 6c65 732e 2020 5765 2063  the holes.  We c\n+0000fd80: 616c 6c20 7468 6573 6520 686f 6c65 2d66  all these hole-f\n+0000fd90: 696c 6c69 6e67 2070 6f6c 7967 6f6e 7320  illing polygons \n+0000fda0: 2265 6e64 7322 2e20 2049 6e20 7468 6973  \"ends\".  In this\n+0000fdb0: 206d 616e 6e65 722c 0a27 7377 6565 7027   manner,.'sweep'\n+0000fdc0: 2066 6f72 6d73 2074 6865 2062 6f75 6e64   forms the bound\n+0000fdd0: 6172 7920 6f66 2061 2074 6872 6565 2d64  ary of a three-d\n+0000fde0: 696d 656e 7369 6f6e 616c 206f 626a 6563  imensional objec\n+0000fdf0: 7420 6672 6f6d 2061 0a74 776f 2d64 696d  t from a.two-dim\n+0000fe00: 656e 7369 6f6e 616c 2070 6f6c 7967 6f6e  ensional polygon\n+0000fe10: 2e0a 0a20 2020 5468 6520 6f72 6465 7220  ...   The order \n+0000fe20: 6f66 2076 6572 7469 6365 7320 6f66 2065  of vertices of e\n+0000fe30: 6e64 2070 6f6c 7967 6f6e 7320 6973 2069  nd polygons is i\n+0000fe40: 6d70 6f72 7461 6e74 2066 6f72 2063 6f72  mportant for cor\n+0000fe50: 7265 6374 0a63 756c 6c69 6e67 2061 7320  rect.culling as \n+0000fe60: 6465 7363 7269 6265 6420 6162 6f76 652e  described above.\n+0000fe70: 2020 416e 2065 7861 6374 2063 6f70 7920    An exact copy \n+0000fe80: 6f66 2074 6865 206f 7269 6769 6e61 6c20  of the original \n+0000fe90: 706f 6c79 676f 6e20 7769 7468 0a76 6572  polygon with.ver\n+0000fea0: 7465 7820 6f72 6465 7220 696e 7461 6374  tex order intact\n+0000feb0: 2066 6f72 6d73 2074 6865 2066 6972 7374   forms the first\n+0000fec0: 2065 6e64 2070 6f6c 7967 6f6e 2e20 2054   end polygon.  T\n+0000fed0: 6865 206f 7468 6572 2065 6e64 2070 6f6c  he other end pol\n+0000fee0: 7967 6f6e 0a72 6573 756c 7473 2066 726f  ygon.results fro\n+0000fef0: 6d20 7472 616e 7366 6f72 6d69 6e67 2061  m transforming a\n+0000ff00: 6e64 2074 6865 2072 6576 6572 7369 6e67  nd the reversing\n+0000ff10: 2074 6865 206f 7264 6572 206f 6620 7665   the order of ve\n+0000ff20: 7274 6963 6573 2069 6e20 7468 650a 6f72  rtices in the.or\n+0000ff30: 6967 696e 616c 2e20 2054 6865 2074 7261  iginal.  The tra\n+0000ff40: 6e73 666f 726d 2070 6c61 6365 7320 7468  nsform places th\n+0000ff50: 6520 6f72 6967 696e 616c 2070 6f6c 7967  e original polyg\n+0000ff60: 6f6e 2061 7420 7468 6520 756e 636f 7665  on at the uncove\n+0000ff70: 7265 640a 686f 6c65 3b20 6974 2069 730a  red.hole; it is.\n+0000ff80: 2020 2020 2054 5f31 5e6e 2074 6865 6e20       T_1^n then \n+0000ff90: 545f 325e 6e20 7468 656e 202e 2e2e 2074  T_2^n then ... t\n+0000ffa0: 6865 6e20 545f 525e 6e2e 0a49 6620 7468  hen T_R^n..If th\n+0000ffb0: 6572 6520 6172 6520 6e6f 206f 7074 696f  ere are no optio\n+0000ffc0: 6e73 206f 6e20 7468 6520 7377 6570 7420  ns on the swept \n+0000ffd0: 706f 6c79 676f 6e2c 2074 6865 6e20 7468  polygon, then th\n+0000ffe0: 6520 2773 7765 6570 2720 6f70 7469 6f6e  e 'sweep' option\n+0000fff0: 730a 6172 6520 636f 7069 6564 2074 6f20  s.are copied to \n+00010000: 6561 6368 206f 7574 7075 7420 706f 6c79  each output poly\n+00010010: 676f 6e2e 2020 4966 2074 6865 2073 7765  gon.  If the swe\n+00010020: 7074 2070 6f6c 7967 6f6e 2064 6f65 7320  pt polygon does \n+00010030: 6861 7665 0a6f 7074 696f 6e73 2c20 7468  have.options, th\n+00010040: 6573 6520 6172 6520 636f 7069 6564 2074  ese are copied t\n+00010050: 6f20 7468 6520 656e 6473 3b20 7468 6520  o the ends; the \n+00010060: 7377 6565 7020 6f70 7469 6f6e 7320 6172  sweep options ar\n+00010070: 6520 636f 7069 6564 2074 6f0a 7468 6520  e copied to.the \n+00010080: 626f 6479 2070 6f6c 7967 6f6e 732e 2020  body polygons.  \n+00010090: 496e 2074 6869 7320 6d61 6e6e 6572 2c20  In this manner, \n+000100a0: 626f 6479 2061 6e64 2065 6e64 7320 6d61  body and ends ma\n+000100b0: 7920 6265 2064 7261 776e 2077 6974 680a  y be drawn with.\n+000100c0: 6469 6666 6572 656e 7420 6368 6172 6163  different charac\n+000100d0: 7465 7269 7374 6963 7320 7375 6368 2061  teristics such a\n+000100e0: 7320 2766 696c 6c63 6f6c 6f72 272e 0a0a  s 'fillcolor'...\n+000100f0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n+00010100: 6e66 6f2c 2020 4e6f 6465 3a20 5377 6570  nfo,  Node: Swep\n+00010110: 7420 626c 6f63 6b73 2c20 204e 6578 743a  t blocks,  Next:\n+00010120: 2053 7765 6570 2066 6163 6520 7370 6c69   Sweep face spli\n+00010130: 7474 696e 672c 2020 5072 6576 3a20 5377  tting,  Prev: Sw\n+00010140: 6570 7420 706f 6c79 676f 6e73 2c20 2055  ept polygons,  U\n+00010150: 703a 2053 7765 6570 730a 0a33 2e32 2e36  p: Sweeps..3.2.6\n+00010160: 2e34 2053 7765 7074 2062 6c6f 636b 730a  .4 Swept blocks.\n+00010170: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+00010180: 2e2e 2e2e 0a0a 5468 6520 7377 6570 7420  ......The swept \n+00010190: 6f62 6a65 6374 2053 5745 5054 5f4f 424a  object SWEPT_OBJ\n+000101a0: 4543 5420 6d61 7920 616c 736f 2062 6520  ECT may also be \n+000101b0: 616e 7920 636f 6c6c 6563 7469 6f6e 206f  any collection o\n+000101c0: 6620 706f 6c79 6c69 6e65 730a 616e 6420  f polylines.and \n+000101d0: 706f 6c79 676f 6e73 2e20 2054 6869 7320  polygons.  This \n+000101e0: 6d61 7920 6265 2061 2062 6c6f 636b 2063  may be a block c\n+000101f0: 6f6d 706f 7365 6420 6f66 2027 6c69 6e65  omposed of 'line\n+00010200: 2720 616e 642f 6f72 2027 706f 6c79 676f  ' and/or 'polygo\n+00010210: 6e27 0a63 6f6d 6d61 6e64 7320 696e 2062  n'.commands in b\n+00010220: 7261 6365 7320 277b 207d 272c 206f 7220  races '{ }', or \n+00010230: 6974 206d 6179 2062 6520 7468 6520 7265  it may be the re\n+00010240: 7375 6c74 206f 6620 6120 2772 6570 6561  sult of a 'repea\n+00010250: 7427 2c20 616e 6f74 6865 720a 2773 7765  t', another.'swe\n+00010260: 6570 272c 2065 7463 2e20 2054 6865 2073  ep', etc.  The s\n+00010270: 7765 6570 2061 6374 7320 696e 6465 7065  weep acts indepe\n+00010280: 6e64 656e 746c 7920 6f6e 2065 6163 6820  ndently on each \n+00010290: 6f62 6a65 6374 2069 6e20 7468 6520 626c  object in the bl\n+000102a0: 6f63 6b0a 6578 6163 746c 7920 6173 2069  ock.exactly as i\n+000102b0: 6620 6974 2077 6572 6520 6120 7369 6e67  f it were a sing\n+000102c0: 6c65 2073 7765 7074 206f 626a 6563 7420  le swept object \n+000102d0: 6465 7363 7269 6265 6420 6162 6f76 6520  described above \n+000102e0: 696e 202a 6e6f 7465 0a53 7765 7074 206c  in *note.Swept l\n+000102f0: 696e 6573 3a3a 2061 6e64 202a 6e6f 7465  ines:: and *note\n+00010300: 2053 7765 7074 2070 6f6c 7967 6f6e 733a   Swept polygons:\n+00010310: 3a2e 0a0a 1f0a 4669 6c65 3a20 736b 6574  :.....File: sket\n+00010320: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n+00010330: 5377 6565 7020 6661 6365 2073 706c 6974  Sweep face split\n+00010340: 7469 6e67 2c20 2050 7265 763a 2053 7765  ting,  Prev: Swe\n+00010350: 7074 2062 6c6f 636b 732c 2020 5570 3a20  pt blocks,  Up: \n+00010360: 5377 6565 7073 0a0a 332e 322e 362e 3520  Sweeps..3.2.6.5 \n+00010370: 5377 6565 7020 6661 6365 2073 706c 6974  Sweep face split\n+00010380: 7469 6e67 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e  ting............\n 00010390: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n-000103a0: 2e2e 2e0a 0a42 6566 6f72 6520 7365 6e64  .....Before send\n-000103b0: 696e 6720 6561 6368 2066 6f75 722d 7369  ing each four-si\n-000103c0: 6465 6420 626f 6479 2070 6f6c 7967 6f6e  ded body polygon\n-000103d0: 206f 6620 6120 2773 7765 6570 2720 746f   of a 'sweep' to\n-000103e0: 2074 6865 206f 7574 7075 742c 0a27 736b   the output,.'sk\n-000103f0: 6574 6368 2720 7465 7374 7320 746f 2073  etch' tests to s\n-00010400: 6565 2069 6620 6974 2069 7320 726f 7567  ee if it is roug\n-00010410: 686c 7920 706c 616e 6172 2e20 2053 696e  hly planar.  Sin\n-00010420: 6365 2070 6c61 6e61 7269 7479 2069 730a  ce planarity is.\n-00010430: 6e65 6365 7373 6172 7920 666f 7220 7072  necessary for pr\n-00010440: 6f70 6572 2066 756e 6374 696f 6e69 6e67  oper functioning\n-00010450: 206f 6620 7468 6520 6869 6464 656e 2073   of the hidden s\n-00010460: 7572 6661 6365 2061 6c67 6f72 6974 686d  urface algorithm\n-00010470: 2c0a 2277 6172 7065 6422 2070 6f6c 7967  ,.\"warped\" polyg\n-00010480: 6f6e 7320 6172 6520 6175 746f 6d61 7469  ons are automati\n-00010490: 6361 6c6c 7920 7370 6c69 7420 696e 746f  cally split into\n-000104a0: 2074 776f 2074 7269 616e 676c 6573 2e0a   two triangles..\n-000104b0: 0a20 2020 486f 6c65 2d66 696c 6c69 6e67  .   Hole-filling\n-000104c0: 2070 6f6c 7967 6f6e 7320 7072 6f64 7563   polygons produc\n-000104d0: 6564 2062 7920 636c 6f73 7572 652d 7461  ed by closure-ta\n-000104e0: 6767 6564 206c 696e 6520 7377 6565 7073  gged line sweeps\n-000104f0: 2061 7265 206e 6f74 0a73 706c 6974 2e20   are not.split. \n-00010500: 204e 6f72 2061 7265 206f 7269 6769 6e61   Nor are origina\n-00010510: 6c20 706f 6c79 676f 6e73 2069 6e20 706f  l polygons in po\n-00010520: 6c79 676f 6e20 7377 6565 7073 2e20 2049  lygon sweeps.  I\n-00010530: 7420 6973 2074 6865 2075 7365 7227 730a  t is the user's.\n-00010540: 7265 7370 6f6e 7369 6269 6c69 7479 2074  responsibility t\n-00010550: 6f20 656e 7375 7265 2074 6865 7365 2061  o ensure these a\n-00010560: 7265 2070 6c61 6e61 722e 0a0a 1f0a 4669  re planar.....Fi\n-00010570: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n-00010580: 2020 4e6f 6465 3a20 426c 6f63 6b73 2c20    Node: Blocks, \n-00010590: 204e 6578 743a 2052 6570 6561 7473 2c20   Next: Repeats, \n-000105a0: 2050 7265 763a 2053 7765 6570 732c 2020   Prev: Sweeps,  \n-000105b0: 5570 3a20 4472 6177 6162 6c65 730a 0a33  Up: Drawables..3\n-000105c0: 2e32 2e37 2042 6c6f 636b 730a 2d2d 2d2d  .2.7 Blocks.----\n-000105d0: 2d2d 2d2d 2d2d 2d2d 0a0a 416e 7920 7365  --------..Any se\n-000105e0: 7175 656e 6365 206f 6620 6472 6177 6162  quence of drawab\n-000105f0: 6c65 7320 6d61 7920 6265 2067 726f 7570  les may be group\n-00010600: 6564 2069 6e20 6120 2262 6c6f 636b 2220  ed in a \"block\" \n-00010610: 6d65 7265 6c79 2062 790a 656e 636c 6f73  merely by.enclos\n-00010620: 696e 6720 7468 656d 2069 6e20 6272 6163  ing them in brac\n-00010630: 6573 2027 7b20 7d27 2e20 2041 2062 6c6f  es '{ }'.  A blo\n-00010640: 636b 2069 7320 6974 7365 6c66 2064 7261  ck is itself dra\n-00010650: 7761 626c 652e 2020 4120 6b65 7920 7573  wable.  A key us\n-00010660: 650a 6f66 2062 6c6f 636b 7320 6973 2074  e.of blocks is t\n-00010670: 6f20 6578 7465 6e64 2074 6865 2065 6666  o extend the eff\n-00010680: 6563 7420 6f66 2061 2073 696e 676c 6520  ect of a single \n-00010690: 2764 6566 272c 202a 6e6f 7465 0a44 6566  'def', *note.Def\n-000106a0: 696e 6974 696f 6e73 3a3a 2c20 2770 7574  initions::, 'put\n-000106b0: 2720 2a6e 6f74 6520 5075 7473 3a3a 2c20  ' *note Puts::, \n-000106c0: 2773 7765 6570 2720 2a6e 6f74 6520 5377  'sweep' *note Sw\n-000106d0: 6565 7073 3a3a 2c20 6f72 2027 7265 7065  eeps::, or 'repe\n-000106e0: 6174 270a 2a6e 6f74 6520 5265 7065 6174  at'.*note Repeat\n-000106f0: 733a 3a20 746f 2069 6e63 6c75 6465 2073  s:: to include s\n-00010700: 6576 6572 616c 206f 626a 6563 7473 2072  everal objects r\n-00010710: 6174 6865 7220 7468 616e 206f 6e65 2e0a  ather than one..\n-00010720: 0a20 2020 4465 6669 6e69 7469 6f6e 7320  .   Definitions \n-00010730: 282a 4e6f 7465 2044 6566 696e 6974 696f  (*Note Definitio\n-00010740: 6e73 3a3a 2e29 2020 696e 7369 6465 2061  ns::.)  inside a\n-00010750: 2062 6c6f 636b 2068 6176 6520 226c 6578   block have \"lex\n-00010760: 6963 616c 0a73 636f 7065 2220 6578 7465  ical.scope\" exte\n-00010770: 6e64 696e 6720 6672 6f6d 2074 6865 2070  nding from the p\n-00010780: 6c61 6365 206f 6620 6465 6669 6e69 7469  lace of definiti\n-00010790: 6f6e 2074 6f20 7468 6520 656e 6420 6f66  on to the end of\n-000107a0: 2074 6865 2062 6c6f 636b 2e0a 0a1f 0a46   the block.....F\n-000107b0: 696c 653a 2073 6b65 7463 682e 696e 666f  ile: sketch.info\n-000107c0: 2c20 204e 6f64 653a 2052 6570 6561 7473  ,  Node: Repeats\n-000107d0: 2c20 204e 6578 743a 2050 7574 732c 2020  ,  Next: Puts,  \n-000107e0: 5072 6576 3a20 426c 6f63 6b73 2c20 2055  Prev: Blocks,  U\n-000107f0: 703a 2044 7261 7761 626c 6573 0a0a 332e  p: Drawables..3.\n-00010800: 322e 3820 5265 7065 6174 730a 2d2d 2d2d  2.8 Repeats.----\n-00010810: 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74  ---------..*Synt\n-00010820: 6178 3a2a 0a20 2020 2020 7265 7065 6174  ax:*.     repeat\n-00010830: 207b 204e 2c20 545f 312c 2054 5f32 2c20   { N, T_1, T_2, \n-00010840: 2e2e 2e2c 2054 5f52 207d 2052 4550 4541  ..., T_R } REPEA\n-00010850: 5445 445f 4f42 4a45 4354 0a54 6865 2072  TED_OBJECT.The r\n-00010860: 6570 6561 7420 6d61 6b65 7320 4e20 7472  epeat makes N tr\n-00010870: 616e 7366 6f72 6d65 6420 636f 7069 6573  ansformed copies\n-00010880: 206f 6620 5245 5045 4154 4544 5f4f 424a   of REPEATED_OBJ\n-00010890: 4543 5420 2869 6e63 6c75 6469 6e67 2074  ECT (including t\n-000108a0: 6865 0a6f 7269 6769 6e61 6c29 2e20 2054  he.original).  T\n-000108b0: 6865 2054 5f49 2061 7265 2074 7261 6e73  he T_I are trans\n-000108c0: 666f 726d 732e 2020 5468 6520 6b27 7468  forms.  The k'th\n-000108d0: 2063 6f70 7920 6f66 2074 6865 0a52 4550   copy of the.REP\n-000108e0: 4541 5445 445f 4f42 4a45 4354 2028 666f  EATED_OBJECT (fo\n-000108f0: 7220 6b3d 302c 312c 2e2e 2e2c 6e2d 3129  r k=0,1,...,n-1)\n-00010900: 2069 7320 7072 6f64 7563 6564 2069 6e20   is produced in \n-00010910: 7468 6520 7361 6d65 206d 616e 6e65 7220  the same manner \n-00010920: 6173 0a66 6f72 2027 7377 6565 7027 7320  as.for 'sweep's \n-00010930: 6465 7363 7269 6265 6420 696e 202a 6e6f  described in *no\n-00010940: 7465 2053 7765 6570 733a 3a2e 2020 5468  te Sweeps::.  Th\n-00010950: 6973 2069 7320 7265 7065 6174 6564 2068  is is repeated h\n-00010960: 6572 6520 286e 6f20 7075 6e0a 696e 7465  ere (no pun.inte\n-00010970: 6e64 6564 2920 666f 7220 636f 6e76 656e  nded) for conven\n-00010980: 6965 6e63 652e 2020 546f 206d 616b 6520  ience.  To make \n-00010990: 7468 6520 6b27 7468 2063 6f70 792c 2074  the k'th copy, t\n-000109a0: 6865 2066 6f6c 6c6f 7769 6e67 0a74 7261  he following.tra\n-000109b0: 6e73 666f 726d 2069 7320 6170 706c 6965  nsform is applie\n-000109c0: 6420 746f 2074 6865 206f 7269 6769 6e61  d to the origina\n-000109d0: 6c20 6f62 6a65 6374 2e0a 2020 2020 2054  l object..     T\n-000109e0: 5f31 5e6b 2074 6865 6e20 545f 325e 6b20  _1^k then T_2^k \n-000109f0: 7468 656e 202e 2e2e 2074 6865 6e20 545f  then ... then T_\n-00010a00: 525e 6b0a 4865 7265 2054 5e6b 206d 6561  R^k.Here T^k mea\n-00010a10: 6e73 2022 7472 616e 7366 6f72 6d20 5420  ns \"transform T \n-00010a20: 6170 706c 6965 6420 6b20 7469 6d65 732e  applied k times.\n-00010a30: 220a 0a1f 0a46 696c 653a 2073 6b65 7463  \"....File: sketc\n-00010a40: 682e 696e 666f 2c20 204e 6f64 653a 2050  h.info,  Node: P\n-00010a50: 7574 732c 2020 5072 6576 3a20 5265 7065  uts,  Prev: Repe\n-00010a60: 6174 732c 2020 5570 3a20 4472 6177 6162  ats,  Up: Drawab\n-00010a70: 6c65 730a 0a33 2e32 2e39 2050 7574 730a  les..3.2.9 Puts.\n-00010a80: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e  ----------..*Syn\n-00010a90: 7461 783a 2a0a 2020 2020 2070 7574 207b  tax:*.     put {\n-00010aa0: 2054 207d 2050 5554 5f4f 424a 4543 540a   T } PUT_OBJECT.\n-00010ab0: 5075 7420 6d65 7265 6c79 2061 7070 6c69  Put merely appli\n-00010ac0: 6573 2074 7261 6e73 666f 726d 2054 2074  es transform T t\n-00010ad0: 6f20 7468 6520 6472 6177 6162 6c65 2050  o the drawable P\n-00010ae0: 5554 5f4f 424a 4543 542e 0a0a 1f0a 4669  UT_OBJECT.....Fi\n-00010af0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n-00010b00: 2020 4e6f 6465 3a20 4465 6669 6e69 7469    Node: Definiti\n-00010b10: 6f6e 732c 2020 4e65 7874 3a20 476c 6f62  ons,  Next: Glob\n-00010b20: 616c 2065 6e76 6972 6f6e 6d65 6e74 2c20  al environment, \n-00010b30: 2050 7265 763a 2044 7261 7761 626c 6573   Prev: Drawables\n-00010b40: 2c20 2055 703a 2049 6e70 7574 206c 616e  ,  Up: Input lan\n-00010b50: 6775 6167 650a 0a33 2e33 2044 6566 696e  guage..3.3 Defin\n-00010b60: 6974 696f 6e73 0a3d 3d3d 3d3d 3d3d 3d3d  itions.=========\n-00010b70: 3d3d 3d3d 3d3d 0a0a 4465 6669 6e69 7469  ======..Definiti\n-00010b80: 6f6e 7320 6769 7665 206e 616d 6573 2074  ons give names t\n-00010b90: 6f20 2773 6b65 7463 6827 206f 626a 6563  o 'sketch' objec\n-00010ba0: 7473 2e20 2044 6566 696e 6974 696f 6e73  ts.  Definitions\n-00010bb0: 2061 6c6f 6e65 2061 7265 0a62 656e 6967   alone are.benig\n-00010bc0: 6e2e 2020 4120 2773 6b65 7463 6827 2069  n.  A 'sketch' i\n-00010bd0: 6e70 7574 2066 696c 6520 636f 6e73 6973  nput file consis\n-00010be0: 7469 6e67 2065 6e74 6972 656c 7920 6f66  ting entirely of\n-00010bf0: 2064 6566 696e 6974 696f 6e73 2077 696c   definitions wil\n-00010c00: 6c0a 6765 6e65 7261 7465 206e 6f20 6472  l.generate no dr\n-00010c10: 6177 696e 672e 2020 4f6e 6c79 2077 6865  awing.  Only whe\n-00010c20: 6e20 6465 6669 6e69 7469 6f6e 7320 6172  n definitions ar\n-00010c30: 6520 2272 6566 6572 656e 6365 6422 2064  e \"referenced\" d\n-00010c40: 6f20 7468 6579 0a70 6f74 656e 7469 616c  o they.potential\n-00010c50: 6c79 206c 6561 6420 746f 2069 6e6b 206f  ly lead to ink o\n-00010c60: 6e20 7468 6520 6472 6177 696e 672e 0a0a  n the drawing...\n-00010c70: 2020 2054 6865 2069 6e74 656e 7420 6f66     The intent of\n-00010c80: 2064 6566 696e 6974 696f 6e73 2069 7320   definitions is \n-00010c90: 746f 206d 616b 6520 2773 6b65 7463 6827  to make 'sketch'\n-00010ca0: 2063 6f64 6520 6d6f 7265 2063 6f6e 6369   code more conci\n-00010cb0: 7365 2061 6e64 0a72 6561 6461 626c 652e  se and.readable.\n-00010cc0: 2020 5468 6572 6520 6973 206e 6f20 696e    There is no in\n-00010cd0: 7075 7420 6669 6c65 2065 6d70 6c6f 7969  put file employi\n-00010ce0: 6e67 2064 6566 696e 6974 696f 6e73 2074  ng definitions t\n-00010cf0: 6861 7420 636f 756c 6420 6e6f 740a 6265  hat could not.be\n-00010d00: 2072 652d 7772 6974 7465 6e20 7769 7468   re-written with\n-00010d10: 6f75 7420 7468 656d 2e0a 0a20 2020 4465  out them...   De\n-00010d20: 6669 6e61 626c 6520 6f62 6a65 6374 7320  finable objects \n-00010d30: 696e 636c 7564 6520 616e 7920 7265 7375  include any resu\n-00010d40: 6c74 206f 6620 616e 2061 6666 696e 6520  lt of an affine \n-00010d50: 6172 6974 686d 6574 6963 0a65 7870 7265  arithmetic.expre\n-00010d60: 7373 696f 6e20 2873 6361 6c61 722c 2070  ssion (scalar, p\n-00010d70: 6f69 6e74 2c20 7665 6374 6f72 2c20 6f72  oint, vector, or\n-00010d80: 2074 7261 6e73 666f 726d 292c 2061 6e79   transform), any\n-00010d90: 2064 7261 7761 626c 6520 6f62 6a65 6374   drawable object\n-00010da0: 0a28 646f 7473 2c20 6c69 6e65 2c20 6375  .(dots, line, cu\n-00010db0: 7276 652c 2070 6f6c 7967 6f6e 2c20 626c  rve, polygon, bl\n-00010dc0: 6f63 6b2c 2073 7765 6570 2c20 7075 742c  ock, sweep, put,\n-00010dd0: 2072 6570 6561 742c 206f 7220 7370 6563   repeat, or spec\n-00010de0: 6961 6c29 2c20 616e 640a 6f70 7469 6f6e  ial), and.option\n-00010df0: 2073 7472 696e 6773 2e20 2049 6e20 6164   strings.  In ad\n-00010e00: 6469 7469 6f6e 2c20 2274 6167 2064 6566  dition, \"tag def\n-00010e10: 696e 6974 696f 6e73 222c 2077 6869 6368  initions\", which\n-00010e20: 2068 6176 6520 6e6f 0a61 7373 6f63 6961   have no.associa\n-00010e30: 7465 6420 6f62 6a65 6374 2061 7420 616c  ted object at al\n-00010e40: 6c2c 2061 6c6c 6f77 2074 6865 206d 6561  l, allow the mea\n-00010e50: 6e69 6e67 206f 6620 6f74 6865 7220 6465  ning of other de\n-00010e60: 6669 6e69 7469 6f6e 7320 746f 2062 650a  finitions to be.\n-00010e70: 7365 6c65 6374 6564 2066 726f 6d20 6120  selected from a \n-00010e80: 7365 7420 6f66 2061 6c74 6572 6e61 7469  set of alternati\n-00010e90: 7665 732e 2020 5369 6e63 6520 7461 6773  ves.  Since tags\n-00010ea0: 206d 6179 2062 6520 6465 6669 6e65 6420   may be defined \n-00010eb0: 2861 6e64 0a75 6e64 6566 696e 6564 2920  (and.undefined) \n-00010ec0: 696e 2074 6865 2063 6f6d 6d61 6e64 206c  in the command l\n-00010ed0: 696e 6520 6f66 2027 736b 6574 6368 272c  ine of 'sketch',\n-00010ee0: 2074 6865 7920 6361 6e20 6265 2061 6e20   they can be an \n-00010ef0: 6169 6420 696e 2074 6865 0a73 6372 6970  aid in the.scrip\n-00010f00: 742d 6472 6976 656e 2070 7265 7061 7261  t-driven prepara\n-00010f10: 7469 6f6e 206f 6620 646f 6375 6d65 6e74  tion of document\n-00010f20: 732e 0a0a 2a20 4d65 6e75 3a0a 0a2a 2046  s...* Menu:..* F\n-00010f30: 6f72 6d73 206f 6620 6465 6669 6e69 7469  orms of definiti\n-00010f40: 6f6e 733a 3a20 2020 2020 2020 2044 6966  ons::        Dif\n-00010f50: 6665 7265 6e74 2064 6566 7320 666f 7220  ferent defs for \n-00010f60: 6469 6666 6572 656e 7420 7075 7270 6f73  different purpos\n-00010f70: 6573 2e0a 2a20 466f 726d 7320 6f66 2072  es..* Forms of r\n-00010f80: 6566 6572 656e 6365 733a 3a20 2020 2020  eferences::     \n-00010f90: 2020 2020 486f 7720 7265 6665 7265 6e63      How referenc\n-00010fa0: 6573 2064 656e 6f74 6520 7479 7065 732e  es denote types.\n-00010fb0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n-00010fc0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 466f  .info,  Node: Fo\n-00010fd0: 726d 7320 6f66 2064 6566 696e 6974 696f  rms of definitio\n-00010fe0: 6e73 2c20 204e 6578 743a 2046 6f72 6d73  ns,  Next: Forms\n-00010ff0: 206f 6620 7265 6665 7265 6e63 6573 2c20   of references, \n-00011000: 2050 7265 763a 2044 6566 696e 6974 696f   Prev: Definitio\n-00011010: 6e73 2c20 2055 703a 2044 6566 696e 6974  ns,  Up: Definit\n-00011020: 696f 6e73 0a0a 332e 332e 3120 466f 726d  ions..3.3.1 Form\n-00011030: 7320 6f66 2064 6566 696e 6974 696f 6e73  s of definitions\n-00011040: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  .---------------\n-00011050: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a44 6566  -----------..Def\n-00011060: 696e 6974 696f 6e73 2068 6176 6520 7468  initions have th\n-00011070: 7265 6520 706f 7373 6962 6c65 2066 6f72  ree possible for\n-00011080: 6d73 2c20 2273 696d 706c 6522 2c20 2277  ms, \"simple\", \"w\n-00011090: 6974 6820 616c 7465 726e 6174 6976 6573  ith alternatives\n-000110a0: 222c 0a61 6e64 2022 7461 6722 2061 7320  \",.and \"tag\" as \n-000110b0: 7368 6f77 6e20 6865 7265 2069 6e20 6f72  shown here in or\n-000110c0: 6465 722e 0a0a 2a53 796e 7461 783a 2a0a  der...*Syntax:*.\n-000110d0: 2020 2020 2064 6566 2049 4420 4f42 4a45       def ID OBJE\n-000110e0: 4354 2020 2520 7369 6d70 6c65 2064 6566  CT  % simple def\n-000110f0: 0a20 2020 2020 6465 6620 4944 203c 5441  .     def ID <TA\n-00011100: 475f 313e 204f 424a 4543 545f 3120 2025  G_1> OBJECT_1  %\n-00011110: 2064 6566 2077 6974 6820 616c 7465 726e   def with altern\n-00011120: 6174 6976 6573 0a20 2020 2020 2020 2020  atives.         \n-00011130: 2020 203c 5441 475f 323e 204f 424a 4543     <TAG_2> OBJEC\n-00011140: 545f 320a 2020 2020 2020 2020 2020 2020  T_2.            \n-00011150: 2e2e 2e0a 2020 2020 2020 2020 2020 2020  ....            \n-00011160: 3c3e 2044 4546 4155 4c54 5f4f 424a 4543  <> DEFAULT_OBJEC\n-00011170: 540a 2020 2020 2064 6566 2049 4420 3c3e  T.     def ID <>\n-00011180: 2020 2520 7461 6720 6465 660a 5468 6520    % tag def.The \n-00011190: 7369 6d70 6c65 2064 6566 696e 6974 696f  simple definitio\n-000111a0: 6e20 6d65 7265 6c79 2061 7373 6f63 6961  n merely associa\n-000111b0: 7465 7320 4f42 4a45 4354 2077 6974 6820  tes OBJECT with \n-000111c0: 7468 6520 6964 656e 7469 6669 6572 2049  the identifier I\n-000111d0: 442e 0a0a 2020 2054 6865 2064 6566 696e  D...   The defin\n-000111e0: 6974 696f 6e20 7769 7468 2061 6c74 6572  ition with alter\n-000111f0: 6e61 7469 7665 7320 6173 736f 6369 6174  natives associat\n-00011200: 6573 204f 424a 4543 545f 4920 7769 7468  es OBJECT_I with\n-00011210: 2049 442c 2077 6865 7265 0a54 4147 5f49   ID, where.TAG_I\n-00011220: 2069 7320 7468 6520 6669 7273 7420 6465   is the first de\n-00011230: 6669 6e65 6420 7461 6720 696e 2074 6865  fined tag in the\n-00011240: 206c 6973 7420 6f66 2061 6c74 6572 6e61   list of alterna\n-00011250: 7469 7665 2074 6167 0a72 6566 6572 656e  tive tag.referen\n-00011260: 6365 732e 2020 4966 206e 6f20 7461 6720  ces.  If no tag \n-00011270: 696e 2074 6865 206c 6973 7420 6973 2064  in the list is d\n-00011280: 6566 696e 6564 2c20 7468 656e 2044 4546  efined, then DEF\n-00011290: 4155 4c54 5f4f 424a 4543 5420 6973 0a61  AULT_OBJECT is.a\n-000112a0: 7373 6f63 6961 7465 6420 7769 7468 2069  ssociated with i\n-000112b0: 6465 6e74 6966 6965 7220 4944 2e0a 0a20  dentifier ID... \n-000112c0: 2020 5468 6520 6669 6e61 6c20 666f 726d    The final form\n-000112d0: 2064 6566 696e 6573 2049 4420 6173 2061   defines ID as a\n-000112e0: 2074 6167 2e20 2041 6e6f 7468 6572 2077   tag.  Another w\n-000112f0: 6179 2074 6f20 6465 6669 6e65 2061 2074  ay to define a t\n-00011300: 6167 2069 730a 7769 7468 2074 6865 2027  ag is.with the '\n-00011310: 2d44 2720 636f 6d6d 616e 6420 6c69 6e65  -D' command line\n-00011320: 206f 7074 696f 6e2e 2020 2a4e 6f74 6520   option.  *Note \n-00011330: 436f 6d6d 616e 6420 6c69 6e65 3a3a 2e0a  Command line::..\n-00011340: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n-00011350: 696e 666f 2c20 204e 6f64 653a 2046 6f72  info,  Node: For\n-00011360: 6d73 206f 6620 7265 6665 7265 6e63 6573  ms of references\n-00011370: 2c20 2050 7265 763a 2046 6f72 6d73 206f  ,  Prev: Forms o\n-00011380: 6620 6465 6669 6e69 7469 6f6e 732c 2020  f definitions,  \n-00011390: 5570 3a20 4465 6669 6e69 7469 6f6e 730a  Up: Definitions.\n-000113a0: 0a33 2e33 2e32 2046 6f72 6d73 206f 6620  .3.3.2 Forms of \n-000113b0: 7265 6665 7265 6e63 6573 0a2d 2d2d 2d2d  references.-----\n+000103a0: 2e0a 0a42 6566 6f72 6520 7365 6e64 696e  ...Before sendin\n+000103b0: 6720 6561 6368 2066 6f75 722d 7369 6465  g each four-side\n+000103c0: 6420 626f 6479 2070 6f6c 7967 6f6e 206f  d body polygon o\n+000103d0: 6620 6120 2773 7765 6570 2720 746f 2074  f a 'sweep' to t\n+000103e0: 6865 206f 7574 7075 742c 0a27 736b 6574  he output,.'sket\n+000103f0: 6368 2720 7465 7374 7320 746f 2073 6565  ch' tests to see\n+00010400: 2069 6620 6974 2069 7320 726f 7567 686c   if it is roughl\n+00010410: 7920 706c 616e 6172 2e20 2053 696e 6365  y planar.  Since\n+00010420: 2070 6c61 6e61 7269 7479 2069 730a 6e65   planarity is.ne\n+00010430: 6365 7373 6172 7920 666f 7220 7072 6f70  cessary for prop\n+00010440: 6572 2066 756e 6374 696f 6e69 6e67 206f  er functioning o\n+00010450: 6620 7468 6520 6869 6464 656e 2073 7572  f the hidden sur\n+00010460: 6661 6365 2061 6c67 6f72 6974 686d 2c0a  face algorithm,.\n+00010470: 2277 6172 7065 6422 2070 6f6c 7967 6f6e  \"warped\" polygon\n+00010480: 7320 6172 6520 6175 746f 6d61 7469 6361  s are automatica\n+00010490: 6c6c 7920 7370 6c69 7420 696e 746f 2074  lly split into t\n+000104a0: 776f 2074 7269 616e 676c 6573 2e0a 0a20  wo triangles... \n+000104b0: 2020 486f 6c65 2d66 696c 6c69 6e67 2070    Hole-filling p\n+000104c0: 6f6c 7967 6f6e 7320 7072 6f64 7563 6564  olygons produced\n+000104d0: 2062 7920 636c 6f73 7572 652d 7461 6767   by closure-tagg\n+000104e0: 6564 206c 696e 6520 7377 6565 7073 2061  ed line sweeps a\n+000104f0: 7265 206e 6f74 0a73 706c 6974 2e20 204e  re not.split.  N\n+00010500: 6f72 2061 7265 206f 7269 6769 6e61 6c20  or are original \n+00010510: 706f 6c79 676f 6e73 2069 6e20 706f 6c79  polygons in poly\n+00010520: 676f 6e20 7377 6565 7073 2e20 2049 7420  gon sweeps.  It \n+00010530: 6973 2074 6865 2075 7365 7227 730a 7265  is the user's.re\n+00010540: 7370 6f6e 7369 6269 6c69 7479 2074 6f20  sponsibility to \n+00010550: 656e 7375 7265 2074 6865 7365 2061 7265  ensure these are\n+00010560: 2070 6c61 6e61 722e 0a0a 1f0a 4669 6c65   planar.....File\n+00010570: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n+00010580: 4e6f 6465 3a20 426c 6f63 6b73 2c20 204e  Node: Blocks,  N\n+00010590: 6578 743a 2052 6570 6561 7473 2c20 2050  ext: Repeats,  P\n+000105a0: 7265 763a 2053 7765 6570 732c 2020 5570  rev: Sweeps,  Up\n+000105b0: 3a20 4472 6177 6162 6c65 730a 0a33 2e32  : Drawables..3.2\n+000105c0: 2e37 2042 6c6f 636b 730a 2d2d 2d2d 2d2d  .7 Blocks.------\n+000105d0: 2d2d 2d2d 2d2d 0a0a 416e 7920 7365 7175  ------..Any sequ\n+000105e0: 656e 6365 206f 6620 6472 6177 6162 6c65  ence of drawable\n+000105f0: 7320 6d61 7920 6265 2067 726f 7570 6564  s may be grouped\n+00010600: 2069 6e20 6120 2262 6c6f 636b 2220 6d65   in a \"block\" me\n+00010610: 7265 6c79 2062 790a 656e 636c 6f73 696e  rely by.enclosin\n+00010620: 6720 7468 656d 2069 6e20 6272 6163 6573  g them in braces\n+00010630: 2027 7b20 7d27 2e20 2041 2062 6c6f 636b   '{ }'.  A block\n+00010640: 2069 7320 6974 7365 6c66 2064 7261 7761   is itself drawa\n+00010650: 626c 652e 2020 4120 6b65 7920 7573 650a  ble.  A key use.\n+00010660: 6f66 2062 6c6f 636b 7320 6973 2074 6f20  of blocks is to \n+00010670: 6578 7465 6e64 2074 6865 2065 6666 6563  extend the effec\n+00010680: 7420 6f66 2061 2073 696e 676c 6520 2764  t of a single 'd\n+00010690: 6566 272c 202a 6e6f 7465 0a44 6566 696e  ef', *note.Defin\n+000106a0: 6974 696f 6e73 3a3a 2c20 2770 7574 2720  itions::, 'put' \n+000106b0: 2a6e 6f74 6520 5075 7473 3a3a 2c20 2773  *note Puts::, 's\n+000106c0: 7765 6570 2720 2a6e 6f74 6520 5377 6565  weep' *note Swee\n+000106d0: 7073 3a3a 2c20 6f72 2027 7265 7065 6174  ps::, or 'repeat\n+000106e0: 270a 2a6e 6f74 6520 5265 7065 6174 733a  '.*note Repeats:\n+000106f0: 3a20 746f 2069 6e63 6c75 6465 2073 6576  : to include sev\n+00010700: 6572 616c 206f 626a 6563 7473 2072 6174  eral objects rat\n+00010710: 6865 7220 7468 616e 206f 6e65 2e0a 0a20  her than one... \n+00010720: 2020 4465 6669 6e69 7469 6f6e 7320 282a    Definitions (*\n+00010730: 4e6f 7465 2044 6566 696e 6974 696f 6e73  Note Definitions\n+00010740: 3a3a 2e29 2020 696e 7369 6465 2061 2062  ::.)  inside a b\n+00010750: 6c6f 636b 2068 6176 6520 226c 6578 6963  lock have \"lexic\n+00010760: 616c 0a73 636f 7065 2220 6578 7465 6e64  al.scope\" extend\n+00010770: 696e 6720 6672 6f6d 2074 6865 2070 6c61  ing from the pla\n+00010780: 6365 206f 6620 6465 6669 6e69 7469 6f6e  ce of definition\n+00010790: 2074 6f20 7468 6520 656e 6420 6f66 2074   to the end of t\n+000107a0: 6865 2062 6c6f 636b 2e0a 0a1f 0a46 696c  he block.....Fil\n+000107b0: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n+000107c0: 204e 6f64 653a 2052 6570 6561 7473 2c20   Node: Repeats, \n+000107d0: 204e 6578 743a 2050 7574 732c 2020 5072   Next: Puts,  Pr\n+000107e0: 6576 3a20 426c 6f63 6b73 2c20 2055 703a  ev: Blocks,  Up:\n+000107f0: 2044 7261 7761 626c 6573 0a0a 332e 322e   Drawables..3.2.\n+00010800: 3820 5265 7065 6174 730a 2d2d 2d2d 2d2d  8 Repeats.------\n+00010810: 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178  -------..*Syntax\n+00010820: 3a2a 0a20 2020 2020 7265 7065 6174 207b  :*.     repeat {\n+00010830: 204e 2c20 545f 312c 2054 5f32 2c20 2e2e   N, T_1, T_2, ..\n+00010840: 2e2c 2054 5f52 207d 2052 4550 4541 5445  ., T_R } REPEATE\n+00010850: 445f 4f42 4a45 4354 0a54 6865 2072 6570  D_OBJECT.The rep\n+00010860: 6561 7420 6d61 6b65 7320 4e20 7472 616e  eat makes N tran\n+00010870: 7366 6f72 6d65 6420 636f 7069 6573 206f  sformed copies o\n+00010880: 6620 5245 5045 4154 4544 5f4f 424a 4543  f REPEATED_OBJEC\n+00010890: 5420 2869 6e63 6c75 6469 6e67 2074 6865  T (including the\n+000108a0: 0a6f 7269 6769 6e61 6c29 2e20 2054 6865  .original).  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To make th\n+00010990: 6520 6b27 7468 2063 6f70 792c 2074 6865  e k'th copy, the\n+000109a0: 2066 6f6c 6c6f 7769 6e67 0a74 7261 6e73   following.trans\n+000109b0: 666f 726d 2069 7320 6170 706c 6965 6420  form is applied \n+000109c0: 746f 2074 6865 206f 7269 6769 6e61 6c20  to the original \n+000109d0: 6f62 6a65 6374 2e0a 2020 2020 2054 5f31  object..     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Det\n-00011660: 6169 6c73 206f 6620 2773 6b65 7463 6827  ails of 'sketch'\n-00011670: 2073 796e 7461 7820 6d61 6b65 2069 7420   syntax make it \n-00011680: 696d 706f 7373 6962 6c65 2066 6f72 2074  impossible for t\n-00011690: 6865 7365 2074 776f 0a72 6566 6572 656e  hese two.referen\n-000116a0: 6365 2074 7970 6573 2074 6f20 6265 2063  ce types to be c\n-000116b0: 6f6e 6675 7365 642e 2020 5468 6520 7370  onfused.  The sp\n-000116c0: 6563 6961 6c20 6d75 6c74 6970 6c65 2072  ecial multiple r\n-000116d0: 6566 6572 656e 6365 0a27 5b49 4431 2c49  eference.'[ID1,I\n-000116e0: 4432 2c2e 2e2e 2c49 444e 5d27 2061 6374  D2,...,IDN]' act\n-000116f0: 7320 6173 2069 6620 7468 6520 7265 7370  s as if the resp\n-00011700: 6563 7469 7665 206c 6973 7473 206f 6620  ective lists of \n-00011710: 6f70 7469 6f6e 7320 7765 7265 0a63 6f6e  options were.con\n-00011720: 6361 7465 6e61 7465 642e 0a0a 1f0a 4669  catenated.....Fi\n-00011730: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n-00011740: 2020 4e6f 6465 3a20 476c 6f62 616c 2065    Node: Global e\n-00011750: 6e76 6972 6f6e 6d65 6e74 2c20 2050 7265  nvironment,  Pre\n-00011760: 763a 2044 6566 696e 6974 696f 6e73 2c20  v: Definitions, \n-00011770: 2055 703a 2049 6e70 7574 206c 616e 6775   Up: Input langu\n-00011780: 6167 650a 0a33 2e34 2047 6c6f 6261 6c20  age..3.4 Global \n-00011790: 656e 7669 726f 6e6d 656e 740a 3d3d 3d3d  environment.====\n+00011560: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 7363 616c  -----------.scal\n+00011570: 6172 2020 2020 2020 2749 4427 0a70 6f69  ar      'ID'.poi\n+00011580: 6e74 2020 2020 2020 2027 2849 4429 270a  nt       '(ID)'.\n+00011590: 7665 6374 6f72 2020 2020 2020 275b 4944  vector      '[ID\n+000115a0: 5d27 0a74 7261 6e73 666f 726d 2020 2027  ]'.transform   '\n+000115b0: 5b5b 4944 5d5d 270a 6472 6177 6162 6c65  [[ID]]'.drawable\n+000115c0: 2020 2020 277b 4944 7d27 0a6f 7074 696f      '{ID}'.optio\n+000115d0: 6e73 2020 2020 2027 5b49 445d 2720 6f72  ns     '[ID]' or\n+000115e0: 2027 5b49 4431 2c2e 2e2e 2c49 444e 5d27   '[ID1,...,IDN]'\n+000115f0: 0a74 6167 2020 2020 2020 2020 2027 3c49  .tag         '<I\n+00011600: 443e 270a 0a4e 6f74 6520 7468 6174 2073  D>'..Note that s\n+00011610: 7175 6172 6520 6272 6163 6b65 7473 2027  quare brackets '\n+00011620: 5b20 5d27 2061 7265 2075 7365 6420 626f  [ ]' are used bo\n+00011630: 7468 2066 6f72 2076 6563 746f 7220 616e  th for vector an\n+00011640: 6420 666f 7220 6f70 7469 6f6e 730a 7265  d for options.re\n+00011650: 6665 7265 6e63 6573 2e20 2044 6574 6169  ferences.  Detai\n+00011660: 6c73 206f 6620 2773 6b65 7463 6827 2073  ls of 'sketch' s\n+00011670: 796e 7461 7820 6d61 6b65 2069 7420 696d  yntax make it im\n+00011680: 706f 7373 6962 6c65 2066 6f72 2074 6865  possible for the\n+00011690: 7365 2074 776f 0a72 6566 6572 656e 6365  se two.reference\n+000116a0: 2074 7970 6573 2074 6f20 6265 2063 6f6e   types to be con\n+000116b0: 6675 7365 642e 2020 5468 6520 7370 6563  fused.  The spec\n+000116c0: 6961 6c20 6d75 6c74 6970 6c65 2072 6566  ial multiple ref\n+000116d0: 6572 656e 6365 0a27 5b49 4431 2c49 4432  erence.'[ID1,ID2\n+000116e0: 2c2e 2e2e 2c49 444e 5d27 2061 6374 7320  ,...,IDN]' acts \n+000116f0: 6173 2069 6620 7468 6520 7265 7370 6563  as if the respec\n+00011700: 7469 7665 206c 6973 7473 206f 6620 6f70  tive lists of op\n+00011710: 7469 6f6e 7320 7765 7265 0a63 6f6e 6361  tions were.conca\n+00011720: 7465 6e61 7465 642e 0a0a 1f0a 4669 6c65  tenated.....File\n+00011730: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n+00011740: 4e6f 6465 3a20 476c 6f62 616c 2065 6e76  Node: Global env\n+00011750: 6972 6f6e 6d65 6e74 2c20 2050 7265 763a  ironment,  Prev:\n+00011760: 2044 6566 696e 6974 696f 6e73 2c20 2055   Definitions,  U\n+00011770: 703a 2049 6e70 7574 206c 616e 6775 6167  p: Input languag\n+00011780: 650a 0a33 2e34 2047 6c6f 6261 6c20 656e  e..3.4 Global en\n+00011790: 7669 726f 6e6d 656e 740a 3d3d 3d3d 3d3d  vironment.======\n 000117a0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n-000117b0: 3d3d 0a0a 416e 206f 7074 696f 6e61 6c20  ==..An optional \n-000117c0: 676c 6f62 616c 2065 6e76 6972 6f6e 6d65  global environme\n-000117d0: 6e74 2062 6c6f 636b 2070 726f 7669 6465  nt block provide\n-000117e0: 7320 6120 6665 7720 7761 7973 2074 6f20  s a few ways to \n-000117f0: 6166 6665 6374 2074 6865 0a65 6e74 6972  affect the.entir\n-00011800: 6520 7363 656e 652e 2020 5468 6520 626c  e scene.  The bl\n-00011810: 6f63 6b20 6d75 7374 2061 7070 6561 7220  ock must appear \n-00011820: 6173 2074 6865 206c 6173 7420 7465 7874  as the last text\n-00011830: 2069 6e20 7468 6520 2773 6b65 7463 6827   in the 'sketch'\n-00011840: 0a69 6e70 7574 2066 696c 652e 2020 4974  .input file.  It\n-00011850: 206d 6179 2069 6e63 6c75 6465 2064 6566   may include def\n-00011860: 696e 6974 696f 6e73 2c20 6275 7420 6e6f  initions, but no\n-00011870: 7465 2074 6861 7420 7072 6576 696f 7573  te that previous\n-00011880: 0a64 6566 696e 6974 696f 6e73 2061 7420  .definitions at \n-00011890: 7468 6520 746f 7020 6c65 7665 6c20 286e  the top level (n\n-000118a0: 6f74 206e 6573 7465 6420 696e 7369 6465  ot nested inside\n-000118b0: 2062 6c6f 636b 7329 2061 7265 2061 6c73   blocks) are als\n-000118c0: 6f0a 6176 6169 6c61 626c 652e 0a0a 2a53  o.available...*S\n-000118d0: 796e 7461 783a 2a0a 2020 2020 2067 6c6f  yntax:*.     glo\n-000118e0: 6261 6c20 7b20 454e 5649 524f 4e4d 454e  bal { ENVIRONMEN\n-000118f0: 545f 5345 5454 494e 4753 207d 0a54 6865  T_SETTINGS }.The\n-00011900: 2063 6f6e 7465 6e74 7320 6f66 2045 4e56   contents of ENV\n-00011910: 4952 4f4e 4d45 4e54 5f53 4554 5449 4e47  IRONMENT_SETTING\n-00011920: 5320 6172 6520 6469 7363 7573 7365 6420  S are discussed \n-00011930: 696e 2074 6865 2073 6563 7469 6f6e 7320  in the sections \n-00011940: 7468 6174 0a66 6f6c 6c6f 772e 0a0a 2a20  that.follow...* \n-00011950: 4d65 6e75 3a0a 0a2a 2047 6c6f 6261 6c20  Menu:..* Global \n-00011960: 6f70 7469 6f6e 733a 3a20 2020 2020 2020  options::       \n-00011970: 2020 2020 2020 2041 7474 7269 6275 7465         Attribute\n-00011980: 7320 6f66 2074 6865 2065 6e74 6972 6520  s of the entire \n-00011990: 6472 6177 696e 672e 0a2a 2043 616d 6572  drawing..* Camer\n-000119a0: 613a 3a20 2020 2020 2020 2020 2020 2020  a::             \n-000119b0: 2020 2020 2020 2020 2041 2066 696e 616c           A final\n-000119c0: 2063 616d 6572 6120 7472 616e 7366 6f72   camera transfor\n-000119d0: 6d61 7469 6f6e 206f 6620 7468 6520 7363  mation of the sc\n-000119e0: 656e 652e 0a2a 2050 6963 7475 7265 2062  ene..* Picture b\n-000119f0: 6f78 3a3a 2020 2020 2020 2020 2020 2020  ox::            \n-00011a00: 2020 2020 2053 6574 7469 6e67 2074 6865       Setting the\n-00011a10: 2062 6f75 6e64 696e 6720 626f 7820 616e   bounding box an\n-00011a20: 6420 3264 2063 6c69 7070 696e 672e 0a2a  d 2d clipping..*\n-00011a30: 2046 7261 6d65 3a3a 2020 2020 2020 2020   Frame::        \n-00011a40: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n-00011a50: 6464 696e 6720 6120 626f 7820 6172 6f75  dding a box arou\n-00011a60: 6e64 2074 6865 2064 7261 7769 6e67 2e0a  nd the drawing..\n-00011a70: 2a20 4c61 6e67 7561 6765 3a3a 2020 2020  * Language::    \n-00011a80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00011a90: 5365 7474 696e 6720 7468 6520 6f75 7470  Setting the outp\n-00011aa0: 7574 206c 616e 6775 6167 652e 0a0a 1f0a  ut language.....\n-00011ab0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n-00011ac0: 6f2c 2020 4e6f 6465 3a20 476c 6f62 616c  o,  Node: Global\n-00011ad0: 206f 7074 696f 6e73 2c20 204e 6578 743a   options,  Next:\n-00011ae0: 2043 616d 6572 612c 2020 5072 6576 3a20   Camera,  Prev: \n-00011af0: 476c 6f62 616c 2065 6e76 6972 6f6e 6d65  Global environme\n-00011b00: 6e74 2c20 2055 703a 2047 6c6f 6261 6c20  nt,  Up: Global \n-00011b10: 656e 7669 726f 6e6d 656e 740a 0a33 2e34  environment..3.4\n-00011b20: 2e31 2047 6c6f 6261 6c20 6f70 7469 6f6e  .1 Global option\n-00011b30: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  s.--------------\n-00011b40: 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 783a  ------..*Syntax:\n-00011b50: 2a0a 2020 2020 2073 6574 205b 204f 5054  *.     set [ OPT\n-00011b60: 494f 4e53 205d 0a54 6865 2063 6f6e 7465  IONS ].The conte\n-00011b70: 6e74 7320 6f66 204f 5054 494f 4e53 2c20  nts of OPTIONS, \n-00011b80: 6578 6365 7074 2066 6f72 2027 736b 6574  except for 'sket\n-00011b90: 6368 2720 696e 7465 726e 616c 206f 7074  ch' internal opt\n-00011ba0: 696f 6e73 2c20 6172 650a 636f 7069 6564  ions, are.copied\n-00011bb0: 2061 732d 6973 2074 6f20 6120 5c70 7373   as-is to a \\pss\n-00011bc0: 6574 2074 6861 7420 6170 7065 6172 7320  et that appears \n-00011bd0: 6265 666f 7265 2061 6e79 7468 696e 6720  before anything \n-00011be0: 656c 7365 2069 6e20 7468 6520 6f75 7470  else in the outp\n-00011bf0: 7574 0a66 696c 652e 2020 5468 6973 2069  ut.file.  This i\n-00011c00: 7320 6120 676f 6f64 2070 6c61 6365 2074  s a good place t\n-00011c10: 6f20 7365 7420 2775 6e69 7427 2c20 6120  o set 'unit', a \n-00011c20: 6465 6661 756c 7420 276c 696e 6577 6964  default 'linewid\n-00011c30: 7468 272c 2065 7463 2e0a 0a20 2020 496e  th', etc...   In\n-00011c40: 7465 726e 616c 206f 7074 696f 6e73 2077  ternal options w\n-00011c50: 6f72 6b20 6f6e 2061 6c6c 206f 626a 6563  ork on all objec\n-00011c60: 7473 2077 6865 7265 2074 6865 7920 6d61  ts where they ma\n-00011c70: 6b65 2073 656e 7365 2e20 2054 6869 730a  ke sense.  This.\n-00011c80: 696e 636c 7564 6573 2027 6375 6c6c 2720  includes 'cull' \n-00011c90: 616e 6420 2773 706c 6974 2720 2862 7574  and 'split' (but\n-00011ca0: 206e 6f74 2027 6c61 7927 292e 2020 2a4e   not 'lay').  *N\n-00011cb0: 6f74 6520 496e 7465 726e 616c 206f 7074  ote Internal opt\n-00011cc0: 696f 6e73 3a3a 2e0a 0a1f 0a46 696c 653a  ions::.....File:\n-00011cd0: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n-00011ce0: 6f64 653a 2043 616d 6572 612c 2020 4e65  ode: Camera,  Ne\n-00011cf0: 7874 3a20 5069 6374 7572 6520 626f 782c  xt: Picture box,\n-00011d00: 2020 5072 6576 3a20 476c 6f62 616c 206f    Prev: Global o\n-00011d10: 7074 696f 6e73 2c20 2055 703a 2047 6c6f  ptions,  Up: Glo\n-00011d20: 6261 6c20 656e 7669 726f 6e6d 656e 740a  bal environment.\n-00011d30: 0a33 2e34 2e32 2043 616d 6572 610a 2d2d  .3.4.2 Camera.--\n-00011d40: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e  ----------..*Syn\n-00011d50: 7461 783a 2a0a 2020 2020 2063 616d 6572  tax:*.     camer\n-00011d60: 6120 5452 414e 5346 4f52 4d5f 4558 5052  a TRANSFORM_EXPR\n-00011d70: 4553 5349 4f4e 0a20 2020 5468 6520 5452  ESSION.   The TR\n-00011d80: 414e 5346 4f52 4d5f 4558 5052 4553 5349  ANSFORM_EXPRESSI\n-00011d90: 4f4e 2069 7320 6170 706c 6965 6420 6166  ON is applied af\n-00011da0: 7465 7220 616c 6c20 6f74 6865 7220 7472  ter all other tr\n-00011db0: 616e 7366 6f72 6d61 7469 6f6e 730a 6f66  ansformations.of\n-00011dc0: 2074 6865 2073 6365 6e65 2e20 2054 6869   the scene.  Thi\n-00011dd0: 7320 6973 2063 7572 7265 6e74 6c79 206f  s is currently o\n-00011de0: 6e6c 7920 7573 6566 756c 2066 6f72 2074  nly useful for t\n-00011df0: 7261 6e73 666f 726d 696e 6720 7468 650a  ransforming the.\n-00011e00: 626f 756e 6469 6e67 2062 6f78 2e20 202a  bounding box.  *\n-00011e10: 4e6f 7465 2050 6963 7475 7265 2062 6f78  Note Picture box\n-00011e20: 3a3a 2e20 2049 7420 7769 6c6c 2070 6c61  ::.  It will pla\n-00011e30: 7920 6120 726f 6c65 2069 6e20 616e 7920  y a role in any \n-00011e40: 6675 7475 7265 0a69 6d70 6c65 6d65 6e74  future.implement\n-00011e50: 6174 696f 6e20 6f66 2063 6c69 7070 696e  ation of clippin\n-00011e60: 672e 0a0a 1f0a 4669 6c65 3a20 736b 6574  g.....File: sket\n-00011e70: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n-00011e80: 5069 6374 7572 6520 626f 782c 2020 4e65  Picture box,  Ne\n-00011e90: 7874 3a20 4672 616d 652c 2020 5072 6576  xt: Frame,  Prev\n-00011ea0: 3a20 4361 6d65 7261 2c20 2055 703a 2047  : Camera,  Up: G\n-00011eb0: 6c6f 6261 6c20 656e 7669 726f 6e6d 656e  lobal environmen\n-00011ec0: 740a 0a33 2e34 2e33 2050 6963 7475 7265  t..3.4.3 Picture\n-00011ed0: 2062 6f78 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d   box.-----------\n-00011ee0: 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 783a  ------..*Syntax:\n-00011ef0: 2a0a 2020 2020 2070 6963 7475 7265 626f  *.     picturebo\n-00011f00: 785b 4241 5345 4c49 4e45 5d0a 2020 2020  x[BASELINE].    \n-00011f10: 2070 6963 7475 7265 626f 785b 4241 5345   picturebox[BASE\n-00011f20: 4c49 4e45 5d20 2850 3129 2850 3229 0a54  LINE] (P1)(P2).T\n-00011f30: 6865 2066 6972 7374 2066 6f72 6d20 6f66  he first form of\n-00011f40: 2027 7069 6374 7572 6562 6f78 2720 6361   'picturebox' ca\n-00011f50: 7573 6573 2061 2073 6361 6c61 7220 4241  uses a scalar BA\n-00011f60: 5345 4c49 4e45 2066 7261 6374 696f 6e20  SELINE fraction \n-00011f70: 746f 2062 650a 656d 6974 7465 6420 696e  to be.emitted in\n-00011f80: 2074 6865 2027 7073 7069 6374 7572 6527   the 'pspicture'\n-00011f90: 2065 6e76 6972 6f6e 6d65 6e74 206f 6620   environment of \n-00011fa0: 7468 6520 6f75 7470 7574 2e20 2053 6565  the output.  See\n-00011fb0: 2027 5053 5472 6963 6b73 270a 646f 6375   'PSTricks'.docu\n-00011fc0: 6d65 6e74 6174 696f 6e20 666f 7220 2770  mentation for 'p\n-00011fd0: 7370 6963 7475 7265 272e 0a0a 2020 2049  spicture'...   I\n-00011fe0: 6e20 7468 6520 7365 636f 6e64 2066 6f72  n the second for\n-00011ff0: 6d2c 2074 6865 2042 4153 454c 494e 4520  m, the BASELINE \n-00012000: 6672 6163 7469 6f6e 2069 7320 6f70 7469  fraction is opti\n-00012010: 6f6e 616c 2c20 616e 6420 7468 6520 7477  onal, and the tw\n-00012020: 6f0a 706f 696e 7473 2074 6861 7420 666f  o.points that fo\n-00012030: 6c6c 6f77 2064 6566 696e 6520 7468 6520  llow define the \n-00012040: 6469 6167 6f6e 616c 206f 6620 6120 7468  diagonal of a th\n-00012050: 7265 652d 6469 6d65 6e73 696f 6e61 6c20  ree-dimensional \n-00012060: 626f 756e 6469 6e67 0a62 6f78 2066 6f72  bounding.box for\n-00012070: 2074 6865 2063 6f6d 706c 6574 6564 2073   the completed s\n-00012080: 6365 6e65 2e20 2054 6865 2070 6172 616c  cene.  The paral\n-00012090: 6c65 6c20 7072 6f6a 6563 7469 6f6e 206f  lel projection o\n-000120a0: 6620 7468 6520 626f 756e 6469 6e67 0a62  f the bounding.b\n-000120b0: 6f78 2064 6574 6572 6d69 6e65 7320 7468  ox determines th\n-000120c0: 6520 636f 726e 6572 7320 6f66 2074 6865  e corners of the\n-000120d0: 2064 7261 7769 6e67 2773 2027 7073 7069   drawing's 'pspi\n-000120e0: 6374 7572 652a 2720 656e 7669 726f 6e6d  cture*' environm\n-000120f0: 656e 742c 0a77 6869 6368 2069 7320 7573  ent,.which is us\n-00012100: 6564 2069 6e20 706c 6163 6520 6f66 2027  ed in place of '\n-00012110: 7073 7069 6374 7572 6527 2e20 2054 6869  pspicture'.  Thi\n-00012120: 7320 6361 7573 6573 2050 6f73 7453 6372  s causes PostScr\n-00012130: 6970 7420 746f 2063 6c69 700a 7468 6520  ipt to clip.the \n-00012140: 6669 6e61 6c20 6472 6177 696e 6720 746f  final drawing to\n-00012150: 2074 6865 2062 6f75 6e64 696e 6720 626f   the bounding bo\n-00012160: 7820 696e 2032 642e 2020 4966 2074 6865  x in 2d.  If the\n-00012170: 7265 2069 7320 6120 2763 616d 6572 6127  re is a 'camera'\n-00012180: 0a73 7065 6369 6669 6564 2c20 7468 6520  .specified, the \n-00012190: 6361 6d65 7261 2074 7261 6e66 6f72 6d61  camera tranforma\n-000121a0: 7469 6f6e 2069 7320 6170 706c 6965 6420  tion is applied \n-000121b0: 746f 2074 6865 2062 6f75 6e64 696e 6720  to the bounding \n-000121c0: 626f 782c 2061 6e64 0a74 6865 2027 7073  box, and.the 'ps\n-000121d0: 7069 6374 7572 6527 2069 7320 7365 7420  picture' is set \n-000121e0: 6a75 7374 206c 6172 6765 2065 6e6f 7567  just large enoug\n-000121f0: 6820 746f 2069 6e63 6c75 6465 2074 6865  h to include the\n-00012200: 2074 7261 6e73 666f 726d 6564 2062 6f78   transformed box\n-00012210: 2e0a 0a20 2020 5768 656e 206e 6f20 626f  ...   When no bo\n-00012220: 756e 6469 6e67 2062 6f78 2069 7320 6769  unding box is gi\n-00012230: 7665 6e2c 2027 736b 6574 6368 2720 636f  ven, 'sketch' co\n-00012240: 6d70 7574 6573 206f 6e65 2061 7574 6f6d  mputes one autom\n-00012250: 6174 6963 616c 6c79 2e0a 0a1f 0a46 696c  atically.....Fil\n-00012260: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n-00012270: 204e 6f64 653a 2046 7261 6d65 2c20 204e   Node: Frame,  N\n-00012280: 6578 743a 204c 616e 6775 6167 652c 2020  ext: Language,  \n-00012290: 5072 6576 3a20 5069 6374 7572 6520 626f  Prev: Picture bo\n-000122a0: 782c 2020 5570 3a20 476c 6f62 616c 2065  x,  Up: Global e\n-000122b0: 6e76 6972 6f6e 6d65 6e74 0a0a 332e 342e  nvironment..3.4.\n-000122c0: 3420 4672 616d 650a 2d2d 2d2d 2d2d 2d2d  4 Frame.--------\n-000122d0: 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a 0a20  ---..*Syntax:*. \n-000122e0: 2020 2020 6672 616d 6520 5b4f 5054 494f      frame [OPTIO\n-000122f0: 4e53 5d0a 4361 7573 6573 2061 205c 7073  NS].Causes a \\ps\n-00012300: 6672 616d 6562 6f78 2074 6f20 7375 7272  framebox to surr\n-00012310: 6f75 6e64 2074 6865 2027 7073 7069 6374  ound the 'pspict\n-00012320: 7572 6527 2065 6e76 6972 6f6e 6d65 6e74  ure' environment\n-00012330: 2069 6e20 7468 650a 6f75 7470 7574 2e20   in the.output. \n-00012340: 2049 6620 4f50 5449 4f4e 5320 6172 6520   If OPTIONS are \n-00012350: 7072 6573 656e 742c 2074 6865 7920 6172  present, they ar\n-00012360: 6520 636f 7069 6564 2061 732d 6973 2e20  e copied as-is. \n-00012370: 204e 6f72 6d61 6c6c 7920 6f6e 650a 776f   Normally one.wo\n-00012380: 756c 6420 7761 6e74 2074 6f20 7365 7420  uld want to set \n-00012390: 276c 696e 6577 6964 7468 272c 2027 6c69  'linewidth', 'li\n-000123a0: 6e65 7374 796c 6527 2c20 276c 696e 6563  nestyle', 'linec\n-000123b0: 6f6c 6f72 272c 2065 7463 2e20 2049 660a  olor', etc.  If.\n-000123c0: 6f6d 6974 7465 642c 2074 6865 6e20 2766  omitted, then 'f\n-000123d0: 7261 6d65 7365 703d 3070 7427 2069 7320  ramesep=0pt' is \n-000123e0: 6164 6465 6420 736f 2074 6861 7420 7468  added so that th\n-000123f0: 6520 6672 616d 6520 7469 6768 746c 7920  e frame tightly \n-00012400: 6875 6773 2074 6865 0a27 7073 7069 6374  hugs the.'pspict\n-00012410: 7572 6527 2e0a 0a1f 0a46 696c 653a 2073  ure'.....File: s\n-00012420: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n-00012430: 653a 204c 616e 6775 6167 652c 2020 5072  e: Language,  Pr\n-00012440: 6576 3a20 4672 616d 652c 2020 5570 3a20  ev: Frame,  Up: \n-00012450: 476c 6f62 616c 2065 6e76 6972 6f6e 6d65  Global environme\n-00012460: 6e74 0a0a 332e 342e 3520 4c61 6e67 7561  nt..3.4.5 Langua\n-00012470: 6765 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ge.-------------\n-00012480: 2d0a 0a20 2020 2020 6c61 6e67 7561 6765  -..     language\n-00012490: 2074 696b 7a0a 2020 2020 206c 616e 6775   tikz.     langu\n-000124a0: 6167 6520 7469 6b7a 2c20 636f 6e74 6578  age tikz, contex\n-000124b0: 740a 2020 2020 206c 616e 6775 6167 6520  t.     language \n-000124c0: 7073 7472 6963 6b73 0a20 2020 2020 6c61  pstricks.     la\n-000124d0: 6e67 7561 6765 2070 7374 7269 636b 732c  nguage pstricks,\n-000124e0: 206c 6174 6578 0a53 6574 7320 7468 6520   latex.Sets the \n-000124f0: 6f75 7470 7574 206c 616e 6775 6167 6520  output language \n-00012500: 6765 6e65 7261 7465 6420 6279 2027 736b  generated by 'sk\n-00012510: 6574 6368 272e 2020 5468 6520 7365 7420  etch'.  The set \n-00012520: 6f66 206f 7074 696f 6e73 0a75 6e64 6572  of options.under\n-00012530: 7374 6f6f 6420 6279 2073 6b65 7463 6820  stood by sketch \n-00012540: 616c 736f 2063 6861 6e67 6573 2e20 2046  also changes.  F\n-00012550: 6f72 2065 7861 6d70 6c65 2c20 7468 6520  or example, the \n-00012560: 2750 5354 7269 636b 7327 206f 7074 696f  'PSTricks' optio\n-00012570: 6e0a 276c 696e 6577 6964 7468 2720 7769  n.'linewidth' wi\n-00012580: 6c6c 206e 6f74 2062 6520 7072 6f70 6572  ll not be proper\n-00012590: 6c79 2068 616e 646c 6564 2069 6620 276c  ly handled if 'l\n-000125a0: 616e 6775 6167 6527 2069 7320 7365 7420  anguage' is set \n-000125b0: 746f 2027 7469 6b7a 272e 0a53 696d 696c  to 'tikz'..Simil\n-000125c0: 6172 6c79 2c20 7468 6520 2754 696b 5a27  arly, the 'TikZ'\n-000125d0: 206f 7074 696f 6e20 276c 696e 6520 7374   option 'line st\n-000125e0: 796c 6527 2028 6e6f 7465 2074 6865 2073  yle' (note the s\n-000125f0: 7061 6365 2920 7769 6c6c 206e 6f74 2062  pace) will not b\n-00012600: 650a 7072 6f70 6572 6c79 2068 616e 646c  e.properly handl\n-00012610: 6564 2069 6620 276c 616e 6775 6167 6527  ed if 'language'\n-00012620: 2069 7320 7365 7420 746f 2027 7073 7472   is set to 'pstr\n-00012630: 6963 6b73 272e 2020 4966 206e 6f20 6c61  icks'.  If no la\n-00012640: 6e67 7561 6765 2069 730a 7370 6563 6966  nguage is.specif\n-00012650: 6965 642c 2074 6865 2064 6566 6175 6c74  ied, the default\n-00012660: 2027 7073 7472 6963 6b73 2720 6973 2075   'pstricks' is u\n-00012670: 7365 642e 0a0a 2020 2041 6e20 6f70 7469  sed...   An opti\n-00012680: 6f6e 616c 2063 6f6d 6d61 2066 6f6c 6c6f  onal comma follo\n-00012690: 7765 6420 6279 2027 6c61 7465 7827 206f  wed by 'latex' o\n-000126a0: 7220 2763 6f6e 7465 7874 2720 7370 6563  r 'context' spec\n-000126b0: 6966 6965 7320 7468 650a 6d61 6372 6f20  ifies the.macro \n-000126c0: 7061 636b 6167 6520 7468 6174 2074 6865  package that the\n-000126d0: 206f 7574 7075 7420 7368 6f75 6c64 2061   output should a\n-000126e0: 7373 756d 652e 2020 5468 6973 2061 6666  ssume.  This aff\n-000126f0: 6563 7473 2074 6865 2027 7069 6374 7572  ects the 'pictur\n-00012700: 6527 0a65 6e76 6972 6f6e 6d65 6e74 2063  e'.environment c\n-00012710: 6f6d 6d61 6e64 7320 656d 6974 7465 6420  ommands emitted \n-00012720: 616e 6420 7468 6520 646f 6375 6d65 6e74  and the document\n-00012730: 2074 656d 706c 6174 6520 7573 6564 2077   template used w\n-00012740: 6974 6820 7468 650a 272d 5427 206f 7074  ith the.'-T' opt\n-00012750: 696f 6e2e 2020 2a4e 6f74 6520 436f 6d6d  ion.  *Note Comm\n-00012760: 616e 6420 6c69 6e65 3a3a 2e20 204e 6f74  and line::.  Not\n-00012770: 6520 7468 6174 2061 7420 7468 6520 7469  e that at the ti\n-00012780: 6d65 2074 6869 7320 6d61 6e75 616c 0a77  me this manual.w\n-00012790: 6173 2067 656e 6572 6174 6564 2c20 2750  as generated, 'P\n-000127a0: 5354 7269 636b 7327 2077 6173 206e 6f74  STricks' was not\n-000127b0: 2073 7570 706f 7274 6564 2062 7920 4c61   supported by La\n-000127c0: 5465 5820 6f72 2062 7920 2743 6f6e 5465  TeX or by 'ConTe\n-000127d0: 5874 272e 0a0a 1f0a 4669 6c65 3a20 736b  Xt'.....File: sk\n-000127e0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n-000127f0: 3a20 4275 696c 6469 6e67 2061 2064 7261  : Building a dra\n-00012800: 7769 6e67 2c20 204e 6578 743a 2043 6f6d  wing,  Next: Com\n-00012810: 6d61 6e64 206c 696e 652c 2020 5072 6576  mand line,  Prev\n-00012820: 3a20 496e 7075 7420 6c61 6e67 7561 6765  : Input language\n-00012830: 2c20 2055 703a 2054 6f70 0a0a 3420 4275  ,  Up: Top..4 Bu\n-00012840: 696c 6469 6e67 2061 2064 7261 7769 6e67  ilding a drawing\n-00012850: 0a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  .***************\n-00012860: 2a2a 2a2a 2a0a 0a53 7563 6365 7373 6675  *****..Successfu\n-00012870: 6c20 6472 6177 696e 6773 2077 6974 6820  l drawings with \n-00012880: 2773 6b65 7463 6827 2061 6e64 2077 6974  'sketch' and wit\n-00012890: 6820 616e 7920 7363 656e 6520 6465 7363  h any scene desc\n-000128a0: 7269 7074 696f 6e0a 6c61 6e67 7561 6765  ription.language\n-000128b0: 2072 6571 7569 7265 2074 6861 7420 7468   require that th\n-000128c0: 6520 7573 6572 2064 6576 656c 6f70 2061  e user develop a\n-000128d0: 6e20 6163 6375 7261 7465 206d 656e 7461  n accurate menta\n-000128e0: 6c20 7069 6374 7572 6520 6f66 2068 6572  l picture of her\n-000128f0: 0a63 6f64 6520 616e 6420 6974 7320 6d65  .code and its me\n-00012900: 616e 696e 672e 2020 5468 6973 2069 6d61  aning.  This ima\n-00012910: 6765 2069 7320 6265 7374 2062 7569 6c74  ge is best built\n-00012920: 2069 6e20 736d 616c 6c20 7069 6563 6573   in small pieces\n-00012930: 2e0a 5468 6572 6566 6f72 652c 2027 736b  ..Therefore, 'sk\n-00012940: 6574 6368 2720 696e 7075 7473 2061 7265  etch' inputs are\n-00012950: 2062 6573 7420 6372 6561 7465 6420 696e   best created in\n-00012960: 2073 6d61 6c6c 2069 6e63 7265 6d65 6e74   small increment\n-00012970: 7320 7769 7468 0a66 7265 7175 656e 7420  s with.frequent \n-00012980: 7061 7573 6573 2074 6f20 636f 6d70 696c  pauses to compil\n-00012990: 6520 616e 6420 7669 6577 2074 6865 2072  e and view the r\n-000129a0: 6573 756c 7473 2e20 2043 6172 6566 756c  esults.  Careful\n-000129b0: 2063 6f6d 6d65 6e74 7320 696e 0a74 6865   comments in.the\n-000129c0: 2069 6e70 7574 206f 6674 656e 2068 656c   input often hel\n-000129d0: 7020 6173 2061 2073 6365 6e65 2067 726f  p as a scene gro\n-000129e0: 7773 2069 6e20 636f 6d70 6c65 7869 7479  ws in complexity\n-000129f0: 2e0a 0a2a 204d 656e 753a 0a0a 2a20 4f76  ...* Menu:..* Ov\n-00012a00: 6572 7669 6577 3a3a 2020 2020 2020 2020  erview::        \n-00012a10: 2020 2020 2020 2020 2020 2020 4275 696c              Buil\n-00012a20: 6469 6e67 2061 2073 7562 7374 616e 7469  ding a substanti\n-00012a30: 616c 2064 7261 7769 6e67 2e0a 2a20 4120  al drawing..* A \n-00012a40: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n-00012a50: 673a 3a20 2020 2020 2020 2020 416e 2065  g::         An e\n-00012a60: 7861 6d70 6c65 2077 6974 6820 6669 6e65  xample with fine\n-00012a70: 2070 6c61 6365 6d65 6e74 2e0a 2a20 4120   placement..* A \n-00012a80: 6869 6572 6172 6368 6963 616c 206d 6f64  hierarchical mod\n-00012a90: 656c 3a3a 2020 2020 2020 2020 416e 2065  el::        An e\n-00012aa0: 7861 6d70 6c65 2077 6974 6820 7377 6565  xample with swee\n-00012ab0: 7073 2061 6e64 2070 7574 732e 0a2a 2043  ps and puts..* C\n-00012ac0: 6176 6561 7473 3a3a 2020 2020 2020 2020  aveats::        \n-00012ad0: 2020 2020 2020 2020 2020 2020 2057 6865               Whe\n-00012ae0: 7265 2074 726f 7562 6c65 2063 616e 206f  re trouble can o\n-00012af0: 6363 7572 2e0a 0a1f 0a46 696c 653a 2073  ccur.....File: s\n-00012b00: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n-00012b10: 653a 204f 7665 7276 6965 772c 2020 4e65  e: Overview,  Ne\n-00012b20: 7874 3a20 4120 7465 6368 6e69 6361 6c20  xt: A technical \n-00012b30: 6472 6177 696e 672c 2020 5072 6576 3a20  drawing,  Prev: \n-00012b40: 4275 696c 6469 6e67 2061 2064 7261 7769  Building a drawi\n-00012b50: 6e67 2c20 2055 703a 2042 7569 6c64 696e  ng,  Up: Buildin\n-00012b60: 6720 6120 6472 6177 696e 670a 0a34 2e31  g a drawing..4.1\n-00012b70: 204f 7665 7276 6965 770a 3d3d 3d3d 3d3d   Overview.======\n-00012b80: 3d3d 3d3d 3d3d 0a0a 4173 2061 6e20 6f76  ======..As an ov\n-00012b90: 6572 7669 6577 2c20 6c65 7427 7320 6465  erview, let's de\n-00012ba0: 7665 6c6f 7020 6120 6469 6167 7261 6d20  velop a diagram \n-00012bb0: 7468 6174 2073 686f 7773 2068 6f77 2061  that shows how a\n-00012bc0: 2070 6572 7370 6563 7469 7665 0a70 726f   perspective.pro\n-00012bd0: 6a65 6374 696f 6e20 7472 616e 7366 6f72  jection transfor\n-00012be0: 6d20 776f 726b 732e 2020 5765 276c 6c20  m works.  We'll \n-00012bf0: 7374 6172 7420 7769 7468 2074 6865 2074  start with the t\n-00012c00: 7261 6469 7469 6f6e 616c 2072 6566 6572  raditional refer\n-00012c10: 656e 6365 0a6f 626a 6563 7420 7573 6564  ence.object used\n-00012c20: 2069 6e20 636f 6d70 7574 6572 2067 7261   in computer gra\n-00012c30: 7068 6963 7320 7465 7874 626f 6f6b 732c  phics textbooks,\n-00012c40: 2061 2068 6f75 7365 2d73 6861 7065 6420   a house-shaped \n-00012c50: 7072 6973 6d2e 2020 4265 6769 6e0a 6279  prism.  Begin.by\n-00012c60: 2064 6566 696e 696e 6720 7468 6520 706f   defining the po\n-00012c70: 696e 7473 206f 6620 7468 6520 686f 7573  ints of the hous\n-00012c80: 652e 2020 5261 7468 6572 2074 6861 6e20  e.  Rather than \n-00012c90: 6465 6669 6e69 6e67 2074 6865 2066 6163  defining the fac\n-00012ca0: 6573 206f 660a 7468 6520 686f 7573 6520  es of.the house \n-00012cb0: 6173 2070 6f6c 7967 6f6e 7320 616e 6420  as polygons and \n-00012cc0: 7472 616e 7366 6f72 6d69 6e67 2074 686f  transforming tho\n-00012cd0: 7365 2c20 7765 2061 7265 2067 6f69 6e67  se, we are going\n-00012ce0: 2074 6f20 7472 616e 7366 6f72 6d0a 7468   to transform.th\n-00012cf0: 6520 706f 696e 7473 2074 6865 6d73 656c  e points themsel\n-00012d00: 7665 7320 7769 7468 2027 736b 6574 6368  ves with 'sketch\n-00012d10: 2720 6172 6974 686d 6574 6963 2073 6f20  ' arithmetic so \n-00012d20: 7468 6174 2077 6520 6861 7665 206e 616d  that we have nam\n-00012d30: 6573 2066 6f72 0a74 6865 2074 7261 6e73  es for.the trans\n-00012d40: 666f 726d 6564 2070 6f69 6e74 7320 6c61  formed points la\n-00012d50: 7465 722e 0a20 2025 2072 6967 6874 2073  ter..  % right s\n-00012d60: 6964 6520 286f 7574 7369 6465 2074 6f20  ide (outside to \n-00012d70: 7269 6768 7429 0a20 2064 6566 2052 3120  right).  def R1 \n-00012d80: 2831 2c31 2c31 2920 6465 6620 5232 2028  (1,1,1) def R2 (\n-00012d90: 312c 2d31 2c31 2920 6465 6620 5233 2028  1,-1,1) def R3 (\n-00012da0: 312c 2d31 2c2d 3129 2064 6566 2052 3420  1,-1,-1) def R4 \n-00012db0: 2831 2c31 2c2d 3129 0a20 2064 6566 2052  (1,1,-1).  def R\n-00012dc0: 3520 2831 2c31 2e35 2c30 290a 0a20 2025  5 (1,1.5,0)..  %\n-00012dd0: 206c 6566 7420 7369 6465 2028 6f75 7473   left side (outs\n-00012de0: 6964 6520 746f 2072 6967 6874 2d2d 6261  ide to right--ba\n-00012df0: 636b 7761 7264 290a 2020 6465 6620 5720  ckward).  def W \n-00012e00: 205b 322c 302c 305d 0a20 2064 6566 204c   [2,0,0].  def L\n-00012e10: 3120 2852 3129 2d5b 575d 2064 6566 204c  1 (R1)-[W] def L\n-00012e20: 3220 2852 3229 2d5b 575d 2064 6566 204c  2 (R2)-[W] def L\n-00012e30: 3320 2852 3329 2d5b 575d 2064 6566 204c  3 (R3)-[W] def L\n-00012e40: 3420 2852 3429 2d5b 575d 0a20 2064 6566  4 (R4)-[W].  def\n-00012e50: 204c 3520 2852 3529 2d5b 575d 0a54 6f20   L5 (R5)-[W].To \n-00012e60: 6164 6420 6120 646f 6f72 2074 6f20 7468  add a door to th\n-00012e70: 6520 686f 7573 652c 2077 6520 7573 6520  e house, we use \n-00012e80: 6120 706f 6c79 676f 6e20 736c 6967 6874  a polygon slight\n-00012e90: 6c79 2069 6e20 6672 6f6e 7420 6f66 2074  ly in front of t\n-00012ea0: 6865 0a66 6f72 656d 6f73 7420 6661 6365  he.foremost face\n-00012eb0: 206f 6620 7468 6520 686f 7573 652e 0a20   of the house.. \n-00012ec0: 2025 2064 6f6f 720a 2020 6465 6620 6520   % door.  def e \n-00012ed0: 2e30 310a 2020 6465 6620 4431 2028 302c  .01.  def D1 (0,\n-00012ee0: 2d31 2c31 2b65 2920 6465 6620 4432 2028  -1,1+e) def D2 (\n-00012ef0: 2e35 2c2d 312c 312b 6529 2064 6566 2044  .5,-1,1+e) def D\n-00012f00: 3320 282e 352c 302c 312b 6529 2064 6566  3 (.5,0,1+e) def\n-00012f10: 2044 3420 2830 2c30 2c31 2b65 290a 4e6f   D4 (0,0,1+e).No\n-00012f20: 7720 6c65 7427 7320 6372 6561 7465 2061  w let's create a\n-00012f30: 206e 6577 2073 6574 206f 6620 706f 696e   new set of poin\n-00012f40: 7473 2074 6861 7420 6172 6520 6120 746f  ts that are a to\n-00012f50: 2d62 652d 6465 7465 726d 696e 6564 0a74  -be-determined.t\n-00012f60: 7261 6e73 666f 726d 206f 6620 7468 6520  ransform of the \n-00012f70: 6f72 6967 696e 616c 732e 0a20 2064 6566  originals..  def\n-00012f80: 2068 7020 7363 616c 6528 3129 2025 2068   hp scale(1) % h\n-00012f90: 6f75 7365 2070 6f73 6974 696f 6e65 720a  ouse positioner.\n-00012fa0: 2020 6465 6620 7052 3120 5b5b 6870 5d5d    def pR1 [[hp]]\n-00012fb0: 2a28 5231 2920 6465 6620 7052 3220 5b5b  *(R1) def pR2 [[\n-00012fc0: 6870 5d5d 2a28 5232 2920 6465 6620 7052  hp]]*(R2) def pR\n-00012fd0: 3320 5b5b 6870 5d5d 2a28 5233 290a 2020  3 [[hp]]*(R3).  \n-00012fe0: 6465 6620 7052 3420 5b5b 6870 5d5d 2a28  def pR4 [[hp]]*(\n-00012ff0: 5234 2920 6465 6620 7052 3520 5b5b 6870  R4) def pR5 [[hp\n-00013000: 5d5d 2a28 5235 290a 2020 6465 6620 704c  ]]*(R5).  def pL\n-00013010: 3120 5b5b 6870 5d5d 2a28 4c31 2920 6465  1 [[hp]]*(L1) de\n-00013020: 6620 704c 3220 5b5b 6870 5d5d 2a28 4c32  f pL2 [[hp]]*(L2\n-00013030: 2920 6465 6620 704c 3320 5b5b 6870 5d5d  ) def pL3 [[hp]]\n-00013040: 2a28 4c33 290a 2020 6465 6620 704c 3420  *(L3).  def pL4 \n-00013050: 5b5b 6870 5d5d 2a28 4c34 2920 6465 6620  [[hp]]*(L4) def \n-00013060: 704c 3520 5b5b 6870 5d5d 2a28 4c35 290a  pL5 [[hp]]*(L5).\n-00013070: 2020 6465 6620 7044 3120 5b5b 6870 5d5d    def pD1 [[hp]]\n-00013080: 2a28 4431 2920 6465 6620 7044 3220 5b5b  *(D1) def pD2 [[\n-00013090: 6870 5d5d 2a28 4432 2920 6465 6620 7044  hp]]*(D2) def pD\n-000130a0: 3320 5b5b 6870 5d5d 2a28 4433 290a 2020  3 [[hp]]*(D3).  \n-000130b0: 6465 6620 7044 3420 5b5b 6870 5d5d 2a28  def pD4 [[hp]]*(\n-000130c0: 4434 2920 0a4e 6f74 6520 7468 6520 7573  D4) .Note the us\n-000130d0: 6520 6f66 2061 2022 7472 616e 7366 6f72  e of a \"transfor\n-000130e0: 6d20 6465 6669 6e69 7469 6f6e 2220 616e  m definition\" an\n-000130f0: 6420 2274 7261 6e73 666f 726d 2072 6566  d \"transform ref\n-00013100: 6572 656e 6365 7322 2e0a 4e6f 7720 6465  erences\"..Now de\n-00013110: 6669 6e65 2074 6865 2073 6576 656e 2070  fine the seven p\n-00013120: 6f6c 7967 6f6e 616c 2066 6163 6573 206f  olygonal faces o\n-00013130: 6620 7468 6520 686f 7573 6520 616e 6420  f the house and \n-00013140: 7468 6520 646f 6f72 2075 7369 6e67 2074  the door using t\n-00013150: 6865 0a74 7261 6e73 666f 726d 6564 2070  he.transformed p\n-00013160: 6f69 6e74 7320 6173 2076 6572 7469 6365  oints as vertice\n-00013170: 732e 2020 4265 2063 6172 6566 756c 2077  s.  Be careful w\n-00013180: 6974 6820 7665 7274 6578 206f 7264 6572  ith vertex order\n-00013190: 210a 2020 6465 6620 7267 7420 706f 6c79  !.  def rgt poly\n-000131a0: 676f 6e20 2870 5231 2928 7052 3229 2870  gon (pR1)(pR2)(p\n-000131b0: 5233 2928 7052 3429 2870 5235 290a 2020  R3)(pR4)(pR5).  \n-000131c0: 6465 6620 6c66 7420 706f 6c79 676f 6e20  def lft polygon \n-000131d0: 2870 4c35 2928 704c 3429 2870 4c33 2928  (pL5)(pL4)(pL3)(\n-000131e0: 704c 3229 2870 4c31 290a 2020 6465 6620  pL2)(pL1).  def \n-000131f0: 6672 7420 706f 6c79 676f 6e20 2870 5232  frt polygon (pR2\n-00013200: 2928 7052 3129 2870 4c31 2928 704c 3229  )(pR1)(pL1)(pL2)\n-00013210: 0a20 2064 6566 2062 636b 2070 6f6c 7967  .  def bck polyg\n-00013220: 6f6e 2028 7052 3429 2870 5233 2928 704c  on (pR4)(pR3)(pL\n-00013230: 3329 2870 4c34 290a 2020 6465 6620 7466  3)(pL4).  def tf\n-00013240: 7220 706f 6c79 676f 6e20 2870 5231 2928  r polygon (pR1)(\n-00013250: 7052 3529 2870 4c35 2928 704c 3129 0a20  pR5)(pL5)(pL1). \n-00013260: 2064 6566 2074 626b 2070 6f6c 7967 6f6e   def tbk polygon\n-00013270: 2028 7052 3529 2870 5234 2928 704c 3429   (pR5)(pR4)(pL4)\n-00013280: 2870 4c35 290a 2020 6465 6620 626f 7420  (pL5).  def bot \n-00013290: 706f 6c79 676f 6e20 2870 5232 2928 704c  polygon (pR2)(pL\n-000132a0: 3229 2870 4c33 2928 7052 3329 0a20 2064  2)(pL3)(pR3).  d\n-000132b0: 6566 2064 6f6f 7220 706f 6c79 676f 6e5b  ef door polygon[\n-000132c0: 6669 6c6c 636f 6c6f 723d 6272 6f77 6e5d  fillcolor=brown]\n-000132d0: 2028 7044 3129 2870 4432 2928 7044 3329   (pD1)(pD2)(pD3)\n-000132e0: 2870 4434 290a 2020 6465 6620 686f 7573  (pD4).  def hous\n-000132f0: 6520 7b20 7b72 6774 7d7b 6c66 747d 7b66  e { {rgt}{lft}{f\n-00013300: 7274 7d7b 6263 6b7d 7b74 6672 7d7b 7462  rt}{bck}{tfr}{tb\n-00013310: 6b7d 7b62 6f74 7d7b 646f 6f72 7d20 7d0a  k}{bot}{door} }.\n-00013320: 2020 2054 696d 6520 666f 7220 6120 7361     Time for a sa\n-00013330: 6e69 7479 2063 6865 636b 2e20 2041 6464  nity check.  Add\n-00013340: 2074 6865 206c 696e 650a 2020 7b68 6f75   the line.  {hou\n-00013350: 7365 7d0a 616e 6420 7468 6973 2069 7320  se}.and this is \n-00013360: 7768 6174 2077 6520 6765 742e 0a0a 0008  what we get.....\n-00013370: 5b69 6d61 6765 2073 7263 3d22 6578 3133  [image src=\"ex13\n-00013380: 302e 706e 6722 2074 6578 743d 2249 6d61  0.png\" text=\"Ima\n-00013390: 6765 2065 7831 3330 206f 6d69 7474 6564  ge ex130 omitted\n-000133a0: 2069 6e20 7465 7874 2076 6572 7369 6f6e   in text version\n-000133b0: 206f 6620 7468 6973 2064 6f63 756d 656e   of this documen\n-000133c0: 742e 2200 085d 0a0a 5468 6973 2069 7320  t.\"..]..This is \n-000133d0: 636f 7272 6563 742c 2062 7574 2064 6f65  correct, but doe\n-000133e0: 7320 6e6f 7420 7265 7665 616c 2076 6572  s not reveal ver\n-000133f0: 7920 6d75 6368 2e20 2043 6f6d 6d6f 6e20  y much.  Common \n-00013400: 6572 726f 7273 2061 7265 0a6d 6973 706c  errors are.mispl\n-00013410: 6163 6564 2076 6572 7469 6365 7320 616e  aced vertices an\n-00013420: 6420 706f 6c79 676f 6e73 206d 6973 7369  d polygons missi\n-00013430: 6e67 2065 6e74 6972 656c 7920 6475 6520  ng entirely due \n-00013440: 746f 2069 6e63 6f72 7265 6374 2076 6572  to incorrect ver\n-00013450: 7465 780a 6f72 6465 722e 2020 546f 2072  tex.order.  To r\n-00013460: 756c 6520 7468 6573 6520 6f75 742c 206c  ule these out, l\n-00013470: 6574 2773 2069 6e73 7065 6374 2061 6c6c  et's inspect all\n-00013480: 2073 6964 6573 206f 6620 7468 6520 686f   sides of the ho\n-00013490: 7573 652e 2020 5468 6973 0a69 7320 6e6f  use.  This.is no\n-000134a0: 7420 6861 7264 2e20 204d 6572 656c 7920  t hard.  Merely \n-000134b0: 7265 706c 6163 6520 7468 6520 7265 6665  replace the refe\n-000134c0: 7265 6e63 6520 7b68 6f75 7365 7d20 7769  rence {house} wi\n-000134d0: 7468 2061 2027 7265 7065 6174 272e 0a2a  th a 'repeat'..*\n-000134e0: 4e6f 7465 2052 6570 6561 7473 3a3a 2e0a  Note Repeats::..\n-000134f0: 2020 7265 7065 6174 207b 2031 332c 2072    repeat { 13, r\n-00013500: 6f74 6174 6528 3330 2c20 5b31 2c32 2c33  otate(30, [1,2,3\n-00013510: 5d29 2c20 7472 616e 736c 6174 6528 5b33  ]), translate([3\n-00013520: 2c30 2c30 5d29 207d 207b 686f 7573 657d  ,0,0]) } {house}\n-00013530: 0a00 085b 696d 6167 6520 7372 633d 2265  ...[image src=\"e\n-00013540: 7831 3430 2e70 6e67 2220 7465 7874 3d22  x140.png\" text=\"\n-00013550: 496d 6167 6520 6578 3134 3020 6f6d 6974  Image ex140 omit\n-00013560: 7465 6420 696e 2074 6578 7420 7665 7273  ted in text vers\n-00013570: 696f 6e20 6f66 2074 6869 7320 646f 6375  ion of this docu\n-00013580: 6d65 6e74 2e22 0008 5d0a 0a41 6761 696e  ment.\"..]..Again\n-00013590: 2074 6869 6e67 7320 6c6f 6f6b 2063 6f72   things look cor\n-000135a0: 7265 6374 2e20 204e 6f74 6520 7468 6174  rect.  Note that\n-000135b0: 2074 6865 2068 6964 6465 6e20 7375 7266   the hidden surf\n-000135c0: 6163 6520 616c 676f 7269 7468 6d0a 6861  ace algorithm.ha\n-000135d0: 6e64 6c65 7320 696e 7465 7273 6563 7469  ndles intersecti\n-000135e0: 6e67 2070 6f6c 7967 6f6e 7320 636f 7272  ng polygons corr\n-000135f0: 6563 746c 7920 7768 6572 6520 736f 6d65  ectly where some\n-00013600: 2063 6f70 6965 7320 6f66 2074 6865 2068   copies of the h\n-00013610: 6f75 7365 0a6f 7665 726c 6170 2e0a 0a20  ouse.overlap... \n-00013620: 2020 4c65 7427 7320 6c61 7920 6f75 7420    Let's lay out \n-00013630: 7468 6520 6765 6f6d 6574 7279 206f 6620  the geometry of \n-00013640: 7065 7273 7065 6374 6976 6520 7072 6f6a  perspective proj\n-00013650: 6563 7469 6f6e 206f 6620 7468 6520 686f  ection of the ho\n-00013660: 7573 650a 6f6e 746f 2061 2070 6c61 6e65  use.onto a plane\n-00013670: 2077 6974 6820 7261 7973 2070 6173 7369   with rays passi\n-00013680: 6e67 2074 6872 6f75 6768 2074 6865 206f  ng through the o\n-00013690: 7269 6769 6e2e 2020 4265 6769 6e20 6279  rigin.  Begin by\n-000136a0: 2070 6f73 6974 696f 6e69 6e67 0a74 6865   positioning.the\n-000136b0: 2068 6f75 7365 2074 7765 6c76 6520 756e   house twelve un\n-000136c0: 6974 7320 6261 636b 206f 6e20 7468 6520  its back on the \n-000136d0: 6e65 6761 7469 7665 207a 2d61 7869 7320  negative z-axis \n-000136e0: 616e 6420 6164 6469 6e67 2061 2073 6574  and adding a set\n-000136f0: 206f 660a 636f 6f72 6469 6e61 7465 2061   of.coordinate a\n-00013700: 7865 732e 2020 546f 206d 6f76 6520 7468  xes.  To move th\n-00013710: 6520 686f 7573 6520 7765 206e 6565 6420  e house we need \n-00013720: 6f6e 6c79 2063 6861 6e67 6520 7468 6520  only change the \n-00013730: 2268 6f75 7365 0a70 6f73 6974 696f 6e69  \"house.positioni\n-00013740: 6e67 2220 7472 616e 7366 6f72 6d20 6465  ng\" transform de\n-00013750: 6669 6e65 6420 6561 726c 6965 722e 0a20  fined earlier.. \n-00013760: 2064 6566 2068 7020 726f 7461 7465 282d   def hp rotate(-\n-00013770: 3430 2c20 5b30 2c31 2c30 5d29 2074 6865  40, [0,1,0]) the\n-00013780: 6e20 7472 616e 736c 6174 6528 5b30 2c30  n translate([0,0\n-00013790: 2c2d 3132 5d29 0a20 2064 6566 2061 7865  ,-12]).  def axe\n-000137a0: 7320 7b0a 2020 2020 6465 6620 737a 2031  s {.    def sz 1\n-000137b0: 0a20 2020 206c 696e 6520 5b61 7272 6f77  .    line [arrow\n-000137c0: 733d 3c2d 3e5d 2028 737a 2c30 2c30 2928  s=<->] (sz,0,0)(\n-000137d0: 4f29 2830 2c73 7a2c 3029 0a20 2020 206c  O)(0,sz,0).    l\n-000137e0: 696e 6520 5b61 7272 6f77 733d 2d3e 5d20  ine [arrows=->] \n-000137f0: 2028 4f29 2830 2c30 2c73 7a29 0a20 2020   (O)(0,0,sz).   \n-00013800: 206c 696e 6520 5b6c 696e 6577 6964 7468   line [linewidth\n-00013810: 3d2e 3270 742c 6c69 6e65 636f 6c6f 723d  =.2pt,linecolor=\n-00013820: 626c 7565 2c6c 696e 6573 7479 6c65 3d64  blue,linestyle=d\n-00013830: 6173 6865 645d 2028 4f29 2830 2c30 2c2d  ashed] (O)(0,0,-\n-00013840: 3130 290a 2020 2020 7370 6563 6961 6c20  10).    special \n-00013850: 7c5c 7570 7574 5b72 5d23 317b 2478 247d  |\\uput[r]#1{$x$}\n-00013860: 5c75 7075 745b 755d 2332 7b24 7924 7d5c  \\uput[u]#2{$y$}\\\n-00013870: 7570 7574 5b6c 5d23 337b 247a 247d 7c0a  uput[l]#3{$z$}|.\n-00013880: 2020 2020 2020 2873 7a2c 302c 3029 2830        (sz,0,0)(0\n-00013890: 2c73 7a2c 3029 2830 2c30 2c73 7a29 0a20  ,sz,0)(0,0,sz). \n-000138a0: 207d 0a0a 2020 2054 696d 6520 666f 7220   }..   Time for \n-000138b0: 616e 6f74 6865 7220 7465 7374 2e20 204c  another test.  L\n-000138c0: 6574 2773 2062 7569 6c64 2061 2072 6561  et's build a rea\n-000138d0: 6c20 7669 6577 2074 7261 6e73 666f 726d  l view transform\n-000138e0: 2c20 6372 6561 7469 6e67 2061 0a22 7669  , creating a.\"vi\n-000138f0: 7274 7561 6c20 6361 6d65 7261 2220 746f  rtual camera\" to\n-00013900: 206c 6f6f 6b20 6174 2074 6865 2073 6365   look at the sce\n-00013910: 6e65 2077 6520 6172 6520 636f 6e73 7472  ne we are constr\n-00013920: 7563 7469 6e67 2e20 2052 6570 6c61 6365  ucting.  Replace\n-00013930: 2074 6865 0a27 7265 7065 6174 2720 7769   the.'repeat' wi\n-00013940: 7468 0a20 2064 6566 2065 7965 2028 3130  th.  def eye (10\n-00013950: 2c34 2c31 3029 0a20 2064 6566 206c 6f6f  ,4,10).  def loo\n-00013960: 6b5f 6174 2028 302c 302c 2d35 290a 2020  k_at (0,0,-5).  \n-00013970: 7075 7420 7b20 7669 6577 2828 6579 6529  put { view((eye)\n-00013980: 2c20 286c 6f6f 6b5f 6174 2929 207d 207b  , (look_at)) } {\n-00013990: 207b 686f 7573 657d 7b61 7865 737d 207d   {house}{axes} }\n-000139a0: 0a20 2020 5468 6520 2276 6965 7720 7472  .   The \"view tr\n-000139b0: 616e 7366 6f72 6d22 2072 6570 6f73 6974  ansform\" reposit\n-000139c0: 696f 6e73 2074 6865 2073 6365 6e65 2073  ions the scene s\n-000139d0: 6f20 7468 6174 2074 6865 2070 6f69 6e74  o that the point\n-000139e0: 2027 6579 6527 2069 730a 6174 2074 6865   'eye' is.at the\n-000139f0: 206f 7269 6769 6e20 616e 6420 7468 6520   origin and the \n-00013a00: 6469 7265 6374 696f 6e20 6672 6f6d 2027  direction from '\n-00013a10: 6579 6527 2074 6f20 276c 6f6f 6b5f 6174  eye' to 'look_at\n-00013a20: 2720 6973 2074 6865 206e 6567 6174 6976  ' is the negativ\n-00013a30: 650a 7a2d 6178 6973 2e20 2054 6869 7320  e.z-axis.  This \n-00013a40: 7265 7175 6972 6573 2061 2072 6f74 6174  requires a rotat\n-00013a50: 696f 6e20 616e 6420 6120 7472 616e 736c  ion and a transl\n-00013a60: 6174 696f 6e20 7468 6174 2061 7265 2061  ation that are a\n-00013a70: 6c6c 2070 6163 6b65 640a 696e 746f 2074  ll packed.into t\n-00013a80: 6865 2063 6f6e 7374 7275 6374 6f72 2027  he constructor '\n-00013a90: 7669 6577 272e 0a0a 0008 5b69 6d61 6765  view'.....[image\n-00013aa0: 2073 7263 3d22 6578 3135 302e 706e 6722   src=\"ex150.png\"\n-00013ab0: 2074 6578 743d 2249 6d61 6765 2065 7831   text=\"Image ex1\n-00013ac0: 3530 206f 6d69 7474 6564 2069 6e20 7465  50 omitted in te\n-00013ad0: 7874 2076 6572 7369 6f6e 206f 6620 7468  xt version of th\n-00013ae0: 6973 2064 6f63 756d 656e 742e 2200 085d  is document.\"..]\n-00013af0: 0a0a 5468 6973 2069 7320 7374 6172 7469  ..This is starti\n-00013b00: 6e67 2074 6f20 6c6f 6f6b 2067 6f6f 6421  ng to look good!\n-00013b10: 2020 4164 6420 7468 6520 7072 6f6a 6563    Add the projec\n-00013b20: 7469 6f6e 2070 6c61 6e65 2068 616c 6620  tion plane half \n-00013b30: 7761 790a 6265 7477 6565 6e20 7468 6520  way.between the \n-00013b40: 6f72 6967 696e 2061 6e64 2074 6865 2068  origin and the h\n-00013b50: 6f75 7365 2061 7420 7a3d 2d35 2e20 2057  ouse at z=-5.  W\n-00013b60: 6527 6c6c 2074 7279 2074 6865 2061 6e67  e'll try the ang\n-00013b70: 6c65 2061 7267 756d 656e 740a 6665 6174  le argument.feat\n-00013b80: 7572 6520 6f66 2027 7370 6563 6961 6c27  ure of 'special'\n-00013b90: 2074 6f20 706f 7369 7469 6f6e 2061 206c   to position a l\n-00013ba0: 6162 656c 2e0a 2020 6465 6620 7020 3520  abel..  def p 5 \n-00013bb0: 2520 7072 6f6a 6563 7469 6f6e 2064 6973  % projection dis\n-00013bc0: 7461 6e63 6520 2870 6c61 6e65 2061 7420  tance (plane at \n-00013bd0: 7a3d 2d70 290a 2020 6465 6620 7072 6f6a  z=-p).  def proj\n-00013be0: 6563 7469 6f6e 5f70 6c61 6e65 207b 0a20  ection_plane {. \n-00013bf0: 2020 2064 6566 2073 7a20 312e 350a 2020     def sz 1.5.  \n-00013c00: 2020 706f 6c79 676f 6e20 282d 737a 2c2d    polygon (-sz,-\n-00013c10: 737a 2c2d 7029 2873 7a2c 2d73 7a2c 2d70  sz,-p)(sz,-sz,-p\n-00013c20: 2928 737a 2c73 7a2c 2d70 2928 2d73 7a2c  )(sz,sz,-p)(-sz,\n-00013c30: 737a 2c2d 7029 0a20 2020 2073 7065 6369  sz,-p).    speci\n-00013c40: 616c 207c 5c72 7075 745b 625d 2331 2d32  al |\\rput[b]#1-2\n-00013c50: 2333 7b5c 666f 6f74 6e6f 7465 7369 7a65  #3{\\footnotesize\n-00013c60: 5c73 6620 7072 6f6a 6563 7469 6f6e 2070  \\sf projection p\n-00013c70: 6c61 6e65 7d7c 200a 2020 2020 2020 282d  lane}| .      (-\n-00013c80: 737a 2c2d 737a 2c2d 7029 2873 7a2c 2d73  sz,-sz,-p)(sz,-s\n-00013c90: 7a2c 2d70 2928 302c 2d73 7a2b 2e31 2c2d  z,-p)(0,-sz+.1,-\n-00013ca0: 7029 0a20 207d 0a41 6464 207b 7072 6f6a  p).  }.Add {proj\n-00013cb0: 6563 7469 6f6e 5f70 6c61 6e65 7d20 746f  ection_plane} to\n-00013cc0: 2074 6865 206c 6973 7420 6f66 206f 626a   the list of obj\n-00013cd0: 6563 7473 2069 6e20 7468 6520 2770 7574  ects in the 'put\n-00013ce0: 2720 6162 6f76 652e 0a0a 0008 5b69 6d61  ' above.....[ima\n-00013cf0: 6765 2073 7263 3d22 6578 3136 302e 706e  ge src=\"ex160.pn\n-00013d00: 6722 2074 6578 743d 2249 6d61 6765 2065  g\" text=\"Image e\n-00013d10: 7831 3630 206f 6d69 7474 6564 2069 6e20  x160 omitted in \n-00013d20: 7465 7874 2076 6572 7369 6f6e 206f 6620  text version of \n-00013d30: 7468 6973 2064 6f63 756d 656e 742e 2200  this document.\".\n-00013d40: 085d 0a0a 2020 2054 6865 2077 6179 2077  .]..   The way w\n-00013d50: 6520 636f 6e73 7472 7563 7465 6420 7468  e constructed th\n-00013d60: 6520 706f 696e 7473 206f 6620 7468 6520  e points of the \n-00013d70: 686f 7573 6520 6e6f 7720 6d61 6b65 7320  house now makes \n-00013d80: 6974 2065 6173 7920 746f 0a64 7261 7720  it easy to.draw \n-00013d90: 7261 7973 206f 6620 7072 6f6a 6563 7469  rays of projecti\n-00013da0: 6f6e 2e20 2057 6527 6c6c 2063 6173 7420  on.  We'll cast \n-00013db0: 6f6e 6520 7261 7920 6672 6f6d 2065 7665  one ray from eve\n-00013dc0: 7279 2076 6973 6962 6c65 2076 6572 7465  ry visible verte\n-00013dd0: 780a 6f66 2074 6865 2068 6f75 7365 2061  x.of the house a\n-00013de0: 6e64 2064 6566 696e 6520 6f70 7469 6f6e  nd define option\n-00013df0: 7320 736f 2074 6865 2061 7070 6561 7261  s so the appeara\n-00013e00: 6e63 6520 6f66 2061 6c6c 2072 6179 7320  nce of all rays \n-00013e10: 6361 6e20 6265 0a63 6861 6e67 6564 2061  can be.changed a\n-00013e20: 7420 7468 6520 7361 6d65 2074 696d 652e  t the same time.\n-00013e30: 0a20 2064 6566 2070 726f 6a65 6374 696f  .  def projectio\n-00013e40: 6e5f 7261 7973 207b 0a20 2020 2064 6566  n_rays {.    def\n-00013e50: 2072 6179 6f70 7420 5b6c 696e 6577 6964   rayopt [linewid\n-00013e60: 7468 3d2e 3370 742c 6c69 6e65 636f 6c6f  th=.3pt,linecolo\n-00013e70: 723d 6c69 6768 7467 7261 795d 0a20 2020  r=lightgray].   \n-00013e80: 206c 696e 6520 5b72 6179 6f70 745d 284f   line [rayopt](O\n-00013e90: 2928 7052 3129 206c 696e 6520 5b72 6179  )(pR1) line [ray\n-00013ea0: 6f70 745d 284f 2928 7052 3229 206c 696e  opt](O)(pR2) lin\n-00013eb0: 655b 7261 796f 7074 5d28 4f29 2870 5233  e[rayopt](O)(pR3\n-00013ec0: 290a 2020 2020 6c69 6e65 205b 7261 796f  ).    line [rayo\n-00013ed0: 7074 5d28 4f29 2870 5234 2920 6c69 6e65  pt](O)(pR4) line\n-00013ee0: 205b 7261 796f 7074 5d28 4f29 2870 5235   [rayopt](O)(pR5\n-00013ef0: 290a 2020 2020 6c69 6e65 205b 7261 796f  ).    line [rayo\n-00013f00: 7074 5d28 4f29 2870 4c31 2920 6c69 6e65  pt](O)(pL1) line\n-00013f10: 205b 7261 796f 7074 5d28 4f29 2870 4c32   [rayopt](O)(pL2\n-00013f20: 2920 6c69 6e65 5b72 6179 6f70 745d 284f  ) line[rayopt](O\n-00013f30: 2928 704c 3529 0a20 2020 206c 696e 6520  )(pL5).    line \n-00013f40: 5b72 6179 6f70 745d 284f 2928 7044 3129  [rayopt](O)(pD1)\n-00013f50: 206c 696e 6520 5b72 6179 6f70 745d 284f   line [rayopt](O\n-00013f60: 2928 7044 3229 200a 2020 2020 6c69 6e65  )(pD2) .    line\n-00013f70: 205b 7261 796f 7074 5d28 4f29 2870 4433   [rayopt](O)(pD3\n-00013f80: 2920 6c69 6e65 205b 7261 796f 7074 5d28  ) line [rayopt](\n-00013f90: 4f29 2870 4434 2920 0a20 207d 0a54 6865  O)(pD4) .  }.The\n-00013fa0: 2072 6573 756c 7420 6973 2073 686f 776e   result is shown\n-00013fb0: 2068 6572 652e 0a0a 0008 5b69 6d61 6765   here.....[image\n-00013fc0: 2073 7263 3d22 6578 3137 302e 706e 6722   src=\"ex170.png\"\n-00013fd0: 2074 6578 743d 2249 6d61 6765 2065 7831   text=\"Image ex1\n-00013fe0: 3730 206f 6d69 7474 6564 2069 6e20 7465  70 omitted in te\n-00013ff0: 7874 2076 6572 7369 6f6e 206f 6620 7468  xt version of th\n-00014000: 6973 2064 6f63 756d 656e 742e 2200 085d  is document.\"..]\n-00014010: 0a0a 5468 6520 7261 7973 2070 6965 7263  ..The rays pierc\n-00014020: 6520 7468 6520 7072 6f6a 6563 7469 6f6e  e the projection\n-00014030: 2070 6c61 6e65 2061 7420 7468 6520 636f   plane at the co\n-00014040: 7272 6573 706f 6e64 696e 6720 706f 696e  rresponding poin\n-00014050: 7473 206f 6e20 7468 650a 7065 7273 7065  ts on the.perspe\n-00014060: 6374 6976 6520 696d 6167 6520 7765 2061  ctive image we a\n-00014070: 7265 2074 7279 696e 6720 746f 2064 7261  re trying to dra\n-00014080: 772e 2020 416c 6272 6563 6874 2044 c3bc  w.  Albrecht D..\n-00014090: 7265 7220 616e 6420 6869 730a 5265 6e61  rer and his.Rena\n-000140a0: 6973 7361 6e63 6520 636f 6e74 656d 706f  issance contempo\n-000140b0: 7261 7269 6573 2068 6164 2074 6865 2073  raries had the s\n-000140c0: 616d 6520 6964 6561 2069 6e20 7468 6520  ame idea in the \n-000140d0: 6561 726c 7920 3135 3030 2773 2e0a 0a00  early 1500's....\n-000140e0: 085b 696d 6167 6520 7372 633d 2264 7565  .[image src=\"due\n-000140f0: 7265 722e 706e 6722 2074 6578 743d 2249  rer.png\" text=\"I\n-00014100: 6d61 6765 206f 6620 4475 6572 6572 2773  mage of Duerer's\n-00014110: 2070 6572 7370 6563 7469 7665 2063 6f6d   perspective com\n-00014120: 7075 7465 7220 6f6d 6974 7465 6420 696e  puter omitted in\n-00014130: 2074 6578 7420 7665 7273 696f 6e20 6f66   text version of\n-00014140: 2074 6869 7320 646f 6375 6d65 6e74 2e22   this document.\"\n-00014150: 0008 5d0a 0a20 2020 416c 6c20 7468 6174  ..]..   