{"diffoscope-json-version": 1, "source1": "/srv/reproducible-results/rbuild-debian/r-b-build.OjGYvgV4/b1/sketch_0.3.7-13_amd64.changes", "source2": "/srv/reproducible-results/rbuild-debian/r-b-build.OjGYvgV4/b2/sketch_0.3.7-13_amd64.changes", "unified_diff": null, "details": [{"source1": "Files", "source2": "Files", "unified_diff": "@@ -1,4 +1,4 @@\n \n- 2d3893da88857ab6fe4e889a15562458 199012 debug optional sketch-dbgsym_0.3.7-13_amd64.deb\n- a28b35e057a4bcc0e07518b0f74e4726 1164592 doc optional sketch-doc_0.3.7-13_all.deb\n- 8f170211d08171542d965243cf17df70 64012 graphics optional sketch_0.3.7-13_amd64.deb\n+ b4b709efc0549e9df8d91b24806656ba 199012 debug optional sketch-dbgsym_0.3.7-13_amd64.deb\n+ 96c18ff0ed05147a00c97e42a557779f 1164624 doc optional sketch-doc_0.3.7-13_all.deb\n+ 7c034e7cf152efa02d70fcce60b28292 63960 graphics optional sketch_0.3.7-13_amd64.deb\n"}, {"source1": "sketch-doc_0.3.7-13_all.deb", "source2": "sketch-doc_0.3.7-13_all.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 2025-10-25 10:55:00.000000 debian-binary\n -rw-r--r-- 0 0 0 4276 2025-10-25 10:55:00.000000 control.tar.xz\n--rw-r--r-- 0 0 0 1160124 2025-10-25 10:55:00.000000 data.tar.xz\n+-rw-r--r-- 0 0 0 1160156 2025-10-25 10:55:00.000000 data.tar.xz\n"}, {"source1": "control.tar.xz", "source2": "control.tar.xz", "unified_diff": null, "details": [{"source1": "control.tar", "source2": "control.tar", "unified_diff": null, "details": [{"source1": "./md5sums", "source2": "./md5sums", "unified_diff": null, "details": [{"source1": "./md5sums", "source2": "./md5sums", "comments": ["Files differ"], "unified_diff": null}]}]}]}, {"source1": "data.tar.xz", "source2": "data.tar.xz", "unified_diff": null, "details": [{"source1": "data.tar", "source2": "data.tar", "unified_diff": null, "details": [{"source1": "file list", "source2": "file list", "unified_diff": "@@ -128,12 +128,12 @@\n -rw-r--r-- 0 root (0) root (0) 2431 2025-10-25 10:55:00.000000 ./usr/share/doc/sketch-doc/sketch/ex220.png\n -rw-r--r-- 0 root (0) root (0) 2846 2025-10-25 10:55:00.000000 ./usr/share/doc/sketch-doc/sketch/ex230.png\n -rw-r--r-- 0 root (0) root (0) 3579 2025-10-25 10:55:00.000000 ./usr/share/doc/sketch-doc/sketch/ex240.png\n -rw-r--r-- 0 root (0) root (0) 2116 2025-10-25 10:55:00.000000 ./usr/share/doc/sketch-doc/sketch/ex250.png\n -rw-r--r-- 0 root (0) root (0) 2032 2025-10-25 10:55:00.000000 ./usr/share/doc/sketch-doc/sketch/ex260.png\n -rw-r--r-- 0 root (0) root (0) 66246 2012-02-25 02:28:13.000000 ./usr/share/doc/sketch-doc/sketch/index.html\n -rw-r--r-- 0 root (0) root (0) 9205 2025-10-25 10:55:00.000000 ./usr/share/doc/sketch-doc/sketch/transparent.png\n--rw-r--r-- 0 root (0) root (0) 706954 2025-10-25 10:55:00.000000 ./usr/share/doc/sketch-doc/sketch.pdf.gz\n+-rw-r--r-- 0 root (0) root (0) 706992 2025-10-25 10:55:00.000000 ./usr/share/doc/sketch-doc/sketch.pdf.gz\n drwxr-xr-x 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/share/doc-base/\n -rw-r--r-- 0 root (0) root (0) 398 2025-10-25 09:00:00.000000 ./usr/share/doc-base/sketch-doc.sketch\n drwxr-xr-x 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/share/info/\n--rw-r--r-- 0 root (0) root (0) 40123 2025-10-25 10:55:00.000000 ./usr/share/info/sketch.info.gz\n+-rw-r--r-- 0 root (0) root (0) 40126 2025-10-25 10:55:00.000000 ./usr/share/info/sketch.info.gz\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), Friday, November 27, 2026\n+Version 0.3 (build 7), Sunday, October 26, 2025\n \n Gene Ressler\n \n \fCopyright c 2005 to 2012 Eugene K. Ressler.\n-This manual is for sketch, version 0.3 (build 7), Friday, November 27, 2026, a program that\n+This manual is for sketch, version 0.3 (build 7), Sunday, October 26, 2025, 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. You can redistribute it and/or modify it under the terms of the\n GNU General Public License as published by the Free Software Foundation; either version\n 3, or (at your option) any later version.\n Sketch is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;\n"}]}]}, {"source1": "./usr/share/info/sketch.info.gz", "source2": "./usr/share/info/sketch.info.gz", "unified_diff": null, "details": [{"source1": "sketch.info", "source2": "sketch.info", "has_internal_linenos": true, "unified_diff": "@@ -5,9794 +5,9793 @@\n 00000040: 682e 7465 7869 2e0a 0a43 6f70 7972 6967 h.texi...Copyrig\n 00000050: 6874 20c2 a920 3230 3035 2074 6f20 3230 ht .. 2005 to 20\n 00000060: 3132 2045 7567 656e 6520 4b2e 2052 6573 12 Eugene K. Res\n 00000070: 736c 6572 2e0a 0a20 2020 5468 6973 206d sler... 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4b65 7920 r things..* Key \n-00001020: 616e 6420 7265 7365 7276 6564 2077 6f72 and reserved wor\n-00001030: 6473 3a3a 2020 2020 2020 4e61 6d65 7320 ds:: Names \n-00001040: 796f 7520 7368 6f75 6c64 6e27 7420 7573 you shouldn't us\n-00001050: 652e 0a2a 204c 6974 6572 616c 733a 3a20 e..* Literals:: \n+000000b0: 2c20 5375 6e64 6179 2c20 4f63 746f 6265 , Sunday, Octobe\n+000000c0: 720a 3236 2c20 3230 3235 2c20 6120 7072 r.26, 2025, a pr\n+000000d0: 6f67 7261 6d20 7468 6174 2063 6f6e 7665 ogram that conve\n+000000e0: 7274 7320 6465 7363 7269 7074 696f 6e73 rts descriptions\n+000000f0: 206f 6620 7369 6d70 6c65 0a74 6872 6565 of simple.three\n+00000100: 2d64 696d 656e 7369 6f6e 616c 2073 6365 -dimensional sce\n+00000110: 6e65 7320 696e 746f 206c 696e 6520 6472 nes into line dr\n+00000120: 6177 696e 6773 2e20 2054 6869 7320 7665 awings. 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You can redi\n+000001d0: 7374 7269 6275 7465 2069 7420 616e 642f stribute it and/\n+000001e0: 6f72 206d 6f64 6966 7920 6974 0a75 6e64 or modify it.und\n+000001f0: 6572 2074 6865 2074 6572 6d73 206f 6620 er the terms of \n+00000200: 7468 6520 474e 5520 4765 6e65 7261 6c20 the GNU General \n+00000210: 5075 626c 6963 204c 6963 656e 7365 2061 Public License a\n+00000220: 7320 7075 626c 6973 6865 6420 6279 2074 s published by t\n+00000230: 6865 0a46 7265 6520 536f 6674 7761 7265 he.Free Software\n+00000240: 2046 6f75 6e64 6174 696f 6e3b 2065 6974 Foundation; eit\n+00000250: 6865 7220 7665 7273 696f 6e20 332c 206f her version 3, o\n+00000260: 7220 2861 7420 796f 7572 206f 7074 696f r (at your optio\n+00000270: 6e29 2061 6e79 0a6c 6174 6572 2076 6572 n) any.later ver\n+00000280: 7369 6f6e 2e0a 0a20 2020 536b 6574 6368 sion... 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See the \n+00000340: 474e 5520 4765 6e65 7261 6c20 5075 626c GNU General Publ\n+00000350: 6963 204c 6963 656e 7365 2066 6f72 0a6d ic License for.m\n+00000360: 6f72 6520 6465 7461 696c 732e 0a0a 2020 ore details... \n+00000370: 2059 6f75 2073 686f 756c 6420 6861 7665 You should have\n+00000380: 2072 6563 6569 7665 6420 6120 636f 7079 received a copy\n+00000390: 206f 6620 7468 6520 474e 5520 4765 6e65 of the GNU Gene\n+000003a0: 7261 6c20 5075 626c 6963 204c 6963 656e ral Public Licen\n+000003b0: 7365 0a61 6c6f 6e67 2077 6974 6820 e280 se.along with ..\n+000003c0: 9873 6b65 7463 68e2 8099 3b20 7365 6520 .sketch...; see \n+000003d0: 7468 6520 6669 6c65 2043 4f50 5949 4e47 the file COPYING\n+000003e0: 2e74 7874 2e20 2049 6620 6e6f 742c 2073 .txt. If not, s\n+000003f0: 6565 0a68 7474 703a 2f2f 7777 772e 676e ee.http://www.gn\n+00000400: 752e 6f72 672f 636f 7079 6c65 6674 2e0a u.org/copyleft..\n+00000410: 0a49 4e46 4f2d 4449 522d 5345 4354 494f .INFO-DIR-SECTIO\n+00000420: 4e20 5465 580a 5354 4152 542d 494e 464f N TeX.START-INFO\n+00000430: 2d44 4952 2d45 4e54 5259 0a2a 2053 6b65 -DIR-ENTRY.* Ske\n+00000440: 7463 683a 2028 736b 6574 6368 292e 2020 tch: (sketch). \n+00000450: 2020 2020 2020 2020 2020 2053 696d 706c Simpl\n+00000460: 6520 3344 2073 6b65 7463 6869 6e67 2066 e 3D sketching f\n+00000470: 6f72 2054 6558 0a45 4e44 2d49 4e46 4f2d or TeX.END-INFO-\n+00000480: 4449 522d 454e 5452 590a 0a1f 0a46 696c DIR-ENTRY....Fil\n+00000490: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n+000004a0: 204e 6f64 653a 2054 6f70 2c20 204e 6578 Node: Top, Nex\n+000004b0: 743a 2041 626f 7574 2073 6b65 7463 682c t: About sketch,\n+000004c0: 2020 5072 6576 3a20 2864 6972 292c 2020 Prev: (dir), \n+000004d0: 5570 3a20 2864 6972 290a 0a53 6b65 7463 Up: (dir)..Sketc\n+000004e0: 680a 2a2a 2a2a 2a2a 0a0a 436f 7079 7269 h.******..Copyri\n+000004f0: 6768 7420 c2a9 2032 3030 3520 746f 2032 ght .. 2005 to 2\n+00000500: 3031 3220 4575 6765 6e65 204b 2e20 5265 012 Eugene K. Re\n+00000510: 7373 6c65 722e 0a0a 2020 2054 6869 7320 ssler... This \n+00000520: 6d61 6e75 616c 2069 7320 666f 7220 e280 manual is for ..\n+00000530: 9873 6b65 7463 68e2 8099 2c20 7665 7273 .sketch..., vers\n+00000540: 696f 6e20 302e 3320 2862 7569 6c64 2037 ion 0.3 (build 7\n+00000550: 292c 2053 756e 6461 792c 204f 6374 6f62 ), Sunday, Octob\n+00000560: 6572 0a32 362c 2032 3032 352c 2061 2070 er.26, 2025, a p\n+00000570: 726f 6772 616d 2074 6861 7420 636f 6e76 rogram that conv\n+00000580: 6572 7473 2064 6573 6372 6970 7469 6f6e erts description\n+00000590: 7320 6f66 2073 696d 706c 650a 7468 7265 s of simple.thre\n+000005a0: 652d 6469 6d65 6e73 696f 6e61 6c20 7363 e-dimensional sc\n+000005b0: 656e 6573 2069 6e74 6f20 6c69 6e65 2064 enes into line d\n+000005c0: 7261 7769 6e67 732e 2020 5468 6973 2076 rawings. This v\n+000005d0: 6572 7369 6f6e 2067 656e 6572 6174 6573 ersion generates\n+000005e0: 0ae2 8098 5053 5472 6963 6b73 e280 9920 ....PSTricks... \n+000005f0: 6f72 20e2 8098 5047 462f 5469 6b5a e280 or ...PGF/TikZ..\n+00000600: 9920 636f 6465 2073 7569 7461 626c 6520 . code suitable \n+00000610: 666f 7220 7573 6520 7769 7468 2074 6865 for use with the\n+00000620: 2054 6558 2064 6f63 756d 656e 740a 7072 TeX document.pr\n+00000630: 6f63 6573 7369 6e67 2073 7973 7465 6d2e ocessing system.\n+00000640: 0a0a 2020 20e2 8098 536b 6574 6368 e280 .. ...Sketch..\n+00000650: 9920 6973 2066 7265 6520 736f 6674 7761 . is free softwa\n+00000660: 7265 2e20 2059 6f75 2063 616e 2072 6564 re. You can red\n+00000670: 6973 7472 6962 7574 6520 6974 2061 6e64 istribute it and\n+00000680: 2f6f 7220 6d6f 6469 6679 2069 740a 756e /or modify it.un\n+00000690: 6465 7220 7468 6520 7465 726d 7320 6f66 der the terms of\n+000006a0: 2074 6865 2047 4e55 2047 656e 6572 616c the GNU General\n+000006b0: 2050 7562 6c69 6320 4c69 6365 6e73 6520 Public License \n+000006c0: 6173 2070 7562 6c69 7368 6564 2062 7920 as published by \n+000006d0: 7468 650a 4672 6565 2053 6f66 7477 6172 the.Free Softwar\n+000006e0: 6520 466f 756e 6461 7469 6f6e 3b20 6569 e Foundation; ei\n+000006f0: 7468 6572 2076 6572 7369 6f6e 2033 2c20 ther version 3, \n+00000700: 6f72 2028 6174 2079 6f75 7220 6f70 7469 or (at your opti\n+00000710: 6f6e 2920 616e 790a 6c61 7465 7220 7665 on) any.later ve\n+00000720: 7273 696f 6e2e 0a0a 2020 2053 6b65 7463 rsion... Sketc\n+00000730: 6820 6973 2064 6973 7472 6962 7574 6564 h is distributed\n+00000740: 2069 6e20 7468 6520 686f 7065 2074 6861 in the hope tha\n+00000750: 7420 6974 2077 696c 6c20 6265 2075 7365 t it will be use\n+00000760: 6675 6c2c 2062 7574 2057 4954 484f 5554 ful, but WITHOUT\n+00000770: 0a41 4e59 2057 4152 5241 4e54 593b 2077 .ANY WARRANTY; w\n+00000780: 6974 686f 7574 2065 7665 6e20 7468 6520 ithout even the \n+00000790: 696d 706c 6965 6420 7761 7272 616e 7479 implied warranty\n+000007a0: 206f 6620 4d45 5243 4841 4e54 4142 494c of MERCHANTABIL\n+000007b0: 4954 5920 6f72 0a46 4954 4e45 5353 2046 ITY or.FITNESS F\n+000007c0: 4f52 2041 2050 4152 5449 4355 4c41 5220 OR A PARTICULAR \n+000007d0: 5055 5250 4f53 452e 2053 6565 2074 6865 PURPOSE. See the\n+000007e0: 2047 4e55 2047 656e 6572 616c 2050 7562 GNU General Pub\n+000007f0: 6c69 6320 4c69 6365 6e73 6520 666f 720a lic License for.\n+00000800: 6d6f 7265 2064 6574 6169 6c73 2e0a 0a20 more details... \n+00000810: 2020 596f 7520 7368 6f75 6c64 2068 6176 You should hav\n+00000820: 6520 7265 6365 6976 6564 2061 2063 6f70 e received a cop\n+00000830: 7920 6f66 2074 6865 2047 4e55 2047 656e y of the GNU Gen\n+00000840: 6572 616c 2050 7562 6c69 6320 4c69 6365 eral Public Lice\n+00000850: 6e73 650a 616c 6f6e 6720 7769 7468 20e2 nse.along with .\n+00000860: 8098 736b 6574 6368 e280 993b 2073 6565 ..sketch...; see\n+00000870: 2074 6865 2066 696c 6520 434f 5059 494e the file COPYIN\n+00000880: 472e 7478 742e 2020 4966 206e 6f74 2c20 G.txt. If not, \n+00000890: 7365 650a 6874 7470 3a2f 2f77 7777 2e67 see.http://www.g\n+000008a0: 6e75 2e6f 7267 2f63 6f70 796c 6566 742e nu.org/copyleft.\n+000008b0: 0a0a 2a20 4d65 6e75 3a0a 0a2a 2041 626f ..* Menu:..* Abo\n+000008c0: 7574 2073 6b65 7463 683a 3a20 2020 2020 ut sketch:: \n+000008d0: 2020 2020 2020 2020 2020 2057 6879 2073 Why s\n+000008e0: 6b65 7463 6820 6578 6973 7473 2061 6e64 ketch exists and\n+000008f0: 2077 6861 7420 6974 2064 6f65 732e 0a2a what it does..*\n+00000900: 2049 6e74 726f 6475 6374 696f 6e20 6279 Introduction by\n+00000910: 2065 7861 6d70 6c65 3a3a 2020 2020 204d example:: M\n+00000920: 6f73 7420 6665 6174 7572 6573 2073 686f ost features sho\n+00000930: 776e 2061 7320 776f 726b 696e 6720 636f wn as working co\n+00000940: 6465 2e0a 2a20 496e 7075 7420 6c61 6e67 de..* Input lang\n+00000950: 7561 6765 3a3a 2020 2020 2020 2020 2020 uage:: \n+00000960: 2020 2020 5379 6e74 6178 2061 6e64 2073 Syntax and s\n+00000970: 656d 616e 7469 6373 206f 6620 e280 9873 emantics of ...s\n+00000980: 6b65 7463 68e2 8099 2063 6f6d 6d61 6e64 ketch... command\n+00000990: 732e 0a2a 2042 7569 6c64 696e 6720 6120 s..* Building a \n+000009a0: 6472 6177 696e 673a 3a20 2020 2020 2020 drawing:: \n+000009b0: 2020 2048 6f77 2074 6f20 7573 6520 e280 How to use ..\n+000009c0: 9873 6b65 7463 68e2 8099 2070 726f 6475 .sketch... produ\n+000009d0: 6374 6976 656c 792e 0a2a 2043 6f6d 6d61 ctively..* Comma\n+000009e0: 6e64 206c 696e 653a 3a20 2020 2020 2020 nd line:: \n+000009f0: 2020 2020 2020 2020 204f 7074 696f 6e73 Options\n+00000a00: 2061 6e64 2074 6865 6972 2075 7361 6765 and their usage\n+00000a10: 2e0a 2a20 496e 7374 616c 6c69 6e67 2073 ..* Installing s\n+00000a20: 6b65 7463 683a 3a20 2020 2020 2020 2020 ketch:: \n+00000a30: 2020 4275 696c 6469 6e67 2061 6e64 2069 Building and i\n+00000a40: 6e73 7461 6c6c 696e 6720 6672 6f6d 2073 nstalling from s\n+00000a50: 6f75 7263 6573 2e0a 2a20 496e 6465 7820 ources..* Index \n+00000a60: 6f66 2073 796e 7461 783a 3a0a 2a20 496e of syntax::.* In\n+00000a70: 6465 783a 3a0a 0a20 2d2d 2054 6865 2044 dex::.. -- The D\n+00000a80: 6574 6169 6c65 6420 4e6f 6465 204c 6973 etailed Node Lis\n+00000a90: 7469 6e67 202d 2d0a 0a41 626f 7574 2073 ting --..About s\n+00000aa0: 6b65 7463 680a 0a2a 2052 6570 6f72 7469 ketch..* Reporti\n+00000ab0: 6e67 2062 7567 733a 3a20 2020 2020 2020 ng bugs:: \n+00000ac0: 2020 2020 2020 204c 6574 2075 7365 206b Let use k\n+00000ad0: 6e6f 7720 7768 6174 2773 2077 726f 6e67 now what's wrong\n+00000ae0: 210a 2a20 436f 6e74 7269 6275 7469 6f6e !.* Contribution\n+00000af0: 733a 3a20 2020 2020 2020 2020 2020 2020 s:: \n+00000b00: 2020 486f 7720 796f 7520 6361 6e20 6865 How you can he\n+00000b10: 6c70 2e2e 2e2e 0a0a 496e 7472 6f64 7563 lp......Introduc\n+00000b20: 7469 6f6e 2062 7920 6578 616d 706c 650a tion by example.\n+00000b30: 0a2a 2048 656c 6c6f 2077 6f72 6c64 3a3a .* Hello world::\n+00000b40: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00000b50: 2053 696d 706c 6573 7420 706f 7373 6962 Simplest possib\n+00000b60: 6c65 20e2 8098 736b 6574 6368 e280 9920 le ...sketch... \n+00000b70: 7072 6f67 7261 6d2e 0a2a 2044 7261 7769 program..* Drawi\n+00000b80: 6e67 206f 7074 696f 6e73 3a3a 2020 2020 ng options:: \n+00000b90: 2020 2020 2020 2020 2043 6f6e 7472 6f6c Control\n+00000ba0: 6c69 6e67 206f 626a 6563 7420 6170 7065 ling object appe\n+00000bb0: 6172 616e 6365 2e0a 2a20 4472 6177 696e arance..* Drawin\n+00000bc0: 6720 6120 736f 6c69 643a 3a20 2020 2020 g a solid:: \n+00000bd0: 2020 2020 2020 2020 4472 6177 696e 6720 Drawing \n+00000be0: 616e 206f 626a 6563 7420 7769 7468 2033 an object with 3\n+00000bf0: 6420 6170 7065 6172 616e 6365 2e0a 2a20 d appearance..* \n+00000c00: 5370 6563 6961 6c20 6f62 6a65 6374 733a Special objects:\n+00000c10: 3a20 2020 2020 2020 2020 2020 2020 4c61 : La\n+00000c20: 7969 6e67 2054 6558 206f 7665 722c 2069 ying TeX over, i\n+00000c30: 6e2c 206f 7220 756e 6465 7220 6472 6177 n, or under draw\n+00000c40: 696e 6773 2e0a 2a20 4f62 6a65 6374 2074 ings..* Object t\n+00000c50: 7261 6e73 666f 726d 733a 3a20 2020 2020 ransforms:: \n+00000c60: 2020 2020 2020 526f 7461 7465 2c20 7472 Rotate, tr\n+00000c70: 616e 736c 6174 652c 2073 6361 6c65 2c20 anslate, scale, \n+00000c80: 616e 6420 6f74 6865 7273 2e0a 2a20 5265 and others..* Re\n+00000c90: 7065 6174 6564 206f 626a 6563 7473 3a3a peated objects::\n+00000ca0: 2020 2020 2020 2020 2020 2020 4d61 6b69 Maki\n+00000cb0: 6e67 2074 7261 6e73 666f 726d 6564 2063 ng transformed c\n+00000cc0: 6f70 6965 732e 0a2a 2053 7765 7074 206f opies..* Swept o\n+00000cd0: 626a 6563 7473 3a3a 2020 2020 2020 2020 bjects:: \n+00000ce0: 2020 2020 2020 2053 7765 6570 696e 6720 Sweeping \n+00000cf0: 6f62 6a65 6374 7320 696e 2073 7061 6365 objects in space\n+00000d00: 2074 6f20 6d61 6b65 206e 6577 2073 6861 to make new sha\n+00000d10: 7065 732e 0a0a 5377 6570 7420 6f62 6a65 pes...Swept obje\n+00000d20: 6374 730a 0a2a 2050 6f69 6e74 2073 7765 cts..* Point swe\n+00000d30: 6570 733a 3a20 2020 2020 2020 2020 2020 eps:: \n+00000d40: 2020 2020 2053 7765 7074 2070 6f69 6e74 Swept point\n+00000d50: 7320 6d61 6b65 206c 696e 6573 2061 6e64 s make lines and\n+00000d60: 2070 6f6c 7967 6f6e 732e 0a2a 2050 6f6c polygons..* Pol\n+00000d70: 796c 696e 6520 7377 6565 7073 3a3a 2020 yline sweeps:: \n+00000d80: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n+00000d90: 206c 696e 6573 206d 616b 6520 7375 7266 lines make surf\n+00000da0: 6163 6573 2e0a 2a20 4e65 7374 6564 2073 aces..* Nested s\n+00000db0: 7765 6570 733a 3a20 2020 2020 2020 2020 weeps:: \n+00000dc0: 2020 2020 2020 5377 6570 7420 7377 6565 Swept swee\n+00000dd0: 7073 2061 7265 2075 7365 6675 6c21 0a2a ps are useful!.*\n+00000de0: 2050 6f6c 7967 6f6e 2073 7765 6570 733a Polygon sweeps:\n+00000df0: 3a20 2020 2020 2020 2020 2020 2020 2053 : S\n+00000e00: 7765 7074 2070 6f6c 7967 6f6e 7320 6d61 wept polygons ma\n+00000e10: 6b65 2073 6f6c 6964 732e 2e2e 0a2a 2050 ke solids....* P\n+00000e20: 6f6c 796c 696e 6520 7377 6565 7073 2077 olyline sweeps w\n+00000e30: 6974 6820 636c 6f73 7572 653a 3a20 2061 ith closure:: a\n+00000e40: 6e64 2073 6f20 646f 2063 6c6f 7365 6420 nd so do closed \n+00000e50: 706f 6c79 6c69 6e65 2073 7765 6570 732e polyline sweeps.\n+00000e60: 0a2a 2041 6666 696e 6520 6172 6974 686d .* Affine arithm\n+00000e70: 6574 6963 3a3a 2020 2020 2020 2020 2020 etic:: \n+00000e80: 2053 6b65 7463 6820 7573 6566 756c 206d Sketch useful m\n+00000e90: 6174 6820 6578 7072 6573 7369 6f6e 2e0a ath expression..\n+00000ea0: 2a20 4d6f 7265 2074 6f20 6c65 6172 6e3a * More to learn:\n+00000eb0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00000ec0: 4368 6563 6b20 6f75 7420 7468 6520 4d6f Check out the Mo\n+00000ed0: 6269 7573 2073 7472 6970 210a 0a49 6e70 bius strip!..Inp\n+00000ee0: 7574 206c 616e 6775 6167 650a 0a2a 204c ut language..* L\n+00000ef0: 616e 6775 6167 6520 6261 7369 6373 3a3a anguage basics::\n+00000f00: 2020 2020 2020 2020 2020 2020 2043 6173 Cas\n+00000f10: 652c 2073 7061 6365 2c20 636f 6d6d 656e e, space, commen\n+00000f20: 7473 2c20 696e 636c 7564 6520 6669 6c65 ts, include file\n+00000f30: 732e 0a2a 2044 7261 7761 626c 6573 3a3a s..* Drawables::\n+00000f40: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00000f50: 2020 2054 6869 6e67 7320 7468 6174 2063 Things that c\n+00000f60: 616e 2062 6520 6472 6177 6e2e 0a2a 2044 an be drawn..* D\n+00000f70: 6566 696e 6974 696f 6e73 3a3a 2020 2020 efinitions:: \n+00000f80: 2020 2020 2020 2020 2020 2020 2047 6976 Giv\n+00000f90: 696e 6720 7468 696e 6773 206e 616d 6573 ing things names\n+00000fa0: 2e0a 2a20 476c 6f62 616c 2065 6e76 6972 ..* Global envir\n+00000fb0: 6f6e 6d65 6e74 3a3a 2020 2020 2020 2020 onment:: \n+00000fc0: 2020 4166 6665 6374 2074 6865 2065 6e74 Affect the ent\n+00000fd0: 6972 6520 6472 6177 696e 672e 0a0a 4261 ire drawing...Ba\n+00000fe0: 7369 6373 0a0a 2a20 4964 656e 7469 6669 sics..* Identifi\n+00000ff0: 6572 733a 3a20 2020 2020 2020 2020 2020 ers:: \n+00001000: 2020 2020 2020 4e61 6d65 7320 666f 7220 Names for \n+00001010: 7468 696e 6773 2e0a 2a20 4b65 7920 616e things..* Key an\n+00001020: 6420 7265 7365 7276 6564 2077 6f72 6473 d reserved words\n+00001030: 3a3a 2020 2020 2020 4e61 6d65 7320 796f :: Names yo\n+00001040: 7520 7368 6f75 6c64 6e27 7420 7573 652e u shouldn't use.\n+00001050: 0a2a 204c 6974 6572 616c 733a 3a20 2020 .* Literals:: \n 00001060: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00001070: 2020 2043 6f6e 7374 616e 7473 2061 6e64 Constants and\n-00001080: 2063 6f6e 7374 7275 6374 6f72 732e 0a2a constructors..*\n-00001090: 2041 7269 7468 6d65 7469 633a 3a20 2020 Arithmetic:: \n-000010a0: 2020 2020 2020 2020 2020 2020 2020 2052 R\n-000010b0: 756c 6573 2066 6f72 2065 7870 7265 7373 ules for express\n-000010c0: 696f 6e73 2e0a 2a20 4f70 7469 6f6e 733a ions..* Options:\n-000010d0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-000010e0: 2020 2020 2020 4d6f 6469 6679 696e 6720 Modifying \n-000010f0: 6f62 6a65 6374 2061 7070 6561 7261 6e63 object appearanc\n-00001100: 652e 0a0a 4c69 7465 7261 6c73 0a0a 2a20 e...Literals..* \n-00001110: 5363 616c 6172 206c 6974 6572 616c 733a Scalar literals:\n-00001120: 3a20 2020 2020 2020 2020 2020 2020 4a75 : Ju\n-00001130: 7374 2074 6865 206e 756d 6265 7273 2e0a st the numbers..\n-00001140: 2a20 506f 696e 7420 616e 6420 7665 6374 * Point and vect\n-00001150: 6f72 206c 6974 6572 616c 733a 3a20 2020 or literals:: \n-00001160: 3364 2071 7561 6e74 6974 6965 732e 0a2a 3d quantities..*\n-00001170: 2054 7261 6e73 666f 726d 206c 6974 6572 Transform liter\n-00001180: 616c 733a 3a20 2020 2020 2020 2020 204d als:: M\n-00001190: 6174 7269 7820 666f 726d 2e0a 0a41 7269 atrix form...Ari\n-000011a0: 7468 6d65 7469 6320 6578 7072 6573 7369 thmetic expressi\n-000011b0: 6f6e 730a 0a2a 2054 776f 2d6f 7065 7261 ons..* Two-opera\n-000011c0: 6e64 2028 6269 6e61 7279 2920 666f 726d nd (binary) form\n-000011d0: 733a 3a20 2041 206f 7020 420a 2a20 556e s:: A op B.* Un\n-000011e0: 6172 7920 666f 726d 733a 3a20 2020 2020 ary forms:: \n-000011f0: 2020 2020 2020 2020 2020 2020 6f70 2041 op A\n-00001200: 2028 616e 6420 6f74 6865 7273 290a 0a4f (and others)..O\n-00001210: 7074 696f 6e73 0a0a 2a20 5053 5472 6963 ptions..* PSTric\n-00001220: 6b73 206f 7074 696f 6e73 3a3a 2020 2020 ks options:: \n-00001230: 2020 2020 2020 2020 4f70 7469 6f6e 7320 Options \n-00001240: 696e 6865 7269 7465 6420 6672 6f6d 20e2 inherited from .\n-00001250: 8098 5053 5472 6963 6b73 e280 992e 0a2a ..PSTricks.....*\n-00001260: 2054 696b 5a2f 5047 4620 6f70 7469 6f6e TikZ/PGF option\n-00001270: 733a 3a20 2020 2020 2020 2020 2020 204f s:: O\n-00001280: 7074 696f 6e73 2069 6e68 6572 6974 6564 ptions inherited\n-00001290: 2066 726f 6d20 e280 9854 696b 5a2f 5047 from ...TikZ/PG\n-000012a0: 46e2 8099 2e0a 2a20 446f 7473 2069 6e20 F.....* Dots in \n-000012b0: 5469 6b5a 2f50 4746 3a3a 2020 2020 2020 TikZ/PGF:: \n-000012c0: 2020 2020 2020 536b 6574 6368 2075 7365 Sketch use\n-000012d0: 7320 e280 9854 696b 5a2f 5047 46e2 8099 s ...TikZ/PGF...\n-000012e0: 2063 6972 636c 6573 2066 6f72 2064 6f74 circles for dot\n-000012f0: 732e 0a2a 2054 696b 5a2f 5047 4620 7573 s..* TikZ/PGF us\n-00001300: 6572 2d64 6566 696e 6564 2073 7479 6c65 er-defined style\n-00001310: 733a 3a20 2053 7570 706f 7274 2066 6f72 s:: Support for\n-00001320: 20e2 8098 5469 6b5a 2f50 4746 e280 9920 ...TikZ/PGF... \n-00001330: 6e61 6d65 642c 2075 7365 722d 6465 6669 named, user-defi\n-00001340: 6e65 6420 7374 796c 6573 2e0a 2a20 5472 ned styles..* Tr\n-00001350: 616e 7370 6172 656e 6379 3a3a 2020 2020 ansparency:: \n-00001360: 2020 2020 2020 2020 2020 2020 5365 652d See-\n-00001370: 7468 726f 7567 6820 706f 6c79 676f 6e73 through polygons\n-00001380: 2e0a 2a20 496e 7465 726e 616c 206f 7074 ..* Internal opt\n-00001390: 696f 6e73 3a3a 2020 2020 2020 2020 2020 ions:: \n-000013a0: 2020 4f70 7469 6f6e 7320 7573 6564 2062 Options used b\n-000013b0: 7920 e280 9873 6b65 7463 68e2 8099 2e0a y ...sketch.....\n-000013c0: 0a50 6f69 6e74 206c 6973 7473 0a0a 2a20 .Point lists..* \n-000013d0: 4472 6177 6162 6c65 733a 3a20 2020 2020 Drawables:: \n-000013e0: 2020 2020 2020 2020 2020 2020 2020 5468 Th\n-000013f0: 696e 6773 2074 6861 7420 6172 6520 6472 ings that are dr\n-00001400: 6177 6e2e 0a2a 2044 6566 696e 6974 696f awn..* Definitio\n-00001410: 6e73 3a3a 2020 2020 2020 2020 2020 2020 ns:: \n-00001420: 2020 2020 2054 6869 6e67 7320 7769 7468 Things with\n-00001430: 206e 616d 6573 2e0a 0a44 7261 7761 626c names...Drawabl\n-00001440: 6573 0a0a 2a20 446f 7473 3a3a 2020 2020 es..* Dots:: \n+00001070: 2043 6f6e 7374 616e 7473 2061 6e64 2063 Constants and c\n+00001080: 6f6e 7374 7275 6374 6f72 732e 0a2a 2041 onstructors..* A\n+00001090: 7269 7468 6d65 7469 633a 3a20 2020 2020 rithmetic:: \n+000010a0: 2020 2020 2020 2020 2020 2020 2052 756c Rul\n+000010b0: 6573 2066 6f72 2065 7870 7265 7373 696f es for expressio\n+000010c0: 6e73 2e0a 2a20 4f70 7469 6f6e 733a 3a20 ns..* Options:: \n+000010d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000010e0: 2020 2020 4d6f 6469 6679 696e 6720 6f62 Modifying ob\n+000010f0: 6a65 6374 2061 7070 6561 7261 6e63 652e ject appearance.\n+00001100: 0a0a 4c69 7465 7261 6c73 0a0a 2a20 5363 ..Literals..* Sc\n+00001110: 616c 6172 206c 6974 6572 616c 733a 3a20 alar literals:: \n+00001120: 2020 2020 2020 2020 2020 2020 4a75 7374 Just\n+00001130: 2074 6865 206e 756d 6265 7273 2e0a 2a20 the numbers..* \n+00001140: 506f 696e 7420 616e 6420 7665 6374 6f72 Point and vector\n+00001150: 206c 6974 6572 616c 733a 3a20 2020 3364 literals:: 3d\n+00001160: 2071 7561 6e74 6974 6965 732e 0a2a 2054 quantities..* T\n+00001170: 7261 6e73 666f 726d 206c 6974 6572 616c ransform literal\n+00001180: 733a 3a20 2020 2020 2020 2020 204d 6174 s:: Mat\n+00001190: 7269 7820 666f 726d 2e0a 0a41 7269 7468 rix form...Arith\n+000011a0: 6d65 7469 6320 6578 7072 6573 7369 6f6e metic expression\n+000011b0: 730a 0a2a 2054 776f 2d6f 7065 7261 6e64 s..* Two-operand\n+000011c0: 2028 6269 6e61 7279 2920 666f 726d 733a (binary) forms:\n+000011d0: 3a20 2041 206f 7020 420a 2a20 556e 6172 : A op B.* Unar\n+000011e0: 7920 666f 726d 733a 3a20 2020 2020 2020 y forms:: \n+000011f0: 2020 2020 2020 2020 2020 6f70 2041 2028 op A (\n+00001200: 616e 6420 6f74 6865 7273 290a 0a4f 7074 and others)..Opt\n+00001210: 696f 6e73 0a0a 2a20 5053 5472 6963 6b73 ions..* PSTricks\n+00001220: 206f 7074 696f 6e73 3a3a 2020 2020 2020 options:: \n+00001230: 2020 2020 2020 4f70 7469 6f6e 7320 696e Options in\n+00001240: 6865 7269 7465 6420 6672 6f6d 20e2 8098 herited from ...\n+00001250: 5053 5472 6963 6b73 e280 992e 0a2a 2054 PSTricks.....* T\n+00001260: 696b 5a2f 5047 4620 6f70 7469 6f6e 733a ikZ/PGF options:\n+00001270: 3a20 2020 2020 2020 2020 2020 204f 7074 : Opt\n+00001280: 696f 6e73 2069 6e68 6572 6974 6564 2066 ions inherited f\n+00001290: 726f 6d20 e280 9854 696b 5a2f 5047 46e2 rom ...TikZ/PGF.\n+000012a0: 8099 2e0a 2a20 446f 7473 2069 6e20 5469 ....* Dots in Ti\n+000012b0: 6b5a 2f50 4746 3a3a 2020 2020 2020 2020 kZ/PGF:: \n+000012c0: 2020 2020 536b 6574 6368 2075 7365 7320 Sketch uses \n+000012d0: e280 9854 696b 5a2f 5047 46e2 8099 2063 ...TikZ/PGF... c\n+000012e0: 6972 636c 6573 2066 6f72 2064 6f74 732e ircles for dots.\n+000012f0: 0a2a 2054 696b 5a2f 5047 4620 7573 6572 .* TikZ/PGF user\n+00001300: 2d64 6566 696e 6564 2073 7479 6c65 733a -defined styles:\n+00001310: 3a20 2053 7570 706f 7274 2066 6f72 20e2 : Support for .\n+00001320: 8098 5469 6b5a 2f50 4746 e280 9920 6e61 ..TikZ/PGF... na\n+00001330: 6d65 642c 2075 7365 722d 6465 6669 6e65 med, user-define\n+00001340: 6420 7374 796c 6573 2e0a 2a20 5472 616e d styles..* Tran\n+00001350: 7370 6172 656e 6379 3a3a 2020 2020 2020 sparency:: \n+00001360: 2020 2020 2020 2020 2020 5365 652d 7468 See-th\n+00001370: 726f 7567 6820 706f 6c79 676f 6e73 2e0a rough polygons..\n+00001380: 2a20 496e 7465 726e 616c 206f 7074 696f * Internal optio\n+00001390: 6e73 3a3a 2020 2020 2020 2020 2020 2020 ns:: \n+000013a0: 4f70 7469 6f6e 7320 7573 6564 2062 7920 Options used by \n+000013b0: e280 9873 6b65 7463 68e2 8099 2e0a 0a50 ...sketch......P\n+000013c0: 6f69 6e74 206c 6973 7473 0a0a 2a20 4472 oint lists..* Dr\n+000013d0: 6177 6162 6c65 733a 3a20 2020 2020 2020 awables:: \n+000013e0: 2020 2020 2020 2020 2020 2020 5468 696e Thin\n+000013f0: 6773 2074 6861 7420 6172 6520 6472 6177 gs that are draw\n+00001400: 6e2e 0a2a 2044 6566 696e 6974 696f 6e73 n..* Definitions\n+00001410: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n+00001420: 2020 2054 6869 6e67 7320 7769 7468 206e Things with n\n+00001430: 616d 6573 2e0a 0a44 7261 7761 626c 6573 ames...Drawables\n+00001440: 0a0a 2a20 446f 7473 3a3a 2020 2020 2020 ..* Dots:: \n 00001450: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00001460: 2020 2020 4472 6177 2064 6f74 732e 0a2a Draw dots..*\n-00001470: 204c 696e 6573 3a3a 2020 2020 2020 2020 Lines:: \n-00001480: 2020 2020 2020 2020 2020 2020 2020 2044 D\n-00001490: 7261 7720 706f 6c79 6c69 6e65 732e 0a2a raw polylines..*\n-000014a0: 2043 7572 7665 733a 3a20 2020 2020 2020 Curves:: \n-000014b0: 2020 2020 2020 2020 2020 2020 2020 2044 D\n-000014c0: 7261 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Dra\n+00001490: 7720 706f 6c79 6c69 6e65 732e 0a2a 2043 w polylines..* C\n+000014a0: 7572 7665 733a 3a20 2020 2020 2020 2020 urves:: \n+000014b0: 2020 2020 2020 2020 2020 2020 2044 7261 Dra\n+000014c0: 7720 6375 7276 6573 2e0a 2a20 506f 6c79 w curves..* Poly\n+000014d0: 676f 6e73 3a3a 2020 2020 2020 2020 2020 gons:: \n+000014e0: 2020 2020 2020 2020 2020 4472 6177 2070 Draw p\n+000014f0: 6f6c 7967 6f6e 732e 0a2a 2053 7065 6369 olygons..* Speci\n+00001500: 616c 733a 3a20 2020 2020 2020 2020 2020 als:: \n+00001510: 2020 2020 2020 2020 2045 6d62 6564 2072 Embed r\n+00001520: 6177 204c 6154 6558 2061 6e64 20e2 8098 aw LaTeX and ...\n+00001530: 5053 5472 6963 6b73 e280 992e 0a2a 2053 PSTricks.....* S\n+00001540: 7765 6570 733a 3a20 2020 2020 2020 2020 weeps:: \n+00001550: 2020 2020 2020 2020 2020 2020 2044 7261 Dra\n+00001560: 7720 7377 6565 7073 206f 6620 646f 7473 w sweeps of dots\n+00001570: 2061 6e64 2070 6f6c 796c 696e 6573 2e0a and polylines..\n+00001580: 2a20 426c 6f63 6b73 3a3a 2020 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One can easi\n-00002020: 6c79 0a69 6e63 6c75 6465 2061 7262 6974 ly.include arbit\n-00002030: 7261 7279 20e2 8098 5053 5472 6963 6b73 rary ...PSTricks\n-00002040: e280 9920 6f72 20e2 8098 5469 6b5a 2f50 ... or ...TikZ/P\n-00002050: 4746 e280 9920 6472 6177 696e 6773 2061 GF... drawings a\n-00002060: 6e64 2074 6578 7420 6f76 6572 2c20 696e nd text over, in\n-00002070: 2c0a 6f72 2075 6e64 6572 20e2 8098 736b ,.or under ...sk\n-00002080: 6574 6368 e280 9920 6472 6177 696e 6773 etch... drawings\n-00002090: 2c20 7072 6f76 6964 696e 6720 6163 6365 , providing acce\n-000020a0: 7373 2074 6f20 7468 6520 6675 6c6c 2070 ss to the full p\n-000020b0: 6f77 6572 206f 6620 4c61 5465 580a 7465 ower of LaTeX.te\n-000020c0: 7874 2061 6e64 206d 6174 6865 6d61 7469 xt and mathemati\n-000020d0: 6373 2066 6f72 6d61 7474 696e 6720 696e cs formatting in\n-000020e0: 2061 2074 6872 6565 2d64 696d 656e 7369 a three-dimensi\n-000020f0: 6f6e 616c 2073 6574 7469 6e67 2e0a 0a1f onal setting....\n-00002100: 0a46 696c 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6574 7469 6e67 2074 6865 2062 6f75 6e64 etting the bound\n+00001900: 696e 6720 626f 7820 616e 6420 3264 2063 ing box and 2d c\n+00001910: 6c69 7070 696e 672e 0a2a 2046 7261 6d65 lipping..* Frame\n+00001920: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n+00001930: 2020 2020 2020 2020 2041 6464 696e 6720 Adding \n+00001940: 6120 626f 7820 6172 6f75 6e64 2074 6865 a box around the\n+00001950: 2064 7261 7769 6e67 2e0a 2a20 4c61 6e67 drawing..* Lang\n+00001960: 7561 6765 3a3a 2020 2020 2020 2020 2020 uage:: \n+00001970: 2020 2020 2020 2020 2020 5365 7474 696e Settin\n+00001980: 6720 7468 6520 6f75 7470 7574 206c 616e g the output lan\n+00001990: 6775 6167 652e 0a0a 4275 696c 6469 6e67 guage...Building\n+000019a0: 2061 2064 7261 7769 6e67 0a0a 2a20 4f76 a drawing..* Ov\n+000019b0: 6572 7669 6577 3a3a 2020 2020 2020 2020 erview:: \n+000019c0: 2020 2020 2020 2020 2020 2020 4275 696c Buil\n+000019d0: 6469 6e67 2061 2073 7562 7374 616e 7469 ding a substanti\n+000019e0: 616c 2064 7261 7769 6e67 2e0a 2a20 4120 al drawing..* A \n+000019f0: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n+00001a00: 673a 3a20 2020 2020 2020 2020 416e 2065 g:: An e\n+00001a10: 7861 6d70 6c65 2077 6974 6820 6669 6e65 xample with fine\n+00001a20: 2070 6c61 6365 6d65 6e74 2e0a 2a20 4120 placement..* A \n+00001a30: 6869 6572 6172 6368 6963 616c 206d 6f64 hierarchical mod\n+00001a40: 656c 3a3a 2020 2020 2020 2020 416e 2065 el:: An e\n+00001a50: 7861 6d70 6c65 2077 6974 6820 7377 6565 xample with swee\n+00001a60: 7073 2061 6e64 2070 7574 732e 0a2a 2043 ps and puts..* C\n+00001a70: 6176 6561 7473 3a3a 2020 2020 2020 2020 aveats:: \n+00001a80: 2020 2020 2020 2020 2020 2020 2057 6865 Whe\n+00001a90: 7265 2074 726f 7562 6c65 2063 616e 206f re trouble can o\n+00001aa0: 6363 7572 2e0a 0a43 6176 6561 7473 0a0a ccur...Caveats..\n+00001ab0: 2a20 4c69 6d69 7473 206f 6e20 6572 726f * Limits on erro\n+00001ac0: 7220 6465 7465 6374 696f 6e3a 3a20 2020 r detection:: \n+00001ad0: 5768 6174 2073 6b65 7463 6820 646f 6573 What sketch does\n+00001ae0: 6e27 7420 646f 2e0a 2a20 436c 6970 7069 n't do..* Clippi\n+00001af0: 6e67 3a3a 2020 2020 2020 2020 2020 2020 ng:: \n+00001b00: 2020 2020 2020 2020 4e6f 2063 6c69 7070 No clipp\n+00001b10: 696e 6720 6174 2070 7265 7365 6e74 2e0a ing at present..\n+00001b20: 2a20 4869 6464 656e 2073 7572 6661 6365 * Hidden surface\n+00001b30: 2072 656d 6f76 616c 3a3a 2020 2020 2020 removal:: \n+00001b40: 496d 7065 7266 6563 7469 6f6e 7320 746f Imperfections to\n+00001b50: 2066 6978 2e0a 0a48 6964 6465 6e20 7375 fix...Hidden su\n+00001b60: 7266 6163 6520 7265 6d6f 7661 6c20 616e rface removal an\n+00001b70: 6420 706f 6c79 676f 6e20 7370 6c69 7474 d polygon splitt\n+00001b80: 696e 670a 0a2a 2053 7461 7469 7374 6963 ing..* Statistic\n+00001b90: 733a 3a20 2020 2020 2020 2020 2020 2020 s:: \n+00001ba0: 2020 2020 2050 6572 666f 726d 616e 6365 Performance\n+00001bb0: 206e 756d 6265 7273 206f 6e20 6465 7074 numbers on dept\n+00001bc0: 6820 736f 7274 2e0a 2a20 4275 6773 2061 h sort..* Bugs a\n+00001bd0: 6e64 2061 6e6f 6d61 6c69 6573 3a3a 2020 nd anomalies:: \n+00001be0: 2020 2020 2020 2020 496d 7065 7266 6563 Imperfec\n+00001bf0: 7469 6f6e 7320 696e 2074 6869 7320 696d tions in this im\n+00001c00: 706c 656d 656e 7461 7469 6f6e 2e0a 0a1f plementation....\n+00001c10: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+00001c20: 666f 2c20 204e 6f64 653a 2041 626f 7574 fo, Node: About\n+00001c30: 2073 6b65 7463 682c 2020 4e65 7874 3a20 sketch, Next: \n+00001c40: 496e 7472 6f64 7563 7469 6f6e 2062 7920 Introduction by \n+00001c50: 6578 616d 706c 652c 2020 5072 6576 3a20 example, Prev: \n+00001c60: 546f 702c 2020 5570 3a20 546f 700a 0a31 Top, Up: Top..1\n+00001c70: 2041 626f 7574 2073 6b65 7463 680a 2a2a About sketch.**\n+00001c80: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 0a0a 2a20 ************..* \n+00001c90: 4d65 6e75 3a0a 0a2a 2052 6570 6f72 7469 Menu:..* Reporti\n+00001ca0: 6e67 2062 7567 733a 3a20 2020 2020 2020 ng bugs:: \n+00001cb0: 2020 2020 2020 204c 6574 2075 7365 206b Let use k\n+00001cc0: 6e6f 7720 7768 6174 2773 2077 726f 6e67 now what's wrong\n+00001cd0: 210a 2a20 436f 6e74 7269 6275 7469 6f6e !.* Contribution\n+00001ce0: 733a 3a20 2020 2020 2020 2020 2020 2020 s:: \n+00001cf0: 2020 486f 7720 796f 7520 6361 6e20 6865 How you can he\n+00001d00: 6c70 2e2e 2e2e 0a0a e280 9853 6b65 7463 lp.........Sketc\n+00001d10: 68e2 8099 2069 7320 6120 736d 616c 6c2c h... is a small,\n+00001d20: 2073 696d 706c 6520 7379 7374 656d 2066 simple system f\n+00001d30: 6f72 2070 726f 6475 6369 6e67 206c 696e or producing lin\n+00001d40: 6520 6472 6177 696e 6773 206f 6620 7477 e drawings of tw\n+00001d50: 6f2d 0a6f 7220 7468 7265 652d 6469 6d65 o-.or three-dime\n+00001d60: 6e73 696f 6e61 6c20 6f62 6a65 6374 7320 nsional objects \n+00001d70: 616e 6420 7363 656e 6573 2e20 2049 7420 and scenes. It \n+00001d80: 6265 6761 6e20 6173 2061 2077 6179 2074 began as a way t\n+00001d90: 6f20 6d61 6b65 0a69 6c6c 7573 7472 6174 o make.illustrat\n+00001da0: 696f 6e73 2066 6f72 2061 2074 6578 7462 ions for a textb\n+00001db0: 6f6f 6b20 6166 7465 7220 7765 2063 6f75 ook after we cou\n+00001dc0: 6c64 2066 696e 6420 6e6f 2073 7569 7461 ld find no suita\n+00001dd0: 626c 6520 746f 6f6c 2066 6f72 0a74 6869 ble tool for.thi\n+00001de0: 7320 7075 7270 6f73 652e 2020 4578 6973 s purpose. Exis\n+00001df0: 7469 6e67 2073 6365 6e65 2070 726f 6365 ting scene proce\n+00001e00: 7373 6f72 7320 656d 7068 6173 697a 6564 ssors emphasized\n+00001e10: 2047 5549 7320 616e 642f 6f72 0a70 686f GUIs and/or.pho\n+00001e20: 746f 2d72 6561 6c69 736d 2c20 626f 7468 to-realism, both\n+00001e30: 2075 6e2d 7573 6566 756c 2074 6f20 7573 un-useful to us\n+00001e40: 2e20 2057 6520 7761 6e74 6564 2074 6f20 . We wanted to \n+00001e50: 7072 6f64 7563 6520 6669 6e65 6c79 0a77 produce finely.w\n+00001e60: 726f 7567 6874 2c20 6d61 7468 656d 6174 rought, mathemat\n+00001e70: 6963 616c 6c79 2d62 6173 6564 2069 6c6c ically-based ill\n+00001e80: 7573 7472 6174 696f 6e73 2077 6974 6820 ustrations with \n+00001e90: 6e6f 2065 7874 7261 6e65 6f75 7320 6465 no extraneous de\n+00001ea0: 7461 696c 2e0a 0a20 2020 e280 9853 6b65 tail... ...Ske\n+00001eb0: 7463 68e2 8099 2061 6363 6570 7473 2061 tch... accepts a\n+00001ec0: 2074 696e 7920 7363 656e 6520 6465 7363 tiny scene desc\n+00001ed0: 7269 7074 696f 6e20 6c61 6e67 7561 6765 ription language\n+00001ee0: 2061 6e64 2067 656e 6572 6174 6573 0ae2 and generates..\n+00001ef0: 8098 5053 5472 6963 6b73 e280 9920 6f72 ..PSTricks... or\n+00001f00: 20e2 8098 5469 6b5a 2f50 4746 e280 9920 ...TikZ/PGF... \n+00001f10: 636f 6465 2066 6f72 204c 6154 6558 2e20 code for LaTeX. \n+00001f20: 2054 6865 20e2 8098 736b 6574 6368 e280 The ...sketch..\n+00001f30: 9920 6c61 6e67 7561 6765 2069 730a 7369 . language is.si\n+00001f40: 6d69 6c61 7220 746f 20e2 8098 5053 5472 milar to ...PSTr\n+00001f50: 6963 6b73 e280 992c 206d 616b 696e 6720 icks..., making \n+00001f60: 6974 2065 6173 7920 746f 206c 6561 726e it easy to learn\n+00001f70: 2066 6f72 2063 7572 7265 6e74 20e2 8098 for current ...\n+00001f80: 5053 5472 6963 6b73 e280 990a 7573 6572 PSTricks....user\n+00001f90: 732e 2020 5365 6520 7777 772e 7073 7472 s. See www.pstr\n+00001fa0: 6963 6b73 2e64 6520 666f 7220 696e 666f icks.de for info\n+00001fb0: 726d 6174 696f 6e20 6f6e 20e2 8098 5053 rmation on ...PS\n+00001fc0: 5472 6963 6b73 e280 992e 2020 e280 9854 Tricks.... ...T\n+00001fd0: 696b 5a2f 5047 46e2 8099 0a69 7320 7369 ikZ/PGF....is si\n+00001fe0: 6d69 6c61 722e 2020 5365 6520 6874 7470 milar. See http\n+00001ff0: 3a2f 2f73 6f75 7263 6566 6f72 6765 2e6e ://sourceforge.n\n+00002000: 6574 2f70 726f 6a65 6374 732f 7067 662e et/projects/pgf.\n+00002010: 2020 4f6e 6520 6361 6e20 6561 7369 6c79 One can easily\n+00002020: 0a69 6e63 6c75 6465 2061 7262 6974 7261 .include arbitra\n+00002030: 7279 20e2 8098 5053 5472 6963 6b73 e280 ry ...PSTricks..\n+00002040: 9920 6f72 20e2 8098 5469 6b5a 2f50 4746 . or ...TikZ/PGF\n+00002050: e280 9920 6472 6177 696e 6773 2061 6e64 ... drawings and\n+00002060: 2074 6578 7420 6f76 6572 2c20 696e 2c0a text over, in,.\n+00002070: 6f72 2075 6e64 6572 20e2 8098 736b 6574 or under ...sket\n+00002080: 6368 e280 9920 6472 6177 696e 6773 2c20 ch... drawings, \n+00002090: 7072 6f76 6964 696e 6720 6163 6365 7373 providing access\n+000020a0: 2074 6f20 7468 6520 6675 6c6c 2070 6f77 to the full pow\n+000020b0: 6572 206f 6620 4c61 5465 580a 7465 7874 er of LaTeX.text\n+000020c0: 2061 6e64 206d 6174 6865 6d61 7469 6373 and mathematics\n+000020d0: 2066 6f72 6d61 7474 696e 6720 696e 2061 formatting in a\n+000020e0: 2074 6872 6565 2d64 696d 656e 7369 6f6e three-dimension\n+000020f0: 616c 2073 6574 7469 6e67 2e0a 0a1f 0a46 al setting.....F\n+00002100: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+00002110: 2c20 204e 6f64 653a 2052 6570 6f72 7469 , Node: Reporti\n+00002120: 6e67 2062 7567 732c 2020 4e65 7874 3a20 ng bugs, Next: \n+00002130: 436f 6e74 7269 6275 7469 6f6e 732c 2020 Contributions, \n+00002140: 5072 6576 3a20 4162 6f75 7420 736b 6574 Prev: About sket\n+00002150: 6368 2c20 2055 703a 2041 626f 7574 2073 ch, Up: About s\n+00002160: 6b65 7463 680a 0a31 2e31 2052 6570 6f72 ketch..1.1 Repor\n+00002170: 7469 6e67 2062 7567 7320 616e 6420 7265 ting bugs and re\n+00002180: 636f 6d6d 656e 6469 6e67 2069 6d70 726f commending impro\n+00002190: 7665 6d65 6e74 732e 0a3d 3d3d 3d3d 3d3d vements..=======\n 000021a0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ================\n 000021b0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ================\n-000021c0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a 5468 ============..Th\n-000021d0: 6520 6772 6f75 7020 6874 7470 3a2f 2f67 e group http://g\n-000021e0: 726f 7570 732e 676f 6f67 6c65 2e63 6f6d roups.google.com\n-000021f0: 2f67 726f 7570 2f73 6b65 7463 682d 7573 /group/sketch-us\n-00002200: 6572 7320 6973 2074 6865 2062 6573 7420 ers is the best \n-00002210: 706c 6163 650a 746f 2072 6570 6f72 7420 place.to report \n-00002220: 6275 6773 2061 6e64 206d 616b 6520 696d bugs and make im\n-00002230: 7072 6f76 656d 656e 7473 2e20 2041 2073 provements. A s\n-00002240: 6563 6f6e 6420 6d65 7468 6f64 2074 6861 econd method tha\n-00002250: 7420 7769 6c6c 0a70 726f 6261 626c 7920 t will.probably \n-00002260: 7072 6f64 7563 6520 6120 736c 6f77 6572 produce a slower\n-00002270: 2072 6573 706f 6e73 6520 6973 2065 6d61 response is ema\n-00002280: 696c 2074 6f20 736b 6574 6368 4066 726f il to sketch@fro\n-00002290: 6e74 6965 726e 6574 2e6e 6574 2e0a 5765 ntiernet.net..We\n-000022a0: 2077 696c 6c20 7472 7920 746f 2072 6573 will try to res\n-000022b0: 706f 6e64 2c20 6275 7420 6361 6e27 7420 pond, but can't \n-000022c0: 7072 6f6d 6973 652e 2020 496e 2061 6e79 promise. In any\n-000022d0: 2065 7665 6e74 2c20 646f 6e27 7420 6265 event, don't be\n-000022e0: 0a6f 6666 656e 6465 6420 6966 2061 2072 .offended if a r\n-000022f0: 6570 6c79 2069 7320 6e6f 7420 666f 7274 eply is not fort\n-00002300: 6863 6f6d 696e 672e 2020 5765 2772 6520 hcoming. We're \n-00002310: 6a75 7374 2062 7573 7920 616e 6420 7769 just busy and wi\n-00002320: 6c6c 2067 6574 2074 6f0a 796f 7572 2073 ll get to.your s\n-00002330: 7567 6765 7374 696f 6e20 6576 656e 7475 uggestion eventu\n-00002340: 616c 6c79 2e0a 0a20 2020 466f 7220 6275 ally... 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(T\n-00003100: 6865 2061 7865 7320 6861 7665 2062 6565 he axes have bee\n-00003110: 6e20 6164 6465 6420 696e 206c 6967 6874 n added in light\n-00003120: 2067 7261 792e 290a 0a00 085b 696d 6167 gray.)....[imag\n-00003130: 6520 7372 633d 2265 7830 3230 2e70 6e67 e src=\"ex020.png\n-00003140: 2220 7465 7874 3d22 496d 6167 6520 6578 \" text=\"Image ex\n-00003150: 3032 3020 6f6d 6974 7465 6420 696e 2074 020 omitted in t\n-00003160: 6578 7420 7665 7273 696f 6e20 6f66 2074 ext version of t\n-00003170: 6869 7320 646f 6375 6d65 6e74 2e22 0008 his document.\"..\n-00003180: 5d0a 0a49 7420 6973 2069 6d70 6f72 7461 ]..It is importa\n-00003190: 6e74 2074 6f20 6b6e 6f77 2074 6861 7420 nt to know that \n-000031a0: 6f6e 6c79 2074 6865 2022 6f75 7473 6964 only the \"outsid\n-000031b0: 6522 206f 6620 6120 706f 6c79 676f 6e20 e\" of a polygon \n-000031c0: 6973 206e 6f72 6d61 6c6c 790a 6472 6177 is normally.draw\n-000031d0: 6e2e 2020 5468 6520 e280 9c6f 7574 7369 n. 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It \n-000032c0: 776f 756c 6420 6861 7665 2062 6565 6e0a would have been.\n-000032d0: e280 9c63 756c 6c65 64e2 809d 2066 726f ...culled... fro\n-000032e0: 6d20 7468 6520 7363 656e 652e 2020 5468 m the scene. Th\n-000032f0: 6973 2063 756c 6c69 6e67 2062 6568 6176 is culling behav\n-00003300: 696f 7220 6d61 7920 7365 656d 2073 7472 ior may seem str\n-00003310: 616e 6765 2c20 6275 740a 7374 6179 2074 ange, but.stay t\n-00003320: 756e 6564 2e0a 0a20 2020 2d2d 2d2d 2d2d uned... ------\n-00003330: 2d2d 2d2d 2046 6f6f 746e 6f74 6573 202d ---- Footnotes -\n-00003340: 2d2d 2d2d 2d2d 2d2d 2d0a 0a20 2020 2831 ---------.. (1\n-00003350: 2920 4f72 2066 6f72 2045 7572 6f70 6561 ) Or for Europea\n-00003360: 6e20 7573 6572 7320 6f66 2041 3420 7369 n users of A4 si\n-00003370: 7a65 2070 6170 6572 2c20 e280 982d 5465 ze paper, ...-Te\n-00003380: e280 992e 0a0a 1f0a 4669 6c65 3a20 736b ........File: sk\n-00003390: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-000033a0: 3a20 4472 6177 696e 6720 6f70 7469 6f6e : Drawing option\n-000033b0: 732c 2020 4e65 7874 3a20 4472 6177 696e s, Next: Drawin\n-000033c0: 6720 6120 736f 6c69 642c 2020 5072 6576 g a solid, Prev\n-000033d0: 3a20 4865 6c6c 6f20 776f 726c 642c 2020 : Hello world, \n-000033e0: 5570 3a20 496e 7472 6f64 7563 7469 6f6e Up: Introduction\n-000033f0: 2062 7920 6578 616d 706c 650a 0a32 2e32 by example..2.2\n-00003400: 204f 7074 696f 6e73 0a3d 3d3d 3d3d 3d3d Options.=======\n-00003410: 3d3d 3d3d 0a0a 4d61 6e79 20e2 8098 5053 ====..Many ...PS\n-00003420: 5472 6963 6b73 e280 9920 616e 6420 e280 Tricks... and ..\n-00003430: 9854 696b 5a2f 5047 46e2 8099 206f 7074 .TikZ/PGF... opt\n-00003440: 696f 6e73 2077 6f72 6b20 6a75 7374 2066 ions work just f\n-00003450: 696e 6520 696e 20e2 8098 736b 6574 6368 ine in ...sketch\n-00003460: e280 992e 2020 4966 0a67 656e 6572 6174 .... If.generat\n-00003470: 696e 6720 e280 9850 5354 7269 636b 73e2 ing ...PSTricks.\n-00003480: 8099 2c20 7468 6520 636f 6465 0a20 2070 .., the code. p\n-00003490: 6f6c 7967 6f6e 5b66 696c 6c63 6f6c 6f72 olygon[fillcolor\n-000034a0: 3d6c 6967 6874 6772 6179 2c6c 696e 6577 =lightgray,linew\n-000034b0: 6964 7468 3d33 7074 5d28 302c 302c 3129 idth=3pt](0,0,1)\n-000034c0: 2831 2c30 2c30 2928 302c 312c 3029 0a20 (1,0,0)(0,1,0). \n-000034d0: 206c 696e 655b 6c69 6e65 7374 796c 653d line[linestyle=\n-000034e0: 646f 7474 6564 5d28 2d31 2c2d 312c 2d31 dotted](-1,-1,-1\n-000034f0: 2928 322c 322c 3229 0a70 726f 6475 6365 )(2,2,2).produce\n-00003500: 730a 0a00 085b 696d 6167 6520 7372 633d s....[image src=\n-00003510: 2265 7830 3330 2e70 6e67 2220 7465 7874 \"ex030.png\" text\n-00003520: 3d22 496d 6167 6520 6578 3033 3020 6f6d =\"Image ex030 om\n-00003530: 6974 7465 6420 696e 2074 6578 7420 7665 itted in text ve\n-00003540: 7273 696f 6e20 6f66 2074 6869 7320 646f rsion of this do\n-00003550: 6375 6d65 6e74 2e22 0008 5d0a 0a20 2020 cument.\"..].. \n-00003560: 546f 2070 726f 6475 6365 20e2 8098 5469 To produce ...Ti\n-00003570: 6b5a 2f50 4746 e280 992c 2074 6865 2063 kZ/PGF..., the c\n-00003580: 6f72 7265 7370 6f6e 6469 6e67 2063 6f64 orresponding cod\n-00003590: 6520 6973 0a20 2070 6f6c 7967 6f6e 5b66 e is. polygon[f\n-000035a0: 696c 6c3d 6c69 6768 7467 7261 792c 6c69 ill=lightgray,li\n-000035b0: 6e65 2077 6964 7468 3d33 7074 5d28 302c ne width=3pt](0,\n-000035c0: 302c 3129 2831 2c30 2c30 2928 302c 312c 0,1)(1,0,0)(0,1,\n-000035d0: 3029 0a20 206c 696e 655b 7374 796c 653d 0). line[style=\n-000035e0: 646f 7474 6564 5d28 2d31 2c2d 312c 2d31 dotted](-1,-1,-1\n-000035f0: 2928 322c 322c 3229 0a20 2067 6c6f 6261 )(2,2,2). globa\n-00003600: 6c20 7b20 6c61 6e67 7561 6765 2074 696b l { language tik\n-00003610: 7a20 7d0a 5468 6520 6669 6e61 6c20 e280 z }.The final ..\n-00003620: 9867 6c6f 6261 6ce2 8099 2069 6e73 7472 .global... instr\n-00003630: 7563 7473 20e2 8098 736b 6574 6368 e280 ucts ...sketch..\n-00003640: 9920 746f 2070 726f 6475 6365 20e2 8098 . to produce ...\n-00003650: 5469 6b5a 2f50 4746 e280 9920 636f 6465 TikZ/PGF... code\n-00003660: 2061 730a 6f75 7470 7574 2072 6174 6865 as.output rathe\n-00003670: 7220 7468 616e 2074 6865 2064 6566 6175 r than the defau\n-00003680: 6c74 2c20 e280 9850 5354 7269 636b 73e2 lt, ...PSTricks.\n-00003690: 8099 2e20 204e 6f74 6520 7468 6174 20e2 ... Note that .\n-000036a0: 8098 706f 6c79 676f 6ee2 8099 2066 696c ..polygon... fil\n-000036b0: 6c0a 636f 6c6f 7220 616e 6420 e280 986c l.color and ...l\n-000036c0: 696e 65e2 8099 2073 7479 6c65 206f 7074 ine... style opt\n-000036d0: 696f 6e73 2062 6f74 6820 636f 6e66 6f72 ions both confor\n-000036e0: 6d20 746f 20e2 8098 5469 6b5a e280 9920 m to ...TikZ... \n-000036f0: 7379 6e74 6178 2072 756c 6573 2e20 2054 syntax rules. T\n-00003700: 6865 0a72 6573 756c 7469 6e67 20e2 8098 he.resulting ...\n-00003710: 5469 6b5a 2f50 4746 e280 9920 6f75 7470 TikZ/PGF... outp\n-00003720: 7574 2069 730a 2020 5c62 6567 696e 7b74 ut is. \\begin{t\n-00003730: 696b 7a70 6963 7475 7265 7d5b 6a6f 696e ikzpicture}[join\n-00003740: 3d72 6f75 6e64 5d0a 2020 5c64 7261 775b =round]. \\draw[\n-00003750: 646f 7474 6564 5d28 2d31 2c2d 3129 2d2d dotted](-1,-1)--\n-00003760: 282e 3333 332c 2e33 3333 293b 0a20 205c (.333,.333);. \\\n-00003770: 6669 6c6c 6472 6177 5b66 696c 6c3d 6c69 filldraw[fill=li\n-00003780: 6768 7467 7261 792c 6c69 6e65 2077 6964 ghtgray,line wid\n-00003790: 7468 3d33 7074 5d28 302c 3029 2d2d 2831 th=3pt](0,0)--(1\n-000037a0: 2c30 292d 2d28 302c 3129 2d2d 6379 636c ,0)--(0,1)--cycl\n-000037b0: 653b 0a20 205c 6472 6177 5b64 6f74 7465 e;. \\draw[dotte\n-000037c0: 645d 282e 3333 332c 2e33 3333 292d 2d28 d](.333,.333)--(\n-000037d0: 322c 3229 3b0a 2020 5c65 6e64 7b74 696b 2,2);. \\end{tik\n-000037e0: 7a70 6963 7475 7265 7d0a 5468 6520 7265 zpicture}.The re\n-000037f0: 6d61 696e 696e 6720 6578 616d 706c 6573 maining examples\n-00003800: 206f 6620 7468 6973 206d 616e 7561 6c20 of this manual \n-00003810: 6172 6520 696e 2050 5354 7269 636b 7320 are in PSTricks \n-00003820: 7374 796c 652e 0a0a 1f0a 4669 6c65 3a20 style.....File: \n-00003830: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n-00003840: 6465 3a20 4472 6177 696e 6720 6120 736f de: Drawing a so\n-00003850: 6c69 642c 2020 4e65 7874 3a20 5370 6563 lid, Next: Spec\n-00003860: 6961 6c20 6f62 6a65 6374 732c 2020 5072 ial objects, Pr\n-00003870: 6576 3a20 4472 6177 696e 6720 6f70 7469 ev: Drawing opti\n-00003880: 6f6e 732c 2020 5570 3a20 496e 7472 6f64 ons, Up: Introd\n-00003890: 7563 7469 6f6e 2062 7920 6578 616d 706c uction by exampl\n-000038a0: 650a 0a32 2e33 2044 7261 7769 6e67 2061 e..2.3 Drawing a\n-000038b0: 2073 6f6c 6964 0a3d 3d3d 3d3d 3d3d 3d3d solid.=========\n-000038c0: 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a 4c65 7427 ==========..Let'\n-000038d0: 7320 7472 7920 736f 6d65 7468 696e 6720 s try something \n-000038e0: 6d6f 7265 2065 7863 6974 696e 672e 2020 more exciting. \n-000038f0: e280 9853 6b65 7463 68e2 8099 2068 6173 ...Sketch... has\n-00003900: 206e 6f20 6e6f 7469 6f6e 206f 6620 6120 no notion of a \n-00003910: 736f 6c69 642c 0a62 7574 2070 6f6c 7967 solid,.but polyg\n-00003920: 6f6e 616c 20e2 809c 6661 6365 73e2 809d onal ...faces...\n-00003930: 2063 616e 2062 6520 7573 6564 2074 6f20 can be used to \n-00003940: 7265 7072 6573 656e 7420 7468 6520 626f represent the bo\n-00003950: 756e 6461 7279 206f 6620 6120 736f 6c69 undary of a soli\n-00003960: 642e 0a54 6f20 7468 6520 7072 6576 696f d..To the previo\n-00003970: 7573 2065 7861 6d70 6c65 2c20 6c65 7427 us example, let'\n-00003980: 7320 6164 6420 7468 7265 6520 6d6f 7265 s add three more\n-00003990: 2074 7269 616e 6775 6c61 7220 706f 6c79 triangular poly\n-000039a0: 676f 6e73 2074 6f0a 6d61 6b65 2074 6865 gons to.make the\n-000039b0: 2066 6163 6573 206f 6620 616e 2069 7272 faces of an irr\n-000039c0: 6567 756c 6172 2074 6574 7261 6865 6472 egular tetrahedr\n-000039d0: 6f6e 2e0a 2020 2520 7665 7274 6963 6573 on.. % vertices\n-000039e0: 206f 6620 7468 6520 7465 7472 6168 6564 of the tetrahed\n-000039f0: 726f 6e0a 2020 6465 6620 7031 2028 302c ron. def p1 (0,\n-00003a00: 302c 3129 2064 6566 2070 3220 2831 2c30 0,1) def p2 (1,0\n-00003a10: 2c30 290a 2020 6465 6620 7033 2028 302c ,0). def p3 (0,\n-00003a20: 312c 3029 2064 6566 2070 3420 282d 2e33 1,0) def p4 (-.3\n-00003a30: 2c2d 2e35 2c2d 2e38 290a 0a20 2025 2066 ,-.5,-.8).. % f\n-00003a40: 6163 6573 206f 6620 7468 6520 7465 7472 aces of the tetr\n-00003a50: 6168 6564 726f 6e2e 0a20 2070 6f6c 7967 ahedron.. polyg\n-00003a60: 6f6e 2870 3129 2870 3229 2870 3329 2025 on(p1)(p2)(p3) %\n-00003a70: 206f 7269 6769 6e61 6c20 6672 6f6e 7420 original front \n-00003a80: 706f 6c79 676f 6e0a 2020 706f 6c79 676f polygon. polygo\n-00003a90: 6e28 7031 2928 7034 2928 7032 2920 2520 n(p1)(p4)(p2) % \n-00003aa0: 626f 7474 6f6d 0a20 2070 6f6c 7967 6f6e bottom. polygon\n-00003ab0: 2870 3129 2870 3329 2870 3429 2025 206c (p1)(p3)(p4) % l\n-00003ac0: 6566 740a 2020 706f 6c79 676f 6e28 7033 eft. polygon(p3\n-00003ad0: 2928 7032 2928 7034 2920 2520 7265 6172 )(p2)(p4) % rear\n-00003ae0: 0a0a 2020 2520 6c69 6e65 2074 6f20 7069 .. % line to pi\n-00003af0: 6572 6365 2074 6865 2074 6574 7261 6865 erce the tetrahe\n-00003b00: 6472 6f6e 0a20 206c 696e 655b 6c69 6e65 dron. line[line\n-00003b10: 636f 6c6f 723d 7265 645d 282d 312c 2d31 color=red](-1,-1\n-00003b20: 2c2d 3129 2832 2c32 2c32 290a 5468 6973 ,-1)(2,2,2).This\n-00003b30: 2065 7861 6d70 6c65 2075 7365 7320 e280 example uses ..\n-00003b40: 9c64 6566 696e 6974 696f 6e73 e280 9d2c .definitions...,\n-00003b50: 2077 6869 6368 2062 6567 696e 2077 6974 which begin wit\n-00003b60: 6820 e280 9864 6566 e280 992e 2020 5468 h ...def.... Th\n-00003b70: 6573 6520 e280 9c64 6566 696e 65e2 809d ese ...define...\n-00003b80: 0a6f 7220 6769 7665 206e 616d 6573 2074 .or give names t\n-00003b90: 6f20 706f 696e 7473 2c20 7768 6963 6820 o points, which \n-00003ba0: 6172 6520 7468 656e 2061 7661 696c 6162 are then availab\n-00003bb0: 6c65 2061 7320 e280 9c72 6566 6572 656e le as ...referen\n-00003bc0: 6365 73e2 809d 2062 790a 656e 636c 6f73 ces... by.enclos\n-00003bd0: 696e 6720 7468 6520 6e61 6d65 7320 696e ing the names in\n-00003be0: 2070 6172 656e 7468 6573 6573 2c20 652e parentheses, e.\n-00003bf0: 672e 2028 666f 6f29 2e20 2054 6865 2070 g. (foo). The p\n-00003c00: 6172 656e 7468 6573 6573 2064 656e 6f74 arentheses denot\n-00003c10: 650a 7468 6174 2074 6865 206e 616d 6573 e.that the names\n-00003c20: 2072 6566 6572 2074 6f20 706f 696e 7473 refer to points\n-00003c30: 3b20 7468 6579 2061 7265 2072 6571 7569 ; they are requi\n-00003c40: 7265 642e 2020 5468 6572 6520 6361 6e20 red. There can \n-00003c50: 6265 206e 6f0a 7768 6974 6520 7370 6163 be no.white spac\n-00003c60: 6520 6265 7477 6565 6e20 7468 656d 2061 e between them a\n-00003c70: 6e64 2074 6865 206e 616d 652e 0a0a 2020 nd the name... \n-00003c80: 2041 7320 796f 7520 6361 6e20 7365 652c As you can see,\n-00003c90: 2063 6f6d 6d65 6e74 7320 7374 6172 7420 comments start \n-00003ca0: 7769 7468 2025 2061 7320 696e 2054 6558 with % as in TeX\n-00003cb0: 2061 6e64 2065 7874 656e 6420 746f 2074 and extend to t\n-00003cc0: 6865 2065 6e64 0a6f 6620 7468 6520 6c69 he end.of the li\n-00003cd0: 6e65 2028 7468 6f75 6768 2023 2077 696c ne (though # wil\n-00003ce0: 6c20 776f 726b 2061 7320 7765 6c6c 292e l work as well).\n-00003cf0: 2020 5768 6974 6520 7370 6163 652c 2069 White space, i\n-00003d00: 6e63 6c75 6469 6e67 0a73 7061 6365 732c ncluding.spaces,\n-00003d10: 2074 6162 7320 616e 6420 626c 616e 6b20 tabs and blank \n-00003d20: 6c69 6e65 732c 2068 6173 206e 6f20 6566 lines, has no ef\n-00003d30: 6665 6374 2069 6e20 7468 6520 e280 9873 fect in the ...s\n-00003d40: 6b65 7463 68e2 8099 206c 616e 6775 6167 ketch... languag\n-00003d50: 652e 0a0a 0008 5b69 6d61 6765 2073 7263 e.....[image src\n-00003d60: 3d22 6578 3034 302e 706e 6722 2074 6578 =\"ex040.png\" tex\n-00003d70: 743d 2249 6d61 6765 2065 7830 3430 206f t=\"Image ex040 o\n-00003d80: 6d69 7474 6564 2069 6e20 7465 7874 2076 mitted in text v\n-00003d90: 6572 7369 6f6e 206f 6620 7468 6973 2064 ersion of this d\n-00003da0: 6f63 756d 656e 742e 2200 085d 0a0a 4966 ocument.\"..]..If\n-00003db0: 2077 6520 6c6f 6f6b 2069 6e73 6964 6520 we look inside \n-00003dc0: 7468 6520 5465 5820 6669 6c65 2070 726f the TeX file pro\n-00003dd0: 6475 6365 6420 6279 20e2 8098 736b 6574 duced by ...sket\n-00003de0: 6368 e280 992c 2074 6865 7265 2077 696c ch..., there wil\n-00003df0: 6c20 6265 206f 6e6c 790a 7468 7265 6520 l be only.three \n-00003e00: 706f 6c79 676f 6e73 2e20 2054 6865 2066 polygons. The f\n-00003e10: 6f75 7274 6820 6861 7320 6265 656e 2063 ourth has been c\n-00003e20: 756c 6c65 6420 6265 6361 7573 6520 6974 ulled because it\n-00003e30: 2069 7320 6120 2262 6163 6b20 6661 6365 is a \"back face\n-00003e40: 220a 6f66 2074 6865 2074 6574 7261 6865 \".of the tetrahe\n-00003e50: 6472 6f6e 2c20 696e 7669 7369 626c 6520 dron, invisible \n-00003e60: 746f 206f 7572 2076 6965 772e 2020 4974 to our view. It\n-00003e70: 2069 7320 756e 6e65 6365 7373 6172 792c is unnecessary,\n-00003e80: 2061 6e64 2073 6f20 6974 0a69 7320 7265 and so it.is re\n-00003e90: 6d6f 7665 642e 0a0a 2020 2049 6e20 736f moved... In so\n-00003ea0: 6d65 2064 7261 7769 6e67 732c 2070 6f6c me drawings, pol\n-00003eb0: 7967 6f6e 7320 6163 7420 6173 207a 6572 ygons act as zer\n-00003ec0: 6f2d 7468 6963 6b6e 6573 7320 736f 6c69 o-thickness soli\n-00003ed0: 6420 7375 7266 6163 6573 2077 6974 680a d surfaces with.\n-00003ee0: 626f 7468 2073 6964 6573 2076 6973 6962 both sides visib\n-00003ef0: 6c65 2072 6174 6865 7220 7468 616e 2061 le rather than a\n-00003f00: 7320 7468 6520 6661 6365 7320 6f66 2073 s the faces of s\n-00003f10: 6f6c 6964 206f 626a 6563 7473 2c20 7768 olid objects, wh\n-00003f20: 6572 6520 6261 636b 0a66 6163 6573 2063 ere back.faces c\n-00003f30: 616e 2062 6520 6375 6c6c 6564 2e20 2046 an be culled. F\n-00003f40: 6f72 207a 6572 6f2d 7468 6963 6b6e 6573 or zero-thicknes\n-00003f50: 7320 736f 6c69 6473 2c20 6375 6c6c 696e s solids, cullin\n-00003f60: 6720 6973 2061 2070 726f 626c 656d 2e0a g is a problem..\n-00003f70: 4f6e 6520 736f 6c75 7469 6f6e 2069 7320 One solution is \n-00003f80: 746f 2075 7365 2061 2070 6169 7220 6f66 to use a pair of\n-00003f90: 20e2 8098 736b 6574 6368 e280 9920 706f ...sketch... po\n-00003fa0: 6c79 676f 6e73 2066 6f72 2065 6163 680a lygons for each.\n-00003fb0: 7a65 726f 2d74 6869 636b 6e65 7373 2066 zero-thickness f\n-00003fc0: 6163 652c 2069 6465 6e74 6963 616c 2065 ace, identical e\n-00003fd0: 7863 6570 7420 7769 7468 206f 7070 6f73 xcept with oppos\n-00003fe0: 6974 6520 7665 7274 6578 206f 7264 6572 ite vertex order\n-00003ff0: 732e 2020 5468 6973 0a69 7320 756e 7769 s. This.is unwi\n-00004000: 656c 6479 2061 6e64 2065 7870 656e 7369 eldy and expensi\n-00004010: 7665 2e20 2041 2062 6574 7465 7220 7761 ve. A better wa\n-00004020: 7920 6973 2074 6f20 7365 7420 7468 6520 y is to set the \n-00004030: e280 9873 6b65 7463 68e2 8099 2069 6e74 ...sketch... int\n-00004040: 6572 6e61 6c0a 6f70 7469 6f6e 20e2 8098 ernal.option ...\n-00004050: 6375 6c6c e280 9920 746f 20e2 8098 6661 cull... to ...fa\n-00004060: 6c73 65e2 8099 2069 6e20 7468 6520 7573 lse... in the us\n-00004070: 7561 6c20 e280 9850 5354 7269 636b 73e2 ual ...PSTricks.\n-00004080: 8099 206d 616e 6e65 722e 0a20 2070 6f6c .. manner.. pol\n-00004090: 7967 6f6e 5b63 756c 6c3d 6661 6c73 655d ygon[cull=false]\n-000040a0: 2870 3129 2870 3229 2870 3329 0a54 6865 (p1)(p2)(p3).The\n-000040b0: 2066 6f6c 6c6f 7769 6e67 2073 686f 7773 following shows\n-000040c0: 2074 6865 2073 616d 6520 6865 6c69 7820 the same helix \n-000040d0: 7368 6170 6520 6472 6177 6e20 6669 7273 shape drawn firs\n-000040e0: 7420 7769 7468 2063 756c 6c3d 7472 7565 t with cull=true\n-000040f0: 2028 7468 650a 6465 6661 756c 7429 2061 (the.default) a\n-00004100: 6e64 2074 6865 6e20 6375 6c6c 3d66 616c nd then cull=fal\n-00004110: 7365 2e0a 0a00 085b 696d 6167 6520 7372 se.....[image sr\n-00004120: 633d 2265 7830 3435 2e70 6e67 2220 7465 c=\"ex045.png\" te\n-00004130: 7874 3d22 496d 6167 6520 6578 3034 3520 xt=\"Image ex045 \n-00004140: 6f6d 6974 7465 6420 696e 2074 6578 7420 omitted in text \n-00004150: 7665 7273 696f 6e20 6f66 2074 6869 7320 version of this \n-00004160: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a57 document.\"..]..W\n-00004170: 6527 6c6c 2073 6f6f 6e20 7365 6520 686f e'll soon see ho\n-00004180: 7720 746f 2070 726f 6475 6365 2074 6865 w to produce the\n-00004190: 7365 2068 656c 6978 6573 2077 6974 6820 se helixes with \n-000041a0: 6120 6665 7720 6c69 6e65 7320 6f66 20e2 a few lines of .\n-000041b0: 8098 736b 6574 6368 e280 990a 6c61 6e67 ..sketch....lang\n-000041c0: 7561 6765 2063 6f64 652e 0a0a 2020 2049 uage code... I\n-000041d0: 7420 6d61 7920 6265 2074 656d 7074 696e t may be temptin\n-000041e0: 6720 746f 2074 7572 6e20 6375 6c6c 696e g to turn cullin\n-000041f0: 6720 6f66 6620 6772 6174 7569 746f 7573 g off gratuitous\n-00004200: 6c79 2073 6f20 7468 6174 2076 6572 7465 ly so that verte\n-00004210: 780a 6f72 6465 7220 6361 6e20 6265 2069 x.order can be i\n-00004220: 676e 6f72 6564 2e20 2054 6869 7320 6973 gnored. This is\n-00004230: 206e 6f74 2061 2067 6f6f 6420 6964 6561 not a good idea\n-00004240: 2062 6563 6175 7365 206f 7574 7075 7420 because output \n-00004250: 6669 6c65 2073 697a 650a 616e 6420 5465 file size.and Te\n-00004260: 5820 616e 6420 506f 7374 7363 7269 7074 X and Postscript\n-00004270: 2070 726f 6365 7373 696e 6720 7469 6d65 processing time\n-00004280: 2062 6f74 6820 6465 7065 6e64 206f 6e20 both depend on \n-00004290: 7468 6520 6e75 6d62 6572 206f 660a 6f75 the number of.ou\n-000042a0: 7470 7574 2070 6f6c 7967 6f6e 732e 2020 tput polygons. \n-000042b0: 4375 6c6c 696e 6720 7573 7561 6c6c 7920 Culling usually \n-000042c0: 696d 7072 6f76 6573 2070 6572 666f 726d improves perform\n-000042d0: 616e 6365 2062 7920 6120 6661 6374 6f72 ance by a factor\n-000042e0: 206f 660a 7477 6f2e 2020 4f6e 2074 6865 of.two. On the\n-000042f0: 206f 7468 6572 2068 616e 642c 2067 6c6f other hand, glo\n-00004300: 6261 6c6c 7920 7365 7474 696e 6720 e280 bally setting ..\n-00004310: 9863 756c 6c3d 6661 6c73 65e2 8099 2069 .cull=false... i\n-00004320: 7320 7265 6173 6f6e 6162 6c65 0a77 6869 s reasonable.whi\n-00004330: 6c65 2064 6562 7567 6769 6e67 2e20 2053 le debugging. S\n-00004340: 6565 202a 6e6f 7465 2047 6c6f 6261 6c20 ee *note Global \n-00004350: 6f70 7469 6f6e 733a 3a20 616e 6420 2a6e options:: and *n\n-00004360: 6f74 6520 4c69 6d69 7473 206f 6e20 6572 ote Limits on er\n-00004370: 726f 720a 6465 7465 6374 696f 6e3a 3a2e ror.detection::.\n-00004380: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n-00004390: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5370 .info, Node: Sp\n-000043a0: 6563 6961 6c20 6f62 6a65 6374 732c 2020 ecial objects, \n-000043b0: 4e65 7874 3a20 4f62 6a65 6374 2074 7261 Next: Object tra\n-000043c0: 6e73 666f 726d 732c 2020 5072 6576 3a20 nsforms, Prev: \n-000043d0: 4472 6177 696e 6720 6120 736f 6c69 642c Drawing a solid,\n-000043e0: 2020 5570 3a20 496e 7472 6f64 7563 7469 Up: Introducti\n-000043f0: 6f6e 2062 7920 6578 616d 706c 650a 0a32 on by example..2\n-00004400: 2e34 2053 7065 6369 616c 206f 626a 6563 .4 Special objec\n-00004410: 7473 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ts.=============\n-00004420: 3d3d 3d3d 3d3d 0a0a 5765 2063 616e 2061 ======..We can a\n-00004430: 6464 206c 6162 656c 7320 746f 2061 2064 dd labels to a d\n-00004440: 7261 7769 6e67 2062 7920 7573 696e 6720 rawing by using \n-00004450: 7370 6563 6961 6c20 6f62 6a65 6374 732c special objects,\n-00004460: 2077 6869 6368 2070 726f 7669 6465 2061 which provide a\n-00004470: 0a77 6179 2074 6f20 656d 6265 6420 7261 .way to embed ra\n-00004480: 7720 4c61 5465 5820 616e 6420 e280 9850 w LaTeX and ...P\n-00004490: 5354 7269 636b 73e2 8099 2063 6f64 652e STricks... code.\n-000044a0: 2020 4164 6469 6e67 2074 6869 7320 746f Adding this to\n-000044b0: 2074 6865 0a74 6574 7261 6865 6472 6f6e the.tetrahedron\n-000044c0: 2064 6f65 7320 7468 6520 7472 6963 6b2e does the trick.\n-000044d0: 0a20 2073 7065 6369 616c 207c 5c66 6f6f . special |\\foo\n-000044e0: 746e 6f74 6573 697a 650a 2020 2020 2020 tnotesize. \n-000044f0: 2020 2020 205c 7570 7574 7b32 7074 7d5b \\uput{2pt}[\n-00004500: 7572 5d23 317b 2450 3124 7d0a 2020 2020 ur]#1{$P1$}. \n-00004510: 2020 2020 2020 205c 7570 7574 5b72 5d23 \\uput[r]#\n-00004520: 327b 2450 3224 7d0a 2020 2020 2020 2020 2{$P2$}. \n-00004530: 2020 205c 7570 7574 5b75 5d23 337b 2450 \\uput[u]#3{$P\n-00004540: 3324 7d0a 2020 2020 2020 2020 2020 205c 3$}. \\\n-00004550: 7570 7574 5b64 5d23 347b 2450 3424 7d7c uput[d]#4{$P4$}|\n-00004560: 0a20 2020 2028 7031 2928 7032 2928 7033 . (p1)(p2)(p3\n-00004570: 2928 7034 290a 4865 7265 2069 7320 7468 )(p4).Here is th\n-00004580: 6520 7265 7375 6c74 2e0a 0a00 085b 696d e result.....[im\n-00004590: 6167 6520 7372 633d 2265 7830 3432 2e70 age src=\"ex042.p\n-000045a0: 6e67 2220 7465 7874 3d22 496d 6167 6520 ng\" text=\"Image \n-000045b0: 6578 3034 3220 6f6d 6974 7465 6420 696e ex042 omitted in\n-000045c0: 2074 6578 7420 7665 7273 696f 6e20 6f66 text version of\n-000045d0: 2074 6869 7320 646f 6375 6d65 6e74 2e22 this document.\"\n-000045e0: 0008 5d0a 0a20 2020 5468 6572 6520 6172 ..].. There ar\n-000045f0: 6520 7365 7665 7261 6c20 6465 7461 696c e several detail\n-00004600: 7320 746f 206e 6f74 6520 6865 7265 2e20 s to note here. \n-00004610: 2046 6972 7374 2c20 7468 6520 7175 6f74 First, the quot\n-00004620: 696e 670a 636f 6e76 656e 7469 6f6e 2066 ing.convention f\n-00004630: 6f72 2074 6865 2072 6177 2063 6f64 6520 or the raw code \n-00004640: 6973 2073 696d 696c 6172 2074 6f20 7468 is similar to th\n-00004650: 6520 4c61 5465 5820 5c76 6572 6220 636f e LaTeX \\verb co\n-00004660: 6d6d 616e 642e 2020 5468 650a 6669 7273 mmand. The.firs\n-00004670: 7420 6e6f 6e2d 7768 6974 6520 7370 6163 t non-white spac\n-00004680: 6520 6368 6172 6163 7465 7220 666f 6c6c e character foll\n-00004690: 6f77 696e 6720 7370 6563 6961 6c20 6973 owing special is\n-000046a0: 2075 6e64 6572 7374 6f6f 6420 746f 2062 understood to b\n-000046b0: 650a 7468 6520 7175 6f74 6520 6368 6172 e.the quote char\n-000046c0: 6163 7465 722c 2069 6e20 7468 6973 2063 acter, in this c\n-000046d0: 6173 6520 e280 987c e280 992e 2020 5468 ase ...|.... Th\n-000046e0: 6520 7261 7720 7465 7874 2063 6f6e 7469 e raw text conti\n-000046f0: 6e75 6573 2075 6e74 696c 0a74 6869 7320 nues until.this \n-00004700: 6368 6172 6163 7465 7220 7265 6375 7273 character recurs\n-00004710: 2e0a 0a20 2020 5365 636f 6e64 2c20 7468 ... Second, th\n-00004720: 6520 6172 6775 6d65 6e74 2072 6566 6572 e argument refer\n-00004730: 656e 6365 7320 2331 2c20 2332 2c20 2333 ences #1, #2, #3\n-00004740: 2c20 616e 6420 2334 2072 6566 6572 2074 , and #4 refer t\n-00004750: 6f20 706f 696e 742c 0a76 6563 746f 722c o point,.vector,\n-00004760: 206f 7220 7363 616c 6172 2076 616c 7565 or scalar value\n-00004770: 7320 696e 2074 6865 206c 6973 7420 7468 s in the list th\n-00004780: 6174 2066 6f6c 6c6f 772e 2020 5468 6973 at follow. This\n-00004790: 2069 7320 7369 6d69 6c61 7220 746f 0a54 is similar to.T\n-000047a0: 6558 206d 6163 726f 2073 796e 7461 782e eX macro syntax.\n-000047b0: 2020 5468 6520 7472 616e 7366 6f72 6d65 The transforme\n-000047c0: 6420 616e 6420 7477 6f2d 6469 6d65 6e73 d and two-dimens\n-000047d0: 696f 6e61 6c20 7072 6f6a 6563 7469 6f6e ional projection\n-000047e0: 7320 6f66 0a74 6865 7365 2074 6872 6565 s of.these three\n-000047f0: 2d64 696d 656e 7369 6f6e 616c 2070 6f69 -dimensional poi\n-00004800: 6e74 7320 6172 6520 7375 6273 7469 7475 nts are substitu\n-00004810: 7465 6420 696e 2074 6865 2066 696e 616c ted in the final\n-00004820: 206f 7574 7075 742e 2020 416e 0a61 7267 output. 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With opti\n-00004e80: 6f6e 20e2 8098 6c61 793d 756e 6465 72e2 on ...lay=under.\n-00004e90: 8099 2c20 6120 7370 6563 6961 6c20 6973 .., a special is\n-00004ea0: 2064 7261 776e 205f 6265 666f 7265 5f2c drawn _before_,\n-00004eb0: 2068 656e 6365 2061 7070 6561 7273 0a5f hence appears._\n-00004ec0: 756e 6465 725f 2061 6e79 206f 6620 7468 under_ any of th\n-00004ed0: 6520 6f62 6a65 6374 7320 6861 6e64 6c65 e objects handle\n-00004ee0: 6420 6279 2074 6865 2068 6964 6465 6e20 d by the hidden \n-00004ef0: 7375 7266 6163 6520 616c 676f 7269 7468 surface algorith\n-00004f00: 6d2e 0a54 6869 7320 6973 2068 6f77 2074 m..This is how t\n-00004f10: 6865 206c 6967 6874 2067 7261 7920 6178 he light gray ax\n-00004f20: 6573 2077 6572 6520 6164 6465 6420 746f es were added to\n-00004f30: 2074 6865 2022 6865 6c6c 6f20 776f 726c the \"hello worl\n-00004f40: 6422 2065 7861 6d70 6c65 0a2a 6e6f 7465 d\" example.*note\n-00004f50: 2048 656c 6c6f 2077 6f72 6c64 3a3a 2e0a Hello world::..\n-00004f60: 0a20 2020 5370 6563 6961 6c20 6f62 6a65 . Special obje\n-00004f70: 6374 7320 6172 6520 706f 7765 7266 756c cts are powerful\n-00004f80: 2c20 7769 7468 206d 616e 7920 706f 7373 , with many poss\n-00004f90: 6962 6c65 2075 7365 732e 0a0a 1f0a 4669 ible uses.....Fi\n-00004fa0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n-00004fb0: 2020 4e6f 6465 3a20 4f62 6a65 6374 2074 Node: Object t\n-00004fc0: 7261 6e73 666f 726d 732c 2020 4e65 7874 ransforms, Next\n-00004fd0: 3a20 5265 7065 6174 6564 206f 626a 6563 : Repeated objec\n-00004fe0: 7473 2c20 2050 7265 763a 2053 7065 6369 ts, Prev: Speci\n-00004ff0: 616c 206f 626a 6563 7473 2c20 2055 703a al objects, Up:\n-00005000: 2049 6e74 726f 6475 6374 696f 6e20 6279 Introduction by\n-00005010: 2065 7861 6d70 6c65 0a0a 322e 3520 5472 example..2.5 Tr\n-00005020: 616e 7366 6f72 6d73 0a3d 3d3d 3d3d 3d3d ansforms.=======\n-00005030: 3d3d 3d3d 3d3d 3d0a 0a4e 6f77 206c 6574 =======..Now let\n-00005040: 2773 2061 6464 2061 2073 6563 6f6e 6420 's add a second \n-00005050: 636f 7079 206f 6620 7468 6520 7069 6572 copy of the pier\n-00005060: 6365 6420 7465 7472 6168 6564 726f 6e2e ced tetrahedron.\n-00005070: 2020 5765 276c 6c20 726f 7461 7465 0a74 We'll rotate.t\n-00005080: 6865 2063 6f70 7920 3930 2064 6567 7265 he copy 90 degre\n-00005090: 6573 2061 626f 7574 2074 6865 2078 2d61 es about the x-a\n-000050a0: 7869 7320 7769 7468 2074 6865 206f 7269 xis with the ori\n-000050b0: 6769 6e20 6173 20e2 809c 6365 6e74 6572 gin as ...center\n-000050c0: 206f 660a 726f 7461 7469 6f6e e280 9d20 of.rotation... \n-000050d0: 736f 2077 6520 6361 6e20 7365 6520 7468 so we can see th\n-000050e0: 6520 6261 636b 2c20 7468 656e 2074 7261 e back, then tra\n-000050f0: 6e73 6c61 7465 2069 7420 746f 2074 6865 nslate it to the\n-00005100: 2072 6967 6874 2d2d 696e 2074 6865 0a70 right--in the.p\n-00005110: 6f73 6974 6976 6520 782d 6469 7265 6374 ositive x-direct\n-00005120: 696f 6e2d 2d73 6f20 6974 2064 6f65 736e ion--so it doesn\n-00005130: 2774 2063 6f6c 6c69 6465 2077 6974 6820 't collide with \n-00005140: 7468 6520 6f72 6967 696e 616c 2e20 2054 the original. T\n-00005150: 6f20 6865 6c70 0a75 7320 7365 6520 7768 o help.us see wh\n-00005160: 6174 2773 2067 6f69 6e67 206f 6e2c 206d at's going on, m\n-00005170: 616b 6520 7468 6520 6261 636b 2073 6964 ake the back sid\n-00005180: 6520 6772 6179 2e0a 2020 6465 6620 7069 e gray.. def pi\n-00005190: 6572 6365 645f 7465 7472 6168 6564 726f erced_tetrahedro\n-000051a0: 6e20 7b0a 2020 2020 6465 6620 7031 2028 n {. def p1 (\n-000051b0: 302c 302c 3129 2064 6566 2070 3220 2831 0,0,1) def p2 (1\n-000051c0: 2c30 2c30 290a 2020 2020 6465 6620 7033 ,0,0). def p3\n-000051d0: 2028 302c 312c 3029 2064 6566 2070 3420 (0,1,0) def p4 \n-000051e0: 282d 2e33 2c2d 2e35 2c2d 2e38 290a 2020 (-.3,-.5,-.8). \n-000051f0: 2020 706f 6c79 676f 6e28 7031 2928 7032 polygon(p1)(p2\n-00005200: 2928 7033 2920 2020 2020 2020 2020 2020 )(p3) \n-00005210: 2020 2020 2020 2020 2020 2025 206f 7269 % ori\n-00005220: 6769 6e61 6c0a 2020 2020 706f 6c79 676f ginal. polygo\n-00005230: 6e28 7031 2928 7034 2928 7032 2920 2020 n(p1)(p4)(p2) \n+000021c0: 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a 5468 6520 ==========..The \n+000021d0: 6772 6f75 7020 6874 7470 3a2f 2f67 726f group http://gro\n+000021e0: 7570 732e 676f 6f67 6c65 2e63 6f6d 2f67 ups.google.com/g\n+000021f0: 726f 7570 2f73 6b65 7463 682d 7573 6572 roup/sketch-user\n+00002200: 7320 6973 2074 6865 2062 6573 7420 706c s is the best pl\n+00002210: 6163 650a 746f 2072 6570 6f72 7420 6275 ace.to report bu\n+00002220: 6773 2061 6e64 206d 616b 6520 696d 7072 gs and make impr\n+00002230: 6f76 656d 656e 7473 2e20 2041 2073 6563 ovements. 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We're ju\n+00002310: 7374 2062 7573 7920 616e 6420 7769 6c6c st busy and will\n+00002320: 2067 6574 2074 6f0a 796f 7572 2073 7567 get to.your sug\n+00002330: 6765 7374 696f 6e20 6576 656e 7475 616c gestion eventual\n+00002340: 6c79 2e0a 0a20 2020 466f 7220 6275 6773 ly... 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W\n+00002440: 6520 7573 6520 6f76 6572 616c 6c20 766f e use overall vo\n+00002450: 7465 2074 616c 6c69 6573 2074 6f20 6465 te tallies to de\n+00002460: 6369 6465 2077 6861 7420 746f 2064 6f20 cide what to do \n+00002470: 6e65 7874 2061 730a 7265 736f 7572 6365 next as.resource\n+00002480: 7320 7065 726d 6974 2e20 2057 6520 7265 s permit. We re\n+00002490: 7365 7276 6520 7468 6520 7269 6768 7420 serve the right \n+000024a0: 746f 2061 7373 6967 6e20 616e 7920 6e75 to assign any nu\n+000024b0: 6d62 6572 206f 6620 766f 7465 7320 746f mber of votes to\n+000024c0: 0a73 7567 6765 7374 696f 6e73 2066 726f .suggestions fro\n+000024d0: 6d20 7065 6f70 6c65 2077 686f 2068 6176 m people who hav\n+000024e0: 6520 6265 656e 2068 656c 7066 756c 2061 e been helpful a\n+000024f0: 6e64 2073 7570 706f 7274 6976 6520 696e nd supportive in\n+00002500: 2074 6865 0a70 6173 742e 0a0a 1f0a 4669 the.past.....Fi\n+00002510: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n+00002520: 2020 4e6f 6465 3a20 436f 6e74 7269 6275 Node: Contribu\n+00002530: 7469 6f6e 732c 2020 5072 6576 3a20 5265 tions, Prev: Re\n+00002540: 706f 7274 696e 6720 6275 6773 2c20 2055 porting bugs, U\n+00002550: 703a 2041 626f 7574 2073 6b65 7463 680a p: About sketch.\n+00002560: 0a31 2e32 2043 6f6e 7472 6962 7574 696f .1.2 Contributio\n+00002570: 6e73 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ns.=============\n+00002580: 3d3d 3d3d 0a0a 4966 2079 6f75 2069 6e74 ====..If you int\n+00002590: 656e 6420 746f 2069 6d70 6c65 6d65 6e74 end to implement\n+000025a0: 2061 6e20 656e 6861 6e63 656d 656e 7420 an enhancement \n+000025b0: 6f66 2079 6f75 7220 6f77 6e2c 2074 6861 of your own, tha\n+000025c0: 7427 7320 7465 7272 6966 6963 210a 436f t's terrific!.Co\n+000025d0: 6e73 6964 6572 2063 6f6c 6c61 626f 7261 nsider collabora\n+000025e0: 7469 6e67 2077 6974 6820 7573 2066 6972 ting with us fir\n+000025f0: 7374 2074 6f20 7365 6520 6966 2077 6527 st to see if we'\n+00002600: 7265 2061 6c72 6561 6479 2077 6f72 6b69 re already worki\n+00002610: 6e67 206f 6e0a 796f 7572 2069 6465 6120 ng on.your idea \n+00002620: 6f72 2069 6620 7765 2063 616e 2075 7365 or if we can use\n+00002630: 2079 6f75 7220 776f 726b 2069 6e20 7468 your work in th\n+00002640: 6520 6f66 6669 6369 616c 2072 656c 6561 e official relea\n+00002650: 7365 2e0a 0a00 085b 696d 6167 6520 7372 se.....[image sr\n+00002660: 633d 2265 7830 3030 2e70 6e67 2220 7465 c=\"ex000.png\" te\n+00002670: 7874 3d22 496d 6167 6520 6578 3030 3020 xt=\"Image ex000 \n+00002680: 6f6d 6974 7465 6420 696e 2074 6578 7420 omitted in text \n+00002690: 7665 7273 696f 6e20 6f66 2074 6869 7320 version of this \n+000026a0: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a1f document.\"..]...\n+000026b0: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+000026c0: 666f 2c20 204e 6f64 653a 2049 6e74 726f fo, Node: Intro\n+000026d0: 6475 6374 696f 6e20 6279 2065 7861 6d70 duction by examp\n+000026e0: 6c65 2c20 204e 6578 743a 2049 6e70 7574 le, Next: Input\n+000026f0: 206c 616e 6775 6167 652c 2020 5072 6576 language, Prev\n+00002700: 3a20 4162 6f75 7420 736b 6574 6368 2c20 : About sketch, \n+00002710: 2055 703a 2054 6f70 0a0a 3220 496e 7472 Up: Top..2 Intr\n+00002720: 6f64 7563 7469 6f6e 2062 7920 6578 616d oduction by exam\n+00002730: 706c 650a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a ple.************\n+00002740: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a0a 0a54 *************..T\n+00002750: 6865 20e2 8098 736b 6574 6368 e280 9920 he ...sketch... \n+00002760: 696e 7075 7420 6c61 6e67 7561 6765 2077 input language w\n+00002770: 696c 6c20 7365 656d 2066 616d 696c 6961 ill seem familia\n+00002780: 7220 746f 2075 7365 7273 206f 6620 7468 r to users of th\n+00002790: 650a e280 9850 5354 7269 636b 73e2 8099 e....PSTricks...\n+000027a0: 2070 6163 6b61 6765 2066 6f72 204c 6154 package for LaT\n+000027b0: 6558 2e20 2054 6865 2066 6f6c 6c6f 7769 eX. The followi\n+000027c0: 6e67 2070 726f 6772 616d 2064 7261 7773 ng program draws\n+000027d0: 2061 2074 7269 616e 6775 6c61 720a 706f a triangular.po\n+000027e0: 6c79 676f 6e20 7069 6572 6365 6420 6279 lygon pierced by\n+000027f0: 2061 206c 696e 652e 0a20 2070 6f6c 7967 a line.. polyg\n+00002800: 6f6e 2830 2c30 2c31 2928 312c 302c 3029 on(0,0,1)(1,0,0)\n+00002810: 2830 2c31 2c30 290a 2020 6c69 6e65 282d (0,1,0). line(-\n+00002820: 312c 2d31 2c2d 3129 2832 2c32 2c32 290a 1,-1,-1)(2,2,2).\n+00002830: 5468 6520 636f 6f72 6469 6e61 7465 2073 The coordinate s\n+00002840: 7973 7465 6d20 6973 2061 2073 7461 6e64 ystem is a stand\n+00002850: 6172 6420 7269 6768 742d 6861 6e64 6564 ard right-handed\n+00002860: 2043 6172 7465 7369 616e 206f 6e65 2e0a Cartesian one..\n+00002870: 0a00 085b 696d 6167 6520 7372 633d 2265 ...[image src=\"e\n+00002880: 7830 3130 2e70 6e67 2220 7465 7874 3d22 x010.png\" text=\"\n+00002890: 496d 6167 6520 6578 3031 3020 6f6d 6974 Image ex010 omit\n+000028a0: 7465 6420 696e 2074 6578 7420 7665 7273 ted in text vers\n+000028b0: 696f 6e20 6f66 2074 6869 7320 646f 6375 ion of this docu\n+000028c0: 6d65 6e74 2e22 0008 5d0a 0a2a 204d 656e ment.\"..]..* Men\n+000028d0: 753a 0a0a 2a20 4865 6c6c 6f20 776f 726c u:..* Hello worl\n+000028e0: 643a 3a20 2020 2020 2020 2020 2020 2020 d:: \n+000028f0: 2020 2020 5369 6d70 6c65 7374 2070 6f73 Simplest pos\n+00002900: 7369 626c 6520 e280 9873 6b65 7463 68e2 sible ...sketch.\n+00002910: 8099 2070 726f 6772 616d 2e0a 2a20 4472 .. program..* Dr\n+00002920: 6177 696e 6720 6f70 7469 6f6e 733a 3a20 awing options:: \n+00002930: 2020 2020 2020 2020 2020 2020 436f 6e74 Cont\n+00002940: 726f 6c6c 696e 6720 6f62 6a65 6374 2061 rolling object a\n+00002950: 7070 6561 7261 6e63 652e 0a2a 2044 7261 ppearance..* Dra\n+00002960: 7769 6e67 2061 2073 6f6c 6964 3a3a 2020 wing a solid:: \n+00002970: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n+00002980: 6e67 2061 6e20 6f62 6a65 6374 2077 6974 ng an object wit\n+00002990: 6820 3364 2061 7070 6561 7261 6e63 652e h 3d appearance.\n+000029a0: 0a2a 2053 7065 6369 616c 206f 626a 6563 .* Special objec\n+000029b0: 7473 3a3a 2020 2020 2020 2020 2020 2020 ts:: \n+000029c0: 204c 6179 696e 6720 5465 5820 6f76 6572 Laying TeX over\n+000029d0: 2c20 696e 2c20 6f72 2075 6e64 6572 2064 , in, or under d\n+000029e0: 7261 7769 6e67 732e 0a2a 204f 626a 6563 rawings..* Objec\n+000029f0: 7420 7472 616e 7366 6f72 6d73 3a3a 2020 t transforms:: \n+00002a00: 2020 2020 2020 2020 2052 6f74 6174 652c Rotate,\n+00002a10: 2074 7261 6e73 6c61 7465 2c20 7363 616c translate, scal\n+00002a20: 652c 2061 6e64 206f 7468 6572 732e 0a2a e, and others..*\n+00002a30: 2052 6570 6561 7465 6420 6f62 6a65 6374 Repeated object\n+00002a40: 733a 3a20 2020 2020 2020 2020 2020 204d s:: M\n+00002a50: 616b 696e 6720 7472 616e 7366 6f72 6d65 aking transforme\n+00002a60: 6420 636f 7069 6573 2e0a 2a20 5377 6570 d copies..* Swep\n+00002a70: 7420 6f62 6a65 6374 733a 3a20 2020 2020 t objects:: \n+00002a80: 2020 2020 2020 2020 2020 5377 6565 7069 Sweepi\n+00002a90: 6e67 206f 626a 6563 7473 2069 6e20 7370 ng objects in sp\n+00002aa0: 6163 6520 746f 206d 616b 6520 6e65 7720 ace to make new \n+00002ab0: 7368 6170 6573 2e0a 0a1f 0a46 696c 653a shapes.....File:\n+00002ac0: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n+00002ad0: 6f64 653a 2048 656c 6c6f 2077 6f72 6c64 ode: Hello world\n+00002ae0: 2c20 204e 6578 743a 2044 7261 7769 6e67 , Next: Drawing\n+00002af0: 206f 7074 696f 6e73 2c20 2050 7265 763a options, Prev:\n+00002b00: 2049 6e74 726f 6475 6374 696f 6e20 6279 Introduction by\n+00002b10: 2065 7861 6d70 6c65 2c20 2055 703a 2049 example, Up: I\n+00002b20: 6e74 726f 6475 6374 696f 6e20 6279 2065 ntroduction by e\n+00002b30: 7861 6d70 6c65 0a0a 322e 3120 4865 6c6c xample..2.1 Hell\n+00002b40: 6f20 776f 726c 640a 3d3d 3d3d 3d3d 3d3d o world.========\n+00002b50: 3d3d 3d3d 3d3d 3d0a 0a54 6865 20e2 8098 =======..The ...\n+00002b60: 736b 6574 6368 e280 9920 7072 6f67 7261 sketch... progra\n+00002b70: 6d20 6162 6f76 6520 6973 206e 6561 726c m above is nearl\n+00002b80: 7920 7468 6520 7369 6d70 6c65 7374 206f y the simplest o\n+00002b90: 6e65 2070 6f73 7369 626c 652c 2074 6865 ne possible, the\n+00002ba0: 0a65 7175 6976 616c 656e 7420 6f66 2061 .equivalent of a\n+00002bb0: 2022 6865 6c6c 6f20 776f 726c 6422 2070 \"hello world\" p\n+00002bc0: 726f 6772 616d 2079 6f75 206d 6967 6874 rogram you might\n+00002bd0: 2066 696e 6420 6174 2074 6865 2073 7461 find at the sta\n+00002be0: 7274 206f 6620 610a 7072 6f67 7261 6d6d rt of a.programm\n+00002bf0: 696e 6720 6c61 6e67 7561 6765 2074 6578 ing language tex\n+00002c00: 742e 2020 4966 2069 7420 6973 2073 6176 t. If it is sav\n+00002c10: 6564 2069 6e20 7468 6520 6669 6c65 20e2 ed in the file .\n+00002c20: 8098 7369 6d70 6c65 2e73 6be2 8099 2c20 ..simple.sk..., \n+00002c30: 7468 656e 0a74 6865 2063 6f6d 6d61 6e64 then.the command\n+00002c40: 0a20 2073 6b65 7463 6820 7369 6d70 6c65 . sketch simple\n+00002c50: 2e73 6b20 2d6f 2073 696d 706c 652e 7465 .sk -o simple.te\n+00002c60: 780a 6372 6561 7465 7320 6120 6669 6c65 x.creates a file\n+00002c70: 20e2 8098 7369 6d70 6c65 2e74 6578 e280 ...simple.tex..