All that\n-00014160: 2773 206c 6566 7420 6973 2074 6f20 6669  's left is to fi\n-00014170: 6e64 2061 2077 6179 2074 6f20 636f 6e6e  nd a way to conn\n-00014180: 6563 7420 7468 6520 706f 696e 7473 206f  ect the points o\n-00014190: 6620 7468 6520 686f 7573 650a 6f6e 2074  f the house.on t\n-000141a0: 6865 2070 726f 6a65 6374 696f 6e20 706c  he projection pl\n-000141b0: 616e 652e 2020 5765 2063 6f75 6c64 2070  ane.  We could p\n-000141c0: 756c 6c20 6f75 7420 6120 676f 6f64 2063  ull out a good c\n-000141d0: 6f6d 7075 7465 7220 6772 6170 6869 6373  omputer graphics\n-000141e0: 0a74 6578 742c 2066 696e 6420 7468 6520  .text, find the \n-000141f0: 6e65 6365 7373 6172 7920 6d61 7472 6978  necessary matrix\n-00014200: 2c20 616e 6420 656e 7465 7220 6974 206f  , and enter it o\n-00014210: 7572 7365 6c76 6573 2061 7320 6120 7472  urselves as a tr\n-00014220: 616e 7366 6f72 6d0a 6c69 7465 7261 6c2e  ansform.literal.\n-00014230: 2020 2a4e 6f74 6520 5472 616e 7366 6f72    *Note Transfor\n-00014240: 6d20 6c69 7465 7261 6c73 3a3a 2e20 2054  m literals::.  T\n-00014250: 6861 7420 776f 726b 2069 7320 616c 7265  hat work is alre\n-00014260: 6164 7920 646f 6e65 2c0a 686f 7765 7665  ady done,.howeve\n-00014270: 722e 2020 5765 2063 616e 2075 7365 2074  r.  We can use t\n-00014280: 6865 2027 7072 6f6a 6563 7428 7029 2720  he 'project(p)' \n-00014290: 636f 6e73 7472 7563 746f 722e 0a0a 2020  constructor...  \n-000142a0: 2054 6865 7265 2061 7265 2073 7469 6c6c   There are still\n-000142b0: 2073 6f6d 6520 6465 7461 696c 7320 7468   some details th\n-000142c0: 6174 2072 6571 7569 7265 2063 6172 652e  at require care.\n-000142d0: 2020 5072 6f6a 6563 7469 6f6e 2077 696c    Projection wil\n-000142e0: 6c0a 666c 6174 7465 6e20 7768 6174 6576  l.flatten whatev\n-000142f0: 6572 2069 7320 7472 616e 7366 6f72 6d65  er is transforme\n-00014300: 6420 6f6e 746f 2074 6865 2070 6c61 6e65  d onto the plane\n-00014310: 207a 3d2d 702e 2020 5468 6572 6566 6f72   z=-p.  Therefor\n-00014320: 6520 616e 7920 7061 7274 0a6f 6620 7468  e any part.of th\n-00014330: 6520 686f 7573 6520 636f 756c 6420 6469  e house could di\n-00014340: 7361 7070 6561 7220 6265 6869 6e64 2074  sappear behind t\n-00014350: 6865 2070 726f 6a65 6374 696f 6e20 706c  he projection pl\n-00014360: 616e 6520 2874 6865 2068 6964 6465 6e0a  ane (the hidden.\n-00014370: 7375 7266 6163 6520 616c 676f 7269 7468  surface algorith\n-00014380: 6d20 6f72 6465 7273 206f 626a 6563 7473  m orders objects\n-00014390: 2061 7420 7468 6520 7361 6d65 2064 6570   at the same dep\n-000143a0: 7468 2061 7262 6974 7261 7269 6c79 292e  th arbitrarily).\n-000143b0: 2020 5468 650a 646f 6f72 206d 6179 2061    The.door may a\n-000143c0: 6c73 6f20 6469 7361 7070 6561 7220 6265  lso disappear be\n-000143d0: 6869 6e64 2074 6865 2066 726f 6e74 206f  hind the front o\n-000143e0: 6620 7468 6520 686f 7573 652e 2020 546f  f the house.  To\n-000143f0: 206d 616b 6520 7375 7265 0a65 7665 7279   make sure.every\n-00014400: 7468 696e 6720 7265 6d61 696e 7320 7669  thing remains vi\n-00014410: 7369 626c 652c 2077 6527 6c6c 2070 6c61  sible, we'll pla\n-00014420: 6365 2074 6865 2068 6f75 7365 2061 2074  ce the house a t\n-00014430: 696e 7920 6269 7420 696e 2066 726f 6e74  iny bit in front\n-00014440: 206f 660a 7468 6520 7072 6f6a 6563 7469   of.the projecti\n-00014450: 6f6e 2070 6c61 6e65 2061 6e64 2061 2073  on plane and a s\n-00014460: 6563 6f6e 6420 636f 7079 206f 6620 7468  econd copy of th\n-00014470: 6520 646f 6f72 2069 6e20 6672 6f6e 7420  e door in front \n-00014480: 6f66 2074 6865 0a68 6f75 7365 2e0a 2020  of the.house..  \n-00014490: 6465 6620 7072 6f6a 6563 7469 6f6e 207b  def projection {\n-000144a0: 0a20 2020 2025 2065 2069 7320 6120 736d  .    % e is a sm\n-000144b0: 616c 6c20 6e75 6d62 6572 2064 6566 696e  all number defin\n-000144c0: 6564 2061 626f 7665 0a20 2020 2070 7574  ed above.    put\n-000144d0: 207b 2070 726f 6a65 6374 2870 2920 7468   { project(p) th\n-000144e0: 656e 2074 7261 6e73 6c61 7465 285b 302c  en translate([0,\n-000144f0: 302c 312a 655d 2920 7d20 7b68 6f75 7365  0,1*e]) } {house\n-00014500: 7d0a 2020 2020 7075 7420 7b20 7072 6f6a  }.    put { proj\n-00014510: 6563 7428 7029 2074 6865 6e20 7472 616e  ect(p) then tran\n-00014520: 736c 6174 6528 5b30 2c30 2c32 2a65 5d29  slate([0,0,2*e])\n-00014530: 207d 207b 646f 6f72 7d0a 2020 7d0a 0a00   } {door}.  }...\n-00014540: 085b 696d 6167 6520 7372 633d 2265 7831  .[image src=\"ex1\n-00014550: 3830 2e70 6e67 2220 7465 7874 3d22 496d  80.png\" text=\"Im\n-00014560: 6167 6520 6578 3138 3020 6f6d 6974 7465  age ex180 omitte\n-00014570: 6420 696e 2074 6578 7420 7665 7273 696f  d in text versio\n-00014580: 6e20 6f66 2074 6869 7320 646f 6375 6d65  n of this docume\n-00014590: 6e74 2e22 0008 5d0a 0a20 2020 4966 2079  nt.\"..]..   If y\n-000145a0: 6f75 2068 6176 6520 7374 7564 6965 6420  ou have studied \n-000145b0: 616e 6420 756e 6465 7273 7461 6e64 2061  and understand a\n-000145c0: 6c6c 2074 6869 732c 2079 6f75 2061 7265  ll this, you are\n-000145d0: 2077 656c 6c20 6f6e 2074 6865 2077 6179   well on the way\n-000145e0: 0a74 6f20 7375 6363 6573 7320 7769 7468  .to success with\n-000145f0: 2027 736b 6574 6368 272e 2020 4e6f 7420   'sketch'.  Not \n-00014600: 7368 6f77 6e20 6172 6520 7468 6520 3230  shown are the 20\n-00014610: 206f 7220 736f 2069 7465 7261 7469 6f6e   or so iteration\n-00014620: 7320 7468 6174 0a77 6572 6520 7265 7175  s that.were requ\n-00014630: 6972 6564 2074 6f20 6669 6e64 2061 2072  ired to find a r\n-00014640: 6561 736f 6e61 626c 6520 7669 6577 696e  easonable viewin\n-00014650: 6720 616e 676c 6520 616e 6420 686f 7573  g angle and hous\n-00014660: 6520 706f 7369 7469 6f6e 2c0a 6574 632e  e position,.etc.\n-00014670: 2020 4e6f 6e65 7468 656c 6573 732c 2074    Nonetheless, t\n-00014680: 6869 7320 6472 6177 696e 6720 7761 7320  his drawing was \n-00014690: 636f 6d70 6c65 7465 6420 696e 2061 626f  completed in abo\n-000146a0: 7574 2061 6e20 686f 7572 2e20 2057 6869  ut an hour.  Whi\n-000146b0: 6c65 2061 0a47 5549 2074 6f6f 6c20 6d61  le a.GUI tool ma\n-000146c0: 7920 6861 7665 2062 6565 6e20 6120 6c69  y have been a li\n-000146d0: 7474 6c65 2066 6173 7465 722c 2069 7420  ttle faster, it \n-000146e0: 6973 2075 6e6c 696b 656c 7920 7468 6174  is unlikely that\n-000146f0: 2061 206e 6577 0a64 7261 7769 6e67 2c20   a new.drawing, \n-00014700: 6974 7365 6c66 2061 2070 6572 7370 6563  itself a perspec\n-00014710: 7469 7665 2070 726f 6a65 6374 696f 6e20  tive projection \n-00014720: 6f66 2074 6865 2073 6365 6e65 2c20 636f  of the scene, co\n-00014730: 756c 6420 6265 0a67 656e 6572 6174 6564  uld be.generated\n-00014740: 2077 6974 6820 7477 6f20 6d6f 7265 206d   with two more m\n-00014750: 696e 7574 6573 2720 776f 726b 2120 204a  inutes' work!  J\n-00014760: 7573 7420 6368 616e 6765 2074 6865 2076  ust change the v\n-00014770: 6965 7720 7472 616e 7366 6f72 6d0a 746f  iew transform.to\n-00014780: 0a20 2070 7574 207b 2076 6965 7728 2865  .  put { view((e\n-00014790: 7965 292c 2028 6c6f 6f6b 5f61 7429 2920  ye), (look_at)) \n-000147a0: 7468 656e 2070 6572 7370 6563 7469 7665  then perspective\n-000147b0: 2839 2920 7d20 7b20 2e2e 2e0a 616e 6420  (9) } { ....and \n-000147c0: 7072 6f64 7563 6520 7468 6973 2e0a 0a00  produce this....\n-000147d0: 085b 696d 6167 6520 7372 633d 2265 7831  .[image src=\"ex1\n-000147e0: 3930 2e70 6e67 2220 7465 7874 3d22 496d  90.png\" text=\"Im\n-000147f0: 6167 6520 6578 3139 3020 6f6d 6974 7465  age ex190 omitte\n-00014800: 6420 696e 2074 6578 7420 7665 7273 696f  d in text versio\n-00014810: 6e20 6f66 2074 6869 7320 646f 6375 6d65  n of this docume\n-00014820: 6e74 2e22 0008 5d0a 0a1f 0a46 696c 653a  nt.\"..]....File:\n-00014830: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n-00014840: 6f64 653a 2041 2074 6563 686e 6963 616c  ode: A technical\n-00014850: 2064 7261 7769 6e67 2c20 204e 6578 743a   drawing,  Next:\n-00014860: 2041 2068 6965 7261 7263 6869 6361 6c20   A hierarchical \n-00014870: 6d6f 6465 6c2c 2020 5072 6576 3a20 4f76  model,  Prev: Ov\n-00014880: 6572 7669 6577 2c20 2055 703a 2042 7569  erview,  Up: Bui\n-00014890: 6c64 696e 6720 6120 6472 6177 696e 670a  lding a drawing.\n-000148a0: 0a34 2e32 2041 2074 6563 686e 6963 616c  .4.2 A technical\n-000148b0: 2064 7261 7769 6e67 0a3d 3d3d 3d3d 3d3d   drawing.=======\n-000148c0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n-000148d0: 0a0a 4c65 7427 7320 6c6f 6f6b 2061 7420  ..Let's look at \n-000148e0: 6120 6472 6177 696e 6720 7468 6174 2072  a drawing that r\n-000148f0: 6570 7265 7365 6e74 7320 7468 6520 6b69  epresents the ki\n-00014900: 6e64 206f 6620 7072 6f62 6c65 6d20 2773  nd of problem 's\n-00014910: 6b65 7463 6827 2077 6173 0a6d 6561 6e74  ketch' was.meant\n-00014920: 2074 6f20 736f 6c76 652d 2d61 2070 6169   to solve--a pai\n-00014930: 7220 6f66 2074 6578 7462 6f6f 6b20 6669  r of textbook fi\n-00014940: 6775 7265 7320 7265 6761 7264 696e 6720  gures regarding \n-00014950: 6120 706f 6c79 676f 6e61 6c0a 6170 7072  a polygonal.appr\n-00014960: 6f78 696d 6174 696f 6e20 6f66 2061 2074  oximation of a t\n-00014970: 7275 6e63 6174 6564 2063 6f6e 652e 2020  runcated cone.  \n-00014980: 4865 7265 2061 7265 2074 6865 2070 6963  Here are the pic\n-00014990: 7475 7265 7320 7765 2077 696c 6c0a 7072  tures we will.pr\n-000149a0: 6f64 7563 652e 0a0a 0008 5b69 6d61 6765  oduce.....[image\n-000149b0: 2073 7263 3d22 6578 3235 302e 706e 6722   src=\"ex250.png\"\n-000149c0: 2074 6578 743d 2249 6d61 6765 2065 7832   text=\"Image ex2\n-000149d0: 3530 206f 6d69 7474 6564 2069 6e20 7465  50 omitted in te\n-000149e0: 7874 2076 6572 7369 6f6e 206f 6620 7468  xt version of th\n-000149f0: 6973 2064 6f63 756d 656e 742e 2200 085d  is document.\"..]\n-00014a00: 2020 2020 2000 085b 696d 6167 6520 7372       ..[image sr\n-00014a10: 633d 2265 7832 3630 2e70 6e67 2220 7465  c=\"ex260.png\" te\n-00014a20: 7874 3d22 496d 6167 6520 6578 3236 3020  xt=\"Image ex260 \n-00014a30: 6f6d 6974 7465 6420 696e 2074 6578 7420  omitted in text \n-00014a40: 7665 7273 696f 6e20 6f66 2074 6869 7320  version of this \n-00014a50: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a20  document.\"..].. \n-00014a60: 2020 5468 6520 636f 6e65 2073 6861 7065    The cone shape\n-00014a70: 2069 7320 6a75 7374 2061 2073 7765 7074   is just a swept\n-00014a80: 206c 696e 6520 7769 7468 206e 6f20 636c   line with no cl\n-00014a90: 6f73 7572 6520 7461 6720 616e 6420 6375  osure tag and cu\n-00014aa0: 6c6c 696e 670a 7475 726e 6564 206f 6666  lling.turned off\n-00014ab0: 2e20 2042 6567 696e 2062 7920 7365 7474  .  Begin by sett\n-00014ac0: 696e 6720 7570 2073 6f6d 6520 7573 6566  ing up some usef\n-00014ad0: 756c 2063 6f6e 7374 616e 7473 2e0a 2020  ul constants..  \n-00014ae0: 6465 6620 4f20 2830 2c30 2c30 2920 6465  def O (0,0,0) de\n-00014af0: 6620 4920 5b31 2c30 2c30 5d20 6465 6620  f I [1,0,0] def \n-00014b00: 4a20 5b30 2c31 2c30 5d20 6465 6620 4b20  J [0,1,0] def K \n-00014b10: 5b30 2c30 2c31 5d0a 2020 6465 6620 7030  [0,0,1].  def p0\n-00014b20: 2028 312c 3229 2064 6566 2070 3120 2831   (1,2) def p1 (1\n-00014b30: 2e35 2c30 2920 6465 6620 4e20 380a 2020  .5,0) def N 8.  \n-00014b40: 6465 6620 7365 675f 726f 7420 726f 7461  def seg_rot rota\n-00014b50: 7465 2833 3630 202f 204e 2c20 5b4a 5d29  te(360 / N, [J])\n-00014b60: 0a54 6865 2070 6f69 6e74 7320 2770 3027  .The points 'p0'\n-00014b70: 2061 6e64 2027 7031 2720 6172 6520 7468   and 'p1' are th\n-00014b80: 6520 656e 6420 706f 696e 7473 206f 6620  e end points of \n-00014b90: 7468 6520 6c69 6e65 2074 6f20 6265 2073  the line to be s\n-00014ba0: 7765 7074 2e0a 5468 6520 6465 6669 6e69  wept..The defini\n-00014bb0: 7469 6f6e 2027 7365 675f 726f 7427 2069  tion 'seg_rot' i\n-00014bc0: 7320 7468 6520 7377 6565 7020 7472 616e  s the sweep tran\n-00014bd0: 7366 6f72 6d61 7469 6f6e 2e20 2057 6974  sformation.  Wit\n-00014be0: 6820 7468 6573 652c 2074 6865 0a63 6f6e  h these, the.con\n-00014bf0: 6520 6974 7365 6c66 2069 7320 7369 6d70  e itself is simp\n-00014c00: 6c65 2e0a 2020 7377 6565 705b 6375 6c6c  le..  sweep[cull\n-00014c10: 3d66 616c 7365 5d20 7b20 4e2c 205b 5b73  =false] { N, [[s\n-00014c20: 6567 5f72 6f74 5d5d 207d 206c 696e 6528  eg_rot]] } line(\n-00014c30: 7030 2928 7031 290a 0a20 2020 5468 6520  p0)(p1)..   The \n-00014c40: 6178 6573 2061 7265 206e 6578 7420 616e  axes are next an\n-00014c50: 6420 696e 636c 7564 6520 616e 2069 6e74  d include an int\n-00014c60: 6572 6573 696e 6720 7472 6963 6b20 7468  eresing trick th\n-00014c70: 6174 2073 686f 7773 2074 6865 0a68 6964  at shows the.hid\n-00014c80: 6465 6e20 7061 7274 7320 6173 2064 6f74  den parts as dot\n-00014c90: 7465 6420 6c69 6e65 732e 2020 5468 6520  ted lines.  The \n-00014ca0: 7365 6372 6574 2069 7320 6472 6177 2074  secret is draw t\n-00014cb0: 6865 2061 7865 7320 7477 6963 652d 2d73  he axes twice--s\n-00014cc0: 6f6c 6964 0a6c 696e 6573 2077 6974 6820  olid.lines with \n-00014cd0: 7468 6520 6e6f 726d 616c 2068 6964 6465  the normal hidde\n-00014ce0: 6e20 7375 7266 6163 6520 616c 676f 7269  n surface algori\n-00014cf0: 7468 6d20 696e 2065 6666 6563 742c 2061  thm in effect, a\n-00014d00: 6e64 2074 6865 6e0a 646f 7474 6564 2077  nd then.dotted w\n-00014d10: 6974 6820 7468 6520 6f70 7469 6f6e 2027  ith the option '\n-00014d20: 6c61 793d 6f76 6572 2720 736f 2074 6861  lay=over' so tha\n-00014d30: 7420 6e6f 2070 6f6c 7967 6f6e 7320 6361  t no polygons ca\n-00014d40: 6e20 6869 6465 2074 6865 6d2e 0a20 2064  n hide them..  d\n-00014d50: 6566 2061 7820 2864 782c 302c 3029 2025  ef ax (dx,0,0) %\n-00014d60: 2074 6970 7320 6f66 2074 6865 2061 7865   tips of the axe\n-00014d70: 730a 2020 6465 6620 6179 2028 302c 6479  s.  def ay (0,dy\n-00014d80: 2c30 290a 2020 6465 6620 617a 2028 302c  ,0).  def az (0,\n-00014d90: 302c 647a 290a 2020 6c69 6e65 5b61 7272  0,dz).  line[arr\n-00014da0: 6f77 733d 3c2d 3e2c 6c69 6e65 7769 6474  ows=<->,linewidt\n-00014db0: 683d 2e34 7074 5d28 6178 2928 4f29 2861  h=.4pt](ax)(O)(a\n-00014dc0: 7929 0a20 206c 696e 655b 6172 726f 7773  y).  line[arrows\n-00014dd0: 3d2d 3e2c 6c69 6e65 7769 6474 683d 2e34  =->,linewidth=.4\n-00014de0: 7074 5d28 4f29 2861 7a29 0a20 2025 2072  pt](O)(az).  % r\n-00014df0: 6570 6561 7420 646f 7474 6564 2061 7320  epeat dotted as \n-00014e00: 616e 206f 7665 726c 6179 2074 6f20 6869  an overlay to hi\n-00014e10: 6e74 2061 7420 7468 6520 6869 6464 656e  nt at the hidden\n-00014e20: 206c 696e 6573 0a20 206c 696e 655b 6c61   lines.  line[la\n-00014e30: 793d 6f76 6572 2c6c 696e 6573 7479 6c65  y=over,linestyle\n-00014e40: 3d64 6f74 7465 642c 6c69 6e65 7769 6474  =dotted,linewidt\n-00014e50: 683d 2e34 7074 5d28 6178 2928 4f29 2861  h=.4pt](ax)(O)(a\n-00014e60: 7929 0a20 206c 696e 655b 6c61 793d 6f76  y).  line[lay=ov\n-00014e70: 6572 2c6c 696e 6573 7479 6c65 3d64 6f74  er,linestyle=dot\n-00014e80: 7465 642c 6c69 6e65 7769 6474 683d 2e34  ted,linewidth=.4\n-00014e90: 7074 5d28 4f29 2861 7a29 0a20 2073 7065  pt](O)(az).  spe\n-00014ea0: 6369 616c 7c5c 666f 6f74 6e6f 7465 7369  cial|\\footnotesi\n-00014eb0: 7a65 0a20 2020 2020 2020 2020 205c 7570  ze.          \\up\n-00014ec0: 7574 5b64 5d23 317b 2478 247d 5c75 7075  ut[d]#1{$x$}\\upu\n-00014ed0: 745b 755d 2332 7b24 7924 7d5c 7570 7574  t[u]#2{$y$}\\uput\n-00014ee0: 5b6c 5d23 337b 247a 247d 7c0a 2020 2020  [l]#3{$z$}|.    \n-00014ef0: 2861 7829 2861 7929 2861 7a29 0a54 6865  (ax)(ay)(az).The\n-00014f00: 206c 6162 656c 7320 6172 6520 6170 706c   labels are appl\n-00014f10: 6965 6420 7769 7468 2027 5053 5472 6963  ied with 'PSTric\n-00014f20: 6b73 2720 7370 6563 6961 6c20 6f62 6a65  ks' special obje\n-00014f30: 6374 7320 6173 2075 7375 616c 2e0a 0a20  cts as usual... \n-00014f40: 2020 466f 7220 7468 6520 6865 6967 6874    For the height\n-00014f50: 2064 696d 656e 7369 6f6e 206d 6172 6b2c   dimension mark,\n-00014f60: 2074 6865 2070 6f77 6572 206f 6620 6166   the power of af\n-00014f70: 6669 6e65 2061 7269 7468 6574 6963 2069  fine arithetic i\n-00014f80: 7320 7665 7279 0a68 656c 7066 756c 2e0a  s very.helpful..\n-00014f90: 2020 6465 6620 6864 696d 5f72 6566 2075    def hdim_ref u\n-00014fa0: 6e69 7428 2870 3129 202d 2028 4f29 2920  nit((p1) - (O)) \n-00014fb0: 7468 656e 205b 5b73 6567 5f72 6f74 5d5d  then [[seg_rot]]\n-00014fc0: 5e32 0a20 2064 6566 2063 3020 2870 3029  ^2.  def c0 (p0)\n-00014fd0: 2074 6865 6e20 7363 616c 6528 5b4a 5d29   then scale([J])\n-00014fe0: 0a20 2064 6566 2068 3030 2028 6330 2920  .  def h00 (c0) \n-00014ff0: 2b20 312e 3120 2a20 5b68 6469 6d5f 7265  + 1.1 * [hdim_re\n-00015000: 665d 0a20 2064 6566 2068 3031 2028 6330  f].  def h01 (c0\n-00015010: 2920 2b20 312e 3920 2a20 5b68 6469 6d5f  ) + 1.9 * [hdim_\n-00015020: 7265 665d 0a20 2064 6566 2068 3032 2028  ref].  def h02 (\n-00015030: 6330 2920 2b20 312e 3820 2a20 5b68 6469  c0) + 1.8 * [hdi\n-00015040: 6d5f 7265 665d 0a20 206c 696e 6528 6830  m_ref].  line(h0\n-00015050: 3029 2868 3031 290a 2020 6465 6620 6831  0)(h01).  def h1\n-00015060: 3020 284f 2920 2b20 312e 3620 2a20 5b68  0 (O) + 1.6 * [h\n-00015070: 6469 6d5f 7265 665d 0a20 2064 6566 2068  dim_ref].  def h\n-00015080: 3131 2028 4f29 202b 2031 2e39 202a 205b  11 (O) + 1.9 * [\n-00015090: 6864 696d 5f72 6566 5d0a 2020 6465 6620  hdim_ref].  def \n-000150a0: 6831 3220 284f 2920 2b20 312e 3820 2a20  h12 (O) + 1.8 * \n-000150b0: 5b68 6469 6d5f 7265 665d 0a20 206c 696e  [hdim_ref].  lin\n-000150c0: 6528 6831 3029 2868 3131 290a 2020 6c69  e(h10)(h11).  li\n-000150d0: 6e65 5b61 7272 6f77 733d 3c2d 3e5d 2868  ne[arrows=<->](h\n-000150e0: 3032 2928 6831 3229 0a20 2064 6566 2068  02)(h12).  def h\n-000150f0: 6d32 2028 2868 3032 2920 2d20 284f 2920  m2 ((h02) - (O) \n-00015100: 2b20 2868 3132 2920 2d20 284f 2929 202f  + (h12) - (O)) /\n-00015110: 2032 202b 2028 4f29 0a20 2073 7065 6369   2 + (O).  speci\n-00015120: 616c 7c5c 666f 6f74 6e6f 7465 7369 7a65  al|\\footnotesize\n-00015130: 5c72 7075 742a 2331 7b24 6824 7d7c 2868  \\rput*#1{$h$}|(h\n-00015140: 6d32 290a 2020 2054 6865 2067 656e 6572  m2).   The gener\n-00015150: 616c 2069 6465 6120 656d 706c 6f79 6564  al idea employed\n-00015160: 2068 6572 6520 6973 2074 6f20 636f 6d70   here is to comp\n-00015170: 7574 6520 6120 756e 6974 2022 7265 6665  ute a unit \"refe\n-00015180: 7265 6e63 650a 7665 6374 6f72 2220 7061  rence.vector\" pa\n-00015190: 7261 6c6c 656c 2074 6f20 7468 6520 787a  rallel to the xz\n-000151a0: 2d70 6c61 6e65 2069 6e20 7468 6520 6465  -plane in the de\n-000151b0: 7369 7265 6420 6469 7265 6374 696f 6e20  sired direction \n-000151c0: 6f66 2074 6865 0a64 696d 656e 7369 6f6e  of the.dimension\n-000151d0: 2066 726f 6d20 7468 6520 6f72 6967 696e   from the origin\n-000151e0: 2e20 2054 6865 2074 7261 6e73 666f 726d  .  The transform\n-000151f0: 6174 696f 6e20 275b 5b73 6567 5f72 6f74  ation '[[seg_rot\n-00015200: 5d5d 5e32 2720 726f 7461 7465 730a 7477  ]]^2' rotates.tw\n-00015210: 6f20 7365 676d 656e 7473 2061 626f 7574  o segments about\n-00015220: 2074 6865 2079 2d61 7869 732e 2020 5768   the y-axis.  Wh\n-00015230: 656e 2061 7070 6c69 6564 2074 6f20 2728  en applied to '(\n-00015240: 7031 2920 2d20 284f 2927 2c20 7468 650a  p1) - (O)', the.\n-00015250: 7265 7375 6c74 696e 6720 7665 6374 6f72  resulting vector\n-00015260: 2070 6f69 6e74 7320 746f 2074 6865 2072   points to the r\n-00015270: 6967 6874 2061 7320 7368 6f77 6e2e 2020  ight as shown.  \n-00015280: 496e 2074 6869 7320 6d61 6e6e 6572 2c20  In this manner, \n-00015290: 7765 2063 616e 0a70 6963 6b20 616e 7920  we can.pick any \n-000152a0: 7665 7274 6578 2061 7320 7468 6520 6c6f  vertex as the lo\n-000152b0: 6361 7469 6f6e 206f 6620 7468 6520 6865  cation of the he\n-000152c0: 6967 6874 2064 696d 656e 7369 6f6e 206c  ight dimension l\n-000152d0: 696e 6573 2062 7920 7661 7279 696e 670a  ines by varying.\n-000152e0: 7468 6520 6578 706f 6e65 6e74 206f 6620  the exponent of \n-000152f0: 275b 5b73 6567 5f72 6f74 5d5d 272e 2020  '[[seg_rot]]'.  \n-00015300: 5468 6973 2069 7320 6f6e 6c79 206f 6e65  This is only one\n-00015310: 206f 6620 6d61 6e79 2070 6f73 7369 626c   of many possibl\n-00015320: 650a 7374 7261 7465 6769 6573 2e0a 0a20  e.strategies... \n-00015330: 2020 5468 6520 636f 6d70 7574 6174 696f    The computatio\n-00015340: 6e20 6f66 2027 686d 3227 2069 7320 6120  n of 'hm2' is a \n-00015350: 7573 6566 756c 2069 6469 6f6d 2066 6f72  useful idiom for\n-00015360: 2066 696e 6469 6e67 2074 6865 2063 656e   finding the cen\n-00015370: 7472 6f69 640a 6f66 2061 2073 6574 206f  troid.of a set o\n-00015380: 6620 706f 696e 7473 2e0a 0a20 2020 5468  f points...   Th\n-00015390: 6520 7477 6f20 7261 6469 7573 206d 6172  e two radius mar\n-000153a0: 6b73 2061 7265 2064 6f6e 6520 7369 6d69  ks are done simi\n-000153b0: 6c61 726c 792c 2073 6f20 7765 2070 7265  larly, so we pre\n-000153c0: 7365 6e74 2074 6865 2063 6f64 650a 7769  sent the code.wi\n-000153d0: 7468 6f75 7420 636f 6d6d 656e 742e 0a20  thout comment.. \n-000153e0: 2025 2072 6164 6975 7320 6d65 6173 7572   % radius measur\n-000153f0: 656d 656e 7420 6d61 726b 730a 2020 6465  ement marks.  de\n-00015400: 6620 6761 7020 5b30 2c2e 322c 305d 2020  f gap [0,.2,0]  \n-00015410: 2520 7573 6564 2074 6f20 6372 6561 7465  % used to create\n-00015420: 2073 6d61 6c6c 2076 6572 7469 6361 6c20   small vertical \n-00015430: 6761 7073 0a0a 2020 2520 6669 7273 7420  gaps..  % first \n-00015440: 7231 0a20 2064 6566 2075 7031 205b 302c  r1.  def up1 [0,\n-00015450: 332e 312c 305d 2025 2074 6963 6b20 7269  3.1,0] % tick ri\n-00015460: 7365 7320 6162 6f76 6520 6469 6d65 6e73  ses above dimens\n-00015470: 696f 6e20 6120 6c69 7474 6c65 0a20 2064  ion a little.  d\n-00015480: 6566 2072 3120 2828 7031 2920 7468 656e  ef r1 ((p1) then\n-00015490: 205b 5b73 6567 5f72 6f74 5d5d 5e2d 3229   [[seg_rot]]^-2)\n-000154a0: 202b 205b 7570 315d 0a20 2064 6566 2072   + [up1].  def r\n-000154b0: 3163 2028 7231 2920 7468 656e 2073 6361  1c (r1) then sca\n-000154c0: 6c65 285b 4a5d 290a 2020 6465 6620 7231  le([J]).  def r1\n-000154d0: 7420 2872 3129 202b 205b 6761 705d 0a20  t (r1) + [gap]. \n-000154e0: 2064 6566 2072 3162 2028 2872 3174 2920   def r1b ((r1t) \n-000154f0: 7468 656e 2073 6361 6c65 285b 312c 302c  then scale([1,0,\n-00015500: 315d 2929 202b 205b 6761 705d 0a20 206c  1])) + [gap].  l\n-00015510: 696e 655b 6172 726f 7773 3d3c 2d3e 5d28  ine[arrows=<->](\n-00015520: 7231 6329 2872 3129 2020 2520 6469 6d65  r1c)(r1)  % dime\n-00015530: 6e73 696f 6e20 6c69 6e65 0a20 206c 696e  nsion line.  lin\n-00015540: 6528 7231 6229 2872 3174 2920 2020 2020  e(r1b)(r1t)     \n-00015550: 2020 2020 2020 2020 2520 7469 636b 0a20          % tick. \n-00015560: 2064 6566 2072 316d 2028 2872 3129 202d   def r1m ((r1) -\n-00015570: 2028 4f29 202b 2028 7231 6329 202d 2028   (O) + (r1c) - (\n-00015580: 4f29 2920 2f20 3220 2b20 284f 2920 2520  O)) / 2 + (O) % \n-00015590: 6c61 6265 6c20 706f 7369 7469 6f6e 0a20  label position. \n-000155a0: 2073 7065 6369 616c 207c 5c66 6f6f 746e   special |\\footn\n-000155b0: 6f74 6573 697a 655c 7270 7574 2a23 317b  otesize\\rput*#1{\n-000155c0: 2472 5f31 247d 7c28 7231 6d29 2020 2520  $r_1$}|(r1m)  % \n-000155d0: 6c61 6265 6c0a 0a20 2025 2073 616d 6520  label..  % same \n-000155e0: 6472 696c 6c20 666f 7220 7230 2c20 6275  drill for r0, bu\n-000155f0: 7420 6d75 7374 2070 726f 6a65 6374 2064  t must project d\n-00015600: 6f77 6e20 6669 7273 740a 2020 6465 6620  own first.  def \n-00015610: 7570 3020 5b30 2c32 2e37 2c30 5d0a 2020  up0 [0,2.7,0].  \n-00015620: 6465 6620 7230 2028 2870 3029 2074 6865  def r0 ((p0) the\n-00015630: 6e20 7363 616c 6528 5b31 2c30 2c31 5d29  n scale([1,0,1])\n-00015640: 2074 6865 6e20 5b5b 7365 675f 726f 745d   then [[seg_rot]\n-00015650: 5d5e 2d32 2920 2b20 5b75 7030 5d0a 2020  ]^-2) + [up0].  \n-00015660: 6465 6620 7230 6320 2872 3029 2074 6865  def r0c (r0) the\n-00015670: 6e20 7363 616c 6528 5b4a 5d29 0a20 2064  n scale([J]).  d\n-00015680: 6566 2072 3074 2028 7230 2920 2b20 5b67  ef r0t (r0) + [g\n-00015690: 6170 5d0a 2020 6465 6620 7230 6220 2828  ap].  def r0b ((\n-000156a0: 7030 2920 7468 656e 205b 5b73 6567 5f72  p0) then [[seg_r\n-000156b0: 6f74 5d5d 5e2d 3229 202b 205b 6761 705d  ot]]^-2) + [gap]\n-000156c0: 0a20 206c 696e 655b 6172 726f 7773 3d3c  .  line[arrows=<\n-000156d0: 2d3e 5d28 7230 6329 2872 3029 0a20 206c  ->](r0c)(r0).  l\n-000156e0: 696e 6528 7230 6229 2872 3074 290a 2020  ine(r0b)(r0t).  \n-000156f0: 6465 6620 7230 6d20 2828 7230 2920 2d20  def r0m ((r0) - \n-00015700: 284f 2920 2b20 2872 3063 2920 2d20 284f  (O) + (r0c) - (O\n-00015710: 2929 202f 2032 202b 2028 4f29 0a20 2073  )) / 2 + (O).  s\n-00015720: 7065 6369 616c 207c 5c66 6f6f 746e 6f74  pecial |\\footnot\n-00015730: 6573 697a 655c 7270 7574 2a23 317b 2472  esize\\rput*#1{$r\n-00015740: 5f30 247d 7c28 7230 6d29 0a0a 2020 2054  _0$}|(r0m)..   T\n-00015750: 6865 2073 6563 6f6e 6420 6472 6177 696e  he second drawin\n-00015760: 6720 7573 6573 2074 6865 2073 616d 6520  g uses the same \n-00015770: 7465 6368 6e69 7175 6573 2e20 204f 6e6c  techniques.  Onl\n-00015780: 7920 7468 6520 6d65 7468 6f64 2066 6f72  y the method for\n-00015790: 0a64 7261 7769 6e67 2074 6865 2065 6c6c  .drawing the ell\n-000157a0: 6970 7469 6361 6c20 6172 6320 6973 206e  iptical arc is n\n-000157b0: 6577 2e20 2048 6572 6520 6973 2074 6865  ew.  Here is the\n-000157c0: 2063 6f64 652e 0a20 2064 6566 206d 6964   code..  def mid\n-000157d0: 2028 2870 3030 292d 284f 292b 2870 3130   ((p00)-(O)+(p10\n-000157e0: 292d 284f 292b 2870 3131 292d 284f 292b  )-(O)+(p11)-(O)+\n-000157f0: 2870 3031 292d 284f 2929 2f34 2b28 4f29  (p01)-(O))/4+(O)\n-00015800: 0a20 2073 7065 6369 616c 7c5c 7270 7574  .  special|\\rput\n-00015810: 2331 7b5c 7073 6375 7374 6f6d 7b0a 2020  #1{\\pscustom{.  \n-00015820: 2020 5c73 6361 6c65 7b31 2031 2e33 7d0a    \\scale{1 1.3}.\n-00015830: 2020 2020 5c70 7361 7263 5b61 7272 6f77      \\psarc[arrow\n-00015840: 6c65 6e67 7468 3d2e 355d 7b2d 3e7d 7b2e  length=.5]{->}{.\n-00015850: 3235 7d7b 2d36 307d 7b32 3430 7d7d 7d7c  25}{-60}{240}}}|\n-00015860: 0a20 2020 205b 6c61 793d 6f76 6572 5d28  .    [lay=over](\n-00015870: 6d69 6429 0a57 6520 636f 756c 6420 6861  mid).We could ha\n-00015880: 7665 2073 7765 7074 2061 2070 6f69 6e74  ve swept a point\n-00015890: 2074 6f20 6d61 6b65 2074 6865 2061 7263   to make the arc\n-000158a0: 2077 6974 6820 2773 6b65 7463 6827 2c20   with 'sketch', \n-000158b0: 6275 7420 7573 696e 6720 610a 2750 5354  but using a.'PST\n-000158c0: 7269 636b 7327 2063 7573 746f 6d20 6772  ricks' custom gr\n-000158d0: 6170 6869 6320 7761 7320 7369 6d70 6c65  aphic was simple\n-000158e0: 722e 2020 4167 6169 6e20 7765 2063 6f6d  r.  Again we com\n-000158f0: 7075 7465 6420 7468 6520 6365 6e74 726f  puted the centro\n-00015900: 6964 0a6f 6620 7468 6520 7175 6164 7269  id.of the quadri\n-00015910: 6c61 7465 7261 6c20 6279 2061 7665 7261  lateral by avera\n-00015920: 6769 6e67 2070 6f69 6e74 732e 2020 4e6f  ging points.  No\n-00015930: 7465 2074 6861 7420 7363 616c 696e 6720  te that scaling \n-00015940: 696e 0a50 6f73 7473 6372 6970 7420 6469  in.Postscript di\n-00015950: 7374 6f72 7473 2074 6865 2061 7272 6f77  storts the arrow\n-00015960: 6865 6164 2c20 6275 7420 696e 2074 6869  head, but in thi\n-00015970: 7320 6361 7365 2074 6865 2064 6973 746f  s case the disto\n-00015980: 7274 696f 6e0a 6163 7475 616c 6c79 206c  rtion.actually l\n-00015990: 6f6f 6b73 2062 6574 7465 7220 696e 2074  ooks better in t\n-000159a0: 6865 2070 726f 6a65 6374 696f 6e20 6f66  he projection of\n-000159b0: 2074 6865 2073 6c61 6e74 6564 2066 6163   the slanted fac\n-000159c0: 652e 2020 4120 2773 6b65 7463 6827 0a61  e.  A 'sketch'.a\n-000159d0: 7272 6f77 6865 6164 2077 6f75 6c64 206e  rrowhead would n\n-000159e0: 6f74 2068 6176 6520 6265 656e 2064 6973  ot have been dis\n-000159f0: 746f 7274 6564 2e0a 0a20 2020 5468 6520  torted...   The \n-00015a00: 636f 6d70 6c65 7465 2063 6f64 6520 666f  complete code fo\n-00015a10: 7220 7468 6973 2065 7861 6d70 6c65 2c20  r this example, \n-00015a20: 7768 6963 6820 6472 6177 7320 6569 7468  which draws eith\n-00015a30: 6572 2066 6967 7572 650a 6465 7065 6e64  er figure.depend\n-00015a40: 696e 6720 6f6e 2074 6865 2064 6566 696e  ing on the defin\n-00015a50: 6974 696f 6e20 6f66 2074 6865 2074 6167  ition of the tag\n-00015a60: 2027 3c6c 6162 656c 6564 3e27 2c20 6973   '<labeled>', is\n-00015a70: 2069 6e63 6c75 6465 6420 696e 2074 6865   included in the\n-00015a80: 0a27 736b 6574 6368 2720 6469 7374 7269  .'sketch' distri\n-00015a90: 6275 7469 6f6e 2069 6e20 7468 6520 6669  bution in the fi\n-00015aa0: 6c65 2027 7472 756e 6361 7465 6463 6f6e  le 'truncatedcon\n-00015ab0: 652e 736b 272e 0a0a 1f0a 4669 6c65 3a20  e.sk'.....File: \n-00015ac0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n-00015ad0: 6465 3a20 4120 6869 6572 6172 6368 6963  de: A hierarchic\n-00015ae0: 616c 206d 6f64 656c 2c20 204e 6578 743a  al model,  Next:\n-00015af0: 2043 6176 6561 7473 2c20 2050 7265 763a   Caveats,  Prev:\n-00015b00: 2041 2074 6563 686e 6963 616c 2064 7261   A technical dra\n-00015b10: 7769 6e67 2c20 2055 703a 2042 7569 6c64  wing,  Up: Build\n-00015b20: 696e 6720 6120 6472 6177 696e 670a 0a34  ing a drawing..4\n-00015b30: 2e33 2041 2068 6965 7261 7263 6869 6361  .3 A hierarchica\n-00015b40: 6c20 6d6f 6465 6c0a 3d3d 3d3d 3d3d 3d3d  l model.========\n-00015b50: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d  ================\n-00015b60: 0a0a 5768 696c 6520 2773 6b65 7463 6827  ..While 'sketch'\n-00015b70: 2077 6173 206e 6576 6572 206d 6561 6e74   was never meant\n-00015b80: 2074 6f20 6265 2061 2067 656f 6d65 7472   to be a geometr\n-00015b90: 6963 206d 6f64 656c 696e 6720 6c61 6e67  ic modeling lang\n-00015ba0: 7561 6765 2c20 6974 0a63 6f6d 6573 2066  uage, it.comes f\n-00015bb0: 6169 726c 7920 636c 6f73 652e 2020 5468  airly close.  Th\n-00015bc0: 6520 666f 6c6c 6f77 696e 6720 6578 616d  e following exam\n-00015bd0: 706c 6520 7075 7473 2061 6c6c 2077 6520  ple puts all we \n-00015be0: 6861 7665 2073 6565 6e20 746f 2077 6f72  have seen to wor\n-00015bf0: 6b0a 696e 2061 2076 6572 7920 7369 6d70  k.in a very simp\n-00015c00: 6c65 206d 6f64 656c 206f 6620 7468 6520  le model of the \n-00015c10: 6875 6d61 6e20 6861 6e64 2e20 2053 7461  human hand.  Sta\n-00015c20: 7274 2062 7920 7377 6565 7069 6e67 2061  rt by sweeping a\n-00015c30: 206c 696e 6520 746f 0a6d 616b 6520 6120   line to.make a \n-00015c40: 7472 756e 6361 7465 6420 636f 6e65 2c20  truncated cone, \n-00015c50: 7768 6963 6820 7769 6c6c 2062 6520 636f  which will be co\n-00015c60: 7069 6564 206f 7665 7220 616e 6420 6f76  pied over and ov\n-00015c70: 6572 2061 6761 696e 2074 6f20 6d61 6b65  er again to make\n-00015c80: 0a74 6865 2073 6567 6d65 6e74 7320 6f66  .the segments of\n-00015c90: 2066 696e 6765 7273 2e0a 2020 6465 6620   fingers..  def \n-00015ca0: 4f20 2830 2c30 2c30 2920 2520 6f72 6967  O (0,0,0) % orig\n-00015cb0: 696e 0a20 2064 6566 2049 205b 312c 302c  in.  def I [1,0,\n-00015cc0: 305d 2064 6566 204a 205b 302c 312c 305d  0] def J [0,1,0]\n-00015cd0: 2064 6566 204b 205b 302c 302c 315d 2025   def K [0,0,1] %\n-00015ce0: 2063 616e 6f6e 6963 616c 2075 6e69 7420   canonical unit \n-00015cf0: 7665 6374 6f72 730a 2020 6465 6620 7365  vectors.  def se\n-00015d00: 676d 656e 7420 7b0a 2020 2020 6465 6620  gment {.    def \n-00015d10: 6e5f 6661 6365 7320 380a 2020 2020 7377  n_faces 8.    sw\n-00015d20: 6565 7020 7b20 6e5f 6661 6365 733c 3e2c  eep { n_faces<>,\n-00015d30: 2072 6f74 6174 6528 3336 3020 2f20 6e5f   rotate(360 / n_\n-00015d40: 6661 6365 732c 205b 4a5d 2920 7d20 0a20  faces, [J]) } . \n-00015d50: 2020 2020 206c 696e 6528 7072 6f78 696d       line(proxim\n-00015d60: 616c 5f72 6164 2c20 3029 2864 6973 7461  al_rad, 0)(dista\n-00015d70: 6c5f 7261 642c 2064 6973 7461 6c5f 6c65  l_rad, distal_le\n-00015d80: 6e29 0a20 207d 0a49 6e20 6861 6e64 2061  n).  }.In hand a\n-00015d90: 6e61 746f 6d79 2c20 5f64 6973 7461 6c5f  natomy, _distal_\n-00015da0: 2069 7320 2261 7420 7468 6520 7469 7022   is \"at the tip\"\n-00015db0: 2061 6e64 205f 7072 6f78 696d 616c 5f20   and _proximal_ \n-00015dc0: 6973 2022 696e 2074 6865 2061 7265 610a  is \"in the area.\n-00015dd0: 6f66 2074 6865 2070 616c 6d2e 2220 2057  of the palm.\"  W\n-00015de0: 6520 6861 7665 206f 6d69 7474 6564 2061  e have omitted a\n-00015df0: 6c6c 2074 6865 2073 6361 6c61 7220 636f  ll the scalar co\n-00015e00: 6e73 7461 6e74 732e 2020 596f 7520 6361  nstants.  You ca\n-00015e10: 6e20 6669 6e64 0a74 6865 6d20 696e 2027  n find.them in '\n-00015e20: 6861 6e64 2e73 6b27 2c20 7768 6963 6820  hand.sk', which \n-00015e30: 6973 2070 726f 7669 6465 6420 696e 2074  is provided in t\n-00015e40: 6865 2027 736b 6574 6368 2720 6469 7374  he 'sketch' dist\n-00015e50: 7269 6275 7469 6f6e 2e0a 0a20 2020 5765  ribution...   We\n-00015e60: 2061 6c73 6f20 6e65 6564 2061 2070 726f   also need a pro\n-00015e70: 746f 7479 7069 6361 6c20 7370 6865 7265  totypical sphere\n-00015e80: 2074 6f20 7573 6520 666f 7220 7468 6520   to use for the \n-00015e90: 6a6f 696e 7473 2074 6865 6d73 656c 7665  joints themselve\n-00015ea0: 732e 0a20 2064 6566 206a 6f69 6e74 5f73  s..  def joint_s\n-00015eb0: 7068 6572 6520 7b0a 2020 2020 6465 6620  phere {.    def \n-00015ec0: 6e5f 6a6f 696e 745f 6661 6365 7320 380a  n_joint_faces 8.\n-00015ed0: 2020 2020 7377 6565 7020 5b66 696c 6c63      sweep [fillc\n-00015ee0: 6f6c 6f72 3d72 6564 5d20 7b20 6e5f 6a6f  olor=red] { n_jo\n-00015ef0: 696e 745f 6661 6365 732c 2072 6f74 6174  int_faces, rotat\n-00015f00: 6528 3336 3020 2f20 6e5f 6a6f 696e 745f  e(360 / n_joint_\n-00015f10: 6661 6365 732c 205b 4a5d 2920 7d0a 2020  faces, [J]) }.  \n-00015f20: 2020 2020 7377 6565 7020 7b20 6e5f 6a6f      sweep { n_jo\n-00015f30: 696e 745f 6661 6365 732c 2072 6f74 6174  int_faces, rotat\n-00015f40: 6528 3138 3020 2f20 6e5f 6a6f 696e 745f  e(180 / n_joint_\n-00015f50: 6661 6365 7329 207d 200a 2020 2020 2020  faces) } .      \n-00015f60: 2020 2830 2c20 2d6a 6f69 6e74 5f72 6164    (0, -joint_rad\n-00015f70: 290a 2020 7d0a 0a20 2020 5765 276c 6c20  ).  }..   We'll \n-00015f80: 6e6f 7720 6465 7369 676e 2074 6865 2069  now design the i\n-00015f90: 6e64 6578 2066 696e 6765 7220 286e 756d  ndex finger (num\n-00015fa0: 6265 7220 3120 696e 206f 7572 206e 6f74  ber 1 in our not\n-00015fb0: 6174 696f 6e61 6c0a 636f 6e76 656e 7469  ational.conventi\n-00015fc0: 6f6e 3b20 6669 6e67 6572 2030 2069 7320  on; finger 0 is \n-00015fd0: 7468 6520 7468 756d 6229 2e20 2054 6865  the thumb).  The\n-00015fe0: 2064 6973 7461 6c20 726f 7461 7469 6f6e   distal rotation\n-00015ff0: 2066 6f72 2074 6865 2066 696e 6765 720a   for the finger.\n-00016000: 6170 706c 6965 7320 6f6e 6c79 2074 6f20  applies only to \n-00016010: 7468 6520 7469 702c 2073 6f20 7765 2064  the tip, so we d\n-00016020: 6566 696e 6520 7468 6520 666f 6c6c 6f77  efine the follow\n-00016030: 696e 672e 0a20 2064 6566 2064 6973 7461  ing..  def dista\n-00016040: 6c5f 3120 7b0a 2020 2020 7075 7420 7b20  l_1 {.    put { \n-00016050: 7472 616e 736c 6174 6528 6a6f 696e 745f  translate(joint_\n-00016060: 6761 7020 2a20 6a6f 696e 745f 7261 6420  gap * joint_rad \n-00016070: 2a20 5b4a 5d29 200a 2020 2020 2020 2020  * [J]) .        \n-00016080: 2020 7468 656e 2072 6f74 6174 6528 6469    then rotate(di\n-00016090: 7374 616c 5f31 5f72 6f74 2c20 5b49 5d29  stal_1_rot, [I])\n-000160a0: 200a 2020 2020 2020 2020 2020 7468 656e   .          then\n-000160b0: 2074 7261 6e73 6c61 7465 2828 6469 7374   translate((dist\n-000160c0: 616c 5f6c 656e 202b 206a 6f69 6e74 5f67  al_len + joint_g\n-000160d0: 6170 202a 206a 6f69 6e74 5f72 6164 2920  ap * joint_rad) \n-000160e0: 2a20 5b4a 5d29 207d 0a20 2020 2020 207b  * [J]) }.      {\n-000160f0: 7365 676d 656e 747d 0a20 2020 2070 7574  segment}.    put\n-00016100: 207b 2072 6f74 6174 6528 6469 7374 616c   { rotate(distal\n-00016110: 5f31 5f72 6f74 202f 2032 2c20 5b49 5d29  _1_rot / 2, [I])\n-00016120: 0a20 2020 2020 2020 2020 2074 6865 6e20  .          then \n-00016130: 7472 616e 736c 6174 6528 2864 6973 7461  translate((dista\n-00016140: 6c5f 6c65 6e20 2b20 6a6f 696e 745f 6761  l_len + joint_ga\n-00016150: 7020 2a20 6a6f 696e 745f 7261 6429 202a  p * joint_rad) *\n-00016160: 205b 4a5d 2920 7d20 0a20 2020 2020 207b   [J]) } .      {\n-00016170: 6a6f 696e 745f 7370 6865 7265 7d0a 2020  joint_sphere}.  \n-00016180: 2020 7075 7420 7b20 7363 616c 6528 205b    put { scale( [\n-00016190: 4a5d 202b 2070 726f 7869 6d61 6c5f 6469  J] + proximal_di\n-000161a0: 7374 616c 5f72 6174 696f 202a 2028 5b49  stal_ratio * ([I\n-000161b0: 5d2b 5b4b 5d29 2029 207d 0a20 2020 2020  ]+[K]) ) }.     \n-000161c0: 207b 7365 676d 656e 747d 0a20 207d 2020   {segment}.  }  \n-000161d0: 0a54 6865 2069 6465 6e74 6966 6965 7273  .The identifiers\n-000161e0: 2068 6572 6520 6172 6520 666f 7220 7369   here are for si\n-000161f0: 7a65 2061 6e64 206c 6f63 6174 696f 6e20  ze and location \n-00016200: 636f 6e73 7461 6e74 732e 2020 5468 6520  constants.  The \n-00016210: 6578 6365 7074 696f 6e0a 6973 2027 6469  exception.is 'di\n-00016220: 7374 616c 5f72 6f74 5f31 272e 2020 5468  stal_rot_1'.  Th\n-00016230: 6973 2072 6f74 6174 696f 6e20 7061 7261  is rotation para\n-00016240: 6d65 7465 7220 6d6f 6465 6c73 2074 6865  meter models the\n-00016250: 2066 6c65 7869 6e67 206f 6620 7468 650a   flexing of the.\n-00016260: 6669 6e67 6572 2074 6970 2e20 2054 6865  finger tip.  The\n-00016270: 2066 6972 7374 2027 7075 7427 206d 616b   first 'put' mak\n-00016280: 6573 2061 2063 6f70 7920 6f66 2074 6865  es a copy of the\n-00016290: 2066 696e 6765 7220 7365 676d 656e 7420   finger segment \n-000162a0: 7468 6174 2069 730a 7472 616e 736c 6174  that is.translat\n-000162b0: 6564 2075 7077 6172 6420 6a75 7374 2066  ed upward just f\n-000162c0: 6172 2065 6e6f 7567 6820 746f 206d 616b  ar enough to mak\n-000162d0: 6520 726f 6f6d 2066 6f72 2074 6865 2073  e room for the s\n-000162e0: 7068 6572 6963 616c 206a 6f69 6e74 2e0a  pherical joint..\n-000162f0: 5468 656e 2069 7420 6170 706c 6965 7320  Then it applies \n-00016300: 7468 6520 6469 7374 616c 2072 6f74 6174  the distal rotat\n-00016310: 696f 6e2e 2020 4669 6e61 6c6c 7920 6974  ion.  Finally it\n-00016320: 2074 7261 6e73 6c61 7465 7320 7468 6520   translates the \n-00016330: 7768 6f6c 650a 6173 7365 6d62 6c79 2075  whole.assembly u\n-00016340: 7077 6172 6420 6167 6169 6e20 746f 206d  pward again to m\n-00016350: 616b 6520 726f 6f6d 2066 6f72 2074 6865  ake room for the\n-00016360: 206d 6964 646c 6520 7068 6c61 6e67 6573   middle phlanges\n-00016370: 2028 7468 6520 6e65 7874 0a62 6f6e 6520   (the next.bone \n-00016380: 746f 7761 7264 2074 6865 2070 616c 6d29  toward the palm)\n-00016390: 2e20 2054 6865 2073 6563 6f6e 6420 2770  .  The second 'p\n-000163a0: 7574 2720 706f 7369 7469 6f6e 7320 7468  ut' positions th\n-000163b0: 6520 7370 6865 7265 2e20 2054 6865 7265  e sphere.  There\n-000163c0: 2069 730a 6120 726f 7461 7469 6f6e 2074   is.a rotation t\n-000163d0: 6f20 706c 6163 6520 7468 6520 6772 6964  o place the grid\n-000163e0: 206f 6e20 7468 6520 7370 6865 7265 2073   on the sphere s\n-000163f0: 7572 6661 6365 2061 7420 616e 206e 6963  urface at an nic\n-00016400: 6520 616e 676c 652c 0a74 6865 6e20 6120  e angle,.then a \n-00016410: 7472 616e 736c 6174 696f 6e20 746f 2074  translation to t\n-00016420: 6865 2062 6173 6520 6f66 2074 6865 2064  he base of the d\n-00016430: 6973 7461 6c20 7068 6c61 6e67 6573 2c20  istal phlanges, \n-00016440: 7768 6963 6820 6973 2061 6c73 6f0a 6365  which is also.ce\n-00016450: 6e74 6572 206f 6620 6974 7320 726f 7461  nter of its rota\n-00016460: 7469 6f6e 2e20 2046 696e 616c 6c79 2c20  tion.  Finally, \n-00016470: 7468 6520 6c61 7374 2027 7075 7427 2070  the last 'put' p\n-00016480: 6f73 6974 696f 6e73 2074 6865 206d 6964  ositions the mid\n-00016490: 646c 650a 7365 676d 656e 7420 6974 7365  dle.segment itse\n-000164a0: 6c66 2e0a 0a20 2020 5468 6520 6d69 6464  lf...   The midd\n-000164b0: 6c65 206a 6f69 6e74 2069 7320 7468 6520  le joint is the \n-000164c0: 6e65 7874 206f 6e65 2064 6f77 6e2c 2077  next one down, w\n-000164d0: 6974 6820 726f 7461 7469 6f6e 2061 6e67  ith rotation ang\n-000164e0: 6c65 0a27 6d69 6464 6c65 5f72 6f74 5f31  le.'middle_rot_1\n-000164f0: 272e 2020 5768 656e 2074 6869 7320 616e  '.  When this an\n-00016500: 676c 6520 6368 616e 6765 732c 2077 6520  gle changes, we \n-00016510: 6e65 6564 2061 6c6c 2074 6865 206f 626a  need all the obj\n-00016520: 6563 7473 2069 6e0a 2764 6973 7461 6c5f  ects in.'distal_\n-00016530: 3127 2074 6f20 726f 7461 7465 2061 7320  1' to rotate as \n-00016540: 6120 756e 6974 2e20 2054 6869 7320 6973  a unit.  This is\n-00016550: 2074 6865 2072 6561 736f 6e69 6e67 2062   the reasoning b\n-00016560: 6568 696e 6420 7468 6520 6e65 7874 0a64  ehind the next.d\n-00016570: 6566 696e 6974 696f 6e2e 0a20 2064 6566  efinition..  def\n-00016580: 2066 696e 6765 725f 3120 7b0a 2020 2020   finger_1 {.    \n-00016590: 7075 7420 7b20 7472 616e 736c 6174 6528  put { translate(\n-000165a0: 6a6f 696e 745f 6761 7020 2a20 6a6f 696e  joint_gap * join\n-000165b0: 745f 7261 6420 2a20 5b4a 5d29 0a20 2020  t_rad * [J]).   \n-000165c0: 2020 2020 2020 2074 6865 6e20 726f 7461         then rota\n-000165d0: 7465 286d 6964 646c 655f 315f 726f 742c  te(middle_1_rot,\n-000165e0: 205b 495d 290a 2020 2020 2020 2020 2020   [I]).          \n-000165f0: 7468 656e 2074 7261 6e73 6c61 7465 2828  then translate((\n-00016600: 6d69 6464 6c65 5f72 6174 696f 202a 2064  middle_ratio * d\n-00016610: 6973 7461 6c5f 6c65 6e20 2b20 0a20 2020  istal_len + .   \n+000117b0: 0a0a 416e 206f 7074 696f 6e61 6c20 676c  ..An optional gl\n+000117c0: 6f62 616c 2065 6e76 6972 6f6e 6d65 6e74  obal environment\n+000117d0: 2062 6c6f 636b 2070 726f 7669 6465 7320   block provides \n+000117e0: 6120 6665 7720 7761 7973 2074 6f20 6166  a few ways to af\n+000117f0: 6665 6374 2074 6865 0a65 6e74 6972 6520  fect the.entire \n+00011800: 7363 656e 652e 2020 5468 6520 626c 6f63  scene.  The bloc\n+00011810: 6b20 6d75 7374 2061 7070 6561 7220 6173  k must appear as\n+00011820: 2074 6865 206c 6173 7420 7465 7874 2069   the last text i\n+00011830: 6e20 7468 6520 2773 6b65 7463 6827 0a69  n the 'sketch'.i\n+00011840: 6e70 7574 2066 696c 652e 2020 4974 206d  nput file.  It m\n+00011850: 6179 2069 6e63 6c75 6465 2064 6566 696e  ay include defin\n+00011860: 6974 696f 6e73 2c20 6275 7420 6e6f 7465  itions, but note\n+00011870: 2074 6861 7420 7072 6576 696f 7573 0a64   that previous.d\n+00011880: 6566 696e 6974 696f 6e73 2061 7420 7468  efinitions at th\n+00011890: 6520 746f 7020 6c65 7665 6c20 286e 6f74  e top level (not\n+000118a0: 206e 6573 7465 6420 696e 7369 6465 2062   nested inside b\n+000118b0: 6c6f 636b 7329 2061 7265 2061 6c73 6f0a  locks) are also.\n+000118c0: 6176 6169 6c61 626c 652e 0a0a 2a53 796e  available...*Syn\n+000118d0: 7461 783a 2a0a 2020 2020 2067 6c6f 6261  tax:*.     globa\n+000118e0: 6c20 7b20 454e 5649 524f 4e4d 454e 545f  l { ENVIRONMENT_\n+000118f0: 5345 5454 494e 4753 207d 0a54 6865 2063  SETTINGS }.The c\n+00011900: 6f6e 7465 6e74 7320 6f66 2045 4e56 4952  ontents of ENVIR\n+00011910: 4f4e 4d45 4e54 5f53 4554 5449 4e47 5320  ONMENT_SETTINGS \n+00011920: 6172 6520 6469 7363 7573 7365 6420 696e  are discussed in\n+00011930: 2074 6865 2073 6563 7469 6f6e 7320 7468   the sections th\n+00011940: 6174 0a66 6f6c 6c6f 772e 0a0a 2a20 4d65  at.follow...* Me\n+00011950: 6e75 3a0a 0a2a 2047 6c6f 6261 6c20 6f70  nu:..* Global op\n+00011960: 7469 6f6e 733a 3a20 2020 2020 2020 2020  tions::         \n+00011970: 2020 2020 2041 7474 7269 6275 7465 7320       Attributes \n+00011980: 6f66 2074 6865 2065 6e74 6972 6520 6472  of the entire dr\n+00011990: 6177 696e 672e 0a2a 2043 616d 6572 613a  awing..* Camera:\n+000119a0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000119b0: 2020 2020 2020 2041 2066 696e 616c 2063         A final c\n+000119c0: 616d 6572 6120 7472 616e 7366 6f72 6d61  amera transforma\n+000119d0: 7469 6f6e 206f 6620 7468 6520 7363 656e  tion of the scen\n+000119e0: 652e 0a2a 2050 6963 7475 7265 2062 6f78  e..* Picture box\n+000119f0: 3a3a 2020 2020 2020 2020 2020 2020 2020  ::              \n+00011a00: 2020 2053 6574 7469 6e67 2074 6865 2062     Setting the b\n+00011a10: 6f75 6e64 696e 6720 626f 7820 616e 6420  ounding box and \n+00011a20: 3264 2063 6c69 7070 696e 672e 0a2a 2046  2d clipping..* F\n+00011a30: 7261 6d65 3a3a 2020 2020 2020 2020 2020  rame::          \n+00011a40: 2020 2020 2020 2020 2020 2020 2041 6464               Add\n+00011a50: 696e 6720 6120 626f 7820 6172 6f75 6e64  ing a box around\n+00011a60: 2074 6865 2064 7261 7769 6e67 2e0a 2a20   the drawing..* \n+00011a70: 4c61 6e67 7561 6765 3a3a 2020 2020 2020  Language::      \n+00011a80: 2020 2020 2020 2020 2020 2020 2020 5365                Se\n+00011a90: 7474 696e 6720 7468 6520 6f75 7470 7574  tting the output\n+00011aa0: 206c 616e 6775 6167 652e 0a0a 1f0a 4669   language.....Fi\n+00011ab0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n+00011ac0: 2020 4e6f 6465 3a20 476c 6f62 616c 206f    Node: Global o\n+00011ad0: 7074 696f 6e73 2c20 204e 6578 743a 2043  ptions,  Next: C\n+00011ae0: 616d 6572 612c 2020 5072 6576 3a20 476c  amera,  Prev: Gl\n+00011af0: 6f62 616c 2065 6e76 6972 6f6e 6d65 6e74  obal environment\n+00011b00: 2c20 2055 703a 2047 6c6f 6261 6c20 656e  ,  Up: Global en\n+00011b10: 7669 726f 6e6d 656e 740a 0a33 2e34 2e31  vironment..3.4.1\n+00011b20: 2047 6c6f 6261 6c20 6f70 7469 6f6e 730a   Global options.\n+00011b30: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n+00011b40: 2d2d 2d2d 0a0a 2a53 796e 7461 783a 2a0a  ----..*Syntax:*.\n+00011b50: 2020 2020 2073 6574 205b 204f 5054 494f       set [ OPTIO\n+00011b60: 4e53 205d 0a54 6865 2063 6f6e 7465 6e74  NS ].The content\n+00011b70: 7320 6f66 204f 5054 494f 4e53 2c20 6578  s of OPTIONS, ex\n+00011b80: 6365 7074 2066 6f72 2027 736b 6574 6368  cept for 'sketch\n+00011b90: 2720 696e 7465 726e 616c 206f 7074 696f  ' internal optio\n+00011ba0: 6e73 2c20 6172 650a 636f 7069 6564 2061  ns, are.copied a\n+00011bb0: 732d 6973 2074 6f20 6120 5c70 7373 6574  s-is to a \\psset\n+00011bc0: 2074 6861 7420 6170 7065 6172 7320 6265   that appears be\n+00011bd0: 666f 7265 2061 6e79 7468 696e 6720 656c  fore anything el\n+00011be0: 7365 2069 6e20 7468 6520 6f75 7470 7574  se in the output\n+00011bf0: 0a66 696c 652e 2020 5468 6973 2069 7320  .file.  This is \n+00011c00: 6120 676f 6f64 2070 6c61 6365 2074 6f20  a good place to \n+00011c10: 7365 7420 2775 6e69 7427 2c20 6120 6465  set 'unit', a de\n+00011c20: 6661 756c 7420 276c 696e 6577 6964 7468  fault 'linewidth\n+00011c30: 272c 2065 7463 2e0a 0a20 2020 496e 7465  ', etc...   Inte\n+00011c40: 726e 616c 206f 7074 696f 6e73 2077 6f72  rnal options wor\n+00011c50: 6b20 6f6e 2061 6c6c 206f 626a 6563 7473  k on all objects\n+00011c60: 2077 6865 7265 2074 6865 7920 6d61 6b65   where they make\n+00011c70: 2073 656e 7365 2e20 2054 6869 730a 696e   sense.  This.in\n+00011c80: 636c 7564 6573 2027 6375 6c6c 2720 616e  cludes 'cull' an\n+00011c90: 6420 2773 706c 6974 2720 2862 7574 206e  d 'split' (but n\n+00011ca0: 6f74 2027 6c61 7927 292e 2020 2a4e 6f74  ot 'lay').  *Not\n+00011cb0: 6520 496e 7465 726e 616c 206f 7074 696f  e Internal optio\n+00011cc0: 6e73 3a3a 2e0a 0a1f 0a46 696c 653a 2073  ns::.....File: s\n+00011cd0: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n+00011ce0: 653a 2043 616d 6572 612c 2020 4e65 7874  e: Camera,  Next\n+00011cf0: 3a20 5069 6374 7572 6520 626f 782c 2020  : Picture box,  \n+00011d00: 5072 6576 3a20 476c 6f62 616c 206f 7074  Prev: Global opt\n+00011d10: 696f 6e73 2c20 2055 703a 2047 6c6f 6261  ions,  Up: Globa\n+00011d20: 6c20 656e 7669 726f 6e6d 656e 740a 0a33  l environment..3\n+00011d30: 2e34 2e32 2043 616d 6572 610a 2d2d 2d2d  .4.2 Camera.----\n+00011d40: 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461  --------..*Synta\n+00011d50: 783a 2a0a 2020 2020 2063 616d 6572 6120  x:*.     camera \n+00011d60: 5452 414e 5346 4f52 4d5f 4558 5052 4553  TRANSFORM_EXPRES\n+00011d70: 5349 4f4e 0a20 2020 5468 6520 5452 414e  SION.   The TRAN\n+00011d80: 5346 4f52 4d5f 4558 5052 4553 5349 4f4e  SFORM_EXPRESSION\n+00011d90: 2069 7320 6170 706c 6965 6420 6166 7465   is applied afte\n+00011da0: 7220 616c 6c20 6f74 6865 7220 7472 616e  r all other tran\n+00011db0: 7366 6f72 6d61 7469 6f6e 730a 6f66 2074  sformations.of t\n+00011dc0: 6865 2073 6365 6e65 2e20 2054 6869 7320  he scene.  This \n+00011dd0: 6973 2063 7572 7265 6e74 6c79 206f 6e6c  is currently onl\n+00011de0: 7920 7573 6566 756c 2066 6f72 2074 7261  y useful for tra\n+00011df0: 6e73 666f 726d 696e 6720 7468 650a 626f  nsforming the.bo\n+00011e00: 756e 6469 6e67 2062 6f78 2e20 202a 4e6f  unding box.  *No\n+00011e10: 7465 2050 6963 7475 7265 2062 6f78 3a3a  te Picture box::\n+00011e20: 2e20 2049 7420 7769 6c6c 2070 6c61 7920  .  It will play \n+00011e30: 6120 726f 6c65 2069 6e20 616e 7920 6675  a role in any fu\n+00011e40: 7475 7265 0a69 6d70 6c65 6d65 6e74 6174  ture.implementat\n+00011e50: 696f 6e20 6f66 2063 6c69 7070 696e 672e  ion of clipping.\n+00011e60: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368  ....File: sketch\n+00011e70: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5069  .info,  Node: Pi\n+00011e80: 6374 7572 6520 626f 782c 2020 4e65 7874  cture box,  Next\n+00011e90: 3a20 4672 616d 652c 2020 5072 6576 3a20  : Frame,  Prev: \n+00011ea0: 4361 6d65 7261 2c20 2055 703a 2047 6c6f  Camera,  Up: Glo\n+00011eb0: 6261 6c20 656e 7669 726f 6e6d 656e 740a  bal environment.\n+00011ec0: 0a33 2e34 2e33 2050 6963 7475 7265 2062  .3.4.3 Picture b\n+00011ed0: 6f78 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ox.-------------\n+00011ee0: 2d2d 2d2d 0a0a 2a53 796e 7461 783a 2a0a  ----..*Syntax:*.\n+00011ef0: 2020 2020 2070 6963 7475 7265 626f 785b       picturebox[\n+00011f00: 4241 5345 4c49 4e45 5d0a 2020 2020 2070  BASELINE].     p\n+00011f10: 6963 7475 7265 626f 785b 4241 5345 4c49  icturebox[BASELI\n+00011f20: 4e45 5d20 2850 3129 2850 3229 0a54 6865  NE] (P1)(P2).The\n+00011f30: 2066 6972 7374 2066 6f72 6d20 6f66 2027   first form of '\n+00011f40: 7069 6374 7572 6562 6f78 2720 6361 7573  picturebox' caus\n+00011f50: 6573 2061 2073 6361 6c61 7220 4241 5345  es a scalar BASE\n+00011f60: 4c49 4e45 2066 7261 6374 696f 6e20 746f  LINE fraction to\n+00011f70: 2062 650a 656d 6974 7465 6420 696e 2074   be.emitted in t\n+00011f80: 6865 2027 7073 7069 6374 7572 6527 2065  he 'pspicture' e\n+00011f90: 6e76 6972 6f6e 6d65 6e74 206f 6620 7468  nvironment of th\n+00011fa0: 6520 6f75 7470 7574 2e20 2053 6565 2027  e output.  See '\n+00011fb0: 5053 5472 6963 6b73 270a 646f 6375 6d65  PSTricks'.docume\n+00011fc0: 6e74 6174 696f 6e20 666f 7220 2770 7370  ntation for 'psp\n+00011fd0: 6963 7475 7265 272e 0a0a 2020 2049 6e20  icture'...   In \n+00011fe0: 7468 6520 7365 636f 6e64 2066 6f72 6d2c  the second form,\n+00011ff0: 2074 6865 2042 4153 454c 494e 4520 6672   the BASELINE fr\n+00012000: 6163 7469 6f6e 2069 7320 6f70 7469 6f6e  action is option\n+00012010: 616c 2c20 616e 6420 7468 6520 7477 6f0a  al, and the two.\n+00012020: 706f 696e 7473 2074 6861 7420 666f 6c6c  points that foll\n+00012030: 6f77 2064 6566 696e 6520 7468 6520 6469  ow define the di\n+00012040: 6167 6f6e 616c 206f 6620 6120 7468 7265  agonal of a thre\n+00012050: 652d 6469 6d65 6e73 696f 6e61 6c20 626f  e-dimensional bo\n+00012060: 756e 6469 6e67 0a62 6f78 2066 6f72 2074  unding.box for t\n+00012070: 6865 2063 6f6d 706c 6574 6564 2073 6365  he completed sce\n+00012080: 6e65 2e20 2054 6865 2070 6172 616c 6c65  ne.  The paralle\n+00012090: 6c20 7072 6f6a 6563 7469 6f6e 206f 6620  l projection of \n+000120a0: 7468 6520 626f 756e 6469 6e67 0a62 6f78  the bounding.box\n+000120b0: 2064 6574 6572 6d69 6e65 7320 7468 6520   determines the \n+000120c0: 636f 726e 6572 7320 6f66 2074 6865 2064  corners of the d\n+000120d0: 7261 7769 6e67 2773 2027 7073 7069 6374  rawing's 'pspict\n+000120e0: 7572 652a 2720 656e 7669 726f 6e6d 656e  ure*' environmen\n+000120f0: 742c 0a77 6869 6368 2069 7320 7573 6564  t,.which is used\n+00012100: 2069 6e20 706c 6163 6520 6f66 2027 7073   in place of 'ps\n+00012110: 7069 6374 7572 6527 2e20 2054 6869 7320  picture'.  This \n+00012120: 6361 7573 6573 2050 6f73 7453 6372 6970  causes PostScrip\n+00012130: 7420 746f 2063 6c69 700a 7468 6520 6669  t to clip.the fi\n+00012140: 6e61 6c20 6472 6177 696e 6720 746f 2074  nal drawing to t\n+00012150: 6865 2062 6f75 6e64 696e 6720 626f 7820  he bounding box \n+00012160: 696e 2032 642e 2020 4966 2074 6865 7265  in 2d.  If there\n+00012170: 2069 7320 6120 2763 616d 6572 6127 0a73   is a 'camera'.s\n+00012180: 7065 6369 6669 6564 2c20 7468 6520 6361  pecified, the ca\n+00012190: 6d65 7261 2074 7261 6e66 6f72 6d61 7469  mera tranformati\n+000121a0: 6f6e 2069 7320 6170 706c 6965 6420 746f  on is applied to\n+000121b0: 2074 6865 2062 6f75 6e64 696e 6720 626f   the bounding bo\n+000121c0: 782c 2061 6e64 0a74 6865 2027 7073 7069  x, and.the 'pspi\n+000121d0: 6374 7572 6527 2069 7320 7365 7420 6a75  cture' is set ju\n+000121e0: 7374 206c 6172 6765 2065 6e6f 7567 6820  st large enough \n+000121f0: 746f 2069 6e63 6c75 6465 2074 6865 2074  to include the t\n+00012200: 7261 6e73 666f 726d 6564 2062 6f78 2e0a  ransformed box..\n+00012210: 0a20 2020 5768 656e 206e 6f20 626f 756e  .   When no boun\n+00012220: 6469 6e67 2062 6f78 2069 7320 6769 7665  ding box is give\n+00012230: 6e2c 2027 736b 6574 6368 2720 636f 6d70  n, 'sketch' comp\n+00012240: 7574 6573 206f 6e65 2061 7574 6f6d 6174  utes one automat\n+00012250: 6963 616c 6c79 2e0a 0a1f 0a46 696c 653a  ically.....File:\n+00012260: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n+00012270: 6f64 653a 2046 7261 6d65 2c20 204e 6578  ode: Frame,  Nex\n+00012280: 743a 204c 616e 6775 6167 652c 2020 5072  t: Language,  Pr\n+00012290: 6576 3a20 5069 6374 7572 6520 626f 782c  ev: Picture box,\n+000122a0: 2020 5570 3a20 476c 6f62 616c 2065 6e76    Up: Global env\n+000122b0: 6972 6f6e 6d65 6e74 0a0a 332e 342e 3420  ironment..3.4.4 \n+000122c0: 4672 616d 650a 2d2d 2d2d 2d2d 2d2d 2d2d  Frame.----------\n+000122d0: 2d0a 0a2a 5379 6e74 6178 3a2a 0a20 2020  -..*Syntax:*.   \n+000122e0: 2020 6672 616d 6520 5b4f 5054 494f 4e53    frame [OPTIONS\n+000122f0: 5d0a 4361 7573 6573 2061 205c 7073 6672  ].Causes a \\psfr\n+00012300: 616d 6562 6f78 2074 6f20 7375 7272 6f75  amebox to surrou\n+00012310: 6e64 2074 6865 2027 7073 7069 6374 7572  nd the 'pspictur\n+00012320: 6527 2065 6e76 6972 6f6e 6d65 6e74 2069  e' environment i\n+00012330: 6e20 7468 650a 6f75 7470 7574 2e20 2049  n the.output.  I\n+00012340: 6620 4f50 5449 4f4e 5320 6172 6520 7072  f OPTIONS are pr\n+00012350: 6573 656e 742c 2074 6865 7920 6172 6520  esent, they are \n+00012360: 636f 7069 6564 2061 732d 6973 2e20 204e  copied as-is.  N\n+00012370: 6f72 6d61 6c6c 7920 6f6e 650a 776f 756c  ormally one.woul\n+00012380: 6420 7761 6e74 2074 6f20 7365 7420 276c  d want to set 'l\n+00012390: 696e 6577 6964 7468 272c 2027 6c69 6e65  inewidth', 'line\n+000123a0: 7374 796c 6527 2c20 276c 696e 6563 6f6c  style', 'linecol\n+000123b0: 6f72 272c 2065 7463 2e20 2049 660a 6f6d  or', etc.  If.om\n+000123c0: 6974 7465 642c 2074 6865 6e20 2766 7261  itted, then 'fra\n+000123d0: 6d65 7365 703d 3070 7427 2069 7320 6164  mesep=0pt' is ad\n+000123e0: 6465 6420 736f 2074 6861 7420 7468 6520  ded so that the \n+000123f0: 6672 616d 6520 7469 6768 746c 7920 6875  frame tightly hu\n+00012400: 6773 2074 6865 0a27 7073 7069 6374 7572  gs the.'pspictur\n+00012410: 6527 2e0a 0a1f 0a46 696c 653a 2073 6b65  e'.....File: ske\n+00012420: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n+00012430: 204c 616e 6775 6167 652c 2020 5072 6576   Language,  Prev\n+00012440: 3a20 4672 616d 652c 2020 5570 3a20 476c  : Frame,  Up: Gl\n+00012450: 6f62 616c 2065 6e76 6972 6f6e 6d65 6e74  obal environment\n+00012460: 0a0a 332e 342e 3520 4c61 6e67 7561 6765  ..3.4.5 Language\n+00012470: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a  .--------------.\n+00012480: 0a20 2020 2020 6c61 6e67 7561 6765 2074  .     language t\n+00012490: 696b 7a0a 2020 2020 206c 616e 6775 6167  ikz.     languag\n+000124a0: 6520 7469 6b7a 2c20 636f 6e74 6578 740a  e tikz, context.\n+000124b0: 2020 2020 206c 616e 6775 6167 6520 7073       language ps\n+000124c0: 7472 6963 6b73 0a20 2020 2020 6c61 6e67  tricks.     lang\n+000124d0: 7561 6765 2070 7374 7269 636b 732c 206c  uage pstricks, l\n+000124e0: 6174 6578 0a53 6574 7320 7468 6520 6f75  atex.Sets the ou\n+000124f0: 7470 7574 206c 616e 6775 6167 6520 6765  tput language ge\n+00012500: 6e65 7261 7465 6420 6279 2027 736b 6574  nerated by 'sket\n+00012510: 6368 272e 2020 5468 6520 7365 7420 6f66  ch'.  The set of\n+00012520: 206f 7074 696f 6e73 0a75 6e64 6572 7374   options.underst\n+00012530: 6f6f 6420 6279 2073 6b65 7463 6820 616c  ood by sketch al\n+00012540: 736f 2063 6861 6e67 6573 2e20 2046 6f72  so changes.  For\n+00012550: 2065 7861 6d70 6c65 2c20 7468 6520 2750   example, the 'P\n+00012560: 5354 7269 636b 7327 206f 7074 696f 6e0a  STricks' option.\n+00012570: 276c 696e 6577 6964 7468 2720 7769 6c6c  'linewidth' will\n+00012580: 206e 6f74 2062 6520 7072 6f70 6572 6c79   not be properly\n+00012590: 2068 616e 646c 6564 2069 6620 276c 616e   handled if 'lan\n+000125a0: 6775 6167 6527 2069 7320 7365 7420 746f  guage' is set to\n+000125b0: 2027 7469 6b7a 272e 0a53 696d 696c 6172   'tikz'..Similar\n+000125c0: 6c79 2c20 7468 6520 2754 696b 5a27 206f  ly, the 'TikZ' o\n+000125d0: 7074 696f 6e20 276c 696e 6520 7374 796c  ption 'line styl\n+000125e0: 6527 2028 6e6f 7465 2074 6865 2073 7061  e' (note the spa\n+000125f0: 6365 2920 7769 6c6c 206e 6f74 2062 650a  ce) will not be.\n+00012600: 7072 6f70 6572 6c79 2068 616e 646c 6564  properly handled\n+00012610: 2069 6620 276c 616e 6775 6167 6527 2069   if 'language' i\n+00012620: 7320 7365 7420 746f 2027 7073 7472 6963  s set to 'pstric\n+00012630: 6b73 272e 2020 4966 206e 6f20 6c61 6e67  ks'.  If no lang\n+00012640: 7561 6765 2069 730a 7370 6563 6966 6965  uage is.specifie\n+00012650: 642c 2074 6865 2064 6566 6175 6c74 2027  d, the default '\n+00012660: 7073 7472 6963 6b73 2720 6973 2075 7365  pstricks' is use\n+00012670: 642e 0a0a 2020 2041 6e20 6f70 7469 6f6e  d...   An option\n+00012680: 616c 2063 6f6d 6d61 2066 6f6c 6c6f 7765  al comma followe\n+00012690: 6420 6279 2027 6c61 7465 7827 206f 7220  d by 'latex' or \n+000126a0: 2763 6f6e 7465 7874 2720 7370 6563 6966  'context' specif\n+000126b0: 6965 7320 7468 650a 6d61 6372 6f20 7061  ies the.macro pa\n+000126c0: 636b 6167 6520 7468 6174 2074 6865 206f  ckage that the o\n+000126d0: 7574 7075 7420 7368 6f75 6c64 2061 7373  utput should ass\n+000126e0: 756d 652e 2020 5468 6973 2061 6666 6563  ume.  This affec\n+000126f0: 7473 2074 6865 2027 7069 6374 7572 6527  ts the 'picture'\n+00012700: 0a65 6e76 6972 6f6e 6d65 6e74 2063 6f6d  .environment com\n+00012710: 6d61 6e64 7320 656d 6974 7465 6420 616e  mands emitted an\n+00012720: 6420 7468 6520 646f 6375 6d65 6e74 2074  d the document t\n+00012730: 656d 706c 6174 6520 7573 6564 2077 6974  emplate used wit\n+00012740: 6820 7468 650a 272d 5427 206f 7074 696f  h the.'-T' optio\n+00012750: 6e2e 2020 2a4e 6f74 6520 436f 6d6d 616e  n.  *Note Comman\n+00012760: 6420 6c69 6e65 3a3a 2e20 204e 6f74 6520  d line::.  Note \n+00012770: 7468 6174 2061 7420 7468 6520 7469 6d65  that at the time\n+00012780: 2074 6869 7320 6d61 6e75 616c 0a77 6173   this manual.was\n+00012790: 2067 656e 6572 6174 6564 2c20 2750 5354   generated, 'PST\n+000127a0: 7269 636b 7327 2077 6173 206e 6f74 2073  ricks' was not s\n+000127b0: 7570 706f 7274 6564 2062 7920 4c61 5465  upported by LaTe\n+000127c0: 5820 6f72 2062 7920 2743 6f6e 5465 5874  X or by 'ConTeXt\n+000127d0: 272e 0a0a 1f0a 4669 6c65 3a20 736b 6574  '.....File: sket\n+000127e0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20  ch.info,  Node: \n+000127f0: 4275 696c 6469 6e67 2061 2064 7261 7769  Building a drawi\n+00012800: 6e67 2c20 204e 6578 743a 2043 6f6d 6d61  ng,  Next: Comma\n+00012810: 6e64 206c 696e 652c 2020 5072 6576 3a20  nd line,  Prev: \n+00012820: 496e 7075 7420 6c61 6e67 7561 6765 2c20  Input language, \n+00012830: 2055 703a 2054 6f70 0a0a 3420 4275 696c   Up: Top..4 Buil\n+00012840: 6469 6e67 2061 2064 7261 7769 6e67 0a2a  ding a drawing.*\n+00012850: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  ****************\n+00012860: 2a2a 2a0a 0a53 7563 6365 7373 6675 6c20  ***..Successful \n+00012870: 6472 6177 696e 6773 2077 6974 6820 2773  drawings with 's\n+00012880: 6b65 7463 6827 2061 6e64 2077 6974 6820  ketch' and with \n+00012890: 616e 7920 7363 656e 6520 6465 7363 7269  any scene descri\n+000128a0: 7074 696f 6e0a 6c61 6e67 7561 6765 2072  ption.language r\n+000128b0: 6571 7569 7265 2074 6861 7420 7468 6520  equire that the \n+000128c0: 7573 6572 2064 6576 656c 6f70 2061 6e20  user develop an \n+000128d0: 6163 6375 7261 7465 206d 656e 7461 6c20  accurate mental \n+000128e0: 7069 6374 7572 6520 6f66 2068 6572 0a63  picture of her.c\n+000128f0: 6f64 6520 616e 6420 6974 7320 6d65 616e  ode and its mean\n+00012900: 696e 672e 2020 5468 6973 2069 6d61 6765  ing.  This image\n+00012910: 2069 7320 6265 7374 2062 7569 6c74 2069   is best built i\n+00012920: 6e20 736d 616c 6c20 7069 6563 6573 2e0a  n small pieces..\n+00012930: 5468 6572 6566 6f72 652c 2027 736b 6574  Therefore, 'sket\n+00012940: 6368 2720 696e 7075 7473 2061 7265 2062  ch' inputs are b\n+00012950: 6573 7420 6372 6561 7465 6420 696e 2073  est created in s\n+00012960: 6d61 6c6c 2069 6e63 7265 6d65 6e74 7320  mall increments \n+00012970: 7769 7468 0a66 7265 7175 656e 7420 7061  with.frequent pa\n+00012980: 7573 6573 2074 6f20 636f 6d70 696c 6520  uses to compile \n+00012990: 616e 6420 7669 6577 2074 6865 2072 6573  and view the res\n+000129a0: 756c 7473 2e20 2043 6172 6566 756c 2063  ults.  Careful c\n+000129b0: 6f6d 6d65 6e74 7320 696e 0a74 6865 2069  omments in.the i\n+000129c0: 6e70 7574 206f 6674 656e 2068 656c 7020  nput often help \n+000129d0: 6173 2061 2073 6365 6e65 2067 726f 7773  as a scene grows\n+000129e0: 2069 6e20 636f 6d70 6c65 7869 7479 2e0a   in complexity..\n+000129f0: 0a2a 204d 656e 753a 0a0a 2a20 4f76 6572  .* Menu:..* Over\n+00012a00: 7669 6577 3a3a 2020 2020 2020 2020 2020  view::          \n+00012a10: 2020 2020 2020 2020 2020 4275 696c 6469            Buildi\n+00012a20: 6e67 2061 2073 7562 7374 616e 7469 616c  ng a substantial\n+00012a30: 2064 7261 7769 6e67 2e0a 2a20 4120 7465   drawing..* A te\n+00012a40: 6368 6e69 6361 6c20 6472 6177 696e 673a  chnical drawing:\n+00012a50: 3a20 2020 2020 2020 2020 416e 2065 7861  :         An exa\n+00012a60: 6d70 6c65 2077 6974 6820 6669 6e65 2070  mple with fine p\n+00012a70: 6c61 6365 6d65 6e74 2e0a 2a20 4120 6869  lacement..* A hi\n+00012a80: 6572 6172 6368 6963 616c 206d 6f64 656c  erarchical model\n+00012a90: 3a3a 2020 2020 2020 2020 416e 2065 7861  ::        An exa\n+00012aa0: 6d70 6c65 2077 6974 6820 7377 6565 7073  mple with sweeps\n+00012ab0: 2061 6e64 2070 7574 732e 0a2a 2043 6176   and puts..* Cav\n+00012ac0: 6561 7473 3a3a 2020 2020 2020 2020 2020  eats::          \n+00012ad0: 2020 2020 2020 2020 2020 2057 6865 7265             Where\n+00012ae0: 2074 726f 7562 6c65 2063 616e 206f 6363   trouble can occ\n+00012af0: 7572 2e0a 0a1f 0a46 696c 653a 2073 6b65  ur.....File: ske\n+00012b00: 7463 682e 696e 666f 2c20 204e 6f64 653a  tch.info,  Node:\n+00012b10: 204f 7665 7276 6965 772c 2020 4e65 7874   Overview,  Next\n+00012b20: 3a20 4120 7465 6368 6e69 6361 6c20 6472  : A technical dr\n+00012b30: 6177 696e 672c 2020 5072 6576 3a20 4275  awing,  Prev: Bu\n+00012b40: 696c 6469 6e67 2061 2064 7261 7769 6e67  ilding a drawing\n+00012b50: 2c20 2055 703a 2042 7569 6c64 696e 6720  ,  Up: Building \n+00012b60: 6120 6472 6177 696e 670a 0a34 2e31 204f  a drawing..4.1 O\n+00012b70: 7665 7276 6965 770a 3d3d 3d3d 3d3d 3d3d  verview.========\n+00012b80: 3d3d 3d3d 0a0a 4173 2061 6e20 6f76 6572  ====..As an over\n+00012b90: 7669 6577 2c20 6c65 7427 7320 6465 7665  view, let's deve\n+00012ba0: 6c6f 7020 6120 6469 6167 7261 6d20 7468  lop a diagram th\n+00012bb0: 6174 2073 686f 7773 2068 6f77 2061 2070  at shows how a p\n+00012bc0: 6572 7370 6563 7469 7665 0a70 726f 6a65  erspective.proje\n+00012bd0: 6374 696f 6e20 7472 616e 7366 6f72 6d20  ction transform \n+00012be0: 776f 726b 732e 2020 5765 276c 6c20 7374  works.  We'll st\n+00012bf0: 6172 7420 7769 7468 2074 6865 2074 7261  art with the tra\n+00012c00: 6469 7469 6f6e 616c 2072 6566 6572 656e  ditional referen\n+00012c10: 6365 0a6f 626a 6563 7420 7573 6564 2069  ce.object used i\n+00012c20: 6e20 636f 6d70 7574 6572 2067 7261 7068  n computer graph\n+00012c30: 6963 7320 7465 7874 626f 6f6b 732c 2061  ics textbooks, a\n+00012c40: 2068 6f75 7365 2d73 6861 7065 6420 7072   house-shaped pr\n+00012c50: 6973 6d2e 2020 4265 6769 6e0a 6279 2064  ism.  Begin.by d\n+00012c60: 6566 696e 696e 6720 7468 6520 706f 696e  efining the poin\n+00012c70: 7473 206f 6620 7468 6520 686f 7573 652e  ts of the house.\n+00012c80: 2020 5261 7468 6572 2074 6861 6e20 6465    Rather than de\n+00012c90: 6669 6e69 6e67 2074 6865 2066 6163 6573  fining the faces\n+00012ca0: 206f 660a 7468 6520 686f 7573 6520 6173   of.the house as\n+00012cb0: 2070 6f6c 7967 6f6e 7320 616e 6420 7472   polygons and tr\n+00012cc0: 616e 7366 6f72 6d69 6e67 2074 686f 7365  ansforming those\n+00012cd0: 2c20 7765 2061 7265 2067 6f69 6e67 2074  , we are going t\n+00012ce0: 6f20 7472 616e 7366 6f72 6d0a 7468 6520  o transform.the \n+00012cf0: 706f 696e 7473 2074 6865 6d73 656c 7665  points themselve\n+00012d00: 7320 7769 7468 2027 736b 6574 6368 2720  s with 'sketch' \n+00012d10: 6172 6974 686d 6574 6963 2073 6f20 7468  arithmetic so th\n+00012d20: 6174 2077 6520 6861 7665 206e 616d 6573  at we have names\n+00012d30: 2066 6f72 0a74 6865 2074 7261 6e73 666f   for.the transfo\n+00012d40: 726d 6564 2070 6f69 6e74 7320 6c61 7465  rmed points late\n+00012d50: 722e 0a20 2025 2072 6967 6874 2073 6964  r..  % right sid\n+00012d60: 6520 286f 7574 7369 6465 2074 6f20 7269  e (outside to ri\n+00012d70: 6768 7429 0a20 2064 6566 2052 3120 2831  ght).  def R1 (1\n+00012d80: 2c31 2c31 2920 6465 6620 5232 2028 312c  ,1,1) def R2 (1,\n+00012d90: 2d31 2c31 2920 6465 6620 5233 2028 312c  -1,1) def R3 (1,\n+00012da0: 2d31 2c2d 3129 2064 6566 2052 3420 2831  -1,-1) def R4 (1\n+00012db0: 2c31 2c2d 3129 0a20 2064 6566 2052 3520  ,1,-1).  def R5 \n+00012dc0: 2831 2c31 2e35 2c30 290a 0a20 2025 206c  (1,1.5,0)..  % l\n+00012dd0: 6566 7420 7369 6465 2028 6f75 7473 6964  eft side (outsid\n+00012de0: 6520 746f 2072 6967 6874 2d2d 6261 636b  e to right--back\n+00012df0: 7761 7264 290a 2020 6465 6620 5720 205b  ward).  def W  [\n+00012e00: 322c 302c 305d 0a20 2064 6566 204c 3120  2,0,0].  def L1 \n+00012e10: 2852 3129 2d5b 575d 2064 6566 204c 3220  (R1)-[W] def L2 \n+00012e20: 2852 3229 2d5b 575d 2064 6566 204c 3320  (R2)-[W] def L3 \n+00012e30: 2852 3329 2d5b 575d 2064 6566 204c 3420  (R3)-[W] def L4 \n+00012e40: 2852 3429 2d5b 575d 0a20 2064 6566 204c  (R4)-[W].  def L\n+00012e50: 3520 2852 3529 2d5b 575d 0a54 6f20 6164  5 (R5)-[W].To ad\n+00012e60: 6420 6120 646f 6f72 2074 6f20 7468 6520  d a door to the \n+00012e70: 686f 7573 652c 2077 6520 7573 6520 6120  house, we use a \n+00012e80: 706f 6c79 676f 6e20 736c 6967 6874 6c79  polygon slightly\n+00012e90: 2069 6e20 6672 6f6e 7420 6f66 2074 6865   in front of the\n+00012ea0: 0a66 6f72 656d 6f73 7420 6661 6365 206f  .foremost face o\n+00012eb0: 6620 7468 6520 686f 7573 652e 0a20 2025  f the house..  %\n+00012ec0: 2064 6f6f 720a 2020 6465 6620 6520 2e30   door.  def e .0\n+00012ed0: 310a 2020 6465 6620 4431 2028 302c 2d31  1.  def D1 (0,-1\n+00012ee0: 2c31 2b65 2920 6465 6620 4432 2028 2e35  ,1+e) def D2 (.5\n+00012ef0: 2c2d 312c 312b 6529 2064 6566 2044 3320  ,-1,1+e) def D3 \n+00012f00: 282e 352c 302c 312b 6529 2064 6566 2044  (.5,0,1+e) def D\n+00012f10: 3420 2830 2c30 2c31 2b65 290a 4e6f 7720  4 (0,0,1+e).Now \n+00012f20: 6c65 7427 7320 6372 6561 7465 2061 206e  let's create a n\n+00012f30: 6577 2073 6574 206f 6620 706f 696e 7473  ew set of points\n+00012f40: 2074 6861 7420 6172 6520 6120 746f 2d62   that are a to-b\n+00012f50: 652d 6465 7465 726d 696e 6564 0a74 7261  e-determined.tra\n+00012f60: 6e73 666f 726d 206f 6620 7468 6520 6f72  nsform of the or\n+00012f70: 6967 696e 616c 732e 0a20 2064 6566 2068  iginals..  def h\n+00012f80: 7020 7363 616c 6528 3129 2025 2068 6f75  p scale(1) % hou\n+00012f90: 7365 2070 6f73 6974 696f 6e65 720a 2020  se positioner.  \n+00012fa0: 6465 6620 7052 3120 5b5b 6870 5d5d 2a28  def pR1 [[hp]]*(\n+00012fb0: 5231 2920 6465 6620 7052 3220 5b5b 6870  R1) def pR2 [[hp\n+00012fc0: 5d5d 2a28 5232 2920 6465 6620 7052 3320  ]]*(R2) def pR3 \n+00012fd0: 5b5b 6870 5d5d 2a28 5233 290a 2020 6465  [[hp]]*(R3).  de\n+00012fe0: 6620 7052 3420 5b5b 6870 5d5d 2a28 5234  f pR4 [[hp]]*(R4\n+00012ff0: 2920 6465 6620 7052 3520 5b5b 6870 5d5d  ) def pR5 [[hp]]\n+00013000: 2a28 5235 290a 2020 6465 6620 704c 3120  *(R5).  def pL1 \n+00013010: 5b5b 6870 5d5d 2a28 4c31 2920 6465 6620  [[hp]]*(L1) def \n+00013020: 704c 3220 5b5b 6870 5d5d 2a28 4c32 2920  pL2 [[hp]]*(L2) \n+00013030: 6465 6620 704c 3320 5b5b 6870 5d5d 2a28  def pL3 [[hp]]*(\n+00013040: 4c33 290a 2020 6465 6620 704c 3420 5b5b  L3).  def pL4 [[\n+00013050: 6870 5d5d 2a28 4c34 2920 6465 6620 704c  hp]]*(L4) def pL\n+00013060: 3520 5b5b 6870 5d5d 2a28 4c35 290a 2020  5 [[hp]]*(L5).  \n+00013070: 6465 6620 7044 3120 5b5b 6870 5d5d 2a28  def pD1 [[hp]]*(\n+00013080: 4431 2920 6465 6620 7044 3220 5b5b 6870  D1) def pD2 [[hp\n+00013090: 5d5d 2a28 4432 2920 6465 6620 7044 3320  ]]*(D2) def pD3 \n+000130a0: 5b5b 6870 5d5d 2a28 4433 290a 2020 6465  [[hp]]*(D3).  de\n+000130b0: 6620 7044 3420 5b5b 6870 5d5d 2a28 4434  f pD4 [[hp]]*(D4\n+000130c0: 2920 0a4e 6f74 6520 7468 6520 7573 6520  ) .Note the use \n+000130d0: 6f66 2061 2022 7472 616e 7366 6f72 6d20  of a \"transform \n+000130e0: 6465 6669 6e69 7469 6f6e 2220 616e 6420  definition\" and \n+000130f0: 2274 7261 6e73 666f 726d 2072 6566 6572  \"transform refer\n+00013100: 656e 6365 7322 2e0a 4e6f 7720 6465 6669  ences\"..Now defi\n+00013110: 6e65 2074 6865 2073 6576 656e 2070 6f6c  ne the seven pol\n+00013120: 7967 6f6e 616c 2066 6163 6573 206f 6620  ygonal faces of \n+00013130: 7468 6520 686f 7573 6520 616e 6420 7468  the house and th\n+00013140: 6520 646f 6f72 2075 7369 6e67 2074 6865  e door using the\n+00013150: 0a74 7261 6e73 666f 726d 6564 2070 6f69  .transformed poi\n+00013160: 6e74 7320 6173 2076 6572 7469 6365 732e  nts as vertices.\n+00013170: 2020 4265 2063 6172 6566 756c 2077 6974    Be careful wit\n+00013180: 6820 7665 7274 6578 206f 7264 6572 210a  h vertex order!.\n+00013190: 2020 6465 6620 7267 7420 706f 6c79 676f    def rgt polygo\n+000131a0: 6e20 2870 5231 2928 7052 3229 2870 5233  n (pR1)(pR2)(pR3\n+000131b0: 2928 7052 3429 2870 5235 290a 2020 6465  )(pR4)(pR5).  de\n+000131c0: 6620 6c66 7420 706f 6c79 676f 6e20 2870  f lft polygon (p\n+000131d0: 4c35 2928 704c 3429 2870 4c33 2928 704c  L5)(pL4)(pL3)(pL\n+000131e0: 3229 2870 4c31 290a 2020 6465 6620 6672  2)(pL1).  def fr\n+000131f0: 7420 706f 6c79 676f 6e20 2870 5232 2928  t polygon (pR2)(\n+00013200: 7052 3129 2870 4c31 2928 704c 3229 0a20  pR1)(pL1)(pL2). \n+00013210: 2064 6566 2062 636b 2070 6f6c 7967 6f6e   def bck polygon\n+00013220: 2028 7052 3429 2870 5233 2928 704c 3329   (pR4)(pR3)(pL3)\n+00013230: 2870 4c34 290a 2020 6465 6620 7466 7220  (pL4).  def tfr \n+00013240: 706f 6c79 676f 6e20 2870 5231 2928 7052  polygon (pR1)(pR\n+00013250: 3529 2870 4c35 2928 704c 3129 0a20 2064  5)(pL5)(pL1).  d\n+00013260: 6566 2074 626b 2070 6f6c 7967 6f6e 2028  ef tbk polygon (\n+00013270: 7052 3529 2870 5234 2928 704c 3429 2870  pR5)(pR4)(pL4)(p\n+00013280: 4c35 290a 2020 6465 6620 626f 7420 706f  L5).  def bot po\n+00013290: 6c79 676f 6e20 2870 5232 2928 704c 3229  lygon (pR2)(pL2)\n+000132a0: 2870 4c33 2928 7052 3329 0a20 2064 6566  (pL3)(pR3).  def\n+000132b0: 2064 6f6f 7220 706f 6c79 676f 6e5b 6669   door polygon[fi\n+000132c0: 6c6c 636f 6c6f 723d 6272 6f77 6e5d 2028  llcolor=brown] (\n+000132d0: 7044 3129 2870 4432 2928 7044 3329 2870  pD1)(pD2)(pD3)(p\n+000132e0: 4434 290a 2020 6465 6620 686f 7573 6520  D4).  def house \n+000132f0: 7b20 7b72 6774 7d7b 6c66 747d 7b66 7274  { {rgt}{lft}{frt\n+00013300: 7d7b 6263 6b7d 7b74 6672 7d7b 7462 6b7d  }{bck}{tfr}{tbk}\n+00013310: 7b62 6f74 7d7b 646f 6f72 7d20 7d0a 2020  {bot}{door} }.  \n+00013320: 2054 696d 6520 666f 7220 6120 7361 6e69   Time for a sani\n+00013330: 7479 2063 6865 636b 2e20 2041 6464 2074  ty check.  Add t\n+00013340: 6865 206c 696e 650a 2020 7b68 6f75 7365  he line.  {house\n+00013350: 7d0a 616e 6420 7468 6973 2069 7320 7768  }.and this is wh\n+00013360: 6174 2077 6520 6765 742e 0a0a 0008 5b69  at we get.....[i\n+00013370: 6d61 6765 2073 7263 3d22 6578 3133 302e  mage src=\"ex130.\n+00013380: 706e 6722 2074 6578 743d 2249 6d61 6765  png\" text=\"Image\n+00013390: 2065 7831 3330 206f 6d69 7474 6564 2069   ex130 omitted i\n+000133a0: 6e20 7465 7874 2076 6572 7369 6f6e 206f  n text version o\n+000133b0: 6620 7468 6973 2064 6f63 756d 656e 742e  f this document.\n+000133c0: 2200 085d 0a0a 5468 6973 2069 7320 636f  \"..]..This is co\n+000133d0: 7272 6563 742c 2062 7574 2064 6f65 7320  rrect, but does \n+000133e0: 6e6f 7420 7265 7665 616c 2076 6572 7920  not reveal very \n+000133f0: 6d75 6368 2e20 2043 6f6d 6d6f 6e20 6572  much.  Common er\n+00013400: 726f 7273 2061 7265 0a6d 6973 706c 6163  rors are.misplac\n+00013410: 6564 2076 6572 7469 6365 7320 616e 6420  ed vertices and \n+00013420: 706f 6c79 676f 6e73 206d 6973 7369 6e67  polygons missing\n+00013430: 2065 6e74 6972 656c 7920 6475 6520 746f   entirely due to\n+00013440: 2069 6e63 6f72 7265 6374 2076 6572 7465   incorrect verte\n+00013450: 780a 6f72 6465 722e 2020 546f 2072 756c  x.order.  To rul\n+00013460: 6520 7468 6573 6520 6f75 742c 206c 6574  e these out, let\n+00013470: 2773 2069 6e73 7065 6374 2061 6c6c 2073  's inspect all s\n+00013480: 6964 6573 206f 6620 7468 6520 686f 7573  ides of the hous\n+00013490: 652e 2020 5468 6973 0a69 7320 6e6f 7420  e.  This.is not \n+000134a0: 6861 7264 2e20 204d 6572 656c 7920 7265  hard.  Merely re\n+000134b0: 706c 6163 6520 7468 6520 7265 6665 7265  place the refere\n+000134c0: 6e63 6520 7b68 6f75 7365 7d20 7769 7468  nce {house} with\n+000134d0: 2061 2027 7265 7065 6174 272e 0a2a 4e6f   a 'repeat'..*No\n+000134e0: 7465 2052 6570 6561 7473 3a3a 2e0a 2020  te Repeats::..  \n+000134f0: 7265 7065 6174 207b 2031 332c 2072 6f74  repeat { 13, rot\n+00013500: 6174 6528 3330 2c20 5b31 2c32 2c33 5d29  ate(30, [1,2,3])\n+00013510: 2c20 7472 616e 736c 6174 6528 5b33 2c30  , translate([3,0\n+00013520: 2c30 5d29 207d 207b 686f 7573 657d 0a00  ,0]) } {house}..\n+00013530: 085b 696d 6167 6520 7372 633d 2265 7831  .[image src=\"ex1\n+00013540: 3430 2e70 6e67 2220 7465 7874 3d22 496d  40.png\" text=\"Im\n+00013550: 6167 6520 6578 3134 3020 6f6d 6974 7465  age ex140 omitte\n+00013560: 6420 696e 2074 6578 7420 7665 7273 696f  d in text versio\n+00013570: 6e20 6f66 2074 6869 7320 646f 6375 6d65  n of this docume\n+00013580: 6e74 2e22 0008 5d0a 0a41 6761 696e 2074  nt.\"..]..Again t\n+00013590: 6869 6e67 7320 6c6f 6f6b 2063 6f72 7265  hings look corre\n+000135a0: 6374 2e20 204e 6f74 6520 7468 6174 2074  ct.  Note that t\n+000135b0: 6865 2068 6964 6465 6e20 7375 7266 6163  he hidden surfac\n+000135c0: 6520 616c 676f 7269 7468 6d0a 6861 6e64  e algorithm.hand\n+000135d0: 6c65 7320 696e 7465 7273 6563 7469 6e67  les intersecting\n+000135e0: 2070 6f6c 7967 6f6e 7320 636f 7272 6563   polygons correc\n+000135f0: 746c 7920 7768 6572 6520 736f 6d65 2063  tly where some c\n+00013600: 6f70 6965 7320 6f66 2074 6865 2068 6f75  opies of the hou\n+00013610: 7365 0a6f 7665 726c 6170 2e0a 0a20 2020  se.overlap...   \n+00013620: 4c65 7427 7320 6c61 7920 6f75 7420 7468  Let's lay out th\n+00013630: 6520 6765 6f6d 6574 7279 206f 6620 7065  e geometry of pe\n+00013640: 7273 7065 6374 6976 6520 7072 6f6a 6563  rspective projec\n+00013650: 7469 6f6e 206f 6620 7468 6520 686f 7573  tion of the hous\n+00013660: 650a 6f6e 746f 2061 2070 6c61 6e65 2077  e.onto a plane w\n+00013670: 6974 6820 7261 7973 2070 6173 7369 6e67  ith rays passing\n+00013680: 2074 6872 6f75 6768 2074 6865 206f 7269   through the ori\n+00013690: 6769 6e2e 2020 4265 6769 6e20 6279 2070  gin.  Begin by p\n+000136a0: 6f73 6974 696f 6e69 6e67 0a74 6865 2068  ositioning.the h\n+000136b0: 6f75 7365 2074 7765 6c76 6520 756e 6974  ouse twelve unit\n+000136c0: 7320 6261 636b 206f 6e20 7468 6520 6e65  s back on the ne\n+000136d0: 6761 7469 7665 207a 2d61 7869 7320 616e  gative z-axis an\n+000136e0: 6420 6164 6469 6e67 2061 2073 6574 206f  d adding a set o\n+000136f0: 660a 636f 6f72 6469 6e61 7465 2061 7865  f.coordinate axe\n+00013700: 732e 2020 546f 206d 6f76 6520 7468 6520  s.  To move the \n+00013710: 686f 7573 6520 7765 206e 6565 6420 6f6e  house we need on\n+00013720: 6c79 2063 6861 6e67 6520 7468 6520 2268  ly change the \"h\n+00013730: 6f75 7365 0a70 6f73 6974 696f 6e69 6e67  ouse.positioning\n+00013740: 2220 7472 616e 7366 6f72 6d20 6465 6669  \" transform defi\n+00013750: 6e65 6420 6561 726c 6965 722e 0a20 2064  ned earlier..  d\n+00013760: 6566 2068 7020 726f 7461 7465 282d 3430  ef hp rotate(-40\n+00013770: 2c20 5b30 2c31 2c30 5d29 2074 6865 6e20  , [0,1,0]) then \n+00013780: 7472 616e 736c 6174 6528 5b30 2c30 2c2d  translate([0,0,-\n+00013790: 3132 5d29 0a20 2064 6566 2061 7865 7320  12]).  def axes \n+000137a0: 7b0a 2020 2020 6465 6620 737a 2031 0a20  {.    def sz 1. \n+000137b0: 2020 206c 696e 6520 5b61 7272 6f77 733d     line [arrows=\n+000137c0: 3c2d 3e5d 2028 737a 2c30 2c30 2928 4f29  <->] (sz,0,0)(O)\n+000137d0: 2830 2c73 7a2c 3029 0a20 2020 206c 696e  (0,sz,0).    lin\n+000137e0: 6520 5b61 7272 6f77 733d 2d3e 5d20 2028  e [arrows=->]  (\n+000137f0: 4f29 2830 2c30 2c73 7a29 0a20 2020 206c  O)(0,0,sz).    l\n+00013800: 696e 6520 5b6c 696e 6577 6964 7468 3d2e  ine [linewidth=.\n+00013810: 3270 742c 6c69 6e65 636f 6c6f 723d 626c  2pt,linecolor=bl\n+00013820: 7565 2c6c 696e 6573 7479 6c65 3d64 6173  ue,linestyle=das\n+00013830: 6865 645d 2028 4f29 2830 2c30 2c2d 3130  hed] (O)(0,0,-10\n+00013840: 290a 2020 2020 7370 6563 6961 6c20 7c5c  ).    special |\\\n+00013850: 7570 7574 5b72 5d23 317b 2478 247d 5c75  uput[r]#1{$x$}\\u\n+00013860: 7075 745b 755d 2332 7b24 7924 7d5c 7570  put[u]#2{$y$}\\up\n+00013870: 7574 5b6c 5d23 337b 247a 247d 7c0a 2020  ut[l]#3{$z$}|.  \n+00013880: 2020 2020 2873 7a2c 302c 3029 2830 2c73      (sz,0,0)(0,s\n+00013890: 7a2c 3029 2830 2c30 2c73 7a29 0a20 207d  z,0)(0,0,sz).  }\n+000138a0: 0a0a 2020 2054 696d 6520 666f 7220 616e  ..   Time for an\n+000138b0: 6f74 6865 7220 7465 7374 2e20 204c 6574  other test.  Let\n+000138c0: 2773 2062 7569 6c64 2061 2072 6561 6c20  's build a real \n+000138d0: 7669 6577 2074 7261 6e73 666f 726d 2c20  view transform, \n+000138e0: 6372 6561 7469 6e67 2061 0a22 7669 7274  creating a.\"virt\n+000138f0: 7561 6c20 6361 6d65 7261 2220 746f 206c  ual camera\" to l\n+00013900: 6f6f 6b20 6174 2074 6865 2073 6365 6e65  ook at the scene\n+00013910: 2077 6520 6172 6520 636f 6e73 7472 7563   we are construc\n+00013920: 7469 6e67 2e20 2052 6570 6c61 6365 2074  ting.  Replace t\n+00013930: 6865 0a27 7265 7065 6174 2720 7769 7468  he.'repeat' with\n+00013940: 0a20 2064 6566 2065 7965 2028 3130 2c34  .  def eye (10,4\n+00013950: 2c31 3029 0a20 2064 6566 206c 6f6f 6b5f  ,10).  def look_\n+00013960: 6174 2028 302c 302c 2d35 290a 2020 7075  at (0,0,-5).  pu\n+00013970: 7420 7b20 7669 6577 2828 6579 6529 2c20  t { view((eye), \n+00013980: 286c 6f6f 6b5f 6174 2929 207d 207b 207b  (look_at)) } { {\n+00013990: 686f 7573 657d 7b61 7865 737d 207d 0a20  house}{axes} }. \n+000139a0: 2020 5468 6520 2276 6965 7720 7472 616e    The \"view tran\n+000139b0: 7366 6f72 6d22 2072 6570 6f73 6974 696f  sform\" repositio\n+000139c0: 6e73 2074 6865 2073 6365 6e65 2073 6f20  ns the scene so \n+000139d0: 7468 6174 2074 6865 2070 6f69 6e74 2027  that the point '\n+000139e0: 6579 6527 2069 730a 6174 2074 6865 206f  eye' is.at the o\n+000139f0: 7269 6769 6e20 616e 6420 7468 6520 6469  rigin and the di\n+00013a00: 7265 6374 696f 6e20 6672 6f6d 2027 6579  rection from 'ey\n+00013a10: 6527 2074 6f20 276c 6f6f 6b5f 6174 2720  e' to 'look_at' \n+00013a20: 6973 2074 6865 206e 6567 6174 6976 650a  is the negative.\n+00013a30: 7a2d 6178 6973 2e20 2054 6869 7320 7265  z-axis.  This re\n+00013a40: 7175 6972 6573 2061 2072 6f74 6174 696f  quires a rotatio\n+00013a50: 6e20 616e 6420 6120 7472 616e 736c 6174  n and a translat\n+00013a60: 696f 6e20 7468 6174 2061 7265 2061 6c6c  ion that are all\n+00013a70: 2070 6163 6b65 640a 696e 746f 2074 6865   packed.into the\n+00013a80: 2063 6f6e 7374 7275 6374 6f72 2027 7669   constructor 'vi\n+00013a90: 6577 272e 0a0a 0008 5b69 6d61 6765 2073  ew'.....[image s\n+00013aa0: 7263 3d22 6578 3135 302e 706e 6722 2074  rc=\"ex150.png\" t\n+00013ab0: 6578 743d 2249 6d61 6765 2065 7831 3530  ext=\"Image ex150\n+00013ac0: 206f 6d69 7474 6564 2069 6e20 7465 7874   omitted in text\n+00013ad0: 2076 6572 7369 6f6e 206f 6620 7468 6973   version of this\n+00013ae0: 2064 6f63 756d 656e 742e 2200 085d 0a0a   document.\"..]..\n+00013af0: 5468 6973 2069 7320 7374 6172 7469 6e67  This is starting\n+00013b00: 2074 6f20 6c6f 6f6b 2067 6f6f 6421 2020   to look good!  \n+00013b10: 4164 6420 7468 6520 7072 6f6a 6563 7469  Add the projecti\n+00013b20: 6f6e 2070 6c61 6e65 2068 616c 6620 7761  on plane half wa\n+00013b30: 790a 6265 7477 6565 6e20 7468 6520 6f72  y.between the or\n+00013b40: 6967 696e 2061 6e64 2074 6865 2068 6f75  igin and the hou\n+00013b50: 7365 2061 7420 7a3d 2d35 2e20 2057 6527  se at z=-5.  We'\n+00013b60: 6c6c 2074 7279 2074 6865 2061 6e67 6c65  ll try the angle\n+00013b70: 2061 7267 756d 656e 740a 6665 6174 7572   argument.featur\n+00013b80: 6520 6f66 2027 7370 6563 6961 6c27 2074  e of 'special' t\n+00013b90: 6f20 706f 7369 7469 6f6e 2061 206c 6162  o position a lab\n+00013ba0: 656c 2e0a 2020 6465 6620 7020 3520 2520  el..  def p 5 % \n+00013bb0: 7072 6f6a 6563 7469 6f6e 2064 6973 7461  projection dista\n+00013bc0: 6e63 6520 2870 6c61 6e65 2061 7420 7a3d  nce (plane at z=\n+00013bd0: 2d70 290a 2020 6465 6620 7072 6f6a 6563  -p).  def projec\n+00013be0: 7469 6f6e 5f70 6c61 6e65 207b 0a20 2020  tion_plane {.   \n+00013bf0: 2064 6566 2073 7a20 312e 350a 2020 2020   def sz 1.5.    \n+00013c00: 706f 6c79 676f 6e20 282d 737a 2c2d 737a  polygon (-sz,-sz\n+00013c10: 2c2d 7029 2873 7a2c 2d73 7a2c 2d70 2928  ,-p)(sz,-sz,-p)(\n+00013c20: 737a 2c73 7a2c 2d70 2928 2d73 7a2c 737a  sz,sz,-p)(-sz,sz\n+00013c30: 2c2d 7029 0a20 2020 2073 7065 6369 616c  ,-p).    special\n+00013c40: 207c 5c72 7075 745b 625d 2331 2d32 2333   |\\rput[b]#1-2#3\n+00013c50: 7b5c 666f 6f74 6e6f 7465 7369 7a65 5c73  {\\footnotesize\\s\n+00013c60: 6620 7072 6f6a 6563 7469 6f6e 2070 6c61  f projection pla\n+00013c70: 6e65 7d7c 200a 2020 2020 2020 282d 737a  ne}| .      (-sz\n+00013c80: 2c2d 737a 2c2d 7029 2873 7a2c 2d73 7a2c  ,-sz,-p)(sz,-sz,\n+00013c90: 2d70 2928 302c 2d73 7a2b 2e31 2c2d 7029  -p)(0,-sz+.1,-p)\n+00013ca0: 0a20 207d 0a41 6464 207b 7072 6f6a 6563  .  }.Add {projec\n+00013cb0: 7469 6f6e 5f70 6c61 6e65 7d20 746f 2074  tion_plane} to t\n+00013cc0: 6865 206c 6973 7420 6f66 206f 626a 6563  he list of objec\n+00013cd0: 7473 2069 6e20 7468 6520 2770 7574 2720  ts in the 'put' \n+00013ce0: 6162 6f76 652e 0a0a 0008 5b69 6d61 6765  above.....[image\n+00013cf0: 2073 7263 3d22 6578 3136 302e 706e 6722   src=\"ex160.png\"\n+00013d00: 2074 6578 743d 2249 6d61 6765 2065 7831   text=\"Image ex1\n+00013d10: 3630 206f 6d69 7474 6564 2069 6e20 7465  60 omitted in te\n+00013d20: 7874 2076 6572 7369 6f6e 206f 6620 7468  xt version of th\n+00013d30: 6973 2064 6f63 756d 656e 742e 2200 085d  is document.\"..]\n+00013d40: 0a0a 2020 2054 6865 2077 6179 2077 6520  ..   The way we \n+00013d50: 636f 6e73 7472 7563 7465 6420 7468 6520  constructed the \n+00013d60: 706f 696e 7473 206f 6620 7468 6520 686f  points of the ho\n+00013d70: 7573 6520 6e6f 7720 6d61 6b65 7320 6974  use now makes it\n+00013d80: 2065 6173 7920 746f 0a64 7261 7720 7261   easy to.draw ra\n+00013d90: 7973 206f 6620 7072 6f6a 6563 7469 6f6e  ys of projection\n+00013da0: 2e20 2057 6527 6c6c 2063 6173 7420 6f6e  .  We'll cast on\n+00013db0: 6520 7261 7920 6672 6f6d 2065 7665 7279  e ray from every\n+00013dc0: 2076 6973 6962 6c65 2076 6572 7465 780a   visible vertex.\n+00013dd0: 6f66 2074 6865 2068 6f75 7365 2061 6e64  of the house and\n+00013de0: 2064 6566 696e 6520 6f70 7469 6f6e 7320   define options \n+00013df0: 736f 2074 6865 2061 7070 6561 7261 6e63  so the appearanc\n+00013e00: 6520 6f66 2061 6c6c 2072 6179 7320 6361  e of all rays ca\n+00013e10: 6e20 6265 0a63 6861 6e67 6564 2061 7420  n be.changed at \n+00013e20: 7468 6520 7361 6d65 2074 696d 652e 0a20  the same time.. \n+00013e30: 2064 6566 2070 726f 6a65 6374 696f 6e5f   def projection_\n+00013e40: 7261 7973 207b 0a20 2020 2064 6566 2072  rays {.    def r\n+00013e50: 6179 6f70 7420 5b6c 696e 6577 6964 7468  ayopt [linewidth\n+00013e60: 3d2e 3370 742c 6c69 6e65 636f 6c6f 723d  =.3pt,linecolor=\n+00013e70: 6c69 6768 7467 7261 795d 0a20 2020 206c  lightgray].    l\n+00013e80: 696e 6520 5b72 6179 6f70 745d 284f 2928  ine [rayopt](O)(\n+00013e90: 7052 3129 206c 696e 6520 5b72 6179 6f70  pR1) line [rayop\n+00013ea0: 745d 284f 2928 7052 3229 206c 696e 655b  t](O)(pR2) line[\n+00013eb0: 7261 796f 7074 5d28 4f29 2870 5233 290a  rayopt](O)(pR3).\n+00013ec0: 2020 2020 6c69 6e65 205b 7261 796f 7074      line [rayopt\n+00013ed0: 5d28 4f29 2870 5234 2920 6c69 6e65 205b  ](O)(pR4) line [\n+00013ee0: 7261 796f 7074 5d28 4f29 2870 5235 290a  rayopt](O)(pR5).\n+00013ef0: 2020 2020 6c69 6e65 205b 7261 796f 7074      line [rayopt\n+00013f00: 5d28 4f29 2870 4c31 2920 6c69 6e65 205b  ](O)(pL1) line [\n+00013f10: 7261 796f 7074 5d28 4f29 2870 4c32 2920  rayopt](O)(pL2) \n+00013f20: 6c69 6e65 5b72 6179 6f70 745d 284f 2928  line[rayopt](O)(\n+00013f30: 704c 3529 0a20 2020 206c 696e 6520 5b72  pL5).    line [r\n+00013f40: 6179 6f70 745d 284f 2928 7044 3129 206c  ayopt](O)(pD1) l\n+00013f50: 696e 6520 5b72 6179 6f70 745d 284f 2928  ine [rayopt](O)(\n+00013f60: 7044 3229 200a 2020 2020 6c69 6e65 205b  pD2) .    line [\n+00013f70: 7261 796f 7074 5d28 4f29 2870 4433 2920  rayopt](O)(pD3) \n+00013f80: 6c69 6e65 205b 7261 796f 7074 5d28 4f29  line [rayopt](O)\n+00013f90: 2870 4434 2920 0a20 207d 0a54 6865 2072  (pD4) .  }.The r\n+00013fa0: 6573 756c 7420 6973 2073 686f 776e 2068  esult is shown h\n+00013fb0: 6572 652e 0a0a 0008 5b69 6d61 6765 2073  ere.....[image s\n+00013fc0: 7263 3d22 6578 3137 302e 706e 6722 2074  rc=\"ex170.png\" t\n+00013fd0: 6578 743d 2249 6d61 6765 2065 7831 3730  ext=\"Image ex170\n+00013fe0: 206f 6d69 7474 6564 2069 6e20 7465 7874   omitted in text\n+00013ff0: 2076 6572 7369 6f6e 206f 6620 7468 6973   version of this\n+00014000: 2064 6f63 756d 656e 742e 2200 085d 0a0a   document.\"..]..\n+00014010: 5468 6520 7261 7973 2070 6965 7263 6520  The rays pierce \n+00014020: 7468 6520 7072 6f6a 6563 7469 6f6e 2070  the projection p\n+00014030: 6c61 6e65 2061 7420 7468 6520 636f 7272  lane at the corr\n+00014040: 6573 706f 6e64 696e 6720 706f 696e 7473  esponding points\n+00014050: 206f 6e20 7468 650a 7065 7273 7065 6374   on the.perspect\n+00014060: 6976 6520 696d 6167 6520 7765 2061 7265  ive image we are\n+00014070: 2074 7279 696e 6720 746f 2064 7261 772e   trying to draw.\n+00014080: 2020 416c 6272 6563 6874 2044 c3bc 7265    Albrecht D..re\n+00014090: 7220 616e 6420 6869 730a 5265 6e61 6973  r and his.Renais\n+000140a0: 7361 6e63 6520 636f 6e74 656d 706f 7261  sance contempora\n+000140b0: 7269 6573 2068 6164 2074 6865 2073 616d  ries had the sam\n+000140c0: 6520 6964 6561 2069 6e20 7468 6520 6561  e idea in the ea\n+000140d0: 726c 7920 3135 3030 2773 2e0a 0a00 085b  rly 1500's.....[\n+000140e0: 696d 6167 6520 7372 633d 2264 7565 7265  image src=\"duere\n+000140f0: 722e 706e 6722 2074 6578 743d 2249 6d61  r.png\" text=\"Ima\n+00014100: 6765 206f 6620 4475 6572 6572 2773 2070  ge of Duerer's p\n+00014110: 6572 7370 6563 7469 7665 2063 6f6d 7075  erspective compu\n+00014120: 7465 7220 6f6d 6974 7465 6420 696e 2074  ter omitted in t\n+00014130: 6578 7420 7665 7273 696f 6e20 6f66 2074  ext version of t\n+00014140: 6869 7320 646f 6375 6d65 6e74 2e22 0008  his document.\"..\n+00014150: 5d0a 0a20 2020 416c 6c20 7468 6174 2773  ]..   All that's\n+00014160: 206c 6566 7420 6973 2074 6f20 6669 6e64   left is to find\n+00014170: 2061 2077 6179 2074 6f20 636f 6e6e 6563   a way to connec\n+00014180: 7420 7468 6520 706f 696e 7473 206f 6620  t the points of \n+00014190: 7468 6520 686f 7573 650a 6f6e 2074 6865  the house.on the\n+000141a0: 2070 726f 6a65 6374 696f 6e20 706c 616e   projection plan\n+000141b0: 652e 2020 5765 2063 6f75 6c64 2070 756c  e.  We could pul\n+000141c0: 6c20 6f75 7420 6120 676f 6f64 2063 6f6d  l out a good com\n+000141d0: 7075 7465 7220 6772 6170 6869 6373 0a74  puter graphics.t\n+000141e0: 6578 742c 2066 696e 6420 7468 6520 6e65  ext, find the ne\n+000141f0: 6365 7373 6172 7920 6d61 7472 6978 2c20  cessary matrix, \n+00014200: 616e 6420 656e 7465 7220 6974 206f 7572  and enter it our\n+00014210: 7365 6c76 6573 2061 7320 6120 7472 616e  selves as a tran\n+00014220: 7366 6f72 6d0a 6c69 7465 7261 6c2e 2020  sform.literal.  \n+00014230: 2a4e 6f74 6520 5472 616e 7366 6f72 6d20  *Note Transform \n+00014240: 6c69 7465 7261 6c73 3a3a 2e20 2054 6861  literals::.  Tha\n+00014250: 7420 776f 726b 2069 7320 616c 7265 6164  t work is alread\n+00014260: 7920 646f 6e65 2c0a 686f 7765 7665 722e  y done,.however.\n+00014270: 2020 5765 2063 616e 2075 7365 2074 6865    We can use the\n+00014280: 2027 7072 6f6a 6563 7428 7029 2720 636f   'project(p)' co\n+00014290: 6e73 7472 7563 746f 722e 0a0a 2020 2054  nstructor...   T\n+000142a0: 6865 7265 2061 7265 2073 7469 6c6c 2073  here are still s\n+000142b0: 6f6d 6520 6465 7461 696c 7320 7468 6174  ome details that\n+000142c0: 2072 6571 7569 7265 2063 6172 652e 2020   require care.  \n+000142d0: 5072 6f6a 6563 7469 6f6e 2077 696c 6c0a  Projection will.\n+000142e0: 666c 6174 7465 6e20 7768 6174 6576 6572  flatten whatever\n+000142f0: 2069 7320 7472 616e 7366 6f72 6d65 6420   is transformed \n+00014300: 6f6e 746f 2074 6865 2070 6c61 6e65 207a  onto the plane z\n+00014310: 3d2d 702e 2020 5468 6572 6566 6f72 6520  =-p.  Therefore \n+00014320: 616e 7920 7061 7274 0a6f 6620 7468 6520  any part.of the \n+00014330: 686f 7573 6520 636f 756c 6420 6469 7361  house could disa\n+00014340: 7070 6561 7220 6265 6869 6e64 2074 6865  ppear behind the\n+00014350: 2070 726f 6a65 6374 696f 6e20 706c 616e   projection plan\n+00014360: 6520 2874 6865 2068 6964 6465 6e0a 7375  e (the hidden.su\n+00014370: 7266 6163 6520 616c 676f 7269 7468 6d20  rface algorithm \n+00014380: 6f72 6465 7273 206f 626a 6563 7473 2061  orders objects a\n+00014390: 7420 7468 6520 7361 6d65 2064 6570 7468  t the same depth\n+000143a0: 2061 7262 6974 7261 7269 6c79 292e 2020   arbitrarily).  \n+000143b0: 5468 650a 646f 6f72 206d 6179 2061 6c73  The.door may als\n+000143c0: 6f20 6469 7361 7070 6561 7220 6265 6869  o disappear behi\n+000143d0: 6e64 2074 6865 2066 726f 6e74 206f 6620  nd the front of \n+000143e0: 7468 6520 686f 7573 652e 2020 546f 206d  the house.  To m\n+000143f0: 616b 6520 7375 7265 0a65 7665 7279 7468  ake sure.everyth\n+00014400: 696e 6720 7265 6d61 696e 7320 7669 7369  ing remains visi\n+00014410: 626c 652c 2077 6527 6c6c 2070 6c61 6365  ble, we'll place\n+00014420: 2074 6865 2068 6f75 7365 2061 2074 696e   the house a tin\n+00014430: 7920 6269 7420 696e 2066 726f 6e74 206f  y bit in front o\n+00014440: 660a 7468 6520 7072 6f6a 6563 7469 6f6e  f.the projection\n+00014450: 2070 6c61 6e65 2061 6e64 2061 2073 6563   plane and a sec\n+00014460: 6f6e 6420 636f 7079 206f 6620 7468 6520  ond copy of the \n+00014470: 646f 6f72 2069 6e20 6672 6f6e 7420 6f66  door in front of\n+00014480: 2074 6865 0a68 6f75 7365 2e0a 2020 6465   the.house..  de\n+00014490: 6620 7072 6f6a 6563 7469 6f6e 207b 0a20  f projection {. \n+000144a0: 2020 2025 2065 2069 7320 6120 736d 616c     % e is a smal\n+000144b0: 6c20 6e75 6d62 6572 2064 6566 696e 6564  l number defined\n+000144c0: 2061 626f 7665 0a20 2020 2070 7574 207b   above.    put {\n+000144d0: 2070 726f 6a65 6374 2870 2920 7468 656e   project(p) then\n+000144e0: 2074 7261 6e73 6c61 7465 285b 302c 302c   translate([0,0,\n+000144f0: 312a 655d 2920 7d20 7b68 6f75 7365 7d0a  1*e]) } {house}.\n+00014500: 2020 2020 7075 7420 7b20 7072 6f6a 6563      put { projec\n+00014510: 7428 7029 2074 6865 6e20 7472 616e 736c  t(p) then transl\n+00014520: 6174 6528 5b30 2c30 2c32 2a65 5d29 207d  ate([0,0,2*e]) }\n+00014530: 207b 646f 6f72 7d0a 2020 7d0a 0a00 085b   {door}.  }....[\n+00014540: 696d 6167 6520 7372 633d 2265 7831 3830  image src=\"ex180\n+00014550: 2e70 6e67 2220 7465 7874 3d22 496d 6167  .png\" text=\"Imag\n+00014560: 6520 6578 3138 3020 6f6d 6974 7465 6420  e ex180 omitted \n+00014570: 696e 2074 6578 7420 7665 7273 696f 6e20  in text version \n+00014580: 6f66 2074 6869 7320 646f 6375 6d65 6e74  of this document\n+00014590: 2e22 0008 5d0a 0a20 2020 4966 2079 6f75  .\"..]..   If you\n+000145a0: 2068 6176 6520 7374 7564 6965 6420 616e   have studied an\n+000145b0: 6420 756e 6465 7273 7461 6e64 2061 6c6c  d understand all\n+000145c0: 2074 6869 732c 2079 6f75 2061 7265 2077   this, you are w\n+000145d0: 656c 6c20 6f6e 2074 6865 2077 6179 0a74  ell on the way.t\n+000145e0: 6f20 7375 6363 6573 7320 7769 7468 2027  o success with '\n+000145f0: 736b 6574 6368 272e 2020 4e6f 7420 7368  sketch'.  Not sh\n+00014600: 6f77 6e20 6172 6520 7468 6520 3230 206f  own are the 20 o\n+00014610: 7220 736f 2069 7465 7261 7469 6f6e 7320  r so iterations \n+00014620: 7468 6174 0a77 6572 6520 7265 7175 6972  that.were requir\n+00014630: 6564 2074 6f20 6669 6e64 2061 2072 6561  ed to find a rea\n+00014640: 736f 6e61 626c 6520 7669 6577 696e 6720  sonable viewing \n+00014650: 616e 676c 6520 616e 6420 686f 7573 6520  angle and house \n+00014660: 706f 7369 7469 6f6e 2c0a 6574 632e 2020  position,.etc.  \n+00014670: 4e6f 6e65 7468 656c 6573 732c 2074 6869  Nonetheless, thi\n+00014680: 7320 6472 6177 696e 6720 7761 7320 636f  s drawing was co\n+00014690: 6d70 6c65 7465 6420 696e 2061 626f 7574  mpleted in about\n+000146a0: 2061 6e20 686f 7572 2e20 2057 6869 6c65   an hour.  While\n+000146b0: 2061 0a47 5549 2074 6f6f 6c20 6d61 7920   a.GUI tool may \n+000146c0: 6861 7665 2062 6565 6e20 6120 6c69 7474  have been a litt\n+000146d0: 6c65 2066 6173 7465 722c 2069 7420 6973  le faster, it is\n+000146e0: 2075 6e6c 696b 656c 7920 7468 6174 2061   unlikely that a\n+000146f0: 206e 6577 0a64 7261 7769 6e67 2c20 6974   new.drawing, it\n+00014700: 7365 6c66 2061 2070 6572 7370 6563 7469  self a perspecti\n+00014710: 7665 2070 726f 6a65 6374 696f 6e20 6f66  ve projection of\n+00014720: 2074 6865 2073 6365 6e65 2c20 636f 756c   the scene, coul\n+00014730: 6420 6265 0a67 656e 6572 6174 6564 2077  d be.generated w\n+00014740: 6974 6820 7477 6f20 6d6f 7265 206d 696e  ith two more min\n+00014750: 7574 6573 2720 776f 726b 2120 204a 7573  utes' work!  Jus\n+00014760: 7420 6368 616e 6765 2074 6865 2076 6965  t change the vie\n+00014770: 7720 7472 616e 7366 6f72 6d0a 746f 0a20  w transform.to. \n+00014780: 2070 7574 207b 2076 6965 7728 2865 7965   put { view((eye\n+00014790: 292c 2028 6c6f 6f6b 5f61 7429 2920 7468  ), (look_at)) th\n+000147a0: 656e 2070 6572 7370 6563 7469 7665 2839  en perspective(9\n+000147b0: 2920 7d20 7b20 2e2e 2e0a 616e 6420 7072  ) } { ....and pr\n+000147c0: 6f64 7563 6520 7468 6973 2e0a 0a00 085b  oduce this.....[\n+000147d0: 696d 6167 6520 7372 633d 2265 7831 3930  image src=\"ex190\n+000147e0: 2e70 6e67 2220 7465 7874 3d22 496d 6167  .png\" text=\"Imag\n+000147f0: 6520 6578 3139 3020 6f6d 6974 7465 6420  e ex190 omitted \n+00014800: 696e 2074 6578 7420 7665 7273 696f 6e20  in text version \n+00014810: 6f66 2074 6869 7320 646f 6375 6d65 6e74  of this document\n+00014820: 2e22 0008 5d0a 0a1f 0a46 696c 653a 2073  .\"..]....File: s\n+00014830: 6b65 7463 682e 696e 666f 2c20 204e 6f64  ketch.info,  Nod\n+00014840: 653a 2041 2074 6563 686e 6963 616c 2064  e: A technical d\n+00014850: 7261 7769 6e67 2c20 204e 6578 743a 2041  rawing,  Next: A\n+00014860: 2068 6965 7261 7263 6869 6361 6c20 6d6f   hierarchical mo\n+00014870: 6465 6c2c 2020 5072 6576 3a20 4f76 6572  del,  Prev: Over\n+00014880: 7669 6577 2c20 2055 703a 2042 7569 6c64  view,  Up: Build\n+00014890: 696e 6720 6120 6472 6177 696e 670a 0a34  ing a drawing..4\n+000148a0: 2e32 2041 2074 6563 686e 6963 616c 2064  .2 A technical d\n+000148b0: 7261 7769 6e67 0a3d 3d3d 3d3d 3d3d 3d3d  rawing.=========\n+000148c0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a  ==============..\n+000148d0: 4c65 7427 7320 6c6f 6f6b 2061 7420 6120  Let's look at a \n+000148e0: 6472 6177 696e 6720 7468 6174 2072 6570  drawing that rep\n+000148f0: 7265 7365 6e74 7320 7468 6520 6b69 6e64  resents the kind\n+00014900: 206f 6620 7072 6f62 6c65 6d20 2773 6b65   of problem 'ske\n+00014910: 7463 6827 2077 6173 0a6d 6561 6e74 2074  tch' was.meant t\n+00014920: 6f20 736f 6c76 652d 2d61 2070 6169 7220  o solve--a pair \n+00014930: 6f66 2074 6578 7462 6f6f 6b20 6669 6775  of textbook figu\n+00014940: 7265 7320 7265 6761 7264 696e 6720 6120  res regarding a \n+00014950: 706f 6c79 676f 6e61 6c0a 6170 7072 6f78  polygonal.approx\n+00014960: 696d 6174 696f 6e20 6f66 2061 2074 7275  imation of a tru\n+00014970: 6e63 6174 6564 2063 6f6e 652e 2020 4865  ncated cone.  He\n+00014980: 7265 2061 7265 2074 6865 2070 6963 7475  re are the pictu\n+00014990: 7265 7320 7765 2077 696c 6c0a 7072 6f64  res we will.prod\n+000149a0: 7563 652e 0a0a 0008 5b69 6d61 6765 2073  uce.....[image s\n+000149b0: 7263 3d22 6578 3235 302e 706e 6722 2074  rc=\"ex250.png\" t\n+000149c0: 6578 743d 2249 6d61 6765 2065 7832 3530  ext=\"Image ex250\n+000149d0: 206f 6d69 7474 6564 2069 6e20 7465 7874   omitted in text\n+000149e0: 2076 6572 7369 6f6e 206f 6620 7468 6973   version of this\n+000149f0: 2064 6f63 756d 656e 742e 2200 085d 2020   document.\"..]  \n+00014a00: 2020 2000 085b 696d 6167 6520 7372 633d     ..[image src=\n+00014a10: 2265 7832 3630 2e70 6e67 2220 7465 7874  \"ex260.png\" text\n+00014a20: 3d22 496d 6167 6520 6578 3236 3020 6f6d  =\"Image ex260 om\n+00014a30: 6974 7465 6420 696e 2074 6578 7420 7665  itted in text ve\n+00014a40: 7273 696f 6e20 6f66 2074 6869 7320 646f  rsion of this do\n+00014a50: 6375 6d65 6e74 2e22 0008 5d0a 0a20 2020  cument.\"..]..   \n+00014a60: 5468 6520 636f 6e65 2073 6861 7065 2069  The cone shape i\n+00014a70: 7320 6a75 7374 2061 2073 7765 7074 206c  s just a swept l\n+00014a80: 696e 6520 7769 7468 206e 6f20 636c 6f73  ine with no clos\n+00014a90: 7572 6520 7461 6720 616e 6420 6375 6c6c  ure tag and cull\n+00014aa0: 696e 670a 7475 726e 6564 206f 6666 2e20  ing.turned off. \n+00014ab0: 2042 6567 696e 2062 7920 7365 7474 696e   Begin by settin\n+00014ac0: 6720 7570 2073 6f6d 6520 7573 6566 756c  g up some useful\n+00014ad0: 2063 6f6e 7374 616e 7473 2e0a 2020 6465   constants..  de\n+00014ae0: 6620 4f20 2830 2c30 2c30 2920 6465 6620  f O (0,0,0) def \n+00014af0: 4920 5b31 2c30 2c30 5d20 6465 6620 4a20  I [1,0,0] def J \n+00014b00: 5b30 2c31 2c30 5d20 6465 6620 4b20 5b30  [0,1,0] def K [0\n+00014b10: 2c30 2c31 5d0a 2020 6465 6620 7030 2028  ,0,1].  def p0 (\n+00014b20: 312c 3229 2064 6566 2070 3120 2831 2e35  1,2) def p1 (1.5\n+00014b30: 2c30 2920 6465 6620 4e20 380a 2020 6465  ,0) def N 8.  de\n+00014b40: 6620 7365 675f 726f 7420 726f 7461 7465  f seg_rot rotate\n+00014b50: 2833 3630 202f 204e 2c20 5b4a 5d29 0a54  (360 / N, [J]).T\n+00014b60: 6865 2070 6f69 6e74 7320 2770 3027 2061  he points 'p0' a\n+00014b70: 6e64 2027 7031 2720 6172 6520 7468 6520  nd 'p1' are the \n+00014b80: 656e 6420 706f 696e 7473 206f 6620 7468  end points of th\n+00014b90: 6520 6c69 6e65 2074 6f20 6265 2073 7765  e line to be swe\n+00014ba0: 7074 2e0a 5468 6520 6465 6669 6e69 7469  pt..The definiti\n+00014bb0: 6f6e 2027 7365 675f 726f 7427 2069 7320  on 'seg_rot' is \n+00014bc0: 7468 6520 7377 6565 7020 7472 616e 7366  the sweep transf\n+00014bd0: 6f72 6d61 7469 6f6e 2e20 2057 6974 6820  ormation.  With \n+00014be0: 7468 6573 652c 2074 6865 0a63 6f6e 6520  these, the.cone \n+00014bf0: 6974 7365 6c66 2069 7320 7369 6d70 6c65  itself is simple\n+00014c00: 2e0a 2020 7377 6565 705b 6375 6c6c 3d66  ..  sweep[cull=f\n+00014c10: 616c 7365 5d20 7b20 4e2c 205b 5b73 6567  alse] { N, [[seg\n+00014c20: 5f72 6f74 5d5d 207d 206c 696e 6528 7030  _rot]] } line(p0\n+00014c30: 2928 7031 290a 0a20 2020 5468 6520 6178  )(p1)..   The ax\n+00014c40: 6573 2061 7265 206e 6578 7420 616e 6420  es are next and \n+00014c50: 696e 636c 7564 6520 616e 2069 6e74 6572  include an inter\n+00014c60: 6573 696e 6720 7472 6963 6b20 7468 6174  esing trick that\n+00014c70: 2073 686f 7773 2074 6865 0a68 6964 6465   shows the.hidde\n+00014c80: 6e20 7061 7274 7320 6173 2064 6f74 7465  n parts as dotte\n+00014c90: 6420 6c69 6e65 732e 2020 5468 6520 7365  d lines.  The se\n+00014ca0: 6372 6574 2069 7320 6472 6177 2074 6865  cret is draw the\n+00014cb0: 2061 7865 7320 7477 6963 652d 2d73 6f6c   axes twice--sol\n+00014cc0: 6964 0a6c 696e 6573 2077 6974 6820 7468  id.lines with th\n+00014cd0: 6520 6e6f 726d 616c 2068 6964 6465 6e20  e normal hidden \n+00014ce0: 7375 7266 6163 6520 616c 676f 7269 7468  surface algorith\n+00014cf0: 6d20 696e 2065 6666 6563 742c 2061 6e64  m in effect, and\n+00014d00: 2074 6865 6e0a 646f 7474 6564 2077 6974   then.dotted wit\n+00014d10: 6820 7468 6520 6f70 7469 6f6e 2027 6c61  h the option 'la\n+00014d20: 793d 6f76 6572 2720 736f 2074 6861 7420  y=over' so that \n+00014d30: 6e6f 2070 6f6c 7967 6f6e 7320 6361 6e20  no polygons can \n+00014d40: 6869 6465 2074 6865 6d2e 0a20 2064 6566  hide them..  def\n+00014d50: 2061 7820 2864 782c 302c 3029 2025 2074   ax (dx,0,0) % t\n+00014d60: 6970 7320 6f66 2074 6865 2061 7865 730a  ips of the axes.\n+00014d70: 2020 6465 6620 6179 2028 302c 6479 2c30    def ay (0,dy,0\n+00014d80: 290a 2020 6465 6620 617a 2028 302c 302c  ).  def az (0,0,\n+00014d90: 647a 290a 2020 6c69 6e65 5b61 7272 6f77  dz).  line[arrow\n+00014da0: 733d 3c2d 3e2c 6c69 6e65 7769 6474 683d  s=<->,linewidth=\n+00014db0: 2e34 7074 5d28 6178 2928 4f29 2861 7929  .4pt](ax)(O)(ay)\n+00014dc0: 0a20 206c 696e 655b 6172 726f 7773 3d2d  .  line[arrows=-\n+00014dd0: 3e2c 6c69 6e65 7769 6474 683d 2e34 7074  >,linewidth=.4pt\n+00014de0: 5d28 4f29 2861 7a29 0a20 2025 2072 6570  ](O)(az).  % rep\n+00014df0: 6561 7420 646f 7474 6564 2061 7320 616e  eat dotted as an\n+00014e00: 206f 7665 726c 6179 2074 6f20 6869 6e74   overlay to hint\n+00014e10: 2061 7420 7468 6520 6869 6464 656e 206c   at the hidden l\n+00014e20: 696e 6573 0a20 206c 696e 655b 6c61 793d  ines.  line[lay=\n+00014e30: 6f76 6572 2c6c 696e 6573 7479 6c65 3d64  over,linestyle=d\n+00014e40: 6f74 7465 642c 6c69 6e65 7769 6474 683d  otted,linewidth=\n+00014e50: 2e34 7074 5d28 6178 2928 4f29 2861 7929  .4pt](ax)(O)(ay)\n+00014e60: 0a20 206c 696e 655b 6c61 793d 6f76 6572  .  line[lay=over\n+00014e70: 2c6c 696e 6573 7479 6c65 3d64 6f74 7465  ,linestyle=dotte\n+00014e80: 642c 6c69 6e65 7769 6474 683d 2e34 7074  d,linewidth=.4pt\n+00014e90: 5d28 4f29 2861 7a29 0a20 2073 7065 6369  ](O)(az).  speci\n+00014ea0: 616c 7c5c 666f 6f74 6e6f 7465 7369 7a65  al|\\footnotesize\n+00014eb0: 0a20 2020 2020 2020 2020 205c 7570 7574  .          \\uput\n+00014ec0: 5b64 5d23 317b 2478 247d 5c75 7075 745b  [d]#1{$x$}\\uput[\n+00014ed0: 755d 2332 7b24 7924 7d5c 7570 7574 5b6c  u]#2{$y$}\\uput[l\n+00014ee0: 5d23 337b 247a 247d 7c0a 2020 2020 2861  ]#3{$z$}|.    (a\n+00014ef0: 7829 2861 7929 2861 7a29 0a54 6865 206c  x)(ay)(az).The l\n+00014f00: 6162 656c 7320 6172 6520 6170 706c 6965  abels are applie\n+00014f10: 6420 7769 7468 2027 5053 5472 6963 6b73  d with 'PSTricks\n+00014f20: 2720 7370 6563 6961 6c20 6f62 6a65 6374  ' special object\n+00014f30: 7320 6173 2075 7375 616c 2e0a 0a20 2020  s as usual...   \n+00014f40: 466f 7220 7468 6520 6865 6967 6874 2064  For the height d\n+00014f50: 696d 656e 7369 6f6e 206d 6172 6b2c 2074  imension mark, t\n+00014f60: 6865 2070 6f77 6572 206f 6620 6166 6669  he power of affi\n+00014f70: 6e65 2061 7269 7468 6574 6963 2069 7320  ne arithetic is \n+00014f80: 7665 7279 0a68 656c 7066 756c 2e0a 2020  very.helpful..  \n+00014f90: 6465 6620 6864 696d 5f72 6566 2075 6e69  def hdim_ref uni\n+00014fa0: 7428 2870 3129 202d 2028 4f29 2920 7468  t((p1) - (O)) th\n+00014fb0: 656e 205b 5b73 6567 5f72 6f74 5d5d 5e32  en [[seg_rot]]^2\n+00014fc0: 0a20 2064 6566 2063 3020 2870 3029 2074  .  def c0 (p0) t\n+00014fd0: 6865 6e20 7363 616c 6528 5b4a 5d29 0a20  hen scale([J]). \n+00014fe0: 2064 6566 2068 3030 2028 6330 2920 2b20   def h00 (c0) + \n+00014ff0: 312e 3120 2a20 5b68 6469 6d5f 7265 665d  1.1 * [hdim_ref]\n+00015000: 0a20 2064 6566 2068 3031 2028 6330 2920  .  def h01 (c0) \n+00015010: 2b20 312e 3920 2a20 5b68 6469 6d5f 7265  + 1.9 * [hdim_re\n+00015020: 665d 0a20 2064 6566 2068 3032 2028 6330  f].  def h02 (c0\n+00015030: 2920 2b20 312e 3820 2a20 5b68 6469 6d5f  ) + 1.8 * [hdim_\n+00015040: 7265 665d 0a20 206c 696e 6528 6830 3029  ref].  line(h00)\n+00015050: 2868 3031 290a 2020 6465 6620 6831 3020  (h01).  def h10 \n+00015060: 284f 2920 2b20 312e 3620 2a20 5b68 6469  (O) + 1.6 * [hdi\n+00015070: 6d5f 7265 665d 0a20 2064 6566 2068 3131  m_ref].  def h11\n+00015080: 2028 4f29 202b 2031 2e39 202a 205b 6864   (O) + 1.9 * [hd\n+00015090: 696d 5f72 6566 5d0a 2020 6465 6620 6831  im_ref].  def h1\n+000150a0: 3220 284f 2920 2b20 312e 3820 2a20 5b68  2 (O) + 1.8 * [h\n+000150b0: 6469 6d5f 7265 665d 0a20 206c 696e 6528  dim_ref].  line(\n+000150c0: 6831 3029 2868 3131 290a 2020 6c69 6e65  h10)(h11).  line\n+000150d0: 5b61 7272 6f77 733d 3c2d 3e5d 2868 3032  [arrows=<->](h02\n+000150e0: 2928 6831 3229 0a20 2064 6566 2068 6d32  )(h12).  def hm2\n+000150f0: 2028 2868 3032 2920 2d20 284f 2920 2b20   ((h02) - (O) + \n+00015100: 2868 3132 2920 2d20 284f 2929 202f 2032  (h12) - (O)) / 2\n+00015110: 202b 2028 4f29 0a20 2073 7065 6369 616c   + (O).  special\n+00015120: 7c5c 666f 6f74 6e6f 7465 7369 7a65 5c72  |\\footnotesize\\r\n+00015130: 7075 742a 2331 7b24 6824 7d7c 2868 6d32  put*#1{$h$}|(hm2\n+00015140: 290a 2020 2054 6865 2067 656e 6572 616c  ).   The general\n+00015150: 2069 6465 6120 656d 706c 6f79 6564 2068   idea employed h\n+00015160: 6572 6520 6973 2074 6f20 636f 6d70 7574  ere is to comput\n+00015170: 6520 6120 756e 6974 2022 7265 6665 7265  e a unit \"refere\n+00015180: 6e63 650a 7665 6374 6f72 2220 7061 7261  nce.vector\" para\n+00015190: 6c6c 656c 2074 6f20 7468 6520 787a 2d70  llel to the xz-p\n+000151a0: 6c61 6e65 2069 6e20 7468 6520 6465 7369  lane in the desi\n+000151b0: 7265 6420 6469 7265 6374 696f 6e20 6f66  red direction of\n+000151c0: 2074 6865 0a64 696d 656e 7369 6f6e 2066   the.dimension f\n+000151d0: 726f 6d20 7468 6520 6f72 6967 696e 2e20  rom the origin. \n+000151e0: 2054 6865 2074 7261 6e73 666f 726d 6174   The transformat\n+000151f0: 696f 6e20 275b 5b73 6567 5f72 6f74 5d5d  ion '[[seg_rot]]\n+00015200: 5e32 2720 726f 7461 7465 730a 7477 6f20  ^2' rotates.two \n+00015210: 7365 676d 656e 7473 2061 626f 7574 2074  segments about t\n+00015220: 6865 2079 2d61 7869 732e 2020 5768 656e  he y-axis.  When\n+00015230: 2061 7070 6c69 6564 2074 6f20 2728 7031   applied to '(p1\n+00015240: 2920 2d20 284f 2927 2c20 7468 650a 7265  ) - (O)', the.re\n+00015250: 7375 6c74 696e 6720 7665 6374 6f72 2070  sulting vector p\n+00015260: 6f69 6e74 7320 746f 2074 6865 2072 6967  oints to the rig\n+00015270: 6874 2061 7320 7368 6f77 6e2e 2020 496e  ht as shown.  In\n+00015280: 2074 6869 7320 6d61 6e6e 6572 2c20 7765   this manner, we\n+00015290: 2063 616e 0a70 6963 6b20 616e 7920 7665   can.pick any ve\n+000152a0: 7274 6578 2061 7320 7468 6520 6c6f 6361  rtex as the loca\n+000152b0: 7469 6f6e 206f 6620 7468 6520 6865 6967  tion of the heig\n+000152c0: 6874 2064 696d 656e 7369 6f6e 206c 696e  ht dimension lin\n+000152d0: 6573 2062 7920 7661 7279 696e 670a 7468  es by varying.th\n+000152e0: 6520 6578 706f 6e65 6e74 206f 6620 275b  e exponent of '[\n+000152f0: 5b73 6567 5f72 6f74 5d5d 272e 2020 5468  [seg_rot]]'.  Th\n+00015300: 6973 2069 7320 6f6e 6c79 206f 6e65 206f  is is only one o\n+00015310: 6620 6d61 6e79 2070 6f73 7369 626c 650a  f many possible.\n+00015320: 7374 7261 7465 6769 6573 2e0a 0a20 2020  strategies...   \n+00015330: 5468 6520 636f 6d70 7574 6174 696f 6e20  The computation \n+00015340: 6f66 2027 686d 3227 2069 7320 6120 7573  of 'hm2' is a us\n+00015350: 6566 756c 2069 6469 6f6d 2066 6f72 2066  eful idiom for f\n+00015360: 696e 6469 6e67 2074 6865 2063 656e 7472  inding the centr\n+00015370: 6f69 640a 6f66 2061 2073 6574 206f 6620  oid.of a set of \n+00015380: 706f 696e 7473 2e0a 0a20 2020 5468 6520  points...   The \n+00015390: 7477 6f20 7261 6469 7573 206d 6172 6b73  two radius marks\n+000153a0: 2061 7265 2064 6f6e 6520 7369 6d69 6c61   are done simila\n+000153b0: 726c 792c 2073 6f20 7765 2070 7265 7365  rly, so we prese\n+000153c0: 6e74 2074 6865 2063 6f64 650a 7769 7468  nt the code.with\n+000153d0: 6f75 7420 636f 6d6d 656e 742e 0a20 2025  out comment..  %\n+000153e0: 2072 6164 6975 7320 6d65 6173 7572 656d   radius measurem\n+000153f0: 656e 7420 6d61 726b 730a 2020 6465 6620  ent marks.  def \n+00015400: 6761 7020 5b30 2c2e 322c 305d 2020 2520  gap [0,.2,0]  % \n+00015410: 7573 6564 2074 6f20 6372 6561 7465 2073  used to create s\n+00015420: 6d61 6c6c 2076 6572 7469 6361 6c20 6761  mall vertical ga\n+00015430: 7073 0a0a 2020 2520 6669 7273 7420 7231  ps..  % first r1\n+00015440: 0a20 2064 6566 2075 7031 205b 302c 332e  .  def up1 [0,3.\n+00015450: 312c 305d 2025 2074 6963 6b20 7269 7365  1,0] % tick rise\n+00015460: 7320 6162 6f76 6520 6469 6d65 6e73 696f  s above dimensio\n+00015470: 6e20 6120 6c69 7474 6c65 0a20 2064 6566  n a little.  def\n+00015480: 2072 3120 2828 7031 2920 7468 656e 205b   r1 ((p1) then [\n+00015490: 5b73 6567 5f72 6f74 5d5d 5e2d 3229 202b  [seg_rot]]^-2) +\n+000154a0: 205b 7570 315d 0a20 2064 6566 2072 3163   [up1].  def r1c\n+000154b0: 2028 7231 2920 7468 656e 2073 6361 6c65   (r1) then scale\n+000154c0: 285b 4a5d 290a 2020 6465 6620 7231 7420  ([J]).  def r1t \n+000154d0: 2872 3129 202b 205b 6761 705d 0a20 2064  (r1) + [gap].  d\n+000154e0: 6566 2072 3162 2028 2872 3174 2920 7468  ef r1b ((r1t) th\n+000154f0: 656e 2073 6361 6c65 285b 312c 302c 315d  en scale([1,0,1]\n+00015500: 2929 202b 205b 6761 705d 0a20 206c 696e  )) + [gap].  lin\n+00015510: 655b 6172 726f 7773 3d3c 2d3e 5d28 7231  e[arrows=<->](r1\n+00015520: 6329 2872 3129 2020 2520 6469 6d65 6e73  c)(r1)  % dimens\n+00015530: 696f 6e20 6c69 6e65 0a20 206c 696e 6528  ion line.  line(\n+00015540: 7231 6229 2872 3174 2920 2020 2020 2020  r1b)(r1t)       \n+00015550: 2020 2020 2020 2520 7469 636b 0a20 2064        % tick.  d\n+00015560: 6566 2072 316d 2028 2872 3129 202d 2028  ef r1m ((r1) - (\n+00015570: 4f29 202b 2028 7231 6329 202d 2028 4f29  O) + (r1c) - (O)\n+00015580: 2920 2f20 3220 2b20 284f 2920 2520 6c61  ) / 2 + (O) % la\n+00015590: 6265 6c20 706f 7369 7469 6f6e 0a20 2073  bel position.  s\n+000155a0: 7065 6369 616c 207c 5c66 6f6f 746e 6f74  pecial |\\footnot\n+000155b0: 6573 697a 655c 7270 7574 2a23 317b 2472  esize\\rput*#1{$r\n+000155c0: 5f31 247d 7c28 7231 6d29 2020 2520 6c61  _1$}|(r1m)  % la\n+000155d0: 6265 6c0a 0a20 2025 2073 616d 6520 6472  bel..  % same dr\n+000155e0: 696c 6c20 666f 7220 7230 2c20 6275 7420  ill for r0, but \n+000155f0: 6d75 7374 2070 726f 6a65 6374 2064 6f77  must project dow\n+00015600: 6e20 6669 7273 740a 2020 6465 6620 7570  n first.  def up\n+00015610: 3020 5b30 2c32 2e37 2c30 5d0a 2020 6465  0 [0,2.7,0].  de\n+00015620: 6620 7230 2028 2870 3029 2074 6865 6e20  f r0 ((p0) then \n+00015630: 7363 616c 6528 5b31 2c30 2c31 5d29 2074  scale([1,0,1]) t\n+00015640: 6865 6e20 5b5b 7365 675f 726f 745d 5d5e  hen [[seg_rot]]^\n+00015650: 2d32 2920 2b20 5b75 7030 5d0a 2020 6465  -2) + [up0].  de\n+00015660: 6620 7230 6320 2872 3029 2074 6865 6e20  f r0c (r0) then \n+00015670: 7363 616c 6528 5b4a 5d29 0a20 2064 6566  scale([J]).  def\n+00015680: 2072 3074 2028 7230 2920 2b20 5b67 6170   r0t (r0) + [gap\n+00015690: 5d0a 2020 6465 6620 7230 6220 2828 7030  ].  def r0b ((p0\n+000156a0: 2920 7468 656e 205b 5b73 6567 5f72 6f74  ) then [[seg_rot\n+000156b0: 5d5d 5e2d 3229 202b 205b 6761 705d 0a20  ]]^-2) + [gap]. \n+000156c0: 206c 696e 655b 6172 726f 7773 3d3c 2d3e   line[arrows=<->\n+000156d0: 5d28 7230 6329 2872 3029 0a20 206c 696e  ](r0c)(r0).  lin\n+000156e0: 6528 7230 6229 2872 3074 290a 2020 6465  e(r0b)(r0t).  de\n+000156f0: 6620 7230 6d20 2828 7230 2920 2d20 284f  f r0m ((r0) - (O\n+00015700: 2920 2b20 2872 3063 2920 2d20 284f 2929  ) + (r0c) - (O))\n+00015710: 202f 2032 202b 2028 4f29 0a20 2073 7065   / 2 + (O).  spe\n+00015720: 6369 616c 207c 5c66 6f6f 746e 6f74 6573  cial |\\footnotes\n+00015730: 697a 655c 7270 7574 2a23 317b 2472 5f30  ize\\rput*#1{$r_0\n+00015740: 247d 7c28 7230 6d29 0a0a 2020 2054 6865  $}|(r0m)..   The\n+00015750: 2073 6563 6f6e 6420 6472 6177 696e 6720   second drawing \n+00015760: 7573 6573 2074 6865 2073 616d 6520 7465  uses the same te\n+00015770: 6368 6e69 7175 6573 2e20 204f 6e6c 7920  chniques.  Only \n+00015780: 7468 6520 6d65 7468 6f64 2066 6f72 0a64  the method for.d\n+00015790: 7261 7769 6e67 2074 6865 2065 6c6c 6970  rawing the ellip\n+000157a0: 7469 6361 6c20 6172 6320 6973 206e 6577  tical arc is new\n+000157b0: 2e20 2048 6572 6520 6973 2074 6865 2063  .  Here is the c\n+000157c0: 6f64 652e 0a20 2064 6566 206d 6964 2028  ode..  def mid (\n+000157d0: 2870 3030 292d 284f 292b 2870 3130 292d  (p00)-(O)+(p10)-\n+000157e0: 284f 292b 2870 3131 292d 284f 292b 2870  (O)+(p11)-(O)+(p\n+000157f0: 3031 292d 284f 2929 2f34 2b28 4f29 0a20  01)-(O))/4+(O). \n+00015800: 2073 7065 6369 616c 7c5c 7270 7574 2331   special|\\rput#1\n+00015810: 7b5c 7073 6375 7374 6f6d 7b0a 2020 2020  {\\pscustom{.    \n+00015820: 5c73 6361 6c65 7b31 2031 2e33 7d0a 2020  \\scale{1 1.3}.  \n+00015830: 2020 5c70 7361 7263 5b61 7272 6f77 6c65    \\psarc[arrowle\n+00015840: 6e67 7468 3d2e 355d 7b2d 3e7d 7b2e 3235  ngth=.5]{->}{.25\n+00015850: 7d7b 2d36 307d 7b32 3430 7d7d 7d7c 0a20  }{-60}{240}}}|. \n+00015860: 2020 205b 6c61 793d 6f76 6572 5d28 6d69     [lay=over](mi\n+00015870: 6429 0a57 6520 636f 756c 6420 6861 7665  d).We could have\n+00015880: 2073 7765 7074 2061 2070 6f69 6e74 2074   swept a point t\n+00015890: 6f20 6d61 6b65 2074 6865 2061 7263 2077  o make the arc w\n+000158a0: 6974 6820 2773 6b65 7463 6827 2c20 6275  ith 'sketch', bu\n+000158b0: 7420 7573 696e 6720 610a 2750 5354 7269  t using a.'PSTri\n+000158c0: 636b 7327 2063 7573 746f 6d20 6772 6170  cks' custom grap\n+000158d0: 6869 6320 7761 7320 7369 6d70 6c65 722e  hic was simpler.\n+000158e0: 2020 4167 6169 6e20 7765 2063 6f6d 7075    Again we compu\n+000158f0: 7465 6420 7468 6520 6365 6e74 726f 6964  ted the centroid\n+00015900: 0a6f 6620 7468 6520 7175 6164 7269 6c61  .of the quadrila\n+00015910: 7465 7261 6c20 6279 2061 7665 7261 6769  teral by averagi\n+00015920: 6e67 2070 6f69 6e74 732e 2020 4e6f 7465  ng points.  Note\n+00015930: 2074 6861 7420 7363 616c 696e 6720 696e   that scaling in\n+00015940: 0a50 6f73 7473 6372 6970 7420 6469 7374  .Postscript dist\n+00015950: 6f72 7473 2074 6865 2061 7272 6f77 6865  orts the arrowhe\n+00015960: 6164 2c20 6275 7420 696e 2074 6869 7320  ad, but in this \n+00015970: 6361 7365 2074 6865 2064 6973 746f 7274  case the distort\n+00015980: 696f 6e0a 6163 7475 616c 6c79 206c 6f6f  ion.actually loo\n+00015990: 6b73 2062 6574 7465 7220 696e 2074 6865  ks better in the\n+000159a0: 2070 726f 6a65 6374 696f 6e20 6f66 2074   projection of t\n+000159b0: 6865 2073 6c61 6e74 6564 2066 6163 652e  he slanted face.\n+000159c0: 2020 4120 2773 6b65 7463 6827 0a61 7272    A 'sketch'.arr\n+000159d0: 6f77 6865 6164 2077 6f75 6c64 206e 6f74  owhead would not\n+000159e0: 2068 6176 6520 6265 656e 2064 6973 746f   have been disto\n+000159f0: 7274 6564 2e0a 0a20 2020 5468 6520 636f  rted...   The co\n+00015a00: 6d70 6c65 7465 2063 6f64 6520 666f 7220  mplete code for \n+00015a10: 7468 6973 2065 7861 6d70 6c65 2c20 7768  this example, wh\n+00015a20: 6963 6820 6472 6177 7320 6569 7468 6572  ich draws either\n+00015a30: 2066 6967 7572 650a 6465 7065 6e64 696e   figure.dependin\n+00015a40: 6720 6f6e 2074 6865 2064 6566 696e 6974  g on the definit\n+00015a50: 696f 6e20 6f66 2074 6865 2074 6167 2027  ion of the tag '\n+00015a60: 3c6c 6162 656c 6564 3e27 2c20 6973 2069  <labeled>', is i\n+00015a70: 6e63 6c75 6465 6420 696e 2074 6865 0a27  ncluded in the.'\n+00015a80: 736b 6574 6368 2720 6469 7374 7269 6275  sketch' distribu\n+00015a90: 7469 6f6e 2069 6e20 7468 6520 6669 6c65  tion in the file\n+00015aa0: 2027 7472 756e 6361 7465 6463 6f6e 652e   'truncatedcone.\n+00015ab0: 736b 272e 0a0a 1f0a 4669 6c65 3a20 736b  sk'.....File: sk\n+00015ac0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n+00015ad0: 3a20 4120 6869 6572 6172 6368 6963 616c  : A hierarchical\n+00015ae0: 206d 6f64 656c 2c20 204e 6578 743a 2043   model,  Next: C\n+00015af0: 6176 6561 7473 2c20 2050 7265 763a 2041  aveats,  Prev: A\n+00015b00: 2074 6563 686e 6963 616c 2064 7261 7769   technical drawi\n+00015b10: 6e67 2c20 2055 703a 2042 7569 6c64 696e  ng,  Up: Buildin\n+00015b20: 6720 6120 6472 6177 696e 670a 0a34 2e33  g a drawing..4.3\n+00015b30: 2041 2068 6965 7261 7263 6869 6361 6c20   A hierarchical \n+00015b40: 6d6f 6465 6c0a 3d3d 3d3d 3d3d 3d3d 3d3d  model.==========\n+00015b50: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a  ==============..\n+00015b60: 5768 696c 6520 2773 6b65 7463 6827 2077  While 'sketch' w\n+00015b70: 6173 206e 6576 6572 206d 6561 6e74 2074  as never meant t\n+00015b80: 6f20 6265 2061 2067 656f 6d65 7472 6963  o be a geometric\n+00015b90: 206d 6f64 656c 696e 6720 6c61 6e67 7561   modeling langua\n+00015ba0: 6765 2c20 6974 0a63 6f6d 6573 2066 6169  ge, it.comes fai\n+00015bb0: 726c 7920 636c 6f73 652e 2020 5468 6520  rly close.  The \n+00015bc0: 666f 6c6c 6f77 696e 6720 6578 616d 706c  following exampl\n+00015bd0: 6520 7075 7473 2061 6c6c 2077 6520 6861  e puts all we ha\n+00015be0: 7665 2073 6565 6e20 746f 2077 6f72 6b0a  ve seen to work.\n+00015bf0: 696e 2061 2076 6572 7920 7369 6d70 6c65  in a very simple\n+00015c00: 206d 6f64 656c 206f 6620 7468 6520 6875   model of the hu\n+00015c10: 6d61 6e20 6861 6e64 2e20 2053 7461 7274  man hand.  Start\n+00015c20: 2062 7920 7377 6565 7069 6e67 2061 206c   by sweeping a l\n+00015c30: 696e 6520 746f 0a6d 616b 6520 6120 7472  ine to.make a tr\n+00015c40: 756e 6361 7465 6420 636f 6e65 2c20 7768  uncated cone, wh\n+00015c50: 6963 6820 7769 6c6c 2062 6520 636f 7069  ich will be copi\n+00015c60: 6564 206f 7665 7220 616e 6420 6f76 6572  ed over and over\n+00015c70: 2061 6761 696e 2074 6f20 6d61 6b65 0a74   again to make.t\n+00015c80: 6865 2073 6567 6d65 6e74 7320 6f66 2066  he segments of f\n+00015c90: 696e 6765 7273 2e0a 2020 6465 6620 4f20  ingers..  def O \n+00015ca0: 2830 2c30 2c30 2920 2520 6f72 6967 696e  (0,0,0) % origin\n+00015cb0: 0a20 2064 6566 2049 205b 312c 302c 305d  .  def I [1,0,0]\n+00015cc0: 2064 6566 204a 205b 302c 312c 305d 2064   def J [0,1,0] d\n+00015cd0: 6566 204b 205b 302c 302c 315d 2025 2063  ef K [0,0,1] % c\n+00015ce0: 616e 6f6e 6963 616c 2075 6e69 7420 7665  anonical unit ve\n+00015cf0: 6374 6f72 730a 2020 6465 6620 7365 676d  ctors.  def segm\n+00015d00: 656e 7420 7b0a 2020 2020 6465 6620 6e5f  ent {.    def n_\n+00015d10: 6661 6365 7320 380a 2020 2020 7377 6565  faces 8.    swee\n+00015d20: 7020 7b20 6e5f 6661 6365 733c 3e2c 2072  p { n_faces<>, r\n+00015d30: 6f74 6174 6528 3336 3020 2f20 6e5f 6661  otate(360 / n_fa\n+00015d40: 6365 732c 205b 4a5d 2920 7d20 0a20 2020  ces, [J]) } .   \n+00015d50: 2020 206c 696e 6528 7072 6f78 696d 616c     line(proximal\n+00015d60: 5f72 6164 2c20 3029 2864 6973 7461 6c5f  _rad, 0)(distal_\n+00015d70: 7261 642c 2064 6973 7461 6c5f 6c65 6e29  rad, distal_len)\n+00015d80: 0a20 207d 0a49 6e20 6861 6e64 2061 6e61  .  }.In hand ana\n+00015d90: 746f 6d79 2c20 5f64 6973 7461 6c5f 2069  tomy, _distal_ i\n+00015da0: 7320 2261 7420 7468 6520 7469 7022 2061  s \"at the tip\" a\n+00015db0: 6e64 205f 7072 6f78 696d 616c 5f20 6973  nd _proximal_ is\n+00015dc0: 2022 696e 2074 6865 2061 7265 610a 6f66   \"in the area.of\n+00015dd0: 2074 6865 2070 616c 6d2e 2220 2057 6520   the palm.\"  We \n+00015de0: 6861 7665 206f 6d69 7474 6564 2061 6c6c  have omitted all\n+00015df0: 2074 6865 2073 6361 6c61 7220 636f 6e73   the scalar cons\n+00015e00: 7461 6e74 732e 2020 596f 7520 6361 6e20  tants.  You can \n+00015e10: 6669 6e64 0a74 6865 6d20 696e 2027 6861  find.them in 'ha\n+00015e20: 6e64 2e73 6b27 2c20 7768 6963 6820 6973  nd.sk', which is\n+00015e30: 2070 726f 7669 6465 6420 696e 2074 6865   provided in the\n+00015e40: 2027 736b 6574 6368 2720 6469 7374 7269   'sketch' distri\n+00015e50: 6275 7469 6f6e 2e0a 0a20 2020 5765 2061  bution...   We a\n+00015e60: 6c73 6f20 6e65 6564 2061 2070 726f 746f  lso need a proto\n+00015e70: 7479 7069 6361 6c20 7370 6865 7265 2074  typical sphere t\n+00015e80: 6f20 7573 6520 666f 7220 7468 6520 6a6f  o use for the jo\n+00015e90: 696e 7473 2074 6865 6d73 656c 7665 732e  ints themselves.\n+00015ea0: 0a20 2064 6566 206a 6f69 6e74 5f73 7068  .  def joint_sph\n+00015eb0: 6572 6520 7b0a 2020 2020 6465 6620 6e5f  ere {.    def n_\n+00015ec0: 6a6f 696e 745f 6661 6365 7320 380a 2020  joint_faces 8.  \n+00015ed0: 2020 7377 6565 7020 5b66 696c 6c63 6f6c    sweep [fillcol\n+00015ee0: 6f72 3d72 6564 5d20 7b20 6e5f 6a6f 696e  or=red] { n_join\n+00015ef0: 745f 6661 6365 732c 2072 6f74 6174 6528  t_faces, rotate(\n+00015f00: 3336 3020 2f20 6e5f 6a6f 696e 745f 6661  360 / n_joint_fa\n+00015f10: 6365 732c 205b 4a5d 2920 7d0a 2020 2020  ces, [J]) }.    \n+00015f20: 2020 7377 6565 7020 7b20 6e5f 6a6f 696e    sweep { n_join\n+00015f30: 745f 6661 6365 732c 2072 6f74 6174 6528  t_faces, rotate(\n+00015f40: 3138 3020 2f20 6e5f 6a6f 696e 745f 6661  180 / n_joint_fa\n+00015f50: 6365 7329 207d 200a 2020 2020 2020 2020  ces) } .        \n+00015f60: 2830 2c20 2d6a 6f69 6e74 5f72 6164 290a  (0, -joint_rad).\n+00015f70: 2020 7d0a 0a20 2020 5765 276c 6c20 6e6f    }..   We'll no\n+00015f80: 7720 6465 7369 676e 2074 6865 2069 6e64  w design the ind\n+00015f90: 6578 2066 696e 6765 7220 286e 756d 6265  ex finger (numbe\n+00015fa0: 7220 3120 696e 206f 7572 206e 6f74 6174  r 1 in our notat\n+00015fb0: 696f 6e61 6c0a 636f 6e76 656e 7469 6f6e  ional.convention\n+00015fc0: 3b20 6669 6e67 6572 2030 2069 7320 7468  ; finger 0 is th\n+00015fd0: 6520 7468 756d 6229 2e20 2054 6865 2064  e thumb).  The d\n+00015fe0: 6973 7461 6c20 726f 7461 7469 6f6e 2066  istal rotation f\n+00015ff0: 6f72 2074 6865 2066 696e 6765 720a 6170  or the finger.ap\n+00016000: 706c 6965 7320 6f6e 6c79 2074 6f20 7468  plies only to th\n+00016010: 6520 7469 702c 2073 6f20 7765 2064 6566  e tip, so we def\n+00016020: 696e 6520 7468 6520 666f 6c6c 6f77 696e  ine the followin\n+00016030: 672e 0a20 2064 6566 2064 6973 7461 6c5f  g..  def distal_\n+00016040: 3120 7b0a 2020 2020 7075 7420 7b20 7472  1 {.    put { tr\n+00016050: 616e 736c 6174 6528 6a6f 696e 745f 6761  anslate(joint_ga\n+00016060: 7020 2a20 6a6f 696e 745f 7261 6420 2a20  p * joint_rad * \n+00016070: 5b4a 5d29 200a 2020 2020 2020 2020 2020  [J]) .          \n+00016080: 7468 656e 2072 6f74 6174 6528 6469 7374  then rotate(dist\n+00016090: 616c 5f31 5f72 6f74 2c20 5b49 5d29 200a  al_1_rot, [I]) .\n+000160a0: 2020 2020 2020 2020 2020 7468 656e 2074            then t\n+000160b0: 7261 6e73 6c61 7465 2828 6469 7374 616c  ranslate((distal\n+000160c0: 5f6c 656e 202b 206a 6f69 6e74 5f67 6170  _len + joint_gap\n+000160d0: 202a 206a 6f69 6e74 5f72 6164 2920 2a20   * joint_rad) * \n+000160e0: 5b4a 5d29 207d 0a20 2020 2020 207b 7365  [J]) }.      {se\n+000160f0: 676d 656e 747d 0a20 2020 2070 7574 207b  gment}.    put {\n+00016100: 2072 6f74 6174 6528 6469 7374 616c 5f31   rotate(distal_1\n+00016110: 5f72 6f74 202f 2032 2c20 5b49 5d29 0a20  _rot / 2, [I]). \n+00016120: 2020 2020 2020 2020 2074 6865 6e20 7472           then tr\n+00016130: 616e 736c 6174 6528 2864 6973 7461 6c5f  anslate((distal_\n+00016140: 6c65 6e20 2b20 6a6f 696e 745f 6761 7020  len + joint_gap \n+00016150: 2a20 6a6f 696e 745f 7261 6429 202a 205b  * joint_rad) * [\n+00016160: 4a5d 2920 7d20 0a20 2020 2020 207b 6a6f  J]) } .      {jo\n+00016170: 696e 745f 7370 6865 7265 7d0a 2020 2020  int_sphere}.    \n+00016180: 7075 7420 7b20 7363 616c 6528 205b 4a5d  put { scale( [J]\n+00016190: 202b 2070 726f 7869 6d61 6c5f 6469 7374   + proximal_dist\n+000161a0: 616c 5f72 6174 696f 202a 2028 5b49 5d2b  al_ratio * ([I]+\n+000161b0: 5b4b 5d29 2029 207d 0a20 2020 2020 207b  [K]) ) }.      {\n+000161c0: 7365 676d 656e 747d 0a20 207d 2020 0a54  segment}.  }  .T\n+000161d0: 6865 2069 6465 6e74 6966 6965 7273 2068  he identifiers h\n+000161e0: 6572 6520 6172 6520 666f 7220 7369 7a65  ere are for size\n+000161f0: 2061 6e64 206c 6f63 6174 696f 6e20 636f   and location co\n+00016200: 6e73 7461 6e74 732e 2020 5468 6520 6578  nstants.  The ex\n+00016210: 6365 7074 696f 6e0a 6973 2027 6469 7374  ception.is 'dist\n+00016220: 616c 5f72 6f74 5f31 272e 2020 5468 6973  al_rot_1'.  This\n+00016230: 2072 6f74 6174 696f 6e20 7061 7261 6d65   rotation parame\n+00016240: 7465 7220 6d6f 6465 6c73 2074 6865 2066  ter models the f\n+00016250: 6c65 7869 6e67 206f 6620 7468 650a 6669  lexing of the.fi\n+00016260: 6e67 6572 2074 6970 2e20 2054 6865 2066  nger tip.  The f\n+00016270: 6972 7374 2027 7075 7427 206d 616b 6573  irst 'put' makes\n+00016280: 2061 2063 6f70 7920 6f66 2074 6865 2066   a copy of the f\n+00016290: 696e 6765 7220 7365 676d 656e 7420 7468  inger segment th\n+000162a0: 6174 2069 730a 7472 616e 736c 6174 6564  at is.translated\n+000162b0: 2075 7077 6172 6420 6a75 7374 2066 6172   upward just far\n+000162c0: 2065 6e6f 7567 6820 746f 206d 616b 6520   enough to make \n+000162d0: 726f 6f6d 2066 6f72 2074 6865 2073 7068  room for the sph\n+000162e0: 6572 6963 616c 206a 6f69 6e74 2e0a 5468  erical joint..Th\n+000162f0: 656e 2069 7420 6170 706c 6965 7320 7468  en it applies th\n+00016300: 6520 6469 7374 616c 2072 6f74 6174 696f  e distal rotatio\n+00016310: 6e2e 2020 4669 6e61 6c6c 7920 6974 2074  n.  Finally it t\n+00016320: 7261 6e73 6c61 7465 7320 7468 6520 7768  ranslates the wh\n+00016330: 6f6c 650a 6173 7365 6d62 6c79 2075 7077  ole.assembly upw\n+00016340: 6172 6420 6167 6169 6e20 746f 206d 616b  ard again to mak\n+00016350: 6520 726f 6f6d 2066 6f72 2074 6865 206d  e room for the m\n+00016360: 6964 646c 6520 7068 6c61 6e67 6573 2028  iddle phlanges (\n+00016370: 7468 6520 6e65 7874 0a62 6f6e 6520 746f  the next.bone to\n+00016380: 7761 7264 2074 6865 2070 616c 6d29 2e20  ward the palm). \n+00016390: 2054 6865 2073 6563 6f6e 6420 2770 7574   The second 'put\n+000163a0: 2720 706f 7369 7469 6f6e 7320 7468 6520  ' positions the \n+000163b0: 7370 6865 7265 2e20 2054 6865 7265 2069  sphere.  There i\n+000163c0: 730a 6120 726f 7461 7469 6f6e 2074 6f20  s.a rotation to \n+000163d0: 706c 6163 6520 7468 6520 6772 6964 206f  place the grid o\n+000163e0: 6e20 7468 6520 7370 6865 7265 2073 7572  n the sphere sur\n+000163f0: 6661 6365 2061 7420 616e 206e 6963 6520  face at an nice \n+00016400: 616e 676c 652c 0a74 6865 6e20 6120 7472  angle,.then a tr\n+00016410: 616e 736c 6174 696f 6e20 746f 2074 6865  anslation to the\n+00016420: 2062 6173 6520 6f66 2074 6865 2064 6973   base of the dis\n+00016430: 7461 6c20 7068 6c61 6e67 6573 2c20 7768  tal phlanges, wh\n+00016440: 6963 6820 6973 2061 6c73 6f0a 6365 6e74  ich is also.cent\n+00016450: 6572 206f 6620 6974 7320 726f 7461 7469  er of its rotati\n+00016460: 6f6e 2e20 2046 696e 616c 6c79 2c20 7468  on.  Finally, th\n+00016470: 6520 6c61 7374 2027 7075 7427 2070 6f73  e last 'put' pos\n+00016480: 6974 696f 6e73 2074 6865 206d 6964 646c  itions the middl\n+00016490: 650a 7365 676d 656e 7420 6974 7365 6c66  e.segment itself\n+000164a0: 2e0a 0a20 2020 5468 6520 6d69 6464 6c65  ...   The middle\n+000164b0: 206a 6f69 6e74 2069 7320 7468 6520 6e65   joint is the ne\n+000164c0: 7874 206f 6e65 2064 6f77 6e2c 2077 6974  xt one down, wit\n+000164d0: 6820 726f 7461 7469 6f6e 2061 6e67 6c65  h rotation angle\n+000164e0: 0a27 6d69 6464 6c65 5f72 6f74 5f31 272e  .'middle_rot_1'.\n+000164f0: 2020 5768 656e 2074 6869 7320 616e 676c    When this angl\n+00016500: 6520 6368 616e 6765 732c 2077 6520 6e65  e changes, we ne\n+00016510: 6564 2061 6c6c 2074 6865 206f 626a 6563  ed all the objec\n+00016520: 7473 2069 6e0a 2764 6973 7461 6c5f 3127  ts in.'distal_1'\n+00016530: 2074 6f20 726f 7461 7465 2061 7320 6120   to rotate as a \n+00016540: 756e 6974 2e20 2054 6869 7320 6973 2074  unit.  This is t\n+00016550: 6865 2072 6561 736f 6e69 6e67 2062 6568  he reasoning beh\n+00016560: 696e 6420 7468 6520 6e65 7874 0a64 6566  ind the next.def\n+00016570: 696e 6974 696f 6e2e 0a20 2064 6566 2066  inition..  def f\n+00016580: 696e 6765 725f 3120 7b0a 2020 2020 7075  inger_1 {.    pu\n+00016590: 7420 7b20 7472 616e 736c 6174 6528 6a6f  t { translate(jo\n+000165a0: 696e 745f 6761 7020 2a20 6a6f 696e 745f  int_gap * joint_\n+000165b0: 7261 6420 2a20 5b4a 5d29 0a20 2020 2020  rad * [J]).     \n+000165c0: 2020 2020 2074 6865 6e20 726f 7461 7465       then rotate\n+000165d0: 286d 6964 646c 655f 315f 726f 742c 205b  (middle_1_rot, [\n+000165e0: 495d 290a 2020 2020 2020 2020 2020 7468  I]).          th\n+000165f0: 656e 2074 7261 6e73 6c61 7465 2828 6d69  en translate((mi\n+00016600: 6464 6c65 5f72 6174 696f 202a 2064 6973  ddle_ratio * dis\n+00016610: 7461 6c5f 6c65 6e20 2b20 0a20 2020 2020  tal_len + .     \n 00016620: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00016630: 2020 2020 2020 206a 6f69 6e74 5f67 6170         joint_gap\n-00016640: 202a 206a 6f69 6e74 5f72 6164 2920 2a20   * joint_rad) * \n-00016650: 5b4a 5d29 207d 0a20 2020 2020 207b 6469  [J]) }.      {di\n-00016660: 7374 616c 5f31 7d0a 2020 2020 7075 7420  stal_1}.    put \n-00016670: 7b20 7363 616c 6528 7072 6f78 696d 616c  { scale(proximal\n-00016680: 5f64 6973 7461 6c5f 7261 7469 6f29 0a20  _distal_ratio). \n-00016690: 2020 2020 2020 2020 2074 6865 6e20 726f           then ro\n-000166a0: 7461 7465 286d 6964 646c 655f 315f 726f  tate(middle_1_ro\n-000166b0: 7420 2f20 322c 205b 495d 290a 2020 2020  t / 2, [I]).    \n-000166c0: 2020 2020 2020 7468 656e 2074 7261 6e73        then trans\n-000166d0: 6c61 7465 2828 6d69 6464 6c65 5f72 6174  late((middle_rat\n-000166e0: 696f 202a 2064 6973 7461 6c5f 6c65 6e20  io * distal_len \n-000166f0: 2b20 0a20 2020 2020 2020 2020 2020 2020  + .             \n-00016700: 2020 2020 2020 2020 2020 2020 206a 6f69               joi\n-00016710: 6e74 5f67 6170 202a 206a 6f69 6e74 5f72  nt_gap * joint_r\n-00016720: 6164 2920 2a20 5b4a 5d29 207d 200a 2020  ad) * [J]) } .  \n-00016730: 2020 2020 7b6a 6f69 6e74 5f73 7068 6572      {joint_spher\n-00016740: 657d 0a20 2020 2070 7574 207b 2073 6361  e}.    put { sca\n-00016750: 6c65 2820 6d69 6464 6c65 5f72 6174 696f  le( middle_ratio\n-00016760: 202a 205b 4a5d 202b 200a 2020 2020 2020   * [J] + .      \n-00016770: 2020 2020 2020 2020 2020 2070 726f 7869             proxi\n-00016780: 6d61 6c5f 6469 7374 616c 5f72 6174 696f  mal_distal_ratio\n-00016790: 5e32 202a 2028 5b49 5d2b 5b4b 5d29 2029  ^2 * ([I]+[K]) )\n-000167a0: 207d 0a20 2020 2020 207b 7365 676d 656e   }.      {segmen\n-000167b0: 747d 0a20 207d 0a54 6869 7320 6c6f 6f6b  t}.  }.This look\n-000167c0: 7320 7665 7279 2073 696d 696c 6172 2074  s very similar t\n-000167d0: 6f20 7468 6520 7072 6576 696f 7573 2064  o the previous d\n-000167e0: 6566 696e 6974 696f 6e2c 2061 6e64 2069  efinition, and i\n-000167f0: 7420 6973 2e20 2054 6865 0a69 6d70 6f72  t is.  The.impor\n-00016800: 7461 6e74 2064 6966 6665 7265 6e63 6520  tant difference \n-00016810: 6973 2074 6861 7420 7261 7468 6572 2074  is that rather t\n-00016820: 6861 6e20 706f 7369 7469 6f6e 696e 6720  han positioning \n-00016830: 616e 6420 726f 7461 7469 6e67 2061 0a73  and rotating a.s\n-00016840: 696e 676c 6520 7365 676d 656e 742c 2077  ingle segment, w\n-00016850: 6520 706f 7369 7469 6f6e 2061 6e64 2072  e position and r\n-00016860: 6f74 6174 6520 7468 6520 656e 7469 7265  otate the entire\n-00016870: 2022 6173 7365 6d62 6c79 2220 6465 6669   \"assembly\" defi\n-00016880: 6e65 6420 6173 0a27 6469 7374 616c 5f31  ned as.'distal_1\n-00016890: 272e 2020 5468 6520 7265 7374 2069 7320  '.  The rest is \n-000168a0: 6a75 7374 2061 7269 7468 6d65 7469 6320  just arithmetic \n-000168b0: 746f 2063 6f6d 7075 7465 2073 697a 6573  to compute sizes\n-000168c0: 2061 6e64 2070 6f73 6974 696f 6e73 0a74   and positions.t\n-000168d0: 6861 7420 6c6f 6f6b 206e 6963 652e 2020  hat look nice.  \n-000168e0: 5468 6520 6c61 7374 2027 7075 7427 2070  The last 'put' p\n-000168f0: 6c61 6365 7320 616e 2061 7070 726f 7072  laces an appropr\n-00016900: 6961 7465 6c79 2073 6861 7065 6420 7365  iately shaped se\n-00016910: 676d 656e 740a 7468 6174 2069 7320 7468  gment.that is th\n-00016920: 6520 5f70 726f 7869 6d61 6c20 7068 6c61  e _proximal phla\n-00016930: 6e67 6573 5f2c 2074 6865 2062 6f6e 6520  nges_, the bone \n-00016940: 7468 6174 206a 6f69 6e73 2074 6865 2070  that joins the p\n-00016950: 616c 6d20 6f66 2074 6865 0a68 616e 642e  alm of the.hand.\n-00016960: 2020 5468 6973 2063 6f6d 706c 6574 6573    This completes\n-00016970: 2074 6865 2066 696e 6765 7220 6974 7365   the finger itse\n-00016980: 6c66 2e0a 0a20 2020 416c 6c20 7468 6520  lf...   All the \n-00016990: 6f74 6865 7220 6669 6e67 6572 7320 6172  other fingers ar\n-000169a0: 6520 6465 7363 7269 6265 6420 6964 656e  e described iden\n-000169b0: 7469 6361 6c6c 7920 746f 2074 6869 7320  tically to this \n-000169c0: 6f6e 652e 2020 5765 0a61 6363 6f75 6e74  one.  We.account\n-000169d0: 2066 6f72 2074 6865 2066 6163 7420 7468   for the fact th\n-000169e0: 6174 2072 6561 6c20 6669 6e67 6572 7320  at real fingers \n-000169f0: 6172 6520 6469 6666 6572 656e 7420 7369  are different si\n-00016a00: 7a65 7320 696e 2074 6865 206e 6578 740a  zes in the next.\n-00016a10: 7374 6570 2c20 7768 6963 6820 6973 2074  step, which is t\n-00016a20: 6f20 6275 696c 6420 7468 6520 656e 7469  o build the enti\n-00016a30: 7265 2068 616e 642e 0a0a 2020 2054 6865  re hand...   The\n-00016a40: 2027 6861 6e64 2720 6465 6669 6e69 7469   'hand' definiti\n-00016a50: 6f6e 2074 6861 7420 666f 6c6c 6f77 7320  on that follows \n-00016a60: 696e 636c 7564 6573 2061 2073 6563 7469  includes a secti\n-00016a70: 6f6e 2066 6f72 2065 6163 680a 6669 6e67  on for each.fing\n-00016a80: 6572 2e20 2057 6527 6c6c 2063 6f6e 7469  er.  We'll conti\n-00016a90: 6e75 6520 7769 7468 2066 696e 6765 7220  nue with finger \n-00016aa0: 3120 616e 6420 6f6d 6974 2061 6c6c 2074  1 and omit all t\n-00016ab0: 6865 206f 7468 6572 732e 2020 284f 6620  he others.  (Of \n-00016ac0: 6e6f 7465 0a69 7320 7468 6174 2074 6865  note.is that the\n-00016ad0: 2074 6875 6d62 206e 6565 6473 2073 6c69   thumb needs sli\n-00016ae0: 6768 746c 7920 7370 6563 6961 6c20 7472  ghtly special tr\n-00016af0: 6561 746d 656e 742d 2d61 6e20 6578 7472  eatment--an extr\n-00016b00: 6120 726f 7461 7469 6f6e 2074 6f0a 6163  a rotation to.ac\n-00016b10: 636f 756e 7420 666f 7220 6974 7320 6f70  count for its op\n-00016b20: 706f 7369 6e67 2061 6e67 6c65 2e20 2054  posing angle.  T\n-00016b30: 6869 7320 6973 2063 6c65 6172 2069 6e20  his is clear in \n-00016b40: 7468 6520 6675 6c6c 2073 6f75 7263 6520  the full source \n-00016b50: 636f 6465 2e29 0a4e 6f74 2073 7572 7072  code.).Not surpr\n-00016b60: 6973 696e 676c 792c 2074 6865 2027 6861  isingly, the 'ha\n-00016b70: 6e64 2720 6465 6669 6e69 7469 6f6e 206c  nd' definition l\n-00016b80: 6f6f 6b73 2076 6572 7920 6d75 6368 206c  ooks very much l\n-00016b90: 696b 6520 7468 650a 7072 6576 696f 7573  ike the.previous\n-00016ba0: 2074 776f 2e20 2049 7420 7368 6f75 6c64   two.  It should\n-00016bb0: 2062 6520 6e6f 2073 7572 7072 6973 6520   be no surprise \n-00016bc0: 7468 6174 2077 6865 6e20 7468 6520 726f  that when the ro\n-00016bd0: 7461 7469 6f6e 2070 6172 616d 6574 6572  tation parameter\n-00016be0: 0a27 6d65 7461 5f31 5f72 6f74 2720 6368  .'meta_1_rot' ch\n-00016bf0: 616e 6765 732c 2074 6865 2065 6e74 6972  anges, the entir\n-00016c00: 6520 6669 6e67 6572 2072 6f74 6174 6573  e finger rotates\n-00016c10: 2120 2054 6865 7265 2069 7320 616e 2061  !  There is an a\n-00016c20: 6464 6974 696f 6e61 6c0a 726f 7461 7469  dditional.rotati\n-00016c30: 6f6e 2074 6861 7420 616c 6c6f 7773 2074  on that allows t\n-00016c40: 6865 2066 696e 6765 7273 2074 6f20 7370  he fingers to sp\n-00016c50: 7265 6164 206c 6174 6572 616c 6c79 2e20  read laterally. \n-00016c60: 2057 6520 7361 7920 7468 6573 650a 6a6f   We say these.jo\n-00016c70: 696e 7473 206f 6620 7468 6520 7072 6f78  ints of the prox\n-00016c80: 696d 616c 2070 686c 616e 6765 7320 6861  imal phlanges ha\n-00016c90: 7665 2074 776f 205f 6465 6772 6565 7320  ve two _degrees \n-00016ca0: 6f66 2066 7265 6564 6f6d 5f2e 2020 5468  of freedom_.  Th\n-00016cb0: 650a 6a6f 696e 7473 2068 6967 6865 7220  e.joints higher \n-00016cc0: 6f6e 2074 6865 2066 696e 6765 7220 6861  on the finger ha\n-00016cd0: 7665 206f 6e6c 7920 6f6e 652e 2020 4669  ve only one.  Fi\n-00016ce0: 6e61 6c6c 792c 2065 6163 6820 6669 6e67  nally, each fing\n-00016cf0: 6572 2069 730a 7363 616c 6564 2062 7920  er is.scaled by \n-00016d00: 6120 6661 6374 6f72 2074 6f20 6c65 6e64  a factor to lend\n-00016d10: 2069 7420 7072 6f70 6f72 7469 6f6e 2e0a   it proportion..\n-00016d20: 2020 6465 6620 6861 6e64 207b 0a20 2020    def hand {.   \n-00016d30: 2025 2066 696e 6765 7220 3120 5b61 6c6c   % finger 1 [all\n-00016d40: 206f 7468 6572 2066 696e 6765 7273 206f   other fingers o\n-00016d50: 6d69 7474 6564 5d0a 2020 2020 6465 6620  mitted].    def \n-00016d60: 7363 616c 655f 3120 2e38 350a 2020 2020  scale_1 .85.    \n-00016d70: 7075 7420 7b20 7363 616c 6528 7363 616c  put { scale(scal\n-00016d80: 655f 3129 200a 2020 2020 2020 2020 2020  e_1) .          \n-00016d90: 7468 656e 2074 7261 6e73 6c61 7465 2828  then translate((\n-00016da0: 6a6f 696e 745f 6761 7020 2a20 6a6f 696e  joint_gap * join\n-00016db0: 745f 7261 6429 202a 205b 4a5d 290a 0920  t_rad) * [J]).. \n-00016dc0: 2074 6865 6e20 726f 7461 7465 286d 6574   then rotate(met\n-00016dd0: 615f 315f 726f 742c 205b 495d 290a 2020  a_1_rot, [I]).  \n-00016de0: 2020 2020 2020 2020 7468 656e 2072 6f74          then rot\n-00016df0: 6174 6528 2d73 7072 6561 645f 726f 742c  ate(-spread_rot,\n-00016e00: 205b 4b5d 290a 2020 2020 2020 2020 2020   [K]).          \n-00016e10: 7468 656e 2074 7261 6e73 6c61 7465 2828  then translate((\n-00016e20: 7072 6f78 696d 616c 5f31 5f6c 6f63 2920  proximal_1_loc) \n-00016e30: 2d20 284f 2929 207d 200a 2020 2020 2020  - (O)) } .      \n-00016e40: 7b66 696e 6765 725f 317d 0a20 2020 2070  {finger_1}.    p\n-00016e50: 7574 207b 2073 6361 6c65 2873 6361 6c65  ut { scale(scale\n-00016e60: 5f31 202a 2070 726f 7869 6d61 6c5f 6469  _1 * proximal_di\n-00016e70: 7374 616c 5f72 6174 696f 5e32 290a 2020  stal_ratio^2).  \n-00016e80: 2020 2020 2020 2020 7468 656e 2072 6f74          then rot\n-00016e90: 6174 6528 6d65 7461 5f31 5f72 6f74 202f  ate(meta_1_rot /\n-00016ea0: 2032 2c20 5b49 5d29 0a20 2020 2020 2020   2, [I]).       \n-00016eb0: 2020 2074 6865 6e20 726f 7461 7465 282d     then rotate(-\n-00016ec0: 7370 7265 6164 5f72 6f74 2c20 5b4b 5d29  spread_rot, [K])\n-00016ed0: 0a20 2020 2020 2020 2020 2074 6865 6e20  .          then \n-00016ee0: 7472 616e 736c 6174 6528 2870 726f 7869  translate((proxi\n-00016ef0: 6d61 6c5f 315f 6c6f 6329 202d 2028 4f29  mal_1_loc) - (O)\n-00016f00: 2920 7d20 0a20 2020 2020 207b 6a6f 696e  ) } .      {join\n-00016f10: 745f 7370 6865 7265 7d0a 0a20 2020 2025  t_sphere}..    %\n-00016f20: 2070 616c 6d0a 2020 2020 7377 6565 7020   palm.    sweep \n-00016f30: 7b20 312c 2072 6f74 6174 6528 362c 2028  { 1, rotate(6, (\n-00016f40: 302c 3135 2c30 292c 205b 495d 2920 7d0a  0,15,0), [I]) }.\n-00016f50: 2020 2020 2020 7075 7420 7b20 726f 7461        put { rota\n-00016f60: 7465 282d 332c 2028 302c 3135 2c30 292c  te(-3, (0,15,0),\n-00016f70: 205b 495d 2920 7d20 7b0a 2020 2020 2020   [I]) } {.      \n-00016f80: 2020 706f 6c79 676f 6e28 7072 6f78 696d    polygon(proxim\n-00016f90: 616c 5f31 5f6c 6f63 2928 7072 6f78 696d  al_1_loc)(proxim\n-00016fa0: 616c 5f32 5f6c 6f63 290a 2020 2020 2020  al_2_loc).      \n-00016fb0: 2020 2020 2020 2020 2028 7072 6f78 696d           (proxim\n-00016fc0: 616c 5f33 5f6c 6f63 2928 7072 6f78 696d  al_3_loc)(proxim\n-00016fd0: 616c 5f34 5f6c 6f63 290a 2020 2020 2020  al_4_loc).      \n-00016fe0: 2020 2020 2020 2020 2028 6835 2928 6836           (h5)(h6\n-00016ff0: 2928 6836 6129 2868 3929 2868 3130 290a  )(h6a)(h9)(h10).\n-00017000: 2020 2020 2020 2020 706f 6c79 676f 6e28          polygon(\n-00017010: 6836 6129 2868 3729 2868 3829 2868 3929  h6a)(h7)(h8)(h9)\n-00017020: 0a20 2020 7d20 207d 0a54 6865 206c 6173  .   }  }.The las\n-00017030: 7420 7365 6374 696f 6e20 6f66 2074 6865  t section of the\n-00017040: 2064 6566 696e 6974 696f 6e20 6372 6561   definition crea\n-00017050: 7465 7320 7468 6520 706f 6c79 746f 7065  tes the polytope\n-00017060: 2066 6f72 2074 6865 2070 616c 6d20 6f66   for the palm of\n-00017070: 0a74 6865 2068 616e 6420 6279 2027 7377  .the hand by 'sw\n-00017080: 6565 7027 696e 6720 6120 3130 2d73 6964  eep'ing a 10-sid\n-00017090: 6564 2070 6f6c 7967 6f6e 2074 6872 6f75  ed polygon throu\n-000170a0: 6768 2061 2076 6572 7920 7368 6f72 7420  gh a very short \n-000170b0: 6172 630a 2839 2064 6567 7265 6573 292e  arc.(9 degrees).\n-000170c0: 2020 5468 6973 2070 726f 7669 6465 7320    This provides \n-000170d0: 6120 7765 6467 652d 7368 6170 6564 2070  a wedge-shaped p\n-000170e0: 726f 6669 6c65 2077 6865 6e20 7669 6577  rofile when view\n-000170f0: 6564 2066 726f 6d20 7468 650a 7369 6465  ed from the.side\n-00017100: 2e20 2054 6865 2074 6869 636b 2065 6e64  .  The thick end\n-00017110: 206f 6620 7468 6520 7765 6467 6520 6973   of the wedge is\n-00017120: 2074 6865 2077 7269 7374 2e20 2042 6563   the wrist.  Bec\n-00017130: 6175 7365 2074 6865 2070 6f6c 7967 6f6e  ause the polygon\n-00017140: 2069 730a 636f 6e63 6176 652c 2069 7420   is.concave, it \n-00017150: 6973 2073 706c 6974 2069 6e74 6f20 696e  is split into in\n-00017160: 746f 2074 776f 2063 6f6e 7665 7820 7368  to two convex sh\n-00017170: 6170 6573 2077 6974 6820 6e69 6e65 2061  apes with nine a\n-00017180: 6e64 2066 6f75 720a 7665 7274 6963 6573  nd four.vertices\n-00017190: 2e0a 0a20 2020 5765 2063 616e 206e 6f77  ...   We can now\n-000171a0: 2068 6176 6520 6675 6e20 706f 7369 7469   have fun positi\n-000171b0: 6f6e 696e 6720 7468 6520 6861 6e64 2062  oning the hand b\n-000171c0: 7920 6164 6a75 7374 696e 6720 7468 6520  y adjusting the \n-000171d0: 7661 7269 6f75 730a 726f 7461 7469 6f6e  various.rotation\n-000171e0: 2061 6e67 6c65 732e 2020 5468 6520 636f   angles.  The co\n-000171f0: 6d70 6c65 7465 2073 6f75 7263 6520 696e  mplete source in\n-00017200: 636c 7564 6573 2064 6566 696e 6974 696f  cludes definitio\n-00017210: 6e73 2077 6974 680a 616c 7465 726e 6174  ns with.alternat\n-00017220: 6976 6573 2074 6861 7420 696e 636c 7564  ives that includ\n-00017230: 6520 7468 6520 666f 6c6c 6f77 696e 6720  e the following \n-00017240: 7669 6577 7320 616e 6420 6d6f 7265 2e0a  views and more..\n-00017250: 0a00 085b 696d 6167 6520 7372 633d 2265  ...[image src=\"e\n-00017260: 7832 3130 2e70 6e67 2220 7465 7874 3d22  x210.png\" text=\"\n-00017270: 496d 6167 6520 6578 3231 3020 6f6d 6974  Image ex210 omit\n-00017280: 7465 6420 696e 2074 6578 7420 7665 7273  ted in text vers\n-00017290: 696f 6e20 6f66 2074 6869 7320 646f 6375  ion of this docu\n-000172a0: 6d65 6e74 2e22 0008 5d00 085b 696d 6167  ment.\"..]..[imag\n-000172b0: 6520 7372 633d 2265 7832 3230 2e70 6e67  e src=\"ex220.png\n-000172c0: 2220 7465 7874 3d22 496d 6167 6520 6578  \" text=\"Image ex\n-000172d0: 3232 3020 6f6d 6974 7465 6420 696e 2074  220 omitted in t\n-000172e0: 6578 7420 7665 7273 696f 6e20 6f66 2074  ext version of t\n-000172f0: 6869 7320 646f 6375 6d65 6e74 2e22 0008  his document.\"..\n-00017300: 5d00 085b 696d 6167 6520 7372 633d 2265  ]..[image src=\"e\n-00017310: 7832 3330 2e70 6e67 2220 7465 7874 3d22  x230.png\" text=\"\n-00017320: 496d 6167 6520 6578 3233 3020 6f6d 6974  Image ex230 omit\n-00017330: 7465 6420 696e 2074 6578 7420 7665 7273  ted in text vers\n-00017340: 696f 6e20 6f66 2074 6869 7320 646f 6375  ion of this docu\n-00017350: 6d65 6e74 2e22 0008 5d00 085b 696d 6167  ment.\"..]..[imag\n-00017360: 6520 7372 633d 2265 7832 3430 2e70 6e67  e src=\"ex240.png\n-00017370: 2220 7465 7874 3d22 496d 6167 6520 6578  \" text=\"Image ex\n-00017380: 3234 3020 6f6d 6974 7465 6420 696e 2074  240 omitted in t\n-00017390: 6578 7420 7665 7273 696f 6e20 6f66 2074  ext version of t\n-000173a0: 6869 7320 646f 6375 6d65 6e74 2e22 0008  his document.\"..\n-000173b0: 5d0a 0a1f 0a46 696c 653a 2073 6b65 7463  ]....File: sketc\n-000173c0: 682e 696e 666f 2c20 204e 6f64 653a 2043  h.info,  Node: C\n-000173d0: 6176 6561 7473 2c20 2050 7265 763a 2041  aveats,  Prev: A\n-000173e0: 2068 6965 7261 7263 6869 6361 6c20 6d6f   hierarchical mo\n-000173f0: 6465 6c2c 2020 5570 3a20 4275 696c 6469  del,  Up: Buildi\n-00017400: 6e67 2061 2064 7261 7769 6e67 0a0a 342e  ng a drawing..4.\n-00017410: 3420 4361 7665 6174 730a 3d3d 3d3d 3d3d  4 Caveats.======\n-00017420: 3d3d 3d3d 3d0a 0a27 536b 6574 6368 2720  =====..'Sketch' \n-00017430: 6973 2061 2066 6169 726c 7920 706f 7765  is a fairly powe\n-00017440: 7266 756c 2074 6f6f 6c20 666f 7220 6472  rful tool for dr\n-00017450: 6177 696e 672c 2062 7574 2c20 6a75 7374  awing, but, just\n-00017460: 2061 7320 7769 7468 2054 6558 2c0a 7468   as with TeX,.th\n-00017470: 6520 706f 7765 7220 746f 2063 7265 6174  e power to creat\n-00017480: 6520 6265 6175 7469 6675 6c20 7265 7375  e beautiful resu\n-00017490: 6c74 7320 636f 6d65 7320 616c 6f6e 6720  lts comes along \n-000174a0: 7769 7468 2074 6865 2070 6f77 6572 2074  with the power t\n-000174b0: 6f20 6d61 6b65 0a6d 6973 7461 6b65 732e  o make.mistakes.\n-000174c0: 2020 5468 6520 666f 6c6c 6f77 696e 6720    The following \n-000174d0: 6172 6520 736f 6d65 2070 6f69 6e74 7320  are some points \n-000174e0: 7768 6572 6520 6361 7265 2069 7320 6e65  where care is ne\n-000174f0: 6365 7373 6172 7920 616e 640a 7768 6572  cessary and.wher\n-00017500: 6520 7468 6520 6375 7272 656e 7420 7665  e the current ve\n-00017510: 7273 696f 6e20 6f66 2027 736b 6574 6368  rsion of 'sketch\n-00017520: 2720 6973 206c 696d 6974 6564 206f 7220  ' is limited or \n-00017530: 6861 7320 6b6e 6f77 6e20 6275 6773 2e0a  has known bugs..\n-00017540: 0a2a 204d 656e 753a 0a0a 2a20 4c69 6d69  .* Menu:..* Limi\n-00017550: 7473 206f 6e20 6572 726f 7220 6465 7465  ts on error dete\n-00017560: 6374 696f 6e3a 3a20 2020 5768 6174 2073  ction::   What s\n-00017570: 6b65 7463 6820 646f 6573 6e27 7420 646f  ketch doesn't do\n-00017580: 2e0a 2a20 436c 6970 7069 6e67 3a3a 2020  ..* Clipping::  \n+00016630: 2020 2020 206a 6f69 6e74 5f67 6170 202a       joint_gap *\n+00016640: 206a 6f69 6e74 5f72 6164 2920 2a20 5b4a   joint_rad) * [J\n+00016650: 5d29 207d 0a20 2020 2020 207b 6469 7374  ]) }.      {dist\n+00016660: 616c 5f31 7d0a 2020 2020 7075 7420 7b20  al_1}.    put { \n+00016670: 7363 616c 6528 7072 6f78 696d 616c 5f64  scale(proximal_d\n+00016680: 6973 7461 6c5f 7261 7469 6f29 0a20 2020  istal_ratio).   \n+00016690: 2020 2020 2020 2074 6865 6e20 726f 7461         then rota\n+000166a0: 7465 286d 6964 646c 655f 315f 726f 7420  te(middle_1_rot \n+000166b0: 2f20 322c 205b 495d 290a 2020 2020 2020  / 2, [I]).      \n+000166c0: 2020 2020 7468 656e 2074 7261 6e73 6c61      then transla\n+000166d0: 7465 2828 6d69 6464 6c65 5f72 6174 696f  te((middle_ratio\n+000166e0: 202a 2064 6973 7461 6c5f 6c65 6e20 2b20   * distal_len + \n+000166f0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+00016700: 2020 2020 2020 2020 2020 206a 6f69 6e74             joint\n+00016710: 5f67 6170 202a 206a 6f69 6e74 5f72 6164  _gap * joint_rad\n+00016720: 2920 2a20 5b4a 5d29 207d 200a 2020 2020  ) * [J]) } .    \n+00016730: 2020 7b6a 6f69 6e74 5f73 7068 6572 657d    {joint_sphere}\n+00016740: 0a20 2020 2070 7574 207b 2073 6361 6c65  .    put { scale\n+00016750: 2820 6d69 6464 6c65 5f72 6174 696f 202a  ( middle_ratio *\n+00016760: 205b 4a5d 202b 200a 2020 2020 2020 2020   [J] + .        \n+00016770: 2020 2020 2020 2020 2070 726f 7869 6d61           proxima\n+00016780: 6c5f 6469 7374 616c 5f72 6174 696f 5e32  l_distal_ratio^2\n+00016790: 202a 2028 5b49 5d2b 5b4b 5d29 2029 207d   * ([I]+[K]) ) }\n+000167a0: 0a20 2020 2020 207b 7365 676d 656e 747d  .      {segment}\n+000167b0: 0a20 207d 0a54 6869 7320 6c6f 6f6b 7320  .  }.This looks \n+000167c0: 7665 7279 2073 696d 696c 6172 2074 6f20  very similar to \n+000167d0: 7468 6520 7072 6576 696f 7573 2064 6566  the previous def\n+000167e0: 696e 6974 696f 6e2c 2061 6e64 2069 7420  inition, and it \n+000167f0: 6973 2e20 2054 6865 0a69 6d70 6f72 7461  is.  The.importa\n+00016800: 6e74 2064 6966 6665 7265 6e63 6520 6973  nt difference is\n+00016810: 2074 6861 7420 7261 7468 6572 2074 6861   that rather tha\n+00016820: 6e20 706f 7369 7469 6f6e 696e 6720 616e  n positioning an\n+00016830: 6420 726f 7461 7469 6e67 2061 0a73 696e  d rotating a.sin\n+00016840: 676c 6520 7365 676d 656e 742c 2077 6520  gle segment, we \n+00016850: 706f 7369 7469 6f6e 2061 6e64 2072 6f74  position and rot\n+00016860: 6174 6520 7468 6520 656e 7469 7265 2022  ate the entire \"\n+00016870: 6173 7365 6d62 6c79 2220 6465 6669 6e65  assembly\" define\n+00016880: 6420 6173 0a27 6469 7374 616c 5f31 272e  d as.'distal_1'.\n+00016890: 2020 5468 6520 7265 7374 2069 7320 6a75    The rest is ju\n+000168a0: 7374 2061 7269 7468 6d65 7469 6320 746f  st arithmetic to\n+000168b0: 2063 6f6d 7075 7465 2073 697a 6573 2061   compute sizes a\n+000168c0: 6e64 2070 6f73 6974 696f 6e73 0a74 6861  nd positions.tha\n+000168d0: 7420 6c6f 6f6b 206e 6963 652e 2020 5468  t look nice.  Th\n+000168e0: 6520 6c61 7374 2027 7075 7427 2070 6c61  e last 'put' pla\n+000168f0: 6365 7320 616e 2061 7070 726f 7072 6961  ces an appropria\n+00016900: 7465 6c79 2073 6861 7065 6420 7365 676d  tely shaped segm\n+00016910: 656e 740a 7468 6174 2069 7320 7468 6520  ent.that is the \n+00016920: 5f70 726f 7869 6d61 6c20 7068 6c61 6e67  _proximal phlang\n+00016930: 6573 5f2c 2074 6865 2062 6f6e 6520 7468  es_, the bone th\n+00016940: 6174 206a 6f69 6e73 2074 6865 2070 616c  at joins the pal\n+00016950: 6d20 6f66 2074 6865 0a68 616e 642e 2020  m of the.hand.  \n+00016960: 5468 6973 2063 6f6d 706c 6574 6573 2074  This completes t\n+00016970: 6865 2066 696e 6765 7220 6974 7365 6c66  he finger itself\n+00016980: 2e0a 0a20 2020 416c 6c20 7468 6520 6f74  ...   All the ot\n+00016990: 6865 7220 6669 6e67 6572 7320 6172 6520  her fingers are \n+000169a0: 6465 7363 7269 6265 6420 6964 656e 7469  described identi\n+000169b0: 6361 6c6c 7920 746f 2074 6869 7320 6f6e  cally to this on\n+000169c0: 652e 2020 5765 0a61 6363 6f75 6e74 2066  e.  We.account f\n+000169d0: 6f72 2074 6865 2066 6163 7420 7468 6174  or the fact that\n+000169e0: 2072 6561 6c20 6669 6e67 6572 7320 6172   real fingers ar\n+000169f0: 6520 6469 6666 6572 656e 7420 7369 7a65  e different size\n+00016a00: 7320 696e 2074 6865 206e 6578 740a 7374  s in the next.st\n+00016a10: 6570 2c20 7768 6963 6820 6973 2074 6f20  ep, which is to \n+00016a20: 6275 696c 6420 7468 6520 656e 7469 7265  build the entire\n+00016a30: 2068 616e 642e 0a0a 2020 2054 6865 2027   hand...   The '\n+00016a40: 6861 6e64 2720 6465 6669 6e69 7469 6f6e  hand' definition\n+00016a50: 2074 6861 7420 666f 6c6c 6f77 7320 696e   that follows in\n+00016a60: 636c 7564 6573 2061 2073 6563 7469 6f6e  cludes a section\n+00016a70: 2066 6f72 2065 6163 680a 6669 6e67 6572   for each.finger\n+00016a80: 2e20 2057 6527 6c6c 2063 6f6e 7469 6e75  .  We'll continu\n+00016a90: 6520 7769 7468 2066 696e 6765 7220 3120  e with finger 1 \n+00016aa0: 616e 6420 6f6d 6974 2061 6c6c 2074 6865  and omit all the\n+00016ab0: 206f 7468 6572 732e 2020 284f 6620 6e6f   others.  (Of no\n+00016ac0: 7465 0a69 7320 7468 6174 2074 6865 2074  te.is that the t\n+00016ad0: 6875 6d62 206e 6565 6473 2073 6c69 6768  humb needs sligh\n+00016ae0: 746c 7920 7370 6563 6961 6c20 7472 6561  tly special trea\n+00016af0: 746d 656e 742d 2d61 6e20 6578 7472 6120  tment--an extra \n+00016b00: 726f 7461 7469 6f6e 2074 6f0a 6163 636f  rotation to.acco\n+00016b10: 756e 7420 666f 7220 6974 7320 6f70 706f  unt for its oppo\n+00016b20: 7369 6e67 2061 6e67 6c65 2e20 2054 6869  sing angle.  Thi\n+00016b30: 7320 6973 2063 6c65 6172 2069 6e20 7468  s is clear in th\n+00016b40: 6520 6675 6c6c 2073 6f75 7263 6520 636f  e full source co\n+00016b50: 6465 2e29 0a4e 6f74 2073 7572 7072 6973  de.).Not surpris\n+00016b60: 696e 676c 792c 2074 6865 2027 6861 6e64  ingly, the 'hand\n+00016b70: 2720 6465 6669 6e69 7469 6f6e 206c 6f6f  ' definition loo\n+00016b80: 6b73 2076 6572 7920 6d75 6368 206c 696b  ks very much lik\n+00016b90: 6520 7468 650a 7072 6576 696f 7573 2074  e the.previous t\n+00016ba0: 776f 2e20 2049 7420 7368 6f75 6c64 2062  wo.  It should b\n+00016bb0: 6520 6e6f 2073 7572 7072 6973 6520 7468  e no surprise th\n+00016bc0: 6174 2077 6865 6e20 7468 6520 726f 7461  at when the rota\n+00016bd0: 7469 6f6e 2070 6172 616d 6574 6572 0a27  tion parameter.'\n+00016be0: 6d65 7461 5f31 5f72 6f74 2720 6368 616e  meta_1_rot' chan\n+00016bf0: 6765 732c 2074 6865 2065 6e74 6972 6520  ges, the entire \n+00016c00: 6669 6e67 6572 2072 6f74 6174 6573 2120  finger rotates! \n+00016c10: 2054 6865 7265 2069 7320 616e 2061 6464   There is an add\n+00016c20: 6974 696f 6e61 6c0a 726f 7461 7469 6f6e  itional.rotation\n+00016c30: 2074 6861 7420 616c 6c6f 7773 2074 6865   that allows the\n+00016c40: 2066 696e 6765 7273 2074 6f20 7370 7265   fingers to spre\n+00016c50: 6164 206c 6174 6572 616c 6c79 2e20 2057  ad laterally.  W\n+00016c60: 6520 7361 7920 7468 6573 650a 6a6f 696e  e say these.join\n+00016c70: 7473 206f 6620 7468 6520 7072 6f78 696d  ts of the proxim\n+00016c80: 616c 2070 686c 616e 6765 7320 6861 7665  al phlanges have\n+00016c90: 2074 776f 205f 6465 6772 6565 7320 6f66   two _degrees of\n+00016ca0: 2066 7265 6564 6f6d 5f2e 2020 5468 650a   freedom_.  The.\n+00016cb0: 6a6f 696e 7473 2068 6967 6865 7220 6f6e  joints higher on\n+00016cc0: 2074 6865 2066 696e 6765 7220 6861 7665   the finger have\n+00016cd0: 206f 6e6c 7920 6f6e 652e 2020 4669 6e61   only one.  Fina\n+00016ce0: 6c6c 792c 2065 6163 6820 6669 6e67 6572  lly, each finger\n+00016cf0: 2069 730a 7363 616c 6564 2062 7920 6120   is.scaled by a \n+00016d00: 6661 6374 6f72 2074 6f20 6c65 6e64 2069  factor to lend i\n+00016d10: 7420 7072 6f70 6f72 7469 6f6e 2e0a 2020  t proportion..  \n+00016d20: 6465 6620 6861 6e64 207b 0a20 2020 2025  def hand {.    %\n+00016d30: 2066 696e 6765 7220 3120 5b61 6c6c 206f   finger 1 [all o\n+00016d40: 7468 6572 2066 696e 6765 7273 206f 6d69  ther fingers omi\n+00016d50: 7474 6564 5d0a 2020 2020 6465 6620 7363  tted].    def sc\n+00016d60: 616c 655f 3120 2e38 350a 2020 2020 7075  ale_1 .85.    pu\n+00016d70: 7420 7b20 7363 616c 6528 7363 616c 655f  t { scale(scale_\n+00016d80: 3129 200a 2020 2020 2020 2020 2020 7468  1) .          th\n+00016d90: 656e 2074 7261 6e73 6c61 7465 2828 6a6f  en translate((jo\n+00016da0: 696e 745f 6761 7020 2a20 6a6f 696e 745f  int_gap * joint_\n+00016db0: 7261 6429 202a 205b 4a5d 290a 0920 2074  rad) * [J])..  t\n+00016dc0: 6865 6e20 726f 7461 7465 286d 6574 615f  hen rotate(meta_\n+00016dd0: 315f 726f 742c 205b 495d 290a 2020 2020  1_rot, [I]).    \n+00016de0: 2020 2020 2020 7468 656e 2072 6f74 6174        then rotat\n+00016df0: 6528 2d73 7072 6561 645f 726f 742c 205b  e(-spread_rot, [\n+00016e00: 4b5d 290a 2020 2020 2020 2020 2020 7468  K]).          th\n+00016e10: 656e 2074 7261 6e73 6c61 7465 2828 7072  en translate((pr\n+00016e20: 6f78 696d 616c 5f31 5f6c 6f63 2920 2d20  oximal_1_loc) - \n+00016e30: 284f 2929 207d 200a 2020 2020 2020 7b66  (O)) } .      {f\n+00016e40: 696e 6765 725f 317d 0a20 2020 2070 7574  inger_1}.    put\n+00016e50: 207b 2073 6361 6c65 2873 6361 6c65 5f31   { scale(scale_1\n+00016e60: 202a 2070 726f 7869 6d61 6c5f 6469 7374   * proximal_dist\n+00016e70: 616c 5f72 6174 696f 5e32 290a 2020 2020  al_ratio^2).    \n+00016e80: 2020 2020 2020 7468 656e 2072 6f74 6174        then rotat\n+00016e90: 6528 6d65 7461 5f31 5f72 6f74 202f 2032  e(meta_1_rot / 2\n+00016ea0: 2c20 5b49 5d29 0a20 2020 2020 2020 2020  , [I]).         \n+00016eb0: 2074 6865 6e20 726f 7461 7465 282d 7370   then rotate(-sp\n+00016ec0: 7265 6164 5f72 6f74 2c20 5b4b 5d29 0a20  read_rot, [K]). \n+00016ed0: 2020 2020 2020 2020 2074 6865 6e20 7472           then tr\n+00016ee0: 616e 736c 6174 6528 2870 726f 7869 6d61  anslate((proxima\n+00016ef0: 6c5f 315f 6c6f 6329 202d 2028 4f29 2920  l_1_loc) - (O)) \n+00016f00: 7d20 0a20 2020 2020 207b 6a6f 696e 745f  } .      {joint_\n+00016f10: 7370 6865 7265 7d0a 0a20 2020 2025 2070  sphere}..    % p\n+00016f20: 616c 6d0a 2020 2020 7377 6565 7020 7b20  alm.    sweep { \n+00016f30: 312c 2072 6f74 6174 6528 362c 2028 302c  1, rotate(6, (0,\n+00016f40: 3135 2c30 292c 205b 495d 2920 7d0a 2020  15,0), [I]) }.  \n+00016f50: 2020 2020 7075 7420 7b20 726f 7461 7465      put { rotate\n+00016f60: 282d 332c 2028 302c 3135 2c30 292c 205b  (-3, (0,15,0), [\n+00016f70: 495d 2920 7d20 7b0a 2020 2020 2020 2020  I]) } {.        \n+00016f80: 706f 6c79 676f 6e28 7072 6f78 696d 616c  polygon(proximal\n+00016f90: 5f31 5f6c 6f63 2928 7072 6f78 696d 616c  _1_loc)(proximal\n+00016fa0: 5f32 5f6c 6f63 290a 2020 2020 2020 2020  _2_loc).        \n+00016fb0: 2020 2020 2020 2028 7072 6f78 696d 616c         (proximal\n+00016fc0: 5f33 5f6c 6f63 2928 7072 6f78 696d 616c  _3_loc)(proximal\n+00016fd0: 5f34 5f6c 6f63 290a 2020 2020 2020 2020  _4_loc).        \n+00016fe0: 2020 2020 2020 2028 6835 2928 6836 2928         (h5)(h6)(\n+00016ff0: 6836 6129 2868 3929 2868 3130 290a 2020  h6a)(h9)(h10).  \n+00017000: 2020 2020 2020 706f 6c79 676f 6e28 6836        polygon(h6\n+00017010: 6129 2868 3729 2868 3829 2868 3929 0a20  a)(h7)(h8)(h9). \n+00017020: 2020 7d20 207d 0a54 6865 206c 6173 7420    }  }.The last \n+00017030: 7365 6374 696f 6e20 6f66 2074 6865 2064  section of the d\n+00017040: 6566 696e 6974 696f 6e20 6372 6561 7465  efinition create\n+00017050: 7320 7468 6520 706f 6c79 746f 7065 2066  s the polytope f\n+00017060: 6f72 2074 6865 2070 616c 6d20 6f66 0a74  or the palm of.t\n+00017070: 6865 2068 616e 6420 6279 2027 7377 6565  he hand by 'swee\n+00017080: 7027 696e 6720 6120 3130 2d73 6964 6564  p'ing a 10-sided\n+00017090: 2070 6f6c 7967 6f6e 2074 6872 6f75 6768   polygon through\n+000170a0: 2061 2076 6572 7920 7368 6f72 7420 6172   a very short ar\n+000170b0: 630a 2839 2064 6567 7265 6573 292e 2020  c.(9 degrees).  \n+000170c0: 5468 6973 2070 726f 7669 6465 7320 6120  This provides a \n+000170d0: 7765 6467 652d 7368 6170 6564 2070 726f  wedge-shaped pro\n+000170e0: 6669 6c65 2077 6865 6e20 7669 6577 6564  file when viewed\n+000170f0: 2066 726f 6d20 7468 650a 7369 6465 2e20   from the.side. \n+00017100: 2054 6865 2074 6869 636b 2065 6e64 206f   The thick end o\n+00017110: 6620 7468 6520 7765 6467 6520 6973 2074  f the wedge is t\n+00017120: 6865 2077 7269 7374 2e20 2042 6563 6175  he wrist.  Becau\n+00017130: 7365 2074 6865 2070 6f6c 7967 6f6e 2069  se the polygon i\n+00017140: 730a 636f 6e63 6176 652c 2069 7420 6973  s.concave, it is\n+00017150: 2073 706c 6974 2069 6e74 6f20 696e 746f   split into into\n+00017160: 2074 776f 2063 6f6e 7665 7820 7368 6170   two convex shap\n+00017170: 6573 2077 6974 6820 6e69 6e65 2061 6e64  es with nine and\n+00017180: 2066 6f75 720a 7665 7274 6963 6573 2e0a   four.vertices..\n+00017190: 0a20 2020 5765 2063 616e 206e 6f77 2068  .   We can now h\n+000171a0: 6176 6520 6675 6e20 706f 7369 7469 6f6e  ave fun position\n+000171b0: 696e 6720 7468 6520 6861 6e64 2062 7920  ing the hand by \n+000171c0: 6164 6a75 7374 696e 6720 7468 6520 7661  adjusting the va\n+000171d0: 7269 6f75 730a 726f 7461 7469 6f6e 2061  rious.rotation a\n+000171e0: 6e67 6c65 732e 2020 5468 6520 636f 6d70  ngles.  The comp\n+000171f0: 6c65 7465 2073 6f75 7263 6520 696e 636c  lete source incl\n+00017200: 7564 6573 2064 6566 696e 6974 696f 6e73  udes definitions\n+00017210: 2077 6974 680a 616c 7465 726e 6174 6976   with.alternativ\n+00017220: 6573 2074 6861 7420 696e 636c 7564 6520  es that include \n+00017230: 7468 6520 666f 6c6c 6f77 696e 6720 7669  the following vi\n+00017240: 6577 7320 616e 6420 6d6f 7265 2e0a 0a00  ews and more....\n+00017250: 085b 696d 6167 6520 7372 633d 2265 7832  .[image src=\"ex2\n+00017260: 3130 2e70 6e67 2220 7465 7874 3d22 496d  10.png\" text=\"Im\n+00017270: 6167 6520 6578 3231 3020 6f6d 6974 7465  age ex210 omitte\n+00017280: 6420 696e 2074 6578 7420 7665 7273 696f  d in text versio\n+00017290: 6e20 6f66 2074 6869 7320 646f 6375 6d65  n of this docume\n+000172a0: 6e74 2e22 0008 5d00 085b 696d 6167 6520  nt.\"..]..[image \n+000172b0: 7372 633d 2265 7832 3230 2e70 6e67 2220  src=\"ex220.png\" \n+000172c0: 7465 7874 3d22 496d 6167 6520 6578 3232  text=\"Image ex22\n+000172d0: 3020 6f6d 6974 7465 6420 696e 2074 6578  0 omitted in tex\n+000172e0: 7420 7665 7273 696f 6e20 6f66 2074 6869  t version of thi\n+000172f0: 7320 646f 6375 6d65 6e74 2e22 0008 5d00  s document.\"..].\n+00017300: 085b 696d 6167 6520 7372 633d 2265 7832  .[image src=\"ex2\n+00017310: 3330 2e70 6e67 2220 7465 7874 3d22 496d  30.png\" text=\"Im\n+00017320: 6167 6520 6578 3233 3020 6f6d 6974 7465  age ex230 omitte\n+00017330: 6420 696e 2074 6578 7420 7665 7273 696f  d in text versio\n+00017340: 6e20 6f66 2074 6869 7320 646f 6375 6d65  n of this docume\n+00017350: 6e74 2e22 0008 5d00 085b 696d 6167 6520  nt.\"..]..[image \n+00017360: 7372 633d 2265 7832 3430 2e70 6e67 2220  src=\"ex240.png\" \n+00017370: 7465 7874 3d22 496d 6167 6520 6578 3234  text=\"Image ex24\n+00017380: 3020 6f6d 6974 7465 6420 696e 2074 6578  0 omitted in tex\n+00017390: 7420 7665 7273 696f 6e20 6f66 2074 6869  t version of thi\n+000173a0: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a  s document.\"..].\n+000173b0: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n+000173c0: 696e 666f 2c20 204e 6f64 653a 2043 6176  info,  Node: Cav\n+000173d0: 6561 7473 2c20 2050 7265 763a 2041 2068  eats,  Prev: A h\n+000173e0: 6965 7261 7263 6869 6361 6c20 6d6f 6465  ierarchical mode\n+000173f0: 6c2c 2020 5570 3a20 4275 696c 6469 6e67  l,  Up: Building\n+00017400: 2061 2064 7261 7769 6e67 0a0a 342e 3420   a drawing..4.4 \n+00017410: 4361 7665 6174 730a 3d3d 3d3d 3d3d 3d3d  Caveats.========\n+00017420: 3d3d 3d0a 0a27 536b 6574 6368 2720 6973  ===..'Sketch' is\n+00017430: 2061 2066 6169 726c 7920 706f 7765 7266   a fairly powerf\n+00017440: 756c 2074 6f6f 6c20 666f 7220 6472 6177  ul tool for draw\n+00017450: 696e 672c 2062 7574 2c20 6a75 7374 2061  ing, but, just a\n+00017460: 7320 7769 7468 2054 6558 2c0a 7468 6520  s with TeX,.the \n+00017470: 706f 7765 7220 746f 2063 7265 6174 6520  power to create \n+00017480: 6265 6175 7469 6675 6c20 7265 7375 6c74  beautiful result\n+00017490: 7320 636f 6d65 7320 616c 6f6e 6720 7769  s comes along wi\n+000174a0: 7468 2074 6865 2070 6f77 6572 2074 6f20  th the power to \n+000174b0: 6d61 6b65 0a6d 6973 7461 6b65 732e 2020  make.mistakes.  \n+000174c0: 5468 6520 666f 6c6c 6f77 696e 6720 6172  The following ar\n+000174d0: 6520 736f 6d65 2070 6f69 6e74 7320 7768  e some points wh\n+000174e0: 6572 6520 6361 7265 2069 7320 6e65 6365  ere care is nece\n+000174f0: 7373 6172 7920 616e 640a 7768 6572 6520  ssary and.where \n+00017500: 7468 6520 6375 7272 656e 7420 7665 7273  the current vers\n+00017510: 696f 6e20 6f66 2027 736b 6574 6368 2720  ion of 'sketch' \n+00017520: 6973 206c 696d 6974 6564 206f 7220 6861  is limited or ha\n+00017530: 7320 6b6e 6f77 6e20 6275 6773 2e0a 0a2a  s known bugs...*\n+00017540: 204d 656e 753a 0a0a 2a20 4c69 6d69 7473   Menu:..* Limits\n+00017550: 206f 6e20 6572 726f 7220 6465 7465 6374   on error detect\n+00017560: 696f 6e3a 3a20 2020 5768 6174 2073 6b65  ion::   What ske\n+00017570: 7463 6820 646f 6573 6e27 7420 646f 2e0a  tch doesn't do..\n+00017580: 2a20 436c 6970 7069 6e67 3a3a 2020 2020  * Clipping::    \n 00017590: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000175a0: 2020 4e6f 2063 6c69 7070 696e 6720 6174    No clipping at\n-000175b0: 2070 7265 7365 6e74 2e0a 2a20 4869 6464   present..