\n+00002c80: 9920 636f 6e74 6169 6e69 6e67 20e2 8098 . containing ...\n+00002c90: 5053 5472 6963 6b73 e280 9920 636f 6d6d PSTricks... comm\n+00002ca0: 616e 6473 2074 6f20 6472 6177 2074 6865 ands to draw the\n+00002cb0: 7365 0a6f 626a 6563 7473 206f 6e20 7061 se.objects on pa\n+00002cc0: 7065 722e 2020 5468 6520 636f 6e74 656e per. The conten\n+00002cd0: 7473 206f 6620 e280 9873 696d 706c 652e ts of ...simple.\n+00002ce0: 7465 78e2 8099 206c 6f6f 6b20 6c69 6b65 tex... look like\n+00002cf0: 2074 6869 732e 0a20 205c 6265 6769 6e7b this.. \\begin{\n+00002d00: 7073 7069 6374 7572 657d 282d 312c 2d31 pspicture}(-1,-1\n+00002d10: 2928 322c 3229 0a20 205c 7073 7456 6572 )(2,2). \\pstVer\n+00002d20: 627b 3120 7365 746c 696e 656a 6f69 6e7d b{1 setlinejoin}\n+00002d30: 0a20 205c 7073 6c69 6e65 282d 312c 2d31 . \\psline(-1,-1\n+00002d40: 2928 2e33 3333 2c2e 3333 3329 0a20 205c )(.333,.333). \\\n+00002d50: 7073 706f 6c79 676f 6e5b 6669 6c6c 7374 pspolygon[fillst\n+00002d60: 796c 653d 736f 6c69 642c 6669 6c6c 636f yle=solid,fillco\n+00002d70: 6c6f 723d 7768 6974 655d 2830 2c30 2928 lor=white](0,0)(\n+00002d80: 312c 3029 2830 2c31 290a 2020 5c70 736c 1,0)(0,1). \\psl\n+00002d90: 696e 6528 2e33 3333 2c2e 3333 3329 2832 ine(.333,.333)(2\n+00002da0: 2c32 290a 2020 5c65 6e64 7b70 7370 6963 ,2). \\end{pspic\n+00002db0: 7475 7265 7d0a 5468 6520 6869 6464 656e ture}.The hidden\n+00002dc0: 2073 7572 6661 6365 2061 6c67 6f72 6974 surface algorit\n+00002dd0: 686d 206f 6620 e280 9873 6b65 7463 68e2 hm of ...sketch.\n+00002de0: 8099 2068 6173 2073 706c 6974 2074 6865 .. has split the\n+00002df0: 206c 696e 6520 696e 746f 2074 776f 0a70 line into two.p\n+00002e00: 6965 6365 7320 616e 6420 6f72 6465 7265 ieces and ordere\n+00002e10: 6420 7468 6520 7468 7265 6520 7265 7375 d the three resu\n+00002e20: 6c74 696e 6720 6f62 6a65 6374 7320 736f lting objects so\n+00002e30: 2074 6861 7420 7468 6520 636f 7272 6563 that the correc\n+00002e40: 740a 706f 7274 696f 6e20 6f66 2074 6865 t.portion of the\n+00002e50: 206c 696e 6520 6973 2068 6964 6465 6e2e line is hidden.\n+00002e60: 0a0a 2020 2049 6620 796f 7527 7665 206e .. If you've n\n+00002e70: 6f74 6963 6564 2074 6861 7420 7468 6520 oticed that the \n+00002e80: 7072 6f6a 6563 7469 6f6e 2077 6520 6172 projection we ar\n+00002e90: 6520 7573 696e 6720 7365 656d 7320 6571 e using seems eq\n+00002ea0: 7569 7661 6c65 6e74 0a74 6f20 6572 6173 uivalent.to eras\n+00002eb0: 696e 6720 7468 6520 7a2d 636f 6f72 6469 ing the z-coordi\n+00002ec0: 6e61 7465 206f 6620 7468 6520 7468 7265 nate of the thre\n+00002ed0: 652d 6469 6d65 6e73 696f 6e61 6c20 696e e-dimensional in\n+00002ee0: 7075 7420 706f 696e 7473 2c20 7061 740a put points, pat.\n+00002ef0: 796f 7572 7365 6c66 206f 6e20 7468 6520 yourself on the \n+00002f00: 6261 636b 2e20 2059 6f75 2061 7265 2063 back. You are c\n+00002f10: 6f72 7265 6374 2e20 2054 6869 7320 6973 orrect. This is\n+00002f20: 2063 616c 6c65 6420 6120 e280 9c70 6172 called a ...par\n+00002f30: 616c 6c65 6c0a 7072 6f6a 6563 7469 6f6e allel.projection\n+00002f40: e280 9d2e 2020 5468 6520 7a2d 636f 6f72 .... The z-coor\n+00002f50: 6469 6e61 7465 2061 7869 7320 6973 2070 dinate axis is p\n+00002f60: 6f69 6e74 696e 6720 7374 7261 6967 6874 ointing straight\n+00002f70: 206f 7574 206f 6620 7468 650a 7061 7065 out of the.pape\n+00002f80: 7220 6174 2075 732c 2077 6869 6c65 2074 r at us, while t\n+00002f90: 6865 2078 2d20 616e 6420 792d 6178 6573 he x- and y-axes\n+00002fa0: 2070 6f69 6e74 2074 6f20 7468 6520 7269 point to the ri\n+00002fb0: 6768 7420 616e 6420 7570 2061 7320 7573 ght and up as us\n+00002fc0: 7561 6c2e 0a0a 2020 2054 6865 2072 6573 ual... The res\n+00002fd0: 756c 7469 6e67 2070 6963 7475 7265 2066 ulting picture f\n+00002fe0: 696c 6520 6361 6e20 6265 2069 6e63 6c75 ile can be inclu\n+00002ff0: 6465 6420 696e 2061 204c 6154 6558 2064 ded in a LaTeX d\n+00003000: 6f63 756d 656e 7420 7769 7468 0a5c 696e ocument with.\\in\n+00003010: 7075 747b 7369 6d70 6c65 7d2e 2020 416c put{simple}. Al\n+00003020: 7465 726e 6174 656c 792c 2061 6464 696e ternately, addin\n+00003030: 6720 7468 6520 636f 6d6d 616e 6420 6c69 g the command li\n+00003040: 6e65 206f 7074 696f 6e20 e280 982d 54e2 ne option ...-T.\n+00003050: 8099 2831 290a 6361 7573 6573 2074 6865 ..(1).causes the\n+00003060: 20e2 8098 7073 7069 6374 7572 65e2 8099 ...pspicture...\n+00003070: 2074 6f20 6265 2077 7261 7070 6564 2069 to be wrapped i\n+00003080: 6e20 6120 7368 6f72 7420 6275 7420 636f n a short but co\n+00003090: 6d70 6c65 7465 2064 6f63 756d 656e 742c mplete document,\n+000030a0: 0a72 6561 6479 2074 6f20 7275 6e20 7468 .ready to run th\n+000030b0: 6f75 6768 204c 6154 6558 2e20 2049 6e20 ough LaTeX. In \n+000030c0: 6120 6669 6e69 7368 6564 2c20 7479 7065 a finished, type\n+000030d0: 7365 7420 646f 6375 6d65 6e74 2c20 7468 set document, th\n+000030e0: 6520 7069 6374 7572 650a 6c6f 6f6b 7320 e picture.looks \n+000030f0: 6c69 6b65 2074 6869 732e 2020 2854 6865 like this. (The\n+00003100: 2061 7865 7320 6861 7665 2062 6565 6e20 axes have been \n+00003110: 6164 6465 6420 696e 206c 6967 6874 2067 added in light g\n+00003120: 7261 792e 290a 0a00 085b 696d 6167 6520 ray.)....[image \n+00003130: 7372 633d 2265 7830 3230 2e70 6e67 2220 src=\"ex020.png\" \n+00003140: 7465 7874 3d22 496d 6167 6520 6578 3032 text=\"Image ex02\n+00003150: 3020 6f6d 6974 7465 6420 696e 2074 6578 0 omitted in tex\n+00003160: 7420 7665 7273 696f 6e20 6f66 2074 6869 t version of thi\n+00003170: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a s document.\"..].\n+00003180: 0a49 7420 6973 2069 6d70 6f72 7461 6e74 .It is important\n+00003190: 2074 6f20 6b6e 6f77 2074 6861 7420 6f6e to know that on\n+000031a0: 6c79 2074 6865 2022 6f75 7473 6964 6522 ly the \"outside\"\n+000031b0: 206f 6620 6120 706f 6c79 676f 6e20 6973 of a polygon is\n+000031c0: 206e 6f72 6d61 6c6c 790a 6472 6177 6e2e normally.drawn.\n+000031d0: 2020 5468 6520 e280 9c6f 7574 7369 6465 The ...outside\n+000031e0: e280 9d20 6973 2077 6865 7265 2074 6865 ... is where the\n+000031f0: 2076 6572 7469 6365 7320 6769 7665 6e20 vertices given \n+00003200: 696e 2074 6865 20e2 8098 706f 6c79 676f in the ...polygo\n+00003210: 6ee2 8099 0a63 6f6d 6d61 6e64 2061 7070 n....command app\n+00003220: 6561 7220 696e 205f 636f 756e 7465 722d ear in _counter-\n+00003230: 636c 6f63 6b77 6973 655f 206f 7264 6572 clockwise_ order\n+00003240: 2e20 2054 6875 732c 2069 6620 7468 6520 . Thus, if the \n+00003250: 636f 6d6d 616e 6420 6162 6f76 650a 6861 command above.ha\n+00003260: 6420 6265 656e 0a20 2070 6f6c 7967 6f6e d been. polygon\n+00003270: 2830 2c31 2c30 2928 312c 302c 3029 2830 (0,1,0)(1,0,0)(0\n+00003280: 2c30 2c31 290a 7468 6520 706f 6c79 676f ,0,1).the polygo\n+00003290: 6e20 776f 756c 6420 6e6f 7420 6170 7065 n would not appe\n+000032a0: 6172 2069 6e20 7468 6520 7069 6374 7572 ar in the pictur\n+000032b0: 6520 6174 2061 6c6c 2e20 2049 7420 776f e at all. It wo\n+000032c0: 756c 6420 6861 7665 2062 6565 6e0a e280 uld have been...\n+000032d0: 9c63 756c 6c65 64e2 809d 2066 726f 6d20 .culled... from \n+000032e0: 7468 6520 7363 656e 652e 2020 5468 6973 the scene. This\n+000032f0: 2063 756c 6c69 6e67 2062 6568 6176 696f culling behavio\n+00003300: 7220 6d61 7920 7365 656d 2073 7472 616e r may seem stran\n+00003310: 6765 2c20 6275 740a 7374 6179 2074 756e ge, but.stay tun\n+00003320: 6564 2e0a 0a20 2020 2d2d 2d2d 2d2d 2d2d ed... --------\n+00003330: 2d2d 2046 6f6f 746e 6f74 6573 202d 2d2d -- Footnotes ---\n+00003340: 2d2d 2d2d 2d2d 2d0a 0a20 2020 2831 2920 -------.. (1) \n+00003350: 4f72 2066 6f72 2045 7572 6f70 6561 6e20 Or for European \n+00003360: 7573 6572 7320 6f66 2041 3420 7369 7a65 users of A4 size\n+00003370: 2070 6170 6572 2c20 e280 982d 5465 e280 paper, ...-Te..\n+00003380: 992e 0a0a 1f0a 4669 6c65 3a20 736b 6574 ......File: sket\n+00003390: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n+000033a0: 4472 6177 696e 6720 6f70 7469 6f6e 732c Drawing options,\n+000033b0: 2020 4e65 7874 3a20 4472 6177 696e 6720 Next: Drawing \n+000033c0: 6120 736f 6c69 642c 2020 5072 6576 3a20 a solid, Prev: \n+000033d0: 4865 6c6c 6f20 776f 726c 642c 2020 5570 Hello world, Up\n+000033e0: 3a20 496e 7472 6f64 7563 7469 6f6e 2062 : Introduction b\n+000033f0: 7920 6578 616d 706c 650a 0a32 2e32 204f y example..2.2 O\n+00003400: 7074 696f 6e73 0a3d 3d3d 3d3d 3d3d 3d3d ptions.=========\n+00003410: 3d3d 0a0a 4d61 6e79 20e2 8098 5053 5472 ==..Many ...PSTr\n+00003420: 6963 6b73 e280 9920 616e 6420 e280 9854 icks... and ...T\n+00003430: 696b 5a2f 5047 46e2 8099 206f 7074 696f ikZ/PGF... optio\n+00003440: 6e73 2077 6f72 6b20 6a75 7374 2066 696e ns work just fin\n+00003450: 6520 696e 20e2 8098 736b 6574 6368 e280 e in ...sketch..\n+00003460: 992e 2020 4966 0a67 656e 6572 6174 696e .. If.generatin\n+00003470: 6720 e280 9850 5354 7269 636b 73e2 8099 g ...PSTricks...\n+00003480: 2c20 7468 6520 636f 6465 0a20 2070 6f6c , the code. pol\n+00003490: 7967 6f6e 5b66 696c 6c63 6f6c 6f72 3d6c ygon[fillcolor=l\n+000034a0: 6967 6874 6772 6179 2c6c 696e 6577 6964 ightgray,linewid\n+000034b0: 7468 3d33 7074 5d28 302c 302c 3129 2831 th=3pt](0,0,1)(1\n+000034c0: 2c30 2c30 2928 302c 312c 3029 0a20 206c ,0,0)(0,1,0). l\n+000034d0: 696e 655b 6c69 6e65 7374 796c 653d 646f ine[linestyle=do\n+000034e0: 7474 6564 5d28 2d31 2c2d 312c 2d31 2928 tted](-1,-1,-1)(\n+000034f0: 322c 322c 3229 0a70 726f 6475 6365 730a 2,2,2).produces.\n+00003500: 0a00 085b 696d 6167 6520 7372 633d 2265 ...[image src=\"e\n+00003510: 7830 3330 2e70 6e67 2220 7465 7874 3d22 x030.png\" text=\"\n+00003520: 496d 6167 6520 6578 3033 3020 6f6d 6974 Image ex030 omit\n+00003530: 7465 6420 696e 2074 6578 7420 7665 7273 ted in text vers\n+00003540: 696f 6e20 6f66 2074 6869 7320 646f 6375 ion of this docu\n+00003550: 6d65 6e74 2e22 0008 5d0a 0a20 2020 546f ment.\"..].. To\n+00003560: 2070 726f 6475 6365 20e2 8098 5469 6b5a produce ...TikZ\n+00003570: 2f50 4746 e280 992c 2074 6865 2063 6f72 /PGF..., the cor\n+00003580: 7265 7370 6f6e 6469 6e67 2063 6f64 6520 responding code \n+00003590: 6973 0a20 2070 6f6c 7967 6f6e 5b66 696c is. polygon[fil\n+000035a0: 6c3d 6c69 6768 7467 7261 792c 6c69 6e65 l=lightgray,line\n+000035b0: 2077 6964 7468 3d33 7074 5d28 302c 302c width=3pt](0,0,\n+000035c0: 3129 2831 2c30 2c30 2928 302c 312c 3029 1)(1,0,0)(0,1,0)\n+000035d0: 0a20 206c 696e 655b 7374 796c 653d 646f . line[style=do\n+000035e0: 7474 6564 5d28 2d31 2c2d 312c 2d31 2928 tted](-1,-1,-1)(\n+000035f0: 322c 322c 3229 0a20 2067 6c6f 6261 6c20 2,2,2). global \n+00003600: 7b20 6c61 6e67 7561 6765 2074 696b 7a20 { language tikz \n+00003610: 7d0a 5468 6520 6669 6e61 6c20 e280 9867 }.The final ...g\n+00003620: 6c6f 6261 6ce2 8099 2069 6e73 7472 7563 lobal... instruc\n+00003630: 7473 20e2 8098 736b 6574 6368 e280 9920 ts ...sketch... \n+00003640: 746f 2070 726f 6475 6365 20e2 8098 5469 to produce ...Ti\n+00003650: 6b5a 2f50 4746 e280 9920 636f 6465 2061 kZ/PGF... code a\n+00003660: 730a 6f75 7470 7574 2072 6174 6865 7220 s.output rather \n+00003670: 7468 616e 2074 6865 2064 6566 6175 6c74 than the default\n+00003680: 2c20 e280 9850 5354 7269 636b 73e2 8099 , ...PSTricks...\n+00003690: 2e20 204e 6f74 6520 7468 6174 20e2 8098 . Note that ...\n+000036a0: 706f 6c79 676f 6ee2 8099 2066 696c 6c0a polygon... fill.\n+000036b0: 636f 6c6f 7220 616e 6420 e280 986c 696e color and ...lin\n+000036c0: 65e2 8099 2073 7479 6c65 206f 7074 696f e... style optio\n+000036d0: 6e73 2062 6f74 6820 636f 6e66 6f72 6d20 ns both conform \n+000036e0: 746f 20e2 8098 5469 6b5a e280 9920 7379 to ...TikZ... sy\n+000036f0: 6e74 6178 2072 756c 6573 2e20 2054 6865 ntax rules. The\n+00003700: 0a72 6573 756c 7469 6e67 20e2 8098 5469 .resulting ...Ti\n+00003710: 6b5a 2f50 4746 e280 9920 6f75 7470 7574 kZ/PGF... output\n+00003720: 2069 730a 2020 5c62 6567 696e 7b74 696b is. \\begin{tik\n+00003730: 7a70 6963 7475 7265 7d5b 6a6f 696e 3d72 zpicture}[join=r\n+00003740: 6f75 6e64 5d0a 2020 5c64 7261 775b 646f ound]. \\draw[do\n+00003750: 7474 6564 5d28 2d31 2c2d 3129 2d2d 282e tted](-1,-1)--(.\n+00003760: 3333 332c 2e33 3333 293b 0a20 205c 6669 333,.333);. \\fi\n+00003770: 6c6c 6472 6177 5b66 696c 6c3d 6c69 6768 lldraw[fill=ligh\n+00003780: 7467 7261 792c 6c69 6e65 2077 6964 7468 tgray,line width\n+00003790: 3d33 7074 5d28 302c 3029 2d2d 2831 2c30 =3pt](0,0)--(1,0\n+000037a0: 292d 2d28 302c 3129 2d2d 6379 636c 653b )--(0,1)--cycle;\n+000037b0: 0a20 205c 6472 6177 5b64 6f74 7465 645d . \\draw[dotted]\n+000037c0: 282e 3333 332c 2e33 3333 292d 2d28 322c (.333,.333)--(2,\n+000037d0: 3229 3b0a 2020 5c65 6e64 7b74 696b 7a70 2);. \\end{tikzp\n+000037e0: 6963 7475 7265 7d0a 5468 6520 7265 6d61 icture}.The rema\n+000037f0: 696e 696e 6720 6578 616d 706c 6573 206f ining examples o\n+00003800: 6620 7468 6973 206d 616e 7561 6c20 6172 f this manual ar\n+00003810: 6520 696e 2050 5354 7269 636b 7320 7374 e in PSTricks st\n+00003820: 796c 652e 0a0a 1f0a 4669 6c65 3a20 736b yle.....File: sk\n+00003830: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n+00003840: 3a20 4472 6177 696e 6720 6120 736f 6c69 : Drawing a soli\n+00003850: 642c 2020 4e65 7874 3a20 5370 6563 6961 d, Next: Specia\n+00003860: 6c20 6f62 6a65 6374 732c 2020 5072 6576 l objects, Prev\n+00003870: 3a20 4472 6177 696e 6720 6f70 7469 6f6e : Drawing option\n+00003880: 732c 2020 5570 3a20 496e 7472 6f64 7563 s, Up: Introduc\n+00003890: 7469 6f6e 2062 7920 6578 616d 706c 650a tion by example.\n+000038a0: 0a32 2e33 2044 7261 7769 6e67 2061 2073 .2.3 Drawing a s\n+000038b0: 6f6c 6964 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d olid.===========\n+000038c0: 3d3d 3d3d 3d3d 3d3d 0a0a 4c65 7427 7320 ========..Let's \n+000038d0: 7472 7920 736f 6d65 7468 696e 6720 6d6f try something mo\n+000038e0: 7265 2065 7863 6974 696e 672e 2020 e280 re exciting. ..\n+000038f0: 9853 6b65 7463 68e2 8099 2068 6173 206e .Sketch... has n\n+00003900: 6f20 6e6f 7469 6f6e 206f 6620 6120 736f o notion of a so\n+00003910: 6c69 642c 0a62 7574 2070 6f6c 7967 6f6e lid,.but polygon\n+00003920: 616c 20e2 809c 6661 6365 73e2 809d 2063 al ...faces... c\n+00003930: 616e 2062 6520 7573 6564 2074 6f20 7265 an be used to re\n+00003940: 7072 6573 656e 7420 7468 6520 626f 756e present the boun\n+00003950: 6461 7279 206f 6620 6120 736f 6c69 642e dary of a solid.\n+00003960: 0a54 6f20 7468 6520 7072 6576 696f 7573 .To the previous\n+00003970: 2065 7861 6d70 6c65 2c20 6c65 7427 7320 example, let's \n+00003980: 6164 6420 7468 7265 6520 6d6f 7265 2074 add three more t\n+00003990: 7269 616e 6775 6c61 7220 706f 6c79 676f riangular polygo\n+000039a0: 6e73 2074 6f0a 6d61 6b65 2074 6865 2066 ns to.make the f\n+000039b0: 6163 6573 206f 6620 616e 2069 7272 6567 aces of an irreg\n+000039c0: 756c 6172 2074 6574 7261 6865 6472 6f6e ular tetrahedron\n+000039d0: 2e0a 2020 2520 7665 7274 6963 6573 206f .. % vertices o\n+000039e0: 6620 7468 6520 7465 7472 6168 6564 726f f the tetrahedro\n+000039f0: 6e0a 2020 6465 6620 7031 2028 302c 302c n. def p1 (0,0,\n+00003a00: 3129 2064 6566 2070 3220 2831 2c30 2c30 1) def p2 (1,0,0\n+00003a10: 290a 2020 6465 6620 7033 2028 302c 312c ). def p3 (0,1,\n+00003a20: 3029 2064 6566 2070 3420 282d 2e33 2c2d 0) def p4 (-.3,-\n+00003a30: 2e35 2c2d 2e38 290a 0a20 2025 2066 6163 .5,-.8).. % fac\n+00003a40: 6573 206f 6620 7468 6520 7465 7472 6168 es of the tetrah\n+00003a50: 6564 726f 6e2e 0a20 2070 6f6c 7967 6f6e edron.. polygon\n+00003a60: 2870 3129 2870 3229 2870 3329 2025 206f (p1)(p2)(p3) % o\n+00003a70: 7269 6769 6e61 6c20 6672 6f6e 7420 706f riginal front po\n+00003a80: 6c79 676f 6e0a 2020 706f 6c79 676f 6e28 lygon. polygon(\n+00003a90: 7031 2928 7034 2928 7032 2920 2520 626f p1)(p4)(p2) % bo\n+00003aa0: 7474 6f6d 0a20 2070 6f6c 7967 6f6e 2870 ttom. polygon(p\n+00003ab0: 3129 2870 3329 2870 3429 2025 206c 6566 1)(p3)(p4) % lef\n+00003ac0: 740a 2020 706f 6c79 676f 6e28 7033 2928 t. polygon(p3)(\n+00003ad0: 7032 2928 7034 2920 2520 7265 6172 0a0a p2)(p4) % rear..\n+00003ae0: 2020 2520 6c69 6e65 2074 6f20 7069 6572 % line to pier\n+00003af0: 6365 2074 6865 2074 6574 7261 6865 6472 ce the tetrahedr\n+00003b00: 6f6e 0a20 206c 696e 655b 6c69 6e65 636f on. line[lineco\n+00003b10: 6c6f 723d 7265 645d 282d 312c 2d31 2c2d lor=red](-1,-1,-\n+00003b20: 3129 2832 2c32 2c32 290a 5468 6973 2065 1)(2,2,2).This e\n+00003b30: 7861 6d70 6c65 2075 7365 7320 e280 9c64 xample uses ...d\n+00003b40: 6566 696e 6974 696f 6e73 e280 9d2c 2077 efinitions..., w\n+00003b50: 6869 6368 2062 6567 696e 2077 6974 6820 hich begin with \n+00003b60: e280 9864 6566 e280 992e 2020 5468 6573 ...def.... Thes\n+00003b70: 6520 e280 9c64 6566 696e 65e2 809d 0a6f e ...define....o\n+00003b80: 7220 6769 7665 206e 616d 6573 2074 6f20 r give names to \n+00003b90: 706f 696e 7473 2c20 7768 6963 6820 6172 points, which ar\n+00003ba0: 6520 7468 656e 2061 7661 696c 6162 6c65 e then available\n+00003bb0: 2061 7320 e280 9c72 6566 6572 656e 6365 as ...reference\n+00003bc0: 73e2 809d 2062 790a 656e 636c 6f73 696e s... by.enclosin\n+00003bd0: 6720 7468 6520 6e61 6d65 7320 696e 2070 g the names in p\n+00003be0: 6172 656e 7468 6573 6573 2c20 652e 672e arentheses, e.g.\n+00003bf0: 2028 666f 6f29 2e20 2054 6865 2070 6172 (foo). The par\n+00003c00: 656e 7468 6573 6573 2064 656e 6f74 650a entheses denote.\n+00003c10: 7468 6174 2074 6865 206e 616d 6573 2072 that the names r\n+00003c20: 6566 6572 2074 6f20 706f 696e 7473 3b20 efer to points; \n+00003c30: 7468 6579 2061 7265 2072 6571 7569 7265 they are require\n+00003c40: 642e 2020 5468 6572 6520 6361 6e20 6265 d. There can be\n+00003c50: 206e 6f0a 7768 6974 6520 7370 6163 6520 no.white space \n+00003c60: 6265 7477 6565 6e20 7468 656d 2061 6e64 between them and\n+00003c70: 2074 6865 206e 616d 652e 0a0a 2020 2041 the name... A\n+00003c80: 7320 796f 7520 6361 6e20 7365 652c 2063 s you can see, c\n+00003c90: 6f6d 6d65 6e74 7320 7374 6172 7420 7769 omments start wi\n+00003ca0: 7468 2025 2061 7320 696e 2054 6558 2061 th % as in TeX a\n+00003cb0: 6e64 2065 7874 656e 6420 746f 2074 6865 nd extend to the\n+00003cc0: 2065 6e64 0a6f 6620 7468 6520 6c69 6e65 end.of the line\n+00003cd0: 2028 7468 6f75 6768 2023 2077 696c 6c20 (though # will \n+00003ce0: 776f 726b 2061 7320 7765 6c6c 292e 2020 work as well). \n+00003cf0: 5768 6974 6520 7370 6163 652c 2069 6e63 White space, inc\n+00003d00: 6c75 6469 6e67 0a73 7061 6365 732c 2074 luding.spaces, t\n+00003d10: 6162 7320 616e 6420 626c 616e 6b20 6c69 abs and blank li\n+00003d20: 6e65 732c 2068 6173 206e 6f20 6566 6665 nes, has no effe\n+00003d30: 6374 2069 6e20 7468 6520 e280 9873 6b65 ct in the ...ske\n+00003d40: 7463 68e2 8099 206c 616e 6775 6167 652e tch... language.\n+00003d50: 0a0a 0008 5b69 6d61 6765 2073 7263 3d22 ....[image src=\"\n+00003d60: 6578 3034 302e 706e 6722 2074 6578 743d ex040.png\" text=\n+00003d70: 2249 6d61 6765 2065 7830 3430 206f 6d69 \"Image ex040 omi\n+00003d80: 7474 6564 2069 6e20 7465 7874 2076 6572 tted in text ver\n+00003d90: 7369 6f6e 206f 6620 7468 6973 2064 6f63 sion of this doc\n+00003da0: 756d 656e 742e 2200 085d 0a0a 4966 2077 ument.\"..]..If w\n+00003db0: 6520 6c6f 6f6b 2069 6e73 6964 6520 7468 e look inside th\n+00003dc0: 6520 5465 5820 6669 6c65 2070 726f 6475 e TeX file produ\n+00003dd0: 6365 6420 6279 20e2 8098 736b 6574 6368 ced by ...sketch\n+00003de0: e280 992c 2074 6865 7265 2077 696c 6c20 ..., there will \n+00003df0: 6265 206f 6e6c 790a 7468 7265 6520 706f be only.three po\n+00003e00: 6c79 676f 6e73 2e20 2054 6865 2066 6f75 lygons. The fou\n+00003e10: 7274 6820 6861 7320 6265 656e 2063 756c rth has been cul\n+00003e20: 6c65 6420 6265 6361 7573 6520 6974 2069 led because it i\n+00003e30: 7320 6120 2262 6163 6b20 6661 6365 220a s a \"back face\".\n+00003e40: 6f66 2074 6865 2074 6574 7261 6865 6472 of the tetrahedr\n+00003e50: 6f6e 2c20 696e 7669 7369 626c 6520 746f on, invisible to\n+00003e60: 206f 7572 2076 6965 772e 2020 4974 2069 our view. It i\n+00003e70: 7320 756e 6e65 6365 7373 6172 792c 2061 s unnecessary, a\n+00003e80: 6e64 2073 6f20 6974 0a69 7320 7265 6d6f nd so it.is remo\n+00003e90: 7665 642e 0a0a 2020 2049 6e20 736f 6d65 ved... In some\n+00003ea0: 2064 7261 7769 6e67 732c 2070 6f6c 7967 drawings, polyg\n+00003eb0: 6f6e 7320 6163 7420 6173 207a 6572 6f2d ons act as zero-\n+00003ec0: 7468 6963 6b6e 6573 7320 736f 6c69 6420 thickness solid \n+00003ed0: 7375 7266 6163 6573 2077 6974 680a 626f surfaces with.bo\n+00003ee0: 7468 2073 6964 6573 2076 6973 6962 6c65 th sides visible\n+00003ef0: 2072 6174 6865 7220 7468 616e 2061 7320 rather than as \n+00003f00: 7468 6520 6661 6365 7320 6f66 2073 6f6c the faces of sol\n+00003f10: 6964 206f 626a 6563 7473 2c20 7768 6572 id objects, wher\n+00003f20: 6520 6261 636b 0a66 6163 6573 2063 616e e back.faces can\n+00003f30: 2062 6520 6375 6c6c 6564 2e20 2046 6f72 be culled. For\n+00003f40: 207a 6572 6f2d 7468 6963 6b6e 6573 7320 zero-thickness \n+00003f50: 736f 6c69 6473 2c20 6375 6c6c 696e 6720 solids, culling \n+00003f60: 6973 2061 2070 726f 626c 656d 2e0a 4f6e is a problem..On\n+00003f70: 6520 736f 6c75 7469 6f6e 2069 7320 746f e solution is to\n+00003f80: 2075 7365 2061 2070 6169 7220 6f66 20e2 use a pair of .\n+00003f90: 8098 736b 6574 6368 e280 9920 706f 6c79 ..sketch... poly\n+00003fa0: 676f 6e73 2066 6f72 2065 6163 680a 7a65 gons for each.ze\n+00003fb0: 726f 2d74 6869 636b 6e65 7373 2066 6163 ro-thickness fac\n+00003fc0: 652c 2069 6465 6e74 6963 616c 2065 7863 e, identical exc\n+00003fd0: 6570 7420 7769 7468 206f 7070 6f73 6974 ept with opposit\n+00003fe0: 6520 7665 7274 6578 206f 7264 6572 732e e vertex orders.\n+00003ff0: 2020 5468 6973 0a69 7320 756e 7769 656c This.is unwiel\n+00004000: 6479 2061 6e64 2065 7870 656e 7369 7665 dy and expensive\n+00004010: 2e20 2041 2062 6574 7465 7220 7761 7920 . A better way \n+00004020: 6973 2074 6f20 7365 7420 7468 6520 e280 is to set the ..\n+00004030: 9873 6b65 7463 68e2 8099 2069 6e74 6572 .sketch... inter\n+00004040: 6e61 6c0a 6f70 7469 6f6e 20e2 8098 6375 nal.option ...cu\n+00004050: 6c6c e280 9920 746f 20e2 8098 6661 6c73 ll... to ...fals\n+00004060: 65e2 8099 2069 6e20 7468 6520 7573 7561 e... in the usua\n+00004070: 6c20 e280 9850 5354 7269 636b 73e2 8099 l ...PSTricks...\n+00004080: 206d 616e 6e65 722e 0a20 2070 6f6c 7967 manner.. polyg\n+00004090: 6f6e 5b63 756c 6c3d 6661 6c73 655d 2870 on[cull=false](p\n+000040a0: 3129 2870 3229 2870 3329 0a54 6865 2066 1)(p2)(p3).The f\n+000040b0: 6f6c 6c6f 7769 6e67 2073 686f 7773 2074 ollowing shows t\n+000040c0: 6865 2073 616d 6520 6865 6c69 7820 7368 he same helix sh\n+000040d0: 6170 6520 6472 6177 6e20 6669 7273 7420 ape drawn first \n+000040e0: 7769 7468 2063 756c 6c3d 7472 7565 2028 with cull=true (\n+000040f0: 7468 650a 6465 6661 756c 7429 2061 6e64 the.default) and\n+00004100: 2074 6865 6e20 6375 6c6c 3d66 616c 7365 then cull=false\n+00004110: 2e0a 0a00 085b 696d 6167 6520 7372 633d .....[image src=\n+00004120: 2265 7830 3435 2e70 6e67 2220 7465 7874 \"ex045.png\" text\n+00004130: 3d22 496d 6167 6520 6578 3034 3520 6f6d =\"Image ex045 om\n+00004140: 6974 7465 6420 696e 2074 6578 7420 7665 itted in text ve\n+00004150: 7273 696f 6e20 6f66 2074 6869 7320 646f rsion of this do\n+00004160: 6375 6d65 6e74 2e22 0008 5d0a 0a57 6527 cument.\"..]..We'\n+00004170: 6c6c 2073 6f6f 6e20 7365 6520 686f 7720 ll soon see how \n+00004180: 746f 2070 726f 6475 6365 2074 6865 7365 to produce these\n+00004190: 2068 656c 6978 6573 2077 6974 6820 6120 helixes with a \n+000041a0: 6665 7720 6c69 6e65 7320 6f66 20e2 8098 few lines of ...\n+000041b0: 736b 6574 6368 e280 990a 6c61 6e67 7561 sketch....langua\n+000041c0: 6765 2063 6f64 652e 0a0a 2020 2049 7420 ge code... It \n+000041d0: 6d61 7920 6265 2074 656d 7074 696e 6720 may be tempting \n+000041e0: 746f 2074 7572 6e20 6375 6c6c 696e 6720 to turn culling \n+000041f0: 6f66 6620 6772 6174 7569 746f 7573 6c79 off gratuitously\n+00004200: 2073 6f20 7468 6174 2076 6572 7465 780a so that vertex.\n+00004210: 6f72 6465 7220 6361 6e20 6265 2069 676e order can be ign\n+00004220: 6f72 6564 2e20 2054 6869 7320 6973 206e ored. This is n\n+00004230: 6f74 2061 2067 6f6f 6420 6964 6561 2062 ot a good idea b\n+00004240: 6563 6175 7365 206f 7574 7075 7420 6669 ecause output fi\n+00004250: 6c65 2073 697a 650a 616e 6420 5465 5820 le size.and TeX \n+00004260: 616e 6420 506f 7374 7363 7269 7074 2070 and Postscript p\n+00004270: 726f 6365 7373 696e 6720 7469 6d65 2062 rocessing time b\n+00004280: 6f74 6820 6465 7065 6e64 206f 6e20 7468 oth depend on th\n+00004290: 6520 6e75 6d62 6572 206f 660a 6f75 7470 e number of.outp\n+000042a0: 7574 2070 6f6c 7967 6f6e 732e 2020 4375 ut polygons. Cu\n+000042b0: 6c6c 696e 6720 7573 7561 6c6c 7920 696d lling usually im\n+000042c0: 7072 6f76 6573 2070 6572 666f 726d 616e proves performan\n+000042d0: 6365 2062 7920 6120 6661 6374 6f72 206f ce by a factor o\n+000042e0: 660a 7477 6f2e 2020 4f6e 2074 6865 206f f.two. On the o\n+000042f0: 7468 6572 2068 616e 642c 2067 6c6f 6261 ther hand, globa\n+00004300: 6c6c 7920 7365 7474 696e 6720 e280 9863 lly setting ...c\n+00004310: 756c 6c3d 6661 6c73 65e2 8099 2069 7320 ull=false... is \n+00004320: 7265 6173 6f6e 6162 6c65 0a77 6869 6c65 reasonable.while\n+00004330: 2064 6562 7567 6769 6e67 2e20 2053 6565 debugging. See\n+00004340: 202a 6e6f 7465 2047 6c6f 6261 6c20 6f70 *note Global op\n+00004350: 7469 6f6e 733a 3a20 616e 6420 2a6e 6f74 tions:: and *not\n+00004360: 6520 4c69 6d69 7473 206f 6e20 6572 726f e Limits on erro\n+00004370: 720a 6465 7465 6374 696f 6e3a 3a2e 0a0a r.detection::...\n+00004380: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+00004390: 6e66 6f2c 2020 4e6f 6465 3a20 5370 6563 nfo, Node: Spec\n+000043a0: 6961 6c20 6f62 6a65 6374 732c 2020 4e65 ial objects, Ne\n+000043b0: 7874 3a20 4f62 6a65 6374 2074 7261 6e73 xt: Object trans\n+000043c0: 666f 726d 732c 2020 5072 6576 3a20 4472 forms, Prev: Dr\n+000043d0: 6177 696e 6720 6120 736f 6c69 642c 2020 awing a solid, \n+000043e0: 5570 3a20 496e 7472 6f64 7563 7469 6f6e Up: Introduction\n+000043f0: 2062 7920 6578 616d 706c 650a 0a32 2e34 by example..2.4\n+00004400: 2053 7065 6369 616c 206f 626a 6563 7473 Special objects\n+00004410: 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d .===============\n+00004420: 3d3d 3d3d 0a0a 5765 2063 616e 2061 6464 ====..We can add\n+00004430: 206c 6162 656c 7320 746f 2061 2064 7261 labels to a dra\n+00004440: 7769 6e67 2062 7920 7573 696e 6720 7370 wing by using sp\n+00004450: 6563 6961 6c20 6f62 6a65 6374 732c 2077 ecial objects, w\n+00004460: 6869 6368 2070 726f 7669 6465 2061 0a77 hich provide a.w\n+00004470: 6179 2074 6f20 656d 6265 6420 7261 7720 ay to embed raw \n+00004480: 4c61 5465 5820 616e 6420 e280 9850 5354 LaTeX and ...PST\n+00004490: 7269 636b 73e2 8099 2063 6f64 652e 2020 ricks... code. \n+000044a0: 4164 6469 6e67 2074 6869 7320 746f 2074 Adding this to t\n+000044b0: 6865 0a74 6574 7261 6865 6472 6f6e 2064 he.tetrahedron d\n+000044c0: 6f65 7320 7468 6520 7472 6963 6b2e 0a20 oes the trick.. \n+000044d0: 2073 7065 6369 616c 207c 5c66 6f6f 746e special |\\footn\n+000044e0: 6f74 6573 697a 650a 2020 2020 2020 2020 otesize. \n+000044f0: 2020 205c 7570 7574 7b32 7074 7d5b 7572 \\uput{2pt}[ur\n+00004500: 5d23 317b 2450 3124 7d0a 2020 2020 2020 ]#1{$P1$}. \n+00004510: 2020 2020 205c 7570 7574 5b72 5d23 327b \\uput[r]#2{\n+00004520: 2450 3224 7d0a 2020 2020 2020 2020 2020 $P2$}. \n+00004530: 205c 7570 7574 5b75 5d23 337b 2450 3324 \\uput[u]#3{$P3$\n+00004540: 7d0a 2020 2020 2020 2020 2020 205c 7570 }. \\up\n+00004550: 7574 5b64 5d23 347b 2450 3424 7d7c 0a20 ut[d]#4{$P4$}|. \n+00004560: 2020 2028 7031 2928 7032 2928 7033 2928 (p1)(p2)(p3)(\n+00004570: 7034 290a 4865 7265 2069 7320 7468 6520 p4).Here is the \n+00004580: 7265 7375 6c74 2e0a 0a00 085b 696d 6167 result.....[imag\n+00004590: 6520 7372 633d 2265 7830 3432 2e70 6e67 e src=\"ex042.png\n+000045a0: 2220 7465 7874 3d22 496d 6167 6520 6578 \" text=\"Image ex\n+000045b0: 3034 3220 6f6d 6974 7465 6420 696e 2074 042 omitted in t\n+000045c0: 6578 7420 7665 7273 696f 6e20 6f66 2074 ext version of t\n+000045d0: 6869 7320 646f 6375 6d65 6e74 2e22 0008 his document.\"..\n+000045e0: 5d0a 0a20 2020 5468 6572 6520 6172 6520 ].. There are \n+000045f0: 7365 7665 7261 6c20 6465 7461 696c 7320 several details \n+00004600: 746f 206e 6f74 6520 6865 7265 2e20 2046 to note here. F\n+00004610: 6972 7374 2c20 7468 6520 7175 6f74 696e irst, the quotin\n+00004620: 670a 636f 6e76 656e 7469 6f6e 2066 6f72 g.convention for\n+00004630: 2074 6865 2072 6177 2063 6f64 6520 6973 the raw code is\n+00004640: 2073 696d 696c 6172 2074 6f20 7468 6520 similar to the \n+00004650: 4c61 5465 5820 5c76 6572 6220 636f 6d6d LaTeX \\verb comm\n+00004660: 616e 642e 2020 5468 650a 6669 7273 7420 and. 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Second, the \n+00004720: 6172 6775 6d65 6e74 2072 6566 6572 656e argument referen\n+00004730: 6365 7320 2331 2c20 2332 2c20 2333 2c20 ces #1, #2, #3, \n+00004740: 616e 6420 2334 2072 6566 6572 2074 6f20 and #4 refer to \n+00004750: 706f 696e 742c 0a76 6563 746f 722c 206f point,.vector, o\n+00004760: 7220 7363 616c 6172 2076 616c 7565 7320 r scalar values \n+00004770: 696e 2074 6865 206c 6973 7420 7468 6174 in the list that\n+00004780: 2066 6f6c 6c6f 772e 2020 5468 6973 2069 follow. This i\n+00004790: 7320 7369 6d69 6c61 7220 746f 0a54 6558 s similar to.TeX\n+000047a0: 206d 6163 726f 2073 796e 7461 782e 2020 macro syntax. \n+000047b0: 5468 6520 7472 616e 7366 6f72 6d65 6420 The transformed \n+000047c0: 616e 6420 7477 6f2d 6469 6d65 6e73 696f and two-dimensio\n+000047d0: 6e61 6c20 7072 6f6a 6563 7469 6f6e 7320 nal projections \n+000047e0: 6f66 0a74 6865 7365 2074 6872 6565 2d64 of.these three-d\n+000047f0: 696d 656e 7369 6f6e 616c 2070 6f69 6e74 imensional point\n+00004800: 7320 6172 6520 7375 6273 7469 7475 7465 s are substitute\n+00004810: 6420 696e 2074 6865 2066 696e 616c 206f d in the final o\n+00004820: 7574 7075 742e 2020 416e 0a61 7267 756d utput. An.argum\n+00004830: 656e 7420 7265 6665 7265 6e63 6520 6f66 ent reference of\n+00004840: 2074 6865 2066 6f72 6d20 2331 2d32 2069 the form #1-2 i\n+00004850: 7320 7265 706c 6163 6564 2077 6974 6820 s replaced with \n+00004860: 7468 6520 616e 676c 6520 696e 0a64 6567 the angle in.deg\n+00004870: 7265 6573 206f 6620 7468 6520 7477 6f2d rees of the two-\n+00004880: 6469 6d65 6e73 696f 6e61 6c20 7665 6374 dimensional vect\n+00004890: 6f72 2074 6861 7420 636f 6e6e 6563 7473 or that connects\n+000048a0: 2074 6865 2070 726f 6a65 6374 696f 6e73 the projections\n+000048b0: 206f 660a 7468 6520 7477 6f20 7265 7370 of.the two resp\n+000048c0: 6563 7469 7665 2061 7267 756d 656e 7420 ective argument \n+000048d0: 706f 696e 7473 2c20 6865 7265 2023 3120 points, here #1 \n+000048e0: 616e 6420 2332 2e20 2054 6865 2073 7562 and #2. The sub\n+000048f0: 7374 6974 7574 6564 0a61 6e67 6c65 2069 stituted.angle i\n+00004900: 7320 656e 636c 6f73 6564 2069 6e20 6375 s enclosed in cu\n+00004910: 726c 7920 6272 6163 6573 20e2 8098 7b20 rly braces ...{ \n+00004920: 7de2 8099 2e20 2057 6865 6e20 e280 9854 }.... When ...T\n+00004930: 696b 5a2f 5047 46e2 8099 206f 7574 7075 ikZ/PGF... outpu\n+00004940: 7420 6973 0a62 6569 6e67 2067 656e 6572 t is.being gener\n+00004950: 6174 6564 2c20 7468 6520 616e 676c 6520 ated, the angle \n+00004960: 6973 2072 6f75 6e64 6564 2074 6f20 7468 is rounded to th\n+00004970: 6520 6e65 6172 6573 7420 6465 6772 6565 e nearest degree\n+00004980: 2062 6563 6175 7365 0a6e 6f6e 2d69 6e74 because.non-int\n+00004990: 6567 6572 2061 6e67 6c65 7320 6172 6520 eger angles are \n+000049a0: 6e6f 7420 616c 6c6f 7765 6420 6279 20e2 not allowed by .\n+000049b0: 8098 5469 6b5a 2f50 4746 e280 9920 7072 ..TikZ/PGF... pr\n+000049c0: 696d 6974 6976 6573 2e0a 0a20 2020 4173 imitives... As\n+000049d0: 206f 6620 5665 7273 696f 6e20 302e 3320 of Version 0.3 \n+000049e0: 6f66 20e2 8098 736b 6574 6368 e280 992c of ...sketch...,\n+000049f0: 2073 7065 6369 616c 2061 7267 756d 656e special argumen\n+00004a00: 7473 206d 6179 2062 6520 7363 616c 6172 ts may be scalar\n+00004a10: 7320 6f72 0a76 6563 746f 7273 2069 6e20 s or.vectors in \n+00004a20: 6164 6469 7469 6f6e 2074 6f20 706f 696e addition to poin\n+00004a30: 7473 2e20 2052 6566 6572 656e 6365 7320 ts. References \n+00004a40: 746f 2073 6361 6c61 7220 6172 6775 6d65 to scalar argume\n+00004a50: 6e74 7320 6172 650a 6d65 7265 6c79 2072 nts are.merely r\n+00004a60: 6570 6c61 6365 6420 7769 7468 2061 206e eplaced with a n\n+00004a70: 756d 6265 7220 666f 726d 6174 7465 6420 umber formatted \n+00004a80: 6a75 7374 2061 7320 616e 7920 706f 696e just as any poin\n+00004a90: 7420 636f 6f72 6469 6e61 7465 2e0a 5265 t coordinate..Re\n+00004aa0: 6665 7265 6e63 6573 2074 6f20 7665 6374 ferences to vect\n+00004ab0: 6f72 7320 6265 636f 6d65 2074 776f 2d64 ors become two-d\n+00004ac0: 696d 656e 7369 6f6e 616c 2070 6f69 6e74 imensional point\n+00004ad0: 732e 2020 5468 6520 7469 636b 206f 7065 s. The tick ope\n+00004ae0: 7261 746f 720a 7468 6174 2073 656c 6563 rator.that selec\n+00004af0: 7473 2069 6e64 6976 6964 7561 6c20 636f ts individual co\n+00004b00: 6d70 6f6e 656e 7473 206f 6620 706f 696e mponents of poin\n+00004b10: 7473 2061 6e64 2076 6563 746f 7273 2065 ts and vectors e\n+00004b20: 6c73 6577 6865 7265 2069 6e0a e280 9873 lsewhere in....s\n+00004b30: 6b65 7463 68e2 8099 2028 7365 6520 666f ketch... (see fo\n+00004b40: 7220 6578 616d 706c 6520 2a6e 6f74 6520 r example *note \n+00004b50: 4166 6669 6e65 2061 7269 7468 6d65 7469 Affine arithmeti\n+00004b60: 633a 3a29 2063 616e 2061 6c73 6f20 6265 c::) can also be\n+00004b70: 2061 7070 6c69 6564 0a74 6f20 706f 696e applied.to poin\n+00004b80: 7420 616e 6420 7665 6374 6f72 2061 7267 t and vector arg\n+00004b90: 756d 656e 7420 7265 6665 7265 6e63 6573 ument references\n+00004ba0: 2e20 2041 6c6c 2074 6872 6565 2064 696d . All three dim\n+00004bb0: 656e 7369 6f6e 7320 6f66 2061 0a74 7261 ensions of a.tra\n+00004bc0: 6e73 666f 726d 6564 2070 6f69 6e74 206f nsformed point o\n+00004bd0: 7220 7665 6374 6f72 2063 616e 2061 6c73 r vector can als\n+00004be0: 6f20 6265 2073 7562 7374 6974 7565 6420 o be substitued \n+00004bf0: 7769 7468 20e2 8098 2733 e280 992e 2020 with ...'3.... \n+00004c00: 5365 6520 2a6e 6f74 650a 5370 6563 6961 See *note.Specia\n+00004c10: 6c73 3a3a 2066 6f72 2064 6574 6169 6c73 ls:: for details\n+00004c20: 2e0a 0a20 2020 4279 2064 6566 6175 6c74 ... By default\n+00004c30: 2c20 e280 9873 7065 6369 616c e280 9920 , ...special... \n+00004c40: 6f62 6a65 6374 7320 6172 6520 7072 696e objects are prin\n+00004c50: 7465 6420 6c61 7374 2c20 6f76 6572 6c61 ted last, overla\n+00004c60: 7969 6e67 2061 6c6c 206f 7468 6572 0a6f ying all other.o\n+00004c70: 626a 6563 7473 2069 6e20 7468 6520 7363 bjects in the sc\n+00004c80: 656e 652e 2020 4966 2079 6f75 2073 7065 ene. If you spe\n+00004c90: 6369 6679 2074 6865 2069 6e74 6572 6e61 cify the interna\n+00004ca0: 6c20 6f70 7469 6f6e 20e2 8098 6c61 793d l option ...lay=\n+00004cb0: 696e e280 992c 2074 6865 0a68 6964 6465 in..., the.hidde\n+00004cc0: 6e20 7375 7266 6163 6520 616c 676f 7269 n surface algori\n+00004cd0: 7468 6d20 636f 6e73 6964 6572 7320 7468 thm considers th\n+00004ce0: 6520 656e 7469 7265 2073 7065 6369 616c e entire special\n+00004cf0: 206f 626a 6563 7420 746f 2062 6520 7468 object to be th\n+00004d00: 650a 6669 7273 7420 706f 696e 7420 2823 e.first point (#\n+00004d10: 3129 2069 6e20 7468 6520 6172 6775 6d65 1) in the argume\n+00004d20: 6e74 206c 6973 742e 2020 4966 2074 6861 nt list. If tha\n+00004d30: 7420 706f 696e 7420 6973 2062 6568 696e t point is behin\n+00004d40: 6420 286f 660a 736d 616c 6c65 7220 7a2d d (of.smaller z-\n+00004d50: 636f 6d70 6f6e 656e 7420 7468 616e 2920 component than) \n+00004d60: 616e 7920 6472 6177 6162 6c65 2c20 7468 any drawable, th\n+00004d70: 656e 2074 6865 2065 6e74 6972 6520 7370 en the entire sp\n+00004d80: 6563 6961 6c20 6f62 6a65 6374 0a69 7320 ecial object.is \n+00004d90: 6472 6177 6e20 6265 666f 7265 2074 6861 drawn before tha\n+00004da0: 7420 6472 6177 6162 6c65 2c20 736f 2074 t drawable, so t\n+00004db0: 6865 2064 7261 7761 626c 6520 6f62 7363 he drawable obsc\n+00004dc0: 7572 6573 2070 6172 7473 206f 6620 7468 ures parts of th\n+00004dd0: 650a 7370 6563 6961 6c20 6f62 6a65 6374 e.special object\n+00004de0: 2074 6861 7420 6f76 6572 6c61 7073 2069 that overlaps i\n+00004df0: 742e 2020 496e 206f 7572 2065 7861 6d70 t. In our examp\n+00004e00: 6c65 2c20 7031 2069 7320 7468 6520 6672 le, p1 is the fr\n+00004e10: 6f6e 742d 6d6f 7374 0a70 6f69 6e74 2069 ont-most.point i\n+00004e20: 6e20 7468 6520 7363 656e 6520 2868 6173 n the scene (has\n+00004e30: 2074 6865 206c 6172 6765 7374 207a 2d63 the largest z-c\n+00004e40: 6f6d 706f 6e65 6e74 292c 2073 6f20 6164 omponent), so ad\n+00004e50: 6469 6e67 20e2 8098 6c61 793d 696e e280 ding ...lay=in..\n+00004e60: 9920 6861 730a 6e6f 2065 6666 6563 742e . has.no effect.\n+00004e70: 0a0a 2020 2057 6974 6820 6f70 7469 6f6e .. With option\n+00004e80: 20e2 8098 6c61 793d 756e 6465 72e2 8099 ...lay=under...\n+00004e90: 2c20 6120 7370 6563 6961 6c20 6973 2064 , a special is d\n+00004ea0: 7261 776e 205f 6265 666f 7265 5f2c 2068 rawn _before_, h\n+00004eb0: 656e 6365 2061 7070 6561 7273 0a5f 756e ence appears._un\n+00004ec0: 6465 725f 2061 6e79 206f 6620 7468 6520 der_ any of the \n+00004ed0: 6f62 6a65 6374 7320 6861 6e64 6c65 6420 objects handled \n+00004ee0: 6279 2074 6865 2068 6964 6465 6e20 7375 by the hidden su\n+00004ef0: 7266 6163 6520 616c 676f 7269 7468 6d2e rface algorithm.\n+00004f00: 0a54 6869 7320 6973 2068 6f77 2074 6865 .This is how the\n+00004f10: 206c 6967 6874 2067 7261 7920 6178 6573 light gray axes\n+00004f20: 2077 6572 6520 6164 6465 6420 746f 2074 were added to t\n+00004f30: 6865 2022 6865 6c6c 6f20 776f 726c 6422 he \"hello world\"\n+00004f40: 2065 7861 6d70 6c65 0a2a 6e6f 7465 2048 example.*note H\n+00004f50: 656c 6c6f 2077 6f72 6c64 3a3a 2e0a 0a20 ello world::... \n+00004f60: 2020 5370 6563 6961 6c20 6f62 6a65 6374 Special object\n+00004f70: 7320 6172 6520 706f 7765 7266 756c 2c20 s are powerful, \n+00004f80: 7769 7468 206d 616e 7920 706f 7373 6962 with many possib\n+00004f90: 6c65 2075 7365 732e 0a0a 1f0a 4669 6c65 le uses.....File\n+00004fa0: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n+00004fb0: 4e6f 6465 3a20 4f62 6a65 6374 2074 7261 Node: Object tra\n+00004fc0: 6e73 666f 726d 732c 2020 4e65 7874 3a20 nsforms, Next: \n+00004fd0: 5265 7065 6174 6564 206f 626a 6563 7473 Repeated objects\n+00004fe0: 2c20 2050 7265 763a 2053 7065 6369 616c , Prev: Special\n+00004ff0: 206f 626a 6563 7473 2c20 2055 703a 2049 objects, Up: I\n+00005000: 6e74 726f 6475 6374 696f 6e20 6279 2065 ntroduction by e\n+00005010: 7861 6d70 6c65 0a0a 322e 3520 5472 616e xample..2.5 Tran\n+00005020: 7366 6f72 6d73 0a3d 3d3d 3d3d 3d3d 3d3d sforms.=========\n+00005030: 3d3d 3d3d 3d0a 0a4e 6f77 206c 6574 2773 =====..Now let's\n+00005040: 2061 6464 2061 2073 6563 6f6e 6420 636f add a second co\n+00005050: 7079 206f 6620 7468 6520 7069 6572 6365 py of the pierce\n+00005060: 6420 7465 7472 6168 6564 726f 6e2e 2020 d tetrahedron. \n+00005070: 5765 276c 6c20 726f 7461 7465 0a74 6865 We'll rotate.the\n+00005080: 2063 6f70 7920 3930 2064 6567 7265 6573 copy 90 degrees\n+00005090: 2061 626f 7574 2074 6865 2078 2d61 7869 about the x-axi\n+000050a0: 7320 7769 7468 2074 6865 206f 7269 6769 s with the origi\n+000050b0: 6e20 6173 20e2 809c 6365 6e74 6572 206f n as ...center o\n+000050c0: 660a 726f 7461 7469 6f6e e280 9d20 736f f.rotation... so\n+000050d0: 2077 6520 6361 6e20 7365 6520 7468 6520 we can see the \n+000050e0: 6261 636b 2c20 7468 656e 2074 7261 6e73 back, then trans\n+000050f0: 6c61 7465 2069 7420 746f 2074 6865 2072 late it to the r\n+00005100: 6967 6874 2d2d 696e 2074 6865 0a70 6f73 ight--in the.pos\n+00005110: 6974 6976 6520 782d 6469 7265 6374 696f itive x-directio\n+00005120: 6e2d 2d73 6f20 6974 2064 6f65 736e 2774 n--so it doesn't\n+00005130: 2063 6f6c 6c69 6465 2077 6974 6820 7468 collide with th\n+00005140: 6520 6f72 6967 696e 616c 2e20 2054 6f20 e original. To \n+00005150: 6865 6c70 0a75 7320 7365 6520 7768 6174 help.us see what\n+00005160: 2773 2067 6f69 6e67 206f 6e2c 206d 616b 's going on, mak\n+00005170: 6520 7468 6520 6261 636b 2073 6964 6520 e the back side \n+00005180: 6772 6179 2e0a 2020 6465 6620 7069 6572 gray.. def pier\n+00005190: 6365 645f 7465 7472 6168 6564 726f 6e20 ced_tetrahedron \n+000051a0: 7b0a 2020 2020 6465 6620 7031 2028 302c {. def p1 (0,\n+000051b0: 302c 3129 2064 6566 2070 3220 2831 2c30 0,1) def p2 (1,0\n+000051c0: 2c30 290a 2020 2020 6465 6620 7033 2028 ,0). def p3 (\n+000051d0: 302c 312c 3029 2064 6566 2070 3420 282d 0,1,0) def p4 (-\n+000051e0: 2e33 2c2d 2e35 2c2d 2e38 290a 2020 2020 .3,-.5,-.8). \n+000051f0: 706f 6c79 676f 6e28 7031 2928 7032 2928 polygon(p1)(p2)(\n+00005200: 7033 2920 2020 2020 2020 2020 2020 2020 p3) \n+00005210: 2020 2020 2020 2020 2025 206f 7269 6769 % origi\n+00005220: 6e61 6c0a 2020 2020 706f 6c79 676f 6e28 nal. polygon(\n+00005230: 7031 2928 7034 2928 7032 2920 2020 2020 p1)(p4)(p2) \n 00005240: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00005250: 2020 2025 2062 6f74 746f 6d0a 2020 2020 % bottom. \n-00005260: 706f 6c79 676f 6e28 7031 2928 7033 2928 polygon(p1)(p3)(\n-00005270: 7034 2920 2020 2020 2020 2020 2020 2020 p4) \n-00005280: 2020 2020 2020 2020 2025 206c 6566 740a % left.\n-00005290: 2020 2020 706f 6c79 676f 6e5b 6669 6c6c polygon[fill\n-000052a0: 636f 6c6f 723d 6c69 6768 7467 7261 795d color=lightgray]\n-000052b0: 2870 3329 2870 3229 2870 3429 2025 2072 (p3)(p2)(p4) % r\n-000052c0: 6561 720a 2020 2020 6c69 6e65 5b6c 696e ear. line[lin\n-000052d0: 6563 6f6c 6f72 3d72 6564 5d28 2d31 2c2d ecolor=red](-1,-\n-000052e0: 312c 2d31 2928 322c 322c 3229 0a20 207d 1,-1)(2,2,2). }\n-000052f0: 0a20 207b 7069 6572 6365 645f 7465 7472 . {pierced_tetr\n-00005300: 6168 6564 726f 6e7d 2020 2520 7465 7472 ahedron} % tetr\n-00005310: 6168 6564 726f 6e20 696e 206f 7269 6769 ahedron in origi\n-00005320: 6e61 6c20 706f 7369 7469 6f6e 0a20 2070 nal position. p\n-00005330: 7574 207b 2072 6f74 6174 6528 3930 2c20 ut { rotate(90, \n-00005340: 2830 2c30 2c30 292c 205b 312c 302c 305d (0,0,0), [1,0,0]\n-00005350: 2920 2520 636f 7079 2069 6e20 6e65 7720 ) % copy in new \n-00005360: 706f 7369 7469 6f6e 0a20 2020 2020 2020 position. \n-00005370: 2074 6865 6e20 7472 616e 736c 6174 6528 then translate(\n-00005380: 5b32 2e35 2c30 2c30 5d29 207d 207b 7069 [2.5,0,0]) } {pi\n-00005390: 6572 6365 645f 7465 7472 6168 6564 726f erced_tetrahedro\n-000053a0: 6e7d 0a48 6572 6520 7468 6520 656e 7469 n}.Here the enti\n-000053b0: 7265 2063 6f64 6520 6f66 2074 6865 2070 re code of the p\n-000053c0: 7265 7669 6f75 7320 6578 616d 706c 6520 revious example \n-000053d0: 6861 7320 6265 656e 2077 7261 7070 6564 has been wrapped\n-000053e0: 2069 6e20 610a 6465 6669 6e69 7469 6f6e in a.definition\n-000053f0: 2062 7920 666f 726d 696e 6720 6120 e280 by forming a ..\n-00005400: 9c62 6c6f 636b e280 9d20 7769 7468 2062 .block... with b\n-00005410: 7261 6365 7320 2861 2073 696e 676c 6520 races (a single \n-00005420: 6974 656d 2077 6f75 6c64 206e 6f74 0a6e item would not.n\n-00005430: 6565 6420 7468 656d 292e 2020 5468 6520 eed them). The \n-00005440: 706f 696e 7420 6465 6669 6e69 7469 6f6e point definition\n-00005450: 7320 6e65 7374 6564 2069 6e73 6964 6520 s nested inside \n-00005460: 7468 6520 6272 6163 6573 2061 7265 0ae2 the braces are..\n-00005470: 809c 6c65 7869 6361 6c6c 7920 7363 6f70 ..lexically scop\n-00005480: 6564 e280 9d2e 2020 5468 6569 7220 6d65 ed.... Their me\n-00005490: 616e 696e 6720 6578 7465 6e64 7320 6f6e aning extends on\n-000054a0: 6c79 2074 6f20 7468 6520 656e 6420 6f66 ly to the end of\n-000054b0: 2074 6865 2062 6c6f 636b 2e0a 5468 6520 the block..The \n-000054c0: 6f75 7465 7220 6465 6620 6973 2063 616c outer def is cal\n-000054d0: 6c65 6420 6120 e280 9c64 7261 7761 626c led a ...drawabl\n-000054e0: 65e2 809d 2064 6566 696e 6974 696f 6e20 e... definition \n-000054f0: 6265 6361 7573 6520 6974 2064 6573 6372 because it descr\n-00005500: 6962 6573 0a73 6f6d 6574 6869 6e67 2074 ibes.something t\n-00005510: 6861 7420 6361 6e20 6265 2064 7261 776e hat can be drawn\n-00005520: 2e0a 0a20 2020 4120 6472 6177 6162 6c65 ... A drawable\n-00005530: 2064 6566 696e 6974 696f 6e20 6279 2069 definition by i\n-00005540: 7473 656c 6620 6361 7573 6573 206e 6f74 tself causes not\n-00005550: 6869 6e67 2074 6f20 6861 7070 656e 2075 hing to happen u\n-00005560: 6e74 696c 2069 7473 0a6e 616d 6520 6973 ntil its.name is\n-00005570: 2072 6566 6572 656e 6365 642e 2020 4472 referenced. Dr\n-00005580: 6177 6162 6c65 2072 6566 6572 656e 6365 awable reference\n-00005590: 7320 6d75 7374 2062 6520 656e 636c 6f73 s must be enclos\n-000055a0: 6564 2069 6e20 6375 726c 790a 6272 6163 ed in curly.brac\n-000055b0: 6573 2c20 652e 672e 207b 666f 6f7d 2c20 es, e.g. {foo}, \n-000055c0: 7769 7468 206e 6f20 696e 7465 7276 656e with no interven\n-000055d0: 696e 6720 7768 6974 6520 7370 6163 652e ing white space.\n-000055e0: 2020 496e 2074 6865 2063 6f64 6520 6162 In the code ab\n-000055f0: 6f76 652c 0a74 6865 2066 6972 7374 2072 ove,.the first r\n-00005600: 6566 6572 656e 6365 207b 7069 6572 6365 eference {pierce\n-00005610: 645f 7465 7472 6168 6564 726f 6e7d 2069 d_tetrahedron} i\n-00005620: 7320 6120 706c 6169 6e20 6f6e 652e 2020 s a plain one. \n-00005630: 4974 7320 6566 6665 6374 2069 730a 6d65 Its effect is.me\n-00005640: 7265 6c79 2074 6f20 6475 706c 6963 6174 rely to duplicat\n-00005650: 6520 7468 6520 6561 726c 6965 7220 6472 e the earlier dr\n-00005660: 6177 696e 672e 2020 416c 6d6f 7374 2061 awing. Almost a\n-00005670: 6e79 2073 6572 6965 7320 6f66 20e2 8098 ny series of ...\n-00005680: 736b 6574 6368 e280 990a 636f 6d6d 616e sketch....comman\n-00005690: 6473 2073 7475 6666 206d 6179 2062 6520 ds stuff may be \n-000056a0: 7265 706c 6163 6564 2077 6974 6820 6465 replaced with de\n-000056b0: 6620 666f 6f20 7b20 7374 7566 6620 7d20 f foo { stuff } \n-000056c0: 7b66 6f6f 7d20 7769 7468 6f75 740a 6368 {foo} without.ch\n-000056d0: 616e 6769 6e67 2069 7473 206d 6561 6e69 anging its meani\n-000056e0: 6e67 2e0a 0a20 2020 5468 6520 7075 7420 ng... The put \n-000056f0: 636f 6d6d 616e 6420 7375 7070 6c69 6573 command supplies\n-00005700: 2061 2073 6563 6f6e 6420 7265 6665 7265 a second refere\n-00005710: 6e63 652c 2074 6869 7320 7469 6d65 2077 nce, this time w\n-00005720: 6974 6820 610a e280 9c74 7261 6e73 666f ith a....transfo\n-00005730: 726d e280 9d20 6170 706c 6965 6420 6669 rm... applied fi\n-00005740: 7273 742e 2020 5468 6520 726f 7461 7465 rst. The rotate\n-00005750: 2074 7261 6e73 666f 726d 2074 7572 6e73 transform turns\n-00005760: 2074 6865 2074 6574 7261 6865 6472 6f6e the tetrahedron\n-00005770: 0a39 3020 6465 6772 6565 7320 6162 6f75 .90 degrees abou\n-00005780: 7420 7468 6520 6f72 6967 696e 2e20 2054 t the origin. T\n-00005790: 6865 2061 7869 7320 6f66 2072 6f74 6174 he axis of rotat\n-000057a0: 696f 6e20 6973 2074 6865 2076 6563 746f ion is the vecto\n-000057b0: 720a 5b31 2c30 2c30 5d2e 2020 4279 2074 r.[1,0,0]. By t\n-000057c0: 6865 20e2 809c 7269 6768 7420 6861 6e64 he ...right hand\n-000057d0: 2072 756c 65e2 809d 2c20 7468 6973 2063 rule..., this c\n-000057e0: 6175 7365 7320 7468 6520 746f 7020 6f66 auses the top of\n-000057f0: 2074 6865 0a74 6574 7261 6865 6472 6f6e the.tetrahedron\n-00005800: 2074 6f20 726f 7461 7465 2074 6f77 6172 to rotate towar\n-00005810: 6420 7468 6520 7669 6577 6572 2061 6e64 d the viewer and\n-00005820: 2074 6865 2062 6f74 746f 6d20 6177 6179 the bottom away\n-00005830: 2e20 2054 6865 2072 756c 650a 7265 6365 . The rule.rece\n-00005840: 6976 6573 2069 7473 206e 616d 6520 6672 ives its name fr\n-00005850: 6f6d 2074 6865 2066 6f6c 6c6f 7769 6e67 om the following\n-00005860: 2064 6566 696e 6974 696f 6e3a 0a20 2020 definition:. \n-00005870: 2020 2a52 6967 6874 2068 616e 6420 7275 *Right hand ru\n-00005880: 6c65 2e2a 2020 4966 2074 6865 2072 6967 le.* If the rig\n-00005890: 6874 2068 616e 6420 6973 2077 7261 7070 ht hand is wrapp\n-000058a0: 6564 2061 726f 756e 6420 616e 7920 6178 ed around any ax\n-000058b0: 6973 0a20 2020 2020 7769 7468 2074 6865 is. with the\n-000058c0: 2074 6875 6d62 2070 6f69 6e74 696e 6720 thumb pointing \n-000058d0: 696e 2074 6865 2061 7869 7320 6469 7265 in the axis dire\n-000058e0: 6374 696f 6e2c 2074 6865 6e20 7468 6520 ction, then the \n-000058f0: 6669 6e67 6572 730a 2020 2020 2063 7572 fingers. cur\n-00005900: 6c20 696e 2074 6865 2064 6972 6563 7469 l in the directi\n-00005910: 6f6e 206f 6620 706f 7369 7469 7665 2072 on of positive r\n-00005920: 6f74 6174 696f 6e20 6162 6f75 7420 7468 otation about th\n-00005930: 6174 2061 7869 732e 0a20 2020 5468 6520 at axis.. The \n-00005940: 7472 616e 736c 6174 6520 7472 616e 7366 translate transf\n-00005950: 6f72 6d20 6d6f 7665 7320 7468 6520 7079 orm moves the py\n-00005960: 7261 6d69 6420 6c61 7465 7261 6c6c 7920 ramid laterally \n-00005970: 746f 2074 6865 2072 6967 6874 2062 790a to the right by.\n-00005980: 6164 6469 6e67 2074 6865 2076 6563 746f adding the vecto\n-00005990: 7220 5b32 2e35 2c30 2c30 5d20 746f 2065 r [2.5,0,0] to e\n-000059a0: 6163 6820 7665 7274 6578 2063 6f6f 7264 ach vertex coord\n-000059b0: 696e 6174 652e 2020 5468 6520 7265 7375 inate. The resu\n-000059c0: 6c74 2069 730a 7368 6f77 6e20 6865 7265 lt is.shown here\n-000059d0: 2e0a 0a00 085b 696d 6167 6520 7372 633d .....[image src=\n-000059e0: 2265 7830 3530 2e70 6e67 2220 7465 7874 \"ex050.png\" text\n-000059f0: 3d22 496d 6167 6520 6578 3035 3020 6f6d =\"Image ex050 om\n-00005a00: 6974 7465 6420 696e 2074 6578 7420 7665 itted in text ve\n-00005a10: 7273 696f 6e20 6f66 2074 6869 7320 646f rsion of this do\n-00005a20: 6375 6d65 6e74 2e22 0008 5d0a 0a1f 0a46 cument.\"..]....F\n-00005a30: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n-00005a40: 2c20 204e 6f64 653a 2052 6570 6561 7465 , Node: Repeate\n-00005a50: 6420 6f62 6a65 6374 732c 2020 4e65 7874 d objects, Next\n-00005a60: 3a20 5377 6570 7420 6f62 6a65 6374 732c : Swept objects,\n-00005a70: 2020 5072 6576 3a20 4f62 6a65 6374 2074 Prev: Object t\n-00005a80: 7261 6e73 666f 726d 732c 2020 5570 3a20 ransforms, Up: \n-00005a90: 496e 7472 6f64 7563 7469 6f6e 2062 7920 Introduction by \n-00005aa0: 6578 616d 706c 650a 0a32 2e36 2052 6570 example..2.6 Rep\n-00005ab0: 6561 7465 6420 6f62 6a65 6374 730a 3d3d eated objects.==\n+00005250: 2025 2062 6f74 746f 6d0a 2020 2020 706f % bottom. po\n+00005260: 6c79 676f 6e28 7031 2928 7033 2928 7034 lygon(p1)(p3)(p4\n+00005270: 2920 2020 2020 2020 2020 2020 2020 2020 ) \n+00005280: 2020 2020 2020 2025 206c 6566 740a 2020 % left. \n+00005290: 2020 706f 6c79 676f 6e5b 6669 6c6c 636f polygon[fillco\n+000052a0: 6c6f 723d 6c69 6768 7467 7261 795d 2870 lor=lightgray](p\n+000052b0: 3329 2870 3229 2870 3429 2025 2072 6561 3)(p2)(p4) % rea\n+000052c0: 720a 2020 2020 6c69 6e65 5b6c 696e 6563 r. line[linec\n+000052d0: 6f6c 6f72 3d72 6564 5d28 2d31 2c2d 312c olor=red](-1,-1,\n+000052e0: 2d31 2928 322c 322c 3229 0a20 207d 0a20 -1)(2,2,2). }. \n+000052f0: 207b 7069 6572 6365 645f 7465 7472 6168 {pierced_tetrah\n+00005300: 6564 726f 6e7d 2020 2520 7465 7472 6168 edron} % tetrah\n+00005310: 6564 726f 6e20 696e 206f 7269 6769 6e61 edron in origina\n+00005320: 6c20 706f 7369 7469 6f6e 0a20 2070 7574 l position. put\n+00005330: 207b 2072 6f74 6174 6528 3930 2c20 2830 { rotate(90, (0\n+00005340: 2c30 2c30 292c 205b 312c 302c 305d 2920 ,0,0), [1,0,0]) \n+00005350: 2520 636f 7079 2069 6e20 6e65 7720 706f % copy in new po\n+00005360: 7369 7469 6f6e 0a20 2020 2020 2020 2074 sition. t\n+00005370: 6865 6e20 7472 616e 736c 6174 6528 5b32 hen translate([2\n+00005380: 2e35 2c30 2c30 5d29 207d 207b 7069 6572 .5,0,0]) } {pier\n+00005390: 6365 645f 7465 7472 6168 6564 726f 6e7d ced_tetrahedron}\n+000053a0: 0a48 6572 6520 7468 6520 656e 7469 7265 .Here the entire\n+000053b0: 2063 6f64 6520 6f66 2074 6865 2070 7265 code of the pre\n+000053c0: 7669 6f75 7320 6578 616d 706c 6520 6861 vious example ha\n+000053d0: 7320 6265 656e 2077 7261 7070 6564 2069 s been wrapped i\n+000053e0: 6e20 610a 6465 6669 6e69 7469 6f6e 2062 n a.definition b\n+000053f0: 7920 666f 726d 696e 6720 6120 e280 9c62 y forming a ...b\n+00005400: 6c6f 636b e280 9d20 7769 7468 2062 7261 lock... with bra\n+00005410: 6365 7320 2861 2073 696e 676c 6520 6974 ces (a single it\n+00005420: 656d 2077 6f75 6c64 206e 6f74 0a6e 6565 em would not.nee\n+00005430: 6420 7468 656d 292e 2020 5468 6520 706f d them). The po\n+00005440: 696e 7420 6465 6669 6e69 7469 6f6e 7320 int definitions \n+00005450: 6e65 7374 6564 2069 6e73 6964 6520 7468 nested inside th\n+00005460: 6520 6272 6163 6573 2061 7265 0ae2 809c e braces are....\n+00005470: 6c65 7869 6361 6c6c 7920 7363 6f70 6564 lexically scoped\n+00005480: e280 9d2e 2020 5468 6569 7220 6d65 616e .... Their mean\n+00005490: 696e 6720 6578 7465 6e64 7320 6f6e 6c79 ing extends only\n+000054a0: 2074 6f20 7468 6520 656e 6420 6f66 2074 to the end of t\n+000054b0: 6865 2062 6c6f 636b 2e0a 5468 6520 6f75 he block..The ou\n+000054c0: 7465 7220 6465 6620 6973 2063 616c 6c65 ter def is calle\n+000054d0: 6420 6120 e280 9c64 7261 7761 626c 65e2 d a ...drawable.\n+000054e0: 809d 2064 6566 696e 6974 696f 6e20 6265 .. definition be\n+000054f0: 6361 7573 6520 6974 2064 6573 6372 6962 cause it describ\n+00005500: 6573 0a73 6f6d 6574 6869 6e67 2074 6861 es.something tha\n+00005510: 7420 6361 6e20 6265 2064 7261 776e 2e0a t can be drawn..\n+00005520: 0a20 2020 4120 6472 6177 6162 6c65 2064 . A drawable d\n+00005530: 6566 696e 6974 696f 6e20 6279 2069 7473 efinition by its\n+00005540: 656c 6620 6361 7573 6573 206e 6f74 6869 elf causes nothi\n+00005550: 6e67 2074 6f20 6861 7070 656e 2075 6e74 ng to happen unt\n+00005560: 696c 2069 7473 0a6e 616d 6520 6973 2072 il its.name is r\n+00005570: 6566 6572 656e 6365 642e 2020 4472 6177 eferenced. Draw\n+00005580: 6162 6c65 2072 6566 6572 656e 6365 7320 able references \n+00005590: 6d75 7374 2062 6520 656e 636c 6f73 6564 must be enclosed\n+000055a0: 2069 6e20 6375 726c 790a 6272 6163 6573 in curly.braces\n+000055b0: 2c20 652e 672e 207b 666f 6f7d 2c20 7769 , e.g. {foo}, wi\n+000055c0: 7468 206e 6f20 696e 7465 7276 656e 696e th no intervenin\n+000055d0: 6720 7768 6974 6520 7370 6163 652e 2020 g white space. \n+000055e0: 496e 2074 6865 2063 6f64 6520 6162 6f76 In the code abov\n+000055f0: 652c 0a74 6865 2066 6972 7374 2072 6566 e,.the first ref\n+00005600: 6572 656e 6365 207b 7069 6572 6365 645f erence {pierced_\n+00005610: 7465 7472 6168 6564 726f 6e7d 2069 7320 tetrahedron} is \n+00005620: 6120 706c 6169 6e20 6f6e 652e 2020 4974 a plain one. It\n+00005630: 7320 6566 6665 6374 2069 730a 6d65 7265 s effect is.mere\n+00005640: 6c79 2074 6f20 6475 706c 6963 6174 6520 ly to duplicate \n+00005650: 7468 6520 6561 726c 6965 7220 6472 6177 the earlier draw\n+00005660: 696e 672e 2020 416c 6d6f 7374 2061 6e79 ing. Almost any\n+00005670: 2073 6572 6965 7320 6f66 20e2 8098 736b series of ...sk\n+00005680: 6574 6368 e280 990a 636f 6d6d 616e 6473 etch....commands\n+00005690: 2073 7475 6666 206d 6179 2062 6520 7265 stuff may be re\n+000056a0: 706c 6163 6564 2077 6974 6820 6465 6620 placed with def \n+000056b0: 666f 6f20 7b20 7374 7566 6620 7d20 7b66 foo { stuff } {f\n+000056c0: 6f6f 7d20 7769 7468 6f75 740a 6368 616e oo} without.chan\n+000056d0: 6769 6e67 2069 7473 206d 6561 6e69 6e67 ging its meaning\n+000056e0: 2e0a 0a20 2020 5468 6520 7075 7420 636f ... The put co\n+000056f0: 6d6d 616e 6420 7375 7070 6c69 6573 2061 mmand supplies a\n+00005700: 2073 6563 6f6e 6420 7265 6665 7265 6e63 second referenc\n+00005710: 652c 2074 6869 7320 7469 6d65 2077 6974 e, this time wit\n+00005720: 6820 610a e280 9c74 7261 6e73 666f 726d h a....transform\n+00005730: e280 9d20 6170 706c 6965 6420 6669 7273 ... applied firs\n+00005740: 742e 2020 5468 6520 726f 7461 7465 2074 t. The rotate t\n+00005750: 7261 6e73 666f 726d 2074 7572 6e73 2074 ransform turns t\n+00005760: 6865 2074 6574 7261 6865 6472 6f6e 0a39 he tetrahedron.9\n+00005770: 3020 6465 6772 6565 7320 6162 6f75 7420 0 degrees about \n+00005780: 7468 6520 6f72 6967 696e 2e20 2054 6865 the origin. The\n+00005790: 2061 7869 7320 6f66 2072 6f74 6174 696f axis of rotatio\n+000057a0: 6e20 6973 2074 6865 2076 6563 746f 720a n is the vector.\n+000057b0: 5b31 2c30 2c30 5d2e 2020 4279 2074 6865 [1,0,0]. By the\n+000057c0: 20e2 809c 7269 6768 7420 6861 6e64 2072 ...right hand r\n+000057d0: 756c 65e2 809d 2c20 7468 6973 2063 6175 ule..., this cau\n+000057e0: 7365 7320 7468 6520 746f 7020 6f66 2074 ses the top of t\n+000057f0: 6865 0a74 6574 7261 6865 6472 6f6e 2074 he.tetrahedron t\n+00005800: 6f20 726f 7461 7465 2074 6f77 6172 6420 o rotate toward \n+00005810: 7468 6520 7669 6577 6572 2061 6e64 2074 the viewer and t\n+00005820: 6865 2062 6f74 746f 6d20 6177 6179 2e20 he bottom away. \n+00005830: 2054 6865 2072 756c 650a 7265 6365 6976 The rule.receiv\n+00005840: 6573 2069 7473 206e 616d 6520 6672 6f6d es its name from\n+00005850: 2074 6865 2066 6f6c 6c6f 7769 6e67 2064 the following d\n+00005860: 6566 696e 6974 696f 6e3a 0a20 2020 2020 efinition:. \n+00005870: 2a52 6967 6874 2068 616e 6420 7275 6c65 *Right hand rule\n+00005880: 2e2a 2020 4966 2074 6865 2072 6967 6874 .* If the right\n+00005890: 2068 616e 6420 6973 2077 7261 7070 6564 hand is wrapped\n+000058a0: 2061 726f 756e 6420 616e 7920 6178 6973 around any axis\n+000058b0: 0a20 2020 2020 7769 7468 2074 6865 2074 . with the t\n+000058c0: 6875 6d62 2070 6f69 6e74 696e 6720 696e humb pointing in\n+000058d0: 2074 6865 2061 7869 7320 6469 7265 6374 the axis direct\n+000058e0: 696f 6e2c 2074 6865 6e20 7468 6520 6669 ion, then the fi\n+000058f0: 6e67 6572 730a 2020 2020 2063 7572 6c20 ngers. curl \n+00005900: 696e 2074 6865 2064 6972 6563 7469 6f6e in the direction\n+00005910: 206f 6620 706f 7369 7469 7665 2072 6f74 of positive rot\n+00005920: 6174 696f 6e20 6162 6f75 7420 7468 6174 ation about that\n+00005930: 2061 7869 732e 0a20 2020 5468 6520 7472 axis.. The tr\n+00005940: 616e 736c 6174 6520 7472 616e 7366 6f72 anslate transfor\n+00005950: 6d20 6d6f 7665 7320 7468 6520 7079 7261 m moves the pyra\n+00005960: 6d69 6420 6c61 7465 7261 6c6c 7920 746f mid laterally to\n+00005970: 2074 6865 2072 6967 6874 2062 790a 6164 the right by.ad\n+00005980: 6469 6e67 2074 6865 2076 6563 746f 7220 ding the vector \n+00005990: 5b32 2e35 2c30 2c30 5d20 746f 2065 6163 [2.5,0,0] to eac\n+000059a0: 6820 7665 7274 6578 2063 6f6f 7264 696e h vertex coordin\n+000059b0: 6174 652e 2020 5468 6520 7265 7375 6c74 ate. The result\n+000059c0: 2069 730a 7368 6f77 6e20 6865 7265 2e0a is.shown here..\n+000059d0: 0a00 085b 696d 6167 6520 7372 633d 2265 ...[image src=\"e\n+000059e0: 7830 3530 2e70 6e67 2220 7465 7874 3d22 x050.png\" text=\"\n+000059f0: 496d 6167 6520 6578 3035 3020 6f6d 6974 Image ex050 omit\n+00005a00: 7465 6420 696e 2074 6578 7420 7665 7273 ted in text vers\n+00005a10: 696f 6e20 6f66 2074 6869 7320 646f 6375 ion of this docu\n+00005a20: 6d65 6e74 2e22 0008 5d0a 0a1f 0a46 696c ment.\"..]....Fil\n+00005a30: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n+00005a40: 204e 6f64 653a 2052 6570 6561 7465 6420 Node: Repeated \n+00005a50: 6f62 6a65 6374 732c 2020 4e65 7874 3a20 objects, Next: \n+00005a60: 5377 6570 7420 6f62 6a65 6374 732c 2020 Swept objects, \n+00005a70: 5072 6576 3a20 4f62 6a65 6374 2074 7261 Prev: Object tra\n+00005a80: 6e73 666f 726d 732c 2020 5570 3a20 496e nsforms, Up: In\n+00005a90: 7472 6f64 7563 7469 6f6e 2062 7920 6578 troduction by ex\n+00005aa0: 616d 706c 650a 0a32 2e36 2052 6570 6561 ample..2.6 Repea\n+00005ab0: 7465 6420 6f62 6a65 6374 730a 3d3d 3d3d ted objects.====\n 00005ac0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ================\n-00005ad0: 3d3d 0a0a 546f 2064 7261 7720 7365 7665 ==..To draw seve\n-00005ae0: 6e20 696e 7374 616e 6365 7320 6f66 2074 n instances of t\n-00005af0: 6865 2074 6574 7261 6865 6472 6f6e 2c20 he tetrahedron, \n-00005b00: 6561 6368 2064 6966 6665 7269 6e67 2066 each differing f\n-00005b10: 726f 6d20 7468 6520 6c61 7374 0a62 7920 rom the last.by \n-00005b20: 7468 6520 7361 6d65 2074 7261 6e73 666f the same transfo\n-00005b30: 726d 2c20 7265 706c 6163 6520 7468 6520 rm, replace the \n-00005b40: 6c61 7374 2074 776f 2063 6f6d 6d61 6e64 last two command\n-00005b50: 7320 6f66 2074 6865 2070 7265 7669 6f75 s of the previou\n-00005b60: 730a 6578 616d 706c 6520 7769 7468 0a20 s.example with. \n-00005b70: 2072 6570 6561 7420 7b20 372c 2072 6f74 repeat { 7, rot\n-00005b80: 6174 6528 3135 2c20 2830 2c30 2c30 292c ate(15, (0,0,0),\n-00005b90: 205b 312c 302c 305d 2920 2520 636f 7079 [1,0,0]) % copy\n-00005ba0: 2069 6e20 6e65 7720 706f 7369 7469 6f6e in new position\n-00005bb0: 0a20 2020 2020 2020 2020 2020 2020 2074 . t\n-00005bc0: 6865 6e20 7472 616e 736c 6174 6528 5b32 hen translate([2\n-00005bd0: 2c30 2c30 5d29 207d 207b 7069 6572 6365 ,0,0]) } {pierce\n-00005be0: 645f 7465 7472 6168 6564 726f 6e7d 0a41 d_tetrahedron}.A\n-00005bf0: 6e64 2074 6865 2072 6573 756c 742e 2e2e nd the result...\n-00005c00: 0a0a 0008 5b69 6d61 6765 2073 7263 3d22 ....[image src=\"\n-00005c10: 6578 3036 302e 706e 6722 2074 6578 743d ex060.png\" text=\n-00005c20: 2249 6d61 6765 2065 7830 3630 206f 6d69 \"Image ex060 omi\n-00005c30: 7474 6564 2069 6e20 7465 7874 2076 6572 tted in text ver\n-00005c40: 7369 6f6e 206f 6620 7468 6973 2064 6f63 sion of this doc\n-00005c50: 756d 656e 742e 2200 085d 0a0a 1f0a 4669 ument.\"..]....Fi\n-00005c60: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n-00005c70: 2020 4e6f 6465 3a20 5377 6570 7420 6f62 Node: Swept ob\n-00005c80: 6a65 6374 732c 2020 5072 6576 3a20 5265 jects, Prev: Re\n-00005c90: 7065 6174 6564 206f 626a 6563 7473 2c20 peated objects, \n-00005ca0: 2055 703a 2049 6e74 726f 6475 6374 696f Up: Introductio\n-00005cb0: 6e20 6279 2065 7861 6d70 6c65 0a0a 322e n by example..2.\n-00005cc0: 3720 5377 6570 7420 6f62 6a65 6374 730a 7 Swept objects.\n-00005cd0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ================\n-00005ce0: 3d0a 0a4d 616e 7920 6661 6d69 6c69 6172 =..Many familiar\n-00005cf0: 2073 6861 7065 7320 6361 6e20 6265 2067 shapes can be g\n-00005d00: 656e 6572 6174 6564 2062 7920 7377 6565 enerated by swee\n-00005d10: 7069 6e67 2073 696d 706c 6572 206f 6e65 ping simpler one\n-00005d20: 7320 7468 726f 7567 680a 7370 6163 6520 s through.space \n-00005d30: 616e 6420 636f 6e73 6964 6572 696e 6720 and considering \n-00005d40: 7468 6520 7265 7375 6c74 696e 6720 7061 the resulting pa\n-00005d50: 7468 2c20 7375 7266 6163 652c 206f 7220 th, surface, or \n-00005d60: 766f 6c75 6d65 2e20 20e2 8098 536b 6574 volume. ...Sket\n-00005d70: 6368 e280 990a 696d 706c 656d 656e 7473 ch....implements\n-00005d80: 2074 6869 7320 6964 6561 2069 6e20 7468 this idea in th\n-00005d90: 6520 7377 6565 7020 636f 6d6d 616e 642e e sweep command.\n-00005da0: 0a20 2064 6566 206e 5f73 6567 7320 380a . def n_segs 8.\n-00005db0: 2020 7377 6565 7020 7b20 6e5f 7365 6773 sweep { n_segs\n-00005dc0: 2c20 726f 7461 7465 2831 3830 202f 206e , rotate(180 / n\n-00005dd0: 5f73 6567 732c 2028 302c 302c 3029 2c20 _segs, (0,0,0), \n-00005de0: 5b30 2c30 2c31 5d29 207d 2028 312c 302c [0,0,1]) } (1,0,\n-00005df0: 3029 0a54 6869 7320 636f 6465 2073 7765 0).This code swe\n-00005e00: 6570 7320 7468 6520 706f 696e 7420 2831 eps the point (1\n-00005e10: 2c30 2c30 2920 6569 6768 7420 7469 6d65 ,0,0) eight time\n-00005e20: 7320 6279 2072 6f74 6174 696e 6720 6974 s by rotating it\n-00005e30: 2031 3830 2f38 203d 0a32 322e 3520 6465 180/8 =.22.5 de\n-00005e40: 6772 6565 7320 6561 6368 2074 696d 6520 grees each time \n-00005e50: 616e 6420 636f 6e6e 6563 7469 6e67 2074 and connecting t\n-00005e60: 6865 2072 6573 756c 7469 6e67 2070 6f69 he resulting poi\n-00005e70: 6e74 7320 7769 7468 206c 696e 650a 7365 nts with line.se\n-00005e80: 676d 656e 7473 2e20 2054 6865 2064 6566 gments. The def\n-00005e90: 2075 7365 6420 6865 7265 2069 7320 6120 used here is a \n-00005ea0: e280 9c73 6361 6c61 72e2 809d 2064 6566 ...scalar... def\n-00005eb0: 696e 6974 696f 6e2e 2020 5265 6665 7265 inition. Refere\n-00005ec0: 6e63 6573 2074 6f0a 7363 616c 6172 7320 nces to.scalars \n-00005ed0: 6861 7665 206e 6f20 656e 636c 6f73 696e have no enclosin\n-00005ee0: 6720 6272 6163 6b65 7473 2061 7420 616c g brackets at al\n-00005ef0: 6c2e 0a0a 2a20 4d65 6e75 3a0a 0a2a 2050 l...* Menu:..* P\n-00005f00: 6f69 6e74 2073 7765 6570 733a 3a20 2020 oint sweeps:: \n-00005f10: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n-00005f20: 7074 2070 6f69 6e74 7320 6d61 6b65 206c pt points make l\n-00005f30: 696e 6573 2061 6e64 2070 6f6c 7967 6f6e ines and polygon\n-00005f40: 732e 0a2a 2050 6f6c 796c 696e 6520 7377 s..* Polyline sw\n-00005f50: 6565 7073 3a3a 2020 2020 2020 2020 2020 eeps:: \n-00005f60: 2020 2053 7765 7074 206c 696e 6573 206d Swept lines m\n-00005f70: 616b 6520 7375 7266 6163 6573 2e0a 2a20 ake surfaces..* \n-00005f80: 4e65 7374 6564 2073 7765 6570 733a 3a20 Nested sweeps:: \n-00005f90: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n-00005fa0: 6570 7420 7377 6565 7073 2061 7265 2075 ept sweeps are u\n-00005fb0: 7365 6675 6c21 0a2a 2050 6f6c 7967 6f6e seful!.* Polygon\n-00005fc0: 2073 7765 6570 733a 3a20 2020 2020 2020 sweeps:: \n-00005fd0: 2020 2020 2020 2053 7765 7074 2070 6f6c Swept pol\n-00005fe0: 7967 6f6e 7320 6d61 6b65 2073 6f6c 6964 ygons make solid\n-00005ff0: 732e 2e2e 0a2a 2050 6f6c 796c 696e 6520 s....* Polyline \n-00006000: 7377 6565 7073 2077 6974 6820 636c 6f73 sweeps with clos\n-00006010: 7572 653a 3a20 2061 6e64 2073 6f20 646f ure:: and so do\n-00006020: 2063 6c6f 7365 6420 706f 6c79 6c69 6e65 closed polyline\n-00006030: 2073 7765 6570 732e 0a2a 2041 6666 696e sweeps..* Affin\n-00006040: 6520 6172 6974 686d 6574 6963 3a3a 2020 e arithmetic:: \n-00006050: 2020 2020 2020 2020 2053 6b65 7463 6820 Sketch \n-00006060: 7573 6566 756c 206d 6174 6820 6578 7072 useful math expr\n-00006070: 6573 7369 6f6e 2e0a 2a20 4d6f 7265 2074 ession..* More t\n-00006080: 6f20 6c65 6172 6e3a 3a20 2020 2020 2020 o learn:: \n-00006090: 2020 2020 2020 2020 4368 6563 6b20 6f75 Check ou\n-000060a0: 7420 7468 6520 4d6f 6269 7573 2073 7472 t the Mobius str\n-000060b0: 6970 210a 0a1f 0a46 696c 653a 2073 6b65 ip!....File: ske\n-000060c0: 7463 682e 696e 666f 2c20 204e 6f64 653a tch.info, Node:\n-000060d0: 2050 6f69 6e74 2073 7765 6570 732c 2020 Point sweeps, \n-000060e0: 4e65 7874 3a20 506f 6c79 6c69 6e65 2073 Next: Polyline s\n-000060f0: 7765 6570 732c 2020 5072 6576 3a20 5377 weeps, Prev: Sw\n-00006100: 6570 7420 6f62 6a65 6374 732c 2020 5570 ept objects, Up\n-00006110: 3a20 5377 6570 7420 6f62 6a65 6374 730a : Swept objects.\n-00006120: 0a32 2e37 2e31 2050 6f69 6e74 2073 7765 .2.7.1 Point swe\n-00006130: 6570 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d eps.------------\n-00006140: 2d2d 2d2d 2d2d 0a0a 5377 6565 7069 6e67 ------..Sweeping\n-00006150: 2061 2070 6f69 6e74 206d 616b 6573 2061 a point makes a\n-00006160: 206f 6e65 2d64 696d 656e 7369 6f6e 616c one-dimensional\n-00006170: 2070 6174 682c 2077 6869 6368 2069 7320 path, which is \n-00006180: 6120 706f 6c79 6c69 6e65 2e0a 5369 6e63 a polyline..Sinc\n-00006190: 6520 7765 2068 6176 6520 7377 6570 7420 e we have swept \n-000061a0: 7769 7468 2061 2072 6f74 6174 696f 6e2c with a rotation,\n-000061b0: 2074 6865 2072 6573 756c 7420 6973 2061 the result is a\n-000061c0: 2063 6972 6375 6c61 7220 6172 632e 2020 circular arc. \n-000061d0: 4865 7265 0a69 7320 7768 6174 2069 7420 Here.is what it \n-000061e0: 6c6f 6f6b 7320 6c69 6b65 2e0a 0a00 085b looks like.....[\n-000061f0: 696d 6167 6520 7372 633d 2265 7830 3730 image src=\"ex070\n-00006200: 2e70 6e67 2220 7465 7874 3d22 496d 6167 .png\" text=\"Imag\n-00006210: 6520 6578 3037 3020 6f6d 6974 7465 6420 e ex070 omitted \n-00006220: 696e 2074 6578 7420 7665 7273 696f 6e20 in text version \n-00006230: 6f66 2074 6869 7320 646f 6375 6d65 6e74 of this document\n-00006240: 2e22 0008 5d0a 0a20 2020 5468 6973 2069 .\"..].. This i\n-00006250: 7320 7468 6520 6669 7273 7420 6578 616d s the first exam\n-00006260: 706c 6520 7765 2068 6176 6520 7365 656e ple we have seen\n-00006270: 206f 6620 e280 9873 6b65 7463 68e2 8099 of ...sketch...\n-00006280: 2061 7269 7468 6d65 7469 632e 2020 5468 arithmetic. Th\n-00006290: 650a 6578 7072 6573 7369 6f6e 2031 3830 e.expression 180\n-000062a0: 202f 206e 5f73 6567 7320 6361 7573 6573 / n_segs causes\n-000062b0: 2074 6865 2065 6967 6874 2072 6f74 6174 the eight rotat\n-000062c0: 696f 6e73 2074 6f20 6164 6420 746f 2031 ions to add to 1\n-000062d0: 3830 2e20 2049 660a 796f 7527 7265 2070 80. If.you're p\n-000062e0: 6179 696e 6720 6174 7465 6e74 696f 6e2c aying attention,\n-000062f0: 2079 6f75 276c 6c20 6861 7665 2061 6c72 you'll have alr\n-00006300: 6561 6479 206e 6f74 6564 2074 6861 7420 eady noted that \n-00006310: 7468 6572 6520 6172 6520 5f6e 696e 655f there are _nine_\n-00006320: 0a70 6f69 6e74 732c 2070 726f 6475 6369 .points, produci\n-00006330: 6e67 2065 6967 6874 206c 696e 6520 7365 ng eight line se\n-00006340: 676d 656e 7473 2e0a 0a20 2020 596f 7520 gments... You \n-00006350: 6361 6e20 6361 7573 6520 7468 6520 7377 can cause the sw\n-00006360: 6570 7420 706f 696e 7420 746f 2067 656e ept point to gen\n-00006370: 6572 6174 6520 6120 7369 6e67 6c65 2070 erate a single p\n-00006380: 6f6c 7967 6f6e 2072 6174 6865 720a 7468 olygon rather.th\n-00006390: 616e 2061 2070 6f6c 796c 696e 6520 6279 an a polyline by\n-000063a0: 2075 7369 6e67 2074 6865 20e2 809c 636c using the ...cl\n-000063b0: 6f73 7572 6520 7461 67e2 809d 203c 3e20 osure tag... <> \n-000063c0: 6166 7465 7220 7468 6520 6e75 6d62 6572 after the number\n-000063d0: 206f 6620 7377 6570 740a 6f62 6a65 6374 of swept.object\n-000063e0: 732e 2020 436f 6465 2061 6e64 2072 6573 s. Code and res\n-000063f0: 756c 7420 666f 6c6c 6f77 0a20 2064 6566 ult follow. def\n-00006400: 206e 5f73 6567 7320 380a 2020 7377 6565 n_segs 8. swee\n-00006410: 7020 7b20 6e5f 7365 6773 3c3e 2c20 726f p { n_segs<>, ro\n-00006420: 7461 7465 2831 3830 202f 206e 5f73 6567 tate(180 / n_seg\n-00006430: 732c 2028 302c 302c 3029 2c20 5b30 2c30 s, (0,0,0), [0,0\n-00006440: 2c31 5d29 207d 2028 312c 302c 3029 0a00 ,1]) } (1,0,0)..\n-00006450: 085b 696d 6167 6520 7372 633d 2265 7830 .[image src=\"ex0\n-00006460: 3830 2e70 6e67 2220 7465 7874 3d22 496d 80.png\" text=\"Im\n-00006470: 6167 6520 6578 3038 3020 6f6d 6974 7465 age ex080 omitte\n-00006480: 6420 696e 2074 6578 7420 7665 7273 696f d in text versio\n-00006490: 6e20 6f66 2074 6869 7320 646f 6375 6d65 n of this docume\n-000064a0: 6e74 2e22 0008 5d0a 0a1f 0a46 696c 653a nt.\"..]....File:\n-000064b0: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-000064c0: 6f64 653a 2050 6f6c 796c 696e 6520 7377 ode: Polyline sw\n-000064d0: 6565 7073 2c20 204e 6578 743a 204e 6573 eeps, Next: Nes\n-000064e0: 7465 6420 7377 6565 7073 2c20 2050 7265 ted sweeps, Pre\n-000064f0: 763a 2050 6f69 6e74 2073 7765 6570 732c v: Point sweeps,\n-00006500: 2020 5570 3a20 5377 6570 7420 6f62 6a65 Up: Swept obje\n-00006510: 6374 730a 0a32 2e37 2e32 2050 6f6c 796c cts..2.7.2 Polyl\n-00006520: 696e 6520 7377 6565 7073 0a2d 2d2d 2d2d ine sweeps.-----\n-00006530: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-00006540: 0a0a 5377 6565 7069 6e67 2061 2070 6f6c ..Sweeping a pol\n-00006550: 796c 696e 6520 7072 6f64 7563 6573 2061 yline produces a\n-00006560: 2073 7572 6661 6365 2063 6f6d 706f 7365 surface compose\n-00006570: 6420 6f66 206d 616e 7920 6661 6365 732e d of many faces.\n-00006580: 2020 5468 650a 756e 6272 6f6b 656e 2068 The.unbroken h\n-00006590: 656c 6978 2069 6e20 7468 6520 6578 616d elix in the exam\n-000065a0: 706c 6520 2a6e 6f74 6520 4865 6c69 7820 ple *note Helix \n-000065b0: 7769 7468 2063 756c 6c20 7365 7420 6661 with cull set fa\n-000065c0: 6c73 6520 7468 656e 0a74 7275 653a 3a20 lse then.true:: \n-000065d0: 6973 2070 726f 6475 6365 6420 6279 2074 is produced by t\n-000065e0: 6869 7320 636f 6465 2028 706c 7573 2061 his code (plus a\n-000065f0: 2073 7572 726f 756e 6469 6e67 2070 7574 surrounding put\n-00006600: 2072 6f74 6174 696f 6e20 746f 206d 616b rotation to mak\n-00006610: 650a 616e 2069 6e74 6572 6573 7469 6e67 e.an interesting\n-00006620: 2076 6965 773b 2074 6869 7320 6861 7320 view; this has \n-00006630: 6265 656e 206f 6d69 7474 6564 292e 0a20 been omitted).. \n-00006640: 2064 6566 204b 205b 302c 302c 315d 0a20 def K [0,0,1]. \n-00006650: 2073 7765 6570 5b63 756c 6c3d 6661 6c73 sweep[cull=fals\n-00006660: 655d 207b 0a20 2020 2036 302c 200a 2020 e] {. 60, . \n-00006670: 2020 726f 7461 7465 2831 302c 2028 302c rotate(10, (0,\n-00006680: 302c 3029 2c20 5b4b 5d29 2074 6865 6e20 0,0), [K]) then \n-00006690: 7472 616e 736c 6174 6528 312f 3620 2a20 translate(1/6 * \n-000066a0: 5b4b 5d29 200a 2020 7d20 6c69 6e65 5b6c [K]) . } line[l\n-000066b0: 696e 6577 6964 7468 3d32 7074 5d28 2d31 inewidth=2pt](-1\n-000066c0: 2c30 2928 312c 3029 0a41 6761 696e 2c20 ,0)(1,0).Again, \n-000066d0: 3630 2073 6567 6d65 6e74 7320 6f66 2074 60 segments of t\n-000066e0: 6865 2068 656c 6978 2061 7265 2070 726f he helix are pro\n-000066f0: 6475 6365 6420 6279 2063 6f6e 6e65 6374 duced by connect\n-00006700: 696e 6720 3631 2069 6e73 7461 6e63 6573 ing 61 instances\n-00006710: 0a6f 6620 7468 6520 7377 6570 7420 6c69 .of the swept li\n-00006720: 6e65 2e20 204f 7074 696f 6e73 2061 7070 ne. Options app\n-00006730: 6c69 6564 2074 6f20 7468 6520 7377 6565 lied to the swee\n-00006740: 702c 2068 6572 6520 6375 6c6c 3d66 616c p, here cull=fal\n-00006750: 7365 2c20 6172 650a 7472 6561 7465 6420 se, are.treated \n-00006760: 6173 206f 7074 696f 6e73 2066 6f72 2074 as options for t\n-00006770: 6865 2067 656e 6572 6174 6564 2070 6f6c he generated pol\n-00006780: 7967 6f6e 206f 7220 706f 6c79 6c69 6e65 ygon or polyline\n-00006790: 2e20 204f 7074 696f 6e73 206f 660a 7468 . Options of.th\n-000067a0: 6520 7377 6570 7420 6c69 6e65 2069 7473 e swept line its\n-000067b0: 656c 662c 2068 6572 6520 6c69 6e65 7769 elf, here linewi\n-000067c0: 6474 683d 3270 742c 2061 7265 2069 676e dth=2pt, are ign\n-000067d0: 6f72 6564 2c20 7468 6f75 6768 2077 6974 ored, though wit\n-000067e0: 6820 610a 7761 726e 696e 672e 2020 5468 h a.warning. Th\n-000067f0: 6973 2064 6566 2069 7320 6120 e280 9c76 is def is a ...v\n-00006800: 6563 746f 72e2 809d 2064 6566 696e 6974 ector... definit\n-00006810: 696f 6e2c 2077 6869 6368 206d 7573 7420 ion, which must \n-00006820: 6265 2072 6566 6572 656e 6365 640a 7769 be referenced.wi\n-00006830: 7468 2073 7175 6172 6520 6272 6163 6b65 th square bracke\n-00006840: 7473 2c20 652e 672e 205b 666f 6f5d 2e0a ts, e.g. [foo]..\n-00006850: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n-00006860: 696e 666f 2c20 204e 6f64 653a 204e 6573 info, Node: Nes\n-00006870: 7465 6420 7377 6565 7073 2c20 204e 6578 ted sweeps, Nex\n-00006880: 743a 2050 6f6c 7967 6f6e 2073 7765 6570 t: Polygon sweep\n-00006890: 732c 2020 5072 6576 3a20 506f 6c79 6c69 s, Prev: Polyli\n-000068a0: 6e65 2073 7765 6570 732c 2020 5570 3a20 ne sweeps, Up: \n-000068b0: 5377 6570 7420 6f62 6a65 6374 730a 0a32 Swept objects..2\n-000068c0: 2e37 2e33 204e 6573 7465 6420 7377 6565 .7.3 Nested swee\n-000068d0: 7073 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ps.-------------\n-000068e0: 2d2d 2d2d 2d2d 0a0a 5768 656e 2074 6865 ------..When the\n-000068f0: 2063 656e 7465 7220 706f 696e 7420 6f66 center point of\n-00006900: 2072 6f74 6174 696f 6e20 6973 206f 6d69 rotation is omi\n-00006910: 7474 6564 2c20 7468 6520 6f72 6967 696e tted, the origin\n-00006920: 2069 7320 6173 7375 6d65 642e 0a57 6865 is assumed..Whe\n-00006930: 6e20 6120 706f 696e 7420 6861 7320 6f6e n a point has on\n-00006940: 6c79 2074 776f 2063 6f6f 7264 696e 6174 ly two coordinat\n-00006950: 6573 2c20 7468 6579 2061 7265 2074 616b es, they are tak\n-00006960: 656e 2061 7320 7820 616e 6420 792c 2077 en as x and y, w\n-00006970: 6974 680a 7a3d 3020 6173 7375 6d65 642e ith.z=0 assumed.\n-00006980: 2020 4120 746f 726f 6964 2069 7320 7468 A toroid is th\n-00006990: 6572 6566 6f72 6520 6f62 7461 696e 6564 erefore obtained\n-000069a0: 2077 6974 6820 7468 6973 2063 6f64 652e with this code.\n-000069b0: 0a20 2064 6566 206e 5f74 6f72 6f69 645f . def n_toroid_\n-000069c0: 7365 6773 2032 3020 2020 6465 6620 6e5f segs 20 def n_\n-000069d0: 6369 7263 6c65 5f73 6567 7320 3136 0a20 circle_segs 16. \n-000069e0: 2064 6566 2072 5f6d 696e 6f72 2031 2020 def r_minor 1 \n-000069f0: 2020 2020 2020 2020 6465 6620 725f 6d61 def r_ma\n-00006a00: 6a6f 7220 312e 350a 2020 7377 6565 7020 jor 1.5. sweep \n-00006a10: 7b20 6e5f 746f 726f 6964 5f73 6567 732c { n_toroid_segs,\n-00006a20: 2072 6f74 6174 6528 3336 3020 2f20 6e5f rotate(360 / n_\n-00006a30: 746f 726f 6964 5f73 6567 732c 205b 302c toroid_segs, [0,\n-00006a40: 312c 305d 2920 7d0a 2020 2020 7377 6565 1,0]) }. swee\n-00006a50: 7020 7b20 6e5f 6369 7263 6c65 5f73 6567 p { n_circle_seg\n-00006a60: 732c 2072 6f74 6174 6528 3336 3020 2f20 s, rotate(360 / \n-00006a70: 6e5f 6369 7263 6c65 5f73 6567 732c 2028 n_circle_segs, (\n-00006a80: 725f 6d61 6a6f 722c 302c 3029 2920 7d20 r_major,0,0)) } \n-00006a90: 0a20 2020 2020 2028 725f 6d61 6a6f 7220 . (r_major \n-00006aa0: 2b20 725f 6d69 6e6f 722c 2030 290a 2020 + r_minor, 0). \n-00006ab0: 2046 6f72 2069 6e74 7569 7469 6f6e 2c20 For intuition, \n-00006ac0: 7468 6520 6964 6561 206f 6620 7468 6520 the idea of the \n-00006ad0: 636f 6465 2069 7320 746f 2073 6b65 7463 code is to sketc\n-00006ae0: 6820 6120 6369 7263 6c65 2074 6f20 7468 h a circle to th\n-00006af0: 650a 7269 6768 7420 6f66 2074 6865 206f e.right of the o\n-00006b00: 7269 6769 6e20 696e 2074 6865 2078 792d rigin in the xy-\n-00006b10: 706c 616e 652c 2074 6865 6e20 726f 7461 plane, then rota\n-00006b20: 7465 2074 6861 7420 6369 7263 6c65 2022 te that circle \"\n-00006b30: 6f75 7420 6f66 2074 6865 0a70 6c61 6e65 out of the.plane\n-00006b40: 2220 6162 6f75 7420 7468 6520 792d 6178 \" about the y-ax\n-00006b50: 6973 2074 6f20 6d61 6b65 2074 6865 2066 is to make the f\n-00006b60: 696e 616c 2066 6967 7572 652e 2020 5468 inal figure. Th\n-00006b70: 6973 2070 726f 6475 6365 7320 7468 650a is produces the.\n-00006b80: 666f 6c6c 6f77 696e 672e 2020 2841 2076 following. (A v\n-00006b90: 6965 7720 726f 7461 7469 6f6e 2061 6e64 iew rotation and\n-00006ba0: 2073 6f6d 6520 6178 6573 2068 6176 6520 some axes have \n-00006bb0: 6265 656e 2061 6464 6564 2e29 0a0a 0008 been added.)....\n-00006bc0: 5b69 6d61 6765 2073 7263 3d22 6578 3039 [image src=\"ex09\n-00006bd0: 302e 706e 6722 2074 6578 743d 2249 6d61 0.png\" text=\"Ima\n-00006be0: 6765 2065 7830 3930 206f 6d69 7474 6564 ge ex090 omitted\n-00006bf0: 2069 6e20 7465 7874 2076 6572 7369 6f6e in text version\n-00006c00: 206f 6620 7468 6973 2064 6f63 756d 656e of this documen\n-00006c10: 742e 2200 085d 0a0a 2020 2054 6869 7320 t.\"..].. This \n-00006c20: 6578 616d 706c 6520 616c 736f 2073 686f example also sho\n-00006c30: 7773 2074 6861 7420 7468 6520 7377 6570 ws that the swep\n-00006c40: 7420 6f62 6a65 6374 206d 6179 2069 7473 t object may its\n-00006c50: 656c 6620 6265 2061 6e6f 7468 6572 0ae2 elf be another..\n-00006c60: 8098 7377 6565 70e2 8099 2e20 2049 6e20 ..sweep.... In \n-00006c70: 6661 6374 2c20 6974 206d 6179 2062 6520 fact, it may be \n-00006c80: 5f61 6e79 5f20 e280 9873 6b65 7463 68e2 _any_ ...sketch.\n-00006c90: 8099 2065 7870 7265 7373 696f 6e20 7468 .. expression th\n-00006ca0: 6174 2072 6573 756c 7473 2069 6e20 610a at results in a.\n-00006cb0: 6c69 7374 206f 6620 6f6e 6520 6f72 206d list of one or m\n-00006cc0: 6f72 6520 706f 696e 7473 206f 722c 2061 ore points or, a\n-00006cd0: 6c74 6572 6e61 7465 6c79 2c20 6120 6c69 lternately, a li\n-00006ce0: 7374 206f 6620 6f6e 6520 6f72 206d 6f72 st of one or mor\n-00006cf0: 650a 706f 6c79 6c69 6e65 7320 616e 6420 e.polylines and \n-00006d00: 706f 6c79 676f 6e73 2e20 2054 6865 206c polygons. The l\n-00006d10: 6174 7465 7220 6b69 6e64 206f 6620 6c69 atter kind of li\n-00006d20: 7374 2063 616e 2062 6520 6372 6561 7465 st can be create\n-00006d30: 6420 7769 7468 2061 0a7b 207d 2d65 6e63 d with a.{ }-enc\n-00006d40: 6c6f 7365 6420 626c 6f63 6b2c 2070 6572 losed block, per\n-00006d50: 6861 7073 2066 6f6c 6c6f 7769 6e67 2061 haps following a\n-00006d60: 2070 7574 206f 7220 7265 7065 6174 2e0a put or repeat..\n-00006d70: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n-00006d80: 696e 666f 2c20 204e 6f64 653a 2050 6f6c info, Node: Pol\n-00006d90: 7967 6f6e 2073 7765 6570 732c 2020 4e65 ygon sweeps, Ne\n-00006da0: 7874 3a20 506f 6c79 6c69 6e65 2073 7765 xt: Polyline swe\n-00006db0: 6570 7320 7769 7468 2063 6c6f 7375 7265 eps with closure\n-00006dc0: 2c20 2050 7265 763a 204e 6573 7465 6420 , Prev: Nested \n-00006dd0: 7377 6565 7073 2c20 2055 703a 2053 7765 sweeps, Up: Swe\n-00006de0: 7074 206f 626a 6563 7473 0a0a 322e 372e pt objects..2.7.\n-00006df0: 3420 506f 6c79 676f 6e20 7377 6565 7073 4 Polygon sweeps\n-00006e00: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d .---------------\n-00006e10: 2d2d 2d2d 2d0a 0a53 7765 6570 696e 6720 -----..Sweeping \n-00006e20: 6120 706f 6c79 676f 6e20 6372 6561 7465 a polygon create\n-00006e30: 7320 6120 636c 6f73 6564 2073 7572 6661 s a closed surfa\n-00006e40: 6365 2077 6974 6820 706f 6c79 676f 6e73 ce with polygons\n-00006e50: 2061 7420 7468 6520 656e 6473 2c0a 7768 at the ends,.wh\n-00006e60: 6963 6820 6172 6520 6a75 7374 2063 6f70 ich are just cop\n-00006e70: 6965 7320 6f66 2074 6865 206f 7269 6769 ies of the origi\n-00006e80: 6e61 6c2c 2061 7070 726f 7072 6961 7465 nal, appropriate\n-00006e90: 6c79 2070 6f73 6974 696f 6e65 642e 2020 ly positioned. \n-00006ea0: 2a4e 6f74 650a 536f 6c69 6420 636f 696c *Note.Solid coil\n-00006eb0: 2065 7861 6d70 6c65 3a3a 2e20 204f 7074 example::. Opt\n-00006ec0: 696f 6e73 206f 6e20 7468 6520 7377 6570 ions on the swep\n-00006ed0: 7420 706f 6c79 676f 6e2c 2069 6620 7468 t polygon, if th\n-00006ee0: 6579 2065 7869 7374 2c20 6172 650a 6170 ey exist, are.ap\n-00006ef0: 706c 6965 6420 746f 2074 6865 2065 6e64 plied to the end\n-00006f00: 732e 2020 4f74 6865 7277 6973 6520 7468 s. Otherwise th\n-00006f10: 6520 7377 6565 7020 6f70 7469 6f6e 7320 e sweep options \n-00006f20: 6172 6520 7573 6564 2074 6872 6f75 6768 are used through\n-00006f30: 6f75 742e 0a0a 1f0a 4669 6c65 3a20 736b out.....File: sk\n-00006f40: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-00006f50: 3a20 506f 6c79 6c69 6e65 2073 7765 6570 : Polyline sweep\n-00006f60: 7320 7769 7468 2063 6c6f 7375 7265 2c20 s with closure, \n-00006f70: 204e 6578 743a 2041 6666 696e 6520 6172 Next: Affine ar\n-00006f80: 6974 686d 6574 6963 2c20 2050 7265 763a ithmetic, Prev:\n-00006f90: 2050 6f6c 7967 6f6e 2073 7765 6570 732c Polygon sweeps,\n-00006fa0: 2020 5570 3a20 5377 6570 7420 6f62 6a65 Up: Swept obje\n-00006fb0: 6374 730a 0a32 2e37 2e35 2050 6f6c 796c cts..2.7.5 Polyl\n-00006fc0: 696e 6520 7377 6565 7073 2077 6974 6820 ine sweeps with \n-00006fd0: 636c 6f73 7572 650a 2d2d 2d2d 2d2d 2d2d closure.--------\n+00005ad0: 0a0a 546f 2064 7261 7720 7365 7665 6e20 ..To draw seven \n+00005ae0: 696e 7374 616e 6365 7320 6f66 2074 6865 instances of the\n+00005af0: 2074 6574 7261 6865 6472 6f6e 2c20 6561 tetrahedron, ea\n+00005b00: 6368 2064 6966 6665 7269 6e67 2066 726f ch differing fro\n+00005b10: 6d20 7468 6520 6c61 7374 0a62 7920 7468 m the last.by th\n+00005b20: 6520 7361 6d65 2074 7261 6e73 666f 726d e same transform\n+00005b30: 2c20 7265 706c 6163 6520 7468 6520 6c61 , replace the la\n+00005b40: 7374 2074 776f 2063 6f6d 6d61 6e64 7320 st two commands \n+00005b50: 6f66 2074 6865 2070 7265 7669 6f75 730a of the previous.\n+00005b60: 6578 616d 706c 6520 7769 7468 0a20 2072 example with. r\n+00005b70: 6570 6561 7420 7b20 372c 2072 6f74 6174 epeat { 7, rotat\n+00005b80: 6528 3135 2c20 2830 2c30 2c30 292c 205b e(15, (0,0,0), [\n+00005b90: 312c 302c 305d 2920 2520 636f 7079 2069 1,0,0]) % copy i\n+00005ba0: 6e20 6e65 7720 706f 7369 7469 6f6e 0a20 n new position. \n+00005bb0: 2020 2020 2020 2020 2020 2020 2074 6865 the\n+00005bc0: 6e20 7472 616e 736c 6174 6528 5b32 2c30 n translate([2,0\n+00005bd0: 2c30 5d29 207d 207b 7069 6572 6365 645f ,0]) } {pierced_\n+00005be0: 7465 7472 6168 6564 726f 6e7d 0a41 6e64 tetrahedron}.And\n+00005bf0: 2074 6865 2072 6573 756c 742e 2e2e 0a0a the result.....\n+00005c00: 0008 5b69 6d61 6765 2073 7263 3d22 6578 ..[image src=\"ex\n+00005c10: 3036 302e 706e 6722 2074 6578 743d 2249 060.png\" text=\"I\n+00005c20: 6d61 6765 2065 7830 3630 206f 6d69 7474 mage ex060 omitt\n+00005c30: 6564 2069 6e20 7465 7874 2076 6572 7369 ed in text versi\n+00005c40: 6f6e 206f 6620 7468 6973 2064 6f63 756d on of this docum\n+00005c50: 656e 742e 2200 085d 0a0a 1f0a 4669 6c65 ent.\"..]....File\n+00005c60: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n+00005c70: 4e6f 6465 3a20 5377 6570 7420 6f62 6a65 Node: Swept obje\n+00005c80: 6374 732c 2020 5072 6576 3a20 5265 7065 cts, Prev: Repe\n+00005c90: 6174 6564 206f 626a 6563 7473 2c20 2055 ated objects, U\n+00005ca0: 703a 2049 6e74 726f 6475 6374 696f 6e20 p: Introduction \n+00005cb0: 6279 2065 7861 6d70 6c65 0a0a 322e 3720 by example..2.7 \n+00005cc0: 5377 6570 7420 6f62 6a65 6374 730a 3d3d Swept objects.==\n+00005cd0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a ===============.\n+00005ce0: 0a4d 616e 7920 6661 6d69 6c69 6172 2073 .Many familiar s\n+00005cf0: 6861 7065 7320 6361 6e20 6265 2067 656e hapes can be gen\n+00005d00: 6572 6174 6564 2062 7920 7377 6565 7069 erated by sweepi\n+00005d10: 6e67 2073 696d 706c 6572 206f 6e65 7320 ng simpler ones \n+00005d20: 7468 726f 7567 680a 7370 6163 6520 616e through.space an\n+00005d30: 6420 636f 6e73 6964 6572 696e 6720 7468 d considering th\n+00005d40: 6520 7265 7375 6c74 696e 6720 7061 7468 e resulting path\n+00005d50: 2c20 7375 7266 6163 652c 206f 7220 766f , surface, or vo\n+00005d60: 6c75 6d65 2e20 20e2 8098 536b 6574 6368 lume. ...Sketch\n+00005d70: e280 990a 696d 706c 656d 656e 7473 2074 ....implements t\n+00005d80: 6869 7320 6964 6561 2069 6e20 7468 6520 his idea in the \n+00005d90: 7377 6565 7020 636f 6d6d 616e 642e 0a20 sweep command.. \n+00005da0: 2064 6566 206e 5f73 6567 7320 380a 2020 def n_segs 8. \n+00005db0: 7377 6565 7020 7b20 6e5f 7365 6773 2c20 sweep { n_segs, \n+00005dc0: 726f 7461 7465 2831 3830 202f 206e 5f73 rotate(180 / n_s\n+00005dd0: 6567 732c 2028 302c 302c 3029 2c20 5b30 egs, (0,0,0), [0\n+00005de0: 2c30 2c31 5d29 207d 2028 312c 302c 3029 ,0,1]) } (1,0,0)\n+00005df0: 0a54 6869 7320 636f 6465 2073 7765 6570 .This code sweep\n+00005e00: 7320 7468 6520 706f 696e 7420 2831 2c30 s the point (1,0\n+00005e10: 2c30 2920 6569 6768 7420 7469 6d65 7320 ,0) eight times \n+00005e20: 6279 2072 6f74 6174 696e 6720 6974 2031 by rotating it 1\n+00005e30: 3830 2f38 203d 0a32 322e 3520 6465 6772 80/8 =.22.5 degr\n+00005e40: 6565 7320 6561 6368 2074 696d 6520 616e ees each time an\n+00005e50: 6420 636f 6e6e 6563 7469 6e67 2074 6865 d connecting the\n+00005e60: 2072 6573 756c 7469 6e67 2070 6f69 6e74 resulting point\n+00005e70: 7320 7769 7468 206c 696e 650a 7365 676d s with line.segm\n+00005e80: 656e 7473 2e20 2054 6865 2064 6566 2075 ents. The def u\n+00005e90: 7365 6420 6865 7265 2069 7320 6120 e280 sed here is a ..\n+00005ea0: 9c73 6361 6c61 72e2 809d 2064 6566 696e .scalar... defin\n+00005eb0: 6974 696f 6e2e 2020 5265 6665 7265 6e63 ition. Referenc\n+00005ec0: 6573 2074 6f0a 7363 616c 6172 7320 6861 es to.scalars ha\n+00005ed0: 7665 206e 6f20 656e 636c 6f73 696e 6720 ve no enclosing \n+00005ee0: 6272 6163 6b65 7473 2061 7420 616c 6c2e brackets at all.\n+00005ef0: 0a0a 2a20 4d65 6e75 3a0a 0a2a 2050 6f69 ..* Menu:..* Poi\n+00005f00: 6e74 2073 7765 6570 733a 3a20 2020 2020 nt sweeps:: \n+00005f10: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n+00005f20: 2070 6f69 6e74 7320 6d61 6b65 206c 696e points make lin\n+00005f30: 6573 2061 6e64 2070 6f6c 7967 6f6e 732e es and polygons.\n+00005f40: 0a2a 2050 6f6c 796c 696e 6520 7377 6565 .* Polyline swee\n+00005f50: 7073 3a3a 2020 2020 2020 2020 2020 2020 ps:: \n+00005f60: 2053 7765 7074 206c 696e 6573 206d 616b Swept lines mak\n+00005f70: 6520 7375 7266 6163 6573 2e0a 2a20 4e65 e surfaces..* Ne\n+00005f80: 7374 6564 2073 7765 6570 733a 3a20 2020 sted sweeps:: \n+00005f90: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n+00005fa0: 7420 7377 6565 7073 2061 7265 2075 7365 t sweeps are use\n+00005fb0: 6675 6c21 0a2a 2050 6f6c 7967 6f6e 2073 ful!.* Polygon s\n+00005fc0: 7765 6570 733a 3a20 2020 2020 2020 2020 weeps:: \n+00005fd0: 2020 2020 2053 7765 7074 2070 6f6c 7967 Swept polyg\n+00005fe0: 6f6e 7320 6d61 6b65 2073 6f6c 6964 732e ons make solids.\n+00005ff0: 2e2e 0a2a 2050 6f6c 796c 696e 6520 7377 ...* Polyline sw\n+00006000: 6565 7073 2077 6974 6820 636c 6f73 7572 eeps with closur\n+00006010: 653a 3a20 2061 6e64 2073 6f20 646f 2063 e:: and so do c\n+00006020: 6c6f 7365 6420 706f 6c79 6c69 6e65 2073 losed polyline s\n+00006030: 7765 6570 732e 0a2a 2041 6666 696e 6520 weeps..* Affine \n+00006040: 6172 6974 686d 6574 6963 3a3a 2020 2020 arithmetic:: \n+00006050: 2020 2020 2020 2053 6b65 7463 6820 7573 Sketch us\n+00006060: 6566 756c 206d 6174 6820 6578 7072 6573 eful math expres\n+00006070: 7369 6f6e 2e0a 2a20 4d6f 7265 2074 6f20 sion..* More to \n+00006080: 6c65 6172 6e3a 3a20 2020 2020 2020 2020 learn:: \n+00006090: 2020 2020 2020 4368 6563 6b20 6f75 7420 Check out \n+000060a0: 7468 6520 4d6f 6269 7573 2073 7472 6970 the Mobius strip\n+000060b0: 210a 0a1f 0a46 696c 653a 2073 6b65 7463 !....File: sketc\n+000060c0: 682e 696e 666f 2c20 204e 6f64 653a 2050 h.info, Node: P\n+000060d0: 6f69 6e74 2073 7765 6570 732c 2020 4e65 oint sweeps, Ne\n+000060e0: 7874 3a20 506f 6c79 6c69 6e65 2073 7765 xt: Polyline swe\n+000060f0: 6570 732c 2020 5072 6576 3a20 5377 6570 eps, Prev: Swep\n+00006100: 7420 6f62 6a65 6374 732c 2020 5570 3a20 t objects, Up: \n+00006110: 5377 6570 7420 6f62 6a65 6374 730a 0a32 Swept objects..2\n+00006120: 2e37 2e31 2050 6f69 6e74 2073 7765 6570 .7.1 Point sweep\n+00006130: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d s.--------------\n+00006140: 2d2d 2d2d 0a0a 5377 6565 7069 6e67 2061 ----..Sweeping a\n+00006150: 2070 6f69 6e74 206d 616b 6573 2061 206f point makes a o\n+00006160: 6e65 2d64 696d 656e 7369 6f6e 616c 2070 ne-dimensional p\n+00006170: 6174 682c 2077 6869 6368 2069 7320 6120 ath, which is a \n+00006180: 706f 6c79 6c69 6e65 2e0a 5369 6e63 6520 polyline..Since \n+00006190: 7765 2068 6176 6520 7377 6570 7420 7769 we have swept wi\n+000061a0: 7468 2061 2072 6f74 6174 696f 6e2c 2074 th a rotation, t\n+000061b0: 6865 2072 6573 756c 7420 6973 2061 2063 he result is a c\n+000061c0: 6972 6375 6c61 7220 6172 632e 2020 4865 ircular arc. He\n+000061d0: 7265 0a69 7320 7768 6174 2069 7420 6c6f re.is what it lo\n+000061e0: 6f6b 7320 6c69 6b65 2e0a 0a00 085b 696d oks like.....[im\n+000061f0: 6167 6520 7372 633d 2265 7830 3730 2e70 age src=\"ex070.p\n+00006200: 6e67 2220 7465 7874 3d22 496d 6167 6520 ng\" text=\"Image \n+00006210: 6578 3037 3020 6f6d 6974 7465 6420 696e ex070 omitted in\n+00006220: 2074 6578 7420 7665 7273 696f 6e20 6f66 text version of\n+00006230: 2074 6869 7320 646f 6375 6d65 6e74 2e22 this document.\"\n+00006240: 0008 5d0a 0a20 2020 5468 6973 2069 7320 ..].. This is \n+00006250: 7468 6520 6669 7273 7420 6578 616d 706c the first exampl\n+00006260: 6520 7765 2068 6176 6520 7365 656e 206f e we have seen o\n+00006270: 6620 e280 9873 6b65 7463 68e2 8099 2061 f ...sketch... a\n+00006280: 7269 7468 6d65 7469 632e 2020 5468 650a rithmetic. The.\n+00006290: 6578 7072 6573 7369 6f6e 2031 3830 202f expression 180 /\n+000062a0: 206e 5f73 6567 7320 6361 7573 6573 2074 n_segs causes t\n+000062b0: 6865 2065 6967 6874 2072 6f74 6174 696f he eight rotatio\n+000062c0: 6e73 2074 6f20 6164 6420 746f 2031 3830 ns to add to 180\n+000062d0: 2e20 2049 660a 796f 7527 7265 2070 6179 . If.you're pay\n+000062e0: 696e 6720 6174 7465 6e74 696f 6e2c 2079 ing attention, y\n+000062f0: 6f75 276c 6c20 6861 7665 2061 6c72 6561 ou'll have alrea\n+00006300: 6479 206e 6f74 6564 2074 6861 7420 7468 dy noted that th\n+00006310: 6572 6520 6172 6520 5f6e 696e 655f 0a70 ere are _nine_.p\n+00006320: 6f69 6e74 732c 2070 726f 6475 6369 6e67 oints, producing\n+00006330: 2065 6967 6874 206c 696e 6520 7365 676d eight line segm\n+00006340: 656e 7473 2e0a 0a20 2020 596f 7520 6361 ents... You ca\n+00006350: 6e20 6361 7573 6520 7468 6520 7377 6570 n cause the swep\n+00006360: 7420 706f 696e 7420 746f 2067 656e 6572 t point to gener\n+00006370: 6174 6520 6120 7369 6e67 6c65 2070 6f6c ate a single pol\n+00006380: 7967 6f6e 2072 6174 6865 720a 7468 616e ygon rather.than\n+00006390: 2061 2070 6f6c 796c 696e 6520 6279 2075 a polyline by u\n+000063a0: 7369 6e67 2074 6865 20e2 809c 636c 6f73 sing the ...clos\n+000063b0: 7572 6520 7461 67e2 809d 203c 3e20 6166 ure tag... <> af\n+000063c0: 7465 7220 7468 6520 6e75 6d62 6572 206f ter the number o\n+000063d0: 6620 7377 6570 740a 6f62 6a65 6374 732e f swept.objects.\n+000063e0: 2020 436f 6465 2061 6e64 2072 6573 756c Code and resul\n+000063f0: 7420 666f 6c6c 6f77 0a20 2064 6566 206e t follow. def n\n+00006400: 5f73 6567 7320 380a 2020 7377 6565 7020 _segs 8. sweep \n+00006410: 7b20 6e5f 7365 6773 3c3e 2c20 726f 7461 { n_segs<>, rota\n+00006420: 7465 2831 3830 202f 206e 5f73 6567 732c te(180 / n_segs,\n+00006430: 2028 302c 302c 3029 2c20 5b30 2c30 2c31 (0,0,0), [0,0,1\n+00006440: 5d29 207d 2028 312c 302c 3029 0a00 085b ]) } (1,0,0)...[\n+00006450: 696d 6167 6520 7372 633d 2265 7830 3830 image src=\"ex080\n+00006460: 2e70 6e67 2220 7465 7874 3d22 496d 6167 .png\" text=\"Imag\n+00006470: 6520 6578 3038 3020 6f6d 6974 7465 6420 e ex080 omitted \n+00006480: 696e 2074 6578 7420 7665 7273 696f 6e20 in text version \n+00006490: 6f66 2074 6869 7320 646f 6375 6d65 6e74 of this document\n+000064a0: 2e22 0008 5d0a 0a1f 0a46 696c 653a 2073 .\"..]....File: s\n+000064b0: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+000064c0: 653a 2050 6f6c 796c 696e 6520 7377 6565 e: Polyline swee\n+000064d0: 7073 2c20 204e 6578 743a 204e 6573 7465 ps, Next: Neste\n+000064e0: 6420 7377 6565 7073 2c20 2050 7265 763a d sweeps, Prev:\n+000064f0: 2050 6f69 6e74 2073 7765 6570 732c 2020 Point sweeps, \n+00006500: 5570 3a20 5377 6570 7420 6f62 6a65 6374 Up: Swept object\n+00006510: 730a 0a32 2e37 2e32 2050 6f6c 796c 696e s..2.7.2 Polylin\n+00006520: 6520 7377 6565 7073 0a2d 2d2d 2d2d 2d2d e sweeps.-------\n+00006530: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a --------------..\n+00006540: 5377 6565 7069 6e67 2061 2070 6f6c 796c Sweeping a polyl\n+00006550: 696e 6520 7072 6f64 7563 6573 2061 2073 ine produces a s\n+00006560: 7572 6661 6365 2063 6f6d 706f 7365 6420 urface composed \n+00006570: 6f66 206d 616e 7920 6661 6365 732e 2020 of many faces. \n+00006580: 5468 650a 756e 6272 6f6b 656e 2068 656c The.unbroken hel\n+00006590: 6978 2069 6e20 7468 6520 6578 616d 706c ix in the exampl\n+000065a0: 6520 2a6e 6f74 6520 4865 6c69 7820 7769 e *note Helix wi\n+000065b0: 7468 2063 756c 6c20 7365 7420 6661 6c73 th cull set fals\n+000065c0: 6520 7468 656e 0a74 7275 653a 3a20 6973 e then.true:: is\n+000065d0: 2070 726f 6475 6365 6420 6279 2074 6869 produced by thi\n+000065e0: 7320 636f 6465 2028 706c 7573 2061 2073 s code (plus a s\n+000065f0: 7572 726f 756e 6469 6e67 2070 7574 2072 urrounding put r\n+00006600: 6f74 6174 696f 6e20 746f 206d 616b 650a otation to make.\n+00006610: 616e 2069 6e74 6572 6573 7469 6e67 2076 an interesting v\n+00006620: 6965 773b 2074 6869 7320 6861 7320 6265 iew; this has be\n+00006630: 656e 206f 6d69 7474 6564 292e 0a20 2064 en omitted).. d\n+00006640: 6566 204b 205b 302c 302c 315d 0a20 2073 ef K [0,0,1]. s\n+00006650: 7765 6570 5b63 756c 6c3d 6661 6c73 655d weep[cull=false]\n+00006660: 207b 0a20 2020 2036 302c 200a 2020 2020 {. 60, . \n+00006670: 726f 7461 7465 2831 302c 2028 302c 302c rotate(10, (0,0,\n+00006680: 3029 2c20 5b4b 5d29 2074 6865 6e20 7472 0), [K]) then tr\n+00006690: 616e 736c 6174 6528 312f 3620 2a20 5b4b anslate(1/6 * [K\n+000066a0: 5d29 200a 2020 7d20 6c69 6e65 5b6c 696e ]) . } line[lin\n+000066b0: 6577 6964 7468 3d32 7074 5d28 2d31 2c30 ewidth=2pt](-1,0\n+000066c0: 2928 312c 3029 0a41 6761 696e 2c20 3630 )(1,0).Again, 60\n+000066d0: 2073 6567 6d65 6e74 7320 6f66 2074 6865 segments of the\n+000066e0: 2068 656c 6978 2061 7265 2070 726f 6475 helix are produ\n+000066f0: 6365 6420 6279 2063 6f6e 6e65 6374 696e ced by connectin\n+00006700: 6720 3631 2069 6e73 7461 6e63 6573 0a6f g 61 instances.o\n+00006710: 6620 7468 6520 7377 6570 7420 6c69 6e65 f the swept line\n+00006720: 2e20 204f 7074 696f 6e73 2061 7070 6c69 . Options appli\n+00006730: 6564 2074 6f20 7468 6520 7377 6565 702c ed to the sweep,\n+00006740: 2068 6572 6520 6375 6c6c 3d66 616c 7365 here cull=false\n+00006750: 2c20 6172 650a 7472 6561 7465 6420 6173 , are.treated as\n+00006760: 206f 7074 696f 6e73 2066 6f72 2074 6865 options for the\n+00006770: 2067 656e 6572 6174 6564 2070 6f6c 7967 generated polyg\n+00006780: 6f6e 206f 7220 706f 6c79 6c69 6e65 2e20 on or polyline. \n+00006790: 204f 7074 696f 6e73 206f 660a 7468 6520 Options of.the \n+000067a0: 7377 6570 7420 6c69 6e65 2069 7473 656c swept line itsel\n+000067b0: 662c 2068 6572 6520 6c69 6e65 7769 6474 f, here linewidt\n+000067c0: 683d 3270 742c 2061 7265 2069 676e 6f72 h=2pt, are ignor\n+000067d0: 6564 2c20 7468 6f75 6768 2077 6974 6820 ed, though with \n+000067e0: 610a 7761 726e 696e 672e 2020 5468 6973 a.warning. This\n+000067f0: 2064 6566 2069 7320 6120 e280 9c76 6563 def is a ...vec\n+00006800: 746f 72e2 809d 2064 6566 696e 6974 696f tor... definitio\n+00006810: 6e2c 2077 6869 6368 206d 7573 7420 6265 n, which must be\n+00006820: 2072 6566 6572 656e 6365 640a 7769 7468 referenced.with\n+00006830: 2073 7175 6172 6520 6272 6163 6b65 7473 square brackets\n+00006840: 2c20 652e 672e 205b 666f 6f5d 2e0a 0a1f , e.g. [foo]....\n+00006850: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+00006860: 666f 2c20 204e 6f64 653a 204e 6573 7465 fo, Node: Neste\n+00006870: 6420 7377 6565 7073 2c20 204e 6578 743a d sweeps, Next:\n+00006880: 2050 6f6c 7967 6f6e 2073 7765 6570 732c Polygon sweeps,\n+00006890: 2020 5072 6576 3a20 506f 6c79 6c69 6e65 Prev: Polyline\n+000068a0: 2073 7765 6570 732c 2020 5570 3a20 5377 sweeps, Up: Sw\n+000068b0: 6570 7420 6f62 6a65 6374 730a 0a32 2e37 ept objects..2.7\n+000068c0: 2e33 204e 6573 7465 6420 7377 6565 7073 .3 Nested sweeps\n+000068d0: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d .---------------\n+000068e0: 2d2d 2d2d 0a0a 5768 656e 2074 6865 2063 ----..When the c\n+000068f0: 656e 7465 7220 706f 696e 7420 6f66 2072 enter point of r\n+00006900: 6f74 6174 696f 6e20 6973 206f 6d69 7474 otation is omitt\n+00006910: 6564 2c20 7468 6520 6f72 6967 696e 2069 ed, the origin i\n+00006920: 7320 6173 7375 6d65 642e 0a57 6865 6e20 s assumed..When \n+00006930: 6120 706f 696e 7420 6861 7320 6f6e 6c79 a point has only\n+00006940: 2074 776f 2063 6f6f 7264 696e 6174 6573 two coordinates\n+00006950: 2c20 7468 6579 2061 7265 2074 616b 656e , they are taken\n+00006960: 2061 7320 7820 616e 6420 792c 2077 6974 as x and y, wit\n+00006970: 680a 7a3d 3020 6173 7375 6d65 642e 2020 h.z=0 assumed. \n+00006980: 4120 746f 726f 6964 2069 7320 7468 6572 A toroid is ther\n+00006990: 6566 6f72 6520 6f62 7461 696e 6564 2077 efore obtained w\n+000069a0: 6974 6820 7468 6973 2063 6f64 652e 0a20 ith this code.. \n+000069b0: 2064 6566 206e 5f74 6f72 6f69 645f 7365 def n_toroid_se\n+000069c0: 6773 2032 3020 2020 6465 6620 6e5f 6369 gs 20 def n_ci\n+000069d0: 7263 6c65 5f73 6567 7320 3136 0a20 2064 rcle_segs 16. d\n+000069e0: 6566 2072 5f6d 696e 6f72 2031 2020 2020 ef r_minor 1 \n+000069f0: 2020 2020 2020 6465 6620 725f 6d61 6a6f def r_majo\n+00006a00: 7220 312e 350a 2020 7377 6565 7020 7b20 r 1.5. sweep { \n+00006a10: 6e5f 746f 726f 6964 5f73 6567 732c 2072 n_toroid_segs, r\n+00006a20: 6f74 6174 6528 3336 3020 2f20 6e5f 746f otate(360 / n_to\n+00006a30: 726f 6964 5f73 6567 732c 205b 302c 312c roid_segs, [0,1,\n+00006a40: 305d 2920 7d0a 2020 2020 7377 6565 7020 0]) }. sweep \n+00006a50: 7b20 6e5f 6369 7263 6c65 5f73 6567 732c { n_circle_segs,\n+00006a60: 2072 6f74 6174 6528 3336 3020 2f20 6e5f rotate(360 / n_\n+00006a70: 6369 7263 6c65 5f73 6567 732c 2028 725f circle_segs, (r_\n+00006a80: 6d61 6a6f 722c 302c 3029 2920 7d20 0a20 major,0,0)) } . \n+00006a90: 2020 2020 2028 725f 6d61 6a6f 7220 2b20 (r_major + \n+00006aa0: 725f 6d69 6e6f 722c 2030 290a 2020 2046 r_minor, 0). F\n+00006ab0: 6f72 2069 6e74 7569 7469 6f6e 2c20 7468 or intuition, th\n+00006ac0: 6520 6964 6561 206f 6620 7468 6520 636f e idea of the co\n+00006ad0: 6465 2069 7320 746f 2073 6b65 7463 6820 de is to sketch \n+00006ae0: 6120 6369 7263 6c65 2074 6f20 7468 650a a circle to the.\n+00006af0: 7269 6768 7420 6f66 2074 6865 206f 7269 right of the ori\n+00006b00: 6769 6e20 696e 2074 6865 2078 792d 706c gin in the xy-pl\n+00006b10: 616e 652c 2074 6865 6e20 726f 7461 7465 ane, then rotate\n+00006b20: 2074 6861 7420 6369 7263 6c65 2022 6f75 that circle \"ou\n+00006b30: 7420 6f66 2074 6865 0a70 6c61 6e65 2220 t of the.plane\" \n+00006b40: 6162 6f75 7420 7468 6520 792d 6178 6973 about the y-axis\n+00006b50: 2074 6f20 6d61 6b65 2074 6865 2066 696e to make the fin\n+00006b60: 616c 2066 6967 7572 652e 2020 5468 6973 al figure. This\n+00006b70: 2070 726f 6475 6365 7320 7468 650a 666f produces the.fo\n+00006b80: 6c6c 6f77 696e 672e 2020 2841 2076 6965 llowing. (A vie\n+00006b90: 7720 726f 7461 7469 6f6e 2061 6e64 2073 w rotation and s\n+00006ba0: 6f6d 6520 6178 6573 2068 6176 6520 6265 ome axes have be\n+00006bb0: 656e 2061 6464 6564 2e29 0a0a 0008 5b69 en added.)....[i\n+00006bc0: 6d61 6765 2073 7263 3d22 6578 3039 302e mage src=\"ex090.\n+00006bd0: 706e 6722 2074 6578 743d 2249 6d61 6765 png\" text=\"Image\n+00006be0: 2065 7830 3930 206f 6d69 7474 6564 2069 ex090 omitted i\n+00006bf0: 6e20 7465 7874 2076 6572 7369 6f6e 206f n text version o\n+00006c00: 6620 7468 6973 2064 6f63 756d 656e 742e f this document.\n+00006c10: 2200 085d 0a0a 2020 2054 6869 7320 6578 \"..].. This ex\n+00006c20: 616d 706c 6520 616c 736f 2073 686f 7773 ample also shows\n+00006c30: 2074 6861 7420 7468 6520 7377 6570 7420 that the swept \n+00006c40: 6f62 6a65 6374 206d 6179 2069 7473 656c object may itsel\n+00006c50: 6620 6265 2061 6e6f 7468 6572 0ae2 8098 f be another....\n+00006c60: 7377 6565 70e2 8099 2e20 2049 6e20 6661 sweep.... In fa\n+00006c70: 6374 2c20 6974 206d 6179 2062 6520 5f61 ct, it may be _a\n+00006c80: 6e79 5f20 e280 9873 6b65 7463 68e2 8099 ny_ ...sketch...\n+00006c90: 2065 7870 7265 7373 696f 6e20 7468 6174 expression that\n+00006ca0: 2072 6573 756c 7473 2069 6e20 610a 6c69 results in a.li\n+00006cb0: 7374 206f 6620 6f6e 6520 6f72 206d 6f72 st of one or mor\n+00006cc0: 6520 706f 696e 7473 206f 722c 2061 6c74 e points or, alt\n+00006cd0: 6572 6e61 7465 6c79 2c20 6120 6c69 7374 ernately, a list\n+00006ce0: 206f 6620 6f6e 6520 6f72 206d 6f72 650a of one or more.\n+00006cf0: 706f 6c79 6c69 6e65 7320 616e 6420 706f polylines and po\n+00006d00: 6c79 676f 6e73 2e20 2054 6865 206c 6174 lygons. The lat\n+00006d10: 7465 7220 6b69 6e64 206f 6620 6c69 7374 ter kind of list\n+00006d20: 2063 616e 2062 6520 6372 6561 7465 6420 can be created \n+00006d30: 7769 7468 2061 0a7b 207d 2d65 6e63 6c6f with a.{ }-enclo\n+00006d40: 7365 6420 626c 6f63 6b2c 2070 6572 6861 sed block, perha\n+00006d50: 7073 2066 6f6c 6c6f 7769 6e67 2061 2070 ps following a p\n+00006d60: 7574 206f 7220 7265 7065 6174 2e0a 0a1f ut or repeat....\n+00006d70: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+00006d80: 666f 2c20 204e 6f64 653a 2050 6f6c 7967 fo, Node: Polyg\n+00006d90: 6f6e 2073 7765 6570 732c 2020 4e65 7874 on sweeps, Next\n+00006da0: 3a20 506f 6c79 6c69 6e65 2073 7765 6570 : Polyline sweep\n+00006db0: 7320 7769 7468 2063 6c6f 7375 7265 2c20 s with closure, \n+00006dc0: 2050 7265 763a 204e 6573 7465 6420 7377 Prev: Nested sw\n+00006dd0: 6565 7073 2c20 2055 703a 2053 7765 7074 eeps, Up: Swept\n+00006de0: 206f 626a 6563 7473 0a0a 322e 372e 3420 objects..2.7.4 \n+00006df0: 506f 6c79 676f 6e20 7377 6565 7073 0a2d Polygon sweeps.-\n+00006e00: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n+00006e10: 2d2d 2d0a 0a53 7765 6570 696e 6720 6120 ---..Sweeping a \n+00006e20: 706f 6c79 676f 6e20 6372 6561 7465 7320 polygon creates \n+00006e30: 6120 636c 6f73 6564 2073 7572 6661 6365 a closed surface\n+00006e40: 2077 6974 6820 706f 6c79 676f 6e73 2061 with polygons a\n+00006e50: 7420 7468 6520 656e 6473 2c0a 7768 6963 t the ends,.whic\n+00006e60: 6820 6172 6520 6a75 7374 2063 6f70 6965 h are just copie\n+00006e70: 7320 6f66 2074 6865 206f 7269 6769 6e61 s of the origina\n+00006e80: 6c2c 2061 7070 726f 7072 6961 7465 6c79 l, appropriately\n+00006e90: 2070 6f73 6974 696f 6e65 642e 2020 2a4e positioned. *N\n+00006ea0: 6f74 650a 536f 6c69 6420 636f 696c 2065 ote.Solid coil e\n+00006eb0: 7861 6d70 6c65 3a3a 2e20 204f 7074 696f xample::. Optio\n+00006ec0: 6e73 206f 6e20 7468 6520 7377 6570 7420 ns on the swept \n+00006ed0: 706f 6c79 676f 6e2c 2069 6620 7468 6579 polygon, if they\n+00006ee0: 2065 7869 7374 2c20 6172 650a 6170 706c exist, are.appl\n+00006ef0: 6965 6420 746f 2074 6865 2065 6e64 732e ied to the ends.\n+00006f00: 2020 4f74 6865 7277 6973 6520 7468 6520 Otherwise the \n+00006f10: 7377 6565 7020 6f70 7469 6f6e 7320 6172 sweep options ar\n+00006f20: 6520 7573 6564 2074 6872 6f75 6768 6f75 e used throughou\n+00006f30: 742e 0a0a 1f0a 4669 6c65 3a20 736b 6574 t.....File: sket\n+00006f40: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n+00006f50: 506f 6c79 6c69 6e65 2073 7765 6570 7320 Polyline sweeps \n+00006f60: 7769 7468 2063 6c6f 7375 7265 2c20 204e with closure, N\n+00006f70: 6578 743a 2041 6666 696e 6520 6172 6974 ext: Affine arit\n+00006f80: 686d 6574 6963 2c20 2050 7265 763a 2050 hmetic, Prev: P\n+00006f90: 6f6c 7967 6f6e 2073 7765 6570 732c 2020 olygon sweeps, \n+00006fa0: 5570 3a20 5377 6570 7420 6f62 6a65 6374 Up: Swept object\n+00006fb0: 730a 0a32 2e37 2e35 2050 6f6c 796c 696e s..2.7.5 Polylin\n+00006fc0: 6520 7377 6565 7073 2077 6974 6820 636c e sweeps with cl\n+00006fd0: 6f73 7572 650a 2d2d 2d2d 2d2d 2d2d 2d2d osure.----------\n 00006fe0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-00006ff0: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 4120 706f ----------..A po\n-00007000: 6c79 6c69 6e65 2073 7765 6570 2077 6974 lyline sweep wit\n-00007010: 6820 6120 636c 6f73 7572 6520 7461 6720 h a closure tag \n-00007020: 6372 6561 7465 7320 616e 6f74 6865 7220 creates another \n-00007030: 6b69 6e64 206f 6620 636c 6f73 6564 0a73 kind of closed.s\n-00007040: 7572 6661 6365 2e20 2046 6972 7374 2c20 urface. First, \n-00007050: 7468 6520 706f 6c79 6c69 6e65 2073 6567 the polyline seg\n-00007060: 6d65 6e74 7320 6172 6520 636f 6e6e 6563 ments are connec\n-00007070: 7465 6420 6279 2066 6163 6573 2c20 6a75 ted by faces, ju\n-00007080: 7374 2061 730a 7769 7468 6f75 7420 7468 st as.without th\n-00007090: 6520 636c 6f73 7572 6520 7461 672e 2020 e closure tag. \n-000070a0: 5468 656e 2c20 6561 6368 2073 6574 206f Then, each set o\n-000070b0: 6620 656e 6420 706f 696e 7473 2069 7320 f end points is \n-000070c0: 6a6f 696e 6564 2074 6f20 6d61 6b65 0a61 joined to make.a\n-000070d0: 2070 6f6c 7967 6f6e 2c20 6f6e 6520 666f polygon, one fo\n-000070e0: 7220 6561 6368 2065 6e64 2e20 2041 2063 r each end. A c\n-000070f0: 6f64 6520 666f 7220 7365 7665 7261 6c20 ode for several \n-00007100: 7669 6577 7320 6f66 2061 2063 796c 696e views of a cylin\n-00007110: 6472 6963 616c 0a70 7269 736d 2066 6f6c drical.prism fol\n-00007120: 6c6f 7773 2e0a 2020 6465 6620 6e5f 6379 lows.. def n_cy\n-00007130: 6c5f 7365 6773 2032 3020 2064 6566 206e l_segs 20 def n\n-00007140: 5f76 6965 7773 2035 2020 6465 6620 4920 _views 5 def I \n-00007150: 5b31 2c30 2c30 5d0a 2020 6465 6620 656e [1,0,0]. def en\n-00007160: 646f 7074 7320 5b66 696c 6c63 6f6c 6f72 dopts [fillcolor\n-00007170: 3d6c 6967 6874 6772 6179 5d0a 2020 7265 =lightgray]. re\n-00007180: 7065 6174 207b 206e 5f76 6965 7773 2c20 peat { n_views, \n-00007190: 726f 7461 7465 2831 3830 2f6e 5f76 6965 rotate(180/n_vie\n-000071a0: 7773 2c20 5b49 5d29 2074 6865 6e20 7472 ws, [I]) then tr\n-000071b0: 616e 736c 6174 6528 5b49 5d20 2a20 322e anslate([I] * 2.\n-000071c0: 3129 207d 200a 2020 2020 7377 6565 705b 1) } . sweep[\n-000071d0: 656e 646f 7074 735d 7b20 6e5f 6379 6c5f endopts]{ n_cyl_\n-000071e0: 7365 6773 3c3e 2c20 726f 7461 7465 2833 segs<>, rotate(3\n-000071f0: 3630 2f6e 5f63 796c 5f73 6567 732c 205b 60/n_cyl_segs, [\n-00007200: 302c 312c 305d 2920 7d20 0a20 2020 2020 0,1,0]) } . \n-00007210: 206c 696e 655b 6669 6c6c 636f 6c6f 723d line[fillcolor=\n-00007220: 7768 6974 655d 2831 2c2d 3129 2831 2c31 white](1,-1)(1,1\n-00007230: 290a 4974 2070 726f 6475 6365 7320 7468 ).It produces th\n-00007240: 6973 2064 7261 7769 6e67 2e0a 0a00 085b is drawing.....[\n-00007250: 696d 6167 6520 7372 633d 2265 7831 3130 image src=\"ex110\n-00007260: 2e70 6e67 2220 7465 7874 3d22 496d 6167 .png\" text=\"Imag\n-00007270: 6520 6578 3131 3020 6f6d 6974 7465 6420 e ex110 omitted \n-00007280: 696e 2074 6578 7420 7665 7273 696f 6e20 in text version \n-00007290: 6f66 2074 6869 7320 646f 6375 6d65 6e74 of this document\n-000072a0: 2e22 0008 5d0a 0a54 6865 206f 7074 696f .\"..]..The optio\n-000072b0: 6e73 206f 6620 7468 6520 7377 6570 7420 ns of the swept \n-000072c0: 6c69 6e65 2c20 6966 2061 6e79 2c20 6172 line, if any, ar\n-000072d0: 6520 6170 706c 6965 6420 746f 2074 6865 e applied to the\n-000072e0: 2066 6163 6573 2070 726f 6475 6365 640a faces produced.\n-000072f0: 6279 2073 7765 6570 696e 6720 7468 6520 by sweeping the \n-00007300: 6c69 6e65 2c20 6275 7420 6e6f 7420 7468 line, but not th\n-00007310: 6520 656e 6420 706f 6c79 676f 6e73 2e20 e end polygons. \n-00007320: 204f 7468 6572 7769 7365 2c20 7468 6520 Otherwise, the \n-00007330: 7377 6565 700a 6f70 7469 6f6e 7320 6172 sweep.options ar\n-00007340: 6520 6170 706c 6965 6420 7468 726f 7567 e applied throug\n-00007350: 686f 7574 2e20 2054 6865 2064 6566 2069 hout. The def i\n-00007360: 6e20 7468 6973 2065 7861 6d70 6c65 2069 n this example i\n-00007370: 7320 616e 20e2 809c 6f70 7469 6f6e e280 s an ...option..\n-00007380: 9d0a 6465 6669 6e69 7469 6f6e 2e20 2052 ..definition. R\n-00007390: 6566 6572 656e 6365 7320 746f 206f 7074 eferences to opt\n-000073a0: 696f 6e73 206d 7573 7420 6265 2065 6e63 ions must be enc\n-000073b0: 6c6f 7365 6420 696e 2073 7175 6172 6520 losed in square \n-000073c0: 6272 6163 6b65 7473 2c0a 652e 672e 2020 brackets,.e.g. \n-000073d0: 205b 666f 6f5d 2e20 2059 6f75 2063 616e [foo]. You can\n-000073e0: 2063 6f6e 6361 7465 6e61 7465 2073 6576 concatenate sev\n-000073f0: 6572 616c 2073 6574 7320 6f66 206f 7074 eral sets of opt\n-00007400: 696f 6e73 2077 6974 6820 6120 7369 6e67 ions with a sing\n-00007410: 6c65 0a72 6566 6572 656e 6365 2c20 652e le.reference, e.\n-00007420: 672e 2020 205b 636f 6c6f 722c 2073 697a g. [color, siz\n-00007430: 652c 2073 7479 6c65 5d20 2077 6f75 6c64 e, style] would\n-00007440: 2063 6175 7365 2074 6865 206f 7074 696f cause the optio\n-00007450: 6e0a 6465 6669 6e69 7469 6f6e 7320 666f n.definitions fo\n-00007460: 7220 e280 9863 6f6c 6f72 e280 992c 20e2 r ...color..., .\n-00007470: 8098 7369 7a65 e280 992c 2061 6e64 20e2 ..size..., and .\n-00007480: 8098 7374 796c 65e2 8099 2074 6f20 6170 ..style... to ap\n-00007490: 7065 6172 2069 6e20 7365 7175 656e 6365 pear in sequence\n-000074a0: 2069 6e0a 7468 6520 6f75 7470 7574 2063 in.the output c\n-000074b0: 7265 6174 6564 2062 7920 7468 6520 e280 reated by the ..\n-000074c0: 9873 6b65 7463 68e2 8099 2063 6f6d 6d61 .sketch... comma\n-000074d0: 6e64 2063 6f6e 7461 696e 696e 6720 7468 nd containing th\n-000074e0: 6520 7265 6665 7265 6e63 652e 0a48 6170 e reference..Hap\n-000074f0: 7069 6c79 2c20 7468 6520 7379 6e74 6178 pily, the syntax\n-00007500: 206f 6620 e280 9873 6b65 7463 68e2 8099 of ...sketch...\n-00007510: 2069 7320 7375 6368 2074 6861 7420 6f70 is such that op\n-00007520: 7469 6f6e 7320 7265 6665 7265 6e63 6573 tions references\n-00007530: 2063 616e 0a6e 6576 6572 2062 6520 636f can.never be co\n-00007540: 6e66 7573 6564 2077 6974 6820 7665 6374 nfused with vect\n-00007550: 6f72 2072 6566 6572 656e 6365 732e 2020 or references. \n-00007560: 5768 696c 6520 6e6f 7420 6170 7061 7265 While not appare\n-00007570: 6e74 2069 6e20 7468 6973 0a65 7861 6d70 nt in this.examp\n-00007580: 6c65 2c20 6f70 7469 6f6e 7320 7265 6665 le, options refe\n-00007590: 7265 6e63 6573 2061 7265 2075 7365 6675 rences are usefu\n-000075a0: 6c20 7768 656e 2064 6566 696e 696e 6720 l when defining \n-000075b0: 6d61 6e79 206f 626a 6563 7473 2077 6974 many objects wit\n-000075c0: 6820 610a 7369 6d69 6c61 7220 6170 7065 h a.similar appe\n-000075d0: 6172 616e 6365 2e0a 0a1f 0a46 696c 653a arance.....File:\n-000075e0: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-000075f0: 6f64 653a 2041 6666 696e 6520 6172 6974 ode: Affine arit\n-00007600: 686d 6574 6963 2c20 204e 6578 743a 204d hmetic, Next: M\n-00007610: 6f72 6520 746f 206c 6561 726e 2c20 2050 ore to learn, P\n-00007620: 7265 763a 2050 6f6c 796c 696e 6520 7377 rev: Polyline sw\n-00007630: 6565 7073 2077 6974 6820 636c 6f73 7572 eeps with closur\n-00007640: 652c 2020 5570 3a20 5377 6570 7420 6f62 e, Up: Swept ob\n-00007650: 6a65 6374 730a 0a32 2e37 2e36 2041 6666 jects..2.7.6 Aff\n-00007660: 696e 6520 6172 6974 686d 6574 6963 0a2d ine arithmetic.-\n+00006ff0: 2d2d 2d2d 2d2d 2d2d 0a0a 4120 706f 6c79 --------..A poly\n+00007000: 6c69 6e65 2073 7765 6570 2077 6974 6820 line sweep with \n+00007010: 6120 636c 6f73 7572 6520 7461 6720 6372 a closure tag cr\n+00007020: 6561 7465 7320 616e 6f74 6865 7220 6b69 eates another ki\n+00007030: 6e64 206f 6620 636c 6f73 6564 0a73 7572 nd of closed.sur\n+00007040: 6661 6365 2e20 2046 6972 7374 2c20 7468 face. First, th\n+00007050: 6520 706f 6c79 6c69 6e65 2073 6567 6d65 e polyline segme\n+00007060: 6e74 7320 6172 6520 636f 6e6e 6563 7465 nts are connecte\n+00007070: 6420 6279 2066 6163 6573 2c20 6a75 7374 d by faces, just\n+00007080: 2061 730a 7769 7468 6f75 7420 7468 6520 as.without the \n+00007090: 636c 6f73 7572 6520 7461 672e 2020 5468 closure tag. Th\n+000070a0: 656e 2c20 6561 6368 2073 6574 206f 6620 en, each set of \n+000070b0: 656e 6420 706f 696e 7473 2069 7320 6a6f end points is jo\n+000070c0: 696e 6564 2074 6f20 6d61 6b65 0a61 2070 ined to make.a p\n+000070d0: 6f6c 7967 6f6e 2c20 6f6e 6520 666f 7220 olygon, one for \n+000070e0: 6561 6368 2065 6e64 2e20 2041 2063 6f64 each end. A cod\n+000070f0: 6520 666f 7220 7365 7665 7261 6c20 7669 e for several vi\n+00007100: 6577 7320 6f66 2061 2063 796c 696e 6472 ews of a cylindr\n+00007110: 6963 616c 0a70 7269 736d 2066 6f6c 6c6f ical.prism follo\n+00007120: 7773 2e0a 2020 6465 6620 6e5f 6379 6c5f ws.. def n_cyl_\n+00007130: 7365 6773 2032 3020 2064 6566 206e 5f76 segs 20 def n_v\n+00007140: 6965 7773 2035 2020 6465 6620 4920 5b31 iews 5 def I [1\n+00007150: 2c30 2c30 5d0a 2020 6465 6620 656e 646f ,0,0]. def endo\n+00007160: 7074 7320 5b66 696c 6c63 6f6c 6f72 3d6c pts [fillcolor=l\n+00007170: 6967 6874 6772 6179 5d0a 2020 7265 7065 ightgray]. repe\n+00007180: 6174 207b 206e 5f76 6965 7773 2c20 726f at { n_views, ro\n+00007190: 7461 7465 2831 3830 2f6e 5f76 6965 7773 tate(180/n_views\n+000071a0: 2c20 5b49 5d29 2074 6865 6e20 7472 616e , [I]) then tran\n+000071b0: 736c 6174 6528 5b49 5d20 2a20 322e 3129 slate([I] * 2.1)\n+000071c0: 207d 200a 2020 2020 7377 6565 705b 656e } . sweep[en\n+000071d0: 646f 7074 735d 7b20 6e5f 6379 6c5f 7365 dopts]{ n_cyl_se\n+000071e0: 6773 3c3e 2c20 726f 7461 7465 2833 3630 gs<>, rotate(360\n+000071f0: 2f6e 5f63 796c 5f73 6567 732c 205b 302c /n_cyl_segs, [0,\n+00007200: 312c 305d 2920 7d20 0a20 2020 2020 206c 1,0]) } . l\n+00007210: 696e 655b 6669 6c6c 636f 6c6f 723d 7768 ine[fillcolor=wh\n+00007220: 6974 655d 2831 2c2d 3129 2831 2c31 290a ite](1,-1)(1,1).\n+00007230: 4974 2070 726f 6475 6365 7320 7468 6973 It produces this\n+00007240: 2064 7261 7769 6e67 2e0a 0a00 085b 696d drawing.....[im\n+00007250: 6167 6520 7372 633d 2265 7831 3130 2e70 age src=\"ex110.p\n+00007260: 6e67 2220 7465 7874 3d22 496d 6167 6520 ng\" text=\"Image \n+00007270: 6578 3131 3020 6f6d 6974 7465 6420 696e ex110 omitted in\n+00007280: 2074 6578 7420 7665 7273 696f 6e20 6f66 text version of\n+00007290: 2074 6869 7320 646f 6375 6d65 6e74 2e22 this document.\"\n+000072a0: 0008 5d0a 0a54 6865 206f 7074 696f 6e73 ..]..The options\n+000072b0: 206f 6620 7468 6520 7377 6570 7420 6c69 of the swept li\n+000072c0: 6e65 2c20 6966 2061 6e79 2c20 6172 6520 ne, if any, are \n+000072d0: 6170 706c 6965 6420 746f 2074 6865 2066 applied to the f\n+000072e0: 6163 6573 2070 726f 6475 6365 640a 6279 aces produced.by\n+000072f0: 2073 7765 6570 696e 6720 7468 6520 6c69 sweeping the li\n+00007300: 6e65 2c20 6275 7420 6e6f 7420 7468 6520 ne, but not the \n+00007310: 656e 6420 706f 6c79 676f 6e73 2e20 204f end polygons. O\n+00007320: 7468 6572 7769 7365 2c20 7468 6520 7377 therwise, the sw\n+00007330: 6565 700a 6f70 7469 6f6e 7320 6172 6520 eep.options are \n+00007340: 6170 706c 6965 6420 7468 726f 7567 686f applied througho\n+00007350: 7574 2e20 2054 6865 2064 6566 2069 6e20 ut. The def in \n+00007360: 7468 6973 2065 7861 6d70 6c65 2069 7320 this example is \n+00007370: 616e 20e2 809c 6f70 7469 6f6e e280 9d0a an ...option....\n+00007380: 6465 6669 6e69 7469 6f6e 2e20 2052 6566 definition. Ref\n+00007390: 6572 656e 6365 7320 746f 206f 7074 696f erences to optio\n+000073a0: 6e73 206d 7573 7420 6265 2065 6e63 6c6f ns must be enclo\n+000073b0: 7365 6420 696e 2073 7175 6172 6520 6272 sed in square br\n+000073c0: 6163 6b65 7473 2c0a 652e 672e 2020 205b ackets,.e.g. [\n+000073d0: 666f 6f5d 2e20 2059 6f75 2063 616e 2063 foo]. You can c\n+000073e0: 6f6e 6361 7465 6e61 7465 2073 6576 6572 oncatenate sever\n+000073f0: 616c 2073 6574 7320 6f66 206f 7074 696f al sets of optio\n+00007400: 6e73 2077 6974 6820 6120 7369 6e67 6c65 ns with a single\n+00007410: 0a72 6566 6572 656e 6365 2c20 652e 672e .reference, e.g.\n+00007420: 2020 205b 636f 6c6f 722c 2073 697a 652c [color, size,\n+00007430: 2073 7479 6c65 5d20 2077 6f75 6c64 2063 style] would c\n+00007440: 6175 7365 2074 6865 206f 7074 696f 6e0a ause the option.\n+00007450: 6465 6669 6e69 7469 6f6e 7320 666f 7220 definitions for \n+00007460: e280 9863 6f6c 6f72 e280 992c 20e2 8098 ...color..., ...\n+00007470: 7369 7a65 e280 992c 2061 6e64 20e2 8098 size..., and ...\n+00007480: 7374 796c 65e2 8099 2074 6f20 6170 7065 style... to appe\n+00007490: 6172 2069 6e20 7365 7175 656e 6365 2069 ar in sequence i\n+000074a0: 6e0a 7468 6520 6f75 7470 7574 2063 7265 n.the output cre\n+000074b0: 6174 6564 2062 7920 7468 6520 e280 9873 ated by the ...s\n+000074c0: 6b65 7463 68e2 8099 2063 6f6d 6d61 6e64 ketch... command\n+000074d0: 2063 6f6e 7461 696e 696e 6720 7468 6520 containing the \n+000074e0: 7265 6665 7265 6e63 652e 0a48 6170 7069 reference..Happi\n+000074f0: 6c79 2c20 7468 6520 7379 6e74 6178 206f ly, the syntax o\n+00007500: 6620 e280 9873 6b65 7463 68e2 8099 2069 f ...sketch... i\n+00007510: 7320 7375 6368 2074 6861 7420 6f70 7469 s such that opti\n+00007520: 6f6e 7320 7265 6665 7265 6e63 6573 2063 ons references c\n+00007530: 616e 0a6e 6576 6572 2062 6520 636f 6e66 an.never be conf\n+00007540: 7573 6564 2077 6974 6820 7665 6374 6f72 used with vector\n+00007550: 2072 6566 6572 656e 6365 732e 2020 5768 references. Wh\n+00007560: 696c 6520 6e6f 7420 6170 7061 7265 6e74 ile not apparent\n+00007570: 2069 6e20 7468 6973 0a65 7861 6d70 6c65 in this.example\n+00007580: 2c20 6f70 7469 6f6e 7320 7265 6665 7265 , options refere\n+00007590: 6e63 6573 2061 7265 2075 7365 6675 6c20 nces are useful \n+000075a0: 7768 656e 2064 6566 696e 696e 6720 6d61 when defining ma\n+000075b0: 6e79 206f 626a 6563 7473 2077 6974 6820 ny objects with \n+000075c0: 610a 7369 6d69 6c61 7220 6170 7065 6172 a.similar appear\n+000075d0: 616e 6365 2e0a 0a1f 0a46 696c 653a 2073 ance.....File: s\n+000075e0: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+000075f0: 653a 2041 6666 696e 6520 6172 6974 686d e: Affine arithm\n+00007600: 6574 6963 2c20 204e 6578 743a 204d 6f72 etic, Next: Mor\n+00007610: 6520 746f 206c 6561 726e 2c20 2050 7265 e to learn, Pre\n+00007620: 763a 2050 6f6c 796c 696e 6520 7377 6565 v: Polyline swee\n+00007630: 7073 2077 6974 6820 636c 6f73 7572 652c ps with closure,\n+00007640: 2020 5570 3a20 5377 6570 7420 6f62 6a65 Up: Swept obje\n+00007650: 6374 730a 0a32 2e37 2e36 2041 6666 696e cts..2.7.6 Affin\n+00007660: 6520 6172 6974 686d 6574 6963 0a2d 2d2d e arithmetic.---\n 00007670: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-00007680: 2d2d 2d2d 2d2d 0a0a 5468 6520 6172 6974 ------..The arit\n-00007690: 686d 6574 6963 205b 495d 202a 2032 2e31 hmetic [I] * 2.1\n-000076a0: 2061 626f 7665 2068 696e 7473 2061 7420 above hints at \n-000076b0: 6120 6c61 7267 6572 2074 7275 7468 2e20 a larger truth. \n-000076c0: 20e2 8098 536b 6574 6368 e280 990a 6f70 ...Sketch....op\n-000076d0: 6572 6174 6f72 7320 776f 726b 206f 6e20 erators work on \n-000076e0: 7363 616c 6172 732c 2076 6563 746f 7273 scalars, vectors\n-000076f0: 2c20 706f 696e 7473 2c20 616e 6420 7472 , points, and tr\n-00007700: 616e 7366 6f72 6d73 2061 6363 6f72 6469 ansforms accordi\n-00007710: 6e67 2074 6f0a 7468 6520 6765 6e65 7261 ng to.the genera\n-00007720: 6c20 7275 6c65 7320 6f66 20e2 809c 6166 l rules of ...af\n-00007730: 6669 6e65 2061 6c67 6562 7261 e280 9d2e fine algebra....\n-00007740: 2020 5468 6973 2063 616e 2062 6520 6865 This can be he\n-00007750: 6c70 6675 6c20 666f 7220 7365 7474 696e lpful for settin\n-00007760: 670a 7570 2064 6961 6772 616d 7320 7769 g.up diagrams wi\n-00007770: 7468 2063 6f6d 7075 7465 6420 6765 6f6d th computed geom\n-00007780: 6574 7279 2e20 2046 6f72 2065 7861 6d70 etry. For examp\n-00007790: 6c65 2c20 6966 2079 6f75 2068 6176 6520 le, if you have \n-000077a0: 7472 6961 6e67 6c65 0a76 6572 7469 6365 triangle.vertice\n-000077b0: 7320 2870 3129 2074 6872 6f75 6768 2028 s (p1) through (\n-000077c0: 7033 2920 616e 6420 6e65 6564 2074 6f20 p3) and need to \n-000077d0: 6472 6177 2061 2075 6e69 7420 6e6f 726d draw a unit norm\n-000077e0: 616c 2076 6563 746f 720a 706f 696e 7469 al vector.pointi\n-000077f0: 6e67 206f 7574 206f 6620 7468 6520 6365 ng out of the ce\n-00007800: 6e74 6572 206f 6620 7468 6520 7472 6961 nter of the tria\n-00007810: 6e67 6c65 2c20 7468 6973 2063 6f64 6520 ngle, this code \n-00007820: 646f 6573 2074 6865 2074 7269 636b 2e0a does the trick..\n-00007830: 2020 6465 6620 7031 2028 312c 302c 3029 def p1 (1,0,0)\n-00007840: 2020 6465 6620 7032 2028 302c 302e 352c def p2 (0,0.5,\n-00007850: 3029 2020 6465 6620 7033 2028 2d30 2e35 0) def p3 (-0.5\n-00007860: 2c2d 312c 3229 0a20 2064 6566 204f 2028 ,-1,2). def O (\n-00007870: 302c 302c 3029 0a20 2064 6566 204e 2075 0,0,0). def N u\n-00007880: 6e69 7428 2028 2870 3329 202d 2028 7032 nit( ((p3) - (p2\n-00007890: 2929 202a 2028 2870 3129 202d 2028 7032 )) * ((p1) - (p2\n-000078a0: 2929 2029 0a20 2064 6566 206e 3120 2828 )) ). def n1 ((\n-000078b0: 7031 292d 284f 2920 2b20 2870 3229 2d28 p1)-(O) + (p2)-(\n-000078c0: 4f29 202b 2028 7033 292d 284f 2929 202f O) + (p3)-(O)) /\n-000078d0: 2033 202b 2028 4f29 0a20 2064 6566 206e 3 + (O). def n\n-000078e0: 3220 286e 3129 2b5b 4e5d 0a20 2070 6f6c 2 (n1)+[N]. pol\n-000078f0: 7967 6f6e 2870 3129 2870 3229 2870 3329 ygon(p1)(p2)(p3)\n-00007900: 0a20 206c 696e 655b 6172 726f 7773 3d2a . line[arrows=*\n-00007910: 2d3e 5d28 6e31 2928 6e32 290a 5468 6520 ->](n1)(n2).The \n-00007920: 6669 7273 7420 6c69 6e65 2063 6f6d 7075 first line compu\n-00007930: 7465 7320 7468 6520 6372 6f73 7320 7072 tes the cross pr\n-00007940: 6f64 7563 7420 6f66 2074 776f 2065 6467 oduct of two edg\n-00007950: 6520 7665 6374 6f72 7320 6f66 2074 6865 e vectors of the\n-00007960: 0a74 7269 616e 676c 6520 616e 6420 7363 .triangle and sc\n-00007970: 616c 6573 2069 7420 746f 2075 6e69 7420 ales it to unit \n-00007980: 6c65 6e67 7468 2e20 2054 6865 2073 6563 length. The sec\n-00007990: 6f6e 6420 636f 6d70 7574 6573 2074 6865 ond computes the\n-000079a0: 2061 7665 7261 6765 0a6f 6620 7468 6520 average.of the \n-000079b0: 7665 7274 6963 6573 2e20 204e 6f74 6520 vertices. Note \n-000079c0: 7468 6174 2073 7562 7472 6163 7469 6f6e that subtraction\n-000079d0: 2061 6e64 2061 6464 6974 696f 6e20 6f66 and addition of\n-000079e0: 2074 6865 206f 7269 6769 6e0a 6566 6665 the origin.effe\n-000079f0: 6374 6976 656c 7920 636f 6e76 6572 7420 ctively convert \n-00007a00: 7665 6374 6f72 7320 746f 2070 6f69 6e74 vectors to point\n-00007a10: 7320 616e 6420 5f76 6963 6520 7665 7273 s and _vice vers\n-00007a20: 615f 2e20 2054 6865 206c 696e 650a 636f a_. The line.co\n-00007a30: 6d6d 616e 6420 6472 6177 7320 7468 6520 mmand draws the \n-00007a40: 6e6f 726d 616c 2061 7420 7468 6520 636f normal at the co\n-00007a50: 7272 6563 7420 7370 6f74 2e0a 0a00 085b rrect spot.....[\n-00007a60: 696d 6167 6520 7372 633d 2265 7831 3030 image src=\"ex100\n-00007a70: 2e70 6e67 2220 7465 7874 3d22 496d 6167 .png\" text=\"Imag\n-00007a80: 6520 6578 3130 3020 6f6d 6974 7465 6420 e ex100 omitted \n-00007a90: 696e 2074 6578 7420 7665 7273 696f 6e20 in text version \n-00007aa0: 6f66 2074 6869 7320 646f 6375 6d65 6e74 of this document\n-00007ab0: 2e22 0008 5d0a 0a20 2020 5477 6f20 6361 .\"..].. Two ca\n-00007ac0: 7665 6174 7320 7265 6761 7264 696e 6720 veats regarding \n-00007ad0: 7468 6973 2065 7861 6d70 6c65 2072 656d this example rem\n-00007ae0: 6169 6e2e 2020 4669 7273 742c 2074 6865 ain. First, the\n-00007af0: 206f 6e6c 7920 7761 7920 746f 0a75 7365 only way to.use\n-00007b00: 20e2 8098 5053 5472 6963 6b73 e280 992d ...PSTricks...-\n-00007b10: 7374 796c 6520 6172 726f 7773 2069 7320 style arrows is \n-00007b20: 7769 7468 2061 7272 6f77 733d 2e20 2054 with arrows=. T\n-00007b30: 6865 2061 6c74 6572 6e61 7469 7665 2073 he alternative s\n-00007b40: 796e 7461 7820 666f 720a e280 9850 5354 yntax for....PST\n-00007b50: 7269 636b 73e2 8099 2061 7272 6f77 7320 ricks... arrows \n-00007b60: 6973 206e 6f74 2061 6c6c 6f77 6564 2069 is not allowed i\n-00007b70: 6e20 736b 6574 6368 2e20 2053 6563 6f6e n sketch. Secon\n-00007b80: 642c 2079 6f75 206d 6967 6874 206c 696b d, you might lik\n-00007b90: 6520 746f 0a65 6c69 6d69 6e61 7465 2074 e to.eliminate t\n-00007ba0: 6865 2074 6869 7264 2064 6566 2061 6e64 he third def and\n-00007bb0: 2077 7269 7465 2069 6e73 7465 6164 2074 write instead t\n-00007bc0: 6865 2066 6f6c 6c6f 7769 6e67 2e0a 2020 he following.. \n-00007bd0: 6c69 6e65 5b61 7272 6f77 733d 2a2d 3e5d line[arrows=*->]\n-00007be0: 286e 3129 2028 6e31 292b 5b4e 5d0a 5468 (n1) (n1)+[N].Th\n-00007bf0: 6973 2069 7320 6e6f 7420 616c 6c6f 7765 is is not allowe\n-00007c00: 642e 2020 5468 6520 706f 696e 7420 6c69 d. The point li\n-00007c10: 7374 7320 696e 2064 7261 7761 626c 6573 sts in drawables\n-00007c20: 206d 6179 2063 6f6e 7369 7374 206f 6e6c may consist onl\n-00007c30: 7920 6f66 0a65 7870 6c69 6369 7420 706f y of.explicit po\n-00007c40: 696e 7473 206f 7220 706f 696e 7420 7265 ints or point re\n-00007c50: 6665 7265 6e63 6573 2e20 2059 6f75 206d ferences. You m\n-00007c60: 6179 2c20 686f 7765 7665 722c 2075 7365 ay, however, use\n-00007c70: 2061 7269 7468 6d65 7469 630a 746f 2063 arithmetic.to c\n-00007c80: 616c 6375 6c61 7465 2070 6f69 6e74 2063 alculate point c\n-00007c90: 6f6d 706f 6e65 6e74 732e 2020 5468 6520 omponents. The \n-00007ca0: 666f 6c6c 6f77 696e 6720 776f 726b 732c following works,\n-00007cb0: 2074 686f 7567 6820 6974 2773 2061 0a6c though it's a.l\n-00007cc0: 6974 746c 6520 6375 6d62 6572 736f 6d65 ittle cumbersome\n-00007cd0: 2e0a 2020 6c69 6e65 5b61 7272 6f77 733d .. line[arrows=\n-00007ce0: 2a2d 3e5d 286e 3129 2828 6e31 2927 782b *->](n1)((n1)'x+\n-00007cf0: 284e 2927 782c 2028 6e31 2927 792b 284e (N)'x, (n1)'y+(N\n-00007d00: 2927 792c 2028 6e31 2927 7a2b 284e 2927 )'y, (n1)'z+(N)'\n-00007d10: 7a29 0a4f 6276 696f 7573 6c79 2c20 7468 z).Obviously, th\n-00007d20: 6520 e280 9c74 6963 6b20 6f70 6572 6174 e ...tick operat\n-00007d30: 6f72 e280 9d20 e280 9827 78e2 8099 2065 or... ...'x... e\n-00007d40: 7874 7261 6374 7320 636f 6d70 6f6e 656e xtracts componen\n-00007d50: 7473 206f 6620 706f 696e 7473 2061 6e64 ts of points and\n-00007d60: 0a76 6563 746f 7273 2e0a 0a1f 0a46 696c .vectors.....Fil\n-00007d70: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n-00007d80: 204e 6f64 653a 204d 6f72 6520 746f 206c Node: More to l\n-00007d90: 6561 726e 2c20 2050 7265 763a 2041 6666 earn, Prev: Aff\n-00007da0: 696e 6520 6172 6974 686d 6574 6963 2c20 ine arithmetic, \n-00007db0: 2055 703a 2053 7765 7074 206f 626a 6563 Up: Swept objec\n-00007dc0: 7473 0a0a 322e 372e 3720 4d6f 7265 2074 ts..2.7.7 More t\n-00007dd0: 6f20 6c65 6172 6e0a 2d2d 2d2d 2d2d 2d2d o learn.--------\n-00007de0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a54 6869 -----------..Thi\n-00007df0: 7320 6973 206e 6f74 2074 6865 2065 6e64 s is not the end\n-00007e00: 206f 6620 7468 6520 7374 6f72 7920 6f6e of the story on\n-00007e10: 2073 7765 6570 7321 2020 5765 2069 6e76 sweeps! We inv\n-00007e20: 6974 6520 7468 6520 7265 6164 6572 2069 ite the reader i\n-00007e30: 6e74 6f0a 7468 6520 6d61 696e 2062 6f64 nto.the main bod\n-00007e40: 7920 6f66 2074 6869 7320 646f 6375 6d65 y of this docume\n-00007e50: 6e74 6174 696f 6e20 2a6e 6f74 6520 5377 ntation *note Sw\n-00007e60: 6565 7073 3a3a 2074 6f20 6c65 6172 6e20 eeps:: to learn \n-00007e70: 6d6f 7265 2e0a 0a00 085b 696d 6167 6520 more.....[image \n-00007e80: 7372 633d 2265 7831 3230 2e70 6e67 2220 src=\"ex120.png\" \n-00007e90: 7465 7874 3d22 496d 6167 6520 6578 3132 text=\"Image ex12\n-00007ea0: 3020 6f6d 6974 7465 6420 696e 2074 6578 0 omitted in tex\n-00007eb0: 7420 7665 7273 696f 6e20 6f66 2074 6869 t version of thi\n-00007ec0: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a s document.\"..].\n-00007ed0: 0a57 686f 206b 6e6f 7773 2077 6865 7265 .Who knows where\n-00007ee0: 2079 6f75 276c 6c20 6669 6e69 7368 3f0a you'll finish?.\n-00007ef0: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n-00007f00: 696e 666f 2c20 204e 6f64 653a 2049 6e70 info, Node: Inp\n-00007f10: 7574 206c 616e 6775 6167 652c 2020 4e65 ut language, Ne\n-00007f20: 7874 3a20 4275 696c 6469 6e67 2061 2064 xt: Building a d\n-00007f30: 7261 7769 6e67 2c20 2050 7265 763a 2049 rawing, Prev: I\n-00007f40: 6e74 726f 6475 6374 696f 6e20 6279 2065 ntroduction by e\n-00007f50: 7861 6d70 6c65 2c20 2055 703a 2054 6f70 xample, Up: Top\n-00007f60: 0a0a 3320 496e 7075 7420 6c61 6e67 7561 ..3 Input langua\n-00007f70: 6765 0a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a ge.*************\n-00007f80: 2a2a 2a0a 0a54 6869 7320 6368 6170 7465 ***..This chapte\n-00007f90: 7220 6465 7363 7269 6265 7320 7468 6520 r describes the \n-00007fa0: e280 9873 6b65 7463 68e2 8099 2069 6e70 ...sketch... inp\n-00007fb0: 7574 206c 616e 6775 6167 6520 696e 2064 ut language in d\n-00007fc0: 6574 6169 6c2e 0a0a 2a20 4d65 6e75 3a0a etail...* Menu:.\n-00007fd0: 0a2a 204c 616e 6775 6167 6520 6261 7369 .* Language basi\n-00007fe0: 6373 3a3a 2020 2020 2020 2020 2020 2020 cs:: \n-00007ff0: 2043 6173 652c 2073 7061 6365 2c20 636f Case, space, co\n-00008000: 6d6d 656e 7473 2c20 696e 636c 7564 6520 mments, include \n-00008010: 6669 6c65 732e 0a2a 2044 7261 7761 626c files..* Drawabl\n-00008020: 6573 3a3a 2020 2020 2020 2020 2020 2020 es:: \n-00008030: 2020 2020 2020 2054 6869 6e67 7320 7468 Things th\n-00008040: 6174 2063 616e 2062 6520 6472 6177 6e2e at can be drawn.\n-00008050: 0a2a 2044 6566 696e 6974 696f 6e73 3a3a .* Definitions::\n-00008060: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00008070: 2047 6976 696e 6720 7468 696e 6773 206e Giving things n\n-00008080: 616d 6573 2e0a 2a20 476c 6f62 616c 2065 ames..* Global e\n-00008090: 6e76 6972 6f6e 6d65 6e74 3a3a 2020 2020 nvironment:: \n-000080a0: 2020 2020 2020 4166 6665 6374 2074 6865 Affect the\n-000080b0: 2065 6e74 6972 6520 6472 6177 696e 672e entire drawing.\n-000080c0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n-000080d0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4c61 .info, Node: La\n-000080e0: 6e67 7561 6765 2062 6173 6963 732c 2020 nguage basics, \n-000080f0: 4e65 7874 3a20 4472 6177 6162 6c65 732c Next: Drawables,\n-00008100: 2020 5072 6576 3a20 496e 7075 7420 6c61 Prev: Input la\n-00008110: 6e67 7561 6765 2c20 2055 703a 2049 6e70 nguage, Up: Inp\n-00008120: 7574 206c 616e 6775 6167 650a 0a33 2e31 ut language..3.1\n-00008130: 2042 6173 6963 730a 3d3d 3d3d 3d3d 3d3d Basics.========\n-00008140: 3d3d 0a0a e280 9853 6b65 7463 68e2 8099 ==.....Sketch...\n-00008150: 2069 6e70 7574 2069 7320 706c 6169 6e20 input is plain \n-00008160: 4153 4349 4920 7465 7874 2c20 7573 7561 ASCII text, usua\n-00008170: 6c6c 7920 7374 6f72 6564 2069 6e20 616e lly stored in an\n-00008180: 2069 6e70 7574 2066 696c 652e 2020 4974 input file. It\n-00008190: 0a64 6573 6372 6962 6573 2061 20e2 809c .describes a ...\n-000081a0: 7363 656e 65e2 809d 2c20 736f 2074 6865 scene..., so the\n-000081b0: 2073 6b65 7463 6820 6c61 6e67 7561 6765 sketch language\n-000081c0: 2069 7320 6120 e280 9c73 6365 6e65 2064 is a ...scene d\n-000081d0: 6573 6372 6970 7469 6f6e 0a6c 616e 6775 escription.langu\n-000081e0: 6167 65e2 809d 2e20 20e2 8098 536b 6574 age.... ...Sket\n-000081f0: 6368 e280 9920 696e 7075 7420 6973 2061 ch... input is a\n-00008200: 6c73 6f20 e280 9c64 6563 6c61 7261 7469 lso ...declarati\n-00008210: 7665 e280 9d2e 2020 4974 206d 6572 656c ve.... It merel\n-00008220: 7920 6465 636c 6172 6573 0a77 6861 7420 y declares.what \n-00008230: 7468 6520 7363 656e 6520 6f75 6768 7420 the scene ought \n-00008240: 746f 206c 6f6f 6b20 6c69 6b65 2077 6865 to look like whe\n-00008250: 6e20 6472 6177 696e 6720 6973 2063 6f6d n drawing is com\n-00008260: 706c 6574 6520 616e 6420 7361 7973 2076 plete and says v\n-00008270: 6572 790a 6c69 7474 6c65 2061 626f 7574 ery.little about\n-00008280: 2068 6f77 20e2 8098 736b 6574 6368 e280 how ...sketch..\n-00008290: 9920 7368 6f75 6c64 2064 6f20 6974 7320 . should do its \n-000082a0: 776f 726b 2e20 20e2 8098 536b 6574 6368 work. ...Sketch\n-000082b0: e280 9920 636f 6d6d 616e 6473 2061 7265 ... commands are\n-000082c0: 206e 6f74 0a65 7865 6375 7465 6420 7365 not.executed se\n-000082d0: 7175 656e 7469 616c 6c79 2061 7320 696e quentially as in\n-000082e0: 2074 6865 2075 7375 616c 2070 726f 6772 the usual progr\n-000082f0: 616d 6d69 6e67 206c 616e 6775 6167 652e amming language.\n-00008300: 2020 5468 6579 206d 6572 656c 790a 636f They merely.co\n-00008310: 6e74 7269 6275 7465 2074 6f20 7468 6174 ntribute to that\n-00008320: 2064 6563 6c61 7261 7469 6f6e 2e0a 0a20 declaration... \n-00008330: 2020 4120 6665 7720 7379 6e74 6163 7469 A few syntacti\n-00008340: 6320 6465 7461 696c 7320 6172 6520 696d c details are im\n-00008350: 706f 7274 616e 742e 2020 4361 7365 2069 portant. Case i\n-00008360: 7320 7369 676e 6966 6963 616e 7420 696e s significant in\n-00008370: 2074 6865 0ae2 8098 736b 6574 6368 e280 the....sketch..\n-00008380: 9920 6c61 6e67 7561 6765 2e20 2057 6974 . language. Wit\n-00008390: 6820 6120 6665 7720 6578 6365 7074 696f h a few exceptio\n-000083a0: 6e73 2c20 7768 6974 6520 7370 6163 6520 ns, white space \n-000083b0: 6973 206e 6f74 2e20 2054 6869 730a 696e is not. This.in\n-000083c0: 636c 7564 6573 206c 696e 6520 6272 6561 cludes line brea\n-000083d0: 6b73 2e20 2043 6f6d 6d65 6e74 7320 6265 ks. Comments be\n-000083e0: 6769 6e20 7769 7468 20e2 8098 25e2 8099 gin with ...%...\n-000083f0: 206f 7220 e280 9823 e280 9920 616e 6420 or ...#... and \n-00008400: 6578 7465 6e64 2074 6f20 7468 650a 656e extend to the.en\n-00008410: 6420 6f66 2074 6865 206c 696e 652e 2020 d of the line. \n-00008420: 596f 7520 6361 6e20 6469 7361 626c 6520 You can disable \n-00008430: 6120 6368 756e 6b20 6f66 2073 796e 7461 a chunk of synta\n-00008440: 6374 6963 616c 6c79 2063 6f72 7265 6374 ctically correct\n-00008450: 0ae2 8098 736b 6574 6368 e280 9920 636f ....sketch... co\n-00008460: 6465 2062 7920 656e 636c 6f73 696e 6720 de by enclosing \n-00008470: 6974 2069 6e20 6120 e280 9864 6566 e280 it in a ...def..\n-00008480: 992e 2020 5468 6572 6520 6973 2061 2073 .. There is a s\n-00008490: 696d 706c 6520 2269 6e63 6c75 6465 0a66 imple \"include.f\n-000084a0: 696c 6522 206d 6563 6861 6e69 736d 2e20 ile\" mechanism. \n-000084b0: 2054 6865 2063 6f6d 6d61 6e64 0a20 2069 The command. i\n-000084c0: 6e70 7574 7b6f 7468 6572 6669 6c65 2e73 nput{otherfile.s\n-000084d0: 6b7d 0a63 6175 7365 7320 7468 6520 636f k}.causes the co\n-000084e0: 6e74 656e 7473 206f 6620 e280 986f 7468 ntents of ...oth\n-000084f0: 6572 6669 6c65 2e73 6be2 8099 2074 6f20 erfile.sk... to \n-00008500: 6265 2069 6e73 6572 7465 6420 6173 2074 be inserted as t\n-00008510: 686f 7567 6820 7468 6579 2077 6572 650a hough they were.\n-00008520: 7061 7274 206f 6620 7468 6520 6375 7272 part of the curr\n-00008530: 656e 7420 6669 6c65 2e0a 0a2a 204d 656e ent file...* Men\n-00008540: 753a 0a0a 2a20 4964 656e 7469 6669 6572 u:..* Identifier\n-00008550: 733a 3a20 2020 2020 2020 2020 2020 2020 s:: \n-00008560: 2020 2020 4e61 6d65 7320 666f 7220 7468 Names for th\n-00008570: 696e 6773 2e0a 2a20 4b65 7920 616e 6420 ings..* Key and \n-00008580: 7265 7365 7276 6564 2077 6f72 6473 3a3a reserved words::\n-00008590: 2020 2020 2020 4e61 6d65 7320 796f 7520 Names you \n-000085a0: 7368 6f75 6c64 6e27 7420 7573 652e 0a2a shouldn't use..*\n-000085b0: 204c 6974 6572 616c 733a 3a20 2020 2020 Literals:: \n-000085c0: 2020 2020 2020 2020 2020 2020 2020 2043 C\n-000085d0: 6f6e 7374 616e 7473 2061 6e64 2063 6f6e onstants and con\n-000085e0: 7374 7275 6374 6f72 732e 0a2a 2041 7269 structors..* Ari\n-000085f0: 7468 6d65 7469 633a 3a20 2020 2020 2020 thmetic:: \n-00008600: 2020 2020 2020 2020 2020 2052 756c 6573 Rules\n-00008610: 2066 6f72 2065 7870 7265 7373 696f 6e73 for expressions\n-00008620: 2e0a 2a20 4f70 7469 6f6e 733a 3a20 2020 ..* Options:: \n+00007680: 2d2d 2d2d 0a0a 5468 6520 6172 6974 686d ----..The arithm\n+00007690: 6574 6963 205b 495d 202a 2032 2e31 2061 etic [I] * 2.1 a\n+000076a0: 626f 7665 2068 696e 7473 2061 7420 6120 bove hints at a \n+000076b0: 6c61 7267 6572 2074 7275 7468 2e20 20e2 larger truth. .\n+000076c0: 8098 536b 6574 6368 e280 990a 6f70 6572 ..Sketch....oper\n+000076d0: 6174 6f72 7320 776f 726b 206f 6e20 7363 ators work on sc\n+000076e0: 616c 6172 732c 2076 6563 746f 7273 2c20 alars, vectors, \n+000076f0: 706f 696e 7473 2c20 616e 6420 7472 616e points, and tran\n+00007700: 7366 6f72 6d73 2061 6363 6f72 6469 6e67 sforms according\n+00007710: 2074 6f0a 7468 6520 6765 6e65 7261 6c20 to.the general \n+00007720: 7275 6c65 7320 6f66 20e2 809c 6166 6669 rules of ...affi\n+00007730: 6e65 2061 6c67 6562 7261 e280 9d2e 2020 ne algebra.... \n+00007740: 5468 6973 2063 616e 2062 6520 6865 6c70 This can be help\n+00007750: 6675 6c20 666f 7220 7365 7474 696e 670a ful for setting.\n+00007760: 7570 2064 6961 6772 616d 7320 7769 7468 up diagrams with\n+00007770: 2063 6f6d 7075 7465 6420 6765 6f6d 6574 computed geomet\n+00007780: 7279 2e20 2046 6f72 2065 7861 6d70 6c65 ry. For example\n+00007790: 2c20 6966 2079 6f75 2068 6176 6520 7472 , if you have tr\n+000077a0: 6961 6e67 6c65 0a76 6572 7469 6365 7320 iangle.vertices \n+000077b0: 2870 3129 2074 6872 6f75 6768 2028 7033 (p1) through (p3\n+000077c0: 2920 616e 6420 6e65 6564 2074 6f20 6472 ) and need to dr\n+000077d0: 6177 2061 2075 6e69 7420 6e6f 726d 616c aw a unit normal\n+000077e0: 2076 6563 746f 720a 706f 696e 7469 6e67 vector.pointing\n+000077f0: 206f 7574 206f 6620 7468 6520 6365 6e74 out of the cent\n+00007800: 6572 206f 6620 7468 6520 7472 6961 6e67 er of the triang\n+00007810: 6c65 2c20 7468 6973 2063 6f64 6520 646f le, this code do\n+00007820: 6573 2074 6865 2074 7269 636b 2e0a 2020 es the trick.. \n+00007830: 6465 6620 7031 2028 312c 302c 3029 2020 def p1 (1,0,0) \n+00007840: 6465 6620 7032 2028 302c 302e 352c 3029 def p2 (0,0.5,0)\n+00007850: 2020 6465 6620 7033 2028 2d30 2e35 2c2d def p3 (-0.5,-\n+00007860: 312c 3229 0a20 2064 6566 204f 2028 302c 1,2). def O (0,\n+00007870: 302c 3029 0a20 2064 6566 204e 2075 6e69 0,0). def N uni\n+00007880: 7428 2028 2870 3329 202d 2028 7032 2929 t( ((p3) - (p2))\n+00007890: 202a 2028 2870 3129 202d 2028 7032 2929 * ((p1) - (p2))\n+000078a0: 2029 0a20 2064 6566 206e 3120 2828 7031 ). def n1 ((p1\n+000078b0: 292d 284f 2920 2b20 2870 3229 2d28 4f29 )-(O) + (p2)-(O)\n+000078c0: 202b 2028 7033 292d 284f 2929 202f 2033 + (p3)-(O)) / 3\n+000078d0: 202b 2028 4f29 0a20 2064 6566 206e 3220 + (O). def n2 \n+000078e0: 286e 3129 2b5b 4e5d 0a20 2070 6f6c 7967 (n1)+[N]. polyg\n+000078f0: 6f6e 2870 3129 2870 3229 2870 3329 0a20 on(p1)(p2)(p3). \n+00007900: 206c 696e 655b 6172 726f 7773 3d2a 2d3e line[arrows=*->\n+00007910: 5d28 6e31 2928 6e32 290a 5468 6520 6669 ](n1)(n2).The fi\n+00007920: 7273 7420 6c69 6e65 2063 6f6d 7075 7465 rst line compute\n+00007930: 7320 7468 6520 6372 6f73 7320 7072 6f64 s the cross prod\n+00007940: 7563 7420 6f66 2074 776f 2065 6467 6520 uct of two edge \n+00007950: 7665 6374 6f72 7320 6f66 2074 6865 0a74 vectors of the.t\n+00007960: 7269 616e 676c 6520 616e 6420 7363 616c riangle and scal\n+00007970: 6573 2069 7420 746f 2075 6e69 7420 6c65 es it to unit le\n+00007980: 6e67 7468 2e20 2054 6865 2073 6563 6f6e ngth. The secon\n+00007990: 6420 636f 6d70 7574 6573 2074 6865 2061 d computes the a\n+000079a0: 7665 7261 6765 0a6f 6620 7468 6520 7665 verage.of the ve\n+000079b0: 7274 6963 6573 2e20 204e 6f74 6520 7468 rtices. Note th\n+000079c0: 6174 2073 7562 7472 6163 7469 6f6e 2061 at subtraction a\n+000079d0: 6e64 2061 6464 6974 696f 6e20 6f66 2074 nd addition of t\n+000079e0: 6865 206f 7269 6769 6e0a 6566 6665 6374 he origin.effect\n+000079f0: 6976 656c 7920 636f 6e76 6572 7420 7665 ively convert ve\n+00007a00: 6374 6f72 7320 746f 2070 6f69 6e74 7320 ctors to points \n+00007a10: 616e 6420 5f76 6963 6520 7665 7273 615f and _vice versa_\n+00007a20: 2e20 2054 6865 206c 696e 650a 636f 6d6d . The line.comm\n+00007a30: 616e 6420 6472 6177 7320 7468 6520 6e6f and draws the no\n+00007a40: 726d 616c 2061 7420 7468 6520 636f 7272 rmal at the corr\n+00007a50: 6563 7420 7370 6f74 2e0a 0a00 085b 696d ect spot.....[im\n+00007a60: 6167 6520 7372 633d 2265 7831 3030 2e70 age src=\"ex100.p\n+00007a70: 6e67 2220 7465 7874 3d22 496d 6167 6520 ng\" text=\"Image \n+00007a80: 6578 3130 3020 6f6d 6974 7465 6420 696e ex100 omitted in\n+00007a90: 2074 6578 7420 7665 7273 696f 6e20 6f66 text version of\n+00007aa0: 2074 6869 7320 646f 6375 6d65 6e74 2e22 this document.\"\n+00007ab0: 0008 5d0a 0a20 2020 5477 6f20 6361 7665 ..].. Two cave\n+00007ac0: 6174 7320 7265 6761 7264 696e 6720 7468 ats regarding th\n+00007ad0: 6973 2065 7861 6d70 6c65 2072 656d 6169 is example remai\n+00007ae0: 6e2e 2020 4669 7273 742c 2074 6865 206f n. First, the o\n+00007af0: 6e6c 7920 7761 7920 746f 0a75 7365 20e2 nly way to.use .\n+00007b00: 8098 5053 5472 6963 6b73 e280 992d 7374 ..PSTricks...-st\n+00007b10: 796c 6520 6172 726f 7773 2069 7320 7769 yle arrows is wi\n+00007b20: 7468 2061 7272 6f77 733d 2e20 2054 6865 th arrows=. The\n+00007b30: 2061 6c74 6572 6e61 7469 7665 2073 796e alternative syn\n+00007b40: 7461 7820 666f 720a e280 9850 5354 7269 tax for....PSTri\n+00007b50: 636b 73e2 8099 2061 7272 6f77 7320 6973 cks... arrows is\n+00007b60: 206e 6f74 2061 6c6c 6f77 6564 2069 6e20 not allowed in \n+00007b70: 736b 6574 6368 2e20 2053 6563 6f6e 642c sketch. Second,\n+00007b80: 2079 6f75 206d 6967 6874 206c 696b 6520 you might like \n+00007b90: 746f 0a65 6c69 6d69 6e61 7465 2074 6865 to.eliminate the\n+00007ba0: 2074 6869 7264 2064 6566 2061 6e64 2077 third def and w\n+00007bb0: 7269 7465 2069 6e73 7465 6164 2074 6865 rite instead the\n+00007bc0: 2066 6f6c 6c6f 7769 6e67 2e0a 2020 6c69 following.. li\n+00007bd0: 6e65 5b61 7272 6f77 733d 2a2d 3e5d 286e ne[arrows=*->](n\n+00007be0: 3129 2028 6e31 292b 5b4e 5d0a 5468 6973 1) (n1)+[N].This\n+00007bf0: 2069 7320 6e6f 7420 616c 6c6f 7765 642e is not allowed.\n+00007c00: 2020 5468 6520 706f 696e 7420 6c69 7374 The point list\n+00007c10: 7320 696e 2064 7261 7761 626c 6573 206d s in drawables m\n+00007c20: 6179 2063 6f6e 7369 7374 206f 6e6c 7920 ay consist only \n+00007c30: 6f66 0a65 7870 6c69 6369 7420 706f 696e of.explicit poin\n+00007c40: 7473 206f 7220 706f 696e 7420 7265 6665 ts or point refe\n+00007c50: 7265 6e63 6573 2e20 2059 6f75 206d 6179 rences. 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The fo\n+00007ca0: 6c6c 6f77 696e 6720 776f 726b 732c 2074 llowing works, t\n+00007cb0: 686f 7567 6820 6974 2773 2061 0a6c 6974 hough it's a.lit\n+00007cc0: 746c 6520 6375 6d62 6572 736f 6d65 2e0a tle cumbersome..\n+00007cd0: 2020 6c69 6e65 5b61 7272 6f77 733d 2a2d line[arrows=*-\n+00007ce0: 3e5d 286e 3129 2828 6e31 2927 782b 284e >](n1)((n1)'x+(N\n+00007cf0: 2927 782c 2028 6e31 2927 792b 284e 2927 )'x, (n1)'y+(N)'\n+00007d00: 792c 2028 6e31 2927 7a2b 284e 2927 7a29 y, (n1)'z+(N)'z)\n+00007d10: 0a4f 6276 696f 7573 6c79 2c20 7468 6520 .Obviously, the \n+00007d20: e280 9c74 6963 6b20 6f70 6572 6174 6f72 ...tick operator\n+00007d30: e280 9d20 e280 9827 78e2 8099 2065 7874 ... ...'x... ext\n+00007d40: 7261 6374 7320 636f 6d70 6f6e 656e 7473 racts components\n+00007d50: 206f 6620 706f 696e 7473 2061 6e64 0a76 of points and.v\n+00007d60: 6563 746f 7273 2e0a 0a1f 0a46 696c 653a ectors.....File:\n+00007d70: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n+00007d80: 6f64 653a 204d 6f72 6520 746f 206c 6561 ode: More to lea\n+00007d90: 726e 2c20 2050 7265 763a 2041 6666 696e rn, Prev: Affin\n+00007da0: 6520 6172 6974 686d 6574 6963 2c20 2055 e arithmetic, U\n+00007db0: 703a 2053 7765 7074 206f 626a 6563 7473 p: Swept objects\n+00007dc0: 0a0a 322e 372e 3720 4d6f 7265 2074 6f20 ..2.7.7 More to \n+00007dd0: 6c65 6172 6e0a 2d2d 2d2d 2d2d 2d2d 2d2d learn.----------\n+00007de0: 2d2d 2d2d 2d2d 2d2d 2d0a 0a54 6869 7320 ---------..This \n+00007df0: 6973 206e 6f74 2074 6865 2065 6e64 206f is not the end o\n+00007e00: 6620 7468 6520 7374 6f72 7920 6f6e 2073 f the story on s\n+00007e10: 7765 6570 7321 2020 5765 2069 6e76 6974 weeps! We invit\n+00007e20: 6520 7468 6520 7265 6164 6572 2069 6e74 e the reader int\n+00007e30: 6f0a 7468 6520 6d61 696e 2062 6f64 7920 o.the main body \n+00007e40: 6f66 2074 6869 7320 646f 6375 6d65 6e74 of this document\n+00007e50: 6174 696f 6e20 2a6e 6f74 6520 5377 6565 ation *note Swee\n+00007e60: 7073 3a3a 2074 6f20 6c65 6172 6e20 6d6f ps:: to learn mo\n+00007e70: 7265 2e0a 0a00 085b 696d 6167 6520 7372 re.....[image sr\n+00007e80: 633d 2265 7831 3230 2e70 6e67 2220 7465 c=\"ex120.png\" te\n+00007e90: 7874 3d22 496d 6167 6520 6578 3132 3020 xt=\"Image ex120 \n+00007ea0: 6f6d 6974 7465 6420 696e 2074 6578 7420 omitted in text \n+00007eb0: 7665 7273 696f 6e20 6f66 2074 6869 7320 version of this \n+00007ec0: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a57 document.\"..]..W\n+00007ed0: 686f 206b 6e6f 7773 2077 6865 7265 2079 ho knows where y\n+00007ee0: 6f75 276c 6c20 6669 6e69 7368 3f0a 0a1f ou'll finish?...\n+00007ef0: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+00007f00: 666f 2c20 204e 6f64 653a 2049 6e70 7574 fo, Node: Input\n+00007f10: 206c 616e 6775 6167 652c 2020 4e65 7874 language, Next\n+00007f20: 3a20 4275 696c 6469 6e67 2061 2064 7261 : Building a dra\n+00007f30: 7769 6e67 2c20 2050 7265 763a 2049 6e74 wing, Prev: Int\n+00007f40: 726f 6475 6374 696f 6e20 6279 2065 7861 roduction by exa\n+00007f50: 6d70 6c65 2c20 2055 703a 2054 6f70 0a0a mple, Up: Top..\n+00007f60: 3320 496e 7075 7420 6c61 6e67 7561 6765 3 Input language\n+00007f70: 0a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a .***************\n+00007f80: 2a0a 0a54 6869 7320 6368 6170 7465 7220 *..This chapter \n+00007f90: 6465 7363 7269 6265 7320 7468 6520 e280 describes the ..\n+00007fa0: 9873 6b65 7463 68e2 8099 2069 6e70 7574 .sketch... input\n+00007fb0: 206c 616e 6775 6167 6520 696e 2064 6574 language in det\n+00007fc0: 6169 6c2e 0a0a 2a20 4d65 6e75 3a0a 0a2a ail...* Menu:..*\n+00007fd0: 204c 616e 6775 6167 6520 6261 7369 6373 Language basics\n+00007fe0: 3a3a 2020 2020 2020 2020 2020 2020 2043 :: C\n+00007ff0: 6173 652c 2073 7061 6365 2c20 636f 6d6d ase, space, comm\n+00008000: 656e 7473 2c20 696e 636c 7564 6520 6669 ents, include fi\n+00008010: 6c65 732e 0a2a 2044 7261 7761 626c 6573 les..* Drawables\n+00008020: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n+00008030: 2020 2020 2054 6869 6e67 7320 7468 6174 Things that\n+00008040: 2063 616e 2062 6520 6472 6177 6e2e 0a2a can be drawn..*\n+00008050: 2044 6566 696e 6974 696f 6e73 3a3a 2020 Definitions:: \n+00008060: 2020 2020 2020 2020 2020 2020 2020 2047 G\n+00008070: 6976 696e 6720 7468 696e 6773 206e 616d iving things nam\n+00008080: 6573 2e0a 2a20 476c 6f62 616c 2065 6e76 es..* Global env\n+00008090: 6972 6f6e 6d65 6e74 3a3a 2020 2020 2020 ironment:: \n+000080a0: 2020 2020 4166 6665 6374 2074 6865 2065 Affect the e\n+000080b0: 6e74 6972 6520 6472 6177 696e 672e 0a0a ntire drawing...\n+000080c0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+000080d0: 6e66 6f2c 2020 4e6f 6465 3a20 4c61 6e67 nfo, Node: Lang\n+000080e0: 7561 6765 2062 6173 6963 732c 2020 4e65 uage basics, Ne\n+000080f0: 7874 3a20 4472 6177 6162 6c65 732c 2020 xt: Drawables, \n+00008100: 5072 6576 3a20 496e 7075 7420 6c61 6e67 Prev: Input lang\n+00008110: 7561 6765 2c20 2055 703a 2049 6e70 7574 uage, Up: Input\n+00008120: 206c 616e 6775 6167 650a 0a33 2e31 2042 language..3.1 B\n+00008130: 6173 6963 730a 3d3d 3d3d 3d3d 3d3d 3d3d asics.==========\n+00008140: 0a0a e280 9853 6b65 7463 68e2 8099 2069 .....Sketch... i\n+00008150: 6e70 7574 2069 7320 706c 6169 6e20 4153 nput is plain AS\n+00008160: 4349 4920 7465 7874 2c20 7573 7561 6c6c CII text, usuall\n+00008170: 7920 7374 6f72 6564 2069 6e20 616e 2069 y stored in an i\n+00008180: 6e70 7574 2066 696c 652e 2020 4974 0a64 nput file. It.d\n+00008190: 6573 6372 6962 6573 2061 20e2 809c 7363 escribes a ...sc\n+000081a0: 656e 65e2 809d 2c20 736f 2074 6865 2073 ene..., so the s\n+000081b0: 6b65 7463 6820 6c61 6e67 7561 6765 2069 ketch language i\n+000081c0: 7320 6120 e280 9c73 6365 6e65 2064 6573 s a ...scene des\n+000081d0: 6372 6970 7469 6f6e 0a6c 616e 6775 6167 cription.languag\n+000081e0: 65e2 809d 2e20 20e2 8098 536b 6574 6368 e.... ...Sketch\n+000081f0: e280 9920 696e 7075 7420 6973 2061 6c73 ... input is als\n+00008200: 6f20 e280 9c64 6563 6c61 7261 7469 7665 o ...declarative\n+00008210: e280 9d2e 2020 4974 206d 6572 656c 7920 .... 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Th\n-00008810: 6520 6c61 7374 2063 6861 7261 6374 6572 e last character\n-00008820: 206d 6179 205f 6e6f 745f 2062 6520 616e may _not_ be an\n-00008830: 2075 6e64 6572 7363 6f72 652e 0a4b 6579 underscore..Key\n-00008840: 776f 7264 7320 6361 6e6e 6f74 2062 6520 words cannot be \n-00008850: 7573 6564 2061 7320 6964 656e 7469 6669 used as identifi\n-00008860: 6572 732c 2061 6e64 2072 6573 6572 7665 ers, and reserve\n-00008870: 6420 776f 7264 7320 6f75 6768 7420 746f d words ought to\n-00008880: 2062 650a 6176 6f69 6465 642e 2020 2a4e be.avoided. *N\n-00008890: 6f74 6520 4b65 7920 616e 6420 7265 7365 ote Key and rese\n-000088a0: 7276 6564 2077 6f72 6473 3a3a 2e0a 0a1f rved words::....\n-000088b0: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n-000088c0: 666f 2c20 204e 6f64 653a 204b 6579 2061 fo, Node: Key a\n-000088d0: 6e64 2072 6573 6572 7665 6420 776f 7264 nd reserved word\n-000088e0: 732c 2020 4e65 7874 3a20 4c69 7465 7261 s, Next: Litera\n-000088f0: 6c73 2c20 2050 7265 763a 2049 6465 6e74 ls, Prev: Ident\n-00008900: 6966 6965 7273 2c20 2055 703a 204c 616e ifiers, Up: Lan\n-00008910: 6775 6167 6520 6261 7369 6373 0a0a 332e guage basics..3.\n-00008920: 312e 3220 4b65 7920 616e 6420 7265 7365 1.2 Key and rese\n-00008930: 7276 6564 2077 6f72 6473 0a2d 2d2d 2d2d rved words.-----\n+00008640: 4d6f 6469 6679 696e 6720 6f62 6a65 6374 Modifying object\n+00008650: 2061 7070 6561 7261 6e63 652e 0a0a 1f0a appearance.....\n+00008660: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n+00008670: 6f2c 2020 4e6f 6465 3a20 4964 656e 7469 o, Node: Identi\n+00008680: 6669 6572 732c 2020 4e65 7874 3a20 4b65 fiers, Next: Ke\n+00008690: 7920 616e 6420 7265 7365 7276 6564 2077 y and reserved w\n+000086a0: 6f72 6473 2c20 2050 7265 763a 204c 616e ords, Prev: Lan\n+000086b0: 6775 6167 6520 6261 7369 6373 2c20 2055 guage basics, U\n+000086c0: 703a 204c 616e 6775 6167 6520 6261 7369 p: Language basi\n+000086d0: 6373 0a0a 332e 312e 3120 4964 656e 7469 cs..3.1.1 Identi\n+000086e0: 6669 6572 730a 2d2d 2d2d 2d2d 2d2d 2d2d fiers.----------\n+000086f0: 2d2d 2d2d 2d2d 2d0a 0a49 6465 6e74 6966 -------..Identif\n+00008700: 6965 7273 2069 6e20 e280 9873 6b65 7463 iers in ...sketc\n+00008710: 68e2 8099 2061 7265 2072 6566 6572 656e h... are referen\n+00008720: 6365 7320 746f 2065 6172 6c69 6572 2d64 ces to earlier-d\n+00008730: 6566 696e 6564 206f 7074 696f 6e73 2c0a efined options,.\n+00008740: 7363 616c 6172 732c 2070 6f69 6e74 732c scalars, points,\n+00008750: 2076 6563 746f 7273 2c20 7472 616e 7366 vectors, transf\n+00008760: 6f72 6d73 2c20 6472 6177 6162 6c65 732c orms, drawables,\n+00008770: 2061 6e64 2074 6167 732e 2020 4465 6669 and tags. 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The \n+00008810: 6c61 7374 2063 6861 7261 6374 6572 206d last character m\n+00008820: 6179 205f 6e6f 745f 2062 6520 616e 2075 ay _not_ be an u\n+00008830: 6e64 6572 7363 6f72 652e 0a4b 6579 776f nderscore..Keywo\n+00008840: 7264 7320 6361 6e6e 6f74 2062 6520 7573 rds cannot be us\n+00008850: 6564 2061 7320 6964 656e 7469 6669 6572 ed as identifier\n+00008860: 732c 2061 6e64 2072 6573 6572 7665 6420 s, and reserved \n+00008870: 776f 7264 7320 6f75 6768 7420 746f 2062 words ought to b\n+00008880: 650a 6176 6f69 6465 642e 2020 2a4e 6f74 e.avoided. *Not\n+00008890: 6520 4b65 7920 616e 6420 7265 7365 7276 e Key and reserv\n+000088a0: 6564 2077 6f72 6473 3a3a 2e0a 0a1f 0a46 ed words::.....F\n+000088b0: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+000088c0: 2c20 204e 6f64 653a 204b 6579 2061 6e64 , Node: Key and\n+000088d0: 2072 6573 6572 7665 6420 776f 7264 732c reserved words,\n+000088e0: 2020 4e65 7874 3a20 4c69 7465 7261 6c73 Next: Literals\n+000088f0: 2c20 2050 7265 763a 2049 6465 6e74 6966 , Prev: Identif\n+00008900: 6965 7273 2c20 2055 703a 204c 616e 6775 iers, Up: Langu\n+00008910: 6167 6520 6261 7369 6373 0a0a 332e 312e age basics..3.1.\n+00008920: 3220 4b65 7920 616e 6420 7265 7365 7276 2 Key and reserv\n+00008930: 6564 2077 6f72 6473 0a2d 2d2d 2d2d 2d2d ed words.-------\n 00008940: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-00008950: 2d2d 2d2d 2d2d 2d0a 0a54 6865 206b 6579 -------..The key\n-00008960: 776f 7264 7320 6f66 20e2 8098 736b 6574 words of ...sket\n-00008970: 6368 e280 9920 6172 6520 e280 9870 6963 ch... are ...pic\n-00008980: 7475 7265 626f 78e2 8099 20e2 8098 6375 turebox... ...cu\n-00008990: 7276 65e2 8099 20e2 8098 6465 66e2 8099 rve... ...def...\n-000089a0: 20e2 8098 646f 7473 e280 9920 e280 9866 ...dots... ...f\n-000089b0: 7261 6d65 e280 990a e280 9867 6c6f 6261 rame.......globa\n-000089c0: 6ce2 8099 20e2 8098 696e 7075 74e2 8099 l... ...input...\n-000089d0: 20e2 8098 6c69 6e65 e280 9920 e280 9870 ...line... ...p\n-000089e0: 6f6c 7967 6f6e e280 9920 e280 9870 7574 olygon... ...put\n-000089f0: e280 9920 e280 9872 6570 6561 74e2 8099 ... ...repeat...\n-00008a00: 20e2 8098 7365 74e2 8099 20e2 8098 7377 ...set... ...sw\n-00008a10: 6565 70e2 8099 2061 6e64 0ae2 8098 7468 eep... and....th\n-00008a20: 656e e280 992e 2020 5468 6520 e280 9873 en.... 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In additi\n-00008aa0: 6f6e 2c20 7468 6572 6520 6172 6520 7265 on, there are re\n-00008ab0: 7365 7276 6564 2077 6f72 6473 2074 6861 served words tha\n-00008ac0: 7420 6361 6e20 6375 7272 656e 746c 7920 t can currently \n-00008ad0: 6265 2064 6566 696e 6564 0a62 7920 7468 be defined.by th\n-00008ae0: 6520 7573 6572 2c20 6275 7420 7769 7468 e user, but with\n-00008af0: 2074 6865 2072 6973 6b20 7468 6174 2066 the risk that f\n-00008b00: 7574 7572 6520 7665 7273 696f 6e73 206f uture versions o\n-00008b10: 6620 e280 9873 6b65 7463 68e2 8099 2077 f ...sketch... w\n-00008b20: 696c 6c0a 7265 6a65 6374 2074 686f 7365 ill.reject those\n-00008b30: 2064 6566 696e 6974 696f 6e73 2e20 2054 definitions. 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The ...ske\n+00008a30: 7463 68e2 8099 2070 6172 7365 7220 7769 tch... parser wi\n+00008a40: 6c6c 206e 6f74 6520 6120 7379 6e74 6178 ll note a syntax\n+00008a50: 2065 7272 6f72 2069 6620 616e 7920 6f66 error if any of\n+00008a60: 2074 6865 7365 0a61 7265 2075 7365 6420 these.are used \n+00008a70: 696e 2070 6c61 6365 206f 6620 6120 7072 in place of a pr\n+00008a80: 6f70 6572 2069 6465 6e74 6966 6965 722e oper identifier.\n+00008a90: 0a0a 2020 2049 6e20 6164 6469 7469 6f6e .. In addition\n+00008aa0: 2c20 7468 6572 6520 6172 6520 7265 7365 , there are rese\n+00008ab0: 7276 6564 2077 6f72 6473 2074 6861 7420 rved words that \n+00008ac0: 6361 6e20 6375 7272 656e 746c 7920 6265 can currently be\n+00008ad0: 2064 6566 696e 6564 0a62 7920 7468 6520 defined.by the \n+00008ae0: 7573 6572 2c20 6275 7420 7769 7468 2074 user, but with t\n+00008af0: 6865 2072 6973 6b20 7468 6174 2066 7574 he risk that fut\n+00008b00: 7572 6520 7665 7273 696f 6e73 206f 6620 ure versions of \n+00008b10: e280 9873 6b65 7463 68e2 8099 2077 696c ...sketch... wil\n+00008b20: 6c0a 7265 6a65 6374 2074 686f 7365 2064 l.reject those d\n+00008b30: 6566 696e 6974 696f 6e73 2e20 2054 6865 efinitions. The\n+00008b40: 2072 6573 6572 7665 6420 776f 7264 7320 reserved words \n+00008b50: 6172 6520 e280 9861 636f 73e2 8099 20e2 are ...acos... .\n+00008b60: 8098 6173 696e e280 9920 e280 9861 7461 ..asin... ...ata\n+00008b70: 6e32 e280 990a e280 9863 6f73 e280 9920 n2.......cos... \n+00008b80: e280 9869 6e76 6572 7365 e280 9920 e280 ...inverse... ..\n+00008b90: 9870 6572 7370 6563 7469 7665 e280 9920 .perspective... \n+00008ba0: e280 9870 726f 6a65 6374 e280 9920 e280 ...project... ..\n+00008bb0: 9872 6f74 6174 65e2 8099 20e2 8098 7363 .rotate... ...sc\n+00008bc0: 616c 65e2 8099 20e2 8098 7369 6ee2 8099 ale... ...sin...\n+00008bd0: 20e2 8098 7370 6563 6961 6ce2 8099 0ae2 ...special.....\n+00008be0: 8098 7371 7274 e280 9920 e280 9874 7261 ..sqrt... ...tra\n+00008bf0: 6e73 6c61 7465 e280 9920 e280 9875 6e69 nslate... ...uni\n+00008c00: 74e2 8099 2061 6e64 20e2 8098 7669 6577 t... and ...view\n+00008c10: e280 992e 0a0a 1f0a 4669 6c65 3a20 736b ........File: sk\n+00008c20: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n+00008c30: 3a20 4c69 7465 7261 6c73 2c20 204e 6578 : Literals, Nex\n+00008c40: 743a 2041 7269 7468 6d65 7469 632c 2020 t: Arithmetic, \n+00008c50: 5072 6576 3a20 4b65 7920 616e 6420 7265 Prev: Key and re\n+00008c60: 7365 7276 6564 2077 6f72 6473 2c20 2055 served words, U\n+00008c70: 703a 204c 616e 6775 6167 6520 6261 7369 p: Language basi\n+00008c80: 6373 0a0a 332e 312e 3320 4c69 7465 7261 cs..3.1.3 Litera\n+00008c90: 6c73 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ls.-------------\n+00008ca0: 2d0a 0a4c 6974 6572 616c 7320 696e 20e2 -..Literals in .\n+00008cb0: 8098 736b 6574 6368 e280 9920 696e 636c ..sketch... incl\n+00008cc0: 7564 6520 7363 616c 6172 732c 2070 6f69 ude scalars, poi\n+00008cd0: 6e74 732c 2076 6563 746f 7273 2c20 616e nts, vectors, an\n+00008ce0: 6420 7472 616e 7366 6f72 6d73 2e0a 4c69 d transforms..Li\n+00008cf0: 7465 7261 6c73 2c20 616c 6f6e 6720 7769 terals, along wi\n+00008d00: 7468 2064 6566 696e 6564 206f 626a 6563 th defined objec\n+00008d10: 7420 7265 6665 7265 6e63 6573 2c20 6172 t references, ar\n+00008d20: 6520 7573 6564 2069 6e20 6172 6974 686d e used in arithm\n+00008d30: 6574 6963 0a65 7870 7265 7373 696f 6e73 etic.expressions\n+00008d40: 2e20 202a 4e6f 7465 2041 7269 7468 6d65 . *Note Arithme\n+00008d50: 7469 633a 3a2e 0a0a 2a20 4d65 6e75 3a0a tic::...* Menu:.\n+00008d60: 0a2a 2053 6361 6c61 7220 6c69 7465 7261 .* Scalar litera\n+00008d70: 6c73 3a3a 2020 2020 2020 2020 2020 2020 ls:: \n+00008d80: 204a 7573 7420 7468 6520 6e75 6d62 6572 Just the number\n+00008d90: 732e 0a2a 2050 6f69 6e74 2061 6e64 2076 s..* Point and v\n+00008da0: 6563 746f 7220 6c69 7465 7261 6c73 3a3a ector literals::\n+00008db0: 2020 2033 6420 7175 616e 7469 7469 6573 3d quantities\n+00008dc0: 2e0a 2a20 5472 616e 7366 6f72 6d20 6c69 ..* Transform li\n+00008dd0: 7465 7261 6c73 3a3a 2020 2020 2020 2020 terals:: \n+00008de0: 2020 4d61 7472 6978 2066 6f72 6d2e 0a0a Matrix form...\n+00008df0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+00008e00: 6e66 6f2c 2020 4e6f 6465 3a20 5363 616c nfo, Node: Scal\n+00008e10: 6172 206c 6974 6572 616c 732c 2020 4e65 ar literals, Ne\n+00008e20: 7874 3a20 506f 696e 7420 616e 6420 7665 xt: Point and ve\n+00008e30: 6374 6f72 206c 6974 6572 616c 732c 2020 ctor literals, \n+00008e40: 5072 6576 3a20 4c69 7465 7261 6c73 2c20 Prev: Literals, \n+00008e50: 2055 703a 204c 6974 6572 616c 730a 0a33 Up: Literals..3\n+00008e60: 2e31 2e33 2e31 2053 6361 6c61 7220 6c69 .1.3.1 Scalar li\n+00008e70: 7465 7261 6c73 0a2e 2e2e 2e2e 2e2e 2e2e terals..........\n+00008e80: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a ................\n+00008e90: 5363 616c 6172 206c 6974 6572 616c 7320 Scalar literals \n+00008ea0: 6172 6520 706f 7369 7469 7665 2066 6c6f are positive flo\n+00008eb0: 6174 696e 6720 706f 696e 7420 6e75 6d62 ating point numb\n+00008ec0: 6572 7320 7769 7468 2073 796e 7461 780a ers with syntax.\n+00008ed0: 6163 636f 7264 696e 6720 746f 2043 2063 according to C c\n+00008ee0: 6f6e 7665 6e74 696f 6e73 2e20 2054 6865 onventions. The\n+00008ef0: 2066 6f6c 6c6f 7769 6e67 2061 7265 2073 following are s\n+00008f00: 6f6d 6520 6578 616d 706c 6573 2e0a 2020 ome examples.. \n+00008f10: 2020 2030 2031 3030 3420 2e30 3031 2038 0 1004 .001 8\n+00008f20: 2e33 3134 3320 332e 2031 2e36 3045 2d31 .3143 3. 1.60E-1\n+00008f30: 3920 362e 3032 652b 3233 0a53 6361 6c61 9 6.02e+23.Scala\n+00008f40: 7220 6c69 7465 7261 6c73 206d 6179 206e r literals may n\n+00008f50: 6f74 2063 6f6e 7461 696e 2065 6d62 6564 ot contain embed\n+00008f60: 6465 6420 7370 6163 6573 2e0a 0a1f 0a46 ded spaces.....F\n+00008f70: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+00008f80: 2c20 204e 6f64 653a 2050 6f69 6e74 2061 , Node: Point a\n+00008f90: 6e64 2076 6563 746f 7220 6c69 7465 7261 nd vector litera\n+00008fa0: 6c73 2c20 204e 6578 743a 2054 7261 6e73 ls, Next: Trans\n+00008fb0: 666f 726d 206c 6974 6572 616c 732c 2020 form literals, \n+00008fc0: 5072 6576 3a20 5363 616c 6172 206c 6974 Prev: Scalar lit\n+00008fd0: 6572 616c 732c 2020 5570 3a20 4c69 7465 erals, Up: Lite\n+00008fe0: 7261 6c73 0a0a 332e 312e 332e 3220 506f rals..3.1.3.2 Po\n+00008ff0: 696e 7420 616e 6420 7665 6374 6f72 206c int and vector l\n+00009000: 6974 6572 616c 730a 2e2e 2e2e 2e2e 2e2e iterals.........