* Hidd\n-000175c0: 656e 2073 7572 6661 6365 2072 656d 6f76  en surface remov\n-000175d0: 616c 3a3a 2020 2020 2020 496d 7065 7266  al::      Imperf\n-000175e0: 6563 7469 6f6e 7320 746f 2066 6978 2e0a  ections to fix..\n-000175f0: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n-00017600: 696e 666f 2c20 204e 6f64 653a 204c 696d  info,  Node: Lim\n-00017610: 6974 7320 6f6e 2065 7272 6f72 2064 6574  its on error det\n-00017620: 6563 7469 6f6e 2c20 204e 6578 743a 2043  ection,  Next: C\n-00017630: 6c69 7070 696e 672c 2020 5072 6576 3a20  lipping,  Prev: \n-00017640: 4361 7665 6174 732c 2020 5570 3a20 4361  Caveats,  Up: Ca\n-00017650: 7665 6174 730a 0a34 2e34 2e31 204c 696d  veats..4.4.1 Lim\n-00017660: 6974 7320 6f6e 2027 736b 6574 6368 2720  its on 'sketch' \n-00017670: 6572 726f 7220 6465 7465 6374 696f 6e0a  error detection.\n+000175a0: 4e6f 2063 6c69 7070 696e 6720 6174 2070  No clipping at p\n+000175b0: 7265 7365 6e74 2e0a 2a20 4869 6464 656e  resent..* Hidden\n+000175c0: 2073 7572 6661 6365 2072 656d 6f76 616c   surface removal\n+000175d0: 3a3a 2020 2020 2020 496d 7065 7266 6563  ::      Imperfec\n+000175e0: 7469 6f6e 7320 746f 2066 6978 2e0a 0a1f  tions to fix....\n+000175f0: 0a46 696c 653a 2073 6b65 7463 682e 696e  .File: sketch.in\n+00017600: 666f 2c20 204e 6f64 653a 204c 696d 6974  fo,  Node: Limit\n+00017610: 7320 6f6e 2065 7272 6f72 2064 6574 6563  s on error detec\n+00017620: 7469 6f6e 2c20 204e 6578 743a 2043 6c69  tion,  Next: Cli\n+00017630: 7070 696e 672c 2020 5072 6576 3a20 4361  pping,  Prev: Ca\n+00017640: 7665 6174 732c 2020 5570 3a20 4361 7665  veats,  Up: Cave\n+00017650: 6174 730a 0a34 2e34 2e31 204c 696d 6974  ats..4.4.1 Limit\n+00017660: 7320 6f6e 2027 736b 6574 6368 2720 6572  s on 'sketch' er\n+00017670: 726f 7220 6465 7465 6374 696f 6e0a 2d2d  ror detection.--\n 00017680: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 00017690: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-000176a0: 2d2d 2d2d 2d2d 2d2d 0a0a 2753 6b65 7463  --------..'Sketc\n-000176b0: 6827 2063 6174 6368 6573 206d 616e 7920  h' catches many \n-000176c0: 6b69 6e64 7320 6f66 2065 7272 6f72 732c  kinds of errors,\n-000176d0: 2062 7574 206e 6f74 2061 6c6c 2e20 2046   but not all.  F\n-000176e0: 6f72 2065 7861 6d70 6c65 2c0a 6f70 7469  or example,.opti\n-000176f0: 6f6e 7320 7468 6174 2073 6b65 7463 6820  ons that sketch \n-00017700: 646f 6573 206e 6f74 2072 6563 6f67 6e69  does not recogni\n-00017710: 7a65 2c20 6576 656e 2069 6e63 6f72 7265  ze, even incorre\n-00017720: 6374 206f 6e65 732c 2061 7265 2071 7569  ct ones, are qui\n-00017730: 6574 6c79 0a63 6f70 6965 6420 746f 2027  etly.copied to '\n-00017740: 5053 5472 6963 6b73 2720 636f 6d6d 616e  PSTricks' comman\n-00017750: 6473 2069 6e20 7468 6520 6f75 7470 7574  ds in the output\n-00017760: 2e20 2049 7420 6973 2061 6c73 6f20 756e  .  It is also un\n-00017770: 666f 7274 756e 6174 656c 790a 6561 7379  fortunately.easy\n-00017780: 2074 6f20 7072 6f64 7563 6520 2773 6b65   to produce 'ske\n-00017790: 7463 6827 2069 6e70 7574 7320 7468 6174  tch' inputs that\n-000177a0: 206c 6561 6420 746f 206e 6f20 7069 6374   lead to no pict\n-000177b0: 7572 6520 6174 2061 6c6c 2028 696d 7072  ure at all (impr\n-000177c0: 6f70 6572 0a76 6572 7465 7820 6f72 6465  oper.vertex orde\n-000177d0: 7269 6e67 2063 6175 7365 7320 6576 6572  ring causes ever\n-000177e0: 7974 6869 6e67 2074 6f20 6265 2063 756c  ything to be cul\n-000177f0: 6c65 6429 2c20 746f 2070 6963 7475 7265  led), to picture\n-00017800: 7320 7468 6174 2061 7265 0a74 6f6f 2062  s that are.too b\n-00017810: 6967 206f 7220 746f 6f20 736d 616c 6c20  ig or too small \n-00017820: 666f 7220 2750 5354 7269 636b 7327 2074  for 'PSTricks' t\n-00017830: 6f20 6472 6177 2028 6475 6520 746f 206c  o draw (due to l\n-00017840: 696d 6974 7320 6f66 2054 6558 206d 6174  imits of TeX mat\n-00017850: 6829 2c0a 616e 6420 7069 6374 7572 6573  h),.and pictures\n-00017860: 2074 6861 7420 6c6f 6f6b 206e 6f74 6869   that look nothi\n-00017870: 6e67 206c 696b 6520 7768 6174 2077 6173  ng like what was\n-00017880: 2069 6e74 656e 6465 642e 2020 4120 7069   intended.  A pi\n-00017890: 6374 7572 6520 7769 7468 0a6f 6e65 206f  cture with.one o\n-000178a0: 6620 7468 6573 6520 7072 6f62 6c65 6d73  f these problems\n-000178b0: 2063 616e 2062 6520 6469 6666 6963 756c   can be difficul\n-000178c0: 7420 746f 2022 6465 6275 672e 2220 2057  t to \"debug.\"  W\n-000178d0: 6520 6f66 6665 7220 7468 650a 666f 6c6c  e offer the.foll\n-000178e0: 6f77 696e 6720 7375 6767 6573 7469 6f6e  owing suggestion\n-000178f0: 732e 0a20 2020 2a20 466f 6c6c 6f77 2074  s..   * Follow t\n-00017900: 6865 2073 7567 6765 7374 6564 2069 6e63  he suggested inc\n-00017910: 7265 6d65 6e74 616c 2064 6576 656c 6f70  remental develop\n-00017920: 6d65 6e74 206d 6574 686f 6420 6465 7363  ment method desc\n-00017930: 7269 6265 6420 696e 0a20 2020 2020 2a6e  ribed in.     *n\n-00017940: 6f74 6520 4f76 6572 7669 6577 3a3a 2e0a  ote Overview::..\n-00017950: 2020 202a 2041 6c77 6179 7320 6d61 696e     * Always main\n-00017960: 7461 696e 206f 6e65 206f 7220 7477 6f20  tain one or two \n-00017970: 6261 636b 2d76 6572 7369 6f6e 7320 6f66  back-versions of\n-00017980: 2061 2064 7261 7769 6e67 2073 6f20 7468   a drawing so th\n-00017990: 6174 2069 7420 6973 0a20 2020 2020 6561  at it is.     ea\n-000179a0: 7379 2074 6f20 6661 6c6c 2062 6163 6b20  sy to fall back \n-000179b0: 746f 2061 206b 6e6f 776e 2d67 6f6f 6420  to a known-good \n-000179c0: 696e 6372 656d 656e 742e 0a20 2020 2a20  increment..   * \n-000179d0: 5768 656e 2075 7369 6e67 2027 7065 7273  When using 'pers\n-000179e0: 7065 6374 6976 6527 2c20 656e 7375 7265  pective', ensure\n-000179f0: 2061 6c6c 2066 696e 616c 6c79 2074 7261   all finally tra\n-00017a00: 6e73 666f 726d 6564 206f 626a 6563 7473  nsformed objects\n-00017a10: 0a20 2020 2020 7361 7469 7366 7920 7a3c  .     satisfy z<\n-00017a20: 3020 616e 642c 2069 6e20 6661 6374 2c20  0 and, in fact, \n-00017a30: 646f 206e 6f74 2063 6f6d 6520 7665 7279  do not come very\n-00017a40: 2063 6c6f 7365 2074 6f20 7468 6520 6f72   close to the or\n-00017a50: 6967 696e 2061 740a 2020 2020 2061 6c6c  igin at.     all\n-00017a60: 2e0a 2020 202a 2054 656d 706f 7261 7269  ..   * Temporari\n-00017a70: 6c79 2075 7365 2027 6375 6c6c 3d66 616c  ly use 'cull=fal\n-00017a80: 7365 2720 746f 2073 6565 2077 6865 7265  se' to see where\n-00017a90: 2076 6572 7465 7820 6f72 6465 7269 6e67   vertex ordering\n-00017aa0: 2070 726f 626c 656d 730a 2020 2020 206c   problems.     l\n-00017ab0: 6965 2e0a 2020 202a 2055 7365 2074 656d  ie..   * Use tem\n-00017ac0: 706f 7261 7279 2063 6861 6e67 6573 206f  porary changes o\n-00017ad0: 6620 636f 6c6f 7220 6f66 206f 6e65 206f  f color of one o\n-00017ae0: 7220 6d6f 7265 206f 626a 6563 7473 2074  r more objects t\n-00017af0: 6f20 656e 7375 7265 0a20 2020 2020 7468  o ensure.     th\n-00017b00: 6174 2079 6f75 7220 756e 6465 7273 7461  at your understa\n-00017b10: 6e64 696e 6720 6f66 2074 6865 2073 6365  nding of the sce\n-00017b20: 6e65 2067 656f 6d65 7472 7920 6973 2063  ne geometry is c\n-00017b30: 6f72 7265 6374 2e0a 2020 202a 2049 6620  orrect..   * If \n-00017b40: 2750 5354 7269 636b 7327 2063 6f6d 706c  'PSTricks' compl\n-00017b50: 6169 6e73 2061 626f 7574 2073 6f6d 6574  ains about somet\n-00017b60: 6869 6e67 2c20 696e 7370 6563 7420 7468  hing, inspect th\n-00017b70: 6520 6f75 7470 7574 0a20 2020 2020 6469  e output.     di\n-00017b80: 7265 6374 6c79 2066 6f72 2063 6c75 6573  rectly for clues\n-00017b90: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463  .....File: sketc\n-00017ba0: 682e 696e 666f 2c20 204e 6f64 653a 2043  h.info,  Node: C\n-00017bb0: 6c69 7070 696e 672c 2020 4e65 7874 3a20  lipping,  Next: \n-00017bc0: 4869 6464 656e 2073 7572 6661 6365 2072  Hidden surface r\n-00017bd0: 656d 6f76 616c 2c20 2050 7265 763a 204c  emoval,  Prev: L\n-00017be0: 696d 6974 7320 6f6e 2065 7272 6f72 2064  imits on error d\n-00017bf0: 6574 6563 7469 6f6e 2c20 2055 703a 2043  etection,  Up: C\n-00017c00: 6176 6561 7473 0a0a 342e 342e 3220 436c  aveats..4.4.2 Cl\n-00017c10: 6970 7069 6e67 0a2d 2d2d 2d2d 2d2d 2d2d  ipping.---------\n-00017c20: 2d2d 2d2d 2d0a 0a54 6865 2063 7572 7265  -----..The curre\n-00017c30: 6e74 2076 6572 7369 6f6e 206f 6620 2773  nt version of 's\n-00017c40: 6b65 7463 6827 2068 6173 206e 6f20 636c  ketch' has no cl\n-00017c50: 6970 7069 6e67 206f 7065 7261 7469 6f6e  ipping operation\n-00017c60: 732e 2020 5468 6520 656e 7469 7265 0a73  s.  The entire.s\n-00017c70: 6365 6e65 2069 7320 616c 7761 7973 2064  cene is always d\n-00017c80: 7261 776e 2e20 2054 6869 7320 6d65 616e  rawn.  This mean\n-00017c90: 7320 7468 6174 2077 6865 6e20 6120 7065  s that when a pe\n-00017ca0: 7273 7065 6374 6976 6520 7472 616e 7366  rspective transf\n-00017cb0: 6f72 6d20 6973 0a65 6d70 6c6f 7965 642c  orm is.employed,\n-00017cc0: 2069 7420 6973 2074 6865 2075 7365 7227   it is the user'\n-00017cd0: 7320 7265 7370 6f6e 7369 6269 6c69 7479  s responsibility\n-00017ce0: 2074 6f20 6d61 6b65 2073 7572 6520 7468   to make sure th\n-00017cf0: 6520 656e 7469 7265 2073 6365 6e65 0a72  e entire scene.r\n-00017d00: 656d 6169 6e73 2069 6e20 6672 6f6e 7420  emains in front \n-00017d10: 6f66 2074 6865 2076 6965 7765 722c 2074  of the viewer, t\n-00017d20: 6865 2072 6567 696f 6e20 7a3c 302e 0a0a  he region z<0...\n-00017d30: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69  ..File: sketch.i\n-00017d40: 6e66 6f2c 2020 4e6f 6465 3a20 4869 6464  nfo,  Node: Hidd\n-00017d50: 656e 2073 7572 6661 6365 2072 656d 6f76  en surface remov\n-00017d60: 616c 2c20 2050 7265 763a 2043 6c69 7070  al,  Prev: Clipp\n-00017d70: 696e 672c 2020 5570 3a20 4361 7665 6174  ing,  Up: Caveat\n-00017d80: 730a 0a34 2e34 2e33 2048 6964 6465 6e20  s..4.4.3 Hidden \n-00017d90: 7375 7266 6163 6520 7265 6d6f 7661 6c20  surface removal \n-00017da0: 616e 6420 706f 6c79 676f 6e20 7370 6c69  and polygon spli\n-00017db0: 7474 696e 670a 2d2d 2d2d 2d2d 2d2d 2d2d  tting.----------\n+000176a0: 2d2d 2d2d 2d2d 0a0a 2753 6b65 7463 6827  ------..'Sketch'\n+000176b0: 2063 6174 6368 6573 206d 616e 7920 6b69   catches many ki\n+000176c0: 6e64 7320 6f66 2065 7272 6f72 732c 2062  nds of errors, b\n+000176d0: 7574 206e 6f74 2061 6c6c 2e20 2046 6f72  ut not all.  For\n+000176e0: 2065 7861 6d70 6c65 2c0a 6f70 7469 6f6e   example,.option\n+000176f0: 7320 7468 6174 2073 6b65 7463 6820 646f  s that sketch do\n+00017700: 6573 206e 6f74 2072 6563 6f67 6e69 7a65  es not recognize\n+00017710: 2c20 6576 656e 2069 6e63 6f72 7265 6374  , even incorrect\n+00017720: 206f 6e65 732c 2061 7265 2071 7569 6574   ones, are quiet\n+00017730: 6c79 0a63 6f70 6965 6420 746f 2027 5053  ly.copied to 'PS\n+00017740: 5472 6963 6b73 2720 636f 6d6d 616e 6473  Tricks' commands\n+00017750: 2069 6e20 7468 6520 6f75 7470 7574 2e20   in the output. \n+00017760: 2049 7420 6973 2061 6c73 6f20 756e 666f   It is also unfo\n+00017770: 7274 756e 6174 656c 790a 6561 7379 2074  rtunately.easy t\n+00017780: 6f20 7072 6f64 7563 6520 2773 6b65 7463  o produce 'sketc\n+00017790: 6827 2069 6e70 7574 7320 7468 6174 206c  h' inputs that l\n+000177a0: 6561 6420 746f 206e 6f20 7069 6374 7572  ead to no pictur\n+000177b0: 6520 6174 2061 6c6c 2028 696d 7072 6f70  e at all (improp\n+000177c0: 6572 0a76 6572 7465 7820 6f72 6465 7269  er.vertex orderi\n+000177d0: 6e67 2063 6175 7365 7320 6576 6572 7974  ng causes everyt\n+000177e0: 6869 6e67 2074 6f20 6265 2063 756c 6c65  hing to be culle\n+000177f0: 6429 2c20 746f 2070 6963 7475 7265 7320  d), to pictures \n+00017800: 7468 6174 2061 7265 0a74 6f6f 2062 6967  that are.too big\n+00017810: 206f 7220 746f 6f20 736d 616c 6c20 666f   or too small fo\n+00017820: 7220 2750 5354 7269 636b 7327 2074 6f20  r 'PSTricks' to \n+00017830: 6472 6177 2028 6475 6520 746f 206c 696d  draw (due to lim\n+00017840: 6974 7320 6f66 2054 6558 206d 6174 6829  its of TeX math)\n+00017850: 2c0a 616e 6420 7069 6374 7572 6573 2074  ,.and pictures t\n+00017860: 6861 7420 6c6f 6f6b 206e 6f74 6869 6e67  hat look nothing\n+00017870: 206c 696b 6520 7768 6174 2077 6173 2069   like what was i\n+00017880: 6e74 656e 6465 642e 2020 4120 7069 6374  ntended.  A pict\n+00017890: 7572 6520 7769 7468 0a6f 6e65 206f 6620  ure with.one of \n+000178a0: 7468 6573 6520 7072 6f62 6c65 6d73 2063  these problems c\n+000178b0: 616e 2062 6520 6469 6666 6963 756c 7420  an be difficult \n+000178c0: 746f 2022 6465 6275 672e 2220 2057 6520  to \"debug.\"  We \n+000178d0: 6f66 6665 7220 7468 650a 666f 6c6c 6f77  offer the.follow\n+000178e0: 696e 6720 7375 6767 6573 7469 6f6e 732e  ing suggestions.\n+000178f0: 0a20 2020 2a20 466f 6c6c 6f77 2074 6865  .   * Follow the\n+00017900: 2073 7567 6765 7374 6564 2069 6e63 7265   suggested incre\n+00017910: 6d65 6e74 616c 2064 6576 656c 6f70 6d65  mental developme\n+00017920: 6e74 206d 6574 686f 6420 6465 7363 7269  nt method descri\n+00017930: 6265 6420 696e 0a20 2020 2020 2a6e 6f74  bed in.     *not\n+00017940: 6520 4f76 6572 7669 6577 3a3a 2e0a 2020  e Overview::..  \n+00017950: 202a 2041 6c77 6179 7320 6d61 696e 7461   * Always mainta\n+00017960: 696e 206f 6e65 206f 7220 7477 6f20 6261  in one or two ba\n+00017970: 636b 2d76 6572 7369 6f6e 7320 6f66 2061  ck-versions of a\n+00017980: 2064 7261 7769 6e67 2073 6f20 7468 6174   drawing so that\n+00017990: 2069 7420 6973 0a20 2020 2020 6561 7379   it is.     easy\n+000179a0: 2074 6f20 6661 6c6c 2062 6163 6b20 746f   to fall back to\n+000179b0: 2061 206b 6e6f 776e 2d67 6f6f 6420 696e   a known-good in\n+000179c0: 6372 656d 656e 742e 0a20 2020 2a20 5768  crement..   * Wh\n+000179d0: 656e 2075 7369 6e67 2027 7065 7273 7065  en using 'perspe\n+000179e0: 6374 6976 6527 2c20 656e 7375 7265 2061  ctive', ensure a\n+000179f0: 6c6c 2066 696e 616c 6c79 2074 7261 6e73  ll finally trans\n+00017a00: 666f 726d 6564 206f 626a 6563 7473 0a20  formed objects. \n+00017a10: 2020 2020 7361 7469 7366 7920 7a3c 3020      satisfy z<0 \n+00017a20: 616e 642c 2069 6e20 6661 6374 2c20 646f  and, in fact, do\n+00017a30: 206e 6f74 2063 6f6d 6520 7665 7279 2063   not come very c\n+00017a40: 6c6f 7365 2074 6f20 7468 6520 6f72 6967  lose to the orig\n+00017a50: 696e 2061 740a 2020 2020 2061 6c6c 2e0a  in at.     all..\n+00017a60: 2020 202a 2054 656d 706f 7261 7269 6c79     * Temporarily\n+00017a70: 2075 7365 2027 6375 6c6c 3d66 616c 7365   use 'cull=false\n+00017a80: 2720 746f 2073 6565 2077 6865 7265 2076  ' to see where v\n+00017a90: 6572 7465 7820 6f72 6465 7269 6e67 2070  ertex ordering p\n+00017aa0: 726f 626c 656d 730a 2020 2020 206c 6965  roblems.     lie\n+00017ab0: 2e0a 2020 202a 2055 7365 2074 656d 706f  ..   * Use tempo\n+00017ac0: 7261 7279 2063 6861 6e67 6573 206f 6620  rary changes of \n+00017ad0: 636f 6c6f 7220 6f66 206f 6e65 206f 7220  color of one or \n+00017ae0: 6d6f 7265 206f 626a 6563 7473 2074 6f20  more objects to \n+00017af0: 656e 7375 7265 0a20 2020 2020 7468 6174  ensure.     that\n+00017b00: 2079 6f75 7220 756e 6465 7273 7461 6e64   your understand\n+00017b10: 696e 6720 6f66 2074 6865 2073 6365 6e65  ing of the scene\n+00017b20: 2067 656f 6d65 7472 7920 6973 2063 6f72   geometry is cor\n+00017b30: 7265 6374 2e0a 2020 202a 2049 6620 2750  rect..   * If 'P\n+00017b40: 5354 7269 636b 7327 2063 6f6d 706c 6169  STricks' complai\n+00017b50: 6e73 2061 626f 7574 2073 6f6d 6574 6869  ns about somethi\n+00017b60: 6e67 2c20 696e 7370 6563 7420 7468 6520  ng, inspect the \n+00017b70: 6f75 7470 7574 0a20 2020 2020 6469 7265  output.     dire\n+00017b80: 6374 6c79 2066 6f72 2063 6c75 6573 2e0a  ctly for clues..\n+00017b90: 0a1f 0a46 696c 653a 2073 6b65 7463 682e  ...File: sketch.\n+00017ba0: 696e 666f 2c20 204e 6f64 653a 2043 6c69  info,  Node: Cli\n+00017bb0: 7070 696e 672c 2020 4e65 7874 3a20 4869  pping,  Next: Hi\n+00017bc0: 6464 656e 2073 7572 6661 6365 2072 656d  dden surface rem\n+00017bd0: 6f76 616c 2c20 2050 7265 763a 204c 696d  oval,  Prev: Lim\n+00017be0: 6974 7320 6f6e 2065 7272 6f72 2064 6574  its on error det\n+00017bf0: 6563 7469 6f6e 2c20 2055 703a 2043 6176  ection,  Up: Cav\n+00017c00: 6561 7473 0a0a 342e 342e 3220 436c 6970  eats..4.4.2 Clip\n+00017c10: 7069 6e67 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d  ping.-----------\n+00017c20: 2d2d 2d0a 0a54 6865 2063 7572 7265 6e74  ---..The current\n+00017c30: 2076 6572 7369 6f6e 206f 6620 2773 6b65   version of 'ske\n+00017c40: 7463 6827 2068 6173 206e 6f20 636c 6970  tch' has no clip\n+00017c50: 7069 6e67 206f 7065 7261 7469 6f6e 732e  ping operations.\n+00017c60: 2020 5468 6520 656e 7469 7265 0a73 6365    The entire.sce\n+00017c70: 6e65 2069 7320 616c 7761 7973 2064 7261  ne is always dra\n+00017c80: 776e 2e20 2054 6869 7320 6d65 616e 7320  wn.  This means \n+00017c90: 7468 6174 2077 6865 6e20 6120 7065 7273  that when a pers\n+00017ca0: 7065 6374 6976 6520 7472 616e 7366 6f72  pective transfor\n+00017cb0: 6d20 6973 0a65 6d70 6c6f 7965 642c 2069  m is.employed, i\n+00017cc0: 7420 6973 2074 6865 2075 7365 7227 7320  t is the user's \n+00017cd0: 7265 7370 6f6e 7369 6269 6c69 7479 2074  responsibility t\n+00017ce0: 6f20 6d61 6b65 2073 7572 6520 7468 6520  o make sure the \n+00017cf0: 656e 7469 7265 2073 6365 6e65 0a72 656d  entire scene.rem\n+00017d00: 6169 6e73 2069 6e20 6672 6f6e 7420 6f66  ains in front of\n+00017d10: 2074 6865 2076 6965 7765 722c 2074 6865   the viewer, the\n+00017d20: 2072 6567 696f 6e20 7a3c 302e 0a0a 1f0a   region z<0.....\n+00017d30: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n+00017d40: 6f2c 2020 4e6f 6465 3a20 4869 6464 656e  o,  Node: Hidden\n+00017d50: 2073 7572 6661 6365 2072 656d 6f76 616c   surface removal\n+00017d60: 2c20 2050 7265 763a 2043 6c69 7070 696e  ,  Prev: Clippin\n+00017d70: 672c 2020 5570 3a20 4361 7665 6174 730a  g,  Up: Caveats.\n+00017d80: 0a34 2e34 2e33 2048 6964 6465 6e20 7375  .4.4.3 Hidden su\n+00017d90: 7266 6163 6520 7265 6d6f 7661 6c20 616e  rface removal an\n+00017da0: 6420 706f 6c79 676f 6e20 7370 6c69 7474  d polygon splitt\n+00017db0: 696e 670a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ing.------------\n 00017dc0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n 00017dd0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d  ----------------\n-00017de0: 2d2d 2d2d 2d2d 2d2d 0a0a 2753 6b65 7463  --------..'Sketc\n-00017df0: 6827 2075 7365 7320 7468 6520 2264 6570  h' uses the \"dep\n-00017e00: 7468 2073 6f72 7420 616c 676f 7269 7468  th sort algorith\n-00017e10: 6d22 2066 6f72 2068 6964 6465 6e20 7375  m\" for hidden su\n-00017e20: 7266 6163 6520 7265 6d6f 7661 6c2e 0a54  rface removal..T\n-00017e30: 6869 7320 6973 2061 2076 6572 7920 6f6c  his is a very ol\n-00017e40: 6420 7465 6368 6e69 7175 6520 6475 6520  d technique due \n-00017e50: 746f 204e 6577 656c 6c2e 2831 2920 2049  to Newell.(1)  I\n-00017e60: 7420 6973 2067 656e 6572 616c 6c79 2072  t is generally r\n-00017e70: 6567 6172 6465 640a 6173 2074 6f6f 2073  egarded.as too s\n-00017e80: 6c6f 7720 666f 7220 7265 616c 2074 696d  low for real tim\n-00017e90: 6520 6772 6170 6869 6373 2c20 6275 7420  e graphics, but \n-00017ea0: 6974 2069 7320 6964 6561 6c20 666f 7220  it is ideal for \n-00017eb0: 6f75 7220 7075 7270 6f73 650a 7768 6572  our purpose.wher\n-00017ec0: 6520 7370 6565 6420 6973 206e 6f74 2076  e speed is not v\n-00017ed0: 6572 7920 696d 706f 7274 616e 742e 2832  ery important.(2\n-00017ee0: 290a 0a20 2020 5468 6520 6465 7074 6820  )..   The depth \n-00017ef0: 736f 7274 2061 6c67 6f72 6974 686d 206d  sort algorithm m\n-00017f00: 6572 656c 7920 736f 7274 7320 6f62 6a65  erely sorts obje\n-00017f10: 6374 7320 6f6e 2061 206b 6579 206f 6620  cts on a key of \n-00017f20: 696e 6372 6561 7369 6e67 0a7a 2d63 6f6f  increasing.z-coo\n-00017f30: 7264 696e 6174 652c 2065 7175 6976 616c  rdinate, equival\n-00017f40: 656e 7420 746f 2064 6563 7265 6173 696e  ent to decreasin\n-00017f50: 6720 6465 7074 682e 2020 4f62 6a65 6374  g depth.  Object\n-00017f60: 7320 6172 6520 7468 656e 2064 7261 776e  s are then drawn\n-00017f70: 2069 6e0a 7468 6520 736f 7274 6564 2073   in.the sorted s\n-00017f80: 6571 7565 6e63 6520 736f 2074 6861 7420  equence so that \n-00017f90: 7468 6f73 6520 6174 2074 6865 2072 6561  those at the rea\n-00017fa0: 7220 6f66 2074 6865 2073 6365 6e65 2061  r of the scene a\n-00017fb0: 7265 0a6f 7665 7277 7269 7474 656e 2062  re.overwritten b\n-00017fc0: 7920 7468 6f73 6520 636c 6f73 6572 2074  y those closer t\n-00017fd0: 6f20 7468 6520 7669 6577 6572 2e20 2053  o the viewer.  S\n-00017fe0: 696e 6365 2074 6869 7320 6973 2061 6c73  ince this is als\n-00017ff0: 6f20 686f 7720 6f69 6c0a 7061 696e 7465  o how oil.painte\n-00018000: 7273 2070 7261 6374 6963 6520 7468 6569  rs practice thei\n-00018010: 7220 6172 742c 2064 6570 7468 2073 6f72  r art, depth sor\n-00018020: 7420 6973 2073 6f6d 6574 696d 6573 2063  t is sometimes c\n-00018030: 616c 6c65 6420 2274 6865 0a70 6169 6e74  alled \"the.paint\n-00018040: 6572 2773 2061 6c67 6f72 6974 686d 2e22  er's algorithm.\"\n-00018050: 0a0a 2020 2049 6e20 736f 6d65 2063 6173  ..   In some cas\n-00018060: 6573 2069 7420 6973 2069 6d70 6f73 7369  es it is impossi\n-00018070: 626c 6520 746f 2073 7472 6963 746c 7920  ble to strictly \n-00018080: 6f72 6465 7220 706f 6c79 676f 6e73 2061  order polygons a\n-00018090: 6363 6f72 6469 6e67 0a74 6f20 6465 7074  ccording.to dept\n-000180a0: 682e 2020 4d6f 7265 6f76 6572 2c20 6576  h.  Moreover, ev\n-000180b0: 656e 2069 6620 6120 636f 7272 6563 7420  en if a correct \n-000180c0: 6465 7074 6820 6f72 6465 7269 6e67 2065  depth ordering e\n-000180d0: 7869 7374 732c 2074 6865 0a63 6f6d 7075  xists, the.compu\n-000180e0: 7461 7469 6f6e 206e 6565 6465 6420 746f  tation needed to\n-000180f0: 2066 696e 6420 6974 206d 6179 2062 6520   find it may be \n-00018100: 746f 6f20 636f 6d70 6c65 7820 616e 6420  too complex and \n-00018110: 736c 6f77 2e20 2049 6e20 7468 6573 650a  slow.  In these.\n-00018120: 6361 7365 732c 2027 736b 6574 6368 2720  cases, 'sketch' \n-00018130: 7370 6c69 7473 206f 6e65 206f 7220 6d6f  splits one or mo\n-00018140: 7265 2070 6f6c 7967 6f6e 7320 696e 746f  re polygons into\n-00018150: 2070 6965 6365 732e 2020 5468 650a 6578   pieces.  The.ex\n-00018160: 7065 6374 6174 696f 6e20 6973 2074 6861  pectation is tha\n-00018170: 7420 7468 6520 6e65 772c 2073 6d61 6c6c  t the new, small\n-00018180: 6572 2070 6f6c 7967 6f6e 7320 7769 6c6c  er polygons will\n-00018190: 2062 6520 7369 6d70 6c65 7220 746f 206f   be simpler to o\n-000181a0: 7264 6572 2e0a 2753 6b65 7463 6827 2075  rder..'Sketch' u\n-000181b0: 7365 7320 6120 4253 5020 2862 696e 6172  ses a BSP (binar\n-000181c0: 7920 7370 6163 6520 7061 7274 6974 696f  y space partitio\n-000181d0: 6e29 2074 6f20 6861 6e64 6c65 2074 6865  n) to handle the\n-000181e0: 2073 706c 6974 7469 6e67 0a6f 7065 7261   splitting.opera\n-000181f0: 7469 6f6e 2e0a 0a2a 204d 656e 753a 0a0a  tion...* Menu:..\n-00018200: 2a20 5374 6174 6973 7469 6373 3a3a 2020  * Statistics::  \n-00018210: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00018220: 5065 7266 6f72 6d61 6e63 6520 6e75 6d62  Performance numb\n-00018230: 6572 7320 6f6e 2064 6570 7468 2073 6f72  ers on depth sor\n-00018240: 742e 0a2a 2042 7567 7320 616e 6420 616e  t..* Bugs and an\n-00018250: 6f6d 616c 6965 733a 3a20 2020 2020 2020  omalies::       \n-00018260: 2020 2049 6d70 6572 6665 6374 696f 6e73     Imperfections\n-00018270: 2069 6e20 7468 6973 2069 6d70 6c65 6d65   in this impleme\n-00018280: 6e74 6174 696f 6e2e 0a0a 2020 202d 2d2d  ntation...   ---\n-00018290: 2d2d 2d2d 2d2d 2d20 466f 6f74 6e6f 7465  ------- Footnote\n-000182a0: 7320 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2020  s ----------..  \n-000182b0: 2028 3129 204e 6577 656c 6c2c 204d 2e45   (1) Newell, M.E\n-000182c0: 2e2c 2052 2e47 2e20 4e65 7765 6c6c 2c20  ., R.G. Newell, \n-000182d0: 616e 6420 542e 4c2e 2053 616e 6368 612c  and T.L. Sancha,\n-000182e0: 2041 2073 6f6c 7574 696f 6e20 746f 2074   A solution to t\n-000182f0: 6865 0a68 6964 6465 6e20 7375 7266 6163  he.hidden surfac\n-00018300: 6520 7072 6f62 6c65 6d2e 2020 5072 6f63  e problem.  Proc\n-00018310: 6565 6469 6e67 7320 6f66 2074 6865 2041  eedings of the A\n-00018320: 434d 2061 6e6e 7561 6c20 636f 6e66 6572  CM annual confer\n-00018330: 656e 6365 202d 0a56 6f6c 756d 6520 312c  ence -.Volume 1,\n-00018340: 2070 6167 6520 3434 332d 3435 302c 2041   page 443-450, A\n-00018350: 434d 2050 7265 7373 2c20 3139 3732 2e0a  CM Press, 1972..\n-00018360: 0a20 2020 2832 2920 5765 2068 6176 6520  .   (2) We have \n-00018370: 7275 6e20 2773 6b65 7463 6827 206f 6e20  run 'sketch' on \n-00018380: 7468 6520 6661 6d6f 7573 2053 7461 6e66  the famous Stanf\n-00018390: 6f72 6420 4275 6e6e 792c 2077 6869 6368  ord Bunny, which\n-000183a0: 2063 6f6e 7369 7374 730a 6f66 206e 6561   consists.of nea\n-000183b0: 726c 7920 3730 2c30 3030 2074 7269 616e  rly 70,000 trian\n-000183c0: 676c 6573 2e20 2052 756e 2074 696d 6520  gles.  Run time \n-000183d0: 7761 7320 6162 6f75 7420 3620 7365 636f  was about 6 seco\n-000183e0: 6e64 732e 2020 4d6f 7374 206f 6620 7468  nds.  Most of th\n-000183f0: 6973 0a77 6173 2073 7065 6e74 2077 7269  is.was spent wri\n-00018400: 7469 6e67 2074 6865 206f 7574 7075 7420  ting the output \n-00018410: 6669 6c65 2072 6174 6865 7220 7468 616e  file rather than\n-00018420: 2069 6e20 7468 6520 6869 6464 656e 2073   in the hidden s\n-00018430: 7572 6661 6365 0a61 6c67 6f72 6974 686d  urface.algorithm\n-00018440: 2e20 204c 6154 6558 2074 6f6f 6b20 6d75  .  LaTeX took mu\n-00018450: 6368 206c 6f6e 6765 7220 746f 2070 726f  ch longer to pro\n-00018460: 6365 7373 2074 6865 2072 6573 756c 7469  cess the resulti\n-00018470: 6e67 2027 5053 5472 6963 6b73 270a 636f  ng 'PSTricks'.co\n-00018480: 6465 2e20 2054 6865 206f 6276 696f 7573  de.  The obvious\n-00018490: 2063 6f6e 636c 7573 696f 6e20 6973 2074   conclusion is t\n-000184a0: 6861 7420 7468 6520 7370 6565 6420 6f66  hat the speed of\n-000184b0: 2074 6865 2064 6570 7468 2073 6f72 740a   the depth sort.\n-000184c0: 616c 676f 7269 7468 6d20 6973 206e 6f74  algorithm is not\n-000184d0: 2061 2077 6f72 7279 2e0a 0a1f 0a46 696c   a worry.....Fil\n-000184e0: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n-000184f0: 204e 6f64 653a 2053 7461 7469 7374 6963   Node: Statistic\n-00018500: 732c 2020 4e65 7874 3a20 4275 6773 2061  s,  Next: Bugs a\n-00018510: 6e64 2061 6e6f 6d61 6c69 6573 2c20 2050  nd anomalies,  P\n-00018520: 7265 763a 2048 6964 6465 6e20 7375 7266  rev: Hidden surf\n-00018530: 6163 6520 7265 6d6f 7661 6c2c 2020 5570  ace removal,  Up\n-00018540: 3a20 4869 6464 656e 2073 7572 6661 6365  : Hidden surface\n-00018550: 2072 656d 6f76 616c 0a0a 342e 342e 332e   removal..4.4.3.\n-00018560: 3120 5374 6174 6973 7469 6373 0a2e 2e2e  1 Statistics....\n-00018570: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a  ................\n-00018580: 0a46 6f72 2074 6865 2063 7572 696f 7573  .For the curious\n-00018590: 2c20 2773 6b65 7463 6827 2077 7269 7465  , 'sketch' write\n-000185a0: 7320 6f6e 6520 6c69 6e65 206f 6620 6465  s one line of de\n-000185b0: 7074 6820 736f 7274 2073 7461 7469 7374  pth sort statist\n-000185c0: 6963 732e 0a48 6572 6520 6973 2061 6e20  ics..Here is an \n-000185d0: 6578 616d 706c 6520 666f 7220 6120 6c61  example for a la\n-000185e0: 7267 6520 636f 6c6c 6563 7469 6f6e 206f  rge collection o\n-000185f0: 6620 7472 6961 6e67 6c65 732e 0a20 2072  f triangles..  r\n-00018600: 656d 6172 6b2c 206e 6f64 653d 3334 3832  emark, node=3482\n-00018610: 3420 7072 6f62 653d 3538 312e 3920 7377  4 probe=581.9 sw\n-00018620: 6170 3d35 2073 706c 6974 3d32 2028 696e  ap=5 split=2 (in\n-00018630: 3d34 206f 7574 3d36 2920 6f6c 733d 3234  =4 out=6) ols=24\n-00018640: 3835 312f 300a 4974 206d 6561 6e73 2074  851/0.It means t\n-00018650: 6861 7420 3334 2c38 3234 206f 626a 6563  hat 34,824 objec\n-00018660: 7473 2077 6572 6520 6465 7074 6820 736f  ts were depth so\n-00018670: 7274 6564 2061 6674 6572 2063 756c 6c69  rted after culli\n-00018680: 6e67 2e20 2046 6f72 2065 6163 682c 0a61  ng.  For each,.a\n-00018690: 6e20 6176 6572 6167 6520 6f66 2035 3831  n average of 581\n-000186a0: 2e39 206f 7468 6572 7320 6861 6420 746f  .9 others had to\n-000186b0: 2062 6520 6368 6563 6b65 6420 746f 2065   be checked to e\n-000186c0: 6e73 7572 6520 7468 6174 2074 6865 2069  nsure that the i\n-000186d0: 6e69 7469 616c 2c0a 6170 7072 6f78 696d  nitial,.approxim\n-000186e0: 6174 6520 6f72 6465 7269 6e67 2077 6173  ate ordering was\n-000186f0: 2063 6f72 7265 6374 2e20 2041 6d6f 6e67   correct.  Among\n-00018700: 2061 6c6c 2074 6865 7365 2063 6865 636b   all these check\n-00018710: 732c 206f 6e6c 7920 350a 7265 7375 6c74  s, only 5.result\n-00018720: 6564 2069 6e20 7377 6170 7320 746f 2072  ed in swaps to r\n-00018730: 656f 7264 6572 2074 6865 2069 6e69 7469  eorder the initi\n-00018740: 616c 2073 6f72 742e 2020 496e 2074 776f  al sort.  In two\n-00018750: 2063 6173 6573 2c20 6120 636f 7272 6563   cases, a correc\n-00018760: 740a 6f72 6465 7269 6e67 2063 6f75 6c64  t.ordering could\n-00018770: 206e 6f74 2062 6520 6465 7465 726d 696e   not be determin\n-00018780: 6564 2c20 736f 2062 696e 6172 7920 7370  ed, so binary sp\n-00018790: 6163 6520 7061 7274 6974 696f 6e73 2077  ace partitions w\n-000187a0: 6572 650a 636f 6e73 7472 7563 7465 6420  ere.constructed \n-000187b0: 666f 7220 7370 6c69 7474 696e 672e 2020  for splitting.  \n-000187c0: 4120 746f 7461 6c20 6f66 2034 206f 626a  A total of 4 obj\n-000187d0: 6563 7473 2028 7472 6961 6e67 6c65 7320  ects (triangles \n-000187e0: 696e 2074 6869 730a 6361 7365 2920 7765  in this.case) we\n-000187f0: 7265 2069 6e73 6572 7465 6420 696e 2074  re inserted in t\n-00018800: 6865 2070 6172 7469 7469 6f6e 732c 2061  he partitions, a\n-00018810: 6e64 2036 2070 6f6c 7967 6f6e 7320 7765  nd 6 polygons we\n-00018820: 7265 2070 726f 6475 6365 642e 0a46 696e  re produced..Fin\n-00018830: 616c 6c79 2c20 3234 2c38 3531 2022 6c61  ally, 24,851 \"la\n-00018840: 7374 2072 6573 6f72 7422 2070 6f6c 7967  st resort\" polyg\n-00018850: 6f6e 206f 7665 726c 6170 2063 6865 636b  on overlap check\n-00018860: 7320 7765 7265 2070 6572 666f 726d 6564  s were performed\n-00018870: 0a61 6674 6572 2073 696d 706c 6572 2c20  .after simpler, \n-00018880: 6661 7374 6572 2063 6865 636b 7320 6661  faster checks fa\n-00018890: 696c 6564 2074 6f20 7969 656c 6420 636f  iled to yield co\n-000188a0: 6e63 6c75 7369 7665 2072 6573 756c 7473  nclusive results\n-000188b0: 2e20 2054 6865 0a66 696e 616c 202f 3020  .  The.final /0 \n-000188c0: 6973 2066 6f72 206c 696e 652d 706f 6c79  is for line-poly\n-000188d0: 676f 6e20 6f76 6572 6c61 7020 6368 6563  gon overlap chec\n-000188e0: 6b73 2e20 2046 6f72 2063 6f6d 7061 7269  ks.  For compari\n-000188f0: 736f 6e2c 2074 6865 0a73 7461 7469 7374  son, the.statist\n-00018900: 6963 7320 666f 7220 7468 6520 6c61 7374  ics for the last\n-00018910: 2066 6967 7572 6520 696e 202a 6e6f 7465   figure in *note\n-00018920: 204f 7665 7276 6965 773a 3a20 666f 6c6c   Overview:: foll\n-00018930: 6f77 2e0a 2020 7265 6d61 726b 2c20 6e6f  ow..  remark, no\n-00018940: 6465 3d32 3720 7072 6f62 653d 3134 2e36  de=27 probe=14.6\n-00018950: 2073 7761 703d 3336 2073 706c 6974 3d31   swap=36 split=1\n-00018960: 3520 2869 6e3d 3330 206f 7574 3d34 3529  5 (in=30 out=45)\n-00018970: 206f 6c73 3d30 2f36 390a 4e6f 7465 2074   ols=0/69.Note t\n-00018980: 6861 7420 7468 6572 6520 7761 7320 7072  hat there was pr\n-00018990: 6f70 6f72 7469 6f6e 616c 6c79 206d 7563  oportionally muc\n-000189a0: 6820 6d6f 7265 2073 7761 7070 696e 6720  h more swapping \n-000189b0: 616e 6420 7370 6c69 7474 696e 670a 6163  and splitting.ac\n-000189c0: 7469 7669 7479 2069 6e20 7468 6973 2068  tivity in this h\n-000189d0: 6967 686c 7920 636f 6e6e 6563 7465 6420  ighly connected \n-000189e0: 7363 656e 652e 0a0a 1f0a 4669 6c65 3a20  scene.....File: \n-000189f0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n-00018a00: 6465 3a20 4275 6773 2061 6e64 2061 6e6f  de: Bugs and ano\n-00018a10: 6d61 6c69 6573 2c20 2050 7265 763a 2053  malies,  Prev: S\n-00018a20: 7461 7469 7374 6963 732c 2020 5570 3a20  tatistics,  Up: \n-00018a30: 4869 6464 656e 2073 7572 6661 6365 2072  Hidden surface r\n-00018a40: 656d 6f76 616c 0a0a 342e 342e 332e 3220  emoval..4.4.3.2 \n-00018a50: 4275 6773 2061 6e64 2061 6e6f 6d61 6c69  Bugs and anomali\n-00018a60: 6573 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  es..............\n-00018a70: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a50  ...............P\n-00018a80: 6f6c 7967 6f6e 2061 6e64 206c 696e 6520  olygon and line \n-00018a90: 7370 6c69 7474 696e 6720 6361 6e20 626f  splitting can bo\n-00018aa0: 7468 2063 6175 7365 2061 6e6f 6d61 6c69  th cause anomali\n-00018ab0: 6573 2069 6e20 7468 6520 6f75 7470 7574  es in the output\n-00018ac0: 2e0a 2750 5354 7269 636b 7327 2064 6173  ..'PSTricks' das\n-00018ad0: 6820 7061 7474 6572 6e73 2c20 7370 6563  h patterns, spec\n-00018ae0: 6966 6965 6420 7769 7468 2027 6c69 6e65  ified with 'line\n-00018af0: 7374 796c 653d 6461 7368 6564 272c 2063  style=dashed', c\n-00018b00: 616e 2062 650a 6469 7372 7570 7465 6420  an be.disrupted \n-00018b10: 6279 2073 706c 6974 7469 6e67 2e20 2054  by splitting.  T\n-00018b20: 6869 7320 6f63 6375 7273 2077 6865 6e20  his occurs when \n-00018b30: 7468 6520 6465 7074 6820 736f 7274 2067  the depth sort g\n-00018b40: 6976 6573 2075 7020 746f 6f0a 6561 726c  ives up too.earl\n-00018b50: 7920 616e 6420 7370 6c69 7473 2061 206c  y and splits a l\n-00018b60: 696e 6520 7768 6572 6520 6974 2069 7320  ine where it is \n-00018b70: 6e6f 7420 7265 616c 6c79 206e 6563 6573  not really neces\n-00018b80: 7361 7279 2e20 2041 2077 6f72 6b61 726f  sary.  A workaro\n-00018b90: 756e 640a 6973 2074 6f20 7573 6520 6772  und.is to use gr\n-00018ba0: 6179 206f 7220 6669 6e65 6c79 2064 6f74  ay or finely dot\n-00018bb0: 7465 6420 6c69 6e65 7320 696e 7374 6561  ted lines instea\n-00018bc0: 642e 2020 4966 2079 6f75 7220 6472 6177  d.  If your draw\n-00018bd0: 696e 6720 6973 0a73 6d61 6c6c 2c20 796f  ing is.small, yo\n-00018be0: 7520 6361 6e20 616c 736f 2065 6469 7420  u can also edit \n-00018bf0: 7468 6520 2773 6b65 7463 6827 206f 7574  the 'sketch' out\n-00018c00: 7075 7420 6279 2068 616e 6420 746f 206d  put by hand to m\n-00018c10: 6572 6765 2074 6865 2070 6965 6365 730a  erge the pieces.\n-00018c20: 6f66 2074 6865 206f 6666 656e 6469 6e67  of the offending\n-00018c30: 206c 696e 652e 0a0a 2020 2041 6e6f 7468   line...   Anoth\n-00018c40: 6572 2061 6e6f 6d61 6c79 2069 7320 7469  er anomaly is ti\n-00018c50: 6e79 2028 6f72 2069 6e20 6465 6765 6e65  ny (or in degene\n-00018c60: 7261 7465 2063 6173 6573 206e 6f74 2d73  rate cases not-s\n-00018c70: 6f2d 7469 6e79 2920 6e6f 7463 6865 730a  o-tiny) notches.\n-00018c80: 696e 2074 6865 206c 696e 6573 2074 6861  in the lines tha\n-00018c90: 7420 626f 7264 6572 2073 706c 6974 2070  t border split p\n-00018ca0: 6f6c 7967 6f6e 732e 2020 5468 6573 6520  olygons.  These \n-00018cb0: 6465 7269 7665 2066 726f 6d20 7468 6520  derive from the \n-00018cc0: 7761 7920 6561 6368 0a70 6f6c 7967 6f6e  way each.polygon\n-00018cd0: 2069 7320 7061 696e 7465 643a 2066 6972   is painted: fir\n-00018ce0: 7374 2c20 616c 6c20 7069 7865 6c73 2077  st, all pixels w\n-00018cf0: 6974 6869 6e20 7468 6520 626f 756e 6461  ithin the bounda\n-00018d00: 7279 2061 7265 2022 6669 6c6c 6564 220a  ry are \"filled\".\n-00018d10: 7769 7468 2063 6f6c 6f72 2028 7065 7268  with color (perh\n-00018d20: 6170 7320 7768 6974 6529 2c20 7468 656e  aps white), then\n-00018d30: 2074 6865 2073 616d 6520 626f 756e 6461   the same bounda\n-00018d40: 7279 2069 7320 2273 7472 6f6b 6564 2220  ry is \"stroked\" \n-00018d50: 2861 0a50 6f73 7473 6372 6970 7420 7465  (a.Postscript te\n-00018d60: 726d 2920 7769 7468 2061 206c 696e 652e  rm) with a line.\n-00018d70: 2020 5468 6520 7265 7375 6c74 2069 7320    The result is \n-00018d80: 7468 6174 2068 616c 6620 7468 6520 6c69  that half the li\n-00018d90: 6e65 206c 6965 730a 696e 7369 6465 2074  ne lies.inside t\n-00018da0: 6865 2062 6f75 6e64 6172 7920 616e 6420  he boundary and \n-00018db0: 6861 6c66 206f 7574 7369 6465 2c20 7768  half outside, wh\n-00018dc0: 696c 6520 7468 6520 5061 696e 7465 7227  ile the Painter'\n-00018dd0: 7320 616c 676f 7269 7468 6d0a 6173 7375  s algorithm.assu\n-00018de0: 6d65 7320 7468 6520 706f 6c79 676f 6e20  mes the polygon \n-00018df0: 6c69 6573 2065 6e74 6972 656c 7920 7769  lies entirely wi\n-00018e00: 7468 696e 2069 7473 2062 6f75 6e64 6172  thin its boundar\n-00018e10: 792e 2020 5468 6520 6e6f 7463 6865 7320  y.  The notches \n-00018e20: 6172 650a 6475 6520 746f 206f 6e65 2070  are.due to one p\n-00018e30: 6f6c 7967 6f6e 2066 696c 6c20 6f70 6572  olygon fill oper\n-00018e40: 6174 696f 6e20 6f76 6572 7772 6974 696e  ation overwritin\n-00018e50: 6720 7468 6520 616c 7265 6164 792d 6472  g the already-dr\n-00018e60: 6177 6e20 696e 7369 6465 0a6f 6620 7468  awn inside.of th\n-00018e70: 6520 626f 7264 6572 206f 6620 616e 6f74  e border of anot\n-00018e80: 6865 7220 706f 6c79 676f 6e2e 2831 2920  her polygon.(1) \n-00018e90: 204f 6e65 2077 6f72 6b61 726f 756e 6420   One workaround \n-00018ea0: 6973 2074 6f20 6d61 6b65 2062 6f72 6465  is to make borde\n-00018eb0: 720a 6c69 6e65 7320 7665 7279 2074 6869  r.lines very thi\n-00018ec0: 6e2e 2020 496e 2066 6163 7420 276c 696e  n.  In fact 'lin\n-00018ed0: 6577 6964 7468 3d30 7074 2720 6973 2067  ewidth=0pt' is g\n-00018ee0: 7561 7261 6e74 6565 6420 746f 2065 6c69  uaranteed to eli\n-00018ef0: 6d69 6e61 7465 0a74 6869 7320 7072 6f62  minate.this prob\n-00018f00: 6c65 6d2c 2074 686f 7567 6820 7468 6973  lem, though this\n-00018f10: 2072 6573 756c 7473 2069 6e20 7468 6520   results in the \n-00018f20: 7468 696e 6e65 7374 206c 696e 6520 796f  thinnest line yo\n-00018f30: 7572 206f 7574 7075 740a 6465 7669 6365  ur output.device\n-00018f40: 2063 616e 2064 7261 772c 2077 6869 6368   can draw, which\n-00018f50: 2069 7320 7573 7561 6c6c 7920 746f 6f20   is usually too \n-00018f60: 7468 696e 2e20 2059 6f75 206d 6967 6874  thin.  You might\n-00018f70: 2067 6574 206c 7563 6b79 2062 790a 6d65   get lucky by.me\n-00018f80: 7265 6c79 2072 656f 7264 6572 696e 6720  rely reordering \n-00018f90: 7468 696e 6773 2069 6e20 7468 6520 696e  things in the in\n-00018fa0: 7075 7420 6669 6c65 2c20 7768 6963 6820  put file, which \n-00018fb0: 6973 206c 696b 656c 7920 746f 206d 6f76  is likely to mov\n-00018fc0: 6520 7468 650a 7370 6c69 7473 2074 6f20  e the.splits to \n-00018fd0: 6469 6666 6572 656e 7420 706c 6163 6573  different places\n-00018fe0: 2e20 2054 6865 206f 6e6c 7920 7375 7265  .  The only sure\n-00018ff0: 2d66 6972 6520 736f 6c75 7469 6f6e 2069  -fire solution i\n-00019000: 7320 7072 6574 7479 0a74 6572 7269 626c  s pretty.terribl\n-00019010: 653a 2063 7573 746f 6d20 6669 7420 2773  e: custom fit 's\n-00019020: 7065 6369 616c 2720 6f76 6572 6c61 7920  pecial' overlay \n-00019030: 6c69 6e65 7320 2877 6974 6820 275c 7073  lines (with '\\ps\n-00019040: 6c69 6e65 2729 2074 6f20 636f 7665 720a  line') to cover.\n-00019050: 7468 6520 6e6f 7463 6865 732e 0a0a 2020  the notches...  \n-00019060: 2050 6f6c 7967 6f6e 2073 706c 6974 7469   Polygon splitti\n-00019070: 6e67 2061 6c73 6f20 6272 6561 6b73 2027  ng also breaks '\n-00019080: 5053 5472 6963 6b73 2720 6861 7463 6820  PSTricks' hatch \n-00019090: 7061 7474 6572 6e73 2e20 2054 6865 206f  patterns.  The o\n-000190a0: 6e6c 790a 6b6e 6f77 6e20 776f 726b 6172  nly.known workar\n-000190b0: 6f75 6e64 2069 7320 746f 2073 7562 7374  ound is to subst\n-000190c0: 6974 7574 6520 6120 736f 6c69 6420 6669  itute a solid fi\n-000190d0: 6c6c 2066 6f72 2074 6865 2068 6174 6368  ll for the hatch\n-000190e0: 2e0a 0a20 2020 2d2d 2d2d 2d2d 2d2d 2d2d  ...   ----------\n-000190f0: 2046 6f6f 746e 6f74 6573 202d 2d2d 2d2d   Footnotes -----\n-00019100: 2d2d 2d2d 2d0a 0a20 2020 2831 2920 4920  -----..   (1) I \n-00019110: 6b6e 6f77 2068 6f77 2074 6f20 6669 7820  know how to fix \n-00019120: 7468 6973 2070 726f 626c 656d 2c20 6275  this problem, bu\n-00019130: 7420 4920 646f 6e27 7420 6c69 6b65 206d  t I don't like m\n-00019140: 7920 736f 6c75 7469 6f6e 2c20 616e 640a  y solution, and.\n-00019150: 4927 6d20 696e 7465 7265 7374 6564 2069  I'm interested i\n-00019160: 6e20 796f 7572 732e 0a0a 1f0a 4669 6c65  n yours.....File\n-00019170: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020  : sketch.info,  \n-00019180: 4e6f 6465 3a20 436f 6d6d 616e 6420 6c69  Node: Command li\n-00019190: 6e65 2c20 204e 6578 743a 2049 6e73 7461  ne,  Next: Insta\n-000191a0: 6c6c 696e 6720 736b 6574 6368 2c20 2050  lling sketch,  P\n-000191b0: 7265 763a 2042 7569 6c64 696e 6720 6120  rev: Building a \n-000191c0: 6472 6177 696e 672c 2020 5570 3a20 546f  drawing,  Up: To\n-000191d0: 700a 0a35 2043 6f6d 6d61 6e64 206c 696e  p..5 Command lin\n-000191e0: 650a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  e.**************\n-000191f0: 0a0a 2a53 796e 6f70 7369 733a 2a0a 2020  ..*Synopsis:*.  \n-00019200: 2020 2073 6b65 7463 6820 5b2d 685d 5b2d     sketch [-h][-\n-00019210: 5620 782e 795d 5b2d 765d 5b2d 625d 5b2d  V x.y][-v][-b][-\n-00019220: 645d 5b74 2064 6f63 746d 705d 5b2d 545b  d][t doctmp][-T[\n-00019230: 757c 655d 5b70 5b50 7c54 5d5b 4c7c 435d  u|e][p[P|T][L|C]\n-00019240: 5d5d 5b2d 6f20 6f75 7470 7574 2e74 6578  ]][-o output.tex\n-00019250: 5d0a 2020 2020 2020 205b 2d44 2054 4147  ].       [-D TAG\n-00019260: 202e 2e2e 5d20 696e 7075 7431 2e73 6b20   ...] input1.sk \n-00019270: 5b2d 5520 5441 4720 2e2e 2e5d 2069 6e70  [-U TAG ...] inp\n-00019280: 7574 322e 736b 202e 2e2e 0a0a 2a44 6573  ut2.sk .....*Des\n-00019290: 6372 6970 7469 6f6e 2a20 5072 6f63 6573  cription* Proces\n-000192a0: 7365 7320 7468 6520 2773 6b65 7463 6827  ses the 'sketch'\n-000192b0: 2069 6e70 7574 2066 696c 6573 2069 6e20   input files in \n-000192c0: 6f72 6465 7220 746f 2070 726f 6475 6365  order to produce\n-000192d0: 0a27 5053 5472 6963 6b73 2720 6f75 7470  .'PSTricks' outp\n-000192e0: 7574 2063 6f64 6520 7375 6974 6162 6c65  ut code suitable\n-000192f0: 2066 6f72 2069 6e63 6c75 7369 6f6e 2069   for inclusion i\n-00019300: 6e20 6120 5465 5820 6f72 204c 6154 6558  n a TeX or LaTeX\n-00019310: 0a64 6f63 756d 656e 742e 0a0a 2a4f 7074  .document...*Opt\n-00019320: 696f 6e73 3a2a 0a27 2d68 270a 2020 2020  ions:*.'-h'.    \n-00019330: 2050 7269 6e74 2061 2073 686f 7274 2063   Print a short c\n-00019340: 6174 616c 6f67 206f 6620 6f70 7469 6f6e  atalog of option\n-00019350: 732e 0a27 2d56 270a 2020 2020 2053 6574  s..'-V'.     Set\n-00019360: 2074 6865 2027 5053 5472 6963 6b73 2720   the 'PSTricks' \n-00019370: 7665 7273 696f 6e20 6173 7375 6d65 6420  version assumed \n-00019380: 666f 7220 6f75 7470 7574 2070 7572 706f  for output purpo\n-00019390: 7365 7320 746f 2027 782e 7927 2c0a 2020  ses to 'x.y',.  \n-000193a0: 2020 2066 6f72 2065 7861 6d70 6c65 2031     for example 1\n-000193b0: 2e31 392e 2020 5573 7561 6c6c 7920 6e65  .19.  Usually ne\n-000193c0: 6564 6564 206f 6e6c 7920 6966 2079 6f75  eded only if you\n-000193d0: 7220 2750 5354 7269 636b 7327 2069 7320  r 'PSTricks' is \n-000193e0: 6f6c 640a 2020 2020 2063 6f6d 7061 7265  old.     compare\n-000193f0: 6420 746f 2079 6f75 7220 2773 6b65 7463  d to your 'sketc\n-00019400: 6827 2e20 2055 7365 2027 2d76 2720 746f  h'.  Use '-v' to\n-00019410: 2073 6565 2077 6861 7420 2773 6b65 7463   see what 'sketc\n-00019420: 6827 2061 7373 756d 6573 0a20 2020 2020  h' assumes.     \n-00019430: 6279 2064 6566 6175 6c74 2e0a 272d 7627  by default..'-v'\n-00019440: 0a20 2020 2020 5072 696e 7420 7665 7273  .     Print vers\n-00019450: 696f 6e20 696e 666f 726d 6174 696f 6e20  ion information \n-00019460: 746f 2073 7461 6e64 6172 6420 6f75 7470  to standard outp\n-00019470: 7574 2c20 696e 636c 7564 696e 6720 7468  ut, including th\n-00019480: 6520 7665 7273 696f 6e0a 2020 2020 206f  e version.     o\n-00019490: 6620 2750 5354 7269 636b 7327 2061 7373  f 'PSTricks' ass\n-000194a0: 756d 6564 2066 6f72 206f 7574 7075 7420  umed for output \n-000194b0: 2863 616e 2062 6520 6368 616e 6765 6420  (can be changed \n-000194c0: 7769 7468 2027 2d56 2720 6162 6f76 6529  with '-V' above)\n-000194d0: 2e0a 272d 6227 0a20 2020 2020 5573 6520  ..'-b'.     Use \n-000194e0: 6120 4253 5020 282a 4e6f 7465 2048 6964  a BSP (*Note Hid\n-000194f0: 6465 6e20 7375 7266 6163 6520 7265 6d6f  den surface remo\n-00019500: 7661 6c3a 3a2e 2920 2066 6f72 205f 616c  val::.)  for _al\n-00019510: 6c5f 2068 6964 6465 6e0a 2020 2020 2073  l_ hidden.     s\n-00019520: 7572 6661 6365 2072 656d 6f76 616c 2072  urface removal r\n-00019530: 6174 6865 7220 7468 616e 2074 6865 2064  ather than the d\n-00019540: 6566 6175 6c74 2c20 7768 6963 6820 6973  efault, which is\n-00019550: 2074 6865 2064 6570 7468 2073 6f72 740a   the depth sort.\n-00019560: 2020 2020 2061 6c67 6f72 6974 686d 2077       algorithm w\n-00019570: 6974 6820 4253 5073 2075 7365 6420 6f6e  ith BSPs used on\n-00019580: 6c79 2066 6f72 2063 7963 6c65 2072 6573  ly for cycle res\n-00019590: 6f6c 7574 696f 6e2e 2020 5468 6973 206d  olution.  This m\n-000195a0: 6179 0a20 2020 2020 7072 6f64 7563 6520  ay.     produce \n-000195b0: 636f 7272 6563 7420 6f75 7470 7574 2069  correct output i\n-000195c0: 6e20 6365 7274 6169 6e20 6465 6765 6e65  n certain degene\n-000195d0: 7261 7465 2063 6173 6573 2077 6865 7265  rate cases where\n-000195e0: 2074 6865 2064 6570 7468 0a20 2020 2020   the depth.     \n-000195f0: 736f 7274 2063 616e 6e6f 742c 2062 7574  sort cannot, but\n-00019600: 2069 7420 616c 736f 206c 6561 6473 2074   it also leads t\n-00019610: 6f20 6d61 6e79 2067 7261 7475 6974 6f75  o many gratuitou\n-00019620: 7320 7370 6c69 7473 2c20 6865 6e63 650a  s splits, hence.\n-00019630: 2020 2020 206d 6f72 6520 616e 6f6d 616c       more anomal\n-00019640: 6965 7320 2a6e 6f74 6520 4275 6773 2061  ies *note Bugs a\n-00019650: 6e64 2061 6e6f 6d61 6c69 6573 3a3a 2061  nd anomalies:: a\n-00019660: 6e64 2062 6967 206f 7574 7075 7420 6669  nd big output fi\n-00019670: 6c65 732e 0a27 2d64 270a 2020 2020 2052  les..'-d'.     R\n-00019680: 756e 2027 736b 6574 6368 2727 7320 7061  un 'sketch''s pa\n-00019690: 7273 6572 2069 6e20 6465 6275 6767 696e  rser in debuggin\n-000196a0: 6720 6d6f 6465 2e20 2054 6869 7320 6973  g mode.  This is\n-000196b0: 2070 7269 6d61 7269 6c79 2066 6f72 0a20   primarily for. \n-000196c0: 2020 2020 6465 7665 6c6f 706d 656e 742e      development.\n-000196d0: 0a27 2d74 270a 2020 2020 2055 7365 2063  .'-t'.     Use c\n-000196e0: 6f6e 7465 6e74 7320 6f66 2066 696c 6520  ontents of file \n-000196f0: 2764 6f63 746d 7027 2061 7320 6120 646f  'doctmp' as a do\n-00019700: 6375 6d65 6e74 2074 656d 706c 6174 6520  cument template \n-00019710: 696e 2077 6869 6368 2074 6f0a 2020 2020  in which to.    \n-00019720: 2065 6e63 6c6f 7365 2027 5053 5472 6963   enclose 'PSTric\n-00019730: 6b73 2720 6f75 7470 7574 2063 6f64 652e  ks' output code.\n-00019740: 2020 5468 6520 636f 6465 2069 7320 696e    The code is in\n-00019750: 7365 7274 6564 2069 6e20 706c 6163 6520  serted in place \n-00019760: 6f66 0a20 2020 2020 7468 6520 6669 7273  of.     the firs\n-00019770: 7420 696e 7374 616e 6365 206f 6620 7468  t instance of th\n-00019780: 6520 6573 6361 7065 2073 7472 696e 6720  e escape string \n-00019790: 2525 534b 4554 4348 5f4f 5554 5055 5425  %%SKETCH_OUTPUT%\n-000197a0: 252e 0a27 2d54 270a 2020 2020 2043 6175  %..'-T'.     Cau\n-000197b0: 7365 7320 2750 5354 7269 636b 7327 206f  ses 'PSTricks' o\n-000197c0: 7574 7075 7420 746f 2062 6520 656e 636c  utput to be encl\n-000197d0: 6f73 6564 2069 6e20 6465 6661 756c 7420  osed in default \n-000197e0: 5553 2064 6f63 756d 656e 740a 2020 2020  US document.    \n-000197f0: 2074 656d 706c 6174 6520 7465 7874 2e20   template text. \n-00019800: 204f 7074 696f 6e20 272d 5475 2720 6973   Option '-Tu' is\n-00019810: 2061 2073 796e 6f6e 796d 2e20 204f 7074   a synonym.  Opt\n-00019820: 696f 6e20 272d 5465 2720 6361 7573 6573  ion '-Te' causes\n-00019830: 2074 6865 0a20 2020 2020 4575 726f 2073   the.     Euro s\n-00019840: 7461 6e64 6172 6420 646f 6375 6d65 6e74  tandard document\n-00019850: 2074 656d 706c 6174 6520 746f 2062 6520   template to be \n-00019860: 7573 6564 2e20 2041 2027 7027 2061 7070  used.  A 'p' app\n-00019870: 656e 6465 6420 746f 2061 6e79 0a20 2020  ended to any.   \n-00019880: 2020 6f66 2074 6865 7365 206f 7074 696f    of these optio\n-00019890: 6e73 2063 6175 7365 7320 7468 6520 7265  ns causes the re\n-000198a0: 7370 6563 7469 7665 2064 6566 6175 6c74  spective default\n-000198b0: 2027 5053 5472 6963 6b73 2720 646f 6375   'PSTricks' docu\n-000198c0: 6d65 6e74 0a20 2020 2020 7465 6d70 6c61  ment.     templa\n-000198d0: 7465 2074 6f20 6265 2070 7269 6e74 6564  te to be printed\n-000198e0: 2074 6f20 7374 616e 6461 7264 206f 7574   to standard out\n-000198f0: 7075 742e 2020 416e 2061 7070 656e 6465  put.  An appende\n-00019900: 6420 2750 2720 6973 2061 0a20 2020 2020  d 'P' is a.     \n-00019910: 7379 6e6f 6e79 6d2e 2020 416e 2061 7070  synonym.  An app\n-00019920: 656e 6465 6420 2754 2720 6361 7573 6573  ended 'T' causes\n-00019930: 2074 6865 2074 6865 2027 5469 6b5a 2f50   the the 'TikZ/P\n-00019940: 4746 2720 7465 6d70 6c61 7465 2074 6f20  GF' template to \n-00019950: 6265 0a20 2020 2020 7072 696e 7465 642e  be.     printed.\n-00019960: 2020 416e 2061 7070 656e 6465 6420 274c    An appended 'L\n-00019970: 2720 7072 696e 7473 2074 6865 204c 6154  ' prints the LaT\n-00019980: 6558 2076 6572 7369 6f6e 206f 6620 7468  eX version of th\n-00019990: 6520 646f 6375 6d65 6e74 0a20 2020 2020  e document.     \n-000199a0: 7465 6d70 6c61 7465 2c20 6120 7379 6e6f  template, a syno\n-000199b0: 6e79 6d20 666f 7220 7468 6520 6465 6661  nym for the defa\n-000199c0: 756c 742e 2020 4120 2743 2720 7072 696e  ult.  A 'C' prin\n-000199d0: 7473 2074 6865 2027 436f 6e54 6558 7427  ts the 'ConTeXt'\n-000199e0: 0a20 2020 2020 7465 6d70 6c61 7465 2e0a  .     template..\n-000199f0: 272d 6f27 0a20 2020 2020 5573 6520 276f  '-o'.     Use 'o\n-00019a00: 7574 7075 742e 7465 7827 2061 7320 7468  utput.tex' as th\n-00019a10: 6520 6f75 7470 7574 2066 696c 652e 2020  e output file.  \n-00019a20: 5468 6520 6465 6661 756c 7420 6973 2073  The default is s\n-00019a30: 7461 6e64 6172 640a 2020 2020 206f 7574  tandard.     out\n-00019a40: 7075 742e 0a27 2d44 270a 2020 2020 2044  put..'-D'.     D\n-00019a50: 6566 696e 6520 6120 7461 6720 666f 7220  efine a tag for \n-00019a60: 7075 7270 6f73 6573 206f 6620 7365 6c65  purposes of sele\n-00019a70: 6374 696e 6720 6465 6669 6e69 7469 6f6e  cting definition\n-00019a80: 2061 6c74 6572 6e61 7469 7665 732e 0a20   alternatives.. \n-00019a90: 2020 2020 2a4e 6f74 6520 4465 6669 6e69      *Note Defini\n-00019aa0: 7469 6f6e 733a 3a2e 2020 5468 6520 6465  tions::.  The de\n-00019ab0: 6669 6e69 7469 6f6e 2061 7070 6c69 6573  finition applies\n-00019ac0: 2066 6f72 2061 6c6c 2069 6e70 7574 2066   for all input f\n-00019ad0: 696c 6573 0a20 2020 2020 7468 6174 2066  iles.     that f\n-00019ae0: 6f6c 6c6f 7720 756e 6c65 7373 2074 6865  ollow unless the\n-00019af0: 2074 6167 2069 7320 756e 6465 6669 6e65   tag is undefine\n-00019b00: 6420 7769 7468 2027 2d55 272e 0a27 696e  d with '-U'..'in\n-00019b10: 7075 7469 2e73 6b27 0a20 2020 2020 496e  puti.sk'.     In\n-00019b20: 7075 7420 6669 6c65 732c 2072 6561 6420  put files, read \n-00019b30: 696e 2074 6865 2073 6571 7565 6e63 6520  in the sequence \n-00019b40: 7468 6579 2061 7265 2067 6976 656e 2e0a  they are given..\n-00019b50: 272d 5527 0a20 2020 2020 556e 2d64 6566  '-U'.     Un-def\n-00019b60: 696e 6520 6120 7461 6720 666f 7220 7075  ine a tag for pu\n-00019b70: 7270 6f73 6573 206f 6620 7365 6c65 6374  rposes of select\n-00019b80: 696e 6720 6465 6669 6e69 7469 6f6e 2061  ing definition a\n-00019b90: 6c74 6572 6e61 7469 7665 732e 0a0a 1f0a  lternatives.....\n-00019ba0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66  File: sketch.inf\n-00019bb0: 6f2c 2020 4e6f 6465 3a20 496e 7374 616c  o,  Node: Instal\n-00019bc0: 6c69 6e67 2073 6b65 7463 682c 2020 4e65  ling sketch,  Ne\n-00019bd0: 7874 3a20 496e 6465 7820 6f66 2073 796e  xt: Index of syn\n-00019be0: 7461 782c 2020 5072 6576 3a20 436f 6d6d  tax,  Prev: Comm\n-00019bf0: 616e 6420 6c69 6e65 2c20 2055 703a 2054  and line,  Up: T\n-00019c00: 6f70 0a0a 3620 4275 696c 6469 6e67 2061  op..6 Building a\n-00019c10: 6e64 2069 6e73 7461 6c6c 696e 6720 2773  nd installing 's\n-00019c20: 6b65 7463 6827 0a2a 2a2a 2a2a 2a2a 2a2a  ketch'.*********\n+00017de0: 2d2d 2d2d 2d2d 0a0a 2753 6b65 7463 6827  ------..'Sketch'\n+00017df0: 2075 7365 7320 7468 6520 2264 6570 7468   uses the \"depth\n+00017e00: 2073 6f72 7420 616c 676f 7269 7468 6d22   sort algorithm\"\n+00017e10: 2066 6f72 2068 6964 6465 6e20 7375 7266   for hidden surf\n+00017e20: 6163 6520 7265 6d6f 7661 6c2e 0a54 6869  ace removal..Thi\n+00017e30: 7320 6973 2061 2076 6572 7920 6f6c 6420  s is a very old \n+00017e40: 7465 6368 6e69 7175 6520 6475 6520 746f  technique due to\n+00017e50: 204e 6577 656c 6c2e 2831 2920 2049 7420   Newell.(1)  It \n+00017e60: 6973 2067 656e 6572 616c 6c79 2072 6567  is generally reg\n+00017e70: 6172 6465 640a 6173 2074 6f6f 2073 6c6f  arded.as too slo\n+00017e80: 7720 666f 7220 7265 616c 2074 696d 6520  w for real time \n+00017e90: 6772 6170 6869 6373 2c20 6275 7420 6974  graphics, but it\n+00017ea0: 2069 7320 6964 6561 6c20 666f 7220 6f75   is ideal for ou\n+00017eb0: 7220 7075 7270 6f73 650a 7768 6572 6520  r purpose.where \n+00017ec0: 7370 6565 6420 6973 206e 6f74 2076 6572  speed is not ver\n+00017ed0: 7920 696d 706f 7274 616e 742e 2832 290a  y important.(2).\n+00017ee0: 0a20 2020 5468 6520 6465 7074 6820 736f  .   The depth so\n+00017ef0: 7274 2061 6c67 6f72 6974 686d 206d 6572  rt algorithm mer\n+00017f00: 656c 7920 736f 7274 7320 6f62 6a65 6374  ely sorts object\n+00017f10: 7320 6f6e 2061 206b 6579 206f 6620 696e  s on a key of in\n+00017f20: 6372 6561 7369 6e67 0a7a 2d63 6f6f 7264  creasing.z-coord\n+00017f30: 696e 6174 652c 2065 7175 6976 616c 656e  inate, equivalen\n+00017f40: 7420 746f 2064 6563 7265 6173 696e 6720  t to decreasing \n+00017f50: 6465 7074 682e 2020 4f62 6a65 6374 7320  depth.  Objects \n+00017f60: 6172 6520 7468 656e 2064 7261 776e 2069  are then drawn i\n+00017f70: 6e0a 7468 6520 736f 7274 6564 2073 6571  n.the sorted seq\n+00017f80: 7565 6e63 6520 736f 2074 6861 7420 7468  uence so that th\n+00017f90: 6f73 6520 6174 2074 6865 2072 6561 7220  ose at the rear \n+00017fa0: 6f66 2074 6865 2073 6365 6e65 2061 7265  of the scene are\n+00017fb0: 0a6f 7665 7277 7269 7474 656e 2062 7920  .overwritten by \n+00017fc0: 7468 6f73 6520 636c 6f73 6572 2074 6f20  those closer to \n+00017fd0: 7468 6520 7669 6577 6572 2e20 2053 696e  the viewer.  Sin\n+00017fe0: 6365 2074 6869 7320 6973 2061 6c73 6f20  ce this is also \n+00017ff0: 686f 7720 6f69 6c0a 7061 696e 7465 7273  how oil.painters\n+00018000: 2070 7261 6374 6963 6520 7468 6569 7220   practice their \n+00018010: 6172 742c 2064 6570 7468 2073 6f72 7420  art, depth sort \n+00018020: 6973 2073 6f6d 6574 696d 6573 2063 616c  is sometimes cal\n+00018030: 6c65 6420 2274 6865 0a70 6169 6e74 6572  led \"the.painter\n+00018040: 2773 2061 6c67 6f72 6974 686d 2e22 0a0a  's algorithm.\"..\n+00018050: 2020 2049 6e20 736f 6d65 2063 6173 6573     In some cases\n+00018060: 2069 7420 6973 2069 6d70 6f73 7369 626c   it is impossibl\n+00018070: 6520 746f 2073 7472 6963 746c 7920 6f72  e to strictly or\n+00018080: 6465 7220 706f 6c79 676f 6e73 2061 6363  der polygons acc\n+00018090: 6f72 6469 6e67 0a74 6f20 6465 7074 682e  ording.to depth.\n+000180a0: 2020 4d6f 7265 6f76 6572 2c20 6576 656e    Moreover, even\n+000180b0: 2069 6620 6120 636f 7272 6563 7420 6465   if a correct de\n+000180c0: 7074 6820 6f72 6465 7269 6e67 2065 7869  pth ordering exi\n+000180d0: 7374 732c 2074 6865 0a63 6f6d 7075 7461  sts, the.computa\n+000180e0: 7469 6f6e 206e 6565 6465 6420 746f 2066  tion needed to f\n+000180f0: 696e 6420 6974 206d 6179 2062 6520 746f  ind it may be to\n+00018100: 6f20 636f 6d70 6c65 7820 616e 6420 736c  o complex and sl\n+00018110: 6f77 2e20 2049 6e20 7468 6573 650a 6361  ow.  In these.ca\n+00018120: 7365 732c 2027 736b 6574 6368 2720 7370  ses, 'sketch' sp\n+00018130: 6c69 7473 206f 6e65 206f 7220 6d6f 7265  lits one or more\n+00018140: 2070 6f6c 7967 6f6e 7320 696e 746f 2070   polygons into p\n+00018150: 6965 6365 732e 2020 5468 650a 6578 7065  ieces.  The.expe\n+00018160: 6374 6174 696f 6e20 6973 2074 6861 7420  ctation is that \n+00018170: 7468 6520 6e65 772c 2073 6d61 6c6c 6572  the new, smaller\n+00018180: 2070 6f6c 7967 6f6e 7320 7769 6c6c 2062   polygons will b\n+00018190: 6520 7369 6d70 6c65 7220 746f 206f 7264  e simpler to ord\n+000181a0: 6572 2e0a 2753 6b65 7463 6827 2075 7365  er..'Sketch' use\n+000181b0: 7320 6120 4253 5020 2862 696e 6172 7920  s a BSP (binary \n+000181c0: 7370 6163 6520 7061 7274 6974 696f 6e29  space partition)\n+000181d0: 2074 6f20 6861 6e64 6c65 2074 6865 2073   to handle the s\n+000181e0: 706c 6974 7469 6e67 0a6f 7065 7261 7469  plitting.operati\n+000181f0: 6f6e 2e0a 0a2a 204d 656e 753a 0a0a 2a20  on...* Menu:..* \n+00018200: 5374 6174 6973 7469 6373 3a3a 2020 2020  Statistics::    \n+00018210: 2020 2020 2020 2020 2020 2020 2020 5065                Pe\n+00018220: 7266 6f72 6d61 6e63 6520 6e75 6d62 6572  rformance number\n+00018230: 7320 6f6e 2064 6570 7468 2073 6f72 742e  s on depth sort.\n+00018240: 0a2a 2042 7567 7320 616e 6420 616e 6f6d  .* Bugs and anom\n+00018250: 616c 6965 733a 3a20 2020 2020 2020 2020  alies::         \n+00018260: 2049 6d70 6572 6665 6374 696f 6e73 2069   Imperfections i\n+00018270: 6e20 7468 6973 2069 6d70 6c65 6d65 6e74  n this implement\n+00018280: 6174 696f 6e2e 0a0a 2020 202d 2d2d 2d2d  ation...   -----\n+00018290: 2d2d 2d2d 2d20 466f 6f74 6e6f 7465 7320  ----- Footnotes \n+000182a0: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2020 2028  ----------..   (\n+000182b0: 3129 204e 6577 656c 6c2c 204d 2e45 2e2c  1) Newell, M.E.,\n+000182c0: 2052 2e47 2e20 4e65 7765 6c6c 2c20 616e   R.G. Newell, an\n+000182d0: 6420 542e 4c2e 2053 616e 6368 612c 2041  d T.L. Sancha, A\n+000182e0: 2073 6f6c 7574 696f 6e20 746f 2074 6865   solution to the\n+000182f0: 0a68 6964 6465 6e20 7375 7266 6163 6520  .hidden surface \n+00018300: 7072 6f62 6c65 6d2e 2020 5072 6f63 6565  problem.  Procee\n+00018310: 6469 6e67 7320 6f66 2074 6865 2041 434d  dings of the ACM\n+00018320: 2061 6e6e 7561 6c20 636f 6e66 6572 656e   annual conferen\n+00018330: 6365 202d 0a56 6f6c 756d 6520 312c 2070  ce -.Volume 1, p\n+00018340: 6167 6520 3434 332d 3435 302c 2041 434d  age 443-450, ACM\n+00018350: 2050 7265 7373 2c20 3139 3732 2e0a 0a20   Press, 1972... \n+00018360: 2020 2832 2920 5765 2068 6176 6520 7275    (2) We have ru\n+00018370: 6e20 2773 6b65 7463 6827 206f 6e20 7468  n 'sketch' on th\n+00018380: 6520 6661 6d6f 7573 2053 7461 6e66 6f72  e famous Stanfor\n+00018390: 6420 4275 6e6e 792c 2077 6869 6368 2063  d Bunny, which c\n+000183a0: 6f6e 7369 7374 730a 6f66 206e 6561 726c  onsists.of nearl\n+000183b0: 7920 3730 2c30 3030 2074 7269 616e 676c  y 70,000 triangl\n+000183c0: 6573 2e20 2052 756e 2074 696d 6520 7761  es.  Run time wa\n+000183d0: 7320 6162 6f75 7420 3620 7365 636f 6e64  s about 6 second\n+000183e0: 732e 2020 4d6f 7374 206f 6620 7468 6973  s.  Most of this\n+000183f0: 0a77 6173 2073 7065 6e74 2077 7269 7469  .was spent writi\n+00018400: 6e67 2074 6865 206f 7574 7075 7420 6669  ng the output fi\n+00018410: 6c65 2072 6174 6865 7220 7468 616e 2069  le rather than i\n+00018420: 6e20 7468 6520 6869 6464 656e 2073 7572  n the hidden sur\n+00018430: 6661 6365 0a61 6c67 6f72 6974 686d 2e20  face.algorithm. \n+00018440: 204c 6154 6558 2074 6f6f 6b20 6d75 6368   LaTeX took much\n+00018450: 206c 6f6e 6765 7220 746f 2070 726f 6365   longer to proce\n+00018460: 7373 2074 6865 2072 6573 756c 7469 6e67  ss the resulting\n+00018470: 2027 5053 5472 6963 6b73 270a 636f 6465   'PSTricks'.code\n+00018480: 2e20 2054 6865 206f 6276 696f 7573 2063  .  The obvious c\n+00018490: 6f6e 636c 7573 696f 6e20 6973 2074 6861  onclusion is tha\n+000184a0: 7420 7468 6520 7370 6565 6420 6f66 2074  t the speed of t\n+000184b0: 6865 2064 6570 7468 2073 6f72 740a 616c  he depth sort.al\n+000184c0: 676f 7269 7468 6d20 6973 206e 6f74 2061  gorithm is not a\n+000184d0: 2077 6f72 7279 2e0a 0a1f 0a46 696c 653a   worry.....File:\n+000184e0: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n+000184f0: 6f64 653a 2053 7461 7469 7374 6963 732c  ode: Statistics,\n+00018500: 2020 4e65 7874 3a20 4275 6773 2061 6e64    Next: Bugs and\n+00018510: 2061 6e6f 6d61 6c69 6573 2c20 2050 7265   anomalies,  Pre\n+00018520: 763a 2048 6964 6465 6e20 7375 7266 6163  v: Hidden surfac\n+00018530: 6520 7265 6d6f 7661 6c2c 2020 5570 3a20  e removal,  Up: \n+00018540: 4869 6464 656e 2073 7572 6661 6365 2072  Hidden surface r\n+00018550: 656d 6f76 616c 0a0a 342e 342e 332e 3120  emoval..4.4.3.1 \n+00018560: 5374 6174 6973 7469 6373 0a2e 2e2e 2e2e  Statistics......\n+00018570: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a46  ...............F\n+00018580: 6f72 2074 6865 2063 7572 696f 7573 2c20  or the curious, \n+00018590: 2773 6b65 7463 6827 2077 7269 7465 7320  'sketch' writes \n+000185a0: 6f6e 6520 6c69 6e65 206f 6620 6465 7074  one line of dept\n+000185b0: 6820 736f 7274 2073 7461 7469 7374 6963  h sort statistic\n+000185c0: 732e 0a48 6572 6520 6973 2061 6e20 6578  s..Here is an ex\n+000185d0: 616d 706c 6520 666f 7220 6120 6c61 7267  ample for a larg\n+000185e0: 6520 636f 6c6c 6563 7469 6f6e 206f 6620  e collection of \n+000185f0: 7472 6961 6e67 6c65 732e 0a20 2072 656d  triangles..  rem\n+00018600: 6172 6b2c 206e 6f64 653d 3334 3832 3420  ark, node=34824 \n+00018610: 7072 6f62 653d 3538 312e 3920 7377 6170  probe=581.9 swap\n+00018620: 3d35 2073 706c 6974 3d32 2028 696e 3d34  =5 split=2 (in=4\n+00018630: 206f 7574 3d36 2920 6f6c 733d 3234 3835   out=6) ols=2485\n+00018640: 312f 300a 4974 206d 6561 6e73 2074 6861  1/0.It means tha\n+00018650: 7420 3334 2c38 3234 206f 626a 6563 7473  t 34,824 objects\n+00018660: 2077 6572 6520 6465 7074 6820 736f 7274   were depth sort\n+00018670: 6564 2061 6674 6572 2063 756c 6c69 6e67  ed after culling\n+00018680: 2e20 2046 6f72 2065 6163 682c 0a61 6e20  .  For each,.an \n+00018690: 6176 6572 6167 6520 6f66 2035 3831 2e39  average of 581.9\n+000186a0: 206f 7468 6572 7320 6861 6420 746f 2062   others had to b\n+000186b0: 6520 6368 6563 6b65 6420 746f 2065 6e73  e checked to ens\n+000186c0: 7572 6520 7468 6174 2074 6865 2069 6e69  ure that the ini\n+000186d0: 7469 616c 2c0a 6170 7072 6f78 696d 6174  tial,.approximat\n+000186e0: 6520 6f72 6465 7269 6e67 2077 6173 2063  e ordering was c\n+000186f0: 6f72 7265 6374 2e20 2041 6d6f 6e67 2061  orrect.  Among a\n+00018700: 6c6c 2074 6865 7365 2063 6865 636b 732c  ll these checks,\n+00018710: 206f 6e6c 7920 350a 7265 7375 6c74 6564   only 5.resulted\n+00018720: 2069 6e20 7377 6170 7320 746f 2072 656f   in swaps to reo\n+00018730: 7264 6572 2074 6865 2069 6e69 7469 616c  rder the initial\n+00018740: 2073 6f72 742e 2020 496e 2074 776f 2063   sort.  In two c\n+00018750: 6173 6573 2c20 6120 636f 7272 6563 740a  ases, a correct.\n+00018760: 6f72 6465 7269 6e67 2063 6f75 6c64 206e  ordering could n\n+00018770: 6f74 2062 6520 6465 7465 726d 696e 6564  ot be determined\n+00018780: 2c20 736f 2062 696e 6172 7920 7370 6163  , so binary spac\n+00018790: 6520 7061 7274 6974 696f 6e73 2077 6572  e partitions wer\n+000187a0: 650a 636f 6e73 7472 7563 7465 6420 666f  e.constructed fo\n+000187b0: 7220 7370 6c69 7474 696e 672e 2020 4120  r splitting.  A \n+000187c0: 746f 7461 6c20 6f66 2034 206f 626a 6563  total of 4 objec\n+000187d0: 7473 2028 7472 6961 6e67 6c65 7320 696e  ts (triangles in\n+000187e0: 2074 6869 730a 6361 7365 2920 7765 7265   this.case) were\n+000187f0: 2069 6e73 6572 7465 6420 696e 2074 6865   inserted in the\n+00018800: 2070 6172 7469 7469 6f6e 732c 2061 6e64   partitions, and\n+00018810: 2036 2070 6f6c 7967 6f6e 7320 7765 7265   6 polygons were\n+00018820: 2070 726f 6475 6365 642e 0a46 696e 616c   produced..Final\n+00018830: 6c79 2c20 3234 2c38 3531 2022 6c61 7374  ly, 24,851 \"last\n+00018840: 2072 6573 6f72 7422 2070 6f6c 7967 6f6e   resort\" polygon\n+00018850: 206f 7665 726c 6170 2063 6865 636b 7320   overlap checks \n+00018860: 7765 7265 2070 6572 666f 726d 6564 0a61  were performed.a\n+00018870: 6674 6572 2073 696d 706c 6572 2c20 6661  fter simpler, fa\n+00018880: 7374 6572 2063 6865 636b 7320 6661 696c  ster checks fail\n+00018890: 6564 2074 6f20 7969 656c 6420 636f 6e63  ed to yield conc\n+000188a0: 6c75 7369 7665 2072 6573 756c 7473 2e20  lusive results. \n+000188b0: 2054 6865 0a66 696e 616c 202f 3020 6973   The.final /0 is\n+000188c0: 2066 6f72 206c 696e 652d 706f 6c79 676f   for line-polygo\n+000188d0: 6e20 6f76 6572 6c61 7020 6368 6563 6b73  n overlap checks\n+000188e0: 2e20 2046 6f72 2063 6f6d 7061 7269 736f  .  For compariso\n+000188f0: 6e2c 2074 6865 0a73 7461 7469 7374 6963  n, the.statistic\n+00018900: 7320 666f 7220 7468 6520 6c61 7374 2066  s for the last f\n+00018910: 6967 7572 6520 696e 202a 6e6f 7465 204f  igure in *note O\n+00018920: 7665 7276 6965 773a 3a20 666f 6c6c 6f77  verview:: follow\n+00018930: 2e0a 2020 7265 6d61 726b 2c20 6e6f 6465  ..  remark, node\n+00018940: 3d32 3720 7072 6f62 653d 3134 2e36 2073  =27 probe=14.6 s\n+00018950: 7761 703d 3336 2073 706c 6974 3d31 3520  wap=36 split=15 \n+00018960: 2869 6e3d 3330 206f 7574 3d34 3529 206f  (in=30 out=45) o\n+00018970: 6c73 3d30 2f36 390a 4e6f 7465 2074 6861  ls=0/69.Note tha\n+00018980: 7420 7468 6572 6520 7761 7320 7072 6f70  t there was prop\n+00018990: 6f72 7469 6f6e 616c 6c79 206d 7563 6820  ortionally much \n+000189a0: 6d6f 7265 2073 7761 7070 696e 6720 616e  more swapping an\n+000189b0: 6420 7370 6c69 7474 696e 670a 6163 7469  d splitting.acti\n+000189c0: 7669 7479 2069 6e20 7468 6973 2068 6967  vity in this hig\n+000189d0: 686c 7920 636f 6e6e 6563 7465 6420 7363  hly connected sc\n+000189e0: 656e 652e 0a0a 1f0a 4669 6c65 3a20 736b  ene.....File: sk\n+000189f0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465  etch.info,  Node\n+00018a00: 3a20 4275 6773 2061 6e64 2061 6e6f 6d61  : Bugs and anoma\n+00018a10: 6c69 6573 2c20 2050 7265 763a 2053 7461  lies,  Prev: Sta\n+00018a20: 7469 7374 6963 732c 2020 5570 3a20 4869  tistics,  Up: Hi\n+00018a30: 6464 656e 2073 7572 6661 6365 2072 656d  dden surface rem\n+00018a40: 6f76 616c 0a0a 342e 342e 332e 3220 4275  oval..4.4.3.2 Bu\n+00018a50: 6773 2061 6e64 2061 6e6f 6d61 6c69 6573  gs and anomalies\n+00018a60: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e  ................\n+00018a70: 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a50 6f6c  .............Pol\n+00018a80: 7967 6f6e 2061 6e64 206c 696e 6520 7370  ygon and line sp\n+00018a90: 6c69 7474 696e 6720 6361 6e20 626f 7468  litting can both\n+00018aa0: 2063 6175 7365 2061 6e6f 6d61 6c69 6573   cause anomalies\n+00018ab0: 2069 6e20 7468 6520 6f75 7470 7574 2e0a   in the output..\n+00018ac0: 2750 5354 7269 636b 7327 2064 6173 6820  'PSTricks' dash \n+00018ad0: 7061 7474 6572 6e73 2c20 7370 6563 6966  patterns, specif\n+00018ae0: 6965 6420 7769 7468 2027 6c69 6e65 7374  ied with 'linest\n+00018af0: 796c 653d 6461 7368 6564 272c 2063 616e  yle=dashed', can\n+00018b00: 2062 650a 6469 7372 7570 7465 6420 6279   be.disrupted by\n+00018b10: 2073 706c 6974 7469 6e67 2e20 2054 6869   splitting.  Thi\n+00018b20: 7320 6f63 6375 7273 2077 6865 6e20 7468  s occurs when th\n+00018b30: 6520 6465 7074 6820 736f 7274 2067 6976  e depth sort giv\n+00018b40: 6573 2075 7020 746f 6f0a 6561 726c 7920  es up too.early \n+00018b50: 616e 6420 7370 6c69 7473 2061 206c 696e  and splits a lin\n+00018b60: 6520 7768 6572 6520 6974 2069 7320 6e6f  e where it is no\n+00018b70: 7420 7265 616c 6c79 206e 6563 6573 7361  t really necessa\n+00018b80: 7279 2e20 2041 2077 6f72 6b61 726f 756e  ry.  A workaroun\n+00018b90: 640a 6973 2074 6f20 7573 6520 6772 6179  d.is to use gray\n+00018ba0: 206f 7220 6669 6e65 6c79 2064 6f74 7465   or finely dotte\n+00018bb0: 6420 6c69 6e65 7320 696e 7374 6561 642e  d lines instead.\n+00018bc0: 2020 4966 2079 6f75 7220 6472 6177 696e    If your drawin\n+00018bd0: 6720 6973 0a73 6d61 6c6c 2c20 796f 7520  g is.small, you \n+00018be0: 6361 6e20 616c 736f 2065 6469 7420 7468  can also edit th\n+00018bf0: 6520 2773 6b65 7463 6827 206f 7574 7075  e 'sketch' outpu\n+00018c00: 7420 6279 2068 616e 6420 746f 206d 6572  t by hand to mer\n+00018c10: 6765 2074 6865 2070 6965 6365 730a 6f66  ge the pieces.of\n+00018c20: 2074 6865 206f 6666 656e 6469 6e67 206c   the offending l\n+00018c30: 696e 652e 0a0a 2020 2041 6e6f 7468 6572  ine...   Another\n+00018c40: 2061 6e6f 6d61 6c79 2069 7320 7469 6e79   anomaly is tiny\n+00018c50: 2028 6f72 2069 6e20 6465 6765 6e65 7261   (or in degenera\n+00018c60: 7465 2063 6173 6573 206e 6f74 2d73 6f2d  te cases not-so-\n+00018c70: 7469 6e79 2920 6e6f 7463 6865 730a 696e  tiny) notches.in\n+00018c80: 2074 6865 206c 696e 6573 2074 6861 7420   the lines that \n+00018c90: 626f 7264 6572 2073 706c 6974 2070 6f6c  border split pol\n+00018ca0: 7967 6f6e 732e 2020 5468 6573 6520 6465  ygons.  These de\n+00018cb0: 7269 7665 2066 726f 6d20 7468 6520 7761  rive from the wa\n+00018cc0: 7920 6561 6368 0a70 6f6c 7967 6f6e 2069  y each.polygon i\n+00018cd0: 7320 7061 696e 7465 643a 2066 6972 7374  s painted: first\n+00018ce0: 2c20 616c 6c20 7069 7865 6c73 2077 6974  , all pixels wit\n+00018cf0: 6869 6e20 7468 6520 626f 756e 6461 7279  hin the boundary\n+00018d00: 2061 7265 2022 6669 6c6c 6564 220a 7769   are \"filled\".wi\n+00018d10: 7468 2063 6f6c 6f72 2028 7065 7268 6170  th color (perhap\n+00018d20: 7320 7768 6974 6529 2c20 7468 656e 2074  s white), then t\n+00018d30: 6865 2073 616d 6520 626f 756e 6461 7279  he same boundary\n+00018d40: 2069 7320 2273 7472 6f6b 6564 2220 2861   is \"stroked\" (a\n+00018d50: 0a50 6f73 7473 6372 6970 7420 7465 726d  .Postscript term\n+00018d60: 2920 7769 7468 2061 206c 696e 652e 2020  ) with a line.  \n+00018d70: 5468 6520 7265 7375 6c74 2069 7320 7468  The result is th\n+00018d80: 6174 2068 616c 6620 7468 6520 6c69 6e65  at half the line\n+00018d90: 206c 6965 730a 696e 7369 6465 2074 6865   lies.inside the\n+00018da0: 2062 6f75 6e64 6172 7920 616e 6420 6861   boundary and ha\n+00018db0: 6c66 206f 7574 7369 6465 2c20 7768 696c  lf outside, whil\n+00018dc0: 6520 7468 6520 5061 696e 7465 7227 7320  e the Painter's \n+00018dd0: 616c 676f 7269 7468 6d0a 6173 7375 6d65  algorithm.assume\n+00018de0: 7320 7468 6520 706f 6c79 676f 6e20 6c69  s the polygon li\n+00018df0: 6573 2065 6e74 6972 656c 7920 7769 7468  es entirely with\n+00018e00: 696e 2069 7473 2062 6f75 6e64 6172 792e  in its boundary.\n+00018e10: 2020 5468 6520 6e6f 7463 6865 7320 6172    The notches ar\n+00018e20: 650a 6475 6520 746f 206f 6e65 2070 6f6c  e.due to one pol\n+00018e30: 7967 6f6e 2066 696c 6c20 6f70 6572 6174  ygon fill operat\n+00018e40: 696f 6e20 6f76 6572 7772 6974 696e 6720  ion overwriting \n+00018e50: 7468 6520 616c 7265 6164 792d 6472 6177  the already-draw\n+00018e60: 6e20 696e 7369 6465 0a6f 6620 7468 6520  n inside.of the \n+00018e70: 626f 7264 6572 206f 6620 616e 6f74 6865  border of anothe\n+00018e80: 7220 706f 6c79 676f 6e2e 2831 2920 204f  r polygon.(1)  O\n+00018e90: 6e65 2077 6f72 6b61 726f 756e 6420 6973  ne workaround is\n+00018ea0: 2074 6f20 6d61 6b65 2062 6f72 6465 720a   to make border.\n+00018eb0: 6c69 6e65 7320 7665 7279 2074 6869 6e2e  lines very thin.\n+00018ec0: 2020 496e 2066 6163 7420 276c 696e 6577    In fact 'linew\n+00018ed0: 6964 7468 3d30 7074 2720 6973 2067 7561  idth=0pt' is gua\n+00018ee0: 7261 6e74 6565 6420 746f 2065 6c69 6d69  ranteed to elimi\n+00018ef0: 6e61 7465 0a74 6869 7320 7072 6f62 6c65  nate.this proble\n+00018f00: 6d2c 2074 686f 7567 6820 7468 6973 2072  m, though this r\n+00018f10: 6573 756c 7473 2069 6e20 7468 6520 7468  esults in the th\n+00018f20: 696e 6e65 7374 206c 696e 6520 796f 7572  innest line your\n+00018f30: 206f 7574 7075 740a 6465 7669 6365 2063   output.device c\n+00018f40: 616e 2064 7261 772c 2077 6869 6368 2069  an draw, which i\n+00018f50: 7320 7573 7561 6c6c 7920 746f 6f20 7468  s usually too th\n+00018f60: 696e 2e20 2059 6f75 206d 6967 6874 2067  in.  You might g\n+00018f70: 6574 206c 7563 6b79 2062 790a 6d65 7265  et lucky by.mere\n+00018f80: 6c79 2072 656f 7264 6572 696e 6720 7468  ly reordering th\n+00018f90: 696e 6773 2069 6e20 7468 6520 696e 7075  ings in the inpu\n+00018fa0: 7420 6669 6c65 2c20 7768 6963 6820 6973  t file, which is\n+00018fb0: 206c 696b 656c 7920 746f 206d 6f76 6520   likely to move \n+00018fc0: 7468 650a 7370 6c69 7473 2074 6f20 6469  the.splits to di\n+00018fd0: 6666 6572 656e 7420 706c 6163 6573 2e20  fferent places. \n+00018fe0: 2054 6865 206f 6e6c 7920 7375 7265 2d66   The only sure-f\n+00018ff0: 6972 6520 736f 6c75 7469 6f6e 2069 7320  ire solution is \n+00019000: 7072 6574 7479 0a74 6572 7269 626c 653a  pretty.terrible:\n+00019010: 2063 7573 746f 6d20 6669 7420 2773 7065   custom fit 'spe\n+00019020: 6369 616c 2720 6f76 6572 6c61 7920 6c69  cial' overlay li\n+00019030: 6e65 7320 2877 6974 6820 275c 7073 6c69  nes (with '\\psli\n+00019040: 6e65 2729 2074 6f20 636f 7665 720a 7468  ne') to cover.th\n+00019050: 6520 6e6f 7463 6865 732e 0a0a 2020 2050  e notches...   P\n+00019060: 6f6c 7967 6f6e 2073 706c 6974 7469 6e67  olygon splitting\n+00019070: 2061 6c73 6f20 6272 6561 6b73 2027 5053   also breaks 'PS\n+00019080: 5472 6963 6b73 2720 6861 7463 6820 7061  Tricks' hatch pa\n+00019090: 7474 6572 6e73 2e20 2054 6865 206f 6e6c  tterns.  The onl\n+000190a0: 790a 6b6e 6f77 6e20 776f 726b 6172 6f75  y.known workarou\n+000190b0: 6e64 2069 7320 746f 2073 7562 7374 6974  nd is to substit\n+000190c0: 7574 6520 6120 736f 6c69 6420 6669 6c6c  ute a solid fill\n+000190d0: 2066 6f72 2074 6865 2068 6174 6368 2e0a   for the hatch..\n+000190e0: 0a20 2020 2d2d 2d2d 2d2d 2d2d 2d2d 2046  .   ---------- F\n+000190f0: 6f6f 746e 6f74 6573 202d 2d2d 2d2d 2d2d  ootnotes -------\n+00019100: 2d2d 2d0a 0a20 2020 2831 2920 4920 6b6e  ---..   (1) I kn\n+00019110: 6f77 2068 6f77 2074 6f20 6669 7820 7468  ow how to fix th\n+00019120: 6973 2070 726f 626c 656d 2c20 6275 7420  is problem, but \n+00019130: 4920 646f 6e27 7420 6c69 6b65 206d 7920  I don't like my \n+00019140: 736f 6c75 7469 6f6e 2c20 616e 640a 4927  solution, and.I'\n+00019150: 6d20 696e 7465 7265 7374 6564 2069 6e20  m interested in \n+00019160: 796f 7572 732e 0a0a 1f0a 4669 6c65 3a20  yours.....File: \n+00019170: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f  sketch.info,  No\n+00019180: 6465 3a20 436f 6d6d 616e 6420 6c69 6e65  de: Command line\n+00019190: 2c20 204e 6578 743a 2049 6e73 7461 6c6c  ,  Next: Install\n+000191a0: 696e 6720 736b 6574 6368 2c20 2050 7265  ing sketch,  Pre\n+000191b0: 763a 2042 7569 6c64 696e 6720 6120 6472  v: Building a dr\n+000191c0: 6177 696e 672c 2020 5570 3a20 546f 700a  awing,  Up: Top.\n+000191d0: 0a35 2043 6f6d 6d61 6e64 206c 696e 650a  .5 Command line.\n+000191e0: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 0a0a  **************..\n+000191f0: 2a53 796e 6f70 7369 733a 2a0a 2020 2020  *Synopsis:*.    \n+00019200: 2073 6b65 7463 6820 5b2d 685d 5b2d 5620   sketch [-h][-V \n+00019210: 782e 795d 5b2d 765d 5b2d 625d 5b2d 645d  x.y][-v][-b][-d]\n+00019220: 5b74 2064 6f63 746d 705d 5b2d 545b 757c  [t doctmp][-T[u|\n+00019230: 655d 5b70 5b50 7c54 5d5b 4c7c 435d 5d5d  e][p[P|T][L|C]]]\n+00019240: 5b2d 6f20 6f75 7470 7574 2e74 6578 5d0a  [-o output.tex].\n+00019250: 2020 2020 2020 205b 2d44 2054 4147 202e         [-D TAG .\n+00019260: 2e2e 5d20 696e 7075 7431 2e73 6b20 5b2d  ..] input1.sk [-\n+00019270: 5520 5441 4720 2e2e 2e5d 2069 6e70 7574  U TAG ...] input\n+00019280: 322e 736b 202e 2e2e 0a0a 2a44 6573 6372  2.sk .....*Descr\n+00019290: 6970 7469 6f6e 2a20 5072 6f63 6573 7365  iption* Processe\n+000192a0: 7320 7468 6520 2773 6b65 7463 6827 2069  s the 'sketch' i\n+000192b0: 6e70 7574 2066 696c 6573 2069 6e20 6f72  nput files in or\n+000192c0: 6465 7220 746f 2070 726f 6475 6365 0a27  der to produce.'\n+000192d0: 5053 5472 6963 6b73 2720 6f75 7470 7574  PSTricks' output\n+000192e0: 2063 6f64 6520 7375 6974 6162 6c65 2066   code suitable f\n+000192f0: 6f72 2069 6e63 6c75 7369 6f6e 2069 6e20  or inclusion in \n+00019300: 6120 5465 5820 6f72 204c 6154 6558 0a64  a TeX or LaTeX.d\n+00019310: 6f63 756d 656e 742e 0a0a 2a4f 7074 696f  ocument...*Optio\n+00019320: 6e73 3a2a 0a27 2d68 270a 2020 2020 2050  ns:*.'-h'.     P\n+00019330: 7269 6e74 2061 2073 686f 7274 2063 6174  rint a short cat\n+00019340: 616c 6f67 206f 6620 6f70 7469 6f6e 732e  alog of options.\n+00019350: 0a27 2d56 270a 2020 2020 2053 6574 2074  .'-V'.     Set t\n+00019360: 6865 2027 5053 5472 6963 6b73 2720 7665  he 'PSTricks' ve\n+00019370: 7273 696f 6e20 6173 7375 6d65 6420 666f  rsion assumed fo\n+00019380: 7220 6f75 7470 7574 2070 7572 706f 7365  r output purpose\n+00019390: 7320 746f 2027 782e 7927 2c0a 2020 2020  s to 'x.y',.    \n+000193a0: 2066 6f72 2065 7861 6d70 6c65 2031 2e31   for example 1.1\n+000193b0: 392e 2020 5573 7561 6c6c 7920 6e65 6564  9.  Usually need\n+000193c0: 6564 206f 6e6c 7920 6966 2079 6f75 7220  ed only if your \n+000193d0: 2750 5354 7269 636b 7327 2069 7320 6f6c  'PSTricks' is ol\n+000193e0: 640a 2020 2020 2063 6f6d 7061 7265 6420  d.     compared \n+000193f0: 746f 2079 6f75 7220 2773 6b65 7463 6827  to your 'sketch'\n+00019400: 2e20 2055 7365 2027 2d76 2720 746f 2073  .  Use '-v' to s\n+00019410: 6565 2077 6861 7420 2773 6b65 7463 6827  ee what 'sketch'\n+00019420: 2061 7373 756d 6573 0a20 2020 2020 6279   assumes.     by\n+00019430: 2064 6566 6175 6c74 2e0a 272d 7627 0a20   default..'-v'. \n+00019440: 2020 2020 5072 696e 7420 7665 7273 696f      Print versio\n+00019450: 6e20 696e 666f 726d 6174 696f 6e20 746f  n information to\n+00019460: 2073 7461 6e64 6172 6420 6f75 7470 7574   standard output\n+00019470: 2c20 696e 636c 7564 696e 6720 7468 6520  , including the \n+00019480: 7665 7273 696f 6e0a 2020 2020 206f 6620  version.     of \n+00019490: 2750 5354 7269 636b 7327 2061 7373 756d  'PSTricks' assum\n+000194a0: 6564 2066 6f72 206f 7574 7075 7420 2863  ed for output (c\n+000194b0: 616e 2062 6520 6368 616e 6765 6420 7769  an be changed wi\n+000194c0: 7468 2027 2d56 2720 6162 6f76 6529 2e0a  th '-V' above)..\n+000194d0: 272d 6227 0a20 2020 2020 5573 6520 6120  '-b'.     Use a \n+000194e0: 4253 5020 282a 4e6f 7465 2048 6964 6465  BSP (*Note Hidde\n+000194f0: 6e20 7375 7266 6163 6520 7265 6d6f 7661  n surface remova\n+00019500: 6c3a 3a2e 2920 2066 6f72 205f 616c 6c5f  l::.)  for _all_\n+00019510: 2068 6964 6465 6e0a 2020 2020 2073 7572   hidden.     sur\n+00019520: 6661 6365 2072 656d 6f76 616c 2072 6174  face removal rat\n+00019530: 6865 7220 7468 616e 2074 6865 2064 6566  her than the def\n+00019540: 6175 6c74 2c20 7768 6963 6820 6973 2074  ault, which is t\n+00019550: 6865 2064 6570 7468 2073 6f72 740a 2020  he depth sort.  \n+00019560: 2020 2061 6c67 6f72 6974 686d 2077 6974     algorithm wit\n+00019570: 6820 4253 5073 2075 7365 6420 6f6e 6c79  h BSPs used only\n+00019580: 2066 6f72 2063 7963 6c65 2072 6573 6f6c   for cycle resol\n+00019590: 7574 696f 6e2e 2020 5468 6973 206d 6179  ution.  This may\n+000195a0: 0a20 2020 2020 7072 6f64 7563 6520 636f  .     produce co\n+000195b0: 7272 6563 7420 6f75 7470 7574 2069 6e20  rrect output in \n+000195c0: 6365 7274 6169 6e20 6465 6765 6e65 7261  certain degenera\n+000195d0: 7465 2063 6173 6573 2077 6865 7265 2074  te cases where t\n+000195e0: 6865 2064 6570 7468 0a20 2020 2020 736f  he depth.     so\n+000195f0: 7274 2063 616e 6e6f 742c 2062 7574 2069  rt cannot, but i\n+00019600: 7420 616c 736f 206c 6561 6473 2074 6f20  t also leads to \n+00019610: 6d61 6e79 2067 7261 7475 6974 6f75 7320  many gratuitous \n+00019620: 7370 6c69 7473 2c20 6865 6e63 650a 2020  splits, hence.  \n+00019630: 2020 206d 6f72 6520 616e 6f6d 616c 6965     more anomalie\n+00019640: 7320 2a6e 6f74 6520 4275 6773 2061 6e64  s *note Bugs and\n+00019650: 2061 6e6f 6d61 6c69 6573 3a3a 2061 6e64   anomalies:: and\n+00019660: 2062 6967 206f 7574 7075 7420 6669 6c65   big output file\n+00019670: 732e 0a27 2d64 270a 2020 2020 2052 756e  s..'-d'.     Run\n+00019680: 2027 736b 6574 6368 2727 7320 7061 7273   'sketch''s pars\n+00019690: 6572 2069 6e20 6465 6275 6767 696e 6720  er in debugging \n+000196a0: 6d6f 6465 2e20 2054 6869 7320 6973 2070  mode.  This is p\n+000196b0: 7269 6d61 7269 6c79 2066 6f72 0a20 2020  rimarily for.   \n+000196c0: 2020 6465 7665 6c6f 706d 656e 742e 0a27    development..'\n+000196d0: 2d74 270a 2020 2020 2055 7365 2063 6f6e  -t'.     Use con\n+000196e0: 7465 6e74 7320 6f66 2066 696c 6520 2764  tents of file 'd\n+000196f0: 6f63 746d 7027 2061 7320 6120 646f 6375  octmp' as a docu\n+00019700: 6d65 6e74 2074 656d 706c 6174 6520 696e  ment template in\n+00019710: 2077 6869 6368 2074 6f0a 2020 2020 2065   which to.     e\n+00019720: 6e63 6c6f 7365 2027 5053 5472 6963 6b73  nclose 'PSTricks\n+00019730: 2720 6f75 7470 7574 2063 6f64 652e 2020  ' output code.  \n+00019740: 5468 6520 636f 6465 2069 7320 696e 7365  The code is inse\n+00019750: 7274 6564 2069 6e20 706c 6163 6520 6f66  rted in place of\n+00019760: 0a20 2020 2020 7468 6520 6669 7273 7420  .     the first \n+00019770: 696e 7374 616e 6365 206f 6620 7468 6520  instance of the \n+00019780: 6573 6361 7065 2073 7472 696e 6720 2525  escape string %%\n+00019790: 534b 4554 4348 5f4f 5554 5055 5425 252e  SKETCH_OUTPUT%%.\n+000197a0: 0a27 2d54 270a 2020 2020 2043 6175 7365  .'-T'.     Cause\n+000197b0: 7320 2750 5354 7269 636b 7327 206f 7574  s 'PSTricks' out\n+000197c0: 7075 7420 746f 2062 6520 656e 636c 6f73  put to be enclos\n+000197d0: 6564 2069 6e20 6465 6661 756c 7420 5553  ed in default US\n+000197e0: 2064 6f63 756d 656e 740a 2020 2020 2074   document.     t\n+000197f0: 656d 706c 6174 6520 7465 7874 2e20 204f  emplate text.  O\n+00019800: 7074 696f 6e20 272d 5475 2720 6973 2061  ption '-Tu' is a\n+00019810: 2073 796e 6f6e 796d 2e20 204f 7074 696f   synonym.  Optio\n+00019820: 6e20 272d 5465 2720 6361 7573 6573 2074  n '-Te' causes t\n+00019830: 6865 0a20 2020 2020 4575 726f 2073 7461  he.     Euro sta\n+00019840: 6e64 6172 6420 646f 6375 6d65 6e74 2074  ndard document t\n+00019850: 656d 706c 6174 6520 746f 2062 6520 7573  emplate to be us\n+00019860: 6564 2e20 2041 2027 7027 2061 7070 656e  ed.  A 'p' appen\n+00019870: 6465 6420 746f 2061 6e79 0a20 2020 2020  ded to any.     \n+00019880: 6f66 2074 6865 7365 206f 7074 696f 6e73  of these options\n+00019890: 2063 6175 7365 7320 7468 6520 7265 7370   causes the resp\n+000198a0: 6563 7469 7665 2064 6566 6175 6c74 2027  ective default '\n+000198b0: 5053 5472 6963 6b73 2720 646f 6375 6d65  PSTricks' docume\n+000198c0: 6e74 0a20 2020 2020 7465 6d70 6c61 7465  nt.     template\n+000198d0: 2074 6f20 6265 2070 7269 6e74 6564 2074   to be printed t\n+000198e0: 6f20 7374 616e 6461 7264 206f 7574 7075  o standard outpu\n+000198f0: 742e 2020 416e 2061 7070 656e 6465 6420  t.  An appended \n+00019900: 2750 2720 6973 2061 0a20 2020 2020 7379  'P' is a.     sy\n+00019910: 6e6f 6e79 6d2e 2020 416e 2061 7070 656e  nonym.  An appen\n+00019920: 6465 6420 2754 2720 6361 7573 6573 2074  ded 'T' causes t\n+00019930: 6865 2074 6865 2027 5469 6b5a 2f50 4746  he the 'TikZ/PGF\n+00019940: 2720 7465 6d70 6c61 7465 2074 6f20 6265  ' template to be\n+00019950: 0a20 2020 2020 7072 696e 7465 642e 2020  .     printed.  \n+00019960: 416e 2061 7070 656e 6465 6420 274c 2720  An appended 'L' \n+00019970: 7072 696e 7473 2074 6865 204c 6154 6558  prints the LaTeX\n+00019980: 2076 6572 7369 6f6e 206f 6620 7468 6520   version of the \n+00019990: 646f 6375 6d65 6e74 0a20 2020 2020 7465  document.     te\n+000199a0: 6d70 6c61 7465 2c20 6120 7379 6e6f 6e79  mplate, a synony\n+000199b0: 6d20 666f 7220 7468 6520 6465 6661 756c  m for the defaul\n+000199c0: 742e 2020 4120 2743 2720 7072 696e 7473  t.  A 'C' prints\n+000199d0: 2074 6865 2027 436f 6e54 6558 7427 0a20   the 'ConTeXt'. \n+000199e0: 2020 2020 7465 6d70 6c61 7465 2e0a 272d      template..'-\n+000199f0: 6f27 0a20 2020 2020 5573 6520 276f 7574  o'.     Use 'out\n+00019a00: 7075 742e 7465 7827 2061 7320 7468 6520  put.tex' as the \n+00019a10: 6f75 7470 7574 2066 696c 652e 2020 5468  output file.  Th\n+00019a20: 6520 6465 6661 756c 7420 6973 2073 7461  e default is sta\n+00019a30: 6e64 6172 640a 2020 2020 206f 7574 7075  ndard.     outpu\n+00019a40: 742e 0a27 2d44 270a 2020 2020 2044 6566  t..'-D'.     Def\n+00019a50: 696e 6520 6120 7461 6720 666f 7220 7075  ine a tag for pu\n+00019a60: 7270 6f73 6573 206f 6620 7365 6c65 6374  rposes of select\n+00019a70: 696e 6720 6465 6669 6e69 7469 6f6e 2061  ing definition a\n+00019a80: 6c74 6572 6e61 7469 7665 732e 0a20 2020  lternatives..   \n+00019a90: 2020 2a4e 6f74 6520 4465 6669 6e69 7469    *Note Definiti\n+00019aa0: 6f6e 733a 3a2e 2020 5468 6520 6465 6669  ons::.  The defi\n+00019ab0: 6e69 7469 6f6e 2061 7070 6c69 6573 2066  nition applies f\n+00019ac0: 6f72 2061 6c6c 2069 6e70 7574 2066 696c  or all input fil\n+00019ad0: 6573 0a20 2020 2020 7468 6174 2066 6f6c  es.     that fol\n+00019ae0: 6c6f 7720 756e 6c65 7373 2074 6865 2074  low unless the t\n+00019af0: 6167 2069 7320 756e 6465 6669 6e65 6420  ag is undefined \n+00019b00: 7769 7468 2027 2d55 272e 0a27 696e 7075  with '-U'..'inpu\n+00019b10: 7469 2e73 6b27 0a20 2020 2020 496e 7075  ti.sk'.     Inpu\n+00019b20: 7420 6669 6c65 732c 2072 6561 6420 696e  t files, read in\n+00019b30: 2074 6865 2073 6571 7565 6e63 6520 7468   the sequence th\n+00019b40: 6579 2061 7265 2067 6976 656e 2e0a 272d  ey are given..'-\n+00019b50: 5527 0a20 2020 2020 556e 2d64 6566 696e  U'.     Un-defin\n+00019b60: 6520 6120 7461 6720 666f 7220 7075 7270  e a tag for purp\n+00019b70: 6f73 6573 206f 6620 7365 6c65 6374 696e  oses of selectin\n+00019b80: 6720 6465 6669 6e69 7469 6f6e 2061 6c74  g definition alt\n+00019b90: 6572 6e61 7469 7665 732e 0a0a 1f0a 4669  ernatives.....Fi\n+00019ba0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c  le: sketch.info,\n+00019bb0: 2020 4e6f 6465 3a20 496e 7374 616c 6c69    Node: Installi\n+00019bc0: 6e67 2073 6b65 7463 682c 2020 4e65 7874  ng sketch,  Next\n+00019bd0: 3a20 496e 6465 7820 6f66 2073 796e 7461  : Index of synta\n+00019be0: 782c 2020 5072 6576 3a20 436f 6d6d 616e  x,  Prev: Comman\n+00019bf0: 6420 6c69 6e65 2c20 2055 703a 2054 6f70  d line,  Up: Top\n+00019c00: 0a0a 3620 4275 696c 6469 6e67 2061 6e64  ..6 Building and\n+00019c10: 2069 6e73 7461 6c6c 696e 6720 2773 6b65   installing 'ske\n+00019c20: 7463 6827 0a2a 2a2a 2a2a 2a2a 2a2a 2a2a  tch'.***********\n 00019c30: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  ****************\n-00019c40: 2a2a 2a2a 2a2a 2a2a 2a0a 0a27 536b 6574  *********..'Sket\n-00019c50: 6368 2720 6973 2073 6f20 736d 616c 6c20  ch' is so small \n-00019c60: 7468 6174 2063 6f6d 7069 6c69 6e67 2062  that compiling b\n-00019c70: 7920 6272 7574 6520 666f 7263 6520 6973  y brute force is\n-00019c80: 2070 726f 6261 626c 7920 6265 7374 2e0a   probably best..\n-00019c90: 5468 6520 666f 6c6c 6f77 696e 6720 636f  The following co\n-00019ca0: 6d6d 616e 6420 6f75 6768 7420 746f 2064  mmand ought to d\n-00019cb0: 6f20 7468 6520 7472 6963 6b20 6f6e 2061  o the trick on a\n-00019cc0: 6e79 2073 7973 7465 6d73 2077 6865 7265  ny systems where\n-00019cd0: 2027 6763 6327 0a69 7320 696e 7374 616c   'gcc'.is instal\n-00019ce0: 6c65 642e 2020 4d61 6b65 2073 7572 6520  led.  Make sure \n-00019cf0: 746f 2066 6972 7374 2063 6861 6e67 6520  to first change \n-00019d00: 6375 7272 656e 7420 6469 7265 6374 6f72  current director\n-00019d10: 6965 7320 746f 2074 6865 0a70 6c61 6365  ies to the.place\n-00019d20: 2077 6865 7265 2079 6f75 2068 6176 6520   where you have \n-00019d30: 756e 7061 636b 6564 2074 6865 2073 6f75  unpacked the sou\n-00019d40: 7263 6573 2e0a 2020 2020 2067 6363 202a  rces..     gcc *\n-00019d50: 2e63 202d 6f20 736b 6574 6368 2e65 7865  .c -o sketch.exe\n-00019d60: 202d 6c6d 0a54 6865 2027 2e65 7865 2720   -lm.The '.exe' \n-00019d70: 6174 2074 6865 2065 6e64 2069 7320 6e65  at the end is ne\n-00019d80: 6365 7373 6172 7920 666f 7220 5769 6e64  cessary for Wind\n-00019d90: 6f77 7320 7379 7374 656d 732e 2020 4472  ows systems.  Dr\n-00019da0: 6f70 2069 7420 6966 2079 6f75 720a 7379  op it if your.sy\n-00019db0: 7374 656d 2069 7320 736f 6d65 2076 6572  stem is some ver\n-00019dc0: 7369 6f6e 206f 6620 556e 6978 2e20 204f  sion of Unix.  O\n-00019dd0: 7468 6572 2043 2063 6f6d 7069 6c65 7273  ther C compilers\n-00019de0: 206f 7567 6874 2074 6f20 776f 726b 2061   ought to work a\n-00019df0: 7320 6a75 7374 0a61 7320 7765 6c6c 2e20  s just.as well. \n-00019e00: 2046 6f72 2065 7861 6d70 6c65 2c0a 2020   For example,.  \n-00019e10: 2020 2063 6c20 2a2e 6320 2d6f 2073 6b65     cl *.c -o ske\n-00019e20: 7463 682e 6578 650a 6973 2074 6865 2063  tch.exe.is the c\n-00019e30: 6f72 7265 6374 2063 6f6d 6d61 6e64 2066  orrect command f\n-00019e40: 6f72 206d 616e 7920 7665 7273 696f 6e73  or many versions\n-00019e50: 206f 6620 4d53 2056 6973 7561 6c20 432e   of MS Visual C.\n-00019e60: 2049 6e20 7468 6520 6c61 7465 7374 0a76   In the latest.v\n-00019e70: 6572 7369 6f6e 732c 204d 6963 726f 736f  ersions, Microso\n-00019e80: 6674 2068 6173 2064 6570 7265 6361 7465  ft has deprecate\n-00019e90: 6420 7468 6520 272d 6f27 206f 7074 696f  d the '-o' optio\n-00019ea0: 6e20 616e 642c 2062 7920 6465 6661 756c  n and, by defaul\n-00019eb0: 742c 2064 6f65 730a 6e6f 7420 6465 6669  t, does.not defi\n-00019ec0: 6e65 2074 6865 2027 5f5f 5354 4443 5f5f  ne the '__STDC__\n-00019ed0: 2720 6d61 6372 6f2e 2020 5468 6973 2063  ' macro.  This c\n-00019ee0: 6175 7365 7320 7072 6f62 6c65 6d73 2077  auses problems w\n-00019ef0: 6974 6820 736f 6d65 0a76 6572 7369 6f6e  ith some.version\n-00019f00: 7320 6f66 2027 666c 6578 272c 2027 6269  s of 'flex', 'bi\n-00019f10: 736f 6e27 2c20 276c 6578 272c 2061 6e64  son', 'lex', and\n-00019f20: 2027 7961 6363 272c 2077 6869 6368 2061   'yacc', which a\n-00019f30: 7265 2075 7365 6420 746f 2063 7265 6174  re used to creat\n-00019f40: 650a 7468 6520 2773 6b65 7463 6827 2073  e.the 'sketch' s\n-00019f50: 6361 6e6e 6572 2061 6e64 2070 6172 7365  canner and parse\n-00019f60: 722e 2020 4974 2773 206e 6561 726c 7920  r.  It's nearly \n-00019f70: 616c 7761 7973 2070 6f73 7369 626c 6520  always possible \n-00019f80: 746f 2066 696e 6420 610a 7365 7420 6f66  to find a.set of\n-00019f90: 206f 7074 696f 6e73 2074 6861 7420 636f   options that co\n-00019fa0: 6d70 696c 6573 2077 6974 6820 6e6f 2065  mpiles with no e\n-00019fb0: 7272 6f72 7320 6f72 2077 6172 6e69 6e67  rrors or warning\n-00019fc0: 732c 2061 6e64 2074 6869 7320 6d65 616e  s, and this mean\n-00019fd0: 730a 2773 6b65 7463 6827 2069 7320 5f76  s.'sketch' is _v\n-00019fe0: 6572 795f 206c 696b 656c 7920 746f 2077  ery_ likely to w\n-00019ff0: 6f72 6b20 636f 7272 6563 746c 792e 2020  ork correctly.  \n-0001a000: 466f 7220 6578 616d 706c 652c 2074 6865  For example, the\n-0001a010: 2056 6973 7561 6c0a 432b 2b20 3230 3035   Visual.C++ 2005\n-0001a020: 2045 7870 7265 7373 2045 6469 7469 6f6e   Express Edition\n-0001a030: 2063 6f6d 7069 6c65 7220 2861 7661 696c   compiler (avail\n-0001a040: 6162 6c65 2066 7265 6520 6f66 2063 6861  able free of cha\n-0001a050: 7267 6520 6672 6f6d 2074 6865 0a4d 6963  rge from the.Mic\n-0001a060: 726f 736f 6674 2077 6562 2073 6974 6529  rosoft web site)\n-0001a070: 2c20 2766 6c65 7827 2076 6572 7369 6f6e  , 'flex' version\n-0001a080: 2032 2e35 2e34 2c20 616e 6420 2762 6973   2.5.4, and 'bis\n-0001a090: 6f6e 2720 7665 7273 696f 6e20 322e 3120  on' version 2.1 \n-0001a0a0: 6275 696c 640a 6572 726f 722d 6672 6565  build.error-free\n-0001a0b0: 2077 6974 680a 2020 2020 2063 6c20 2d44   with.     cl -D\n-0001a0c0: 5959 5f4e 4556 4552 5f49 4e54 4552 4143  YY_NEVER_INTERAC\n-0001a0d0: 5449 5645 3d31 202d 5a61 202d 4f78 202d  TIVE=1 -Za -Ox -\n-0001a0e0: 4665 736b 6574 6368 2e65 7865 202a 2e63  Fesketch.exe *.c\n-0001a0f0: 0a0a 2020 2046 6f72 2070 7572 6973 7473  ..   For purists\n-0001a100: 2c20 7468 6572 6520 6973 2061 6c73 6f20  , there is also \n-0001a110: 6120 276d 616b 6566 696c 6527 2063 6f6d  a 'makefile' com\n-0001a120: 7061 7469 626c 6520 7769 7468 2047 4e55  patible with GNU\n-0001a130: 2027 6d61 6b65 270a 616e 6420 2767 6363   'make'.and 'gcc\n-0001a140: 272e 2020 5468 6520 636f 6d6d 616e 640a  '.  The command.\n-0001a150: 2020 2020 206d 616b 650a 7769 6c6c 2062       make.will b\n-0001a160: 7569 6c64 2074 6865 2065 7865 6375 7461  uild the executa\n-0001a170: 626c 652c 2069 6e63 6c75 6469 6e67 2074  ble, including t\n-0001a180: 6865 2072 6562 7569 6c64 696e 6720 6f66  he rebuilding of\n-0001a190: 2074 6865 2073 6361 6e6e 6572 2061 6e64   the scanner and\n-0001a1a0: 0a70 6172 7365 7220 7769 7468 2027 666c  .parser with 'fl\n-0001a1b0: 6578 2720 616e 6420 2762 6973 6f6e 2720  ex' and 'bison' \n-0001a1c0: 6966 2079 6f75 2068 6176 6520 6368 616e  if you have chan\n-0001a1d0: 6765 6420 2773 6b65 7463 682e 6c27 206f  ged 'sketch.l' o\n-0001a1e0: 720a 2773 6b65 7463 682e 7927 2072 6573  r.'sketch.y' res\n-0001a1f0: 7065 6374 6976 656c 792e 0a0a 2020 2057  pectively...   W\n-0001a200: 6869 6c65 206e 6f74 2065 7373 656e 7469  hile not essenti\n-0001a210: 616c 2c20 6275 696c 6469 6e67 2074 6865  al, building the\n-0001a220: 206d 616e 7561 6c20 6973 2061 6e20 6578   manual is an ex\n-0001a230: 6365 6c6c 656e 7420 7465 7374 206f 6620  cellent test of \n-0001a240: 796f 7572 0a27 736b 6574 6368 2720 696e  your.'sketch' in\n-0001a250: 7374 616c 6c61 7469 6f6e 2e20 2054 6f20  stallation.  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Oth\n+00019dd0: 6572 2043 2063 6f6d 7069 6c65 7273 206f  er C compilers o\n+00019de0: 7567 6874 2074 6f20 776f 726b 2061 7320  ught to work as \n+00019df0: 6a75 7374 0a61 7320 7765 6c6c 2e20 2046  just.as well.  F\n+00019e00: 6f72 2065 7861 6d70 6c65 2c0a 2020 2020  or example,.    \n+00019e10: 2063 6c20 2a2e 6320 2d6f 2073 6b65 7463   cl *.c -o sketc\n+00019e20: 682e 6578 650a 6973 2074 6865 2063 6f72  h.exe.is the cor\n+00019e30: 7265 6374 2063 6f6d 6d61 6e64 2066 6f72  rect command for\n+00019e40: 206d 616e 7920 7665 7273 696f 6e73 206f   many versions o\n+00019e50: 6620 4d53 2056 6973 7561 6c20 432e 2049  f MS Visual C. 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7265 2074 6167   <>, closure tag\n+0001aec0: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n+0001aed0: 2020 2020 2020 2020 5377 6565 7073 2e20          Sweeps. \n+0001aee0: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+0001aef0: 696e 6520 3139 290a 2a20 3c3e 2c20 636c  ine 19).* <>, cl\n+0001af00: 6f73 7572 6520 7461 6720 3c33 3e3a 2020  osure tag <3>:  \n 0001af10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001af20: 2020 2053 7765 7074 2070 6f69 6e74 732e     Swept points.\n-0001af30: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-0001af40: 3629 0a2a 203c 3e2c 2063 6c6f 7375 7265  6).* <>, closure\n-0001af50: 2074 6167 203c 343e 3a20 2020 2020 2020   tag <4>:       \n-0001af60: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n-0001af70: 7420 706f 696e 7473 2e20 2020 2020 2020  t points.       \n-0001af80: 2020 286c 696e 6520 3133 290a 2a20 3c3e    (line 13).* <>\n-0001af90: 2c20 636c 6f73 7572 6520 7461 6720 3c35  , closure tag <5\n-0001afa0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001afb0: 2020 2020 2053 7765 7074 206c 696e 6573       Swept lines\n-0001afc0: 2e20 2020 2020 2020 2020 2028 6c69 6e65  .          (line\n-0001afd0: 2020 3629 0a2a 203c 3e2c 2063 6c6f 7375    6).* <>, closu\n-0001afe0: 7265 2074 6167 203c 363e 3a20 2020 2020  re tag <6>:     \n-0001aff0: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n-0001b000: 6570 7420 6c69 6e65 732e 2020 2020 2020  ept lines.      \n-0001b010: 2020 2020 286c 696e 6520 3238 290a 2a20      (line 28).* \n-0001b020: 3c3e 2c20 636c 6f73 7572 6520 7461 6720  <>, closure tag \n-0001b030: 3c37 3e3a 2020 2020 2020 2020 2020 2020  <7>:            \n-0001b040: 2020 2020 2020 2053 7765 6570 2066 6163         Sweep fac\n-0001b050: 6520 7370 6c69 7474 696e 672e 2028 6c69  e splitting. (li\n-0001b060: 6e65 2031 3129 0a2a 203c 666f 6f3e 2c20  ne 11).* <foo>, \n-0001b070: 7461 6720 7265 6665 7265 6e63 653a 2020  tag reference:  \n-0001b080: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b090: 466f 726d 7320 6f66 2064 6566 696e 6974  Forms of definit\n-0001b0a0: 696f 6e73 2e20 286c 696e 6520 3230 290a  ions. (line 20).\n-0001b0b0: 2a20 3c66 6f6f 3e2c 2074 6167 2072 6566  * <foo>, tag ref\n-0001b0c0: 6572 656e 6365 203c 313e 3a20 2020 2020  erence <1>:     \n-0001b0d0: 2020 2020 2020 2020 2046 6f72 6d73 206f           Forms o\n-0001b0e0: 6620 7265 6665 7265 6e63 6573 2e20 2028  f references.  (\n-0001b0f0: 6c69 6e65 2031 3929 0a2a 205b 666f 6f2c  line 19).* [foo,\n-0001b100: 2e2e 2e2c 6261 725d 2c20 6d75 6c74 6970  ...,bar], multip\n-0001b110: 6c65 206f 7074 696f 6e73 2072 6566 6572  le options refer\n-0001b120: 656e 6365 3a20 466f 726d 7320 6f66 2072  ence: Forms of r\n-0001b130: 6566 6572 656e 6365 732e 0a20 2020 2020  eferences..     \n+0001af20: 2053 7765 7074 2070 6f69 6e74 732e 2020   Swept points.  \n+0001af30: 2020 2020 2020 2028 6c69 6e65 2020 3629         (line  6)\n+0001af40: 0a2a 203c 3e2c 2063 6c6f 7375 7265 2074  .* <>, closure t\n+0001af50: 6167 203c 343e 3a20 2020 2020 2020 2020  ag <4>:         \n+0001af60: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n+0001af70: 706f 696e 7473 2e20 2020 2020 2020 2020  points.         \n+0001af80: 286c 696e 6520 3133 290a 2a20 3c3e 2c20  (line 13).* <>, \n+0001af90: 636c 6f73 7572 6520 7461 6720 3c35 3e3a  closure tag <5>:\n+0001afa0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001afb0: 2020 2053 7765 7074 206c 696e 6573 2e20     Swept lines. \n+0001afc0: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+0001afd0: 3629 0a2a 203c 3e2c 2063 6c6f 7375 7265  6).* <>, closure\n+0001afe0: 2074 6167 203c 363e 3a20 2020 2020 2020   tag <6>:       \n+0001aff0: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n+0001b000: 7420 6c69 6e65 732e 2020 2020 2020 2020  t lines.        \n+0001b010: 2020 286c 696e 6520 3238 290a 2a20 3c3e    (line 28).* <>\n+0001b020: 2c20 636c 6f73 7572 6520 7461 6720 3c37  , closure tag <7\n+0001b030: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001b040: 2020 2020 2053 7765 6570 2066 6163 6520       Sweep face \n+0001b050: 7370 6c69 7474 696e 672e 2028 6c69 6e65  splitting. (line\n+0001b060: 2031 3129 0a2a 203c 666f 6f3e 2c20 7461   11).* <foo>, ta\n+0001b070: 6720 7265 6665 7265 6e63 653a 2020 2020  g reference:    \n+0001b080: 2020 2020 2020 2020 2020 2020 2020 466f                Fo\n+0001b090: 726d 7320 6f66 2064 6566 696e 6974 696f  rms of definitio\n+0001b0a0: 6e73 2e20 286c 696e 6520 3230 290a 2a20  ns. (line 20).* \n+0001b0b0: 3c66 6f6f 3e2c 2074 6167 2072 6566 6572  <foo>, tag refer\n+0001b0c0: 656e 6365 203c 313e 3a20 2020 2020 2020  ence <1>:       \n+0001b0d0: 2020 2020 2020 2046 6f72 6d73 206f 6620         Forms of \n+0001b0e0: 7265 6665 7265 6e63 6573 2e20 2028 6c69  references.  (li\n+0001b0f0: 6e65 2031 3929 0a2a 205b 666f 6f2c 2e2e  ne 19).* [foo,..\n+0001b100: 2e2c 6261 725d 2c20 6d75 6c74 6970 6c65  .,bar], multiple\n+0001b110: 206f 7074 696f 6e73 2072 6566 6572 656e   options referen\n+0001b120: 6365 3a20 466f 726d 7320 6f66 2072 6566  ce: Forms of ref\n+0001b130: 6572 656e 6365 732e 0a20 2020 2020 2020  erences..       \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 2020 2020 286c 696e 6520            (line \n-0001b180: 3138 290a 2a20 5b66 6f6f 5d2c 206f 7074  18).* [foo], opt\n-0001b190: 696f 6e73 2072 6566 6572 656e 6365 3a20  ions reference: \n-0001b1a0: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n-0001b1b0: 796c 696e 6520 7377 6565 7073 2077 6974  yline sweeps wit\n-0001b1c0: 6820 636c 6f73 7572 652e 0a20 2020 2020  h closure..     \n+0001b170: 2020 2020 2020 2020 286c 696e 6520 3138          (line 18\n+0001b180: 290a 2a20 5b66 6f6f 5d2c 206f 7074 696f  ).* [foo], optio\n+0001b190: 6e73 2072 6566 6572 656e 6365 3a20 2020  ns reference:   \n+0001b1a0: 2020 2020 2020 2020 2020 2050 6f6c 796c             Polyl\n+0001b1b0: 696e 6520 7377 6565 7073 2077 6974 6820  ine sweeps with \n+0001b1c0: 636c 6f73 7572 652e 0a20 2020 2020 2020  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 2020 2020 286c 696e 6520            (line \n-0001b210: 3234 290a 2a20 5b66 6f6f 5d2c 206f 7074  24).* [foo], opt\n-0001b220: 696f 6e73 2072 6566 6572 656e 6365 203c  ions reference <\n-0001b230: 313e 3a20 2020 2020 2020 2020 2046 6f72  1>:          For\n-0001b240: 6d73 206f 6620 7265 6665 7265 6e63 6573  ms of references\n-0001b250: 2e20 2028 6c69 6e65 2031 3829 0a2a 205b  .  (line 18).* [\n-0001b260: 666f 6f5d 2c20 7665 6374 6f72 2072 6566  foo], vector ref\n-0001b270: 6572 656e 6365 3a20 2020 2020 2020 2020  erence:         \n-0001b280: 2020 2020 2020 506f 6c79 6c69 6e65 2073        Polyline s\n-0001b290: 7765 6570 732e 2020 2020 2020 286c 696e  weeps.      (lin\n-0001b2a0: 6520 3230 290a 2a20 5b66 6f6f 5d2c 2076  e 20).* [foo], v\n-0001b2b0: 6563 746f 7220 7265 6665 7265 6e63 6520  ector reference \n-0001b2c0: 3c31 3e3a 2020 2020 2020 2020 2020 2046  <1>:           F\n-0001b2d0: 6f72 6d73 206f 6620 7265 6665 7265 6e63  orms of referenc\n-0001b2e0: 6573 2e20 2028 6c69 6e65 2031 3529 0a2a  es.  (line 15).*\n-0001b2f0: 205b 5b20 5d5b 205d 5b20 5d5b 205d 5d2c   [[ ][ ][ ][ ]],\n-0001b300: 2074 7261 6e73 666f 726d 206c 6974 6572   transform liter\n-0001b310: 616c 3a20 2020 2020 5472 616e 7366 6f72  al:     Transfor\n-0001b320: 6d20 6c69 7465 7261 6c73 2e20 2020 286c  m literals.   (l\n-0001b330: 696e 6520 3437 290a 2a20 5b5b 205d 5b20  ine 47).* [[ ][ \n-0001b340: 5d5b 205d 5b20 5d5d 2c20 7472 616e 7366  ][ ][ ]], transf\n-0001b350: 6f72 6d20 6c69 7465 7261 6c20 3c31 3e3a  orm literal <1>:\n-0001b360: 2054 7261 6e73 666f 726d 206c 6974 6572   Transform liter\n-0001b370: 616c 732e 2020 2028 6c69 6e65 2035 3329  als.   (line 53)\n-0001b380: 0a2a 205b 5b66 6f6f 5d5d 2c20 7472 616e  .* [[foo]], tran\n-0001b390: 7366 6f72 6d20 7265 6665 7265 6e63 653a  sform reference:\n-0001b3a0: 2020 2020 2020 2020 2020 466f 726d 7320            Forms \n-0001b3b0: 6f66 2072 6566 6572 656e 6365 732e 2020  of references.  \n-0001b3c0: 286c 696e 6520 3136 290a 2a20 5b5b 666f  (line 16).* [[fo\n-0001b3d0: 6f5d 5d2c 2074 7261 6e73 666f 726d 2072  o]], transform r\n-0001b3e0: 6566 6572 656e 6365 203c 313e 3a20 2020  eference <1>:   \n-0001b3f0: 2020 204f 7665 7276 6965 772e 2020 2020     Overview.    \n-0001b400: 2020 2020 2020 2020 2028 6c69 6e65 2033           (line 3\n-0001b410: 3529 0a2a 205b 5b66 6f6f 5d5d 2c20 7472  5).* [[foo]], tr\n-0001b420: 616e 7366 6f72 6d20 7265 6665 7265 6e63  ansform referenc\n-0001b430: 6520 3c32 3e3a 2020 2020 2020 4f76 6572  e <2>:      Over\n-0001b440: 7669 6577 2e20 2020 2020 2020 2020 2020  view.           \n-0001b450: 2020 286c 696e 6520 3335 290a 2a20 5e2c    (line 35).* ^,\n-0001b460: 2065 7870 6f6e 656e 7469 6174 696f 6e20   exponentiation \n-0001b470: 6f70 6572 6174 6f72 3a20 2020 2020 2020  operator:       \n-0001b480: 2020 2020 2054 776f 2d6f 7065 7261 6e64       Two-operand\n-0001b490: 2028 6269 6e61 7279 2920 666f 726d 732e   (binary) forms.\n-0001b4a0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+0001b200: 2020 2020 2020 2020 286c 696e 6520 3234          (line 24\n+0001b210: 290a 2a20 5b66 6f6f 5d2c 206f 7074 696f  ).* [foo], optio\n+0001b220: 6e73 2072 6566 6572 656e 6365 203c 313e  ns reference <1>\n+0001b230: 3a20 2020 2020 2020 2020 2046 6f72 6d73  :          Forms\n+0001b240: 206f 6620 7265 6665 7265 6e63 6573 2e20   of references. \n+0001b250: 2028 6c69 6e65 2031 3829 0a2a 205b 666f   (line 18).* [fo\n+0001b260: 6f5d 2c20 7665 6374 6f72 2072 6566 6572  o], vector refer\n+0001b270: 656e 6365 3a20 2020 2020 2020 2020 2020  ence:           \n+0001b280: 2020 2020 506f 6c79 6c69 6e65 2073 7765      Polyline swe\n+0001b290: 6570 732e 2020 2020 2020 286c 696e 6520  eps.      (line \n+0001b2a0: 3230 290a 2a20 5b66 6f6f 5d2c 2076 6563  20).* [foo], vec\n+0001b2b0: 746f 7220 7265 6665 7265 6e63 6520 3c31  tor reference <1\n+0001b2c0: 3e3a 2020 2020 2020 2020 2020 2046 6f72  >:           For\n+0001b2d0: 6d73 206f 6620 7265 6665 7265 6e63 6573  ms of references\n+0001b2e0: 2e20 2028 6c69 6e65 2031 3529 0a2a 205b  .  (line 15).* [\n+0001b2f0: 5b20 5d5b 205d 5b20 5d5b 205d 5d2c 2074  [ ][ ][ ][ ]], t\n+0001b300: 7261 6e73 666f 726d 206c 6974 6572 616c  ransform literal\n+0001b310: 3a20 2020 2020 5472 616e 7366 6f72 6d20  :     Transform \n+0001b320: 6c69 7465 7261 6c73 2e20 2020 286c 696e  literals.   (lin\n+0001b330: 6520 3437 290a 2a20 5b5b 205d 5b20 5d5b  e 47).* [[ ][ ][\n+0001b340: 205d 5b20 5d5d 2c20 7472 616e 7366 6f72   ][ ]], transfor\n+0001b350: 6d20 6c69 7465 7261 6c20 3c31 3e3a 2054  m literal <1>: T\n+0001b360: 7261 6e73 666f 726d 206c 6974 6572 616c  ransform literal\n+0001b370: 732e 2020 2028 6c69 6e65 2035 3329 0a2a  s.   (line 53).*\n+0001b380: 205b 5b66 6f6f 5d5d 2c20 7472 616e 7366   [[foo]], transf\n+0001b390: 6f72 6d20 7265 6665 7265 6e63 653a 2020  orm reference:  \n+0001b3a0: 2020 2020 2020 2020 466f 726d 7320 6f66          Forms of\n+0001b3b0: 2072 6566 6572 656e 6365 732e 2020 286c   references.  (l\n+0001b3c0: 696e 6520 3136 290a 2a20 5b5b 666f 6f5d  ine 16).* [[foo]\n+0001b3d0: 5d2c 2074 7261 6e73 666f 726d 2072 6566  ], transform ref\n+0001b3e0: 6572 656e 6365 203c 313e 3a20 2020 2020  erence <1>:     \n+0001b3f0: 204f 7665 7276 6965 772e 2020 2020 2020   Overview.      \n+0001b400: 2020 2020 2020 2028 6c69 6e65 2033 3529         (line 35)\n+0001b410: 0a2a 205b 5b66 6f6f 5d5d 2c20 7472 616e  .* [[foo]], tran\n+0001b420: 7366 6f72 6d20 7265 6665 7265 6e63 6520  sform reference \n+0001b430: 3c32 3e3a 2020 2020 2020 4f76 6572 7669  <2>:      Overvi\n+0001b440: 6577 2e20 2020 2020 2020 2020 2020 2020  ew.             \n+0001b450: 286c 696e 6520 3335 290a 2a20 5e2c 2065  (line 35).* ^, e\n+0001b460: 7870 6f6e 656e 7469 6174 696f 6e20 6f70  xponentiation op\n+0001b470: 6572 6174 6f72 3a20 2020 2020 2020 2020  erator:         \n+0001b480: 2020 2054 776f 2d6f 7065 7261 6e64 2028     Two-operand (\n+0001b490: 6269 6e61 7279 2920 666f 726d 732e 0a20  binary) forms.. \n+0001b4a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020                  \n-0001b4e0: 286c 696e 6520 3237 290a 2a20 7b20 7d2c  (line 27).* { },\n-0001b4f0: 2062 6c6f 636b 2064 7261 7761 626c 653a   block drawable:\n+0001b4d0: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+0001b4e0: 696e 6520 3237 290a 2a20 7b20 7d2c 2062  ine 27).* { }, b\n+0001b4f0: 6c6f 636b 2064 7261 7761 626c 653a 2020  lock drawable:  \n 0001b500: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b510: 2020 204f 626a 6563 7420 7472 616e 7366     Object transf\n-0001b520: 6f72 6d73 2e20 2020 2028 6c69 6e65 2032  orms.    (line 2\n-0001b530: 3429 0a2a 207b 207d 2c20 626c 6f63 6b20  4).* { }, block \n-0001b540: 6472 6177 6162 6c65 203c 313e 3a20 2020  drawable <1>:   \n-0001b550: 2020 2020 2020 2020 2020 2020 4e65 7374              Nest\n-0001b560: 6564 2073 7765 6570 732e 2020 2020 2020  ed sweeps.      \n-0001b570: 2020 286c 696e 6520 3235 290a 2a20 7b20    (line 25).* { \n-0001b580: 7d2c 2062 6c6f 636b 2064 7261 7761 626c  }, block drawabl\n-0001b590: 6520 3c32 3e3a 2020 2020 2020 2020 2020  e <2>:          \n-0001b5a0: 2020 2020 2053 7765 7074 2062 6c6f 636b       Swept block\n-0001b5b0: 732e 2020 2020 2020 2020 2028 6c69 6e65  s.         (line\n-0001b5c0: 2020 3729 0a2a 207b 207d 2c20 626c 6f63    7).* { }, bloc\n-0001b5d0: 6b20 6472 6177 6162 6c65 203c 333e 3a20  k drawable <3>: \n-0001b5e0: 2020 2020 2020 2020 2020 2020 2020 426c                Bl\n-0001b5f0: 6f63 6b73 2e20 2020 2020 2020 2020 2020  ocks.           \n-0001b600: 2020 2020 286c 696e 6520 2036 290a 2a20      (line  6).* \n-0001b610: 7b20 7d2c 2062 6c6f 636b 2064 7261 7761  { }, block drawa\n-0001b620: 626c 6520 3c34 3e3a 2020 2020 2020 2020  ble <4>:        \n-0001b630: 2020 2020 2020 204f 7665 7276 6965 772e         Overview.\n-0001b640: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n-0001b650: 6e65 2033 3729 0a2a 207b 666f 6f7d 2c20  ne 37).* {foo}, \n-0001b660: 6472 6177 6162 6c65 2072 6566 6572 656e  drawable referen\n-0001b670: 6365 3a20 2020 2020 2020 2020 2020 2020  ce:             \n-0001b680: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n-0001b690: 732e 2020 2020 286c 696e 6520 3333 290a  s.    (line 33).\n-0001b6a0: 2a20 7b66 6f6f 7d2c 2064 7261 7761 626c  * {foo}, drawabl\n-0001b6b0: 6520 7265 6665 7265 6e63 6520 3c31 3e3a  e reference <1>:\n-0001b6c0: 2020 2020 2020 2020 2046 6f72 6d73 206f           Forms o\n-0001b6d0: 6620 7265 6665 7265 6e63 6573 2e20 2028  f references.  (\n-0001b6e0: 6c69 6e65 2031 3729 0a2a 207b 666f 6f7d  line 17).* {foo}\n-0001b6f0: 2c20 6472 6177 6162 6c65 2072 6566 6572  , drawable refer\n-0001b700: 656e 6365 203c 323e 3a20 2020 2020 2020  ence <2>:       \n-0001b710: 2020 4f76 6572 7669 6577 2e20 2020 2020    Overview.     \n-0001b720: 2020 2020 2020 2020 286c 696e 6520 3437          (line 47\n-0001b730: 290a 2a20 7b66 6f6f 7d2c 2064 7261 7761  ).* {foo}, drawa\n-0001b740: 626c 6520 7265 6665 7265 6e63 6520 3c33  ble reference <3\n-0001b750: 3e3a 2020 2020 2020 2020 204f 7665 7276  >:         Overv\n-0001b760: 6965 772e 2020 2020 2020 2020 2020 2020  iew.            \n-0001b770: 2028 6c69 6e65 2035 3729 0a2a 207c 587c   (line 57).* |X|\n-0001b780: 2c20 6d61 676e 6974 7564 6520 6f70 6572  , magnitude oper\n-0001b790: 6174 6f72 3a20 2020 2020 2020 2020 2020  ator:           \n-0001b7a0: 2020 2020 556e 6172 7920 666f 726d 732e      Unary forms.\n-0001b7b0: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-0001b7c0: 3132 290a 2a20 6163 6f73 3a20 2020 2020  12).* acos:     \n+0001b510: 204f 626a 6563 7420 7472 616e 7366 6f72   Object transfor\n+0001b520: 6d73 2e20 2020 2028 6c69 6e65 2032 3429  ms.    (line 24)\n+0001b530: 0a2a 207b 207d 2c20 626c 6f63 6b20 6472  .* { }, block dr\n+0001b540: 6177 6162 6c65 203c 313e 3a20 2020 2020  awable <1>:     \n+0001b550: 2020 2020 2020 2020 2020 4e65 7374 6564            Nested\n+0001b560: 2073 7765 6570 732e 2020 2020 2020 2020   sweeps.        \n+0001b570: 286c 696e 6520 3235 290a 2a20 7b20 7d2c  (line 25).* { },\n+0001b580: 2062 6c6f 636b 2064 7261 7761 626c 6520   block drawable \n+0001b590: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n+0001b5a0: 2020 2053 7765 7074 2062 6c6f 636b 732e     Swept blocks.\n+0001b5b0: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+0001b5c0: 3729 0a2a 207b 207d 2c20 626c 6f63 6b20  7).* { }, block \n+0001b5d0: 6472 6177 6162 6c65 203c 333e 3a20 2020  drawable <3>:   \n+0001b5e0: 2020 2020 2020 2020 2020 2020 426c 6f63              Bloc\n+0001b5f0: 6b73 2e20 2020 2020 2020 2020 2020 2020  ks.             \n+0001b600: 2020 286c 696e 6520 2036 290a 2a20 7b20    (line  6).* { \n+0001b610: 7d2c 2062 6c6f 636b 2064 7261 7761 626c  }, block drawabl\n+0001b620: 6520 3c34 3e3a 2020 2020 2020 2020 2020  e <4>:          \n+0001b630: 2020 2020 204f 7665 7276 6965 772e 2020       Overview.  \n+0001b640: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001b650: 2033 3729 0a2a 207b 666f 6f7d 2c20 6472   37).* {foo}, dr\n+0001b660: 6177 6162 6c65 2072 6566 6572 656e 6365  awable reference\n+0001b670: 3a20 2020 2020 2020 2020 2020 2020 4f62  :             Ob\n+0001b680: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n+0001b690: 2020 2020 286c 696e 6520 3333 290a 2a20      (line 33).* \n+0001b6a0: 7b66 6f6f 7d2c 2064 7261 7761 626c 6520  {foo}, drawable \n+0001b6b0: 7265 6665 7265 6e63 6520 3c31 3e3a 2020  reference <1>:  \n+0001b6c0: 2020 2020 2020 2046 6f72 6d73 206f 6620         Forms of \n+0001b6d0: 7265 6665 7265 6e63 6573 2e20 2028 6c69  references.  (li\n+0001b6e0: 6e65 2031 3729 0a2a 207b 666f 6f7d 2c20  ne 17).* {foo}, \n+0001b6f0: 6472 6177 6162 6c65 2072 6566 6572 656e  drawable referen\n+0001b700: 6365 203c 323e 3a20 2020 2020 2020 2020  ce <2>:         \n+0001b710: 4f76 6572 7669 6577 2e20 2020 2020 2020  Overview.       \n+0001b720: 2020 2020 2020 286c 696e 6520 3437 290a        (line 47).\n+0001b730: 2a20 7b66 6f6f 7d2c 2064 7261 7761 626c  * {foo}, drawabl\n+0001b740: 6520 7265 6665 7265 6e63 6520 3c33 3e3a  e reference <3>:\n+0001b750: 2020 2020 2020 2020 204f 7665 7276 6965           Overvie\n+0001b760: 772e 2020 2020 2020 2020 2020 2020 2028  w.             (\n+0001b770: 6c69 6e65 2035 3729 0a2a 207c 587c 2c20  line 57).* |X|, \n+0001b780: 6d61 676e 6974 7564 6520 6f70 6572 6174  magnitude operat\n+0001b790: 6f72 3a20 2020 2020 2020 2020 2020 2020  or:             \n+0001b7a0: 2020 556e 6172 7920 666f 726d 732e 2020    Unary forms.  \n+0001b7b0: 2020 2020 2020 2020 286c 696e 6520 3132          (line 12\n+0001b7c0: 290a 2a20 6163 6f73 3a20 2020 2020 2020  ).* acos:       \n 0001b7d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b7e0: 2020 2020 2020 2020 2020 2020 2055 6e61               Una\n-0001b7f0: 7279 2066 6f72 6d73 2e20 2020 2020 2020  ry forms.       \n-0001b800: 2020 2028 6c69 6e65 2031 3829 0a2a 2061     (line 18).* a\n-0001b810: 7272 6f77 733a 2020 2020 2020 2020 2020  rrows:          \n+0001b7e0: 2020 2020 2020 2020 2020 2055 6e61 7279             Unary\n+0001b7f0: 2066 6f72 6d73 2e20 2020 2020 2020 2020   forms.         \n+0001b800: 2028 6c69 6e65 2031 3829 0a2a 2061 7272   (line 18).* arr\n+0001b810: 6f77 733a 2020 2020 2020 2020 2020 2020  ows:            \n 0001b820: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b830: 2020 2020 2020 4166 6669 6e65 2061 7269        Affine ari\n-0001b840: 7468 6d65 7469 632e 2020 2020 286c 696e  thmetic.    (lin\n-0001b850: 6520 3131 290a 2a20 6172 726f 7773 203c  e 11).* arrows <\n-0001b860: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-0001b870: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n-0001b880: 6666 696e 6520 6172 6974 686d 6574 6963  ffine arithmetic\n-0001b890: 2e20 2020 2028 6c69 6e65 2032 3829 0a2a  .    (line 28).*\n-0001b8a0: 2061 7272 6f77 7320 3c32 3e3a 2020 2020   arrows <2>:    \n+0001b830: 2020 2020 4166 6669 6e65 2061 7269 7468      Affine arith\n+0001b840: 6d65 7469 632e 2020 2020 286c 696e 6520  metic.    (line \n+0001b850: 3131 290a 2a20 6172 726f 7773 203c 313e  11).* arrows <1>\n+0001b860: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001b870: 2020 2020 2020 2020 2020 2020 2041 6666               Aff\n+0001b880: 696e 6520 6172 6974 686d 6574 6963 2e20  ine arithmetic. \n+0001b890: 2020 2028 6c69 6e65 2032 3829 0a2a 2061     (line 28).* a\n+0001b8a0: 7272 6f77 7320 3c32 3e3a 2020 2020 2020  rrows <2>:      \n 0001b8b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b8c0: 2020 2020 2020 2020 4f76 6572 7669 6577          Overview\n-0001b8d0: 2e20 2020 2020 2020 2020 2020 2020 286c  .             (l\n-0001b8e0: 696e 6520 3639 290a 2a20 6172 726f 7773  ine 69).* arrows\n-0001b8f0: 203c 333e 3a20 2020 2020 2020 2020 2020   <3>:           \n-0001b900: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b910: 2041 2074 6563 686e 6963 616c 2064 7261   A technical dra\n-0001b920: 7769 6e67 2e20 2028 6c69 6e65 2032 3629  wing.  (line 26)\n-0001b930: 0a2a 2061 7272 6f77 7320 3c34 3e3a 2020  .* arrows <4>:  \n+0001b8c0: 2020 2020 2020 4f76 6572 7669 6577 2e20        Overview. \n+0001b8d0: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+0001b8e0: 6520 3639 290a 2a20 6172 726f 7773 203c  e 69).* arrows <\n+0001b8f0: 333e 3a20 2020 2020 2020 2020 2020 2020  3>:             \n+0001b900: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+0001b910: 2074 6563 686e 6963 616c 2064 7261 7769   technical drawi\n+0001b920: 6e67 2e20 2028 6c69 6e65 2032 3629 0a2a  ng.  (line 26).*\n+0001b930: 2061 7272 6f77 7320 3c34 3e3a 2020 2020   arrows <4>:    \n 0001b940: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b950: 2020 2020 2020 2020 2020 4120 7465 6368            A tech\n-0001b960: 6e69 6361 6c20 6472 6177 696e 672e 2020  nical drawing.  \n-0001b970: 286c 696e 6520 3638 290a 2a20 6173 696e  (line 68).* asin\n-0001b980: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001b950: 2020 2020 2020 2020 4120 7465 6368 6e69          A techni\n+0001b960: 6361 6c20 6472 6177 696e 672e 2020 286c  cal drawing.  (l\n+0001b970: 696e 6520 3638 290a 2a20 6173 696e 3a20  ine 68).* asin: \n+0001b980: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001b990: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b9a0: 2020 2055 6e61 7279 2066 6f72 6d73 2e20     Unary forms. \n-0001b9b0: 2020 2020 2020 2020 2028 6c69 6e65 2031           (line 1\n-0001b9c0: 3729 0a2a 2061 7461 6e32 3a20 2020 2020  7).* atan2:     \n+0001b9a0: 2055 6e61 7279 2066 6f72 6d73 2e20 2020   Unary forms.   \n+0001b9b0: 2020 2020 2020 2028 6c69 6e65 2031 3729         (line 17)\n+0001b9c0: 0a2a 2061 7461 6e32 3a20 2020 2020 2020  .* atan2:       \n 0001b9d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001b9e0: 2020 2020 2020 2020 2020 2020 556e 6172              Unar\n-0001b9f0: 7920 666f 726d 732e 2020 2020 2020 2020  y forms.        \n-0001ba00: 2020 286c 696e 6520 3139 290a 2a20 6361    (line 19).* ca\n-0001ba10: 6d65 7261 3a20 2020 2020 2020 2020 2020  mera:           \n+0001b9e0: 2020 2020 2020 2020 2020 556e 6172 7920            Unary \n+0001b9f0: 666f 726d 732e 2020 2020 2020 2020 2020  forms.          \n+0001ba00: 286c 696e 6520 3139 290a 2a20 6361 6d65  (line 19).* came\n+0001ba10: 7261 3a20 2020 2020 2020 2020 2020 2020  ra:             \n 0001ba20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ba30: 2020 2020 2043 616d 6572 612e 2020 2020       Camera.    \n-0001ba40: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-0001ba50: 2020 3629 0a2a 2063 6f6e 7465 7874 3a20    6).* context: \n+0001ba30: 2020 2043 616d 6572 612e 2020 2020 2020     Camera.      \n+0001ba40: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+0001ba50: 3629 0a2a 2063 6f6e 7465 7874 3a20 2020  6).* context:   \n 0001ba60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ba70: 2020 2020 2020 2020 2020 2020 2020 4c61                La\n-0001ba80: 6e67 7561 6765 2e20 2020 2020 2020 2020  nguage.         \n-0001ba90: 2020 2020 286c 696e 6520 3137 290a 2a20      (line 17).* \n-0001baa0: 636f 733a 2020 2020 2020 2020 2020 2020  cos:            \n+0001ba70: 2020 2020 2020 2020 2020 2020 4c61 6e67              Lang\n+0001ba80: 7561 6765 2e20 2020 2020 2020 2020 2020  uage.           \n+0001ba90: 2020 286c 696e 6520 3137 290a 2a20 636f    (line 17).* co\n+0001baa0: 733a 2020 2020 2020 2020 2020 2020 2020  s:              \n 0001bab0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bac0: 2020 2020 2020 2055 6e61 7279 2066 6f72         Unary for\n-0001bad0: 6d73 2e20 2020 2020 2020 2020 2028 6c69  ms.          (li\n-0001bae0: 6e65 2031 3629 0a2a 2063 756c 6c3a 2020  ne 16).* cull:  \n+0001bac0: 2020 2020 2055 6e61 7279 2066 6f72 6d73       Unary forms\n+0001bad0: 2e20 2020 2020 2020 2020 2028 6c69 6e65  .          (line\n+0001bae0: 2031 3629 0a2a 2063 756c 6c3a 2020 2020   16).* cull:    \n 0001baf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bb00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bb10: 4472 6177 696e 6720 6120 736f 6c69 642e  Drawing a solid.\n-0001bb20: 2020 2020 2020 286c 696e 6520 3435 290a        (line 45).\n-0001bb30: 2a20 6375 6c6c 203c 313e 3a20 2020 2020  * cull <1>:     \n+0001bb00: 2020 2020 2020 2020 2020 2020 2020 4472                Dr\n+0001bb10: 6177 696e 6720 6120 736f 6c69 642e 2020  awing a solid.  \n+0001bb20: 2020 2020 286c 696e 6520 3435 290a 2a20      (line 45).* \n+0001bb30: 6375 6c6c 203c 313e 3a20 2020 2020 2020  cull <1>:       \n 0001bb40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bb50: 2020 2020 2020 2020 2050 6f6c 796c 696e           Polylin\n-0001bb60: 6520 7377 6565 7073 2e20 2020 2020 2028  e sweeps.      (\n-0001bb70: 6c69 6e65 2020 3929 0a2a 2063 756c 6c20  line  9).* cull \n-0001bb80: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n+0001bb50: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n+0001bb60: 7377 6565 7073 2e20 2020 2020 2028 6c69  sweeps.      (li\n+0001bb70: 6e65 2020 3929 0a2a 2063 756c 6c20 3c32  ne  9).* cull <2\n+0001bb80: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n 0001bb90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bba0: 2020 5472 616e 7370 6172 656e 6379 2e20    Transparency. \n-0001bbb0: 2020 2020 2020 2020 286c 696e 6520 3135          (line 15\n-0001bbc0: 290a 2a20 6375 6c6c 203c 333e 3a20 2020  ).* cull <3>:   \n+0001bba0: 5472 616e 7370 6172 656e 6379 2e20 2020  Transparency.   \n+0001bbb0: 2020 2020 2020 286c 696e 6520 3135 290a        (line 15).\n+0001bbc0: 2a20 6375 6c6c 203c 333e 3a20 2020 2020  * cull <3>:     \n 0001bbd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bbe0: 2020 2020 2020 2020 2020 2041 2074 6563             A tec\n-0001bbf0: 686e 6963 616c 2064 7261 7769 6e67 2e20  hnical drawing. \n-0001bc00: 2028 6c69 6e65 2032 3029 0a2a 2063 756c   (line 20).* cul\n-0001bc10: 6c20 3c34 3e3a 2020 2020 2020 2020 2020  l <4>:          \n+0001bbe0: 2020 2020 2020 2020 2041 2074 6563 686e           A techn\n+0001bbf0: 6963 616c 2064 7261 7769 6e67 2e20 2028  ical drawing.  (\n+0001bc00: 6c69 6e65 2032 3029 0a2a 2063 756c 6c20  line 20).* cull \n+0001bc10: 3c34 3e3a 2020 2020 2020 2020 2020 2020  <4>:            \n 0001bc20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bc30: 2020 2020 496e 7465 726e 616c 206f 7074      Internal opt\n-0001bc40: 696f 6e73 2e20 2020 2020 286c 696e 6520  ions.     (line \n-0001bc50: 2037 290a 2a20 6375 6c6c 203c 353e 3a20   7).* cull <5>: \n+0001bc30: 2020 496e 7465 726e 616c 206f 7074 696f    Internal optio\n+0001bc40: 6e73 2e20 2020 2020 286c 696e 6520 2037  ns.     (line  7\n+0001bc50: 290a 2a20 6375 6c6c 203c 353e 3a20 2020  ).* cull <5>:   \n 0001bc60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bc70: 2020 2020 2020 2020 2020 2020 2047 6c6f               Glo\n-0001bc80: 6261 6c20 6f70 7469 6f6e 732e 2020 2020  bal options.    \n-0001bc90: 2020 2028 6c69 6e65 2031 3329 0a2a 2063     (line 13).* c\n-0001bca0: 7572 7665 3a20 2020 2020 2020 2020 2020  urve:           \n+0001bc70: 2020 2020 2020 2020 2020 2047 6c6f 6261             Globa\n+0001bc80: 6c20 6f70 7469 6f6e 732e 2020 2020 2020  l options.      \n+0001bc90: 2028 6c69 6e65 2031 3329 0a2a 2063 7572   (line 13).* cur\n+0001bca0: 7665 3a20 2020 2020 2020 2020 2020 2020  ve:             \n 0001bcb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bcc0: 2020 2020 2020 4375 7276 6573 2e20 2020        Curves.   \n-0001bcd0: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-0001bce0: 6520 2036 290a 2a20 6465 663a 2020 2020  e  6).* def:    \n+0001bcc0: 2020 2020 4375 7276 6573 2e20 2020 2020      Curves.     \n+0001bcd0: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+0001bce0: 2036 290a 2a20 6465 663a 2020 2020 2020   6).* def:      \n 0001bcf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bd00: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n-0001bd10: 7261 7769 6e67 2061 2073 6f6c 6964 2e20  rawing a solid. \n-0001bd20: 2020 2020 2028 6c69 6e65 2020 3929 0a2a       (line  9).*\n-0001bd30: 2064 6566 203c 313e 3a20 2020 2020 2020   def <1>:       \n+0001bd00: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n+0001bd10: 7769 6e67 2061 2073 6f6c 6964 2e20 2020  wing a solid.   \n+0001bd20: 2020 2028 6c69 6e65 2020 3929 0a2a 2064     (line  9).* d\n+0001bd30: 6566 203c 313e 3a20 2020 2020 2020 2020  ef <1>:         \n 0001bd40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bd50: 2020 2020 2020 2020 4472 6177 696e 6720          Drawing \n-0001bd60: 6120 736f 6c69 642e 2020 2020 2020 286c  a solid.      (l\n-0001bd70: 696e 6520 3232 290a 2a20 6465 6620 3c32  ine 22).* def <2\n-0001bd80: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001bd90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bda0: 204f 626a 6563 7420 7472 616e 7366 6f72   Object transfor\n-0001bdb0: 6d73 2e20 2020 2028 6c69 6e65 2031 3029  ms.    (line 10)\n-0001bdc0: 0a2a 2064 6566 203c 333e 3a20 2020 2020  .* def <3>:     \n+0001bd50: 2020 2020 2020 4472 6177 696e 6720 6120        Drawing a \n+0001bd60: 736f 6c69 642e 2020 2020 2020 286c 696e  solid.      (lin\n+0001bd70: 6520 3232 290a 2a20 6465 6620 3c32 3e3a  e 22).* def <2>:\n+0001bd80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001bd90: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n+0001bda0: 626a 6563 7420 7472 616e 7366 6f72 6d73  bject transforms\n+0001bdb0: 2e20 2020 2028 6c69 6e65 2031 3029 0a2a  .    (line 10).*\n+0001bdc0: 2064 6566 203c 333e 3a20 2020 2020 2020   def <3>:       \n 0001bdd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bde0: 2020 2020 2020 2020 2020 506f 696e 7420            Point \n-0001bdf0: 7377 6565 7073 2e20 2020 2020 2020 2020  sweeps.         \n-0001be00: 286c 696e 6520 3139 290a 2a20 6465 6620  (line 19).* def \n-0001be10: 3c34 3e3a 2020 2020 2020 2020 2020 2020  <4>:            \n+0001bde0: 2020 2020 2020 2020 506f 696e 7420 7377          Point sw\n+0001bdf0: 6565 7073 2e20 2020 2020 2020 2020 286c  eeps.         (l\n+0001be00: 696e 6520 3139 290a 2a20 6465 6620 3c34  ine 19).* def <4\n+0001be10: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n 0001be20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001be30: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n-0001be40: 7073 2e20 2020 2020 2028 6c69 6e65 2020  ps.      (line  \n-0001be50: 3929 0a2a 2064 6566 203c 353e 3a20 2020  9).* def <5>:   \n+0001be30: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n+0001be40: 2e20 2020 2020 2028 6c69 6e65 2020 3929  .      (line  9)\n+0001be50: 0a2a 2064 6566 203c 353e 3a20 2020 2020  .* def <5>:     \n 0001be60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001be70: 2020 2020 2020 2020 2020 2020 4e65 7374              Nest\n-0001be80: 6564 2073 7765 6570 732e 2020 2020 2020  ed sweeps.      \n-0001be90: 2020 286c 696e 6520 2038 290a 2a20 6465    (line  8).* de\n-0001bea0: 6620 3c36 3e3a 2020 2020 2020 2020 2020  f <6>:          \n+0001be70: 2020 2020 2020 2020 2020 4e65 7374 6564            Nested\n+0001be80: 2073 7765 6570 732e 2020 2020 2020 2020   sweeps.        \n+0001be90: 286c 696e 6520 2038 290a 2a20 6465 6620  (line  8).* def \n+0001bea0: 3c36 3e3a 2020 2020 2020 2020 2020 2020  <6>:            \n 0001beb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bec0: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n-0001bed0: 6565 7073 2077 6974 6820 636c 6f73 7572  eeps with closur\n-0001bee0: 652e 0a20 2020 2020 2020 2020 2020 2020  e..             \n+0001bec0: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n+0001bed0: 7073 2077 6974 6820 636c 6f73 7572 652e  ps with closure.\n+0001bee0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \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 2020                  \n-0001bf20: 2020 286c 696e 6520 3130 290a 2a20 6465    (line 10).* de\n-0001bf30: 6620 3c37 3e3a 2020 2020 2020 2020 2020  f <7>:          \n+0001bf20: 286c 696e 6520 3130 290a 2a20 6465 6620  (line 10).* def \n+0001bf30: 3c37 3e3a 2020 2020 2020 2020 2020 2020  <7>:            \n 0001bf40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bf50: 2020 2020 2041 6666 696e 6520 6172 6974       Affine arit\n-0001bf60: 686d 6574 6963 2e20 2020 2028 6c69 6e65  hmetic.    (line\n-0001bf70: 2031 3129 0a2a 2064 6566 203c 383e 3a20   11).* def <8>: \n+0001bf50: 2020 2041 6666 696e 6520 6172 6974 686d     Affine arithm\n+0001bf60: 6574 6963 2e20 2020 2028 6c69 6e65 2031  etic.    (line 1\n+0001bf70: 3129 0a2a 2064 6566 203c 383e 3a20 2020  1).* def <8>:   \n 0001bf80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bf90: 2020 2020 2020 2020 2020 2020 2020 4f76                Ov\n-0001bfa0: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n-0001bfb0: 2020 2020 286c 696e 6520 3132 290a 2a20      (line 12).* \n-0001bfc0: 6465 6620 3c39 3e3a 2020 2020 2020 2020  def <9>:        \n+0001bf90: 2020 2020 2020 2020 2020 2020 4f76 6572              Over\n+0001bfa0: 7669 6577 2e20 2020 2020 2020 2020 2020  view.           \n+0001bfb0: 2020 286c 696e 6520 3132 290a 2a20 6465    (line 12).* de\n+0001bfc0: 6620 3c39 3e3a 2020 2020 2020 2020 2020  f <9>:          \n 0001bfd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001bfe0: 2020 2020 2020 204f 7665 7276 6965 772e         Overview.\n-0001bff0: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n-0001c000: 6e65 2033 3729 0a2a 2064 6566 203c 3130  ne 37).* def <10\n-0001c010: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001c020: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c030: 4f76 6572 7669 6577 2e20 2020 2020 2020  Overview.       \n-0001c040: 2020 2020 2020 286c 696e 6520 3639 290a        (line 69).\n-0001c050: 2a20 6465 6620 3c31 313e 3a20 2020 2020  * def <11>:     \n+0001bfe0: 2020 2020 204f 7665 7276 6965 772e 2020       Overview.  \n+0001bff0: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001c000: 2033 3729 0a2a 2064 6566 203c 3130 3e3a   37).* def <10>:\n+0001c010: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c020: 2020 2020 2020 2020 2020 2020 2020 4f76                Ov\n+0001c030: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n+0001c040: 2020 2020 286c 696e 6520 3639 290a 2a20      (line 69).* \n+0001c050: 6465 6620 3c31 313e 3a20 2020 2020 2020  def <11>:       \n 0001c060: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c070: 2020 2020 2020 2020 2041 2074 6563 686e           A techn\n-0001c080: 6963 616c 2064 7261 7769 6e67 2e20 2028  ical drawing.  (\n-0001c090: 6c69 6e65 2031 3429 0a2a 2064 6566 203c  line 14).* def <\n-0001c0a0: 3132 3e3a 2020 2020 2020 2020 2020 2020  12>:            \n+0001c070: 2020 2020 2020 2041 2074 6563 686e 6963         A technic\n+0001c080: 616c 2064 7261 7769 6e67 2e20 2028 6c69  al drawing.  (li\n+0001c090: 6e65 2031 3429 0a2a 2064 6566 203c 3132  ne 14).* def <12\n+0001c0a0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n 0001c0b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c0c0: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n-0001c0d0: 6177 696e 672e 2020 286c 696e 6520 3236  awing.  (line 26\n-0001c0e0: 290a 2a20 6465 6620 3c31 333e 3a20 2020  ).* def <13>:   \n+0001c0c0: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n+0001c0d0: 696e 672e 2020 286c 696e 6520 3236 290a  ing.  (line 26).\n+0001c0e0: 2a20 6465 6620 3c31 333e 3a20 2020 2020  * def <13>:     \n 0001c0f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c100: 2020 2020 2020 2020 2020 2041 2074 6563             A tec\n-0001c110: 686e 6963 616c 2064 7261 7769 6e67 2e20  hnical drawing. \n-0001c120: 2028 6c69 6e65 2034 3129 0a2a 2064 6566   (line 41).* def\n-0001c130: 203c 3134 3e3a 2020 2020 2020 2020 2020   <14>:          \n+0001c100: 2020 2020 2020 2020 2041 2074 6563 686e           A techn\n+0001c110: 6963 616c 2064 7261 7769 6e67 2e20 2028  ical drawing.  (\n+0001c120: 6c69 6e65 2034 3129 0a2a 2064 6566 203c  line 41).* def <\n+0001c130: 3134 3e3a 2020 2020 2020 2020 2020 2020  14>:            \n 0001c140: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c150: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n-0001c160: 6472 6177 696e 672e 2020 286c 696e 6520  drawing.  (line \n-0001c170: 3638 290a 2a20 6465 6620 3c31 353e 3a20  68).* def <15>: \n+0001c150: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n+0001c160: 6177 696e 672e 2020 286c 696e 6520 3638  awing.  (line 68\n+0001c170: 290a 2a20 6465 6620 3c31 353e 3a20 2020  ).* def <15>:   \n 0001c180: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c190: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n-0001c1a0: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n-0001c1b0: 2e20 2028 6c69 6e65 2039 3529 0a2a 2064  .  (line 95).* d\n-0001c1c0: 6566 203c 3136 3e3a 2020 2020 2020 2020  ef <16>:        \n+0001c190: 2020 2020 2020 2020 2020 2041 2074 6563             A tec\n+0001c1a0: 686e 6963 616c 2064 7261 7769 6e67 2e20  hnical drawing. \n+0001c1b0: 2028 6c69 6e65 2039 3529 0a2a 2064 6566   (line 95).* def\n+0001c1c0: 203c 3136 3e3a 2020 2020 2020 2020 2020   <16>:          \n 0001c1d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c1e0: 2020 2020 2020 4120 6869 6572 6172 6368        A hierarch\n-0001c1f0: 6963 616c 206d 6f64 656c 2e20 286c 696e  ical model. (lin\n-0001c200: 6520 3130 290a 2a20 6465 6620 3c31 373e  e 10).* def <17>\n-0001c210: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001c220: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n-0001c230: 2068 6965 7261 7263 6869 6361 6c20 6d6f   hierarchical mo\n-0001c240: 6465 6c2e 2028 6c69 6e65 2032 3329 0a2a  del. (line 23).*\n-0001c250: 2064 6566 203c 3138 3e3a 2020 2020 2020   def <18>:      \n+0001c1e0: 2020 2020 4120 6869 6572 6172 6368 6963      A hierarchic\n+0001c1f0: 616c 206d 6f64 656c 2e20 286c 696e 6520  al model. (line \n+0001c200: 3130 290a 2a20 6465 6620 3c31 373e 3a20  10).* def <17>: \n+0001c210: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c220: 2020 2020 2020 2020 2020 2020 2041 2068               A h\n+0001c230: 6965 7261 7263 6869 6361 6c20 6d6f 6465  ierarchical mode\n+0001c240: 6c2e 2028 6c69 6e65 2032 3329 0a2a 2064  l. (line 23).* d\n+0001c250: 6566 203c 3138 3e3a 2020 2020 2020 2020  ef <18>:        \n 0001c260: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c270: 2020 2020 2020 2020 4120 6869 6572 6172          A hierar\n-0001c280: 6368 6963 616c 206d 6f64 656c 2e20 286c  chical model. (l\n-0001c290: 696e 6520 3332 290a 2a20 646f 7473 3a20  ine 32).* dots: \n+0001c270: 2020 2020 2020 4120 6869 6572 6172 6368        A hierarch\n+0001c280: 6963 616c 206d 6f64 656c 2e20 286c 696e  ical model. (lin\n+0001c290: 6520 3332 290a 2a20 646f 7473 3a20 2020  e 32).* dots:   \n 0001c2a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c2b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c2c0: 2044 6f74 732e 2020 2020 2020 2020 2020   Dots.          \n-0001c2d0: 2020 2020 2020 2028 6c69 6e65 2020 3629         (line  6)\n-0001c2e0: 0a2a 2066 696c 6c20 6f70 6163 6974 793a  .* fill opacity:\n+0001c2b0: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n+0001c2c0: 6f74 732e 2020 2020 2020 2020 2020 2020  ots.            \n+0001c2d0: 2020 2020 2028 6c69 6e65 2020 3629 0a2a       (line  6).*\n+0001c2e0: 2066 696c 6c20 6f70 6163 6974 793a 2020   fill opacity:  \n 0001c2f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c300: 2020 2020 2020 2020 2020 5472 616e 7370            Transp\n-0001c310: 6172 656e 6379 2e20 2020 2020 2020 2020  arency.         \n-0001c320: 286c 696e 6520 3130 290a 2a20 6669 6c6c  (line 10).* fill\n-0001c330: 2073 7479 6c65 3a20 2020 2020 2020 2020   style:         \n+0001c300: 2020 2020 2020 2020 5472 616e 7370 6172          Transpar\n+0001c310: 656e 6379 2e20 2020 2020 2020 2020 286c  ency.         (l\n+0001c320: 696e 6520 3130 290a 2a20 6669 6c6c 2073  ine 10).* fill s\n+0001c330: 7479 6c65 3a20 2020 2020 2020 2020 2020  tyle:           \n 0001c340: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c350: 2020 2054 696b 5a2f 5047 4620 7573 6572     TikZ/PGF user\n-0001c360: 2d64 6566 696e 6564 2073 7479 6c65 732e  -defined styles.\n-0001c370: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+0001c350: 2054 696b 5a2f 5047 4620 7573 6572 2d64   TikZ/PGF user-d\n+0001c360: 6566 696e 6564 2073 7479 6c65 732e 0a20  efined styles.. \n+0001c370: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020                  \n-0001c3b0: 286c 696e 6520 3235 290a 2a20 6669 6c6c  (line 25).* fill\n-0001c3c0: 636f 6c6f 723a 2020 2020 2020 2020 2020  color:          \n+0001c3a0: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+0001c3b0: 696e 6520 3235 290a 2a20 6669 6c6c 636f  ine 25).* fillco\n+0001c3c0: 6c6f 723a 2020 2020 2020 2020 2020 2020  lor:            \n 0001c3d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c3e0: 2020 204f 626a 6563 7420 7472 616e 7366     Object transf\n-0001c3f0: 6f72 6d73 2e20 2020 2028 6c69 6e65 2031  orms.    (line 1\n-0001c400: 3029 0a2a 2066 696c 6c63 6f6c 6f72 203c  0).* fillcolor <\n-0001c410: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-0001c420: 2020 2020 2020 2020 2020 2020 506f 6c79              Poly\n-0001c430: 6c69 6e65 2073 7765 6570 7320 7769 7468  line sweeps with\n-0001c440: 2063 6c6f 7375 7265 2e0a 2020 2020 2020   closure..      \n+0001c3e0: 204f 626a 6563 7420 7472 616e 7366 6f72   Object transfor\n+0001c3f0: 6d73 2e20 2020 2028 6c69 6e65 2031 3029  ms.    (line 10)\n+0001c400: 0a2a 2066 696c 6c63 6f6c 6f72 203c 313e  .* fillcolor <1>\n+0001c410: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001c420: 2020 2020 2020 2020 2020 506f 6c79 6c69            Polyli\n+0001c430: 6e65 2073 7765 6570 7320 7769 7468 2063  ne sweeps with c\n+0001c440: 6c6f 7375 7265 2e0a 2020 2020 2020 2020  losure..        \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 2020 2020 2028 6c69 6e65 2031           (line 1\n-0001c490: 3029 0a2a 2066 696c 6c63 6f6c 6f72 203c  0).* fillcolor <\n-0001c4a0: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n-0001c4b0: 2020 2020 2020 2020 2020 2020 4f76 6572              Over\n-0001c4c0: 7669 6577 2e20 2020 2020 2020 2020 2020  view.           \n-0001c4d0: 2020 286c 696e 6520 3337 290a 2a20 6672    (line 37).* fr\n-0001c4e0: 616d 653a 2020 2020 2020 2020 2020 2020  ame:            \n+0001c480: 2020 2020 2020 2028 6c69 6e65 2031 3029         (line 10)\n+0001c490: 0a2a 2066 696c 6c63 6f6c 6f72 203c 323e  .* fillcolor <2>\n+0001c4a0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001c4b0: 2020 2020 2020 2020 2020 4f76 6572 7669            Overvi\n+0001c4c0: 6577 2e20 2020 2020 2020 2020 2020 2020  ew.             \n+0001c4d0: 286c 696e 6520 3337 290a 2a20 6672 616d  (line 37).* fram\n+0001c4e0: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n 0001c4f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c500: 2020 2020 2046 7261 6d65 2e20 2020 2020       Frame.     \n-0001c510: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-0001c520: 2020 3629 0a2a 2066 7261 6d65 7365 703a    6).* framesep:\n+0001c500: 2020 2046 7261 6d65 2e20 2020 2020 2020     Frame.       \n+0001c510: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+0001c520: 3629 0a2a 2066 7261 6d65 7365 703a 2020  6).* framesep:  \n 0001c530: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c540: 2020 2020 2020 2020 2020 2020 2020 4672                Fr\n-0001c550: 616d 652e 2020 2020 2020 2020 2020 2020  ame.            \n-0001c560: 2020 2020 286c 696e 6520 3131 290a 2a20      (line 11).* \n-0001c570: 676c 6f62 616c 3a20 2020 2020 2020 2020  global:         \n+0001c540: 2020 2020 2020 2020 2020 2020 4672 616d              Fram\n+0001c550: 652e 2020 2020 2020 2020 2020 2020 2020  e.              \n+0001c560: 2020 286c 696e 6520 3131 290a 2a20 676c    (line 11).* gl\n+0001c570: 6f62 616c 3a20 2020 2020 2020 2020 2020  obal:           \n 0001c580: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c590: 2020 2020 2020 2047 6c6f 6261 6c20 656e         Global en\n-0001c5a0: 7669 726f 6e6d 656e 742e 2020 2028 6c69  vironment.   (li\n-0001c5b0: 6e65 2031 3229 0a2a 2069 6e70 7574 3a20  ne 12).* input: \n+0001c590: 2020 2020 2047 6c6f 6261 6c20 656e 7669       Global envi\n+0001c5a0: 726f 6e6d 656e 742e 2020 2028 6c69 6e65  ronment.   (line\n+0001c5b0: 2031 3229 0a2a 2069 6e70 7574 3a20 2020   12).* input:   \n 0001c5c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c5d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c5e0: 4c61 6e67 7561 6765 2062 6173 6963 732e  Language basics.\n-0001c5f0: 2020 2020 2020 286c 696e 6520 3139 290a        (line 19).\n-0001c600: 2a20 696e 7665 7273 653a 2020 2020 2020  * inverse:      \n+0001c5d0: 2020 2020 2020 2020 2020 2020 2020 4c61                La\n+0001c5e0: 6e67 7561 6765 2062 6173 6963 732e 2020  nguage basics.  \n+0001c5f0: 2020 2020 286c 696e 6520 3139 290a 2a20      (line 19).* \n+0001c600: 696e 7665 7273 653a 2020 2020 2020 2020  inverse:        \n 0001c610: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c620: 2020 2020 2020 2020 2055 6e61 7279 2066           Unary f\n-0001c630: 6f72 6d73 2e20 2020 2020 2020 2020 2028  orms.          (\n-0001c640: 6c69 6e65 2032 3129 0a2a 206c 616e 6775  line 21).* langu\n-0001c650: 6167 653a 2020 2020 2020 2020 2020 2020  age:            \n+0001c620: 2020 2020 2020 2055 6e61 7279 2066 6f72         Unary for\n+0001c630: 6d73 2e20 2020 2020 2020 2020 2028 6c69  ms.          (li\n+0001c640: 6e65 2032 3129 0a2a 206c 616e 6775 6167  ne 21).* languag\n+0001c650: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n 0001c660: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c670: 2020 4c61 6e67 7561 6765 2e20 2020 2020    Language.     \n-0001c680: 2020 2020 2020 2020 286c 696e 6520 2036          (line  6\n-0001c690: 290a 2a20 6c61 7465 783a 2020 2020 2020  ).* latex:      \n+0001c670: 4c61 6e67 7561 6765 2e20 2020 2020 2020  Language.       \n+0001c680: 2020 2020 2020 286c 696e 6520 2036 290a        (line  6).\n+0001c690: 2a20 6c61 7465 783a 2020 2020 2020 2020  * latex:        \n 0001c6a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c6b0: 2020 2020 2020 2020 2020 204c 616e 6775             Langu\n-0001c6c0: 6167 652e 2020 2020 2020 2020 2020 2020  age.            \n-0001c6d0: 2028 6c69 6e65 2031 3729 0a2a 206c 6179   (line 17).* lay\n-0001c6e0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001c6b0: 2020 2020 2020 2020 204c 616e 6775 6167           Languag\n+0001c6c0: 652e 2020 2020 2020 2020 2020 2020 2028  e.             (\n+0001c6d0: 6c69 6e65 2031 3729 0a2a 206c 6179 3a20  line 17).* lay: \n+0001c6e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001c6f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c700: 2020 2020 5370 6563 6961 6c20 6f62 6a65      Special obje\n-0001c710: 6374 732e 2020 2020 2020 286c 696e 6520  cts.      (line \n-0001c720: 3438 290a 2a20 6c61 7920 3c31 3e3a 2020  48).* lay <1>:  \n+0001c700: 2020 5370 6563 6961 6c20 6f62 6a65 6374    Special object\n+0001c710: 732e 2020 2020 2020 286c 696e 6520 3438  s.      (line 48\n+0001c720: 290a 2a20 6c61 7920 3c31 3e3a 2020 2020  ).* lay <1>:    \n 0001c730: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c740: 2020 2020 2020 2020 2020 2020 2054 696b               Tik\n-0001c750: 5a2f 5047 4620 7573 6572 2d64 6566 696e  Z/PGF user-defin\n-0001c760: 6564 2073 7479 6c65 732e 0a20 2020 2020  ed styles..     \n+0001c740: 2020 2020 2020 2020 2020 2054 696b 5a2f             TikZ/\n+0001c750: 5047 4620 7573 6572 2d64 6566 696e 6564  PGF user-defined\n+0001c760: 2073 7479 6c65 732e 0a20 2020 2020 2020   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 2020 2020 286c 696e 6520            (line \n-0001c7b0: 3336 290a 2a20 6c61 7920 3c32 3e3a 2020  36).* lay <2>:  \n+0001c7a0: 2020 2020 2020 2020 286c 696e 6520 3336          (line 36\n+0001c7b0: 290a 2a20 6c61 7920 3c32 3e3a 2020 2020  ).* lay <2>:    \n 0001c7c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c7d0: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n-0001c7e0: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n-0001c7f0: 2e20 2028 6c69 6e65 2032 3629 0a2a 206c  .  (line 26).* l\n-0001c800: 6179 203c 333e 3a20 2020 2020 2020 2020  ay <3>:         \n+0001c7d0: 2020 2020 2020 2020 2020 2041 2074 6563             A tec\n+0001c7e0: 686e 6963 616c 2064 7261 7769 6e67 2e20  hnical drawing. \n+0001c7f0: 2028 6c69 6e65 2032 3629 0a2a 206c 6179   (line 26).* lay\n+0001c800: 203c 333e 3a20 2020 2020 2020 2020 2020   <3>:           \n 0001c810: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c820: 2020 2020 2020 4120 7465 6368 6e69 6361        A technica\n-0001c830: 6c20 6472 6177 696e 672e 2020 286c 696e  l drawing.  (lin\n-0001c840: 6520 3236 290a 2a20 6c61 7920 3c34 3e3a  e 26).* lay <4>:\n+0001c820: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n+0001c830: 6472 6177 696e 672e 2020 286c 696e 6520  drawing.  (line \n+0001c840: 3236 290a 2a20 6c61 7920 3c34 3e3a 2020  26).* lay <4>:  \n 0001c850: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c860: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n-0001c870: 2074 6563 686e 6963 616c 2064 7261 7769   technical drawi\n-0001c880: 6e67 2e20 2028 6c69 6e65 2039 3529 0a2a  ng.  (line 95).*\n-0001c890: 206c 6179 203c 353e 3a20 2020 2020 2020   lay <5>:       \n+0001c860: 2020 2020 2020 2020 2020 2020 2041 2074               A t\n+0001c870: 6563 686e 6963 616c 2064 7261 7769 6e67  echnical drawing\n+0001c880: 2e20 2028 6c69 6e65 2039 3529 0a2a 206c  .  (line 95).* l\n+0001c890: 6179 203c 353e 3a20 2020 2020 2020 2020  ay <5>:         \n 0001c8a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c8b0: 2020 2020 2020 2020 496e 7465 726e 616c          Internal\n-0001c8c0: 206f 7074 696f 6e73 2e20 2020 2020 286c   options.     (l\n-0001c8d0: 696e 6520 2037 290a 2a20 6c61 7920 3c36  ine  7).* lay <6\n-0001c8e0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001c8f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c900: 2053 7065 6369 616c 732e 2020 2020 2020   Specials.      \n-0001c910: 2020 2020 2020 2028 6c69 6e65 2034 3229         (line 42)\n-0001c920: 0a2a 206c 6179 203c 373e 3a20 2020 2020  .* lay <7>:     \n+0001c8b0: 2020 2020 2020 496e 7465 726e 616c 206f        Internal o\n+0001c8c0: 7074 696f 6e73 2e20 2020 2020 286c 696e  ptions.     (lin\n+0001c8d0: 6520 2037 290a 2a20 6c61 7920 3c36 3e3a  e  7).* lay <6>:\n+0001c8e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001c8f0: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n+0001c900: 7065 6369 616c 732e 2020 2020 2020 2020  pecials.        \n+0001c910: 2020 2020 2028 6c69 6e65 2034 3229 0a2a       (line 42).*\n+0001c920: 206c 6179 203c 373e 3a20 2020 2020 2020   lay <7>:       \n 0001c930: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c940: 2020 2020 2020 2020 2020 476c 6f62 616c            Global\n-0001c950: 206f 7074 696f 6e73 2e20 2020 2020 2020   options.       \n-0001c960: 286c 696e 6520 3133 290a 2a20 6c69 6e65  (line 13).* line\n-0001c970: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001c940: 2020 2020 2020 2020 476c 6f62 616c 206f          Global o\n+0001c950: 7074 696f 6e73 2e20 2020 2020 2020 286c  ptions.       (l\n+0001c960: 696e 6520 3133 290a 2a20 6c69 6e65 3a20  ine 13).* line: \n+0001c970: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001c980: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c990: 2020 2044 7261 7769 6e67 206f 7074 696f     Drawing optio\n-0001c9a0: 6e73 2e20 2020 2020 2028 6c69 6e65 2020  ns.      (line  \n-0001c9b0: 3729 0a2a 206c 696e 6520 3c31 3e3a 2020  7).* line <1>:  \n+0001c990: 2044 7261 7769 6e67 206f 7074 696f 6e73   Drawing options\n+0001c9a0: 2e20 2020 2020 2028 6c69 6e65 2020 3729  .      (line  7)\n+0001c9b0: 0a2a 206c 696e 6520 3c31 3e3a 2020 2020  .* line <1>:    \n 0001c9c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001c9d0: 2020 2020 2020 2020 2020 2020 4f62 6a65              Obje\n-0001c9e0: 6374 2074 7261 6e73 666f 726d 732e 2020  ct transforms.  \n-0001c9f0: 2020 286c 696e 6520 3130 290a 2a20 6c69    (line 10).* li\n-0001ca00: 6e65 203c 323e 3a20 2020 2020 2020 2020  ne <2>:         \n+0001c9d0: 2020 2020 2020 2020 2020 4f62 6a65 6374            Object\n+0001c9e0: 2074 7261 6e73 666f 726d 732e 2020 2020   transforms.    \n+0001c9f0: 286c 696e 6520 3130 290a 2a20 6c69 6e65  (line 10).* line\n+0001ca00: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n 0001ca10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ca20: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n-0001ca30: 6565 7073 2077 6974 6820 636c 6f73 7572  eeps with closur\n-0001ca40: 652e 0a20 2020 2020 2020 2020 2020 2020  e..             \n+0001ca20: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n+0001ca30: 7073 2077 6974 6820 636c 6f73 7572 652e  ps with closure.\n+0001ca40: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \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 2020                  \n-0001ca80: 2020 286c 696e 6520 3130 290a 2a20 6c69    (line 10).* li\n-0001ca90: 6e65 203c 333e 3a20 2020 2020 2020 2020  ne <3>:         \n+0001ca80: 286c 696e 6520 3130 290a 2a20 6c69 6e65  (line 10).* line\n+0001ca90: 203c 333e 3a20 2020 2020 2020 2020 2020   <3>:           \n 0001caa0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cab0: 2020 2020 2041 6666 696e 6520 6172 6974       Affine arit\n-0001cac0: 686d 6574 6963 2e20 2020 2028 6c69 6e65  hmetic.    (line\n-0001cad0: 2031 3129 0a2a 206c 696e 6520 3c34 3e3a   11).* line <4>:\n+0001cab0: 2020 2041 6666 696e 6520 6172 6974 686d     Affine arithm\n+0001cac0: 6574 6963 2e20 2020 2028 6c69 6e65 2031  etic.    (line 1\n+0001cad0: 3129 0a2a 206c 696e 6520 3c34 3e3a 2020  1).* line <4>:  \n 0001cae0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001caf0: 2020 2020 2020 2020 2020 2020 2020 4c69                Li\n-0001cb00: 6e65 732e 2020 2020 2020 2020 2020 2020  nes.            \n-0001cb10: 2020 2020 286c 696e 6520 2036 290a 2a20      (line  6).* \n-0001cb20: 6c69 6e65 203c 353e 3a20 2020 2020 2020  line <5>:       \n+0001caf0: 2020 2020 2020 2020 2020 2020 4c69 6e65              Line\n+0001cb00: 732e 2020 2020 2020 2020 2020 2020 2020  s.              \n+0001cb10: 2020 286c 696e 6520 2036 290a 2a20 6c69    (line  6).* li\n+0001cb20: 6e65 203c 353e 3a20 2020 2020 2020 2020  ne <5>:         \n 0001cb30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cb40: 2020 2020 2020 2053 7765 7074 2062 6c6f         Swept blo\n-0001cb50: 636b 732e 2020 2020 2020 2020 2028 6c69  cks.         (li\n-0001cb60: 6e65 2020 3729 0a2a 206c 696e 6520 3c36  ne  7).* line <6\n-0001cb70: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001cb80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cb90: 4f76 6572 7669 6577 2e20 2020 2020 2020  Overview.       \n-0001cba0: 2020 2020 2020 286c 696e 6520 3639 290a        (line 69).\n-0001cbb0: 2a20 6c69 6e65 203c 373e 3a20 2020 2020  * line <7>:     \n+0001cb40: 2020 2020 2053 7765 7074 2062 6c6f 636b       Swept block\n+0001cb50: 732e 2020 2020 2020 2020 2028 6c69 6e65  s.         (line\n+0001cb60: 2020 3729 0a2a 206c 696e 6520 3c36 3e3a    7).* line <6>:\n+0001cb70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001cb80: 2020 2020 2020 2020 2020 2020 2020 4f76                Ov\n+0001cb90: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n+0001cba0: 2020 2020 286c 696e 6520 3639 290a 2a20      (line 69).* \n+0001cbb0: 6c69 6e65 203c 373e 3a20 2020 2020 2020  line <7>:       \n 0001cbc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cbd0: 2020 2020 2020 2020 2041 2074 6563 686e           A techn\n-0001cbe0: 6963 616c 2064 7261 7769 6e67 2e20 2028  ical drawing.  (\n-0001cbf0: 6c69 6e65 2032 3029 0a2a 206c 696e 6520  line 20).* line \n-0001cc00: 3c38 3e3a 2020 2020 2020 2020 2020 2020  <8>:            \n+0001cbd0: 2020 2020 2020 2041 2074 6563 686e 6963         A technic\n+0001cbe0: 616c 2064 7261 7769 6e67 2e20 2028 6c69  al drawing.  (li\n+0001cbf0: 6e65 2032 3029 0a2a 206c 696e 6520 3c38  ne 20).* line <8\n+0001cc00: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n 0001cc10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cc20: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n-0001cc30: 6177 696e 672e 2020 286c 696e 6520 3236  awing.  (line 26\n-0001cc40: 290a 2a20 6c69 6e65 203c 393e 3a20 2020  ).* line <9>:   \n+0001cc20: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n+0001cc30: 696e 672e 2020 286c 696e 6520 3236 290a  ing.  (line 26).\n+0001cc40: 2a20 6c69 6e65 203c 393e 3a20 2020 2020  * line <9>:     \n 0001cc50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cc60: 2020 2020 2020 2020 2020 2041 2074 6563             A tec\n-0001cc70: 686e 6963 616c 2064 7261 7769 6e67 2e20  hnical drawing. \n-0001cc80: 2028 6c69 6e65 2034 3129 0a2a 206c 696e   (line 41).* lin\n-0001cc90: 6520 3c31 303e 3a20 2020 2020 2020 2020  e <10>:         \n+0001cc60: 2020 2020 2020 2020 2041 2074 6563 686e           A techn\n+0001cc70: 6963 616c 2064 7261 7769 6e67 2e20 2028  ical drawing.  (\n+0001cc80: 6c69 6e65 2034 3129 0a2a 206c 696e 6520  line 41).* line \n+0001cc90: 3c31 303e 3a20 2020 2020 2020 2020 2020  <10>:           \n 0001cca0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ccb0: 2020 2020 4120 7465 6368 6e69 6361 6c20      A technical \n-0001ccc0: 6472 6177 696e 672e 2020 286c 696e 6520  drawing.  (line \n-0001ccd0: 3638 290a 2a20 6c69 6e65 203c 3131 3e3a  68).* line <11>:\n+0001ccb0: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n+0001ccc0: 6177 696e 672e 2020 286c 696e 6520 3638  awing.  (line 68\n+0001ccd0: 290a 2a20 6c69 6e65 203c 3131 3e3a 2020  ).* line <11>:  \n 0001cce0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ccf0: 2020 2020 2020 2020 2020 2020 2041 2068               A h\n-0001cd00: 6965 7261 7263 6869 6361 6c20 6d6f 6465  ierarchical mode\n-0001cd10: 6c2e 2028 6c69 6e65 2031 3029 0a2a 206c  l. (line 10).* l\n-0001cd20: 696e 6520 7374 796c 653a 2020 2020 2020  ine style:      \n+0001ccf0: 2020 2020 2020 2020 2020 2041 2068 6965             A hie\n+0001cd00: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e  rarchical model.\n+0001cd10: 2028 6c69 6e65 2031 3029 0a2a 206c 696e   (line 10).* lin\n+0001cd20: 6520 7374 796c 653a 2020 2020 2020 2020  e style:        \n 0001cd30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cd40: 2020 2020 2020 5469 6b5a 2f50 4746 2075        TikZ/PGF u\n-0001cd50: 7365 722d 6465 6669 6e65 6420 7374 796c  ser-defined styl\n-0001cd60: 6573 2e0a 2020 2020 2020 2020 2020 2020  es..            \n+0001cd40: 2020 2020 5469 6b5a 2f50 4746 2075 7365      TikZ/PGF use\n+0001cd50: 722d 6465 6669 6e65 6420 7374 796c 6573  r-defined styles\n+0001cd60: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020                  \n-0001cda0: 2020 2028 6c69 6e65 2032 3529 0a2a 206c     (line 25).* l\n-0001cdb0: 696e 6563 6f6c 6f72 3a20 2020 2020 2020  inecolor:       \n+0001cda0: 2028 6c69 6e65 2032 3529 0a2a 206c 696e   (line 25).* lin\n+0001cdb0: 6563 6f6c 6f72 3a20 2020 2020 2020 2020  ecolor:         \n 0001cdc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cdd0: 2020 2020 2020 4f62 6a65 6374 2074 7261        Object tra\n-0001cde0: 6e73 666f 726d 732e 2020 2020 286c 696e  nsforms.    (lin\n-0001cdf0: 6520 3130 290a 2a20 6c69 6e65 636f 6c6f  e 10).* linecolo\n-0001ce00: 7220 3c31 3e3a 2020 2020 2020 2020 2020  r <1>:          \n-0001ce10: 2020 2020 2020 2020 2020 2020 2020 2046                 F\n-0001ce20: 7261 6d65 2e20 2020 2020 2020 2020 2020  rame.           \n-0001ce30: 2020 2020 2028 6c69 6e65 2031 3029 0a2a       (line 10).*\n-0001ce40: 206c 696e 6563 6f6c 6f72 203c 323e 3a20   linecolor <2>: \n+0001cdd0: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n+0001cde0: 666f 726d 732e 2020 2020 286c 696e 6520  forms.    (line \n+0001cdf0: 3130 290a 2a20 6c69 6e65 636f 6c6f 7220  10).* linecolor \n+0001ce00: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n+0001ce10: 2020 2020 2020 2020 2020 2020 2046 7261               Fra\n+0001ce20: 6d65 2e20 2020 2020 2020 2020 2020 2020  me.             \n+0001ce30: 2020 2028 6c69 6e65 2031 3029 0a2a 206c     (line 10).* l\n+0001ce40: 696e 6563 6f6c 6f72 203c 323e 3a20 2020  inecolor <2>:   \n 0001ce50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ce60: 2020 2020 2020 2020 4f76 6572 7669 6577          Overview\n-0001ce70: 2e20 2020 2020 2020 2020 2020 2020 286c  .             (l\n-0001ce80: 696e 6520 3639 290a 2a20 6c69 6e65 7374  ine 69).* linest\n-0001ce90: 796c 653a 2020 2020 2020 2020 2020 2020  yle:            \n-0001cea0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ceb0: 2046 7261 6d65 2e20 2020 2020 2020 2020   Frame.         \n-0001cec0: 2020 2020 2020 2028 6c69 6e65 2031 3029         (line 10)\n-0001ced0: 0a2a 206c 696e 6573 7479 6c65 203c 313e  .* linestyle <1>\n-0001cee0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001cef0: 2020 2020 2020 2020 2020 4f76 6572 7669            Overvi\n-0001cf00: 6577 2e20 2020 2020 2020 2020 2020 2020  ew.             \n-0001cf10: 286c 696e 6520 3639 290a 2a20 6c69 6e65  (line 69).* line\n-0001cf20: 7374 796c 6520 3c32 3e3a 2020 2020 2020  style <2>:      \n+0001ce60: 2020 2020 2020 4f76 6572 7669 6577 2e20        Overview. \n+0001ce70: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+0001ce80: 6520 3639 290a 2a20 6c69 6e65 7374 796c  e 69).* linestyl\n+0001ce90: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n+0001cea0: 2020 2020 2020 2020 2020 2020 2020 2046                 F\n+0001ceb0: 7261 6d65 2e20 2020 2020 2020 2020 2020  rame.           \n+0001cec0: 2020 2020 2028 6c69 6e65 2031 3029 0a2a       (line 10).*\n+0001ced0: 206c 696e 6573 7479 6c65 203c 313e 3a20   linestyle <1>: \n+0001cee0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001cef0: 2020 2020 2020 2020 4f76 6572 7669 6577          Overview\n+0001cf00: 2e20 2020 2020 2020 2020 2020 2020 286c  .             (l\n+0001cf10: 696e 6520 3639 290a 2a20 6c69 6e65 7374  ine 69).* linest\n+0001cf20: 796c 6520 3c32 3e3a 2020 2020 2020 2020  yle <2>:        \n 0001cf30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cf40: 2020 2041 2074 6563 686e 6963 616c 2064     A technical d\n-0001cf50: 7261 7769 6e67 2e20 2028 6c69 6e65 2032  rawing.  (line 2\n-0001cf60: 3629 0a2a 206c 696e 6573 7479 6c65 203c  6).* linestyle <\n-0001cf70: 333e 3a20 2020 2020 2020 2020 2020 2020  3>:             \n-0001cf80: 2020 2020 2020 2020 2020 2020 4275 6773              Bugs\n-0001cf90: 2061 6e64 2061 6e6f 6d61 6c69 6573 2e20   and anomalies. \n-0001cfa0: 2020 286c 696e 6520 2037 290a 2a20 6c69    (line  7).* li\n-0001cfb0: 6e65 7769 6474 683a 2020 2020 2020 2020  newidth:        \n+0001cf40: 2041 2074 6563 686e 6963 616c 2064 7261   A technical dra\n+0001cf50: 7769 6e67 2e20 2028 6c69 6e65 2032 3629  wing.  (line 26)\n+0001cf60: 0a2a 206c 696e 6573 7479 6c65 203c 333e  .* linestyle <3>\n+0001cf70: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001cf80: 2020 2020 2020 2020 2020 4275 6773 2061            Bugs a\n+0001cf90: 6e64 2061 6e6f 6d61 6c69 6573 2e20 2020  nd anomalies.   \n+0001cfa0: 286c 696e 6520 2037 290a 2a20 6c69 6e65  (line  7).* line\n+0001cfb0: 7769 6474 683a 2020 2020 2020 2020 2020  width:          \n 0001cfc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001cfd0: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n-0001cfe0: 6565 7073 2e20 2020 2020 2028 6c69 6e65  eeps.      (line\n-0001cff0: 2020 3929 0a2a 206c 696e 6577 6964 7468    9).* linewidth\n-0001d000: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-0001d010: 2020 2020 2020 2020 2020 2020 2020 4672                Fr\n-0001d020: 616d 652e 2020 2020 2020 2020 2020 2020  ame.            \n-0001d030: 2020 2020 286c 696e 6520 3130 290a 2a20      (line 10).* \n-0001d040: 6c69 6e65 7769 6474 6820 3c32 3e3a 2020  linewidth <2>:  \n+0001cfd0: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n+0001cfe0: 7073 2e20 2020 2020 2028 6c69 6e65 2020  ps.      (line  \n+0001cff0: 3929 0a2a 206c 696e 6577 6964 7468 203c  9).* linewidth <\n+0001d000: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+0001d010: 2020 2020 2020 2020 2020 2020 4672 616d              Fram\n+0001d020: 652e 2020 2020 2020 2020 2020 2020 2020  e.              \n+0001d030: 2020 286c 696e 6520 3130 290a 2a20 6c69    (line 10).* li\n+0001d040: 6e65 7769 6474 6820 3c32 3e3a 2020 2020  newidth <2>:    \n 0001d050: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d060: 2020 2020 2020 204f 7665 7276 6965 772e         Overview.\n-0001d070: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n-0001d080: 6e65 2036 3929 0a2a 206c 696e 6577 6964  ne 69).* linewid\n-0001d090: 7468 203c 333e 3a20 2020 2020 2020 2020  th <3>:         \n-0001d0a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d0b0: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n-0001d0c0: 696e 672e 2020 286c 696e 6520 3236 290a  ing.  (line 26).\n-0001d0d0: 2a20 6f70 6163 6974 793a 2020 2020 2020  * opacity:      \n+0001d060: 2020 2020 204f 7665 7276 6965 772e 2020       Overview.  \n+0001d070: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001d080: 2036 3929 0a2a 206c 696e 6577 6964 7468   69).* linewidth\n+0001d090: 203c 333e 3a20 2020 2020 2020 2020 2020   <3>:           \n+0001d0a0: 2020 2020 2020 2020 2020 2020 2020 4120                A \n+0001d0b0: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n+0001d0c0: 672e 2020 286c 696e 6520 3236 290a 2a20  g.  (line 26).* \n+0001d0d0: 6f70 6163 6974 793a 2020 2020 2020 2020  opacity:        \n 0001d0e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d0f0: 2020 2020 2020 2020 2054 7261 6e73 7061           Transpa\n-0001d100: 7265 6e63 792e 2020 2020 2020 2020 2028  rency.         (\n-0001d110: 6c69 6e65 2031 3029 0a2a 2070 6572 7370  line 10).* persp\n-0001d120: 6563 7469 7665 3a20 2020 2020 2020 2020  ective:         \n+0001d0f0: 2020 2020 2020 2054 7261 6e73 7061 7265         Transpare\n+0001d100: 6e63 792e 2020 2020 2020 2020 2028 6c69  ncy.         (li\n+0001d110: 6e65 2031 3029 0a2a 2070 6572 7370 6563  ne 10).* perspec\n+0001d120: 7469 7665 3a20 2020 2020 2020 2020 2020  tive:           \n 0001d130: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d140: 2020 5472 616e 7366 6f72 6d20 6c69 7465    Transform lite\n-0001d150: 7261 6c73 2e20 2020 286c 696e 6520 3231  rals.   (line 21\n-0001d160: 290a 2a20 7069 6374 7572 6562 6f78 3a20  ).* picturebox: \n+0001d140: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n+0001d150: 6c73 2e20 2020 286c 696e 6520 3231 290a  ls.   (line 21).\n+0001d160: 2a20 7069 6374 7572 6562 6f78 3a20 2020  * picturebox:   \n 0001d170: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d180: 2020 2020 2020 2020 2020 2050 6963 7475             Pictu\n-0001d190: 7265 2062 6f78 2e20 2020 2020 2020 2020  re box.         \n-0001d1a0: 2028 6c69 6e65 2020 3629 0a2a 2070 6f69   (line  6).* poi\n-0001d1b0: 6e74 206c 6973 743a 2020 2020 2020 2020  nt list:        \n+0001d180: 2020 2020 2020 2020 2050 6963 7475 7265           Picture\n+0001d190: 2062 6f78 2e20 2020 2020 2020 2020 2028   box.          (\n+0001d1a0: 6c69 6e65 2020 3629 0a2a 2070 6f69 6e74  line  6).* point\n+0001d1b0: 206c 6973 743a 2020 2020 2020 2020 2020   list:          \n 0001d1c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d1d0: 2020 2020 496e 7465 726e 616c 206f 7074      Internal opt\n-0001d1e0: 696f 6e73 2e20 2020 2020 286c 696e 6520  ions.     (line \n-0001d1f0: 3234 290a 2a20 706f 6c79 676f 6e3a 2020  24).* polygon:  \n+0001d1d0: 2020 496e 7465 726e 616c 206f 7074 696f    Internal optio\n+0001d1e0: 6e73 2e20 2020 2020 286c 696e 6520 3234  ns.     (line 24\n+0001d1f0: 290a 2a20 706f 6c79 676f 6e3a 2020 2020  ).* polygon:    \n 0001d200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d210: 2020 2020 2020 2020 2020 2020 2048 656c               Hel\n-0001d220: 6c6f 2077 6f72 6c64 2e20 2020 2020 2020  lo world.       \n-0001d230: 2020 2028 6c69 6e65 2033 3829 0a2a 2070     (line 38).* p\n-0001d240: 6f6c 7967 6f6e 203c 313e 3a20 2020 2020  olygon <1>:     \n+0001d210: 2020 2020 2020 2020 2020 2048 656c 6c6f             Hello\n+0001d220: 2077 6f72 6c64 2e20 2020 2020 2020 2020   world.         \n+0001d230: 2028 6c69 6e65 2033 3829 0a2a 2070 6f6c   (line 38).* pol\n+0001d240: 7967 6f6e 203c 313e 3a20 2020 2020 2020  ygon <1>:       \n 0001d250: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d260: 2020 2020 2020 4472 6177 696e 6720 6120        Drawing a \n-0001d270: 736f 6c69 642e 2020 2020 2020 286c 696e  solid.      (lin\n-0001d280: 6520 2039 290a 2a20 706f 6c79 676f 6e20  e  9).* polygon \n-0001d290: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n-0001d2a0: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n-0001d2b0: 626a 6563 7420 7472 616e 7366 6f72 6d73  bject transforms\n-0001d2c0: 2e20 2020 2028 6c69 6e65 2031 3029 0a2a  .    (line 10).*\n-0001d2d0: 2070 6f6c 7967 6f6e 203c 333e 3a20 2020   polygon <3>:   \n+0001d260: 2020 2020 4472 6177 696e 6720 6120 736f      Drawing a so\n+0001d270: 6c69 642e 2020 2020 2020 286c 696e 6520  lid.      (line \n+0001d280: 2039 290a 2a20 706f 6c79 676f 6e20 3c32   9).* polygon <2\n+0001d290: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001d2a0: 2020 2020 2020 2020 2020 2020 204f 626a               Obj\n+0001d2b0: 6563 7420 7472 616e 7366 6f72 6d73 2e20  ect transforms. \n+0001d2c0: 2020 2028 6c69 6e65 2031 3029 0a2a 2070     (line 10).