\n 00009010: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-00009020: 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a50 6f69 .............Poi\n-00009030: 6e74 7320 616e 6420 7665 6374 6f72 206c nts and vector l\n-00009040: 6974 6572 616c 7320 6861 7665 2074 6865 iterals have the\n-00009050: 7365 2066 6f72 6d73 2072 6573 7065 6374 se forms respect\n-00009060: 6976 656c 792e 0a20 2020 2020 2858 2c59 ively.. (X,Y\n-00009070: 2c5a 2920 205b 582c 592c 5a5d 0a45 6163 ,Z) [X,Y,Z].Eac\n-00009080: 6820 6f66 2074 6865 2063 6f6d 706f 6e65 h of the compone\n-00009090: 6e74 7320 6973 2069 7473 656c 6620 6120 nts is itself a \n-000090a0: 7363 616c 6172 2065 7870 7265 7373 696f scalar expressio\n-000090b0: 6e2e 2020 5468 6520 7a2d 636f 6d70 6f6e n. The z-compon\n-000090c0: 656e 7473 0a61 7265 206f 7074 696f 6e61 ents.are optiona\n-000090d0: 6c20 616e 6420 6465 6661 756c 7420 746f l and default to\n-000090e0: 207a 6572 6f2e 0a0a 1f0a 4669 6c65 3a20 zero.....File: \n-000090f0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n-00009100: 6465 3a20 5472 616e 7366 6f72 6d20 6c69 de: Transform li\n-00009110: 7465 7261 6c73 2c20 2050 7265 763a 2050 terals, Prev: P\n-00009120: 6f69 6e74 2061 6e64 2076 6563 746f 7220 oint and vector \n-00009130: 6c69 7465 7261 6c73 2c20 2055 703a 204c literals, Up: L\n-00009140: 6974 6572 616c 730a 0a33 2e31 2e33 2e33 iterals..3.1.3.3\n-00009150: 2054 7261 6e73 666f 726d 206c 6974 6572 Transform liter\n-00009160: 616c 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e als.............\n-00009170: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a ................\n-00009180: 4d6f 7374 2074 7261 6e73 666f 726d 206c Most transform l\n-00009190: 6974 6572 616c 7320 6172 6520 666f 726d iterals are form\n-000091a0: 6564 2062 7920 e280 9c63 6f6e 7374 7275 ed by ...constru\n-000091b0: 6374 6f72 73e2 809d 2e20 2054 6865 7365 ctors.... These\n-000091c0: 2061 7265 0a73 756d 6d61 7269 7a65 6420 are.summarized \n-000091d0: 696e 2074 6865 2066 6f6c 6c6f 7769 6e67 in the following\n-000091e0: 2074 6162 6c65 2e0a 436f 6e73 7472 7563 table..Construc\n-000091f0: 746f 7220 2020 2020 2020 2020 2020 2020 tor \n-00009200: 2020 2020 2020 2020 2020 2020 5061 7261 Para\n-00009210: 6d20 7479 7065 7320 2020 2020 2020 2020 m types \n-00009220: 2020 4465 7363 7269 7074 696f 6e0a 2d2d Description.--\n+00009020: 2e2e 2e2e 2e2e 2e2e 2e0a 0a50 6f69 6e74 ...........Point\n+00009030: 7320 616e 6420 7665 6374 6f72 206c 6974 s and vector lit\n+00009040: 6572 616c 7320 6861 7665 2074 6865 7365 erals have these\n+00009050: 2066 6f72 6d73 2072 6573 7065 6374 6976 forms respectiv\n+00009060: 656c 792e 0a20 2020 2020 2858 2c59 2c5a ely.. (X,Y,Z\n+00009070: 2920 205b 582c 592c 5a5d 0a45 6163 6820 ) [X,Y,Z].Each \n+00009080: 6f66 2074 6865 2063 6f6d 706f 6e65 6e74 of the component\n+00009090: 7320 6973 2069 7473 656c 6620 6120 7363 s is itself a sc\n+000090a0: 616c 6172 2065 7870 7265 7373 696f 6e2e alar expression.\n+000090b0: 2020 5468 6520 7a2d 636f 6d70 6f6e 656e The z-componen\n+000090c0: 7473 0a61 7265 206f 7074 696f 6e61 6c20 ts.are optional \n+000090d0: 616e 6420 6465 6661 756c 7420 746f 207a and default to z\n+000090e0: 6572 6f2e 0a0a 1f0a 4669 6c65 3a20 736b ero.....File: sk\n+000090f0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n+00009100: 3a20 5472 616e 7366 6f72 6d20 6c69 7465 : Transform lite\n+00009110: 7261 6c73 2c20 2050 7265 763a 2050 6f69 rals, Prev: Poi\n+00009120: 6e74 2061 6e64 2076 6563 746f 7220 6c69 nt and vector li\n+00009130: 7465 7261 6c73 2c20 2055 703a 204c 6974 terals, Up: Lit\n+00009140: 6572 616c 730a 0a33 2e31 2e33 2e33 2054 erals..3.1.3.3 T\n+00009150: 7261 6e73 666f 726d 206c 6974 6572 616c ransform literal\n+00009160: 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e s...............\n+00009170: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 4d6f ..............Mo\n+00009180: 7374 2074 7261 6e73 666f 726d 206c 6974 st transform lit\n+00009190: 6572 616c 7320 6172 6520 666f 726d 6564 erals are formed\n+000091a0: 2062 7920 e280 9c63 6f6e 7374 7275 6374 by ...construct\n+000091b0: 6f72 73e2 809d 2e20 2054 6865 7365 2061 ors.... These a\n+000091c0: 7265 0a73 756d 6d61 7269 7a65 6420 696e re.summarized in\n+000091d0: 2074 6865 2066 6f6c 6c6f 7769 6e67 2074 the following t\n+000091e0: 6162 6c65 2e0a 436f 6e73 7472 7563 746f able..Constructo\n+000091f0: 7220 2020 2020 2020 2020 2020 2020 2020 r \n+00009200: 2020 2020 2020 2020 2020 5061 7261 6d20 Param \n+00009210: 7479 7065 7320 2020 2020 2020 2020 2020 types \n+00009220: 4465 7363 7269 7074 696f 6e0a 2d2d 2d2d Description.----\n 00009230: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 00009240: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 00009250: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 00009260: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 00009270: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 00009280: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-00009290: 2d2d 2d2d 2d2d 2d2d 2d0a e280 9872 6f74 ---------....rot\n-000092a0: 6174 6528 412c 502c 5829 e280 9920 2020 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2020 2020 202a 4e6f 7465 2052 *Note R\n+000093b0: 6967 6874 2068 616e 6420 7275 6c65 3a3a ight hand rule::\n+000093c0: 2e20 20e2 8098 50e2 8099 2061 6e64 20e2 . ...P... and .\n+000093d0: 8098 58e2 8099 2061 7265 2062 6f74 680a ..X... are both.\n+000093e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000093f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009400: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009410: 2020 2020 2020 2020 2020 2020 6f70 7469 opti\n-00009420: 6f6e 616c 2061 6e64 2064 6566 6175 6c74 onal and default\n-00009430: 2074 6f20 7468 6520 6f72 6967 696e 2061 to the origin a\n-00009440: 6e64 2074 6865 0a20 2020 2020 2020 2020 nd the. \n+00009410: 2020 2020 2020 2020 2020 6f70 7469 6f6e option\n+00009420: 616c 2061 6e64 2064 6566 6175 6c74 2074 al and default t\n+00009430: 6f20 7468 6520 6f72 6967 696e 2061 6e64 o the origin and\n+00009440: 2074 6865 0a20 2020 2020 2020 2020 2020 the. \n 00009450: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009460: 2020 2020 2020 2020 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equivalent to ..\n-00009e90: 9876 6965 7728 452c 0a20 2020 2020 2020 .view(E,. \n+00009e60: 2020 2020 2020 2020 2054 6869 7320 666f This fo\n+00009e70: 726d 206f 6620 7669 6577 2069 7320 6571 rm of view is eq\n+00009e80: 7569 7661 6c65 6e74 2074 6f20 e280 9876 uivalent to ...v\n+00009e90: 6965 7728 452c 0a20 2020 2020 2020 2020 iew(E,. \n 00009ea0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009eb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009ec0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009ed0: 2020 2028 4c29 2d28 4529 2c20 5529 e280 (L)-(E), U)..\n-00009ee0: 992c 2077 6865 7265 20e2 8098 284c 292d ., where ...(L)-\n-00009ef0: 2845 29e2 8099 2069 7320 6120 6469 7265 (E)... is a dire\n-00009f00: 6374 696f 6e0a 2020 2020 2020 2020 2020 ction. \n+00009ed0: 2028 4c29 2d28 4529 2c20 5529 e280 992c (L)-(E), U)...,\n+00009ee0: 2077 6865 7265 20e2 8098 284c 292d 2845 where ...(L)-(E\n+00009ef0: 29e2 8099 2069 7320 6120 6469 7265 6374 )... is a direct\n+00009f00: 696f 6e0a 2020 2020 2020 2020 2020 2020 ion. \n 00009f10: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009f20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009f30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009f40: 7665 6374 6f72 2e20 20e2 8098 55e2 8099 vector. ...U...\n-00009f50: 2069 7320 6f70 7469 6f6e 616c 2061 6e64 is optional and\n-00009f60: 2064 6566 6175 6c74 7320 746f 0a20 2020 defaults to. \n+00009f30: 2020 2020 2020 2020 2020 2020 2020 7665 ve\n+00009f40: 6374 6f72 2e20 20e2 8098 55e2 8099 2069 ctor. ...U... i\n+00009f50: 7320 6f70 7469 6f6e 616c 2061 6e64 2064 s optional and d\n+00009f60: 6566 6175 6c74 7320 746f 0a20 2020 2020 efaults to. \n 00009f70: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009f80: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009f90: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009fa0: 2020 2020 2020 205b 302c 312c 305d 2e0a [0,1,0]..\n-00009fb0: e280 985b 5b61 5f7b 3131 7d2c 615f 7b31 ...[[a_{11},a_{1\n-00009fc0: 327d 2c61 5f7b 3133 7d2c 615f 7b31 347d 2},a_{13},a_{14}\n-00009fd0: 5de2 8099 2020 2020 3136 2073 6361 6c61 ]... 16 scala\n-00009fe0: 7273 2020 2020 2020 2020 2020 2020 4469 rs Di\n-00009ff0: 7265 6374 2074 7261 6e73 666f 726d 206d rect transform m\n-0000a000: 6174 7269 7820 6465 6669 6e69 7469 6f6e atrix definition\n-0000a010: 2e20 2045 6163 6820 6f66 0ae2 8098 205b . Each of.... [\n-0000a020: 615f 7b32 317d 2c61 5f7b 3232 7d2c 615f a_{21},a_{22},a_\n-0000a030: 7b32 337d 2c61 5f7b 3234 7d5d e280 9920 {23},a_{24}]... \n+00009fa0: 2020 2020 205b 302c 312c 305d 2e0a e280 [0,1,0]....\n+00009fb0: 985b 5b61 5f7b 3131 7d2c 615f 7b31 327d .[[a_{11},a_{12}\n+00009fc0: 2c61 5f7b 3133 7d2c 615f 7b31 347d 5de2 ,a_{13},a_{14}].\n+00009fd0: 8099 2020 2020 3136 2073 6361 6c61 7273 .. 16 scalars\n+00009fe0: 2020 2020 2020 2020 2020 2020 4469 7265 Dire\n+00009ff0: 6374 2074 7261 6e73 666f 726d 206d 6174 ct transform mat\n+0000a000: 7269 7820 6465 6669 6e69 7469 6f6e 2e20 rix definition. \n+0000a010: 2045 6163 6820 6f66 0ae2 8098 205b 615f Each of.... [a_\n+0000a020: 7b32 317d 2c61 5f7b 3232 7d2c 615f 7b32 {21},a_{22},a_{2\n+0000a030: 337d 2c61 5f7b 3234 7d5d e280 9920 2020 3},a_{24}]... \n 0000a040: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000a050: 2020 2020 2020 2020 2074 6865 2061 5f7b the a_{\n-0000a060: 696a 7d20 6973 2061 2073 6361 6c61 7220 ij} is a scalar \n-0000a070: 6578 7072 6573 7369 6f6e 2e20 2053 6565 expression. See\n-0000a080: 2074 6578 740a e280 9820 5b61 5f7b 3331 text.... [a_{31\n-0000a090: 7d2c 615f 7b33 327d 2c61 5f7b 3333 7d2c },a_{32},a_{33},\n-0000a0a0: 615f 7b33 347d 5de2 8099 2020 2020 2020 a_{34}]... \n+0000a050: 2020 2020 2020 2074 6865 2061 5f7b 696a the a_{ij\n+0000a060: 7d20 6973 2061 2073 6361 6c61 7220 6578 } is a scalar ex\n+0000a070: 7072 6573 7369 6f6e 2e20 2053 6565 2074 pression. See t\n+0000a080: 6578 740a e280 9820 5b61 5f7b 3331 7d2c ext.... [a_{31},\n+0000a090: 615f 7b33 327d 2c61 5f7b 3333 7d2c 615f a_{32},a_{33},a_\n+0000a0a0: 7b33 347d 5de2 8099 2020 2020 2020 2020 {34}]... \n 0000a0b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000a0c0: 2020 2020 666f 7220 6465 7461 696c 732e for details.\n-0000a0d0: 0ae2 8098 205b 615f 7b34 317d 2c61 5f7b .... [a_{41},a_{\n-0000a0e0: 3432 7d2c 615f 7b34 337d 2c61 5f7b 3434 42},a_{43},a_{44\n-0000a0f0: 7d5d 5de2 8099 0a54 6865 20e2 8098 7072 }]]....The ...pr\n-0000a100: 6f6a 6563 74e2 8099 2063 6f6e 7374 7275 oject... constru\n-0000a110: 6374 6f72 2069 7320 6e6f 7420 6765 6e65 ctor is not gene\n-0000a120: 7261 6c6c 7920 7573 6566 756c 2062 6563 rally useful bec\n-0000a130: 6175 7365 2069 7420 6465 6665 6174 730a ause it defeats.\n-0000a140: 6869 6464 656e 2073 7572 6661 6365 2072 hidden surface r\n-0000a150: 656d 6f76 616c 2062 7920 636f 6c6c 6170 emoval by collap\n-0000a160: 7369 6e67 2074 6865 2073 6365 6e65 206f sing the scene o\n-0000a170: 6e74 6f20 6120 7369 6e67 6c65 2070 6c61 nto a single pla\n-0000a180: 6e65 2e20 2049 740a 6973 2061 2073 7065 ne. It.is a spe\n-0000a190: 6369 616c 2070 7572 706f 7365 2074 7261 cial purpose tra\n-0000a1a0: 6e73 666f 726d 2066 6f72 2064 7261 7769 nsform for drawi\n-0000a1b0: 6e67 2070 6963 7475 7265 7320 6f66 2073 ng pictures of s\n-0000a1c0: 6365 6e65 7320 7768 6572 650a 7468 7265 cenes where.thre\n-0000a1d0: 652d 6469 6d65 6e73 696f 6e61 6c20 6f62 e-dimensional ob\n-0000a1e0: 6a65 6374 7320 6172 6520 6265 696e 6720 jects are being \n-0000a1f0: 7072 6f6a 6563 7465 6420 6f6e 746f 2070 projected onto p\n-0000a200: 6c61 6e65 732e 2020 5365 652c 2066 6f72 lanes. See, for\n-0000a210: 0a65 7861 6d70 6c65 2c20 2a6e 6f74 6520 .example, *note \n-0000a220: 4f76 6572 7669 6577 3a3a 2e0a 0a20 2020 Overview::... \n-0000a230: 5468 6520 6469 7265 6374 2074 7261 6e73 The direct trans\n-0000a240: 666f 726d 2063 6f6e 7374 7275 6374 6f72 form constructor\n-0000a250: 2061 6c6c 6f77 7320 6469 7265 6374 2065 allows direct e\n-0000a260: 6e74 7279 206f 6620 6120 3478 340a 7472 ntry of a 4x4.tr\n-0000a270: 616e 7366 6f72 6d61 7469 6f6e 206d 6174 ansformation mat\n-0000a280: 7269 782e 2020 4d6f 7374 2033 6420 6772 rix. Most 3d gr\n-0000a290: 6170 6869 6373 2073 7973 7465 6d73 2c20 aphics systems, \n-0000a2a0: 696e 636c 7564 696e 6720 e280 9873 6b65 including ...ske\n-0000a2b0: 7463 68e2 8099 2c0a 7573 6520 342d 6469 tch...,.use 4-di\n-0000a2c0: 6d65 6e73 696f 6e61 6c20 686f 6d6f 6765 mensional homoge\n-0000a2d0: 6e65 6f75 7320 636f 6f72 6469 6e61 7465 neous coordinate\n-0000a2e0: 7320 696e 7465 726e 616c 6c79 2e20 2054 s internally. T\n-0000a2f0: 6865 7365 2061 7265 0a74 7261 6e73 666f hese are.transfo\n-0000a300: 726d 6564 2062 7920 6d75 6c74 6970 6c69 rmed by multipli\n-0000a310: 6361 7469 6f6e 2077 6974 6820 3478 3420 cation with 4x4 \n-0000a320: 6d61 7472 6963 6573 2e20 2054 6865 2062 matrices. The b\n-0000a330: 7569 6c74 2d69 6e0a 636f 6e73 7472 7563 uilt-in.construc\n-0000a340: 746f 7273 2028 e280 9872 6f74 6174 65e2 tors (...rotate.\n-0000a350: 8099 2c20 e280 9873 6361 6c65 e280 992c .., ...scale...,\n-0000a360: 2065 7463 2e29 2020 6172 6520 616c 6c20 etc.) are all \n-0000a370: 7472 616e 736c 6174 6564 2069 6e74 6572 translated inter\n-0000a380: 6e61 6c6c 7920 746f 0a73 7563 6820 3478 nally to.such 4x\n-0000a390: 3420 6d61 7472 6963 6573 2e20 2046 6f72 4 matrices. For\n-0000a3a0: 206d 6f72 6520 696e 666f 726d 6174 696f more informatio\n-0000a3b0: 6e20 6f6e 2068 6f6d 6f67 656e 656f 7573 n on homogeneous\n-0000a3c0: 2063 6f6f 7264 696e 6174 650a 7472 616e coordinate.tran\n-0000a3d0: 7366 6f72 6d61 7469 6f6e 732c 2073 6565 sformations, see\n-0000a3e0: 2061 6e79 2067 6f6f 6420 636f 6d70 7574 any good comput\n-0000a3f0: 6572 2067 7261 7068 6963 7320 7465 7874 er graphics text\n-0000a400: 626f 6f6b 2e20 2054 6865 2064 6972 6563 book. The direc\n-0000a410: 740a 7472 616e 7366 6f72 6d20 6665 6174 t.transform feat\n-0000a420: 7572 6520 6f66 20e2 8098 736b 6574 6368 ure of ...sketch\n-0000a430: e280 9920 616c 6c6f 7773 2079 6f75 2074 ... allows you t\n-0000a440: 6f20 656e 7465 7220 6120 6d61 7472 6978 o enter a matrix\n-0000a450: 206f 6620 796f 7572 206f 776e 0a63 686f of your own.cho\n-0000a460: 6963 652e 2020 5468 6572 6520 6172 6520 ice. There are \n-0000a470: 6e6f 7420 6d61 6e79 2063 6173 6573 2077 not many cases w\n-0000a480: 6865 7265 2074 6869 7320 6973 2075 7365 here this is use\n-0000a490: 6675 6c2c 2062 7574 2069 6620 796f 7520 ful, but if you \n-0000a4a0: 646f 0a6e 6565 6420 6974 2c20 796f 7520 do.need it, you \n-0000a4b0: 6e65 6564 2069 7420 6261 646c 7921 0a0a need it badly!..\n-0000a4c0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n-0000a4d0: 6e66 6f2c 2020 4e6f 6465 3a20 4172 6974 nfo, Node: Arit\n-0000a4e0: 686d 6574 6963 2c20 204e 6578 743a 204f hmetic, Next: O\n-0000a4f0: 7074 696f 6e73 2c20 2050 7265 763a 204c ptions, Prev: L\n-0000a500: 6974 6572 616c 732c 2020 5570 3a20 4c61 iterals, Up: La\n-0000a510: 6e67 7561 6765 2062 6173 6963 730a 0a33 nguage basics..3\n-0000a520: 2e31 2e34 2041 7269 7468 6d65 7469 6320 .1.4 Arithmetic \n-0000a530: 6578 7072 6573 7369 6f6e 730a 2d2d 2d2d expressions.----\n+0000a0c0: 2020 666f 7220 6465 7461 696c 732e 0ae2 for details...\n+0000a0d0: 8098 205b 615f 7b34 317d 2c61 5f7b 3432 .. [a_{41},a_{42\n+0000a0e0: 7d2c 615f 7b34 337d 2c61 5f7b 3434 7d5d },a_{43},a_{44}]\n+0000a0f0: 5de2 8099 0a54 6865 20e2 8098 7072 6f6a ]....The ...proj\n+0000a100: 6563 74e2 8099 2063 6f6e 7374 7275 6374 ect... construct\n+0000a110: 6f72 2069 7320 6e6f 7420 6765 6e65 7261 or is not genera\n+0000a120: 6c6c 7920 7573 6566 756c 2062 6563 6175 lly useful becau\n+0000a130: 7365 2069 7420 6465 6665 6174 730a 6869 se it defeats.hi\n+0000a140: 6464 656e 2073 7572 6661 6365 2072 656d dden surface rem\n+0000a150: 6f76 616c 2062 7920 636f 6c6c 6170 7369 oval by collapsi\n+0000a160: 6e67 2074 6865 2073 6365 6e65 206f 6e74 ng the scene ont\n+0000a170: 6f20 6120 7369 6e67 6c65 2070 6c61 6e65 o a single plane\n+0000a180: 2e20 2049 740a 6973 2061 2073 7065 6369 . It.is a speci\n+0000a190: 616c 2070 7572 706f 7365 2074 7261 6e73 al purpose trans\n+0000a1a0: 666f 726d 2066 6f72 2064 7261 7769 6e67 form for drawing\n+0000a1b0: 2070 6963 7475 7265 7320 6f66 2073 6365 pictures of sce\n+0000a1c0: 6e65 7320 7768 6572 650a 7468 7265 652d nes where.three-\n+0000a1d0: 6469 6d65 6e73 696f 6e61 6c20 6f62 6a65 dimensional obje\n+0000a1e0: 6374 7320 6172 6520 6265 696e 6720 7072 cts are being pr\n+0000a1f0: 6f6a 6563 7465 6420 6f6e 746f 2070 6c61 ojected onto pla\n+0000a200: 6e65 732e 2020 5365 652c 2066 6f72 0a65 nes. See, for.e\n+0000a210: 7861 6d70 6c65 2c20 2a6e 6f74 6520 4f76 xample, *note Ov\n+0000a220: 6572 7669 6577 3a3a 2e0a 0a20 2020 5468 erview::... Th\n+0000a230: 6520 6469 7265 6374 2074 7261 6e73 666f e direct transfo\n+0000a240: 726d 2063 6f6e 7374 7275 6374 6f72 2061 rm constructor a\n+0000a250: 6c6c 6f77 7320 6469 7265 6374 2065 6e74 llows direct ent\n+0000a260: 7279 206f 6620 6120 3478 340a 7472 616e ry of a 4x4.tran\n+0000a270: 7366 6f72 6d61 7469 6f6e 206d 6174 7269 sformation matri\n+0000a280: 782e 2020 4d6f 7374 2033 6420 6772 6170 x. Most 3d grap\n+0000a290: 6869 6373 2073 7973 7465 6d73 2c20 696e hics systems, in\n+0000a2a0: 636c 7564 696e 6720 e280 9873 6b65 7463 cluding ...sketc\n+0000a2b0: 68e2 8099 2c0a 7573 6520 342d 6469 6d65 h...,.use 4-dime\n+0000a2c0: 6e73 696f 6e61 6c20 686f 6d6f 6765 6e65 nsional homogene\n+0000a2d0: 6f75 7320 636f 6f72 6469 6e61 7465 7320 ous coordinates \n+0000a2e0: 696e 7465 726e 616c 6c79 2e20 2054 6865 internally. The\n+0000a2f0: 7365 2061 7265 0a74 7261 6e73 666f 726d se are.transform\n+0000a300: 6564 2062 7920 6d75 6c74 6970 6c69 6361 ed by multiplica\n+0000a310: 7469 6f6e 2077 6974 6820 3478 3420 6d61 tion with 4x4 ma\n+0000a320: 7472 6963 6573 2e20 2054 6865 2062 7569 trices. The bui\n+0000a330: 6c74 2d69 6e0a 636f 6e73 7472 7563 746f lt-in.constructo\n+0000a340: 7273 2028 e280 9872 6f74 6174 65e2 8099 rs (...rotate...\n+0000a350: 2c20 e280 9873 6361 6c65 e280 992c 2065 , ...scale..., e\n+0000a360: 7463 2e29 2020 6172 6520 616c 6c20 7472 tc.) are all tr\n+0000a370: 616e 736c 6174 6564 2069 6e74 6572 6e61 anslated interna\n+0000a380: 6c6c 7920 746f 0a73 7563 6820 3478 3420 lly to.such 4x4 \n+0000a390: 6d61 7472 6963 6573 2e20 2046 6f72 206d matrices. For m\n+0000a3a0: 6f72 6520 696e 666f 726d 6174 696f 6e20 ore information \n+0000a3b0: 6f6e 2068 6f6d 6f67 656e 656f 7573 2063 on homogeneous c\n+0000a3c0: 6f6f 7264 696e 6174 650a 7472 616e 7366 oordinate.transf\n+0000a3d0: 6f72 6d61 7469 6f6e 732c 2073 6565 2061 ormations, see a\n+0000a3e0: 6e79 2067 6f6f 6420 636f 6d70 7574 6572 ny good computer\n+0000a3f0: 2067 7261 7068 6963 7320 7465 7874 626f graphics textbo\n+0000a400: 6f6b 2e20 2054 6865 2064 6972 6563 740a ok. The direct.\n+0000a410: 7472 616e 7366 6f72 6d20 6665 6174 7572 transform featur\n+0000a420: 6520 6f66 20e2 8098 736b 6574 6368 e280 e of ...sketch..\n+0000a430: 9920 616c 6c6f 7773 2079 6f75 2074 6f20 . allows you to \n+0000a440: 656e 7465 7220 6120 6d61 7472 6978 206f enter a matrix o\n+0000a450: 6620 796f 7572 206f 776e 0a63 686f 6963 f your own.choic\n+0000a460: 652e 2020 5468 6572 6520 6172 6520 6e6f e. There are no\n+0000a470: 7420 6d61 6e79 2063 6173 6573 2077 6865 t many cases whe\n+0000a480: 7265 2074 6869 7320 6973 2075 7365 6675 re this is usefu\n+0000a490: 6c2c 2062 7574 2069 6620 796f 7520 646f l, but if you do\n+0000a4a0: 0a6e 6565 6420 6974 2c20 796f 7520 6e65 .need it, you ne\n+0000a4b0: 6564 2069 7420 6261 646c 7921 0a0a 1f0a ed it badly!....\n+0000a4c0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n+0000a4d0: 6f2c 2020 4e6f 6465 3a20 4172 6974 686d o, Node: Arithm\n+0000a4e0: 6574 6963 2c20 204e 6578 743a 204f 7074 etic, Next: Opt\n+0000a4f0: 696f 6e73 2c20 2050 7265 763a 204c 6974 ions, Prev: Lit\n+0000a500: 6572 616c 732c 2020 5570 3a20 4c61 6e67 erals, Up: Lang\n+0000a510: 7561 6765 2062 6173 6963 730a 0a33 2e31 uage basics..3.1\n+0000a520: 2e34 2041 7269 7468 6d65 7469 6320 6578 .4 Arithmetic ex\n+0000a530: 7072 6573 7369 6f6e 730a 2d2d 2d2d 2d2d pressions.------\n 0000a540: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-0000a550: 2d2d 2d2d 2d2d 2d2d 0a0a 4172 6974 686d --------..Arithm\n-0000a560: 6574 6963 2065 7870 7265 7373 696f 6e73 etic expressions\n-0000a570: 206f 7665 7220 e280 9873 6b65 7463 68e2 over ...sketch.\n-0000a580: 8099 206c 6974 6572 616c 7320 616e 6420 .. literals and \n-0000a590: 6465 6669 6e65 6420 6964 656e 7469 6669 defined identifi\n-0000a5a0: 6572 730a 6172 6520 7375 6d6d 6172 697a ers.are summariz\n-0000a5b0: 6564 2069 6e20 7468 6520 666f 6c6c 6f77 ed in the follow\n-0000a5c0: 696e 6720 7461 626c 6573 2e0a 0a2a 204d ing tables...* M\n-0000a5d0: 656e 753a 0a0a 2a20 5477 6f2d 6f70 6572 enu:..* Two-oper\n-0000a5e0: 616e 6420 2862 696e 6172 7929 2066 6f72 and (binary) for\n-0000a5f0: 6d73 3a3a 2020 4120 6f70 2042 0a2a 2055 ms:: A op B.* U\n-0000a600: 6e61 7279 2066 6f72 6d73 3a3a 2020 2020 nary forms:: \n-0000a610: 2020 2020 2020 2020 2020 2020 206f 7020 op \n-0000a620: 4120 2861 6e64 206f 7468 6572 7329 0a0a A (and others)..\n-0000a630: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n-0000a640: 6e66 6f2c 2020 4e6f 6465 3a20 5477 6f2d nfo, Node: Two-\n-0000a650: 6f70 6572 616e 6420 2862 696e 6172 7929 operand (binary)\n-0000a660: 2066 6f72 6d73 2c20 204e 6578 743a 2055 forms, Next: U\n-0000a670: 6e61 7279 2066 6f72 6d73 2c20 2050 7265 nary forms, Pre\n-0000a680: 763a 2041 7269 7468 6d65 7469 632c 2020 v: Arithmetic, \n-0000a690: 5570 3a20 4172 6974 686d 6574 6963 0a0a Up: Arithmetic..\n-0000a6a0: 332e 312e 342e 3120 5477 6f2d 6f70 6572 3.1.4.1 Two-oper\n-0000a6b0: 616e 6420 2862 696e 6172 7929 2066 6f72 and (binary) for\n-0000a6c0: 6d73 2061 6e64 2070 7265 6365 6465 6e63 ms and precedenc\n-0000a6d0: 650a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e e...............\n+0000a550: 2d2d 2d2d 2d2d 0a0a 4172 6974 686d 6574 ------..Arithmet\n+0000a560: 6963 2065 7870 7265 7373 696f 6e73 206f ic expressions o\n+0000a570: 7665 7220 e280 9873 6b65 7463 68e2 8099 ver ...sketch...\n+0000a580: 206c 6974 6572 616c 7320 616e 6420 6465 literals and de\n+0000a590: 6669 6e65 6420 6964 656e 7469 6669 6572 fined identifier\n+0000a5a0: 730a 6172 6520 7375 6d6d 6172 697a 6564 s.are summarized\n+0000a5b0: 2069 6e20 7468 6520 666f 6c6c 6f77 696e in the followin\n+0000a5c0: 6720 7461 626c 6573 2e0a 0a2a 204d 656e g tables...* Men\n+0000a5d0: 753a 0a0a 2a20 5477 6f2d 6f70 6572 616e u:..* Two-operan\n+0000a5e0: 6420 2862 696e 6172 7929 2066 6f72 6d73 d (binary) forms\n+0000a5f0: 3a3a 2020 4120 6f70 2042 0a2a 2055 6e61 :: A op B.* Una\n+0000a600: 7279 2066 6f72 6d73 3a3a 2020 2020 2020 ry forms:: \n+0000a610: 2020 2020 2020 2020 2020 206f 7020 4120 op A \n+0000a620: 2861 6e64 206f 7468 6572 7329 0a0a 1f0a (and others)....\n+0000a630: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n+0000a640: 6f2c 2020 4e6f 6465 3a20 5477 6f2d 6f70 o, Node: Two-op\n+0000a650: 6572 616e 6420 2862 696e 6172 7929 2066 erand (binary) f\n+0000a660: 6f72 6d73 2c20 204e 6578 743a 2055 6e61 orms, Next: Una\n+0000a670: 7279 2066 6f72 6d73 2c20 2050 7265 763a ry forms, Prev:\n+0000a680: 2041 7269 7468 6d65 7469 632c 2020 5570 Arithmetic, Up\n+0000a690: 3a20 4172 6974 686d 6574 6963 0a0a 332e : Arithmetic..3.\n+0000a6a0: 312e 342e 3120 5477 6f2d 6f70 6572 616e 1.4.1 Two-operan\n+0000a6b0: 6420 2862 696e 6172 7929 2066 6f72 6d73 d (binary) forms\n+0000a6c0: 2061 6e64 2070 7265 6365 6465 6e63 650a and precedence.\n+0000a6d0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n 0000a6e0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n 0000a6f0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000a700: 2e2e 2e0a 0a4d 6f73 7420 7477 6f2d 6f70 .....Most two-op\n-0000a710: 6572 616e 6420 6269 6e61 7279 2066 6f72 erand binary for\n-0000a720: 6d73 2068 6176 6520 6d65 616e 696e 6773 ms have meanings\n-0000a730: 2064 6570 656e 6465 6e74 206f 6e20 7468 dependent on th\n-0000a740: 6520 7479 7065 7320 6f66 0a74 6865 6972 e types of.their\n-0000a750: 2061 7267 756d 656e 7473 2e20 2041 6e20 arguments. An \n-0000a760: 6578 6861 7573 7469 7665 2073 756d 6d61 exhaustive summa\n-0000a770: 7279 206f 6620 7468 6520 706f 7373 6962 ry of the possib\n-0000a780: 696c 6974 6965 7320 6973 2067 6976 656e ilities is given\n-0000a790: 2069 6e0a 7468 6520 666f 6c6c 6f77 696e in.the followin\n-0000a7a0: 6720 7461 626c 652e 0a4c 6566 7420 2020 g table..Left \n-0000a7b0: 2020 2020 204f 7020 2020 2020 2020 5269 Op Ri\n-0000a7c0: 6768 7420 2020 2020 2020 5265 7375 6c74 ght Result\n-0000a7d0: 2020 2020 2020 4465 7363 7269 7074 696f Descriptio\n-0000a7e0: 6e0a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d n.--------------\n+0000a700: 2e0a 0a4d 6f73 7420 7477 6f2d 6f70 6572 ...Most two-oper\n+0000a710: 616e 6420 6269 6e61 7279 2066 6f72 6d73 and binary forms\n+0000a720: 2068 6176 6520 6d65 616e 696e 6773 2064 have meanings d\n+0000a730: 6570 656e 6465 6e74 206f 6e20 7468 6520 ependent on the \n+0000a740: 7479 7065 7320 6f66 0a74 6865 6972 2061 types of.their a\n+0000a750: 7267 756d 656e 7473 2e20 2041 6e20 6578 rguments. An ex\n+0000a760: 6861 7573 7469 7665 2073 756d 6d61 7279 haustive summary\n+0000a770: 206f 6620 7468 6520 706f 7373 6962 696c of the possibil\n+0000a780: 6974 6965 7320 6973 2067 6976 656e 2069 ities is given i\n+0000a790: 6e0a 7468 6520 666f 6c6c 6f77 696e 6720 n.the following \n+0000a7a0: 7461 626c 652e 0a4c 6566 7420 2020 2020 table..Left \n+0000a7b0: 2020 204f 7020 2020 2020 2020 5269 6768 Op Righ\n+0000a7c0: 7420 2020 2020 2020 5265 7375 6c74 2020 t Result \n+0000a7d0: 2020 2020 4465 7363 7269 7074 696f 6e0a Description.\n+0000a7e0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a7f0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a800: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a810: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a820: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a830: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a840: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-0000a850: 2d2d 2d2d 2d2d 2d2d 0a73 6361 6c61 7220 --------.scalar \n-0000a860: 2020 2020 20e2 8098 2be2 8099 2020 2020 ...+... \n-0000a870: 2020 7363 616c 6172 2020 2020 2020 7363 scalar sc\n-0000a880: 616c 6172 2020 2020 2020 5363 616c 6172 alar Scalar\n-0000a890: 2073 756d 2e0a 7665 6374 6f72 2020 2020 sum..vector \n-0000a8a0: 2020 e280 982b e280 9920 2020 2020 2076 ...+... v\n-0000a8b0: 6563 746f 7220 2020 2020 2076 6563 746f ector vecto\n-0000a8c0: 7220 2020 2020 2056 6563 746f 7220 7375 r Vector su\n-0000a8d0: 6d2e 0a70 6f69 6e74 2020 2020 2020 20e2 m..point .\n-0000a8e0: 8098 2be2 8099 2020 2020 2020 7665 6374 ..+... vect\n-0000a8f0: 6f72 2020 2020 2020 706f 696e 7420 2020 or point \n-0000a900: 2020 2020 506f 696e 742d 7665 6374 6f72 Point-vector\n-0000a910: 2061 6666 696e 6520 7375 6d2e 0a76 6563 affine sum..vec\n-0000a920: 746f 7220 2020 2020 20e2 8098 2be2 8099 tor ...+...\n-0000a930: 2020 2020 2020 706f 696e 7420 2020 2020 point \n-0000a940: 2020 2220 2020 2020 2020 2020 2020 220a \" \".\n-0000a950: 7363 616c 6172 2020 2020 2020 e280 982d scalar ...-\n-0000a960: e280 9920 2020 2020 2073 6361 6c61 7220 ... scalar \n-0000a970: 2020 2020 2073 6361 6c61 7220 2020 2020 scalar \n-0000a980: 2053 6361 6c61 7220 6469 6666 6572 656e Scalar differen\n-0000a990: 6365 2e0a 7665 6374 6f72 2020 2020 2020 ce..vector \n-0000a9a0: e280 982d e280 9920 2020 2020 2076 6563 ...-... vec\n-0000a9b0: 746f 7220 2020 2020 2076 6563 746f 7220 tor vector \n-0000a9c0: 2020 2020 2056 6563 746f 7220 6469 6666 Vector diff\n-0000a9d0: 6572 656e 6365 2e0a 706f 696e 7420 2020 erence..point \n-0000a9e0: 2020 2020 e280 982d e280 9920 2020 2020 ...-... \n-0000a9f0: 2070 6f69 6e74 2020 2020 2020 2076 6563 point vec\n-0000aa00: 746f 7220 2020 2020 2050 6f69 6e74 2d70 tor Point-p\n-0000aa10: 6f69 6e74 2061 6666 696e 6520 6469 6666 oint affine diff\n-0000aa20: 6572 656e 6365 2e0a 706f 696e 7420 2020 erence..point \n-0000aa30: 2020 2020 e280 982d e280 9920 2020 2020 ...-... \n-0000aa40: 2076 6563 746f 7220 2020 2020 2070 6f69 vector poi\n-0000aa50: 6e74 2020 2020 2020 2050 6f69 6e74 2d76 nt Point-v\n-0000aa60: 6563 746f 7220 6166 6669 6e65 2064 6966 ector affine dif\n-0000aa70: 6665 7265 6e63 652e 0a73 6361 6c61 7220 ference..scalar \n-0000aa80: 2020 2020 20e2 8098 2ae2 8099 206f 7220 ...*... or \n-0000aa90: 2020 7363 616c 6172 2020 2020 2020 7363 scalar sc\n-0000aaa0: 616c 6172 2020 2020 2020 5363 616c 6172 alar Scalar\n-0000aab0: 2070 726f 6475 6374 2e0a 2020 2020 2020 product.. \n-0000aac0: 2020 2020 2020 e280 982e e280 990a 7363 ........sc\n-0000aad0: 616c 6172 2020 2020 2020 e280 982a e280 alar ...*..\n-0000aae0: 9920 6f72 2020 2076 6563 746f 7220 2020 . or vector \n-0000aaf0: 2020 2076 6563 746f 7220 2020 2020 2053 vector S\n-0000ab00: 6361 6c61 722d 7665 6374 6f72 2070 726f calar-vector pro\n-0000ab10: 6475 6374 2e0a 2020 2020 2020 2020 2020 duct.. \n-0000ab20: 2020 e280 982e e280 990a 7665 6374 6f72 ........vector\n-0000ab30: 2020 2020 2020 e280 982a e280 9920 6f72 ...*... or\n-0000ab40: 2020 2073 6361 6c61 7220 2020 2020 2022 scalar \"\n-0000ab50: 2020 2020 2020 2020 2020 2022 0a20 2020 \". \n-0000ab60: 2020 2020 2020 2020 20e2 8098 2ee2 8099 .......\n-0000ab70: 0a76 6563 746f 7220 2020 2020 20e2 8098 .vector ...\n-0000ab80: 2ae2 8099 2020 2020 2020 7665 6374 6f72 *... vector\n-0000ab90: 2020 2020 2020 7665 6374 6f72 2020 2020 vector \n-0000aba0: 2020 5665 6374 6f72 2063 726f 7373 2d70 Vector cross-p\n-0000abb0: 726f 6475 6374 2e0a 7665 6374 6f72 2020 roduct..vector \n-0000abc0: 2020 2020 e280 982e e280 9920 2020 2020 ....... \n-0000abd0: 2076 6563 746f 7220 2020 2020 2073 6361 vector sca\n-0000abe0: 6c61 7220 2020 2020 2056 6563 746f 7220 lar Vector \n-0000abf0: 646f 7420 7072 6f64 7563 742e 0a73 6361 dot product..sca\n-0000ac00: 6c61 7220 2020 2020 20e2 8098 5ee2 8099 lar ...^...\n-0000ac10: 2020 2020 2020 7363 616c 6172 2020 2020 scalar \n-0000ac20: 2020 7363 616c 6172 2020 2020 2020 5261 scalar Ra\n-0000ac30: 6973 6520 7363 616c 6172 2074 6f20 7363 ise scalar to sc\n-0000ac40: 616c 6172 2070 6f77 6572 2e0a 7472 616e alar power..tran\n-0000ac50: 7366 6f72 6d20 2020 e280 985e e280 9920 sform ...^... \n-0000ac60: 2020 2020 2069 6e74 6567 6572 2020 2020 integer \n-0000ac70: 2074 7261 6e73 666f 726d 2020 2052 6169 transform Rai\n-0000ac80: 7365 2074 7261 6e73 666f 726d 2074 6f20 se transform to \n-0000ac90: 696e 7465 6765 7220 706f 7765 722e 0a74 integer power..t\n-0000aca0: 7261 6e73 666f 726d 2020 20e2 8098 2ae2 ransform ...*.\n-0000acb0: 8099 206f 7220 2020 706f 696e 7420 2020 .. or point \n-0000acc0: 2020 2020 706f 696e 7420 2020 2020 2020 point \n-0000acd0: 4166 6669 6e65 2070 6f69 6e74 2074 7261 Affine point tra\n-0000ace0: 6e73 666f 726d 2028 7269 6768 742d 746f nsform (right-to\n-0000acf0: 2d6c 6566 7429 2e0a 2020 2020 2020 2020 -left).. \n-0000ad00: 2020 2020 e280 982e e280 990a 7472 616e ........tran\n-0000ad10: 7366 6f72 6d20 2020 e280 982a e280 9920 sform ...*... \n-0000ad20: 6f72 2020 2076 6563 746f 7220 2020 2020 or vector \n-0000ad30: 2076 6563 746f 7220 2020 2020 2041 6666 vector Aff\n-0000ad40: 696e 6520 7665 6374 6f72 2074 7261 6e73 ine vector trans\n-0000ad50: 666f 726d 2028 7269 6768 742d 746f 2d6c form (right-to-l\n-0000ad60: 6566 7429 2e0a 2020 2020 2020 2020 2020 eft).. \n-0000ad70: 2020 e280 982e e280 990a 7472 616e 7366 ........transf\n-0000ad80: 6f72 6d20 2020 e280 982a e280 9920 6f72 orm ...*... or\n-0000ad90: 2020 2074 7261 6e73 666f 726d 2020 2074 transform t\n-0000ada0: 7261 6e73 666f 726d 2020 2054 7261 6e73 ransform Trans\n-0000adb0: 666f 726d 2063 6f6d 706f 7369 7469 6f6e form composition\n-0000adc0: 2028 7269 6768 742d 746f 2d6c 6566 7429 (right-to-left)\n-0000add0: 2e0a 2020 2020 2020 2020 2020 2020 e280 .. ..\n-0000ade0: 982e e280 990a 706f 696e 7420 2020 2020 ......point \n-0000adf0: 2020 e280 9874 6865 6ee2 8099 2020 2074 ...then... t\n-0000ae00: 7261 6e73 666f 726d 2020 2070 6f69 6e74 ransform point\n-0000ae10: 2020 2020 2020 2041 6666 696e 6520 706f Affine po\n-0000ae20: 696e 7420 7472 616e 7366 6f72 6d20 286c int transform (l\n-0000ae30: 6566 742d 746f 2d72 6967 6874 292e 0a76 eft-to-right)..v\n-0000ae40: 6563 746f 7220 2020 2020 20e2 8098 7468 ector ...th\n-0000ae50: 656e e280 9920 2020 7472 616e 7366 6f72 en... transfor\n-0000ae60: 6d20 2020 7665 6374 6f72 2020 2020 2020 m vector \n-0000ae70: 4166 6669 6e65 2076 6563 746f 7220 7472 Affine vector tr\n-0000ae80: 616e 7366 6f72 6d20 286c 6566 742d 746f ansform (left-to\n-0000ae90: 2d72 6967 6874 292e 0a74 7261 6e73 666f -right)..transfo\n-0000aea0: 726d 2020 20e2 8098 7468 656e e280 9920 rm ...then... \n-0000aeb0: 2020 7472 616e 7366 6f72 6d20 2020 7472 transform tr\n-0000aec0: 616e 7366 6f72 6d20 2020 5472 616e 7366 ansform Transf\n-0000aed0: 6f72 6d20 636f 6d70 6f73 6974 696f 6e20 orm composition \n-0000aee0: 286c 6566 742d 746f 2d72 6967 6874 292e (left-to-right).\n-0000aef0: 0a73 6361 6c61 7220 2020 2020 20e2 8098 .scalar ...\n-0000af00: 2fe2 8099 2020 2020 2020 7363 616c 6172 /... scalar\n-0000af10: 2020 2020 2020 7363 616c 6172 2020 2020 scalar \n-0000af20: 2020 5363 616c 6172 2064 6976 6973 696f Scalar divisio\n-0000af30: 6e2e 0a76 6563 746f 7220 2020 2020 20e2 n..vector .\n-0000af40: 8098 2fe2 8099 2020 2020 2020 7363 616c ../... scal\n-0000af50: 6172 2020 2020 2020 7665 6374 6f72 2020 ar vector \n-0000af60: 2020 2020 5665 6374 6f72 2063 6f6d 706f Vector compo\n-0000af70: 6e65 6e74 2d77 6973 6520 6469 7669 7369 nent-wise divisi\n-0000af80: 6f6e 2062 7920 7363 616c 6172 2e0a 706f on by scalar..po\n-0000af90: 696e 7420 2020 2020 2020 e280 9827 e280 int ...'..\n-0000afa0: 9920 2020 2020 20e2 8098 78e2 8099 2c20 . ...x..., \n-0000afb0: e280 9879 e280 992c 2020 2073 6361 6c61 ...y..., scala\n-0000afc0: 7220 2020 2020 2050 6f69 6e74 2063 6f6d r Point com\n-0000afd0: 706f 6e65 6e74 2065 7874 7261 6374 696f ponent extractio\n-0000afe0: 6e2e 0a20 2020 2020 2020 2020 2020 2020 n.. \n-0000aff0: 2020 2020 2020 2020 6f72 20e2 8098 7ae2 or ...z.\n-0000b000: 8099 0a76 6563 746f 7220 2020 2020 20e2 ...vector .\n-0000b010: 8098 27e2 8099 2020 2020 2020 e280 9878 ..'... ...x\n-0000b020: e280 992c 20e2 8098 79e2 8099 2c20 2020 ..., ...y..., \n-0000b030: 7363 616c 6172 2020 2020 2020 5665 6374 scalar Vect\n-0000b040: 6f72 2063 6f6d 706f 6e65 6e74 2065 7874 or component ext\n-0000b050: 7261 6374 696f 6e2e 0a20 2020 2020 2020 raction.. \n-0000b060: 2020 2020 2020 2020 2020 2020 2020 6f72 or\n-0000b070: 20e2 8098 7ae2 8099 0a0a 4f70 6572 6174 ...z.....Operat\n-0000b080: 6f72 2070 7265 6365 6465 6e63 6520 6973 or precedence is\n-0000b090: 2073 686f 776e 2069 6e20 7468 6973 2074 shown in this t\n-0000b0a0: 6162 6c65 2e0a 4f70 2020 2020 2020 2050 able..Op P\n-0000b0b0: 7265 6365 6465 6e63 650a 2d2d 2d2d 2d2d recedence.------\n+0000a850: 2d2d 2d2d 2d2d 0a73 6361 6c61 7220 2020 ------.scalar \n+0000a860: 2020 20e2 8098 2be2 8099 2020 2020 2020 ...+... \n+0000a870: 7363 616c 6172 2020 2020 2020 7363 616c scalar scal\n+0000a880: 6172 2020 2020 2020 5363 616c 6172 2073 ar Scalar s\n+0000a890: 756d 2e0a 7665 6374 6f72 2020 2020 2020 um..vector \n+0000a8a0: e280 982b e280 9920 2020 2020 2076 6563 ...+... vec\n+0000a8b0: 746f 7220 2020 2020 2076 6563 746f 7220 tor vector \n+0000a8c0: 2020 2020 2056 6563 746f 7220 7375 6d2e Vector sum.\n+0000a8d0: 0a70 6f69 6e74 2020 2020 2020 20e2 8098 .point ...\n+0000a8e0: 2be2 8099 2020 2020 2020 7665 6374 6f72 +... vector\n+0000a8f0: 2020 2020 2020 706f 696e 7420 2020 2020 point \n+0000a900: 2020 506f 696e 742d 7665 6374 6f72 2061 Point-vector a\n+0000a910: 6666 696e 6520 7375 6d2e 0a76 6563 746f ffine sum..vecto\n+0000a920: 7220 2020 2020 20e2 8098 2be2 8099 2020 r ...+... \n+0000a930: 2020 2020 706f 696e 7420 2020 2020 2020 point \n+0000a940: 2220 2020 2020 2020 2020 2020 220a 7363 \" \".sc\n+0000a950: 616c 6172 2020 2020 2020 e280 982d e280 alar ...-..\n+0000a960: 9920 2020 2020 2073 6361 6c61 7220 2020 . scalar \n+0000a970: 2020 2073 6361 6c61 7220 2020 2020 2053 scalar S\n+0000a980: 6361 6c61 7220 6469 6666 6572 656e 6365 calar difference\n+0000a990: 2e0a 7665 6374 6f72 2020 2020 2020 e280 ..vector ..\n+0000a9a0: 982d e280 9920 2020 2020 2076 6563 746f .-... vecto\n+0000a9b0: 7220 2020 2020 2076 6563 746f 7220 2020 r vector \n+0000a9c0: 2020 2056 6563 746f 7220 6469 6666 6572 Vector differ\n+0000a9d0: 656e 6365 2e0a 706f 696e 7420 2020 2020 ence..point \n+0000a9e0: 2020 e280 982d e280 9920 2020 2020 2070 ...-... p\n+0000a9f0: 6f69 6e74 2020 2020 2020 2076 6563 746f oint vecto\n+0000aa00: 7220 2020 2020 2050 6f69 6e74 2d70 6f69 r Point-poi\n+0000aa10: 6e74 2061 6666 696e 6520 6469 6666 6572 nt affine differ\n+0000aa20: 656e 6365 2e0a 706f 696e 7420 2020 2020 ence..point \n+0000aa30: 2020 e280 982d e280 9920 2020 2020 2076 ...-... v\n+0000aa40: 6563 746f 7220 2020 2020 2070 6f69 6e74 ector point\n+0000aa50: 2020 2020 2020 2050 6f69 6e74 2d76 6563 Point-vec\n+0000aa60: 746f 7220 6166 6669 6e65 2064 6966 6665 tor affine diffe\n+0000aa70: 7265 6e63 652e 0a73 6361 6c61 7220 2020 rence..scalar \n+0000aa80: 2020 20e2 8098 2ae2 8099 206f 7220 2020 ...*... or \n+0000aa90: 7363 616c 6172 2020 2020 2020 7363 616c scalar scal\n+0000aaa0: 6172 2020 2020 2020 5363 616c 6172 2070 ar Scalar p\n+0000aab0: 726f 6475 6374 2e0a 2020 2020 2020 2020 roduct.. \n+0000aac0: 2020 2020 e280 982e e280 990a 7363 616c ........scal\n+0000aad0: 6172 2020 2020 2020 e280 982a e280 9920 ar ...*... \n+0000aae0: 6f72 2020 2076 6563 746f 7220 2020 2020 or vector \n+0000aaf0: 2076 6563 746f 7220 2020 2020 2053 6361 vector Sca\n+0000ab00: 6c61 722d 7665 6374 6f72 2070 726f 6475 lar-vector produ\n+0000ab10: 6374 2e0a 2020 2020 2020 2020 2020 2020 ct.. \n+0000ab20: e280 982e e280 990a 7665 6374 6f72 2020 ........vector \n+0000ab30: 2020 2020 e280 982a e280 9920 6f72 2020 ...*... or \n+0000ab40: 2073 6361 6c61 7220 2020 2020 2022 2020 scalar \" \n+0000ab50: 2020 2020 2020 2020 2022 0a20 2020 2020 \". \n+0000ab60: 2020 2020 2020 20e2 8098 2ee2 8099 0a76 ........v\n+0000ab70: 6563 746f 7220 2020 2020 20e2 8098 2ae2 ector ...*.\n+0000ab80: 8099 2020 2020 2020 7665 6374 6f72 2020 .. vector \n+0000ab90: 2020 2020 7665 6374 6f72 2020 2020 2020 vector \n+0000aba0: 5665 6374 6f72 2063 726f 7373 2d70 726f Vector cross-pro\n+0000abb0: 6475 6374 2e0a 7665 6374 6f72 2020 2020 duct..vector \n+0000abc0: 2020 e280 982e e280 9920 2020 2020 2076 ....... v\n+0000abd0: 6563 746f 7220 2020 2020 2073 6361 6c61 ector scala\n+0000abe0: 7220 2020 2020 2056 6563 746f 7220 646f r Vector do\n+0000abf0: 7420 7072 6f64 7563 742e 0a73 6361 6c61 t product..scala\n+0000ac00: 7220 2020 2020 20e2 8098 5ee2 8099 2020 r ...^... \n+0000ac10: 2020 2020 7363 616c 6172 2020 2020 2020 scalar \n+0000ac20: 7363 616c 6172 2020 2020 2020 5261 6973 scalar Rais\n+0000ac30: 6520 7363 616c 6172 2074 6f20 7363 616c e scalar to scal\n+0000ac40: 6172 2070 6f77 6572 2e0a 7472 616e 7366 ar power..transf\n+0000ac50: 6f72 6d20 2020 e280 985e e280 9920 2020 orm ...^... \n+0000ac60: 2020 2069 6e74 6567 6572 2020 2020 2074 integer t\n+0000ac70: 7261 6e73 666f 726d 2020 2052 6169 7365 ransform Raise\n+0000ac80: 2074 7261 6e73 666f 726d 2074 6f20 696e transform to in\n+0000ac90: 7465 6765 7220 706f 7765 722e 0a74 7261 teger power..tra\n+0000aca0: 6e73 666f 726d 2020 20e2 8098 2ae2 8099 nsform ...*...\n+0000acb0: 206f 7220 2020 706f 696e 7420 2020 2020 or point \n+0000acc0: 2020 706f 696e 7420 2020 2020 2020 4166 point Af\n+0000acd0: 6669 6e65 2070 6f69 6e74 2074 7261 6e73 fine point trans\n+0000ace0: 666f 726d 2028 7269 6768 742d 746f 2d6c form (right-to-l\n+0000acf0: 6566 7429 2e0a 2020 2020 2020 2020 2020 eft).. \n+0000ad00: 2020 e280 982e e280 990a 7472 616e 7366 ........transf\n+0000ad10: 6f72 6d20 2020 e280 982a e280 9920 6f72 orm ...*... or\n+0000ad20: 2020 2076 6563 746f 7220 2020 2020 2076 vector v\n+0000ad30: 6563 746f 7220 2020 2020 2041 6666 696e ector Affin\n+0000ad40: 6520 7665 6374 6f72 2074 7261 6e73 666f e vector transfo\n+0000ad50: 726d 2028 7269 6768 742d 746f 2d6c 6566 rm (right-to-lef\n+0000ad60: 7429 2e0a 2020 2020 2020 2020 2020 2020 t).. \n+0000ad70: e280 982e e280 990a 7472 616e 7366 6f72 ........transfor\n+0000ad80: 6d20 2020 e280 982a e280 9920 6f72 2020 m ...*... or \n+0000ad90: 2074 7261 6e73 666f 726d 2020 2074 7261 transform tra\n+0000ada0: 6e73 666f 726d 2020 2054 7261 6e73 666f nsform Transfo\n+0000adb0: 726d 2063 6f6d 706f 7369 7469 6f6e 2028 rm composition (\n+0000adc0: 7269 6768 742d 746f 2d6c 6566 7429 2e0a right-to-left)..\n+0000add0: 2020 2020 2020 2020 2020 2020 e280 982e ....\n+0000ade0: e280 990a 706f 696e 7420 2020 2020 2020 ....point \n+0000adf0: e280 9874 6865 6ee2 8099 2020 2074 7261 ...then... tra\n+0000ae00: 6e73 666f 726d 2020 2070 6f69 6e74 2020 nsform point \n+0000ae10: 2020 2020 2041 6666 696e 6520 706f 696e Affine poin\n+0000ae20: 7420 7472 616e 7366 6f72 6d20 286c 6566 t transform (lef\n+0000ae30: 742d 746f 2d72 6967 6874 292e 0a76 6563 t-to-right)..vec\n+0000ae40: 746f 7220 2020 2020 20e2 8098 7468 656e tor ...then\n+0000ae50: e280 9920 2020 7472 616e 7366 6f72 6d20 ... transform \n+0000ae60: 2020 7665 6374 6f72 2020 2020 2020 4166 vector Af\n+0000ae70: 6669 6e65 2076 6563 746f 7220 7472 616e fine vector tran\n+0000ae80: 7366 6f72 6d20 286c 6566 742d 746f 2d72 sform (left-to-r\n+0000ae90: 6967 6874 292e 0a74 7261 6e73 666f 726d ight)..transform\n+0000aea0: 2020 20e2 8098 7468 656e e280 9920 2020 ...then... \n+0000aeb0: 7472 616e 7366 6f72 6d20 2020 7472 616e transform tran\n+0000aec0: 7366 6f72 6d20 2020 5472 616e 7366 6f72 sform Transfor\n+0000aed0: 6d20 636f 6d70 6f73 6974 696f 6e20 286c m composition (l\n+0000aee0: 6566 742d 746f 2d72 6967 6874 292e 0a73 eft-to-right)..s\n+0000aef0: 6361 6c61 7220 2020 2020 20e2 8098 2fe2 calar .../.\n+0000af00: 8099 2020 2020 2020 7363 616c 6172 2020 .. scalar \n+0000af10: 2020 2020 7363 616c 6172 2020 2020 2020 scalar \n+0000af20: 5363 616c 6172 2064 6976 6973 696f 6e2e Scalar division.\n+0000af30: 0a76 6563 746f 7220 2020 2020 20e2 8098 .vector ...\n+0000af40: 2fe2 8099 2020 2020 2020 7363 616c 6172 /... scalar\n+0000af50: 2020 2020 2020 7665 6374 6f72 2020 2020 vector \n+0000af60: 2020 5665 6374 6f72 2063 6f6d 706f 6e65 Vector compone\n+0000af70: 6e74 2d77 6973 6520 6469 7669 7369 6f6e nt-wise division\n+0000af80: 2062 7920 7363 616c 6172 2e0a 706f 696e by scalar..poin\n+0000af90: 7420 2020 2020 2020 e280 9827 e280 9920 t ...'... \n+0000afa0: 2020 2020 20e2 8098 78e2 8099 2c20 e280 ...x..., ..\n+0000afb0: 9879 e280 992c 2020 2073 6361 6c61 7220 .y..., scalar \n+0000afc0: 2020 2020 2050 6f69 6e74 2063 6f6d 706f Point compo\n+0000afd0: 6e65 6e74 2065 7874 7261 6374 696f 6e2e nent extraction.\n+0000afe0: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n+0000aff0: 2020 2020 2020 6f72 20e2 8098 7ae2 8099 or ...z...\n+0000b000: 0a76 6563 746f 7220 2020 2020 20e2 8098 .vector ...\n+0000b010: 27e2 8099 2020 2020 2020 e280 9878 e280 '... ...x..\n+0000b020: 992c 20e2 8098 79e2 8099 2c20 2020 7363 ., ...y..., sc\n+0000b030: 616c 6172 2020 2020 2020 5665 6374 6f72 alar Vector\n+0000b040: 2063 6f6d 706f 6e65 6e74 2065 7874 7261 component extra\n+0000b050: 6374 696f 6e2e 0a20 2020 2020 2020 2020 ction.. \n+0000b060: 2020 2020 2020 2020 2020 2020 6f72 20e2 or .\n+0000b070: 8098 7ae2 8099 0a0a 4f70 6572 6174 6f72 ..z.....Operator\n+0000b080: 2070 7265 6365 6465 6e63 6520 6973 2073 precedence is s\n+0000b090: 686f 776e 2069 6e20 7468 6973 2074 6162 hown in this tab\n+0000b0a0: 6c65 2e0a 4f70 2020 2020 2020 2050 7265 le..Op Pre\n+0000b0b0: 6365 6465 6e63 650a 2d2d 2d2d 2d2d 2d2d cedence.--------\n 0000b0c0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000b0d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-0000b0e0: 2d2d 2d2d 0ae2 8098 27e2 8099 2020 2020 ----....'... \n-0000b0f0: 2020 6869 6768 6573 7420 286d 6f73 7420 highest (most \n-0000b100: 7469 6768 746c 7920 6269 6e64 696e 6729 tightly binding)\n-0000b110: 0ae2 8098 5ee2 8099 0ae2 8098 2de2 8099 ....^.......-...\n-0000b120: 2020 2020 2020 2875 6e61 7279 206e 6567 (unary neg\n-0000b130: 6174 696f 6e29 0ae2 8098 2ae2 8099 0ae2 ation)....*.....\n-0000b140: 8098 2ee2 8099 0ae2 8098 2fe2 8099 0ae2 ........../.....\n-0000b150: 8098 2be2 8099 0ae2 8098 2de2 8099 0ae2 ..+.......-.....\n-0000b160: 8098 7468 656e e280 9920 2020 6c6f 7765 ..then... lowe\n-0000b170: 7374 2028 6c65 6173 7420 7469 6768 746c st (least tightl\n-0000b180: 7920 6269 6e64 696e 6729 0a0a 416c 6c20 y binding)..All \n-0000b190: 6f70 6572 6174 696f 6e73 2061 7265 206c operations are l\n-0000b1a0: 6566 742d 6173 736f 6369 6174 6976 6520 eft-associative \n-0000b1b0: 6578 6365 7074 2066 6f72 20e2 8098 5ee2 except for ...^.\n-0000b1c0: 8099 2e20 2050 6172 656e 7468 6573 6573 ... Parentheses\n-0000b1d0: 20e2 8098 2820 29e2 8099 0a61 7265 2075 ...( )....are u\n-0000b1e0: 7365 6420 666f 7220 6772 6f75 7069 6e67 sed for grouping\n-0000b1f0: 2074 6f20 6f76 6572 7269 6465 2070 7265 to override pre\n-0000b200: 6365 6465 6e63 6520 696e 2074 6865 2075 cedence in the u\n-0000b210: 7375 616c 2077 6179 2e0a 0a20 2020 4173 sual way... As\n-0000b220: 2079 6f75 2063 616e 2073 6565 2c20 7468 you can see, th\n-0000b230: 6520 646f 7420 6f70 6572 6174 6f72 20e2 e dot operator .\n-0000b240: 8098 2ee2 8099 2069 7320 7573 7561 6c6c ...... is usuall\n-0000b250: 7920 6120 7379 6e6f 6e79 6d20 666f 720a y a synonym for.\n-0000b260: 7275 6e2d 6f66 2d74 6865 2d6d 696c 6c20 run-of-the-mill \n-0000b270: 6d75 6c74 6970 6c69 6361 7469 6f6e 2c20 multiplication, \n-0000b280: e280 982a e280 992e 2020 5468 6520 6d65 ...*.... The me\n-0000b290: 616e 696e 6773 2064 6966 6665 7220 6f6e anings differ on\n-0000b2a0: 6c79 2066 6f72 0a76 6563 746f 7220 6f70 ly for.vector op\n-0000b2b0: 6572 616e 6473 2e20 2054 6865 20e2 8098 erands. The ...\n-0000b2c0: 7468 656e e280 9920 6f70 6572 6174 6f72 then... operator\n-0000b2d0: 206d 6572 656c 7920 7265 7665 7273 6573 merely reverses\n-0000b2e0: 2074 6865 206f 7065 7261 6e64 206f 7264 the operand ord\n-0000b2f0: 6572 0a77 6974 6820 7265 7370 6563 7420 er.with respect \n-0000b300: 746f 206e 6f72 6d61 6c20 6d75 6c74 6970 to normal multip\n-0000b310: 6c69 6361 7469 6f6e 20e2 8098 2ae2 8099 lication ...*...\n-0000b320: 2e20 2054 6865 2069 6e74 656e 7420 6865 . The intent he\n-0000b330: 7265 2069 7320 746f 206d 616b 650a 636f re is to make.co\n-0000b340: 6d70 6f73 6974 696f 6e73 2072 6561 6420 mpositions read \n-0000b350: 6d6f 7265 206e 6174 7572 616c 6c79 2e20 more naturally. \n-0000b360: 2054 6865 2063 6f64 650a 2020 2020 2028 The code. (\n-0000b370: 312c 322c 3329 2074 6865 6e20 7363 616c 1,2,3) then scal\n-0000b380: 6528 3229 2074 6865 6e20 726f 7461 7465 e(2) then rotate\n-0000b390: 2833 3029 2074 6865 6e20 7472 616e 736c (30) then transl\n-0000b3a0: 6174 6528 5b31 2c33 2c30 5d29 0a65 7870 ate([1,3,0]).exp\n-0000b3b0: 7265 7373 6573 2061 2073 6572 6965 7320 resses a series \n-0000b3c0: 6f66 2073 7563 6365 7373 6976 6520 6d6f of successive mo\n-0000b3d0: 6469 6669 6361 7469 6f6e 7320 746f 2074 difications to t\n-0000b3e0: 6865 2070 6f69 6e74 2c20 7768 6572 6561 he point, wherea\n-0000b3f0: 7320 7468 650a 6571 7569 7661 6c65 6e74 s the.equivalent\n-0000b400: 2066 6f72 6d0a 2020 2020 2074 7261 6e73 form. trans\n-0000b410: 6c61 7465 285b 312c 332c 305d 2920 2a20 late([1,3,0]) * \n-0000b420: 726f 7461 7465 2833 3029 202a 2073 6361 rotate(30) * sca\n-0000b430: 6c65 2832 2920 2a20 2831 2c32 2c33 290a le(2) * (1,2,3).\n-0000b440: 7769 6c6c 2062 6520 696e 7475 6974 6976 will be intuitiv\n-0000b450: 6520 6f6e 6c79 2074 6f20 6d61 7468 656d e only to mathem\n-0000b460: 6174 6963 6961 6e73 2028 616e 6420 7065 aticians (and pe\n-0000b470: 7268 6170 7320 4172 6162 6963 206c 616e rhaps Arabic lan\n-0000b480: 6775 6167 650a 7265 6164 6572 7329 2e0a guage.readers)..\n-0000b490: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n-0000b4a0: 696e 666f 2c20 204e 6f64 653a 2055 6e61 info, Node: Una\n-0000b4b0: 7279 2066 6f72 6d73 2c20 2050 7265 763a ry forms, Prev:\n-0000b4c0: 2054 776f 2d6f 7065 7261 6e64 2028 6269 Two-operand (bi\n-0000b4d0: 6e61 7279 2920 666f 726d 732c 2020 5570 nary) forms, Up\n-0000b4e0: 3a20 4172 6974 686d 6574 6963 0a0a 332e : Arithmetic..3.\n-0000b4f0: 312e 342e 3220 556e 6172 7920 666f 726d 1.4.2 Unary form\n-0000b500: 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e s...............\n-0000b510: 2e2e 2e2e 2e0a 0a55 6e61 7279 206f 7220 .......Unary or \n-0000b520: 6f6e 652d 6f70 6572 616e 6420 666f 726d one-operand form\n-0000b530: 7320 6172 6520 7375 6d6d 6172 697a 6564 s are summarized\n-0000b540: 2069 6e20 7468 6520 666f 6c6c 6f77 696e in the followin\n-0000b550: 6720 7461 626c 652c 2077 6865 7265 0ae2 g table, where..\n-0000b560: 8098 58e2 8099 2073 7461 6e64 7320 666f ..X... stands fo\n-0000b570: 7220 7468 6520 6f70 6572 616e 642e 0a4f r the operand..O\n-0000b580: 7020 2020 2020 2020 2020 2020 2020 4f70 p Op\n-0000b590: 6572 616e 6420 2020 2020 5265 7375 6c74 erand Result\n-0000b5a0: 2020 2020 2020 4465 7363 7269 7074 696f Descriptio\n-0000b5b0: 6e0a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d n.--------------\n+0000b0e0: 2d2d 0ae2 8098 27e2 8099 2020 2020 2020 --....'... \n+0000b0f0: 6869 6768 6573 7420 286d 6f73 7420 7469 highest (most ti\n+0000b100: 6768 746c 7920 6269 6e64 696e 6729 0ae2 ghtly binding)..\n+0000b110: 8098 5ee2 8099 0ae2 8098 2de2 8099 2020 ..^.......-... \n+0000b120: 2020 2020 2875 6e61 7279 206e 6567 6174 (unary negat\n+0000b130: 696f 6e29 0ae2 8098 2ae2 8099 0ae2 8098 ion)....*.......\n+0000b140: 2ee2 8099 0ae2 8098 2fe2 8099 0ae2 8098 ......../.......\n+0000b150: 2be2 8099 0ae2 8098 2de2 8099 0ae2 8098 +.......-.......\n+0000b160: 7468 656e e280 9920 2020 6c6f 7765 7374 then... lowest\n+0000b170: 2028 6c65 6173 7420 7469 6768 746c 7920 (least tightly \n+0000b180: 6269 6e64 696e 6729 0a0a 416c 6c20 6f70 binding)..All op\n+0000b190: 6572 6174 696f 6e73 2061 7265 206c 6566 erations are lef\n+0000b1a0: 742d 6173 736f 6369 6174 6976 6520 6578 t-associative ex\n+0000b1b0: 6365 7074 2066 6f72 20e2 8098 5ee2 8099 cept for ...^...\n+0000b1c0: 2e20 2050 6172 656e 7468 6573 6573 20e2 . Parentheses .\n+0000b1d0: 8098 2820 29e2 8099 0a61 7265 2075 7365 ..( )....are use\n+0000b1e0: 6420 666f 7220 6772 6f75 7069 6e67 2074 d for grouping t\n+0000b1f0: 6f20 6f76 6572 7269 6465 2070 7265 6365 o override prece\n+0000b200: 6465 6e63 6520 696e 2074 6865 2075 7375 dence in the usu\n+0000b210: 616c 2077 6179 2e0a 0a20 2020 4173 2079 al way... As y\n+0000b220: 6f75 2063 616e 2073 6565 2c20 7468 6520 ou can see, the \n+0000b230: 646f 7420 6f70 6572 6174 6f72 20e2 8098 dot operator ...\n+0000b240: 2ee2 8099 2069 7320 7573 7561 6c6c 7920 .... is usually \n+0000b250: 6120 7379 6e6f 6e79 6d20 666f 720a 7275 a synonym for.ru\n+0000b260: 6e2d 6f66 2d74 6865 2d6d 696c 6c20 6d75 n-of-the-mill mu\n+0000b270: 6c74 6970 6c69 6361 7469 6f6e 2c20 e280 ltiplication, ..\n+0000b280: 982a e280 992e 2020 5468 6520 6d65 616e .*.... The mean\n+0000b290: 696e 6773 2064 6966 6665 7220 6f6e 6c79 ings differ only\n+0000b2a0: 2066 6f72 0a76 6563 746f 7220 6f70 6572 for.vector oper\n+0000b2b0: 616e 6473 2e20 2054 6865 20e2 8098 7468 ands. The ...th\n+0000b2c0: 656e e280 9920 6f70 6572 6174 6f72 206d en... operator m\n+0000b2d0: 6572 656c 7920 7265 7665 7273 6573 2074 erely reverses t\n+0000b2e0: 6865 206f 7065 7261 6e64 206f 7264 6572 he operand order\n+0000b2f0: 0a77 6974 6820 7265 7370 6563 7420 746f .with respect to\n+0000b300: 206e 6f72 6d61 6c20 6d75 6c74 6970 6c69 normal multipli\n+0000b310: 6361 7469 6f6e 20e2 8098 2ae2 8099 2e20 cation ...*.... \n+0000b320: 2054 6865 2069 6e74 656e 7420 6865 7265 The intent here\n+0000b330: 2069 7320 746f 206d 616b 650a 636f 6d70 is to make.comp\n+0000b340: 6f73 6974 696f 6e73 2072 6561 6420 6d6f ositions read mo\n+0000b350: 7265 206e 6174 7572 616c 6c79 2e20 2054 re naturally. T\n+0000b360: 6865 2063 6f64 650a 2020 2020 2028 312c he code. (1,\n+0000b370: 322c 3329 2074 6865 6e20 7363 616c 6528 2,3) then scale(\n+0000b380: 3229 2074 6865 6e20 726f 7461 7465 2833 2) then rotate(3\n+0000b390: 3029 2074 6865 6e20 7472 616e 736c 6174 0) then translat\n+0000b3a0: 6528 5b31 2c33 2c30 5d29 0a65 7870 7265 e([1,3,0]).expre\n+0000b3b0: 7373 6573 2061 2073 6572 6965 7320 6f66 sses a series of\n+0000b3c0: 2073 7563 6365 7373 6976 6520 6d6f 6469 successive modi\n+0000b3d0: 6669 6361 7469 6f6e 7320 746f 2074 6865 fications to the\n+0000b3e0: 2070 6f69 6e74 2c20 7768 6572 6561 7320 point, whereas \n+0000b3f0: 7468 650a 6571 7569 7661 6c65 6e74 2066 the.equivalent f\n+0000b400: 6f72 6d0a 2020 2020 2074 7261 6e73 6c61 orm. transla\n+0000b410: 7465 285b 312c 332c 305d 2920 2a20 726f te([1,3,0]) * ro\n+0000b420: 7461 7465 2833 3029 202a 2073 6361 6c65 tate(30) * scale\n+0000b430: 2832 2920 2a20 2831 2c32 2c33 290a 7769 (2) * (1,2,3).wi\n+0000b440: 6c6c 2062 6520 696e 7475 6974 6976 6520 ll be intuitive \n+0000b450: 6f6e 6c79 2074 6f20 6d61 7468 656d 6174 only to mathemat\n+0000b460: 6963 6961 6e73 2028 616e 6420 7065 7268 icians (and perh\n+0000b470: 6170 7320 4172 6162 6963 206c 616e 6775 aps Arabic langu\n+0000b480: 6167 650a 7265 6164 6572 7329 2e0a 0a1f age.readers)....\n+0000b490: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+0000b4a0: 666f 2c20 204e 6f64 653a 2055 6e61 7279 fo, Node: Unary\n+0000b4b0: 2066 6f72 6d73 2c20 2050 7265 763a 2054 forms, Prev: T\n+0000b4c0: 776f 2d6f 7065 7261 6e64 2028 6269 6e61 wo-operand (bina\n+0000b4d0: 7279 2920 666f 726d 732c 2020 5570 3a20 ry) forms, Up: \n+0000b4e0: 4172 6974 686d 6574 6963 0a0a 332e 312e Arithmetic..3.1.\n+0000b4f0: 342e 3220 556e 6172 7920 666f 726d 730a 4.2 Unary forms.\n+0000b500: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n+0000b510: 2e2e 2e0a 0a55 6e61 7279 206f 7220 6f6e .....Unary or on\n+0000b520: 652d 6f70 6572 616e 6420 666f 726d 7320 e-operand forms \n+0000b530: 6172 6520 7375 6d6d 6172 697a 6564 2069 are summarized i\n+0000b540: 6e20 7468 6520 666f 6c6c 6f77 696e 6720 n the following \n+0000b550: 7461 626c 652c 2077 6865 7265 0ae2 8098 table, where....\n+0000b560: 58e2 8099 2073 7461 6e64 7320 666f 7220 X... stands for \n+0000b570: 7468 6520 6f70 6572 616e 642e 0a4f 7020 the operand..Op \n+0000b580: 2020 2020 2020 2020 2020 2020 4f70 6572 Oper\n+0000b590: 616e 6420 2020 2020 5265 7375 6c74 2020 and Result \n+0000b5a0: 2020 2020 4465 7363 7269 7074 696f 6e0a Description.\n+0000b5b0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000b5c0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000b5d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000b5e0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000b5f0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-0000b600: 2d2d 2d2d 2d2d 0ae2 8098 2d58 e280 9920 ------....-X... \n-0000b610: 2020 2020 2020 2020 2020 7363 616c 6172 scalar\n-0000b620: 2020 2020 2020 7363 616c 6172 2020 2020 scalar \n-0000b630: 2020 556e 6172 7920 7363 616c 6172 206e Unary scalar n\n-0000b640: 6567 6174 696f 6e2e 0ae2 8098 2d58 e280 egation.....-X..\n-0000b650: 9920 2020 2020 2020 2020 2020 7665 6374 . vect\n-0000b660: 6f72 2020 2020 2020 7665 6374 6f72 2020 or vector \n-0000b670: 2020 2020 556e 6172 7920 7665 6374 6f72 Unary vector\n-0000b680: 206e 6567 6174 696f 6e2e 0ae2 8098 7c58 negation.....|X\n-0000b690: 7ce2 8099 2020 2020 2020 2020 2020 7665 |... ve\n-0000b6a0: 6374 6f72 2020 2020 2020 7363 616c 6172 ctor scalar\n-0000b6b0: 2020 2020 2020 5665 6374 6f72 206c 656e Vector len\n-0000b6c0: 6774 682e 0ae2 8098 756e 6974 2858 29e2 gth.....unit(X).\n-0000b6d0: 8099 2020 2020 2020 7665 6374 6f72 2020 .. vector \n-0000b6e0: 2020 2020 7665 6374 6f72 2020 2020 2020 vector \n-0000b6f0: 556e 6974 2076 6563 746f 7220 7769 7468 Unit vector with\n-0000b700: 2073 616d 6520 6469 7265 6374 696f 6e2e same direction.\n-0000b710: 0ae2 8098 7371 7274 2858 29e2 8099 2020 ....sqrt(X)... \n-0000b720: 2020 2020 7363 616c 6172 2020 2020 2020 scalar \n-0000b730: 7363 616c 6172 2020 2020 2020 5363 616c scalar Scal\n-0000b740: 6172 2073 7175 6172 6520 726f 6f74 2e0a ar square root..\n-0000b750: e280 9873 696e 2858 29e2 8099 2020 2020 ...sin(X)... \n-0000b760: 2020 2073 6361 6c61 7220 2020 2020 2073 scalar s\n-0000b770: 6361 6c61 7220 2020 2020 2054 7269 676f calar Trigo\n-0000b780: 6e6f 6d65 7472 6963 2073 696e 6520 28e2 nometric sine (.\n-0000b790: 8098 58e2 8099 2069 6e20 6465 6772 6565 ..X... in degree\n-0000b7a0: 7329 2e0a e280 9863 6f73 2858 29e2 8099 s).....cos(X)...\n-0000b7b0: 2020 2020 2020 2073 6361 6c61 7220 2020 scalar \n-0000b7c0: 2020 2073 6361 6c61 7220 2020 2020 2054 scalar T\n-0000b7d0: 7269 676f 6e6f 6d65 7472 6963 2063 6f73 rigonometric cos\n-0000b7e0: 696e 6520 28e2 8098 58e2 8099 2069 6e20 ine (...X... in \n-0000b7f0: 6465 6772 6565 7329 2e0a e280 9861 7369 degrees).....asi\n-0000b800: 6e28 5829 e280 9920 2020 2020 2073 6361 n(X)... sca\n-0000b810: 6c61 7220 2020 2020 2073 6361 6c61 7220 lar scalar \n-0000b820: 2020 2020 2049 6e76 6572 7365 2073 696e Inverse sin\n-0000b830: 6520 28e2 8098 58e2 8099 2069 6e20 6465 e (...X... in de\n-0000b840: 6772 6565 7329 2e0a e280 9861 636f 7328 grees).....acos(\n-0000b850: 5829 e280 9920 2020 2020 2073 6361 6c61 X)... scala\n-0000b860: 7220 2020 2020 2073 6361 6c61 7220 2020 r scalar \n-0000b870: 2020 2049 6e76 6572 7365 2063 6f73 696e Inverse cosin\n-0000b880: 6520 28e2 8098 58e2 8099 2069 6e20 6465 e (...X... in de\n-0000b890: 6772 6565 7329 2e0a e280 9861 7461 6e32 grees).....atan2\n-0000b8a0: 2858 2c59 29e2 8099 2020 2073 6361 6c61 (X,Y)... scala\n-0000b8b0: 7220 2020 2020 2073 6361 6c61 7220 2020 r scalar \n-0000b8c0: 2020 2050 6f6c 6172 2061 6e67 6c65 2069 Polar angle i\n-0000b8d0: 6e20 6465 6772 6565 7320 6f66 2076 6563 n degrees of vec\n-0000b8e0: 746f 7220 5b58 2c59 5d2e 0ae2 8098 696e tor [X,Y].....in\n-0000b8f0: 7665 7273 6528 5829 e280 9920 2020 7472 verse(X)... tr\n-0000b900: 616e 7366 6f72 6d20 2020 7472 616e 7366 ansform transf\n-0000b910: 6f72 6d20 2020 496e 7665 7273 6520 7472 orm Inverse tr\n-0000b920: 616e 7366 6f72 6d2e 0a0a 4572 726f 7273 ansform...Errors\n-0000b930: 2061 7265 2072 6570 6f72 7465 6420 7768 are reported wh\n-0000b940: 656e 20e2 8098 7c58 7ce2 8099 2c20 e280 en ...|X|..., ..\n-0000b950: 9875 6e69 74e2 8099 2c20 e280 9861 7369 .unit..., ...asi\n-0000b960: 6ee2 8099 2c20 e280 9861 636f 73e2 8099 n..., ...acos...\n-0000b970: 2c20 e280 9873 7172 74e2 8099 2c20 e280 , ...sqrt..., ..\n-0000b980: 9861 7461 6e32 e280 992c 0a61 6e64 20e2 .atan2...,.and .\n-0000b990: 8098 696e 7665 7273 65e2 8099 2066 6169 ..inverse... fai\n-0000b9a0: 6c20 6475 6520 746f 206f 7065 7261 6e64 l due to operand\n-0000b9b0: 7320 6f75 7473 6964 6520 7468 6569 7220 s outside their \n-0000b9c0: 7265 7370 6563 7469 7665 2064 6f6d 6169 respective domai\n-0000b9d0: 6e73 2e0a 0a1f 0a46 696c 653a 2073 6b65 ns.....File: ske\n-0000b9e0: 7463 682e 696e 666f 2c20 204e 6f64 653a tch.info, Node:\n-0000b9f0: 204f 7074 696f 6e73 2c20 2050 7265 763a Options, Prev:\n-0000ba00: 2041 7269 7468 6d65 7469 632c 2020 5570 Arithmetic, Up\n-0000ba10: 3a20 4c61 6e67 7561 6765 2062 6173 6963 : Language basic\n-0000ba20: 730a 0a33 2e31 2e35 204f 7074 696f 6e73 s..3.1.5 Options\n-0000ba30: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a .-------------..\n-0000ba40: 2a53 796e 7461 783a 2a0a 2020 2020 205b *Syntax:*. [\n-0000ba50: 4b45 5931 3d56 414c 312c 4b45 5932 3d56 KEY1=VAL1,KEY2=V\n-0000ba60: 414c 322c 2e2e 2e5d 0a4f 7074 696f 6e73 AL2,...].Options\n-0000ba70: 2061 7265 2075 7365 6420 746f 2073 7065 are used to spe\n-0000ba80: 6369 6679 2064 6574 6169 6c73 206f 6620 cify details of \n-0000ba90: 7468 6520 6170 7065 6172 616e 6365 206f the appearance o\n-0000baa0: 6620 6472 6177 6162 6c65 732e 2020 4173 f drawables. As\n-0000bab0: 0a73 686f 776e 2061 626f 7665 2c20 7468 .shown above, th\n-0000bac0: 6579 2061 7265 2067 6976 656e 2061 7320 ey are given as \n-0000bad0: 636f 6d6d 612d 7365 7061 7261 7465 6420 comma-separated \n-0000bae0: 6b65 792d 7661 6c75 6520 7061 6972 732e key-value pairs.\n-0000baf0: 0a0a 2a20 4d65 6e75 3a0a 0a2a 2050 5354 ..* Menu:..* PST\n-0000bb00: 7269 636b 7320 6f70 7469 6f6e 733a 3a20 ricks options:: \n-0000bb10: 2020 2020 2020 2020 2020 204f 7074 696f Optio\n-0000bb20: 6e73 2069 6e68 6572 6974 6564 2066 726f ns inherited fro\n-0000bb30: 6d20 e280 9850 5354 7269 636b 73e2 8099 m ...PSTricks...\n-0000bb40: 2e0a 2a20 5469 6b5a 2f50 4746 206f 7074 ..* TikZ/PGF opt\n-0000bb50: 696f 6e73 3a3a 2020 2020 2020 2020 2020 ions:: \n-0000bb60: 2020 4f70 7469 6f6e 7320 696e 6865 7269 Options inheri\n-0000bb70: 7465 6420 6672 6f6d 20e2 8098 5469 6b5a ted from ...TikZ\n-0000bb80: 2f50 4746 e280 992e 0a2a 2044 6f74 7320 /PGF.....* Dots \n-0000bb90: 696e 2054 696b 5a2f 5047 463a 3a20 2020 in TikZ/PGF:: \n-0000bba0: 2020 2020 2020 2020 2053 6b65 7463 6820 Sketch \n-0000bbb0: 7573 6573 20e2 8098 5469 6b5a 2f50 4746 uses ...TikZ/PGF\n-0000bbc0: e280 9920 6369 7263 6c65 7320 666f 7220 ... circles for \n-0000bbd0: 646f 7473 2e0a 2a20 5469 6b5a 2f50 4746 dots..* TikZ/PGF\n-0000bbe0: 2075 7365 722d 6465 6669 6e65 6420 7374 user-defined st\n-0000bbf0: 796c 6573 3a3a 2020 5375 7070 6f72 7420 yles:: Support \n-0000bc00: 666f 7220 e280 9854 696b 5a2f 5047 46e2 for ...TikZ/PGF.\n-0000bc10: 8099 206e 616d 6564 2c20 7573 6572 2d64 .. named, user-d\n-0000bc20: 6566 696e 6564 2073 7479 6c65 732e 0a2a efined styles..*\n-0000bc30: 2054 7261 6e73 7061 7265 6e63 793a 3a20 Transparency:: \n-0000bc40: 2020 2020 2020 2020 2020 2020 2020 2053 S\n-0000bc50: 6565 2d74 6872 6f75 6768 2070 6f6c 7967 ee-through polyg\n-0000bc60: 6f6e 732e 0a2a 2049 6e74 6572 6e61 6c20 ons..* Internal \n-0000bc70: 6f70 7469 6f6e 733a 3a20 2020 2020 2020 options:: \n-0000bc80: 2020 2020 204f 7074 696f 6e73 2075 7365 Options use\n-0000bc90: 6420 6279 20e2 8098 736b 6574 6368 e280 d by ...sketch..\n-0000bca0: 992e 0a0a 1f0a 4669 6c65 3a20 736b 6574 ......File: sket\n-0000bcb0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n-0000bcc0: 5053 5472 6963 6b73 206f 7074 696f 6e73 PSTricks options\n-0000bcd0: 2c20 204e 6578 743a 2054 696b 5a2f 5047 , Next: TikZ/PG\n-0000bce0: 4620 6f70 7469 6f6e 732c 2020 5072 6576 F options, Prev\n-0000bcf0: 3a20 4f70 7469 6f6e 732c 2020 5570 3a20 : Options, Up: \n-0000bd00: 4f70 7469 6f6e 730a 0a33 2e31 2e35 2e31 Options..3.1.5.1\n-0000bd10: 20e2 8098 5053 5472 6963 6b73 e280 9920 ...PSTricks... \n-0000bd20: 6f70 7469 6f6e 730a 2e2e 2e2e 2e2e 2e2e options.........\n+0000b600: 2d2d 2d2d 0ae2 8098 2d58 e280 9920 2020 ----....-X... \n+0000b610: 2020 2020 2020 2020 7363 616c 6172 2020 scalar \n+0000b620: 2020 2020 7363 616c 6172 2020 2020 2020 scalar \n+0000b630: 556e 6172 7920 7363 616c 6172 206e 6567 Unary scalar neg\n+0000b640: 6174 696f 6e2e 0ae2 8098 2d58 e280 9920 ation.....-X... \n+0000b650: 2020 2020 2020 2020 2020 7665 6374 6f72 vector\n+0000b660: 2020 2020 2020 7665 6374 6f72 2020 2020 vector \n+0000b670: 2020 556e 6172 7920 7665 6374 6f72 206e Unary vector n\n+0000b680: 6567 6174 696f 6e2e 0ae2 8098 7c58 7ce2 egation.....|X|.\n+0000b690: 8099 2020 2020 2020 2020 2020 7665 6374 .. vect\n+0000b6a0: 6f72 2020 2020 2020 7363 616c 6172 2020 or scalar \n+0000b6b0: 2020 2020 5665 6374 6f72 206c 656e 6774 Vector lengt\n+0000b6c0: 682e 0ae2 8098 756e 6974 2858 29e2 8099 h.....unit(X)...\n+0000b6d0: 2020 2020 2020 7665 6374 6f72 2020 2020 vector \n+0000b6e0: 2020 7665 6374 6f72 2020 2020 2020 556e vector Un\n+0000b6f0: 6974 2076 6563 746f 7220 7769 7468 2073 it vector with s\n+0000b700: 616d 6520 6469 7265 6374 696f 6e2e 0ae2 ame direction...\n+0000b710: 8098 7371 7274 2858 29e2 8099 2020 2020 ..sqrt(X)... \n+0000b720: 2020 7363 616c 6172 2020 2020 2020 7363 scalar sc\n+0000b730: 616c 6172 2020 2020 2020 5363 616c 6172 alar Scalar\n+0000b740: 2073 7175 6172 6520 726f 6f74 2e0a e280 square root....\n+0000b750: 9873 696e 2858 29e2 8099 2020 2020 2020 .sin(X)... \n+0000b760: 2073 6361 6c61 7220 2020 2020 2073 6361 scalar sca\n+0000b770: 6c61 7220 2020 2020 2054 7269 676f 6e6f lar Trigono\n+0000b780: 6d65 7472 6963 2073 696e 6520 28e2 8098 metric sine (...\n+0000b790: 58e2 8099 2069 6e20 6465 6772 6565 7329 X... in degrees)\n+0000b7a0: 2e0a e280 9863 6f73 2858 29e2 8099 2020 .....cos(X)... \n+0000b7b0: 2020 2020 2073 6361 6c61 7220 2020 2020 scalar \n+0000b7c0: 2073 6361 6c61 7220 2020 2020 2054 7269 scalar Tri\n+0000b7d0: 676f 6e6f 6d65 7472 6963 2063 6f73 696e gonometric cosin\n+0000b7e0: 6520 28e2 8098 58e2 8099 2069 6e20 6465 e (...X... in de\n+0000b7f0: 6772 6565 7329 2e0a e280 9861 7369 6e28 grees).....asin(\n+0000b800: 5829 e280 9920 2020 2020 2073 6361 6c61 X)... scala\n+0000b810: 7220 2020 2020 2073 6361 6c61 7220 2020 r scalar \n+0000b820: 2020 2049 6e76 6572 7365 2073 696e 6520 Inverse sine \n+0000b830: 28e2 8098 58e2 8099 2069 6e20 6465 6772 (...X... in degr\n+0000b840: 6565 7329 2e0a e280 9861 636f 7328 5829 ees).....acos(X)\n+0000b850: e280 9920 2020 2020 2073 6361 6c61 7220 ... scalar \n+0000b860: 2020 2020 2073 6361 6c61 7220 2020 2020 scalar \n+0000b870: 2049 6e76 6572 7365 2063 6f73 696e 6520 Inverse cosine \n+0000b880: 28e2 8098 58e2 8099 2069 6e20 6465 6772 (...X... in degr\n+0000b890: 6565 7329 2e0a e280 9861 7461 6e32 2858 ees).....atan2(X\n+0000b8a0: 2c59 29e2 8099 2020 2073 6361 6c61 7220 ,Y)... scalar \n+0000b8b0: 2020 2020 2073 6361 6c61 7220 2020 2020 scalar \n+0000b8c0: 2050 6f6c 6172 2061 6e67 6c65 2069 6e20 Polar angle in \n+0000b8d0: 6465 6772 6565 7320 6f66 2076 6563 746f degrees of vecto\n+0000b8e0: 7220 5b58 2c59 5d2e 0ae2 8098 696e 7665 r [X,Y].....inve\n+0000b8f0: 7273 6528 5829 e280 9920 2020 7472 616e rse(X)... tran\n+0000b900: 7366 6f72 6d20 2020 7472 616e 7366 6f72 sform transfor\n+0000b910: 6d20 2020 496e 7665 7273 6520 7472 616e m Inverse tran\n+0000b920: 7366 6f72 6d2e 0a0a 4572 726f 7273 2061 sform...Errors a\n+0000b930: 7265 2072 6570 6f72 7465 6420 7768 656e re reported when\n+0000b940: 20e2 8098 7c58 7ce2 8099 2c20 e280 9875 ...|X|..., ...u\n+0000b950: 6e69 74e2 8099 2c20 e280 9861 7369 6ee2 nit..., ...asin.\n+0000b960: 8099 2c20 e280 9861 636f 73e2 8099 2c20 .., ...acos..., \n+0000b970: e280 9873 7172 74e2 8099 2c20 e280 9861 ...sqrt..., ...a\n+0000b980: 7461 6e32 e280 992c 0a61 6e64 20e2 8098 tan2...,.and ...\n+0000b990: 696e 7665 7273 65e2 8099 2066 6169 6c20 inverse... fail \n+0000b9a0: 6475 6520 746f 206f 7065 7261 6e64 7320 due to operands \n+0000b9b0: 6f75 7473 6964 6520 7468 6569 7220 7265 outside their re\n+0000b9c0: 7370 6563 7469 7665 2064 6f6d 6169 6e73 spective domains\n+0000b9d0: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n+0000b9e0: 682e 696e 666f 2c20 204e 6f64 653a 204f h.info, Node: O\n+0000b9f0: 7074 696f 6e73 2c20 2050 7265 763a 2041 ptions, Prev: A\n+0000ba00: 7269 7468 6d65 7469 632c 2020 5570 3a20 rithmetic, Up: \n+0000ba10: 4c61 6e67 7561 6765 2062 6173 6963 730a Language basics.\n+0000ba20: 0a33 2e31 2e35 204f 7074 696f 6e73 0a2d .3.1.5 Options.-\n+0000ba30: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 ------------..*S\n+0000ba40: 796e 7461 783a 2a0a 2020 2020 205b 4b45 yntax:*. [KE\n+0000ba50: 5931 3d56 414c 312c 4b45 5932 3d56 414c Y1=VAL1,KEY2=VAL\n+0000ba60: 322c 2e2e 2e5d 0a4f 7074 696f 6e73 2061 2,...].Options a\n+0000ba70: 7265 2075 7365 6420 746f 2073 7065 6369 re used to speci\n+0000ba80: 6679 2064 6574 6169 6c73 206f 6620 7468 fy details of th\n+0000ba90: 6520 6170 7065 6172 616e 6365 206f 6620 e appearance of \n+0000baa0: 6472 6177 6162 6c65 732e 2020 4173 0a73 drawables. As.s\n+0000bab0: 686f 776e 2061 626f 7665 2c20 7468 6579 hown above, they\n+0000bac0: 2061 7265 2067 6976 656e 2061 7320 636f are given as co\n+0000bad0: 6d6d 612d 7365 7061 7261 7465 6420 6b65 mma-separated ke\n+0000bae0: 792d 7661 6c75 6520 7061 6972 732e 0a0a y-value pairs...\n+0000baf0: 2a20 4d65 6e75 3a0a 0a2a 2050 5354 7269 * Menu:..* PSTri\n+0000bb00: 636b 7320 6f70 7469 6f6e 733a 3a20 2020 cks options:: \n+0000bb10: 2020 2020 2020 2020 204f 7074 696f 6e73 Options\n+0000bb20: 2069 6e68 6572 6974 6564 2066 726f 6d20 inherited from \n+0000bb30: e280 9850 5354 7269 636b 73e2 8099 2e0a ...PSTricks.....\n+0000bb40: 2a20 5469 6b5a 2f50 4746 206f 7074 696f * TikZ/PGF optio\n+0000bb50: 6e73 3a3a 2020 2020 2020 2020 2020 2020 ns:: \n+0000bb60: 4f70 7469 6f6e 7320 696e 6865 7269 7465 Options inherite\n+0000bb70: 6420 6672 6f6d 20e2 8098 5469 6b5a 2f50 d from ...TikZ/P\n+0000bb80: 4746 e280 992e 0a2a 2044 6f74 7320 696e GF.....* Dots in\n+0000bb90: 2054 696b 5a2f 5047 463a 3a20 2020 2020 TikZ/PGF:: \n+0000bba0: 2020 2020 2020 2053 6b65 7463 6820 7573 Sketch us\n+0000bbb0: 6573 20e2 8098 5469 6b5a 2f50 4746 e280 es ...TikZ/PGF..\n+0000bbc0: 9920 6369 7263 6c65 7320 666f 7220 646f . circles for do\n+0000bbd0: 7473 2e0a 2a20 5469 6b5a 2f50 4746 2075 ts..* TikZ/PGF u\n+0000bbe0: 7365 722d 6465 6669 6e65 6420 7374 796c ser-defined styl\n+0000bbf0: 6573 3a3a 2020 5375 7070 6f72 7420 666f es:: Support fo\n+0000bc00: 7220 e280 9854 696b 5a2f 5047 46e2 8099 r ...TikZ/PGF...\n+0000bc10: 206e 616d 6564 2c20 7573 6572 2d64 6566 named, user-def\n+0000bc20: 696e 6564 2073 7479 6c65 732e 0a2a 2054 ined styles..* T\n+0000bc30: 7261 6e73 7061 7265 6e63 793a 3a20 2020 ransparency:: \n+0000bc40: 2020 2020 2020 2020 2020 2020 2053 6565 See\n+0000bc50: 2d74 6872 6f75 6768 2070 6f6c 7967 6f6e -through polygon\n+0000bc60: 732e 0a2a 2049 6e74 6572 6e61 6c20 6f70 s..* Internal op\n+0000bc70: 7469 6f6e 733a 3a20 2020 2020 2020 2020 tions:: \n+0000bc80: 2020 204f 7074 696f 6e73 2075 7365 6420 Options used \n+0000bc90: 6279 20e2 8098 736b 6574 6368 e280 992e by ...sketch....\n+0000bca0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n+0000bcb0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5053 .info, Node: PS\n+0000bcc0: 5472 6963 6b73 206f 7074 696f 6e73 2c20 Tricks options, \n+0000bcd0: 204e 6578 743a 2054 696b 5a2f 5047 4620 Next: TikZ/PGF \n+0000bce0: 6f70 7469 6f6e 732c 2020 5072 6576 3a20 options, Prev: \n+0000bcf0: 4f70 7469 6f6e 732c 2020 5570 3a20 4f70 Options, Up: Op\n+0000bd00: 7469 6f6e 730a 0a33 2e31 2e35 2e31 20e2 tions..3.1.5.1 .\n+0000bd10: 8098 5053 5472 6963 6b73 e280 9920 6f70 ..PSTricks... op\n+0000bd20: 7469 6f6e 730a 2e2e 2e2e 2e2e 2e2e 2e2e tions...........\n 0000bd30: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000bd40: 2e2e 0a0a 5768 656e 20e2 8098 6c61 6e67 ....When ...lang\n-0000bd50: 7561 6765 2070 7374 7269 636b 73e2 8099 uage pstricks...\n-0000bd60: 2069 7320 7365 6c65 6374 6564 2028 7468 is selected (th\n-0000bd70: 6520 6465 6661 756c 7429 2c20 7065 726d e default), perm\n-0000bd80: 6973 7369 626c 650a 6b65 792d 7661 6c75 issible.key-valu\n-0000bd90: 6520 7061 6972 7320 696e 636c 7564 6520 e pairs include \n-0000bda0: 616c 6c20 7468 6f73 6520 666f 7220 7369 all those for si\n-0000bdb0: 6d69 6c61 7220 e280 9850 5354 7269 636b milar ...PSTrick\n-0000bdc0: 73e2 8099 206f 626a 6563 7473 2e20 2046 s... objects. F\n-0000bdd0: 6f72 0a65 7861 6d70 6c65 2c20 6120 706f or.example, a po\n-0000bde0: 6c79 676f 6e20 6d69 6768 7420 6861 7665 lygon might have\n-0000bdf0: 2074 6865 206f 7074 696f 6e73 0a20 205b the options. [\n-0000be00: 6c69 6e65 7769 6474 683d 3170 742c 6c69 linewidth=1pt,li\n-0000be10: 6e65 636f 6c6f 723d 626c 7565 2c66 696c necolor=blue,fil\n-0000be20: 6c63 6f6c 6f72 3d63 7961 6e5d 0ae2 8098 lcolor=cyan]....\n-0000be30: 536b 6574 6368 e280 9920 6d65 7265 6c79 Sketch... merely\n-0000be40: 2070 6173 7365 7320 7468 6573 6520 6f6e passes these on\n-0000be50: 2074 6f20 e280 9850 5354 7269 636b 73e2 to ...PSTricks.\n-0000be60: 8099 2077 6974 686f 7574 2063 6865 636b .. without check\n-0000be70: 696e 6720 6f72 0a6d 6f64 6966 6963 6174 ing or.modificat\n-0000be80: 696f 6e2e 2020 4f70 7469 6f6e 206c 6973 ion. Option lis\n-0000be90: 7473 2061 7265 2061 6c77 6179 7320 6f70 ts are always op\n-0000bea0: 7469 6f6e 616c 2e20 2041 206d 6973 7369 tional. A missi\n-0000beb0: 6e67 206f 7074 696f 6e73 206c 6973 740a ng options list.\n-0000bec0: 6973 2065 7175 6976 616c 656e 7420 746f is equivalent to\n-0000bed0: 2061 6e20 656d 7074 7920 6f6e 6520 e280 an empty one ..\n-0000bee0: 985b 5de2 8099 2e0a 0a20 2020 5768 656e .[]...... When\n-0000bef0: 2061 20e2 8098 706f 6c79 676f 6ee2 8099 a ...polygon...\n-0000bf00: 2068 6173 206f 7074 696f 6e73 2066 6f72 has options for\n-0000bf10: 2062 6f74 6820 6974 7320 6661 6365 2061 both its face a\n-0000bf20: 6e64 2069 7473 2065 6467 6573 2c20 616e nd its edges, an\n-0000bf30: 6420 7468 650a 706f 6c79 676f 6e20 6973 d the.polygon is\n-0000bf40: 2073 706c 6974 2062 7920 7468 6520 6869 split by the hi\n-0000bf50: 6464 656e 2073 7572 6661 6365 2061 6c67 dden surface alg\n-0000bf60: 6f72 6974 686d 2c20 e280 9873 6b65 7463 orithm, ...sketc\n-0000bf70: 68e2 8099 206d 7573 7420 636f 7079 2074 h... must copy t\n-0000bf80: 6865 0a65 6467 6520 6f70 7469 6f6e 7320 he.edge options \n-0000bf90: 746f 20e2 8098 7073 6c69 6e65 e280 9973 to ...psline...s\n-0000bfa0: 2066 6f72 2074 6865 2065 6467 6520 7365 for the edge se\n-0000bfb0: 676d 656e 7473 2061 6e64 2074 6865 2066 gments and the f\n-0000bfc0: 6163 6520 6f70 7469 6f6e 7320 746f 0ae2 ace options to..\n-0000bfd0: 8098 7073 706f 6c79 676f 6ee2 8099 732e ..pspolygon...s.\n-0000bfe0: 2020 4f70 7469 6f6e 7320 6b6e 6f77 6e20 Options known \n-0000bff0: 746f 20e2 8098 736b 6574 6368 e280 9920 to ...sketch... \n-0000c000: 666f 7220 7075 7270 6f73 6573 206f 6620 for purposes of \n-0000c010: 7468 6973 2073 706c 6974 7469 6e67 0a6f this splitting.o\n-0000c020: 7065 7261 7469 6f6e 2069 6e63 6c75 6465 peration include\n-0000c030: 20e2 8098 6172 726f 7773 e280 992c 20e2 ...arrows..., .\n-0000c040: 8098 6461 7368 e280 992c 20e2 8098 646f ..dash..., ...do\n-0000c050: 7473 6570 e280 992c 20e2 8098 6669 6c6c tsep..., ...fill\n-0000c060: 636f 6c6f 72e2 8099 2c20 e280 9866 696c color..., ...fil\n-0000c070: 6c73 7479 6c65 e280 992c 0ae2 8098 6c69 lstyle...,....li\n-0000c080: 6e65 636f 6c6f 72e2 8099 2c20 e280 986c necolor..., ...l\n-0000c090: 696e 6573 7479 6c65 e280 992c 20e2 8098 inestyle..., ...\n-0000c0a0: 6c69 6e65 7769 6474 68e2 8099 2c20 e280 linewidth..., ..\n-0000c0b0: 986f 7061 6369 7479 e280 992c 20e2 8098 .opacity..., ...\n-0000c0c0: 7368 6f77 706f 696e 7473 e280 992c 0ae2 showpoints...,..\n-0000c0d0: 8098 7374 726f 6b65 6f70 6163 6974 79e2 ..strokeopacity.\n-0000c0e0: 8099 2c20 616e 6420 e280 9874 7261 6e73 .., and ...trans\n-0000c0f0: 7061 6c70 6861 e280 992e 0a0a 1f0a 4669 palpha........Fi\n-0000c100: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n-0000c110: 2020 4e6f 6465 3a20 5469 6b5a 2f50 4746 Node: TikZ/PGF\n-0000c120: 206f 7074 696f 6e73 2c20 204e 6578 743a options, Next:\n-0000c130: 2044 6f74 7320 696e 2054 696b 5a2f 5047 Dots in TikZ/PG\n-0000c140: 462c 2020 5072 6576 3a20 5053 5472 6963 F, Prev: PSTric\n-0000c150: 6b73 206f 7074 696f 6e73 2c20 2055 703a ks options, Up:\n-0000c160: 204f 7074 696f 6e73 0a0a 332e 312e 352e Options..3.1.5.\n-0000c170: 3220 e280 9854 696b 5a2f 5047 46e2 8099 2 ...TikZ/PGF...\n-0000c180: 206f 7074 696f 6e73 0a2e 2e2e 2e2e 2e2e options........\n+0000bd40: 0a0a 5768 656e 20e2 8098 6c61 6e67 7561 ..When ...langua\n+0000bd50: 6765 2070 7374 7269 636b 73e2 8099 2069 ge pstricks... i\n+0000bd60: 7320 7365 6c65 6374 6564 2028 7468 6520 s selected (the \n+0000bd70: 6465 6661 756c 7429 2c20 7065 726d 6973 default), permis\n+0000bd80: 7369 626c 650a 6b65 792d 7661 6c75 6520 sible.key-value \n+0000bd90: 7061 6972 7320 696e 636c 7564 6520 616c pairs include al\n+0000bda0: 6c20 7468 6f73 6520 666f 7220 7369 6d69 l those for simi\n+0000bdb0: 6c61 7220 e280 9850 5354 7269 636b 73e2 lar ...PSTricks.\n+0000bdc0: 8099 206f 626a 6563 7473 2e20 2046 6f72 .. objects. For\n+0000bdd0: 0a65 7861 6d70 6c65 2c20 6120 706f 6c79 .example, a poly\n+0000bde0: 676f 6e20 6d69 6768 7420 6861 7665 2074 gon might have t\n+0000bdf0: 6865 206f 7074 696f 6e73 0a20 205b 6c69 he options. [li\n+0000be00: 6e65 7769 6474 683d 3170 742c 6c69 6e65 newidth=1pt,line\n+0000be10: 636f 6c6f 723d 626c 7565 2c66 696c 6c63 color=blue,fillc\n+0000be20: 6f6c 6f72 3d63 7961 6e5d 0ae2 8098 536b olor=cyan]....Sk\n+0000be30: 6574 6368 e280 9920 6d65 7265 6c79 2070 etch... merely p\n+0000be40: 6173 7365 7320 7468 6573 6520 6f6e 2074 asses these on t\n+0000be50: 6f20 e280 9850 5354 7269 636b 73e2 8099 o ...PSTricks...\n+0000be60: 2077 6974 686f 7574 2063 6865 636b 696e without checkin\n+0000be70: 6720 6f72 0a6d 6f64 6966 6963 6174 696f g or.modificatio\n+0000be80: 6e2e 2020 4f70 7469 6f6e 206c 6973 7473 n. Option lists\n+0000be90: 2061 7265 2061 6c77 6179 7320 6f70 7469 are always opti\n+0000bea0: 6f6e 616c 2e20 2041 206d 6973 7369 6e67 onal. A missing\n+0000beb0: 206f 7074 696f 6e73 206c 6973 740a 6973 options list.is\n+0000bec0: 2065 7175 6976 616c 656e 7420 746f 2061 equivalent to a\n+0000bed0: 6e20 656d 7074 7920 6f6e 6520 e280 985b n empty one ...[\n+0000bee0: 5de2 8099 2e0a 0a20 2020 5768 656e 2061 ]...... When a\n+0000bef0: 20e2 8098 706f 6c79 676f 6ee2 8099 2068 ...polygon... h\n+0000bf00: 6173 206f 7074 696f 6e73 2066 6f72 2062 as options for b\n+0000bf10: 6f74 6820 6974 7320 6661 6365 2061 6e64 oth its face and\n+0000bf20: 2069 7473 2065 6467 6573 2c20 616e 6420 its edges, and \n+0000bf30: 7468 650a 706f 6c79 676f 6e20 6973 2073 the.polygon is s\n+0000bf40: 706c 6974 2062 7920 7468 6520 6869 6464 plit by the hidd\n+0000bf50: 656e 2073 7572 6661 6365 2061 6c67 6f72 en surface algor\n+0000bf60: 6974 686d 2c20 e280 9873 6b65 7463 68e2 ithm, ...sketch.\n+0000bf70: 8099 206d 7573 7420 636f 7079 2074 6865 .. must copy the\n+0000bf80: 0a65 6467 6520 6f70 7469 6f6e 7320 746f .edge options to\n+0000bf90: 20e2 8098 7073 6c69 6e65 e280 9973 2066 ...psline...s f\n+0000bfa0: 6f72 2074 6865 2065 6467 6520 7365 676d or the edge segm\n+0000bfb0: 656e 7473 2061 6e64 2074 6865 2066 6163 ents and the fac\n+0000bfc0: 6520 6f70 7469 6f6e 7320 746f 0ae2 8098 e options to....\n+0000bfd0: 7073 706f 6c79 676f 6ee2 8099 732e 2020 pspolygon...s. \n+0000bfe0: 4f70 7469 6f6e 7320 6b6e 6f77 6e20 746f Options known to\n+0000bff0: 20e2 8098 736b 6574 6368 e280 9920 666f ...sketch... fo\n+0000c000: 7220 7075 7270 6f73 6573 206f 6620 7468 r purposes of th\n+0000c010: 6973 2073 706c 6974 7469 6e67 0a6f 7065 is splitting.ope\n+0000c020: 7261 7469 6f6e 2069 6e63 6c75 6465 20e2 ration include .\n+0000c030: 8098 6172 726f 7773 e280 992c 20e2 8098 ..arrows..., ...\n+0000c040: 6461 7368 e280 992c 20e2 8098 646f 7473 dash..., ...dots\n+0000c050: 6570 e280 992c 20e2 8098 6669 6c6c 636f ep..., ...fillco\n+0000c060: 6c6f 72e2 8099 2c20 e280 9866 696c 6c73 lor..., ...fills\n+0000c070: 7479 6c65 e280 992c 0ae2 8098 6c69 6e65 tyle...,....line\n+0000c080: 636f 6c6f 72e2 8099 2c20 e280 986c 696e color..., ...lin\n+0000c090: 6573 7479 6c65 e280 992c 20e2 8098 6c69 estyle..., ...li\n+0000c0a0: 6e65 7769 6474 68e2 8099 2c20 e280 986f newidth..., ...o\n+0000c0b0: 7061 6369 7479 e280 992c 20e2 8098 7368 pacity..., ...sh\n+0000c0c0: 6f77 706f 696e 7473 e280 992c 0ae2 8098 owpoints...,....\n+0000c0d0: 7374 726f 6b65 6f70 6163 6974 79e2 8099 strokeopacity...\n+0000c0e0: 2c20 616e 6420 e280 9874 7261 6e73 7061 , and ...transpa\n+0000c0f0: 6c70 6861 e280 992e 0a0a 1f0a 4669 6c65 lpha........File\n+0000c100: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n+0000c110: 4e6f 6465 3a20 5469 6b5a 2f50 4746 206f Node: TikZ/PGF o\n+0000c120: 7074 696f 6e73 2c20 204e 6578 743a 2044 ptions, Next: D\n+0000c130: 6f74 7320 696e 2054 696b 5a2f 5047 462c ots in TikZ/PGF,\n+0000c140: 2020 5072 6576 3a20 5053 5472 6963 6b73 Prev: PSTricks\n+0000c150: 206f 7074 696f 6e73 2c20 2055 703a 204f options, Up: O\n+0000c160: 7074 696f 6e73 0a0a 332e 312e 352e 3220 ptions..3.1.5.2 \n+0000c170: e280 9854 696b 5a2f 5047 46e2 8099 206f ...TikZ/PGF... o\n+0000c180: 7074 696f 6e73 0a2e 2e2e 2e2e 2e2e 2e2e ptions..........\n 0000c190: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000c1a0: 2e2e 2e0a 0ae2 8098 5469 6b5a 2f50 4746 ........TikZ/PGF\n-0000c1b0: e280 9920 6f70 7469 6f6e 7320 6172 6520 ... options are \n-0000c1c0: 6861 6e64 6c65 6420 6d75 6368 2061 7320 handled much as \n-0000c1d0: 666f 7220 e280 9850 5354 7269 636b 73e2 for ...PSTricks.\n-0000c1e0: 8099 2e20 2054 686f 7567 680a e280 9854 ... Though....T\n-0000c1f0: 696b 5a2f 5047 46e2 8099 206f 6674 656e ikZ/PGF... often\n-0000c200: 2061 6c6c 6f77 7320 636f 6c6f 7273 2061 allows colors a\n-0000c210: 6e64 2073 7479 6c65 7320 746f 2062 6520 nd styles to be \n-0000c220: 6769 7665 6e20 7769 7468 6f75 740a 636f given without.co\n-0000c230: 7272 6573 706f 6e64 696e 6720 6b65 7973 rresponding keys\n-0000c240: 2c20 666f 7220 6578 616d 706c 652c 0a20 , for example,. \n-0000c250: 205c 6472 6177 5b72 6564 2c75 6c74 7261 \\draw[red,ultra\n-0000c260: 2074 6869 636b 5d28 302c 3029 2d2d 2831 thick](0,0)--(1\n-0000c270: 2c31 293b 0a74 6869 7320 6973 206e 6f74 ,1);.this is not\n-0000c280: 2070 6572 6d69 7474 6564 2069 6e20 e280 permitted in ..\n-0000c290: 9873 6b65 7463 68e2 8099 2e20 2054 6f20 .sketch.... To \n-0000c2a0: 6472 6177 2061 2072 6564 2c20 756c 7472 draw a red, ultr\n-0000c2b0: 612d 7468 6963 6b20 6c69 6e65 2069 6e0a a-thick line in.\n-0000c2c0: e280 9873 6b65 7463 68e2 8099 2c20 7468 ...sketch..., th\n-0000c2d0: 6520 666f 726d 2069 730a 2020 6c69 6e65 e form is. line\n-0000c2e0: 5b64 7261 773d 7265 642c 7374 796c 653d [draw=red,style=\n-0000c2f0: 756c 7472 6120 7468 6963 6b5d 2830 2c30 ultra thick](0,0\n-0000c300: 2928 312c 3129 0a0a 2020 204a 7573 7420 )(1,1).. Just \n-0000c310: 6173 2066 6f72 20e2 8098 5053 5472 6963 as for ...PSTric\n-0000c320: 6b73 e280 992c 2077 6865 6e20 6120 e280 ks..., when a ..\n-0000c330: 9870 6f6c 7967 6f6e e280 9920 6861 7320 .polygon... has \n-0000c340: 6f70 7469 6f6e 7320 666f 7220 626f 7468 options for both\n-0000c350: 2069 7473 0a66 6163 6520 616e 6420 6974 its.face and it\n-0000c360: 7320 6564 6765 732c 2061 6e64 2074 6865 s edges, and the\n-0000c370: 2070 6f6c 7967 6f6e 2069 7320 7370 6c69 polygon is spli\n-0000c380: 7420 6279 2074 6865 2068 6964 6465 6e20 t by the hidden \n-0000c390: 7375 7266 6163 650a 616c 676f 7269 7468 surface.algorith\n-0000c3a0: 6d2c 20e2 8098 736b 6574 6368 e280 9920 m, ...sketch... \n-0000c3b0: 6d75 7374 2063 6f70 7920 7468 6520 6564 must copy the ed\n-0000c3c0: 6765 206f 7074 696f 6e73 2074 6f20 e280 ge options to ..