* p\n+0001d2d0: 6f6c 7967 6f6e 203c 333e 3a20 2020 2020  olygon <3>:     \n 0001d2e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d2f0: 2020 2020 2020 2020 4166 6669 6e65 2061          Affine a\n-0001d300: 7269 7468 6d65 7469 632e 2020 2020 286c  rithmetic.    (l\n-0001d310: 696e 6520 3131 290a 2a20 706f 6c79 676f  ine 11).* polygo\n-0001d320: 6e20 3c34 3e3a 2020 2020 2020 2020 2020  n <4>:          \n-0001d330: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d340: 2050 6f6c 7967 6f6e 732e 2020 2020 2020   Polygons.      \n-0001d350: 2020 2020 2020 2028 6c69 6e65 2020 3629         (line  6)\n-0001d360: 0a2a 2070 6f6c 7967 6f6e 203c 353e 3a20  .* polygon <5>: \n+0001d2f0: 2020 2020 2020 4166 6669 6e65 2061 7269        Affine ari\n+0001d300: 7468 6d65 7469 632e 2020 2020 286c 696e  thmetic.    (lin\n+0001d310: 6520 3131 290a 2a20 706f 6c79 676f 6e20  e 11).* polygon \n+0001d320: 3c34 3e3a 2020 2020 2020 2020 2020 2020  <4>:            \n+0001d330: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n+0001d340: 6f6c 7967 6f6e 732e 2020 2020 2020 2020  olygons.        \n+0001d350: 2020 2020 2028 6c69 6e65 2020 3629 0a2a       (line  6).*\n+0001d360: 2070 6f6c 7967 6f6e 203c 353e 3a20 2020   polygon <5>:   \n 0001d370: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d380: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n-0001d390: 626c 6f63 6b73 2e20 2020 2020 2020 2020  blocks.         \n-0001d3a0: 286c 696e 6520 2037 290a 2a20 706f 6c79  (line  7).* poly\n-0001d3b0: 676f 6e20 3c36 3e3a 2020 2020 2020 2020  gon <6>:        \n+0001d380: 2020 2020 2020 2020 5377 6570 7420 626c          Swept bl\n+0001d390: 6f63 6b73 2e20 2020 2020 2020 2020 286c  ocks.         (l\n+0001d3a0: 696e 6520 2037 290a 2a20 706f 6c79 676f  ine  7).* polygo\n+0001d3b0: 6e20 3c36 3e3a 2020 2020 2020 2020 2020  n <6>:          \n 0001d3c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d3d0: 2020 204f 7665 7276 6965 772e 2020 2020     Overview.    \n-0001d3e0: 2020 2020 2020 2020 2028 6c69 6e65 2033           (line 3\n-0001d3f0: 3729 0a2a 2070 726f 6a65 6374 3a20 2020  7).* project:   \n+0001d3d0: 204f 7665 7276 6965 772e 2020 2020 2020   Overview.      \n+0001d3e0: 2020 2020 2020 2028 6c69 6e65 2033 3729         (line 37)\n+0001d3f0: 0a2a 2070 726f 6a65 6374 3a20 2020 2020  .* project:     \n 0001d400: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d410: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n-0001d420: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n-0001d430: 2020 286c 696e 6520 3138 290a 2a20 7072    (line 18).* pr\n-0001d440: 6f6a 6563 7420 3c31 3e3a 2020 2020 2020  oject <1>:      \n+0001d410: 2020 2020 2020 2020 2020 5472 616e 7366            Transf\n+0001d420: 6f72 6d20 6c69 7465 7261 6c73 2e20 2020  orm literals.   \n+0001d430: 286c 696e 6520 3138 290a 2a20 7072 6f6a  (line 18).* proj\n+0001d440: 6563 7420 3c31 3e3a 2020 2020 2020 2020  ect <1>:        \n 0001d450: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d460: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n-0001d470: 6974 6572 616c 732e 2020 2028 6c69 6e65  iterals.   (line\n-0001d480: 2031 3929 0a2a 2070 726f 6a65 6374 203c   19).* project <\n-0001d490: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n-0001d4a0: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n-0001d4b0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n-0001d4c0: 2e20 2020 286c 696e 6520 3437 290a 2a20  .   (line 47).* \n-0001d4d0: 7073 7472 6963 6b73 3a20 2020 2020 2020  pstricks:       \n+0001d460: 2020 2054 7261 6e73 666f 726d 206c 6974     Transform lit\n+0001d470: 6572 616c 732e 2020 2028 6c69 6e65 2031  erals.   (line 1\n+0001d480: 3929 0a2a 2070 726f 6a65 6374 203c 323e  9).* project <2>\n+0001d490: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001d4a0: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n+0001d4b0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n+0001d4c0: 2020 286c 696e 6520 3437 290a 2a20 7073    (line 47).* ps\n+0001d4d0: 7472 6963 6b73 3a20 2020 2020 2020 2020  tricks:         \n 0001d4e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d4f0: 2020 2020 2020 204c 616e 6775 6167 652e         Language.\n-0001d500: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n-0001d510: 6e65 2031 3029 0a2a 2070 7574 3a20 2020  ne 10).* put:   \n+0001d4f0: 2020 2020 204c 616e 6775 6167 652e 2020       Language.  \n+0001d500: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001d510: 2031 3029 0a2a 2070 7574 3a20 2020 2020   10).* put:     \n 0001d520: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d530: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d540: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n-0001d550: 732e 2020 2020 286c 696e 6520 3130 290a  s.    (line 10).\n-0001d560: 2a20 7075 7420 3c31 3e3a 2020 2020 2020  * put <1>:      \n+0001d530: 2020 2020 2020 2020 2020 2020 2020 4f62                Ob\n+0001d540: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n+0001d550: 2020 2020 286c 696e 6520 3130 290a 2a20      (line 10).* \n+0001d560: 7075 7420 3c31 3e3a 2020 2020 2020 2020  put <1>:        \n 0001d570: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d580: 2020 2020 2020 2020 204e 6573 7465 6420           Nested \n-0001d590: 7377 6565 7073 2e20 2020 2020 2020 2028  sweeps.        (\n-0001d5a0: 6c69 6e65 2032 3529 0a2a 2070 7574 203c  line 25).* put <\n-0001d5b0: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n+0001d580: 2020 2020 2020 204e 6573 7465 6420 7377         Nested sw\n+0001d590: 6565 7073 2e20 2020 2020 2020 2028 6c69  eeps.        (li\n+0001d5a0: 6e65 2032 3529 0a2a 2070 7574 203c 323e  ne 25).* put <2>\n+0001d5b0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n 0001d5c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d5d0: 2020 5075 7473 2e20 2020 2020 2020 2020    Puts.         \n-0001d5e0: 2020 2020 2020 2020 286c 696e 6520 2036          (line  6\n-0001d5f0: 290a 2a20 7075 7420 3c33 3e3a 2020 2020  ).* put <3>:    \n+0001d5d0: 5075 7473 2e20 2020 2020 2020 2020 2020  Puts.           \n+0001d5e0: 2020 2020 2020 286c 696e 6520 2036 290a        (line  6).\n+0001d5f0: 2a20 7075 7420 3c33 3e3a 2020 2020 2020  * put <3>:      \n 0001d600: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d610: 2020 2020 2020 2020 2020 2041 2068 6965             A hie\n-0001d620: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e  rarchical model.\n-0001d630: 2028 6c69 6e65 2033 3229 0a2a 2072 6570   (line 32).* rep\n-0001d640: 6561 743a 2020 2020 2020 2020 2020 2020  eat:            \n+0001d610: 2020 2020 2020 2020 2041 2068 6965 7261           A hiera\n+0001d620: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028  rchical model. (\n+0001d630: 6c69 6e65 2033 3229 0a2a 2072 6570 6561  line 32).* repea\n+0001d640: 743a 2020 2020 2020 2020 2020 2020 2020  t:              \n 0001d650: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d660: 2020 2020 5265 7065 6174 6564 206f 626a      Repeated obj\n-0001d670: 6563 7473 2e20 2020 2020 286c 696e 6520  ects.     (line \n-0001d680: 2038 290a 2a20 7265 7065 6174 203c 313e   8).* repeat <1>\n-0001d690: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001d6a0: 2020 2020 2020 2020 2020 2020 204e 6573               Nes\n-0001d6b0: 7465 6420 7377 6565 7073 2e20 2020 2020  ted sweeps.     \n-0001d6c0: 2020 2028 6c69 6e65 2032 3529 0a2a 2072     (line 25).* r\n-0001d6d0: 6570 6561 7420 3c32 3e3a 2020 2020 2020  epeat <2>:      \n+0001d660: 2020 5265 7065 6174 6564 206f 626a 6563    Repeated objec\n+0001d670: 7473 2e20 2020 2020 286c 696e 6520 2038  ts.     (line  8\n+0001d680: 290a 2a20 7265 7065 6174 203c 313e 3a20  ).* repeat <1>: \n+0001d690: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d6a0: 2020 2020 2020 2020 2020 204e 6573 7465             Neste\n+0001d6b0: 6420 7377 6565 7073 2e20 2020 2020 2020  d sweeps.       \n+0001d6c0: 2028 6c69 6e65 2032 3529 0a2a 2072 6570   (line 25).* rep\n+0001d6d0: 6561 7420 3c32 3e3a 2020 2020 2020 2020  eat <2>:        \n 0001d6e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d6f0: 2020 2020 2020 506f 6c79 6c69 6e65 2073        Polyline s\n-0001d700: 7765 6570 7320 7769 7468 2063 6c6f 7375  weeps with closu\n-0001d710: 7265 2e0a 2020 2020 2020 2020 2020 2020  re..            \n+0001d6f0: 2020 2020 506f 6c79 6c69 6e65 2073 7765      Polyline swe\n+0001d700: 6570 7320 7769 7468 2063 6c6f 7375 7265  eps with closure\n+0001d710: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020                  \n-0001d750: 2020 2028 6c69 6e65 2031 3029 0a2a 2072     (line 10).* r\n-0001d760: 6570 6561 7420 3c33 3e3a 2020 2020 2020  epeat <3>:      \n+0001d750: 2028 6c69 6e65 2031 3029 0a2a 2072 6570   (line 10).* rep\n+0001d760: 6561 7420 3c33 3e3a 2020 2020 2020 2020  eat <3>:        \n 0001d770: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d780: 2020 2020 2020 5265 7065 6174 732e 2020        Repeats.  \n-0001d790: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-0001d7a0: 6520 2036 290a 2a20 7265 7065 6174 203c  e  6).* repeat <\n-0001d7b0: 343e 3a20 2020 2020 2020 2020 2020 2020  4>:             \n-0001d7c0: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n-0001d7d0: 7665 7276 6965 772e 2020 2020 2020 2020  verview.        \n-0001d7e0: 2020 2020 2028 6c69 6e65 2035 3729 0a2a       (line 57).*\n-0001d7f0: 2072 6f74 6174 653a 2020 2020 2020 2020   rotate:        \n+0001d780: 2020 2020 5265 7065 6174 732e 2020 2020      Repeats.    \n+0001d790: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+0001d7a0: 2036 290a 2a20 7265 7065 6174 203c 343e   6).* repeat <4>\n+0001d7b0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001d7c0: 2020 2020 2020 2020 2020 2020 204f 7665               Ove\n+0001d7d0: 7276 6965 772e 2020 2020 2020 2020 2020  rview.          \n+0001d7e0: 2020 2028 6c69 6e65 2035 3729 0a2a 2072     (line 57).* r\n+0001d7f0: 6f74 6174 653a 2020 2020 2020 2020 2020  otate:          \n 0001d800: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d810: 2020 2020 2020 2020 4f62 6a65 6374 2074          Object t\n-0001d820: 7261 6e73 666f 726d 732e 2020 2020 286c  ransforms.    (l\n-0001d830: 696e 6520 3130 290a 2a20 726f 7461 7465  ine 10).* rotate\n-0001d840: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-0001d850: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d860: 204f 626a 6563 7420 7472 616e 7366 6f72   Object transfor\n-0001d870: 6d73 2e20 2020 2028 6c69 6e65 2033 3929  ms.    (line 39)\n-0001d880: 0a2a 2072 6f74 6174 6520 3c32 3e3a 2020  .* rotate <2>:  \n+0001d810: 2020 2020 2020 4f62 6a65 6374 2074 7261        Object tra\n+0001d820: 6e73 666f 726d 732e 2020 2020 286c 696e  nsforms.    (lin\n+0001d830: 6520 3130 290a 2a20 726f 7461 7465 203c  e 10).* rotate <\n+0001d840: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+0001d850: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n+0001d860: 626a 6563 7420 7472 616e 7366 6f72 6d73  bject transforms\n+0001d870: 2e20 2020 2028 6c69 6e65 2033 3929 0a2a  .    (line 39).*\n+0001d880: 2072 6f74 6174 6520 3c32 3e3a 2020 2020   rotate <2>:    \n 0001d890: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d8a0: 2020 2020 2020 2020 2020 5265 7065 6174            Repeat\n-0001d8b0: 6564 206f 626a 6563 7473 2e20 2020 2020  ed objects.     \n-0001d8c0: 286c 696e 6520 2038 290a 2a20 726f 7461  (line  8).* rota\n-0001d8d0: 7465 203c 333e 3a20 2020 2020 2020 2020  te <3>:         \n+0001d8a0: 2020 2020 2020 2020 5265 7065 6174 6564          Repeated\n+0001d8b0: 206f 626a 6563 7473 2e20 2020 2020 286c   objects.     (l\n+0001d8c0: 696e 6520 2038 290a 2a20 726f 7461 7465  ine  8).* rotate\n+0001d8d0: 203c 333e 3a20 2020 2020 2020 2020 2020   <3>:           \n 0001d8e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d8f0: 2020 2053 7765 7074 206f 626a 6563 7473     Swept objects\n-0001d900: 2e20 2020 2020 2020 2028 6c69 6e65 2020  .        (line  \n-0001d910: 3829 0a2a 2072 6f74 6174 6520 3c34 3e3a  8).* rotate <4>:\n+0001d8f0: 2053 7765 7074 206f 626a 6563 7473 2e20   Swept objects. \n+0001d900: 2020 2020 2020 2028 6c69 6e65 2020 3829         (line  8)\n+0001d910: 0a2a 2072 6f74 6174 6520 3c34 3e3a 2020  .* rotate <4>:  \n 0001d920: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d930: 2020 2020 2020 2020 2020 2020 506f 696e              Poin\n-0001d940: 7420 7377 6565 7073 2e20 2020 2020 2020  t sweeps.       \n-0001d950: 2020 286c 696e 6520 3139 290a 2a20 726f    (line 19).* ro\n-0001d960: 7461 7465 203c 353e 3a20 2020 2020 2020  tate <5>:       \n+0001d930: 2020 2020 2020 2020 2020 506f 696e 7420            Point \n+0001d940: 7377 6565 7073 2e20 2020 2020 2020 2020  sweeps.         \n+0001d950: 286c 696e 6520 3139 290a 2a20 726f 7461  (line 19).* rota\n+0001d960: 7465 203c 353e 3a20 2020 2020 2020 2020  te <5>:         \n 0001d970: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001d980: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n-0001d990: 6565 7073 2e20 2020 2020 2028 6c69 6e65  eeps.      (line\n-0001d9a0: 2020 3929 0a2a 2072 6f74 6174 6520 3c36    9).* rotate <6\n-0001d9b0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001d9c0: 2020 2020 2020 2020 2020 2020 2020 4e65                Ne\n-0001d9d0: 7374 6564 2073 7765 6570 732e 2020 2020  sted sweeps.    \n-0001d9e0: 2020 2020 286c 696e 6520 2038 290a 2a20      (line  8).* \n-0001d9f0: 726f 7461 7465 203c 373e 3a20 2020 2020  rotate <7>:     \n+0001d980: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n+0001d990: 7073 2e20 2020 2020 2028 6c69 6e65 2020  ps.      (line  \n+0001d9a0: 3929 0a2a 2072 6f74 6174 6520 3c36 3e3a  9).* rotate <6>:\n+0001d9b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001d9c0: 2020 2020 2020 2020 2020 2020 4e65 7374              Nest\n+0001d9d0: 6564 2073 7765 6570 732e 2020 2020 2020  ed sweeps.      \n+0001d9e0: 2020 286c 696e 6520 2038 290a 2a20 726f    (line  8).* ro\n+0001d9f0: 7461 7465 203c 373e 3a20 2020 2020 2020  tate <7>:       \n 0001da00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001da10: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n-0001da20: 7377 6565 7073 2077 6974 6820 636c 6f73  sweeps with clos\n-0001da30: 7572 652e 0a20 2020 2020 2020 2020 2020  ure..           \n+0001da10: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n+0001da20: 6565 7073 2077 6974 6820 636c 6f73 7572  eeps with closur\n+0001da30: 652e 0a20 2020 2020 2020 2020 2020 2020  e..             \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: 2020 2020 286c 696e 6520 3130 290a 2a20      (line 10).* \n-0001da80: 726f 7461 7465 203c 383e 3a20 2020 2020  rotate <8>:     \n+0001da70: 2020 286c 696e 6520 3130 290a 2a20 726f    (line 10).* ro\n+0001da80: 7461 7465 203c 383e 3a20 2020 2020 2020  tate <8>:       \n 0001da90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001daa0: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n-0001dab0: 206c 6974 6572 616c 732e 2020 2028 6c69   literals.   (li\n-0001dac0: 6e65 2031 3029 0a2a 2072 6f74 6174 6520  ne 10).* rotate \n-0001dad0: 3c39 3e3a 2020 2020 2020 2020 2020 2020  <9>:            \n-0001dae0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001daf0: 4f76 6572 7669 6577 2e20 2020 2020 2020  Overview.       \n-0001db00: 2020 2020 2020 286c 696e 6520 3537 290a        (line 57).\n-0001db10: 2a20 726f 7461 7465 203c 3130 3e3a 2020  * rotate <10>:  \n+0001daa0: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n+0001dab0: 6974 6572 616c 732e 2020 2028 6c69 6e65  iterals.   (line\n+0001dac0: 2031 3029 0a2a 2072 6f74 6174 6520 3c39   10).* rotate <9\n+0001dad0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001dae0: 2020 2020 2020 2020 2020 2020 2020 4f76                Ov\n+0001daf0: 6572 7669 6577 2e20 2020 2020 2020 2020  erview.         \n+0001db00: 2020 2020 286c 696e 6520 3537 290a 2a20      (line 57).* \n+0001db10: 726f 7461 7465 203c 3130 3e3a 2020 2020  rotate <10>:    \n 0001db20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001db30: 2020 2020 2020 2020 204f 7665 7276 6965           Overvie\n-0001db40: 772e 2020 2020 2020 2020 2020 2020 2028  w.             (\n-0001db50: 6c69 6e65 2036 3929 0a2a 2072 6f74 6174  line 69).* rotat\n-0001db60: 6520 3c31 313e 3a20 2020 2020 2020 2020  e <11>:         \n+0001db30: 2020 2020 2020 204f 7665 7276 6965 772e         Overview.\n+0001db40: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n+0001db50: 6e65 2036 3929 0a2a 2072 6f74 6174 6520  ne 69).* rotate \n+0001db60: 3c31 313e 3a20 2020 2020 2020 2020 2020  <11>:           \n 0001db70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001db80: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n-0001db90: 6177 696e 672e 2020 286c 696e 6520 3134  awing.  (line 14\n-0001dba0: 290a 2a20 726f 7461 7465 203c 3132 3e3a  ).* rotate <12>:\n+0001db80: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n+0001db90: 696e 672e 2020 286c 696e 6520 3134 290a  ing.  (line 14).\n+0001dba0: 2a20 726f 7461 7465 203c 3132 3e3a 2020  * rotate <12>:  \n 0001dbb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dbc0: 2020 2020 2020 2020 2020 2041 2068 6965             A hie\n-0001dbd0: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e  rarchical model.\n-0001dbe0: 2028 6c69 6e65 2031 3029 0a2a 2072 6f74   (line 10).* rot\n-0001dbf0: 6174 6520 3c31 333e 3a20 2020 2020 2020  ate <13>:       \n+0001dbc0: 2020 2020 2020 2020 2041 2068 6965 7261           A hiera\n+0001dbd0: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028  rchical model. (\n+0001dbe0: 6c69 6e65 2031 3029 0a2a 2072 6f74 6174  line 10).* rotat\n+0001dbf0: 6520 3c31 333e 3a20 2020 2020 2020 2020  e <13>:         \n 0001dc00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dc10: 2020 2020 4120 6869 6572 6172 6368 6963      A hierarchic\n-0001dc20: 616c 206d 6f64 656c 2e20 286c 696e 6520  al model. (line \n-0001dc30: 3233 290a 2a20 726f 7461 7465 203c 3134  23).* rotate <14\n-0001dc40: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001dc50: 2020 2020 2020 2020 2020 2020 2041 2068               A h\n-0001dc60: 6965 7261 7263 6869 6361 6c20 6d6f 6465  ierarchical mode\n-0001dc70: 6c2e 2028 6c69 6e65 2033 3229 0a2a 2073  l. (line 32).* s\n-0001dc80: 6361 6c65 3a20 2020 2020 2020 2020 2020  cale:           \n+0001dc10: 2020 4120 6869 6572 6172 6368 6963 616c    A hierarchical\n+0001dc20: 206d 6f64 656c 2e20 286c 696e 6520 3233   model. (line 23\n+0001dc30: 290a 2a20 726f 7461 7465 203c 3134 3e3a  ).* rotate <14>:\n+0001dc40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001dc50: 2020 2020 2020 2020 2020 2041 2068 6965             A hie\n+0001dc60: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e  rarchical model.\n+0001dc70: 2028 6c69 6e65 2033 3229 0a2a 2073 6361   (line 32).* sca\n+0001dc80: 6c65 3a20 2020 2020 2020 2020 2020 2020  le:             \n 0001dc90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dca0: 2020 2020 2020 5472 616e 7366 6f72 6d20        Transform \n-0001dcb0: 6c69 7465 7261 6c73 2e20 2020 286c 696e  literals.   (lin\n-0001dcc0: 6520 3136 290a 2a20 7363 616c 6520 3c31  e 16).* scale <1\n-0001dcd0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001dce0: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n-0001dcf0: 7261 6e73 666f 726d 206c 6974 6572 616c  ransform literal\n-0001dd00: 732e 2020 2028 6c69 6e65 2031 3729 0a2a  s.   (line 17).*\n-0001dd10: 2073 6361 6c65 203c 323e 3a20 2020 2020   scale <2>:     \n+0001dca0: 2020 2020 5472 616e 7366 6f72 6d20 6c69      Transform li\n+0001dcb0: 7465 7261 6c73 2e20 2020 286c 696e 6520  terals.   (line \n+0001dcc0: 3136 290a 2a20 7363 616c 6520 3c31 3e3a  16).* scale <1>:\n+0001dcd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001dce0: 2020 2020 2020 2020 2020 2020 2054 7261               Tra\n+0001dcf0: 6e73 666f 726d 206c 6974 6572 616c 732e  nsform literals.\n+0001dd00: 2020 2028 6c69 6e65 2031 3729 0a2a 2073     (line 17).* s\n+0001dd10: 6361 6c65 203c 323e 3a20 2020 2020 2020  cale <2>:       \n 0001dd20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dd30: 2020 2020 2020 2020 4120 7465 6368 6e69          A techni\n-0001dd40: 6361 6c20 6472 6177 696e 672e 2020 286c  cal drawing.  (l\n-0001dd50: 696e 6520 3431 290a 2a20 7363 616c 6520  ine 41).* scale \n-0001dd60: 3c33 3e3a 2020 2020 2020 2020 2020 2020  <3>:            \n-0001dd70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dd80: 2041 2074 6563 686e 6963 616c 2064 7261   A technical dra\n-0001dd90: 7769 6e67 2e20 2028 6c69 6e65 2036 3829  wing.  (line 68)\n-0001dda0: 0a2a 2073 6361 6c65 203c 343e 3a20 2020  .* scale <4>:   \n+0001dd30: 2020 2020 2020 4120 7465 6368 6e69 6361        A technica\n+0001dd40: 6c20 6472 6177 696e 672e 2020 286c 696e  l drawing.  (lin\n+0001dd50: 6520 3431 290a 2a20 7363 616c 6520 3c33  e 41).* scale <3\n+0001dd60: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001dd70: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+0001dd80: 2074 6563 686e 6963 616c 2064 7261 7769   technical drawi\n+0001dd90: 6e67 2e20 2028 6c69 6e65 2036 3829 0a2a  ng.  (line 68).*\n+0001dda0: 2073 6361 6c65 203c 343e 3a20 2020 2020   scale <4>:     \n 0001ddb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ddc0: 2020 2020 2020 2020 2020 4120 6869 6572            A hier\n-0001ddd0: 6172 6368 6963 616c 206d 6f64 656c 2e20  archical model. \n-0001dde0: 286c 696e 6520 3332 290a 2a20 7365 743a  (line 32).* set:\n+0001ddc0: 2020 2020 2020 2020 4120 6869 6572 6172          A hierar\n+0001ddd0: 6368 6963 616c 206d 6f64 656c 2e20 286c  chical model. (l\n+0001dde0: 696e 6520 3332 290a 2a20 7365 743a 2020  ine 32).* set:  \n 0001ddf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001de00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001de10: 2020 2047 6c6f 6261 6c20 6f70 7469 6f6e     Global option\n-0001de20: 732e 2020 2020 2020 2028 6c69 6e65 2020  s.       (line  \n-0001de30: 3629 0a2a 2073 696e 3a20 2020 2020 2020  6).* sin:       \n+0001de10: 2047 6c6f 6261 6c20 6f70 7469 6f6e 732e   Global options.\n+0001de20: 2020 2020 2020 2028 6c69 6e65 2020 3629         (line  6)\n+0001de30: 0a2a 2073 696e 3a20 2020 2020 2020 2020  .* sin:         \n 0001de40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001de50: 2020 2020 2020 2020 2020 2020 556e 6172              Unar\n-0001de60: 7920 666f 726d 732e 2020 2020 2020 2020  y forms.        \n-0001de70: 2020 286c 696e 6520 3135 290a 2a20 7370    (line 15).* sp\n-0001de80: 6563 6961 6c3a 2020 2020 2020 2020 2020  ecial:          \n+0001de50: 2020 2020 2020 2020 2020 556e 6172 7920            Unary \n+0001de60: 666f 726d 732e 2020 2020 2020 2020 2020  forms.          \n+0001de70: 286c 696e 6520 3135 290a 2a20 7370 6563  (line 15).* spec\n+0001de80: 6961 6c3a 2020 2020 2020 2020 2020 2020  ial:            \n 0001de90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dea0: 2020 2020 2053 7065 6369 616c 206f 626a       Special obj\n-0001deb0: 6563 7473 2e20 2020 2020 2028 6c69 6e65  ects.      (line\n-0001dec0: 2020 3629 0a2a 2073 7065 6369 616c 203c    6).* special <\n-0001ded0: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-0001dee0: 2020 2020 2020 2020 2020 2020 2020 5370                Sp\n-0001def0: 6563 6961 6c73 2e20 2020 2020 2020 2020  ecials.         \n-0001df00: 2020 2020 286c 696e 6520 2036 290a 2a20      (line  6).* \n-0001df10: 7370 6563 6961 6c20 3c32 3e3a 2020 2020  special <2>:    \n+0001dea0: 2020 2053 7065 6369 616c 206f 626a 6563     Special objec\n+0001deb0: 7473 2e20 2020 2020 2028 6c69 6e65 2020  ts.      (line  \n+0001dec0: 3629 0a2a 2073 7065 6369 616c 203c 313e  6).* special <1>\n+0001ded0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001dee0: 2020 2020 2020 2020 2020 2020 5370 6563              Spec\n+0001def0: 6961 6c73 2e20 2020 2020 2020 2020 2020  ials.           \n+0001df00: 2020 286c 696e 6520 2036 290a 2a20 7370    (line  6).* sp\n+0001df10: 6563 6961 6c20 3c32 3e3a 2020 2020 2020  ecial <2>:      \n 0001df20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001df30: 2020 2020 2020 204f 7665 7276 6965 772e         Overview.\n-0001df40: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n-0001df50: 6e65 2036 3929 0a2a 2073 7065 6369 616c  ne 69).* special\n-0001df60: 203c 333e 3a20 2020 2020 2020 2020 2020   <3>:           \n-0001df70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001df80: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n-0001df90: 696e 672e 2020 286c 696e 6520 3236 290a  ing.  (line 26).\n-0001dfa0: 2a20 7370 6563 6961 6c20 3c34 3e3a 2020  * special <4>:  \n+0001df30: 2020 2020 204f 7665 7276 6965 772e 2020       Overview.  \n+0001df40: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+0001df50: 2036 3929 0a2a 2073 7065 6369 616c 203c   69).* special <\n+0001df60: 333e 3a20 2020 2020 2020 2020 2020 2020  3>:             \n+0001df70: 2020 2020 2020 2020 2020 2020 2020 4120                A \n+0001df80: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n+0001df90: 672e 2020 286c 696e 6520 3236 290a 2a20  g.  (line 26).* \n+0001dfa0: 7370 6563 6961 6c20 3c34 3e3a 2020 2020  special <4>:    \n 0001dfb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001dfc0: 2020 2020 2020 2020 2041 2074 6563 686e           A techn\n-0001dfd0: 6963 616c 2064 7261 7769 6e67 2e20 2028  ical drawing.  (\n-0001dfe0: 6c69 6e65 2034 3129 0a2a 2073 7065 6369  line 41).* speci\n-0001dff0: 616c 203c 353e 3a20 2020 2020 2020 2020  al <5>:         \n+0001dfc0: 2020 2020 2020 2041 2074 6563 686e 6963         A technic\n+0001dfd0: 616c 2064 7261 7769 6e67 2e20 2028 6c69  al drawing.  (li\n+0001dfe0: 6e65 2034 3129 0a2a 2073 7065 6369 616c  ne 41).* special\n+0001dff0: 203c 353e 3a20 2020 2020 2020 2020 2020   <5>:           \n 0001e000: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e010: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n-0001e020: 6177 696e 672e 2020 286c 696e 6520 3638  awing.  (line 68\n-0001e030: 290a 2a20 7370 6563 6961 6c20 3c36 3e3a  ).* special <6>:\n+0001e010: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n+0001e020: 696e 672e 2020 286c 696e 6520 3638 290a  ing.  (line 68).\n+0001e030: 2a20 7370 6563 6961 6c20 3c36 3e3a 2020  * special <6>:  \n 0001e040: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e050: 2020 2020 2020 2020 2020 2041 2074 6563             A tec\n-0001e060: 686e 6963 616c 2064 7261 7769 6e67 2e20  hnical drawing. \n-0001e070: 2028 6c69 6e65 2039 3529 0a2a 2073 706c   (line 95).* spl\n-0001e080: 6974 3a20 2020 2020 2020 2020 2020 2020  it:             \n+0001e050: 2020 2020 2020 2020 2041 2074 6563 686e           A techn\n+0001e060: 6963 616c 2064 7261 7769 6e67 2e20 2028  ical drawing.  (\n+0001e070: 6c69 6e65 2039 3529 0a2a 2073 706c 6974  line 95).* split\n+0001e080: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n 0001e090: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e0a0: 2020 2020 496e 7465 726e 616c 206f 7074      Internal opt\n-0001e0b0: 696f 6e73 2e20 2020 2020 286c 696e 6520  ions.     (line \n-0001e0c0: 2037 290a 2a20 7370 6c69 7420 3c31 3e3a   7).* split <1>:\n+0001e0a0: 2020 496e 7465 726e 616c 206f 7074 696f    Internal optio\n+0001e0b0: 6e73 2e20 2020 2020 286c 696e 6520 2037  ns.     (line  7\n+0001e0c0: 290a 2a20 7370 6c69 7420 3c31 3e3a 2020  ).* split <1>:  \n 0001e0d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e0e0: 2020 2020 2020 2020 2020 2020 2047 6c6f               Glo\n-0001e0f0: 6261 6c20 6f70 7469 6f6e 732e 2020 2020  bal options.    \n-0001e100: 2020 2028 6c69 6e65 2031 3329 0a2a 2073     (line 13).* s\n-0001e110: 7172 743a 2020 2020 2020 2020 2020 2020  qrt:            \n+0001e0e0: 2020 2020 2020 2020 2020 2047 6c6f 6261             Globa\n+0001e0f0: 6c20 6f70 7469 6f6e 732e 2020 2020 2020  l options.      \n+0001e100: 2028 6c69 6e65 2031 3329 0a2a 2073 7172   (line 13).* sqr\n+0001e110: 743a 2020 2020 2020 2020 2020 2020 2020  t:              \n 0001e120: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e130: 2020 2020 2020 556e 6172 7920 666f 726d        Unary form\n-0001e140: 732e 2020 2020 2020 2020 2020 286c 696e  s.          (lin\n-0001e150: 6520 3134 290a 2a20 7377 6565 703a 2020  e 14).* sweep:  \n+0001e130: 2020 2020 556e 6172 7920 666f 726d 732e      Unary forms.\n+0001e140: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+0001e150: 3134 290a 2a20 7377 6565 703a 2020 2020  14).* sweep:    \n 0001e160: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e170: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n-0001e180: 7765 7074 206f 626a 6563 7473 2e20 2020  wept objects.   \n-0001e190: 2020 2020 2028 6c69 6e65 2020 3829 0a2a       (line  8).*\n-0001e1a0: 2073 7765 6570 203c 313e 3a20 2020 2020   sweep <1>:     \n+0001e170: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n+0001e180: 7074 206f 626a 6563 7473 2e20 2020 2020  pt objects.     \n+0001e190: 2020 2028 6c69 6e65 2020 3829 0a2a 2073     (line  8).* s\n+0001e1a0: 7765 6570 203c 313e 3a20 2020 2020 2020  weep <1>:       \n 0001e1b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e1c0: 2020 2020 2020 2020 506f 696e 7420 7377          Point sw\n-0001e1d0: 6565 7073 2e20 2020 2020 2020 2020 286c  eeps.         (l\n-0001e1e0: 696e 6520 3139 290a 2a20 7377 6565 7020  ine 19).* sweep \n-0001e1f0: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n-0001e200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e210: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n-0001e220: 2e20 2020 2020 2028 6c69 6e65 2020 3929  .      (line  9)\n-0001e230: 0a2a 2073 7765 6570 203c 333e 3a20 2020  .* sweep <3>:   \n+0001e1c0: 2020 2020 2020 506f 696e 7420 7377 6565        Point swee\n+0001e1d0: 7073 2e20 2020 2020 2020 2020 286c 696e  ps.         (lin\n+0001e1e0: 6520 3139 290a 2a20 7377 6565 7020 3c32  e 19).* sweep <2\n+0001e1f0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001e200: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n+0001e210: 6f6c 796c 696e 6520 7377 6565 7073 2e20  olyline sweeps. \n+0001e220: 2020 2020 2028 6c69 6e65 2020 3929 0a2a       (line  9).*\n+0001e230: 2073 7765 6570 203c 333e 3a20 2020 2020   sweep <3>:     \n 0001e240: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e250: 2020 2020 2020 2020 2020 4e65 7374 6564            Nested\n-0001e260: 2073 7765 6570 732e 2020 2020 2020 2020   sweeps.        \n-0001e270: 286c 696e 6520 2038 290a 2a20 7377 6565  (line  8).* swee\n-0001e280: 7020 3c34 3e3a 2020 2020 2020 2020 2020  p <4>:          \n+0001e250: 2020 2020 2020 2020 4e65 7374 6564 2073          Nested s\n+0001e260: 7765 6570 732e 2020 2020 2020 2020 286c  weeps.        (l\n+0001e270: 696e 6520 2038 290a 2a20 7377 6565 7020  ine  8).* sweep \n+0001e280: 3c34 3e3a 2020 2020 2020 2020 2020 2020  <4>:            \n 0001e290: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e2a0: 2020 204e 6573 7465 6420 7377 6565 7073     Nested sweeps\n-0001e2b0: 2e20 2020 2020 2020 2028 6c69 6e65 2032  .        (line 2\n-0001e2c0: 3229 0a2a 2073 7765 6570 203c 353e 3a20  2).* sweep <5>: \n+0001e2a0: 204e 6573 7465 6420 7377 6565 7073 2e20   Nested sweeps. \n+0001e2b0: 2020 2020 2020 2028 6c69 6e65 2032 3229         (line 22)\n+0001e2c0: 0a2a 2073 7765 6570 203c 353e 3a20 2020  .* sweep <5>:   \n 0001e2d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e2e0: 2020 2020 2020 2020 2020 2020 506f 6c79              Poly\n-0001e2f0: 6c69 6e65 2073 7765 6570 7320 7769 7468  line sweeps with\n-0001e300: 2063 6c6f 7375 7265 2e0a 2020 2020 2020   closure..      \n+0001e2e0: 2020 2020 2020 2020 2020 506f 6c79 6c69            Polyli\n+0001e2f0: 6e65 2073 7765 6570 7320 7769 7468 2063  ne sweeps with c\n+0001e300: 6c6f 7375 7265 2e0a 2020 2020 2020 2020  losure..        \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 2020 2020 2028 6c69 6e65 2031           (line 1\n-0001e350: 3029 0a2a 2073 7765 6570 203c 363e 3a20  0).* sweep <6>: \n+0001e340: 2020 2020 2020 2028 6c69 6e65 2031 3029         (line 10)\n+0001e350: 0a2a 2073 7765 6570 203c 363e 3a20 2020  .* sweep <6>:   \n 0001e360: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e370: 2020 2020 2020 2020 2020 2020 5377 6565              Swee\n-0001e380: 7073 2e20 2020 2020 2020 2020 2020 2020  ps.             \n-0001e390: 2020 286c 696e 6520 2036 290a 2a20 7377    (line  6).* sw\n-0001e3a0: 6565 7020 3c37 3e3a 2020 2020 2020 2020  eep <7>:        \n+0001e370: 2020 2020 2020 2020 2020 5377 6565 7073            Sweeps\n+0001e380: 2e20 2020 2020 2020 2020 2020 2020 2020  .               \n+0001e390: 286c 696e 6520 2036 290a 2a20 7377 6565  (line  6).* swee\n+0001e3a0: 7020 3c37 3e3a 2020 2020 2020 2020 2020  p <7>:          \n 0001e3b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e3c0: 2020 2020 2041 2074 6563 686e 6963 616c       A technical\n-0001e3d0: 2064 7261 7769 6e67 2e20 2028 6c69 6e65   drawing.  (line\n-0001e3e0: 2032 3029 0a2a 2073 7765 6570 203c 383e   20).* sweep <8>\n-0001e3f0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001e400: 2020 2020 2020 2020 2020 2020 2020 4120                A \n-0001e410: 6869 6572 6172 6368 6963 616c 206d 6f64  hierarchical mod\n-0001e420: 656c 2e20 286c 696e 6520 3130 290a 2a20  el. (line 10).* \n-0001e430: 7377 6565 7020 3c39 3e3a 2020 2020 2020  sweep <9>:      \n+0001e3c0: 2020 2041 2074 6563 686e 6963 616c 2064     A technical d\n+0001e3d0: 7261 7769 6e67 2e20 2028 6c69 6e65 2032  rawing.  (line 2\n+0001e3e0: 3029 0a2a 2073 7765 6570 203c 383e 3a20  0).* sweep <8>: \n+0001e3f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e400: 2020 2020 2020 2020 2020 2020 4120 6869              A hi\n+0001e410: 6572 6172 6368 6963 616c 206d 6f64 656c  erarchical model\n+0001e420: 2e20 286c 696e 6520 3130 290a 2a20 7377  . (line 10).* sw\n+0001e430: 6565 7020 3c39 3e3a 2020 2020 2020 2020  eep <9>:        \n 0001e440: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e450: 2020 2020 2020 2041 2068 6965 7261 7263         A hierarc\n-0001e460: 6869 6361 6c20 6d6f 6465 6c2e 2028 6c69  hical model. (li\n-0001e470: 6e65 2032 3329 0a2a 2074 6865 6e3a 2020  ne 23).* then:  \n+0001e450: 2020 2020 2041 2068 6965 7261 7263 6869       A hierarchi\n+0001e460: 6361 6c20 6d6f 6465 6c2e 2028 6c69 6e65  cal model. (line\n+0001e470: 2032 3329 0a2a 2074 6865 6e3a 2020 2020   23).* then:    \n 0001e480: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e490: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e4a0: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n-0001e4b0: 732e 2020 2020 286c 696e 6520 3130 290a  s.    (line 10).\n-0001e4c0: 2a20 7468 656e 203c 313e 3a20 2020 2020  * then <1>:     \n+0001e490: 2020 2020 2020 2020 2020 2020 2020 4f62                Ob\n+0001e4a0: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n+0001e4b0: 2020 2020 286c 696e 6520 3130 290a 2a20      (line 10).* \n+0001e4c0: 7468 656e 203c 313e 3a20 2020 2020 2020  then <1>:       \n 0001e4d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e4e0: 2020 2020 2020 2020 2050 6f6c 796c 696e           Polylin\n-0001e4f0: 6520 7377 6565 7073 2077 6974 6820 636c  e sweeps with cl\n-0001e500: 6f73 7572 652e 0a20 2020 2020 2020 2020  osure..         \n+0001e4e0: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n+0001e4f0: 7377 6565 7073 2077 6974 6820 636c 6f73  sweeps with clos\n+0001e500: 7572 652e 0a20 2020 2020 2020 2020 2020  ure..           \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 2020 2020 286c 696e 6520 3130 290a        (line 10).\n-0001e550: 2a20 7468 656e 203c 323e 3a20 2020 2020  * then <2>:     \n+0001e540: 2020 2020 286c 696e 6520 3130 290a 2a20      (line 10).* \n+0001e550: 7468 656e 203c 323e 3a20 2020 2020 2020  then <2>:       \n 0001e560: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e570: 2020 2020 2020 2020 2054 776f 2d6f 7065           Two-ope\n-0001e580: 7261 6e64 2028 6269 6e61 7279 2920 666f  rand (binary) fo\n-0001e590: 726d 732e 0a20 2020 2020 2020 2020 2020  rms..           \n+0001e570: 2020 2020 2020 2054 776f 2d6f 7065 7261         Two-opera\n+0001e580: 6e64 2028 6269 6e61 7279 2920 666f 726d  nd (binary) form\n+0001e590: 732e 0a20 2020 2020 2020 2020 2020 2020  s..             \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: 2020 2020 286c 696e 6520 3336 290a 2a20      (line 36).* \n-0001e5e0: 7468 656e 203c 333e 3a20 2020 2020 2020  then <3>:       \n+0001e5d0: 2020 286c 696e 6520 3336 290a 2a20 7468    (line 36).* th\n+0001e5e0: 656e 203c 333e 3a20 2020 2020 2020 2020  en <3>:         \n 0001e5f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e600: 2020 2020 2020 2054 776f 2d6f 7065 7261         Two-opera\n-0001e610: 6e64 2028 6269 6e61 7279 2920 666f 726d  nd (binary) form\n-0001e620: 732e 0a20 2020 2020 2020 2020 2020 2020  s..             \n+0001e600: 2020 2020 2054 776f 2d6f 7065 7261 6e64       Two-operand\n+0001e610: 2028 6269 6e61 7279 2920 666f 726d 732e   (binary) forms.\n+0001e620: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \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 2020                  \n-0001e660: 2020 286c 696e 6520 3633 290a 2a20 7469    (line 63).* ti\n-0001e670: 6b7a 3a20 2020 2020 2020 2020 2020 2020  kz:             \n+0001e660: 286c 696e 6520 3633 290a 2a20 7469 6b7a  (line 63).* tikz\n+0001e670: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n 0001e680: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e690: 2020 2020 204c 616e 6775 6167 652e 2020       Language.  \n-0001e6a0: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-0001e6b0: 2031 3029 0a2a 2074 7261 6e73 6c61 7465   10).* translate\n-0001e6c0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001e6d0: 2020 2020 2020 2020 2020 2020 2020 4f62                Ob\n-0001e6e0: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n-0001e6f0: 2020 2020 286c 696e 6520 3130 290a 2a20      (line 10).* \n-0001e700: 7472 616e 736c 6174 6520 3c31 3e3a 2020  translate <1>:  \n+0001e690: 2020 204c 616e 6775 6167 652e 2020 2020     Language.    \n+0001e6a0: 2020 2020 2020 2020 2028 6c69 6e65 2031           (line 1\n+0001e6b0: 3029 0a2a 2074 7261 6e73 6c61 7465 3a20  0).* translate: \n+0001e6c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e6d0: 2020 2020 2020 2020 2020 2020 4f62 6a65              Obje\n+0001e6e0: 6374 2074 7261 6e73 666f 726d 732e 2020  ct transforms.  \n+0001e6f0: 2020 286c 696e 6520 3130 290a 2a20 7472    (line 10).* tr\n+0001e700: 616e 736c 6174 6520 3c31 3e3a 2020 2020  anslate <1>:    \n 0001e710: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e720: 2020 2020 2020 204f 626a 6563 7420 7472         Object tr\n-0001e730: 616e 7366 6f72 6d73 2e20 2020 2028 6c69  ansforms.    (li\n-0001e740: 6e65 2034 3729 0a2a 2074 7261 6e73 6c61  ne 47).* transla\n-0001e750: 7465 203c 323e 3a20 2020 2020 2020 2020  te <2>:         \n-0001e760: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e770: 5265 7065 6174 6564 206f 626a 6563 7473  Repeated objects\n-0001e780: 2e20 2020 2020 286c 696e 6520 2038 290a  .     (line  8).\n-0001e790: 2a20 7472 616e 736c 6174 6520 3c33 3e3a  * translate <3>:\n+0001e720: 2020 2020 204f 626a 6563 7420 7472 616e       Object tran\n+0001e730: 7366 6f72 6d73 2e20 2020 2028 6c69 6e65  sforms.    (line\n+0001e740: 2034 3729 0a2a 2074 7261 6e73 6c61 7465   47).* translate\n+0001e750: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n+0001e760: 2020 2020 2020 2020 2020 2020 2020 5265                Re\n+0001e770: 7065 6174 6564 206f 626a 6563 7473 2e20  peated objects. \n+0001e780: 2020 2020 286c 696e 6520 2038 290a 2a20      (line  8).* \n+0001e790: 7472 616e 736c 6174 6520 3c33 3e3a 2020  translate <3>:  \n 0001e7a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e7b0: 2020 2020 2020 2020 2050 6f6c 796c 696e           Polylin\n-0001e7c0: 6520 7377 6565 7073 2e20 2020 2020 2028  e sweeps.      (\n-0001e7d0: 6c69 6e65 2020 3929 0a2a 2074 7261 6e73  line  9).* trans\n-0001e7e0: 6c61 7465 203c 343e 3a20 2020 2020 2020  late <4>:       \n+0001e7b0: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n+0001e7c0: 7377 6565 7073 2e20 2020 2020 2028 6c69  sweeps.      (li\n+0001e7d0: 6e65 2020 3929 0a2a 2074 7261 6e73 6c61  ne  9).* transla\n+0001e7e0: 7465 203c 343e 3a20 2020 2020 2020 2020  te <4>:         \n 0001e7f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e800: 2020 506f 6c79 6c69 6e65 2073 7765 6570    Polyline sweep\n-0001e810: 7320 7769 7468 2063 6c6f 7375 7265 2e0a  s with closure..\n+0001e800: 506f 6c79 6c69 6e65 2073 7765 6570 7320  Polyline sweeps \n+0001e810: 7769 7468 2063 6c6f 7375 7265 2e0a 2020  with closure..  \n 0001e820: 2020 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 2020 2020 2028                 (\n-0001e860: 6c69 6e65 2031 3029 0a2a 2074 7261 6e73  line 10).* trans\n-0001e870: 6c61 7465 203c 353e 3a20 2020 2020 2020  late <5>:       \n+0001e850: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n+0001e860: 6e65 2031 3029 0a2a 2074 7261 6e73 6c61  ne 10).* transla\n+0001e870: 7465 203c 353e 3a20 2020 2020 2020 2020  te <5>:         \n 0001e880: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e890: 2020 5472 616e 7366 6f72 6d20 6c69 7465    Transform lite\n-0001e8a0: 7261 6c73 2e20 2020 286c 696e 6520 3135  rals.   (line 15\n-0001e8b0: 290a 2a20 7472 616e 736c 6174 6520 3c36  ).* translate <6\n-0001e8c0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001e8d0: 2020 2020 2020 2020 2020 204f 7665 7276             Overv\n-0001e8e0: 6965 772e 2020 2020 2020 2020 2020 2020  iew.            \n-0001e8f0: 2028 6c69 6e65 2035 3729 0a2a 2074 7261   (line 57).* tra\n-0001e900: 6e73 6c61 7465 203c 373e 3a20 2020 2020  nslate <7>:     \n+0001e890: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n+0001e8a0: 6c73 2e20 2020 286c 696e 6520 3135 290a  ls.   (line 15).\n+0001e8b0: 2a20 7472 616e 736c 6174 6520 3c36 3e3a  * translate <6>:\n+0001e8c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001e8d0: 2020 2020 2020 2020 204f 7665 7276 6965           Overvie\n+0001e8e0: 772e 2020 2020 2020 2020 2020 2020 2028  w.             (\n+0001e8f0: 6c69 6e65 2035 3729 0a2a 2074 7261 6e73  line 57).* trans\n+0001e900: 6c61 7465 203c 373e 3a20 2020 2020 2020  late <7>:       \n 0001e910: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e920: 2020 2020 4f76 6572 7669 6577 2e20 2020      Overview.   \n-0001e930: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-0001e940: 3639 290a 2a20 7472 616e 736c 6174 6520  69).* translate \n-0001e950: 3c38 3e3a 2020 2020 2020 2020 2020 2020  <8>:            \n-0001e960: 2020 2020 2020 2020 2020 2020 2041 2068               A h\n-0001e970: 6965 7261 7263 6869 6361 6c20 6d6f 6465  ierarchical mode\n-0001e980: 6c2e 2028 6c69 6e65 2033 3229 0a2a 2074  l. (line 32).* t\n-0001e990: 7261 6e73 7061 6c70 6861 3a20 2020 2020  ranspalpha:     \n+0001e920: 2020 4f76 6572 7669 6577 2e20 2020 2020    Overview.     \n+0001e930: 2020 2020 2020 2020 286c 696e 6520 3639          (line 69\n+0001e940: 290a 2a20 7472 616e 736c 6174 6520 3c38  ).* translate <8\n+0001e950: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001e960: 2020 2020 2020 2020 2020 2041 2068 6965             A hie\n+0001e970: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e  rarchical model.\n+0001e980: 2028 6c69 6e65 2033 3229 0a2a 2074 7261   (line 32).* tra\n+0001e990: 6e73 7061 6c70 6861 3a20 2020 2020 2020  nspalpha:       \n 0001e9a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e9b0: 2020 2020 2020 5472 616e 7370 6172 656e        Transparen\n-0001e9c0: 6379 2e20 2020 2020 2020 2020 286c 696e  cy.         (lin\n-0001e9d0: 6520 3130 290a 2a20 756e 6974 3a20 2020  e 10).* unit:   \n+0001e9b0: 2020 2020 5472 616e 7370 6172 656e 6379      Transparency\n+0001e9c0: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n+0001e9d0: 3130 290a 2a20 756e 6974 3a20 2020 2020  10).* unit:     \n 0001e9e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001e9f0: 2020 2020 2020 2020 2020 2020 2020 2055                 U\n-0001ea00: 6e61 7279 2066 6f72 6d73 2e20 2020 2020  nary forms.     \n-0001ea10: 2020 2020 2028 6c69 6e65 2031 3329 0a2a       (line 13).*\n-0001ea20: 2075 6e69 7420 3c31 3e3a 2020 2020 2020   unit <1>:      \n+0001e9f0: 2020 2020 2020 2020 2020 2020 2055 6e61               Una\n+0001ea00: 7279 2066 6f72 6d73 2e20 2020 2020 2020  ry forms.       \n+0001ea10: 2020 2028 6c69 6e65 2031 3329 0a2a 2075     (line 13).* u\n+0001ea20: 6e69 7420 3c31 3e3a 2020 2020 2020 2020  nit <1>:        \n 0001ea30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ea40: 2020 2020 2020 2020 4120 7465 6368 6e69          A techni\n-0001ea50: 6361 6c20 6472 6177 696e 672e 2020 286c  cal drawing.  (l\n-0001ea60: 696e 6520 3431 290a 2a20 7669 6577 3a20  ine 41).* view: \n+0001ea40: 2020 2020 2020 4120 7465 6368 6e69 6361        A technica\n+0001ea50: 6c20 6472 6177 696e 672e 2020 286c 696e  l drawing.  (lin\n+0001ea60: 6520 3431 290a 2a20 7669 6577 3a20 2020  e 41).* view:   \n 0001ea70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ea80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ea90: 2054 7261 6e73 666f 726d 206c 6974 6572   Transform liter\n-0001eaa0: 616c 732e 2020 2028 6c69 6e65 2032 3529  als.   (line 25)\n-0001eab0: 0a2a 2076 6965 7720 3c31 3e3a 2020 2020  .* view <1>:    \n+0001ea80: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n+0001ea90: 7261 6e73 666f 726d 206c 6974 6572 616c  ransform literal\n+0001eaa0: 732e 2020 2028 6c69 6e65 2032 3529 0a2a  s.   (line 25).*\n+0001eab0: 2076 6965 7720 3c31 3e3a 2020 2020 2020   view <1>:      \n 0001eac0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ead0: 2020 2020 2020 2020 2020 5472 616e 7366            Transf\n-0001eae0: 6f72 6d20 6c69 7465 7261 6c73 2e20 2020  orm literals.   \n-0001eaf0: 286c 696e 6520 3335 290a 0a1f 0a46 696c  (line 35)....Fil\n-0001eb00: 653a 2073 6b65 7463 682e 696e 666f 2c20  e: sketch.info, \n-0001eb10: 204e 6f64 653a 2049 6e64 6578 2c20 2050   Node: Index,  P\n-0001eb20: 7265 763a 2049 6e64 6578 206f 6620 7379  rev: Index of sy\n-0001eb30: 6e74 6178 2c20 2055 703a 2054 6f70 0a0a  ntax,  Up: Top..\n-0001eb40: 496e 6465 7820 6f66 2063 6f6e 6365 7074  Index of concept\n-0001eb50: 730a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  s.**************\n-0001eb60: 2a2a 2a0a 0a00 085b 696e 6465 7800 085d  ***....[index..]\n-0001eb70: 0a2a 204d 656e 753a 0a0a 2a20 6166 6669  .* Menu:..* affi\n-0001eb80: 6e65 2061 7269 7468 6d65 7469 633a 2020  ne arithmetic:  \n+0001ead0: 2020 2020 2020 2020 5472 616e 7366 6f72          Transfor\n+0001eae0: 6d20 6c69 7465 7261 6c73 2e20 2020 286c  m literals.   (l\n+0001eaf0: 696e 6520 3335 290a 0a1f 0a46 696c 653a  ine 35)....File:\n+0001eb00: 2073 6b65 7463 682e 696e 666f 2c20 204e   sketch.info,  N\n+0001eb10: 6f64 653a 2049 6e64 6578 2c20 2050 7265  ode: Index,  Pre\n+0001eb20: 763a 2049 6e64 6578 206f 6620 7379 6e74  v: Index of synt\n+0001eb30: 6178 2c20 2055 703a 2054 6f70 0a0a 496e  ax,  Up: Top..In\n+0001eb40: 6465 7820 6f66 2063 6f6e 6365 7074 730a  dex of concepts.\n+0001eb50: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a  ****************\n+0001eb60: 2a0a 0a00 085b 696e 6465 7800 085d 0a2a  *....[index..].*\n+0001eb70: 204d 656e 753a 0a0a 2a20 6166 6669 6e65   Menu:..* affine\n+0001eb80: 2061 7269 7468 6d65 7469 633a 2020 2020   arithmetic:    \n 0001eb90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001eba0: 2020 2041 6666 696e 6520 6172 6974 686d     Affine arithm\n-0001ebb0: 6574 6963 2e20 2020 286c 696e 6520 2020  etic.   (line   \n-0001ebc0: 3829 0a2a 2061 6666 696e 6520 6172 6974  8).* affine arit\n-0001ebd0: 686d 6574 6963 203c 313e 3a20 2020 2020  hmetic <1>:     \n-0001ebe0: 2020 2020 2020 2020 2020 2020 4120 7465              A te\n-0001ebf0: 6368 6e69 6361 6c20 6472 6177 696e 672e  chnical drawing.\n-0001ec00: 2028 6c69 6e65 2020 3430 290a 2a20 616c   (line  40).* al\n-0001ec10: 7465 726e 6174 6976 6573 2c20 6465 6669  ternatives, defi\n-0001ec20: 6e69 7469 6f6e 3a20 2020 2020 2020 2020  nition:         \n-0001ec30: 2020 2020 2046 6f72 6d73 206f 6620 6465       Forms of de\n-0001ec40: 6669 6e69 7469 6f6e 732e 0a20 2020 2020  finitions..     \n+0001eba0: 2041 6666 696e 6520 6172 6974 686d 6574   Affine arithmet\n+0001ebb0: 6963 2e20 2020 286c 696e 6520 2020 3829  ic.   (line   8)\n+0001ebc0: 0a2a 2061 6666 696e 6520 6172 6974 686d  .* affine arithm\n+0001ebd0: 6574 6963 203c 313e 3a20 2020 2020 2020  etic <1>:       \n+0001ebe0: 2020 2020 2020 2020 2020 4120 7465 6368            A tech\n+0001ebf0: 6e69 6361 6c20 6472 6177 696e 672e 2028  nical drawing. (\n+0001ec00: 6c69 6e65 2020 3430 290a 2a20 616c 7465  line  40).* alte\n+0001ec10: 726e 6174 6976 6573 2c20 6465 6669 6e69  rnatives, defini\n+0001ec20: 7469 6f6e 3a20 2020 2020 2020 2020 2020  tion:           \n+0001ec30: 2020 2046 6f72 6d73 206f 6620 6465 6669     Forms of defi\n+0001ec40: 6e69 7469 6f6e 732e 0a20 2020 2020 2020  nitions..       \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 2020 2020 2028 6c69 6e65 2020           (line  \n-0001ec90: 2036 290a 2a20 6172 6775 6d65 6e74 2c20   6).* argument, \n-0001eca0: 7370 6563 6961 6c3a 2020 2020 2020 2020  special:        \n-0001ecb0: 2020 2020 2020 2020 2020 2020 2053 7065               Spe\n-0001ecc0: 6369 616c 206f 626a 6563 7473 2e20 2020  cial objects.   \n-0001ecd0: 2020 286c 696e 6520 2032 3529 0a2a 2061    (line  25).* a\n-0001ece0: 7267 756d 656e 742c 2073 7065 6369 616c  rgument, special\n-0001ecf0: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-0001ed00: 2020 2020 2020 5370 6563 6961 6c73 2e20        Specials. \n-0001ed10: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-0001ed20: 2020 3130 290a 2a20 6173 736f 6369 6174    10).* associat\n-0001ed30: 6976 6974 792c 206f 7065 7261 746f 723a  ivity, operator:\n-0001ed40: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n-0001ed50: 776f 2d6f 7065 7261 6e64 2028 6269 6e61  wo-operand (bina\n-0001ed60: 7279 2920 666f 726d 732e 0a20 2020 2020  ry) forms..     \n+0001ec80: 2020 2020 2020 2028 6c69 6e65 2020 2036         (line   6\n+0001ec90: 290a 2a20 6172 6775 6d65 6e74 2c20 7370  ).* argument, sp\n+0001eca0: 6563 6961 6c3a 2020 2020 2020 2020 2020  ecial:          \n+0001ecb0: 2020 2020 2020 2020 2020 2053 7065 6369             Speci\n+0001ecc0: 616c 206f 626a 6563 7473 2e20 2020 2020  al objects.     \n+0001ecd0: 286c 696e 6520 2032 3529 0a2a 2061 7267  (line  25).* arg\n+0001ece0: 756d 656e 742c 2073 7065 6369 616c 203c  ument, special <\n+0001ecf0: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+0001ed00: 2020 2020 5370 6563 6961 6c73 2e20 2020      Specials.   \n+0001ed10: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+0001ed20: 3130 290a 2a20 6173 736f 6369 6174 6976  10).* associativ\n+0001ed30: 6974 792c 206f 7065 7261 746f 723a 2020  ity, operator:  \n+0001ed40: 2020 2020 2020 2020 2020 2020 2054 776f               Two\n+0001ed50: 2d6f 7065 7261 6e64 2028 6269 6e61 7279  -operand (binary\n+0001ed60: 2920 666f 726d 732e 0a20 2020 2020 2020  ) 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 2020 2020 2028 6c69 6e65 2020           (line  \n-0001edb0: 3538 290a 2a20 6178 6973 2c20 726f 7461  58).* axis, rota\n-0001edc0: 7469 6f6e 3a20 2020 2020 2020 2020 2020  tion:           \n-0001edd0: 2020 2020 2020 2020 2020 2020 204f 626a               Obj\n-0001ede0: 6563 7420 7472 616e 7366 6f72 6d73 2e20  ect transforms. \n-0001edf0: 2020 286c 696e 6520 2034 3029 0a2a 2062    (line  40).* b\n-0001ee00: 6163 6b20 6661 6365 3a20 2020 2020 2020  ack face:       \n+0001eda0: 2020 2020 2020 2028 6c69 6e65 2020 3538         (line  58\n+0001edb0: 290a 2a20 6178 6973 2c20 726f 7461 7469  ).* axis, rotati\n+0001edc0: 6f6e 3a20 2020 2020 2020 2020 2020 2020  on:             \n+0001edd0: 2020 2020 2020 2020 2020 204f 626a 6563             Objec\n+0001ede0: 7420 7472 616e 7366 6f72 6d73 2e20 2020  t transforms.   \n+0001edf0: 286c 696e 6520 2034 3029 0a2a 2062 6163  (line  40).* bac\n+0001ee00: 6b20 6661 6365 3a20 2020 2020 2020 2020  k face:         \n 0001ee10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ee20: 2020 2020 2020 4472 6177 696e 6720 6120        Drawing a \n-0001ee30: 736f 6c69 642e 2020 2020 2028 6c69 6e65  solid.     (line\n-0001ee40: 2020 3335 290a 2a20 6261 7365 6c69 6e65    35).* baseline\n-0001ee50: 2066 7261 6374 696f 6e3a 2020 2020 2020   fraction:      \n-0001ee60: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n-0001ee70: 6963 7475 7265 2062 6f78 2e20 2020 2020  icture box.     \n-0001ee80: 2020 2020 286c 696e 6520 2031 3029 0a2a      (line  10).*\n-0001ee90: 2062 696e 6172 7920 666f 726d 3a20 2020   binary form:   \n+0001ee20: 2020 2020 4472 6177 696e 6720 6120 736f      Drawing a so\n+0001ee30: 6c69 642e 2020 2020 2028 6c69 6e65 2020  lid.     (line  \n+0001ee40: 3335 290a 2a20 6261 7365 6c69 6e65 2066  35).* baseline f\n+0001ee50: 7261 6374 696f 6e3a 2020 2020 2020 2020  raction:        \n+0001ee60: 2020 2020 2020 2020 2020 2020 2050 6963               Pic\n+0001ee70: 7475 7265 2062 6f78 2e20 2020 2020 2020  ture box.       \n+0001ee80: 2020 286c 696e 6520 2031 3029 0a2a 2062    (line  10).* b\n+0001ee90: 696e 6172 7920 666f 726d 3a20 2020 2020  inary form:     \n 0001eea0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001eeb0: 2020 2020 2020 2020 5477 6f2d 6f70 6572          Two-oper\n-0001eec0: 616e 6420 2862 696e 6172 7929 2066 6f72  and (binary) for\n-0001eed0: 6d73 2e0a 2020 2020 2020 2020 2020 2020  ms..            \n+0001eeb0: 2020 2020 2020 5477 6f2d 6f70 6572 616e        Two-operan\n+0001eec0: 6420 2862 696e 6172 7929 2066 6f72 6d73  d (binary) forms\n+0001eed0: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020                  \n-0001ef10: 2020 286c 696e 6520 2020 3629 0a2a 2062    (line   6).* b\n-0001ef20: 696e 6172 7920 7370 6163 6520 7061 7274  inary space part\n-0001ef30: 6974 696f 6e3a 2020 2020 2020 2020 2020  ition:          \n-0001ef40: 2020 2020 2020 4869 6464 656e 2073 7572        Hidden sur\n-0001ef50: 6661 6365 2072 656d 6f76 616c 2e0a 2020  face removal..  \n+0001ef10: 286c 696e 6520 2020 3629 0a2a 2062 696e  (line   6).* bin\n+0001ef20: 6172 7920 7370 6163 6520 7061 7274 6974  ary space partit\n+0001ef30: 696f 6e3a 2020 2020 2020 2020 2020 2020  ion:            \n+0001ef40: 2020 2020 4869 6464 656e 2073 7572 6661      Hidden surfa\n+0001ef50: 6365 2072 656d 6f76 616c 2e0a 2020 2020  ce 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 2020 2020 286c 696e              (lin\n-0001efa0: 6520 2032 3329 0a2a 2062 696e 6172 7920  e  23).* binary \n-0001efb0: 7370 6163 6520 7061 7274 6974 696f 6e20  space partition \n-0001efc0: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n-0001efd0: 5374 6174 6973 7469 6373 2e20 2020 2020  Statistics.     \n-0001efe0: 2020 2020 2028 6c69 6e65 2020 3133 290a       (line  13).\n-0001eff0: 2a20 6269 6e61 7279 2073 7061 6365 2070  * binary space p\n-0001f000: 6172 7469 7469 6f6e 203c 323e 3a20 2020  artition <2>:   \n-0001f010: 2020 2020 2020 2020 2043 6f6d 6d61 6e64           Command\n-0001f020: 206c 696e 652e 2020 2020 2020 2020 286c   line.        (l\n-0001f030: 696e 6520 2032 3629 0a2a 2062 6c6f 636b  ine  26).* block\n-0001f040: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+0001ef90: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+0001efa0: 2032 3329 0a2a 2062 696e 6172 7920 7370   23).* binary sp\n+0001efb0: 6163 6520 7061 7274 6974 696f 6e20 3c31  ace partition <1\n+0001efc0: 3e3a 2020 2020 2020 2020 2020 2020 5374  >:            St\n+0001efd0: 6174 6973 7469 6373 2e20 2020 2020 2020  atistics.       \n+0001efe0: 2020 2028 6c69 6e65 2020 3133 290a 2a20     (line  13).* \n+0001eff0: 6269 6e61 7279 2073 7061 6365 2070 6172  binary space par\n+0001f000: 7469 7469 6f6e 203c 323e 3a20 2020 2020  tition <2>:     \n+0001f010: 2020 2020 2020 2043 6f6d 6d61 6e64 206c         Command l\n+0001f020: 696e 652e 2020 2020 2020 2020 286c 696e  ine.        (lin\n+0001f030: 6520 2032 3629 0a2a 2062 6c6f 636b 3a20  e  26).* block: \n+0001f040: 2020 2020 2020 2020 2020 2020 2020 2020                  \n 0001f050: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f060: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n-0001f070: 726d 732e 2020 2028 6c69 6e65 2020 3234  rms.   (line  24\n-0001f080: 290a 2a20 626c 6f63 6b20 3c31 3e3a 2020  ).* block <1>:  \n+0001f060: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n+0001f070: 732e 2020 2028 6c69 6e65 2020 3234 290a  s.   (line  24).\n+0001f080: 2a20 626c 6f63 6b20 3c31 3e3a 2020 2020  * block <1>:    \n 0001f090: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f0a0: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-0001f0b0: 2062 6c6f 636b 732e 2020 2020 2020 2020   blocks.        \n-0001f0c0: 286c 696e 6520 2020 3729 0a2a 2062 6c6f  (line   7).* blo\n-0001f0d0: 636b 203c 323e 3a20 2020 2020 2020 2020  ck <2>:         \n+0001f0a0: 2020 2020 2020 2020 2053 7765 7074 2062           Swept b\n+0001f0b0: 6c6f 636b 732e 2020 2020 2020 2020 286c  locks.        (l\n+0001f0c0: 696e 6520 2020 3729 0a2a 2062 6c6f 636b  ine   7).* block\n+0001f0d0: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n 0001f0e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f0f0: 2020 2020 426c 6f63 6b73 2e20 2020 2020      Blocks.     \n-0001f100: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-0001f110: 2036 290a 2a20 626c 6f63 6b20 7377 6565   6).* block swee\n-0001f120: 703a 2020 2020 2020 2020 2020 2020 2020  p:              \n-0001f130: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n-0001f140: 7074 2062 6c6f 636b 732e 2020 2020 2020  pt blocks.      \n-0001f150: 2020 286c 696e 6520 2020 3629 0a2a 2062    (line   6).* b\n-0001f160: 6f64 7920 706f 6c79 676f 6e3a 2020 2020  ody polygon:    \n+0001f0f0: 2020 426c 6f63 6b73 2e20 2020 2020 2020    Blocks.       \n+0001f100: 2020 2020 2020 2028 6c69 6e65 2020 2036         (line   6\n+0001f110: 290a 2a20 626c 6f63 6b20 7377 6565 703a  ).* block sweep:\n+0001f120: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f130: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n+0001f140: 2062 6c6f 636b 732e 2020 2020 2020 2020   blocks.        \n+0001f150: 286c 696e 6520 2020 3629 0a2a 2062 6f64  (line   6).* bod\n+0001f160: 7920 706f 6c79 676f 6e3a 2020 2020 2020  y polygon:      \n 0001f170: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f180: 2020 2020 2020 496e 7465 726e 616c 206f        Internal o\n-0001f190: 7074 696f 6e73 2e20 2020 2028 6c69 6e65  ptions.    (line\n-0001f1a0: 2020 3136 290a 2a20 626f 6479 2070 6f6c    16).* body pol\n-0001f1b0: 7967 6f6e 203c 313e 3a20 2020 2020 2020  ygon <1>:       \n-0001f1c0: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n-0001f1d0: 7765 7074 206c 696e 6573 2e20 2020 2020  wept lines.     \n-0001f1e0: 2020 2020 286c 696e 6520 2031 3029 0a2a      (line  10).*\n-0001f1f0: 2062 6f64 7920 706f 6c79 676f 6e20 3c32   body polygon <2\n-0001f200: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001f210: 2020 2020 2020 2020 5377 6570 7420 706f          Swept po\n-0001f220: 6c79 676f 6e73 2e20 2020 2020 2028 6c69  lygons.      (li\n-0001f230: 6e65 2020 2039 290a 2a20 626f 756e 6469  ne   9).* boundi\n-0001f240: 6e67 2062 6f78 3a20 2020 2020 2020 2020  ng box:         \n-0001f250: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f260: 2050 6963 7475 7265 2062 6f78 2e20 2020   Picture box.   \n-0001f270: 2020 2020 2020 286c 696e 6520 2031 3529        (line  15)\n-0001f280: 0a2a 2042 5350 2c20 6269 6e61 7279 2073  .* BSP, binary s\n-0001f290: 7061 6365 2070 6172 7469 7469 6f6e 3a20  pace partition: \n-0001f2a0: 2020 2020 2020 2020 2020 4869 6464 656e            Hidden\n-0001f2b0: 2073 7572 6661 6365 2072 656d 6f76 616c   surface removal\n-0001f2c0: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+0001f180: 2020 2020 496e 7465 726e 616c 206f 7074      Internal opt\n+0001f190: 696f 6e73 2e20 2020 2028 6c69 6e65 2020  ions.    (line  \n+0001f1a0: 3136 290a 2a20 626f 6479 2070 6f6c 7967  16).* body polyg\n+0001f1b0: 6f6e 203c 313e 3a20 2020 2020 2020 2020  on <1>:         \n+0001f1c0: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n+0001f1d0: 7074 206c 696e 6573 2e20 2020 2020 2020  pt lines.       \n+0001f1e0: 2020 286c 696e 6520 2031 3029 0a2a 2062    (line  10).* b\n+0001f1f0: 6f64 7920 706f 6c79 676f 6e20 3c32 3e3a  ody polygon <2>:\n+0001f200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f210: 2020 2020 2020 5377 6570 7420 706f 6c79        Swept poly\n+0001f220: 676f 6e73 2e20 2020 2020 2028 6c69 6e65  gons.      (line\n+0001f230: 2020 2039 290a 2a20 626f 756e 6469 6e67     9).* bounding\n+0001f240: 2062 6f78 3a20 2020 2020 2020 2020 2020   box:           \n+0001f250: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n+0001f260: 6963 7475 7265 2062 6f78 2e20 2020 2020  icture box.     \n+0001f270: 2020 2020 286c 696e 6520 2031 3529 0a2a      (line  15).*\n+0001f280: 2042 5350 2c20 6269 6e61 7279 2073 7061   BSP, binary spa\n+0001f290: 6365 2070 6172 7469 7469 6f6e 3a20 2020  ce partition:   \n+0001f2a0: 2020 2020 2020 2020 4869 6464 656e 2073          Hidden s\n+0001f2b0: 7572 6661 6365 2072 656d 6f76 616c 2e0a  urface removal..\n+0001f2c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020                  \n-0001f300: 286c 696e 6520 2032 3329 0a2a 2042 5350  (line  23).* BSP\n-0001f310: 2c20 6269 6e61 7279 2073 7061 6365 2070  , binary space p\n-0001f320: 6172 7469 7469 6f6e 203c 313e 3a20 2020  artition <1>:   \n-0001f330: 2020 2020 436f 6d6d 616e 6420 6c69 6e65      Command line\n-0001f340: 2e20 2020 2020 2020 2028 6c69 6e65 2020  .        (line  \n-0001f350: 3236 290a 2a20 6361 6d65 7261 3a20 2020  26).* camera:   \n+0001f2f0: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+0001f300: 696e 6520 2032 3329 0a2a 2042 5350 2c20  ine  23).* BSP, \n+0001f310: 6269 6e61 7279 2073 7061 6365 2070 6172  binary space par\n+0001f320: 7469 7469 6f6e 203c 313e 3a20 2020 2020  tition <1>:     \n+0001f330: 2020 436f 6d6d 616e 6420 6c69 6e65 2e20    Command line. \n+0001f340: 2020 2020 2020 2028 6c69 6e65 2020 3236         (line  26\n+0001f350: 290a 2a20 6361 6d65 7261 3a20 2020 2020  ).* camera:     \n 0001f360: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f370: 2020 2020 2020 2020 2020 2020 2043 616d               Cam\n-0001f380: 6572 612e 2020 2020 2020 2020 2020 2020  era.            \n-0001f390: 2020 286c 696e 6520 2020 3629 0a2a 2063    (line   6).* c\n-0001f3a0: 656e 7465 7220 6f66 2072 6f74 6174 696f  enter of rotatio\n-0001f3b0: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n-0001f3c0: 2020 2020 2020 4f62 6a65 6374 2074 7261        Object tra\n-0001f3d0: 6e73 666f 726d 732e 2020 2028 6c69 6e65  nsforms.   (line\n-0001f3e0: 2020 2038 290a 2a20 6365 6e74 6572 206f     8).* center o\n-0001f3f0: 6620 726f 7461 7469 6f6e 203c 313e 3a20  f rotation <1>: \n-0001f400: 2020 2020 2020 2020 2020 2020 2020 204e                 N\n-0001f410: 6573 7465 6420 7377 6565 7073 2e20 2020  ested sweeps.   \n-0001f420: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-0001f430: 2063 656e 7472 6f69 643a 2020 2020 2020   centroid:      \n+0001f370: 2020 2020 2020 2020 2020 2043 616d 6572             Camer\n+0001f380: 612e 2020 2020 2020 2020 2020 2020 2020  a.              \n+0001f390: 286c 696e 6520 2020 3629 0a2a 2063 656e  (line   6).* cen\n+0001f3a0: 7465 7220 6f66 2072 6f74 6174 696f 6e3a  ter of rotation:\n+0001f3b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f3c0: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n+0001f3d0: 666f 726d 732e 2020 2028 6c69 6e65 2020  forms.   (line  \n+0001f3e0: 2038 290a 2a20 6365 6e74 6572 206f 6620   8).* center of \n+0001f3f0: 726f 7461 7469 6f6e 203c 313e 3a20 2020  rotation <1>:   \n+0001f400: 2020 2020 2020 2020 2020 2020 204e 6573               Nes\n+0001f410: 7465 6420 7377 6565 7073 2e20 2020 2020  ted sweeps.     \n+0001f420: 2020 286c 696e 6520 2020 3629 0a2a 2063    (line   6).* c\n+0001f430: 656e 7472 6f69 643a 2020 2020 2020 2020  entroid:        \n 0001f440: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f450: 2020 2020 2020 2020 4120 7465 6368 6e69          A techni\n-0001f460: 6361 6c20 6472 6177 696e 672e 2028 6c69  cal drawing. (li\n-0001f470: 6e65 2020 3634 290a 2a20 6365 6e74 726f  ne  64).* centro\n-0001f480: 6964 203c 313e 3a20 2020 2020 2020 2020  id <1>:         \n-0001f490: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f4a0: 2041 2074 6563 686e 6963 616c 2064 7261   A technical dra\n-0001f4b0: 7769 6e67 2e20 286c 696e 6520 3130 3229  wing. (line 102)\n-0001f4c0: 0a2a 2063 6c69 7070 696e 673a 2020 2020  .* clipping:    \n+0001f450: 2020 2020 2020 4120 7465 6368 6e69 6361        A technica\n+0001f460: 6c20 6472 6177 696e 672e 2028 6c69 6e65  l drawing. (line\n+0001f470: 2020 3634 290a 2a20 6365 6e74 726f 6964    64).* centroid\n+0001f480: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+0001f490: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+0001f4a0: 2074 6563 686e 6963 616c 2064 7261 7769   technical drawi\n+0001f4b0: 6e67 2e20 286c 696e 6520 3130 3229 0a2a  ng. (line 102).*\n+0001f4c0: 2063 6c69 7070 696e 673a 2020 2020 2020   clipping:      \n 0001f4d0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f4e0: 2020 2020 2020 2020 2020 5069 6374 7572            Pictur\n-0001f4f0: 6520 626f 782e 2020 2020 2020 2020 2028  e box.         (\n-0001f500: 6c69 6e65 2020 3137 290a 2a20 636c 6970  line  17).* clip\n-0001f510: 7069 6e67 203c 313e 3a20 2020 2020 2020  ping <1>:       \n+0001f4e0: 2020 2020 2020 2020 5069 6374 7572 6520          Picture \n+0001f4f0: 626f 782e 2020 2020 2020 2020 2028 6c69  box.         (li\n+0001f500: 6e65 2020 3137 290a 2a20 636c 6970 7069  ne  17).* clippi\n+0001f510: 6e67 203c 313e 3a20 2020 2020 2020 2020  ng <1>:         \n 0001f520: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f530: 2020 2043 6c69 7070 696e 672e 2020 2020     Clipping.    \n-0001f540: 2020 2020 2020 2020 286c 696e 6520 2020          (line   \n-0001f550: 3629 0a2a 2063 6c6f 7375 7265 2074 6167  6).* closure tag\n-0001f560: 2c20 3c3e 3a20 2020 2020 2020 2020 2020  , <>:           \n-0001f570: 2020 2020 2020 2020 2020 2020 506f 696e              Poin\n-0001f580: 7420 7377 6565 7073 2e20 2020 2020 2020  t sweeps.       \n-0001f590: 2028 6c69 6e65 2020 3138 290a 2a20 636c   (line  18).* cl\n-0001f5a0: 6f73 7572 6520 7461 672c 203c 3e20 3c31  osure tag, <> <1\n-0001f5b0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001f5c0: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n-0001f5d0: 6565 7073 2077 6974 6820 636c 6f73 7572  eeps with closur\n-0001f5e0: 652e 0a20 2020 2020 2020 2020 2020 2020  e..             \n+0001f530: 2043 6c69 7070 696e 672e 2020 2020 2020   Clipping.      \n+0001f540: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+0001f550: 0a2a 2063 6c6f 7375 7265 2074 6167 2c20  .* closure tag, \n+0001f560: 3c3e 3a20 2020 2020 2020 2020 2020 2020  <>:             \n+0001f570: 2020 2020 2020 2020 2020 506f 696e 7420            Point \n+0001f580: 7377 6565 7073 2e20 2020 2020 2020 2028  sweeps.        (\n+0001f590: 6c69 6e65 2020 3138 290a 2a20 636c 6f73  line  18).* clos\n+0001f5a0: 7572 6520 7461 672c 203c 3e20 3c31 3e3a  ure tag, <> <1>:\n+0001f5b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f5c0: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n+0001f5d0: 7073 2077 6974 6820 636c 6f73 7572 652e  ps with closure.\n+0001f5e0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \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 2020 2020                  \n-0001f620: 2028 6c69 6e65 2020 2036 290a 2a20 636c   (line   6).* cl\n-0001f630: 6f73 7572 6520 7461 672c 203c 3e20 3c32  osure tag, <> <2\n-0001f640: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-0001f650: 2020 2020 2053 7765 6570 732e 2020 2020       Sweeps.    \n-0001f660: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-0001f670: 2031 3929 0a2a 2063 6c6f 7375 7265 2074   19).* closure t\n-0001f680: 6167 2c20 3c3e 203c 333e 3a20 2020 2020  ag, <> <3>:     \n-0001f690: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n-0001f6a0: 6570 7420 706f 696e 7473 2e20 2020 2020  ept points.     \n-0001f6b0: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n-0001f6c0: 636c 6f73 7572 6520 7461 672c 203c 3e20  closure tag, <> \n-0001f6d0: 3c34 3e3a 2020 2020 2020 2020 2020 2020  <4>:            \n-0001f6e0: 2020 2020 2020 2053 7765 7074 2070 6f69         Swept poi\n-0001f6f0: 6e74 732e 2020 2020 2020 2020 286c 696e  nts.        (lin\n-0001f700: 6520 2031 3329 0a2a 2063 6c6f 7375 7265  e  13).* closure\n-0001f710: 2074 6167 2c20 3c3e 203c 353e 3a20 2020   tag, <> <5>:   \n-0001f720: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f730: 5377 6570 7420 6c69 6e65 732e 2020 2020  Swept lines.    \n-0001f740: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n-0001f750: 2a20 636c 6f73 7572 6520 7461 672c 203c  * closure tag, <\n-0001f760: 3e20 3c36 3e3a 2020 2020 2020 2020 2020  > <6>:          \n-0001f770: 2020 2020 2020 2020 2053 7765 7074 206c           Swept l\n-0001f780: 696e 6573 2e20 2020 2020 2020 2020 286c  ines.         (l\n-0001f790: 696e 6520 2032 3829 0a2a 2063 6c6f 7375  ine  28).* closu\n-0001f7a0: 7265 2074 6167 2c20 3c3e 203c 373e 3a20  re tag, <> <7>: \n+0001f610: 2020 2020 2020 2020 2020 2020 2020 2028                 (\n+0001f620: 6c69 6e65 2020 2036 290a 2a20 636c 6f73  line   6).* clos\n+0001f630: 7572 6520 7461 672c 203c 3e20 3c32 3e3a  ure tag, <> <2>:\n+0001f640: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f650: 2020 2053 7765 6570 732e 2020 2020 2020     Sweeps.      \n+0001f660: 2020 2020 2020 2020 286c 696e 6520 2031          (line  1\n+0001f670: 3929 0a2a 2063 6c6f 7375 7265 2074 6167  9).* closure tag\n+0001f680: 2c20 3c3e 203c 333e 3a20 2020 2020 2020  , <> <3>:       \n+0001f690: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n+0001f6a0: 7420 706f 696e 7473 2e20 2020 2020 2020  t points.       \n+0001f6b0: 2028 6c69 6e65 2020 2036 290a 2a20 636c   (line   6).* cl\n+0001f6c0: 6f73 7572 6520 7461 672c 203c 3e20 3c34  osure tag, <> <4\n+0001f6d0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001f6e0: 2020 2020 2053 7765 7074 2070 6f69 6e74       Swept point\n+0001f6f0: 732e 2020 2020 2020 2020 286c 696e 6520  s.        (line \n+0001f700: 2031 3329 0a2a 2063 6c6f 7375 7265 2074   13).* closure t\n+0001f710: 6167 2c20 3c3e 203c 353e 3a20 2020 2020  ag, <> <5>:     \n+0001f720: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n+0001f730: 6570 7420 6c69 6e65 732e 2020 2020 2020  ept lines.      \n+0001f740: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n+0001f750: 636c 6f73 7572 6520 7461 672c 203c 3e20  closure tag, <> \n+0001f760: 3c36 3e3a 2020 2020 2020 2020 2020 2020  <6>:            \n+0001f770: 2020 2020 2020 2053 7765 7074 206c 696e         Swept lin\n+0001f780: 6573 2e20 2020 2020 2020 2020 286c 696e  es.         (lin\n+0001f790: 6520 2032 3829 0a2a 2063 6c6f 7375 7265  e  28).* closure\n+0001f7a0: 2074 6167 2c20 3c3e 203c 373e 3a20 2020   tag, <> <7>:   \n 0001f7b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f7c0: 2020 5377 6565 7020 6661 6365 2073 706c    Sweep face spl\n-0001f7d0: 6974 7469 6e67 2e0a 2020 2020 2020 2020  itting..        \n+0001f7c0: 5377 6565 7020 6661 6365 2073 706c 6974  Sweep face split\n+0001f7d0: 7469 6e67 2e0a 2020 2020 2020 2020 2020  ting..          \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 2020 2020 286c 696e 6520 2031 3129        (line  11)\n-0001f820: 0a2a 2063 6f6d 6d61 6e64 206c 696e 6520  .* command line \n-0001f830: 6f70 7469 6f6e 3a20 2020 2020 2020 2020  option:         \n-0001f840: 2020 2020 2020 2020 2020 4865 6c6c 6f20            Hello \n-0001f850: 776f 726c 642e 2020 2020 2020 2020 2028  world.         (\n-0001f860: 6c69 6e65 2020 3330 290a 2a20 636f 6d6d  line  30).* comm\n-0001f870: 616e 6420 6c69 6e65 206f 7074 696f 6e73  and line options\n-0001f880: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-0001f890: 2020 2043 6f6d 6d61 6e64 206c 696e 652e     Command line.\n-0001f8a0: 2020 2020 2020 2020 286c 696e 6520 2031          (line  1\n-0001f8b0: 3429 0a2a 2063 6f6d 6d61 6e64 206c 696e  4).* command lin\n-0001f8c0: 652c 2073 6b65 7463 683a 2020 2020 2020  e, sketch:      \n-0001f8d0: 2020 2020 2020 2020 2020 2020 4865 6c6c              Hell\n-0001f8e0: 6f20 776f 726c 642e 2020 2020 2020 2020  o world.        \n-0001f8f0: 2028 6c69 6e65 2020 2039 290a 2a20 636f   (line   9).* co\n-0001f900: 6d6d 616e 6420 6c69 6e65 2c20 736b 6574  mmand line, sket\n-0001f910: 6368 203c 313e 3a20 2020 2020 2020 2020  ch <1>:         \n-0001f920: 2020 2020 2043 6f6d 6d61 6e64 206c 696e       Command lin\n-0001f930: 652e 2020 2020 2020 2020 286c 696e 6520  e.        (line \n-0001f940: 2020 3629 0a2a 2063 6f6d 6d65 6e74 733a    6).* comments:\n+0001f810: 2020 2020 286c 696e 6520 2031 3129 0a2a      (line  11).*\n+0001f820: 2063 6f6d 6d61 6e64 206c 696e 6520 6f70   command line op\n+0001f830: 7469 6f6e 3a20 2020 2020 2020 2020 2020  tion:           \n+0001f840: 2020 2020 2020 2020 4865 6c6c 6f20 776f          Hello wo\n+0001f850: 726c 642e 2020 2020 2020 2020 2028 6c69  rld.         (li\n+0001f860: 6e65 2020 3330 290a 2a20 636f 6d6d 616e  ne  30).* comman\n+0001f870: 6420 6c69 6e65 206f 7074 696f 6e73 3a20  d line options: \n+0001f880: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001f890: 2043 6f6d 6d61 6e64 206c 696e 652e 2020   Command line.  \n+0001f8a0: 2020 2020 2020 286c 696e 6520 2031 3429        (line  14)\n+0001f8b0: 0a2a 2063 6f6d 6d61 6e64 206c 696e 652c  .* command line,\n+0001f8c0: 2073 6b65 7463 683a 2020 2020 2020 2020   sketch:        \n+0001f8d0: 2020 2020 2020 2020 2020 4865 6c6c 6f20            Hello \n+0001f8e0: 776f 726c 642e 2020 2020 2020 2020 2028  world.         (\n+0001f8f0: 6c69 6e65 2020 2039 290a 2a20 636f 6d6d  line   9).* comm\n+0001f900: 616e 6420 6c69 6e65 2c20 736b 6574 6368  and line, sketch\n+0001f910: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+0001f920: 2020 2043 6f6d 6d61 6e64 206c 696e 652e     Command line.\n+0001f930: 2020 2020 2020 2020 286c 696e 6520 2020          (line   \n+0001f940: 3629 0a2a 2063 6f6d 6d65 6e74 733a 2020  6).* comments:  \n 0001f950: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f960: 2020 2020 2020 2020 2020 2020 2020 4472                Dr\n-0001f970: 6177 696e 6720 6120 736f 6c69 642e 2020  awing a solid.  \n-0001f980: 2020 2028 6c69 6e65 2020 3238 290a 2a20     (line  28).* \n-0001f990: 636f 6d6d 656e 7473 203c 313e 3a20 2020  comments <1>:   \n+0001f960: 2020 2020 2020 2020 2020 2020 4472 6177              Draw\n+0001f970: 696e 6720 6120 736f 6c69 642e 2020 2020  ing a solid.    \n+0001f980: 2028 6c69 6e65 2020 3238 290a 2a20 636f   (line  28).* co\n+0001f990: 6d6d 656e 7473 203c 313e 3a20 2020 2020  mments <1>:     \n 0001f9a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001f9b0: 2020 2020 2020 204c 616e 6775 6167 6520         Language \n-0001f9c0: 6261 7369 6373 2e20 2020 2020 286c 696e  basics.     (lin\n-0001f9d0: 6520 2031 3829 0a2a 2063 6f6e 7374 7275  e  18).* constru\n-0001f9e0: 6374 6f72 3a20 2020 2020 2020 2020 2020  ctor:           \n-0001f9f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fa00: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n-0001fa10: 6c73 2e20 2028 6c69 6e65 2020 2036 290a  ls.  (line   6).\n-0001fa20: 2a20 636f 6f72 6469 6e61 7465 2073 7973  * coordinate sys\n-0001fa30: 7465 6d2c 2072 6967 6874 2d68 616e 6465  tem, right-hande\n-0001fa40: 643a 2020 2020 2020 2049 6e74 726f 6475  d:       Introdu\n-0001fa50: 6374 696f 6e20 6279 2065 7861 6d70 6c65  ction by example\n-0001fa60: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+0001f9b0: 2020 2020 204c 616e 6775 6167 6520 6261       Language ba\n+0001f9c0: 7369 6373 2e20 2020 2020 286c 696e 6520  sics.     (line \n+0001f9d0: 2031 3829 0a2a 2063 6f6e 7374 7275 6374   18).* construct\n+0001f9e0: 6f72 3a20 2020 2020 2020 2020 2020 2020  or:             \n+0001f9f0: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n+0001fa00: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n+0001fa10: 2e20 2028 6c69 6e65 2020 2036 290a 2a20  .  (line   6).* \n+0001fa20: 636f 6f72 6469 6e61 7465 2073 7973 7465  coordinate syste\n+0001fa30: 6d2c 2072 6967 6874 2d68 616e 6465 643a  m, right-handed:\n+0001fa40: 2020 2020 2020 2049 6e74 726f 6475 6374         Introduct\n+0001fa50: 696f 6e20 6279 2065 7861 6d70 6c65 2e0a  ion by example..\n+0001fa60: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020                  \n-0001faa0: 286c 696e 6520 2031 3129 0a2a 2063 6f75  (line  11).* cou\n-0001fab0: 6e74 6572 2d63 6c6f 636b 7769 7365 2070  nter-clockwise p\n-0001fac0: 6f6c 7967 6f6e 2076 6572 7465 7820 6f72  olygon vertex or\n-0001fad0: 6465 723a 2048 656c 6c6f 2077 6f72 6c64  der: Hello world\n-0001fae0: 2e20 2020 2020 2020 2028 6c69 6e65 2020  .        (line  \n-0001faf0: 3339 290a 2a20 6375 6c6c 696e 673a 2020  39).* culling:  \n+0001fa90: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+0001faa0: 696e 6520 2031 3129 0a2a 2063 6f75 6e74  ine  11).* count\n+0001fab0: 6572 2d63 6c6f 636b 7769 7365 2070 6f6c  er-clockwise pol\n+0001fac0: 7967 6f6e 2076 6572 7465 7820 6f72 6465  ygon vertex orde\n+0001fad0: 723a 2048 656c 6c6f 2077 6f72 6c64 2e20  r: Hello world. \n+0001fae0: 2020 2020 2020 2028 6c69 6e65 2020 3339         (line  39\n+0001faf0: 290a 2a20 6375 6c6c 696e 673a 2020 2020  ).* culling:    \n 0001fb00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fb10: 2020 2020 2020 2020 2020 2020 2048 656c               Hel\n-0001fb20: 6c6f 2077 6f72 6c64 2e20 2020 2020 2020  lo world.       \n-0001fb30: 2020 286c 696e 6520 2034 3329 0a2a 2063    (line  43).* c\n-0001fb40: 756c 6c69 6e67 203c 313e 3a20 2020 2020  ulling <1>:     \n+0001fb10: 2020 2020 2020 2020 2020 2048 656c 6c6f             Hello\n+0001fb20: 2077 6f72 6c64 2e20 2020 2020 2020 2020   world.         \n+0001fb30: 286c 696e 6520 2034 3329 0a2a 2063 756c  (line  43).* cul\n+0001fb40: 6c69 6e67 203c 313e 3a20 2020 2020 2020  ling <1>:       \n 0001fb50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fb60: 2020 2020 2020 4472 6177 696e 6720 6120        Drawing a \n-0001fb70: 736f 6c69 642e 2020 2020 2028 6c69 6e65  solid.     (line\n-0001fb80: 2020 3335 290a 2a20 6375 6c6c 696e 6720    35).* culling \n-0001fb90: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n-0001fba0: 2020 2020 2020 2020 2020 2020 2020 2044                 D\n-0001fbb0: 7261 7769 6e67 2061 2073 6f6c 6964 2e20  rawing a solid. \n-0001fbc0: 2020 2020 286c 696e 6520 2034 3129 0a2a      (line  41).*\n-0001fbd0: 2063 756c 6c69 6e67 203c 333e 3a20 2020   culling <3>:   \n+0001fb60: 2020 2020 4472 6177 696e 6720 6120 736f      Drawing a so\n+0001fb70: 6c69 642e 2020 2020 2028 6c69 6e65 2020  lid.     (line  \n+0001fb80: 3335 290a 2a20 6375 6c6c 696e 6720 3c32  35).* culling <2\n+0001fb90: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+0001fba0: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n+0001fbb0: 7769 6e67 2061 2073 6f6c 6964 2e20 2020  wing a solid.   \n+0001fbc0: 2020 286c 696e 6520 2034 3129 0a2a 2063    (line  41).* c\n+0001fbd0: 756c 6c69 6e67 203c 333e 3a20 2020 2020  ulling <3>:     \n 0001fbe0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fbf0: 2020 2020 2020 2020 5377 6570 7420 6c69          Swept li\n-0001fc00: 6e65 732e 2020 2020 2020 2020 2028 6c69  nes.         (li\n-0001fc10: 6e65 2020 3136 290a 2a20 6465 636c 6172  ne  16).* declar\n-0001fc20: 6174 6976 6520 6c61 6e67 7561 6765 3a20  ative language: \n-0001fc30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fc40: 204c 616e 6775 6167 6520 6261 7369 6373   Language basics\n-0001fc50: 2e20 2020 2020 286c 696e 6520 2020 3829  .     (line   8)\n-0001fc60: 0a2a 2064 6566 696e 6974 696f 6e3a 2020  .* definition:  \n+0001fbf0: 2020 2020 2020 5377 6570 7420 6c69 6e65        Swept line\n+0001fc00: 732e 2020 2020 2020 2020 2028 6c69 6e65  s.         (line\n+0001fc10: 2020 3136 290a 2a20 6465 636c 6172 6174    16).* declarat\n+0001fc20: 6976 6520 6c61 6e67 7561 6765 3a20 2020  ive language:   \n+0001fc30: 2020 2020 2020 2020 2020 2020 2020 204c                 L\n+0001fc40: 616e 6775 6167 6520 6261 7369 6373 2e20  anguage basics. \n+0001fc50: 2020 2020 286c 696e 6520 2020 3829 0a2a      (line   8).*\n+0001fc60: 2064 6566 696e 6974 696f 6e3a 2020 2020   definition:    \n 0001fc70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fc80: 2020 2020 2020 2020 2020 4472 6177 696e            Drawin\n-0001fc90: 6720 6120 736f 6c69 642e 2020 2020 2028  g a solid.     (\n-0001fca0: 6c69 6e65 2020 3232 290a 2a20 6465 6669  line  22).* defi\n-0001fcb0: 6e69 7469 6f6e 203c 313e 3a20 2020 2020  nition <1>:     \n+0001fc80: 2020 2020 2020 2020 4472 6177 696e 6720          Drawing \n+0001fc90: 6120 736f 6c69 642e 2020 2020 2028 6c69  a solid.     (li\n+0001fca0: 6e65 2020 3232 290a 2a20 6465 6669 6e69  ne  22).* defini\n+0001fcb0: 7469 6f6e 203c 313e 3a20 2020 2020 2020  tion <1>:       \n 0001fcc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001fcd0: 2020 2044 6566 696e 6974 696f 6e73 2e20     Definitions. \n-0001fce0: 2020 2020 2020 2020 286c 696e 6520 2020          (line   \n-0001fcf0: 3629 0a2a 2064 6566 696e 6974 696f 6e20  6).* definition \n-0001fd00: 7769 7468 2061 6c74 6572 6e61 7469 7665  with alternative\n-0001fd10: 733a 2020 2020 2020 2020 2020 466f 726d  s:          Form\n-0001fd20: 7320 6f66 2064 6566 696e 6974 696f 6e73  s of definitions\n-0001fd30: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+0001fcd0: 2044 6566 696e 6974 696f 6e73 2e20 2020   Definitions.   \n+0001fce0: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+0001fcf0: 0a2a 2064 6566 696e 6974 696f 6e20 7769  .* definition wi\n+0001fd00: 7468 2061 6c74 6572 6e61 7469 7665 733a  th alternatives:\n+0001fd10: 2020 2020 2020 2020 2020 466f 726d 7320            Forms \n+0001fd20: 6f66 2064 6566 696e 6974 696f 6e73 2e0a  of definitions..\n+0001fd30: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020                  \n-0001fd70: 286c 696e 6520 2020 3629 0a2a 2064 6566  (line   6).* def\n-0001fd80: 696e 6974 696f 6e2c 2064 7261 7761 626c  inition, drawabl\n-0001fd90: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n-0001fda0: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n-0001fdb0: 666f 726d 732e 2020 2028 6c69 6e65 2020  forms.   (line  \n-0001fdc0: 3237 290a 2a20 6465 6669 6e69 7469 6f6e  27).