\n-0000c3d0: 9870 736c 696e 65e2 8099 7320 666f 7220 .psline...s for \n-0000c3e0: 7468 6520 6564 6765 0a73 6567 6d65 6e74 the edge.segment\n-0000c3f0: 7320 616e 6420 7468 6520 6661 6365 206f s and the face o\n-0000c400: 7074 696f 6e73 2074 6f20 e280 9870 7370 ptions to ...psp\n-0000c410: 6f6c 7967 6f6e e280 9973 2e20 20e2 8098 olygon...s. ...\n-0000c420: 5469 6b5a 2f50 4746 e280 9920 6f70 7469 TikZ/PGF... opti\n-0000c430: 6f6e 7320 6b6e 6f77 6e0a 746f 20e2 8098 ons known.to ...\n-0000c440: 736b 6574 6368 e280 9920 666f 7220 7075 sketch... for pu\n-0000c450: 7270 6f73 6573 206f 6620 7468 6973 2073 rposes of this s\n-0000c460: 706c 6974 7469 6e67 206f 7065 7261 7469 plitting operati\n-0000c470: 6f6e 2069 6e63 6c75 6465 20e2 8098 6172 on include ...ar\n-0000c480: 726f 7773 e280 992c 0ae2 8098 6361 70e2 rows...,....cap.\n-0000c490: 8099 2c20 e280 9863 6f6c 6f72 e280 992c .., ...color...,\n-0000c4a0: 20e2 8098 6461 7368 2070 6174 7465 726e ...dash pattern\n-0000c4b0: e280 992c 20e2 8098 6461 7368 2070 6861 ..., ...dash pha\n-0000c4c0: 7365 e280 992c 20e2 8098 646f 7562 6c65 se..., ...double\n-0000c4d0: e280 992c 20e2 8098 646f 7562 6c65 0a64 ..., ...double.d\n-0000c4e0: 6973 7461 6e63 65e2 8099 2c20 e280 9864 istance..., ...d\n-0000c4f0: 7261 77e2 8099 2c20 e280 9864 7261 7720 raw..., ...draw \n-0000c500: 6f70 6163 6974 79e2 8099 2c20 e280 9866 opacity..., ...f\n-0000c510: 696c 6ce2 8099 2c20 e280 9866 696c 6c20 ill..., ...fill \n-0000c520: 6f70 6163 6974 79e2 8099 2c20 e280 986a opacity..., ...j\n-0000c530: 6f69 6ee2 8099 2c20 e280 986c 696e 650a oin..., ...line.\n-0000c540: 7769 6474 68e2 8099 2c20 e280 986d 6974 width..., ...mit\n-0000c550: 6572 206c 696d 6974 e280 992c 20e2 8098 er limit..., ...\n-0000c560: 7061 7474 6572 6ee2 8099 2c20 e280 9870 pattern..., ...p\n-0000c570: 6174 7465 726e 2063 6f6c 6f72 e280 992c attern color...,\n-0000c580: 2061 6e64 20e2 8098 7374 796c 65e2 8099 and ...style...\n-0000c590: 2e0a 0a20 2020 5468 6520 e280 9873 7479 ... The ...sty\n-0000c5a0: 6c65 e280 9920 6f70 7469 6f6e 2063 616e le... option can\n-0000c5b0: 2063 6f6e 7461 696e 2062 6f74 6820 6661 contain both fa\n-0000c5c0: 6365 2061 6e64 2065 6467 6520 696e 666f ce and edge info\n-0000c5d0: 726d 6174 696f 6e2c 2073 6f0a e280 9873 rmation, so....s\n-0000c5e0: 6b65 7463 68e2 8099 206d 7573 7420 6368 ketch... must ch\n-0000c5f0: 6563 6b20 7468 6520 7374 796c 6520 7661 eck the style va\n-0000c600: 6c75 652e 2020 5661 6c75 6573 206b 6e6f lue. Values kno\n-0000c610: 776e 2074 6f20 e280 9873 6b65 7463 68e2 wn to ...sketch.\n-0000c620: 8099 2069 6e63 6c75 6465 0ae2 8098 6461 .. include....da\n-0000c630: 7368 6564 e280 992c 20e2 8098 6465 6e73 shed..., ...dens\n-0000c640: 656c 7920 6461 7368 6564 e280 992c 20e2 ely dashed..., .\n-0000c650: 8098 6465 6e73 656c 7920 646f 7474 6564 ..densely dotted\n-0000c660: e280 992c 20e2 8098 646f 7474 6564 e280 ..., ...dotted..\n-0000c670: 992c 20e2 8098 646f 7562 6c65 e280 992c ., ...double...,\n-0000c680: 0ae2 8098 6c6f 6f73 656c 7920 6461 7368 ....loosely dash\n-0000c690: 6564 e280 992c 20e2 8098 6c6f 6f73 656c ed..., ...loosel\n-0000c6a0: 7920 646f 7474 6564 e280 992c 20e2 8098 y dotted..., ...\n-0000c6b0: 6e65 6172 6c79 206f 7061 7175 65e2 8099 nearly opaque...\n-0000c6c0: 2c20 e280 986e 6561 726c 790a 7472 616e , ...nearly.tran\n-0000c6d0: 7370 6172 656e 74e2 8099 2c20 e280 9873 sparent..., ...s\n-0000c6e0: 656d 6974 6869 636b e280 992c 20e2 8098 emithick..., ...\n-0000c6f0: 7365 6d69 7472 616e 7370 6172 656e 74e2 semitransparent.\n-0000c700: 8099 2c20 e280 9873 6f6c 6964 e280 992c .., ...solid...,\n-0000c710: 20e2 8098 7468 6963 6be2 8099 2c20 e280 ...thick..., ..\n-0000c720: 9874 6869 6ee2 8099 2c0a e280 9874 7261 .thin...,....tra\n-0000c730: 6e73 7061 7265 6e74 e280 992c 20e2 8098 nsparent..., ...\n-0000c740: 756c 7472 6120 6e65 6172 6c79 2074 7261 ultra nearly tra\n-0000c750: 6e73 7061 7265 6e74 e280 992c 20e2 8098 nsparent..., ...\n-0000c760: 756c 7472 6120 7468 6963 6be2 8099 2c20 ultra thick..., \n-0000c770: e280 9875 6c74 7261 2074 6869 6ee2 8099 ...ultra thin...\n-0000c780: 2c0a e280 9876 6572 7920 6e65 6172 6c79 ,....very nearly\n-0000c790: 2074 7261 6e73 7061 7265 6e74 e280 992c transparent...,\n-0000c7a0: 20e2 8098 7665 7279 2074 6869 636b e280 ...very thick..\n-0000c7b0: 992c 2061 6e64 20e2 8098 7665 7279 2074 ., and ...very t\n-0000c7c0: 6869 6ee2 8099 2e0a 0a1f 0a46 696c 653a hin........File:\n-0000c7d0: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-0000c7e0: 6f64 653a 2044 6f74 7320 696e 2054 696b ode: Dots in Tik\n-0000c7f0: 5a2f 5047 462c 2020 4e65 7874 3a20 5469 Z/PGF, Next: Ti\n-0000c800: 6b5a 2f50 4746 2075 7365 722d 6465 6669 kZ/PGF user-defi\n-0000c810: 6e65 6420 7374 796c 6573 2c20 2050 7265 ned styles, Pre\n-0000c820: 763a 2054 696b 5a2f 5047 4620 6f70 7469 v: TikZ/PGF opti\n-0000c830: 6f6e 732c 2020 5570 3a20 4f70 7469 6f6e ons, Up: Option\n-0000c840: 730a 0a33 2e31 2e35 2e33 2044 6f74 7320 s..3.1.5.3 Dots \n-0000c850: 696e 20e2 8098 5469 6b5a 2f50 4746 e280 in ...TikZ/PGF..\n-0000c860: 990a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000c870: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a e280 ................\n-0000c880: 9854 696b 5a2f 5047 46e2 8099 2064 6f65 .TikZ/PGF... doe\n-0000c890: 7320 6e6f 7420 6861 7665 2061 20e2 8098 s not have a ...\n-0000c8a0: 646f 7473 e280 9920 636f 6d6d 616e 6420 dots... command \n-0000c8b0: 6173 2064 6f65 7320 5053 5472 6963 6b73 as does PSTricks\n-0000c8c0: 2e20 2049 6e73 7465 6164 2c0a e280 9853 . Instead,....S\n-0000c8d0: 6b65 7463 68e2 8099 2065 6d69 7473 2064 ketch... emits d\n-0000c8e0: 6f74 7320 6173 20e2 8098 6669 6c6c 6472 ots as ...filldr\n-0000c8f0: 6177 e280 9920 6369 7263 6c65 732e 2020 aw... circles. \n-0000c900: 5468 6520 6469 616d 6574 6572 206d 6179 The diameter may\n-0000c910: 2062 6520 7365 740a 7573 696e 6720 7468 be set.using th\n-0000c920: 6520 6f70 7469 6f6e 20e2 8098 646f 7473 e option ...dots\n-0000c930: 697a 65e2 8099 2062 6f72 726f 7765 6420 ize... borrowed \n-0000c940: 6672 6f6d 2050 5354 7269 636b 732e 2020 from PSTricks. \n-0000c950: 5468 6520 e280 9864 6f74 7369 7a65 e280 The ...dotsize..\n-0000c960: 9920 6f70 7469 6f6e 0a77 696c 6c20 6265 . option.will be\n-0000c970: 2072 656d 6f76 6564 2066 726f 6d20 7468 removed from th\n-0000c980: 6520 6f70 7469 6f6e 206c 6973 7420 696e e option list in\n-0000c990: 2074 6865 206f 7574 7075 7420 e280 9866 the output ...f\n-0000c9a0: 696c 6c64 7261 77e2 8099 2063 6f6d 6d61 illdraw... comma\n-0000c9b0: 6e64 2e0a 4f74 6865 7220 6f70 7469 6f6e nd..Other option\n-0000c9c0: 7320 776f 726b 2069 6e20 7468 6520 6578 s work in the ex\n-0000c9d0: 7065 6374 6564 2077 6179 2e20 2046 6f72 pected way. For\n-0000c9e0: 2065 7861 6d70 6c65 2c20 e280 9866 696c example, ...fil\n-0000c9f0: 6ce2 8099 2073 6574 7320 6669 6c6c 0a63 l... sets fill.c\n-0000ca00: 6f6c 6f72 2061 6e64 20e2 8098 636f 6c6f olor and ...colo\n-0000ca10: 72e2 8099 2073 6574 7320 6c69 6e65 2063 r... sets line c\n-0000ca20: 6f6c 6f72 206f 6620 7468 6520 6369 7263 olor of the circ\n-0000ca30: 6c65 732e 0a0a 1f0a 4669 6c65 3a20 736b les.....File: sk\n-0000ca40: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-0000ca50: 3a20 5469 6b5a 2f50 4746 2075 7365 722d : TikZ/PGF user-\n-0000ca60: 6465 6669 6e65 6420 7374 796c 6573 2c20 defined styles, \n-0000ca70: 204e 6578 743a 2054 7261 6e73 7061 7265 Next: Transpare\n-0000ca80: 6e63 792c 2020 5072 6576 3a20 446f 7473 ncy, Prev: Dots\n-0000ca90: 2069 6e20 5469 6b5a 2f50 4746 2c20 2055 in TikZ/PGF, U\n-0000caa0: 703a 204f 7074 696f 6e73 0a0a 332e 312e p: Options..3.1.\n-0000cab0: 352e 3420 e280 9854 696b 5a2f 5047 46e2 5.4 ...TikZ/PGF.\n-0000cac0: 8099 2075 7365 722d 6465 6669 6e65 6420 .. user-defined \n-0000cad0: 7374 796c 6573 0a2e 2e2e 2e2e 2e2e 2e2e styles..........\n+0000c1a0: 2e0a 0ae2 8098 5469 6b5a 2f50 4746 e280 ......TikZ/PGF..\n+0000c1b0: 9920 6f70 7469 6f6e 7320 6172 6520 6861 . options are ha\n+0000c1c0: 6e64 6c65 6420 6d75 6368 2061 7320 666f ndled much as fo\n+0000c1d0: 7220 e280 9850 5354 7269 636b 73e2 8099 r ...PSTricks...\n+0000c1e0: 2e20 2054 686f 7567 680a e280 9854 696b . Though....Tik\n+0000c1f0: 5a2f 5047 46e2 8099 206f 6674 656e 2061 Z/PGF... often a\n+0000c200: 6c6c 6f77 7320 636f 6c6f 7273 2061 6e64 llows colors and\n+0000c210: 2073 7479 6c65 7320 746f 2062 6520 6769 styles to be gi\n+0000c220: 7665 6e20 7769 7468 6f75 740a 636f 7272 ven without.corr\n+0000c230: 6573 706f 6e64 696e 6720 6b65 7973 2c20 esponding keys, \n+0000c240: 666f 7220 6578 616d 706c 652c 0a20 205c for example,. \\\n+0000c250: 6472 6177 5b72 6564 2c75 6c74 7261 2074 draw[red,ultra t\n+0000c260: 6869 636b 5d28 302c 3029 2d2d 2831 2c31 hick](0,0)--(1,1\n+0000c270: 293b 0a74 6869 7320 6973 206e 6f74 2070 );.this is not p\n+0000c280: 6572 6d69 7474 6564 2069 6e20 e280 9873 ermitted in ...s\n+0000c290: 6b65 7463 68e2 8099 2e20 2054 6f20 6472 ketch.... To dr\n+0000c2a0: 6177 2061 2072 6564 2c20 756c 7472 612d aw a red, ultra-\n+0000c2b0: 7468 6963 6b20 6c69 6e65 2069 6e0a e280 thick line in...\n+0000c2c0: 9873 6b65 7463 68e2 8099 2c20 7468 6520 .sketch..., the \n+0000c2d0: 666f 726d 2069 730a 2020 6c69 6e65 5b64 form is. line[d\n+0000c2e0: 7261 773d 7265 642c 7374 796c 653d 756c raw=red,style=ul\n+0000c2f0: 7472 6120 7468 6963 6b5d 2830 2c30 2928 tra thick](0,0)(\n+0000c300: 312c 3129 0a0a 2020 204a 7573 7420 6173 1,1).. Just as\n+0000c310: 2066 6f72 20e2 8098 5053 5472 6963 6b73 for ...PSTricks\n+0000c320: e280 992c 2077 6865 6e20 6120 e280 9870 ..., when a ...p\n+0000c330: 6f6c 7967 6f6e e280 9920 6861 7320 6f70 olygon... has op\n+0000c340: 7469 6f6e 7320 666f 7220 626f 7468 2069 tions for both i\n+0000c350: 7473 0a66 6163 6520 616e 6420 6974 7320 ts.face and its \n+0000c360: 6564 6765 732c 2061 6e64 2074 6865 2070 edges, and the p\n+0000c370: 6f6c 7967 6f6e 2069 7320 7370 6c69 7420 olygon is split \n+0000c380: 6279 2074 6865 2068 6964 6465 6e20 7375 by the hidden su\n+0000c390: 7266 6163 650a 616c 676f 7269 7468 6d2c rface.algorithm,\n+0000c3a0: 20e2 8098 736b 6574 6368 e280 9920 6d75 ...sketch... mu\n+0000c3b0: 7374 2063 6f70 7920 7468 6520 6564 6765 st copy the edge\n+0000c3c0: 206f 7074 696f 6e73 2074 6f20 e280 9870 options to ...p\n+0000c3d0: 736c 696e 65e2 8099 7320 666f 7220 7468 sline...s for th\n+0000c3e0: 6520 6564 6765 0a73 6567 6d65 6e74 7320 e edge.segments \n+0000c3f0: 616e 6420 7468 6520 6661 6365 206f 7074 and the face opt\n+0000c400: 696f 6e73 2074 6f20 e280 9870 7370 6f6c ions to ...pspol\n+0000c410: 7967 6f6e e280 9973 2e20 20e2 8098 5469 ygon...s. ...Ti\n+0000c420: 6b5a 2f50 4746 e280 9920 6f70 7469 6f6e kZ/PGF... option\n+0000c430: 7320 6b6e 6f77 6e0a 746f 20e2 8098 736b s known.to ...sk\n+0000c440: 6574 6368 e280 9920 666f 7220 7075 7270 etch... for purp\n+0000c450: 6f73 6573 206f 6620 7468 6973 2073 706c oses of this spl\n+0000c460: 6974 7469 6e67 206f 7065 7261 7469 6f6e itting operation\n+0000c470: 2069 6e63 6c75 6465 20e2 8098 6172 726f include ...arro\n+0000c480: 7773 e280 992c 0ae2 8098 6361 70e2 8099 ws...,....cap...\n+0000c490: 2c20 e280 9863 6f6c 6f72 e280 992c 20e2 , ...color..., .\n+0000c4a0: 8098 6461 7368 2070 6174 7465 726e e280 ..dash pattern..\n+0000c4b0: 992c 20e2 8098 6461 7368 2070 6861 7365 ., ...dash phase\n+0000c4c0: e280 992c 20e2 8098 646f 7562 6c65 e280 ..., ...double..\n+0000c4d0: 992c 20e2 8098 646f 7562 6c65 0a64 6973 ., ...double.dis\n+0000c4e0: 7461 6e63 65e2 8099 2c20 e280 9864 7261 tance..., ...dra\n+0000c4f0: 77e2 8099 2c20 e280 9864 7261 7720 6f70 w..., ...draw op\n+0000c500: 6163 6974 79e2 8099 2c20 e280 9866 696c acity..., ...fil\n+0000c510: 6ce2 8099 2c20 e280 9866 696c 6c20 6f70 l..., ...fill op\n+0000c520: 6163 6974 79e2 8099 2c20 e280 986a 6f69 acity..., ...joi\n+0000c530: 6ee2 8099 2c20 e280 986c 696e 650a 7769 n..., ...line.wi\n+0000c540: 6474 68e2 8099 2c20 e280 986d 6974 6572 dth..., ...miter\n+0000c550: 206c 696d 6974 e280 992c 20e2 8098 7061 limit..., ...pa\n+0000c560: 7474 6572 6ee2 8099 2c20 e280 9870 6174 ttern..., ...pat\n+0000c570: 7465 726e 2063 6f6c 6f72 e280 992c 2061 tern color..., a\n+0000c580: 6e64 20e2 8098 7374 796c 65e2 8099 2e0a nd ...style.....\n+0000c590: 0a20 2020 5468 6520 e280 9873 7479 6c65 . The ...style\n+0000c5a0: e280 9920 6f70 7469 6f6e 2063 616e 2063 ... option can c\n+0000c5b0: 6f6e 7461 696e 2062 6f74 6820 6661 6365 ontain both face\n+0000c5c0: 2061 6e64 2065 6467 6520 696e 666f 726d and edge inform\n+0000c5d0: 6174 696f 6e2c 2073 6f0a e280 9873 6b65 ation, so....ske\n+0000c5e0: 7463 68e2 8099 206d 7573 7420 6368 6563 tch... must chec\n+0000c5f0: 6b20 7468 6520 7374 796c 6520 7661 6c75 k the style valu\n+0000c600: 652e 2020 5661 6c75 6573 206b 6e6f 776e e. Values known\n+0000c610: 2074 6f20 e280 9873 6b65 7463 68e2 8099 to ...sketch...\n+0000c620: 2069 6e63 6c75 6465 0ae2 8098 6461 7368 include....dash\n+0000c630: 6564 e280 992c 20e2 8098 6465 6e73 656c ed..., ...densel\n+0000c640: 7920 6461 7368 6564 e280 992c 20e2 8098 y dashed..., ...\n+0000c650: 6465 6e73 656c 7920 646f 7474 6564 e280 densely dotted..\n+0000c660: 992c 20e2 8098 646f 7474 6564 e280 992c ., ...dotted...,\n+0000c670: 20e2 8098 646f 7562 6c65 e280 992c 0ae2 ...double...,..\n+0000c680: 8098 6c6f 6f73 656c 7920 6461 7368 6564 ..loosely dashed\n+0000c690: e280 992c 20e2 8098 6c6f 6f73 656c 7920 ..., ...loosely \n+0000c6a0: 646f 7474 6564 e280 992c 20e2 8098 6e65 dotted..., ...ne\n+0000c6b0: 6172 6c79 206f 7061 7175 65e2 8099 2c20 arly opaque..., \n+0000c6c0: e280 986e 6561 726c 790a 7472 616e 7370 ...nearly.transp\n+0000c6d0: 6172 656e 74e2 8099 2c20 e280 9873 656d arent..., ...sem\n+0000c6e0: 6974 6869 636b e280 992c 20e2 8098 7365 ithick..., ...se\n+0000c6f0: 6d69 7472 616e 7370 6172 656e 74e2 8099 mitransparent...\n+0000c700: 2c20 e280 9873 6f6c 6964 e280 992c 20e2 , ...solid..., .\n+0000c710: 8098 7468 6963 6be2 8099 2c20 e280 9874 ..thick..., ...t\n+0000c720: 6869 6ee2 8099 2c0a e280 9874 7261 6e73 hin...,....trans\n+0000c730: 7061 7265 6e74 e280 992c 20e2 8098 756c parent..., ...ul\n+0000c740: 7472 6120 6e65 6172 6c79 2074 7261 6e73 tra nearly trans\n+0000c750: 7061 7265 6e74 e280 992c 20e2 8098 756c parent..., ...ul\n+0000c760: 7472 6120 7468 6963 6be2 8099 2c20 e280 tra thick..., ..\n+0000c770: 9875 6c74 7261 2074 6869 6ee2 8099 2c0a .ultra thin...,.\n+0000c780: e280 9876 6572 7920 6e65 6172 6c79 2074 ...very nearly t\n+0000c790: 7261 6e73 7061 7265 6e74 e280 992c 20e2 ransparent..., .\n+0000c7a0: 8098 7665 7279 2074 6869 636b e280 992c ..very thick...,\n+0000c7b0: 2061 6e64 20e2 8098 7665 7279 2074 6869 and ...very thi\n+0000c7c0: 6ee2 8099 2e0a 0a1f 0a46 696c 653a 2073 n........File: s\n+0000c7d0: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+0000c7e0: 653a 2044 6f74 7320 696e 2054 696b 5a2f e: Dots in TikZ/\n+0000c7f0: 5047 462c 2020 4e65 7874 3a20 5469 6b5a PGF, Next: TikZ\n+0000c800: 2f50 4746 2075 7365 722d 6465 6669 6e65 /PGF user-define\n+0000c810: 6420 7374 796c 6573 2c20 2050 7265 763a d styles, Prev:\n+0000c820: 2054 696b 5a2f 5047 4620 6f70 7469 6f6e TikZ/PGF option\n+0000c830: 732c 2020 5570 3a20 4f70 7469 6f6e 730a s, Up: Options.\n+0000c840: 0a33 2e31 2e35 2e33 2044 6f74 7320 696e .3.1.5.3 Dots in\n+0000c850: 20e2 8098 5469 6b5a 2f50 4746 e280 990a ...TikZ/PGF....\n+0000c860: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n+0000c870: 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a e280 9854 ...............T\n+0000c880: 696b 5a2f 5047 46e2 8099 2064 6f65 7320 ikZ/PGF... does \n+0000c890: 6e6f 7420 6861 7665 2061 20e2 8098 646f not have a ...do\n+0000c8a0: 7473 e280 9920 636f 6d6d 616e 6420 6173 ts... command as\n+0000c8b0: 2064 6f65 7320 5053 5472 6963 6b73 2e20 does PSTricks. \n+0000c8c0: 2049 6e73 7465 6164 2c0a e280 9853 6b65 Instead,....Ske\n+0000c8d0: 7463 68e2 8099 2065 6d69 7473 2064 6f74 tch... emits dot\n+0000c8e0: 7320 6173 20e2 8098 6669 6c6c 6472 6177 s as ...filldraw\n+0000c8f0: e280 9920 6369 7263 6c65 732e 2020 5468 ... circles. Th\n+0000c900: 6520 6469 616d 6574 6572 206d 6179 2062 e diameter may b\n+0000c910: 6520 7365 740a 7573 696e 6720 7468 6520 e set.using the \n+0000c920: 6f70 7469 6f6e 20e2 8098 646f 7473 697a option ...dotsiz\n+0000c930: 65e2 8099 2062 6f72 726f 7765 6420 6672 e... borrowed fr\n+0000c940: 6f6d 2050 5354 7269 636b 732e 2020 5468 om PSTricks. Th\n+0000c950: 6520 e280 9864 6f74 7369 7a65 e280 9920 e ...dotsize... \n+0000c960: 6f70 7469 6f6e 0a77 696c 6c20 6265 2072 option.will be r\n+0000c970: 656d 6f76 6564 2066 726f 6d20 7468 6520 emoved from the \n+0000c980: 6f70 7469 6f6e 206c 6973 7420 696e 2074 option list in t\n+0000c990: 6865 206f 7574 7075 7420 e280 9866 696c he output ...fil\n+0000c9a0: 6c64 7261 77e2 8099 2063 6f6d 6d61 6e64 ldraw... command\n+0000c9b0: 2e0a 4f74 6865 7220 6f70 7469 6f6e 7320 ..Other options \n+0000c9c0: 776f 726b 2069 6e20 7468 6520 6578 7065 work in the expe\n+0000c9d0: 6374 6564 2077 6179 2e20 2046 6f72 2065 cted way. For e\n+0000c9e0: 7861 6d70 6c65 2c20 e280 9866 696c 6ce2 xample, ...fill.\n+0000c9f0: 8099 2073 6574 7320 6669 6c6c 0a63 6f6c .. sets fill.col\n+0000ca00: 6f72 2061 6e64 20e2 8098 636f 6c6f 72e2 or and ...color.\n+0000ca10: 8099 2073 6574 7320 6c69 6e65 2063 6f6c .. sets line col\n+0000ca20: 6f72 206f 6620 7468 6520 6369 7263 6c65 or of the circle\n+0000ca30: 732e 0a0a 1f0a 4669 6c65 3a20 736b 6574 s.....File: sket\n+0000ca40: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n+0000ca50: 5469 6b5a 2f50 4746 2075 7365 722d 6465 TikZ/PGF user-de\n+0000ca60: 6669 6e65 6420 7374 796c 6573 2c20 204e fined styles, N\n+0000ca70: 6578 743a 2054 7261 6e73 7061 7265 6e63 ext: Transparenc\n+0000ca80: 792c 2020 5072 6576 3a20 446f 7473 2069 y, Prev: Dots i\n+0000ca90: 6e20 5469 6b5a 2f50 4746 2c20 2055 703a n TikZ/PGF, Up:\n+0000caa0: 204f 7074 696f 6e73 0a0a 332e 312e 352e Options..3.1.5.\n+0000cab0: 3420 e280 9854 696b 5a2f 5047 46e2 8099 4 ...TikZ/PGF...\n+0000cac0: 2075 7365 722d 6465 6669 6e65 6420 7374 user-defined st\n+0000cad0: 796c 6573 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e yles............\n 0000cae0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000caf0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0ae2 ................\n-0000cb00: 8098 5469 6b5a 2f50 4746 e280 9920 616c ..TikZ/PGF... al\n-0000cb10: 6c6f 7773 206e 616d 6564 2073 7479 6c65 lows named style\n-0000cb20: 7320 6465 6669 6e65 6420 6279 2074 6865 s defined by the\n-0000cb30: 2075 7365 722c 2066 6f72 2065 7861 6d70 user, for examp\n-0000cb40: 6c65 0a20 205c 7469 6b7a 7374 796c 657b le. \\tikzstyle{\n-0000cb50: 6d79 706f 6c79 676f 6e73 7479 6c65 7d20 mypolygonstyle} \n-0000cb60: 3d20 5b66 696c 6c3d 626c 7565 2132 302c = [fill=blue!20,\n-0000cb70: 6669 6c6c 206f 7061 6369 7479 3d30 2e38 fill opacity=0.8\n-0000cb80: 5d20 200a 2020 5c74 696b 7a73 7479 6c65 ] . \\tikzstyle\n-0000cb90: 7b6d 796c 696e 6573 7479 6c65 7d20 3d20 {mylinestyle} = \n-0000cba0: 5b72 6564 2132 302c 6461 7368 6564 5d0a [red!20,dashed].\n-0000cbb0: 5369 6e63 6520 e280 9873 6b65 7463 68e2 Since ...sketch.\n-0000cbc0: 8099 2068 6173 206e 6f20 696e 666f 726d .. has no inform\n-0000cbd0: 6174 696f 6e20 6f6e 2074 6865 2063 6f6e ation on the con\n-0000cbe0: 7465 6e74 7320 6f66 2073 7563 6820 7374 tents of such st\n-0000cbf0: 796c 6573 2c20 6974 0a6f 6d69 7473 2074 yles, it.omits t\n-0000cc00: 6865 6d20 656e 7469 7265 6c79 2066 726f hem entirely fro\n-0000cc10: 6d20 6c69 6e65 732c 2070 6f6c 7967 6f6e m lines, polygon\n-0000cc20: 732c 2061 6e64 2074 6865 6972 2065 6467 s, and their edg\n-0000cc30: 6573 2064 7572 696e 6720 6f70 7469 6f6e es during option\n-0000cc40: 0a73 706c 6974 7469 6e67 2e20 2046 6f72 .splitting. For\n-0000cc50: 2065 7861 6d70 6c65 2c0a 2020 706f 6c79 example,. poly\n-0000cc60: 676f 6e5b 7374 796c 653d 6d79 706f 6c79 gon[style=mypoly\n-0000cc70: 676f 6e73 7479 6c65 2c73 7479 6c65 3d74 gonstyle,style=t\n-0000cc80: 6869 636b 5d28 302c 302c 3129 2831 2c30 hick](0,0,1)(1,0\n-0000cc90: 2c30 2928 302c 312c 3029 0a20 206c 696e ,0)(0,1,0). lin\n-0000cca0: 655b 7374 796c 653d 6d79 6c69 6e65 7374 e[style=mylinest\n-0000ccb0: 796c 655d 282d 312c 2d31 2c2d 3129 2832 yle](-1,-1,-1)(2\n-0000ccc0: 2c32 2c32 290a 7072 6f64 7563 6573 2074 ,2,2).produces t\n-0000ccd0: 6865 20e2 8098 5469 6b5a e280 9920 6f75 he ...TikZ... ou\n-0000cce0: 7470 7574 0a20 205c 6472 6177 282d 312c tput. \\draw(-1,\n-0000ccf0: 2d31 292d 2d28 2e33 3333 2c2e 3333 3329 -1)--(.333,.333)\n-0000cd00: 3b0a 2020 5c66 696c 6c64 7261 775b 7468 ;. \\filldraw[th\n-0000cd10: 6963 6b2c 6669 6c6c 3d77 6869 7465 5d28 ick,fill=white](\n-0000cd20: 302c 3029 2d2d 2831 2c30 292d 2d28 302c 0,0)--(1,0)--(0,\n-0000cd30: 3129 2d2d 6379 636c 653b 0a20 205c 6472 1)--cycle;. \\dr\n-0000cd40: 6177 282e 3333 332c 2e33 3333 292d 2d28 aw(.333,.333)--(\n-0000cd50: 322c 3229 3b0a 4e6f 7465 2074 6861 7420 2,2);.Note that \n-0000cd60: 7468 6520 7573 6572 2d64 6566 696e 6564 the user-defined\n-0000cd70: 2073 7479 6c65 7320 6172 6520 6e6f 7420 styles are not \n-0000cd80: 7072 6573 656e 742e 2020 536b 6574 6368 present. Sketch\n-0000cd90: 2061 6c73 6f20 6973 7375 6573 0a77 6172 also issues.war\n-0000cda0: 6e69 6e67 733a 0a20 2077 6172 6e69 6e67 nings:. warning\n-0000cdb0: 2c20 756e 6b6e 6f77 6e20 706f 6c79 676f , unknown polygo\n-0000cdc0: 6e20 6f70 7469 6f6e 2073 7479 6c65 3d6d n option style=m\n-0000cdd0: 7970 6f6c 7967 6f6e 7374 796c 6520 7769 ypolygonstyle wi\n-0000cde0: 6c6c 2062 6520 6967 6e6f 7265 640a 2020 ll be ignored. \n-0000cdf0: 7761 726e 696e 672c 2075 6e6b 6e6f 776e warning, unknown\n-0000ce00: 206c 696e 6520 6f70 7469 6f6e 2073 7479 line option sty\n-0000ce10: 6c65 3d6d 796c 696e 6573 7479 6c65 2077 le=mylinestyle w\n-0000ce20: 696c 6c20 6265 2069 676e 6f72 6564 0a0a ill be ignored..\n-0000ce30: 2020 2054 6865 2072 656d 6564 7920 6973 The remedy is\n-0000ce40: 2074 6f20 7374 6174 6520 6578 706c 6963 to state explic\n-0000ce50: 6974 6c79 2077 6865 7468 6572 2061 2075 itly whether a u\n-0000ce60: 7365 722d 6465 6669 6e65 6420 7374 796c ser-defined styl\n-0000ce70: 6520 7368 6f75 6c64 0a62 6520 6174 7463 e should.be attc\n-0000ce80: 6865 6420 746f 2070 6f6c 7967 6f6e 7320 hed to polygons \n-0000ce90: 6f72 206c 696e 6573 2069 6e20 7468 6520 or lines in the \n-0000cea0: e280 9854 696b 5ae2 8099 206f 7574 7075 ...TikZ... outpu\n-0000ceb0: 7420 7573 696e 670a 5f70 7365 7564 6f2d t using._pseudo-\n-0000cec0: 6f70 7469 6f6e 735f 20e2 8098 6669 6c6c options_ ...fill\n-0000ced0: 2073 7479 6c65 e280 9920 616e 6420 e280 style... and ..\n-0000cee0: 986c 696e 6520 7374 796c 65e2 8099 2c0a .line style...,.\n-0000cef0: 2020 706f 6c79 676f 6e5b 6669 6c6c 2073 polygon[fill s\n-0000cf00: 7479 6c65 3d6d 7970 6f6c 7967 6f6e 7374 tyle=mypolygonst\n-0000cf10: 796c 652c 7374 796c 653d 7468 6963 6b5d yle,style=thick]\n-0000cf20: 2830 2c30 2c31 2928 312c 302c 3029 2830 (0,0,1)(1,0,0)(0\n-0000cf30: 2c31 2c30 290a 2020 6c69 6e65 5b6c 696e ,1,0). line[lin\n-0000cf40: 6520 7374 796c 653d 6d79 6c69 6e65 7374 e style=mylinest\n-0000cf50: 796c 655d 282d 312c 2d31 2c2d 3129 2832 yle](-1,-1,-1)(2\n-0000cf60: 2c32 2c32 290a 4e6f 772c 2074 6865 206f ,2,2).Now, the o\n-0000cf70: 7574 7075 7420 6973 0a20 205c 6472 6177 utput is. \\draw\n-0000cf80: 5b6d 796c 696e 6573 7479 6c65 5d28 2d31 [mylinestyle](-1\n-0000cf90: 2c2d 3129 2d2d 282e 3333 332c 2e33 3333 ,-1)--(.333,.333\n-0000cfa0: 293b 0a20 205c 6669 6c6c 6472 6177 5b6d );. \\filldraw[m\n-0000cfb0: 7970 6f6c 7967 6f6e 7374 796c 652c 7468 ypolygonstyle,th\n-0000cfc0: 6963 6b5d 2830 2c30 292d 2d28 312c 3029 ick](0,0)--(1,0)\n-0000cfd0: 2d2d 2830 2c31 292d 2d63 7963 6c65 3b0a --(0,1)--cycle;.\n-0000cfe0: 2020 5c64 7261 775b 6d79 6c69 6e65 7374 \\draw[mylinest\n-0000cff0: 796c 655d 282e 3333 332c 2e33 3333 292d yle](.333,.333)-\n-0000d000: 2d28 322c 3229 3b0a 0a20 2020 4120 7573 -(2,2);.. A us\n-0000d010: 6566 756c 2074 6563 686e 6971 7565 2069 eful technique i\n-0000d020: 7320 746f 2069 6e63 6c75 6465 2075 7365 s to include use\n-0000d030: 722d 6465 6669 6e65 6420 7374 796c 6520 r-defined style \n-0000d040: 6465 6669 6e69 7469 6f6e 7320 696e 0ae2 definitions in..\n-0000d050: 8098 736b 6574 6368 e280 9920 636f 6465 ..sketch... code\n-0000d060: 2061 7320 e280 9873 7065 6369 616c e280 as ...special..\n-0000d070: 9973 2077 6974 6820 6f70 7469 6f6e 20e2 .s with option .\n-0000d080: 8098 5b6c 6179 3d75 6e64 6572 5de2 8099 ..[lay=under]...\n-0000d090: 2074 6f20 656e 7375 7265 2074 6861 7420 to ensure that \n-0000d0a0: 7468 650a 7374 796c 6573 2061 7265 2065 the.styles are e\n-0000d0b0: 6d69 7474 6564 2066 6972 7374 2069 6e20 mitted first in \n-0000d0c0: 7468 6520 6f75 7470 7574 2c20 6265 666f the output, befo\n-0000d0d0: 7265 2061 6e79 2075 7365 7320 6f66 2074 re any uses of t\n-0000d0e0: 6865 2073 7479 6c65 0a6e 616d 6573 2e20 he style.names. \n-0000d0f0: 2028 3129 2020 466f 7220 6578 616d 706c (1) For exampl\n-0000d100: 652c 0a20 2073 7065 6369 616c 7c5c 7469 e,. special|\\ti\n-0000d110: 6b7a 7374 796c 657b 6d79 706f 6c79 676f kzstyle{mypolygo\n-0000d120: 6e73 7479 6c65 7d20 3d20 5b66 696c 6c3d nstyle} = [fill=\n-0000d130: 626c 7565 2132 302c 6669 6c6c 206f 7061 blue!20,fill opa\n-0000d140: 6369 7479 3d30 2e38 5d7c 5b6c 6179 3d75 city=0.8]|[lay=u\n-0000d150: 6e64 6572 5d0a 2020 7370 6563 6961 6c7c nder]. special|\n-0000d160: 5c74 696b 7a73 7479 6c65 7b6d 796c 696e \\tikzstyle{mylin\n-0000d170: 6573 7479 6c65 7d20 3d20 5b72 6564 2132 estyle} = [red!2\n-0000d180: 302c 6461 7368 6564 5d7c 5b6c 6179 3d75 0,dashed]|[lay=u\n-0000d190: 6e64 6572 5d0a 5468 6520 6175 7468 6f72 nder].The author\n-0000d1a0: 2069 7320 7265 7370 6f6e 7369 626c 6520 is responsible \n-0000d1b0: 666f 7220 7573 696e 6720 7468 6520 6b65 for using the ke\n-0000d1c0: 792c 20e2 8098 6c69 6e65 2073 7479 6c65 y, ...line style\n-0000d1d0: e280 9920 6f72 20e2 8098 6669 6c6c 0a73 ... or ...fill.s\n-0000d1e0: 7479 6c65 e280 992c 2074 6861 7420 6d61 tyle..., that ma\n-0000d1f0: 7463 6865 7320 7468 6520 636f 6e74 656e tches the conten\n-0000d200: 7420 6f66 2074 6865 2073 7479 6c65 2064 t of the style d\n-0000d210: 6566 696e 6974 696f 6e2e 0a0a 2020 202d efinition... -\n-0000d220: 2d2d 2d2d 2d2d 2d2d 2d20 466f 6f74 6e6f --------- Footno\n-0000d230: 7465 7320 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a tes ----------..\n-0000d240: 2020 2028 3129 2054 6869 7320 636c 6576 (1) This clev\n-0000d250: 6572 2074 7269 636b 2069 7320 6475 6520 er trick is due \n-0000d260: 746f 204b 6a65 6c6c 204d 6167 6e65 2046 to Kjell Magne F\n-0000d270: 6175 736b 652e 0a0a 1f0a 4669 6c65 3a20 auske.....File: \n-0000d280: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n-0000d290: 6465 3a20 5472 616e 7370 6172 656e 6379 de: Transparency\n-0000d2a0: 2c20 204e 6578 743a 2049 6e74 6572 6e61 , Next: Interna\n-0000d2b0: 6c20 6f70 7469 6f6e 732c 2020 5072 6576 l options, Prev\n-0000d2c0: 3a20 5469 6b5a 2f50 4746 2075 7365 722d : TikZ/PGF user-\n-0000d2d0: 6465 6669 6e65 6420 7374 796c 6573 2c20 defined styles, \n-0000d2e0: 2055 703a 204f 7074 696f 6e73 0a0a 332e Up: Options..3.\n-0000d2f0: 312e 352e 3520 5472 616e 7370 6172 656e 1.5.5 Transparen\n-0000d300: 6379 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e cy..............\n-0000d310: 2e2e 2e2e 2e2e 2e0a 0a42 6f74 6820 e280 .........Both ..\n-0000d320: 9850 5354 7269 636b 73e2 8099 2061 6e64 .PSTricks... and\n-0000d330: 20e2 8098 5469 6b5a 2f50 4746 e280 9920 ...TikZ/PGF... \n-0000d340: 7375 7070 6f72 7420 706f 6c79 676f 6e20 support polygon \n-0000d350: 6f70 7469 6f6e 7320 7468 6174 2068 6176 options that hav\n-0000d360: 6520 7468 650a 6566 6665 6374 206f 6620 e the.effect of \n-0000d370: 6d61 6b69 6e67 2074 6865 2070 6f6c 7967 making the polyg\n-0000d380: 6f6e 2061 7070 6561 7220 7472 616e 7370 on appear transp\n-0000d390: 6172 656e 742e 2020 466f 7220 e280 9850 arent. For ...P\n-0000d3a0: 5354 7269 636b 73e2 8099 2c0a 6b65 7977 STricks...,.keyw\n-0000d3b0: 6f72 6420 e280 9874 7261 6e73 7061 6c70 ord ...transpalp\n-0000d3c0: 6861 e280 9920 7761 7320 7573 6564 2064 ha... was used d\n-0000d3d0: 7572 696e 6720 696e 6974 6961 6c20 6465 uring initial de\n-0000d3e0: 7665 6c6f 706d 656e 7420 6f66 0a74 7261 velopment of.tra\n-0000d3f0: 6e73 7061 7265 6e63 7920 6665 6174 7572 nsparency featur\n-0000d400: 6573 2c20 616e 6420 e280 986f 7061 6369 es, and ...opaci\n-0000d410: 7479 e280 9920 7761 7320 6164 6f70 7465 ty... was adopte\n-0000d420: 6420 6c61 7465 722e 2020 e280 9853 6b65 d later. ...Ske\n-0000d430: 7463 68e2 8099 2068 6f6e 6f72 730a 626f tch... honors.bo\n-0000d440: 7468 2e20 20e2 8098 5469 6b5a 2f50 4746 th. ...TikZ/PGF\n-0000d450: e280 9920 7573 6573 20e2 8098 6f70 6163 ... uses ...opac\n-0000d460: 6974 79e2 8099 206f 6e6c 792e 2020 5768 ity... only. Wh\n-0000d470: 656e 2074 7261 6e73 7061 7265 6e74 2070 en transparent p\n-0000d480: 6f6c 7967 6f6e 7320 6172 6520 696e 0a74 olygons are in.t\n-0000d490: 6865 2066 6f72 6567 726f 756e 642c 206f he foreground, o\n-0000d4a0: 626a 6563 7473 2062 6568 696e 6420 7468 bjects behind th\n-0000d4b0: 656d 2028 6472 6177 6e20 6561 726c 6965 em (drawn earlie\n-0000d4c0: 7229 2061 7265 2076 6973 6962 6c65 2077 r) are visible w\n-0000d4d0: 6974 680a 636f 6c6f 7220 7375 6264 7565 ith.color subdue\n-0000d4e0: 6420 616e 6420 7469 6e74 6564 2e20 2054 d and tinted. T\n-0000d4f0: 6865 2068 6964 6465 6e20 7375 7266 6163 he hidden surfac\n-0000d500: 6520 616c 676f 7269 7468 6d20 6f66 20e2 e algorithm of .\n-0000d510: 8098 736b 6574 6368 e280 990a 776f 726b ..sketch....work\n-0000d520: 7320 7765 6c6c 2077 6974 6820 7375 6368 s well with such\n-0000d530: 2074 7261 6e73 7061 7265 6e74 2070 6f6c transparent pol\n-0000d540: 7967 6f6e 732e 0a0a 2020 204e 6f74 6520 ygons... Note \n-0000d550: 7468 6174 2063 756c 6c3d 6661 6c73 6520 that cull=false \n-0000d560: 6d75 7374 2062 6520 7573 6564 2066 6f72 must be used for\n-0000d570: 2072 6561 722d 6661 6369 6e67 2070 6f6c rear-facing pol\n-0000d580: 7967 6f6e 7320 746f 2062 650a 7669 7369 ygons to be.visi\n-0000d590: 626c 6520 7768 656e 2070 6f73 6974 696f ble when positio\n-0000d5a0: 6e65 6420 6265 6869 6e64 206f 7468 6572 ned behind other\n-0000d5b0: 2074 7261 6e73 7061 7265 6e74 2073 7572 transparent sur\n-0000d5c0: 6661 6365 732e 0a0a 1f0a 4669 6c65 3a20 faces.....File: \n-0000d5d0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n-0000d5e0: 6465 3a20 496e 7465 726e 616c 206f 7074 de: Internal opt\n-0000d5f0: 696f 6e73 2c20 2050 7265 763a 2054 7261 ions, Prev: Tra\n-0000d600: 6e73 7061 7265 6e63 792c 2020 5570 3a20 nsparency, Up: \n-0000d610: 4f70 7469 6f6e 730a 0a33 2e31 2e35 2e36 Options..3.1.5.6\n-0000d620: 2049 6e74 6572 6e61 6c20 6f70 7469 6f6e Internal option\n-0000d630: 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e s...............\n-0000d640: 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 5468 6572 ............Ther\n-0000d650: 6520 6172 6520 616c 736f 205f 696e 7465 e are also _inte\n-0000d660: 726e 616c 5f20 6f70 7469 6f6e 7320 7573 rnal_ options us\n-0000d670: 6564 206f 6e6c 7920 6279 20e2 8098 736b ed only by ...sk\n-0000d680: 6574 6368 e280 9920 616e 6420 6e6f 7420 etch... and not \n-0000d690: 7061 7373 6564 0a6f 6e20 746f 20e2 8098 passed.on to ...\n-0000d6a0: 5053 5472 6963 6b73 e280 992e 2020 5468 PSTricks.... Th\n-0000d6b0: 6573 6520 6172 6520 7375 6d6d 6172 697a ese are summariz\n-0000d6c0: 6564 2069 6e20 7468 6520 666f 6c6c 6f77 ed in the follow\n-0000d6d0: 696e 6720 7461 626c 652e 0a4b 6579 2020 ing table..Key \n-0000d6e0: 2020 2020 2050 6f73 7369 626c 6520 7661 Possible va\n-0000d6f0: 6c75 6573 2020 2020 2020 2020 2044 6573 lues Des\n-0000d700: 6372 6970 7469 6f6e 0a2d 2d2d 2d2d 2d2d cription.-------\n+0000caf0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0ae2 8098 ................\n+0000cb00: 5469 6b5a 2f50 4746 e280 9920 616c 6c6f TikZ/PGF... allo\n+0000cb10: 7773 206e 616d 6564 2073 7479 6c65 7320 ws named styles \n+0000cb20: 6465 6669 6e65 6420 6279 2074 6865 2075 defined by the u\n+0000cb30: 7365 722c 2066 6f72 2065 7861 6d70 6c65 ser, for example\n+0000cb40: 0a20 205c 7469 6b7a 7374 796c 657b 6d79 . \\tikzstyle{my\n+0000cb50: 706f 6c79 676f 6e73 7479 6c65 7d20 3d20 polygonstyle} = \n+0000cb60: 5b66 696c 6c3d 626c 7565 2132 302c 6669 [fill=blue!20,fi\n+0000cb70: 6c6c 206f 7061 6369 7479 3d30 2e38 5d20 ll opacity=0.8] \n+0000cb80: 200a 2020 5c74 696b 7a73 7479 6c65 7b6d . \\tikzstyle{m\n+0000cb90: 796c 696e 6573 7479 6c65 7d20 3d20 5b72 ylinestyle} = [r\n+0000cba0: 6564 2132 302c 6461 7368 6564 5d0a 5369 ed!20,dashed].Si\n+0000cbb0: 6e63 6520 e280 9873 6b65 7463 68e2 8099 nce ...sketch...\n+0000cbc0: 2068 6173 206e 6f20 696e 666f 726d 6174 has no informat\n+0000cbd0: 696f 6e20 6f6e 2074 6865 2063 6f6e 7465 ion on the conte\n+0000cbe0: 6e74 7320 6f66 2073 7563 6820 7374 796c nts of such styl\n+0000cbf0: 6573 2c20 6974 0a6f 6d69 7473 2074 6865 es, it.omits the\n+0000cc00: 6d20 656e 7469 7265 6c79 2066 726f 6d20 m entirely from \n+0000cc10: 6c69 6e65 732c 2070 6f6c 7967 6f6e 732c lines, polygons,\n+0000cc20: 2061 6e64 2074 6865 6972 2065 6467 6573 and their edges\n+0000cc30: 2064 7572 696e 6720 6f70 7469 6f6e 0a73 during option.s\n+0000cc40: 706c 6974 7469 6e67 2e20 2046 6f72 2065 plitting. 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A usef\n+0000d010: 756c 2074 6563 686e 6971 7565 2069 7320 ul technique is \n+0000d020: 746f 2069 6e63 6c75 6465 2075 7365 722d to include user-\n+0000d030: 6465 6669 6e65 6420 7374 796c 6520 6465 defined style de\n+0000d040: 6669 6e69 7469 6f6e 7320 696e 0ae2 8098 finitions in....\n+0000d050: 736b 6574 6368 e280 9920 636f 6465 2061 sketch... code a\n+0000d060: 7320 e280 9873 7065 6369 616c e280 9973 s ...special...s\n+0000d070: 2077 6974 6820 6f70 7469 6f6e 20e2 8098 with option ...\n+0000d080: 5b6c 6179 3d75 6e64 6572 5de2 8099 2074 [lay=under]... t\n+0000d090: 6f20 656e 7375 7265 2074 6861 7420 7468 o ensure that th\n+0000d0a0: 650a 7374 796c 6573 2061 7265 2065 6d69 e.styles are emi\n+0000d0b0: 7474 6564 2066 6972 7374 2069 6e20 7468 tted first in th\n+0000d0c0: 6520 6f75 7470 7574 2c20 6265 666f 7265 e output, before\n+0000d0d0: 2061 6e79 2075 7365 7320 6f66 2074 6865 any uses of the\n+0000d0e0: 2073 7479 6c65 0a6e 616d 6573 2e20 2028 style.names. (\n+0000d0f0: 3129 2020 466f 7220 6578 616d 706c 652c 1) For example,\n+0000d100: 0a20 2073 7065 6369 616c 7c5c 7469 6b7a . special|\\tikz\n+0000d110: 7374 796c 657b 6d79 706f 6c79 676f 6e73 style{mypolygons\n+0000d120: 7479 6c65 7d20 3d20 5b66 696c 6c3d 626c tyle} = [fill=bl\n+0000d130: 7565 2132 302c 6669 6c6c 206f 7061 6369 ue!20,fill opaci\n+0000d140: 7479 3d30 2e38 5d7c 5b6c 6179 3d75 6e64 ty=0.8]|[lay=und\n+0000d150: 6572 5d0a 2020 7370 6563 6961 6c7c 5c74 er]. special|\\t\n+0000d160: 696b 7a73 7479 6c65 7b6d 796c 696e 6573 ikzstyle{mylines\n+0000d170: 7479 6c65 7d20 3d20 5b72 6564 2132 302c tyle} = [red!20,\n+0000d180: 6461 7368 6564 5d7c 5b6c 6179 3d75 6e64 dashed]|[lay=und\n+0000d190: 6572 5d0a 5468 6520 6175 7468 6f72 2069 er].The author i\n+0000d1a0: 7320 7265 7370 6f6e 7369 626c 6520 666f s responsible fo\n+0000d1b0: 7220 7573 696e 6720 7468 6520 6b65 792c r using the key,\n+0000d1c0: 20e2 8098 6c69 6e65 2073 7479 6c65 e280 ...line style..\n+0000d1d0: 9920 6f72 20e2 8098 6669 6c6c 0a73 7479 . or ...fill.sty\n+0000d1e0: 6c65 e280 992c 2074 6861 7420 6d61 7463 le..., that matc\n+0000d1f0: 6865 7320 7468 6520 636f 6e74 656e 7420 hes the content \n+0000d200: 6f66 2074 6865 2073 7479 6c65 2064 6566 of the style def\n+0000d210: 696e 6974 696f 6e2e 0a0a 2020 202d 2d2d inition... ---\n+0000d220: 2d2d 2d2d 2d2d 2d20 466f 6f74 6e6f 7465 ------- Footnote\n+0000d230: 7320 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2020 s ----------.. \n+0000d240: 2028 3129 2054 6869 7320 636c 6576 6572 (1) This clever\n+0000d250: 2074 7269 636b 2069 7320 6475 6520 746f trick is due to\n+0000d260: 204b 6a65 6c6c 204d 6167 6e65 2046 6175 Kjell Magne Fau\n+0000d270: 736b 652e 0a0a 1f0a 4669 6c65 3a20 736b ske.....File: sk\n+0000d280: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n+0000d290: 3a20 5472 616e 7370 6172 656e 6379 2c20 : Transparency, \n+0000d2a0: 204e 6578 743a 2049 6e74 6572 6e61 6c20 Next: Internal \n+0000d2b0: 6f70 7469 6f6e 732c 2020 5072 6576 3a20 options, Prev: \n+0000d2c0: 5469 6b5a 2f50 4746 2075 7365 722d 6465 TikZ/PGF user-de\n+0000d2d0: 6669 6e65 6420 7374 796c 6573 2c20 2055 fined styles, U\n+0000d2e0: 703a 204f 7074 696f 6e73 0a0a 332e 312e p: Options..3.1.\n+0000d2f0: 352e 3520 5472 616e 7370 6172 656e 6379 5.5 Transparency\n+0000d300: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n+0000d310: 2e2e 2e2e 2e0a 0a42 6f74 6820 e280 9850 .......Both ...P\n+0000d320: 5354 7269 636b 73e2 8099 2061 6e64 20e2 STricks... and .\n+0000d330: 8098 5469 6b5a 2f50 4746 e280 9920 7375 ..TikZ/PGF... su\n+0000d340: 7070 6f72 7420 706f 6c79 676f 6e20 6f70 pport polygon op\n+0000d350: 7469 6f6e 7320 7468 6174 2068 6176 6520 tions that have \n+0000d360: 7468 650a 6566 6665 6374 206f 6620 6d61 the.effect of ma\n+0000d370: 6b69 6e67 2074 6865 2070 6f6c 7967 6f6e king the polygon\n+0000d380: 2061 7070 6561 7220 7472 616e 7370 6172 appear transpar\n+0000d390: 656e 742e 2020 466f 7220 e280 9850 5354 ent. For ...PST\n+0000d3a0: 7269 636b 73e2 8099 2c0a 6b65 7977 6f72 ricks...,.keywor\n+0000d3b0: 6420 e280 9874 7261 6e73 7061 6c70 6861 d ...transpalpha\n+0000d3c0: e280 9920 7761 7320 7573 6564 2064 7572 ... was used dur\n+0000d3d0: 696e 6720 696e 6974 6961 6c20 6465 7665 ing initial deve\n+0000d3e0: 6c6f 706d 656e 7420 6f66 0a74 7261 6e73 lopment of.trans\n+0000d3f0: 7061 7265 6e63 7920 6665 6174 7572 6573 parency features\n+0000d400: 2c20 616e 6420 e280 986f 7061 6369 7479 , and ...opacity\n+0000d410: e280 9920 7761 7320 6164 6f70 7465 6420 ... was adopted \n+0000d420: 6c61 7465 722e 2020 e280 9853 6b65 7463 later. ...Sketc\n+0000d430: 68e2 8099 2068 6f6e 6f72 730a 626f 7468 h... honors.both\n+0000d440: 2e20 20e2 8098 5469 6b5a 2f50 4746 e280 . ...TikZ/PGF..\n+0000d450: 9920 7573 6573 20e2 8098 6f70 6163 6974 . uses ...opacit\n+0000d460: 79e2 8099 206f 6e6c 792e 2020 5768 656e y... only. When\n+0000d470: 2074 7261 6e73 7061 7265 6e74 2070 6f6c transparent pol\n+0000d480: 7967 6f6e 7320 6172 6520 696e 0a74 6865 ygons are in.the\n+0000d490: 2066 6f72 6567 726f 756e 642c 206f 626a foreground, obj\n+0000d4a0: 6563 7473 2062 6568 696e 6420 7468 656d ects behind them\n+0000d4b0: 2028 6472 6177 6e20 6561 726c 6965 7229 (drawn earlier)\n+0000d4c0: 2061 7265 2076 6973 6962 6c65 2077 6974 are visible wit\n+0000d4d0: 680a 636f 6c6f 7220 7375 6264 7565 6420 h.color subdued \n+0000d4e0: 616e 6420 7469 6e74 6564 2e20 2054 6865 and tinted. The\n+0000d4f0: 2068 6964 6465 6e20 7375 7266 6163 6520 hidden surface \n+0000d500: 616c 676f 7269 7468 6d20 6f66 20e2 8098 algorithm of ...\n+0000d510: 736b 6574 6368 e280 990a 776f 726b 7320 sketch....works \n+0000d520: 7765 6c6c 2077 6974 6820 7375 6368 2074 well with such t\n+0000d530: 7261 6e73 7061 7265 6e74 2070 6f6c 7967 ransparent polyg\n+0000d540: 6f6e 732e 0a0a 2020 204e 6f74 6520 7468 ons... 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The default \n+0000da50: 7661 6c75 6520 e280 9874 7275 65e2 8099 value ...true...\n+0000da60: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n 0000da70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000da80: 2020 2020 2063 6175 7365 7320 2277 6172 causes \"war\n-0000da90: 7065 6422 2070 6f6c 7967 6f6e 7320 746f ped\" polygons to\n-0000daa0: 2062 6520 7370 6c69 7420 696e 746f 2074 be split into t\n-0000dab0: 7269 616e 676c 6573 2c20 7768 6963 680a riangles, which.\n+0000da80: 2020 2063 6175 7365 7320 2277 6172 7065 causes \"warpe\n+0000da90: 6422 2070 6f6c 7967 6f6e 7320 746f 2062 d\" polygons to b\n+0000daa0: 6520 7370 6c69 7420 696e 746f 2074 7269 e split into tri\n+0000dab0: 616e 676c 6573 2c20 7768 6963 680a 2020 angles, which. \n 0000dac0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0000dad0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000dae0: 2020 6176 6f69 6473 206d 6973 7461 6b65 avoids mistake\n-0000daf0: 7320 6279 2074 6865 2068 6964 6465 6e20 s by the hidden \n-0000db00: 7375 7266 6163 6520 616c 676f 7269 7468 surface algorith\n-0000db10: 6d2e 0a0a 332e 312e 3620 506f 696e 7420 m...3.1.6 Point \n-0000db20: 6c69 7374 730a 2d2d 2d2d 2d2d 2d2d 2d2d lists.----------\n-0000db30: 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 -------..*Syntax\n-0000db40: 3a2a 0a20 2020 2020 2858 312c 5931 2c5a :*. 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Any po\n-0000dc00: 696e 7420 6d61 7920 6861 7665 2074 6865 int may have the\n-0000dc10: 207a 2d63 6f6d 706f 6e65 6e74 206f 6d69 z-component omi\n-0000dc20: 7474 6564 3b20 6974 2077 696c 6c20 6465 tted; it will de\n-0000dc30: 6661 756c 740a 746f 207a 3d30 2e0a 0a2a fault.to z=0...*\n-0000dc40: 204d 656e 753a 0a0a 2a20 4472 6177 6162 Menu:..* Drawab\n-0000dc50: 6c65 733a 3a20 2020 2020 2020 2020 2020 les:: \n-0000dc60: 2020 2020 2020 2020 5468 696e 6773 2074 Things t\n-0000dc70: 6861 7420 6172 6520 6472 6177 6e2e 0a2a hat are drawn..*\n-0000dc80: 2044 6566 696e 6974 696f 6e73 3a3a 2020 Definitions:: \n-0000dc90: 2020 2020 2020 2020 2020 2020 2020 2054 T\n-0000dca0: 6869 6e67 7320 7769 7468 206e 616d 6573 hings with names\n-0000dcb0: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n-0000dcc0: 682e 696e 666f 2c20 204e 6f64 653a 2044 h.info, Node: D\n-0000dcd0: 7261 7761 626c 6573 2c20 204e 6578 743a rawables, Next:\n-0000dce0: 2044 6566 696e 6974 696f 6e73 2c20 2050 Definitions, P\n-0000dcf0: 7265 763a 204c 616e 6775 6167 6520 6261 rev: Language ba\n-0000dd00: 7369 6373 2c20 2055 703a 2049 6e70 7574 sics, Up: Input\n-0000dd10: 206c 616e 6775 6167 650a 0a33 2e32 2044 language..3.2 D\n-0000dd20: 7261 7761 626c 6573 0a3d 3d3d 3d3d 3d3d rawables.=======\n-0000dd30: 3d3d 3d3d 3d3d 0a0a 4472 6177 6162 6c65 ======..Drawable\n-0000dd40: 7320 6172 6520 7369 6d70 6c79 20e2 8098 s are simply ...\n-0000dd50: 736b 6574 6368 e280 9920 6f62 6a65 6374 sketch... object\n-0000dd60: 7320 7468 6174 206d 6967 6874 2061 7070 s that might app\n-0000dd70: 6561 7220 696e 2074 6865 2064 7261 7769 ear in the drawi\n-0000dd80: 6e67 2e0a 5468 6579 2069 6e63 6c75 6465 ng..They include\n-0000dd90: 2064 6f74 732c 2070 6f6c 796c 696e 6573 dots, polylines\n-0000dda0: 2c20 6375 7276 6573 2c20 706f 6c79 676f , curves, polygo\n-0000ddb0: 6e73 2c20 616e 6420 6d6f 7265 2063 6f6d ns, and more com\n-0000ddc0: 706c 6578 206f 626a 6563 7473 0a74 6861 plex objects.tha\n-0000ddd0: 7420 6172 6520 6275 696c 7420 7570 2066 t are built up f\n-0000dde0: 726f 6d20 7369 6d70 6c65 7220 6f6e 6573 rom simpler ones\n-0000ddf0: 2069 6e20 7661 7269 6f75 7320 7761 7973 in various ways\n-0000de00: 2e20 2046 696e 616c 6c79 2c20 e280 9c73 . Finally, ...s\n-0000de10: 7065 6369 616c e280 9d0a 6f62 6a65 6374 pecial....object\n-0000de20: 7320 6172 6520 7468 6f73 6520 636f 6d70 s are those comp\n-0000de30: 6f73 6564 206f 6620 4c61 5465 5820 6f72 osed of LaTeX or\n-0000de40: 20e2 8098 5053 5472 6963 6b73 e280 9920 ...PSTricks... \n-0000de50: 636f 6465 2c20 7065 7268 6170 730a 696e code, perhaps.in\n-0000de60: 636c 7564 696e 6720 636f 6f72 6469 6e61 cluding coordina\n-0000de70: 7465 7320 616e 6420 616e 676c 6573 2063 tes and angles c\n-0000de80: 6f6d 7075 7465 6420 6279 20e2 8098 736b omputed by ...sk\n-0000de90: 6574 6368 e280 992e 0a0a 2a20 4d65 6e75 etch......* Menu\n-0000dea0: 3a0a 0a2a 2044 6f74 733a 3a20 2020 2020 :..* Dots:: \n+0000dae0: 6176 6f69 6473 206d 6973 7461 6b65 7320 avoids mistakes \n+0000daf0: 6279 2074 6865 2068 6964 6465 6e20 7375 by the hidden su\n+0000db00: 7266 6163 6520 616c 676f 7269 7468 6d2e rface algorithm.\n+0000db10: 0a0a 332e 312e 3620 506f 696e 7420 6c69 ..3.1.6 Point li\n+0000db20: 7374 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d sts.------------\n+0000db30: 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a -----..*Syntax:*\n+0000db40: 0a20 2020 2020 2858 312c 5931 2c5a 3129 . 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446f 7473 2c20 204e 6578 Node: Dots, Nex\n-0000e0c0: 743a 204c 696e 6573 2c20 2050 7265 763a t: Lines, Prev:\n-0000e0d0: 2044 7261 7761 626c 6573 2c20 2055 703a Drawables, Up:\n-0000e0e0: 2044 7261 7761 626c 6573 0a0a 332e 322e Drawables..3.2.\n-0000e0f0: 3120 446f 7473 0a2d 2d2d 2d2d 2d2d 2d2d 1 Dots.---------\n-0000e100: 2d0a 0a2a 5379 6e74 6178 3a2a 0a20 2020 -..*Syntax:*. \n-0000e110: 2020 646f 7473 5b4f 5054 494f 4e53 5d20 dots[OPTIONS] \n-0000e120: 504f 494e 545f 4c49 5354 0a54 6869 7320 POINT_LIST.This \n-0000e130: 636f 6d6d 616e 6420 6973 2074 6865 2074 command is the t\n-0000e140: 6872 6565 2d64 696d 656e 7369 6f6e 616c hree-dimensional\n-0000e150: 2065 7175 6976 616c 656e 7420 6f66 2074 equivalent of t\n-0000e160: 6865 20e2 8098 5053 5472 6963 6b73 e280 he ...PSTricks..\n-0000e170: 990a 636f 6d6d 616e 6420 e280 985c 7073 ..command ...\\ps\n-0000e180: 646f 7473 e280 992e 0a0a 1f0a 4669 6c65 dots........File\n-0000e190: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n-0000e1a0: 4e6f 6465 3a20 4c69 6e65 732c 2020 4e65 Node: Lines, Ne\n-0000e1b0: 7874 3a20 4375 7276 6573 2c20 2050 7265 xt: Curves, Pre\n-0000e1c0: 763a 2044 6f74 732c 2020 5570 3a20 4472 v: Dots, Up: Dr\n-0000e1d0: 6177 6162 6c65 730a 0a33 2e32 2e32 204c awables..3.2.2 L\n-0000e1e0: 696e 6573 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d ines.-----------\n-0000e1f0: 0a0a 2a53 796e 7461 783a 2a0a 2020 2020 ..*Syntax:*. \n-0000e200: 206c 696e 655b 4f50 5449 4f4e 535d 2050 line[OPTIONS] P\n-0000e210: 4f49 4e54 5f4c 4953 540a 5468 6973 2063 OINT_LIST.This c\n-0000e220: 6f6d 6d61 6e64 2069 7320 7468 6520 7468 ommand is the th\n-0000e230: 7265 652d 6469 6d65 6e73 696f 6e61 6c20 ree-dimensional \n-0000e240: 6571 7569 7661 6c65 6e74 206f 6620 7468 equivalent of th\n-0000e250: 6520 e280 9850 5354 7269 636b 73e2 8099 e ...PSTricks...\n-0000e260: 0a63 6f6d 6d61 6e64 20e2 8098 5c70 736c .command ...\\psl\n-0000e270: 696e 65e2 8099 2e0a 0a1f 0a46 696c 653a ine........File:\n-0000e280: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-0000e290: 6f64 653a 2043 7572 7665 732c 2020 4e65 ode: Curves, Ne\n-0000e2a0: 7874 3a20 506f 6c79 676f 6e73 2c20 2050 xt: Polygons, P\n-0000e2b0: 7265 763a 204c 696e 6573 2c20 2055 703a rev: Lines, Up:\n-0000e2c0: 2044 7261 7761 626c 6573 0a0a 332e 322e Drawables..3.2.\n-0000e2d0: 3320 4375 7276 6573 0a2d 2d2d 2d2d 2d2d 3 Curves.-------\n-0000e2e0: 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a -----..*Syntax:*\n-0000e2f0: 0a20 2020 2020 6375 7276 655b 4f50 5449 . curve[OPTI\n-0000e300: 4f4e 535d 2050 4f49 4e54 5f4c 4953 540a ONS] POINT_LIST.\n-0000e310: 5468 6973 2063 6f6d 6d61 6e64 2069 7320 This command is \n-0000e320: 7468 6520 7468 7265 652d 6469 6d65 6e73 the three-dimens\n-0000e330: 696f 6e61 6c20 6571 7569 7661 6c65 6e74 ional equivalent\n-0000e340: 206f 6620 7468 6520 e280 9850 5354 7269 of the ...PSTri\n-0000e350: 636b 73e2 8099 0a63 6f6d 6d61 6e64 20e2 cks....command .\n-0000e360: 8098 5c70 7363 7572 7665 e280 992e 2020 ..\\pscurve.... \n-0000e370: 4974 2069 7320 6e6f 7420 696d 706c 656d It is not implem\n-0000e380: 656e 7465 6420 696e 2074 6865 2063 7572 ented in the cur\n-0000e390: 7265 6e74 2076 6572 7369 6f6e 206f 660a rent version of.\n-0000e3a0: e280 9873 6b65 7463 68e2 8099 2e0a 0a1f ...sketch.......\n-0000e3b0: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n-0000e3c0: 666f 2c20 204e 6f64 653a 2050 6f6c 7967 fo, Node: Polyg\n-0000e3d0: 6f6e 732c 2020 4e65 7874 3a20 5370 6563 ons, Next: Spec\n-0000e3e0: 6961 6c73 2c20 2050 7265 763a 2043 7572 ials, Prev: Cur\n-0000e3f0: 7665 732c 2020 5570 3a20 4472 6177 6162 ves, Up: Drawab\n-0000e400: 6c65 730a 0a33 2e32 2e34 2050 6f6c 7967 les..3.2.4 Polyg\n-0000e410: 6f6e 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ons.------------\n-0000e420: 2d2d 0a0a 2a53 796e 7461 783a 2a0a 2020 --..*Syntax:*. \n-0000e430: 2020 2070 6f6c 7967 6f6e 5b4f 5054 494f polygon[OPTIO\n-0000e440: 4e53 5d20 504f 494e 545f 4c49 5354 0a54 NS] POINT_LIST.T\n-0000e450: 6869 7320 636f 6d6d 616e 6420 6973 2074 his command is t\n-0000e460: 6865 2074 6872 6565 2d64 696d 656e 7369 he three-dimensi\n-0000e470: 6f6e 616c 2065 7175 6976 616c 656e 7420 onal equivalent \n-0000e480: 6f66 2074 6865 20e2 8098 5053 5472 6963 of the ...PSTric\n-0000e490: 6b73 e280 990a 636f 6d6d 616e 6420 e280 ks....command ..\n-0000e4a0: 985c 7073 706f 6c79 676f 6ee2 8099 2e20 .\\pspolygon.... \n-0000e4b0: 2054 6865 20e2 8098 736b 6574 6368 e280 The ...sketch..\n-0000e4c0: 9920 6869 6464 656e 2073 7572 6661 6365 . hidden surface\n-0000e4d0: 2061 6c67 6f72 6974 686d 2061 7373 756d algorithm assum\n-0000e4e0: 6573 0a74 6861 7420 706f 6c79 676f 6e73 es.that polygons\n-0000e4f0: 2061 7265 2063 6f6e 7665 7820 616e 6420 are convex and \n-0000e500: 706c 616e 6172 2e20 2049 6e20 7072 6163 planar. In prac\n-0000e510: 7469 6365 2c20 6472 6177 696e 6773 206d tice, drawings m\n-0000e520: 6179 2077 656c 6c0a 7475 726e 206f 7574 ay well.turn out\n-0000e530: 2063 6f72 7265 6374 6c79 2065 7665 6e20 correctly even \n-0000e540: 6966 2074 6865 7365 2061 7373 756d 7074 if these assumpt\n-0000e550: 696f 6e73 2061 7265 2076 696f 6c61 7465 ions are violate\n-0000e560: 642e 0a0a 1f0a 4669 6c65 3a20 736b 6574 d.....File: sket\n-0000e570: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n-0000e580: 5370 6563 6961 6c73 2c20 204e 6578 743a Specials, Next:\n-0000e590: 2053 7765 6570 732c 2020 5072 6576 3a20 Sweeps, Prev: \n-0000e5a0: 506f 6c79 676f 6e73 2c20 2055 703a 2044 Polygons, Up: D\n-0000e5b0: 7261 7761 626c 6573 0a0a 332e 322e 3520 rawables..3.2.5 \n-0000e5c0: 5370 6563 6961 6c73 0a2d 2d2d 2d2d 2d2d Specials.-------\n-0000e5d0: 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 -------..*Syntax\n-0000e5e0: 3a2a 0a20 2020 2020 7370 6563 6961 6c20 :*. special \n-0000e5f0: 2452 4157 5f54 4558 5424 5b4f 5054 494f $RAW_TEXT$[OPTIO\n-0000e600: 4e53 5d20 4152 475f 4c49 5354 0a48 6572 NS] ARG_LIST.Her\n-0000e610: 6520 e280 9824 e280 9920 6361 6e20 6265 e ...$... can be\n-0000e620: 2061 6e79 2063 6861 7261 6374 6572 2061 any character a\n-0000e630: 6e64 2069 7320 7573 6564 2074 6f20 6465 nd is used to de\n-0000e640: 6c69 6d69 7420 7468 6520 7374 6172 7420 limit the start \n-0000e650: 616e 6420 656e 640a 6f66 2052 4157 5f54 and end.of RAW_T\n-0000e660: 4558 542e 2020 5468 6520 636f 6d6d 616e EXT. The comman\n-0000e670: 6420 656d 6265 6473 2052 4157 5f54 4558 d embeds RAW_TEX\n-0000e680: 5420 696e 2074 6865 20e2 8098 736b 6574 T in the ...sket\n-0000e690: 6368 e280 9920 6f75 7470 7574 2061 6674 ch... output aft\n-0000e6a0: 6572 0a70 6572 666f 726d 696e 6720 7375 er.performing su\n-0000e6b0: 6273 7469 7475 7469 6f6e 7320 6173 2066 bstitutions as f\n-0000e6c0: 6f6c 6c6f 7773 2e0a 2020 20e2 80a2 20e2 ollows.. ... .\n-0000e6d0: 8098 2349 e280 9920 7768 6572 6520 4920 ..#I... where I \n-0000e6e0: 6973 2061 2070 6f73 6974 6976 6520 696e is a positive in\n-0000e6f0: 7465 6765 7220 6973 2072 6570 6c61 6365 teger is replace\n-0000e700: 6420 6279 2074 6865 2049 2774 6820 7661 d by the I'th va\n-0000e710: 6c75 6520 696e 0a20 2020 2020 4152 475f lue in. ARG_\n-0000e720: 4c49 5354 2e20 2050 6f69 6e74 2061 6e64 LIST. Point and\n-0000e730: 2076 6563 746f 7220 6172 6775 6d65 6e74 vector argument\n-0000e740: 7320 6265 636f 6d65 2074 776f 2d64 696d s become two-dim\n-0000e750: 656e 7369 6f6e 616c 0a20 2020 2020 706f ensional. po\n-0000e760: 696e 7473 2c20 7768 6963 6820 6172 6520 ints, which are \n-0000e770: 7468 6520 7472 616e 7366 6f72 6d65 6420 the transformed \n-0000e780: 3364 2061 7267 756d 656e 7473 2070 726f 3d arguments pro\n-0000e790: 6a65 6374 6564 206f 6e74 6f20 7468 650a jected onto the.\n-0000e7a0: 2020 2020 2058 2d59 2070 6c61 6e65 2e20 X-Y plane. \n-0000e7b0: 2054 6869 7320 616c 6c6f 7773 2074 776f This allows two\n-0000e7c0: 2d64 696d 656e 7469 6f6e 616c 206f 7574 -dimentional out\n-0000e7d0: 7075 7420 656c 656d 656e 7473 2073 7563 put elements suc\n-0000e7e0: 6820 6173 0a20 2020 2020 6c61 6265 6c73 h as. labels\n-0000e7f0: 2074 6f20 6265 2065 6173 696c 7920 706f to be easily po\n-0000e800: 7369 7469 6f6e 6564 2077 6974 6820 7265 sitioned with re\n-0000e810: 7370 6563 7420 746f 2074 6872 6565 2d64 spect to three-d\n-0000e820: 696d 656e 7369 6f6e 616c 0a20 2020 2020 imensional. \n-0000e830: 6665 6174 7572 6573 2069 6e20 7468 6520 features in the \n-0000e840: 6472 6177 696e 672e 2020 5363 616c 6172 drawing. Scalar\n-0000e850: 2061 7267 756d 656e 7473 2061 7265 2073 arguments are s\n-0000e860: 7562 7369 7475 7465 6420 6469 7265 6374 ubsituted direct\n-0000e870: 6c79 2e0a 2020 2020 204e 6f20 7472 616e ly.. No tran\n-0000e880: 7366 6f72 6d61 7469 6f6e 2069 7320 6170 sformation is ap\n-0000e890: 706c 6965 642e 0a20 2020 e280 a220 e280 plied.. ... ..\n-0000e8a0: 9823 7b49 7de2 8099 2069 7320 616c 736f .#{I}... is also\n-0000e8b0: 2072 6570 6c61 6365 6420 6173 2061 626f replaced as abo\n-0000e8c0: 7665 2e0a 2020 20e2 80a2 20e2 8098 2349 ve.. ... ...#I\n-0000e8d0: 2732 e280 9920 6973 2072 6570 6c61 6365 '2... is replace\n-0000e8e0: 6420 6173 2061 626f 7665 2066 6f72 2070 d as above for p\n-0000e8f0: 6f69 6e74 7320 6f72 2076 6563 746f 7273 oints or vectors\n-0000e900: 2e20 2049 7420 6973 2061 6e20 6572 726f . It is an erro\n-0000e910: 720a 2020 2020 2066 6f72 2074 6865 2049 r. for the I\n-0000e920: 2774 6820 6172 6775 6d65 6e74 2074 6f20 'th argument to \n-0000e930: 6265 2061 2073 6361 6c61 722e 0a20 2020 be a scalar.. \n-0000e940: e280 a220 e280 9823 4927 78e2 8099 2c20 ... ...#I'x..., \n-0000e950: e280 9823 4927 79e2 8099 2c20 6f72 20e2 ...#I'y..., or .\n-0000e960: 8098 2349 277a e280 9920 6973 2072 6570 ..#I'z... is rep\n-0000e970: 6c61 6365 642c 2072 6573 7065 6374 6976 laced, respectiv\n-0000e980: 656c 792c 2062 7920 7468 6520 7363 616c ely, by the scal\n-0000e990: 6172 0a20 2020 2020 582c 2059 2c20 6f72 ar. X, Y, or\n-0000e9a0: 205a 2d63 6f6f 7264 696e 6174 6520 6f66 Z-coordinate of\n-0000e9b0: 2074 6865 2061 7267 756d 656e 7420 706f the argument po\n-0000e9c0: 696e 7420 6f72 2076 6563 746f 722e 2020 int or vector. \n-0000e9d0: 4974 2069 7320 616e 0a20 2020 2020 6572 It is an. er\n-0000e9e0: 726f 7220 666f 7220 7468 6520 4927 7468 ror for the I'th\n-0000e9f0: 2061 7267 756d 656e 7420 746f 2062 6520 argument to be \n-0000ea00: 6120 7363 616c 6172 2e0a 2020 20e2 80a2 a scalar.. ...\n-0000ea10: 20e2 8098 2349 2733 e280 9920 6973 2072 ...#I'3... is r\n-0000ea20: 6570 6c61 6365 6420 6279 2074 6865 2074 eplaced by the t\n-0000ea30: 6872 6565 2d64 696d 656e 7369 6f6e 616c hree-dimensional\n-0000ea40: 2074 7261 6e73 666f 726d 6564 2061 7267 transformed arg\n-0000ea50: 756d 656e 742e 0a20 2020 2020 4e6f 7465 ument.. Note\n-0000ea60: 2074 6861 7420 6966 2061 2070 6572 7370 that if a persp\n-0000ea70: 6563 7469 7665 2074 7261 6e73 666f 726d ective transform\n-0000ea80: 6174 696f 6e20 6861 7320 6265 656e 2061 ation has been a\n-0000ea90: 7070 6c69 6564 2c20 7468 650a 2020 2020 pplied, the. \n-0000eaa0: 205a 2d63 6f6f 7264 696e 6174 6520 6861 Z-coordinate ha\n-0000eab0: 7320 6c69 7474 6c65 2067 656f 6d65 7472 s little geometr\n-0000eac0: 6963 2073 6967 6e69 6669 6361 6e63 652c ic significance,\n-0000ead0: 2074 686f 7567 6820 6974 0a20 2020 2020 though it. \n-0000eae0: 6163 6375 7261 7465 6c79 2069 6e64 6963 accurately indic\n-0000eaf0: 6174 6573 2072 656c 6174 6976 6520 6465 ates relative de\n-0000eb00: 7074 682e 0a20 2020 e280 a220 e280 9823 pth.. ... ...#\n-0000eb10: 492d 4ae2 8099 2077 6865 7265 2049 2061 I-J... where I a\n-0000eb20: 6e64 204a 2061 7265 2070 6f73 6974 6976 nd J are positiv\n-0000eb30: 6520 696e 7465 6765 7273 2069 7320 7265 e integers is re\n-0000eb40: 706c 6163 6564 2062 7920 6120 7374 7269 placed by a stri\n-0000eb50: 6e67 0a20 2020 2020 e280 987b 414e 474c ng. ...{ANGL\n-0000eb60: 457d e280 9920 7768 6572 6520 414e 474c E}... where ANGL\n-0000eb70: 4520 6973 2074 6865 2070 6f6c 6172 2061 E is the polar a\n-0000eb80: 6e67 6c65 206f 6620 6120 7665 6374 6f72 ngle of a vector\n-0000eb90: 2066 726f 6d20 7468 6520 4927 7468 0a20 from the I'th. \n-0000eba0: 2020 2020 706f 696e 7420 696e 2050 4f49 point in POI\n-0000ebb0: 4e54 5f4c 4953 5420 746f 2074 6865 204a NT_LIST to the J\n-0000ebc0: 2774 6820 706f 696e 7420 7072 6f6a 6563 'th point projec\n-0000ebd0: 7465 6420 696e 746f 2074 6865 2078 2d79 ted into the x-y\n-0000ebe0: 2070 6c61 6e65 2e0a 2020 2020 2049 7420 plane.. It \n-0000ebf0: 6973 2061 6e20 6572 726f 7220 666f 7220 is an error for \n-0000ec00: 7468 6520 4927 7468 206f 7220 4a27 7468 the I'th or J'th\n-0000ec10: 2061 7267 756d 656e 7420 746f 2062 6520 argument to be \n-0000ec20: 6120 7363 616c 6172 206f 7220 610a 2020 a scalar or a. \n-0000ec30: 2020 2076 6563 746f 722e 0a20 2020 e280 vector.. ..\n-0000ec40: a220 e280 9823 7b49 2d4a 7de2 8099 2069 . ...#{I-J}... i\n-0000ec50: 7320 616c 736f 2072 6570 6c61 6365 6420 s also replaced \n-0000ec60: 6173 2061 626f 7665 2e0a 2020 20e2 80a2 as above.. ...\n-0000ec70: 20e2 8098 2323 e280 9920 6973 2072 6570 ...##... is rep\n-0000ec80: 6c61 6365 6420 7769 7468 20e2 8098 23e2 laced with ...#.\n-0000ec90: 8099 2e0a 5468 6520 666f 726d 7320 7769 ....The forms wi\n-0000eca0: 7468 2062 7261 6365 7320 e280 987b 207d th braces ...{ }\n-0000ecb0: e280 9920 6172 6520 7573 6566 756c 2077 ... are useful w\n-0000ecc0: 6865 6e20 7468 6520 6172 6775 6d65 6e74 hen the argument\n-0000ecd0: 2069 7320 696d 6d65 6469 6174 656c 790a is immediately.\n-0000ece0: 666f 6c6c 6f77 6564 2062 7920 6120 6469 followed by a di\n-0000ecf0: 6769 7420 6f72 2061 2074 6963 6b20 6368 git or a tick ch\n-0000ed00: 6172 6163 7465 7220 7468 6174 2069 7320 aracter that is \n-0000ed10: 7061 7274 206f 6620 7468 6520 5465 5820 part of the TeX \n-0000ed20: 636f 6465 2e0a 0a20 2020 5468 6520 6f6e code... The on\n-0000ed30: 6c79 2075 7365 6675 6c20 6f70 7469 6f6e ly useful option\n-0000ed40: 206f 6620 e280 9873 7065 6369 616c e280 of ...special..\n-0000ed50: 9920 6973 20e2 8098 6c61 79e2 8099 2c20 . is ...lay..., \n-0000ed60: 7768 6963 6820 6465 7465 726d 696e 6573 which determines\n-0000ed70: 2069 6620 7468 650a 7375 6273 7469 7475 if the.substitu\n-0000ed80: 6564 2072 6177 2074 6578 7420 6973 2065 ed raw text is e\n-0000ed90: 6d69 7474 6564 2062 6566 6f72 652c 2061 mitted before, a\n-0000eda0: 6674 6572 2c20 6f72 2075 7369 6e67 2074 fter, or using t\n-0000edb0: 6865 2066 6972 7374 2070 6f69 6e74 0a69 he first point.i\n-0000edc0: 6e20 504f 494e 545f 4c49 5354 2061 7320 n POINT_LIST as \n-0000edd0: 616e 2069 6e64 6963 6174 6f72 206f 6620 an indicator of \n-0000ede0: 6465 7074 682e 2020 5468 6573 6520 6f63 depth. These oc\n-0000edf0: 6375 722c 2072 6573 7065 6374 6976 656c cur, respectivel\n-0000ee00: 792c 2077 6974 680a e280 986c 6179 3d75 y, with....lay=u\n-0000ee10: 6e64 6572 e280 992c 20e2 8098 6c61 793d nder..., ...lay=\n-0000ee20: 6f76 6572 e280 992c 2061 6e64 20e2 8098 over..., and ...\n-0000ee30: 6c61 793d 696e e280 992e 2020 5365 6520 lay=in.... See \n-0000ee40: 2a6e 6f74 6520 5370 6563 6961 6c20 6f62 *note Special ob\n-0000ee50: 6a65 6374 733a 3a20 616e 640a 2a6e 6f74 jects:: and.*not\n-0000ee60: 6520 5469 6b5a 2f50 4746 2075 7365 722d e TikZ/PGF user-\n-0000ee70: 6465 6669 6e65 6420 7374 796c 6573 3a3a defined styles::\n-0000ee80: 2066 6f72 2065 7861 6d70 6c65 732e 2020 for examples. \n-0000ee90: 2a4e 6f74 6520 496e 7465 726e 616c 0a6f *Note Internal.o\n-0000eea0: 7074 696f 6e73 3a3a 2e0a 0a1f 0a46 696c ptions::.....Fil\n-0000eeb0: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n-0000eec0: 204e 6f64 653a 2053 7765 6570 732c 2020 Node: Sweeps, \n-0000eed0: 4e65 7874 3a20 426c 6f63 6b73 2c20 2050 Next: Blocks, P\n-0000eee0: 7265 763a 2053 7065 6369 616c 732c 2020 rev: Specials, \n-0000eef0: 5570 3a20 4472 6177 6162 6c65 730a 0a33 Up: Drawables..3\n-0000ef00: 2e32 2e36 2053 7765 6570 730a 2d2d 2d2d .2.6 Sweeps.----\n-0000ef10: 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 --------..*Synta\n-0000ef20: 783a 2a0a 2020 2020 2073 7765 6570 207b x:*. sweep {\n-0000ef30: 204e 2c20 545f 312c 2054 5f32 2c20 2e2e N, T_1, T_2, ..\n-0000ef40: 2e2c 2054 5f52 207d 5b4f 5054 494f 4e53 ., T_R }[OPTIONS\n-0000ef50: 5d20 5357 4550 545f 4f42 4a45 4354 0a20 ] SWEPT_OBJECT. \n-0000ef60: 2020 2020 7377 6565 7020 7b20 4e3c 3e2c sweep { N<>,\n-0000ef70: 2054 5f31 2c20 545f 322c 202e 2e2e 2c20 T_1, T_2, ..., \n-0000ef80: 545f 5220 7d5b 4f50 5449 4f4e 535d 2053 T_R }[OPTIONS] S\n-0000ef90: 5745 5054 5f4f 424a 4543 540a 5468 6520 WEPT_OBJECT.The \n-0000efa0: 7377 6565 7020 636f 6e6e 6563 7473 204e sweep connects N\n-0000efb0: 2028 6f72 2070 6572 6861 7073 204e 2b31 (or perhaps N+1\n-0000efc0: 2920 636f 7069 6573 206f 6620 5357 4550 ) copies of SWEP\n-0000efd0: 545f 4f42 4a45 4354 2069 6e20 6f72 6465 T_OBJECT in orde\n-0000efe0: 7220 746f 0a63 7265 6174 6520 6120 6e65 r to.create a ne\n-0000eff0: 7720 6f62 6a65 6374 206f 6620 6869 6768 w object of high\n-0000f000: 6572 2064 696d 656e 7369 6f6e 2e20 2054 er dimension. T\n-0000f010: 6865 2054 5f49 2028 666f 7220 6920 6265 he T_I (for i be\n-0000f020: 7477 6565 6e20 3120 616e 640a 7229 2061 tween 1 and.r) a\n-0000f030: 7265 2074 7261 6e73 666f 726d 732e 2020 re transforms. \n-0000f040: 5468 6520 6b27 7468 2063 6f70 7920 6f66 The k'th copy of\n-0000f050: 2053 5745 5054 5f4f 424a 4543 5420 6973 SWEPT_OBJECT is\n-0000f060: 2070 726f 6475 6365 6420 6279 0a61 7070 produced by.app\n-0000f070: 6c79 696e 6720 7468 6520 666f 6c6c 6f77 lying the follow\n-0000f080: 696e 6720 7472 616e 7366 6f72 6d20 746f ing transform to\n-0000f090: 2074 6865 206f 7269 6769 6e61 6c2e 0a20 the original.. \n-0000f0a0: 2020 2020 545f 315e 6b20 7468 656e 2054 T_1^k then T\n-0000f0b0: 5f32 5e6b 2074 6865 6e20 2e2e 2e20 7468 _2^k then ... th\n-0000f0c0: 656e 2054 5f52 5e6b 0a48 6572 6520 545e en T_R^k.Here T^\n-0000f0d0: 6b20 6d65 616e 7320 2274 7261 6e73 666f k means \"transfo\n-0000f0e0: 726d 2054 2061 7070 6c69 6564 206b 2074 rm T applied k t\n-0000f0f0: 696d 6573 2e22 2020 5468 6520 6f72 6967 imes.\" The orig\n-0000f100: 696e 616c 206f 626a 6563 7420 6973 0a74 inal object is.t\n-0000f110: 6865 207a 6572 6f27 7468 2063 6f70 792c he zero'th copy,\n-0000f120: 2077 6974 6820 6b3d 3020 616e 6420 6566 with k=0 and ef\n-0000f130: 6665 6374 6976 656c 7920 6e6f 2074 7261 fectively no tra\n-0000f140: 6e73 666f 726d 2061 7070 6c69 6564 2028 nsform applied (\n-0000f150: 545e 303d 492c 0a74 6865 2069 6465 6e74 T^0=I,.the ident\n-0000f160: 6974 7920 7472 616e 7366 6f72 6d29 2e0a ity transform)..\n-0000f170: 0a20 2020 5468 6520 6d65 7468 6f64 206f . The method o\n-0000f180: 6620 636f 6e6e 6563 7469 6e67 2074 6865 f connecting the\n-0000f190: 2063 6f70 6965 7320 6465 7065 6e64 7320 copies depends \n-0000f1a0: 6f6e 2074 6865 2074 7970 6520 6f66 0a53 on the type of.S\n-0000f1b0: 5745 5054 5f4f 424a 4543 5420 616e 6420 WEPT_OBJECT and \n-0000f1c0: 6f6e 2077 6865 7468 6572 2074 6865 2063 on whether the c\n-0000f1d0: 6c6f 7375 7265 2074 6167 20e2 8098 3c3e losure tag ...<>\n-0000f1e0: e280 9920 6973 2070 7265 7365 6e74 206f ... is present o\n-0000f1f0: 7220 6e6f 742e 0a0a 2020 2041 6e20 6578 r not... An ex\n-0000f200: 616d 706c 6520 6f66 2061 2073 7765 6570 ample of a sweep\n-0000f210: 2077 6865 7265 2072 3d32 2069 7320 7468 where r=2 is th\n-0000f220: 6520 4d6f 6269 7573 2066 6967 7572 6520 e Mobius figure \n-0000f230: 6174 202a 6e6f 7465 204d 6f72 6520 746f at *note More to\n-0000f240: 0a6c 6561 726e 3a3a 2e0a 0a2a 204d 656e .learn::...* Men\n-0000f250: 753a 0a0a 2a20 5377 6570 7420 706f 696e u:..* Swept poin\n-0000f260: 7473 3a3a 2020 2020 2020 2020 2020 2020 ts:: \n-0000f270: 2020 2020 5377 6570 7420 706f 696e 7473 Swept points\n-0000f280: 206d 616b 6520 6c69 6e65 7320 6f72 2070 make lines or p\n-0000f290: 6f6c 7967 6f6e 732e 0a2a 2053 7765 7074 olygons..* Swept\n-0000f2a0: 206c 696e 6573 3a3a 2020 2020 2020 2020 lines:: \n-0000f2b0: 2020 2020 2020 2020 2053 7765 7074 206c Swept l\n-0000f2c0: 696e 6573 206d 616b 6520 6f70 656e 206f ines make open o\n-0000f2d0: 7220 636c 6f73 6564 2073 7572 6661 6365 r closed surface\n-0000f2e0: 732e 0a2a 2053 7765 7074 2070 6f6c 7967 s..* Swept polyg\n-0000f2f0: 6f6e 733a 3a20 2020 2020 2020 2020 2020 ons:: \n-0000f300: 2020 2053 7765 7074 2070 6f6c 7967 6f6e Swept polygon\n-0000f310: 7320 6d61 6b65 2063 6c6f 7365 6420 7375 s make closed su\n-0000f320: 7266 6163 6573 2e0a 2a20 5377 6570 7420 rfaces..* Swept \n-0000f330: 626c 6f63 6b73 3a3a 2020 2020 2020 2020 blocks:: \n-0000f340: 2020 2020 2020 2020 5377 6570 7420 626c Swept bl\n-0000f350: 6f63 6b20 e289 a120 626c 6f63 6b20 6f66 ock ... block of\n-0000f360: 2073 7765 6570 732e 0a2a 2053 7765 6570 sweeps..* Sweep\n-0000f370: 2066 6163 6520 7370 6c69 7474 696e 673a face splitting:\n-0000f380: 3a20 2020 2020 2020 2046 6978 696e 6720 : Fixing \n-0000f390: 7761 7270 6564 2066 6163 6573 2077 6974 warped faces wit\n-0000f3a0: 6820 7472 6961 6e67 6c65 732e 0a0a 1f0a h triangles.....\n-0000f3b0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n-0000f3c0: 6f2c 2020 4e6f 6465 3a20 5377 6570 7420 o, Node: Swept \n-0000f3d0: 706f 696e 7473 2c20 204e 6578 743a 2053 points, Next: S\n-0000f3e0: 7765 7074 206c 696e 6573 2c20 2050 7265 wept lines, Pre\n-0000f3f0: 763a 2053 7765 6570 732c 2020 5570 3a20 v: Sweeps, Up: \n-0000f400: 5377 6565 7073 0a0a 332e 322e 362e 3120 Sweeps..3.2.6.1 \n-0000f410: 5377 6570 7420 706f 696e 7473 0a2e 2e2e Swept points....\n-0000f420: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000f430: 2e0a 0a49 6620 5357 4550 545f 4f42 4a45 ...If SWEPT_OBJE\n-0000f440: 4354 2069 7320 6120 706f 696e 7420 6c69 CT is a point li\n-0000f450: 7374 2061 6e64 2074 6865 7265 2069 7320 st and there is \n-0000f460: 6e6f 2063 6c6f 7375 7265 2074 6167 2c20 no closure tag, \n-0000f470: 7468 656e 0ae2 8098 7377 6565 70e2 8099 then....sweep...\n-0000f480: 2063 6f6e 6e65 6374 7320 4e2b 3120 7375 connects N+1 su\n-0000f490: 6363 6573 7369 7665 2063 6f70 6965 7320 ccessive copies \n-0000f4a0: 6f66 2065 6163 6820 706f 696e 7420 2869 of each point (i\n-0000f4b0: 6e63 6c75 6469 6e67 2074 6865 0a6f 7269 ncluding the.ori\n-0000f4c0: 6769 6e61 6c29 2077 6974 6820 7374 7261 ginal) with stra\n-0000f4d0: 6967 6874 206c 696e 6520 7365 676d 656e ight line segmen\n-0000f4e0: 7473 2074 6f20 666f 726d 2061 2070 6f6c ts to form a pol\n-0000f4f0: 796c 696e 652e 2020 4966 2074 6865 7265 yline. If there\n-0000f500: 2061 7265 0a6d 2070 6f69 6e74 7320 696e are.m points in\n-0000f510: 2074 6865 206f 7269 6769 6e61 6c20 706f the original po\n-0000f520: 696e 7420 6c69 7374 2c20 7468 656e 206d int list, then m\n-0000f530: 2070 6f6c 796c 696e 6573 2077 6974 6820 polylines with \n-0000f540: 4e20 7365 676d 656e 7473 0a65 6163 6820 N segments.each \n-0000f550: 6172 6520 666f 726d 6564 2062 7920 7468 are formed by th\n-0000f560: 6520 7377 6565 702e 2020 496e 2074 6869 e sweep. In thi\n-0000f570: 7320 6d61 6e6e 6572 2c20 e280 9873 7765 s manner, ...swe\n-0000f580: 6570 e280 9920 666f 726d 7320 6120 7365 ep... forms a se\n-0000f590: 7420 6f66 0a6f 6e65 2d64 696d 656e 7369 t of.one-dimensi\n-0000f5a0: 6f6e 616c 206f 626a 6563 7473 2028 706f onal objects (po\n-0000f5b0: 6c79 6c69 6e65 7329 2066 726f 6d20 7a65 lylines) from ze\n-0000f5c0: 726f 2d64 696d 656e 7369 6f6e 616c 206f ro-dimensional o\n-0000f5d0: 6e65 7320 2870 6f69 6e74 7329 2e0a 0a20 nes (points)... \n-0000f5e0: 2020 5768 656e 2074 6865 7265 205f 6973 When there _is\n-0000f5f0: 5f20 6120 636c 6f73 7572 6520 7461 672c _ a closure tag,\n-0000f600: 20e2 8098 7377 6565 70e2 8099 2063 6f6e ...sweep... con\n-0000f610: 6e65 6374 7320 4e20 7375 6363 6573 7369 nects N successi\n-0000f620: 7665 2063 6f70 6965 730a 6f66 2065 6163 ve copies.of eac\n-0000f630: 6820 706f 696e 7420 2869 6e63 6c75 6469 h point (includi\n-0000f640: 6e67 2074 6865 206f 7269 6769 6e61 6c29 ng the original)\n-0000f650: 2077 6974 6820 7374 7261 6967 6874 206c with straight l\n-0000f660: 696e 6520 7365 676d 656e 7473 2061 6e64 ine segments and\n-0000f670: 0a66 696e 616c 6c79 2063 6f6e 6e65 6374 .finally connect\n-0000f680: 7320 7468 6520 6c61 7374 2063 6f70 7920 s the last copy \n-0000f690: 6261 636b 2074 6f20 7468 6520 6f72 6967 back to the orig\n-0000f6a0: 696e 616c 2074 6f20 666f 726d 2061 2070 inal to form a p\n-0000f6b0: 6f6c 7967 6f6e 0a77 6974 6820 4e20 7369 olygon.with N si\n-0000f6c0: 6465 732e 2020 4966 2074 6865 7265 2061 des. If there a\n-0000f6d0: 7265 206d 2070 6f69 6e74 7320 696e 2074 re m points in t\n-0000f6e0: 6865 206f 7269 6769 6e61 6c20 706f 696e he original poin\n-0000f6f0: 7420 6c69 7374 2c20 7468 656e 206d 0a70 t list, then m.p\n-0000f700: 6f6c 7967 6f6e 7320 7769 7468 204e 2073 olygons with N s\n-0000f710: 6964 6573 2065 6163 6820 6172 6520 666f ides each are fo\n-0000f720: 726d 6564 2062 7920 7468 6520 7377 6565 rmed by the swee\n-0000f730: 702e 2020 496e 2074 6869 7320 6d61 6e6e p. In this mann\n-0000f740: 6572 2c0a e280 9873 7765 6570 e280 9920 er,....sweep... \n-0000f750: 666f 726d 7320 6120 7365 7420 6f66 2074 forms a set of t\n-0000f760: 776f 2d64 696d 656e 7369 6f6e 616c 206f wo-dimensional o\n-0000f770: 626a 6563 7473 2028 706f 6c79 676f 6e73 bjects (polygons\n-0000f780: 2920 6672 6f6d 0a7a 6572 6f2d 6469 6d65 ) from.zero-dime\n-0000f790: 6e73 696f 6e61 6c20 6f6e 6573 2028 706f nsional ones (po\n-0000f7a0: 696e 7473 292e 0a0a 2020 204f 7074 696f ints)... Optio\n-0000f7b0: 6e73 206f 6620 7468 6520 e280 9873 7765 ns of the ...swe\n-0000f7c0: 6570 e280 9920 6172 6520 636f 7069 6564 ep... are copied\n-0000f7d0: 2064 6972 6563 746c 7920 746f 2074 6865 directly to the\n-0000f7e0: 2072 6573 756c 7469 6e67 0a70 6f6c 796c resulting.polyl\n-0000f7f0: 696e 6528 7329 2e0a 0a1f 0a46 696c 653a ine(s).....File:\n-0000f800: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-0000f810: 6f64 653a 2053 7765 7074 206c 696e 6573 ode: Swept lines\n-0000f820: 2c20 204e 6578 743a 2053 7765 7074 2070 , Next: Swept p\n-0000f830: 6f6c 7967 6f6e 732c 2020 5072 6576 3a20 olygons, Prev: \n-0000f840: 5377 6570 7420 706f 696e 7473 2c20 2055 Swept points, U\n-0000f850: 703a 2053 7765 6570 730a 0a33 2e32 2e36 p: Sweeps..3.2.6\n-0000f860: 2e32 2053 7765 7074 206c 696e 6573 0a2e .2 Swept lines..\n+0000dec0: 2044 7261 7720 646f 7473 2e0a 2a20 4c69 Draw dots..* Li\n+0000ded0: 6e65 733a 3a20 2020 2020 2020 2020 2020 nes:: \n+0000dee0: 2020 2020 2020 2020 2020 2020 4472 6177 Draw\n+0000def0: 2070 6f6c 796c 696e 6573 2e0a 2a20 4375 polylines..* Cu\n+0000df00: 7276 6573 3a3a 2020 2020 2020 2020 2020 rves:: \n+0000df10: 2020 2020 2020 2020 2020 2020 4472 6177 Draw\n+0000df20: 2063 7572 7665 732e 0a2a 2050 6f6c 7967 curves..* Polyg\n+0000df30: 6f6e 733a 3a20 2020 2020 2020 2020 2020 ons:: \n+0000df40: 2020 2020 2020 2020 2044 7261 7720 706f Draw po\n+0000df50: 6c79 676f 6e73 2e0a 2a20 5370 6563 6961 lygons..* Specia\n+0000df60: 6c73 3a3a 2020 2020 2020 2020 2020 2020 ls:: \n+0000df70: 2020 2020 2020 2020 456d 6265 6420 7261 Embed ra\n+0000df80: 7720 4c61 5465 5820 616e 6420 e280 9850 w LaTeX and ...P\n+0000df90: 5354 7269 636b 73e2 8099 2e0a 2a20 5377 STricks.....* Sw\n+0000dfa0: 6565 7073 3a3a 2020 2020 2020 2020 2020 eeps:: \n+0000dfb0: 2020 2020 2020 2020 2020 2020 4472 6177 Draw\n+0000dfc0: 2073 7765 6570 7320 6f66 2064 6f74 7320 sweeps of dots \n+0000dfd0: 616e 6420 706f 6c79 6c69 6e65 732e 0a2a and polylines..*\n+0000dfe0: 2042 6c6f 636b 733a 3a20 2020 2020 2020 Blocks:: \n+0000dff0: 2020 2020 2020 2020 2020 2020 2020 2047 G\n+0000e000: 726f 7570 206f 7468 6572 2064 7261 7761 roup other drawa\n+0000e010: 626c 6573 2e0a 2a20 5265 7065 6174 733a bles..* Repeats:\n+0000e020: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0000e030: 2020 2020 2020 4472 6177 2074 7261 6e73 Draw trans\n+0000e040: 666f 726d 6564 2063 6f70 6965 7320 6f66 formed copies of\n+0000e050: 206f 626a 6563 7473 2e0a 2a20 5075 7473 objects..* Puts\n+0000e060: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n+0000e070: 2020 2020 2020 2020 2020 4472 6177 206f Draw o\n+0000e080: 6e65 206f 626a 6563 7420 7472 616e 7366 ne object transf\n+0000e090: 6f72 6d65 642e 0a0a 1f0a 4669 6c65 3a20 ormed.....File: \n+0000e0a0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n+0000e0b0: 6465 3a20 446f 7473 2c20 204e 6578 743a de: Dots, Next:\n+0000e0c0: 204c 696e 6573 2c20 2050 7265 763a 2044 Lines, Prev: D\n+0000e0d0: 7261 7761 626c 6573 2c20 2055 703a 2044 rawables, Up: D\n+0000e0e0: 7261 7761 626c 6573 0a0a 332e 322e 3120 rawables..3.2.1 \n+0000e0f0: 446f 7473 0a2d 2d2d 2d2d 2d2d 2d2d 2d0a Dots.----------.\n+0000e100: 0a2a 5379 6e74 6178 3a2a 0a20 2020 2020 .*Syntax:*. \n+0000e110: 646f 7473 5b4f 5054 494f 4e53 5d20 504f dots[OPTIONS] PO\n+0000e120: 494e 545f 4c49 5354 0a54 6869 7320 636f INT_LIST.This co\n+0000e130: 6d6d 616e 6420 6973 2074 6865 2074 6872 mmand is the thr\n+0000e140: 6565 2d64 696d 656e 7369 6f6e 616c 2065 ee-dimensional e\n+0000e150: 7175 6976 616c 656e 7420 6f66 2074 6865 quivalent of the\n+0000e160: 20e2 8098 5053 5472 6963 6b73 e280 990a ...PSTricks....\n+0000e170: 636f 6d6d 616e 6420 e280 985c 7073 646f command ...\\psdo\n+0000e180: 7473 e280 992e 0a0a 1f0a 4669 6c65 3a20 ts........File: \n+0000e190: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n+0000e1a0: 6465 3a20 4c69 6e65 732c 2020 4e65 7874 de: Lines, Next\n+0000e1b0: 3a20 4375 7276 6573 2c20 2050 7265 763a : Curves, Prev:\n+0000e1c0: 2044 6f74 732c 2020 5570 3a20 4472 6177 Dots, Up: Draw\n+0000e1d0: 6162 6c65 730a 0a33 2e32 2e32 204c 696e ables..3.2.2 Lin\n+0000e1e0: 6573 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a es.-----------..\n+0000e1f0: 2a53 796e 7461 783a 2a0a 2020 2020 206c *Syntax:*. l\n+0000e200: 696e 655b 4f50 5449 4f4e 535d 2050 4f49 ine[OPTIONS] POI\n+0000e210: 4e54 5f4c 4953 540a 5468 6973 2063 6f6d NT_LIST.This com\n+0000e220: 6d61 6e64 2069 7320 7468 6520 7468 7265 mand is the thre\n+0000e230: 652d 6469 6d65 6e73 696f 6e61 6c20 6571 e-dimensional eq\n+0000e240: 7569 7661 6c65 6e74 206f 6620 7468 6520 uivalent of the \n+0000e250: e280 9850 5354 7269 636b 73e2 8099 0a63 ...PSTricks....c\n+0000e260: 6f6d 6d61 6e64 20e2 8098 5c70 736c 696e ommand ...\\pslin\n+0000e270: 65e2 8099 2e0a 0a1f 0a46 696c 653a 2073 e........File: s\n+0000e280: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+0000e290: 653a 2043 7572 7665 732c 2020 4e65 7874 e: Curves, Next\n+0000e2a0: 3a20 506f 6c79 676f 6e73 2c20 2050 7265 : Polygons, Pre\n+0000e2b0: 763a 204c 696e 6573 2c20 2055 703a 2044 v: Lines, Up: D\n+0000e2c0: 7261 7761 626c 6573 0a0a 332e 322e 3320 rawables..3.2.3 \n+0000e2d0: 4375 7276 6573 0a2d 2d2d 2d2d 2d2d 2d2d Curves.---------\n+0000e2e0: 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a 0a20 ---..*Syntax:*. \n+0000e2f0: 2020 2020 6375 7276 655b 4f50 5449 4f4e curve[OPTION\n+0000e300: 535d 2050 4f49 4e54 5f4c 4953 540a 5468 S] POINT_LIST.Th\n+0000e310: 6973 2063 6f6d 6d61 6e64 2069 7320 7468 is command is th\n+0000e320: 6520 7468 7265 652d 6469 6d65 6e73 696f e three-dimensio\n+0000e330: 6e61 6c20 6571 7569 7661 6c65 6e74 206f nal equivalent o\n+0000e340: 6620 7468 6520 e280 9850 5354 7269 636b f the ...PSTrick\n+0000e350: 73e2 8099 0a63 6f6d 6d61 6e64 20e2 8098 s....command ...\n+0000e360: 5c70 7363 7572 7665 e280 992e 2020 4974 \\pscurve.... It\n+0000e370: 2069 7320 6e6f 7420 696d 706c 656d 656e is not implemen\n+0000e380: 7465 6420 696e 2074 6865 2063 7572 7265 ted in the curre\n+0000e390: 6e74 2076 6572 7369 6f6e 206f 660a e280 nt version of...\n+0000e3a0: 9873 6b65 7463 68e2 8099 2e0a 0a1f 0a46 .sketch........F\n+0000e3b0: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+0000e3c0: 2c20 204e 6f64 653a 2050 6f6c 7967 6f6e , Node: Polygon\n+0000e3d0: 732c 2020 4e65 7874 3a20 5370 6563 6961 s, Next: Specia\n+0000e3e0: 6c73 2c20 2050 7265 763a 2043 7572 7665 ls, Prev: Curve\n+0000e3f0: 732c 2020 5570 3a20 4472 6177 6162 6c65 s, Up: Drawable\n+0000e400: 730a 0a33 2e32 2e34 2050 6f6c 7967 6f6e s..3.2.4 Polygon\n+0000e410: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d s.--------------\n+0000e420: 0a0a 2a53 796e 7461 783a 2a0a 2020 2020 ..*Syntax:*. \n+0000e430: 2070 6f6c 7967 6f6e 5b4f 5054 494f 4e53 polygon[OPTIONS\n+0000e440: 5d20 504f 494e 545f 4c49 5354 0a54 6869 ] POINT_LIST.Thi\n+0000e450: 7320 636f 6d6d 616e 6420 6973 2074 6865 s command is the\n+0000e460: 2074 6872 6565 2d64 696d 656e 7369 6f6e three-dimension\n+0000e470: 616c 2065 7175 6976 616c 656e 7420 6f66 al equivalent of\n+0000e480: 2074 6865 20e2 8098 5053 5472 6963 6b73 the ...PSTricks\n+0000e490: e280 990a 636f 6d6d 616e 6420 e280 985c ....command ...\\\n+0000e4a0: 7073 706f 6c79 676f 6ee2 8099 2e20 2054 pspolygon.... T\n+0000e4b0: 6865 20e2 8098 736b 6574 6368 e280 9920 he ...sketch... \n+0000e4c0: 6869 6464 656e 2073 7572 6661 6365 2061 hidden surface a\n+0000e4d0: 6c67 6f72 6974 686d 2061 7373 756d 6573 lgorithm assumes\n+0000e4e0: 0a74 6861 7420 706f 6c79 676f 6e73 2061 .that polygons a\n+0000e4f0: 7265 2063 6f6e 7665 7820 616e 6420 706c re convex and pl\n+0000e500: 616e 6172 2e20 2049 6e20 7072 6163 7469 anar. In practi\n+0000e510: 6365 2c20 6472 6177 696e 6773 206d 6179 ce, drawings may\n+0000e520: 2077 656c 6c0a 7475 726e 206f 7574 2063 well.turn out c\n+0000e530: 6f72 7265 6374 6c79 2065 7665 6e20 6966 orrectly even if\n+0000e540: 2074 6865 7365 2061 7373 756d 7074 696f these assumptio\n+0000e550: 6e73 2061 7265 2076 696f 6c61 7465 642e ns are violated.\n+0000e560: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n+0000e570: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5370 .info, Node: Sp\n+0000e580: 6563 6961 6c73 2c20 204e 6578 743a 2053 ecials, Next: S\n+0000e590: 7765 6570 732c 2020 5072 6576 3a20 506f weeps, Prev: Po\n+0000e5a0: 6c79 676f 6e73 2c20 2055 703a 2044 7261 lygons, Up: Dra\n+0000e5b0: 7761 626c 6573 0a0a 332e 322e 3520 5370 wables..3.2.5 Sp\n+0000e5c0: 6563 6961 6c73 0a2d 2d2d 2d2d 2d2d 2d2d ecials.---------\n+0000e5d0: 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a -----..*Syntax:*\n+0000e5e0: 0a20 2020 2020 7370 6563 6961 6c20 2452 . special $R\n+0000e5f0: 4157 5f54 4558 5424 5b4f 5054 494f 4e53 AW_TEXT$[OPTIONS\n+0000e600: 5d20 4152 475f 4c49 5354 0a48 6572 6520 ] ARG_LIST.Here \n+0000e610: e280 9824 e280 9920 6361 6e20 6265 2061 ...$... can be a\n+0000e620: 6e79 2063 6861 7261 6374 6572 2061 6e64 ny character and\n+0000e630: 2069 7320 7573 6564 2074 6f20 6465 6c69 is used to deli\n+0000e640: 6d69 7420 7468 6520 7374 6172 7420 616e mit the start an\n+0000e650: 6420 656e 640a 6f66 2052 4157 5f54 4558 d end.of RAW_TEX\n+0000e660: 542e 2020 5468 6520 636f 6d6d 616e 6420 T. The command \n+0000e670: 656d 6265 6473 2052 4157 5f54 4558 5420 embeds RAW_TEXT \n+0000e680: 696e 2074 6865 20e2 8098 736b 6574 6368 in the ...sketch\n+0000e690: e280 9920 6f75 7470 7574 2061 6674 6572 ... output after\n+0000e6a0: 0a70 6572 666f 726d 696e 6720 7375 6273 .performing subs\n+0000e6b0: 7469 7475 7469 6f6e 7320 6173 2066 6f6c titutions as fol\n+0000e6c0: 6c6f 7773 2e0a 2020 20e2 80a2 20e2 8098 lows.. ... ...\n+0000e6d0: 2349 e280 9920 7768 6572 6520 4920 6973 #I... where I is\n+0000e6e0: 2061 2070 6f73 6974 6976 6520 696e 7465 a positive inte\n+0000e6f0: 6765 7220 6973 2072 6570 6c61 6365 6420 ger is replaced \n+0000e700: 6279 2074 6865 2049 2774 6820 7661 6c75 by the I'th valu\n+0000e710: 6520 696e 0a20 2020 2020 4152 475f 4c49 e in. ARG_LI\n+0000e720: 5354 2e20 2050 6f69 6e74 2061 6e64 2076 ST. Point and v\n+0000e730: 6563 746f 7220 6172 6775 6d65 6e74 7320 ector arguments \n+0000e740: 6265 636f 6d65 2074 776f 2d64 696d 656e become two-dimen\n+0000e750: 7369 6f6e 616c 0a20 2020 2020 706f 696e sional. poin\n+0000e760: 7473 2c20 7768 6963 6820 6172 6520 7468 ts, which are th\n+0000e770: 6520 7472 616e 7366 6f72 6d65 6420 3364 e transformed 3d\n+0000e780: 2061 7267 756d 656e 7473 2070 726f 6a65 arguments proje\n+0000e790: 6374 6564 206f 6e74 6f20 7468 650a 2020 cted onto the. \n+0000e7a0: 2020 2058 2d59 2070 6c61 6e65 2e20 2054 X-Y plane. T\n+0000e7b0: 6869 7320 616c 6c6f 7773 2074 776f 2d64 his allows two-d\n+0000e7c0: 696d 656e 7469 6f6e 616c 206f 7574 7075 imentional outpu\n+0000e7d0: 7420 656c 656d 656e 7473 2073 7563 6820 t elements such \n+0000e7e0: 6173 0a20 2020 2020 6c61 6265 6c73 2074 as. labels t\n+0000e7f0: 6f20 6265 2065 6173 696c 7920 706f 7369 o be easily posi\n+0000e800: 7469 6f6e 6564 2077 6974 6820 7265 7370 tioned with resp\n+0000e810: 6563 7420 746f 2074 6872 6565 2d64 696d ect to three-dim\n+0000e820: 656e 7369 6f6e 616c 0a20 2020 2020 6665 ensional. fe\n+0000e830: 6174 7572 6573 2069 6e20 7468 6520 6472 atures in the dr\n+0000e840: 6177 696e 672e 2020 5363 616c 6172 2061 awing. Scalar a\n+0000e850: 7267 756d 656e 7473 2061 7265 2073 7562 rguments are sub\n+0000e860: 7369 7475 7465 6420 6469 7265 6374 6c79 situted directly\n+0000e870: 2e0a 2020 2020 204e 6f20 7472 616e 7366 .. No transf\n+0000e880: 6f72 6d61 7469 6f6e 2069 7320 6170 706c ormation is appl\n+0000e890: 6965 642e 0a20 2020 e280 a220 e280 9823 ied.. ... ...#\n+0000e8a0: 7b49 7de2 8099 2069 7320 616c 736f 2072 {I}... is also r\n+0000e8b0: 6570 6c61 6365 6420 6173 2061 626f 7665 eplaced as above\n+0000e8c0: 2e0a 2020 20e2 80a2 20e2 8098 2349 2732 .. ... ...#I'2\n+0000e8d0: e280 9920 6973 2072 6570 6c61 6365 6420 ... is replaced \n+0000e8e0: 6173 2061 626f 7665 2066 6f72 2070 6f69 as above for poi\n+0000e8f0: 6e74 7320 6f72 2076 6563 746f 7273 2e20 nts or vectors. \n+0000e900: 2049 7420 6973 2061 6e20 6572 726f 720a It is an error.\n+0000e910: 2020 2020 2066 6f72 2074 6865 2049 2774 for the I't\n+0000e920: 6820 6172 6775 6d65 6e74 2074 6f20 6265 h argument to be\n+0000e930: 2061 2073 6361 6c61 722e 0a20 2020 e280 a scalar.. ..