* definition\n-0001fdd0: 2c20 6f70 7469 6f6e 733a 2020 2020 2020  , options:      \n-0001fde0: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n-0001fdf0: 796c 696e 6520 7377 6565 7073 2077 6974  yline sweeps wit\n-0001fe00: 6820 636c 6f73 7572 652e 0a20 2020 2020  h closure..     \n+0001fd60: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+0001fd70: 696e 6520 2020 3629 0a2a 2064 6566 696e  ine   6).* defin\n+0001fd80: 6974 696f 6e2c 2064 7261 7761 626c 653a  ition, drawable:\n+0001fd90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001fda0: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n+0001fdb0: 726d 732e 2020 2028 6c69 6e65 2020 3237  rms.   (line  27\n+0001fdc0: 290a 2a20 6465 6669 6e69 7469 6f6e 2c20  ).* definition, \n+0001fdd0: 6f70 7469 6f6e 733a 2020 2020 2020 2020  options:        \n+0001fde0: 2020 2020 2020 2020 2020 2050 6f6c 796c             Polyl\n+0001fdf0: 696e 6520 7377 6565 7073 2077 6974 6820  ine sweeps with \n+0001fe00: 636c 6f73 7572 652e 0a20 2020 2020 2020  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 2020 2020 2028 6c69 6e65 2020           (line  \n-0001fe50: 3233 290a 2a20 6465 6669 6e69 7469 6f6e  23).* definition\n-0001fe60: 2c20 706f 696e 743a 2020 2020 2020 2020  , point:        \n-0001fe70: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n-0001fe80: 7769 6e67 2061 2073 6f6c 6964 2e20 2020  wing a solid.   \n-0001fe90: 2020 286c 696e 6520 2032 3329 0a2a 2064    (line  23).* d\n-0001fea0: 6566 696e 6974 696f 6e2c 2073 6361 6c61  efinition, scala\n-0001feb0: 723a 2020 2020 2020 2020 2020 2020 2020  r:              \n-0001fec0: 2020 2020 2020 5377 6570 7420 6f62 6a65        Swept obje\n-0001fed0: 6374 732e 2020 2020 2020 2028 6c69 6e65  cts.       (line\n-0001fee0: 2020 3133 290a 2a20 6465 6669 6e69 7469    13).* definiti\n-0001fef0: 6f6e 2c20 7369 6d70 6c65 3a20 2020 2020  on, simple:     \n-0001ff00: 2020 2020 2020 2020 2020 2020 2020 2046                 F\n-0001ff10: 6f72 6d73 206f 6620 6465 6669 6e69 7469  orms of definiti\n-0001ff20: 6f6e 732e 0a20 2020 2020 2020 2020 2020  ons..           \n+0001fe40: 2020 2020 2020 2028 6c69 6e65 2020 3233         (line  23\n+0001fe50: 290a 2a20 6465 6669 6e69 7469 6f6e 2c20  ).* definition, \n+0001fe60: 706f 696e 743a 2020 2020 2020 2020 2020  point:          \n+0001fe70: 2020 2020 2020 2020 2020 2044 7261 7769             Drawi\n+0001fe80: 6e67 2061 2073 6f6c 6964 2e20 2020 2020  ng a solid.     \n+0001fe90: 286c 696e 6520 2032 3329 0a2a 2064 6566  (line  23).* def\n+0001fea0: 696e 6974 696f 6e2c 2073 6361 6c61 723a  inition, scalar:\n+0001feb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+0001fec0: 2020 2020 5377 6570 7420 6f62 6a65 6374      Swept object\n+0001fed0: 732e 2020 2020 2020 2028 6c69 6e65 2020  s.       (line  \n+0001fee0: 3133 290a 2a20 6465 6669 6e69 7469 6f6e  13).* definition\n+0001fef0: 2c20 7369 6d70 6c65 3a20 2020 2020 2020  , simple:       \n+0001ff00: 2020 2020 2020 2020 2020 2020 2046 6f72               For\n+0001ff10: 6d73 206f 6620 6465 6669 6e69 7469 6f6e  ms of definition\n+0001ff20: 732e 0a20 2020 2020 2020 2020 2020 2020  s..             \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 2020                  \n-0001ff60: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n-0001ff70: 6465 6669 6e69 7469 6f6e 2c20 7461 673a  definition, tag:\n+0001ff60: 2028 6c69 6e65 2020 2036 290a 2a20 6465   (line   6).* de\n+0001ff70: 6669 6e69 7469 6f6e 2c20 7461 673a 2020  finition, tag:  \n 0001ff80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ff90: 2020 2020 2020 2044 6566 696e 6974 696f         Definitio\n-0001ffa0: 6e73 2e20 2020 2020 2020 2020 286c 696e  ns.         (lin\n-0001ffb0: 6520 2031 3829 0a2a 2064 6566 696e 6974  e  18).* definit\n-0001ffc0: 696f 6e2c 2074 6167 203c 313e 3a20 2020  ion, tag <1>:   \n-0001ffd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-0001ffe0: 466f 726d 7320 6f66 2064 6566 696e 6974  Forms of definit\n-0001fff0: 696f 6e73 2e0a 2020 2020 2020 2020 2020  ions..          \n+0001ff90: 2020 2020 2044 6566 696e 6974 696f 6e73       Definitions\n+0001ffa0: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n+0001ffb0: 2031 3829 0a2a 2064 6566 696e 6974 696f   18).* definitio\n+0001ffc0: 6e2c 2074 6167 203c 313e 3a20 2020 2020  n, tag <1>:     \n+0001ffd0: 2020 2020 2020 2020 2020 2020 2020 466f                Fo\n+0001ffe0: 726d 7320 6f66 2064 6566 696e 6974 696f  rms of definitio\n+0001fff0: 6e73 2e0a 2020 2020 2020 2020 2020 2020  ns..            \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: 2020 2020 286c 696e 6520 2020 3729 0a2a      (line   7).*\n-00020040: 2064 6566 696e 6974 696f 6e2c 2074 6167   definition, tag\n-00020050: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n-00020060: 2020 2020 2020 2020 436f 6d6d 616e 6420          Command \n-00020070: 6c69 6e65 2e20 2020 2020 2020 2028 6c69  line.        (li\n-00020080: 6e65 2020 3533 290a 2a20 6465 6669 6e69  ne  53).* defini\n-00020090: 7469 6f6e 2c20 7472 616e 7366 6f72 6d3a  tion, transform:\n-000200a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000200b0: 204f 7665 7276 6965 772e 2020 2020 2020   Overview.      \n-000200c0: 2020 2020 2020 286c 696e 6520 2033 3529        (line  35)\n-000200d0: 0a2a 2064 6566 696e 6974 696f 6e2c 2076  .* definition, v\n-000200e0: 6563 746f 723a 2020 2020 2020 2020 2020  ector:          \n-000200f0: 2020 2020 2020 2020 2020 506f 6c79 6c69            Polyli\n-00020100: 6e65 2073 7765 6570 732e 2020 2020 2028  ne sweeps.     (\n-00020110: 6c69 6e65 2020 3139 290a 2a20 6465 7074  line  19).* dept\n-00020120: 6820 736f 7274 3a20 2020 2020 2020 2020  h sort:         \n+00020030: 2020 286c 696e 6520 2020 3729 0a2a 2064    (line   7).* d\n+00020040: 6566 696e 6974 696f 6e2c 2074 6167 203c  efinition, tag <\n+00020050: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n+00020060: 2020 2020 2020 436f 6d6d 616e 6420 6c69        Command li\n+00020070: 6e65 2e20 2020 2020 2020 2028 6c69 6e65  ne.        (line\n+00020080: 2020 3533 290a 2a20 6465 6669 6e69 7469    53).* definiti\n+00020090: 6f6e 2c20 7472 616e 7366 6f72 6d3a 2020  on, transform:  \n+000200a0: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n+000200b0: 7665 7276 6965 772e 2020 2020 2020 2020  verview.        \n+000200c0: 2020 2020 286c 696e 6520 2033 3529 0a2a      (line  35).*\n+000200d0: 2064 6566 696e 6974 696f 6e2c 2076 6563   definition, vec\n+000200e0: 746f 723a 2020 2020 2020 2020 2020 2020  tor:            \n+000200f0: 2020 2020 2020 2020 506f 6c79 6c69 6e65          Polyline\n+00020100: 2073 7765 6570 732e 2020 2020 2028 6c69   sweeps.     (li\n+00020110: 6e65 2020 3139 290a 2a20 6465 7074 6820  ne  19).* depth \n+00020120: 736f 7274 3a20 2020 2020 2020 2020 2020  sort:           \n 00020130: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020140: 2020 2049 6e74 6572 6e61 6c20 6f70 7469     Internal opti\n-00020150: 6f6e 732e 2020 2020 286c 696e 6520 2031  ons.    (line  1\n-00020160: 3329 0a2a 2064 6570 7468 2073 6f72 7420  3).* depth sort \n-00020170: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n-00020180: 2020 2020 2020 2020 2020 2020 4869 6464              Hidd\n-00020190: 656e 2073 7572 6661 6365 2072 656d 6f76  en surface remov\n-000201a0: 616c 2e0a 2020 2020 2020 2020 2020 2020  al..            \n+00020140: 2049 6e74 6572 6e61 6c20 6f70 7469 6f6e   Internal option\n+00020150: 732e 2020 2020 286c 696e 6520 2031 3329  s.    (line  13)\n+00020160: 0a2a 2064 6570 7468 2073 6f72 7420 3c31  .* depth sort <1\n+00020170: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+00020180: 2020 2020 2020 2020 2020 4869 6464 656e            Hidden\n+00020190: 2073 7572 6661 6365 2072 656d 6f76 616c   surface removal\n+000201a0: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020                  \n-000201e0: 2020 286c 696e 6520 2020 3629 0a2a 2064    (line   6).* d\n-000201f0: 6570 7468 2073 6f72 7420 3c32 3e3a 2020  epth sort <2>:  \n+000201e0: 286c 696e 6520 2020 3629 0a2a 2064 6570  (line   6).* dep\n+000201f0: 7468 2073 6f72 7420 3c32 3e3a 2020 2020  th sort <2>:    \n 00020200: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020210: 2020 2020 2020 4275 6773 2061 6e64 2061        Bugs and a\n-00020220: 6e6f 6d61 6c69 6573 2e20 2028 6c69 6e65  nomalies.  (line\n-00020230: 2020 2038 290a 2a20 6469 7265 6374 2074     8).* direct t\n-00020240: 7261 6e73 666f 726d 3a20 2020 2020 2020  ransform:       \n-00020250: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n-00020260: 7261 6e73 666f 726d 206c 6974 6572 616c  ransform literal\n-00020270: 732e 2020 286c 696e 6520 2034 3729 0a2a  s.  (line  47).*\n-00020280: 2064 6972 6563 7420 7472 616e 7366 6f72   direct transfor\n-00020290: 6d20 3c31 3e3a 2020 2020 2020 2020 2020  m <1>:          \n-000202a0: 2020 2020 2020 2020 5472 616e 7366 6f72          Transfor\n-000202b0: 6d20 6c69 7465 7261 6c73 2e20 2028 6c69  m literals.  (li\n-000202c0: 6e65 2020 3533 290a 2a20 646f 6375 6d65  ne  53).* docume\n-000202d0: 6e74 2074 656d 706c 6174 653a 2020 2020  nt template:    \n-000202e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000202f0: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020   Hello world.   \n-00020300: 2020 2020 2020 286c 696e 6520 2033 3229        (line  32)\n-00020310: 0a2a 2064 6f63 756d 656e 7420 7465 6d70  .* document temp\n-00020320: 6c61 7465 203c 313e 3a20 2020 2020 2020  late <1>:       \n-00020330: 2020 2020 2020 2020 2020 436f 6d6d 616e            Comman\n-00020340: 6420 6c69 6e65 2e20 2020 2020 2020 2028  d line.        (\n-00020350: 6c69 6e65 2020 3336 290a 2a20 6472 6177  line  36).* draw\n-00020360: 6162 6c65 3a20 2020 2020 2020 2020 2020  able:           \n+00020210: 2020 2020 4275 6773 2061 6e64 2061 6e6f      Bugs and ano\n+00020220: 6d61 6c69 6573 2e20 2028 6c69 6e65 2020  malies.  (line  \n+00020230: 2038 290a 2a20 6469 7265 6374 2074 7261   8).* direct tra\n+00020240: 6e73 666f 726d 3a20 2020 2020 2020 2020  nsform:         \n+00020250: 2020 2020 2020 2020 2020 2020 2054 7261               Tra\n+00020260: 6e73 666f 726d 206c 6974 6572 616c 732e  nsform literals.\n+00020270: 2020 286c 696e 6520 2034 3729 0a2a 2064    (line  47).* d\n+00020280: 6972 6563 7420 7472 616e 7366 6f72 6d20  irect transform \n+00020290: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n+000202a0: 2020 2020 2020 5472 616e 7366 6f72 6d20        Transform \n+000202b0: 6c69 7465 7261 6c73 2e20 2028 6c69 6e65  literals.  (line\n+000202c0: 2020 3533 290a 2a20 646f 6375 6d65 6e74    53).* document\n+000202d0: 2074 656d 706c 6174 653a 2020 2020 2020   template:      \n+000202e0: 2020 2020 2020 2020 2020 2020 2020 2048                 H\n+000202f0: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020  ello world.     \n+00020300: 2020 2020 286c 696e 6520 2033 3229 0a2a      (line  32).*\n+00020310: 2064 6f63 756d 656e 7420 7465 6d70 6c61   document templa\n+00020320: 7465 203c 313e 3a20 2020 2020 2020 2020  te <1>:         \n+00020330: 2020 2020 2020 2020 436f 6d6d 616e 6420          Command \n+00020340: 6c69 6e65 2e20 2020 2020 2020 2028 6c69  line.        (li\n+00020350: 6e65 2020 3336 290a 2a20 6472 6177 6162  ne  36).* drawab\n+00020360: 6c65 3a20 2020 2020 2020 2020 2020 2020  le:             \n 00020370: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020380: 2020 204f 626a 6563 7420 7472 616e 7366     Object transf\n-00020390: 6f72 6d73 2e20 2020 286c 696e 6520 2032  orms.   (line  2\n-000203a0: 3729 0a2a 2064 7261 7761 626c 6520 3c31  7).* drawable <1\n-000203b0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-000203c0: 2020 2020 2020 2020 2020 2020 4472 6177              Draw\n-000203d0: 6162 6c65 732e 2020 2020 2020 2020 2020  ables.          \n-000203e0: 2028 6c69 6e65 2020 2036 290a 2a20 6472   (line   6).* dr\n-000203f0: 6177 6162 6c65 2064 6566 696e 6974 696f  awable definitio\n-00020400: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n-00020410: 2020 2020 204f 626a 6563 7420 7472 616e       Object tran\n-00020420: 7366 6f72 6d73 2e20 2020 286c 696e 6520  sforms.   (line \n-00020430: 2032 3729 0a2a 2064 7261 7761 626c 6520   27).* drawable \n-00020440: 7265 6665 7265 6e63 653a 2020 2020 2020  reference:      \n-00020450: 2020 2020 2020 2020 2020 2020 2020 466f                Fo\n-00020460: 726d 7320 6f66 2072 6566 6572 656e 6365  rms of reference\n-00020470: 732e 2028 6c69 6e65 2020 3137 290a 2a20  s. (line  17).* \n-00020480: 656e 6420 706f 6c79 676f 6e3a 2020 2020  end polygon:    \n+00020380: 204f 626a 6563 7420 7472 616e 7366 6f72   Object transfor\n+00020390: 6d73 2e20 2020 286c 696e 6520 2032 3729  ms.   (line  27)\n+000203a0: 0a2a 2064 7261 7761 626c 6520 3c31 3e3a  .* drawable <1>:\n+000203b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000203c0: 2020 2020 2020 2020 2020 4472 6177 6162            Drawab\n+000203d0: 6c65 732e 2020 2020 2020 2020 2020 2028  les.           (\n+000203e0: 6c69 6e65 2020 2036 290a 2a20 6472 6177  line   6).* draw\n+000203f0: 6162 6c65 2064 6566 696e 6974 696f 6e3a  able definition:\n+00020400: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020410: 2020 204f 626a 6563 7420 7472 616e 7366     Object transf\n+00020420: 6f72 6d73 2e20 2020 286c 696e 6520 2032  orms.   (line  2\n+00020430: 3729 0a2a 2064 7261 7761 626c 6520 7265  7).* drawable re\n+00020440: 6665 7265 6e63 653a 2020 2020 2020 2020  ference:        \n+00020450: 2020 2020 2020 2020 2020 2020 466f 726d              Form\n+00020460: 7320 6f66 2072 6566 6572 656e 6365 732e  s of references.\n+00020470: 2028 6c69 6e65 2020 3137 290a 2a20 656e   (line  17).* en\n+00020480: 6420 706f 6c79 676f 6e3a 2020 2020 2020  d polygon:      \n 00020490: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000204a0: 2020 2020 2020 2053 7765 7074 206c 696e         Swept lin\n-000204b0: 6573 2e20 2020 2020 2020 2020 286c 696e  es.         (lin\n-000204c0: 6520 2033 3829 0a2a 2065 6e64 2070 6f6c  e  38).* end pol\n-000204d0: 7967 6f6e 203c 313e 3a20 2020 2020 2020  ygon <1>:       \n-000204e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000204f0: 5377 6570 7420 706f 6c79 676f 6e73 2e20  Swept polygons. \n-00020500: 2020 2020 2028 6c69 6e65 2020 3135 290a       (line  15).\n-00020510: 2a20 6661 6365 733a 2020 2020 2020 2020  * faces:        \n+000204a0: 2020 2020 2053 7765 7074 206c 696e 6573       Swept lines\n+000204b0: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n+000204c0: 2033 3829 0a2a 2065 6e64 2070 6f6c 7967   38).* end polyg\n+000204d0: 6f6e 203c 313e 3a20 2020 2020 2020 2020  on <1>:         \n+000204e0: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n+000204f0: 6570 7420 706f 6c79 676f 6e73 2e20 2020  ept polygons.   \n+00020500: 2020 2028 6c69 6e65 2020 3135 290a 2a20     (line  15).* \n+00020510: 6661 6365 733a 2020 2020 2020 2020 2020  faces:          \n 00020520: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020530: 2020 2020 2020 2020 2044 7261 7769 6e67           Drawing\n-00020540: 2061 2073 6f6c 6964 2e20 2020 2020 286c   a solid.     (l\n-00020550: 696e 6520 2020 3729 0a2a 2066 6163 6573  ine   7).* faces\n-00020560: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+00020530: 2020 2020 2020 2044 7261 7769 6e67 2061         Drawing a\n+00020540: 2073 6f6c 6964 2e20 2020 2020 286c 696e   solid.     (lin\n+00020550: 6520 2020 3729 0a2a 2066 6163 6573 203c  e   7).* faces <\n+00020560: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n 00020570: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020580: 2020 506f 6c79 6c69 6e65 2073 7765 6570    Polyline sweep\n-00020590: 732e 2020 2020 2028 6c69 6e65 2020 2036  s.     (line   6\n-000205a0: 290a 2a20 6669 6c65 2c20 696e 636c 7564  ).* file, includ\n-000205b0: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n-000205c0: 2020 2020 2020 2020 2020 204c 616e 6775             Langu\n-000205d0: 6167 6520 6261 7369 6373 2e20 2020 2020  age basics.     \n-000205e0: 286c 696e 6520 2031 3929 0a2a 2066 696c  (line  19).* fil\n-000205f0: 652c 2069 6e70 7574 3a20 2020 2020 2020  e, input:       \n+00020580: 506f 6c79 6c69 6e65 2073 7765 6570 732e  Polyline sweeps.\n+00020590: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n+000205a0: 2a20 6669 6c65 2c20 696e 636c 7564 653a  * file, include:\n+000205b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000205c0: 2020 2020 2020 2020 204c 616e 6775 6167           Languag\n+000205d0: 6520 6261 7369 6373 2e20 2020 2020 286c  e basics.     (l\n+000205e0: 696e 6520 2031 3929 0a2a 2066 696c 652c  ine  19).* file,\n+000205f0: 2069 6e70 7574 3a20 2020 2020 2020 2020   input:         \n 00020600: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020610: 2020 2020 4c61 6e67 7561 6765 2062 6173      Language bas\n-00020620: 6963 732e 2020 2020 2028 6c69 6e65 2020  ics.     (line  \n-00020630: 2036 290a 2a20 6672 616d 6520 626f 783a   6).* frame box:\n+00020610: 2020 4c61 6e67 7561 6765 2062 6173 6963    Language basic\n+00020620: 732e 2020 2020 2028 6c69 6e65 2020 2036  s.     (line   6\n+00020630: 290a 2a20 6672 616d 6520 626f 783a 2020  ).* frame box:  \n 00020640: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020650: 2020 2020 2020 2020 2020 2020 2046 7261               Fra\n-00020660: 6d65 2e20 2020 2020 2020 2020 2020 2020  me.             \n-00020670: 2020 286c 696e 6520 2020 3629 0a2a 2067    (line   6).* g\n-00020680: 6c6f 6261 6c20 6f70 7469 6f6e 733a 2020  lobal options:  \n+00020650: 2020 2020 2020 2020 2020 2046 7261 6d65             Frame\n+00020660: 2e20 2020 2020 2020 2020 2020 2020 2020  .               \n+00020670: 286c 696e 6520 2020 3629 0a2a 2067 6c6f  (line   6).* glo\n+00020680: 6261 6c20 6f70 7469 6f6e 733a 2020 2020  bal options:    \n 00020690: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000206a0: 2020 2020 2020 4472 6177 696e 6720 6f70        Drawing op\n-000206b0: 7469 6f6e 732e 2020 2020 2028 6c69 6e65  tions.     (line\n-000206c0: 2020 3138 290a 2a20 676c 6f62 616c 206f    18).* global o\n-000206d0: 7074 696f 6e73 203c 313e 3a20 2020 2020  ptions <1>:     \n-000206e0: 2020 2020 2020 2020 2020 2020 2020 2047                 G\n-000206f0: 6c6f 6261 6c20 6f70 7469 6f6e 732e 2020  lobal options.  \n-00020700: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-00020710: 2068 656c 6978 3a20 2020 2020 2020 2020   helix:         \n+000206a0: 2020 2020 4472 6177 696e 6720 6f70 7469      Drawing opti\n+000206b0: 6f6e 732e 2020 2020 2028 6c69 6e65 2020  ons.     (line  \n+000206c0: 3138 290a 2a20 676c 6f62 616c 206f 7074  18).* global opt\n+000206d0: 696f 6e73 203c 313e 3a20 2020 2020 2020  ions <1>:       \n+000206e0: 2020 2020 2020 2020 2020 2020 2047 6c6f               Glo\n+000206f0: 6261 6c20 6f70 7469 6f6e 732e 2020 2020  bal options.    \n+00020700: 2020 286c 696e 6520 2020 3629 0a2a 2068    (line   6).* h\n+00020710: 656c 6978 3a20 2020 2020 2020 2020 2020  elix:           \n 00020720: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020730: 2020 2020 2020 2020 4472 6177 696e 6720          Drawing \n-00020740: 6120 736f 6c69 642e 2020 2020 2028 6c69  a solid.     (li\n-00020750: 6e65 2020 3437 290a 2a20 6865 6c69 7820  ne  47).* helix \n-00020760: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n-00020770: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020780: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n-00020790: 2e20 2020 2020 286c 696e 6520 2031 3529  .     (line  15)\n-000207a0: 0a2a 2068 656c 6c6f 2077 6f72 6c64 3a20  .* hello world: \n+00020730: 2020 2020 2020 4472 6177 696e 6720 6120        Drawing a \n+00020740: 736f 6c69 642e 2020 2020 2028 6c69 6e65  solid.     (line\n+00020750: 2020 3437 290a 2a20 6865 6c69 7820 3c31    47).* helix <1\n+00020760: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+00020770: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n+00020780: 6f6c 796c 696e 6520 7377 6565 7073 2e20  olyline sweeps. \n+00020790: 2020 2020 286c 696e 6520 2031 3529 0a2a      (line  15).*\n+000207a0: 2068 656c 6c6f 2077 6f72 6c64 3a20 2020   hello world:   \n 000207b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000207c0: 2020 2020 2020 2020 2020 4865 6c6c 6f20            Hello \n-000207d0: 776f 726c 642e 2020 2020 2020 2020 2028  world.         (\n-000207e0: 6c69 6e65 2020 2037 290a 2a20 6869 6464  line   7).* hidd\n-000207f0: 656e 2073 7572 6661 6365 2061 6c67 6f72  en surface algor\n-00020800: 6974 686d 3a20 2020 2020 2020 2020 2020  ithm:           \n-00020810: 2020 2048 656c 6c6f 2077 6f72 6c64 2e20     Hello world. \n-00020820: 2020 2020 2020 2020 286c 696e 6520 2031          (line  1\n-00020830: 3929 0a2a 2068 6964 6465 6e20 7375 7266  9).* hidden surf\n-00020840: 6163 6520 616c 676f 7269 7468 6d20 3c31  ace algorithm <1\n-00020850: 3e3a 2020 2020 2020 2020 2020 5370 6563  >:          Spec\n-00020860: 6961 6c20 6f62 6a65 6374 732e 2020 2020  ial objects.    \n-00020870: 2028 6c69 6e65 2020 3438 290a 2a20 6869   (line  48).* hi\n-00020880: 6464 656e 2073 7572 6661 6365 2061 6c67  dden surface alg\n-00020890: 6f72 6974 686d 203c 323e 3a20 2020 2020  orithm <2>:     \n-000208a0: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n-000208b0: 6974 6572 616c 732e 2020 286c 696e 6520  iterals.  (line \n-000208c0: 2032 3429 0a2a 2068 6964 6465 6e20 7375   24).* hidden su\n-000208d0: 7266 6163 6520 616c 676f 7269 7468 6d20  rface algorithm \n-000208e0: 3c33 3e3a 2020 2020 2020 2020 2020 4120  <3>:          A \n-000208f0: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n-00020900: 672e 2028 6c69 6e65 2020 3235 290a 2a20  g. (line  25).* \n-00020910: 6869 6464 656e 2073 7572 6661 6365 2061  hidden surface a\n-00020920: 6c67 6f72 6974 686d 203c 343e 3a20 2020  lgorithm <4>:   \n-00020930: 2020 2020 2020 2048 6964 6465 6e20 7375         Hidden su\n-00020940: 7266 6163 6520 7265 6d6f 7661 6c2e 0a20  rface removal.. \n+000207c0: 2020 2020 2020 2020 4865 6c6c 6f20 776f          Hello wo\n+000207d0: 726c 642e 2020 2020 2020 2020 2028 6c69  rld.         (li\n+000207e0: 6e65 2020 2037 290a 2a20 6869 6464 656e  ne   7).* hidden\n+000207f0: 2073 7572 6661 6365 2061 6c67 6f72 6974   surface algorit\n+00020800: 686d 3a20 2020 2020 2020 2020 2020 2020  hm:             \n+00020810: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020   Hello world.   \n+00020820: 2020 2020 2020 286c 696e 6520 2031 3929        (line  19)\n+00020830: 0a2a 2068 6964 6465 6e20 7375 7266 6163  .* hidden surfac\n+00020840: 6520 616c 676f 7269 7468 6d20 3c31 3e3a  e algorithm <1>:\n+00020850: 2020 2020 2020 2020 2020 5370 6563 6961            Specia\n+00020860: 6c20 6f62 6a65 6374 732e 2020 2020 2028  l objects.     (\n+00020870: 6c69 6e65 2020 3438 290a 2a20 6869 6464  line  48).* hidd\n+00020880: 656e 2073 7572 6661 6365 2061 6c67 6f72  en surface algor\n+00020890: 6974 686d 203c 323e 3a20 2020 2020 2020  ithm <2>:       \n+000208a0: 2020 2054 7261 6e73 666f 726d 206c 6974     Transform lit\n+000208b0: 6572 616c 732e 2020 286c 696e 6520 2032  erals.  (line  2\n+000208c0: 3429 0a2a 2068 6964 6465 6e20 7375 7266  4).* hidden surf\n+000208d0: 6163 6520 616c 676f 7269 7468 6d20 3c33  ace algorithm <3\n+000208e0: 3e3a 2020 2020 2020 2020 2020 4120 7465  >:          A te\n+000208f0: 6368 6e69 6361 6c20 6472 6177 696e 672e  chnical drawing.\n+00020900: 2028 6c69 6e65 2020 3235 290a 2a20 6869   (line  25).* hi\n+00020910: 6464 656e 2073 7572 6661 6365 2061 6c67  dden surface alg\n+00020920: 6f72 6974 686d 203c 343e 3a20 2020 2020  orithm <4>:     \n+00020930: 2020 2020 2048 6964 6465 6e20 7375 7266       Hidden surf\n+00020940: 6163 6520 7265 6d6f 7661 6c2e 0a20 2020  ace removal..   \n 00020950: 2020 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 2020 2020 2028 6c69               (li\n-00020990: 6e65 2020 2036 290a 2a20 6869 6572 6172  ne   6).* hierar\n-000209a0: 6368 6963 616c 206d 6f64 656c 3a20 2020  chical model:   \n-000209b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000209c0: 2041 2068 6965 7261 7263 6869 6361 6c20   A hierarchical \n-000209d0: 6d6f 6465 6c2e 0a20 2020 2020 2020 2020  model..         \n+00020980: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+00020990: 2020 2036 290a 2a20 6869 6572 6172 6368     6).* hierarch\n+000209a0: 6963 616c 206d 6f64 656c 3a20 2020 2020  ical model:     \n+000209b0: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+000209c0: 2068 6965 7261 7263 6869 6361 6c20 6d6f   hierarchical mo\n+000209d0: 6465 6c2e 0a20 2020 2020 2020 2020 2020  del..           \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: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n-00020a20: 2a20 6964 656e 7469 6669 6572 733a 2020  * identifiers:  \n+00020a10: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n+00020a20: 6964 656e 7469 6669 6572 733a 2020 2020  identifiers:    \n 00020a30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020a40: 2020 2020 2020 2020 2049 6465 6e74 6966           Identif\n-00020a50: 6965 7273 2e20 2020 2020 2020 2020 286c  iers.         (l\n-00020a60: 696e 6520 2020 3729 0a2a 2069 6e63 6c75  ine   7).* inclu\n-00020a70: 6465 2066 696c 653a 2020 2020 2020 2020  de file:        \n+00020a40: 2020 2020 2020 2049 6465 6e74 6966 6965         Identifie\n+00020a50: 7273 2e20 2020 2020 2020 2020 286c 696e  rs.         (lin\n+00020a60: 6520 2020 3729 0a2a 2069 6e63 6c75 6465  e   7).* include\n+00020a70: 2066 696c 653a 2020 2020 2020 2020 2020   file:          \n 00020a80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020a90: 2020 4c61 6e67 7561 6765 2062 6173 6963    Language basic\n-00020aa0: 732e 2020 2020 2028 6c69 6e65 2020 3139  s.     (line  19\n-00020ab0: 290a 2a20 696e 7075 7420 6669 6c65 3a20  ).* input file: \n+00020a90: 4c61 6e67 7561 6765 2062 6173 6963 732e  Language basics.\n+00020aa0: 2020 2020 2028 6c69 6e65 2020 3139 290a       (line  19).\n+00020ab0: 2a20 696e 7075 7420 6669 6c65 3a20 2020  * input file:   \n 00020ac0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020ad0: 2020 2020 2020 2020 2020 204c 616e 6775             Langu\n-00020ae0: 6167 6520 6261 7369 6373 2e20 2020 2020  age basics.     \n-00020af0: 286c 696e 6520 2020 3629 0a2a 2069 6e74  (line   6).* int\n-00020b00: 6572 6e61 6c20 6f70 7469 6f6e 3a20 2020  ernal option:   \n+00020ad0: 2020 2020 2020 2020 204c 616e 6775 6167           Languag\n+00020ae0: 6520 6261 7369 6373 2e20 2020 2020 286c  e basics.     (l\n+00020af0: 696e 6520 2020 3629 0a2a 2069 6e74 6572  ine   6).* inter\n+00020b00: 6e61 6c20 6f70 7469 6f6e 3a20 2020 2020  nal option:     \n 00020b10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020b20: 2020 2020 5370 6563 6961 6c20 6f62 6a65      Special obje\n-00020b30: 6374 732e 2020 2020 2028 6c69 6e65 2020  cts.     (line  \n-00020b40: 3437 290a 2a20 696e 7465 726e 616c 206f  47).* internal o\n-00020b50: 7074 696f 6e73 3a20 2020 2020 2020 2020  ptions:         \n-00020b60: 2020 2020 2020 2020 2020 2020 2049 6e74               Int\n-00020b70: 6572 6e61 6c20 6f70 7469 6f6e 732e 2020  ernal options.  \n-00020b80: 2020 286c 696e 6520 2020 3629 0a2a 2069    (line   6).* i\n-00020b90: 6e74 6572 6e61 6c20 6f70 7469 6f6e 7320  nternal options \n-00020ba0: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n-00020bb0: 2020 2020 2020 476c 6f62 616c 206f 7074        Global opt\n-00020bc0: 696f 6e73 2e20 2020 2020 2028 6c69 6e65  ions.      (line\n-00020bd0: 2020 3132 290a 2a20 6b65 7977 6f72 6473    12).* keywords\n-00020be0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00020bf0: 2020 2020 2020 2020 2020 2020 2020 204b                 K\n-00020c00: 6579 2061 6e64 2072 6573 6572 7665 6420  ey and reserved \n-00020c10: 776f 7264 732e 0a20 2020 2020 2020 2020  words..         \n+00020b20: 2020 5370 6563 6961 6c20 6f62 6a65 6374    Special object\n+00020b30: 732e 2020 2020 2028 6c69 6e65 2020 3437  s.     (line  47\n+00020b40: 290a 2a20 696e 7465 726e 616c 206f 7074  ).* internal opt\n+00020b50: 696f 6e73 3a20 2020 2020 2020 2020 2020  ions:           \n+00020b60: 2020 2020 2020 2020 2020 2049 6e74 6572             Inter\n+00020b70: 6e61 6c20 6f70 7469 6f6e 732e 2020 2020  nal options.    \n+00020b80: 286c 696e 6520 2020 3629 0a2a 2069 6e74  (line   6).* int\n+00020b90: 6572 6e61 6c20 6f70 7469 6f6e 7320 3c31  ernal options <1\n+00020ba0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+00020bb0: 2020 2020 476c 6f62 616c 206f 7074 696f      Global optio\n+00020bc0: 6e73 2e20 2020 2020 2028 6c69 6e65 2020  ns.      (line  \n+00020bd0: 3132 290a 2a20 6b65 7977 6f72 6473 3a20  12).* keywords: \n+00020be0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020bf0: 2020 2020 2020 2020 2020 2020 204b 6579               Key\n+00020c00: 2061 6e64 2072 6573 6572 7665 6420 776f   and reserved wo\n+00020c10: 7264 732e 0a20 2020 2020 2020 2020 2020  rds..           \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: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n-00020c60: 2a20 6c61 6265 6c73 3a20 2020 2020 2020  * labels:       \n+00020c50: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n+00020c60: 6c61 6265 6c73 3a20 2020 2020 2020 2020  labels:         \n 00020c70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020c80: 2020 2020 2020 2020 2053 7065 6369 616c           Special\n-00020c90: 206f 626a 6563 7473 2e20 2020 2020 286c   objects.     (l\n-00020ca0: 696e 6520 2020 3629 0a2a 206c 616e 6775  ine   6).* langu\n-00020cb0: 6167 652c 2064 6563 6c61 7261 7469 7665  age, declarative\n-00020cc0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00020cd0: 2020 4c61 6e67 7561 6765 2062 6173 6963    Language basic\n-00020ce0: 732e 2020 2020 2028 6c69 6e65 2020 2038  s.     (line   8\n-00020cf0: 290a 2a20 6c61 6e67 7561 6765 2c20 6f75  ).* language, ou\n-00020d00: 7470 7574 3a20 2020 2020 2020 2020 2020  tput:           \n-00020d10: 2020 2020 2020 2020 2020 204c 616e 6775             Langu\n-00020d20: 6167 652e 2020 2020 2020 2020 2020 2020  age.            \n-00020d30: 286c 696e 6520 2020 3629 0a2a 206c 616e  (line   6).* lan\n-00020d40: 6775 6167 652c 2073 6365 6e65 2064 6573  guage, scene des\n-00020d50: 6372 6970 7469 6f6e 3a20 2020 2020 2020  cription:       \n-00020d60: 2020 2020 4c61 6e67 7561 6765 2062 6173      Language bas\n-00020d70: 6963 732e 2020 2020 2028 6c69 6e65 2020  ics.     (line  \n-00020d80: 2038 290a 2a20 6c65 7869 6361 6c20 7363   8).* lexical sc\n-00020d90: 6f70 653a 2020 2020 2020 2020 2020 2020  ope:            \n-00020da0: 2020 2020 2020 2020 2020 2020 204f 626a               Obj\n-00020db0: 6563 7420 7472 616e 7366 6f72 6d73 2e20  ect transforms. \n-00020dc0: 2020 286c 696e 6520 2032 3629 0a2a 206c    (line  26).* l\n-00020dd0: 6578 6963 616c 2073 636f 7065 203c 313e  exical scope <1>\n-00020de0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00020df0: 2020 2020 2020 426c 6f63 6b73 2e20 2020        Blocks.   \n-00020e00: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-00020e10: 2020 3133 290a 2a20 6c69 6e65 2073 7765    13).* line swe\n-00020e20: 6570 3a20 2020 2020 2020 2020 2020 2020  ep:             \n-00020e30: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n-00020e40: 6f6c 796c 696e 6520 7377 6565 7073 2e20  olyline sweeps. \n-00020e50: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-00020e60: 206c 696e 6520 7377 6565 7020 3c31 3e3a   line sweep <1>:\n+00020c80: 2020 2020 2020 2053 7065 6369 616c 206f         Special o\n+00020c90: 626a 6563 7473 2e20 2020 2020 286c 696e  bjects.     (lin\n+00020ca0: 6520 2020 3629 0a2a 206c 616e 6775 6167  e   6).* languag\n+00020cb0: 652c 2064 6563 6c61 7261 7469 7665 3a20  e, declarative: \n+00020cc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020cd0: 4c61 6e67 7561 6765 2062 6173 6963 732e  Language basics.\n+00020ce0: 2020 2020 2028 6c69 6e65 2020 2038 290a       (line   8).\n+00020cf0: 2a20 6c61 6e67 7561 6765 2c20 6f75 7470  * language, outp\n+00020d00: 7574 3a20 2020 2020 2020 2020 2020 2020  ut:             \n+00020d10: 2020 2020 2020 2020 204c 616e 6775 6167           Languag\n+00020d20: 652e 2020 2020 2020 2020 2020 2020 286c  e.            (l\n+00020d30: 696e 6520 2020 3629 0a2a 206c 616e 6775  ine   6).* langu\n+00020d40: 6167 652c 2073 6365 6e65 2064 6573 6372  age, scene descr\n+00020d50: 6970 7469 6f6e 3a20 2020 2020 2020 2020  iption:         \n+00020d60: 2020 4c61 6e67 7561 6765 2062 6173 6963    Language basic\n+00020d70: 732e 2020 2020 2028 6c69 6e65 2020 2038  s.     (line   8\n+00020d80: 290a 2a20 6c65 7869 6361 6c20 7363 6f70  ).* lexical scop\n+00020d90: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n+00020da0: 2020 2020 2020 2020 2020 204f 626a 6563             Objec\n+00020db0: 7420 7472 616e 7366 6f72 6d73 2e20 2020  t transforms.   \n+00020dc0: 286c 696e 6520 2032 3629 0a2a 206c 6578  (line  26).* lex\n+00020dd0: 6963 616c 2073 636f 7065 203c 313e 3a20  ical scope <1>: \n+00020de0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020df0: 2020 2020 426c 6f63 6b73 2e20 2020 2020      Blocks.     \n+00020e00: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+00020e10: 3133 290a 2a20 6c69 6e65 2073 7765 6570  13).* line sweep\n+00020e20: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00020e30: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n+00020e40: 796c 696e 6520 7377 6565 7073 2e20 2020  yline sweeps.   \n+00020e50: 2020 286c 696e 6520 2020 3629 0a2a 206c    (line   6).* l\n+00020e60: 696e 6520 7377 6565 7020 3c31 3e3a 2020  ine sweep <1>:  \n 00020e70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020e80: 2020 2020 2020 2020 5377 6570 7420 6c69          Swept li\n-00020e90: 6e65 732e 2020 2020 2020 2020 2028 6c69  nes.         (li\n-00020ea0: 6e65 2020 2036 290a 2a20 6c69 6e65 2073  ne   6).* line s\n-00020eb0: 7765 6570 203c 323e 3a20 2020 2020 2020  weep <2>:       \n-00020ec0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020ed0: 2041 2074 6563 686e 6963 616c 2064 7261   A technical dra\n-00020ee0: 7769 6e67 2e20 286c 696e 6520 2032 3029  wing. (line  20)\n-00020ef0: 0a2a 206c 6974 6572 616c 2c20 706f 696e  .* literal, poin\n-00020f00: 743a 2020 2020 2020 2020 2020 2020 2020  t:              \n-00020f10: 2020 2020 2020 2020 2020 506f 696e 7420            Point \n-00020f20: 616e 6420 7665 6374 6f72 206c 6974 6572  and vector liter\n-00020f30: 616c 732e 0a20 2020 2020 2020 2020 2020  als..           \n+00020e80: 2020 2020 2020 5377 6570 7420 6c69 6e65        Swept line\n+00020e90: 732e 2020 2020 2020 2020 2028 6c69 6e65  s.         (line\n+00020ea0: 2020 2036 290a 2a20 6c69 6e65 2073 7765     6).* line swe\n+00020eb0: 6570 203c 323e 3a20 2020 2020 2020 2020  ep <2>:         \n+00020ec0: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+00020ed0: 2074 6563 686e 6963 616c 2064 7261 7769   technical drawi\n+00020ee0: 6e67 2e20 286c 696e 6520 2032 3029 0a2a  ng. (line  20).*\n+00020ef0: 206c 6974 6572 616c 2c20 706f 696e 743a   literal, point:\n+00020f00: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00020f10: 2020 2020 2020 2020 506f 696e 7420 616e          Point an\n+00020f20: 6420 7665 6374 6f72 206c 6974 6572 616c  d vector literal\n+00020f30: 732e 0a20 2020 2020 2020 2020 2020 2020  s..             \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 2020                  \n-00020f70: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n-00020f80: 6c69 7465 7261 6c2c 2073 6361 6c61 723a  literal, scalar:\n+00020f70: 2028 6c69 6e65 2020 2036 290a 2a20 6c69   (line   6).* li\n+00020f80: 7465 7261 6c2c 2073 6361 6c61 723a 2020  teral, scalar:  \n 00020f90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020fa0: 2020 2020 2020 2053 6361 6c61 7220 6c69         Scalar li\n-00020fb0: 7465 7261 6c73 2e20 2020 2020 286c 696e  terals.     (lin\n-00020fc0: 6520 2020 3629 0a2a 206c 6974 6572 616c  e   6).* literal\n-00020fd0: 2c20 7472 616e 7366 6f72 6d3a 2020 2020  , transform:    \n-00020fe0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00020ff0: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n-00021000: 6c73 2e20 2028 6c69 6e65 2020 2036 290a  ls.  (line   6).\n-00021010: 2a20 6c69 7465 7261 6c2c 2076 6563 746f  * literal, vecto\n-00021020: 723a 2020 2020 2020 2020 2020 2020 2020  r:              \n-00021030: 2020 2020 2020 2020 2050 6f69 6e74 2061           Point a\n-00021040: 6e64 2076 6563 746f 7220 6c69 7465 7261  nd vector litera\n-00021050: 6c73 2e0a 2020 2020 2020 2020 2020 2020  ls..            \n+00020fa0: 2020 2020 2053 6361 6c61 7220 6c69 7465       Scalar lite\n+00020fb0: 7261 6c73 2e20 2020 2020 286c 696e 6520  rals.     (line \n+00020fc0: 2020 3629 0a2a 206c 6974 6572 616c 2c20    6).* literal, \n+00020fd0: 7472 616e 7366 6f72 6d3a 2020 2020 2020  transform:      \n+00020fe0: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n+00020ff0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n+00021000: 2e20 2028 6c69 6e65 2020 2036 290a 2a20  .  (line   6).* \n+00021010: 6c69 7465 7261 6c2c 2076 6563 746f 723a  literal, vector:\n+00021020: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021030: 2020 2020 2020 2050 6f69 6e74 2061 6e64         Point and\n+00021040: 2076 6563 746f 7220 6c69 7465 7261 6c73   vector literals\n+00021050: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020                  \n-00021090: 2020 286c 696e 6520 2020 3629 0a2a 206e    (line   6).* n\n-000210a0: 6573 7469 6e67 2c20 7377 6570 7420 6f62  esting, swept ob\n-000210b0: 6a65 6374 3a20 2020 2020 2020 2020 2020  ject:           \n-000210c0: 2020 2020 2020 4e65 7374 6564 2073 7765        Nested swe\n-000210d0: 6570 732e 2020 2020 2020 2028 6c69 6e65  eps.       (line\n-000210e0: 2020 3232 290a 2a20 6f6e 652d 6f70 6572    22).* one-oper\n-000210f0: 616e 6420 666f 726d 3a20 2020 2020 2020  and form:       \n-00021100: 2020 2020 2020 2020 2020 2020 2020 2055                 U\n-00021110: 6e61 7279 2066 6f72 6d73 2e20 2020 2020  nary forms.     \n-00021120: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-00021130: 206f 7065 7261 746f 7220 6173 736f 6369   operator associ\n-00021140: 6174 6976 6974 793a 2020 2020 2020 2020  ativity:        \n-00021150: 2020 2020 2020 2020 5477 6f2d 6f70 6572          Two-oper\n-00021160: 616e 6420 2862 696e 6172 7929 2066 6f72  and (binary) for\n-00021170: 6d73 2e0a 2020 2020 2020 2020 2020 2020  ms..            \n+00021090: 286c 696e 6520 2020 3629 0a2a 206e 6573  (line   6).* nes\n+000210a0: 7469 6e67 2c20 7377 6570 7420 6f62 6a65  ting, swept obje\n+000210b0: 6374 3a20 2020 2020 2020 2020 2020 2020  ct:             \n+000210c0: 2020 2020 4e65 7374 6564 2073 7765 6570      Nested sweep\n+000210d0: 732e 2020 2020 2020 2028 6c69 6e65 2020  s.       (line  \n+000210e0: 3232 290a 2a20 6f6e 652d 6f70 6572 616e  22).* one-operan\n+000210f0: 6420 666f 726d 3a20 2020 2020 2020 2020  d form:         \n+00021100: 2020 2020 2020 2020 2020 2020 2055 6e61               Una\n+00021110: 7279 2066 6f72 6d73 2e20 2020 2020 2020  ry forms.       \n+00021120: 2020 286c 696e 6520 2020 3629 0a2a 206f    (line   6).* o\n+00021130: 7065 7261 746f 7220 6173 736f 6369 6174  perator associat\n+00021140: 6976 6974 793a 2020 2020 2020 2020 2020  ivity:          \n+00021150: 2020 2020 2020 5477 6f2d 6f70 6572 616e        Two-operan\n+00021160: 6420 2862 696e 6172 7929 2066 6f72 6d73  d (binary) forms\n+00021170: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020                  \n-000211b0: 2020 286c 696e 6520 2035 3829 0a2a 206f    (line  58).* o\n-000211c0: 7065 7261 746f 7220 7072 6563 6564 656e  perator preceden\n-000211d0: 6365 3a20 2020 2020 2020 2020 2020 2020  ce:             \n-000211e0: 2020 2020 2020 5477 6f2d 6f70 6572 616e        Two-operan\n-000211f0: 6420 2862 696e 6172 7929 2066 6f72 6d73  d (binary) forms\n-00021200: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+000211b0: 286c 696e 6520 2035 3829 0a2a 206f 7065  (line  58).* ope\n+000211c0: 7261 746f 7220 7072 6563 6564 656e 6365  rator precedence\n+000211d0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000211e0: 2020 2020 5477 6f2d 6f70 6572 616e 6420      Two-operand \n+000211f0: 2862 696e 6172 7929 2066 6f72 6d73 2e0a  (binary) forms..\n+00021200: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020                  \n-00021240: 286c 696e 6520 2034 3529 0a2a 206f 7074  (line  45).* opt\n-00021250: 696f 6e3a 2020 2020 2020 2020 2020 2020  ion:            \n+00021230: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+00021240: 696e 6520 2034 3529 0a2a 206f 7074 696f  ine  45).* optio\n+00021250: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n 00021260: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021270: 2020 2020 4472 6177 696e 6720 6f70 7469      Drawing opti\n-00021280: 6f6e 732e 2020 2020 2028 6c69 6e65 2020  ons.     (line  \n-00021290: 2036 290a 2a20 6f70 7469 6f6e 2c20 636f   6).* option, co\n-000212a0: 6d6d 616e 6420 6c69 6e65 3a20 2020 2020  mmand line:     \n-000212b0: 2020 2020 2020 2020 2020 2020 2048 656c               Hel\n-000212c0: 6c6f 2077 6f72 6c64 2e20 2020 2020 2020  lo world.       \n-000212d0: 2020 286c 696e 6520 2033 3029 0a2a 206f    (line  30).* o\n-000212e0: 7074 696f 6e2c 2069 6e74 6572 6e61 6c3a  ption, internal:\n+00021270: 2020 4472 6177 696e 6720 6f70 7469 6f6e    Drawing option\n+00021280: 732e 2020 2020 2028 6c69 6e65 2020 2036  s.     (line   6\n+00021290: 290a 2a20 6f70 7469 6f6e 2c20 636f 6d6d  ).* option, comm\n+000212a0: 616e 6420 6c69 6e65 3a20 2020 2020 2020  and line:       \n+000212b0: 2020 2020 2020 2020 2020 2048 656c 6c6f             Hello\n+000212c0: 2077 6f72 6c64 2e20 2020 2020 2020 2020   world.         \n+000212d0: 286c 696e 6520 2033 3029 0a2a 206f 7074  (line  30).* opt\n+000212e0: 696f 6e2c 2069 6e74 6572 6e61 6c3a 2020  ion, internal:  \n 000212f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021300: 2020 2020 2020 5370 6563 6961 6c20 6f62        Special ob\n-00021310: 6a65 6374 732e 2020 2020 2028 6c69 6e65  jects.     (line\n-00021320: 2020 3437 290a 2a20 6f70 7469 6f6e 733a    47).* options:\n+00021300: 2020 2020 5370 6563 6961 6c20 6f62 6a65      Special obje\n+00021310: 6374 732e 2020 2020 2028 6c69 6e65 2020  cts.     (line  \n+00021320: 3437 290a 2a20 6f70 7469 6f6e 733a 2020  47).* options:  \n 00021330: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021340: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n-00021350: 7074 696f 6e73 2e20 2020 2020 2020 2020  ptions.         \n-00021360: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-00021370: 206f 7074 696f 6e73 2064 6566 696e 6974   options definit\n-00021380: 696f 6e3a 2020 2020 2020 2020 2020 2020  ion:            \n-00021390: 2020 2020 2020 2020 506f 6c79 6c69 6e65          Polyline\n-000213a0: 2073 7765 6570 7320 7769 7468 2063 6c6f   sweeps with clo\n-000213b0: 7375 7265 2e0a 2020 2020 2020 2020 2020  sure..          \n+00021340: 2020 2020 2020 2020 2020 2020 204f 7074               Opt\n+00021350: 696f 6e73 2e20 2020 2020 2020 2020 2020  ions.           \n+00021360: 2020 286c 696e 6520 2020 3629 0a2a 206f    (line   6).* o\n+00021370: 7074 696f 6e73 2064 6566 696e 6974 696f  ptions definitio\n+00021380: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n+00021390: 2020 2020 2020 506f 6c79 6c69 6e65 2073        Polyline s\n+000213a0: 7765 6570 7320 7769 7468 2063 6c6f 7375  weeps with closu\n+000213b0: 7265 2e0a 2020 2020 2020 2020 2020 2020  re..            \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: 2020 2020 286c 696e 6520 2032 3329 0a2a      (line  23).*\n-00021400: 206f 7074 696f 6e73 206d 756c 7469 706c   options multipl\n-00021410: 6520 7265 6665 7265 6e63 653a 2020 2020  e reference:    \n-00021420: 2020 2020 2020 2020 466f 726d 7320 6f66          Forms of\n-00021430: 2072 6566 6572 656e 6365 732e 2028 6c69   references. (li\n-00021440: 6e65 2020 3138 290a 2a20 6f70 7469 6f6e  ne  18).* option\n-00021450: 7320 7265 6665 7265 6e63 653a 2020 2020  s reference:    \n-00021460: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021470: 2046 6f72 6d73 206f 6620 7265 6665 7265   Forms of refere\n-00021480: 6e63 6573 2e20 286c 696e 6520 2031 3829  nces. (line  18)\n-00021490: 0a2a 206f 7074 696f 6e73 2c20 636f 6d6d  .* options, comm\n-000214a0: 616e 6420 6c69 6e65 3a20 2020 2020 2020  and line:       \n-000214b0: 2020 2020 2020 2020 2020 436f 6d6d 616e            Comman\n-000214c0: 6420 6c69 6e65 2e20 2020 2020 2020 2028  d line.        (\n-000214d0: 6c69 6e65 2020 3134 290a 2a20 6f70 7469  line  14).* opti\n-000214e0: 6f6e 732c 2067 6c6f 6261 6c3a 2020 2020  ons, global:    \n+000213f0: 2020 286c 696e 6520 2032 3329 0a2a 206f    (line  23).* o\n+00021400: 7074 696f 6e73 206d 756c 7469 706c 6520  ptions multiple \n+00021410: 7265 6665 7265 6e63 653a 2020 2020 2020  reference:      \n+00021420: 2020 2020 2020 466f 726d 7320 6f66 2072        Forms of r\n+00021430: 6566 6572 656e 6365 732e 2028 6c69 6e65  eferences. (line\n+00021440: 2020 3138 290a 2a20 6f70 7469 6f6e 7320    18).* options \n+00021450: 7265 6665 7265 6e63 653a 2020 2020 2020  reference:      \n+00021460: 2020 2020 2020 2020 2020 2020 2020 2046                 F\n+00021470: 6f72 6d73 206f 6620 7265 6665 7265 6e63  orms of referenc\n+00021480: 6573 2e20 286c 696e 6520 2031 3829 0a2a  es. (line  18).*\n+00021490: 206f 7074 696f 6e73 2c20 636f 6d6d 616e   options, comman\n+000214a0: 6420 6c69 6e65 3a20 2020 2020 2020 2020  d line:         \n+000214b0: 2020 2020 2020 2020 436f 6d6d 616e 6420          Command \n+000214c0: 6c69 6e65 2e20 2020 2020 2020 2028 6c69  line.        (li\n+000214d0: 6e65 2020 3134 290a 2a20 6f70 7469 6f6e  ne  14).* option\n+000214e0: 732c 2067 6c6f 6261 6c3a 2020 2020 2020  s, global:      \n 000214f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021500: 2020 2044 7261 7769 6e67 206f 7074 696f     Drawing optio\n-00021510: 6e73 2e20 2020 2020 286c 696e 6520 2031  ns.     (line  1\n-00021520: 3829 0a2a 206f 7074 696f 6e73 2c20 676c  8).* options, gl\n-00021530: 6f62 616c 203c 313e 3a20 2020 2020 2020  obal <1>:       \n-00021540: 2020 2020 2020 2020 2020 2020 476c 6f62              Glob\n-00021550: 616c 206f 7074 696f 6e73 2e20 2020 2020  al options.     \n-00021560: 2028 6c69 6e65 2020 2036 290a 2a20 6f70   (line   6).* op\n-00021570: 7469 6f6e 732c 2069 6e74 6572 6e61 6c3a  tions, internal:\n+00021500: 2044 7261 7769 6e67 206f 7074 696f 6e73   Drawing options\n+00021510: 2e20 2020 2020 286c 696e 6520 2031 3829  .     (line  18)\n+00021520: 0a2a 206f 7074 696f 6e73 2c20 676c 6f62  .* options, glob\n+00021530: 616c 203c 313e 3a20 2020 2020 2020 2020  al <1>:         \n+00021540: 2020 2020 2020 2020 2020 476c 6f62 616c            Global\n+00021550: 206f 7074 696f 6e73 2e20 2020 2020 2028   options.      (\n+00021560: 6c69 6e65 2020 2036 290a 2a20 6f70 7469  line   6).* opti\n+00021570: 6f6e 732c 2069 6e74 6572 6e61 6c3a 2020  ons, internal:  \n 00021580: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021590: 2020 2020 2049 6e74 6572 6e61 6c20 6f70       Internal op\n-000215a0: 7469 6f6e 732e 2020 2020 286c 696e 6520  tions.    (line \n-000215b0: 2020 3629 0a2a 206f 7074 696f 6e73 2c20    6).* options, \n-000215c0: 696e 7465 726e 616c 203c 313e 3a20 2020  internal <1>:   \n-000215d0: 2020 2020 2020 2020 2020 2020 2020 476c                Gl\n-000215e0: 6f62 616c 206f 7074 696f 6e73 2e20 2020  obal options.   \n-000215f0: 2020 2028 6c69 6e65 2020 3132 290a 2a20     (line  12).* \n-00021600: 6f70 7469 6f6e 732c 2073 7765 6570 3a20  options, sweep: \n+00021590: 2020 2049 6e74 6572 6e61 6c20 6f70 7469     Internal opti\n+000215a0: 6f6e 732e 2020 2020 286c 696e 6520 2020  ons.    (line   \n+000215b0: 3629 0a2a 206f 7074 696f 6e73 2c20 696e  6).* options, in\n+000215c0: 7465 726e 616c 203c 313e 3a20 2020 2020  ternal <1>:     \n+000215d0: 2020 2020 2020 2020 2020 2020 476c 6f62              Glob\n+000215e0: 616c 206f 7074 696f 6e73 2e20 2020 2020  al options.     \n+000215f0: 2028 6c69 6e65 2020 3132 290a 2a20 6f70   (line  12).* op\n+00021600: 7469 6f6e 732c 2073 7765 6570 3a20 2020  tions, sweep:   \n 00021610: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021620: 2020 2020 2020 2050 6f6c 796c 696e 6520         Polyline \n-00021630: 7377 6565 7073 2e20 2020 2020 286c 696e  sweeps.     (lin\n-00021640: 6520 2031 3629 0a2a 206f 7074 696f 6e73  e  16).* options\n-00021650: 2c20 7377 6565 7020 3c31 3e3a 2020 2020  , sweep <1>:    \n-00021660: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021670: 506f 6c79 676f 6e20 7377 6565 7073 2e20  Polygon sweeps. \n-00021680: 2020 2020 2028 6c69 6e65 2020 2039 290a       (line   9).\n-00021690: 2a20 6f70 7469 6f6e 732c 2073 7765 6570  * options, sweep\n-000216a0: 203c 323e 3a20 2020 2020 2020 2020 2020   <2>:           \n-000216b0: 2020 2020 2020 2020 2053 7765 7074 2070           Swept p\n-000216c0: 6f69 6e74 732e 2020 2020 2020 2020 286c  oints.        (l\n-000216d0: 696e 6520 2032 3129 0a2a 206f 7074 696f  ine  21).* optio\n-000216e0: 6e73 2c20 7377 6565 7020 3c33 3e3a 2020  ns, sweep <3>:  \n+00021620: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n+00021630: 6565 7073 2e20 2020 2020 286c 696e 6520  eeps.     (line \n+00021640: 2031 3629 0a2a 206f 7074 696f 6e73 2c20   16).* options, \n+00021650: 7377 6565 7020 3c31 3e3a 2020 2020 2020  sweep <1>:      \n+00021660: 2020 2020 2020 2020 2020 2020 2020 506f                Po\n+00021670: 6c79 676f 6e20 7377 6565 7073 2e20 2020  lygon sweeps.   \n+00021680: 2020 2028 6c69 6e65 2020 2039 290a 2a20     (line   9).* \n+00021690: 6f70 7469 6f6e 732c 2073 7765 6570 203c  options, sweep <\n+000216a0: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n+000216b0: 2020 2020 2020 2053 7765 7074 2070 6f69         Swept poi\n+000216c0: 6e74 732e 2020 2020 2020 2020 286c 696e  nts.        (lin\n+000216d0: 6520 2032 3129 0a2a 206f 7074 696f 6e73  e  21).* options\n+000216e0: 2c20 7377 6565 7020 3c33 3e3a 2020 2020  , sweep <3>:    \n 000216f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021700: 2020 5377 6570 7420 6c69 6e65 732e 2020    Swept lines.  \n-00021710: 2020 2020 2020 2028 6c69 6e65 2020 3235         (line  25\n-00021720: 290a 2a20 6f70 7469 6f6e 732c 2073 7765  ).* options, swe\n-00021730: 6570 203c 343e 3a20 2020 2020 2020 2020  ep <4>:         \n-00021740: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-00021750: 206c 696e 6573 2e20 2020 2020 2020 2020   lines.         \n-00021760: 286c 696e 6520 2034 3829 0a2a 206f 7074  (line  48).* opt\n-00021770: 696f 6e73 2c20 7377 6570 7420 6f62 6a65  ions, swept obje\n-00021780: 6374 3a20 2020 2020 2020 2020 2020 2020  ct:             \n-00021790: 2020 2020 506f 6c79 676f 6e20 7377 6565      Polygon swee\n-000217a0: 7073 2e20 2020 2020 2028 6c69 6e65 2020  ps.      (line  \n-000217b0: 2038 290a 2a20 6f70 7469 6f6e 732c 2073   8).* options, s\n-000217c0: 7765 7074 206f 626a 6563 7420 3c31 3e3a  wept object <1>:\n-000217d0: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n-000217e0: 796c 696e 6520 7377 6565 7073 2077 6974  yline sweeps wit\n-000217f0: 6820 636c 6f73 7572 652e 0a20 2020 2020  h closure..     \n+00021700: 5377 6570 7420 6c69 6e65 732e 2020 2020  Swept lines.    \n+00021710: 2020 2020 2028 6c69 6e65 2020 3235 290a       (line  25).\n+00021720: 2a20 6f70 7469 6f6e 732c 2073 7765 6570  * options, sweep\n+00021730: 203c 343e 3a20 2020 2020 2020 2020 2020   <4>:           \n+00021740: 2020 2020 2020 2020 2053 7765 7074 206c           Swept l\n+00021750: 696e 6573 2e20 2020 2020 2020 2020 286c  ines.         (l\n+00021760: 696e 6520 2034 3829 0a2a 206f 7074 696f  ine  48).* optio\n+00021770: 6e73 2c20 7377 6570 7420 6f62 6a65 6374  ns, swept object\n+00021780: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00021790: 2020 506f 6c79 676f 6e20 7377 6565 7073    Polygon sweeps\n+000217a0: 2e20 2020 2020 2028 6c69 6e65 2020 2038  .      (line   8\n+000217b0: 290a 2a20 6f70 7469 6f6e 732c 2073 7765  ).* options, swe\n+000217c0: 7074 206f 626a 6563 7420 3c31 3e3a 2020  pt object <1>:  \n+000217d0: 2020 2020 2020 2020 2020 2050 6f6c 796c             Polyl\n+000217e0: 696e 6520 7377 6565 7073 2077 6974 6820  ine sweeps with \n+000217f0: 636c 6f73 7572 652e 0a20 2020 2020 2020  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 2020 2020 2028 6c69 6e65 2020           (line  \n-00021840: 3232 290a 2a20 6f70 7469 6f6e 732c 2073  22).* options, s\n-00021850: 7765 7074 206f 626a 6563 7420 3c32 3e3a  wept object <2>:\n-00021860: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n-00021870: 7074 206c 696e 6573 2e20 2020 2020 2020  pt lines.       \n-00021880: 2020 286c 696e 6520 2032 3629 0a2a 206f    (line  26).* o\n-00021890: 7074 696f 6e73 2c20 7377 6570 7420 6f62  ptions, swept ob\n-000218a0: 6a65 6374 203c 333e 3a20 2020 2020 2020  ject <3>:       \n-000218b0: 2020 2020 2020 5377 6570 7420 6c69 6e65        Swept line\n-000218c0: 732e 2020 2020 2020 2020 2028 6c69 6e65  s.         (line\n-000218d0: 2020 3438 290a 2a20 6f72 6465 722c 2070    48).* order, p\n-000218e0: 6f6c 7967 6f6e 2076 6572 7465 783a 2020  olygon vertex:  \n-000218f0: 2020 2020 2020 2020 2020 2020 2020 2048                 H\n-00021900: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020  ello world.     \n-00021910: 2020 2020 286c 696e 6520 2033 3929 0a2a      (line  39).*\n-00021920: 206f 7264 6572 2c20 706f 6c79 676f 6e20   order, polygon \n-00021930: 7665 7274 6578 203c 313e 3a20 2020 2020  vertex <1>:     \n-00021940: 2020 2020 2020 2020 5377 6570 7420 6c69          Swept li\n-00021950: 6e65 732e 2020 2020 2020 2020 2028 6c69  nes.         (li\n-00021960: 6e65 2020 3134 290a 2a20 6f72 6465 722c  ne  14).* order,\n-00021970: 2070 6f6c 7967 6f6e 2076 6572 7465 7820   polygon vertex \n-00021980: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n-00021990: 2053 7765 7074 206c 696e 6573 2e20 2020   Swept lines.   \n-000219a0: 2020 2020 2020 286c 696e 6520 2034 3029        (line  40)\n-000219b0: 0a2a 206f 7264 6572 2c20 706f 6c79 676f  .* order, polygo\n-000219c0: 6e20 7665 7274 6578 203c 333e 3a20 2020  n vertex <3>:   \n-000219d0: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n-000219e0: 706f 6c79 676f 6e73 2e20 2020 2020 2028  polygons.      (\n-000219f0: 6c69 6e65 2020 3139 290a 2a20 6f72 6465  line  19).* orde\n-00021a00: 722c 2070 6f6c 7967 6f6e 2076 6572 7465  r, polygon verte\n-00021a10: 7820 3c34 3e3a 2020 2020 2020 2020 2020  x <4>:          \n-00021a20: 2020 204f 7665 7276 6965 772e 2020 2020     Overview.    \n-00021a30: 2020 2020 2020 2020 286c 696e 6520 2033          (line  3\n-00021a40: 3729 0a2a 206f 7264 6572 2c20 706f 6c79  7).* order, poly\n-00021a50: 676f 6e20 7665 7274 6578 203c 353e 3a20  gon vertex <5>: \n-00021a60: 2020 2020 2020 2020 2020 2020 4f76 6572              Over\n-00021a70: 7669 6577 2e20 2020 2020 2020 2020 2020  view.           \n-00021a80: 2028 6c69 6e65 2020 3535 290a 2a20 6f75   (line  55).* ou\n-00021a90: 7470 7574 206c 616e 6775 6167 653a 2020  tput language:  \n+00021830: 2020 2020 2020 2028 6c69 6e65 2020 3232         (line  22\n+00021840: 290a 2a20 6f70 7469 6f6e 732c 2073 7765  ).* options, swe\n+00021850: 7074 206f 626a 6563 7420 3c32 3e3a 2020  pt object <2>:  \n+00021860: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n+00021870: 206c 696e 6573 2e20 2020 2020 2020 2020   lines.         \n+00021880: 286c 696e 6520 2032 3629 0a2a 206f 7074  (line  26).* opt\n+00021890: 696f 6e73 2c20 7377 6570 7420 6f62 6a65  ions, swept obje\n+000218a0: 6374 203c 333e 3a20 2020 2020 2020 2020  ct <3>:         \n+000218b0: 2020 2020 5377 6570 7420 6c69 6e65 732e      Swept lines.\n+000218c0: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+000218d0: 3438 290a 2a20 6f72 6465 722c 2070 6f6c  48).* order, pol\n+000218e0: 7967 6f6e 2076 6572 7465 783a 2020 2020  ygon vertex:    \n+000218f0: 2020 2020 2020 2020 2020 2020 2048 656c               Hel\n+00021900: 6c6f 2077 6f72 6c64 2e20 2020 2020 2020  lo world.       \n+00021910: 2020 286c 696e 6520 2033 3929 0a2a 206f    (line  39).* o\n+00021920: 7264 6572 2c20 706f 6c79 676f 6e20 7665  rder, polygon ve\n+00021930: 7274 6578 203c 313e 3a20 2020 2020 2020  rtex <1>:       \n+00021940: 2020 2020 2020 5377 6570 7420 6c69 6e65        Swept line\n+00021950: 732e 2020 2020 2020 2020 2028 6c69 6e65  s.         (line\n+00021960: 2020 3134 290a 2a20 6f72 6465 722c 2070    14).* order, p\n+00021970: 6f6c 7967 6f6e 2076 6572 7465 7820 3c32  olygon vertex <2\n+00021980: 3e3a 2020 2020 2020 2020 2020 2020 2053  >:             S\n+00021990: 7765 7074 206c 696e 6573 2e20 2020 2020  wept lines.     \n+000219a0: 2020 2020 286c 696e 6520 2034 3029 0a2a      (line  40).*\n+000219b0: 206f 7264 6572 2c20 706f 6c79 676f 6e20   order, polygon \n+000219c0: 7665 7274 6578 203c 333e 3a20 2020 2020  vertex <3>:     \n+000219d0: 2020 2020 2020 2020 5377 6570 7420 706f          Swept po\n+000219e0: 6c79 676f 6e73 2e20 2020 2020 2028 6c69  lygons.      (li\n+000219f0: 6e65 2020 3139 290a 2a20 6f72 6465 722c  ne  19).* order,\n+00021a00: 2070 6f6c 7967 6f6e 2076 6572 7465 7820   polygon vertex \n+00021a10: 3c34 3e3a 2020 2020 2020 2020 2020 2020  <4>:            \n+00021a20: 204f 7665 7276 6965 772e 2020 2020 2020   Overview.      \n+00021a30: 2020 2020 2020 286c 696e 6520 2033 3729        (line  37)\n+00021a40: 0a2a 206f 7264 6572 2c20 706f 6c79 676f  .* order, polygo\n+00021a50: 6e20 7665 7274 6578 203c 353e 3a20 2020  n vertex <5>:   \n+00021a60: 2020 2020 2020 2020 2020 4f76 6572 7669            Overvi\n+00021a70: 6577 2e20 2020 2020 2020 2020 2020 2028  ew.            (\n+00021a80: 6c69 6e65 2020 3535 290a 2a20 6f75 7470  line  55).* outp\n+00021a90: 7574 206c 616e 6775 6167 653a 2020 2020  ut language:    \n 00021aa0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021ab0: 2020 2020 204c 616e 6775 6167 652e 2020       Language.  \n-00021ac0: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-00021ad0: 2020 3629 0a2a 206f 7574 7369 6465 206f    6).* outside o\n-00021ae0: 6620 6120 706f 6c79 676f 6e3a 2020 2020  f a polygon:    \n-00021af0: 2020 2020 2020 2020 2020 2020 2020 4865                He\n-00021b00: 6c6c 6f20 776f 726c 642e 2020 2020 2020  llo world.      \n-00021b10: 2020 2028 6c69 6e65 2020 3337 290a 2a20     (line  37).* \n-00021b20: 7061 7261 6c6c 656c 2070 726f 6a65 6374  parallel project\n-00021b30: 696f 6e3a 2020 2020 2020 2020 2020 2020  ion:            \n-00021b40: 2020 2020 2020 2048 656c 6c6f 2077 6f72         Hello wor\n-00021b50: 6c64 2e20 2020 2020 2020 2020 286c 696e  ld.         (lin\n-00021b60: 6520 2032 3629 0a2a 2070 6172 616c 6c65  e  26).* paralle\n-00021b70: 6c20 7072 6f6a 6563 7469 6f6e 203c 313e  l projection <1>\n-00021b80: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00021b90: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n-00021ba0: 6c73 2e20 2028 6c69 6e65 2020 3138 290a  ls.  (line  18).\n-00021bb0: 2a20 7061 7261 6c6c 656c 2070 726f 6a65  * parallel proje\n-00021bc0: 6374 696f 6e20 3c32 3e3a 2020 2020 2020  ction <2>:      \n-00021bd0: 2020 2020 2020 2020 2050 6963 7475 7265           Picture\n-00021be0: 2062 6f78 2e20 2020 2020 2020 2020 286c   box.         (l\n-00021bf0: 696e 6520 2031 3529 0a2a 2070 6172 656e  ine  15).* paren\n-00021c00: 7468 6573 6573 3a20 2020 2020 2020 2020  theses:         \n+00021ab0: 2020 204c 616e 6775 6167 652e 2020 2020     Language.    \n+00021ac0: 2020 2020 2020 2020 286c 696e 6520 2020          (line   \n+00021ad0: 3629 0a2a 206f 7574 7369 6465 206f 6620  6).* outside of \n+00021ae0: 6120 706f 6c79 676f 6e3a 2020 2020 2020  a polygon:      \n+00021af0: 2020 2020 2020 2020 2020 2020 4865 6c6c              Hell\n+00021b00: 6f20 776f 726c 642e 2020 2020 2020 2020  o world.        \n+00021b10: 2028 6c69 6e65 2020 3337 290a 2a20 7061   (line  37).* pa\n+00021b20: 7261 6c6c 656c 2070 726f 6a65 6374 696f  rallel projectio\n+00021b30: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n+00021b40: 2020 2020 2048 656c 6c6f 2077 6f72 6c64       Hello world\n+00021b50: 2e20 2020 2020 2020 2020 286c 696e 6520  .         (line \n+00021b60: 2032 3629 0a2a 2070 6172 616c 6c65 6c20   26).* parallel \n+00021b70: 7072 6f6a 6563 7469 6f6e 203c 313e 3a20  projection <1>: \n+00021b80: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n+00021b90: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n+00021ba0: 2e20 2028 6c69 6e65 2020 3138 290a 2a20  .  (line  18).* \n+00021bb0: 7061 7261 6c6c 656c 2070 726f 6a65 6374  parallel project\n+00021bc0: 696f 6e20 3c32 3e3a 2020 2020 2020 2020  ion <2>:        \n+00021bd0: 2020 2020 2020 2050 6963 7475 7265 2062         Picture b\n+00021be0: 6f78 2e20 2020 2020 2020 2020 286c 696e  ox.         (lin\n+00021bf0: 6520 2031 3529 0a2a 2070 6172 656e 7468  e  15).* parenth\n+00021c00: 6573 6573 3a20 2020 2020 2020 2020 2020  eses:           \n 00021c10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021c20: 2020 5477 6f2d 6f70 6572 616e 6420 2862    Two-operand (b\n-00021c30: 696e 6172 7929 2066 6f72 6d73 2e0a 2020  inary) forms..  \n+00021c20: 5477 6f2d 6f70 6572 616e 6420 2862 696e  Two-operand (bin\n+00021c30: 6172 7929 2066 6f72 6d73 2e0a 2020 2020  ary) 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 2020 2020 286c 696e              (lin\n-00021c80: 6520 2035 3829 0a2a 2070 6572 7370 6563  e  58).* perspec\n-00021c90: 7469 7665 2070 726f 6a65 6374 696f 6e3a  tive projection:\n-00021ca0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021cb0: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n-00021cc0: 6c73 2e20 2028 6c69 6e65 2020 3139 290a  ls.  (line  19).\n-00021cd0: 2a20 7065 7273 7065 6374 6976 6520 7072  * perspective pr\n-00021ce0: 6f6a 6563 7469 6f6e 203c 313e 3a20 2020  ojection <1>:   \n-00021cf0: 2020 2020 2020 2020 2054 7261 6e73 666f           Transfo\n-00021d00: 726d 206c 6974 6572 616c 732e 2020 286c  rm literals.  (l\n-00021d10: 696e 6520 2032 3129 0a2a 2070 6572 7370  ine  21).* persp\n-00021d20: 6563 7469 7665 2070 726f 6a65 6374 696f  ective projectio\n-00021d30: 6e20 3c32 3e3a 2020 2020 2020 2020 2020  n <2>:          \n-00021d40: 2020 4f76 6572 7669 6577 2e20 2020 2020    Overview.     \n-00021d50: 2020 2020 2020 2028 6c69 6e65 2020 2037         (line   7\n-00021d60: 290a 2a20 7069 6374 7572 6520 626f 783a  ).* picture box:\n+00021c70: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00021c80: 2035 3829 0a2a 2070 6572 7370 6563 7469   58).* perspecti\n+00021c90: 7665 2070 726f 6a65 6374 696f 6e3a 2020  ve projection:  \n+00021ca0: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n+00021cb0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n+00021cc0: 2e20 2028 6c69 6e65 2020 3139 290a 2a20  .  (line  19).* \n+00021cd0: 7065 7273 7065 6374 6976 6520 7072 6f6a  perspective proj\n+00021ce0: 6563 7469 6f6e 203c 313e 3a20 2020 2020  ection <1>:     \n+00021cf0: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n+00021d00: 206c 6974 6572 616c 732e 2020 286c 696e   literals.  (lin\n+00021d10: 6520 2032 3129 0a2a 2070 6572 7370 6563  e  21).* perspec\n+00021d20: 7469 7665 2070 726f 6a65 6374 696f 6e20  tive projection \n+00021d30: 3c32 3e3a 2020 2020 2020 2020 2020 2020  <2>:            \n+00021d40: 4f76 6572 7669 6577 2e20 2020 2020 2020  Overview.       \n+00021d50: 2020 2020 2028 6c69 6e65 2020 2037 290a       (line   7).\n+00021d60: 2a20 7069 6374 7572 6520 626f 783a 2020  * picture box:  \n 00021d70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021d80: 2020 2020 2020 2020 2020 2050 6963 7475             Pictu\n-00021d90: 7265 2062 6f78 2e20 2020 2020 2020 2020  re box.         \n-00021da0: 286c 696e 6520 2020 3629 0a2a 2070 6c61  (line   6).* pla\n-00021db0: 6e61 7269 7479 206f 6620 706f 6c79 676f  narity of polygo\n-00021dc0: 6e73 3a20 2020 2020 2020 2020 2020 2020  ns:             \n-00021dd0: 2020 2020 506f 6c79 676f 6e73 2e20 2020      Polygons.   \n-00021de0: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-00021df0: 3130 290a 2a20 706c 616e 6172 6974 7920  10).* planarity \n-00021e00: 6f66 2070 6f6c 7967 6f6e 7320 3c31 3e3a  of polygons <1>:\n-00021e10: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n-00021e20: 6570 2066 6163 6520 7370 6c69 7474 696e  ep face splittin\n-00021e30: 672e 0a20 2020 2020 2020 2020 2020 2020  g..             \n+00021d80: 2020 2020 2020 2020 2050 6963 7475 7265           Picture\n+00021d90: 2062 6f78 2e20 2020 2020 2020 2020 286c   box.         (l\n+00021da0: 696e 6520 2020 3629 0a2a 2070 6c61 6e61  ine   6).* plana\n+00021db0: 7269 7479 206f 6620 706f 6c79 676f 6e73  rity of polygons\n+00021dc0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00021dd0: 2020 506f 6c79 676f 6e73 2e20 2020 2020    Polygons.     \n+00021de0: 2020 2020 2020 2028 6c69 6e65 2020 3130         (line  10\n+00021df0: 290a 2a20 706c 616e 6172 6974 7920 6f66  ).* planarity of\n+00021e00: 2070 6f6c 7967 6f6e 7320 3c31 3e3a 2020   polygons <1>:  \n+00021e10: 2020 2020 2020 2020 2020 2053 7765 6570             Sweep\n+00021e20: 2066 6163 6520 7370 6c69 7474 696e 672e   face splitting.\n+00021e30: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \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 2020 2020                  \n-00021e70: 2028 6c69 6e65 2020 2037 290a 2a20 706f   (line   7).* po\n-00021e80: 696e 7420 6465 6669 6e69 7469 6f6e 3a20  int definition: \n+00021e60: 2020 2020 2020 2020 2020 2020 2020 2028                 (\n+00021e70: 6c69 6e65 2020 2037 290a 2a20 706f 696e  line   7).* poin\n+00021e80: 7420 6465 6669 6e69 7469 6f6e 3a20 2020  t definition:   \n 00021e90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021ea0: 2020 2020 2044 7261 7769 6e67 2061 2073       Drawing a s\n-00021eb0: 6f6c 6964 2e20 2020 2020 286c 696e 6520  olid.     (line \n-00021ec0: 2032 3329 0a2a 2070 6f69 6e74 206c 6973   23).* point lis\n-00021ed0: 743a 2020 2020 2020 2020 2020 2020 2020  t:              \n-00021ee0: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n-00021ef0: 6570 7420 706f 696e 7473 2e20 2020 2020  ept points.     \n-00021f00: 2020 2028 6c69 6e65 2020 2039 290a 2a20     (line   9).* \n-00021f10: 706f 696e 7420 6c69 7465 7261 6c3a 2020  point literal:  \n+00021ea0: 2020 2044 7261 7769 6e67 2061 2073 6f6c     Drawing a sol\n+00021eb0: 6964 2e20 2020 2020 286c 696e 6520 2032  id.     (line  2\n+00021ec0: 3329 0a2a 2070 6f69 6e74 206c 6973 743a  3).* point list:\n+00021ed0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00021ee0: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n+00021ef0: 7420 706f 696e 7473 2e20 2020 2020 2020  t points.       \n+00021f00: 2028 6c69 6e65 2020 2039 290a 2a20 706f   (line   9).* po\n+00021f10: 696e 7420 6c69 7465 7261 6c3a 2020 2020  int literal:    \n 00021f20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021f30: 2020 2020 2020 2050 6f69 6e74 2061 6e64         Point and\n-00021f40: 2076 6563 746f 7220 6c69 7465 7261 6c73   vector literals\n-00021f50: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+00021f30: 2020 2020 2050 6f69 6e74 2061 6e64 2076       Point and v\n+00021f40: 6563 746f 7220 6c69 7465 7261 6c73 2e0a  ector literals..\n+00021f50: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020                  \n-00021f90: 286c 696e 6520 2020 3629 0a2a 2070 6f69  (line   6).* poi\n-00021fa0: 6e74 2072 6566 6572 656e 6365 3a20 2020  nt reference:   \n+00021f80: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+00021f90: 696e 6520 2020 3629 0a2a 2070 6f69 6e74  ine   6).* point\n+00021fa0: 2072 6566 6572 656e 6365 3a20 2020 2020   reference:     \n 00021fb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00021fc0: 2020 2020 466f 726d 7320 6f66 2072 6566      Forms of ref\n-00021fd0: 6572 656e 6365 732e 2028 6c69 6e65 2020  erences. (line  \n-00021fe0: 3134 290a 2a20 706f 696e 7420 7377 6565  14).* point swee\n-00021ff0: 703a 2020 2020 2020 2020 2020 2020 2020  p:              \n-00022000: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n-00022010: 7074 206f 626a 6563 7473 2e20 2020 2020  pt objects.     \n-00022020: 2020 286c 696e 6520 2031 3129 0a2a 2070    (line  11).* p\n-00022030: 6f69 6e74 2073 7765 6570 203c 313e 3a20  oint sweep <1>: \n+00021fc0: 2020 466f 726d 7320 6f66 2072 6566 6572    Forms of refer\n+00021fd0: 656e 6365 732e 2028 6c69 6e65 2020 3134  ences. (line  14\n+00021fe0: 290a 2a20 706f 696e 7420 7377 6565 703a  ).* point sweep:\n+00021ff0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022000: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n+00022010: 206f 626a 6563 7473 2e20 2020 2020 2020   objects.       \n+00022020: 286c 696e 6520 2031 3129 0a2a 2070 6f69  (line  11).* poi\n+00022030: 6e74 2073 7765 6570 203c 313e 3a20 2020  nt sweep <1>:   \n 00022040: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022050: 2020 2020 2020 5377 6570 7420 706f 696e        Swept poin\n-00022060: 7473 2e20 2020 2020 2020 2028 6c69 6e65  ts.        (line\n-00022070: 2020 2036 290a 2a20 706f 6c79 676f 6e20     6).* polygon \n-00022080: 7377 6565 703a 2020 2020 2020 2020 2020  sweep:          \n-00022090: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n-000220a0: 6f6c 7967 6f6e 2073 7765 6570 732e 2020  olygon sweeps.  \n-000220b0: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-000220c0: 2070 6f6c 7967 6f6e 2073 7765 6570 203c   polygon sweep <\n-000220d0: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-000220e0: 2020 2020 2020 2020 5377 6570 7420 706f          Swept po\n-000220f0: 6c79 676f 6e73 2e20 2020 2020 2028 6c69  lygons.      (li\n-00022100: 6e65 2020 2036 290a 2a20 706f 6c79 676f  ne   6).* polygo\n-00022110: 6e20 7377 6565 7020 3c32 3e3a 2020 2020  n sweep <2>:    \n-00022120: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022130: 2041 2068 6965 7261 7263 6869 6361 6c20   A hierarchical \n-00022140: 6d6f 6465 6c2e 0a20 2020 2020 2020 2020  model..         \n+00022050: 2020 2020 5377 6570 7420 706f 696e 7473      Swept points\n+00022060: 2e20 2020 2020 2020 2028 6c69 6e65 2020  .        (line  \n+00022070: 2036 290a 2a20 706f 6c79 676f 6e20 7377   6).* polygon sw\n+00022080: 6565 703a 2020 2020 2020 2020 2020 2020  eep:            \n+00022090: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n+000220a0: 7967 6f6e 2073 7765 6570 732e 2020 2020  ygon sweeps.    \n+000220b0: 2020 286c 696e 6520 2020 3629 0a2a 2070    (line   6).* p\n+000220c0: 6f6c 7967 6f6e 2073 7765 6570 203c 313e  olygon sweep <1>\n+000220d0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000220e0: 2020 2020 2020 5377 6570 7420 706f 6c79        Swept poly\n+000220f0: 676f 6e73 2e20 2020 2020 2028 6c69 6e65  gons.      (line\n+00022100: 2020 2036 290a 2a20 706f 6c79 676f 6e20     6).* polygon \n+00022110: 7377 6565 7020 3c32 3e3a 2020 2020 2020  sweep <2>:      \n+00022120: 2020 2020 2020 2020 2020 2020 2020 2041                 A\n+00022130: 2068 6965 7261 7263 6869 6361 6c20 6d6f   hierarchical mo\n+00022140: 6465 6c2e 0a20 2020 2020 2020 2020 2020  del..           \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: 2020 2020 2028 6c69 6e65 2031 3232 290a       (line 122).\n-00022190: 2a20 706f 6c79 676f 6e20 7665 7274 6578  * polygon vertex\n-000221a0: 206f 7264 6572 3a20 2020 2020 2020 2020   order:         \n-000221b0: 2020 2020 2020 2020 2048 656c 6c6f 2077           Hello w\n-000221c0: 6f72 6c64 2e20 2020 2020 2020 2020 286c  orld.         (l\n-000221d0: 696e 6520 2033 3929 0a2a 2070 6f6c 7967  ine  39).* polyg\n-000221e0: 6f6e 2076 6572 7465 7820 6f72 6465 7220  on vertex order \n-000221f0: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n-00022200: 2020 5377 6570 7420 6c69 6e65 732e 2020    Swept lines.  \n-00022210: 2020 2020 2020 2028 6c69 6e65 2020 3134         (line  14\n-00022220: 290a 2a20 706f 6c79 676f 6e20 7665 7274  ).* polygon vert\n-00022230: 6578 206f 7264 6572 203c 323e 3a20 2020  ex order <2>:   \n-00022240: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-00022250: 206c 696e 6573 2e20 2020 2020 2020 2020   lines.         \n-00022260: 286c 696e 6520 2034 3029 0a2a 2070 6f6c  (line  40).* pol\n-00022270: 7967 6f6e 2076 6572 7465 7820 6f72 6465  ygon vertex orde\n-00022280: 7220 3c33 3e3a 2020 2020 2020 2020 2020  r <3>:          \n-00022290: 2020 2020 5377 6570 7420 706f 6c79 676f      Swept polygo\n-000222a0: 6e73 2e20 2020 2020 2028 6c69 6e65 2020  ns.      (line  \n-000222b0: 3139 290a 2a20 706f 6c79 676f 6e20 7665  19).* polygon ve\n-000222c0: 7274 6578 206f 7264 6572 203c 343e 3a20  rtex order <4>: \n-000222d0: 2020 2020 2020 2020 2020 2020 204f 7665               Ove\n-000222e0: 7276 6965 772e 2020 2020 2020 2020 2020  rview.          \n-000222f0: 2020 286c 696e 6520 2033 3729 0a2a 2070    (line  37).* p\n-00022300: 6f6c 7967 6f6e 2076 6572 7465 7820 6f72  olygon vertex or\n-00022310: 6465 7220 3c35 3e3a 2020 2020 2020 2020  der <5>:        \n-00022320: 2020 2020 2020 4f76 6572 7669 6577 2e20        Overview. \n-00022330: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-00022340: 2020 3535 290a 2a20 706f 6c79 676f 6e2c    55).* polygon,\n-00022350: 2062 6f64 793a 2020 2020 2020 2020 2020   body:          \n-00022360: 2020 2020 2020 2020 2020 2020 2020 2049                 I\n-00022370: 6e74 6572 6e61 6c20 6f70 7469 6f6e 732e  nternal options.\n-00022380: 2020 2020 286c 696e 6520 2031 3629 0a2a      (line  16).*\n-00022390: 2070 6f6c 7967 6f6e 2c20 626f 6479 203c   polygon, body <\n-000223a0: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-000223b0: 2020 2020 2020 2020 5377 6570 7420 6c69          Swept li\n-000223c0: 6e65 732e 2020 2020 2020 2020 2028 6c69  nes.         (li\n-000223d0: 6e65 2020 3130 290a 2a20 706f 6c79 676f  ne  10).* polygo\n-000223e0: 6e2c 2062 6f64 7920 3c32 3e3a 2020 2020  n, body <2>:    \n-000223f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022400: 2053 7765 7074 2070 6f6c 7967 6f6e 732e   Swept polygons.\n-00022410: 2020 2020 2020 286c 696e 6520 2020 3929        (line   9)\n-00022420: 0a2a 2070 6f6c 7967 6f6e 2c20 656e 643a  .* polygon, end:\n+00022180: 2020 2028 6c69 6e65 2031 3232 290a 2a20     (line 122).* \n+00022190: 706f 6c79 676f 6e20 7665 7274 6578 206f  polygon vertex o\n+000221a0: 7264 6572 3a20 2020 2020 2020 2020 2020  rder:           \n+000221b0: 2020 2020 2020 2048 656c 6c6f 2077 6f72         Hello wor\n+000221c0: 6c64 2e20 2020 2020 2020 2020 286c 696e  ld.         (lin\n+000221d0: 6520 2033 3929 0a2a 2070 6f6c 7967 6f6e  e  39).* polygon\n+000221e0: 2076 6572 7465 7820 6f72 6465 7220 3c31   vertex order <1\n+000221f0: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+00022200: 5377 6570 7420 6c69 6e65 732e 2020 2020  Swept lines.    \n+00022210: 2020 2020 2028 6c69 6e65 2020 3134 290a       (line  14).\n+00022220: 2a20 706f 6c79 676f 6e20 7665 7274 6578  * polygon vertex\n+00022230: 206f 7264 6572 203c 323e 3a20 2020 2020   order <2>:     \n+00022240: 2020 2020 2020 2020 2053 7765 7074 206c           Swept l\n+00022250: 696e 6573 2e20 2020 2020 2020 2020 286c  ines.         (l\n+00022260: 696e 6520 2034 3029 0a2a 2070 6f6c 7967  ine  40).* polyg\n+00022270: 6f6e 2076 6572 7465 7820 6f72 6465 7220  on vertex order \n+00022280: 3c33 3e3a 2020 2020 2020 2020 2020 2020  <3>:            \n+00022290: 2020 5377 6570 7420 706f 6c79 676f 6e73    Swept polygons\n+000222a0: 2e20 2020 2020 2028 6c69 6e65 2020 3139  .      (line  19\n+000222b0: 290a 2a20 706f 6c79 676f 6e20 7665 7274  ).* polygon vert\n+000222c0: 6578 206f 7264 6572 203c 343e 3a20 2020  ex order <4>:   \n+000222d0: 2020 2020 2020 2020 2020 204f 7665 7276             Overv\n+000222e0: 6965 772e 2020 2020 2020 2020 2020 2020  iew.            \n+000222f0: 286c 696e 6520 2033 3729 0a2a 2070 6f6c  (line  37).* pol\n+00022300: 7967 6f6e 2076 6572 7465 7820 6f72 6465  ygon vertex orde\n+00022310: 7220 3c35 3e3a 2020 2020 2020 2020 2020  r <5>:          \n+00022320: 2020 2020 4f76 6572 7669 6577 2e20 2020      Overview.   \n+00022330: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+00022340: 3535 290a 2a20 706f 6c79 676f 6e2c 2062  55).* polygon, b\n+00022350: 6f64 793a 2020 2020 2020 2020 2020 2020  ody:            \n+00022360: 2020 2020 2020 2020 2020 2020 2049 6e74               Int\n+00022370: 6572 6e61 6c20 6f70 7469 6f6e 732e 2020  ernal options.  \n+00022380: 2020 286c 696e 6520 2031 3629 0a2a 2070    (line  16).* p\n+00022390: 6f6c 7967 6f6e 2c20 626f 6479 203c 313e  olygon, body <1>\n+000223a0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+000223b0: 2020 2020 2020 5377 6570 7420 6c69 6e65        Swept line\n+000223c0: 732e 2020 2020 2020 2020 2028 6c69 6e65  s.         (line\n+000223d0: 2020 3130 290a 2a20 706f 6c79 676f 6e2c    10).* polygon,\n+000223e0: 2062 6f64 7920 3c32 3e3a 2020 2020 2020   body <2>:      \n+000223f0: 2020 2020 2020 2020 2020 2020 2020 2053                 S\n+00022400: 7765 7074 2070 6f6c 7967 6f6e 732e 2020  wept polygons.  \n+00022410: 2020 2020 286c 696e 6520 2020 3929 0a2a      (line   9).*\n+00022420: 2070 6f6c 7967 6f6e 2c20 656e 643a 2020   polygon, end:  \n 00022430: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022440: 2020 2020 2020 2020 2020 5377 6570 7420            Swept \n-00022450: 6c69 6e65 732e 2020 2020 2020 2020 2028  lines.         (\n-00022460: 6c69 6e65 2020 3338 290a 2a20 706f 6c79  line  38).* poly\n-00022470: 676f 6e2c 2065 6e64 203c 313e 3a20 2020  gon, end <1>:   \n+00022440: 2020 2020 2020 2020 5377 6570 7420 6c69          Swept li\n+00022450: 6e65 732e 2020 2020 2020 2020 2028 6c69  nes.         (li\n+00022460: 6e65 2020 3338 290a 2a20 706f 6c79 676f  ne  38).* polygo\n+00022470: 6e2c 2065 6e64 203c 313e 3a20 2020 2020  n, end <1>:     \n 00022480: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022490: 2020 2053 7765 7074 2070 6f6c 7967 6f6e     Swept polygon\n-000224a0: 732e 2020 2020 2020 286c 696e 6520 2031  s.      (line  1\n-000224b0: 3529 0a2a 2070 6f6c 7967 6f6e 2c20 6f75  5).* polygon, ou\n-000224c0: 7473 6964 6520 6f66 3a20 2020 2020 2020  tside of:       \n-000224d0: 2020 2020 2020 2020 2020 2020 4865 6c6c              Hell\n-000224e0: 6f20 776f 726c 642e 2020 2020 2020 2020  o world.        \n-000224f0: 2028 6c69 6e65 2020 3337 290a 2a20 706f   (line  37).* po\n-00022500: 6c79 676f 6e2c 2070 6c61 6e61 723a 2020  lygon, planar:  \n+00022490: 2053 7765 7074 2070 6f6c 7967 6f6e 732e   Swept polygons.\n+000224a0: 2020 2020 2020 286c 696e 6520 2031 3529        (line  15)\n+000224b0: 0a2a 2070 6f6c 7967 6f6e 2c20 6f75 7473  .* polygon, outs\n+000224c0: 6964 6520 6f66 3a20 2020 2020 2020 2020  ide of:         \n+000224d0: 2020 2020 2020 2020 2020 4865 6c6c 6f20            Hello \n+000224e0: 776f 726c 642e 2020 2020 2020 2020 2028  world.         (\n+000224f0: 6c69 6e65 2020 3337 290a 2a20 706f 6c79  line  37).* poly\n+00022500: 676f 6e2c 2070 6c61 6e61 723a 2020 2020  gon, planar:    \n 00022510: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022520: 2020 2020 2050 6f6c 7967 6f6e 732e 2020       Polygons.  \n-00022530: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n-00022540: 2031 3029 0a2a 2070 6f6c 7967 6f6e 2c20   10).* polygon, \n-00022550: 706c 616e 6172 203c 313e 3a20 2020 2020  planar <1>:     \n-00022560: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n-00022570: 6565 7020 6661 6365 2073 706c 6974 7469  eep face splitti\n-00022580: 6e67 2e0a 2020 2020 2020 2020 2020 2020  ng..            \n+00022520: 2020 2050 6f6c 7967 6f6e 732e 2020 2020     Polygons.    \n+00022530: 2020 2020 2020 2020 286c 696e 6520 2031          (line  1\n+00022540: 3029 0a2a 2070 6f6c 7967 6f6e 2c20 706c  0).* polygon, pl\n+00022550: 616e 6172 203c 313e 3a20 2020 2020 2020  anar <1>:       \n+00022560: 2020 2020 2020 2020 2020 2020 5377 6565              Swee\n+00022570: 7020 6661 6365 2073 706c 6974 7469 6e67  p face splitting\n+00022580: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020                  \n-000225c0: 2020 286c 696e 6520 2020 3729 0a2a 2070    (line   7).* p\n-000225d0: 7265 6365 6465 6e63 652c 206f 7065 7261  recedence, opera\n-000225e0: 746f 723a 2020 2020 2020 2020 2020 2020  tor:            \n-000225f0: 2020 2020 2020 5477 6f2d 6f70 6572 616e        Two-operan\n-00022600: 6420 2862 696e 6172 7929 2066 6f72 6d73  d (binary) forms\n-00022610: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \n+000225c0: 286c 696e 6520 2020 3729 0a2a 2070 7265  (line   7).* pre\n+000225d0: 6365 6465 6e63 652c 206f 7065 7261 746f  cedence, operato\n+000225e0: 723a 2020 2020 2020 2020 2020 2020 2020  r:              \n+000225f0: 2020 2020 5477 6f2d 6f70 6572 616e 6420      Two-operand \n+00022600: 2862 696e 6172 7929 2066 6f72 6d73 2e0a  (binary) forms..\n+00022610: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020                  \n-00022650: 286c 696e 6520 2034 3529 0a2a 2070 726f  (line  45).* pro\n-00022660: 6772 616d 2c20 6865 6c6c 6f20 776f 726c  gram, hello worl\n-00022670: 643a 2020 2020 2020 2020 2020 2020 2020  d:              \n-00022680: 2020 2020 4865 6c6c 6f20 776f 726c 642e      Hello world.\n-00022690: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-000226a0: 2037 290a 2a20 7072 6f6a 6563 7469 6f6e   7).* projection\n-000226b0: 2c20 7061 7261 6c6c 656c 3a20 2020 2020  , parallel:     \n-000226c0: 2020 2020 2020 2020 2020 2020 2048 656c               Hel\n-000226d0: 6c6f 2077 6f72 6c64 2e20 2020 2020 2020  lo world.       \n-000226e0: 2020 286c 696e 6520 2032 3629 0a2a 2070    (line  26).* p\n-000226f0: 726f 6a65 6374 696f 6e2c 2070 6172 616c  rojection, paral\n-00022700: 6c65 6c20 3c31 3e3a 2020 2020 2020 2020  lel <1>:        \n-00022710: 2020 2020 2020 5472 616e 7366 6f72 6d20        Transform \n-00022720: 6c69 7465 7261 6c73 2e20 2028 6c69 6e65  literals.  (line\n-00022730: 2020 3138 290a 2a20 7072 6f6a 6563 7469    18).* projecti\n-00022740: 6f6e 2c20 7061 7261 6c6c 656c 203c 323e  on, parallel <2>\n-00022750: 3a20 2020 2020 2020 2020 2020 2020 2050  :              P\n-00022760: 6963 7475 7265 2062 6f78 2e20 2020 2020  icture box.     \n-00022770: 2020 2020 286c 696e 6520 2031 3529 0a2a      (line  15).*\n-00022780: 2070 726f 6a65 6374 696f 6e2c 2070 6572   projection, per\n-00022790: 7370 6563 7469 7665 3a20 2020 2020 2020  spective:       \n-000227a0: 2020 2020 2020 2020 5472 616e 7366 6f72          Transfor\n-000227b0: 6d20 6c69 7465 7261 6c73 2e20 2028 6c69  m literals.  (li\n-000227c0: 6e65 2020 3139 290a 2a20 7072 6f6a 6563  ne  19).