\n+0000e940: a220 e280 9823 4927 78e2 8099 2c20 e280 . ...#I'x..., ..\n+0000e950: 9823 4927 79e2 8099 2c20 6f72 20e2 8098 .#I'y..., or ...\n+0000e960: 2349 277a e280 9920 6973 2072 6570 6c61 #I'z... is repla\n+0000e970: 6365 642c 2072 6573 7065 6374 6976 656c ced, respectivel\n+0000e980: 792c 2062 7920 7468 6520 7363 616c 6172 y, by the scalar\n+0000e990: 0a20 2020 2020 582c 2059 2c20 6f72 205a . X, Y, or Z\n+0000e9a0: 2d63 6f6f 7264 696e 6174 6520 6f66 2074 -coordinate of t\n+0000e9b0: 6865 2061 7267 756d 656e 7420 706f 696e he argument poin\n+0000e9c0: 7420 6f72 2076 6563 746f 722e 2020 4974 t or vector. It\n+0000e9d0: 2069 7320 616e 0a20 2020 2020 6572 726f is an. erro\n+0000e9e0: 7220 666f 7220 7468 6520 4927 7468 2061 r for the I'th a\n+0000e9f0: 7267 756d 656e 7420 746f 2062 6520 6120 rgument to be a \n+0000ea00: 7363 616c 6172 2e0a 2020 20e2 80a2 20e2 scalar.. ... .\n+0000ea10: 8098 2349 2733 e280 9920 6973 2072 6570 ..#I'3... is rep\n+0000ea20: 6c61 6365 6420 6279 2074 6865 2074 6872 laced by the thr\n+0000ea30: 6565 2d64 696d 656e 7369 6f6e 616c 2074 ee-dimensional t\n+0000ea40: 7261 6e73 666f 726d 6564 2061 7267 756d ransformed argum\n+0000ea50: 656e 742e 0a20 2020 2020 4e6f 7465 2074 ent.. Note t\n+0000ea60: 6861 7420 6966 2061 2070 6572 7370 6563 hat if a perspec\n+0000ea70: 7469 7665 2074 7261 6e73 666f 726d 6174 tive transformat\n+0000ea80: 696f 6e20 6861 7320 6265 656e 2061 7070 ion has been app\n+0000ea90: 6c69 6564 2c20 7468 650a 2020 2020 205a lied, the. Z\n+0000eaa0: 2d63 6f6f 7264 696e 6174 6520 6861 7320 -coordinate has \n+0000eab0: 6c69 7474 6c65 2067 656f 6d65 7472 6963 little geometric\n+0000eac0: 2073 6967 6e69 6669 6361 6e63 652c 2074 significance, t\n+0000ead0: 686f 7567 6820 6974 0a20 2020 2020 6163 hough it. ac\n+0000eae0: 6375 7261 7465 6c79 2069 6e64 6963 6174 curately indicat\n+0000eaf0: 6573 2072 656c 6174 6976 6520 6465 7074 es relative dept\n+0000eb00: 682e 0a20 2020 e280 a220 e280 9823 492d h.. ... ...#I-\n+0000eb10: 4ae2 8099 2077 6865 7265 2049 2061 6e64 J... where I and\n+0000eb20: 204a 2061 7265 2070 6f73 6974 6976 6520 J are positive \n+0000eb30: 696e 7465 6765 7273 2069 7320 7265 706c integers is repl\n+0000eb40: 6163 6564 2062 7920 6120 7374 7269 6e67 aced by a string\n+0000eb50: 0a20 2020 2020 e280 987b 414e 474c 457d . ...{ANGLE}\n+0000eb60: e280 9920 7768 6572 6520 414e 474c 4520 ... where ANGLE \n+0000eb70: 6973 2074 6865 2070 6f6c 6172 2061 6e67 is the polar ang\n+0000eb80: 6c65 206f 6620 6120 7665 6374 6f72 2066 le of a vector f\n+0000eb90: 726f 6d20 7468 6520 4927 7468 0a20 2020 rom the I'th. \n+0000eba0: 2020 706f 696e 7420 696e 2050 4f49 4e54 point in POINT\n+0000ebb0: 5f4c 4953 5420 746f 2074 6865 204a 2774 _LIST to the J't\n+0000ebc0: 6820 706f 696e 7420 7072 6f6a 6563 7465 h point projecte\n+0000ebd0: 6420 696e 746f 2074 6865 2078 2d79 2070 d into the x-y p\n+0000ebe0: 6c61 6e65 2e0a 2020 2020 2049 7420 6973 lane.. It is\n+0000ebf0: 2061 6e20 6572 726f 7220 666f 7220 7468 an error for th\n+0000ec00: 6520 4927 7468 206f 7220 4a27 7468 2061 e I'th or J'th a\n+0000ec10: 7267 756d 656e 7420 746f 2062 6520 6120 rgument to be a \n+0000ec20: 7363 616c 6172 206f 7220 610a 2020 2020 scalar or a. \n+0000ec30: 2076 6563 746f 722e 0a20 2020 e280 a220 vector.. ... \n+0000ec40: e280 9823 7b49 2d4a 7de2 8099 2069 7320 ...#{I-J}... is \n+0000ec50: 616c 736f 2072 6570 6c61 6365 6420 6173 also replaced as\n+0000ec60: 2061 626f 7665 2e0a 2020 20e2 80a2 20e2 above.. ... .\n+0000ec70: 8098 2323 e280 9920 6973 2072 6570 6c61 ..##... is repla\n+0000ec80: 6365 6420 7769 7468 20e2 8098 23e2 8099 ced with ...#...\n+0000ec90: 2e0a 5468 6520 666f 726d 7320 7769 7468 ..The forms with\n+0000eca0: 2062 7261 6365 7320 e280 987b 207d e280 braces ...{ }..\n+0000ecb0: 9920 6172 6520 7573 6566 756c 2077 6865 . are useful whe\n+0000ecc0: 6e20 7468 6520 6172 6775 6d65 6e74 2069 n the argument i\n+0000ecd0: 7320 696d 6d65 6469 6174 656c 790a 666f s immediately.fo\n+0000ece0: 6c6c 6f77 6564 2062 7920 6120 6469 6769 llowed by a digi\n+0000ecf0: 7420 6f72 2061 2074 6963 6b20 6368 6172 t or a tick char\n+0000ed00: 6163 7465 7220 7468 6174 2069 7320 7061 acter that is pa\n+0000ed10: 7274 206f 6620 7468 6520 5465 5820 636f rt of the TeX co\n+0000ed20: 6465 2e0a 0a20 2020 5468 6520 6f6e 6c79 de... The only\n+0000ed30: 2075 7365 6675 6c20 6f70 7469 6f6e 206f useful option o\n+0000ed40: 6620 e280 9873 7065 6369 616c e280 9920 f ...special... \n+0000ed50: 6973 20e2 8098 6c61 79e2 8099 2c20 7768 is ...lay..., wh\n+0000ed60: 6963 6820 6465 7465 726d 696e 6573 2069 ich determines i\n+0000ed70: 6620 7468 650a 7375 6273 7469 7475 6564 f the.substitued\n+0000ed80: 2072 6177 2074 6578 7420 6973 2065 6d69 raw text is emi\n+0000ed90: 7474 6564 2062 6566 6f72 652c 2061 6674 tted before, aft\n+0000eda0: 6572 2c20 6f72 2075 7369 6e67 2074 6865 er, or using the\n+0000edb0: 2066 6972 7374 2070 6f69 6e74 0a69 6e20 first point.in \n+0000edc0: 504f 494e 545f 4c49 5354 2061 7320 616e POINT_LIST as an\n+0000edd0: 2069 6e64 6963 6174 6f72 206f 6620 6465 indicator of de\n+0000ede0: 7074 682e 2020 5468 6573 6520 6f63 6375 pth. These occu\n+0000edf0: 722c 2072 6573 7065 6374 6976 656c 792c r, respectively,\n+0000ee00: 2077 6974 680a e280 986c 6179 3d75 6e64 with....lay=und\n+0000ee10: 6572 e280 992c 20e2 8098 6c61 793d 6f76 er..., ...lay=ov\n+0000ee20: 6572 e280 992c 2061 6e64 20e2 8098 6c61 er..., and ...la\n+0000ee30: 793d 696e e280 992e 2020 5365 6520 2a6e y=in.... See *n\n+0000ee40: 6f74 6520 5370 6563 6961 6c20 6f62 6a65 ote Special obje\n+0000ee50: 6374 733a 3a20 616e 640a 2a6e 6f74 6520 cts:: and.*note \n+0000ee60: 5469 6b5a 2f50 4746 2075 7365 722d 6465 TikZ/PGF user-de\n+0000ee70: 6669 6e65 6420 7374 796c 6573 3a3a 2066 fined styles:: f\n+0000ee80: 6f72 2065 7861 6d70 6c65 732e 2020 2a4e or examples. *N\n+0000ee90: 6f74 6520 496e 7465 726e 616c 0a6f 7074 ote Internal.opt\n+0000eea0: 696f 6e73 3a3a 2e0a 0a1f 0a46 696c 653a ions::.....File:\n+0000eeb0: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n+0000eec0: 6f64 653a 2053 7765 6570 732c 2020 4e65 ode: Sweeps, Ne\n+0000eed0: 7874 3a20 426c 6f63 6b73 2c20 2050 7265 xt: Blocks, Pre\n+0000eee0: 763a 2053 7065 6369 616c 732c 2020 5570 v: Specials, Up\n+0000eef0: 3a20 4472 6177 6162 6c65 730a 0a33 2e32 : Drawables..3.2\n+0000ef00: 2e36 2053 7765 6570 730a 2d2d 2d2d 2d2d .6 Sweeps.------\n+0000ef10: 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 783a ------..*Syntax:\n+0000ef20: 2a0a 2020 2020 2073 7765 6570 207b 204e *. sweep { N\n+0000ef30: 2c20 545f 312c 2054 5f32 2c20 2e2e 2e2c , T_1, T_2, ...,\n+0000ef40: 2054 5f52 207d 5b4f 5054 494f 4e53 5d20 T_R }[OPTIONS] \n+0000ef50: 5357 4550 545f 4f42 4a45 4354 0a20 2020 SWEPT_OBJECT. \n+0000ef60: 2020 7377 6565 7020 7b20 4e3c 3e2c 2054 sweep { N<>, T\n+0000ef70: 5f31 2c20 545f 322c 202e 2e2e 2c20 545f _1, T_2, ..., T_\n+0000ef80: 5220 7d5b 4f50 5449 4f4e 535d 2053 5745 R }[OPTIONS] SWE\n+0000ef90: 5054 5f4f 424a 4543 540a 5468 6520 7377 PT_OBJECT.The sw\n+0000efa0: 6565 7020 636f 6e6e 6563 7473 204e 2028 eep connects N (\n+0000efb0: 6f72 2070 6572 6861 7073 204e 2b31 2920 or perhaps N+1) \n+0000efc0: 636f 7069 6573 206f 6620 5357 4550 545f copies of SWEPT_\n+0000efd0: 4f42 4a45 4354 2069 6e20 6f72 6465 7220 OBJECT in order \n+0000efe0: 746f 0a63 7265 6174 6520 6120 6e65 7720 to.create a new \n+0000eff0: 6f62 6a65 6374 206f 6620 6869 6768 6572 object of higher\n+0000f000: 2064 696d 656e 7369 6f6e 2e20 2054 6865 dimension. The\n+0000f010: 2054 5f49 2028 666f 7220 6920 6265 7477 T_I (for i betw\n+0000f020: 6565 6e20 3120 616e 640a 7229 2061 7265 een 1 and.r) are\n+0000f030: 2074 7261 6e73 666f 726d 732e 2020 5468 transforms. Th\n+0000f040: 6520 6b27 7468 2063 6f70 7920 6f66 2053 e k'th copy of S\n+0000f050: 5745 5054 5f4f 424a 4543 5420 6973 2070 WEPT_OBJECT is p\n+0000f060: 726f 6475 6365 6420 6279 0a61 7070 6c79 roduced by.apply\n+0000f070: 696e 6720 7468 6520 666f 6c6c 6f77 696e ing the followin\n+0000f080: 6720 7472 616e 7366 6f72 6d20 746f 2074 g transform to t\n+0000f090: 6865 206f 7269 6769 6e61 6c2e 0a20 2020 he original.. \n+0000f0a0: 2020 545f 315e 6b20 7468 656e 2054 5f32 T_1^k then T_2\n+0000f0b0: 5e6b 2074 6865 6e20 2e2e 2e20 7468 656e ^k then ... then\n+0000f0c0: 2054 5f52 5e6b 0a48 6572 6520 545e 6b20 T_R^k.Here T^k \n+0000f0d0: 6d65 616e 7320 2274 7261 6e73 666f 726d means \"transform\n+0000f0e0: 2054 2061 7070 6c69 6564 206b 2074 696d T applied k tim\n+0000f0f0: 6573 2e22 2020 5468 6520 6f72 6967 696e es.\" The origin\n+0000f100: 616c 206f 626a 6563 7420 6973 0a74 6865 al object is.the\n+0000f110: 207a 6572 6f27 7468 2063 6f70 792c 2077 zero'th copy, w\n+0000f120: 6974 6820 6b3d 3020 616e 6420 6566 6665 ith k=0 and effe\n+0000f130: 6374 6976 656c 7920 6e6f 2074 7261 6e73 ctively no trans\n+0000f140: 666f 726d 2061 7070 6c69 6564 2028 545e form applied (T^\n+0000f150: 303d 492c 0a74 6865 2069 6465 6e74 6974 0=I,.the identit\n+0000f160: 7920 7472 616e 7366 6f72 6d29 2e0a 0a20 y transform)... \n+0000f170: 2020 5468 6520 6d65 7468 6f64 206f 6620 The method of \n+0000f180: 636f 6e6e 6563 7469 6e67 2074 6865 2063 connecting the c\n+0000f190: 6f70 6965 7320 6465 7065 6e64 7320 6f6e opies depends on\n+0000f1a0: 2074 6865 2074 7970 6520 6f66 0a53 5745 the type of.SWE\n+0000f1b0: 5054 5f4f 424a 4543 5420 616e 6420 6f6e PT_OBJECT and on\n+0000f1c0: 2077 6865 7468 6572 2074 6865 2063 6c6f whether the clo\n+0000f1d0: 7375 7265 2074 6167 20e2 8098 3c3e e280 sure tag ...<>..\n+0000f1e0: 9920 6973 2070 7265 7365 6e74 206f 7220 . is present or \n+0000f1f0: 6e6f 742e 0a0a 2020 2041 6e20 6578 616d not... An exam\n+0000f200: 706c 6520 6f66 2061 2073 7765 6570 2077 ple of a sweep w\n+0000f210: 6865 7265 2072 3d32 2069 7320 7468 6520 here r=2 is the \n+0000f220: 4d6f 6269 7573 2066 6967 7572 6520 6174 Mobius figure at\n+0000f230: 202a 6e6f 7465 204d 6f72 6520 746f 0a6c *note More to.l\n+0000f240: 6561 726e 3a3a 2e0a 0a2a 204d 656e 753a earn::...* Menu:\n+0000f250: 0a0a 2a20 5377 6570 7420 706f 696e 7473 ..* Swept points\n+0000f260: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n+0000f270: 2020 5377 6570 7420 706f 696e 7473 206d Swept points m\n+0000f280: 616b 6520 6c69 6e65 7320 6f72 2070 6f6c ake lines or pol\n+0000f290: 7967 6f6e 732e 0a2a 2053 7765 7074 206c ygons..* Swept l\n+0000f2a0: 696e 6573 3a3a 2020 2020 2020 2020 2020 ines:: \n+0000f2b0: 2020 2020 2020 2053 7765 7074 206c 696e Swept lin\n+0000f2c0: 6573 206d 616b 6520 6f70 656e 206f 7220 es make open or \n+0000f2d0: 636c 6f73 6564 2073 7572 6661 6365 732e closed surfaces.\n+0000f2e0: 0a2a 2053 7765 7074 2070 6f6c 7967 6f6e .* Swept polygon\n+0000f2f0: 733a 3a20 2020 2020 2020 2020 2020 2020 s:: \n+0000f300: 2053 7765 7074 2070 6f6c 7967 6f6e 7320 Swept polygons \n+0000f310: 6d61 6b65 2063 6c6f 7365 6420 7375 7266 make closed surf\n+0000f320: 6163 6573 2e0a 2a20 5377 6570 7420 626c aces..* Swept bl\n+0000f330: 6f63 6b73 3a3a 2020 2020 2020 2020 2020 ocks:: \n+0000f340: 2020 2020 2020 5377 6570 7420 626c 6f63 Swept bloc\n+0000f350: 6b20 e289 a120 626c 6f63 6b20 6f66 2073 k ... block of s\n+0000f360: 7765 6570 732e 0a2a 2053 7765 6570 2066 weeps..* Sweep f\n+0000f370: 6163 6520 7370 6c69 7474 696e 673a 3a20 ace splitting:: \n+0000f380: 2020 2020 2020 2046 6978 696e 6720 7761 Fixing wa\n+0000f390: 7270 6564 2066 6163 6573 2077 6974 6820 rped faces with \n+0000f3a0: 7472 6961 6e67 6c65 732e 0a0a 1f0a 4669 triangles.....Fi\n+0000f3b0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n+0000f3c0: 2020 4e6f 6465 3a20 5377 6570 7420 706f Node: Swept po\n+0000f3d0: 696e 7473 2c20 204e 6578 743a 2053 7765 ints, Next: Swe\n+0000f3e0: 7074 206c 696e 6573 2c20 2050 7265 763a pt lines, Prev:\n+0000f3f0: 2053 7765 6570 732c 2020 5570 3a20 5377 Sweeps, Up: Sw\n+0000f400: 6565 7073 0a0a 332e 322e 362e 3120 5377 eeps..3.2.6.1 Sw\n+0000f410: 6570 7420 706f 696e 7473 0a2e 2e2e 2e2e ept points......\n+0000f420: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a ................\n+0000f430: 0a49 6620 5357 4550 545f 4f42 4a45 4354 .If SWEPT_OBJECT\n+0000f440: 2069 7320 6120 706f 696e 7420 6c69 7374 is a point list\n+0000f450: 2061 6e64 2074 6865 7265 2069 7320 6e6f and there is no\n+0000f460: 2063 6c6f 7375 7265 2074 6167 2c20 7468 closure tag, th\n+0000f470: 656e 0ae2 8098 7377 6565 70e2 8099 2063 en....sweep... c\n+0000f480: 6f6e 6e65 6374 7320 4e2b 3120 7375 6363 onnects N+1 succ\n+0000f490: 6573 7369 7665 2063 6f70 6965 7320 6f66 essive copies of\n+0000f4a0: 2065 6163 6820 706f 696e 7420 2869 6e63 each point (inc\n+0000f4b0: 6c75 6469 6e67 2074 6865 0a6f 7269 6769 luding the.origi\n+0000f4c0: 6e61 6c29 2077 6974 6820 7374 7261 6967 nal) with straig\n+0000f4d0: 6874 206c 696e 6520 7365 676d 656e 7473 ht line segments\n+0000f4e0: 2074 6f20 666f 726d 2061 2070 6f6c 796c to form a polyl\n+0000f4f0: 696e 652e 2020 4966 2074 6865 7265 2061 ine. If there a\n+0000f500: 7265 0a6d 2070 6f69 6e74 7320 696e 2074 re.m points in t\n+0000f510: 6865 206f 7269 6769 6e61 6c20 706f 696e he original poin\n+0000f520: 7420 6c69 7374 2c20 7468 656e 206d 2070 t list, then m p\n+0000f530: 6f6c 796c 696e 6573 2077 6974 6820 4e20 olylines with N \n+0000f540: 7365 676d 656e 7473 0a65 6163 6820 6172 segments.each ar\n+0000f550: 6520 666f 726d 6564 2062 7920 7468 6520 e formed by the \n+0000f560: 7377 6565 702e 2020 496e 2074 6869 7320 sweep. In this \n+0000f570: 6d61 6e6e 6572 2c20 e280 9873 7765 6570 manner, ...sweep\n+0000f580: e280 9920 666f 726d 7320 6120 7365 7420 ... forms a set \n+0000f590: 6f66 0a6f 6e65 2d64 696d 656e 7369 6f6e of.one-dimension\n+0000f5a0: 616c 206f 626a 6563 7473 2028 706f 6c79 al objects (poly\n+0000f5b0: 6c69 6e65 7329 2066 726f 6d20 7a65 726f lines) from zero\n+0000f5c0: 2d64 696d 656e 7369 6f6e 616c 206f 6e65 -dimensional one\n+0000f5d0: 7320 2870 6f69 6e74 7329 2e0a 0a20 2020 s (points)... \n+0000f5e0: 5768 656e 2074 6865 7265 205f 6973 5f20 When there _is_ \n+0000f5f0: 6120 636c 6f73 7572 6520 7461 672c 20e2 a closure tag, .\n+0000f600: 8098 7377 6565 70e2 8099 2063 6f6e 6e65 ..sweep... conne\n+0000f610: 6374 7320 4e20 7375 6363 6573 7369 7665 cts N successive\n+0000f620: 2063 6f70 6965 730a 6f66 2065 6163 6820 copies.of each \n+0000f630: 706f 696e 7420 2869 6e63 6c75 6469 6e67 point (including\n+0000f640: 2074 6865 206f 7269 6769 6e61 6c29 2077 the original) w\n+0000f650: 6974 6820 7374 7261 6967 6874 206c 696e ith straight lin\n+0000f660: 6520 7365 676d 656e 7473 2061 6e64 0a66 e segments and.f\n+0000f670: 696e 616c 6c79 2063 6f6e 6e65 6374 7320 inally connects \n+0000f680: 7468 6520 6c61 7374 2063 6f70 7920 6261 the last copy ba\n+0000f690: 636b 2074 6f20 7468 6520 6f72 6967 696e ck to the origin\n+0000f6a0: 616c 2074 6f20 666f 726d 2061 2070 6f6c al to form a pol\n+0000f6b0: 7967 6f6e 0a77 6974 6820 4e20 7369 6465 ygon.with N side\n+0000f6c0: 732e 2020 4966 2074 6865 7265 2061 7265 s. If there are\n+0000f6d0: 206d 2070 6f69 6e74 7320 696e 2074 6865 m points in the\n+0000f6e0: 206f 7269 6769 6e61 6c20 706f 696e 7420 original point \n+0000f6f0: 6c69 7374 2c20 7468 656e 206d 0a70 6f6c list, then m.pol\n+0000f700: 7967 6f6e 7320 7769 7468 204e 2073 6964 ygons with N sid\n+0000f710: 6573 2065 6163 6820 6172 6520 666f 726d es each are form\n+0000f720: 6564 2062 7920 7468 6520 7377 6565 702e ed by the sweep.\n+0000f730: 2020 496e 2074 6869 7320 6d61 6e6e 6572 In this manner\n+0000f740: 2c0a e280 9873 7765 6570 e280 9920 666f ,....sweep... fo\n+0000f750: 726d 7320 6120 7365 7420 6f66 2074 776f rms a set of two\n+0000f760: 2d64 696d 656e 7369 6f6e 616c 206f 626a -dimensional obj\n+0000f770: 6563 7473 2028 706f 6c79 676f 6e73 2920 ects (polygons) \n+0000f780: 6672 6f6d 0a7a 6572 6f2d 6469 6d65 6e73 from.zero-dimens\n+0000f790: 696f 6e61 6c20 6f6e 6573 2028 706f 696e ional ones (poin\n+0000f7a0: 7473 292e 0a0a 2020 204f 7074 696f 6e73 ts)... Options\n+0000f7b0: 206f 6620 7468 6520 e280 9873 7765 6570 of the ...sweep\n+0000f7c0: e280 9920 6172 6520 636f 7069 6564 2064 ... are copied d\n+0000f7d0: 6972 6563 746c 7920 746f 2074 6865 2072 irectly to the r\n+0000f7e0: 6573 756c 7469 6e67 0a70 6f6c 796c 696e esulting.polylin\n+0000f7f0: 6528 7329 2e0a 0a1f 0a46 696c 653a 2073 e(s).....File: s\n+0000f800: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+0000f810: 653a 2053 7765 7074 206c 696e 6573 2c20 e: Swept lines, \n+0000f820: 204e 6578 743a 2053 7765 7074 2070 6f6c Next: Swept pol\n+0000f830: 7967 6f6e 732c 2020 5072 6576 3a20 5377 ygons, Prev: Sw\n+0000f840: 6570 7420 706f 696e 7473 2c20 2055 703a ept points, Up:\n+0000f850: 2053 7765 6570 730a 0a33 2e32 2e36 2e32 Sweeps..3.2.6.2\n+0000f860: 2053 7765 7074 206c 696e 6573 0a2e 2e2e Swept lines....\n 0000f870: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000f880: 2e2e 0a0a 4966 2053 5745 5054 5f4f 424a ....If SWEPT_OBJ\n-0000f890: 4543 5420 6973 2061 2070 6f6c 796c 696e ECT is a polylin\n-0000f8a0: 6520 616e 6420 7468 6572 6520 6973 206e e and there is n\n-0000f8b0: 6f20 636c 6f73 7572 6520 7461 672c 2074 o closure tag, t\n-0000f8c0: 6865 6e20 e280 9873 7765 6570 e280 990a hen ...sweep....\n-0000f8d0: 636f 6e6e 6563 7473 204e 2b31 2073 7563 connects N+1 suc\n-0000f8e0: 6365 7373 6976 6520 636f 7069 6573 206f cessive copies o\n-0000f8f0: 6620 7468 6520 706f 6c79 6c69 6e65 2028 f the polyline (\n-0000f900: 696e 636c 7564 696e 6720 7468 6520 6f72 including the or\n-0000f910: 6967 696e 616c 290a 7769 7468 2066 6f75 iginal).with fou\n-0000f920: 722d 7369 6465 6420 706f 6c79 676f 6e73 r-sided polygons\n-0000f930: 2c20 6561 6368 2070 6169 7220 6f66 2063 , each pair of c\n-0000f940: 6f70 6965 7320 6769 7669 6e67 2072 6973 opies giving ris\n-0000f950: 6520 746f 2061 2022 706f 6c79 676f 6e0a e to a \"polygon.\n-0000f960: 7374 7269 702e 2220 2049 6620 7468 6572 strip.\" If ther\n-0000f970: 6520 6172 6520 6d20 706f 696e 7473 2069 e are m points i\n-0000f980: 6e20 7468 6520 6f72 6967 696e 616c 2070 n the original p\n-0000f990: 6f6c 796c 696e 652c 2074 6865 6e20 286d olyline, then (m\n-0000f9a0: 2d31 294e 0a70 6f6c 7967 6f6e 7320 6172 -1)N.polygons ar\n-0000f9b0: 6520 666f 726d 6564 2062 7920 7468 6520 e formed by the \n-0000f9c0: 7377 6565 702e 2020 5765 2063 616c 6c20 sweep. We call \n-0000f9d0: 7468 6573 6520 e280 9c62 6f64 7920 706f these ...body po\n-0000f9e0: 6c79 676f 6e73 e280 9d2e 2020 496e 0a74 lygons.... In.t\n-0000f9f0: 6869 7320 6d61 6e6e 6572 2c20 e280 9873 his manner, ...s\n-0000fa00: 7765 6570 e280 9920 666f 726d 7320 6120 weep... forms a \n-0000fa10: 7477 6f2d 6469 6d65 6e73 696f 6e61 6c20 two-dimensional \n-0000fa20: 7375 7266 6163 6520 6672 6f6d 2066 726f surface from fro\n-0000fa30: 6d20 610a 6f6e 652d 6469 6d65 6e73 696f m a.one-dimensio\n-0000fa40: 6e61 6c20 706f 6c79 6c69 6e65 2e0a 0a20 nal polyline... \n-0000fa50: 2020 5468 6520 6f72 6465 7220 6f66 2076 The order of v\n-0000fa60: 6572 7469 6365 7320 7072 6f64 7563 6564 ertices produced\n-0000fa70: 2062 7920 e280 9873 7765 6570 e280 9920 by ...sweep... \n-0000fa80: 6973 2069 6d70 6f72 7461 6e74 2e20 2049 is important. I\n-0000fa90: 6620 610a 706f 6c79 676f 6e27 7320 7665 f a.polygon's ve\n-0000faa0: 7274 6963 6573 2064 6f20 6e6f 7420 6170 rtices do not ap\n-0000fab0: 7065 6172 2069 6e20 636f 756e 7465 722d pear in counter-\n-0000fac0: 636c 6f63 6b77 6973 6520 6f72 6465 7220 clockwise order \n-0000fad0: 696e 2074 6865 2066 696e 616c 0a69 6d61 in the final.ima\n-0000fae0: 6765 2c20 7468 6520 706f 6c79 676f 6e20 ge, the polygon \n-0000faf0: 7769 6c6c 2062 6520 6375 6c6c 6564 2028 will be culled (\n-0000fb00: 756e 6c65 7373 20e2 8098 6375 6c6c 3d66 unless ...cull=f\n-0000fb10: 616c 7365 e280 9920 6973 2073 6574 292e alse... is set).\n-0000fb20: 2020 4966 2074 6865 0a70 6f69 6e74 7320 If the.points \n-0000fb30: 696e 2074 6865 206b 2774 6820 636f 7079 in the k'th copy\n-0000fb40: 206f 6620 7468 6520 706f 6c79 6c69 6e65 of the polyline\n-0000fb50: 2061 7265 2050 5f31 2c20 505f 322c 202e are P_1, P_2, .\n-0000fb60: 2e2e 2c20 505f 6d2c 2061 6e64 2074 6865 .., P_m, and the\n-0000fb70: 0a70 6f69 6e74 7320 696e 2074 6865 206e .points in the n\n-0000fb80: 6578 7420 636f 7079 2c20 7468 6520 286b ext copy, the (k\n-0000fb90: 2b31 2973 742c 2061 7265 2050 5f31 272c +1)st, are P_1',\n-0000fba0: 2050 5f32 272c 202e 2e2e 2c20 505f 6d27 P_2', ..., P_m'\n-0000fbb0: 2c20 7468 656e 0a74 6865 2076 6572 7465 , then.the verte\n-0000fbc0: 7820 6f72 6465 7220 6f66 2074 6865 2067 x order of the g\n-0000fbd0: 656e 6572 6174 6564 2070 6f6c 7967 6f6e enerated polygon\n-0000fbe0: 7320 6973 0a20 2020 2020 426f 6479 2070 s is. Body p\n-0000fbf0: 6f6c 7967 6f6e 2031 3a20 505f 3220 505f olygon 1: P_2 P_\n-0000fc00: 3120 505f 3127 2050 5f32 270a 2020 2020 1 P_1' P_2'. \n-0000fc10: 2042 6f64 7920 706f 6c79 676f 6e20 323a Body polygon 2:\n-0000fc20: 2050 5f33 2050 5f32 2050 5f32 2720 505f P_3 P_2 P_2' P_\n-0000fc30: 3327 0a20 2020 2020 2e2e 2e0a 2020 2020 3'. .... \n-0000fc40: 2042 6f64 7920 706f 6c79 676f 6e20 6d2d Body polygon m-\n-0000fc50: 313a 2050 5f6d 2050 5f7b 6d2d 317d 2050 1: P_m P_{m-1} P\n-0000fc60: 5f7b 6d2d 317d 2720 505f 6d27 0a0a 2020 _{m-1}' P_m'.. \n-0000fc70: 204f 7074 696f 6e73 206f 6620 756e 636c Options of uncl\n-0000fc80: 6f73 6564 206c 696e 6520 7377 6565 7073 osed line sweeps\n-0000fc90: 2061 7265 2063 6f70 6965 6420 746f 2065 are copied to e\n-0000fca0: 6163 6820 6f75 7470 7574 2070 6f6c 7967 ach output polyg\n-0000fcb0: 6f6e 2e0a 4f70 7469 6f6e 7320 6f66 2074 on..Options of t\n-0000fcc0: 6865 2073 7765 7074 206c 696e 6520 6172 he swept line ar\n-0000fcd0: 6520 6967 6e6f 7265 642e 0a0a 2020 2057 e ignored... W\n-0000fce0: 6865 6e20 7468 6572 6520 5f69 735f 2061 hen there _is_ a\n-0000fcf0: 2063 6c6f 7375 7265 2074 6167 2c20 7468 closure tag, th\n-0000fd00: 656e 20e2 8098 7377 6565 70e2 8099 2063 en ...sweep... c\n-0000fd10: 6f6e 6e65 6374 7320 4e20 7375 6363 6573 onnects N succes\n-0000fd20: 7369 7665 0a63 6f70 6965 7320 6f66 2074 sive.copies of t\n-0000fd30: 6865 2070 6f6c 796c 696e 6520 2869 6e63 he polyline (inc\n-0000fd40: 6c75 6469 6e67 2074 6865 206f 7269 6769 luding the origi\n-0000fd50: 6e61 6c29 2077 6974 6820 666f 7572 2d73 nal) with four-s\n-0000fd60: 6964 6564 2062 6f64 790a 706f 6c79 676f ided body.polygo\n-0000fd70: 6e73 206a 7573 7420 6173 2074 6865 2063 ns just as the c\n-0000fd80: 6173 6520 7769 7468 206e 6f20 636c 6f73 ase with no clos\n-0000fd90: 7572 6520 7461 672e 2020 4974 2074 6865 ure tag. It the\n-0000fda0: 6e20 636f 6e6e 6563 7473 2074 6865 0a6c n connects the.l\n-0000fdb0: 6173 7420 636f 7079 2062 6163 6b20 746f ast copy back to\n-0000fdc0: 2074 6865 206f 7269 6769 6e61 6c20 746f the original to\n-0000fdd0: 2066 6f72 6d20 6120 7269 6262 6f6e 2d73 form a ribbon-s\n-0000fde0: 6861 7065 6420 7375 7266 6163 6520 7468 haped surface th\n-0000fdf0: 6174 0a63 6c6f 7365 7320 6f6e 2069 7473 at.closes on its\n-0000fe00: 656c 6620 7769 7468 2074 776f 2068 6f6c elf with two hol\n-0000fe10: 6573 2072 656d 6169 6e69 6e67 2e0a 0a20 es remaining... \n-0000fe20: 2020 4669 6e61 6c6c 792c 2074 6865 2073 Finally, the s\n-0000fe30: 7765 6570 2061 6464 7320 7477 6f20 6d6f weep adds two mo\n-0000fe40: 7265 2070 6f6c 7967 6f6e 7320 746f 2073 re polygons to s\n-0000fe50: 6561 6c20 7468 6520 686f 6c65 7320 616e eal the holes an\n-0000fe60: 6420 666f 726d 0a61 2063 6c6f 7365 6420 d form.a closed \n-0000fe70: 7375 7266 6163 6520 7468 6174 2c20 6465 surface that, de\n-0000fe80: 7065 6e64 696e 6720 6f6e 2074 6865 2073 pending on the s\n-0000fe90: 7765 6570 2074 7261 6e73 666f 726d 732c weep transforms,\n-0000fea0: 206d 6179 2072 6570 7265 7365 6e74 0a74 may represent.t\n-0000feb0: 6865 2062 6f75 6e64 6172 7920 6f66 2061 he boundary of a\n-0000fec0: 2073 6f6c 6964 2e20 2049 6e20 7468 6973 solid. In this\n-0000fed0: 206d 616e 6e65 722c 20e2 8098 7377 6565 manner, ...swee\n-0000fee0: 70e2 8099 2066 6f72 6d73 2074 6865 2062 p... forms the b\n-0000fef0: 6f75 6e64 6172 7920 6f66 0a61 2074 6872 oundary of.a thr\n-0000ff00: 6565 2d64 696d 656e 7369 6f6e 616c 206f ee-dimensional o\n-0000ff10: 626a 6563 7420 6672 6f6d 2061 206f 6e65 bject from a one\n-0000ff20: 2d64 696d 656e 7369 6f6e 616c 2070 6f6c -dimensional pol\n-0000ff30: 796c 696e 652e 2020 5765 2063 616c 6c0a yline. We call.\n-0000ff40: 7468 6573 6520 686f 6c65 2d66 696c 6c69 these hole-filli\n-0000ff50: 6e67 2070 6f6c 7967 6f6e 7320 e280 9c65 ng polygons ...e\n-0000ff60: 6e64 73e2 809d 2e0a 0a20 2020 5468 6520 nds...... The \n-0000ff70: 6f72 6465 7220 6f66 2076 6572 7469 6365 order of vertice\n-0000ff80: 7320 6f66 2065 6e64 2070 6f6c 7967 6f6e s of end polygon\n-0000ff90: 7320 6973 2069 6d70 6f72 7461 6e74 2066 s is important f\n-0000ffa0: 6f72 2063 6f72 7265 6374 0a63 756c 6c69 or correct.culli\n-0000ffb0: 6e67 2061 7320 6465 7363 7269 6265 6420 ng as described \n-0000ffc0: 6162 6f76 652e 2020 4966 2050 5f31 5e31 above. If P_1^1\n-0000ffd0: 2c20 505f 315e 322c 202e 2e2e 2c20 505f , P_1^2, ..., P_\n-0000ffe0: 315e 6e20 6172 6520 7468 6520 4e0a 636f 1^n are the N.co\n-0000fff0: 7069 6573 206f 6620 7468 6520 6669 7273 pies of the firs\n-00010000: 7420 706f 6c79 6c69 6e65 2070 6f69 6e74 t polyline point\n-00010010: 2061 6e64 2050 5f6d 5e31 2c20 505f 6d5e and P_m^1, P_m^\n-00010020: 322c 202e 2e2e 202c 505f 6d5e 6e20 6172 2, ... ,P_m^n ar\n-00010030: 6520 7468 650a 4e20 636f 7069 6573 206f e the.N copies o\n-00010040: 6620 7468 6520 6c61 7374 2070 6f6c 796c f the last polyl\n-00010050: 696e 6520 706f 696e 742c 2074 6865 6e20 ine point, then \n-00010060: 7468 6520 656e 6420 706f 6c79 676f 6e20 the end polygon \n-00010070: 7665 7274 6578 206f 7264 6572 0a69 730a vertex order.is.\n-00010080: 2020 2020 2045 6e64 2070 6f6c 7967 6f6e End polygon\n-00010090: 2031 3a20 505f 315e 6e2c 2050 5f31 5e7b 1: P_1^n, P_1^{\n-000100a0: 6e2d 317d 2c20 2e2e 2e20 2c50 5f31 5e31 n-1}, ... ,P_1^1\n-000100b0: 0a20 2020 2020 456e 6420 706f 6c79 676f . End polygo\n-000100c0: 6e20 323a 2050 5f6d 5e31 2c20 505f 6d5e n 2: P_m^1, P_m^\n-000100d0: 322c 202e 2e2e 202c 505f 6d5e 6e0a 0a20 2, ... ,P_m^n.. \n-000100e0: 2020 4966 2074 6865 7265 2061 7265 206e If there are n\n-000100f0: 6f20 6f70 7469 6f6e 7320 6f6e 2074 6865 o options on the\n-00010100: 2073 7765 7074 206c 696e 652c 2074 6865 swept line, the\n-00010110: 6e20 7468 6520 e280 9873 7765 6570 e280 n the ...sweep..\n-00010120: 9920 6f70 7469 6f6e 730a 6172 6520 636f . options.are co\n-00010130: 7069 6564 2074 6f20 6561 6368 206f 7574 pied to each out\n-00010140: 7075 7420 706f 6c79 676f 6e2e 2020 4966 put polygon. If\n-00010150: 2074 6865 2073 7765 7074 206c 696e 6520 the swept line \n-00010160: 646f 6573 2068 6176 6520 6f70 7469 6f6e does have option\n-00010170: 732c 0a74 6865 7365 2061 7265 2063 6f70 s,.these are cop\n-00010180: 6965 6420 746f 2063 6f72 7265 7370 6f6e ied to correspon\n-00010190: 6469 6e67 2062 6f64 7920 706f 6c79 676f ding body polygo\n-000101a0: 6e73 3b20 7468 6520 7377 6565 7020 6f70 ns; the sweep op\n-000101b0: 7469 6f6e 7320 6172 650a 636f 7069 6564 tions are.copied\n-000101c0: 2074 6f20 7468 6520 656e 6420 706f 6c79 to the end poly\n-000101d0: 676f 6e73 2e20 2049 6e20 7468 6973 206d gons. In this m\n-000101e0: 616e 6e65 722c 2062 6f64 7920 616e 6420 anner, body and \n-000101f0: 656e 6473 206d 6179 2062 6520 6472 6177 ends may be draw\n-00010200: 6e0a 7769 7468 2064 6966 6665 7265 6e74 n.with different\n-00010210: 2063 6861 7261 6374 6572 6973 7469 6373 characteristics\n-00010220: 2073 7563 6820 6173 20e2 8098 6669 6c6c such as ...fill\n-00010230: 636f 6c6f 72e2 8099 2e0a 0a1f 0a46 696c color........Fil\n-00010240: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n-00010250: 204e 6f64 653a 2053 7765 7074 2070 6f6c Node: Swept pol\n-00010260: 7967 6f6e 732c 2020 4e65 7874 3a20 5377 ygons, Next: Sw\n-00010270: 6570 7420 626c 6f63 6b73 2c20 2050 7265 ept blocks, Pre\n-00010280: 763a 2053 7765 7074 206c 696e 6573 2c20 v: Swept lines, \n-00010290: 2055 703a 2053 7765 6570 730a 0a33 2e32 Up: Sweeps..3.2\n-000102a0: 2e36 2e33 2053 7765 7074 2070 6f6c 7967 .6.3 Swept polyg\n-000102b0: 6f6e 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ons.............\n-000102c0: 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 4966 2053 ............If S\n-000102d0: 5745 5054 5f4f 424a 4543 5420 6973 2061 WEPT_OBJECT is a\n-000102e0: 2070 6f6c 7967 6f6e 2c20 7468 6520 e280 polygon, the ..\n-000102f0: 9873 7765 6570 e280 9920 636f 6e6e 6563 .sweep... connec\n-00010300: 7473 204e 2b31 2073 7563 6365 7373 6976 ts N+1 successiv\n-00010310: 6520 636f 7069 6573 0a6f 6620 7468 6520 e copies.of the \n-00010320: 636c 6f73 6564 2070 6f6c 796c 696e 6520 closed polyline \n-00010330: 626f 7264 6572 206f 6620 7468 6520 706f border of the po\n-00010340: 6c79 676f 6e20 746f 2066 6f72 6d20 626f lygon to form bo\n-00010350: 6479 2070 6f6c 7967 6f6e 730a 6578 6163 dy polygons.exac\n-00010360: 746c 7920 6173 2074 686f 7567 6820 7468 tly as though th\n-00010370: 6520 626f 7264 6572 2077 6572 6520 6120 e border were a \n-00010380: 7377 6570 7420 706f 6c79 6c69 6e65 2061 swept polyline a\n-00010390: 7320 6465 7363 7269 6265 6420 696e 202a s described in *\n-000103a0: 6e6f 7465 0a53 7765 7074 206c 696e 6573 note.Swept lines\n-000103b0: 3a3a 2e20 2049 6620 7468 6572 6520 6172 ::. If there ar\n-000103c0: 6520 6d20 706f 696e 7473 2069 6e20 7468 e m points in th\n-000103d0: 6520 6f72 6967 696e 616c 2070 6f6c 7967 e original polyg\n-000103e0: 6f6e 2c20 7468 656e 206d 4e0a 626f 6479 on, then mN.body\n-000103f0: 2070 6f6c 7967 6f6e 7320 6172 6520 666f polygons are fo\n-00010400: 726d 6564 2062 7920 7468 6973 2073 7765 rmed by this swe\n-00010410: 6570 2e20 2054 6865 2062 6f64 7920 706f ep. The body po\n-00010420: 6c79 676f 6e73 2066 6f72 6d20 616e 0ae2 lygons form an..\n-00010430: 809c 6578 7472 7573 696f 6ee2 809d 206f ..extrusion... o\n-00010440: 6620 7468 6520 626f 756e 6461 7279 206f f the boundary o\n-00010450: 6620 7468 6520 6f72 6967 696e 616c 2070 f the original p\n-00010460: 6f6c 7967 6f6e 2077 6974 6820 7477 6f20 olygon with two \n-00010470: 686f 6c65 7320 6174 0a74 6865 206f 7065 holes at.the ope\n-00010480: 6e20 656e 6473 2e0a 0a20 2020 4669 6e61 n ends... Fina\n-00010490: 6c6c 792c 2074 6865 2073 7765 6570 2061 lly, the sweep a\n-000104a0: 6464 7320 7477 6f20 636f 7069 6573 206f dds two copies o\n-000104b0: 6620 7468 6520 6f72 6967 696e 616c 2070 f the original p\n-000104c0: 6f6c 7967 6f6e 2074 6f20 636f 7665 720a olygon to cover.\n-000104d0: 7468 6520 686f 6c65 732e 2020 5765 2063 the holes. We c\n-000104e0: 616c 6c20 7468 6573 6520 686f 6c65 2d66 all these hole-f\n-000104f0: 696c 6c69 6e67 2070 6f6c 7967 6f6e 7320 illing polygons \n-00010500: e280 9c65 6e64 73e2 809d 2e20 2049 6e20 ...ends.... In \n-00010510: 7468 6973 206d 616e 6e65 722c 0ae2 8098 this manner,....\n-00010520: 7377 6565 70e2 8099 2066 6f72 6d73 2074 sweep... forms t\n-00010530: 6865 2062 6f75 6e64 6172 7920 6f66 2061 he boundary of a\n-00010540: 2074 6872 6565 2d64 696d 656e 7369 6f6e three-dimension\n-00010550: 616c 206f 626a 6563 7420 6672 6f6d 2061 al object from a\n-00010560: 0a74 776f 2d64 696d 656e 7369 6f6e 616c .two-dimensional\n-00010570: 2070 6f6c 7967 6f6e 2e0a 0a20 2020 5468 polygon... Th\n-00010580: 6520 6f72 6465 7220 6f66 2076 6572 7469 e order of verti\n-00010590: 6365 7320 6f66 2065 6e64 2070 6f6c 7967 ces of end polyg\n-000105a0: 6f6e 7320 6973 2069 6d70 6f72 7461 6e74 ons is important\n-000105b0: 2066 6f72 2063 6f72 7265 6374 0a63 756c for correct.cul\n-000105c0: 6c69 6e67 2061 7320 6465 7363 7269 6265 ling as describe\n-000105d0: 6420 6162 6f76 652e 2020 416e 2065 7861 d above. An exa\n-000105e0: 6374 2063 6f70 7920 6f66 2074 6865 206f ct copy of the o\n-000105f0: 7269 6769 6e61 6c20 706f 6c79 676f 6e20 riginal polygon \n-00010600: 7769 7468 0a76 6572 7465 7820 6f72 6465 with.vertex orde\n-00010610: 7220 696e 7461 6374 2066 6f72 6d73 2074 r intact forms t\n-00010620: 6865 2066 6972 7374 2065 6e64 2070 6f6c he first end pol\n-00010630: 7967 6f6e 2e20 2054 6865 206f 7468 6572 ygon. The other\n-00010640: 2065 6e64 2070 6f6c 7967 6f6e 0a72 6573 end polygon.res\n-00010650: 756c 7473 2066 726f 6d20 7472 616e 7366 ults from transf\n-00010660: 6f72 6d69 6e67 2061 6e64 2074 6865 2072 orming and the r\n-00010670: 6576 6572 7369 6e67 2074 6865 206f 7264 eversing the ord\n-00010680: 6572 206f 6620 7665 7274 6963 6573 2069 er of vertices i\n-00010690: 6e20 7468 650a 6f72 6967 696e 616c 2e20 n the.original. \n-000106a0: 2054 6865 2074 7261 6e73 666f 726d 2070 The transform p\n-000106b0: 6c61 6365 7320 7468 6520 6f72 6967 696e laces the origin\n-000106c0: 616c 2070 6f6c 7967 6f6e 2061 7420 7468 al polygon at th\n-000106d0: 6520 756e 636f 7665 7265 640a 686f 6c65 e uncovered.hole\n-000106e0: 3b20 6974 2069 730a 2020 2020 2054 5f31 ; it is. T_1\n-000106f0: 5e6e 2074 6865 6e20 545f 325e 6e20 7468 ^n then T_2^n th\n-00010700: 656e 202e 2e2e 2074 6865 6e20 545f 525e en ... then T_R^\n-00010710: 6e2e 0a49 6620 7468 6572 6520 6172 6520 n..If there are \n-00010720: 6e6f 206f 7074 696f 6e73 206f 6e20 7468 no options on th\n-00010730: 6520 7377 6570 7420 706f 6c79 676f 6e2c e swept polygon,\n-00010740: 2074 6865 6e20 7468 6520 e280 9873 7765 then the ...swe\n-00010750: 6570 e280 9920 6f70 7469 6f6e 730a 6172 ep... options.ar\n-00010760: 6520 636f 7069 6564 2074 6f20 6561 6368 e copied to each\n-00010770: 206f 7574 7075 7420 706f 6c79 676f 6e2e output polygon.\n-00010780: 2020 4966 2074 6865 2073 7765 7074 2070 If the swept p\n-00010790: 6f6c 7967 6f6e 2064 6f65 7320 6861 7665 olygon does have\n-000107a0: 0a6f 7074 696f 6e73 2c20 7468 6573 6520 .options, these \n-000107b0: 6172 6520 636f 7069 6564 2074 6f20 7468 are copied to th\n-000107c0: 6520 656e 6473 3b20 7468 6520 7377 6565 e ends; the swee\n-000107d0: 7020 6f70 7469 6f6e 7320 6172 6520 636f p options are co\n-000107e0: 7069 6564 2074 6f0a 7468 6520 626f 6479 pied to.the body\n-000107f0: 2070 6f6c 7967 6f6e 732e 2020 496e 2074 polygons. In t\n-00010800: 6869 7320 6d61 6e6e 6572 2c20 626f 6479 his manner, body\n-00010810: 2061 6e64 2065 6e64 7320 6d61 7920 6265 and ends may be\n-00010820: 2064 7261 776e 2077 6974 680a 6469 6666 drawn with.diff\n-00010830: 6572 656e 7420 6368 6172 6163 7465 7269 erent characteri\n-00010840: 7374 6963 7320 7375 6368 2061 7320 e280 stics such as ..\n-00010850: 9866 696c 6c63 6f6c 6f72 e280 992e 0a0a .fillcolor......\n-00010860: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n-00010870: 6e66 6f2c 2020 4e6f 6465 3a20 5377 6570 nfo, Node: Swep\n-00010880: 7420 626c 6f63 6b73 2c20 204e 6578 743a t blocks, Next:\n-00010890: 2053 7765 6570 2066 6163 6520 7370 6c69 Sweep face spli\n-000108a0: 7474 696e 672c 2020 5072 6576 3a20 5377 tting, Prev: Sw\n-000108b0: 6570 7420 706f 6c79 676f 6e73 2c20 2055 ept polygons, U\n-000108c0: 703a 2053 7765 6570 730a 0a33 2e32 2e36 p: Sweeps..3.2.6\n-000108d0: 2e34 2053 7765 7074 2062 6c6f 636b 730a .4 Swept blocks.\n+0000f880: 0a0a 4966 2053 5745 5054 5f4f 424a 4543 ..If SWEPT_OBJEC\n+0000f890: 5420 6973 2061 2070 6f6c 796c 696e 6520 T is a polyline \n+0000f8a0: 616e 6420 7468 6572 6520 6973 206e 6f20 and there is no \n+0000f8b0: 636c 6f73 7572 6520 7461 672c 2074 6865 closure tag, the\n+0000f8c0: 6e20 e280 9873 7765 6570 e280 990a 636f n ...sweep....co\n+0000f8d0: 6e6e 6563 7473 204e 2b31 2073 7563 6365 nnects N+1 succe\n+0000f8e0: 7373 6976 6520 636f 7069 6573 206f 6620 ssive copies of \n+0000f8f0: 7468 6520 706f 6c79 6c69 6e65 2028 696e the polyline (in\n+0000f900: 636c 7564 696e 6720 7468 6520 6f72 6967 cluding the orig\n+0000f910: 696e 616c 290a 7769 7468 2066 6f75 722d inal).with four-\n+0000f920: 7369 6465 6420 706f 6c79 676f 6e73 2c20 sided polygons, \n+0000f930: 6561 6368 2070 6169 7220 6f66 2063 6f70 each pair of cop\n+0000f940: 6965 7320 6769 7669 6e67 2072 6973 6520 ies giving rise \n+0000f950: 746f 2061 2022 706f 6c79 676f 6e0a 7374 to a \"polygon.st\n+0000f960: 7269 702e 2220 2049 6620 7468 6572 6520 rip.\" If there \n+0000f970: 6172 6520 6d20 706f 696e 7473 2069 6e20 are m points in \n+0000f980: 7468 6520 6f72 6967 696e 616c 2070 6f6c the original pol\n+0000f990: 796c 696e 652c 2074 6865 6e20 286d 2d31 yline, then (m-1\n+0000f9a0: 294e 0a70 6f6c 7967 6f6e 7320 6172 6520 )N.polygons are \n+0000f9b0: 666f 726d 6564 2062 7920 7468 6520 7377 formed by the sw\n+0000f9c0: 6565 702e 2020 5765 2063 616c 6c20 7468 eep. We call th\n+0000f9d0: 6573 6520 e280 9c62 6f64 7920 706f 6c79 ese ...body poly\n+0000f9e0: 676f 6e73 e280 9d2e 2020 496e 0a74 6869 gons.... In.thi\n+0000f9f0: 7320 6d61 6e6e 6572 2c20 e280 9873 7765 s manner, ...swe\n+0000fa00: 6570 e280 9920 666f 726d 7320 6120 7477 ep... forms a tw\n+0000fa10: 6f2d 6469 6d65 6e73 696f 6e61 6c20 7375 o-dimensional su\n+0000fa20: 7266 6163 6520 6672 6f6d 2066 726f 6d20 rface from from \n+0000fa30: 610a 6f6e 652d 6469 6d65 6e73 696f 6e61 a.one-dimensiona\n+0000fa40: 6c20 706f 6c79 6c69 6e65 2e0a 0a20 2020 l polyline... \n+0000fa50: 5468 6520 6f72 6465 7220 6f66 2076 6572 The order of ver\n+0000fa60: 7469 6365 7320 7072 6f64 7563 6564 2062 tices produced b\n+0000fa70: 7920 e280 9873 7765 6570 e280 9920 6973 y ...sweep... is\n+0000fa80: 2069 6d70 6f72 7461 6e74 2e20 2049 6620 important. If \n+0000fa90: 610a 706f 6c79 676f 6e27 7320 7665 7274 a.polygon's vert\n+0000faa0: 6963 6573 2064 6f20 6e6f 7420 6170 7065 ices do not appe\n+0000fab0: 6172 2069 6e20 636f 756e 7465 722d 636c ar in counter-cl\n+0000fac0: 6f63 6b77 6973 6520 6f72 6465 7220 696e ockwise order in\n+0000fad0: 2074 6865 2066 696e 616c 0a69 6d61 6765 the final.image\n+0000fae0: 2c20 7468 6520 706f 6c79 676f 6e20 7769 , the polygon wi\n+0000faf0: 6c6c 2062 6520 6375 6c6c 6564 2028 756e ll be culled (un\n+0000fb00: 6c65 7373 20e2 8098 6375 6c6c 3d66 616c less ...cull=fal\n+0000fb10: 7365 e280 9920 6973 2073 6574 292e 2020 se... is set). \n+0000fb20: 4966 2074 6865 0a70 6f69 6e74 7320 696e If the.points in\n+0000fb30: 2074 6865 206b 2774 6820 636f 7079 206f the k'th copy o\n+0000fb40: 6620 7468 6520 706f 6c79 6c69 6e65 2061 f the polyline a\n+0000fb50: 7265 2050 5f31 2c20 505f 322c 202e 2e2e re P_1, P_2, ...\n+0000fb60: 2c20 505f 6d2c 2061 6e64 2074 6865 0a70 , P_m, and the.p\n+0000fb70: 6f69 6e74 7320 696e 2074 6865 206e 6578 oints in the nex\n+0000fb80: 7420 636f 7079 2c20 7468 6520 286b 2b31 t copy, the (k+1\n+0000fb90: 2973 742c 2061 7265 2050 5f31 272c 2050 )st, are P_1', P\n+0000fba0: 5f32 272c 202e 2e2e 2c20 505f 6d27 2c20 _2', ..., P_m', \n+0000fbb0: 7468 656e 0a74 6865 2076 6572 7465 7820 then.the vertex \n+0000fbc0: 6f72 6465 7220 6f66 2074 6865 2067 656e order of the gen\n+0000fbd0: 6572 6174 6564 2070 6f6c 7967 6f6e 7320 erated polygons \n+0000fbe0: 6973 0a20 2020 2020 426f 6479 2070 6f6c is. Body pol\n+0000fbf0: 7967 6f6e 2031 3a20 505f 3220 505f 3120 ygon 1: P_2 P_1 \n+0000fc00: 505f 3127 2050 5f32 270a 2020 2020 2042 P_1' P_2'. B\n+0000fc10: 6f64 7920 706f 6c79 676f 6e20 323a 2050 ody polygon 2: P\n+0000fc20: 5f33 2050 5f32 2050 5f32 2720 505f 3327 _3 P_2 P_2' P_3'\n+0000fc30: 0a20 2020 2020 2e2e 2e0a 2020 2020 2042 . .... B\n+0000fc40: 6f64 7920 706f 6c79 676f 6e20 6d2d 313a ody polygon m-1:\n+0000fc50: 2050 5f6d 2050 5f7b 6d2d 317d 2050 5f7b P_m P_{m-1} P_{\n+0000fc60: 6d2d 317d 2720 505f 6d27 0a0a 2020 204f m-1}' P_m'.. O\n+0000fc70: 7074 696f 6e73 206f 6620 756e 636c 6f73 ptions of unclos\n+0000fc80: 6564 206c 696e 6520 7377 6565 7073 2061 ed line sweeps a\n+0000fc90: 7265 2063 6f70 6965 6420 746f 2065 6163 re copied to eac\n+0000fca0: 6820 6f75 7470 7574 2070 6f6c 7967 6f6e h output polygon\n+0000fcb0: 2e0a 4f70 7469 6f6e 7320 6f66 2074 6865 ..Options of the\n+0000fcc0: 2073 7765 7074 206c 696e 6520 6172 6520 swept line are \n+0000fcd0: 6967 6e6f 7265 642e 0a0a 2020 2057 6865 ignored... Whe\n+0000fce0: 6e20 7468 6572 6520 5f69 735f 2061 2063 n there _is_ a c\n+0000fcf0: 6c6f 7375 7265 2074 6167 2c20 7468 656e losure tag, then\n+0000fd00: 20e2 8098 7377 6565 70e2 8099 2063 6f6e ...sweep... con\n+0000fd10: 6e65 6374 7320 4e20 7375 6363 6573 7369 nects N successi\n+0000fd20: 7665 0a63 6f70 6965 7320 6f66 2074 6865 ve.copies of the\n+0000fd30: 2070 6f6c 796c 696e 6520 2869 6e63 6c75 polyline (inclu\n+0000fd40: 6469 6e67 2074 6865 206f 7269 6769 6e61 ding the origina\n+0000fd50: 6c29 2077 6974 6820 666f 7572 2d73 6964 l) with four-sid\n+0000fd60: 6564 2062 6f64 790a 706f 6c79 676f 6e73 ed body.polygons\n+0000fd70: 206a 7573 7420 6173 2074 6865 2063 6173 just as the cas\n+0000fd80: 6520 7769 7468 206e 6f20 636c 6f73 7572 e with no closur\n+0000fd90: 6520 7461 672e 2020 4974 2074 6865 6e20 e tag. It then \n+0000fda0: 636f 6e6e 6563 7473 2074 6865 0a6c 6173 connects the.las\n+0000fdb0: 7420 636f 7079 2062 6163 6b20 746f 2074 t copy back to t\n+0000fdc0: 6865 206f 7269 6769 6e61 6c20 746f 2066 he original to f\n+0000fdd0: 6f72 6d20 6120 7269 6262 6f6e 2d73 6861 orm a ribbon-sha\n+0000fde0: 7065 6420 7375 7266 6163 6520 7468 6174 ped surface that\n+0000fdf0: 0a63 6c6f 7365 7320 6f6e 2069 7473 656c .closes on itsel\n+0000fe00: 6620 7769 7468 2074 776f 2068 6f6c 6573 f with two holes\n+0000fe10: 2072 656d 6169 6e69 6e67 2e0a 0a20 2020 remaining... \n+0000fe20: 4669 6e61 6c6c 792c 2074 6865 2073 7765 Finally, the swe\n+0000fe30: 6570 2061 6464 7320 7477 6f20 6d6f 7265 ep adds two more\n+0000fe40: 2070 6f6c 7967 6f6e 7320 746f 2073 6561 polygons to sea\n+0000fe50: 6c20 7468 6520 686f 6c65 7320 616e 6420 l the holes and \n+0000fe60: 666f 726d 0a61 2063 6c6f 7365 6420 7375 form.a closed su\n+0000fe70: 7266 6163 6520 7468 6174 2c20 6465 7065 rface that, depe\n+0000fe80: 6e64 696e 6720 6f6e 2074 6865 2073 7765 nding on the swe\n+0000fe90: 6570 2074 7261 6e73 666f 726d 732c 206d ep transforms, m\n+0000fea0: 6179 2072 6570 7265 7365 6e74 0a74 6865 ay represent.the\n+0000feb0: 2062 6f75 6e64 6172 7920 6f66 2061 2073 boundary of a s\n+0000fec0: 6f6c 6964 2e20 2049 6e20 7468 6973 206d olid. In this m\n+0000fed0: 616e 6e65 722c 20e2 8098 7377 6565 70e2 anner, ...sweep.\n+0000fee0: 8099 2066 6f72 6d73 2074 6865 2062 6f75 .. forms the bou\n+0000fef0: 6e64 6172 7920 6f66 0a61 2074 6872 6565 ndary of.a three\n+0000ff00: 2d64 696d 656e 7369 6f6e 616c 206f 626a -dimensional obj\n+0000ff10: 6563 7420 6672 6f6d 2061 206f 6e65 2d64 ect from a one-d\n+0000ff20: 696d 656e 7369 6f6e 616c 2070 6f6c 796c imensional polyl\n+0000ff30: 696e 652e 2020 5765 2063 616c 6c0a 7468 ine. We call.th\n+0000ff40: 6573 6520 686f 6c65 2d66 696c 6c69 6e67 ese hole-filling\n+0000ff50: 2070 6f6c 7967 6f6e 7320 e280 9c65 6e64 polygons ...end\n+0000ff60: 73e2 809d 2e0a 0a20 2020 5468 6520 6f72 s...... The or\n+0000ff70: 6465 7220 6f66 2076 6572 7469 6365 7320 der of vertices \n+0000ff80: 6f66 2065 6e64 2070 6f6c 7967 6f6e 7320 of end polygons \n+0000ff90: 6973 2069 6d70 6f72 7461 6e74 2066 6f72 is important for\n+0000ffa0: 2063 6f72 7265 6374 0a63 756c 6c69 6e67 correct.culling\n+0000ffb0: 2061 7320 6465 7363 7269 6265 6420 6162 as described ab\n+0000ffc0: 6f76 652e 2020 4966 2050 5f31 5e31 2c20 ove. If P_1^1, \n+0000ffd0: 505f 315e 322c 202e 2e2e 2c20 505f 315e P_1^2, ..., P_1^\n+0000ffe0: 6e20 6172 6520 7468 6520 4e0a 636f 7069 n are the N.copi\n+0000fff0: 6573 206f 6620 7468 6520 6669 7273 7420 es of the first \n+00010000: 706f 6c79 6c69 6e65 2070 6f69 6e74 2061 polyline point a\n+00010010: 6e64 2050 5f6d 5e31 2c20 505f 6d5e 322c nd P_m^1, P_m^2,\n+00010020: 202e 2e2e 202c 505f 6d5e 6e20 6172 6520 ... ,P_m^n are \n+00010030: 7468 650a 4e20 636f 7069 6573 206f 6620 the.N copies of \n+00010040: 7468 6520 6c61 7374 2070 6f6c 796c 696e the last polylin\n+00010050: 6520 706f 696e 742c 2074 6865 6e20 7468 e point, then th\n+00010060: 6520 656e 6420 706f 6c79 676f 6e20 7665 e end polygon ve\n+00010070: 7274 6578 206f 7264 6572 0a69 730a 2020 rtex order.is. \n+00010080: 2020 2045 6e64 2070 6f6c 7967 6f6e 2031 End polygon 1\n+00010090: 3a20 505f 315e 6e2c 2050 5f31 5e7b 6e2d : P_1^n, P_1^{n-\n+000100a0: 317d 2c20 2e2e 2e20 2c50 5f31 5e31 0a20 1}, ... ,P_1^1. \n+000100b0: 2020 2020 456e 6420 706f 6c79 676f 6e20 End polygon \n+000100c0: 323a 2050 5f6d 5e31 2c20 505f 6d5e 322c 2: P_m^1, P_m^2,\n+000100d0: 202e 2e2e 202c 505f 6d5e 6e0a 0a20 2020 ... ,P_m^n.. \n+000100e0: 4966 2074 6865 7265 2061 7265 206e 6f20 If there are no \n+000100f0: 6f70 7469 6f6e 7320 6f6e 2074 6865 2073 options on the s\n+00010100: 7765 7074 206c 696e 652c 2074 6865 6e20 wept line, then \n+00010110: 7468 6520 e280 9873 7765 6570 e280 9920 the ...sweep... \n+00010120: 6f70 7469 6f6e 730a 6172 6520 636f 7069 options.are copi\n+00010130: 6564 2074 6f20 6561 6368 206f 7574 7075 ed to each outpu\n+00010140: 7420 706f 6c79 676f 6e2e 2020 4966 2074 t polygon. If t\n+00010150: 6865 2073 7765 7074 206c 696e 6520 646f he swept line do\n+00010160: 6573 2068 6176 6520 6f70 7469 6f6e 732c es have options,\n+00010170: 0a74 6865 7365 2061 7265 2063 6f70 6965 .these are copie\n+00010180: 6420 746f 2063 6f72 7265 7370 6f6e 6469 d to correspondi\n+00010190: 6e67 2062 6f64 7920 706f 6c79 676f 6e73 ng body polygons\n+000101a0: 3b20 7468 6520 7377 6565 7020 6f70 7469 ; the sweep opti\n+000101b0: 6f6e 7320 6172 650a 636f 7069 6564 2074 ons are.copied t\n+000101c0: 6f20 7468 6520 656e 6420 706f 6c79 676f o the end polygo\n+000101d0: 6e73 2e20 2049 6e20 7468 6973 206d 616e ns. In this man\n+000101e0: 6e65 722c 2062 6f64 7920 616e 6420 656e ner, body and en\n+000101f0: 6473 206d 6179 2062 6520 6472 6177 6e0a ds may be drawn.\n+00010200: 7769 7468 2064 6966 6665 7265 6e74 2063 with different c\n+00010210: 6861 7261 6374 6572 6973 7469 6373 2073 haracteristics s\n+00010220: 7563 6820 6173 20e2 8098 6669 6c6c 636f uch as ...fillco\n+00010230: 6c6f 72e2 8099 2e0a 0a1f 0a46 696c 653a lor........File:\n+00010240: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n+00010250: 6f64 653a 2053 7765 7074 2070 6f6c 7967 ode: Swept polyg\n+00010260: 6f6e 732c 2020 4e65 7874 3a20 5377 6570 ons, Next: Swep\n+00010270: 7420 626c 6f63 6b73 2c20 2050 7265 763a t blocks, Prev:\n+00010280: 2053 7765 7074 206c 696e 6573 2c20 2055 Swept lines, U\n+00010290: 703a 2053 7765 6570 730a 0a33 2e32 2e36 p: Sweeps..3.2.6\n+000102a0: 2e33 2053 7765 7074 2070 6f6c 7967 6f6e .3 Swept polygon\n+000102b0: 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e s...............\n+000102c0: 2e2e 2e2e 2e2e 2e2e 0a0a 4966 2053 5745 ..........If SWE\n+000102d0: 5054 5f4f 424a 4543 5420 6973 2061 2070 PT_OBJECT is a p\n+000102e0: 6f6c 7967 6f6e 2c20 7468 6520 e280 9873 olygon, the ...s\n+000102f0: 7765 6570 e280 9920 636f 6e6e 6563 7473 weep... connects\n+00010300: 204e 2b31 2073 7563 6365 7373 6976 6520 N+1 successive \n+00010310: 636f 7069 6573 0a6f 6620 7468 6520 636c copies.of the cl\n+00010320: 6f73 6564 2070 6f6c 796c 696e 6520 626f osed polyline bo\n+00010330: 7264 6572 206f 6620 7468 6520 706f 6c79 rder of the poly\n+00010340: 676f 6e20 746f 2066 6f72 6d20 626f 6479 gon to form body\n+00010350: 2070 6f6c 7967 6f6e 730a 6578 6163 746c polygons.exactl\n+00010360: 7920 6173 2074 686f 7567 6820 7468 6520 y as though the \n+00010370: 626f 7264 6572 2077 6572 6520 6120 7377 border were a sw\n+00010380: 6570 7420 706f 6c79 6c69 6e65 2061 7320 ept polyline as \n+00010390: 6465 7363 7269 6265 6420 696e 202a 6e6f described in *no\n+000103a0: 7465 0a53 7765 7074 206c 696e 6573 3a3a te.Swept lines::\n+000103b0: 2e20 2049 6620 7468 6572 6520 6172 6520 . If there are \n+000103c0: 6d20 706f 696e 7473 2069 6e20 7468 6520 m points in the \n+000103d0: 6f72 6967 696e 616c 2070 6f6c 7967 6f6e original polygon\n+000103e0: 2c20 7468 656e 206d 4e0a 626f 6479 2070 , then mN.body p\n+000103f0: 6f6c 7967 6f6e 7320 6172 6520 666f 726d olygons are form\n+00010400: 6564 2062 7920 7468 6973 2073 7765 6570 ed by this sweep\n+00010410: 2e20 2054 6865 2062 6f64 7920 706f 6c79 . The body poly\n+00010420: 676f 6e73 2066 6f72 6d20 616e 0ae2 809c gons form an....\n+00010430: 6578 7472 7573 696f 6ee2 809d 206f 6620 extrusion... of \n+00010440: 7468 6520 626f 756e 6461 7279 206f 6620 the boundary of \n+00010450: 7468 6520 6f72 6967 696e 616c 2070 6f6c the original pol\n+00010460: 7967 6f6e 2077 6974 6820 7477 6f20 686f ygon with two ho\n+00010470: 6c65 7320 6174 0a74 6865 206f 7065 6e20 les at.the open \n+00010480: 656e 6473 2e0a 0a20 2020 4669 6e61 6c6c ends... Finall\n+00010490: 792c 2074 6865 2073 7765 6570 2061 6464 y, the sweep add\n+000104a0: 7320 7477 6f20 636f 7069 6573 206f 6620 s two copies of \n+000104b0: 7468 6520 6f72 6967 696e 616c 2070 6f6c the original pol\n+000104c0: 7967 6f6e 2074 6f20 636f 7665 720a 7468 ygon to cover.th\n+000104d0: 6520 686f 6c65 732e 2020 5765 2063 616c e holes. We cal\n+000104e0: 6c20 7468 6573 6520 686f 6c65 2d66 696c l these hole-fil\n+000104f0: 6c69 6e67 2070 6f6c 7967 6f6e 7320 e280 ling polygons ..\n+00010500: 9c65 6e64 73e2 809d 2e20 2049 6e20 7468 .ends.... In th\n+00010510: 6973 206d 616e 6e65 722c 0ae2 8098 7377 is manner,....sw\n+00010520: 6565 70e2 8099 2066 6f72 6d73 2074 6865 eep... forms the\n+00010530: 2062 6f75 6e64 6172 7920 6f66 2061 2074 boundary of a t\n+00010540: 6872 6565 2d64 696d 656e 7369 6f6e 616c hree-dimensional\n+00010550: 206f 626a 6563 7420 6672 6f6d 2061 0a74 object from a.t\n+00010560: 776f 2d64 696d 656e 7369 6f6e 616c 2070 wo-dimensional p\n+00010570: 6f6c 7967 6f6e 2e0a 0a20 2020 5468 6520 olygon... The \n+00010580: 6f72 6465 7220 6f66 2076 6572 7469 6365 order of vertice\n+00010590: 7320 6f66 2065 6e64 2070 6f6c 7967 6f6e s of end polygon\n+000105a0: 7320 6973 2069 6d70 6f72 7461 6e74 2066 s is important f\n+000105b0: 6f72 2063 6f72 7265 6374 0a63 756c 6c69 or correct.culli\n+000105c0: 6e67 2061 7320 6465 7363 7269 6265 6420 ng as described \n+000105d0: 6162 6f76 652e 2020 416e 2065 7861 6374 above. An exact\n+000105e0: 2063 6f70 7920 6f66 2074 6865 206f 7269 copy of the ori\n+000105f0: 6769 6e61 6c20 706f 6c79 676f 6e20 7769 ginal polygon wi\n+00010600: 7468 0a76 6572 7465 7820 6f72 6465 7220 th.vertex order \n+00010610: 696e 7461 6374 2066 6f72 6d73 2074 6865 intact forms the\n+00010620: 2066 6972 7374 2065 6e64 2070 6f6c 7967 first end polyg\n+00010630: 6f6e 2e20 2054 6865 206f 7468 6572 2065 on. The other e\n+00010640: 6e64 2070 6f6c 7967 6f6e 0a72 6573 756c nd polygon.resul\n+00010650: 7473 2066 726f 6d20 7472 616e 7366 6f72 ts from transfor\n+00010660: 6d69 6e67 2061 6e64 2074 6865 2072 6576 ming and the rev\n+00010670: 6572 7369 6e67 2074 6865 206f 7264 6572 ersing the order\n+00010680: 206f 6620 7665 7274 6963 6573 2069 6e20 of vertices in \n+00010690: 7468 650a 6f72 6967 696e 616c 2e20 2054 the.original. T\n+000106a0: 6865 2074 7261 6e73 666f 726d 2070 6c61 he transform pla\n+000106b0: 6365 7320 7468 6520 6f72 6967 696e 616c ces the original\n+000106c0: 2070 6f6c 7967 6f6e 2061 7420 7468 6520 polygon at the \n+000106d0: 756e 636f 7665 7265 640a 686f 6c65 3b20 uncovered.hole; \n+000106e0: 6974 2069 730a 2020 2020 2054 5f31 5e6e it is. T_1^n\n+000106f0: 2074 6865 6e20 545f 325e 6e20 7468 656e then T_2^n then\n+00010700: 202e 2e2e 2074 6865 6e20 545f 525e 6e2e ... then T_R^n.\n+00010710: 0a49 6620 7468 6572 6520 6172 6520 6e6f .If there are no\n+00010720: 206f 7074 696f 6e73 206f 6e20 7468 6520 options on the \n+00010730: 7377 6570 7420 706f 6c79 676f 6e2c 2074 swept polygon, t\n+00010740: 6865 6e20 7468 6520 e280 9873 7765 6570 hen the ...sweep\n+00010750: e280 9920 6f70 7469 6f6e 730a 6172 6520 ... options.are \n+00010760: 636f 7069 6564 2074 6f20 6561 6368 206f copied to each o\n+00010770: 7574 7075 7420 706f 6c79 676f 6e2e 2020 utput polygon. \n+00010780: 4966 2074 6865 2073 7765 7074 2070 6f6c If the swept pol\n+00010790: 7967 6f6e 2064 6f65 7320 6861 7665 0a6f ygon does have.o\n+000107a0: 7074 696f 6e73 2c20 7468 6573 6520 6172 ptions, these ar\n+000107b0: 6520 636f 7069 6564 2074 6f20 7468 6520 e copied to the \n+000107c0: 656e 6473 3b20 7468 6520 7377 6565 7020 ends; the sweep \n+000107d0: 6f70 7469 6f6e 7320 6172 6520 636f 7069 options are copi\n+000107e0: 6564 2074 6f0a 7468 6520 626f 6479 2070 ed to.the body p\n+000107f0: 6f6c 7967 6f6e 732e 2020 496e 2074 6869 olygons. In thi\n+00010800: 7320 6d61 6e6e 6572 2c20 626f 6479 2061 s manner, body a\n+00010810: 6e64 2065 6e64 7320 6d61 7920 6265 2064 nd ends may be d\n+00010820: 7261 776e 2077 6974 680a 6469 6666 6572 rawn with.differ\n+00010830: 656e 7420 6368 6172 6163 7465 7269 7374 ent characterist\n+00010840: 6963 7320 7375 6368 2061 7320 e280 9866 ics such as ...f\n+00010850: 696c 6c63 6f6c 6f72 e280 992e 0a0a 1f0a illcolor........\n+00010860: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n+00010870: 6f2c 2020 4e6f 6465 3a20 5377 6570 7420 o, Node: Swept \n+00010880: 626c 6f63 6b73 2c20 204e 6578 743a 2053 blocks, Next: S\n+00010890: 7765 6570 2066 6163 6520 7370 6c69 7474 weep face splitt\n+000108a0: 696e 672c 2020 5072 6576 3a20 5377 6570 ing, Prev: Swep\n+000108b0: 7420 706f 6c79 676f 6e73 2c20 2055 703a t polygons, Up:\n+000108c0: 2053 7765 6570 730a 0a33 2e32 2e36 2e34 Sweeps..3.2.6.4\n+000108d0: 2053 7765 7074 2062 6c6f 636b 730a 2e2e Swept blocks...\n 000108e0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-000108f0: 2e2e 2e2e 0a0a 5468 6520 7377 6570 7420 ......The swept \n-00010900: 6f62 6a65 6374 2053 5745 5054 5f4f 424a object SWEPT_OBJ\n-00010910: 4543 5420 6d61 7920 616c 736f 2062 6520 ECT may also be \n-00010920: 616e 7920 636f 6c6c 6563 7469 6f6e 206f any collection o\n-00010930: 6620 706f 6c79 6c69 6e65 730a 616e 6420 f polylines.and \n-00010940: 706f 6c79 676f 6e73 2e20 2054 6869 7320 polygons. This \n-00010950: 6d61 7920 6265 2061 2062 6c6f 636b 2063 may be a block c\n-00010960: 6f6d 706f 7365 6420 6f66 20e2 8098 6c69 omposed of ...li\n-00010970: 6e65 e280 9920 616e 642f 6f72 20e2 8098 ne... and/or ...\n-00010980: 706f 6c79 676f 6ee2 8099 0a63 6f6d 6d61 polygon....comma\n-00010990: 6e64 7320 696e 2062 7261 6365 7320 e280 nds in braces ..\n-000109a0: 987b 207d e280 992c 206f 7220 6974 206d .{ }..., or it m\n-000109b0: 6179 2062 6520 7468 6520 7265 7375 6c74 ay be the result\n-000109c0: 206f 6620 6120 e280 9872 6570 6561 74e2 of a ...repeat.\n-000109d0: 8099 2c20 616e 6f74 6865 720a e280 9873 .., another....s\n-000109e0: 7765 6570 e280 992c 2065 7463 2e20 2054 weep..., etc. T\n-000109f0: 6865 2073 7765 6570 2061 6374 7320 696e he sweep acts in\n-00010a00: 6465 7065 6e64 656e 746c 7920 6f6e 2065 dependently on e\n-00010a10: 6163 6820 6f62 6a65 6374 2069 6e20 7468 ach object in th\n-00010a20: 6520 626c 6f63 6b0a 6578 6163 746c 7920 e block.exactly \n-00010a30: 6173 2069 6620 6974 2077 6572 6520 6120 as if it were a \n-00010a40: 7369 6e67 6c65 2073 7765 7074 206f 626a single swept obj\n-00010a50: 6563 7420 6465 7363 7269 6265 6420 6162 ect described ab\n-00010a60: 6f76 6520 696e 202a 6e6f 7465 0a53 7765 ove in *note.Swe\n-00010a70: 7074 206c 696e 6573 3a3a 2061 6e64 202a pt lines:: and *\n-00010a80: 6e6f 7465 2053 7765 7074 2070 6f6c 7967 note Swept polyg\n-00010a90: 6f6e 733a 3a2e 0a0a 1f0a 4669 6c65 3a20 ons::.....File: \n-00010aa0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n-00010ab0: 6465 3a20 5377 6565 7020 6661 6365 2073 de: Sweep face s\n-00010ac0: 706c 6974 7469 6e67 2c20 2050 7265 763a plitting, Prev:\n-00010ad0: 2053 7765 7074 2062 6c6f 636b 732c 2020 Swept blocks, \n-00010ae0: 5570 3a20 5377 6565 7073 0a0a 332e 322e Up: Sweeps..3.2.\n-00010af0: 362e 3520 5377 6565 7020 6661 6365 2073 6.5 Sweep face s\n-00010b00: 706c 6974 7469 6e67 0a2e 2e2e 2e2e 2e2e plitting........\n+000108f0: 2e2e 0a0a 5468 6520 7377 6570 7420 6f62 ....The swept ob\n+00010900: 6a65 6374 2053 5745 5054 5f4f 424a 4543 ject SWEPT_OBJEC\n+00010910: 5420 6d61 7920 616c 736f 2062 6520 616e T may also be an\n+00010920: 7920 636f 6c6c 6563 7469 6f6e 206f 6620 y collection of \n+00010930: 706f 6c79 6c69 6e65 730a 616e 6420 706f polylines.and po\n+00010940: 6c79 676f 6e73 2e20 2054 6869 7320 6d61 lygons. This ma\n+00010950: 7920 6265 2061 2062 6c6f 636b 2063 6f6d y be a block com\n+00010960: 706f 7365 6420 6f66 20e2 8098 6c69 6e65 posed of ...line\n+00010970: e280 9920 616e 642f 6f72 20e2 8098 706f ... and/or ...po\n+00010980: 6c79 676f 6ee2 8099 0a63 6f6d 6d61 6e64 lygon....command\n+00010990: 7320 696e 2062 7261 6365 7320 e280 987b s in braces ...{\n+000109a0: 207d e280 992c 206f 7220 6974 206d 6179 }..., or it may\n+000109b0: 2062 6520 7468 6520 7265 7375 6c74 206f be the result o\n+000109c0: 6620 6120 e280 9872 6570 6561 74e2 8099 f a ...repeat...\n+000109d0: 2c20 616e 6f74 6865 720a e280 9873 7765 , another....swe\n+000109e0: 6570 e280 992c 2065 7463 2e20 2054 6865 ep..., etc. The\n+000109f0: 2073 7765 6570 2061 6374 7320 696e 6465 sweep acts inde\n+00010a00: 7065 6e64 656e 746c 7920 6f6e 2065 6163 pendently on eac\n+00010a10: 6820 6f62 6a65 6374 2069 6e20 7468 6520 h object in the \n+00010a20: 626c 6f63 6b0a 6578 6163 746c 7920 6173 block.exactly as\n+00010a30: 2069 6620 6974 2077 6572 6520 6120 7369 if it were a si\n+00010a40: 6e67 6c65 2073 7765 7074 206f 626a 6563 ngle swept objec\n+00010a50: 7420 6465 7363 7269 6265 6420 6162 6f76 t described abov\n+00010a60: 6520 696e 202a 6e6f 7465 0a53 7765 7074 e in *note.Swept\n+00010a70: 206c 696e 6573 3a3a 2061 6e64 202a 6e6f lines:: and *no\n+00010a80: 7465 2053 7765 7074 2070 6f6c 7967 6f6e te Swept polygon\n+00010a90: 733a 3a2e 0a0a 1f0a 4669 6c65 3a20 736b s::.....File: sk\n+00010aa0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n+00010ab0: 3a20 5377 6565 7020 6661 6365 2073 706c : Sweep face spl\n+00010ac0: 6974 7469 6e67 2c20 2050 7265 763a 2053 itting, Prev: S\n+00010ad0: 7765 7074 2062 6c6f 636b 732c 2020 5570 wept blocks, Up\n+00010ae0: 3a20 5377 6565 7073 0a0a 332e 322e 362e : Sweeps..3.2.6.\n+00010af0: 3520 5377 6565 7020 6661 6365 2073 706c 5 Sweep face spl\n+00010b00: 6974 7469 6e67 0a2e 2e2e 2e2e 2e2e 2e2e itting..........\n 00010b10: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-00010b20: 2e2e 2e2e 2e0a 0a42 6566 6f72 6520 7365 .......Before se\n-00010b30: 6e64 696e 6720 6561 6368 2066 6f75 722d nding each four-\n-00010b40: 7369 6465 6420 626f 6479 2070 6f6c 7967 sided body polyg\n-00010b50: 6f6e 206f 6620 6120 e280 9873 7765 6570 on of a ...sweep\n-00010b60: e280 9920 746f 2074 6865 206f 7574 7075 ... to the outpu\n-00010b70: 742c 0ae2 8098 736b 6574 6368 e280 9920 t,....sketch... \n-00010b80: 7465 7374 7320 746f 2073 6565 2069 6620 tests to see if \n-00010b90: 6974 2069 7320 726f 7567 686c 7920 706c it is roughly pl\n-00010ba0: 616e 6172 2e20 2053 696e 6365 2070 6c61 anar. Since pla\n-00010bb0: 6e61 7269 7479 2069 730a 6e65 6365 7373 narity is.necess\n-00010bc0: 6172 7920 666f 7220 7072 6f70 6572 2066 ary for proper f\n-00010bd0: 756e 6374 696f 6e69 6e67 206f 6620 7468 unctioning of th\n-00010be0: 6520 6869 6464 656e 2073 7572 6661 6365 e hidden surface\n-00010bf0: 2061 6c67 6f72 6974 686d 2c0a 2277 6172 algorithm,.\"war\n-00010c00: 7065 6422 2070 6f6c 7967 6f6e 7320 6172 ped\" polygons ar\n-00010c10: 6520 6175 746f 6d61 7469 6361 6c6c 7920 e automatically \n-00010c20: 7370 6c69 7420 696e 746f 2074 776f 2074 split into two t\n-00010c30: 7269 616e 676c 6573 2e0a 0a20 2020 486f riangles... Ho\n-00010c40: 6c65 2d66 696c 6c69 6e67 2070 6f6c 7967 le-filling polyg\n-00010c50: 6f6e 7320 7072 6f64 7563 6564 2062 7920 ons produced by \n-00010c60: 636c 6f73 7572 652d 7461 6767 6564 206c closure-tagged l\n-00010c70: 696e 6520 7377 6565 7073 2061 7265 206e ine sweeps are n\n-00010c80: 6f74 0a73 706c 6974 2e20 204e 6f72 2061 ot.split. Nor a\n-00010c90: 7265 206f 7269 6769 6e61 6c20 706f 6c79 re original poly\n-00010ca0: 676f 6e73 2069 6e20 706f 6c79 676f 6e20 gons in polygon \n-00010cb0: 7377 6565 7073 2e20 2049 7420 6973 2074 sweeps. It is t\n-00010cc0: 6865 2075 7365 7227 730a 7265 7370 6f6e he user's.respon\n-00010cd0: 7369 6269 6c69 7479 2074 6f20 656e 7375 sibility to ensu\n-00010ce0: 7265 2074 6865 7365 2061 7265 2070 6c61 re these are pla\n-00010cf0: 6e61 722e 0a0a 1f0a 4669 6c65 3a20 736b nar.....File: sk\n-00010d00: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-00010d10: 3a20 426c 6f63 6b73 2c20 204e 6578 743a : Blocks, Next:\n-00010d20: 2052 6570 6561 7473 2c20 2050 7265 763a Repeats, Prev:\n-00010d30: 2053 7765 6570 732c 2020 5570 3a20 4472 Sweeps, Up: Dr\n-00010d40: 6177 6162 6c65 730a 0a33 2e32 2e37 2042 awables..3.2.7 B\n-00010d50: 6c6f 636b 730a 2d2d 2d2d 2d2d 2d2d 2d2d locks.----------\n-00010d60: 2d2d 0a0a 416e 7920 7365 7175 656e 6365 --..Any sequence\n-00010d70: 206f 6620 6472 6177 6162 6c65 7320 6d61 of drawables ma\n-00010d80: 7920 6265 2067 726f 7570 6564 2069 6e20 y be grouped in \n-00010d90: 6120 e280 9c62 6c6f 636b e280 9d20 6d65 a ...block... me\n-00010da0: 7265 6c79 2062 790a 656e 636c 6f73 696e rely by.enclosin\n-00010db0: 6720 7468 656d 2069 6e20 6272 6163 6573 g them in braces\n-00010dc0: 20e2 8098 7b20 7de2 8099 2e20 2041 2062 ...{ }.... A b\n-00010dd0: 6c6f 636b 2069 7320 6974 7365 6c66 2064 lock is itself d\n-00010de0: 7261 7761 626c 652e 2020 4120 6b65 7920 rawable. A key \n-00010df0: 7573 650a 6f66 2062 6c6f 636b 7320 6973 use.of blocks is\n-00010e00: 2074 6f20 6578 7465 6e64 2074 6865 2065 to extend the e\n-00010e10: 6666 6563 7420 6f66 2061 2073 696e 676c ffect of a singl\n-00010e20: 6520 e280 9864 6566 e280 992c 202a 6e6f e ...def..., *no\n-00010e30: 7465 0a44 6566 696e 6974 696f 6e73 3a3a te.Definitions::\n-00010e40: 2c20 e280 9870 7574 e280 9920 2a6e 6f74 , ...put... *not\n-00010e50: 6520 5075 7473 3a3a 2c20 e280 9873 7765 e Puts::, ...swe\n-00010e60: 6570 e280 9920 2a6e 6f74 6520 5377 6565 ep... *note Swee\n-00010e70: 7073 3a3a 2c20 6f72 20e2 8098 7265 7065 ps::, or ...repe\n-00010e80: 6174 e280 990a 2a6e 6f74 6520 5265 7065 at....*note Repe\n-00010e90: 6174 733a 3a20 746f 2069 6e63 6c75 6465 ats:: to include\n-00010ea0: 2073 6576 6572 616c 206f 626a 6563 7473 several objects\n-00010eb0: 2072 6174 6865 7220 7468 616e 206f 6e65 rather than one\n-00010ec0: 2e0a 0a20 2020 4465 6669 6e69 7469 6f6e ... Definition\n-00010ed0: 7320 282a 4e6f 7465 2044 6566 696e 6974 s (*Note Definit\n-00010ee0: 696f 6e73 3a3a 2e29 2020 696e 7369 6465 ions::.) inside\n-00010ef0: 2061 2062 6c6f 636b 2068 6176 6520 e280 a block have ..\n-00010f00: 9c6c 6578 6963 616c 0a73 636f 7065 e280 .lexical.scope..\n-00010f10: 9d20 6578 7465 6e64 696e 6720 6672 6f6d . extending from\n-00010f20: 2074 6865 2070 6c61 6365 206f 6620 6465 the place of de\n-00010f30: 6669 6e69 7469 6f6e 2074 6f20 7468 6520 finition to the \n-00010f40: 656e 6420 6f66 2074 6865 2062 6c6f 636b end of the block\n-00010f50: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n-00010f60: 682e 696e 666f 2c20 204e 6f64 653a 2052 h.info, Node: R\n-00010f70: 6570 6561 7473 2c20 204e 6578 743a 2050 epeats, Next: P\n-00010f80: 7574 732c 2020 5072 6576 3a20 426c 6f63 uts, Prev: Bloc\n-00010f90: 6b73 2c20 2055 703a 2044 7261 7761 626c ks, Up: Drawabl\n-00010fa0: 6573 0a0a 332e 322e 3820 5265 7065 6174 es..3.2.8 Repeat\n-00010fb0: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a s.-------------.\n-00010fc0: 0a2a 5379 6e74 6178 3a2a 0a20 2020 2020 .*Syntax:*. \n-00010fd0: 7265 7065 6174 207b 204e 2c20 545f 312c repeat { N, T_1,\n-00010fe0: 2054 5f32 2c20 2e2e 2e2c 2054 5f52 207d T_2, ..., T_R }\n-00010ff0: 2052 4550 4541 5445 445f 4f42 4a45 4354 REPEATED_OBJECT\n-00011000: 0a54 6865 2072 6570 6561 7420 6d61 6b65 .The repeat make\n-00011010: 7320 4e20 7472 616e 7366 6f72 6d65 6420 s N transformed \n-00011020: 636f 7069 6573 206f 6620 5245 5045 4154 copies of REPEAT\n-00011030: 4544 5f4f 424a 4543 5420 2869 6e63 6c75 ED_OBJECT (inclu\n-00011040: 6469 6e67 2074 6865 0a6f 7269 6769 6e61 ding the.origina\n-00011050: 6c29 2e20 2054 6865 2054 5f49 2061 7265 l). The T_I are\n-00011060: 2074 7261 6e73 666f 726d 732e 2020 5468 transforms. Th\n-00011070: 6520 6b27 7468 2063 6f70 7920 6f66 2074 e k'th copy of t\n-00011080: 6865 0a52 4550 4541 5445 445f 4f42 4a45 he.REPEATED_OBJE\n-00011090: 4354 2028 666f 7220 6b3d 302c 312c 2e2e CT (for k=0,1,..\n-000110a0: 2e2c 6e2d 3129 2069 7320 7072 6f64 7563 .,n-1) is produc\n-000110b0: 6564 2069 6e20 7468 6520 7361 6d65 206d ed in the same m\n-000110c0: 616e 6e65 7220 6173 0a66 6f72 20e2 8098 anner as.for ...\n-000110d0: 7377 6565 70e2 8099 7320 6465 7363 7269 sweep...s descri\n-000110e0: 6265 6420 696e 202a 6e6f 7465 2053 7765 bed in *note Swe\n-000110f0: 6570 733a 3a2e 2020 5468 6973 2069 7320 eps::. This is \n-00011100: 7265 7065 6174 6564 2068 6572 6520 286e repeated here (n\n-00011110: 6f20 7075 6e0a 696e 7465 6e64 6564 2920 o pun.intended) \n-00011120: 666f 7220 636f 6e76 656e 6965 6e63 652e for convenience.\n-00011130: 2020 546f 206d 616b 6520 7468 6520 6b27 To make the k'\n-00011140: 7468 2063 6f70 792c 2074 6865 2066 6f6c th copy, the fol\n-00011150: 6c6f 7769 6e67 0a74 7261 6e73 666f 726d lowing.transform\n-00011160: 2069 7320 6170 706c 6965 6420 746f 2074 is applied to t\n-00011170: 6865 206f 7269 6769 6e61 6c20 6f62 6a65 he original obje\n-00011180: 6374 2e0a 2020 2020 2054 5f31 5e6b 2074 ct.. T_1^k t\n-00011190: 6865 6e20 545f 325e 6b20 7468 656e 202e hen T_2^k then .\n-000111a0: 2e2e 2074 6865 6e20 545f 525e 6b0a 4865 .. then T_R^k.He\n-000111b0: 7265 2054 5e6b 206d 6561 6e73 2022 7472 re T^k means \"tr\n-000111c0: 616e 7366 6f72 6d20 5420 6170 706c 6965 ansform T applie\n-000111d0: 6420 6b20 7469 6d65 732e 220a 0a1f 0a46 d k times.\"....F\n-000111e0: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n-000111f0: 2c20 204e 6f64 653a 2050 7574 732c 2020 , Node: Puts, \n-00011200: 5072 6576 3a20 5265 7065 6174 732c 2020 Prev: Repeats, \n-00011210: 5570 3a20 4472 6177 6162 6c65 730a 0a33 Up: Drawables..3\n-00011220: 2e32 2e39 2050 7574 730a 2d2d 2d2d 2d2d .2.9 Puts.------\n-00011230: 2d2d 2d2d 0a0a 2a53 796e 7461 783a 2a0a ----..*Syntax:*.\n-00011240: 2020 2020 2070 7574 207b 2054 207d 2050 put { T } P\n-00011250: 5554 5f4f 424a 4543 540a 5075 7420 6d65 UT_OBJECT.Put me\n-00011260: 7265 6c79 2061 7070 6c69 6573 2074 7261 rely applies tra\n-00011270: 6e73 666f 726d 2054 2074 6f20 7468 6520 nsform T to the \n-00011280: 6472 6177 6162 6c65 2050 5554 5f4f 424a drawable PUT_OBJ\n-00011290: 4543 542e 0a0a 1f0a 4669 6c65 3a20 736b ECT.....File: sk\n-000112a0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-000112b0: 3a20 4465 6669 6e69 7469 6f6e 732c 2020 : Definitions, \n-000112c0: 4e65 7874 3a20 476c 6f62 616c 2065 6e76 Next: Global env\n-000112d0: 6972 6f6e 6d65 6e74 2c20 2050 7265 763a ironment, Prev:\n-000112e0: 2044 7261 7761 626c 6573 2c20 2055 703a Drawables, Up:\n-000112f0: 2049 6e70 7574 206c 616e 6775 6167 650a Input language.\n-00011300: 0a33 2e33 2044 6566 696e 6974 696f 6e73 .3.3 Definitions\n-00011310: 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d .===============\n-00011320: 0a0a 4465 6669 6e69 7469 6f6e 7320 6769 ..Definitions gi\n-00011330: 7665 206e 616d 6573 2074 6f20 e280 9873 ve names to ...s\n-00011340: 6b65 7463 68e2 8099 206f 626a 6563 7473 ketch... objects\n-00011350: 2e20 2044 6566 696e 6974 696f 6e73 2061 . Definitions a\n-00011360: 6c6f 6e65 2061 7265 0a62 656e 6967 6e2e lone are.benign.\n-00011370: 2020 4120 e280 9873 6b65 7463 68e2 8099 A ...sketch...\n-00011380: 2069 6e70 7574 2066 696c 6520 636f 6e73 input file cons\n-00011390: 6973 7469 6e67 2065 6e74 6972 656c 7920 isting entirely \n-000113a0: 6f66 2064 6566 696e 6974 696f 6e73 2077 of definitions w\n-000113b0: 696c 6c0a 6765 6e65 7261 7465 206e 6f20 ill.generate no \n-000113c0: 6472 6177 696e 672e 2020 4f6e 6c79 2077 drawing. Only w\n-000113d0: 6865 6e20 6465 6669 6e69 7469 6f6e 7320 hen definitions \n-000113e0: 6172 6520 e280 9c72 6566 6572 656e 6365 are ...reference\n-000113f0: 64e2 809d 2064 6f20 7468 6579 0a70 6f74 d... do they.pot\n-00011400: 656e 7469 616c 6c79 206c 6561 6420 746f entially lead to\n-00011410: 2069 6e6b 206f 6e20 7468 6520 6472 6177 ink on the draw\n-00011420: 696e 672e 0a0a 2020 2054 6865 2069 6e74 ing... The int\n-00011430: 656e 7420 6f66 2064 6566 696e 6974 696f ent of definitio\n-00011440: 6e73 2069 7320 746f 206d 616b 6520 e280 ns is to make ..\n-00011450: 9873 6b65 7463 68e2 8099 2063 6f64 6520 .sketch... code \n-00011460: 6d6f 7265 2063 6f6e 6369 7365 2061 6e64 more concise and\n-00011470: 0a72 6561 6461 626c 652e 2020 5468 6572 .readable. Ther\n-00011480: 6520 6973 206e 6f20 696e 7075 7420 6669 e is no input fi\n-00011490: 6c65 2065 6d70 6c6f 7969 6e67 2064 6566 le employing def\n-000114a0: 696e 6974 696f 6e73 2074 6861 7420 636f initions that co\n-000114b0: 756c 6420 6e6f 740a 6265 2072 652d 7772 uld not.be re-wr\n-000114c0: 6974 7465 6e20 7769 7468 6f75 7420 7468 itten without th\n-000114d0: 656d 2e0a 0a20 2020 4465 6669 6e61 626c em... 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In addition\n-000115c0: 2c20 e280 9c74 6167 2064 6566 696e 6974 , ...tag definit\n-000115d0: 696f 6e73 e280 9d2c 2077 6869 6368 2068 ions..., which h\n-000115e0: 6176 6520 6e6f 0a61 7373 6f63 6961 7465 ave no.associate\n-000115f0: 6420 6f62 6a65 6374 2061 7420 616c 6c2c d object at all,\n-00011600: 2061 6c6c 6f77 2074 6865 206d 6561 6e69 allow the meani\n-00011610: 6e67 206f 6620 6f74 6865 7220 6465 6669 ng of other defi\n-00011620: 6e69 7469 6f6e 7320 746f 2062 650a 7365 nitions to be.se\n-00011630: 6c65 6374 6564 2066 726f 6d20 6120 7365 lected from a se\n-00011640: 7420 6f66 2061 6c74 6572 6e61 7469 7665 t of alternative\n-00011650: 732e 2020 5369 6e63 6520 7461 6773 206d s. Since tags m\n-00011660: 6179 2062 6520 6465 6669 6e65 6420 2861 ay be defined (a\n-00011670: 6e64 0a75 6e64 6566 696e 6564 2920 696e nd.undefined) in\n-00011680: 2074 6865 2063 6f6d 6d61 6e64 206c 696e the command lin\n-00011690: 6520 6f66 20e2 8098 736b 6574 6368 e280 e of ...sketch..\n-000116a0: 992c 2074 6865 7920 6361 6e20 6265 2061 ., they can be a\n-000116b0: 6e20 6169 6420 696e 2074 6865 0a73 6372 n aid in the.scr\n-000116c0: 6970 742d 6472 6976 656e 2070 7265 7061 ipt-driven prepa\n-000116d0: 7261 7469 6f6e 206f 6620 646f 6375 6d65 ration of docume\n-000116e0: 6e74 732e 0a0a 2a20 4d65 6e75 3a0a 0a2a nts...* Menu:..*\n-000116f0: 2046 6f72 6d73 206f 6620 6465 6669 6e69 Forms of defini\n-00011700: 7469 6f6e 733a 3a20 2020 2020 2020 2044 tions:: D\n-00011710: 6966 6665 7265 6e74 2064 6566 7320 666f ifferent defs fo\n-00011720: 7220 6469 6666 6572 656e 7420 7075 7270 r different purp\n-00011730: 6f73 6573 2e0a 2a20 466f 726d 7320 6f66 oses..* Forms of\n-00011740: 2072 6566 6572 656e 6365 733a 3a20 2020 references:: \n-00011750: 2020 2020 2020 486f 7720 7265 6665 7265 How refere\n-00011760: 6e63 6573 2064 656e 6f74 6520 7479 7065 nces denote type\n-00011770: 732e 0a0a 1f0a 4669 6c65 3a20 736b 6574 s.....File: sket\n-00011780: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n-00011790: 466f 726d 7320 6f66 2064 6566 696e 6974 Forms of definit\n-000117a0: 696f 6e73 2c20 204e 6578 743a 2046 6f72 ions, Next: For\n-000117b0: 6d73 206f 6620 7265 6665 7265 6e63 6573 ms of references\n-000117c0: 2c20 2050 7265 763a 2044 6566 696e 6974 , Prev: Definit\n-000117d0: 696f 6e73 2c20 2055 703a 2044 6566 696e ions, Up: Defin\n-000117e0: 6974 696f 6e73 0a0a 332e 332e 3120 466f itions..3.3.1 Fo\n-000117f0: 726d 7320 6f66 2064 6566 696e 6974 696f rms of definitio\n-00011800: 6e73 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ns.-------------\n-00011810: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a44 -------------..D\n-00011820: 6566 696e 6974 696f 6e73 2068 6176 6520 efinitions have \n-00011830: 7468 7265 6520 706f 7373 6962 6c65 2066 three possible f\n-00011840: 6f72 6d73 2c20 e280 9c73 696d 706c 65e2 orms, ...simple.\n-00011850: 809d 2c20 e280 9c77 6974 6820 616c 7465 .., ...with alte\n-00011860: 726e 6174 6976 6573 e280 9d2c 0a61 6e64 rnatives...,.and\n-00011870: 20e2 809c 7461 67e2 809d 2061 7320 7368 ...tag... as sh\n-00011880: 6f77 6e20 6865 7265 2069 6e20 6f72 6465 own here in orde\n-00011890: 722e 0a0a 2a53 796e 7461 783a 2a0a 2020 r...*Syntax:*. \n-000118a0: 2020 2064 6566 2049 4420 4f42 4a45 4354 def ID OBJECT\n-000118b0: 2020 2520 7369 6d70 6c65 2064 6566 0a20 % simple def. \n-000118c0: 2020 2020 6465 6620 4944 203c 5441 475f def ID OBJECT_1 % d\n-000118e0: 6566 2077 6974 6820 616c 7465 726e 6174 ef with alternat\n-000118f0: 6976 6573 0a20 2020 2020 2020 2020 2020 ives. \n-00011900: 203c 5441 475f 323e 204f 424a 4543 545f OBJECT_\n-00011910: 320a 2020 2020 2020 2020 2020 2020 2e2e 2. ..\n-00011920: 2e0a 2020 2020 2020 2020 2020 2020 3c3e .. <>\n-00011930: 2044 4546 4155 4c54 5f4f 424a 4543 540a DEFAULT_OBJECT.\n-00011940: 2020 2020 2064 6566 2049 4420 3c3e 2020 def ID <> \n-00011950: 2520 7461 6720 6465 660a 5468 6520 7369 % tag def.The si\n-00011960: 6d70 6c65 2064 6566 696e 6974 696f 6e20 mple definition \n-00011970: 6d65 7265 6c79 2061 7373 6f63 6961 7465 merely associate\n-00011980: 7320 4f42 4a45 4354 2077 6974 6820 7468 s OBJECT with th\n-00011990: 6520 6964 656e 7469 6669 6572 2049 442e e identifier ID.\n-000119a0: 0a0a 2020 2054 6865 2064 6566 696e 6974 .. The definit\n-000119b0: 696f 6e20 7769 7468 2061 6c74 6572 6e61 ion with alterna\n-000119c0: 7469 7665 7320 6173 736f 6369 6174 6573 tives associates\n-000119d0: 204f 424a 4543 545f 4920 7769 7468 2049 OBJECT_I with I\n-000119e0: 442c 2077 6865 7265 0a54 4147 5f49 2069 D, where.TAG_I i\n-000119f0: 7320 7468 6520 6669 7273 7420 6465 6669 s the first defi\n-00011a00: 6e65 6420 7461 6720 696e 2074 6865 206c ned tag in the l\n-00011a10: 6973 7420 6f66 2061 6c74 6572 6e61 7469 ist of alternati\n-00011a20: 7665 2074 6167 0a72 6566 6572 656e 6365 ve tag.reference\n-00011a30: 732e 2020 4966 206e 6f20 7461 6720 696e s. If no tag in\n-00011a40: 2074 6865 206c 6973 7420 6973 2064 6566 the list is def\n-00011a50: 696e 6564 2c20 7468 656e 2044 4546 4155 ined, then DEFAU\n-00011a60: 4c54 5f4f 424a 4543 5420 6973 0a61 7373 LT_OBJECT is.ass\n-00011a70: 6f63 6961 7465 6420 7769 7468 2069 6465 ociated with ide\n-00011a80: 6e74 6966 6965 7220 4944 2e0a 0a20 2020 ntifier ID... \n-00011a90: 5468 6520 6669 6e61 6c20 666f 726d 2064 The final form d\n-00011aa0: 6566 696e 6573 2049 4420 6173 2061 2074 efines ID as a t\n-00011ab0: 6167 2e20 2041 6e6f 7468 6572 2077 6179 ag. Another way\n-00011ac0: 2074 6f20 6465 6669 6e65 2061 2074 6167 to define a tag\n-00011ad0: 2069 730a 7769 7468 2074 6865 20e2 8098 is.with the ...\n-00011ae0: 2d44 e280 9920 636f 6d6d 616e 6420 6c69 -D... command li\n-00011af0: 6e65 206f 7074 696f 6e2e 2020 2a4e 6f74 ne option. *Not\n-00011b00: 6520 436f 6d6d 616e 6420 6c69 6e65 3a3a e Command line::\n-00011b10: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n-00011b20: 682e 696e 666f 2c20 204e 6f64 653a 2046 h.info, Node: F\n-00011b30: 6f72 6d73 206f 6620 7265 6665 7265 6e63 orms of referenc\n-00011b40: 6573 2c20 2050 7265 763a 2046 6f72 6d73 es, Prev: Forms\n-00011b50: 206f 6620 6465 6669 6e69 7469 6f6e 732c of definitions,\n-00011b60: 2020 5570 3a20 4465 6669 6e69 7469 6f6e Up: Definition\n-00011b70: 730a 0a33 2e33 2e32 2046 6f72 6d73 206f s..3.3.2 Forms o\n-00011b80: 6620 7265 6665 7265 6e63 6573 0a2d 2d2d f references.---\n+00010b20: 2e2e 2e0a 0a42 6566 6f72 6520 7365 6e64 .....Before send\n+00010b30: 696e 6720 6561 6368 2066 6f75 722d 7369 ing each four-si\n+00010b40: 6465 6420 626f 6479 2070 6f6c 7967 6f6e ded body polygon\n+00010b50: 206f 6620 6120 e280 9873 7765 6570 e280 of a ...sweep..\n+00010b60: 9920 746f 2074 6865 206f 7574 7075 742c . to the output,\n+00010b70: 0ae2 8098 736b 6574 6368 e280 9920 7465 ....sketch... te\n+00010b80: 7374 7320 746f 2073 6565 2069 6620 6974 sts to see if it\n+00010b90: 2069 7320 726f 7567 686c 7920 706c 616e is roughly plan\n+00010ba0: 6172 2e20 2053 696e 6365 2070 6c61 6e61 ar. Since plana\n+00010bb0: 7269 7479 2069 730a 6e65 6365 7373 6172 rity is.necessar\n+00010bc0: 7920 666f 7220 7072 6f70 6572 2066 756e y for proper fun\n+00010bd0: 6374 696f 6e69 6e67 206f 6620 7468 6520 ctioning of the \n+00010be0: 6869 6464 656e 2073 7572 6661 6365 2061 hidden surface a\n+00010bf0: 6c67 6f72 6974 686d 2c0a 2277 6172 7065 lgorithm,.\"warpe\n+00010c00: 6422 2070 6f6c 7967 6f6e 7320 6172 6520 d\" polygons are \n+00010c10: 6175 746f 6d61 7469 6361 6c6c 7920 7370 automatically sp\n+00010c20: 6c69 7420 696e 746f 2074 776f 2074 7269 lit into two tri\n+00010c30: 616e 676c 6573 2e0a 0a20 2020 486f 6c65 angles... Hole\n+00010c40: 2d66 696c 6c69 6e67 2070 6f6c 7967 6f6e -filling polygon\n+00010c50: 7320 7072 6f64 7563 6564 2062 7920 636c s produced by cl\n+00010c60: 6f73 7572 652d 7461 6767 6564 206c 696e osure-tagged lin\n+00010c70: 6520 7377 6565 7073 2061 7265 206e 6f74 e sweeps are not\n+00010c80: 0a73 706c 6974 2e20 204e 6f72 2061 7265 .split. Nor are\n+00010c90: 206f 7269 6769 6e61 6c20 706f 6c79 676f original polygo\n+00010ca0: 6e73 2069 6e20 706f 6c79 676f 6e20 7377 ns in polygon sw\n+00010cb0: 6565 7073 2e20 2049 7420 6973 2074 6865 eeps. It is the\n+00010cc0: 2075 7365 7227 730a 7265 7370 6f6e 7369 user's.responsi\n+00010cd0: 6269 6c69 7479 2074 6f20 656e 7375 7265 bility to ensure\n+00010ce0: 2074 6865 7365 2061 7265 2070 6c61 6e61 these are plana\n+00010cf0: 722e 0a0a 1f0a 4669 6c65 3a20 736b 6574 r.....File: sket\n+00010d00: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n+00010d10: 426c 6f63 6b73 2c20 204e 6578 743a 2052 Blocks, Next: R\n+00010d20: 6570 6561 7473 2c20 2050 7265 763a 2053 epeats, Prev: S\n+00010d30: 7765 6570 732c 2020 5570 3a20 4472 6177 weeps, Up: Draw\n+00010d40: 6162 6c65 730a 0a33 2e32 2e37 2042 6c6f ables..3.2.7 Blo\n+00010d50: 636b 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d cks.------------\n+00010d60: 0a0a 416e 7920 7365 7175 656e 6365 206f ..Any sequence o\n+00010d70: 6620 6472 6177 6162 6c65 7320 6d61 7920 f drawables may \n+00010d80: 6265 2067 726f 7570 6564 2069 6e20 6120 be grouped in a \n+00010d90: e280 9c62 6c6f 636b e280 9d20 6d65 7265 ...block... mere\n+00010da0: 6c79 2062 790a 656e 636c 6f73 696e 6720 ly by.enclosing \n+00010db0: 7468 656d 2069 6e20 6272 6163 6573 20e2 them in braces .\n+00010dc0: 8098 7b20 7de2 8099 2e20 2041 2062 6c6f ..{ }.... A blo\n+00010dd0: 636b 2069 7320 6974 7365 6c66 2064 7261 ck is itself dra\n+00010de0: 7761 626c 652e 2020 4120 6b65 7920 7573 wable. A key us\n+00010df0: 650a 6f66 2062 6c6f 636b 7320 6973 2074 e.of blocks is t\n+00010e00: 6f20 6578 7465 6e64 2074 6865 2065 6666 o extend the eff\n+00010e10: 6563 7420 6f66 2061 2073 696e 676c 6520 ect of a single \n+00010e20: e280 9864 6566 e280 992c 202a 6e6f 7465 ...def..., *note\n+00010e30: 0a44 6566 696e 6974 696f 6e73 3a3a 2c20 .Definitions::, \n+00010e40: e280 9870 7574 e280 9920 2a6e 6f74 6520 ...put... *note \n+00010e50: 5075 7473 3a3a 2c20 e280 9873 7765 6570 Puts::, ...sweep\n+00010e60: e280 9920 2a6e 6f74 6520 5377 6565 7073 ... *note Sweeps\n+00010e70: 3a3a 2c20 6f72 20e2 8098 7265 7065 6174 ::, or ...repeat\n+00010e80: e280 990a 2a6e 6f74 6520 5265 7065 6174 ....*note Repeat\n+00010e90: 733a 3a20 746f 2069 6e63 6c75 6465 2073 s:: to include s\n+00010ea0: 6576 6572 616c 206f 626a 6563 7473 2072 everal objects r\n+00010eb0: 6174 6865 7220 7468 616e 206f 6e65 2e0a ather than one..\n+00010ec0: 0a20 2020 4465 6669 6e69 7469 6f6e 7320 . Definitions \n+00010ed0: 282a 4e6f 7465 2044 6566 696e 6974 696f (*Note Definitio\n+00010ee0: 6e73 3a3a 2e29 2020 696e 7369 6465 2061 ns::.) inside a\n+00010ef0: 2062 6c6f 636b 2068 6176 6520 e280 9c6c block have ...l\n+00010f00: 6578 6963 616c 0a73 636f 7065 e280 9d20 exical.scope... \n+00010f10: 6578 7465 6e64 696e 6720 6672 6f6d 2074 extending from t\n+00010f20: 6865 2070 6c61 6365 206f 6620 6465 6669 he place of defi\n+00010f30: 6e69 7469 6f6e 2074 6f20 7468 6520 656e nition to the en\n+00010f40: 6420 6f66 2074 6865 2062 6c6f 636b 2e0a d of the block..\n+00010f50: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n+00010f60: 696e 666f 2c20 204e 6f64 653a 2052 6570 info, Node: Rep\n+00010f70: 6561 7473 2c20 204e 6578 743a 2050 7574 eats, Next: Put\n+00010f80: 732c 2020 5072 6576 3a20 426c 6f63 6b73 s, Prev: Blocks\n+00010f90: 2c20 2055 703a 2044 7261 7761 626c 6573 , Up: Drawables\n+00010fa0: 0a0a 332e 322e 3820 5265 7065 6174 730a ..3.2.8 Repeats.\n+00010fb0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a -------------..*\n+00010fc0: 5379 6e74 6178 3a2a 0a20 2020 2020 7265 Syntax:*. re\n+00010fd0: 7065 6174 207b 204e 2c20 545f 312c 2054 peat { N, T_1, T\n+00010fe0: 5f32 2c20 2e2e 2e2c 2054 5f52 207d 2052 _2, ..., T_R } R\n+00010ff0: 4550 4541 5445 445f 4f42 4a45 4354 0a54 EPEATED_OBJECT.T\n+00011000: 6865 2072 6570 6561 7420 6d61 6b65 7320 he repeat makes \n+00011010: 4e20 7472 616e 7366 6f72 6d65 6420 636f N transformed co\n+00011020: 7069 6573 206f 6620 5245 5045 4154 4544 pies of REPEATED\n+00011030: 5f4f 424a 4543 5420 2869 6e63 6c75 6469 _OBJECT (includi\n+00011040: 6e67 2074 6865 0a6f 7269 6769 6e61 6c29 ng the.original)\n+00011050: 2e20 2054 6865 2054 5f49 2061 7265 2074 . The T_I are t\n+00011060: 7261 6e73 666f 726d 732e 2020 5468 6520 ransforms. The \n+00011070: 6b27 7468 2063 6f70 7920 6f66 2074 6865 k'th copy of the\n+00011080: 0a52 4550 4541 5445 445f 4f42 4a45 4354 .REPEATED_OBJECT\n+00011090: 2028 666f 7220 6b3d 302c 312c 2e2e 2e2c (for k=0,1,...,\n+000110a0: 6e2d 3129 2069 7320 7072 6f64 7563 6564 n-1) is produced\n+000110b0: 2069 6e20 7468 6520 7361 6d65 206d 616e in the same man\n+000110c0: 6e65 7220 6173 0a66 6f72 20e2 8098 7377 ner as.for ...sw\n+000110d0: 6565 70e2 8099 7320 6465 7363 7269 6265 eep...s describe\n+000110e0: 6420 696e 202a 6e6f 7465 2053 7765 6570 d in *note Sweep\n+000110f0: 733a 3a2e 2020 5468 6973 2069 7320 7265 s::. This is re\n+00011100: 7065 6174 6564 2068 6572 6520 286e 6f20 peated here (no \n+00011110: 7075 6e0a 696e 7465 6e64 6564 2920 666f pun.intended) fo\n+00011120: 7220 636f 6e76 656e 6965 6e63 652e 2020 r convenience. \n+00011130: 546f 206d 616b 6520 7468 6520 6b27 7468 To make the k'th\n+00011140: 2063 6f70 792c 2074 6865 2066 6f6c 6c6f copy, the follo\n+00011150: 7769 6e67 0a74 7261 6e73 666f 726d 2069 wing.transform i\n+00011160: 7320 6170 706c 6965 6420 746f 2074 6865 s applied to the\n+00011170: 206f 7269 6769 6e61 6c20 6f62 6a65 6374 original object\n+00011180: 2e0a 2020 2020 2054 5f31 5e6b 2074 6865 .. T_1^k the\n+00011190: 6e20 545f 325e 6b20 7468 656e 202e 2e2e n T_2^k then ...