* projec\n-000227d0: 7469 6f6e 2c20 7065 7273 7065 6374 6976  tion, perspectiv\n-000227e0: 6520 3c31 3e3a 2020 2020 2020 2020 2020  e <1>:          \n-000227f0: 2054 7261 6e73 666f 726d 206c 6974 6572   Transform liter\n-00022800: 616c 732e 2020 286c 696e 6520 2032 3129  als.  (line  21)\n-00022810: 0a2a 2070 726f 6a65 6374 696f 6e2c 2070  .* projection, p\n-00022820: 6572 7370 6563 7469 7665 203c 323e 3a20  erspective <2>: \n-00022830: 2020 2020 2020 2020 2020 4f76 6572 7669            Overvi\n-00022840: 6577 2e20 2020 2020 2020 2020 2020 2028  ew.            (\n-00022850: 6c69 6e65 2020 2037 290a 2a20 7073 6575  line   7).* pseu\n-00022860: 646f 2d6f 7074 696f 6e73 3a20 2020 2020  do-options:     \n+00022640: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+00022650: 696e 6520 2034 3529 0a2a 2070 726f 6772  ine  45).* progr\n+00022660: 616d 2c20 6865 6c6c 6f20 776f 726c 643a  am, hello world:\n+00022670: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022680: 2020 4865 6c6c 6f20 776f 726c 642e 2020    Hello world.  \n+00022690: 2020 2020 2020 2028 6c69 6e65 2020 2037         (line   7\n+000226a0: 290a 2a20 7072 6f6a 6563 7469 6f6e 2c20  ).* projection, \n+000226b0: 7061 7261 6c6c 656c 3a20 2020 2020 2020  parallel:       \n+000226c0: 2020 2020 2020 2020 2020 2048 656c 6c6f             Hello\n+000226d0: 2077 6f72 6c64 2e20 2020 2020 2020 2020   world.         \n+000226e0: 286c 696e 6520 2032 3629 0a2a 2070 726f  (line  26).* pro\n+000226f0: 6a65 6374 696f 6e2c 2070 6172 616c 6c65  jection, paralle\n+00022700: 6c20 3c31 3e3a 2020 2020 2020 2020 2020  l <1>:          \n+00022710: 2020 2020 5472 616e 7366 6f72 6d20 6c69      Transform li\n+00022720: 7465 7261 6c73 2e20 2028 6c69 6e65 2020  terals.  (line  \n+00022730: 3138 290a 2a20 7072 6f6a 6563 7469 6f6e  18).* projection\n+00022740: 2c20 7061 7261 6c6c 656c 203c 323e 3a20  , parallel <2>: \n+00022750: 2020 2020 2020 2020 2020 2020 2050 6963               Pic\n+00022760: 7475 7265 2062 6f78 2e20 2020 2020 2020  ture box.       \n+00022770: 2020 286c 696e 6520 2031 3529 0a2a 2070    (line  15).* p\n+00022780: 726f 6a65 6374 696f 6e2c 2070 6572 7370  rojection, persp\n+00022790: 6563 7469 7665 3a20 2020 2020 2020 2020  ective:         \n+000227a0: 2020 2020 2020 5472 616e 7366 6f72 6d20        Transform \n+000227b0: 6c69 7465 7261 6c73 2e20 2028 6c69 6e65  literals.  (line\n+000227c0: 2020 3139 290a 2a20 7072 6f6a 6563 7469    19).* projecti\n+000227d0: 6f6e 2c20 7065 7273 7065 6374 6976 6520  on, perspective \n+000227e0: 3c31 3e3a 2020 2020 2020 2020 2020 2054  <1>:           T\n+000227f0: 7261 6e73 666f 726d 206c 6974 6572 616c  ransform literal\n+00022800: 732e 2020 286c 696e 6520 2032 3129 0a2a  s.  (line  21).*\n+00022810: 2070 726f 6a65 6374 696f 6e2c 2070 6572   projection, per\n+00022820: 7370 6563 7469 7665 203c 323e 3a20 2020  spective <2>:   \n+00022830: 2020 2020 2020 2020 4f76 6572 7669 6577          Overview\n+00022840: 2e20 2020 2020 2020 2020 2020 2028 6c69  .            (li\n+00022850: 6e65 2020 2037 290a 2a20 7073 6575 646f  ne   7).* pseudo\n+00022860: 2d6f 7074 696f 6e73 3a20 2020 2020 2020  -options:       \n 00022870: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022880: 2020 2054 696b 5a2f 5047 4620 7573 6572     TikZ/PGF user\n-00022890: 2d64 6566 696e 6564 2073 7479 6c65 732e  -defined styles.\n-000228a0: 0a20 2020 2020 2020 2020 2020 2020 2020  .               \n+00022880: 2054 696b 5a2f 5047 4620 7573 6572 2d64   TikZ/PGF user-d\n+00022890: 6566 696e 6564 2073 7479 6c65 732e 0a20  efined styles.. \n+000228a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \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 2020 2020 2028                 (\n-000228e0: 6c69 6e65 2020 3235 290a 2a20 7073 6672  line  25).* psfr\n-000228f0: 616d 6562 6f78 3a20 2020 2020 2020 2020  amebox:         \n+000228d0: 2020 2020 2020 2020 2020 2020 2028 6c69               (li\n+000228e0: 6e65 2020 3235 290a 2a20 7073 6672 616d  ne  25).* psfram\n+000228f0: 6562 6f78 3a20 2020 2020 2020 2020 2020  ebox:           \n 00022900: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022910: 2020 2046 7261 6d65 2e20 2020 2020 2020     Frame.       \n-00022920: 2020 2020 2020 2020 286c 696e 6520 2020          (line   \n-00022930: 3829 0a2a 2070 7370 6963 7475 7265 3a20  8).* pspicture: \n+00022910: 2046 7261 6d65 2e20 2020 2020 2020 2020   Frame.         \n+00022920: 2020 2020 2020 286c 696e 6520 2020 3829        (line   8)\n+00022930: 0a2a 2070 7370 6963 7475 7265 3a20 2020  .* pspicture:   \n 00022940: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022950: 2020 2020 2020 2020 2020 2020 5069 6374              Pict\n-00022960: 7572 6520 626f 782e 2020 2020 2020 2020  ure box.        \n-00022970: 2028 6c69 6e65 2020 3130 290a 2a20 5053   (line  10).* PS\n-00022980: 5472 6963 6b73 3a20 2020 2020 2020 2020  Tricks:         \n+00022950: 2020 2020 2020 2020 2020 5069 6374 7572            Pictur\n+00022960: 6520 626f 782e 2020 2020 2020 2020 2028  e box.         (\n+00022970: 6c69 6e65 2020 3130 290a 2a20 5053 5472  line  10).* PSTr\n+00022980: 6963 6b73 3a20 2020 2020 2020 2020 2020  icks:           \n 00022990: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000229a0: 2020 2020 2041 626f 7574 2073 6b65 7463       About sketc\n-000229b0: 682e 2020 2020 2020 2020 286c 696e 6520  h.        (line \n-000229c0: 2032 3129 0a2a 2071 756f 7469 6e67 2c20   21).* quoting, \n-000229d0: 7370 6563 6961 6c3a 2020 2020 2020 2020  special:        \n-000229e0: 2020 2020 2020 2020 2020 2020 2020 5370                Sp\n-000229f0: 6563 6961 6c20 6f62 6a65 6374 732e 2020  ecial objects.  \n-00022a00: 2020 2028 6c69 6e65 2020 3230 290a 2a20     (line  20).* \n-00022a10: 7175 6f74 696e 672c 2073 7065 6369 616c  quoting, special\n-00022a20: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-00022a30: 2020 2020 2020 2053 7065 6369 616c 732e         Specials.\n-00022a40: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n-00022a50: 6520 2020 3829 0a2a 2072 6566 6572 656e  e   8).* referen\n-00022a60: 6365 2c20 6472 6177 6162 6c65 3a20 2020  ce, drawable:   \n-00022a70: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022a80: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n-00022a90: 732e 2020 2028 6c69 6e65 2020 3333 290a  s.   (line  33).\n-00022aa0: 2a20 7265 6665 7265 6e63 652c 2064 7261  * reference, dra\n-00022ab0: 7761 626c 6520 3c31 3e3a 2020 2020 2020  wable <1>:      \n-00022ac0: 2020 2020 2020 2020 2046 6f72 6d73 206f           Forms o\n-00022ad0: 6620 7265 6665 7265 6e63 6573 2e20 286c  f references. (l\n-00022ae0: 696e 6520 2031 3729 0a2a 2072 6566 6572  ine  17).* refer\n-00022af0: 656e 6365 2c20 6472 6177 6162 6c65 203c  ence, drawable <\n-00022b00: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n-00022b10: 2020 4f76 6572 7669 6577 2e20 2020 2020    Overview.     \n-00022b20: 2020 2020 2020 2028 6c69 6e65 2020 3437         (line  47\n-00022b30: 290a 2a20 7265 6665 7265 6e63 652c 2064  ).* reference, d\n-00022b40: 7261 7761 626c 6520 3c33 3e3a 2020 2020  rawable <3>:    \n-00022b50: 2020 2020 2020 2020 2020 204f 7665 7276             Overv\n-00022b60: 6965 772e 2020 2020 2020 2020 2020 2020  iew.            \n-00022b70: 286c 696e 6520 2035 3729 0a2a 2072 6566  (line  57).* ref\n-00022b80: 6572 656e 6365 2c20 6d75 6c74 6970 6c65  erence, multiple\n-00022b90: 206f 7074 696f 6e73 3a20 2020 2020 2020   options:       \n-00022ba0: 2020 2020 466f 726d 7320 6f66 2072 6566      Forms of ref\n-00022bb0: 6572 656e 6365 732e 2028 6c69 6e65 2020  erences. (line  \n-00022bc0: 3138 290a 2a20 7265 6665 7265 6e63 652c  18).* reference,\n-00022bd0: 206f 7074 696f 6e73 3a20 2020 2020 2020   options:       \n-00022be0: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n-00022bf0: 796c 696e 6520 7377 6565 7073 2077 6974  yline sweeps wit\n-00022c00: 6820 636c 6f73 7572 652e 0a20 2020 2020  h closure..     \n+000229a0: 2020 2041 626f 7574 2073 6b65 7463 682e     About sketch.\n+000229b0: 2020 2020 2020 2020 286c 696e 6520 2032          (line  2\n+000229c0: 3129 0a2a 2071 756f 7469 6e67 2c20 7370  1).* quoting, sp\n+000229d0: 6563 6961 6c3a 2020 2020 2020 2020 2020  ecial:          \n+000229e0: 2020 2020 2020 2020 2020 2020 5370 6563              Spec\n+000229f0: 6961 6c20 6f62 6a65 6374 732e 2020 2020  ial objects.    \n+00022a00: 2028 6c69 6e65 2020 3230 290a 2a20 7175   (line  20).* qu\n+00022a10: 6f74 696e 672c 2073 7065 6369 616c 203c  oting, special <\n+00022a20: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+00022a30: 2020 2020 2053 7065 6369 616c 732e 2020       Specials.  \n+00022a40: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00022a50: 2020 3829 0a2a 2072 6566 6572 656e 6365    8).* reference\n+00022a60: 2c20 6472 6177 6162 6c65 3a20 2020 2020  , drawable:     \n+00022a70: 2020 2020 2020 2020 2020 2020 2020 4f62                Ob\n+00022a80: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n+00022a90: 2020 2028 6c69 6e65 2020 3333 290a 2a20     (line  33).* \n+00022aa0: 7265 6665 7265 6e63 652c 2064 7261 7761  reference, drawa\n+00022ab0: 626c 6520 3c31 3e3a 2020 2020 2020 2020  ble <1>:        \n+00022ac0: 2020 2020 2020 2046 6f72 6d73 206f 6620         Forms of \n+00022ad0: 7265 6665 7265 6e63 6573 2e20 286c 696e  references. (lin\n+00022ae0: 6520 2031 3729 0a2a 2072 6566 6572 656e  e  17).* referen\n+00022af0: 6365 2c20 6472 6177 6162 6c65 203c 323e  ce, drawable <2>\n+00022b00: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00022b10: 4f76 6572 7669 6577 2e20 2020 2020 2020  Overview.       \n+00022b20: 2020 2020 2028 6c69 6e65 2020 3437 290a       (line  47).\n+00022b30: 2a20 7265 6665 7265 6e63 652c 2064 7261  * reference, dra\n+00022b40: 7761 626c 6520 3c33 3e3a 2020 2020 2020  wable <3>:      \n+00022b50: 2020 2020 2020 2020 204f 7665 7276 6965           Overvie\n+00022b60: 772e 2020 2020 2020 2020 2020 2020 286c  w.            (l\n+00022b70: 696e 6520 2035 3729 0a2a 2072 6566 6572  ine  57).* refer\n+00022b80: 656e 6365 2c20 6d75 6c74 6970 6c65 206f  ence, multiple o\n+00022b90: 7074 696f 6e73 3a20 2020 2020 2020 2020  ptions:         \n+00022ba0: 2020 466f 726d 7320 6f66 2072 6566 6572    Forms of refer\n+00022bb0: 656e 6365 732e 2028 6c69 6e65 2020 3138  ences. (line  18\n+00022bc0: 290a 2a20 7265 6665 7265 6e63 652c 206f  ).* reference, o\n+00022bd0: 7074 696f 6e73 3a20 2020 2020 2020 2020  ptions:         \n+00022be0: 2020 2020 2020 2020 2020 2050 6f6c 796c             Polyl\n+00022bf0: 696e 6520 7377 6565 7073 2077 6974 6820  ine sweeps with \n+00022c00: 636c 6f73 7572 652e 0a20 2020 2020 2020  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 2020 2020 2028 6c69 6e65 2020           (line  \n-00022c50: 3234 290a 2a20 7265 6665 7265 6e63 652c  24).* reference,\n-00022c60: 206f 7074 696f 6e73 203c 313e 3a20 2020   options <1>:   \n-00022c70: 2020 2020 2020 2020 2020 2020 2046 6f72               For\n-00022c80: 6d73 206f 6620 7265 6665 7265 6e63 6573  ms of references\n-00022c90: 2e20 286c 696e 6520 2031 3829 0a2a 2072  . (line  18).* r\n-00022ca0: 6566 6572 656e 6365 2c20 706f 696e 743a  eference, point:\n+00022c40: 2020 2020 2020 2028 6c69 6e65 2020 3234         (line  24\n+00022c50: 290a 2a20 7265 6665 7265 6e63 652c 206f  ).* reference, o\n+00022c60: 7074 696f 6e73 203c 313e 3a20 2020 2020  ptions <1>:     \n+00022c70: 2020 2020 2020 2020 2020 2046 6f72 6d73             Forms\n+00022c80: 206f 6620 7265 6665 7265 6e63 6573 2e20   of references. \n+00022c90: 286c 696e 6520 2031 3829 0a2a 2072 6566  (line  18).* ref\n+00022ca0: 6572 656e 6365 2c20 706f 696e 743a 2020  erence, point:  \n 00022cb0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022cc0: 2020 2020 2020 4472 6177 696e 6720 6120        Drawing a \n-00022cd0: 736f 6c69 642e 2020 2020 2028 6c69 6e65  solid.     (line\n-00022ce0: 2020 3233 290a 2a20 7265 6665 7265 6e63    23).* referenc\n-00022cf0: 652c 2070 6f69 6e74 203c 313e 3a20 2020  e, point <1>:   \n-00022d00: 2020 2020 2020 2020 2020 2020 2020 2046                 F\n-00022d10: 6f72 6d73 206f 6620 7265 6665 7265 6e63  orms of referenc\n-00022d20: 6573 2e20 286c 696e 6520 2031 3429 0a2a  es. (line  14).*\n-00022d30: 2072 6566 6572 656e 6365 2c20 7363 616c   reference, scal\n-00022d40: 6172 3a20 2020 2020 2020 2020 2020 2020  ar:             \n-00022d50: 2020 2020 2020 2020 5377 6570 7420 6f62          Swept ob\n-00022d60: 6a65 6374 732e 2020 2020 2020 2028 6c69  jects.       (li\n-00022d70: 6e65 2020 3133 290a 2a20 7265 6665 7265  ne  13).* refere\n-00022d80: 6e63 652c 2073 6361 6c61 7220 3c31 3e3a  nce, scalar <1>:\n-00022d90: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022da0: 2046 6f72 6d73 206f 6620 7265 6665 7265   Forms of refere\n-00022db0: 6e63 6573 2e20 286c 696e 6520 2031 3329  nces. (line  13)\n-00022dc0: 0a2a 2072 6566 6572 656e 6365 2c20 7461  .* reference, ta\n-00022dd0: 673a 2020 2020 2020 2020 2020 2020 2020  g:              \n-00022de0: 2020 2020 2020 2020 2020 466f 726d 7320            Forms \n-00022df0: 6f66 2064 6566 696e 6974 696f 6e73 2e0a  of definitions..\n+00022cc0: 2020 2020 4472 6177 696e 6720 6120 736f      Drawing a so\n+00022cd0: 6c69 642e 2020 2020 2028 6c69 6e65 2020  lid.     (line  \n+00022ce0: 3233 290a 2a20 7265 6665 7265 6e63 652c  23).* reference,\n+00022cf0: 2070 6f69 6e74 203c 313e 3a20 2020 2020   point <1>:     \n+00022d00: 2020 2020 2020 2020 2020 2020 2046 6f72               For\n+00022d10: 6d73 206f 6620 7265 6665 7265 6e63 6573  ms of references\n+00022d20: 2e20 286c 696e 6520 2031 3429 0a2a 2072  . (line  14).* r\n+00022d30: 6566 6572 656e 6365 2c20 7363 616c 6172  eference, scalar\n+00022d40: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00022d50: 2020 2020 2020 5377 6570 7420 6f62 6a65        Swept obje\n+00022d60: 6374 732e 2020 2020 2020 2028 6c69 6e65  cts.       (line\n+00022d70: 2020 3133 290a 2a20 7265 6665 7265 6e63    13).* referenc\n+00022d80: 652c 2073 6361 6c61 7220 3c31 3e3a 2020  e, scalar <1>:  \n+00022d90: 2020 2020 2020 2020 2020 2020 2020 2046                 F\n+00022da0: 6f72 6d73 206f 6620 7265 6665 7265 6e63  orms of referenc\n+00022db0: 6573 2e20 286c 696e 6520 2031 3329 0a2a  es. (line  13).*\n+00022dc0: 2072 6566 6572 656e 6365 2c20 7461 673a   reference, tag:\n+00022dd0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00022de0: 2020 2020 2020 2020 466f 726d 7320 6f66          Forms of\n+00022df0: 2064 6566 696e 6974 696f 6e73 2e0a 2020   definitions..  \n 00022e00: 2020 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 2020 2020 286c                (l\n-00022e40: 696e 6520 2032 3029 0a2a 2072 6566 6572  ine  20).* refer\n-00022e50: 656e 6365 2c20 7461 6720 3c31 3e3a 2020  ence, tag <1>:  \n+00022e30: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+00022e40: 6520 2032 3029 0a2a 2072 6566 6572 656e  e  20).* referen\n+00022e50: 6365 2c20 7461 6720 3c31 3e3a 2020 2020  ce, tag <1>:    \n 00022e60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00022e70: 2020 466f 726d 7320 6f66 2072 6566 6572    Forms of refer\n-00022e80: 656e 6365 732e 2028 6c69 6e65 2020 3139  ences. (line  19\n-00022e90: 290a 2a20 7265 6665 7265 6e63 652c 2074  ).* reference, t\n-00022ea0: 7261 6e73 666f 726d 3a20 2020 2020 2020  ransform:       \n-00022eb0: 2020 2020 2020 2020 2020 2046 6f72 6d73             Forms\n-00022ec0: 206f 6620 7265 6665 7265 6e63 6573 2e20   of references. \n-00022ed0: 286c 696e 6520 2031 3629 0a2a 2072 6566  (line  16).* ref\n-00022ee0: 6572 656e 6365 2c20 7472 616e 7366 6f72  erence, transfor\n-00022ef0: 6d20 3c31 3e3a 2020 2020 2020 2020 2020  m <1>:          \n-00022f00: 2020 2020 4f76 6572 7669 6577 2e20 2020      Overview.   \n-00022f10: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-00022f20: 3335 290a 2a20 7265 6665 7265 6e63 652c  35).* reference,\n-00022f30: 2076 6563 746f 723a 2020 2020 2020 2020   vector:        \n-00022f40: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n-00022f50: 796c 696e 6520 7377 6565 7073 2e20 2020  yline sweeps.   \n-00022f60: 2020 286c 696e 6520 2032 3029 0a2a 2072    (line  20).* r\n-00022f70: 6566 6572 656e 6365 2c20 7665 6374 6f72  eference, vector\n-00022f80: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-00022f90: 2020 2020 2020 466f 726d 7320 6f66 2072        Forms of r\n-00022fa0: 6566 6572 656e 6365 732e 2028 6c69 6e65  eferences. (line\n-00022fb0: 2020 3135 290a 2a20 7265 7065 6174 6564    15).* repeated\n-00022fc0: 206f 626a 6563 743a 2020 2020 2020 2020   object:        \n-00022fd0: 2020 2020 2020 2020 2020 2020 2020 2052                 R\n-00022fe0: 6570 6561 7473 2e20 2020 2020 2020 2020  epeats.         \n-00022ff0: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-00023000: 2072 6573 6572 7665 6420 776f 7264 733a   reserved words:\n+00022e70: 466f 726d 7320 6f66 2072 6566 6572 656e  Forms of referen\n+00022e80: 6365 732e 2028 6c69 6e65 2020 3139 290a  ces. (line  19).\n+00022e90: 2a20 7265 6665 7265 6e63 652c 2074 7261  * reference, tra\n+00022ea0: 6e73 666f 726d 3a20 2020 2020 2020 2020  nsform:         \n+00022eb0: 2020 2020 2020 2020 2046 6f72 6d73 206f           Forms o\n+00022ec0: 6620 7265 6665 7265 6e63 6573 2e20 286c  f references. (l\n+00022ed0: 696e 6520 2031 3629 0a2a 2072 6566 6572  ine  16).* refer\n+00022ee0: 656e 6365 2c20 7472 616e 7366 6f72 6d20  ence, transform \n+00022ef0: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n+00022f00: 2020 4f76 6572 7669 6577 2e20 2020 2020    Overview.     \n+00022f10: 2020 2020 2020 2028 6c69 6e65 2020 3335         (line  35\n+00022f20: 290a 2a20 7265 6665 7265 6e63 652c 2076  ).* reference, v\n+00022f30: 6563 746f 723a 2020 2020 2020 2020 2020  ector:          \n+00022f40: 2020 2020 2020 2020 2020 2050 6f6c 796c             Polyl\n+00022f50: 696e 6520 7377 6565 7073 2e20 2020 2020  ine sweeps.     \n+00022f60: 286c 696e 6520 2032 3029 0a2a 2072 6566  (line  20).* ref\n+00022f70: 6572 656e 6365 2c20 7665 6374 6f72 203c  erence, vector <\n+00022f80: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+00022f90: 2020 2020 466f 726d 7320 6f66 2072 6566      Forms of ref\n+00022fa0: 6572 656e 6365 732e 2028 6c69 6e65 2020  erences. (line  \n+00022fb0: 3135 290a 2a20 7265 7065 6174 6564 206f  15).* repeated o\n+00022fc0: 626a 6563 743a 2020 2020 2020 2020 2020  bject:          \n+00022fd0: 2020 2020 2020 2020 2020 2020 2052 6570               Rep\n+00022fe0: 6561 7473 2e20 2020 2020 2020 2020 2020  eats.           \n+00022ff0: 2020 286c 696e 6520 2020 3629 0a2a 2072    (line   6).* r\n+00023000: 6573 6572 7665 6420 776f 7264 733a 2020  eserved words:  \n 00023010: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023020: 2020 2020 2020 2020 4b65 7920 616e 6420          Key and \n-00023030: 7265 7365 7276 6564 2077 6f72 6473 2e0a  reserved words..\n+00023020: 2020 2020 2020 4b65 7920 616e 6420 7265        Key and re\n+00023030: 7365 7276 6564 2077 6f72 6473 2e0a 2020  served words..  \n 00023040: 2020 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 2020 2020 286c                (l\n-00023080: 696e 6520 2031 3129 0a2a 2072 6967 6874  ine  11).* right\n-00023090: 2068 616e 6420 7275 6c65 3a20 2020 2020   hand rule:     \n+00023070: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+00023080: 6520 2031 3129 0a2a 2072 6967 6874 2068  e  11).* right h\n+00023090: 616e 6420 7275 6c65 3a20 2020 2020 2020  and rule:       \n 000230a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000230b0: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n-000230c0: 726d 732e 2020 2028 6c69 6e65 2020 3431  rms.   (line  41\n-000230d0: 290a 2a20 7269 6768 742d 6861 6e64 2063  ).* right-hand c\n-000230e0: 6f6f 7264 696e 6174 6520 7379 7374 656d  oordinate system\n-000230f0: 3a20 2020 2020 2020 2020 2049 6e74 726f  :          Intro\n-00023100: 6475 6374 696f 6e20 6279 2065 7861 6d70  duction by examp\n-00023110: 6c65 2e0a 2020 2020 2020 2020 2020 2020  le..            \n+000230b0: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n+000230c0: 732e 2020 2028 6c69 6e65 2020 3431 290a  s.   (line  41).\n+000230d0: 2a20 7269 6768 742d 6861 6e64 2063 6f6f  * right-hand coo\n+000230e0: 7264 696e 6174 6520 7379 7374 656d 3a20  rdinate system: \n+000230f0: 2020 2020 2020 2020 2049 6e74 726f 6475           Introdu\n+00023100: 6374 696f 6e20 6279 2065 7861 6d70 6c65  ction by example\n+00023110: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020                  \n-00023150: 2020 286c 696e 6520 2031 3129 0a2a 2072    (line  11).* r\n-00023160: 6f74 6174 696f 6e3a 2020 2020 2020 2020  otation:        \n+00023150: 286c 696e 6520 2031 3129 0a2a 2072 6f74  (line  11).* rot\n+00023160: 6174 696f 6e3a 2020 2020 2020 2020 2020  ation:          \n 00023170: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023180: 2020 2020 2020 4f62 6a65 6374 2074 7261        Object tra\n-00023190: 6e73 666f 726d 732e 2020 2028 6c69 6e65  nsforms.   (line\n-000231a0: 2020 3339 290a 2a20 726f 7461 7469 6f6e    39).* rotation\n-000231b0: 2074 7261 6e73 666f 726d 3a20 2020 2020   transform:     \n-000231c0: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n-000231d0: 7261 6e73 666f 726d 206c 6974 6572 616c  ransform literal\n-000231e0: 732e 2020 286c 696e 6520 2031 3029 0a2a  s.  (line  10).*\n-000231f0: 2072 6f74 6174 696f 6e20 7472 616e 7366   rotation transf\n-00023200: 6f72 6d20 3c31 3e3a 2020 2020 2020 2020  orm <1>:        \n-00023210: 2020 2020 2020 2020 4120 6869 6572 6172          A hierar\n-00023220: 6368 6963 616c 206d 6f64 656c 2e0a 2020  chical model..  \n+00023180: 2020 2020 4f62 6a65 6374 2074 7261 6e73      Object trans\n+00023190: 666f 726d 732e 2020 2028 6c69 6e65 2020  forms.   (line  \n+000231a0: 3339 290a 2a20 726f 7461 7469 6f6e 2074  39).* rotation t\n+000231b0: 7261 6e73 666f 726d 3a20 2020 2020 2020  ransform:       \n+000231c0: 2020 2020 2020 2020 2020 2020 2054 7261               Tra\n+000231d0: 6e73 666f 726d 206c 6974 6572 616c 732e  nsform literals.\n+000231e0: 2020 286c 696e 6520 2031 3029 0a2a 2072    (line  10).* r\n+000231f0: 6f74 6174 696f 6e20 7472 616e 7366 6f72  otation transfor\n+00023200: 6d20 3c31 3e3a 2020 2020 2020 2020 2020  m <1>:          \n+00023210: 2020 2020 2020 4120 6869 6572 6172 6368        A hierarch\n+00023220: 6963 616c 206d 6f64 656c 2e0a 2020 2020  ical 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 2020 2020 286c 696e              (lin\n-00023270: 6520 2034 3829 0a2a 2072 6f74 6174 696f  e  48).* rotatio\n-00023280: 6e20 7472 616e 7366 6f72 6d20 3c32 3e3a  n transform <2>:\n-00023290: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000232a0: 4120 6869 6572 6172 6368 6963 616c 206d  A hierarchical m\n-000232b0: 6f64 656c 2e0a 2020 2020 2020 2020 2020  odel..          \n+00023260: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00023270: 2034 3829 0a2a 2072 6f74 6174 696f 6e20   48).* rotation \n+00023280: 7472 616e 7366 6f72 6d20 3c32 3e3a 2020  transform <2>:  \n+00023290: 2020 2020 2020 2020 2020 2020 2020 4120                A \n+000232a0: 6869 6572 6172 6368 6963 616c 206d 6f64  hierarchical mod\n+000232b0: 656c 2e0a 2020 2020 2020 2020 2020 2020  el..            \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: 2020 2020 286c 696e 6520 2035 3829 0a2a      (line  58).*\n-00023300: 2072 6f74 6174 696f 6e20 7472 616e 7366   rotation transf\n-00023310: 6f72 6d20 3c33 3e3a 2020 2020 2020 2020  orm <3>:        \n-00023320: 2020 2020 2020 2020 4120 6869 6572 6172          A hierar\n-00023330: 6368 6963 616c 206d 6f64 656c 2e0a 2020  chical model..  \n+000232f0: 2020 286c 696e 6520 2035 3829 0a2a 2072    (line  58).* r\n+00023300: 6f74 6174 696f 6e20 7472 616e 7366 6f72  otation transfor\n+00023310: 6d20 3c33 3e3a 2020 2020 2020 2020 2020  m <3>:          \n+00023320: 2020 2020 2020 4120 6869 6572 6172 6368        A hierarch\n+00023330: 6963 616c 206d 6f64 656c 2e0a 2020 2020  ical 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 2020 2020 286c 696e              (lin\n-00023380: 6520 2037 3829 0a2a 2072 6f74 6174 696f  e  78).* rotatio\n-00023390: 6e20 7472 616e 7366 6f72 6d20 3c34 3e3a  n transform <4>:\n-000233a0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000233b0: 4120 6869 6572 6172 6368 6963 616c 206d  A hierarchical m\n-000233c0: 6f64 656c 2e0a 2020 2020 2020 2020 2020  odel..          \n+00023370: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00023380: 2037 3829 0a2a 2072 6f74 6174 696f 6e20   78).* rotation \n+00023390: 7472 616e 7366 6f72 6d20 3c34 3e3a 2020  transform <4>:  \n+000233a0: 2020 2020 2020 2020 2020 2020 2020 4120                A \n+000233b0: 6869 6572 6172 6368 6963 616c 206d 6f64  hierarchical mod\n+000233c0: 656c 2e0a 2020 2020 2020 2020 2020 2020  el..            \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: 2020 2020 286c 696e 6520 2039 3329 0a2a      (line  93).*\n-00023410: 2072 6f74 6174 696f 6e2c 2063 656e 7465   rotation, cente\n-00023420: 7220 6f66 3a20 2020 2020 2020 2020 2020  r of:           \n-00023430: 2020 2020 2020 2020 4f62 6a65 6374 2074          Object t\n-00023440: 7261 6e73 666f 726d 732e 2020 2028 6c69  ransforms.   (li\n-00023450: 6e65 2020 2038 290a 2a20 726f 7461 7469  ne   8).* rotati\n-00023460: 6f6e 2c20 6365 6e74 6572 206f 6620 3c31  on, center of <1\n-00023470: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-00023480: 204e 6573 7465 6420 7377 6565 7073 2e20   Nested sweeps. \n-00023490: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n-000234a0: 0a2a 2072 756e 6e69 6e67 2073 6b65 7463  .* running sketc\n-000234b0: 683a 2020 2020 2020 2020 2020 2020 2020  h:              \n-000234c0: 2020 2020 2020 2020 2020 4865 6c6c 6f20            Hello \n-000234d0: 776f 726c 642e 2020 2020 2020 2020 2028  world.         (\n-000234e0: 6c69 6e65 2020 2039 290a 2a20 7363 616c  line   9).* scal\n-000234f0: 6172 2064 6566 696e 6974 696f 6e3a 2020  ar definition:  \n+00023400: 2020 286c 696e 6520 2039 3329 0a2a 2072    (line  93).* r\n+00023410: 6f74 6174 696f 6e2c 2063 656e 7465 7220  otation, center \n+00023420: 6f66 3a20 2020 2020 2020 2020 2020 2020  of:             \n+00023430: 2020 2020 2020 4f62 6a65 6374 2074 7261        Object tra\n+00023440: 6e73 666f 726d 732e 2020 2028 6c69 6e65  nsforms.   (line\n+00023450: 2020 2038 290a 2a20 726f 7461 7469 6f6e     8).* rotation\n+00023460: 2c20 6365 6e74 6572 206f 6620 3c31 3e3a  , center of <1>:\n+00023470: 2020 2020 2020 2020 2020 2020 2020 204e                 N\n+00023480: 6573 7465 6420 7377 6565 7073 2e20 2020  ested sweeps.   \n+00023490: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n+000234a0: 2072 756e 6e69 6e67 2073 6b65 7463 683a   running sketch:\n+000234b0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000234c0: 2020 2020 2020 2020 4865 6c6c 6f20 776f          Hello wo\n+000234d0: 726c 642e 2020 2020 2020 2020 2028 6c69  rld.         (li\n+000234e0: 6e65 2020 2039 290a 2a20 7363 616c 6172  ne   9).* scalar\n+000234f0: 2064 6566 696e 6974 696f 6e3a 2020 2020   definition:    \n 00023500: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023510: 2020 2053 7765 7074 206f 626a 6563 7473     Swept objects\n-00023520: 2e20 2020 2020 2020 286c 696e 6520 2031  .       (line  1\n-00023530: 3329 0a2a 2073 6361 6c61 7220 6c69 7465  3).* scalar lite\n-00023540: 7261 6c3a 2020 2020 2020 2020 2020 2020  ral:            \n-00023550: 2020 2020 2020 2020 2020 2020 5363 616c              Scal\n-00023560: 6172 206c 6974 6572 616c 732e 2020 2020  ar literals.    \n-00023570: 2028 6c69 6e65 2020 2036 290a 2a20 7363   (line   6).* sc\n-00023580: 616c 6172 2072 6566 6572 656e 6365 3a20  alar reference: \n+00023510: 2053 7765 7074 206f 626a 6563 7473 2e20   Swept objects. \n+00023520: 2020 2020 2020 286c 696e 6520 2031 3329        (line  13)\n+00023530: 0a2a 2073 6361 6c61 7220 6c69 7465 7261  .* scalar litera\n+00023540: 6c3a 2020 2020 2020 2020 2020 2020 2020  l:              \n+00023550: 2020 2020 2020 2020 2020 5363 616c 6172            Scalar\n+00023560: 206c 6974 6572 616c 732e 2020 2020 2028   literals.     (\n+00023570: 6c69 6e65 2020 2036 290a 2a20 7363 616c  line   6).* scal\n+00023580: 6172 2072 6566 6572 656e 6365 3a20 2020  ar reference:   \n 00023590: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000235a0: 2020 2020 2046 6f72 6d73 206f 6620 7265       Forms of re\n-000235b0: 6665 7265 6e63 6573 2e20 286c 696e 6520  ferences. (line \n-000235c0: 2031 3329 0a2a 2073 6361 6c65 2074 7261   13).* scale tra\n-000235d0: 6e73 666f 726d 3a20 2020 2020 2020 2020  nsform:         \n-000235e0: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n-000235f0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n-00023600: 2e20 2028 6c69 6e65 2020 3136 290a 2a20  .  (line  16).* \n-00023610: 7363 616c 6520 7472 616e 7366 6f72 6d20  scale transform \n-00023620: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n-00023630: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n-00023640: 206c 6974 6572 616c 732e 2020 286c 696e   literals.  (lin\n-00023650: 6520 2031 3729 0a2a 2073 6365 6e65 2064  e  17).* scene d\n-00023660: 6573 6372 6970 7469 6f6e 206c 616e 6775  escription langu\n-00023670: 6167 653a 2020 2020 2020 2020 2020 2020  age:            \n-00023680: 4c61 6e67 7561 6765 2062 6173 6963 732e  Language basics.\n-00023690: 2020 2020 2028 6c69 6e65 2020 2038 290a       (line   8).\n-000236a0: 2a20 7363 656e 6520 6465 7363 7269 7074  * scene descript\n-000236b0: 696f 6e20 6c61 6e67 7561 6765 203c 313e  ion language <1>\n-000236c0: 3a20 2020 2020 2020 2042 7569 6c64 696e  :        Buildin\n-000236d0: 6720 6120 6472 6177 696e 672e 2020 286c  g a drawing.  (l\n-000236e0: 696e 6520 2020 3729 0a2a 2073 636f 7065  ine   7).* scope\n-000236f0: 2c20 6964 656e 7469 6669 6572 3a20 2020  , identifier:   \n+000235a0: 2020 2046 6f72 6d73 206f 6620 7265 6665     Forms of refe\n+000235b0: 7265 6e63 6573 2e20 286c 696e 6520 2031  rences. (line  1\n+000235c0: 3329 0a2a 2073 6361 6c65 2074 7261 6e73  3).* scale trans\n+000235d0: 666f 726d 3a20 2020 2020 2020 2020 2020  form:           \n+000235e0: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n+000235f0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n+00023600: 2028 6c69 6e65 2020 3136 290a 2a20 7363   (line  16).* sc\n+00023610: 616c 6520 7472 616e 7366 6f72 6d20 3c31  ale transform <1\n+00023620: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+00023630: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n+00023640: 6974 6572 616c 732e 2020 286c 696e 6520  iterals.  (line \n+00023650: 2031 3729 0a2a 2073 6365 6e65 2064 6573   17).* scene des\n+00023660: 6372 6970 7469 6f6e 206c 616e 6775 6167  cription languag\n+00023670: 653a 2020 2020 2020 2020 2020 2020 4c61  e:            La\n+00023680: 6e67 7561 6765 2062 6173 6963 732e 2020  nguage basics.  \n+00023690: 2020 2028 6c69 6e65 2020 2038 290a 2a20     (line   8).* \n+000236a0: 7363 656e 6520 6465 7363 7269 7074 696f  scene descriptio\n+000236b0: 6e20 6c61 6e67 7561 6765 203c 313e 3a20  n language <1>: \n+000236c0: 2020 2020 2020 2042 7569 6c64 696e 6720         Building \n+000236d0: 6120 6472 6177 696e 672e 2020 286c 696e  a drawing.  (lin\n+000236e0: 6520 2020 3729 0a2a 2073 636f 7065 2c20  e   7).* scope, \n+000236f0: 6964 656e 7469 6669 6572 3a20 2020 2020  identifier:     \n 00023700: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023710: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n-00023720: 726d 732e 2020 2028 6c69 6e65 2020 3236  rms.   (line  26\n-00023730: 290a 2a20 7363 6f70 652c 2069 6465 6e74  ).* scope, ident\n-00023740: 6966 6965 7220 3c31 3e3a 2020 2020 2020  ifier <1>:      \n-00023750: 2020 2020 2020 2020 2020 2042 6c6f 636b             Block\n-00023760: 732e 2020 2020 2020 2020 2020 2020 2020  s.              \n-00023770: 286c 696e 6520 2031 3329 0a2a 2073 696d  (line  13).* sim\n-00023780: 706c 6520 6465 6669 6e69 7469 6f6e 3a20  ple definition: \n+00023710: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n+00023720: 732e 2020 2028 6c69 6e65 2020 3236 290a  s.   (line  26).\n+00023730: 2a20 7363 6f70 652c 2069 6465 6e74 6966  * scope, identif\n+00023740: 6965 7220 3c31 3e3a 2020 2020 2020 2020  ier <1>:        \n+00023750: 2020 2020 2020 2020 2042 6c6f 636b 732e           Blocks.\n+00023760: 2020 2020 2020 2020 2020 2020 2020 286c                (l\n+00023770: 696e 6520 2031 3329 0a2a 2073 696d 706c  ine  13).* simpl\n+00023780: 6520 6465 6669 6e69 7469 6f6e 3a20 2020  e definition:   \n 00023790: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000237a0: 2020 2020 466f 726d 7320 6f66 2064 6566      Forms of def\n-000237b0: 696e 6974 696f 6e73 2e0a 2020 2020 2020  initions..      \n+000237a0: 2020 466f 726d 7320 6f66 2064 6566 696e    Forms of defin\n+000237b0: 6974 696f 6e73 2e0a 2020 2020 2020 2020  itions..        \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 2020 2020 286c 696e 6520 2020          (line   \n-00023800: 3629 0a2a 2073 6f6c 6964 3a20 2020 2020  6).* solid:     \n+000237f0: 2020 2020 2020 286c 696e 6520 2020 3629        (line   6)\n+00023800: 0a2a 2073 6f6c 6964 3a20 2020 2020 2020  .* solid:       \n 00023810: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023820: 2020 2020 2020 2020 2020 2020 4472 6177              Draw\n-00023830: 696e 6720 6120 736f 6c69 642e 2020 2020  ing a solid.    \n-00023840: 2028 6c69 6e65 2020 2036 290a 2a20 7370   (line   6).* sp\n-00023850: 6563 6961 6c20 6172 6775 6d65 6e74 2073  ecial argument s\n-00023860: 7562 7374 6974 7574 696f 6e3a 2020 2020  ubstitution:    \n-00023870: 2020 2020 2053 7065 6369 616c 206f 626a       Special obj\n-00023880: 6563 7473 2e20 2020 2020 286c 696e 6520  ects.     (line \n-00023890: 2032 3829 0a2a 2073 7065 6369 616c 2061   28).* special a\n-000238a0: 7267 756d 656e 7420 7375 6273 7469 7475  rgument substitu\n-000238b0: 7469 6f6e 203c 313e 3a20 2020 2020 5370  tion <1>:     Sp\n-000238c0: 6563 6961 6c73 2e20 2020 2020 2020 2020  ecials.         \n-000238d0: 2020 2028 6c69 6e65 2020 3130 290a 2a20     (line  10).* \n-000238e0: 7370 6563 6961 6c20 6f62 6a65 6374 3a20  special object: \n+00023820: 2020 2020 2020 2020 2020 4472 6177 696e            Drawin\n+00023830: 6720 6120 736f 6c69 642e 2020 2020 2028  g a solid.     (\n+00023840: 6c69 6e65 2020 2036 290a 2a20 7370 6563  line   6).* spec\n+00023850: 6961 6c20 6172 6775 6d65 6e74 2073 7562  ial argument sub\n+00023860: 7374 6974 7574 696f 6e3a 2020 2020 2020  stitution:      \n+00023870: 2020 2053 7065 6369 616c 206f 626a 6563     Special objec\n+00023880: 7473 2e20 2020 2020 286c 696e 6520 2032  ts.     (line  2\n+00023890: 3829 0a2a 2073 7065 6369 616c 2061 7267  8).* special arg\n+000238a0: 756d 656e 7420 7375 6273 7469 7475 7469  ument substituti\n+000238b0: 6f6e 203c 313e 3a20 2020 2020 5370 6563  on <1>:     Spec\n+000238c0: 6961 6c73 2e20 2020 2020 2020 2020 2020  ials.           \n+000238d0: 2028 6c69 6e65 2020 3130 290a 2a20 7370   (line  10).* sp\n+000238e0: 6563 6961 6c20 6f62 6a65 6374 3a20 2020  ecial object:   \n 000238f0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023900: 2020 2020 2020 2053 7065 6369 616c 206f         Special o\n-00023910: 626a 6563 7473 2e20 2020 2020 286c 696e  bjects.     (lin\n-00023920: 6520 2020 3629 0a2a 2073 7065 6369 616c  e   6).* special\n-00023930: 206f 626a 6563 7473 3a20 2020 2020 2020   objects:       \n-00023940: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023950: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n-00023960: 696e 672e 2028 6c69 6e65 2020 3338 290a  ing. (line  38).\n-00023970: 2a20 7370 6c69 7474 696e 672c 206c 696e  * splitting, lin\n-00023980: 6520 616e 6420 7375 7266 6163 653a 2020  e and surface:  \n-00023990: 2020 2020 2020 2020 2048 656c 6c6f 2077           Hello w\n-000239a0: 6f72 6c64 2e20 2020 2020 2020 2020 286c  orld.         (l\n-000239b0: 696e 6520 2031 3929 0a2a 2073 706c 6974  ine  19).* split\n-000239c0: 7469 6e67 2c20 6c69 6e65 2061 6e64 2073  ting, line and s\n-000239d0: 7572 6661 6365 203c 313e 3a20 2020 2020  urface <1>:     \n-000239e0: 2020 4869 6464 656e 2073 7572 6661 6365    Hidden surface\n-000239f0: 2072 656d 6f76 616c 2e0a 2020 2020 2020   removal..      \n+00023900: 2020 2020 2053 7065 6369 616c 206f 626a       Special obj\n+00023910: 6563 7473 2e20 2020 2020 286c 696e 6520  ects.     (line \n+00023920: 2020 3629 0a2a 2073 7065 6369 616c 206f    6).* special o\n+00023930: 626a 6563 7473 3a20 2020 2020 2020 2020  bjects:         \n+00023940: 2020 2020 2020 2020 2020 2020 2020 4120                A \n+00023950: 7465 6368 6e69 6361 6c20 6472 6177 696e  technical drawin\n+00023960: 672e 2028 6c69 6e65 2020 3338 290a 2a20  g. (line  38).* \n+00023970: 7370 6c69 7474 696e 672c 206c 696e 6520  splitting, line \n+00023980: 616e 6420 7375 7266 6163 653a 2020 2020  and surface:    \n+00023990: 2020 2020 2020 2048 656c 6c6f 2077 6f72         Hello wor\n+000239a0: 6c64 2e20 2020 2020 2020 2020 286c 696e  ld.         (lin\n+000239b0: 6520 2031 3929 0a2a 2073 706c 6974 7469  e  19).* splitti\n+000239c0: 6e67 2c20 6c69 6e65 2061 6e64 2073 7572  ng, line and sur\n+000239d0: 6661 6365 203c 313e 3a20 2020 2020 2020  face <1>:       \n+000239e0: 4869 6464 656e 2073 7572 6661 6365 2072  Hidden surface r\n+000239f0: 656d 6f76 616c 2e0a 2020 2020 2020 2020  emoval..        \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 2020 2020 286c 696e 6520 2032          (line  2\n-00023a40: 3129 0a2a 2073 7562 7374 6974 7574 696f  1).* substitutio\n-00023a50: 6e2c 2073 7065 6369 616c 3a20 2020 2020  n, special:     \n-00023a60: 2020 2020 2020 2020 2020 2020 5370 6563              Spec\n-00023a70: 6961 6c20 6f62 6a65 6374 732e 2020 2020  ial objects.    \n-00023a80: 2028 6c69 6e65 2020 3238 290a 2a20 7375   (line  28).* su\n-00023a90: 7266 6163 653a 2020 2020 2020 2020 2020  rface:          \n+00023a30: 2020 2020 2020 286c 696e 6520 2032 3129        (line  21)\n+00023a40: 0a2a 2073 7562 7374 6974 7574 696f 6e2c  .* substitution,\n+00023a50: 2073 7065 6369 616c 3a20 2020 2020 2020   special:       \n+00023a60: 2020 2020 2020 2020 2020 5370 6563 6961            Specia\n+00023a70: 6c20 6f62 6a65 6374 732e 2020 2020 2028  l objects.     (\n+00023a80: 6c69 6e65 2020 3238 290a 2a20 7375 7266  line  28).* surf\n+00023a90: 6163 653a 2020 2020 2020 2020 2020 2020  ace:            \n 00023aa0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023ab0: 2020 2020 2050 6f6c 796c 696e 6520 7377       Polyline sw\n-00023ac0: 6565 7073 2e20 2020 2020 286c 696e 6520  eeps.     (line \n-00023ad0: 2020 3629 0a2a 2073 7765 6570 3a20 2020    6).* sweep:   \n+00023ab0: 2020 2050 6f6c 796c 696e 6520 7377 6565     Polyline swee\n+00023ac0: 7073 2e20 2020 2020 286c 696e 6520 2020  ps.     (line   \n+00023ad0: 3629 0a2a 2073 7765 6570 3a20 2020 2020  6).* sweep:     \n 00023ae0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023af0: 2020 2020 2020 2020 2020 2020 2020 5377                Sw\n-00023b00: 6570 7420 6f62 6a65 6374 732e 2020 2020  ept objects.    \n-00023b10: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n-00023b20: 7377 6570 7420 626f 636b 3a20 2020 2020  swept bock:     \n+00023af0: 2020 2020 2020 2020 2020 2020 5377 6570              Swep\n+00023b00: 7420 6f62 6a65 6374 732e 2020 2020 2020  t objects.      \n+00023b10: 2028 6c69 6e65 2020 2036 290a 2a20 7377   (line   6).* sw\n+00023b20: 6570 7420 626f 636b 3a20 2020 2020 2020  ept bock:       \n 00023b30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023b40: 2020 2020 2020 2053 7765 7074 2062 6c6f         Swept blo\n-00023b50: 636b 732e 2020 2020 2020 2020 286c 696e  cks.        (lin\n-00023b60: 6520 2020 3629 0a2a 2073 7765 7074 206c  e   6).* swept l\n-00023b70: 696e 653a 2020 2020 2020 2020 2020 2020  ine:            \n-00023b80: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023b90: 506f 6c79 6c69 6e65 2073 7765 6570 732e  Polyline sweeps.\n-00023ba0: 2020 2020 2028 6c69 6e65 2020 2036 290a       (line   6).\n-00023bb0: 2a20 7377 6570 7420 6c69 6e65 203c 313e  * swept line <1>\n-00023bc0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00023bd0: 2020 2020 2020 2020 2053 7765 7074 206c           Swept l\n-00023be0: 696e 6573 2e20 2020 2020 2020 2020 286c  ines.         (l\n-00023bf0: 696e 6520 2020 3629 0a2a 2073 7765 7074  ine   6).* swept\n-00023c00: 206c 696e 6520 3c32 3e3a 2020 2020 2020   line <2>:      \n+00023b40: 2020 2020 2053 7765 7074 2062 6c6f 636b       Swept block\n+00023b50: 732e 2020 2020 2020 2020 286c 696e 6520  s.        (line \n+00023b60: 2020 3629 0a2a 2073 7765 7074 206c 696e    6).* swept lin\n+00023b70: 653a 2020 2020 2020 2020 2020 2020 2020  e:              \n+00023b80: 2020 2020 2020 2020 2020 2020 2020 506f                Po\n+00023b90: 6c79 6c69 6e65 2073 7765 6570 732e 2020  lyline sweeps.  \n+00023ba0: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n+00023bb0: 7377 6570 7420 6c69 6e65 203c 313e 3a20  swept line <1>: \n+00023bc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023bd0: 2020 2020 2020 2053 7765 7074 206c 696e         Swept lin\n+00023be0: 6573 2e20 2020 2020 2020 2020 286c 696e  es.         (lin\n+00023bf0: 6520 2020 3629 0a2a 2073 7765 7074 206c  e   6).* swept l\n+00023c00: 696e 6520 3c32 3e3a 2020 2020 2020 2020  ine <2>:        \n 00023c10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023c20: 2020 4120 7465 6368 6e69 6361 6c20 6472    A technical dr\n-00023c30: 6177 696e 672e 2028 6c69 6e65 2020 3230  awing. (line  20\n-00023c40: 290a 2a20 7377 6570 7420 6f62 6a65 6374  ).* swept object\n-00023c50: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00023c60: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n-00023c70: 206f 626a 6563 7473 2e20 2020 2020 2020   objects.       \n-00023c80: 286c 696e 6520 2020 3629 0a2a 2073 7765  (line   6).* swe\n-00023c90: 7074 206f 626a 6563 7420 3c31 3e3a 2020  pt object <1>:  \n+00023c20: 4120 7465 6368 6e69 6361 6c20 6472 6177  A technical draw\n+00023c30: 696e 672e 2028 6c69 6e65 2020 3230 290a  ing. (line  20).\n+00023c40: 2a20 7377 6570 7420 6f62 6a65 6374 3a20  * swept object: \n+00023c50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023c60: 2020 2020 2020 2020 2053 7765 7074 206f           Swept o\n+00023c70: 626a 6563 7473 2e20 2020 2020 2020 286c  bjects.       (l\n+00023c80: 696e 6520 2020 3629 0a2a 2073 7765 7074  ine   6).* swept\n+00023c90: 206f 626a 6563 7420 3c31 3e3a 2020 2020   object <1>:    \n 00023ca0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023cb0: 2020 2020 5377 6565 7073 2e20 2020 2020      Sweeps.     \n-00023cc0: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n-00023cd0: 2039 290a 2a20 7377 6570 7420 706f 696e   9).* swept poin\n-00023ce0: 743a 2020 2020 2020 2020 2020 2020 2020  t:              \n-00023cf0: 2020 2020 2020 2020 2020 2020 2053 7765               Swe\n-00023d00: 7074 206f 626a 6563 7473 2e20 2020 2020  pt objects.     \n-00023d10: 2020 286c 696e 6520 2031 3129 0a2a 2073    (line  11).* s\n-00023d20: 7765 7074 2070 6f69 6e74 203c 313e 3a20  wept point <1>: \n+00023cb0: 2020 5377 6565 7073 2e20 2020 2020 2020    Sweeps.       \n+00023cc0: 2020 2020 2020 2028 6c69 6e65 2020 2039         (line   9\n+00023cd0: 290a 2a20 7377 6570 7420 706f 696e 743a  ).* swept point:\n+00023ce0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023cf0: 2020 2020 2020 2020 2020 2053 7765 7074             Swept\n+00023d00: 206f 626a 6563 7473 2e20 2020 2020 2020   objects.       \n+00023d10: 286c 696e 6520 2031 3129 0a2a 2073 7765  (line  11).* swe\n+00023d20: 7074 2070 6f69 6e74 203c 313e 3a20 2020  pt point <1>:   \n 00023d30: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023d40: 2020 2020 2020 5377 6570 7420 706f 696e        Swept poin\n-00023d50: 7473 2e20 2020 2020 2020 2028 6c69 6e65  ts.        (line\n-00023d60: 2020 2036 290a 2a20 7377 6570 7420 706f     6).* swept po\n-00023d70: 6c79 676f 6e3a 2020 2020 2020 2020 2020  lygon:          \n-00023d80: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n-00023d90: 6f6c 7967 6f6e 2073 7765 6570 732e 2020  olygon sweeps.  \n-00023da0: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-00023db0: 2073 7765 7074 2070 6f6c 7967 6f6e 203c   swept polygon <\n-00023dc0: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n-00023dd0: 2020 2020 2020 2020 4120 6869 6572 6172          A hierar\n-00023de0: 6368 6963 616c 206d 6f64 656c 2e0a 2020  chical model..  \n+00023d40: 2020 2020 5377 6570 7420 706f 696e 7473      Swept points\n+00023d50: 2e20 2020 2020 2020 2028 6c69 6e65 2020  .        (line  \n+00023d60: 2036 290a 2a20 7377 6570 7420 706f 6c79   6).* swept poly\n+00023d70: 676f 6e3a 2020 2020 2020 2020 2020 2020  gon:            \n+00023d80: 2020 2020 2020 2020 2020 2020 2050 6f6c               Pol\n+00023d90: 7967 6f6e 2073 7765 6570 732e 2020 2020  ygon sweeps.    \n+00023da0: 2020 286c 696e 6520 2020 3629 0a2a 2073    (line   6).* s\n+00023db0: 7765 7074 2070 6f6c 7967 6f6e 203c 313e  wept polygon <1>\n+00023dc0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00023dd0: 2020 2020 2020 4120 6869 6572 6172 6368        A hierarch\n+00023de0: 6963 616c 206d 6f64 656c 2e0a 2020 2020  ical 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 2020 2020 286c 696e              (lin\n-00023e30: 6520 3132 3229 0a2a 2074 6167 2064 6566  e 122).* tag def\n-00023e40: 696e 6974 696f 6e3a 2020 2020 2020 2020  inition:        \n-00023e50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023e60: 4465 6669 6e69 7469 6f6e 732e 2020 2020  Definitions.    \n-00023e70: 2020 2020 2028 6c69 6e65 2020 3138 290a       (line  18).\n-00023e80: 2a20 7461 6720 6465 6669 6e69 7469 6f6e  * tag definition\n-00023e90: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n-00023ea0: 2020 2020 2020 2020 2046 6f72 6d73 206f           Forms o\n-00023eb0: 6620 6465 6669 6e69 7469 6f6e 732e 0a20  f definitions.. \n+00023e20: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00023e30: 3132 3229 0a2a 2074 6167 2064 6566 696e  122).* tag defin\n+00023e40: 6974 696f 6e3a 2020 2020 2020 2020 2020  ition:          \n+00023e50: 2020 2020 2020 2020 2020 2020 2020 4465                De\n+00023e60: 6669 6e69 7469 6f6e 732e 2020 2020 2020  finitions.      \n+00023e70: 2020 2028 6c69 6e65 2020 3138 290a 2a20     (line  18).* \n+00023e80: 7461 6720 6465 6669 6e69 7469 6f6e 203c  tag definition <\n+00023e90: 313e 3a20 2020 2020 2020 2020 2020 2020  1>:             \n+00023ea0: 2020 2020 2020 2046 6f72 6d73 206f 6620         Forms of \n+00023eb0: 6465 6669 6e69 7469 6f6e 732e 0a20 2020  definitions..   \n 00023ec0: 2020 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 2020 2020 2028 6c69               (li\n-00023f00: 6e65 2020 2037 290a 2a20 7461 6720 6465  ne   7).* tag de\n-00023f10: 6669 6e69 7469 6f6e 203c 323e 3a20 2020  finition <2>:   \n-00023f20: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00023f30: 2043 6f6d 6d61 6e64 206c 696e 652e 2020   Command line.  \n-00023f40: 2020 2020 2020 286c 696e 6520 2035 3329        (line  53)\n-00023f50: 0a2a 2074 6167 2072 6566 6572 656e 6365  .* tag reference\n-00023f60: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00023f70: 2020 2020 2020 2020 2020 466f 726d 7320            Forms \n-00023f80: 6f66 2064 6566 696e 6974 696f 6e73 2e0a  of definitions..\n+00023ef0: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+00023f00: 2020 2037 290a 2a20 7461 6720 6465 6669     7).* tag defi\n+00023f10: 6e69 7469 6f6e 203c 323e 3a20 2020 2020  nition <2>:     \n+00023f20: 2020 2020 2020 2020 2020 2020 2020 2043                 C\n+00023f30: 6f6d 6d61 6e64 206c 696e 652e 2020 2020  ommand line.    \n+00023f40: 2020 2020 286c 696e 6520 2035 3329 0a2a      (line  53).*\n+00023f50: 2074 6167 2072 6566 6572 656e 6365 3a20   tag reference: \n+00023f60: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00023f70: 2020 2020 2020 2020 466f 726d 7320 6f66          Forms of\n+00023f80: 2064 6566 696e 6974 696f 6e73 2e0a 2020   definitions..  \n 00023f90: 2020 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 2020 2020 286c                (l\n-00023fd0: 696e 6520 2032 3029 0a2a 2074 6167 2072  ine  20).* tag r\n-00023fe0: 6566 6572 656e 6365 203c 313e 3a20 2020  eference <1>:   \n+00023fc0: 2020 2020 2020 2020 2020 2020 286c 696e              (lin\n+00023fd0: 6520 2032 3029 0a2a 2074 6167 2072 6566  e  20).* tag ref\n+00023fe0: 6572 656e 6365 203c 313e 3a20 2020 2020  erence <1>:     \n 00023ff0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024000: 2020 466f 726d 7320 6f66 2072 6566 6572    Forms of refer\n-00024010: 656e 6365 732e 2028 6c69 6e65 2020 3139  ences. (line  19\n-00024020: 290a 2a20 7465 6d70 6c61 7465 2c20 646f  ).* template, do\n-00024030: 6375 6d65 6e74 3a20 2020 2020 2020 2020  cument:         \n-00024040: 2020 2020 2020 2020 2020 2048 656c 6c6f             Hello\n-00024050: 2077 6f72 6c64 2e20 2020 2020 2020 2020   world.         \n-00024060: 286c 696e 6520 2033 3229 0a2a 2074 656d  (line  32).* tem\n-00024070: 706c 6174 652c 2064 6f63 756d 656e 7420  plate, document \n-00024080: 3c31 3e3a 2020 2020 2020 2020 2020 2020  <1>:            \n-00024090: 2020 2020 436f 6d6d 616e 6420 6c69 6e65      Command line\n-000240a0: 2e20 2020 2020 2020 2028 6c69 6e65 2020  .        (line  \n-000240b0: 3336 290a 2a20 7465 7472 6168 6564 726f  36).* tetrahedro\n-000240c0: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n-000240d0: 2020 2020 2020 2020 2020 2020 2044 7261               Dra\n-000240e0: 7769 6e67 2061 2073 6f6c 6964 2e20 2020  wing a solid.   \n-000240f0: 2020 286c 696e 6520 2020 3929 0a2a 2074    (line   9).* t\n-00024100: 6963 6b20 6f70 6572 6174 6f72 2028 2729  ick operator (')\n-00024110: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00024120: 2020 2020 2020 4166 6669 6e65 2061 7269        Affine ari\n-00024130: 7468 6d65 7469 632e 2020 2028 6c69 6e65  thmetic.   (line\n-00024140: 2020 3337 290a 2a20 7469 636b 206f 7065    37).* tick ope\n-00024150: 7261 746f 7220 2827 2920 3c31 3e3a 2020  rator (') <1>:  \n-00024160: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n-00024170: 776f 2d6f 7065 7261 6e64 2028 6269 6e61  wo-operand (bina\n-00024180: 7279 2920 666f 726d 732e 0a20 2020 2020  ry) forms..     \n+00024000: 466f 726d 7320 6f66 2072 6566 6572 656e  Forms of referen\n+00024010: 6365 732e 2028 6c69 6e65 2020 3139 290a  ces. (line  19).\n+00024020: 2a20 7465 6d70 6c61 7465 2c20 646f 6375  * template, docu\n+00024030: 6d65 6e74 3a20 2020 2020 2020 2020 2020  ment:           \n+00024040: 2020 2020 2020 2020 2048 656c 6c6f 2077           Hello w\n+00024050: 6f72 6c64 2e20 2020 2020 2020 2020 286c  orld.         (l\n+00024060: 696e 6520 2033 3229 0a2a 2074 656d 706c  ine  32).* templ\n+00024070: 6174 652c 2064 6f63 756d 656e 7420 3c31  ate, document <1\n+00024080: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n+00024090: 2020 436f 6d6d 616e 6420 6c69 6e65 2e20    Command line. \n+000240a0: 2020 2020 2020 2028 6c69 6e65 2020 3336         (line  36\n+000240b0: 290a 2a20 7465 7472 6168 6564 726f 6e3a  ).* tetrahedron:\n+000240c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000240d0: 2020 2020 2020 2020 2020 2044 7261 7769             Drawi\n+000240e0: 6e67 2061 2073 6f6c 6964 2e20 2020 2020  ng a solid.     \n+000240f0: 286c 696e 6520 2020 3929 0a2a 2074 6963  (line   9).* tic\n+00024100: 6b20 6f70 6572 6174 6f72 2028 2729 3a20  k operator ('): \n+00024110: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024120: 2020 2020 4166 6669 6e65 2061 7269 7468      Affine arith\n+00024130: 6d65 7469 632e 2020 2028 6c69 6e65 2020  metic.   (line  \n+00024140: 3337 290a 2a20 7469 636b 206f 7065 7261  37).* tick opera\n+00024150: 746f 7220 2827 2920 3c31 3e3a 2020 2020  tor (') <1>:    \n+00024160: 2020 2020 2020 2020 2020 2020 2054 776f               Two\n+00024170: 2d6f 7065 7261 6e64 2028 6269 6e61 7279  -operand (binary\n+00024180: 2920 666f 726d 732e 0a20 2020 2020 2020  ) 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 2020 2020 2028 6c69 6e65 2020           (line  \n-000241d0: 3431 290a 2a20 5469 6b5a 2f50 4746 3a20  41).* TikZ/PGF: \n+000241c0: 2020 2020 2020 2028 6c69 6e65 2020 3431         (line  41\n+000241d0: 290a 2a20 5469 6b5a 2f50 4746 3a20 2020  ).* TikZ/PGF:   \n 000241e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000241f0: 2020 2020 2020 2020 2020 2020 2041 626f               Abo\n-00024200: 7574 2073 6b65 7463 682e 2020 2020 2020  ut sketch.      \n-00024210: 2020 286c 696e 6520 2032 3229 0a2a 2074    (line  22).* t\n-00024220: 6f72 6f69 643a 2020 2020 2020 2020 2020  oroid:          \n+000241f0: 2020 2020 2020 2020 2020 2041 626f 7574             About\n+00024200: 2073 6b65 7463 682e 2020 2020 2020 2020   sketch.        \n+00024210: 286c 696e 6520 2032 3229 0a2a 2074 6f72  (line  22).* tor\n+00024220: 6f69 643a 2020 2020 2020 2020 2020 2020  oid:            \n 00024230: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024240: 2020 2020 2020 4e65 7374 6564 2073 7765        Nested swe\n-00024250: 6570 732e 2020 2020 2020 2028 6c69 6e65  eps.       (line\n-00024260: 2020 2038 290a 2a20 7472 616e 7366 6f72     8).* transfor\n-00024270: 6d3a 2020 2020 2020 2020 2020 2020 2020  m:              \n-00024280: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n-00024290: 626a 6563 7420 7472 616e 7366 6f72 6d73  bject transforms\n-000242a0: 2e20 2020 286c 696e 6520 2020 3629 0a2a  .   (line   6).*\n-000242b0: 2074 7261 6e73 666f 726d 203c 313e 3a20   transform <1>: \n+00024240: 2020 2020 4e65 7374 6564 2073 7765 6570      Nested sweep\n+00024250: 732e 2020 2020 2020 2028 6c69 6e65 2020  s.       (line  \n+00024260: 2038 290a 2a20 7472 616e 7366 6f72 6d3a   8).* transform:\n+00024270: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024280: 2020 2020 2020 2020 2020 2020 204f 626a               Obj\n+00024290: 6563 7420 7472 616e 7366 6f72 6d73 2e20  ect transforms. \n+000242a0: 2020 286c 696e 6520 2020 3629 0a2a 2074    (line   6).* t\n+000242b0: 7261 6e73 666f 726d 203c 313e 3a20 2020  ransform <1>:   \n 000242c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000242d0: 2020 2020 2020 2020 5477 6f2d 6f70 6572          Two-oper\n-000242e0: 616e 6420 2862 696e 6172 7929 2066 6f72  and (binary) for\n-000242f0: 6d73 2e0a 2020 2020 2020 2020 2020 2020  ms..            \n+000242d0: 2020 2020 2020 5477 6f2d 6f70 6572 616e        Two-operan\n+000242e0: 6420 2862 696e 6172 7929 2066 6f72 6d73  d (binary) forms\n+000242f0: 2e0a 2020 2020 2020 2020 2020 2020 2020  ..              \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 2020                  \n-00024330: 2020 286c 696e 6520 2032 3829 0a2a 2074    (line  28).* t\n-00024340: 7261 6e73 666f 726d 203c 323e 3a20 2020  ransform <2>:   \n+00024330: 286c 696e 6520 2032 3829 0a2a 2074 7261  (line  28).* tra\n+00024340: 6e73 666f 726d 203c 323e 3a20 2020 2020  nsform <2>:     \n 00024350: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024360: 2020 2020 2020 5377 6565 7073 2e20 2020        Sweeps.   \n-00024370: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n-00024380: 2020 3131 290a 2a20 7472 616e 7366 6f72    11).* transfor\n-00024390: 6d20 3c33 3e3a 2020 2020 2020 2020 2020  m <3>:          \n-000243a0: 2020 2020 2020 2020 2020 2020 2020 2052                 R\n-000243b0: 6570 6561 7473 2e20 2020 2020 2020 2020  epeats.         \n-000243c0: 2020 2020 286c 696e 6520 2020 3929 0a2a      (line   9).*\n-000243d0: 2074 7261 6e73 666f 726d 203c 343e 3a20   transform <4>: \n+00024360: 2020 2020 5377 6565 7073 2e20 2020 2020      Sweeps.     \n+00024370: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+00024380: 3131 290a 2a20 7472 616e 7366 6f72 6d20  11).* transform \n+00024390: 3c33 3e3a 2020 2020 2020 2020 2020 2020  <3>:            \n+000243a0: 2020 2020 2020 2020 2020 2020 2052 6570               Rep\n+000243b0: 6561 7473 2e20 2020 2020 2020 2020 2020  eats.           \n+000243c0: 2020 286c 696e 6520 2020 3929 0a2a 2074    (line   9).* t\n+000243d0: 7261 6e73 666f 726d 203c 343e 3a20 2020  ransform <4>:   \n 000243e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000243f0: 2020 2020 2020 2020 4f76 6572 7669 6577          Overview\n-00024400: 2e20 2020 2020 2020 2020 2020 2028 6c69  .            (li\n-00024410: 6e65 2020 2037 290a 2a20 7472 616e 7366  ne   7).* transf\n-00024420: 6f72 6d20 6465 6669 6e69 7469 6f6e 3a20  orm definition: \n-00024430: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024440: 204f 7665 7276 6965 772e 2020 2020 2020   Overview.      \n-00024450: 2020 2020 2020 286c 696e 6520 2033 3529        (line  35)\n-00024460: 0a2a 2074 7261 6e73 666f 726d 206c 6974  .* transform lit\n-00024470: 6572 616c 3a20 2020 2020 2020 2020 2020  eral:           \n-00024480: 2020 2020 2020 2020 2020 5472 616e 7366            Transf\n-00024490: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028  orm literals.  (\n-000244a0: 6c69 6e65 2020 2036 290a 2a20 7472 616e  line   6).* tran\n-000244b0: 7366 6f72 6d20 7265 6665 7265 6e63 653a  sform reference:\n+000243f0: 2020 2020 2020 4f76 6572 7669 6577 2e20        Overview. \n+00024400: 2020 2020 2020 2020 2020 2028 6c69 6e65             (line\n+00024410: 2020 2037 290a 2a20 7472 616e 7366 6f72     7).* transfor\n+00024420: 6d20 6465 6669 6e69 7469 6f6e 3a20 2020  m definition:   \n+00024430: 2020 2020 2020 2020 2020 2020 2020 204f                 O\n+00024440: 7665 7276 6965 772e 2020 2020 2020 2020  verview.        \n+00024450: 2020 2020 286c 696e 6520 2033 3529 0a2a      (line  35).*\n+00024460: 2074 7261 6e73 666f 726d 206c 6974 6572   transform liter\n+00024470: 616c 3a20 2020 2020 2020 2020 2020 2020  al:             \n+00024480: 2020 2020 2020 2020 5472 616e 7366 6f72          Transfor\n+00024490: 6d20 6c69 7465 7261 6c73 2e20 2028 6c69  m literals.  (li\n+000244a0: 6e65 2020 2036 290a 2a20 7472 616e 7366  ne   6).* transf\n+000244b0: 6f72 6d20 7265 6665 7265 6e63 653a 2020  orm reference:  \n 000244c0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-000244d0: 2020 2046 6f72 6d73 206f 6620 7265 6665     Forms of refe\n-000244e0: 7265 6e63 6573 2e20 286c 696e 6520 2031  rences. (line  1\n-000244f0: 3629 0a2a 2074 7261 6e73 666f 726d 2072  6).* transform r\n-00024500: 6566 6572 656e 6365 203c 313e 3a20 2020  eference <1>:   \n-00024510: 2020 2020 2020 2020 2020 2020 4f76 6572              Over\n-00024520: 7669 6577 2e20 2020 2020 2020 2020 2020  view.           \n-00024530: 2028 6c69 6e65 2020 3335 290a 2a20 7472   (line  35).* tr\n-00024540: 616e 7366 6f72 6d2c 2064 6972 6563 743a  ansform, direct:\n+000244d0: 2046 6f72 6d73 206f 6620 7265 6665 7265   Forms of refere\n+000244e0: 6e63 6573 2e20 286c 696e 6520 2031 3629  nces. (line  16)\n+000244f0: 0a2a 2074 7261 6e73 666f 726d 2072 6566  .* transform ref\n+00024500: 6572 656e 6365 203c 313e 3a20 2020 2020  erence <1>:     \n+00024510: 2020 2020 2020 2020 2020 4f76 6572 7669            Overvi\n+00024520: 6577 2e20 2020 2020 2020 2020 2020 2028  ew.            (\n+00024530: 6c69 6e65 2020 3335 290a 2a20 7472 616e  line  35).* tran\n+00024540: 7366 6f72 6d2c 2064 6972 6563 743a 2020  sform, direct:  \n 00024550: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024560: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n-00024570: 6974 6572 616c 732e 2020 286c 696e 6520  iterals.  (line \n-00024580: 2034 3729 0a2a 2074 7261 6e73 666f 726d   47).* transform\n-00024590: 2c20 6469 7265 6374 203c 313e 3a20 2020  , direct <1>:   \n-000245a0: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n-000245b0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n-000245c0: 2e20 2028 6c69 6e65 2020 3533 290a 2a20  .  (line  53).* \n-000245d0: 7472 616e 7366 6f72 6d2c 2072 6f74 6174  transform, rotat\n-000245e0: 696f 6e3a 2020 2020 2020 2020 2020 2020  ion:            \n-000245f0: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n-00024600: 206c 6974 6572 616c 732e 2020 286c 696e   literals.  (lin\n-00024610: 6520 2031 3029 0a2a 2074 7261 6e73 666f  e  10).* transfo\n-00024620: 726d 2c20 726f 7461 7469 6f6e 203c 313e  rm, rotation <1>\n-00024630: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00024640: 4120 6869 6572 6172 6368 6963 616c 206d  A hierarchical m\n-00024650: 6f64 656c 2e0a 2020 2020 2020 2020 2020  odel..          \n+00024560: 2020 2054 7261 6e73 666f 726d 206c 6974     Transform lit\n+00024570: 6572 616c 732e 2020 286c 696e 6520 2034  erals.  (line  4\n+00024580: 3729 0a2a 2074 7261 6e73 666f 726d 2c20  7).* transform, \n+00024590: 6469 7265 6374 203c 313e 3a20 2020 2020  direct <1>:     \n+000245a0: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n+000245b0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n+000245c0: 2028 6c69 6e65 2020 3533 290a 2a20 7472   (line  53).* tr\n+000245d0: 616e 7366 6f72 6d2c 2072 6f74 6174 696f  ansform, rotatio\n+000245e0: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n+000245f0: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n+00024600: 6974 6572 616c 732e 2020 286c 696e 6520  iterals.  (line \n+00024610: 2031 3029 0a2a 2074 7261 6e73 666f 726d   10).* transform\n+00024620: 2c20 726f 7461 7469 6f6e 203c 313e 3a20  , rotation <1>: \n+00024630: 2020 2020 2020 2020 2020 2020 2020 4120                A \n+00024640: 6869 6572 6172 6368 6963 616c 206d 6f64  hierarchical mod\n+00024650: 656c 2e0a 2020 2020 2020 2020 2020 2020  el..            \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: 2020 2020 286c 696e 6520 2034 3829 0a2a      (line  48).*\n-000246a0: 2074 7261 6e73 666f 726d 2c20 726f 7461   transform, rota\n-000246b0: 7469 6f6e 203c 323e 3a20 2020 2020 2020  tion <2>:       \n-000246c0: 2020 2020 2020 2020 4120 6869 6572 6172          A hierar\n-000246d0: 6368 6963 616c 206d 6f64 656c 2e0a 2020  chical model..  \n+00024690: 2020 286c 696e 6520 2034 3829 0a2a 2074    (line  48).* t\n+000246a0: 7261 6e73 666f 726d 2c20 726f 7461 7469  ransform, rotati\n+000246b0: 6f6e 203c 323e 3a20 2020 2020 2020 2020  on <2>:         \n+000246c0: 2020 2020 2020 4120 6869 6572 6172 6368        A hierarch\n+000246d0: 6963 616c 206d 6f64 656c 2e0a 2020 2020  ical 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 2020 2020 286c 696e              (lin\n-00024720: 6520 2035 3829 0a2a 2074 7261 6e73 666f  e  58).* transfo\n-00024730: 726d 2c20 726f 7461 7469 6f6e 203c 333e  rm, rotation <3>\n-00024740: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00024750: 4120 6869 6572 6172 6368 6963 616c 206d  A hierarchical m\n-00024760: 6f64 656c 2e0a 2020 2020 2020 2020 2020  odel..          \n+00024710: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00024720: 2035 3829 0a2a 2074 7261 6e73 666f 726d   58).* transform\n+00024730: 2c20 726f 7461 7469 6f6e 203c 333e 3a20  , rotation <3>: \n+00024740: 2020 2020 2020 2020 2020 2020 2020 4120                A \n+00024750: 6869 6572 6172 6368 6963 616c 206d 6f64  hierarchical mod\n+00024760: 656c 2e0a 2020 2020 2020 2020 2020 2020  el..            \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: 2020 2020 286c 696e 6520 2037 3829 0a2a      (line  78).*\n-000247b0: 2074 7261 6e73 666f 726d 2c20 726f 7461   transform, rota\n-000247c0: 7469 6f6e 203c 343e 3a20 2020 2020 2020  tion <4>:       \n-000247d0: 2020 2020 2020 2020 4120 6869 6572 6172          A hierar\n-000247e0: 6368 6963 616c 206d 6f64 656c 2e0a 2020  chical model..  \n+000247a0: 2020 286c 696e 6520 2037 3829 0a2a 2074    (line  78).* t\n+000247b0: 7261 6e73 666f 726d 2c20 726f 7461 7469  ransform, rotati\n+000247c0: 6f6e 203c 343e 3a20 2020 2020 2020 2020  on <4>:         \n+000247d0: 2020 2020 2020 4120 6869 6572 6172 6368        A hierarch\n+000247e0: 6963 616c 206d 6f64 656c 2e0a 2020 2020  ical 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 2020 2020 286c 696e              (lin\n-00024830: 6520 2039 3329 0a2a 2074 7261 6e73 666f  e  93).* transfo\n-00024840: 726d 2c20 7363 616c 653a 2020 2020 2020  rm, scale:      \n-00024850: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024860: 5472 616e 7366 6f72 6d20 6c69 7465 7261  Transform litera\n-00024870: 6c73 2e20 2028 6c69 6e65 2020 3136 290a  ls.  (line  16).\n-00024880: 2a20 7472 616e 7366 6f72 6d2c 2073 6361  * transform, sca\n-00024890: 6c65 203c 313e 3a20 2020 2020 2020 2020  le <1>:         \n-000248a0: 2020 2020 2020 2020 2054 7261 6e73 666f           Transfo\n-000248b0: 726d 206c 6974 6572 616c 732e 2020 286c  rm literals.  (l\n-000248c0: 696e 6520 2031 3729 0a2a 2074 7261 6e73  ine  17).* trans\n-000248d0: 666f 726d 2c20 7472 616e 736c 6174 696f  form, translatio\n-000248e0: 6e3a 2020 2020 2020 2020 2020 2020 2020  n:              \n-000248f0: 2020 4f62 6a65 6374 2074 7261 6e73 666f    Object transfo\n-00024900: 726d 732e 2020 2028 6c69 6e65 2020 3437  rms.   (line  47\n-00024910: 290a 2a20 7472 616e 7366 6f72 6d2c 2074  ).* transform, t\n-00024920: 7261 6e73 6c61 7469 6f6e 203c 313e 3a20  ranslation <1>: \n-00024930: 2020 2020 2020 2020 2020 2054 7261 6e73             Trans\n-00024940: 666f 726d 206c 6974 6572 616c 732e 2020  form literals.  \n-00024950: 286c 696e 6520 2031 3529 0a2a 2074 7261  (line  15).* tra\n-00024960: 6e73 666f 726d 2c20 7472 616e 736c 6174  nsform, translat\n-00024970: 696f 6e20 3c32 3e3a 2020 2020 2020 2020  ion <2>:        \n-00024980: 2020 2020 4120 6869 6572 6172 6368 6963      A hierarchic\n-00024990: 616c 206d 6f64 656c 2e0a 2020 2020 2020  al model..      \n+00024820: 2020 2020 2020 2020 2020 286c 696e 6520            (line \n+00024830: 2039 3329 0a2a 2074 7261 6e73 666f 726d   93).* transform\n+00024840: 2c20 7363 616c 653a 2020 2020 2020 2020  , scale:        \n+00024850: 2020 2020 2020 2020 2020 2020 2020 5472                Tr\n+00024860: 616e 7366 6f72 6d20 6c69 7465 7261 6c73  ansform literals\n+00024870: 2e20 2028 6c69 6e65 2020 3136 290a 2a20  .  (line  16).* \n+00024880: 7472 616e 7366 6f72 6d2c 2073 6361 6c65  transform, scale\n+00024890: 203c 313e 3a20 2020 2020 2020 2020 2020   <1>:           \n+000248a0: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n+000248b0: 206c 6974 6572 616c 732e 2020 286c 696e   literals.  (lin\n+000248c0: 6520 2031 3729 0a2a 2074 7261 6e73 666f  e  17).* transfo\n+000248d0: 726d 2c20 7472 616e 736c 6174 696f 6e3a  rm, translation:\n+000248e0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+000248f0: 4f62 6a65 6374 2074 7261 6e73 666f 726d  Object transform\n+00024900: 732e 2020 2028 6c69 6e65 2020 3437 290a  s.   (line  47).\n+00024910: 2a20 7472 616e 7366 6f72 6d2c 2074 7261  * transform, tra\n+00024920: 6e73 6c61 7469 6f6e 203c 313e 3a20 2020  nslation <1>:   \n+00024930: 2020 2020 2020 2020 2054 7261 6e73 666f           Transfo\n+00024940: 726d 206c 6974 6572 616c 732e 2020 286c  rm literals.  (l\n+00024950: 696e 6520 2031 3529 0a2a 2074 7261 6e73  ine  15).* trans\n+00024960: 666f 726d 2c20 7472 616e 736c 6174 696f  form, translatio\n+00024970: 6e20 3c32 3e3a 2020 2020 2020 2020 2020  n <2>:          \n+00024980: 2020 4120 6869 6572 6172 6368 6963 616c    A hierarchical\n+00024990: 206d 6f64 656c 2e0a 2020 2020 2020 2020   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 2020 2020 286c 696e 6520 2034          (line  4\n-000249e0: 3729 0a2a 2074 7261 6e73 666f 726d 2c20  7).* transform, \n-000249f0: 7669 6577 3a20 2020 2020 2020 2020 2020  view:           \n-00024a00: 2020 2020 2020 2020 2020 2020 5472 616e              Tran\n-00024a10: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20  sform literals. \n-00024a20: 2028 6c69 6e65 2020 3235 290a 2a20 7472   (line  25).* tr\n-00024a30: 616e 7366 6f72 6d2c 2076 6965 7720 3c31  ansform, view <1\n-00024a40: 3e3a 2020 2020 2020 2020 2020 2020 2020  >:              \n-00024a50: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n-00024a60: 6974 6572 616c 732e 2020 286c 696e 6520  iterals.  (line \n-00024a70: 2033 3529 0a2a 2074 7261 6e73 6c61 7469   35).* translati\n-00024a80: 6f6e 2074 7261 6e73 666f 726d 3a20 2020  on transform:   \n-00024a90: 2020 2020 2020 2020 2020 2020 2020 4f62                Ob\n-00024aa0: 6a65 6374 2074 7261 6e73 666f 726d 732e  ject transforms.\n-00024ab0: 2020 2028 6c69 6e65 2020 3437 290a 2a20     (line  47).* \n-00024ac0: 7472 616e 736c 6174 696f 6e20 7472 616e  translation tran\n-00024ad0: 7366 6f72 6d20 3c31 3e3a 2020 2020 2020  sform <1>:      \n-00024ae0: 2020 2020 2020 2054 7261 6e73 666f 726d         Transform\n-00024af0: 206c 6974 6572 616c 732e 2020 286c 696e   literals.  (lin\n-00024b00: 6520 2031 3529 0a2a 2074 7261 6e73 6c61  e  15).* transla\n-00024b10: 7469 6f6e 2074 7261 6e73 666f 726d 203c  tion transform <\n-00024b20: 323e 3a20 2020 2020 2020 2020 2020 2020  2>:             \n-00024b30: 4120 6869 6572 6172 6368 6963 616c 206d  A hierarchical m\n-00024b40: 6f64 656c 2e0a 2020 2020 2020 2020 2020  odel..          \n+000249d0: 2020 2020 2020 286c 696e 6520 2034 3729        (line  47)\n+000249e0: 0a2a 2074 7261 6e73 666f 726d 2c20 7669  .* transform, vi\n+000249f0: 6577 3a20 2020 2020 2020 2020 2020 2020  ew:             \n+00024a00: 2020 2020 2020 2020 2020 5472 616e 7366            Transf\n+00024a10: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028  orm literals.  (\n+00024a20: 6c69 6e65 2020 3235 290a 2a20 7472 616e  line  25).* tran\n+00024a30: 7366 6f72 6d2c 2076 6965 7720 3c31 3e3a  sform, view <1>:\n+00024a40: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024a50: 2020 2054 7261 6e73 666f 726d 206c 6974     Transform lit\n+00024a60: 6572 616c 732e 2020 286c 696e 6520 2033  erals.  (line  3\n+00024a70: 3529 0a2a 2074 7261 6e73 6c61 7469 6f6e  5).* translation\n+00024a80: 2074 7261 6e73 666f 726d 3a20 2020 2020   transform:     \n+00024a90: 2020 2020 2020 2020 2020 2020 4f62 6a65              Obje\n+00024aa0: 6374 2074 7261 6e73 666f 726d 732e 2020  ct transforms.  \n+00024ab0: 2028 6c69 6e65 2020 3437 290a 2a20 7472   (line  47).* tr\n+00024ac0: 616e 736c 6174 696f 6e20 7472 616e 7366  anslation transf\n+00024ad0: 6f72 6d20 3c31 3e3a 2020 2020 2020 2020  orm <1>:        \n+00024ae0: 2020 2020 2054 7261 6e73 666f 726d 206c       Transform l\n+00024af0: 6974 6572 616c 732e 2020 286c 696e 6520  iterals.  (line \n+00024b00: 2031 3529 0a2a 2074 7261 6e73 6c61 7469   15).* translati\n+00024b10: 6f6e 2074 7261 6e73 666f 726d 203c 323e  on transform <2>\n+00024b20: 3a20 2020 2020 2020 2020 2020 2020 4120  :             A \n+00024b30: 6869 6572 6172 6368 6963 616c 206d 6f64  hierarchical mod\n+00024b40: 656c 2e0a 2020 2020 2020 2020 2020 2020  el..            \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: 2020 2020 286c 696e 6520 2034 3729 0a2a      (line  47).*\n-00024b90: 2074 7261 6e73 7061 7265 6e63 793a 2020   transparency:  \n+00024b80: 2020 286c 696e 6520 2034 3729 0a2a 2074    (line  47).* t\n+00024b90: 7261 6e73 7061 7265 6e63 793a 2020 2020  ransparency:    \n 00024ba0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024bb0: 2020 2020 2020 2020 5472 616e 7370 6172          Transpar\n-00024bc0: 656e 6379 2e20 2020 2020 2020 2028 6c69  ency.        (li\n-00024bd0: 6e65 2020 2036 290a 2a20 7477 6f2d 6f70  ne   6).* two-op\n-00024be0: 6572 616e 6420 666f 726d 3a20 2020 2020  erand form:     \n-00024bf0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024c00: 2054 776f 2d6f 7065 7261 6e64 2028 6269   Two-operand (bi\n-00024c10: 6e61 7279 2920 666f 726d 732e 0a20 2020  nary) forms..   \n+00024bb0: 2020 2020 2020 5472 616e 7370 6172 656e        Transparen\n+00024bc0: 6379 2e20 2020 2020 2020 2028 6c69 6e65  cy.        (line\n+00024bd0: 2020 2036 290a 2a20 7477 6f2d 6f70 6572     6).* two-oper\n+00024be0: 616e 6420 666f 726d 3a20 2020 2020 2020  and form:       \n+00024bf0: 2020 2020 2020 2020 2020 2020 2020 2054                 T\n+00024c00: 776f 2d6f 7065 7261 6e64 2028 6269 6e61  wo-operand (bina\n+00024c10: 7279 2920 666f 726d 732e 0a20 2020 2020  ry) 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 2020 2020 2028 6c69 6e65             (line\n-00024c60: 2020 2036 290a 2a20 756e 6172 7920 666f     6).* unary fo\n-00024c70: 726d 3a20 2020 2020 2020 2020 2020 2020  rm:             \n-00024c80: 2020 2020 2020 2020 2020 2020 2020 2055                 U\n-00024c90: 6e61 7279 2066 6f72 6d73 2e20 2020 2020  nary forms.     \n-00024ca0: 2020 2020 286c 696e 6520 2020 3629 0a2a      (line   6).*\n-00024cb0: 2076 6563 746f 723a 2020 2020 2020 2020   vector:        \n+00024c50: 2020 2020 2020 2020 2028 6c69 6e65 2020           (line  \n+00024c60: 2036 290a 2a20 756e 6172 7920 666f 726d   6).* unary form\n+00024c70: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n+00024c80: 2020 2020 2020 2020 2020 2020 2055 6e61               Una\n+00024c90: 7279 2066 6f72 6d73 2e20 2020 2020 2020  ry forms.       \n+00024ca0: 2020 286c 696e 6520 2020 3629 0a2a 2076    (line   6).* v\n+00024cb0: 6563 746f 723a 2020 2020 2020 2020 2020  ector:          \n 00024cc0: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024cd0: 2020 2020 2020 2020 4f62 6a65 6374 2074          Object t\n-00024ce0: 7261 6e73 666f 726d 732e 2020 2028 6c69  ransforms.   (li\n-00024cf0: 6e65 2020 3438 290a 2a20 7665 6374 6f72  ne  48).* vector\n-00024d00: 2064 6566 696e 6974 696f 6e3a 2020 2020   definition:    \n-00024d10: 2020 2020 2020 2020 2020 2020 2020 2020                  \n-00024d20: 2050 6f6c 796c 696e 6520 7377 6565 7073   Polyline sweeps\n-00024d30: 2e20 2020 2020 286c 696e 6520 2031 3929  .     (line  19)\n-00024d40: 0a2a 2076 6563 746f 7220 6c69 7465 7261  .* vector litera\n-00024d50: 6c3a 2020 2020 2020 2020 2020 2020 2020  l:              \n-00024d60: 2020 2020 2020 2020 2020 506f 696e 7420            Point \n-00024d70: 616e 6420 7665 6374 6f72 206c 6974 6572  and vector liter\n-00024d80: 616c 732e 0a20 2020 2020 2020 2020 2020  als..           \n+00024cd0: 2020 2020 2020 4f62 6a65 6374 2074 7261        Object tra\n+00024ce0: 6e73 666f 726d 732e 2020 2028 6c69 6e65  nsforms.   (line\n+00024cf0: 2020 3438 290a 2a20 7665 6374 6f72 2064    48).* vector d\n+00024d00: 6566 696e 6974 696f 6e3a 2020 2020 2020  efinition:      \n+00024d10: 2020 2020 2020 2020 2020 2020 2020 2050                 P\n+00024d20: 6f6c 796c 696e 6520 7377 6565 7073 2e20  olyline sweeps. \n+00024d30: 2020 2020 286c 696e 6520 2031 3929 0a2a      (line  19).*\n+00024d40: 2076 6563 746f 7220 6c69 7465 7261 6c3a   vector literal:\n+00024d50: 2020 2020 2020 2020 2020 2020 2020 2020                  \n+00024d60: 2020 2020 2020 2020 506f 696e 7420 616e          Point an\n+00024d70: 6420 7665 6374 6f72 206c 6974 6572 616c  d vector literal\n+00024d80: 732e 0a20 2020 2020 2020 2020 2020 2020  s..             \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 2020                  \n-00024dc0: 2020 2028 6c69 6e65 2020 2036 290a 2a20     (line   6).* \n-00024dd0: 7665 6374 6f72 2072 6566 6572 656e 6365  vector reference\n-00024de0: 3a20 2020 2020 2020 2020 2020 2020 2020  :               \n-00024df0: 2020 2020 2020 2046 6f72 6d73 206f 6620         Forms of \n-00024e00: 7265 6665 7265 6e63 6573 2e20 286c 696e  references. 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{}", "unified_diff": "@@ -113,16 +113,16 @@\n   0x0001a6e0 66746572 202d5470 2c202725 63270000 fter -Tp, '%c'..\n   0x0001a6f0 756e7265 636f676e 697a6564 206d6f64 unrecognized mod\n   0x0001a700 69666965 72206f66 206f7074 696f6e20 ifier of option \n   0x0001a710 272d5425 63270000 6d697373 696e6720 '-T%c'..missing \n   0x0001a720 50535472 69636b73 206f7220 54696b5a PSTricks or TikZ\n   0x0001a730 20766572 73696f6e 20616674 6572202d  version after -\n   0x0001a740 56000000 302e3320 28627569 6c642037 V...0.3 (build 7\n-  0x0001a750 642c2054 75652046 65622031 38203030 d, Tue Feb 18 00\n-  0x0001a760 3a33323a 30322032 30323529 00000000 :32:02 2025)....\n+  0x0001a750 642c2054 7565204a 616e2031 36203138 d, Tue Jan 16 18\n+  0x0001a760 3a31333a 31392032 30323429 00000000 :13:19 2024)....\n   0x0001a770 25252061 7373756d 65732050 53547269 %% assumes PSTri\n   0x0001a780 636b7320 76657273 696f6e20 25730a00 cks version %s..\n   0x0001a790 25252075 7365202d 5620746f 2073656c %% use -V to sel\n   0x0001a7a0 65637420 6561726c 69657220 76657273 ect earlier vers\n   0x0001a7b0 696f6e73 0a000000 61647661 6e63655f ions....advance_\n   0x0001a7c0 746f5f6e 6578745f 66696c65 5f6e616d to_next_file_nam\n   0x0001a7d0 653a2075 6e657870 65637465 64206f70 e: unexpected op\n@@ -246,16 +246,16 @@\n   0x0001af30 65636961 6c206172 67202874 72792023 ecial arg (try #\n   0x0001af40 23290000 63616e27 74206f70 656e2064 #)..can't open d\n   0x0001af50 6f63756d 656e7420 74656d70 6c617465 ocument template\n   0x0001af60 20272573 25272066 6f722069 6e707574  '%s%' for input\n   0x0001af70 0a000000 25252053 6b657463 68206f75 ....%% Sketch ou\n   0x0001af80 74707574 2c207665 7273696f 6e20302e tput, version 0.\n   0x0001af90 33202862 75696c64 2037642c 20547565 3 (build 7d, Tue\n-  0x0001afa0 20466562 20313820 30303a33 323a3032  Feb 18 00:32:02\n-  0x0001afb0 20323032 35290a25 25204f75 74707574  2025).%% Output\n+  0x0001afa0 204a616e 20313620 31383a31 333a3139  Jan 16 18:13:19\n+  0x0001afb0 20323032 34290a25 25204f75 74707574  2024).%% Output\n   0x0001afc0 206c616e 67756167 653a2025 730a0000  language: %s...\n   0x0001afd0 646f6375 6d656e74 2074656d 706c6174 document templat\n   0x0001afe0 65207769 7468206e 6f206573 63617065 e with no escape\n   0x0001aff0 20272573 27206861 73206265 656e2069  '%s' has been i\n   0x0001b000 676e6f72 65640000 6d6f7265 20746861 gnored..more tha\n   0x0001b010 6e206f6e 65206573 63617065 20696e20 n one escape in \n   0x0001b020 646f6375 6d656e74 2074656d 706c6174 document templat\n"}, {"source1": "readelf --wide --decompress --hex-dump=.gnu_debuglink {}", "source2": "readelf --wide --decompress --hex-dump=.gnu_debuglink {}", "comments": ["error from `readelf --wide --decompress --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 39643230 61633332 64656566 64386164 9d20ac32deefd8ad\n-  0x00000010 31366365 65636433 36326332 37616362 16ceecd362c27acb\n-  0x00000020 34383964 36302e64 65627567 00000000 489d60.debug....\n-  0x00000030 f3228db0                            .\"..\n+  0x00000000 36316337 30623333 37376637 33363536 61c70b3377f73656\n+  0x00000010 61663230 38316634 65613831 30333336 af2081f4ea810336\n+  0x00000020 32326561 39622e64 65627567 00000000 22ea9b.debug....\n+  0x00000030 be0ad7eb                            ....\n \n"}]}]}]}]}, {"source1": "sketch-dbgsym_0.3.7-12_i386.deb", "source2": "sketch-dbgsym_0.3.7-12_i386.deb", "unified_diff": null, "details": [{"source1": "file list", "source2": "file list", "unified_diff": "@@ -1,3 +1,3 @@\n -rw-r--r--   0        0        0        4 2020-11-07 02:36:18.000000 debian-binary\n -rw-r--r--   0        0        0      532 2020-11-07 02:36:18.000000 control.tar.xz\n--rw-r--r--   0        0        0   169460 2020-11-07 02:36:18.000000 data.tar.xz\n+-rw-r--r--   0        0        0   169452 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": "./control", "source2": "./control", "unified_diff": "@@ -5,8 +5,8 @@\n Architecture: i386\n Maintainer: Debian Science Maintainers <debian-science-maintainers@lists.alioth.debian.org>\n Installed-Size: 195\n Depends: sketch (= 1:0.3.7-12)\n Section: debug\n Priority: optional\n Description: debug symbols for sketch\n-Build-Ids: c29d20ac32deefd8ad16ceecd362c27acb489d60\n+Build-Ids: 6f61c70b3377f73656af2081f4ea81033622ea9b\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/c2/9d20ac32deefd8ad16ceecd362c27acb489d60.debug\n+usr/lib/debug/.build-id/6f/61c70b3377f73656af2081f4ea81033622ea9b.debug\n"}]}]}]}, {"source1": "data.tar.xz", "source2": "data.tar.xz", "unified_diff": null, "details": [{"source1": "data.tar", "source2": "data.tar", "unified_diff": null, "details": [{"source1": "file list", "source2": "file list", "unified_diff": "@@ -1,10 +1,10 @@\n drwxr-xr-x   0 root         (0) root         (0)        0 2020-11-07 02:36:18.000000 ./\n drwxr-xr-x   0 root         (0) root         (0)        0 2020-11-07 02:36:18.000000 ./usr/\n drwxr-xr-x   0 root         (0) root         (0)        0 2020-11-07 02:36:18.000000 ./usr/lib/\n drwxr-xr-x   0 root         (0) root         (0)        0 2020-11-07 02:36:18.000000 ./usr/lib/debug/\n drwxr-xr-x   0 root         (0) root         (0)        0 2020-11-07 02:36:18.000000 ./usr/lib/debug/.build-id/\n-drwxr-xr-x   0 root         (0) root         (0)        0 2020-11-07 02:36:18.000000 ./usr/lib/debug/.build-id/c2/\n--rw-r--r--   0 root         (0) root         (0)   188488 2020-11-07 02:36:18.000000 ./usr/lib/debug/.build-id/c2/9d20ac32deefd8ad16ceecd362c27acb489d60.debug\n+drwxr-xr-x   0 root         (0) root         (0)        0 2020-11-07 02:36:18.000000 ./usr/lib/debug/.build-id/6f/\n+-rw-r--r--   0 root         (0) root         (0)   188488 2020-11-07 02:36:18.000000 ./usr/lib/debug/.build-id/6f/61c70b3377f73656af2081f4ea81033622ea9b.debug\n drwxr-xr-x   0 root         (0) root         (0)        0 2020-11-07 02:36:18.000000 ./usr/share/\n drwxr-xr-x   0 root         (0) root         (0)        0 2020-11-07 02:36:18.000000 ./usr/share/doc/\n lrwxrwxrwx   0 root         (0) root         (0)        0 2020-11-07 02:36:18.000000 ./usr/share/doc/sketch-dbgsym -> sketch\n"}, {"source1": "./usr/lib/debug/.build-id/c2/9d20ac32deefd8ad16ceecd362c27acb489d60.debug", "source2": "./usr/lib/debug/.build-id/6f/61c70b3377f73656af2081f4ea81033622ea9b.debug", "comments": ["File has been modified after NT_GNU_BUILD_ID has been applied.", "Files 0% similar despite different names"], "unified_diff": null, "details": [{"source1": "readelf --wide --notes {}", "source2": "readelf --wide --notes {}", "comments": ["error from `readelf --wide --notes {}`:", "readelf: Error: Unable to find program interpreter name"], "unified_diff": "@@ -1,8 +1,8 @@\n \n Displaying notes found in: .note.gnu.build-id\n   Owner                Data size \tDescription\n-  GNU                  0x00000014\tNT_GNU_BUILD_ID (unique build ID bitstring)\t    Build ID: c29d20ac32deefd8ad16ceecd362c27acb489d60\n+  GNU                  0x00000014\tNT_GNU_BUILD_ID (unique build ID bitstring)\t    Build ID: 6f61c70b3377f73656af2081f4ea81033622ea9b\n \n Displaying notes found in: .note.ABI-tag\n   Owner                Data size \tDescription\n   GNU                  0x00000010\tNT_GNU_ABI_TAG (ABI version tag)\t    OS: Linux, ABI: 3.2.0\n"}]}]}]}]}]}