\n+000111a0: 2074 6865 6e20 545f 525e 6b0a 4865 7265 then T_R^k.Here\n+000111b0: 2054 5e6b 206d 6561 6e73 2022 7472 616e T^k means \"tran\n+000111c0: 7366 6f72 6d20 5420 6170 706c 6965 6420 sform T applied \n+000111d0: 6b20 7469 6d65 732e 220a 0a1f 0a46 696c k times.\"....Fil\n+000111e0: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n+000111f0: 204e 6f64 653a 2050 7574 732c 2020 5072 Node: Puts, Pr\n+00011200: 6576 3a20 5265 7065 6174 732c 2020 5570 ev: Repeats, Up\n+00011210: 3a20 4472 6177 6162 6c65 730a 0a33 2e32 : Drawables..3.2\n+00011220: 2e39 2050 7574 730a 2d2d 2d2d 2d2d 2d2d .9 Puts.--------\n+00011230: 2d2d 0a0a 2a53 796e 7461 783a 2a0a 2020 --..*Syntax:*. \n+00011240: 2020 2070 7574 207b 2054 207d 2050 5554 put { T } PUT\n+00011250: 5f4f 424a 4543 540a 5075 7420 6d65 7265 _OBJECT.Put mere\n+00011260: 6c79 2061 7070 6c69 6573 2074 7261 6e73 ly applies trans\n+00011270: 666f 726d 2054 2074 6f20 7468 6520 6472 form T to the dr\n+00011280: 6177 6162 6c65 2050 5554 5f4f 424a 4543 awable PUT_OBJEC\n+00011290: 542e 0a0a 1f0a 4669 6c65 3a20 736b 6574 T.....File: sket\n+000112a0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n+000112b0: 4465 6669 6e69 7469 6f6e 732c 2020 4e65 Definitions, Ne\n+000112c0: 7874 3a20 476c 6f62 616c 2065 6e76 6972 xt: Global envir\n+000112d0: 6f6e 6d65 6e74 2c20 2050 7265 763a 2044 onment, Prev: D\n+000112e0: 7261 7761 626c 6573 2c20 2055 703a 2049 rawables, Up: I\n+000112f0: 6e70 7574 206c 616e 6775 6167 650a 0a33 nput language..3\n+00011300: 2e33 2044 6566 696e 6974 696f 6e73 0a3d .3 Definitions.=\n+00011310: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a ==============..\n+00011320: 4465 6669 6e69 7469 6f6e 7320 6769 7665 Definitions give\n+00011330: 206e 616d 6573 2074 6f20 e280 9873 6b65 names to ...ske\n+00011340: 7463 68e2 8099 206f 626a 6563 7473 2e20 tch... objects. \n+00011350: 2044 6566 696e 6974 696f 6e73 2061 6c6f Definitions alo\n+00011360: 6e65 2061 7265 0a62 656e 6967 6e2e 2020 ne are.benign. \n+00011370: 4120 e280 9873 6b65 7463 68e2 8099 2069 A ...sketch... i\n+00011380: 6e70 7574 2066 696c 6520 636f 6e73 6973 nput file consis\n+00011390: 7469 6e67 2065 6e74 6972 656c 7920 6f66 ting entirely of\n+000113a0: 2064 6566 696e 6974 696f 6e73 2077 696c definitions wil\n+000113b0: 6c0a 6765 6e65 7261 7465 206e 6f20 6472 l.generate no dr\n+000113c0: 6177 696e 672e 2020 4f6e 6c79 2077 6865 awing. 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This is a go\n-00012410: 6f64 2070 6c61 6365 2074 6f20 7365 7420 od place to set \n-00012420: e280 9875 6e69 74e2 8099 2c20 6120 6465 ...unit..., a de\n-00012430: 6661 756c 7420 e280 986c 696e 6577 6964 fault ...linewid\n-00012440: 7468 e280 992c 2065 7463 2e0a 0a20 2020 th..., etc... \n-00012450: 496e 7465 726e 616c 206f 7074 696f 6e73 Internal options\n-00012460: 2077 6f72 6b20 6f6e 2061 6c6c 206f 626a work on all obj\n-00012470: 6563 7473 2077 6865 7265 2074 6865 7920 ects where they \n-00012480: 6d61 6b65 2073 656e 7365 2e20 2054 6869 make sense. Thi\n-00012490: 730a 696e 636c 7564 6573 20e2 8098 6375 s.includes ...cu\n-000124a0: 6c6c e280 9920 616e 6420 e280 9873 706c ll... and ...spl\n-000124b0: 6974 e280 9920 2862 7574 206e 6f74 20e2 it... (but not .\n-000124c0: 8098 6c61 79e2 8099 292e 2020 2a4e 6f74 ..lay...). *Not\n-000124d0: 6520 496e 7465 726e 616c 206f 7074 696f e Internal optio\n-000124e0: 6e73 3a3a 2e0a 0a1f 0a46 696c 653a 2073 ns::.....File: s\n-000124f0: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n-00012500: 653a 2043 616d 6572 612c 2020 4e65 7874 e: Camera, Next\n-00012510: 3a20 5069 6374 7572 6520 626f 782c 2020 : Picture box, \n-00012520: 5072 6576 3a20 476c 6f62 616c 206f 7074 Prev: Global opt\n-00012530: 696f 6e73 2c20 2055 703a 2047 6c6f 6261 ions, Up: Globa\n-00012540: 6c20 656e 7669 726f 6e6d 656e 740a 0a33 l environment..3\n-00012550: 2e34 2e32 2043 616d 6572 610a 2d2d 2d2d .4.2 Camera.----\n-00012560: 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 --------..*Synta\n-00012570: 783a 2a0a 2020 2020 2063 616d 6572 6120 x:*. camera \n-00012580: 5452 414e 5346 4f52 4d5f 4558 5052 4553 TRANSFORM_EXPRES\n-00012590: 5349 4f4e 0a20 2020 5468 6520 5452 414e SION. The TRAN\n-000125a0: 5346 4f52 4d5f 4558 5052 4553 5349 4f4e SFORM_EXPRESSION\n-000125b0: 2069 7320 6170 706c 6965 6420 6166 7465 is applied afte\n-000125c0: 7220 616c 6c20 6f74 6865 7220 7472 616e r all other tran\n-000125d0: 7366 6f72 6d61 7469 6f6e 730a 6f66 2074 sformations.of t\n-000125e0: 6865 2073 6365 6e65 2e20 2054 6869 7320 he scene. This \n-000125f0: 6973 2063 7572 7265 6e74 6c79 206f 6e6c is currently onl\n-00012600: 7920 7573 6566 756c 2066 6f72 2074 7261 y useful for tra\n-00012610: 6e73 666f 726d 696e 6720 7468 650a 626f nsforming the.bo\n-00012620: 756e 6469 6e67 2062 6f78 2e20 202a 4e6f unding box. *No\n-00012630: 7465 2050 6963 7475 7265 2062 6f78 3a3a te Picture box::\n-00012640: 2e20 2049 7420 7769 6c6c 2070 6c61 7920 . It will play \n-00012650: 6120 726f 6c65 2069 6e20 616e 7920 6675 a role in any fu\n-00012660: 7475 7265 0a69 6d70 6c65 6d65 6e74 6174 ture.implementat\n-00012670: 696f 6e20 6f66 2063 6c69 7070 696e 672e ion of clipping.\n-00012680: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n-00012690: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5069 .info, Node: Pi\n-000126a0: 6374 7572 6520 626f 782c 2020 4e65 7874 cture box, Next\n-000126b0: 3a20 4672 616d 652c 2020 5072 6576 3a20 : Frame, Prev: \n-000126c0: 4361 6d65 7261 2c20 2055 703a 2047 6c6f Camera, Up: Glo\n-000126d0: 6261 6c20 656e 7669 726f 6e6d 656e 740a bal environment.\n-000126e0: 0a33 2e34 2e33 2050 6963 7475 7265 2062 .3.4.3 Picture b\n-000126f0: 6f78 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ox.-------------\n-00012700: 2d2d 2d2d 0a0a 2a53 796e 7461 783a 2a0a ----..*Syntax:*.\n-00012710: 2020 2020 2070 6963 7475 7265 626f 785b picturebox[\n-00012720: 4241 5345 4c49 4e45 5d0a 2020 2020 2070 BASELINE]. p\n-00012730: 6963 7475 7265 626f 785b 4241 5345 4c49 icturebox[BASELI\n-00012740: 4e45 5d20 2850 3129 2850 3229 0a54 6865 NE] (P1)(P2).The\n-00012750: 2066 6972 7374 2066 6f72 6d20 6f66 20e2 first form of .\n-00012760: 8098 7069 6374 7572 6562 6f78 e280 9920 ..picturebox... \n-00012770: 6361 7573 6573 2061 2073 6361 6c61 7220 causes a scalar \n-00012780: 4241 5345 4c49 4e45 2066 7261 6374 696f BASELINE fractio\n-00012790: 6e20 746f 2062 650a 656d 6974 7465 6420 n to be.emitted \n-000127a0: 696e 2074 6865 20e2 8098 7073 7069 6374 in the ...pspict\n-000127b0: 7572 65e2 8099 2065 6e76 6972 6f6e 6d65 ure... environme\n-000127c0: 6e74 206f 6620 7468 6520 6f75 7470 7574 nt of the output\n-000127d0: 2e20 2053 6565 20e2 8098 5053 5472 6963 . See ...PSTric\n-000127e0: 6b73 e280 990a 646f 6375 6d65 6e74 6174 ks....documentat\n-000127f0: 696f 6e20 666f 7220 e280 9870 7370 6963 ion for ...pspic\n-00012800: 7475 7265 e280 992e 0a0a 2020 2049 6e20 ture...... In \n-00012810: 7468 6520 7365 636f 6e64 2066 6f72 6d2c the second form,\n-00012820: 2074 6865 2042 4153 454c 494e 4520 6672 the BASELINE fr\n-00012830: 6163 7469 6f6e 2069 7320 6f70 7469 6f6e action is option\n-00012840: 616c 2c20 616e 6420 7468 6520 7477 6f0a al, and the two.\n-00012850: 706f 696e 7473 2074 6861 7420 666f 6c6c points that foll\n-00012860: 6f77 2064 6566 696e 6520 7468 6520 6469 ow define the di\n-00012870: 6167 6f6e 616c 206f 6620 6120 7468 7265 agonal of a thre\n-00012880: 652d 6469 6d65 6e73 696f 6e61 6c20 626f e-dimensional bo\n-00012890: 756e 6469 6e67 0a62 6f78 2066 6f72 2074 unding.box for t\n-000128a0: 6865 2063 6f6d 706c 6574 6564 2073 6365 he completed sce\n-000128b0: 6e65 2e20 2054 6865 2070 6172 616c 6c65 ne. The paralle\n-000128c0: 6c20 7072 6f6a 6563 7469 6f6e 206f 6620 l projection of \n-000128d0: 7468 6520 626f 756e 6469 6e67 0a62 6f78 the bounding.box\n-000128e0: 2064 6574 6572 6d69 6e65 7320 7468 6520 determines the \n-000128f0: 636f 726e 6572 7320 6f66 2074 6865 2064 corners of the d\n-00012900: 7261 7769 6e67 2773 20e2 8098 7073 7069 rawing's ...pspi\n-00012910: 6374 7572 652a e280 9920 656e 7669 726f cture*... enviro\n-00012920: 6e6d 656e 742c 0a77 6869 6368 2069 7320 nment,.which is \n-00012930: 7573 6564 2069 6e20 706c 6163 6520 6f66 used in place of\n-00012940: 20e2 8098 7073 7069 6374 7572 65e2 8099 ...pspicture...\n-00012950: 2e20 2054 6869 7320 6361 7573 6573 2050 . This causes P\n-00012960: 6f73 7453 6372 6970 7420 746f 2063 6c69 ostScript to cli\n-00012970: 700a 7468 6520 6669 6e61 6c20 6472 6177 p.the final draw\n-00012980: 696e 6720 746f 2074 6865 2062 6f75 6e64 ing to the bound\n-00012990: 696e 6720 626f 7820 696e 2032 642e 2020 ing box in 2d. \n-000129a0: 4966 2074 6865 7265 2069 7320 6120 e280 If there is a ..\n-000129b0: 9863 616d 6572 61e2 8099 0a73 7065 6369 .camera....speci\n-000129c0: 6669 6564 2c20 7468 6520 6361 6d65 7261 fied, the camera\n-000129d0: 2074 7261 6e66 6f72 6d61 7469 6f6e 2069 tranformation i\n-000129e0: 7320 6170 706c 6965 6420 746f 2074 6865 s applied to the\n-000129f0: 2062 6f75 6e64 696e 6720 626f 782c 2061 bounding box, a\n-00012a00: 6e64 0a74 6865 20e2 8098 7073 7069 6374 nd.the ...pspict\n-00012a10: 7572 65e2 8099 2069 7320 7365 7420 6a75 ure... is set ju\n-00012a20: 7374 206c 6172 6765 2065 6e6f 7567 6820 st large enough \n-00012a30: 746f 2069 6e63 6c75 6465 2074 6865 2074 to include the t\n-00012a40: 7261 6e73 666f 726d 6564 2062 6f78 2e0a ransformed box..\n-00012a50: 0a20 2020 5768 656e 206e 6f20 626f 756e . When no boun\n-00012a60: 6469 6e67 2062 6f78 2069 7320 6769 7665 ding box is give\n-00012a70: 6e2c 20e2 8098 736b 6574 6368 e280 9920 n, ...sketch... \n-00012a80: 636f 6d70 7574 6573 206f 6e65 2061 7574 computes one aut\n-00012a90: 6f6d 6174 6963 616c 6c79 2e0a 0a1f 0a46 omatically.....F\n-00012aa0: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n-00012ab0: 2c20 204e 6f64 653a 2046 7261 6d65 2c20 , Node: Frame, \n-00012ac0: 204e 6578 743a 204c 616e 6775 6167 652c Next: Language,\n-00012ad0: 2020 5072 6576 3a20 5069 6374 7572 6520 Prev: Picture \n-00012ae0: 626f 782c 2020 5570 3a20 476c 6f62 616c box, Up: Global\n-00012af0: 2065 6e76 6972 6f6e 6d65 6e74 0a0a 332e environment..3.\n-00012b00: 342e 3420 4672 616d 650a 2d2d 2d2d 2d2d 4.4 Frame.------\n-00012b10: 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a -----..*Syntax:*\n-00012b20: 0a20 2020 2020 6672 616d 6520 5b4f 5054 . frame [OPT\n-00012b30: 494f 4e53 5d0a 4361 7573 6573 2061 205c IONS].Causes a \\\n-00012b40: 7073 6672 616d 6562 6f78 2074 6f20 7375 psframebox to su\n-00012b50: 7272 6f75 6e64 2074 6865 20e2 8098 7073 rround the ...ps\n-00012b60: 7069 6374 7572 65e2 8099 2065 6e76 6972 picture... envir\n-00012b70: 6f6e 6d65 6e74 2069 6e20 7468 650a 6f75 onment in the.ou\n-00012b80: 7470 7574 2e20 2049 6620 4f50 5449 4f4e tput. If OPTION\n-00012b90: 5320 6172 6520 7072 6573 656e 742c 2074 S are present, t\n-00012ba0: 6865 7920 6172 6520 636f 7069 6564 2061 hey are copied a\n-00012bb0: 732d 6973 2e20 204e 6f72 6d61 6c6c 7920 s-is. Normally \n-00012bc0: 6f6e 650a 776f 756c 6420 7761 6e74 2074 one.would want t\n-00012bd0: 6f20 7365 7420 e280 986c 696e 6577 6964 o set ...linewid\n-00012be0: 7468 e280 992c 20e2 8098 6c69 6e65 7374 th..., ...linest\n-00012bf0: 796c 65e2 8099 2c20 e280 986c 696e 6563 yle..., ...linec\n-00012c00: 6f6c 6f72 e280 992c 2065 7463 2e20 2049 olor..., etc. I\n-00012c10: 660a 6f6d 6974 7465 642c 2074 6865 6e20 f.omitted, then \n-00012c20: e280 9866 7261 6d65 7365 703d 3070 74e2 ...framesep=0pt.\n-00012c30: 8099 2069 7320 6164 6465 6420 736f 2074 .. is added so t\n-00012c40: 6861 7420 7468 6520 6672 616d 6520 7469 hat the frame ti\n-00012c50: 6768 746c 7920 6875 6773 2074 6865 0ae2 ghtly hugs the..\n-00012c60: 8098 7073 7069 6374 7572 65e2 8099 2e0a ..pspicture.....\n-00012c70: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n-00012c80: 696e 666f 2c20 204e 6f64 653a 204c 616e info, Node: Lan\n-00012c90: 6775 6167 652c 2020 5072 6576 3a20 4672 guage, Prev: Fr\n-00012ca0: 616d 652c 2020 5570 3a20 476c 6f62 616c ame, Up: Global\n-00012cb0: 2065 6e76 6972 6f6e 6d65 6e74 0a0a 332e environment..3.\n-00012cc0: 342e 3520 4c61 6e67 7561 6765 0a2d 2d2d 4.5 Language.---\n-00012cd0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a20 2020 -----------.. \n-00012ce0: 2020 6c61 6e67 7561 6765 2074 696b 7a0a language tikz.\n-00012cf0: 2020 2020 206c 616e 6775 6167 6520 7469 language ti\n-00012d00: 6b7a 2c20 636f 6e74 6578 740a 2020 2020 kz, context. \n-00012d10: 206c 616e 6775 6167 6520 7073 7472 6963 language pstric\n-00012d20: 6b73 0a20 2020 2020 6c61 6e67 7561 6765 ks. language\n-00012d30: 2070 7374 7269 636b 732c 206c 6174 6578 pstricks, latex\n-00012d40: 0a53 6574 7320 7468 6520 6f75 7470 7574 .Sets the output\n-00012d50: 206c 616e 6775 6167 6520 6765 6e65 7261 language genera\n-00012d60: 7465 6420 6279 20e2 8098 736b 6574 6368 ted by ...sketch\n-00012d70: e280 992e 2020 5468 6520 7365 7420 6f66 .... The set of\n-00012d80: 206f 7074 696f 6e73 0a75 6e64 6572 7374 options.underst\n-00012d90: 6f6f 6420 6279 2073 6b65 7463 6820 616c ood by sketch al\n-00012da0: 736f 2063 6861 6e67 6573 2e20 2046 6f72 so changes. For\n-00012db0: 2065 7861 6d70 6c65 2c20 7468 6520 e280 example, the ..\n-00012dc0: 9850 5354 7269 636b 73e2 8099 206f 7074 .PSTricks... opt\n-00012dd0: 696f 6e0a e280 986c 696e 6577 6964 7468 ion....linewidth\n-00012de0: e280 9920 7769 6c6c 206e 6f74 2062 6520 ... will not be \n-00012df0: 7072 6f70 6572 6c79 2068 616e 646c 6564 properly handled\n-00012e00: 2069 6620 e280 986c 616e 6775 6167 65e2 if ...language.\n-00012e10: 8099 2069 7320 7365 7420 746f 20e2 8098 .. is set to ...\n-00012e20: 7469 6b7a e280 992e 0a53 696d 696c 6172 tikz.....Similar\n-00012e30: 6c79 2c20 7468 6520 e280 9854 696b 5ae2 ly, the ...TikZ.\n-00012e40: 8099 206f 7074 696f 6e20 e280 986c 696e .. option ...lin\n-00012e50: 6520 7374 796c 65e2 8099 2028 6e6f 7465 e style... (note\n-00012e60: 2074 6865 2073 7061 6365 2920 7769 6c6c the space) will\n-00012e70: 206e 6f74 2062 650a 7072 6f70 6572 6c79 not be.properly\n-00012e80: 2068 616e 646c 6564 2069 6620 e280 986c handled if ...l\n-00012e90: 616e 6775 6167 65e2 8099 2069 7320 7365 anguage... is se\n-00012ea0: 7420 746f 20e2 8098 7073 7472 6963 6b73 t to ...pstricks\n-00012eb0: e280 992e 2020 4966 206e 6f20 6c61 6e67 .... If no lang\n-00012ec0: 7561 6765 2069 730a 7370 6563 6966 6965 uage is.specifie\n-00012ed0: 642c 2074 6865 2064 6566 6175 6c74 20e2 d, the default .\n-00012ee0: 8098 7073 7472 6963 6b73 e280 9920 6973 ..pstricks... is\n-00012ef0: 2075 7365 642e 0a0a 2020 2041 6e20 6f70 used... An op\n-00012f00: 7469 6f6e 616c 2063 6f6d 6d61 2066 6f6c tional comma fol\n-00012f10: 6c6f 7765 6420 6279 20e2 8098 6c61 7465 lowed by ...late\n-00012f20: 78e2 8099 206f 7220 e280 9863 6f6e 7465 x... or ...conte\n-00012f30: 7874 e280 9920 7370 6563 6966 6965 7320 xt... specifies \n-00012f40: 7468 650a 6d61 6372 6f20 7061 636b 6167 the.macro packag\n-00012f50: 6520 7468 6174 2074 6865 206f 7574 7075 e that the outpu\n-00012f60: 7420 7368 6f75 6c64 2061 7373 756d 652e t should assume.\n-00012f70: 2020 5468 6973 2061 6666 6563 7473 2074 This affects t\n-00012f80: 6865 20e2 8098 7069 6374 7572 65e2 8099 he ...picture...\n-00012f90: 0a65 6e76 6972 6f6e 6d65 6e74 2063 6f6d .environment com\n-00012fa0: 6d61 6e64 7320 656d 6974 7465 6420 616e mands emitted an\n-00012fb0: 6420 7468 6520 646f 6375 6d65 6e74 2074 d the document t\n-00012fc0: 656d 706c 6174 6520 7573 6564 2077 6974 emplate used wit\n-00012fd0: 6820 7468 650a e280 982d 54e2 8099 206f h the....-T... o\n-00012fe0: 7074 696f 6e2e 2020 2a4e 6f74 6520 436f ption. *Note Co\n-00012ff0: 6d6d 616e 6420 6c69 6e65 3a3a 2e20 204e mmand line::. N\n-00013000: 6f74 6520 7468 6174 2061 7420 7468 6520 ote that at the \n-00013010: 7469 6d65 2074 6869 7320 6d61 6e75 616c time this manual\n-00013020: 0a77 6173 2067 656e 6572 6174 6564 2c20 .was generated, \n-00013030: e280 9850 5354 7269 636b 73e2 8099 2077 ...PSTricks... w\n-00013040: 6173 206e 6f74 2073 7570 706f 7274 6564 as not supported\n-00013050: 2062 7920 4c61 5465 5820 6f72 2062 7920 by LaTeX or by \n-00013060: e280 9843 6f6e 5465 5874 e280 992e 0a0a ...ConTeXt......\n-00013070: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n-00013080: 6e66 6f2c 2020 4e6f 6465 3a20 4275 696c nfo, Node: Buil\n-00013090: 6469 6e67 2061 2064 7261 7769 6e67 2c20 ding a drawing, \n-000130a0: 204e 6578 743a 2043 6f6d 6d61 6e64 206c Next: Command l\n-000130b0: 696e 652c 2020 5072 6576 3a20 496e 7075 ine, Prev: Inpu\n-000130c0: 7420 6c61 6e67 7561 6765 2c20 2055 703a t language, Up:\n-000130d0: 2054 6f70 0a0a 3420 4275 696c 6469 6e67 Top..4 Building\n-000130e0: 2061 2064 7261 7769 6e67 0a2a 2a2a 2a2a a drawing.*****\n-000130f0: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a0a ***************.\n-00013100: 0a53 7563 6365 7373 6675 6c20 6472 6177 .Successful draw\n-00013110: 696e 6773 2077 6974 6820 e280 9873 6b65 ings with ...ske\n-00013120: 7463 68e2 8099 2061 6e64 2077 6974 6820 tch... and with \n-00013130: 616e 7920 7363 656e 6520 6465 7363 7269 any scene descri\n-00013140: 7074 696f 6e0a 6c61 6e67 7561 6765 2072 ption.language r\n-00013150: 6571 7569 7265 2074 6861 7420 7468 6520 equire that the \n-00013160: 7573 6572 2064 6576 656c 6f70 2061 6e20 user develop an \n-00013170: 6163 6375 7261 7465 206d 656e 7461 6c20 accurate mental \n-00013180: 7069 6374 7572 6520 6f66 2068 6572 0a63 picture of her.c\n-00013190: 6f64 6520 616e 6420 6974 7320 6d65 616e ode and its mean\n-000131a0: 696e 672e 2020 5468 6973 2069 6d61 6765 ing. This image\n-000131b0: 2069 7320 6265 7374 2062 7569 6c74 2069 is best built i\n-000131c0: 6e20 736d 616c 6c20 7069 6563 6573 2e0a n small pieces..\n-000131d0: 5468 6572 6566 6f72 652c 20e2 8098 736b Therefore, ...sk\n-000131e0: 6574 6368 e280 9920 696e 7075 7473 2061 etch... inputs a\n-000131f0: 7265 2062 6573 7420 6372 6561 7465 6420 re best created \n-00013200: 696e 2073 6d61 6c6c 2069 6e63 7265 6d65 in small increme\n-00013210: 6e74 7320 7769 7468 0a66 7265 7175 656e nts with.frequen\n-00013220: 7420 7061 7573 6573 2074 6f20 636f 6d70 t pauses to comp\n-00013230: 696c 6520 616e 6420 7669 6577 2074 6865 ile and view the\n-00013240: 2072 6573 756c 7473 2e20 2043 6172 6566 results. Caref\n-00013250: 756c 2063 6f6d 6d65 6e74 7320 696e 0a74 ul comments in.t\n-00013260: 6865 2069 6e70 7574 206f 6674 656e 2068 he input often h\n-00013270: 656c 7020 6173 2061 2073 6365 6e65 2067 elp as a scene g\n-00013280: 726f 7773 2069 6e20 636f 6d70 6c65 7869 rows in complexi\n-00013290: 7479 2e0a 0a2a 204d 656e 753a 0a0a 2a20 ty...* Menu:..* \n-000132a0: 4f76 6572 7669 6577 3a3a 2020 2020 2020 Overview:: \n-000132b0: 2020 2020 2020 2020 2020 2020 2020 4275 Bu\n-000132c0: 696c 6469 6e67 2061 2073 7562 7374 616e ilding a substan\n-000132d0: 7469 616c 2064 7261 7769 6e67 2e0a 2a20 tial drawing..* \n-000132e0: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n-000132f0: 696e 673a 3a20 2020 2020 2020 2020 416e ing:: An\n-00013300: 2065 7861 6d70 6c65 2077 6974 6820 6669 example with fi\n-00013310: 6e65 2070 6c61 6365 6d65 6e74 2e0a 2a20 ne placement..* \n-00013320: 4120 6869 6572 6172 6368 6963 616c 206d A hierarchical m\n-00013330: 6f64 656c 3a3a 2020 2020 2020 2020 416e odel:: An\n-00013340: 2065 7861 6d70 6c65 2077 6974 6820 7377 example with sw\n-00013350: 6565 7073 2061 6e64 2070 7574 732e 0a2a eeps and puts..*\n-00013360: 2043 6176 6561 7473 3a3a 2020 2020 2020 Caveats:: \n-00013370: 2020 2020 2020 2020 2020 2020 2020 2057 W\n-00013380: 6865 7265 2074 726f 7562 6c65 2063 616e here trouble can\n-00013390: 206f 6363 7572 2e0a 0a1f 0a46 696c 653a occur.....File:\n-000133a0: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-000133b0: 6f64 653a 204f 7665 7276 6965 772c 2020 ode: Overview, \n-000133c0: 4e65 7874 3a20 4120 7465 6368 6e69 6361 Next: A technica\n-000133d0: 6c20 6472 6177 696e 672c 2020 5072 6576 l drawing, Prev\n-000133e0: 3a20 4275 696c 6469 6e67 2061 2064 7261 : Building a dra\n-000133f0: 7769 6e67 2c20 2055 703a 2042 7569 6c64 wing, Up: Build\n-00013400: 696e 6720 6120 6472 6177 696e 670a 0a34 ing a drawing..4\n-00013410: 2e31 204f 7665 7276 6965 770a 3d3d 3d3d .1 Overview.====\n-00013420: 3d3d 3d3d 3d3d 3d3d 0a0a 4173 2061 6e20 ========..As an \n-00013430: 6f76 6572 7669 6577 2c20 6c65 7427 7320 overview, let's \n-00013440: 6465 7665 6c6f 7020 6120 6469 6167 7261 develop a diagra\n-00013450: 6d20 7468 6174 2073 686f 7773 2068 6f77 m that shows how\n-00013460: 2061 2070 6572 7370 6563 7469 7665 0a70 a perspective.p\n-00013470: 726f 6a65 6374 696f 6e20 7472 616e 7366 rojection transf\n-00013480: 6f72 6d20 776f 726b 732e 2020 5765 276c orm works. We'l\n-00013490: 6c20 7374 6172 7420 7769 7468 2074 6865 l start with the\n-000134a0: 2074 7261 6469 7469 6f6e 616c 2072 6566 traditional ref\n-000134b0: 6572 656e 6365 0a6f 626a 6563 7420 7573 erence.object us\n-000134c0: 6564 2069 6e20 636f 6d70 7574 6572 2067 ed in computer g\n-000134d0: 7261 7068 6963 7320 7465 7874 626f 6f6b raphics textbook\n-000134e0: 732c 2061 2068 6f75 7365 2d73 6861 7065 s, a house-shape\n-000134f0: 6420 7072 6973 6d2e 2020 4265 6769 6e0a d prism. Begin.\n-00013500: 6279 2064 6566 696e 696e 6720 7468 6520 by defining the \n-00013510: 706f 696e 7473 206f 6620 7468 6520 686f points of the ho\n-00013520: 7573 652e 2020 5261 7468 6572 2074 6861 use. Rather tha\n-00013530: 6e20 6465 6669 6e69 6e67 2074 6865 2066 n defining the f\n-00013540: 6163 6573 206f 660a 7468 6520 686f 7573 aces of.the hous\n-00013550: 6520 6173 2070 6f6c 7967 6f6e 7320 616e e as polygons an\n-00013560: 6420 7472 616e 7366 6f72 6d69 6e67 2074 d transforming t\n-00013570: 686f 7365 2c20 7765 2061 7265 2067 6f69 hose, we are goi\n-00013580: 6e67 2074 6f20 7472 616e 7366 6f72 6d0a ng to transform.\n-00013590: 7468 6520 706f 696e 7473 2074 6865 6d73 the points thems\n-000135a0: 656c 7665 7320 7769 7468 20e2 8098 736b elves with ...sk\n-000135b0: 6574 6368 e280 9920 6172 6974 686d 6574 etch... arithmet\n-000135c0: 6963 2073 6f20 7468 6174 2077 6520 6861 ic so that we ha\n-000135d0: 7665 206e 616d 6573 2066 6f72 0a74 6865 ve names for.the\n-000135e0: 2074 7261 6e73 666f 726d 6564 2070 6f69 transformed poi\n-000135f0: 6e74 7320 6c61 7465 722e 0a20 2025 2072 nts later.. % r\n-00013600: 6967 6874 2073 6964 6520 286f 7574 7369 ight side (outsi\n-00013610: 6465 2074 6f20 7269 6768 7429 0a20 2064 de to right). d\n-00013620: 6566 2052 3120 2831 2c31 2c31 2920 6465 ef R1 (1,1,1) de\n-00013630: 6620 5232 2028 312c 2d31 2c31 2920 6465 f R2 (1,-1,1) de\n-00013640: 6620 5233 2028 312c 2d31 2c2d 3129 2064 f R3 (1,-1,-1) d\n-00013650: 6566 2052 3420 2831 2c31 2c2d 3129 0a20 ef R4 (1,1,-1). \n-00013660: 2064 6566 2052 3520 2831 2c31 2e35 2c30 def R5 (1,1.5,0\n-00013670: 290a 0a20 2025 206c 6566 7420 7369 6465 ).. % left side\n-00013680: 2028 6f75 7473 6964 6520 746f 2072 6967 (outside to rig\n-00013690: 6874 2d2d 6261 636b 7761 7264 290a 2020 ht--backward). \n-000136a0: 6465 6620 5720 205b 322c 302c 305d 0a20 def W [2,0,0]. \n-000136b0: 2064 6566 204c 3120 2852 3129 2d5b 575d def L1 (R1)-[W]\n-000136c0: 2064 6566 204c 3220 2852 3229 2d5b 575d def L2 (R2)-[W]\n-000136d0: 2064 6566 204c 3320 2852 3329 2d5b 575d def L3 (R3)-[W]\n-000136e0: 2064 6566 204c 3420 2852 3429 2d5b 575d def L4 (R4)-[W]\n-000136f0: 0a20 2064 6566 204c 3520 2852 3529 2d5b . def L5 (R5)-[\n-00013700: 575d 0a54 6f20 6164 6420 6120 646f 6f72 W].To add a door\n-00013710: 2074 6f20 7468 6520 686f 7573 652c 2077 to the house, w\n-00013720: 6520 7573 6520 6120 706f 6c79 676f 6e20 e use a polygon \n-00013730: 736c 6967 6874 6c79 2069 6e20 6672 6f6e slightly in fron\n-00013740: 7420 6f66 2074 6865 0a66 6f72 656d 6f73 t of the.foremos\n-00013750: 7420 6661 6365 206f 6620 7468 6520 686f t face of the ho\n-00013760: 7573 652e 0a20 2025 2064 6f6f 720a 2020 use.. % door. \n-00013770: 6465 6620 6520 2e30 310a 2020 6465 6620 def e .01. def \n-00013780: 4431 2028 302c 2d31 2c31 2b65 2920 6465 D1 (0,-1,1+e) de\n-00013790: 6620 4432 2028 2e35 2c2d 312c 312b 6529 f D2 (.5,-1,1+e)\n-000137a0: 2064 6566 2044 3320 282e 352c 302c 312b def D3 (.5,0,1+\n-000137b0: 6529 2064 6566 2044 3420 2830 2c30 2c31 e) def D4 (0,0,1\n-000137c0: 2b65 290a 4e6f 7720 6c65 7427 7320 6372 +e).Now let's cr\n-000137d0: 6561 7465 2061 206e 6577 2073 6574 206f eate a new set o\n-000137e0: 6620 706f 696e 7473 2074 6861 7420 6172 f points that ar\n-000137f0: 6520 6120 746f 2d62 652d 6465 7465 726d e a to-be-determ\n-00013800: 696e 6564 0a74 7261 6e73 666f 726d 206f ined.transform o\n-00013810: 6620 7468 6520 6f72 6967 696e 616c 732e f the originals.\n-00013820: 0a20 2064 6566 2068 7020 7363 616c 6528 . def hp scale(\n-00013830: 3129 2025 2068 6f75 7365 2070 6f73 6974 1) % house posit\n-00013840: 696f 6e65 720a 2020 6465 6620 7052 3120 ioner. def pR1 \n-00013850: 5b5b 6870 5d5d 2a28 5231 2920 6465 6620 [[hp]]*(R1) def \n-00013860: 7052 3220 5b5b 6870 5d5d 2a28 5232 2920 pR2 [[hp]]*(R2) \n-00013870: 6465 6620 7052 3320 5b5b 6870 5d5d 2a28 def pR3 [[hp]]*(\n-00013880: 5233 290a 2020 6465 6620 7052 3420 5b5b R3). def pR4 [[\n-00013890: 6870 5d5d 2a28 5234 2920 6465 6620 7052 hp]]*(R4) def pR\n-000138a0: 3520 5b5b 6870 5d5d 2a28 5235 290a 2020 5 [[hp]]*(R5). \n-000138b0: 6465 6620 704c 3120 5b5b 6870 5d5d 2a28 def pL1 [[hp]]*(\n-000138c0: 4c31 2920 6465 6620 704c 3220 5b5b 6870 L1) def pL2 [[hp\n-000138d0: 5d5d 2a28 4c32 2920 6465 6620 704c 3320 ]]*(L2) def pL3 \n-000138e0: 5b5b 6870 5d5d 2a28 4c33 290a 2020 6465 [[hp]]*(L3). de\n-000138f0: 6620 704c 3420 5b5b 6870 5d5d 2a28 4c34 f pL4 [[hp]]*(L4\n-00013900: 2920 6465 6620 704c 3520 5b5b 6870 5d5d ) def pL5 [[hp]]\n-00013910: 2a28 4c35 290a 2020 6465 6620 7044 3120 *(L5). def pD1 \n-00013920: 5b5b 6870 5d5d 2a28 4431 2920 6465 6620 [[hp]]*(D1) def \n-00013930: 7044 3220 5b5b 6870 5d5d 2a28 4432 2920 pD2 [[hp]]*(D2) \n-00013940: 6465 6620 7044 3320 5b5b 6870 5d5d 2a28 def pD3 [[hp]]*(\n-00013950: 4433 290a 2020 6465 6620 7044 3420 5b5b D3). def pD4 [[\n-00013960: 6870 5d5d 2a28 4434 2920 0a4e 6f74 6520 hp]]*(D4) .Note \n-00013970: 7468 6520 7573 6520 6f66 2061 20e2 809c the use of a ...\n-00013980: 7472 616e 7366 6f72 6d20 6465 6669 6e69 transform defini\n-00013990: 7469 6f6e e280 9d20 616e 6420 e280 9c74 tion... and ...t\n-000139a0: 7261 6e73 666f 726d 2072 6566 6572 656e ransform referen\n-000139b0: 6365 73e2 809d 2e0a 4e6f 7720 6465 6669 ces.....Now defi\n-000139c0: 6e65 2074 6865 2073 6576 656e 2070 6f6c ne the seven pol\n-000139d0: 7967 6f6e 616c 2066 6163 6573 206f 6620 ygonal faces of \n-000139e0: 7468 6520 686f 7573 6520 616e 6420 7468 the house and th\n-000139f0: 6520 646f 6f72 2075 7369 6e67 2074 6865 e door using the\n-00013a00: 0a74 7261 6e73 666f 726d 6564 2070 6f69 .transformed poi\n-00013a10: 6e74 7320 6173 2076 6572 7469 6365 732e nts as vertices.\n-00013a20: 2020 4265 2063 6172 6566 756c 2077 6974 Be careful wit\n-00013a30: 6820 7665 7274 6578 206f 7264 6572 210a h vertex order!.\n-00013a40: 2020 6465 6620 7267 7420 706f 6c79 676f def rgt polygo\n-00013a50: 6e20 2870 5231 2928 7052 3229 2870 5233 n (pR1)(pR2)(pR3\n-00013a60: 2928 7052 3429 2870 5235 290a 2020 6465 )(pR4)(pR5). de\n-00013a70: 6620 6c66 7420 706f 6c79 676f 6e20 2870 f lft polygon (p\n-00013a80: 4c35 2928 704c 3429 2870 4c33 2928 704c L5)(pL4)(pL3)(pL\n-00013a90: 3229 2870 4c31 290a 2020 6465 6620 6672 2)(pL1). def fr\n-00013aa0: 7420 706f 6c79 676f 6e20 2870 5232 2928 t polygon (pR2)(\n-00013ab0: 7052 3129 2870 4c31 2928 704c 3229 0a20 pR1)(pL1)(pL2). \n-00013ac0: 2064 6566 2062 636b 2070 6f6c 7967 6f6e def bck polygon\n-00013ad0: 2028 7052 3429 2870 5233 2928 704c 3329 (pR4)(pR3)(pL3)\n-00013ae0: 2870 4c34 290a 2020 6465 6620 7466 7220 (pL4). def tfr \n-00013af0: 706f 6c79 676f 6e20 2870 5231 2928 7052 polygon (pR1)(pR\n-00013b00: 3529 2870 4c35 2928 704c 3129 0a20 2064 5)(pL5)(pL1). d\n-00013b10: 6566 2074 626b 2070 6f6c 7967 6f6e 2028 ef tbk polygon (\n-00013b20: 7052 3529 2870 5234 2928 704c 3429 2870 pR5)(pR4)(pL4)(p\n-00013b30: 4c35 290a 2020 6465 6620 626f 7420 706f L5). def bot po\n-00013b40: 6c79 676f 6e20 2870 5232 2928 704c 3229 lygon (pR2)(pL2)\n-00013b50: 2870 4c33 2928 7052 3329 0a20 2064 6566 (pL3)(pR3). def\n-00013b60: 2064 6f6f 7220 706f 6c79 676f 6e5b 6669 door polygon[fi\n-00013b70: 6c6c 636f 6c6f 723d 6272 6f77 6e5d 2028 llcolor=brown] (\n-00013b80: 7044 3129 2870 4432 2928 7044 3329 2870 pD1)(pD2)(pD3)(p\n-00013b90: 4434 290a 2020 6465 6620 686f 7573 6520 D4). def house \n-00013ba0: 7b20 7b72 6774 7d7b 6c66 747d 7b66 7274 { {rgt}{lft}{frt\n-00013bb0: 7d7b 6263 6b7d 7b74 6672 7d7b 7462 6b7d }{bck}{tfr}{tbk}\n-00013bc0: 7b62 6f74 7d7b 646f 6f72 7d20 7d0a 2020 {bot}{door} }. \n-00013bd0: 2054 696d 6520 666f 7220 6120 7361 6e69 Time for a sani\n-00013be0: 7479 2063 6865 636b 2e20 2041 6464 2074 ty check. Add t\n-00013bf0: 6865 206c 696e 650a 2020 7b68 6f75 7365 he line. {house\n-00013c00: 7d0a 616e 6420 7468 6973 2069 7320 7768 }.and this is wh\n-00013c10: 6174 2077 6520 6765 742e 0a0a 0008 5b69 at we get.....[i\n-00013c20: 6d61 6765 2073 7263 3d22 6578 3133 302e mage src=\"ex130.\n-00013c30: 706e 6722 2074 6578 743d 2249 6d61 6765 png\" text=\"Image\n-00013c40: 2065 7831 3330 206f 6d69 7474 6564 2069 ex130 omitted i\n-00013c50: 6e20 7465 7874 2076 6572 7369 6f6e 206f n text version o\n-00013c60: 6620 7468 6973 2064 6f63 756d 656e 742e f this document.\n-00013c70: 2200 085d 0a0a 5468 6973 2069 7320 636f \"..]..This is co\n-00013c80: 7272 6563 742c 2062 7574 2064 6f65 7320 rrect, but does \n-00013c90: 6e6f 7420 7265 7665 616c 2076 6572 7920 not reveal very \n-00013ca0: 6d75 6368 2e20 2043 6f6d 6d6f 6e20 6572 much. Common er\n-00013cb0: 726f 7273 2061 7265 0a6d 6973 706c 6163 rors are.misplac\n-00013cc0: 6564 2076 6572 7469 6365 7320 616e 6420 ed vertices and \n-00013cd0: 706f 6c79 676f 6e73 206d 6973 7369 6e67 polygons missing\n-00013ce0: 2065 6e74 6972 656c 7920 6475 6520 746f entirely due to\n-00013cf0: 2069 6e63 6f72 7265 6374 2076 6572 7465 incorrect verte\n-00013d00: 780a 6f72 6465 722e 2020 546f 2072 756c x.order. To rul\n-00013d10: 6520 7468 6573 6520 6f75 742c 206c 6574 e these out, let\n-00013d20: 2773 2069 6e73 7065 6374 2061 6c6c 2073 's inspect all s\n-00013d30: 6964 6573 206f 6620 7468 6520 686f 7573 ides of the hous\n-00013d40: 652e 2020 5468 6973 0a69 7320 6e6f 7420 e. This.is not \n-00013d50: 6861 7264 2e20 204d 6572 656c 7920 7265 hard. Merely re\n-00013d60: 706c 6163 6520 7468 6520 7265 6665 7265 place the refere\n-00013d70: 6e63 6520 7b68 6f75 7365 7d20 7769 7468 nce {house} with\n-00013d80: 2061 20e2 8098 7265 7065 6174 e280 992e a ...repeat....\n-00013d90: 0a2a 4e6f 7465 2052 6570 6561 7473 3a3a .*Note Repeats::\n-00013da0: 2e0a 2020 7265 7065 6174 207b 2031 332c .. repeat { 13,\n-00013db0: 2072 6f74 6174 6528 3330 2c20 5b31 2c32 rotate(30, [1,2\n-00013dc0: 2c33 5d29 2c20 7472 616e 736c 6174 6528 ,3]), translate(\n-00013dd0: 5b33 2c30 2c30 5d29 207d 207b 686f 7573 [3,0,0]) } {hous\n-00013de0: 657d 0a00 085b 696d 6167 6520 7372 633d e}...[image src=\n-00013df0: 2265 7831 3430 2e70 6e67 2220 7465 7874 \"ex140.png\" text\n-00013e00: 3d22 496d 6167 6520 6578 3134 3020 6f6d =\"Image ex140 om\n-00013e10: 6974 7465 6420 696e 2074 6578 7420 7665 itted in text ve\n-00013e20: 7273 696f 6e20 6f66 2074 6869 7320 646f rsion of this do\n-00013e30: 6375 6d65 6e74 2e22 0008 5d0a 0a41 6761 cument.\"..]..Aga\n-00013e40: 696e 2074 6869 6e67 7320 6c6f 6f6b 2063 in things look c\n-00013e50: 6f72 7265 6374 2e20 204e 6f74 6520 7468 orrect. Note th\n-00013e60: 6174 2074 6865 2068 6964 6465 6e20 7375 at the hidden su\n-00013e70: 7266 6163 6520 616c 676f 7269 7468 6d0a rface algorithm.\n-00013e80: 6861 6e64 6c65 7320 696e 7465 7273 6563 handles intersec\n-00013e90: 7469 6e67 2070 6f6c 7967 6f6e 7320 636f ting polygons co\n-00013ea0: 7272 6563 746c 7920 7768 6572 6520 736f rrectly where so\n-00013eb0: 6d65 2063 6f70 6965 7320 6f66 2074 6865 me copies of the\n-00013ec0: 2068 6f75 7365 0a6f 7665 726c 6170 2e0a house.overlap..\n-00013ed0: 0a20 2020 4c65 7427 7320 6c61 7920 6f75 . Let's lay ou\n-00013ee0: 7420 7468 6520 6765 6f6d 6574 7279 206f t the geometry o\n-00013ef0: 6620 7065 7273 7065 6374 6976 6520 7072 f perspective pr\n-00013f00: 6f6a 6563 7469 6f6e 206f 6620 7468 6520 ojection of the \n-00013f10: 686f 7573 650a 6f6e 746f 2061 2070 6c61 house.onto a pla\n-00013f20: 6e65 2077 6974 6820 7261 7973 2070 6173 ne with rays pas\n-00013f30: 7369 6e67 2074 6872 6f75 6768 2074 6865 sing through the\n-00013f40: 206f 7269 6769 6e2e 2020 4265 6769 6e20 origin. Begin \n-00013f50: 6279 2070 6f73 6974 696f 6e69 6e67 0a74 by positioning.t\n-00013f60: 6865 2068 6f75 7365 2074 7765 6c76 6520 he house twelve \n-00013f70: 756e 6974 7320 6261 636b 206f 6e20 7468 units back on th\n-00013f80: 6520 6e65 6761 7469 7665 207a 2d61 7869 e negative z-axi\n-00013f90: 7320 616e 6420 6164 6469 6e67 2061 2073 s and adding a s\n-00013fa0: 6574 206f 660a 636f 6f72 6469 6e61 7465 et of.coordinate\n-00013fb0: 2061 7865 732e 2020 546f 206d 6f76 6520 axes. To move \n-00013fc0: 7468 6520 686f 7573 6520 7765 206e 6565 the house we nee\n-00013fd0: 6420 6f6e 6c79 2063 6861 6e67 6520 7468 d only change th\n-00013fe0: 6520 2268 6f75 7365 0a70 6f73 6974 696f e \"house.positio\n-00013ff0: 6e69 6e67 2220 7472 616e 7366 6f72 6d20 ning\" transform \n-00014000: 6465 6669 6e65 6420 6561 726c 6965 722e defined earlier.\n-00014010: 0a20 2064 6566 2068 7020 726f 7461 7465 . def hp rotate\n-00014020: 282d 3430 2c20 5b30 2c31 2c30 5d29 2074 (-40, [0,1,0]) t\n-00014030: 6865 6e20 7472 616e 736c 6174 6528 5b30 hen translate([0\n-00014040: 2c30 2c2d 3132 5d29 0a20 2064 6566 2061 ,0,-12]). def a\n-00014050: 7865 7320 7b0a 2020 2020 6465 6620 737a xes {. def sz\n-00014060: 2031 0a20 2020 206c 696e 6520 5b61 7272 1. line [arr\n-00014070: 6f77 733d 3c2d 3e5d 2028 737a 2c30 2c30 ows=<->] (sz,0,0\n-00014080: 2928 4f29 2830 2c73 7a2c 3029 0a20 2020 )(O)(0,sz,0). \n-00014090: 206c 696e 6520 5b61 7272 6f77 733d 2d3e line [arrows=->\n-000140a0: 5d20 2028 4f29 2830 2c30 2c73 7a29 0a20 ] (O)(0,0,sz). \n-000140b0: 2020 206c 696e 6520 5b6c 696e 6577 6964 line [linewid\n-000140c0: 7468 3d2e 3270 742c 6c69 6e65 636f 6c6f th=.2pt,linecolo\n-000140d0: 723d 626c 7565 2c6c 696e 6573 7479 6c65 r=blue,linestyle\n-000140e0: 3d64 6173 6865 645d 2028 4f29 2830 2c30 =dashed] (O)(0,0\n-000140f0: 2c2d 3130 290a 2020 2020 7370 6563 6961 ,-10). specia\n-00014100: 6c20 7c5c 7570 7574 5b72 5d23 317b 2478 l |\\uput[r]#1{$x\n-00014110: 247d 5c75 7075 745b 755d 2332 7b24 7924 $}\\uput[u]#2{$y$\n-00014120: 7d5c 7570 7574 5b6c 5d23 337b 247a 247d }\\uput[l]#3{$z$}\n-00014130: 7c0a 2020 2020 2020 2873 7a2c 302c 3029 |. (sz,0,0)\n-00014140: 2830 2c73 7a2c 3029 2830 2c30 2c73 7a29 (0,sz,0)(0,0,sz)\n-00014150: 0a20 207d 0a0a 2020 2054 696d 6520 666f . }.. Time fo\n-00014160: 7220 616e 6f74 6865 7220 7465 7374 2e20 r another test. \n-00014170: 204c 6574 2773 2062 7569 6c64 2061 2072 Let's build a r\n-00014180: 6561 6c20 7669 6577 2074 7261 6e73 666f eal view transfo\n-00014190: 726d 2c20 6372 6561 7469 6e67 2061 0ae2 rm, creating a..\n-000141a0: 809c 7669 7274 7561 6c20 6361 6d65 7261 ..virtual camera\n-000141b0: e280 9d20 746f 206c 6f6f 6b20 6174 2074 ... to look at t\n-000141c0: 6865 2073 6365 6e65 2077 6520 6172 6520 he scene we are \n-000141d0: 636f 6e73 7472 7563 7469 6e67 2e20 2052 constructing. R\n-000141e0: 6570 6c61 6365 2074 6865 0ae2 8098 7265 eplace the....re\n-000141f0: 7065 6174 e280 9920 7769 7468 0a20 2064 peat... with. d\n-00014200: 6566 2065 7965 2028 3130 2c34 2c31 3029 ef eye (10,4,10)\n-00014210: 0a20 2064 6566 206c 6f6f 6b5f 6174 2028 . def look_at (\n-00014220: 302c 302c 2d35 290a 2020 7075 7420 7b20 0,0,-5). put { \n-00014230: 7669 6577 2828 6579 6529 2c20 286c 6f6f view((eye), (loo\n-00014240: 6b5f 6174 2929 207d 207b 207b 686f 7573 k_at)) } { {hous\n-00014250: 657d 7b61 7865 737d 207d 0a20 2020 5468 e}{axes} }. Th\n-00014260: 6520 e280 9c76 6965 7720 7472 616e 7366 e ...view transf\n-00014270: 6f72 6de2 809d 2072 6570 6f73 6974 696f orm... repositio\n-00014280: 6e73 2074 6865 2073 6365 6e65 2073 6f20 ns the scene so \n-00014290: 7468 6174 2074 6865 2070 6f69 6e74 20e2 that the point .\n-000142a0: 8098 6579 65e2 8099 2069 730a 6174 2074 ..eye... is.at t\n-000142b0: 6865 206f 7269 6769 6e20 616e 6420 7468 he origin and th\n-000142c0: 6520 6469 7265 6374 696f 6e20 6672 6f6d e direction from\n-000142d0: 20e2 8098 6579 65e2 8099 2074 6f20 e280 ...eye... to ..\n-000142e0: 986c 6f6f 6b5f 6174 e280 9920 6973 2074 .look_at... is t\n-000142f0: 6865 206e 6567 6174 6976 650a 7a2d 6178 he negative.z-ax\n-00014300: 6973 2e20 2054 6869 7320 7265 7175 6972 is. This requir\n-00014310: 6573 2061 2072 6f74 6174 696f 6e20 616e es a rotation an\n-00014320: 6420 6120 7472 616e 736c 6174 696f 6e20 d a translation \n-00014330: 7468 6174 2061 7265 2061 6c6c 2070 6163 that are all pac\n-00014340: 6b65 640a 696e 746f 2074 6865 2063 6f6e ked.into the con\n-00014350: 7374 7275 6374 6f72 20e2 8098 7669 6577 structor ...view\n-00014360: e280 992e 0a0a 0008 5b69 6d61 6765 2073 ........[image s\n-00014370: 7263 3d22 6578 3135 302e 706e 6722 2074 rc=\"ex150.png\" t\n-00014380: 6578 743d 2249 6d61 6765 2065 7831 3530 ext=\"Image ex150\n-00014390: 206f 6d69 7474 6564 2069 6e20 7465 7874 omitted in text\n-000143a0: 2076 6572 7369 6f6e 206f 6620 7468 6973 version of this\n-000143b0: 2064 6f63 756d 656e 742e 2200 085d 0a0a document.\"..]..\n-000143c0: 5468 6973 2069 7320 7374 6172 7469 6e67 This is starting\n-000143d0: 2074 6f20 6c6f 6f6b 2067 6f6f 6421 2020 to look good! \n-000143e0: 4164 6420 7468 6520 7072 6f6a 6563 7469 Add the projecti\n-000143f0: 6f6e 2070 6c61 6e65 2068 616c 6620 7761 on plane half wa\n-00014400: 790a 6265 7477 6565 6e20 7468 6520 6f72 y.between the or\n-00014410: 6967 696e 2061 6e64 2074 6865 2068 6f75 igin and the hou\n-00014420: 7365 2061 7420 7a3d 2d35 2e20 2057 6527 se at z=-5. We'\n-00014430: 6c6c 2074 7279 2074 6865 2061 6e67 6c65 ll try the angle\n-00014440: 2061 7267 756d 656e 740a 6665 6174 7572 argument.featur\n-00014450: 6520 6f66 20e2 8098 7370 6563 6961 6ce2 e of ...special.\n-00014460: 8099 2074 6f20 706f 7369 7469 6f6e 2061 .. to position a\n-00014470: 206c 6162 656c 2e0a 2020 6465 6620 7020 label.. def p \n-00014480: 3520 2520 7072 6f6a 6563 7469 6f6e 2064 5 % projection d\n-00014490: 6973 7461 6e63 6520 2870 6c61 6e65 2061 istance (plane a\n-000144a0: 7420 7a3d 2d70 290a 2020 6465 6620 7072 t z=-p). def pr\n-000144b0: 6f6a 6563 7469 6f6e 5f70 6c61 6e65 207b ojection_plane {\n-000144c0: 0a20 2020 2064 6566 2073 7a20 312e 350a . def sz 1.5.\n-000144d0: 2020 2020 706f 6c79 676f 6e20 282d 737a polygon (-sz\n-000144e0: 2c2d 737a 2c2d 7029 2873 7a2c 2d73 7a2c ,-sz,-p)(sz,-sz,\n-000144f0: 2d70 2928 737a 2c73 7a2c 2d70 2928 2d73 -p)(sz,sz,-p)(-s\n-00014500: 7a2c 737a 2c2d 7029 0a20 2020 2073 7065 z,sz,-p). spe\n-00014510: 6369 616c 207c 5c72 7075 745b 625d 2331 cial |\\rput[b]#1\n-00014520: 2d32 2333 7b5c 666f 6f74 6e6f 7465 7369 -2#3{\\footnotesi\n-00014530: 7a65 5c73 6620 7072 6f6a 6563 7469 6f6e ze\\sf projection\n-00014540: 2070 6c61 6e65 7d7c 200a 2020 2020 2020 plane}| . \n-00014550: 282d 737a 2c2d 737a 2c2d 7029 2873 7a2c (-sz,-sz,-p)(sz,\n-00014560: 2d73 7a2c 2d70 2928 302c 2d73 7a2b 2e31 -sz,-p)(0,-sz+.1\n-00014570: 2c2d 7029 0a20 207d 0a41 6464 207b 7072 ,-p). }.Add {pr\n-00014580: 6f6a 6563 7469 6f6e 5f70 6c61 6e65 7d20 ojection_plane} \n-00014590: 746f 2074 6865 206c 6973 7420 6f66 206f to the list of o\n-000145a0: 626a 6563 7473 2069 6e20 7468 6520 e280 bjects in the ..\n-000145b0: 9870 7574 e280 9920 6162 6f76 652e 0a0a .put... above...\n-000145c0: 0008 5b69 6d61 6765 2073 7263 3d22 6578 ..[image src=\"ex\n-000145d0: 3136 302e 706e 6722 2074 6578 743d 2249 160.png\" text=\"I\n-000145e0: 6d61 6765 2065 7831 3630 206f 6d69 7474 mage ex160 omitt\n-000145f0: 6564 2069 6e20 7465 7874 2076 6572 7369 ed in text versi\n-00014600: 6f6e 206f 6620 7468 6973 2064 6f63 756d on of this docum\n-00014610: 656e 742e 2200 085d 0a0a 2020 2054 6865 ent.\"..].. The\n-00014620: 2077 6179 2077 6520 636f 6e73 7472 7563 way we construc\n-00014630: 7465 6420 7468 6520 706f 696e 7473 206f ted the points o\n-00014640: 6620 7468 6520 686f 7573 6520 6e6f 7720 f the house now \n-00014650: 6d61 6b65 7320 6974 2065 6173 7920 746f makes it easy to\n-00014660: 0a64 7261 7720 7261 7973 206f 6620 7072 .draw rays of pr\n-00014670: 6f6a 6563 7469 6f6e 2e20 2057 6527 6c6c ojection. We'll\n-00014680: 2063 6173 7420 6f6e 6520 7261 7920 6672 cast one ray fr\n-00014690: 6f6d 2065 7665 7279 2076 6973 6962 6c65 om every visible\n-000146a0: 2076 6572 7465 780a 6f66 2074 6865 2068 vertex.of the h\n-000146b0: 6f75 7365 2061 6e64 2064 6566 696e 6520 ouse and define \n-000146c0: 6f70 7469 6f6e 7320 736f 2074 6865 2061 options so the a\n-000146d0: 7070 6561 7261 6e63 6520 6f66 2061 6c6c ppearance of all\n-000146e0: 2072 6179 7320 6361 6e20 6265 0a63 6861 rays can be.cha\n-000146f0: 6e67 6564 2061 7420 7468 6520 7361 6d65 nged at the same\n-00014700: 2074 696d 652e 0a20 2064 6566 2070 726f time.. def pro\n-00014710: 6a65 6374 696f 6e5f 7261 7973 207b 0a20 jection_rays {. \n-00014720: 2020 2064 6566 2072 6179 6f70 7420 5b6c def rayopt [l\n-00014730: 696e 6577 6964 7468 3d2e 3370 742c 6c69 inewidth=.3pt,li\n-00014740: 6e65 636f 6c6f 723d 6c69 6768 7467 7261 necolor=lightgra\n-00014750: 795d 0a20 2020 206c 696e 6520 5b72 6179 y]. line [ray\n-00014760: 6f70 745d 284f 2928 7052 3129 206c 696e opt](O)(pR1) lin\n-00014770: 6520 5b72 6179 6f70 745d 284f 2928 7052 e [rayopt](O)(pR\n-00014780: 3229 206c 696e 655b 7261 796f 7074 5d28 2) line[rayopt](\n-00014790: 4f29 2870 5233 290a 2020 2020 6c69 6e65 O)(pR3). line\n-000147a0: 205b 7261 796f 7074 5d28 4f29 2870 5234 [rayopt](O)(pR4\n-000147b0: 2920 6c69 6e65 205b 7261 796f 7074 5d28 ) line [rayopt](\n-000147c0: 4f29 2870 5235 290a 2020 2020 6c69 6e65 O)(pR5). line\n-000147d0: 205b 7261 796f 7074 5d28 4f29 2870 4c31 [rayopt](O)(pL1\n-000147e0: 2920 6c69 6e65 205b 7261 796f 7074 5d28 ) line [rayopt](\n-000147f0: 4f29 2870 4c32 2920 6c69 6e65 5b72 6179 O)(pL2) line[ray\n-00014800: 6f70 745d 284f 2928 704c 3529 0a20 2020 opt](O)(pL5). \n-00014810: 206c 696e 6520 5b72 6179 6f70 745d 284f line [rayopt](O\n-00014820: 2928 7044 3129 206c 696e 6520 5b72 6179 )(pD1) line [ray\n-00014830: 6f70 745d 284f 2928 7044 3229 200a 2020 opt](O)(pD2) . \n-00014840: 2020 6c69 6e65 205b 7261 796f 7074 5d28 line [rayopt](\n-00014850: 4f29 2870 4433 2920 6c69 6e65 205b 7261 O)(pD3) line [ra\n-00014860: 796f 7074 5d28 4f29 2870 4434 2920 0a20 yopt](O)(pD4) . \n-00014870: 207d 0a54 6865 2072 6573 756c 7420 6973 }.The result is\n-00014880: 2073 686f 776e 2068 6572 652e 0a0a 0008 shown here.....\n-00014890: 5b69 6d61 6765 2073 7263 3d22 6578 3137 [image src=\"ex17\n-000148a0: 302e 706e 6722 2074 6578 743d 2249 6d61 0.png\" text=\"Ima\n-000148b0: 6765 2065 7831 3730 206f 6d69 7474 6564 ge ex170 omitted\n-000148c0: 2069 6e20 7465 7874 2076 6572 7369 6f6e in text version\n-000148d0: 206f 6620 7468 6973 2064 6f63 756d 656e of this documen\n-000148e0: 742e 2200 085d 0a0a 5468 6520 7261 7973 t.\"..]..The rays\n-000148f0: 2070 6965 7263 6520 7468 6520 7072 6f6a pierce the proj\n-00014900: 6563 7469 6f6e 2070 6c61 6e65 2061 7420 ection plane at \n-00014910: 7468 6520 636f 7272 6573 706f 6e64 696e the correspondin\n-00014920: 6720 706f 696e 7473 206f 6e20 7468 650a g points on the.\n-00014930: 7065 7273 7065 6374 6976 6520 696d 6167 perspective imag\n-00014940: 6520 7765 2061 7265 2074 7279 696e 6720 e we are trying \n-00014950: 746f 2064 7261 772e 2020 416c 6272 6563 to draw. Albrec\n-00014960: 6874 2044 c3bc 7265 7220 616e 6420 6869 ht D..rer and hi\n-00014970: 730a 5265 6e61 6973 7361 6e63 6520 636f s.Renaissance co\n-00014980: 6e74 656d 706f 7261 7269 6573 2068 6164 ntemporaries had\n-00014990: 2074 6865 2073 616d 6520 6964 6561 2069 the same idea i\n-000149a0: 6e20 7468 6520 6561 726c 7920 3135 3030 n the early 1500\n-000149b0: 2773 2e0a 0a00 085b 696d 6167 6520 7372 's.....[image sr\n-000149c0: 633d 2264 7565 7265 722e 706e 6722 2074 c=\"duerer.png\" t\n-000149d0: 6578 743d 2249 6d61 6765 206f 6620 4475 ext=\"Image of Du\n-000149e0: 6572 6572 2773 2070 6572 7370 6563 7469 erer's perspecti\n-000149f0: 7665 2063 6f6d 7075 7465 7220 6f6d 6974 ve computer omit\n-00014a00: 7465 6420 696e 2074 6578 7420 7665 7273 ted in text vers\n-00014a10: 696f 6e20 6f66 2074 6869 7320 646f 6375 ion of this docu\n-00014a20: 6d65 6e74 2e22 0008 5d0a 0a20 2020 416c ment.\"..].. Al\n-00014a30: 6c20 7468 6174 2773 206c 6566 7420 6973 l that's left is\n-00014a40: 2074 6f20 6669 6e64 2061 2077 6179 2074 to find a way t\n-00014a50: 6f20 636f 6e6e 6563 7420 7468 6520 706f o connect the po\n-00014a60: 696e 7473 206f 6620 7468 6520 686f 7573 ints of the hous\n-00014a70: 650a 6f6e 2074 6865 2070 726f 6a65 6374 e.on the project\n-00014a80: 696f 6e20 706c 616e 652e 2020 5765 2063 ion plane. We c\n-00014a90: 6f75 6c64 2070 756c 6c20 6f75 7420 6120 ould pull out a \n-00014aa0: 676f 6f64 2063 6f6d 7075 7465 7220 6772 good computer gr\n-00014ab0: 6170 6869 6373 0a74 6578 742c 2066 696e aphics.text, fin\n-00014ac0: 6420 7468 6520 6e65 6365 7373 6172 7920 d the necessary \n-00014ad0: 6d61 7472 6978 2c20 616e 6420 656e 7465 matrix, and ente\n-00014ae0: 7220 6974 206f 7572 7365 6c76 6573 2061 r it ourselves a\n-00014af0: 7320 6120 7472 616e 7366 6f72 6d0a 6c69 s a transform.li\n-00014b00: 7465 7261 6c2e 2020 2a4e 6f74 6520 5472 teral. *Note Tr\n-00014b10: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-00014b20: 3a3a 2e20 2054 6861 7420 776f 726b 2069 ::. That work i\n-00014b30: 7320 616c 7265 6164 7920 646f 6e65 2c0a s already done,.\n-00014b40: 686f 7765 7665 722e 2020 5765 2063 616e however. We can\n-00014b50: 2075 7365 2074 6865 20e2 8098 7072 6f6a use the ...proj\n-00014b60: 6563 7428 7029 e280 9920 636f 6e73 7472 ect(p)... constr\n-00014b70: 7563 746f 722e 0a0a 2020 2054 6865 7265 uctor... There\n-00014b80: 2061 7265 2073 7469 6c6c 2073 6f6d 6520 are still some \n-00014b90: 6465 7461 696c 7320 7468 6174 2072 6571 details that req\n-00014ba0: 7569 7265 2063 6172 652e 2020 5072 6f6a uire care. Proj\n-00014bb0: 6563 7469 6f6e 2077 696c 6c0a 666c 6174 ection will.flat\n-00014bc0: 7465 6e20 7768 6174 6576 6572 2069 7320 ten whatever is \n-00014bd0: 7472 616e 7366 6f72 6d65 6420 6f6e 746f transformed onto\n-00014be0: 2074 6865 2070 6c61 6e65 207a 3d2d 702e the plane z=-p.\n-00014bf0: 2020 5468 6572 6566 6f72 6520 616e 7920 Therefore any \n-00014c00: 7061 7274 0a6f 6620 7468 6520 686f 7573 part.of the hous\n-00014c10: 6520 636f 756c 6420 6469 7361 7070 6561 e could disappea\n-00014c20: 7220 6265 6869 6e64 2074 6865 2070 726f r behind the pro\n-00014c30: 6a65 6374 696f 6e20 706c 616e 6520 2874 jection plane (t\n-00014c40: 6865 2068 6964 6465 6e0a 7375 7266 6163 he hidden.surfac\n-00014c50: 6520 616c 676f 7269 7468 6d20 6f72 6465 e algorithm orde\n-00014c60: 7273 206f 626a 6563 7473 2061 7420 7468 rs objects at th\n-00014c70: 6520 7361 6d65 2064 6570 7468 2061 7262 e same depth arb\n-00014c80: 6974 7261 7269 6c79 292e 2020 5468 650a itrarily). The.\n-00014c90: 646f 6f72 206d 6179 2061 6c73 6f20 6469 door may also di\n-00014ca0: 7361 7070 6561 7220 6265 6869 6e64 2074 sappear behind t\n-00014cb0: 6865 2066 726f 6e74 206f 6620 7468 6520 he front of the \n-00014cc0: 686f 7573 652e 2020 546f 206d 616b 6520 house. To make \n-00014cd0: 7375 7265 0a65 7665 7279 7468 696e 6720 sure.everything \n-00014ce0: 7265 6d61 696e 7320 7669 7369 626c 652c remains visible,\n-00014cf0: 2077 6527 6c6c 2070 6c61 6365 2074 6865 we'll place the\n-00014d00: 2068 6f75 7365 2061 2074 696e 7920 6269 house a tiny bi\n-00014d10: 7420 696e 2066 726f 6e74 206f 660a 7468 t in front of.th\n-00014d20: 6520 7072 6f6a 6563 7469 6f6e 2070 6c61 e projection pla\n-00014d30: 6e65 2061 6e64 2061 2073 6563 6f6e 6420 ne and a second \n-00014d40: 636f 7079 206f 6620 7468 6520 646f 6f72 copy of the door\n-00014d50: 2069 6e20 6672 6f6e 7420 6f66 2074 6865 in front of the\n-00014d60: 0a68 6f75 7365 2e0a 2020 6465 6620 7072 .house.. def pr\n-00014d70: 6f6a 6563 7469 6f6e 207b 0a20 2020 2025 ojection {. %\n-00014d80: 2065 2069 7320 6120 736d 616c 6c20 6e75 e is a small nu\n-00014d90: 6d62 6572 2064 6566 696e 6564 2061 626f mber defined abo\n-00014da0: 7665 0a20 2020 2070 7574 207b 2070 726f ve. put { pro\n-00014db0: 6a65 6374 2870 2920 7468 656e 2074 7261 ject(p) then tra\n-00014dc0: 6e73 6c61 7465 285b 302c 302c 312a 655d nslate([0,0,1*e]\n-00014dd0: 2920 7d20 7b68 6f75 7365 7d0a 2020 2020 ) } {house}. \n-00014de0: 7075 7420 7b20 7072 6f6a 6563 7428 7029 put { project(p)\n-00014df0: 2074 6865 6e20 7472 616e 736c 6174 6528 then translate(\n-00014e00: 5b30 2c30 2c32 2a65 5d29 207d 207b 646f [0,0,2*e]) } {do\n-00014e10: 6f72 7d0a 2020 7d0a 0a00 085b 696d 6167 or}. }....[imag\n-00014e20: 6520 7372 633d 2265 7831 3830 2e70 6e67 e src=\"ex180.png\n-00014e30: 2220 7465 7874 3d22 496d 6167 6520 6578 \" text=\"Image ex\n-00014e40: 3138 3020 6f6d 6974 7465 6420 696e 2074 180 omitted in t\n-00014e50: 6578 7420 7665 7273 696f 6e20 6f66 2074 ext version of t\n-00014e60: 6869 7320 646f 6375 6d65 6e74 2e22 0008 his document.\"..\n-00014e70: 5d0a 0a20 2020 4966 2079 6f75 2068 6176 ].. If you hav\n-00014e80: 6520 7374 7564 6965 6420 616e 6420 756e e studied and un\n-00014e90: 6465 7273 7461 6e64 2061 6c6c 2074 6869 derstand all thi\n-00014ea0: 732c 2079 6f75 2061 7265 2077 656c 6c20 s, you are well \n-00014eb0: 6f6e 2074 6865 2077 6179 0a74 6f20 7375 on the way.to su\n-00014ec0: 6363 6573 7320 7769 7468 20e2 8098 736b ccess with ...sk\n-00014ed0: 6574 6368 e280 992e 2020 4e6f 7420 7368 etch.... Not sh\n-00014ee0: 6f77 6e20 6172 6520 7468 6520 3230 206f own are the 20 o\n-00014ef0: 7220 736f 2069 7465 7261 7469 6f6e 7320 r so iterations \n-00014f00: 7468 6174 0a77 6572 6520 7265 7175 6972 that.were requir\n-00014f10: 6564 2074 6f20 6669 6e64 2061 2072 6561 ed to find a rea\n-00014f20: 736f 6e61 626c 6520 7669 6577 696e 6720 sonable viewing \n-00014f30: 616e 676c 6520 616e 6420 686f 7573 6520 angle and house \n-00014f40: 706f 7369 7469 6f6e 2c0a 6574 632e 2020 position,.etc. \n-00014f50: 4e6f 6e65 7468 656c 6573 732c 2074 6869 Nonetheless, thi\n-00014f60: 7320 6472 6177 696e 6720 7761 7320 636f s drawing was co\n-00014f70: 6d70 6c65 7465 6420 696e 2061 626f 7574 mpleted in about\n-00014f80: 2061 6e20 686f 7572 2e20 2057 6869 6c65 an hour. While\n-00014f90: 2061 0a47 5549 2074 6f6f 6c20 6d61 7920 a.GUI tool may \n-00014fa0: 6861 7665 2062 6565 6e20 6120 6c69 7474 have been a litt\n-00014fb0: 6c65 2066 6173 7465 722c 2069 7420 6973 le faster, it is\n-00014fc0: 2075 6e6c 696b 656c 7920 7468 6174 2061 unlikely that a\n-00014fd0: 206e 6577 0a64 7261 7769 6e67 2c20 6974 new.drawing, it\n-00014fe0: 7365 6c66 2061 2070 6572 7370 6563 7469 self a perspecti\n-00014ff0: 7665 2070 726f 6a65 6374 696f 6e20 6f66 ve projection of\n-00015000: 2074 6865 2073 6365 6e65 2c20 636f 756c the scene, coul\n-00015010: 6420 6265 0a67 656e 6572 6174 6564 2077 d be.generated w\n-00015020: 6974 6820 7477 6f20 6d6f 7265 206d 696e ith two more min\n-00015030: 7574 6573 2720 776f 726b 2120 204a 7573 utes' work! Jus\n-00015040: 7420 6368 616e 6765 2074 6865 2076 6965 t change the vie\n-00015050: 7720 7472 616e 7366 6f72 6d0a 746f 0a20 w transform.to. \n-00015060: 2070 7574 207b 2076 6965 7728 2865 7965 put { view((eye\n-00015070: 292c 2028 6c6f 6f6b 5f61 7429 2920 7468 ), (look_at)) th\n-00015080: 656e 2070 6572 7370 6563 7469 7665 2839 en perspective(9\n-00015090: 2920 7d20 7b20 2e2e 2e0a 616e 6420 7072 ) } { ....and pr\n-000150a0: 6f64 7563 6520 7468 6973 2e0a 0a00 085b oduce this.....[\n-000150b0: 696d 6167 6520 7372 633d 2265 7831 3930 image src=\"ex190\n-000150c0: 2e70 6e67 2220 7465 7874 3d22 496d 6167 .png\" text=\"Imag\n-000150d0: 6520 6578 3139 3020 6f6d 6974 7465 6420 e ex190 omitted \n-000150e0: 696e 2074 6578 7420 7665 7273 696f 6e20 in text version \n-000150f0: 6f66 2074 6869 7320 646f 6375 6d65 6e74 of this document\n-00015100: 2e22 0008 5d0a 0a1f 0a46 696c 653a 2073 .\"..]....File: s\n-00015110: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n-00015120: 653a 2041 2074 6563 686e 6963 616c 2064 e: A technical d\n-00015130: 7261 7769 6e67 2c20 204e 6578 743a 2041 rawing, Next: A\n-00015140: 2068 6965 7261 7263 6869 6361 6c20 6d6f hierarchical mo\n-00015150: 6465 6c2c 2020 5072 6576 3a20 4f76 6572 del, Prev: Over\n-00015160: 7669 6577 2c20 2055 703a 2042 7569 6c64 view, Up: Build\n-00015170: 696e 6720 6120 6472 6177 696e 670a 0a34 ing a drawing..4\n-00015180: 2e32 2041 2074 6563 686e 6963 616c 2064 .2 A technical d\n-00015190: 7261 7769 6e67 0a3d 3d3d 3d3d 3d3d 3d3d rawing.=========\n-000151a0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a ==============..\n-000151b0: 4c65 7427 7320 6c6f 6f6b 2061 7420 6120 Let's look at a \n-000151c0: 6472 6177 696e 6720 7468 6174 2072 6570 drawing that rep\n-000151d0: 7265 7365 6e74 7320 7468 6520 6b69 6e64 resents the kind\n-000151e0: 206f 6620 7072 6f62 6c65 6d20 e280 9873 of problem ...s\n-000151f0: 6b65 7463 68e2 8099 2077 6173 0a6d 6561 ketch... was.mea\n-00015200: 6e74 2074 6f20 736f 6c76 652d 2d61 2070 nt to solve--a p\n-00015210: 6169 7220 6f66 2074 6578 7462 6f6f 6b20 air of textbook \n-00015220: 6669 6775 7265 7320 7265 6761 7264 696e figures regardin\n-00015230: 6720 6120 706f 6c79 676f 6e61 6c0a 6170 g a polygonal.ap\n-00015240: 7072 6f78 696d 6174 696f 6e20 6f66 2061 proximation of a\n-00015250: 2074 7275 6e63 6174 6564 2063 6f6e 652e truncated cone.\n-00015260: 2020 4865 7265 2061 7265 2074 6865 2070 Here are the p\n-00015270: 6963 7475 7265 7320 7765 2077 696c 6c0a ictures we will.\n-00015280: 7072 6f64 7563 652e 0a0a 0008 5b69 6d61 produce.....[ima\n-00015290: 6765 2073 7263 3d22 6578 3235 302e 706e ge src=\"ex250.pn\n-000152a0: 6722 2074 6578 743d 2249 6d61 6765 2065 g\" text=\"Image e\n-000152b0: 7832 3530 206f 6d69 7474 6564 2069 6e20 x250 omitted in \n-000152c0: 7465 7874 2076 6572 7369 6f6e 206f 6620 text version of \n-000152d0: 7468 6973 2064 6f63 756d 656e 742e 2200 this document.\".\n-000152e0: 085d 2020 2020 2000 085b 696d 6167 6520 .] ..[image \n-000152f0: 7372 633d 2265 7832 3630 2e70 6e67 2220 src=\"ex260.png\" \n-00015300: 7465 7874 3d22 496d 6167 6520 6578 3236 text=\"Image ex26\n-00015310: 3020 6f6d 6974 7465 6420 696e 2074 6578 0 omitted in tex\n-00015320: 7420 7665 7273 696f 6e20 6f66 2074 6869 t version of thi\n-00015330: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a s document.\"..].\n-00015340: 0a20 2020 5468 6520 636f 6e65 2073 6861 . The cone sha\n-00015350: 7065 2069 7320 6a75 7374 2061 2073 7765 pe is just a swe\n-00015360: 7074 206c 696e 6520 7769 7468 206e 6f20 pt line with no \n-00015370: 636c 6f73 7572 6520 7461 6720 616e 6420 closure tag and \n-00015380: 6375 6c6c 696e 670a 7475 726e 6564 206f culling.turned o\n-00015390: 6666 2e20 2042 6567 696e 2062 7920 7365 ff. Begin by se\n-000153a0: 7474 696e 6720 7570 2073 6f6d 6520 7573 tting up some us\n-000153b0: 6566 756c 2063 6f6e 7374 616e 7473 2e0a eful constants..\n-000153c0: 2020 6465 6620 4f20 2830 2c30 2c30 2920 def O (0,0,0) \n-000153d0: 6465 6620 4920 5b31 2c30 2c30 5d20 6465 def I [1,0,0] de\n-000153e0: 6620 4a20 5b30 2c31 2c30 5d20 6465 6620 f J [0,1,0] def \n-000153f0: 4b20 5b30 2c30 2c31 5d0a 2020 6465 6620 K [0,0,1]. def \n-00015400: 7030 2028 312c 3229 2064 6566 2070 3120 p0 (1,2) def p1 \n-00015410: 2831 2e35 2c30 2920 6465 6620 4e20 380a (1.5,0) def N 8.\n-00015420: 2020 6465 6620 7365 675f 726f 7420 726f def seg_rot ro\n-00015430: 7461 7465 2833 3630 202f 204e 2c20 5b4a tate(360 / N, [J\n-00015440: 5d29 0a54 6865 2070 6f69 6e74 7320 e280 ]).The points ..\n-00015450: 9870 30e2 8099 2061 6e64 20e2 8098 7031 .p0... and ...p1\n-00015460: e280 9920 6172 6520 7468 6520 656e 6420 ... are the end \n-00015470: 706f 696e 7473 206f 6620 7468 6520 6c69 points of the li\n-00015480: 6e65 2074 6f20 6265 2073 7765 7074 2e0a ne to be swept..\n-00015490: 5468 6520 6465 6669 6e69 7469 6f6e 20e2 The definition .\n-000154a0: 8098 7365 675f 726f 74e2 8099 2069 7320 ..seg_rot... is \n-000154b0: 7468 6520 7377 6565 7020 7472 616e 7366 the sweep transf\n-000154c0: 6f72 6d61 7469 6f6e 2e20 2057 6974 6820 ormation. With \n-000154d0: 7468 6573 652c 2074 6865 0a63 6f6e 6520 these, the.cone \n-000154e0: 6974 7365 6c66 2069 7320 7369 6d70 6c65 itself is simple\n-000154f0: 2e0a 2020 7377 6565 705b 6375 6c6c 3d66 .. sweep[cull=f\n-00015500: 616c 7365 5d20 7b20 4e2c 205b 5b73 6567 alse] { N, [[seg\n-00015510: 5f72 6f74 5d5d 207d 206c 696e 6528 7030 _rot]] } line(p0\n-00015520: 2928 7031 290a 0a20 2020 5468 6520 6178 )(p1).. The ax\n-00015530: 6573 2061 7265 206e 6578 7420 616e 6420 es are next and \n-00015540: 696e 636c 7564 6520 616e 2069 6e74 6572 include an inter\n-00015550: 6573 696e 6720 7472 6963 6b20 7468 6174 esing trick that\n-00015560: 2073 686f 7773 2074 6865 0a68 6964 6465 shows the.hidde\n-00015570: 6e20 7061 7274 7320 6173 2064 6f74 7465 n parts as dotte\n-00015580: 6420 6c69 6e65 732e 2020 5468 6520 7365 d lines. The se\n-00015590: 6372 6574 2069 7320 6472 6177 2074 6865 cret is draw the\n-000155a0: 2061 7865 7320 7477 6963 652d 2d73 6f6c axes twice--sol\n-000155b0: 6964 0a6c 696e 6573 2077 6974 6820 7468 id.lines with th\n-000155c0: 6520 6e6f 726d 616c 2068 6964 6465 6e20 e normal hidden \n-000155d0: 7375 7266 6163 6520 616c 676f 7269 7468 surface algorith\n-000155e0: 6d20 696e 2065 6666 6563 742c 2061 6e64 m in effect, and\n-000155f0: 2074 6865 6e0a 646f 7474 6564 2077 6974 then.dotted wit\n-00015600: 6820 7468 6520 6f70 7469 6f6e 20e2 8098 h the option ...\n-00015610: 6c61 793d 6f76 6572 e280 9920 736f 2074 lay=over... so t\n-00015620: 6861 7420 6e6f 2070 6f6c 7967 6f6e 7320 hat no polygons \n-00015630: 6361 6e20 6869 6465 2074 6865 6d2e 0a20 can hide them.. \n-00015640: 2064 6566 2061 7820 2864 782c 302c 3029 def ax (dx,0,0)\n-00015650: 2025 2074 6970 7320 6f66 2074 6865 2061 % tips of the a\n-00015660: 7865 730a 2020 6465 6620 6179 2028 302c xes. def ay (0,\n-00015670: 6479 2c30 290a 2020 6465 6620 617a 2028 dy,0). def az (\n-00015680: 302c 302c 647a 290a 2020 6c69 6e65 5b61 0,0,dz). line[a\n-00015690: 7272 6f77 733d 3c2d 3e2c 6c69 6e65 7769 rrows=<->,linewi\n-000156a0: 6474 683d 2e34 7074 5d28 6178 2928 4f29 dth=.4pt](ax)(O)\n-000156b0: 2861 7929 0a20 206c 696e 655b 6172 726f (ay). line[arro\n-000156c0: 7773 3d2d 3e2c 6c69 6e65 7769 6474 683d ws=->,linewidth=\n-000156d0: 2e34 7074 5d28 4f29 2861 7a29 0a20 2025 .4pt](O)(az). %\n-000156e0: 2072 6570 6561 7420 646f 7474 6564 2061 repeat dotted a\n-000156f0: 7320 616e 206f 7665 726c 6179 2074 6f20 s an overlay to \n-00015700: 6869 6e74 2061 7420 7468 6520 6869 6464 hint at the hidd\n-00015710: 656e 206c 696e 6573 0a20 206c 696e 655b en lines. line[\n-00015720: 6c61 793d 6f76 6572 2c6c 696e 6573 7479 lay=over,linesty\n-00015730: 6c65 3d64 6f74 7465 642c 6c69 6e65 7769 le=dotted,linewi\n-00015740: 6474 683d 2e34 7074 5d28 6178 2928 4f29 dth=.4pt](ax)(O)\n-00015750: 2861 7929 0a20 206c 696e 655b 6c61 793d (ay). line[lay=\n-00015760: 6f76 6572 2c6c 696e 6573 7479 6c65 3d64 over,linestyle=d\n-00015770: 6f74 7465 642c 6c69 6e65 7769 6474 683d otted,linewidth=\n-00015780: 2e34 7074 5d28 4f29 2861 7a29 0a20 2073 .4pt](O)(az). s\n-00015790: 7065 6369 616c 7c5c 666f 6f74 6e6f 7465 pecial|\\footnote\n-000157a0: 7369 7a65 0a20 2020 2020 2020 2020 205c size. \\\n-000157b0: 7570 7574 5b64 5d23 317b 2478 247d 5c75 uput[d]#1{$x$}\\u\n-000157c0: 7075 745b 755d 2332 7b24 7924 7d5c 7570 put[u]#2{$y$}\\up\n-000157d0: 7574 5b6c 5d23 337b 247a 247d 7c0a 2020 ut[l]#3{$z$}|. \n-000157e0: 2020 2861 7829 2861 7929 2861 7a29 0a54 (ax)(ay)(az).T\n-000157f0: 6865 206c 6162 656c 7320 6172 6520 6170 he labels are ap\n-00015800: 706c 6965 6420 7769 7468 20e2 8098 5053 plied with ...PS\n-00015810: 5472 6963 6b73 e280 9920 7370 6563 6961 Tricks... specia\n-00015820: 6c20 6f62 6a65 6374 7320 6173 2075 7375 l objects as usu\n-00015830: 616c 2e0a 0a20 2020 466f 7220 7468 6520 al... For the \n-00015840: 6865 6967 6874 2064 696d 656e 7369 6f6e height dimension\n-00015850: 206d 6172 6b2c 2074 6865 2070 6f77 6572 mark, the power\n-00015860: 206f 6620 6166 6669 6e65 2061 7269 7468 of affine arith\n-00015870: 6574 6963 2069 7320 7665 7279 0a68 656c etic is very.hel\n-00015880: 7066 756c 2e0a 2020 6465 6620 6864 696d pful.. def hdim\n-00015890: 5f72 6566 2075 6e69 7428 2870 3129 202d _ref unit((p1) -\n-000158a0: 2028 4f29 2920 7468 656e 205b 5b73 6567 (O)) then [[seg\n-000158b0: 5f72 6f74 5d5d 5e32 0a20 2064 6566 2063 _rot]]^2. def c\n-000158c0: 3020 2870 3029 2074 6865 6e20 7363 616c 0 (p0) then scal\n-000158d0: 6528 5b4a 5d29 0a20 2064 6566 2068 3030 e([J]). def h00\n-000158e0: 2028 6330 2920 2b20 312e 3120 2a20 5b68 (c0) + 1.1 * [h\n-000158f0: 6469 6d5f 7265 665d 0a20 2064 6566 2068 dim_ref]. def h\n-00015900: 3031 2028 6330 2920 2b20 312e 3920 2a20 01 (c0) + 1.9 * \n-00015910: 5b68 6469 6d5f 7265 665d 0a20 2064 6566 [hdim_ref]. def\n-00015920: 2068 3032 2028 6330 2920 2b20 312e 3820 h02 (c0) + 1.8 \n-00015930: 2a20 5b68 6469 6d5f 7265 665d 0a20 206c * [hdim_ref]. l\n-00015940: 696e 6528 6830 3029 2868 3031 290a 2020 ine(h00)(h01). \n-00015950: 6465 6620 6831 3020 284f 2920 2b20 312e def h10 (O) + 1.\n-00015960: 3620 2a20 5b68 6469 6d5f 7265 665d 0a20 6 * [hdim_ref]. \n-00015970: 2064 6566 2068 3131 2028 4f29 202b 2031 def h11 (O) + 1\n-00015980: 2e39 202a 205b 6864 696d 5f72 6566 5d0a .9 * [hdim_ref].\n-00015990: 2020 6465 6620 6831 3220 284f 2920 2b20 def h12 (O) + \n-000159a0: 312e 3820 2a20 5b68 6469 6d5f 7265 665d 1.8 * [hdim_ref]\n-000159b0: 0a20 206c 696e 6528 6831 3029 2868 3131 . line(h10)(h11\n-000159c0: 290a 2020 6c69 6e65 5b61 7272 6f77 733d ). line[arrows=\n-000159d0: 3c2d 3e5d 2868 3032 2928 6831 3229 0a20 <->](h02)(h12). \n-000159e0: 2064 6566 2068 6d32 2028 2868 3032 2920 def hm2 ((h02) \n-000159f0: 2d20 284f 2920 2b20 2868 3132 2920 2d20 - (O) + (h12) - \n-00015a00: 284f 2929 202f 2032 202b 2028 4f29 0a20 (O)) / 2 + (O). \n-00015a10: 2073 7065 6369 616c 7c5c 666f 6f74 6e6f special|\\footno\n-00015a20: 7465 7369 7a65 5c72 7075 742a 2331 7b24 tesize\\rput*#1{$\n-00015a30: 6824 7d7c 2868 6d32 290a 2020 2054 6865 h$}|(hm2). The\n-00015a40: 2067 656e 6572 616c 2069 6465 6120 656d general idea em\n-00015a50: 706c 6f79 6564 2068 6572 6520 6973 2074 ployed here is t\n-00015a60: 6f20 636f 6d70 7574 6520 6120 756e 6974 o compute a unit\n-00015a70: 2022 7265 6665 7265 6e63 650a 7665 6374 \"reference.vect\n-00015a80: 6f72 2220 7061 7261 6c6c 656c 2074 6f20 or\" parallel to \n-00015a90: 7468 6520 787a 2d70 6c61 6e65 2069 6e20 the xz-plane in \n-00015aa0: 7468 6520 6465 7369 7265 6420 6469 7265 the desired dire\n-00015ab0: 6374 696f 6e20 6f66 2074 6865 0a64 696d ction of the.dim\n-00015ac0: 656e 7369 6f6e 2066 726f 6d20 7468 6520 ension from the \n-00015ad0: 6f72 6967 696e 2e20 2054 6865 2074 7261 origin. The tra\n-00015ae0: 6e73 666f 726d 6174 696f 6e20 e280 985b nsformation ...[\n-00015af0: 5b73 6567 5f72 6f74 5d5d 5e32 e280 9920 [seg_rot]]^2... \n-00015b00: 726f 7461 7465 730a 7477 6f20 7365 676d rotates.two segm\n-00015b10: 656e 7473 2061 626f 7574 2074 6865 2079 ents about the y\n-00015b20: 2d61 7869 732e 2020 5768 656e 2061 7070 -axis. When app\n-00015b30: 6c69 6564 2074 6f20 e280 9828 7031 2920 lied to ...(p1) \n-00015b40: 2d20 284f 29e2 8099 2c20 7468 650a 7265 - (O)..., the.re\n-00015b50: 7375 6c74 696e 6720 7665 6374 6f72 2070 sulting vector p\n-00015b60: 6f69 6e74 7320 746f 2074 6865 2072 6967 oints to the rig\n-00015b70: 6874 2061 7320 7368 6f77 6e2e 2020 496e ht as shown. In\n-00015b80: 2074 6869 7320 6d61 6e6e 6572 2c20 7765 this manner, we\n-00015b90: 2063 616e 0a70 6963 6b20 616e 7920 7665 can.pick any ve\n-00015ba0: 7274 6578 2061 7320 7468 6520 6c6f 6361 rtex as the loca\n-00015bb0: 7469 6f6e 206f 6620 7468 6520 6865 6967 tion of the heig\n-00015bc0: 6874 2064 696d 656e 7369 6f6e 206c 696e ht dimension lin\n-00015bd0: 6573 2062 7920 7661 7279 696e 670a 7468 es by varying.th\n-00015be0: 6520 6578 706f 6e65 6e74 206f 6620 e280 e exponent of ..\n-00015bf0: 985b 5b73 6567 5f72 6f74 5d5d e280 992e .[[seg_rot]]....\n-00015c00: 2020 5468 6973 2069 7320 6f6e 6c79 206f This is only o\n-00015c10: 6e65 206f 6620 6d61 6e79 2070 6f73 7369 ne of many possi\n-00015c20: 626c 650a 7374 7261 7465 6769 6573 2e0a ble.strategies..\n-00015c30: 0a20 2020 5468 6520 636f 6d70 7574 6174 . The computat\n-00015c40: 696f 6e20 6f66 20e2 8098 686d 32e2 8099 ion of ...hm2...\n-00015c50: 2069 7320 6120 7573 6566 756c 2069 6469 is a useful idi\n-00015c60: 6f6d 2066 6f72 2066 696e 6469 6e67 2074 om for finding t\n-00015c70: 6865 2063 656e 7472 6f69 640a 6f66 2061 he centroid.of a\n-00015c80: 2073 6574 206f 6620 706f 696e 7473 2e0a set of points..\n-00015c90: 0a20 2020 5468 6520 7477 6f20 7261 6469 . The two radi\n-00015ca0: 7573 206d 6172 6b73 2061 7265 2064 6f6e us marks are don\n-00015cb0: 6520 7369 6d69 6c61 726c 792c 2073 6f20 e similarly, so \n-00015cc0: 7765 2070 7265 7365 6e74 2074 6865 2063 we present the c\n-00015cd0: 6f64 650a 7769 7468 6f75 7420 636f 6d6d ode.without comm\n-00015ce0: 656e 742e 0a20 2025 2072 6164 6975 7320 ent.. % radius \n-00015cf0: 6d65 6173 7572 656d 656e 7420 6d61 726b measurement mark\n-00015d00: 730a 2020 6465 6620 6761 7020 5b30 2c2e s. def gap [0,.\n-00015d10: 322c 305d 2020 2520 7573 6564 2074 6f20 2,0] % used to \n-00015d20: 6372 6561 7465 2073 6d61 6c6c 2076 6572 create small ver\n-00015d30: 7469 6361 6c20 6761 7073 0a0a 2020 2520 tical gaps.. % \n-00015d40: 6669 7273 7420 7231 0a20 2064 6566 2075 first r1. def u\n-00015d50: 7031 205b 302c 332e 312c 305d 2025 2074 p1 [0,3.1,0] % t\n-00015d60: 6963 6b20 7269 7365 7320 6162 6f76 6520 ick rises above \n-00015d70: 6469 6d65 6e73 696f 6e20 6120 6c69 7474 dimension a litt\n-00015d80: 6c65 0a20 2064 6566 2072 3120 2828 7031 le. def r1 ((p1\n-00015d90: 2920 7468 656e 205b 5b73 6567 5f72 6f74 ) then [[seg_rot\n-00015da0: 5d5d 5e2d 3229 202b 205b 7570 315d 0a20 ]]^-2) + [up1]. \n-00015db0: 2064 6566 2072 3163 2028 7231 2920 7468 def r1c (r1) th\n-00015dc0: 656e 2073 6361 6c65 285b 4a5d 290a 2020 en scale([J]). \n-00015dd0: 6465 6620 7231 7420 2872 3129 202b 205b def r1t (r1) + [\n-00015de0: 6761 705d 0a20 2064 6566 2072 3162 2028 gap]. def r1b (\n-00015df0: 2872 3174 2920 7468 656e 2073 6361 6c65 (r1t) then scale\n-00015e00: 285b 312c 302c 315d 2929 202b 205b 6761 ([1,0,1])) + [ga\n-00015e10: 705d 0a20 206c 696e 655b 6172 726f 7773 p]. line[arrows\n-00015e20: 3d3c 2d3e 5d28 7231 6329 2872 3129 2020 =<->](r1c)(r1) \n-00015e30: 2520 6469 6d65 6e73 696f 6e20 6c69 6e65 % dimension line\n-00015e40: 0a20 206c 696e 6528 7231 6229 2872 3174 . line(r1b)(r1t\n-00015e50: 2920 2020 2020 2020 2020 2020 2020 2520 ) % \n-00015e60: 7469 636b 0a20 2064 6566 2072 316d 2028 tick. def r1m (\n-00015e70: 2872 3129 202d 2028 4f29 202b 2028 7231 (r1) - (O) + (r1\n-00015e80: 6329 202d 2028 4f29 2920 2f20 3220 2b20 c) - (O)) / 2 + \n-00015e90: 284f 2920 2520 6c61 6265 6c20 706f 7369 (O) % label posi\n-00015ea0: 7469 6f6e 0a20 2073 7065 6369 616c 207c tion. special |\n-00015eb0: 5c66 6f6f 746e 6f74 6573 697a 655c 7270 \\footnotesize\\rp\n-00015ec0: 7574 2a23 317b 2472 5f31 247d 7c28 7231 ut*#1{$r_1$}|(r1\n-00015ed0: 6d29 2020 2520 6c61 6265 6c0a 0a20 2025 m) % label.. %\n-00015ee0: 2073 616d 6520 6472 696c 6c20 666f 7220 same drill for \n-00015ef0: 7230 2c20 6275 7420 6d75 7374 2070 726f r0, but must pro\n-00015f00: 6a65 6374 2064 6f77 6e20 6669 7273 740a ject down first.\n-00015f10: 2020 6465 6620 7570 3020 5b30 2c32 2e37 def up0 [0,2.7\n-00015f20: 2c30 5d0a 2020 6465 6620 7230 2028 2870 ,0]. def r0 ((p\n-00015f30: 3029 2074 6865 6e20 7363 616c 6528 5b31 0) then scale([1\n-00015f40: 2c30 2c31 5d29 2074 6865 6e20 5b5b 7365 ,0,1]) then [[se\n-00015f50: 675f 726f 745d 5d5e 2d32 2920 2b20 5b75 g_rot]]^-2) + [u\n-00015f60: 7030 5d0a 2020 6465 6620 7230 6320 2872 p0]. def r0c (r\n-00015f70: 3029 2074 6865 6e20 7363 616c 6528 5b4a 0) then scale([J\n-00015f80: 5d29 0a20 2064 6566 2072 3074 2028 7230 ]). def r0t (r0\n-00015f90: 2920 2b20 5b67 6170 5d0a 2020 6465 6620 ) + [gap]. def \n-00015fa0: 7230 6220 2828 7030 2920 7468 656e 205b r0b ((p0) then [\n-00015fb0: 5b73 6567 5f72 6f74 5d5d 5e2d 3229 202b [seg_rot]]^-2) +\n-00015fc0: 205b 6761 705d 0a20 206c 696e 655b 6172 [gap]. line[ar\n-00015fd0: 726f 7773 3d3c 2d3e 5d28 7230 6329 2872 rows=<->](r0c)(r\n-00015fe0: 3029 0a20 206c 696e 6528 7230 6229 2872 0). line(r0b)(r\n-00015ff0: 3074 290a 2020 6465 6620 7230 6d20 2828 0t). def r0m ((\n-00016000: 7230 2920 2d20 284f 2920 2b20 2872 3063 r0) - (O) + (r0c\n-00016010: 2920 2d20 284f 2929 202f 2032 202b 2028 ) - (O)) / 2 + (\n-00016020: 4f29 0a20 2073 7065 6369 616c 207c 5c66 O). special |\\f\n-00016030: 6f6f 746e 6f74 6573 697a 655c 7270 7574 ootnotesize\\rput\n-00016040: 2a23 317b 2472 5f30 247d 7c28 7230 6d29 *#1{$r_0$}|(r0m)\n-00016050: 0a0a 2020 2054 6865 2073 6563 6f6e 6420 .. The second \n-00016060: 6472 6177 696e 6720 7573 6573 2074 6865 drawing uses the\n-00016070: 2073 616d 6520 7465 6368 6e69 7175 6573 same techniques\n-00016080: 2e20 204f 6e6c 7920 7468 6520 6d65 7468 . Only the meth\n-00016090: 6f64 2066 6f72 0a64 7261 7769 6e67 2074 od for.drawing t\n-000160a0: 6865 2065 6c6c 6970 7469 6361 6c20 6172 he elliptical ar\n-000160b0: 6320 6973 206e 6577 2e20 2048 6572 6520 c is new. Here \n-000160c0: 6973 2074 6865 2063 6f64 652e 0a20 2064 is the code.. d\n-000160d0: 6566 206d 6964 2028 2870 3030 292d 284f ef mid ((p00)-(O\n-000160e0: 292b 2870 3130 292d 284f 292b 2870 3131 )+(p10)-(O)+(p11\n-000160f0: 292d 284f 292b 2870 3031 292d 284f 2929 )-(O)+(p01)-(O))\n-00016100: 2f34 2b28 4f29 0a20 2073 7065 6369 616c /4+(O). special\n-00016110: 7c5c 7270 7574 2331 7b5c 7073 6375 7374 |\\rput#1{\\pscust\n-00016120: 6f6d 7b0a 2020 2020 5c73 6361 6c65 7b31 om{. \\scale{1\n-00016130: 2031 2e33 7d0a 2020 2020 5c70 7361 7263 1.3}. \\psarc\n-00016140: 5b61 7272 6f77 6c65 6e67 7468 3d2e 355d [arrowlength=.5]\n-00016150: 7b2d 3e7d 7b2e 3235 7d7b 2d36 307d 7b32 {->}{.25}{-60}{2\n-00016160: 3430 7d7d 7d7c 0a20 2020 205b 6c61 793d 40}}}|. [lay=\n-00016170: 6f76 6572 5d28 6d69 6429 0a57 6520 636f over](mid).We co\n-00016180: 756c 6420 6861 7665 2073 7765 7074 2061 uld have swept a\n-00016190: 2070 6f69 6e74 2074 6f20 6d61 6b65 2074 point to make t\n-000161a0: 6865 2061 7263 2077 6974 6820 e280 9873 he arc with ...s\n-000161b0: 6b65 7463 68e2 8099 2c20 6275 7420 7573 ketch..., but us\n-000161c0: 696e 6720 610a e280 9850 5354 7269 636b ing a....PSTrick\n-000161d0: 73e2 8099 2063 7573 746f 6d20 6772 6170 s... custom grap\n-000161e0: 6869 6320 7761 7320 7369 6d70 6c65 722e hic was simpler.\n-000161f0: 2020 4167 6169 6e20 7765 2063 6f6d 7075 Again we compu\n-00016200: 7465 6420 7468 6520 6365 6e74 726f 6964 ted the centroid\n-00016210: 0a6f 6620 7468 6520 7175 6164 7269 6c61 .of the quadrila\n-00016220: 7465 7261 6c20 6279 2061 7665 7261 6769 teral by averagi\n-00016230: 6e67 2070 6f69 6e74 732e 2020 4e6f 7465 ng points. Note\n-00016240: 2074 6861 7420 7363 616c 696e 6720 696e that scaling in\n-00016250: 0a50 6f73 7473 6372 6970 7420 6469 7374 .Postscript dist\n-00016260: 6f72 7473 2074 6865 2061 7272 6f77 6865 orts the arrowhe\n-00016270: 6164 2c20 6275 7420 696e 2074 6869 7320 ad, but in this \n-00016280: 6361 7365 2074 6865 2064 6973 746f 7274 case the distort\n-00016290: 696f 6e0a 6163 7475 616c 6c79 206c 6f6f ion.actually loo\n-000162a0: 6b73 2062 6574 7465 7220 696e 2074 6865 ks better in the\n-000162b0: 2070 726f 6a65 6374 696f 6e20 6f66 2074 projection of t\n-000162c0: 6865 2073 6c61 6e74 6564 2066 6163 652e he slanted face.\n-000162d0: 2020 4120 e280 9873 6b65 7463 68e2 8099 A ...sketch...\n-000162e0: 0a61 7272 6f77 6865 6164 2077 6f75 6c64 .arrowhead would\n-000162f0: 206e 6f74 2068 6176 6520 6265 656e 2064 not have been d\n-00016300: 6973 746f 7274 6564 2e0a 0a20 2020 5468 istorted... Th\n-00016310: 6520 636f 6d70 6c65 7465 2063 6f64 6520 e complete code \n-00016320: 666f 7220 7468 6973 2065 7861 6d70 6c65 for this example\n-00016330: 2c20 7768 6963 6820 6472 6177 7320 6569 , which draws ei\n-00016340: 7468 6572 2066 6967 7572 650a 6465 7065 ther figure.depe\n-00016350: 6e64 696e 6720 6f6e 2074 6865 2064 6566 nding on the def\n-00016360: 696e 6974 696f 6e20 6f66 2074 6865 2074 inition of the t\n-00016370: 6167 20e2 8098 3c6c 6162 656c 6564 3ee2 ag ....\n-00016380: 8099 2c20 6973 2069 6e63 6c75 6465 6420 .., is included \n-00016390: 696e 2074 6865 0ae2 8098 736b 6574 6368 in the....sketch\n-000163a0: e280 9920 6469 7374 7269 6275 7469 6f6e ... distribution\n-000163b0: 2069 6e20 7468 6520 6669 6c65 20e2 8098 in the file ...\n-000163c0: 7472 756e 6361 7465 6463 6f6e 652e 736b truncatedcone.sk\n-000163d0: e280 992e 0a0a 1f0a 4669 6c65 3a20 736b ........File: sk\n-000163e0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-000163f0: 3a20 4120 6869 6572 6172 6368 6963 616c : A hierarchical\n-00016400: 206d 6f64 656c 2c20 204e 6578 743a 2043 model, Next: C\n-00016410: 6176 6561 7473 2c20 2050 7265 763a 2041 aveats, Prev: A\n-00016420: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n-00016430: 6e67 2c20 2055 703a 2042 7569 6c64 696e ng, Up: Buildin\n-00016440: 6720 6120 6472 6177 696e 670a 0a34 2e33 g a drawing..4.3\n-00016450: 2041 2068 6965 7261 7263 6869 6361 6c20 A hierarchical \n-00016460: 6d6f 6465 6c0a 3d3d 3d3d 3d3d 3d3d 3d3d model.==========\n-00016470: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a ==============..\n-00016480: 5768 696c 6520 e280 9873 6b65 7463 68e2 While ...sketch.\n-00016490: 8099 2077 6173 206e 6576 6572 206d 6561 .. was never mea\n-000164a0: 6e74 2074 6f20 6265 2061 2067 656f 6d65 nt to be a geome\n-000164b0: 7472 6963 206d 6f64 656c 696e 6720 6c61 tric modeling la\n-000164c0: 6e67 7561 6765 2c20 6974 0a63 6f6d 6573 nguage, it.comes\n-000164d0: 2066 6169 726c 7920 636c 6f73 652e 2020 fairly close. \n-000164e0: 5468 6520 666f 6c6c 6f77 696e 6720 6578 The following ex\n-000164f0: 616d 706c 6520 7075 7473 2061 6c6c 2077 ample puts all w\n-00016500: 6520 6861 7665 2073 6565 6e20 746f 2077 e have seen to w\n-00016510: 6f72 6b0a 696e 2061 2076 6572 7920 7369 ork.in a very si\n-00016520: 6d70 6c65 206d 6f64 656c 206f 6620 7468 mple model of th\n-00016530: 6520 6875 6d61 6e20 6861 6e64 2e20 2053 e human hand. S\n-00016540: 7461 7274 2062 7920 7377 6565 7069 6e67 tart by sweeping\n-00016550: 2061 206c 696e 6520 746f 0a6d 616b 6520 a line to.make \n-00016560: 6120 7472 756e 6361 7465 6420 636f 6e65 a truncated cone\n-00016570: 2c20 7768 6963 6820 7769 6c6c 2062 6520 , which will be \n-00016580: 636f 7069 6564 206f 7665 7220 616e 6420 copied over and \n-00016590: 6f76 6572 2061 6761 696e 2074 6f20 6d61 over again to ma\n-000165a0: 6b65 0a74 6865 2073 6567 6d65 6e74 7320 ke.the segments \n-000165b0: 6f66 2066 696e 6765 7273 2e0a 2020 6465 of fingers.. de\n-000165c0: 6620 4f20 2830 2c30 2c30 2920 2520 6f72 f O (0,0,0) % or\n-000165d0: 6967 696e 0a20 2064 6566 2049 205b 312c igin. def I [1,\n-000165e0: 302c 305d 2064 6566 204a 205b 302c 312c 0,0] def J [0,1,\n-000165f0: 305d 2064 6566 204b 205b 302c 302c 315d 0] def K [0,0,1]\n-00016600: 2025 2063 616e 6f6e 6963 616c 2075 6e69 % canonical uni\n-00016610: 7420 7665 6374 6f72 730a 2020 6465 6620 t vectors. def \n-00016620: 7365 676d 656e 7420 7b0a 2020 2020 6465 segment {. de\n-00016630: 6620 6e5f 6661 6365 7320 380a 2020 2020 f n_faces 8. \n-00016640: 7377 6565 7020 7b20 6e5f 6661 6365 733c sweep { n_faces<\n-00016650: 3e2c 2072 6f74 6174 6528 3336 3020 2f20 >, rotate(360 / \n-00016660: 6e5f 6661 6365 732c 205b 4a5d 2920 7d20 n_faces, [J]) } \n-00016670: 0a20 2020 2020 206c 696e 6528 7072 6f78 . line(prox\n-00016680: 696d 616c 5f72 6164 2c20 3029 2864 6973 imal_rad, 0)(dis\n-00016690: 7461 6c5f 7261 642c 2064 6973 7461 6c5f tal_rad, distal_\n-000166a0: 6c65 6e29 0a20 207d 0a49 6e20 6861 6e64 len). }.In hand\n-000166b0: 2061 6e61 746f 6d79 2c20 5f64 6973 7461 anatomy, _dista\n-000166c0: 6c5f 2069 7320 2261 7420 7468 6520 7469 l_ is \"at the ti\n-000166d0: 7022 2061 6e64 205f 7072 6f78 696d 616c p\" and _proximal\n-000166e0: 5f20 6973 2022 696e 2074 6865 2061 7265 _ is \"in the are\n-000166f0: 610a 6f66 2074 6865 2070 616c 6d2e 2220 a.of the palm.\" \n-00016700: 2057 6520 6861 7665 206f 6d69 7474 6564 We have omitted\n-00016710: 2061 6c6c 2074 6865 2073 6361 6c61 7220 all the scalar \n-00016720: 636f 6e73 7461 6e74 732e 2020 596f 7520 constants. You \n-00016730: 6361 6e20 6669 6e64 0a74 6865 6d20 696e can find.them in\n-00016740: 20e2 8098 6861 6e64 2e73 6be2 8099 2c20 ...hand.sk..., \n-00016750: 7768 6963 6820 6973 2070 726f 7669 6465 which is provide\n-00016760: 6420 696e 2074 6865 20e2 8098 736b 6574 d in the ...sket\n-00016770: 6368 e280 9920 6469 7374 7269 6275 7469 ch... distributi\n-00016780: 6f6e 2e0a 0a20 2020 5765 2061 6c73 6f20 on... We also \n-00016790: 6e65 6564 2061 2070 726f 746f 7479 7069 need a prototypi\n-000167a0: 6361 6c20 7370 6865 7265 2074 6f20 7573 cal sphere to us\n-000167b0: 6520 666f 7220 7468 6520 6a6f 696e 7473 e for the joints\n-000167c0: 2074 6865 6d73 656c 7665 732e 0a20 2064 themselves.. d\n-000167d0: 6566 206a 6f69 6e74 5f73 7068 6572 6520 ef joint_sphere \n-000167e0: 7b0a 2020 2020 6465 6620 6e5f 6a6f 696e {. def n_join\n-000167f0: 745f 6661 6365 7320 380a 2020 2020 7377 t_faces 8. sw\n-00016800: 6565 7020 5b66 696c 6c63 6f6c 6f72 3d72 eep [fillcolor=r\n-00016810: 6564 5d20 7b20 6e5f 6a6f 696e 745f 6661 ed] { n_joint_fa\n-00016820: 6365 732c 2072 6f74 6174 6528 3336 3020 ces, rotate(360 \n-00016830: 2f20 6e5f 6a6f 696e 745f 6661 6365 732c / n_joint_faces,\n-00016840: 205b 4a5d 2920 7d0a 2020 2020 2020 7377 [J]) }. sw\n-00016850: 6565 7020 7b20 6e5f 6a6f 696e 745f 6661 eep { n_joint_fa\n-00016860: 6365 732c 2072 6f74 6174 6528 3138 3020 ces, rotate(180 \n-00016870: 2f20 6e5f 6a6f 696e 745f 6661 6365 7329 / n_joint_faces)\n-00016880: 207d 200a 2020 2020 2020 2020 2830 2c20 } . (0, \n-00016890: 2d6a 6f69 6e74 5f72 6164 290a 2020 7d0a -joint_rad). }.\n-000168a0: 0a20 2020 5765 276c 6c20 6e6f 7720 6465 . We'll now de\n-000168b0: 7369 676e 2074 6865 2069 6e64 6578 2066 sign the index f\n-000168c0: 696e 6765 7220 286e 756d 6265 7220 3120 inger (number 1 \n-000168d0: 696e 206f 7572 206e 6f74 6174 696f 6e61 in our notationa\n-000168e0: 6c0a 636f 6e76 656e 7469 6f6e 3b20 6669 l.convention; fi\n-000168f0: 6e67 6572 2030 2069 7320 7468 6520 7468 nger 0 is the th\n-00016900: 756d 6229 2e20 2054 6865 2064 6973 7461 umb). The dista\n-00016910: 6c20 726f 7461 7469 6f6e 2066 6f72 2074 l rotation for t\n-00016920: 6865 2066 696e 6765 720a 6170 706c 6965 he finger.applie\n-00016930: 7320 6f6e 6c79 2074 6f20 7468 6520 7469 s only to the ti\n-00016940: 702c 2073 6f20 7765 2064 6566 696e 6520 p, so we define \n-00016950: 7468 6520 666f 6c6c 6f77 696e 672e 0a20 the following.. \n-00016960: 2064 6566 2064 6973 7461 6c5f 3120 7b0a def distal_1 {.\n-00016970: 2020 2020 7075 7420 7b20 7472 616e 736c put { transl\n-00016980: 6174 6528 6a6f 696e 745f 6761 7020 2a20 ate(joint_gap * \n-00016990: 6a6f 696e 745f 7261 6420 2a20 5b4a 5d29 joint_rad * [J])\n-000169a0: 200a 2020 2020 2020 2020 2020 7468 656e . then\n-000169b0: 2072 6f74 6174 6528 6469 7374 616c 5f31 rotate(distal_1\n-000169c0: 5f72 6f74 2c20 5b49 5d29 200a 2020 2020 _rot, [I]) . \n-000169d0: 2020 2020 2020 7468 656e 2074 7261 6e73 then trans\n-000169e0: 6c61 7465 2828 6469 7374 616c 5f6c 656e late((distal_len\n-000169f0: 202b 206a 6f69 6e74 5f67 6170 202a 206a + joint_gap * j\n-00016a00: 6f69 6e74 5f72 6164 2920 2a20 5b4a 5d29 oint_rad) * [J])\n-00016a10: 207d 0a20 2020 2020 207b 7365 676d 656e }. {segmen\n-00016a20: 747d 0a20 2020 2070 7574 207b 2072 6f74 t}. put { rot\n-00016a30: 6174 6528 6469 7374 616c 5f31 5f72 6f74 ate(distal_1_rot\n-00016a40: 202f 2032 2c20 5b49 5d29 0a20 2020 2020 / 2, [I]). \n-00016a50: 2020 2020 2074 6865 6e20 7472 616e 736c then transl\n-00016a60: 6174 6528 2864 6973 7461 6c5f 6c65 6e20 ate((distal_len \n-00016a70: 2b20 6a6f 696e 745f 6761 7020 2a20 6a6f + joint_gap * jo\n-00016a80: 696e 745f 7261 6429 202a 205b 4a5d 2920 int_rad) * [J]) \n-00016a90: 7d20 0a20 2020 2020 207b 6a6f 696e 745f } . {joint_\n-00016aa0: 7370 6865 7265 7d0a 2020 2020 7075 7420 sphere}. put \n-00016ab0: 7b20 7363 616c 6528 205b 4a5d 202b 2070 { scale( [J] + p\n-00016ac0: 726f 7869 6d61 6c5f 6469 7374 616c 5f72 roximal_distal_r\n-00016ad0: 6174 696f 202a 2028 5b49 5d2b 5b4b 5d29 atio * ([I]+[K])\n-00016ae0: 2029 207d 0a20 2020 2020 207b 7365 676d ) }. {segm\n-00016af0: 656e 747d 0a20 207d 2020 0a54 6865 2069 ent}. } .The i\n-00016b00: 6465 6e74 6966 6965 7273 2068 6572 6520 dentifiers here \n-00016b10: 6172 6520 666f 7220 7369 7a65 2061 6e64 are for size and\n-00016b20: 206c 6f63 6174 696f 6e20 636f 6e73 7461 location consta\n-00016b30: 6e74 732e 2020 5468 6520 6578 6365 7074 nts. The except\n-00016b40: 696f 6e0a 6973 20e2 8098 6469 7374 616c ion.is ...distal\n-00016b50: 5f72 6f74 5f31 e280 992e 2020 5468 6973 _rot_1.... This\n-00016b60: 2072 6f74 6174 696f 6e20 7061 7261 6d65 rotation parame\n-00016b70: 7465 7220 6d6f 6465 6c73 2074 6865 2066 ter models the f\n-00016b80: 6c65 7869 6e67 206f 6620 7468 650a 6669 lexing of the.fi\n-00016b90: 6e67 6572 2074 6970 2e20 2054 6865 2066 nger tip. The f\n-00016ba0: 6972 7374 20e2 8098 7075 74e2 8099 206d irst ...put... m\n-00016bb0: 616b 6573 2061 2063 6f70 7920 6f66 2074 akes a copy of t\n-00016bc0: 6865 2066 696e 6765 7220 7365 676d 656e he finger segmen\n-00016bd0: 7420 7468 6174 2069 730a 7472 616e 736c t that is.transl\n-00016be0: 6174 6564 2075 7077 6172 6420 6a75 7374 ated upward just\n-00016bf0: 2066 6172 2065 6e6f 7567 6820 746f 206d far enough to m\n-00016c00: 616b 6520 726f 6f6d 2066 6f72 2074 6865 ake room for the\n-00016c10: 2073 7068 6572 6963 616c 206a 6f69 6e74 spherical joint\n-00016c20: 2e0a 5468 656e 2069 7420 6170 706c 6965 ..Then it applie\n-00016c30: 7320 7468 6520 6469 7374 616c 2072 6f74 s the distal rot\n-00016c40: 6174 696f 6e2e 2020 4669 6e61 6c6c 7920 ation. Finally \n-00016c50: 6974 2074 7261 6e73 6c61 7465 7320 7468 it translates th\n-00016c60: 6520 7768 6f6c 650a 6173 7365 6d62 6c79 e whole.assembly\n-00016c70: 2075 7077 6172 6420 6167 6169 6e20 746f upward again to\n-00016c80: 206d 616b 6520 726f 6f6d 2066 6f72 2074 make room for t\n-00016c90: 6865 206d 6964 646c 6520 7068 6c61 6e67 he middle phlang\n-00016ca0: 6573 2028 7468 6520 6e65 7874 0a62 6f6e es (the next.bon\n-00016cb0: 6520 746f 7761 7264 2074 6865 2070 616c e toward the pal\n-00016cc0: 6d29 2e20 2054 6865 2073 6563 6f6e 6420 m). The second \n-00016cd0: e280 9870 7574 e280 9920 706f 7369 7469 ...put... positi\n-00016ce0: 6f6e 7320 7468 6520 7370 6865 7265 2e20 ons the sphere. \n-00016cf0: 2054 6865 7265 2069 730a 6120 726f 7461 There is.a rota\n-00016d00: 7469 6f6e 2074 6f20 706c 6163 6520 7468 tion to place th\n-00016d10: 6520 6772 6964 206f 6e20 7468 6520 7370 e grid on the sp\n-00016d20: 6865 7265 2073 7572 6661 6365 2061 7420 here surface at \n-00016d30: 616e 206e 6963 6520 616e 676c 652c 0a74 an nice angle,.t\n-00016d40: 6865 6e20 6120 7472 616e 736c 6174 696f hen a translatio\n-00016d50: 6e20 746f 2074 6865 2062 6173 6520 6f66 n to the base of\n-00016d60: 2074 6865 2064 6973 7461 6c20 7068 6c61 the distal phla\n-00016d70: 6e67 6573 2c20 7768 6963 6820 6973 2061 nges, which is a\n-00016d80: 6c73 6f0a 6365 6e74 6572 206f 6620 6974 lso.center of it\n-00016d90: 7320 726f 7461 7469 6f6e 2e20 2046 696e s rotation. Fin\n-00016da0: 616c 6c79 2c20 7468 6520 6c61 7374 20e2 ally, the last .\n-00016db0: 8098 7075 74e2 8099 2070 6f73 6974 696f ..put... positio\n-00016dc0: 6e73 2074 6865 206d 6964 646c 650a 7365 ns the middle.se\n-00016dd0: 676d 656e 7420 6974 7365 6c66 2e0a 0a20 gment itself... \n-00016de0: 2020 5468 6520 6d69 6464 6c65 206a 6f69 The middle joi\n-00016df0: 6e74 2069 7320 7468 6520 6e65 7874 206f nt is the next o\n-00016e00: 6e65 2064 6f77 6e2c 2077 6974 6820 726f ne down, with ro\n-00016e10: 7461 7469 6f6e 2061 6e67 6c65 0ae2 8098 tation angle....\n-00016e20: 6d69 6464 6c65 5f72 6f74 5f31 e280 992e middle_rot_1....\n-00016e30: 2020 5768 656e 2074 6869 7320 616e 676c When this angl\n-00016e40: 6520 6368 616e 6765 732c 2077 6520 6e65 e changes, we ne\n-00016e50: 6564 2061 6c6c 2074 6865 206f 626a 6563 ed all the objec\n-00016e60: 7473 2069 6e0a e280 9864 6973 7461 6c5f ts in....distal_\n-00016e70: 31e2 8099 2074 6f20 726f 7461 7465 2061 1... to rotate a\n-00016e80: 7320 6120 756e 6974 2e20 2054 6869 7320 s a unit. This \n-00016e90: 6973 2074 6865 2072 6561 736f 6e69 6e67 is the reasoning\n-00016ea0: 2062 6568 696e 6420 7468 6520 6e65 7874 behind the next\n-00016eb0: 0a64 6566 696e 6974 696f 6e2e 0a20 2064 .definition.. d\n-00016ec0: 6566 2066 696e 6765 725f 3120 7b0a 2020 ef finger_1 {. \n-00016ed0: 2020 7075 7420 7b20 7472 616e 736c 6174 put { translat\n-00016ee0: 6528 6a6f 696e 745f 6761 7020 2a20 6a6f e(joint_gap * jo\n-00016ef0: 696e 745f 7261 6420 2a20 5b4a 5d29 0a20 int_rad * [J]). \n-00016f00: 2020 2020 2020 2020 2074 6865 6e20 726f then ro\n-00016f10: 7461 7465 286d 6964 646c 655f 315f 726f tate(middle_1_ro\n-00016f20: 742c 205b 495d 290a 2020 2020 2020 2020 t, [I]). \n-00016f30: 2020 7468 656e 2074 7261 6e73 6c61 7465 then translate\n-00016f40: 2828 6d69 6464 6c65 5f72 6174 696f 202a ((middle_ratio *\n-00016f50: 2064 6973 7461 6c5f 6c65 6e20 2b20 0a20 distal_len + . \n+00012250: 2020 2041 6464 696e 6720 6120 626f 7820 Adding a box \n+00012260: 6172 6f75 6e64 2074 6865 2064 7261 7769 around the drawi\n+00012270: 6e67 2e0a 2a20 4c61 6e67 7561 6765 3a3a ng..* Language::\n+00012280: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00012290: 2020 2020 5365 7474 696e 6720 7468 6520 Setting the \n+000122a0: 6f75 7470 7574 206c 616e 6775 6167 652e output language.\n+000122b0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n+000122c0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 476c .info, Node: Gl\n+000122d0: 6f62 616c 206f 7074 696f 6e73 2c20 204e obal options, N\n+000122e0: 6578 743a 2043 616d 6572 612c 2020 5072 ext: Camera, Pr\n+000122f0: 6576 3a20 476c 6f62 616c 2065 6e76 6972 ev: Global envir\n+00012300: 6f6e 6d65 6e74 2c20 2055 703a 2047 6c6f onment, Up: Glo\n+00012310: 6261 6c20 656e 7669 726f 6e6d 656e 740a bal environment.\n+00012320: 0a33 2e34 2e31 2047 6c6f 6261 6c20 6f70 .3.4.1 Global op\n+00012330: 7469 6f6e 730a 2d2d 2d2d 2d2d 2d2d 2d2d tions.----------\n+00012340: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e ----------..*Syn\n+00012350: 7461 783a 2a0a 2020 2020 2073 6574 205b tax:*. set [\n+00012360: 204f 5054 494f 4e53 205d 0a54 6865 2063 OPTIONS ].The c\n+00012370: 6f6e 7465 6e74 7320 6f66 204f 5054 494f ontents of OPTIO\n+00012380: 4e53 2c20 6578 6365 7074 2066 6f72 20e2 NS, except for .\n+00012390: 8098 736b 6574 6368 e280 9920 696e 7465 ..sketch... inte\n+000123a0: 726e 616c 206f 7074 696f 6e73 2c20 6172 rnal options, ar\n+000123b0: 650a 636f 7069 6564 2061 732d 6973 2074 e.copied as-is t\n+000123c0: 6f20 6120 5c70 7373 6574 2074 6861 7420 o a \\psset that \n+000123d0: 6170 7065 6172 7320 6265 666f 7265 2061 appears before a\n+000123e0: 6e79 7468 696e 6720 656c 7365 2069 6e20 nything else in \n+000123f0: 7468 6520 6f75 7470 7574 0a66 696c 652e the output.file.\n+00012400: 2020 5468 6973 2069 7320 6120 676f 6f64 This is a good\n+00012410: 2070 6c61 6365 2074 6f20 7365 7420 e280 place to set ..\n+00012420: 9875 6e69 74e2 8099 2c20 6120 6465 6661 .unit..., a defa\n+00012430: 756c 7420 e280 986c 696e 6577 6964 7468 ult ...linewidth\n+00012440: e280 992c 2065 7463 2e0a 0a20 2020 496e ..., etc... In\n+00012450: 7465 726e 616c 206f 7074 696f 6e73 2077 ternal options w\n+00012460: 6f72 6b20 6f6e 2061 6c6c 206f 626a 6563 ork on all objec\n+00012470: 7473 2077 6865 7265 2074 6865 7920 6d61 ts where they ma\n+00012480: 6b65 2073 656e 7365 2e20 2054 6869 730a ke sense. This.\n+00012490: 696e 636c 7564 6573 20e2 8098 6375 6c6c includes ...cull\n+000124a0: e280 9920 616e 6420 e280 9873 706c 6974 ... and ...split\n+000124b0: e280 9920 2862 7574 206e 6f74 20e2 8098 ... (but not ...\n+000124c0: 6c61 79e2 8099 292e 2020 2a4e 6f74 6520 lay...). *Note \n+000124d0: 496e 7465 726e 616c 206f 7074 696f 6e73 Internal options\n+000124e0: 3a3a 2e0a 0a1f 0a46 696c 653a 2073 6b65 ::.....File: ske\n+000124f0: 7463 682e 696e 666f 2c20 204e 6f64 653a tch.info, Node:\n+00012500: 2043 616d 6572 612c 2020 4e65 7874 3a20 Camera, Next: \n+00012510: 5069 6374 7572 6520 626f 782c 2020 5072 Picture box, Pr\n+00012520: 6576 3a20 476c 6f62 616c 206f 7074 696f ev: Global optio\n+00012530: 6e73 2c20 2055 703a 2047 6c6f 6261 6c20 ns, Up: Global \n+00012540: 656e 7669 726f 6e6d 656e 740a 0a33 2e34 environment..3.4\n+00012550: 2e32 2043 616d 6572 610a 2d2d 2d2d 2d2d .2 Camera.------\n+00012560: 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 783a ------..*Syntax:\n+00012570: 2a0a 2020 2020 2063 616d 6572 6120 5452 *. camera TR\n+00012580: 414e 5346 4f52 4d5f 4558 5052 4553 5349 ANSFORM_EXPRESSI\n+00012590: 4f4e 0a20 2020 5468 6520 5452 414e 5346 ON. The TRANSF\n+000125a0: 4f52 4d5f 4558 5052 4553 5349 4f4e 2069 ORM_EXPRESSION i\n+000125b0: 7320 6170 706c 6965 6420 6166 7465 7220 s applied after \n+000125c0: 616c 6c20 6f74 6865 7220 7472 616e 7366 all other transf\n+000125d0: 6f72 6d61 7469 6f6e 730a 6f66 2074 6865 ormations.of the\n+000125e0: 2073 6365 6e65 2e20 2054 6869 7320 6973 scene. This is\n+000125f0: 2063 7572 7265 6e74 6c79 206f 6e6c 7920 currently only \n+00012600: 7573 6566 756c 2066 6f72 2074 7261 6e73 useful for trans\n+00012610: 666f 726d 696e 6720 7468 650a 626f 756e forming the.boun\n+00012620: 6469 6e67 2062 6f78 2e20 202a 4e6f 7465 ding box. *Note\n+00012630: 2050 6963 7475 7265 2062 6f78 3a3a 2e20 Picture box::. \n+00012640: 2049 7420 7769 6c6c 2070 6c61 7920 6120 It will play a \n+00012650: 726f 6c65 2069 6e20 616e 7920 6675 7475 role in any futu\n+00012660: 7265 0a69 6d70 6c65 6d65 6e74 6174 696f re.implementatio\n+00012670: 6e20 6f66 2063 6c69 7070 696e 672e 0a0a n of clipping...\n+00012680: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+00012690: 6e66 6f2c 2020 4e6f 6465 3a20 5069 6374 nfo, Node: Pict\n+000126a0: 7572 6520 626f 782c 2020 4e65 7874 3a20 ure box, Next: \n+000126b0: 4672 616d 652c 2020 5072 6576 3a20 4361 Frame, Prev: Ca\n+000126c0: 6d65 7261 2c20 2055 703a 2047 6c6f 6261 mera, Up: Globa\n+000126d0: 6c20 656e 7669 726f 6e6d 656e 740a 0a33 l environment..3\n+000126e0: 2e34 2e33 2050 6963 7475 7265 2062 6f78 .4.3 Picture box\n+000126f0: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d .---------------\n+00012700: 2d2d 0a0a 2a53 796e 7461 783a 2a0a 2020 --..*Syntax:*. \n+00012710: 2020 2070 6963 7475 7265 626f 785b 4241 picturebox[BA\n+00012720: 5345 4c49 4e45 5d0a 2020 2020 2070 6963 SELINE]. pic\n+00012730: 7475 7265 626f 785b 4241 5345 4c49 4e45 turebox[BASELINE\n+00012740: 5d20 2850 3129 2850 3229 0a54 6865 2066 ] (P1)(P2).The f\n+00012750: 6972 7374 2066 6f72 6d20 6f66 20e2 8098 irst form of ...\n+00012760: 7069 6374 7572 6562 6f78 e280 9920 6361 picturebox... ca\n+00012770: 7573 6573 2061 2073 6361 6c61 7220 4241 uses a scalar BA\n+00012780: 5345 4c49 4e45 2066 7261 6374 696f 6e20 SELINE fraction \n+00012790: 746f 2062 650a 656d 6974 7465 6420 696e to be.emitted in\n+000127a0: 2074 6865 20e2 8098 7073 7069 6374 7572 the ...pspictur\n+000127b0: 65e2 8099 2065 6e76 6972 6f6e 6d65 6e74 e... environment\n+000127c0: 206f 6620 7468 6520 6f75 7470 7574 2e20 of the output. \n+000127d0: 2053 6565 20e2 8098 5053 5472 6963 6b73 See ...PSTricks\n+000127e0: e280 990a 646f 6375 6d65 6e74 6174 696f ....documentatio\n+000127f0: 6e20 666f 7220 e280 9870 7370 6963 7475 n for ...pspictu\n+00012800: 7265 e280 992e 0a0a 2020 2049 6e20 7468 re...... In th\n+00012810: 6520 7365 636f 6e64 2066 6f72 6d2c 2074 e second form, t\n+00012820: 6865 2042 4153 454c 494e 4520 6672 6163 he BASELINE frac\n+00012830: 7469 6f6e 2069 7320 6f70 7469 6f6e 616c tion is optional\n+00012840: 2c20 616e 6420 7468 6520 7477 6f0a 706f , and the two.po\n+00012850: 696e 7473 2074 6861 7420 666f 6c6c 6f77 ints that follow\n+00012860: 2064 6566 696e 6520 7468 6520 6469 6167 define the diag\n+00012870: 6f6e 616c 206f 6620 6120 7468 7265 652d onal of a three-\n+00012880: 6469 6d65 6e73 696f 6e61 6c20 626f 756e dimensional boun\n+00012890: 6469 6e67 0a62 6f78 2066 6f72 2074 6865 ding.box for the\n+000128a0: 2063 6f6d 706c 6574 6564 2073 6365 6e65 completed scene\n+000128b0: 2e20 2054 6865 2070 6172 616c 6c65 6c20 . The parallel \n+000128c0: 7072 6f6a 6563 7469 6f6e 206f 6620 7468 projection of th\n+000128d0: 6520 626f 756e 6469 6e67 0a62 6f78 2064 e bounding.box d\n+000128e0: 6574 6572 6d69 6e65 7320 7468 6520 636f etermines the co\n+000128f0: 726e 6572 7320 6f66 2074 6865 2064 7261 rners of the dra\n+00012900: 7769 6e67 2773 20e2 8098 7073 7069 6374 wing's ...pspict\n+00012910: 7572 652a e280 9920 656e 7669 726f 6e6d ure*... environm\n+00012920: 656e 742c 0a77 6869 6368 2069 7320 7573 ent,.which is us\n+00012930: 6564 2069 6e20 706c 6163 6520 6f66 20e2 ed in place of .\n+00012940: 8098 7073 7069 6374 7572 65e2 8099 2e20 ..pspicture.... \n+00012950: 2054 6869 7320 6361 7573 6573 2050 6f73 This causes Pos\n+00012960: 7453 6372 6970 7420 746f 2063 6c69 700a tScript to clip.\n+00012970: 7468 6520 6669 6e61 6c20 6472 6177 696e the final drawin\n+00012980: 6720 746f 2074 6865 2062 6f75 6e64 696e g to the boundin\n+00012990: 6720 626f 7820 696e 2032 642e 2020 4966 g box in 2d. If\n+000129a0: 2074 6865 7265 2069 7320 6120 e280 9863 there is a ...c\n+000129b0: 616d 6572 61e2 8099 0a73 7065 6369 6669 amera....specifi\n+000129c0: 6564 2c20 7468 6520 6361 6d65 7261 2074 ed, the camera t\n+000129d0: 7261 6e66 6f72 6d61 7469 6f6e 2069 7320 ranformation is \n+000129e0: 6170 706c 6965 6420 746f 2074 6865 2062 applied to the b\n+000129f0: 6f75 6e64 696e 6720 626f 782c 2061 6e64 ounding box, and\n+00012a00: 0a74 6865 20e2 8098 7073 7069 6374 7572 .the ...pspictur\n+00012a10: 65e2 8099 2069 7320 7365 7420 6a75 7374 e... is set just\n+00012a20: 206c 6172 6765 2065 6e6f 7567 6820 746f large enough to\n+00012a30: 2069 6e63 6c75 6465 2074 6865 2074 7261 include the tra\n+00012a40: 6e73 666f 726d 6564 2062 6f78 2e0a 0a20 nsformed box... \n+00012a50: 2020 5768 656e 206e 6f20 626f 756e 6469 When no boundi\n+00012a60: 6e67 2062 6f78 2069 7320 6769 7665 6e2c ng box is given,\n+00012a70: 20e2 8098 736b 6574 6368 e280 9920 636f ...sketch... co\n+00012a80: 6d70 7574 6573 206f 6e65 2061 7574 6f6d mputes one autom\n+00012a90: 6174 6963 616c 6c79 2e0a 0a1f 0a46 696c atically.....Fil\n+00012aa0: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n+00012ab0: 204e 6f64 653a 2046 7261 6d65 2c20 204e Node: Frame, N\n+00012ac0: 6578 743a 204c 616e 6775 6167 652c 2020 ext: Language, \n+00012ad0: 5072 6576 3a20 5069 6374 7572 6520 626f Prev: Picture bo\n+00012ae0: 782c 2020 5570 3a20 476c 6f62 616c 2065 x, Up: Global e\n+00012af0: 6e76 6972 6f6e 6d65 6e74 0a0a 332e 342e nvironment..3.4.\n+00012b00: 3420 4672 616d 650a 2d2d 2d2d 2d2d 2d2d 4 Frame.--------\n+00012b10: 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a 0a20 ---..*Syntax:*. \n+00012b20: 2020 2020 6672 616d 6520 5b4f 5054 494f frame [OPTIO\n+00012b30: 4e53 5d0a 4361 7573 6573 2061 205c 7073 NS].Causes a \\ps\n+00012b40: 6672 616d 6562 6f78 2074 6f20 7375 7272 framebox to surr\n+00012b50: 6f75 6e64 2074 6865 20e2 8098 7073 7069 ound the ...pspi\n+00012b60: 6374 7572 65e2 8099 2065 6e76 6972 6f6e cture... environ\n+00012b70: 6d65 6e74 2069 6e20 7468 650a 6f75 7470 ment in the.outp\n+00012b80: 7574 2e20 2049 6620 4f50 5449 4f4e 5320 ut. If OPTIONS \n+00012b90: 6172 6520 7072 6573 656e 742c 2074 6865 are present, the\n+00012ba0: 7920 6172 6520 636f 7069 6564 2061 732d y are copied as-\n+00012bb0: 6973 2e20 204e 6f72 6d61 6c6c 7920 6f6e is. Normally on\n+00012bc0: 650a 776f 756c 6420 7761 6e74 2074 6f20 e.would want to \n+00012bd0: 7365 7420 e280 986c 696e 6577 6964 7468 set ...linewidth\n+00012be0: e280 992c 20e2 8098 6c69 6e65 7374 796c ..., ...linestyl\n+00012bf0: 65e2 8099 2c20 e280 986c 696e 6563 6f6c e..., ...linecol\n+00012c00: 6f72 e280 992c 2065 7463 2e20 2049 660a or..., etc. If.\n+00012c10: 6f6d 6974 7465 642c 2074 6865 6e20 e280 omitted, then ..\n+00012c20: 9866 7261 6d65 7365 703d 3070 74e2 8099 .framesep=0pt...\n+00012c30: 2069 7320 6164 6465 6420 736f 2074 6861 is added so tha\n+00012c40: 7420 7468 6520 6672 616d 6520 7469 6768 t the frame tigh\n+00012c50: 746c 7920 6875 6773 2074 6865 0ae2 8098 tly hugs the....\n+00012c60: 7073 7069 6374 7572 65e2 8099 2e0a 0a1f pspicture.......\n+00012c70: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+00012c80: 666f 2c20 204e 6f64 653a 204c 616e 6775 fo, Node: Langu\n+00012c90: 6167 652c 2020 5072 6576 3a20 4672 616d age, Prev: Fram\n+00012ca0: 652c 2020 5570 3a20 476c 6f62 616c 2065 e, Up: Global e\n+00012cb0: 6e76 6972 6f6e 6d65 6e74 0a0a 332e 342e nvironment..3.4.\n+00012cc0: 3520 4c61 6e67 7561 6765 0a2d 2d2d 2d2d 5 Language.-----\n+00012cd0: 2d2d 2d2d 2d2d 2d2d 2d0a 0a20 2020 2020 ---------.. \n+00012ce0: 6c61 6e67 7561 6765 2074 696b 7a0a 2020 language tikz. \n+00012cf0: 2020 206c 616e 6775 6167 6520 7469 6b7a language tikz\n+00012d00: 2c20 636f 6e74 6578 740a 2020 2020 206c , context. l\n+00012d10: 616e 6775 6167 6520 7073 7472 6963 6b73 anguage pstricks\n+00012d20: 0a20 2020 2020 6c61 6e67 7561 6765 2070 . language p\n+00012d30: 7374 7269 636b 732c 206c 6174 6578 0a53 stricks, latex.S\n+00012d40: 6574 7320 7468 6520 6f75 7470 7574 206c ets the output l\n+00012d50: 616e 6775 6167 6520 6765 6e65 7261 7465 anguage generate\n+00012d60: 6420 6279 20e2 8098 736b 6574 6368 e280 d by ...sketch..\n+00012d70: 992e 2020 5468 6520 7365 7420 6f66 206f .. The set of o\n+00012d80: 7074 696f 6e73 0a75 6e64 6572 7374 6f6f ptions.understoo\n+00012d90: 6420 6279 2073 6b65 7463 6820 616c 736f d by sketch also\n+00012da0: 2063 6861 6e67 6573 2e20 2046 6f72 2065 changes. For e\n+00012db0: 7861 6d70 6c65 2c20 7468 6520 e280 9850 xample, the ...P\n+00012dc0: 5354 7269 636b 73e2 8099 206f 7074 696f STricks... optio\n+00012dd0: 6e0a e280 986c 696e 6577 6964 7468 e280 n....linewidth..\n+00012de0: 9920 7769 6c6c 206e 6f74 2062 6520 7072 . will not be pr\n+00012df0: 6f70 6572 6c79 2068 616e 646c 6564 2069 operly handled i\n+00012e00: 6620 e280 986c 616e 6775 6167 65e2 8099 f ...language...\n+00012e10: 2069 7320 7365 7420 746f 20e2 8098 7469 is set to ...ti\n+00012e20: 6b7a e280 992e 0a53 696d 696c 6172 6c79 kz.....Similarly\n+00012e30: 2c20 7468 6520 e280 9854 696b 5ae2 8099 , the ...TikZ...\n+00012e40: 206f 7074 696f 6e20 e280 986c 696e 6520 option ...line \n+00012e50: 7374 796c 65e2 8099 2028 6e6f 7465 2074 style... (note t\n+00012e60: 6865 2073 7061 6365 2920 7769 6c6c 206e he space) will n\n+00012e70: 6f74 2062 650a 7072 6f70 6572 6c79 2068 ot be.properly h\n+00012e80: 616e 646c 6564 2069 6620 e280 986c 616e andled if ...lan\n+00012e90: 6775 6167 65e2 8099 2069 7320 7365 7420 guage... is set \n+00012ea0: 746f 20e2 8098 7073 7472 6963 6b73 e280 to ...pstricks..\n+00012eb0: 992e 2020 4966 206e 6f20 6c61 6e67 7561 .. If no langua\n+00012ec0: 6765 2069 730a 7370 6563 6966 6965 642c ge is.specified,\n+00012ed0: 2074 6865 2064 6566 6175 6c74 20e2 8098 the default ...\n+00012ee0: 7073 7472 6963 6b73 e280 9920 6973 2075 pstricks... is u\n+00012ef0: 7365 642e 0a0a 2020 2041 6e20 6f70 7469 sed... An opti\n+00012f00: 6f6e 616c 2063 6f6d 6d61 2066 6f6c 6c6f onal comma follo\n+00012f10: 7765 6420 6279 20e2 8098 6c61 7465 78e2 wed by ...latex.\n+00012f20: 8099 206f 7220 e280 9863 6f6e 7465 7874 .. or ...context\n+00012f30: e280 9920 7370 6563 6966 6965 7320 7468 ... specifies th\n+00012f40: 650a 6d61 6372 6f20 7061 636b 6167 6520 e.macro package \n+00012f50: 7468 6174 2074 6865 206f 7574 7075 7420 that the output \n+00012f60: 7368 6f75 6c64 2061 7373 756d 652e 2020 should assume. \n+00012f70: 5468 6973 2061 6666 6563 7473 2074 6865 This affects the\n+00012f80: 20e2 8098 7069 6374 7572 65e2 8099 0a65 ...picture....e\n+00012f90: 6e76 6972 6f6e 6d65 6e74 2063 6f6d 6d61 nvironment comma\n+00012fa0: 6e64 7320 656d 6974 7465 6420 616e 6420 nds emitted and \n+00012fb0: 7468 6520 646f 6375 6d65 6e74 2074 656d the document tem\n+00012fc0: 706c 6174 6520 7573 6564 2077 6974 6820 plate used with \n+00012fd0: 7468 650a e280 982d 54e2 8099 206f 7074 the....-T... opt\n+00012fe0: 696f 6e2e 2020 2a4e 6f74 6520 436f 6d6d ion. *Note Comm\n+00012ff0: 616e 6420 6c69 6e65 3a3a 2e20 204e 6f74 and line::. Not\n+00013000: 6520 7468 6174 2061 7420 7468 6520 7469 e that at the ti\n+00013010: 6d65 2074 6869 7320 6d61 6e75 616c 0a77 me this manual.w\n+00013020: 6173 2067 656e 6572 6174 6564 2c20 e280 as generated, ..\n+00013030: 9850 5354 7269 636b 73e2 8099 2077 6173 .PSTricks... was\n+00013040: 206e 6f74 2073 7570 706f 7274 6564 2062 not supported b\n+00013050: 7920 4c61 5465 5820 6f72 2062 7920 e280 y LaTeX or by ..\n+00013060: 9843 6f6e 5465 5874 e280 992e 0a0a 1f0a .ConTeXt........\n+00013070: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n+00013080: 6f2c 2020 4e6f 6465 3a20 4275 696c 6469 o, Node: Buildi\n+00013090: 6e67 2061 2064 7261 7769 6e67 2c20 204e ng a drawing, N\n+000130a0: 6578 743a 2043 6f6d 6d61 6e64 206c 696e ext: Command lin\n+000130b0: 652c 2020 5072 6576 3a20 496e 7075 7420 e, Prev: Input \n+000130c0: 6c61 6e67 7561 6765 2c20 2055 703a 2054 language, Up: T\n+000130d0: 6f70 0a0a 3420 4275 696c 6469 6e67 2061 op..4 Building a\n+000130e0: 2064 7261 7769 6e67 0a2a 2a2a 2a2a 2a2a drawing.*******\n+000130f0: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a0a 0a53 *************..S\n+00013100: 7563 6365 7373 6675 6c20 6472 6177 696e uccessful drawin\n+00013110: 6773 2077 6974 6820 e280 9873 6b65 7463 gs with ...sketc\n+00013120: 68e2 8099 2061 6e64 2077 6974 6820 616e h... and with an\n+00013130: 7920 7363 656e 6520 6465 7363 7269 7074 y scene descript\n+00013140: 696f 6e0a 6c61 6e67 7561 6765 2072 6571 ion.language req\n+00013150: 7569 7265 2074 6861 7420 7468 6520 7573 uire that the us\n+00013160: 6572 2064 6576 656c 6f70 2061 6e20 6163 er develop an ac\n+00013170: 6375 7261 7465 206d 656e 7461 6c20 7069 curate mental pi\n+00013180: 6374 7572 6520 6f66 2068 6572 0a63 6f64 cture of her.cod\n+00013190: 6520 616e 6420 6974 7320 6d65 616e 696e e and its meanin\n+000131a0: 672e 2020 5468 6973 2069 6d61 6765 2069 g. This image i\n+000131b0: 7320 6265 7374 2062 7569 6c74 2069 6e20 s best built in \n+000131c0: 736d 616c 6c20 7069 6563 6573 2e0a 5468 small pieces..Th\n+000131d0: 6572 6566 6f72 652c 20e2 8098 736b 6574 erefore, ...sket\n+000131e0: 6368 e280 9920 696e 7075 7473 2061 7265 ch... inputs are\n+000131f0: 2062 6573 7420 6372 6561 7465 6420 696e best created in\n+00013200: 2073 6d61 6c6c 2069 6e63 7265 6d65 6e74 small increment\n+00013210: 7320 7769 7468 0a66 7265 7175 656e 7420 s with.frequent \n+00013220: 7061 7573 6573 2074 6f20 636f 6d70 696c pauses to compil\n+00013230: 6520 616e 6420 7669 6577 2074 6865 2072 e and view the r\n+00013240: 6573 756c 7473 2e20 2043 6172 6566 756c esults. Careful\n+00013250: 2063 6f6d 6d65 6e74 7320 696e 0a74 6865 comments in.the\n+00013260: 2069 6e70 7574 206f 6674 656e 2068 656c input often hel\n+00013270: 7020 6173 2061 2073 6365 6e65 2067 726f p as a scene gro\n+00013280: 7773 2069 6e20 636f 6d70 6c65 7869 7479 ws in complexity\n+00013290: 2e0a 0a2a 204d 656e 753a 0a0a 2a20 4f76 ...* Menu:..* Ov\n+000132a0: 6572 7669 6577 3a3a 2020 2020 2020 2020 erview:: \n+000132b0: 2020 2020 2020 2020 2020 2020 4275 696c Buil\n+000132c0: 6469 6e67 2061 2073 7562 7374 616e 7469 ding a substanti\n+000132d0: 616c 2064 7261 7769 6e67 2e0a 2a20 4120 al drawing..* A \n+000132e0: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n+000132f0: 673a 3a20 2020 2020 2020 2020 416e 2065 g:: An e\n+00013300: 7861 6d70 6c65 2077 6974 6820 6669 6e65 xample with fine\n+00013310: 2070 6c61 6365 6d65 6e74 2e0a 2a20 4120 placement..* A \n+00013320: 6869 6572 6172 6368 6963 616c 206d 6f64 hierarchical mod\n+00013330: 656c 3a3a 2020 2020 2020 2020 416e 2065 el:: An e\n+00013340: 7861 6d70 6c65 2077 6974 6820 7377 6565 xample with swee\n+00013350: 7073 2061 6e64 2070 7574 732e 0a2a 2043 ps and puts..* C\n+00013360: 6176 6561 7473 3a3a 2020 2020 2020 2020 aveats:: \n+00013370: 2020 2020 2020 2020 2020 2020 2057 6865 Whe\n+00013380: 7265 2074 726f 7562 6c65 2063 616e 206f re trouble can o\n+00013390: 6363 7572 2e0a 0a1f 0a46 696c 653a 2073 ccur.....File: s\n+000133a0: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+000133b0: 653a 204f 7665 7276 6965 772c 2020 4e65 e: Overview, Ne\n+000133c0: 7874 3a20 4120 7465 6368 6e69 6361 6c20 xt: A technical \n+000133d0: 6472 6177 696e 672c 2020 5072 6576 3a20 drawing, Prev: \n+000133e0: 4275 696c 6469 6e67 2061 2064 7261 7769 Building a drawi\n+000133f0: 6e67 2c20 2055 703a 2042 7569 6c64 696e ng, Up: Buildin\n+00013400: 6720 6120 6472 6177 696e 670a 0a34 2e31 g a drawing..4.1\n+00013410: 204f 7665 7276 6965 770a 3d3d 3d3d 3d3d Overview.======\n+00013420: 3d3d 3d3d 3d3d 0a0a 4173 2061 6e20 6f76 ======..As an ov\n+00013430: 6572 7669 6577 2c20 6c65 7427 7320 6465 erview, let's de\n+00013440: 7665 6c6f 7020 6120 6469 6167 7261 6d20 velop a diagram \n+00013450: 7468 6174 2073 686f 7773 2068 6f77 2061 that shows how a\n+00013460: 2070 6572 7370 6563 7469 7665 0a70 726f perspective.pro\n+00013470: 6a65 6374 696f 6e20 7472 616e 7366 6f72 jection transfor\n+00013480: 6d20 776f 726b 732e 2020 5765 276c 6c20 m works. We'll \n+00013490: 7374 6172 7420 7769 7468 2074 6865 2074 start with the t\n+000134a0: 7261 6469 7469 6f6e 616c 2072 6566 6572 raditional refer\n+000134b0: 656e 6365 0a6f 626a 6563 7420 7573 6564 ence.object used\n+000134c0: 2069 6e20 636f 6d70 7574 6572 2067 7261 in computer gra\n+000134d0: 7068 6963 7320 7465 7874 626f 6f6b 732c phics textbooks,\n+000134e0: 2061 2068 6f75 7365 2d73 6861 7065 6420 a house-shaped \n+000134f0: 7072 6973 6d2e 2020 4265 6769 6e0a 6279 prism. Begin.by\n+00013500: 2064 6566 696e 696e 6720 7468 6520 706f defining the po\n+00013510: 696e 7473 206f 6620 7468 6520 686f 7573 ints of the hous\n+00013520: 652e 2020 5261 7468 6572 2074 6861 6e20 e. Rather than \n+00013530: 6465 6669 6e69 6e67 2074 6865 2066 6163 defining the fac\n+00013540: 6573 206f 660a 7468 6520 686f 7573 6520 es of.the house \n+00013550: 6173 2070 6f6c 7967 6f6e 7320 616e 6420 as polygons and \n+00013560: 7472 616e 7366 6f72 6d69 6e67 2074 686f transforming tho\n+00013570: 7365 2c20 7765 2061 7265 2067 6f69 6e67 se, we are going\n+00013580: 2074 6f20 7472 616e 7366 6f72 6d0a 7468 to transform.th\n+00013590: 6520 706f 696e 7473 2074 6865 6d73 656c e points themsel\n+000135a0: 7665 7320 7769 7468 20e2 8098 736b 6574 ves with ...sket\n+000135b0: 6368 e280 9920 6172 6974 686d 6574 6963 ch... arithmetic\n+000135c0: 2073 6f20 7468 6174 2077 6520 6861 7665 so that we have\n+000135d0: 206e 616d 6573 2066 6f72 0a74 6865 2074 names for.the t\n+000135e0: 7261 6e73 666f 726d 6564 2070 6f69 6e74 ransformed point\n+000135f0: 7320 6c61 7465 722e 0a20 2025 2072 6967 s later.. % rig\n+00013600: 6874 2073 6964 6520 286f 7574 7369 6465 ht side (outside\n+00013610: 2074 6f20 7269 6768 7429 0a20 2064 6566 to right). def\n+00013620: 2052 3120 2831 2c31 2c31 2920 6465 6620 R1 (1,1,1) def \n+00013630: 5232 2028 312c 2d31 2c31 2920 6465 6620 R2 (1,-1,1) def \n+00013640: 5233 2028 312c 2d31 2c2d 3129 2064 6566 R3 (1,-1,-1) def\n+00013650: 2052 3420 2831 2c31 2c2d 3129 0a20 2064 R4 (1,1,-1). d\n+00013660: 6566 2052 3520 2831 2c31 2e35 2c30 290a ef R5 (1,1.5,0).\n+00013670: 0a20 2025 206c 6566 7420 7369 6465 2028 . % left side (\n+00013680: 6f75 7473 6964 6520 746f 2072 6967 6874 outside to right\n+00013690: 2d2d 6261 636b 7761 7264 290a 2020 6465 --backward). de\n+000136a0: 6620 5720 205b 322c 302c 305d 0a20 2064 f W [2,0,0]. d\n+000136b0: 6566 204c 3120 2852 3129 2d5b 575d 2064 ef L1 (R1)-[W] d\n+000136c0: 6566 204c 3220 2852 3229 2d5b 575d 2064 ef L2 (R2)-[W] d\n+000136d0: 6566 204c 3320 2852 3329 2d5b 575d 2064 ef L3 (R3)-[W] d\n+000136e0: 6566 204c 3420 2852 3429 2d5b 575d 0a20 ef L4 (R4)-[W]. \n+000136f0: 2064 6566 204c 3520 2852 3529 2d5b 575d def L5 (R5)-[W]\n+00013700: 0a54 6f20 6164 6420 6120 646f 6f72 2074 .To add a door t\n+00013710: 6f20 7468 6520 686f 7573 652c 2077 6520 o the house, we \n+00013720: 7573 6520 6120 706f 6c79 676f 6e20 736c use a polygon sl\n+00013730: 6967 6874 6c79 2069 6e20 6672 6f6e 7420 ightly in front \n+00013740: 6f66 2074 6865 0a66 6f72 656d 6f73 7420 of the.foremost \n+00013750: 6661 6365 206f 6620 7468 6520 686f 7573 face of the hous\n+00013760: 652e 0a20 2025 2064 6f6f 720a 2020 6465 e.. % door. de\n+00013770: 6620 6520 2e30 310a 2020 6465 6620 4431 f e .01. def D1\n+00013780: 2028 302c 2d31 2c31 2b65 2920 6465 6620 (0,-1,1+e) def \n+00013790: 4432 2028 2e35 2c2d 312c 312b 6529 2064 D2 (.5,-1,1+e) d\n+000137a0: 6566 2044 3320 282e 352c 302c 312b 6529 ef D3 (.5,0,1+e)\n+000137b0: 2064 6566 2044 3420 2830 2c30 2c31 2b65 def D4 (0,0,1+e\n+000137c0: 290a 4e6f 7720 6c65 7427 7320 6372 6561 ).Now let's crea\n+000137d0: 7465 2061 206e 6577 2073 6574 206f 6620 te a new set of \n+000137e0: 706f 696e 7473 2074 6861 7420 6172 6520 points that are \n+000137f0: 6120 746f 2d62 652d 6465 7465 726d 696e a to-be-determin\n+00013800: 6564 0a74 7261 6e73 666f 726d 206f 6620 ed.transform of \n+00013810: 7468 6520 6f72 6967 696e 616c 732e 0a20 the originals.. \n+00013820: 2064 6566 2068 7020 7363 616c 6528 3129 def hp scale(1)\n+00013830: 2025 2068 6f75 7365 2070 6f73 6974 696f % house positio\n+00013840: 6e65 720a 2020 6465 6620 7052 3120 5b5b ner. def pR1 [[\n+00013850: 6870 5d5d 2a28 5231 2920 6465 6620 7052 hp]]*(R1) def pR\n+00013860: 3220 5b5b 6870 5d5d 2a28 5232 2920 6465 2 [[hp]]*(R2) de\n+00013870: 6620 7052 3320 5b5b 6870 5d5d 2a28 5233 f pR3 [[hp]]*(R3\n+00013880: 290a 2020 6465 6620 7052 3420 5b5b 6870 ). def pR4 [[hp\n+00013890: 5d5d 2a28 5234 2920 6465 6620 7052 3520 ]]*(R4) def pR5 \n+000138a0: 5b5b 6870 5d5d 2a28 5235 290a 2020 6465 [[hp]]*(R5). de\n+000138b0: 6620 704c 3120 5b5b 6870 5d5d 2a28 4c31 f pL1 [[hp]]*(L1\n+000138c0: 2920 6465 6620 704c 3220 5b5b 6870 5d5d ) def pL2 [[hp]]\n+000138d0: 2a28 4c32 2920 6465 6620 704c 3320 5b5b *(L2) def pL3 [[\n+000138e0: 6870 5d5d 2a28 4c33 290a 2020 6465 6620 hp]]*(L3). def \n+000138f0: 704c 3420 5b5b 6870 5d5d 2a28 4c34 2920 pL4 [[hp]]*(L4) \n+00013900: 6465 6620 704c 3520 5b5b 6870 5d5d 2a28 def pL5 [[hp]]*(\n+00013910: 4c35 290a 2020 6465 6620 7044 3120 5b5b L5). def pD1 [[\n+00013920: 6870 5d5d 2a28 4431 2920 6465 6620 7044 hp]]*(D1) def pD\n+00013930: 3220 5b5b 6870 5d5d 2a28 4432 2920 6465 2 [[hp]]*(D2) de\n+00013940: 6620 7044 3320 5b5b 6870 5d5d 2a28 4433 f pD3 [[hp]]*(D3\n+00013950: 290a 2020 6465 6620 7044 3420 5b5b 6870 ). def pD4 [[hp\n+00013960: 5d5d 2a28 4434 2920 0a4e 6f74 6520 7468 ]]*(D4) .Note th\n+00013970: 6520 7573 6520 6f66 2061 20e2 809c 7472 e use of a ...tr\n+00013980: 616e 7366 6f72 6d20 6465 6669 6e69 7469 ansform definiti\n+00013990: 6f6e e280 9d20 616e 6420 e280 9c74 7261 on... and ...tra\n+000139a0: 6e73 666f 726d 2072 6566 6572 656e 6365 nsform reference\n+000139b0: 73e2 809d 2e0a 4e6f 7720 6465 6669 6e65 s.....Now define\n+000139c0: 2074 6865 2073 6576 656e 2070 6f6c 7967 the seven polyg\n+000139d0: 6f6e 616c 2066 6163 6573 206f 6620 7468 onal faces of th\n+000139e0: 6520 686f 7573 6520 616e 6420 7468 6520 e house and the \n+000139f0: 646f 6f72 2075 7369 6e67 2074 6865 0a74 door using the.t\n+00013a00: 7261 6e73 666f 726d 6564 2070 6f69 6e74 ransformed point\n+00013a10: 7320 6173 2076 6572 7469 6365 732e 2020 s as vertices. \n+00013a20: 4265 2063 6172 6566 756c 2077 6974 6820 Be careful with \n+00013a30: 7665 7274 6578 206f 7264 6572 210a 2020 vertex order!. \n+00013a40: 6465 6620 7267 7420 706f 6c79 676f 6e20 def rgt polygon \n+00013a50: 2870 5231 2928 7052 3229 2870 5233 2928 (pR1)(pR2)(pR3)(\n+00013a60: 7052 3429 2870 5235 290a 2020 6465 6620 pR4)(pR5). def \n+00013a70: 6c66 7420 706f 6c79 676f 6e20 2870 4c35 lft polygon (pL5\n+00013a80: 2928 704c 3429 2870 4c33 2928 704c 3229 )(pL4)(pL3)(pL2)\n+00013a90: 2870 4c31 290a 2020 6465 6620 6672 7420 (pL1). def frt \n+00013aa0: 706f 6c79 676f 6e20 2870 5232 2928 7052 polygon (pR2)(pR\n+00013ab0: 3129 2870 4c31 2928 704c 3229 0a20 2064 1)(pL1)(pL2). d\n+00013ac0: 6566 2062 636b 2070 6f6c 7967 6f6e 2028 ef bck polygon (\n+00013ad0: 7052 3429 2870 5233 2928 704c 3329 2870 pR4)(pR3)(pL3)(p\n+00013ae0: 4c34 290a 2020 6465 6620 7466 7220 706f L4). def tfr po\n+00013af0: 6c79 676f 6e20 2870 5231 2928 7052 3529 lygon (pR1)(pR5)\n+00013b00: 2870 4c35 2928 704c 3129 0a20 2064 6566 (pL5)(pL1). def\n+00013b10: 2074 626b 2070 6f6c 7967 6f6e 2028 7052 tbk polygon (pR\n+00013b20: 3529 2870 5234 2928 704c 3429 2870 4c35 5)(pR4)(pL4)(pL5\n+00013b30: 290a 2020 6465 6620 626f 7420 706f 6c79 ). def bot poly\n+00013b40: 676f 6e20 2870 5232 2928 704c 3229 2870 gon (pR2)(pL2)(p\n+00013b50: 4c33 2928 7052 3329 0a20 2064 6566 2064 L3)(pR3). def d\n+00013b60: 6f6f 7220 706f 6c79 676f 6e5b 6669 6c6c oor polygon[fill\n+00013b70: 636f 6c6f 723d 6272 6f77 6e5d 2028 7044 color=brown] (pD\n+00013b80: 3129 2870 4432 2928 7044 3329 2870 4434 1)(pD2)(pD3)(pD4\n+00013b90: 290a 2020 6465 6620 686f 7573 6520 7b20 ). def house { \n+00013ba0: 7b72 6774 7d7b 6c66 747d 7b66 7274 7d7b {rgt}{lft}{frt}{\n+00013bb0: 6263 6b7d 7b74 6672 7d7b 7462 6b7d 7b62 bck}{tfr}{tbk}{b\n+00013bc0: 6f74 7d7b 646f 6f72 7d20 7d0a 2020 2054 ot}{door} }. T\n+00013bd0: 696d 6520 666f 7220 6120 7361 6e69 7479 ime for a sanity\n+00013be0: 2063 6865 636b 2e20 2041 6464 2074 6865 check. Add the\n+00013bf0: 206c 696e 650a 2020 7b68 6f75 7365 7d0a line. {house}.\n+00013c00: 616e 6420 7468 6973 2069 7320 7768 6174 and this is what\n+00013c10: 2077 6520 6765 742e 0a0a 0008 5b69 6d61 we get.....[ima\n+00013c20: 6765 2073 7263 3d22 6578 3133 302e 706e ge src=\"ex130.pn\n+00013c30: 6722 2074 6578 743d 2249 6d61 6765 2065 g\" text=\"Image e\n+00013c40: 7831 3330 206f 6d69 7474 6564 2069 6e20 x130 omitted in \n+00013c50: 7465 7874 2076 6572 7369 6f6e 206f 6620 text version of \n+00013c60: 7468 6973 2064 6f63 756d 656e 742e 2200 this document.\".\n+00013c70: 085d 0a0a 5468 6973 2069 7320 636f 7272 .]..This is corr\n+00013c80: 6563 742c 2062 7574 2064 6f65 7320 6e6f ect, but does no\n+00013c90: 7420 7265 7665 616c 2076 6572 7920 6d75 t reveal very mu\n+00013ca0: 6368 2e20 2043 6f6d 6d6f 6e20 6572 726f ch. Common erro\n+00013cb0: 7273 2061 7265 0a6d 6973 706c 6163 6564 rs are.misplaced\n+00013cc0: 2076 6572 7469 6365 7320 616e 6420 706f vertices and po\n+00013cd0: 6c79 676f 6e73 206d 6973 7369 6e67 2065 lygons missing e\n+00013ce0: 6e74 6972 656c 7920 6475 6520 746f 2069 ntirely due to i\n+00013cf0: 6e63 6f72 7265 6374 2076 6572 7465 780a ncorrect vertex.\n+00013d00: 6f72 6465 722e 2020 546f 2072 756c 6520 order. To rule \n+00013d10: 7468 6573 6520 6f75 742c 206c 6574 2773 these out, let's\n+00013d20: 2069 6e73 7065 6374 2061 6c6c 2073 6964 inspect all sid\n+00013d30: 6573 206f 6620 7468 6520 686f 7573 652e es of the house.\n+00013d40: 2020 5468 6973 0a69 7320 6e6f 7420 6861 This.is not ha\n+00013d50: 7264 2e20 204d 6572 656c 7920 7265 706c rd. Merely repl\n+00013d60: 6163 6520 7468 6520 7265 6665 7265 6e63 ace the referenc\n+00013d70: 6520 7b68 6f75 7365 7d20 7769 7468 2061 e {house} with a\n+00013d80: 20e2 8098 7265 7065 6174 e280 992e 0a2a ...repeat.....*\n+00013d90: 4e6f 7465 2052 6570 6561 7473 3a3a 2e0a Note Repeats::..\n+00013da0: 2020 7265 7065 6174 207b 2031 332c 2072 repeat { 13, r\n+00013db0: 6f74 6174 6528 3330 2c20 5b31 2c32 2c33 otate(30, [1,2,3\n+00013dc0: 5d29 2c20 7472 616e 736c 6174 6528 5b33 ]), translate([3\n+00013dd0: 2c30 2c30 5d29 207d 207b 686f 7573 657d ,0,0]) } {house}\n+00013de0: 0a00 085b 696d 6167 6520 7372 633d 2265 ...[image src=\"e\n+00013df0: 7831 3430 2e70 6e67 2220 7465 7874 3d22 x140.png\" text=\"\n+00013e00: 496d 6167 6520 6578 3134 3020 6f6d 6974 Image ex140 omit\n+00013e10: 7465 6420 696e 2074 6578 7420 7665 7273 ted in text vers\n+00013e20: 696f 6e20 6f66 2074 6869 7320 646f 6375 ion of this docu\n+00013e30: 6d65 6e74 2e22 0008 5d0a 0a41 6761 696e ment.\"..]..Again\n+00013e40: 2074 6869 6e67 7320 6c6f 6f6b 2063 6f72 things look cor\n+00013e50: 7265 6374 2e20 204e 6f74 6520 7468 6174 rect. Note that\n+00013e60: 2074 6865 2068 6964 6465 6e20 7375 7266 the hidden surf\n+00013e70: 6163 6520 616c 676f 7269 7468 6d0a 6861 ace algorithm.ha\n+00013e80: 6e64 6c65 7320 696e 7465 7273 6563 7469 ndles intersecti\n+00013e90: 6e67 2070 6f6c 7967 6f6e 7320 636f 7272 ng polygons corr\n+00013ea0: 6563 746c 7920 7768 6572 6520 736f 6d65 ectly where some\n+00013eb0: 2063 6f70 6965 7320 6f66 2074 6865 2068 copies of the h\n+00013ec0: 6f75 7365 0a6f 7665 726c 6170 2e0a 0a20 ouse.overlap... \n+00013ed0: 2020 4c65 7427 7320 6c61 7920 6f75 7420 Let's lay out \n+00013ee0: 7468 6520 6765 6f6d 6574 7279 206f 6620 the geometry of \n+00013ef0: 7065 7273 7065 6374 6976 6520 7072 6f6a perspective proj\n+00013f00: 6563 7469 6f6e 206f 6620 7468 6520 686f ection of the ho\n+00013f10: 7573 650a 6f6e 746f 2061 2070 6c61 6e65 use.onto a plane\n+00013f20: 2077 6974 6820 7261 7973 2070 6173 7369 with rays passi\n+00013f30: 6e67 2074 6872 6f75 6768 2074 6865 206f ng through the o\n+00013f40: 7269 6769 6e2e 2020 4265 6769 6e20 6279 rigin. Begin by\n+00013f50: 2070 6f73 6974 696f 6e69 6e67 0a74 6865 positioning.the\n+00013f60: 2068 6f75 7365 2074 7765 6c76 6520 756e house twelve un\n+00013f70: 6974 7320 6261 636b 206f 6e20 7468 6520 its back on the \n+00013f80: 6e65 6761 7469 7665 207a 2d61 7869 7320 negative z-axis \n+00013f90: 616e 6420 6164 6469 6e67 2061 2073 6574 and adding a set\n+00013fa0: 206f 660a 636f 6f72 6469 6e61 7465 2061 of.coordinate a\n+00013fb0: 7865 732e 2020 546f 206d 6f76 6520 7468 xes. To move th\n+00013fc0: 6520 686f 7573 6520 7765 206e 6565 6420 e house we need \n+00013fd0: 6f6e 6c79 2063 6861 6e67 6520 7468 6520 only change the \n+00013fe0: 2268 6f75 7365 0a70 6f73 6974 696f 6e69 \"house.positioni\n+00013ff0: 6e67 2220 7472 616e 7366 6f72 6d20 6465 ng\" transform de\n+00014000: 6669 6e65 6420 6561 726c 6965 722e 0a20 fined earlier.. \n+00014010: 2064 6566 2068 7020 726f 7461 7465 282d def hp rotate(-\n+00014020: 3430 2c20 5b30 2c31 2c30 5d29 2074 6865 40, [0,1,0]) the\n+00014030: 6e20 7472 616e 736c 6174 6528 5b30 2c30 n translate([0,0\n+00014040: 2c2d 3132 5d29 0a20 2064 6566 2061 7865 ,-12]). def axe\n+00014050: 7320 7b0a 2020 2020 6465 6620 737a 2031 s {. def sz 1\n+00014060: 0a20 2020 206c 696e 6520 5b61 7272 6f77 . line [arrow\n+00014070: 733d 3c2d 3e5d 2028 737a 2c30 2c30 2928 s=<->] (sz,0,0)(\n+00014080: 4f29 2830 2c73 7a2c 3029 0a20 2020 206c O)(0,sz,0). l\n+00014090: 696e 6520 5b61 7272 6f77 733d 2d3e 5d20 ine [arrows=->] \n+000140a0: 2028 4f29 2830 2c30 2c73 7a29 0a20 2020 (O)(0,0,sz). \n+000140b0: 206c 696e 6520 5b6c 696e 6577 6964 7468 line [linewidth\n+000140c0: 3d2e 3270 742c 6c69 6e65 636f 6c6f 723d =.2pt,linecolor=\n+000140d0: 626c 7565 2c6c 696e 6573 7479 6c65 3d64 blue,linestyle=d\n+000140e0: 6173 6865 645d 2028 4f29 2830 2c30 2c2d ashed] (O)(0,0,-\n+000140f0: 3130 290a 2020 2020 7370 6563 6961 6c20 10). special \n+00014100: 7c5c 7570 7574 5b72 5d23 317b 2478 247d |\\uput[r]#1{$x$}\n+00014110: 5c75 7075 745b 755d 2332 7b24 7924 7d5c \\uput[u]#2{$y$}\\\n+00014120: 7570 7574 5b6c 5d23 337b 247a 247d 7c0a uput[l]#3{$z$}|.\n+00014130: 2020 2020 2020 2873 7a2c 302c 3029 2830 (sz,0,0)(0\n+00014140: 2c73 7a2c 3029 2830 2c30 2c73 7a29 0a20 ,sz,0)(0,0,sz). \n+00014150: 207d 0a0a 2020 2054 696d 6520 666f 7220 }.. Time for \n+00014160: 616e 6f74 6865 7220 7465 7374 2e20 204c another test. L\n+00014170: 6574 2773 2062 7569 6c64 2061 2072 6561 et's build a rea\n+00014180: 6c20 7669 6577 2074 7261 6e73 666f 726d l view transform\n+00014190: 2c20 6372 6561 7469 6e67 2061 0ae2 809c , creating a....\n+000141a0: 7669 7274 7561 6c20 6361 6d65 7261 e280 virtual camera..\n+000141b0: 9d20 746f 206c 6f6f 6b20 6174 2074 6865 . to look at the\n+000141c0: 2073 6365 6e65 2077 6520 6172 6520 636f scene we are co\n+000141d0: 6e73 7472 7563 7469 6e67 2e20 2052 6570 nstructing. Rep\n+000141e0: 6c61 6365 2074 6865 0ae2 8098 7265 7065 lace the....repe\n+000141f0: 6174 e280 9920 7769 7468 0a20 2064 6566 at... with. def\n+00014200: 2065 7965 2028 3130 2c34 2c31 3029 0a20 eye (10,4,10). \n+00014210: 2064 6566 206c 6f6f 6b5f 6174 2028 302c def look_at (0,\n+00014220: 302c 2d35 290a 2020 7075 7420 7b20 7669 0,-5). put { vi\n+00014230: 6577 2828 6579 6529 2c20 286c 6f6f 6b5f ew((eye), (look_\n+00014240: 6174 2929 207d 207b 207b 686f 7573 657d at)) } { {house}\n+00014250: 7b61 7865 737d 207d 0a20 2020 5468 6520 {axes} }. The \n+00014260: e280 9c76 6965 7720 7472 616e 7366 6f72 ...view transfor\n+00014270: 6de2 809d 2072 6570 6f73 6974 696f 6e73 m... repositions\n+00014280: 2074 6865 2073 6365 6e65 2073 6f20 7468 the scene so th\n+00014290: 6174 2074 6865 2070 6f69 6e74 20e2 8098 at the point ...\n+000142a0: 6579 65e2 8099 2069 730a 6174 2074 6865 eye... is.at the\n+000142b0: 206f 7269 6769 6e20 616e 6420 7468 6520 origin and the \n+000142c0: 6469 7265 6374 696f 6e20 6672 6f6d 20e2 direction from .\n+000142d0: 8098 6579 65e2 8099 2074 6f20 e280 986c ..eye... to ...l\n+000142e0: 6f6f 6b5f 6174 e280 9920 6973 2074 6865 ook_at... is the\n+000142f0: 206e 6567 6174 6976 650a 7a2d 6178 6973 negative.z-axis\n+00014300: 2e20 2054 6869 7320 7265 7175 6972 6573 . This requires\n+00014310: 2061 2072 6f74 6174 696f 6e20 616e 6420 a rotation and \n+00014320: 6120 7472 616e 736c 6174 696f 6e20 7468 a translation th\n+00014330: 6174 2061 7265 2061 6c6c 2070 6163 6b65 at are all packe\n+00014340: 640a 696e 746f 2074 6865 2063 6f6e 7374 d.into the const\n+00014350: 7275 6374 6f72 20e2 8098 7669 6577 e280 ructor ...view..\n+00014360: 992e 0a0a 0008 5b69 6d61 6765 2073 7263 ......[image src\n+00014370: 3d22 6578 3135 302e 706e 6722 2074 6578 =\"ex150.png\" tex\n+00014380: 743d 2249 6d61 6765 2065 7831 3530 206f t=\"Image ex150 o\n+00014390: 6d69 7474 6564 2069 6e20 7465 7874 2076 mitted in text v\n+000143a0: 6572 7369 6f6e 206f 6620 7468 6973 2064 ersion of this d\n+000143b0: 6f63 756d 656e 742e 2200 085d 0a0a 5468 ocument.\"..]..Th\n+000143c0: 6973 2069 7320 7374 6172 7469 6e67 2074 is is starting t\n+000143d0: 6f20 6c6f 6f6b 2067 6f6f 6421 2020 4164 o look good! Ad\n+000143e0: 6420 7468 6520 7072 6f6a 6563 7469 6f6e d the projection\n+000143f0: 2070 6c61 6e65 2068 616c 6620 7761 790a plane half way.\n+00014400: 6265 7477 6565 6e20 7468 6520 6f72 6967 between the orig\n+00014410: 696e 2061 6e64 2074 6865 2068 6f75 7365 in and the house\n+00014420: 2061 7420 7a3d 2d35 2e20 2057 6527 6c6c at z=-5. We'll\n+00014430: 2074 7279 2074 6865 2061 6e67 6c65 2061 try the angle a\n+00014440: 7267 756d 656e 740a 6665 6174 7572 6520 rgument.feature \n+00014450: 6f66 20e2 8098 7370 6563 6961 6ce2 8099 of ...special...\n+00014460: 2074 6f20 706f 7369 7469 6f6e 2061 206c to position a l\n+00014470: 6162 656c 2e0a 2020 6465 6620 7020 3520 abel.. def p 5 \n+00014480: 2520 7072 6f6a 6563 7469 6f6e 2064 6973 % projection dis\n+00014490: 7461 6e63 6520 2870 6c61 6e65 2061 7420 tance (plane at \n+000144a0: 7a3d 2d70 290a 2020 6465 6620 7072 6f6a z=-p). def proj\n+000144b0: 6563 7469 6f6e 5f70 6c61 6e65 207b 0a20 ection_plane {. \n+000144c0: 2020 2064 6566 2073 7a20 312e 350a 2020 def sz 1.5. \n+000144d0: 2020 706f 6c79 676f 6e20 282d 737a 2c2d polygon (-sz,-\n+000144e0: 737a 2c2d 7029 2873 7a2c 2d73 7a2c 2d70 sz,-p)(sz,-sz,-p\n+000144f0: 2928 737a 2c73 7a2c 2d70 2928 2d73 7a2c )(sz,sz,-p)(-sz,\n+00014500: 737a 2c2d 7029 0a20 2020 2073 7065 6369 sz,-p). speci\n+00014510: 616c 207c 5c72 7075 745b 625d 2331 2d32 al |\\rput[b]#1-2\n+00014520: 2333 7b5c 666f 6f74 6e6f 7465 7369 7a65 #3{\\footnotesize\n+00014530: 5c73 6620 7072 6f6a 6563 7469 6f6e 2070 \\sf projection p\n+00014540: 6c61 6e65 7d7c 200a 2020 2020 2020 282d lane}| . (-\n+00014550: 737a 2c2d 737a 2c2d 7029 2873 7a2c 2d73 sz,-sz,-p)(sz,-s\n+00014560: 7a2c 2d70 2928 302c 2d73 7a2b 2e31 2c2d z,-p)(0,-sz+.1,-\n+00014570: 7029 0a20 207d 0a41 6464 207b 7072 6f6a p). }.Add {proj\n+00014580: 6563 7469 6f6e 5f70 6c61 6e65 7d20 746f ection_plane} to\n+00014590: 2074 6865 206c 6973 7420 6f66 206f 626a the list of obj\n+000145a0: 6563 7473 2069 6e20 7468 6520 e280 9870 ects in the ...p\n+000145b0: 7574 e280 9920 6162 6f76 652e 0a0a 0008 ut... above.....\n+000145c0: 5b69 6d61 6765 2073 7263 3d22 6578 3136 [image src=\"ex16\n+000145d0: 302e 706e 6722 2074 6578 743d 2249 6d61 0.png\" text=\"Ima\n+000145e0: 6765 2065 7831 3630 206f 6d69 7474 6564 ge ex160 omitted\n+000145f0: 2069 6e20 7465 7874 2076 6572 7369 6f6e in text version\n+00014600: 206f 6620 7468 6973 2064 6f63 756d 656e of this documen\n+00014610: 742e 2200 085d 0a0a 2020 2054 6865 2077 t.\"..].. The w\n+00014620: 6179 2077 6520 636f 6e73 7472 7563 7465 ay we constructe\n+00014630: 6420 7468 6520 706f 696e 7473 206f 6620 d the points of \n+00014640: 7468 6520 686f 7573 6520 6e6f 7720 6d61 the house now ma\n+00014650: 6b65 7320 6974 2065 6173 7920 746f 0a64 kes it easy to.d\n+00014660: 7261 7720 7261 7973 206f 6620 7072 6f6a raw rays of proj\n+00014670: 6563 7469 6f6e 2e20 2057 6527 6c6c 2063 ection. We'll c\n+00014680: 6173 7420 6f6e 6520 7261 7920 6672 6f6d ast one ray from\n+00014690: 2065 7665 7279 2076 6973 6962 6c65 2076 every visible v\n+000146a0: 6572 7465 780a 6f66 2074 6865 2068 6f75 ertex.of the hou\n+000146b0: 7365 2061 6e64 2064 6566 696e 6520 6f70 se and define op\n+000146c0: 7469 6f6e 7320 736f 2074 6865 2061 7070 tions so the app\n+000146d0: 6561 7261 6e63 6520 6f66 2061 6c6c 2072 earance of all r\n+000146e0: 6179 7320 6361 6e20 6265 0a63 6861 6e67 ays can be.chang\n+000146f0: 6564 2061 7420 7468 6520 7361 6d65 2074 ed at the same t\n+00014700: 696d 652e 0a20 2064 6566 2070 726f 6a65 ime.. def proje\n+00014710: 6374 696f 6e5f 7261 7973 207b 0a20 2020 ction_rays {. \n+00014720: 2064 6566 2072 6179 6f70 7420 5b6c 696e def rayopt [lin\n+00014730: 6577 6964 7468 3d2e 3370 742c 6c69 6e65 ewidth=.3pt,line\n+00014740: 636f 6c6f 723d 6c69 6768 7467 7261 795d color=lightgray]\n+00014750: 0a20 2020 206c 696e 6520 5b72 6179 6f70 . line [rayop\n+00014760: 745d 284f 2928 7052 3129 206c 696e 6520 t](O)(pR1) line \n+00014770: 5b72 6179 6f70 745d 284f 2928 7052 3229 [rayopt](O)(pR2)\n+00014780: 206c 696e 655b 7261 796f 7074 5d28 4f29 line[rayopt](O)\n+00014790: 2870 5233 290a 2020 2020 6c69 6e65 205b (pR3). line [\n+000147a0: 7261 796f 7074 5d28 4f29 2870 5234 2920 rayopt](O)(pR4) \n+000147b0: 6c69 6e65 205b 7261 796f 7074 5d28 4f29 line [rayopt](O)\n+000147c0: 2870 5235 290a 2020 2020 6c69 6e65 205b (pR5). line [\n+000147d0: 7261 796f 7074 5d28 4f29 2870 4c31 2920 rayopt](O)(pL1) \n+000147e0: 6c69 6e65 205b 7261 796f 7074 5d28 4f29 line [rayopt](O)\n+000147f0: 2870 4c32 2920 6c69 6e65 5b72 6179 6f70 (pL2) line[rayop\n+00014800: 745d 284f 2928 704c 3529 0a20 2020 206c t](O)(pL5). l\n+00014810: 696e 6520 5b72 6179 6f70 745d 284f 2928 ine [rayopt](O)(\n+00014820: 7044 3129 206c 696e 6520 5b72 6179 6f70 pD1) line [rayop\n+00014830: 745d 284f 2928 7044 3229 200a 2020 2020 t](O)(pD2) . \n+00014840: 6c69 6e65 205b 7261 796f 7074 5d28 4f29 line [rayopt](O)\n+00014850: 2870 4433 2920 6c69 6e65 205b 7261 796f (pD3) line [rayo\n+00014860: 7074 5d28 4f29 2870 4434 2920 0a20 207d pt](O)(pD4) . }\n+00014870: 0a54 6865 2072 6573 756c 7420 6973 2073 .The result is s\n+00014880: 686f 776e 2068 6572 652e 0a0a 0008 5b69 hown here.....[i\n+00014890: 6d61 6765 2073 7263 3d22 6578 3137 302e mage src=\"ex170.\n+000148a0: 706e 6722 2074 6578 743d 2249 6d61 6765 png\" text=\"Image\n+000148b0: 2065 7831 3730 206f 6d69 7474 6564 2069 ex170 omitted i\n+000148c0: 6e20 7465 7874 2076 6572 7369 6f6e 206f n text version o\n+000148d0: 6620 7468 6973 2064 6f63 756d 656e 742e f this document.\n+000148e0: 2200 085d 0a0a 5468 6520 7261 7973 2070 \"..]..The rays p\n+000148f0: 6965 7263 6520 7468 6520 7072 6f6a 6563 ierce the projec\n+00014900: 7469 6f6e 2070 6c61 6e65 2061 7420 7468 tion plane at th\n+00014910: 6520 636f 7272 6573 706f 6e64 696e 6720 e corresponding \n+00014920: 706f 696e 7473 206f 6e20 7468 650a 7065 points on the.pe\n+00014930: 7273 7065 6374 6976 6520 696d 6167 6520 rspective image \n+00014940: 7765 2061 7265 2074 7279 696e 6720 746f we are trying to\n+00014950: 2064 7261 772e 2020 416c 6272 6563 6874 draw. Albrecht\n+00014960: 2044 c3bc 7265 7220 616e 6420 6869 730a D..rer and his.\n+00014970: 5265 6e61 6973 7361 6e63 6520 636f 6e74 Renaissance cont\n+00014980: 656d 706f 7261 7269 6573 2068 6164 2074 emporaries had t\n+00014990: 6865 2073 616d 6520 6964 6561 2069 6e20 he same idea in \n+000149a0: 7468 6520 6561 726c 7920 3135 3030 2773 the early 1500's\n+000149b0: 2e0a 0a00 085b 696d 6167 6520 7372 633d .....[image src=\n+000149c0: 2264 7565 7265 722e 706e 6722 2074 6578 \"duerer.png\" tex\n+000149d0: 743d 2249 6d61 6765 206f 6620 4475 6572 t=\"Image of Duer\n+000149e0: 6572 2773 2070 6572 7370 6563 7469 7665 er's perspective\n+000149f0: 2063 6f6d 7075 7465 7220 6f6d 6974 7465 computer omitte\n+00014a00: 6420 696e 2074 6578 7420 7665 7273 696f d in text versio\n+00014a10: 6e20 6f66 2074 6869 7320 646f 6375 6d65 n of this docume\n+00014a20: 6e74 2e22 0008 5d0a 0a20 2020 416c 6c20 nt.\"..].. All \n+00014a30: 7468 6174 2773 206c 6566 7420 6973 2074 that's left is t\n+00014a40: 6f20 6669 6e64 2061 2077 6179 2074 6f20 o find a way to \n+00014a50: 636f 6e6e 6563 7420 7468 6520 706f 696e connect the poin\n+00014a60: 7473 206f 6620 7468 6520 686f 7573 650a ts of the house.\n+00014a70: 6f6e 2074 6865 2070 726f 6a65 6374 696f on the projectio\n+00014a80: 6e20 706c 616e 652e 2020 5765 2063 6f75 n plane. We cou\n+00014a90: 6c64 2070 756c 6c20 6f75 7420 6120 676f ld pull out a go\n+00014aa0: 6f64 2063 6f6d 7075 7465 7220 6772 6170 od computer grap\n+00014ab0: 6869 6373 0a74 6578 742c 2066 696e 6420 hics.text, find \n+00014ac0: 7468 6520 6e65 6365 7373 6172 7920 6d61 the necessary ma\n+00014ad0: 7472 6978 2c20 616e 6420 656e 7465 7220 trix, and enter \n+00014ae0: 6974 206f 7572 7365 6c76 6573 2061 7320 it ourselves as \n+00014af0: 6120 7472 616e 7366 6f72 6d0a 6c69 7465 a transform.lite\n+00014b00: 7261 6c2e 2020 2a4e 6f74 6520 5472 616e ral. *Note Tran\n+00014b10: 7366 6f72 6d20 6c69 7465 7261 6c73 3a3a sform literals::\n+00014b20: 2e20 2054 6861 7420 776f 726b 2069 7320 . That work is \n+00014b30: 616c 7265 6164 7920 646f 6e65 2c0a 686f already done,.ho\n+00014b40: 7765 7665 722e 2020 5765 2063 616e 2075 wever. We can u\n+00014b50: 7365 2074 6865 20e2 8098 7072 6f6a 6563 se the ...projec\n+00014b60: 7428 7029 e280 9920 636f 6e73 7472 7563 t(p)... construc\n+00014b70: 746f 722e 0a0a 2020 2054 6865 7265 2061 tor... There a\n+00014b80: 7265 2073 7469 6c6c 2073 6f6d 6520 6465 re still some de\n+00014b90: 7461 696c 7320 7468 6174 2072 6571 7569 tails that requi\n+00014ba0: 7265 2063 6172 652e 2020 5072 6f6a 6563 re care. Projec\n+00014bb0: 7469 6f6e 2077 696c 6c0a 666c 6174 7465 tion will.flatte\n+00014bc0: 6e20 7768 6174 6576 6572 2069 7320 7472 n whatever is tr\n+00014bd0: 616e 7366 6f72 6d65 6420 6f6e 746f 2074 ansformed onto t\n+00014be0: 6865 2070 6c61 6e65 207a 3d2d 702e 2020 he plane z=-p. \n+00014bf0: 5468 6572 6566 6f72 6520 616e 7920 7061 Therefore any pa\n+00014c00: 7274 0a6f 6620 7468 6520 686f 7573 6520 rt.of the house \n+00014c10: 636f 756c 6420 6469 7361 7070 6561 7220 could disappear \n+00014c20: 6265 6869 6e64 2074 6865 2070 726f 6a65 behind the proje\n+00014c30: 6374 696f 6e20 706c 616e 6520 2874 6865 ction plane (the\n+00014c40: 2068 6964 6465 6e0a 7375 7266 6163 6520 hidden.surface \n+00014c50: 616c 676f 7269 7468 6d20 6f72 6465 7273 algorithm orders\n+00014c60: 206f 626a 6563 7473 2061 7420 7468 6520 objects at the \n+00014c70: 7361 6d65 2064 6570 7468 2061 7262 6974 same depth arbit\n+00014c80: 7261 7269 6c79 292e 2020 5468 650a 646f rarily). The.do\n+00014c90: 6f72 206d 6179 2061 6c73 6f20 6469 7361 or may also disa\n+00014ca0: 7070 6561 7220 6265 6869 6e64 2074 6865 ppear behind the\n+00014cb0: 2066 726f 6e74 206f 6620 7468 6520 686f front of the ho\n+00014cc0: 7573 652e 2020 546f 206d 616b 6520 7375 use. To make su\n+00014cd0: 7265 0a65 7665 7279 7468 696e 6720 7265 re.everything re\n+00014ce0: 6d61 696e 7320 7669 7369 626c 652c 2077 mains visible, w\n+00014cf0: 6527 6c6c 2070 6c61 6365 2074 6865 2068 e'll place the h\n+00014d00: 6f75 7365 2061 2074 696e 7920 6269 7420 ouse a tiny bit \n+00014d10: 696e 2066 726f 6e74 206f 660a 7468 6520 in front of.the \n+00014d20: 7072 6f6a 6563 7469 6f6e 2070 6c61 6e65 projection plane\n+00014d30: 2061 6e64 2061 2073 6563 6f6e 6420 636f and a second co\n+00014d40: 7079 206f 6620 7468 6520 646f 6f72 2069 py of the door i\n+00014d50: 6e20 6672 6f6e 7420 6f66 2074 6865 0a68 n front of the.h\n+00014d60: 6f75 7365 2e0a 2020 6465 6620 7072 6f6a ouse.. def proj\n+00014d70: 6563 7469 6f6e 207b 0a20 2020 2025 2065 ection {. % e\n+00014d80: 2069 7320 6120 736d 616c 6c20 6e75 6d62 is a small numb\n+00014d90: 6572 2064 6566 696e 6564 2061 626f 7665 er defined above\n+00014da0: 0a20 2020 2070 7574 207b 2070 726f 6a65 . put { proje\n+00014db0: 6374 2870 2920 7468 656e 2074 7261 6e73 ct(p) then trans\n+00014dc0: 6c61 7465 285b 302c 302c 312a 655d 2920 late([0,0,1*e]) \n+00014dd0: 7d20 7b68 6f75 7365 7d0a 2020 2020 7075 } {house}. pu\n+00014de0: 7420 7b20 7072 6f6a 6563 7428 7029 2074 t { project(p) t\n+00014df0: 6865 6e20 7472 616e 736c 6174 6528 5b30 hen translate([0\n+00014e00: 2c30 2c32 2a65 5d29 207d 207b 646f 6f72 ,0,2*e]) } {door\n+00014e10: 7d0a 2020 7d0a 0a00 085b 696d 6167 6520 }. }....[image \n+00014e20: 7372 633d 2265 7831 3830 2e70 6e67 2220 src=\"ex180.png\" \n+00014e30: 7465 7874 3d22 496d 6167 6520 6578 3138 text=\"Image ex18\n+00014e40: 3020 6f6d 6974 7465 6420 696e 2074 6578 0 omitted in tex\n+00014e50: 7420 7665 7273 696f 6e20 6f66 2074 6869 t version of thi\n+00014e60: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a s document.\"..].\n+00014e70: 0a20 2020 4966 2079 6f75 2068 6176 6520 . 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While a\n+00014f90: 0a47 5549 2074 6f6f 6c20 6d61 7920 6861 .GUI tool may ha\n+00014fa0: 7665 2062 6565 6e20 6120 6c69 7474 6c65 ve been a little\n+00014fb0: 2066 6173 7465 722c 2069 7420 6973 2075 faster, it is u\n+00014fc0: 6e6c 696b 656c 7920 7468 6174 2061 206e nlikely that a n\n+00014fd0: 6577 0a64 7261 7769 6e67 2c20 6974 7365 ew.drawing, itse\n+00014fe0: 6c66 2061 2070 6572 7370 6563 7469 7665 lf a perspective\n+00014ff0: 2070 726f 6a65 6374 696f 6e20 6f66 2074 projection of t\n+00015000: 6865 2073 6365 6e65 2c20 636f 756c 6420 he scene, could \n+00015010: 6265 0a67 656e 6572 6174 6564 2077 6974 be.generated wit\n+00015020: 6820 7477 6f20 6d6f 7265 206d 696e 7574 h two more minut\n+00015030: 6573 2720 776f 726b 2120 204a 7573 7420 es' work! Just \n+00015040: 6368 616e 6765 2074 6865 2076 6965 7720 change the view \n+00015050: 7472 616e 7366 6f72 6d0a 746f 0a20 2070 transform.to. p\n+00015060: 7574 207b 2076 6965 7728 2865 7965 292c ut { view((eye),\n+00015070: 2028 6c6f 6f6b 5f61 7429 2920 7468 656e (look_at)) then\n+00015080: 2070 6572 7370 6563 7469 7665 2839 2920 perspective(9) \n+00015090: 7d20 7b20 2e2e 2e0a 616e 6420 7072 6f64 } { ....and prod\n+000150a0: 7563 6520 7468 6973 2e0a 0a00 085b 696d uce this.....[im\n+000150b0: 6167 6520 7372 633d 2265 7831 3930 2e70 age src=\"ex190.p\n+000150c0: 6e67 2220 7465 7874 3d22 496d 6167 6520 ng\" text=\"Image \n+000150d0: 6578 3139 3020 6f6d 6974 7465 6420 696e ex190 omitted in\n+000150e0: 2074 6578 7420 7665 7273 696f 6e20 6f66 text version of\n+000150f0: 2074 6869 7320 646f 6375 6d65 6e74 2e22 this document.\"\n+00015100: 0008 5d0a 0a1f 0a46 696c 653a 2073 6b65 ..]....File: ske\n+00015110: 7463 682e 696e 666f 2c20 204e 6f64 653a tch.info, Node:\n+00015120: 2041 2074 6563 686e 6963 616c 2064 7261 A technical dra\n+00015130: 7769 6e67 2c20 204e 6578 743a 2041 2068 wing, Next: A h\n+00015140: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n+00015150: 6c2c 2020 5072 6576 3a20 4f76 6572 7669 l, Prev: Overvi\n+00015160: 6577 2c20 2055 703a 2042 7569 6c64 696e ew, Up: Buildin\n+00015170: 6720 6120 6472 6177 696e 670a 0a34 2e32 g a drawing..4.2\n+00015180: 2041 2074 6563 686e 6963 616c 2064 7261 A technical dra\n+00015190: 7769 6e67 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d wing.===========\n+000151a0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a 4c65 ============..Le\n+000151b0: 7427 7320 6c6f 6f6b 2061 7420 6120 6472 t's look at a dr\n+000151c0: 6177 696e 6720 7468 6174 2072 6570 7265 awing that repre\n+000151d0: 7365 6e74 7320 7468 6520 6b69 6e64 206f sents the kind o\n+000151e0: 6620 7072 6f62 6c65 6d20 e280 9873 6b65 f problem ...ske\n+000151f0: 7463 68e2 8099 2077 6173 0a6d 6561 6e74 tch... was.meant\n+00015200: 2074 6f20 736f 6c76 652d 2d61 2070 6169 to solve--a pai\n+00015210: 7220 6f66 2074 6578 7462 6f6f 6b20 6669 r of textbook fi\n+00015220: 6775 7265 7320 7265 6761 7264 696e 6720 gures regarding \n+00015230: 6120 706f 6c79 676f 6e61 6c0a 6170 7072 a polygonal.appr\n+00015240: 6f78 696d 6174 696f 6e20 6f66 2061 2074 oximation of a t\n+00015250: 7275 6e63 6174 6564 2063 6f6e 652e 2020 runcated cone. \n+00015260: 4865 7265 2061 7265 2074 6865 2070 6963 Here are the pic\n+00015270: 7475 7265 7320 7765 2077 696c 6c0a 7072 tures we will.pr\n+00015280: 6f64 7563 652e 0a0a 0008 5b69 6d61 6765 oduce.....[image\n+00015290: 2073 7263 3d22 6578 3235 302e 706e 6722 src=\"ex250.png\"\n+000152a0: 2074 6578 743d 2249 6d61 6765 2065 7832 text=\"Image ex2\n+000152b0: 3530 206f 6d69 7474 6564 2069 6e20 7465 50 omitted in te\n+000152c0: 7874 2076 6572 7369 6f6e 206f 6620 7468 xt version of th\n+000152d0: 6973 2064 6f63 756d 656e 742e 2200 085d is document.\"..]\n+000152e0: 2020 2020 2000 085b 696d 6167 6520 7372 ..[image sr\n+000152f0: 633d 2265 7832 3630 2e70 6e67 2220 7465 c=\"ex260.png\" te\n+00015300: 7874 3d22 496d 6167 6520 6578 3236 3020 xt=\"Image ex260 \n+00015310: 6f6d 6974 7465 6420 696e 2074 6578 7420 omitted in text \n+00015320: 7665 7273 696f 6e20 6f66 2074 6869 7320 version of this \n+00015330: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a20 document.\"..].. \n+00015340: 2020 5468 6520 636f 6e65 2073 6861 7065 The cone shape\n+00015350: 2069 7320 6a75 7374 2061 2073 7765 7074 is just a swept\n+00015360: 206c 696e 6520 7769 7468 206e 6f20 636c line with no cl\n+00015370: 6f73 7572 6520 7461 6720 616e 6420 6375 osure tag and cu\n+00015380: 6c6c 696e 670a 7475 726e 6564 206f 6666 lling.turned off\n+00015390: 2e20 2042 6567 696e 2062 7920 7365 7474 . Begin by sett\n+000153a0: 696e 6720 7570 2073 6f6d 6520 7573 6566 ing up some usef\n+000153b0: 756c 2063 6f6e 7374 616e 7473 2e0a 2020 ul constants.. \n+000153c0: 6465 6620 4f20 2830 2c30 2c30 2920 6465 def O (0,0,0) de\n+000153d0: 6620 4920 5b31 2c30 2c30 5d20 6465 6620 f I [1,0,0] def \n+000153e0: 4a20 5b30 2c31 2c30 5d20 6465 6620 4b20 J [0,1,0] def K \n+000153f0: 5b30 2c30 2c31 5d0a 2020 6465 6620 7030 [0,0,1]. def p0\n+00015400: 2028 312c 3229 2064 6566 2070 3120 2831 (1,2) def p1 (1\n+00015410: 2e35 2c30 2920 6465 6620 4e20 380a 2020 .5,0) def N 8. \n+00015420: 6465 6620 7365 675f 726f 7420 726f 7461 def seg_rot rota\n+00015430: 7465 2833 3630 202f 204e 2c20 5b4a 5d29 te(360 / N, [J])\n+00015440: 0a54 6865 2070 6f69 6e74 7320 e280 9870 .The points ...p\n+00015450: 30e2 8099 2061 6e64 20e2 8098 7031 e280 0... and ...p1..\n+00015460: 9920 6172 6520 7468 6520 656e 6420 706f . are the end po\n+00015470: 696e 7473 206f 6620 7468 6520 6c69 6e65 ints of the line\n+00015480: 2074 6f20 6265 2073 7765 7074 2e0a 5468 to be swept..Th\n+00015490: 6520 6465 6669 6e69 7469 6f6e 20e2 8098 e definition ...\n+000154a0: 7365 675f 726f 74e2 8099 2069 7320 7468 seg_rot... is th\n+000154b0: 6520 7377 6565 7020 7472 616e 7366 6f72 e sweep transfor\n+000154c0: 6d61 7469 6f6e 2e20 2057 6974 6820 7468 mation. With th\n+000154d0: 6573 652c 2074 6865 0a63 6f6e 6520 6974 ese, the.cone it\n+000154e0: 7365 6c66 2069 7320 7369 6d70 6c65 2e0a self is simple..\n+000154f0: 2020 7377 6565 705b 6375 6c6c 3d66 616c sweep[cull=fal\n+00015500: 7365 5d20 7b20 4e2c 205b 5b73 6567 5f72 se] { N, [[seg_r\n+00015510: 6f74 5d5d 207d 206c 696e 6528 7030 2928 ot]] } line(p0)(\n+00015520: 7031 290a 0a20 2020 5468 6520 6178 6573 p1).. The axes\n+00015530: 2061 7265 206e 6578 7420 616e 6420 696e are next and in\n+00015540: 636c 7564 6520 616e 2069 6e74 6572 6573 clude an interes\n+00015550: 696e 6720 7472 6963 6b20 7468 6174 2073 ing trick that s\n+00015560: 686f 7773 2074 6865 0a68 6964 6465 6e20 hows the.hidden \n+00015570: 7061 7274 7320 6173 2064 6f74 7465 6420 parts as dotted \n+00015580: 6c69 6e65 732e 2020 5468 6520 7365 6372 lines. The secr\n+00015590: 6574 2069 7320 6472 6177 2074 6865 2061 et is draw the a\n+000155a0: 7865 7320 7477 6963 652d 2d73 6f6c 6964 xes twice--solid\n+000155b0: 0a6c 696e 6573 2077 6974 6820 7468 6520 .lines with the \n+000155c0: 6e6f 726d 616c 2068 6964 6465 6e20 7375 normal hidden su\n+000155d0: 7266 6163 6520 616c 676f 7269 7468 6d20 rface algorithm \n+000155e0: 696e 2065 6666 6563 742c 2061 6e64 2074 in effect, and t\n+000155f0: 6865 6e0a 646f 7474 6564 2077 6974 6820 hen.dotted with \n+00015600: 7468 6520 6f70 7469 6f6e 20e2 8098 6c61 the option ...la\n+00015610: 793d 6f76 6572 e280 9920 736f 2074 6861 y=over... so tha\n+00015620: 7420 6e6f 2070 6f6c 7967 6f6e 7320 6361 t no polygons ca\n+00015630: 6e20 6869 6465 2074 6865 6d2e 0a20 2064 n hide them.. d\n+00015640: 6566 2061 7820 2864 782c 302c 3029 2025 ef ax (dx,0,0) %\n+00015650: 2074 6970 7320 6f66 2074 6865 2061 7865 tips of the axe\n+00015660: 730a 2020 6465 6620 6179 2028 302c 6479 s. def ay (0,dy\n+00015670: 2c30 290a 2020 6465 6620 617a 2028 302c ,0). def az (0,\n+00015680: 302c 647a 290a 2020 6c69 6e65 5b61 7272 0,dz). line[arr\n+00015690: 6f77 733d 3c2d 3e2c 6c69 6e65 7769 6474 ows=<->,linewidt\n+000156a0: 683d 2e34 7074 5d28 6178 2928 4f29 2861 h=.4pt](ax)(O)(a\n+000156b0: 7929 0a20 206c 696e 655b 6172 726f 7773 y). line[arrows\n+000156c0: 3d2d 3e2c 6c69 6e65 7769 6474 683d 2e34 =->,linewidth=.4\n+000156d0: 7074 5d28 4f29 2861 7a29 0a20 2025 2072 pt](O)(az). % r\n+000156e0: 6570 6561 7420 646f 7474 6564 2061 7320 epeat dotted as \n+000156f0: 616e 206f 7665 726c 6179 2074 6f20 6869 an overlay to hi\n+00015700: 6e74 2061 7420 7468 6520 6869 6464 656e nt at the hidden\n+00015710: 206c 696e 6573 0a20 206c 696e 655b 6c61 lines. line[la\n+00015720: 793d 6f76 6572 2c6c 696e 6573 7479 6c65 y=over,linestyle\n+00015730: 3d64 6f74 7465 642c 6c69 6e65 7769 6474 =dotted,linewidt\n+00015740: 683d 2e34 7074 5d28 6178 2928 4f29 2861 h=.4pt](ax)(O)(a\n+00015750: 7929 0a20 206c 696e 655b 6c61 793d 6f76 y). line[lay=ov\n+00015760: 6572 2c6c 696e 6573 7479 6c65 3d64 6f74 er,linestyle=dot\n+00015770: 7465 642c 6c69 6e65 7769 6474 683d 2e34 ted,linewidth=.4\n+00015780: 7074 5d28 4f29 2861 7a29 0a20 2073 7065 pt](O)(az). spe\n+00015790: 6369 616c 7c5c 666f 6f74 6e6f 7465 7369 cial|\\footnotesi\n+000157a0: 7a65 0a20 2020 2020 2020 2020 205c 7570 ze. \\up\n+000157b0: 7574 5b64 5d23 317b 2478 247d 5c75 7075 ut[d]#1{$x$}\\upu\n+000157c0: 745b 755d 2332 7b24 7924 7d5c 7570 7574 t[u]#2{$y$}\\uput\n+000157d0: 5b6c 5d23 337b 247a 247d 7c0a 2020 2020 [l]#3{$z$}|. \n+000157e0: 2861 7829 2861 7929 2861 7a29 0a54 6865 (ax)(ay)(az).The\n+000157f0: 206c 6162 656c 7320 6172 6520 6170 706c labels are appl\n+00015800: 6965 6420 7769 7468 20e2 8098 5053 5472 ied with ...PSTr\n+00015810: 6963 6b73 e280 9920 7370 6563 6961 6c20 icks... special \n+00015820: 6f62 6a65 6374 7320 6173 2075 7375 616c objects as usual\n+00015830: 2e0a 0a20 2020 466f 7220 7468 6520 6865 ... For the he\n+00015840: 6967 6874 2064 696d 656e 7369 6f6e 206d ight dimension m\n+00015850: 6172 6b2c 2074 6865 2070 6f77 6572 206f ark, the power o\n+00015860: 6620 6166 6669 6e65 2061 7269 7468 6574 f affine arithet\n+00015870: 6963 2069 7320 7665 7279 0a68 656c 7066 ic is very.helpf\n+00015880: 756c 2e0a 2020 6465 6620 6864 696d 5f72 ul.. def hdim_r\n+00015890: 6566 2075 6e69 7428 2870 3129 202d 2028 ef unit((p1) - (\n+000158a0: 4f29 2920 7468 656e 205b 5b73 6567 5f72 O)) then [[seg_r\n+000158b0: 6f74 5d5d 5e32 0a20 2064 6566 2063 3020 ot]]^2. def c0 \n+000158c0: 2870 3029 2074 6865 6e20 7363 616c 6528 (p0) then scale(\n+000158d0: 5b4a 5d29 0a20 2064 6566 2068 3030 2028 [J]). def h00 (\n+000158e0: 6330 2920 2b20 312e 3120 2a20 5b68 6469 c0) + 1.1 * [hdi\n+000158f0: 6d5f 7265 665d 0a20 2064 6566 2068 3031 m_ref]. def h01\n+00015900: 2028 6330 2920 2b20 312e 3920 2a20 5b68 (c0) + 1.9 * [h\n+00015910: 6469 6d5f 7265 665d 0a20 2064 6566 2068 dim_ref]. def h\n+00015920: 3032 2028 6330 2920 2b20 312e 3820 2a20 02 (c0) + 1.8 * \n+00015930: 5b68 6469 6d5f 7265 665d 0a20 206c 696e [hdim_ref]. lin\n+00015940: 6528 6830 3029 2868 3031 290a 2020 6465 e(h00)(h01). de\n+00015950: 6620 6831 3020 284f 2920 2b20 312e 3620 f h10 (O) + 1.6 \n+00015960: 2a20 5b68 6469 6d5f 7265 665d 0a20 2064 * [hdim_ref]. d\n+00015970: 6566 2068 3131 2028 4f29 202b 2031 2e39 ef h11 (O) + 1.9\n+00015980: 202a 205b 6864 696d 5f72 6566 5d0a 2020 * [hdim_ref]. \n+00015990: 6465 6620 6831 3220 284f 2920 2b20 312e def h12 (O) + 1.\n+000159a0: 3820 2a20 5b68 6469 6d5f 7265 665d 0a20 8 * [hdim_ref]. \n+000159b0: 206c 696e 6528 6831 3029 2868 3131 290a line(h10)(h11).\n+000159c0: 2020 6c69 6e65 5b61 7272 6f77 733d 3c2d line[arrows=<-\n+000159d0: 3e5d 2868 3032 2928 6831 3229 0a20 2064 >](h02)(h12). d\n+000159e0: 6566 2068 6d32 2028 2868 3032 2920 2d20 ef hm2 ((h02) - \n+000159f0: 284f 2920 2b20 2868 3132 2920 2d20 284f (O) + (h12) - (O\n+00015a00: 2929 202f 2032 202b 2028 4f29 0a20 2073 )) / 2 + (O). s\n+00015a10: 7065 6369 616c 7c5c 666f 6f74 6e6f 7465 pecial|\\footnote\n+00015a20: 7369 7a65 5c72 7075 742a 2331 7b24 6824 size\\rput*#1{$h$\n+00015a30: 7d7c 2868 6d32 290a 2020 2054 6865 2067 }|(hm2). The g\n+00015a40: 656e 6572 616c 2069 6465 6120 656d 706c eneral idea empl\n+00015a50: 6f79 6564 2068 6572 6520 6973 2074 6f20 oyed here is to \n+00015a60: 636f 6d70 7574 6520 6120 756e 6974 2022 compute a unit \"\n+00015a70: 7265 6665 7265 6e63 650a 7665 6374 6f72 reference.vector\n+00015a80: 2220 7061 7261 6c6c 656c 2074 6f20 7468 \" parallel to th\n+00015a90: 6520 787a 2d70 6c61 6e65 2069 6e20 7468 e xz-plane in th\n+00015aa0: 6520 6465 7369 7265 6420 6469 7265 6374 e desired direct\n+00015ab0: 696f 6e20 6f66 2074 6865 0a64 696d 656e ion of the.dimen\n+00015ac0: 7369 6f6e 2066 726f 6d20 7468 6520 6f72 sion from the or\n+00015ad0: 6967 696e 2e20 2054 6865 2074 7261 6e73 igin. The trans\n+00015ae0: 666f 726d 6174 696f 6e20 e280 985b 5b73 formation ...[[s\n+00015af0: 6567 5f72 6f74 5d5d 5e32 e280 9920 726f eg_rot]]^2... ro\n+00015b00: 7461 7465 730a 7477 6f20 7365 676d 656e tates.two segmen\n+00015b10: 7473 2061 626f 7574 2074 6865 2079 2d61 ts about the y-a\n+00015b20: 7869 732e 2020 5768 656e 2061 7070 6c69 xis. When appli\n+00015b30: 6564 2074 6f20 e280 9828 7031 2920 2d20 ed to ...(p1) - \n+00015b40: 284f 29e2 8099 2c20 7468 650a 7265 7375 (O)..., the.resu\n+00015b50: 6c74 696e 6720 7665 6374 6f72 2070 6f69 lting vector poi\n+00015b60: 6e74 7320 746f 2074 6865 2072 6967 6874 nts to the right\n+00015b70: 2061 7320 7368 6f77 6e2e 2020 496e 2074 as shown. In t\n+00015b80: 6869 7320 6d61 6e6e 6572 2c20 7765 2063 his manner, we c\n+00015b90: 616e 0a70 6963 6b20 616e 7920 7665 7274 an.pick any vert\n+00015ba0: 6578 2061 7320 7468 6520 6c6f 6361 7469 ex as the locati\n+00015bb0: 6f6e 206f 6620 7468 6520 6865 6967 6874 on of the height\n+00015bc0: 2064 696d 656e 7369 6f6e 206c 696e 6573 dimension lines\n+00015bd0: 2062 7920 7661 7279 696e 670a 7468 6520 by varying.the \n+00015be0: 6578 706f 6e65 6e74 206f 6620 e280 985b exponent of ...[\n+00015bf0: 5b73 6567 5f72 6f74 5d5d e280 992e 2020 [seg_rot]].... \n+00015c00: 5468 6973 2069 7320 6f6e 6c79 206f 6e65 This is only one\n+00015c10: 206f 6620 6d61 6e79 2070 6f73 7369 626c of many possibl\n+00015c20: 650a 7374 7261 7465 6769 6573 2e0a 0a20 e.strategies... \n+00015c30: 2020 5468 6520 636f 6d70 7574 6174 696f The computatio\n+00015c40: 6e20 6f66 20e2 8098 686d 32e2 8099 2069 n of ...hm2... i\n+00015c50: 7320 6120 7573 6566 756c 2069 6469 6f6d s a useful idiom\n+00015c60: 2066 6f72 2066 696e 6469 6e67 2074 6865 for finding the\n+00015c70: 2063 656e 7472 6f69 640a 6f66 2061 2073 centroid.of a s\n+00015c80: 6574 206f 6620 706f 696e 7473 2e0a 0a20 et of points... \n+00015c90: 2020 5468 6520 7477 6f20 7261 6469 7573 The two radius\n+00015ca0: 206d 6172 6b73 2061 7265 2064 6f6e 6520 marks are done \n+00015cb0: 7369 6d69 6c61 726c 792c 2073 6f20 7765 similarly, so we\n+00015cc0: 2070 7265 7365 6e74 2074 6865 2063 6f64 present the cod\n+00015cd0: 650a 7769 7468 6f75 7420 636f 6d6d 656e e.without commen\n+00015ce0: 742e 0a20 2025 2072 6164 6975 7320 6d65 t.. % radius me\n+00015cf0: 6173 7572 656d 656e 7420 6d61 726b 730a asurement marks.\n+00015d00: 2020 6465 6620 6761 7020 5b30 2c2e 322c def gap [0,.2,\n+00015d10: 305d 2020 2520 7573 6564 2074 6f20 6372 0] % used to cr\n+00015d20: 6561 7465 2073 6d61 6c6c 2076 6572 7469 eate small verti\n+00015d30: 6361 6c20 6761 7073 0a0a 2020 2520 6669 cal gaps.. % fi\n+00015d40: 7273 7420 7231 0a20 2064 6566 2075 7031 rst r1. def up1\n+00015d50: 205b 302c 332e 312c 305d 2025 2074 6963 [0,3.1,0] % tic\n+00015d60: 6b20 7269 7365 7320 6162 6f76 6520 6469 k rises above di\n+00015d70: 6d65 6e73 696f 6e20 6120 6c69 7474 6c65 mension a little\n+00015d80: 0a20 2064 6566 2072 3120 2828 7031 2920 . def r1 ((p1) \n+00015d90: 7468 656e 205b 5b73 6567 5f72 6f74 5d5d then [[seg_rot]]\n+00015da0: 5e2d 3229 202b 205b 7570 315d 0a20 2064 ^-2) + [up1]. d\n+00015db0: 6566 2072 3163 2028 7231 2920 7468 656e ef r1c (r1) then\n+00015dc0: 2073 6361 6c65 285b 4a5d 290a 2020 6465 scale([J]). de\n+00015dd0: 6620 7231 7420 2872 3129 202b 205b 6761 f r1t (r1) + [ga\n+00015de0: 705d 0a20 2064 6566 2072 3162 2028 2872 p]. def r1b ((r\n+00015df0: 3174 2920 7468 656e 2073 6361 6c65 285b 1t) then scale([\n+00015e00: 312c 302c 315d 2929 202b 205b 6761 705d 1,0,1])) + [gap]\n+00015e10: 0a20 206c 696e 655b 6172 726f 7773 3d3c . line[arrows=<\n+00015e20: 2d3e 5d28 7231 6329 2872 3129 2020 2520 ->](r1c)(r1) % \n+00015e30: 6469 6d65 6e73 696f 6e20 6c69 6e65 0a20 dimension line. \n+00015e40: 206c 696e 6528 7231 6229 2872 3174 2920 line(r1b)(r1t) \n+00015e50: 2020 2020 2020 2020 2020 2020 2520 7469 % ti\n+00015e60: 636b 0a20 2064 6566 2072 316d 2028 2872 ck. def r1m ((r\n+00015e70: 3129 202d 2028 4f29 202b 2028 7231 6329 1) - (O) + (r1c)\n+00015e80: 202d 2028 4f29 2920 2f20 3220 2b20 284f - (O)) / 2 + (O\n+00015e90: 2920 2520 6c61 6265 6c20 706f 7369 7469 ) % label positi\n+00015ea0: 6f6e 0a20 2073 7065 6369 616c 207c 5c66 on. special |\\f\n+00015eb0: 6f6f 746e 6f74 6573 697a 655c 7270 7574 ootnotesize\\rput\n+00015ec0: 2a23 317b 2472 5f31 247d 7c28 7231 6d29 *#1{$r_1$}|(r1m)\n+00015ed0: 2020 2520 6c61 6265 6c0a 0a20 2025 2073 % label.. % s\n+00015ee0: 616d 6520 6472 696c 6c20 666f 7220 7230 ame drill for r0\n+00015ef0: 2c20 6275 7420 6d75 7374 2070 726f 6a65 , but must proje\n+00015f00: 6374 2064 6f77 6e20 6669 7273 740a 2020 ct down first. \n+00015f10: 6465 6620 7570 3020 5b30 2c32 2e37 2c30 def up0 [0,2.7,0\n+00015f20: 5d0a 2020 6465 6620 7230 2028 2870 3029 ]. def r0 ((p0)\n+00015f30: 2074 6865 6e20 7363 616c 6528 5b31 2c30 then scale([1,0\n+00015f40: 2c31 5d29 2074 6865 6e20 5b5b 7365 675f ,1]) then [[seg_\n+00015f50: 726f 745d 5d5e 2d32 2920 2b20 5b75 7030 rot]]^-2) + [up0\n+00015f60: 5d0a 2020 6465 6620 7230 6320 2872 3029 ]. def r0c (r0)\n+00015f70: 2074 6865 6e20 7363 616c 6528 5b4a 5d29 then scale([J])\n+00015f80: 0a20 2064 6566 2072 3074 2028 7230 2920 . def r0t (r0) \n+00015f90: 2b20 5b67 6170 5d0a 2020 6465 6620 7230 + [gap]. def r0\n+00015fa0: 6220 2828 7030 2920 7468 656e 205b 5b73 b ((p0) then [[s\n+00015fb0: 6567 5f72 6f74 5d5d 5e2d 3229 202b 205b eg_rot]]^-2) + [\n+00015fc0: 6761 705d 0a20 206c 696e 655b 6172 726f gap]. line[arro\n+00015fd0: 7773 3d3c 2d3e 5d28 7230 6329 2872 3029 ws=<->](r0c)(r0)\n+00015fe0: 0a20 206c 696e 6528 7230 6229 2872 3074 . line(r0b)(r0t\n+00015ff0: 290a 2020 6465 6620 7230 6d20 2828 7230 ). def r0m ((r0\n+00016000: 2920 2d20 284f 2920 2b20 2872 3063 2920 ) - (O) + (r0c) \n+00016010: 2d20 284f 2929 202f 2032 202b 2028 4f29 - (O)) / 2 + (O)\n+00016020: 0a20 2073 7065 6369 616c 207c 5c66 6f6f . special |\\foo\n+00016030: 746e 6f74 6573 697a 655c 7270 7574 2a23 tnotesize\\rput*#\n+00016040: 317b 2472 5f30 247d 7c28 7230 6d29 0a0a 1{$r_0$}|(r0m)..\n+00016050: 2020 2054 6865 2073 6563 6f6e 6420 6472 The second dr\n+00016060: 6177 696e 6720 7573 6573 2074 6865 2073 awing uses the s\n+00016070: 616d 6520 7465 6368 6e69 7175 6573 2e20 ame techniques. \n+00016080: 204f 6e6c 7920 7468 6520 6d65 7468 6f64 Only the method\n+00016090: 2066 6f72 0a64 7261 7769 6e67 2074 6865 for.drawing the\n+000160a0: 2065 6c6c 6970 7469 6361 6c20 6172 6320 elliptical arc \n+000160b0: 6973 206e 6577 2e20 2048 6572 6520 6973 is new. Here is\n+000160c0: 2074 6865 2063 6f64 652e 0a20 2064 6566 the code.. def\n+000160d0: 206d 6964 2028 2870 3030 292d 284f 292b mid ((p00)-(O)+\n+000160e0: 2870 3130 292d 284f 292b 2870 3131 292d (p10)-(O)+(p11)-\n+000160f0: 284f 292b 2870 3031 292d 284f 2929 2f34 (O)+(p01)-(O))/4\n+00016100: 2b28 4f29 0a20 2073 7065 6369 616c 7c5c +(O). special|\\\n+00016110: 7270 7574 2331 7b5c 7073 6375 7374 6f6d rput#1{\\pscustom\n+00016120: 7b0a 2020 2020 5c73 6361 6c65 7b31 2031 {. \\scale{1 1\n+00016130: 2e33 7d0a 2020 2020 5c70 7361 7263 5b61 .3}. \\psarc[a\n+00016140: 7272 6f77 6c65 6e67 7468 3d2e 355d 7b2d rrowlength=.5]{-\n+00016150: 3e7d 7b2e 3235 7d7b 2d36 307d 7b32 3430 >}{.25}{-60}{240\n+00016160: 7d7d 7d7c 0a20 2020 205b 6c61 793d 6f76 }}}|. [lay=ov\n+00016170: 6572 5d28 6d69 6429 0a57 6520 636f 756c er](mid).We coul\n+00016180: 6420 6861 7665 2073 7765 7074 2061 2070 d have swept a p\n+00016190: 6f69 6e74 2074 6f20 6d61 6b65 2074 6865 oint to make the\n+000161a0: 2061 7263 2077 6974 6820 e280 9873 6b65 arc with ...ske\n+000161b0: 7463 68e2 8099 2c20 6275 7420 7573 696e tch..., but usin\n+000161c0: 6720 610a e280 9850 5354 7269 636b 73e2 g a....PSTricks.\n+000161d0: 8099 2063 7573 746f 6d20 6772 6170 6869 .. custom graphi\n+000161e0: 6320 7761 7320 7369 6d70 6c65 722e 2020 c was simpler. \n+000161f0: 4167 6169 6e20 7765 2063 6f6d 7075 7465 Again we compute\n+00016200: 6420 7468 6520 6365 6e74 726f 6964 0a6f d the centroid.o\n+00016210: 6620 7468 6520 7175 6164 7269 6c61 7465 f the quadrilate\n+00016220: 7261 6c20 6279 2061 7665 7261 6769 6e67 ral by averaging\n+00016230: 2070 6f69 6e74 732e 2020 4e6f 7465 2074 points. Note t\n+00016240: 6861 7420 7363 616c 696e 6720 696e 0a50 hat scaling in.P\n+00016250: 6f73 7473 6372 6970 7420 6469 7374 6f72 ostscript distor\n+00016260: 7473 2074 6865 2061 7272 6f77 6865 6164 ts the arrowhead\n+00016270: 2c20 6275 7420 696e 2074 6869 7320 6361 , but in this ca\n+00016280: 7365 2074 6865 2064 6973 746f 7274 696f se the distortio\n+00016290: 6e0a 6163 7475 616c 6c79 206c 6f6f 6b73 n.actually looks\n+000162a0: 2062 6574 7465 7220 696e 2074 6865 2070 better in the p\n+000162b0: 726f 6a65 6374 696f 6e20 6f66 2074 6865 rojection of the\n+000162c0: 2073 6c61 6e74 6564 2066 6163 652e 2020 slanted face. \n+000162d0: 4120 e280 9873 6b65 7463 68e2 8099 0a61 A ...sketch....a\n+000162e0: 7272 6f77 6865 6164 2077 6f75 6c64 206e rrowhead would n\n+000162f0: 6f74 2068 6176 6520 6265 656e 2064 6973 ot have been dis\n+00016300: 746f 7274 6564 2e0a 0a20 2020 5468 6520 torted... The \n+00016310: 636f 6d70 6c65 7465 2063 6f64 6520 666f complete code fo\n+00016320: 7220 7468 6973 2065 7861 6d70 6c65 2c20 r this example, \n+00016330: 7768 6963 6820 6472 6177 7320 6569 7468 which draws eith\n+00016340: 6572 2066 6967 7572 650a 6465 7065 6e64 er figure.depend\n+00016350: 696e 6720 6f6e 2074 6865 2064 6566 696e ing on the defin\n+00016360: 6974 696f 6e20 6f66 2074 6865 2074 6167 ition of the tag\n+00016370: 20e2 8098 3c6c 6162 656c 6564 3ee2 8099 ......\n+00016380: 2c20 6973 2069 6e63 6c75 6465 6420 696e , is included in\n+00016390: 2074 6865 0ae2 8098 736b 6574 6368 e280 the....sketch..\n+000163a0: 9920 6469 7374 7269 6275 7469 6f6e 2069 . distribution i\n+000163b0: 6e20 7468 6520 6669 6c65 20e2 8098 7472 n the file ...tr\n+000163c0: 756e 6361 7465 6463 6f6e 652e 736b e280 uncatedcone.sk..\n+000163d0: 992e 0a0a 1f0a 4669 6c65 3a20 736b 6574 ......File: sket\n+000163e0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n+000163f0: 4120 6869 6572 6172 6368 6963 616c 206d A hierarchical m\n+00016400: 6f64 656c 2c20 204e 6578 743a 2043 6176 odel, Next: Cav\n+00016410: 6561 7473 2c20 2050 7265 763a 2041 2074 eats, Prev: A t\n+00016420: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n+00016430: 2c20 2055 703a 2042 7569 6c64 696e 6720 , Up: Building \n+00016440: 6120 6472 6177 696e 670a 0a34 2e33 2041 a drawing..4.3 A\n+00016450: 2068 6965 7261 7263 6869 6361 6c20 6d6f hierarchical mo\n+00016460: 6465 6c0a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d del.============\n+00016470: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a 5768 ============..Wh\n+00016480: 696c 6520 e280 9873 6b65 7463 68e2 8099 ile ...sketch...\n+00016490: 2077 6173 206e 6576 6572 206d 6561 6e74 was never meant\n+000164a0: 2074 6f20 6265 2061 2067 656f 6d65 7472 to be a geometr\n+000164b0: 6963 206d 6f64 656c 696e 6720 6c61 6e67 ic modeling lang\n+000164c0: 7561 6765 2c20 6974 0a63 6f6d 6573 2066 uage, it.comes f\n+000164d0: 6169 726c 7920 636c 6f73 652e 2020 5468 airly close. Th\n+000164e0: 6520 666f 6c6c 6f77 696e 6720 6578 616d e following exam\n+000164f0: 706c 6520 7075 7473 2061 6c6c 2077 6520 ple puts all we \n+00016500: 6861 7665 2073 6565 6e20 746f 2077 6f72 have seen to wor\n+00016510: 6b0a 696e 2061 2076 6572 7920 7369 6d70 k.in a very simp\n+00016520: 6c65 206d 6f64 656c 206f 6620 7468 6520 le model of the \n+00016530: 6875 6d61 6e20 6861 6e64 2e20 2053 7461 human hand. Sta\n+00016540: 7274 2062 7920 7377 6565 7069 6e67 2061 rt by sweeping a\n+00016550: 206c 696e 6520 746f 0a6d 616b 6520 6120 line to.make a \n+00016560: 7472 756e 6361 7465 6420 636f 6e65 2c20 truncated cone, \n+00016570: 7768 6963 6820 7769 6c6c 2062 6520 636f which will be co\n+00016580: 7069 6564 206f 7665 7220 616e 6420 6f76 pied over and ov\n+00016590: 6572 2061 6761 696e 2074 6f20 6d61 6b65 er again to make\n+000165a0: 0a74 6865 2073 6567 6d65 6e74 7320 6f66 .the segments of\n+000165b0: 2066 696e 6765 7273 2e0a 2020 6465 6620 fingers.. def \n+000165c0: 4f20 2830 2c30 2c30 2920 2520 6f72 6967 O (0,0,0) % orig\n+000165d0: 696e 0a20 2064 6566 2049 205b 312c 302c in. def I [1,0,\n+000165e0: 305d 2064 6566 204a 205b 302c 312c 305d 0] def J [0,1,0]\n+000165f0: 2064 6566 204b 205b 302c 302c 315d 2025 def K [0,0,1] %\n+00016600: 2063 616e 6f6e 6963 616c 2075 6e69 7420 canonical unit \n+00016610: 7665 6374 6f72 730a 2020 6465 6620 7365 vectors. def se\n+00016620: 676d 656e 7420 7b0a 2020 2020 6465 6620 gment {. def \n+00016630: 6e5f 6661 6365 7320 380a 2020 2020 7377 n_faces 8. sw\n+00016640: 6565 7020 7b20 6e5f 6661 6365 733c 3e2c eep { n_faces<>,\n+00016650: 2072 6f74 6174 6528 3336 3020 2f20 6e5f rotate(360 / n_\n+00016660: 6661 6365 732c 205b 4a5d 2920 7d20 0a20 faces, [J]) } . \n+00016670: 2020 2020 206c 696e 6528 7072 6f78 696d line(proxim\n+00016680: 616c 5f72 6164 2c20 3029 2864 6973 7461 al_rad, 0)(dista\n+00016690: 6c5f 7261 642c 2064 6973 7461 6c5f 6c65 l_rad, distal_le\n+000166a0: 6e29 0a20 207d 0a49 6e20 6861 6e64 2061 n). }.In hand a\n+000166b0: 6e61 746f 6d79 2c20 5f64 6973 7461 6c5f natomy, _distal_\n+000166c0: 2069 7320 2261 7420 7468 6520 7469 7022 is \"at the tip\"\n+000166d0: 2061 6e64 205f 7072 6f78 696d 616c 5f20 and _proximal_ \n+000166e0: 6973 2022 696e 2074 6865 2061 7265 610a is \"in the area.\n+000166f0: 6f66 2074 6865 2070 616c 6d2e 2220 2057 of the palm.\" W\n+00016700: 6520 6861 7665 206f 6d69 7474 6564 2061 e have omitted a\n+00016710: 6c6c 2074 6865 2073 6361 6c61 7220 636f ll the scalar co\n+00016720: 6e73 7461 6e74 732e 2020 596f 7520 6361 nstants. You ca\n+00016730: 6e20 6669 6e64 0a74 6865 6d20 696e 20e2 n find.them in .\n+00016740: 8098 6861 6e64 2e73 6be2 8099 2c20 7768 ..hand.sk..., wh\n+00016750: 6963 6820 6973 2070 726f 7669 6465 6420 ich is provided \n+00016760: 696e 2074 6865 20e2 8098 736b 6574 6368 in the ...sketch\n+00016770: e280 9920 6469 7374 7269 6275 7469 6f6e ... distribution\n+00016780: 2e0a 0a20 2020 5765 2061 6c73 6f20 6e65 ... We also ne\n+00016790: 6564 2061 2070 726f 746f 7479 7069 6361 ed a prototypica\n+000167a0: 6c20 7370 6865 7265 2074 6f20 7573 6520 l sphere to use \n+000167b0: 666f 7220 7468 6520 6a6f 696e 7473 2074 for the joints t\n+000167c0: 6865 6d73 656c 7665 732e 0a20 2064 6566 hemselves.. def\n+000167d0: 206a 6f69 6e74 5f73 7068 6572 6520 7b0a joint_sphere {.\n+000167e0: 2020 2020 6465 6620 6e5f 6a6f 696e 745f def n_joint_\n+000167f0: 6661 6365 7320 380a 2020 2020 7377 6565 faces 8. swee\n+00016800: 7020 5b66 696c 6c63 6f6c 6f72 3d72 6564 p [fillcolor=red\n+00016810: 5d20 7b20 6e5f 6a6f 696e 745f 6661 6365 ] { n_joint_face\n+00016820: 732c 2072 6f74 6174 6528 3336 3020 2f20 s, rotate(360 / \n+00016830: 6e5f 6a6f 696e 745f 6661 6365 732c 205b n_joint_faces, [\n+00016840: 4a5d 2920 7d0a 2020 2020 2020 7377 6565 J]) }. swee\n+00016850: 7020 7b20 6e5f 6a6f 696e 745f 6661 6365 p { n_joint_face\n+00016860: 732c 2072 6f74 6174 6528 3138 3020 2f20 s, rotate(180 / \n+00016870: 6e5f 6a6f 696e 745f 6661 6365 7329 207d n_joint_faces) }\n+00016880: 200a 2020 2020 2020 2020 2830 2c20 2d6a . (0, -j\n+00016890: 6f69 6e74 5f72 6164 290a 2020 7d0a 0a20 oint_rad). }.. \n+000168a0: 2020 5765 276c 6c20 6e6f 7720 6465 7369 We'll now desi\n+000168b0: 676e 2074 6865 2069 6e64 6578 2066 696e gn the index fin\n+000168c0: 6765 7220 286e 756d 6265 7220 3120 696e ger (number 1 in\n+000168d0: 206f 7572 206e 6f74 6174 696f 6e61 6c0a our notational.\n+000168e0: 636f 6e76 656e 7469 6f6e 3b20 6669 6e67 convention; fing\n+000168f0: 6572 2030 2069 7320 7468 6520 7468 756d er 0 is the thum\n+00016900: 6229 2e20 2054 6865 2064 6973 7461 6c20 b). The distal \n+00016910: 726f 7461 7469 6f6e 2066 6f72 2074 6865 rotation for the\n+00016920: 2066 696e 6765 720a 6170 706c 6965 7320 finger.applies \n+00016930: 6f6e 6c79 2074 6f20 7468 6520 7469 702c only to the tip,\n+00016940: 2073 6f20 7765 2064 6566 696e 6520 7468 so we define th\n+00016950: 6520 666f 6c6c 6f77 696e 672e 0a20 2064 e following.. d\n+00016960: 6566 2064 6973 7461 6c5f 3120 7b0a 2020 ef distal_1 {. \n+00016970: 2020 7075 7420 7b20 7472 616e 736c 6174 put { translat\n+00016980: 6528 6a6f 696e 745f 6761 7020 2a20 6a6f e(joint_gap * jo\n+00016990: 696e 745f 7261 6420 2a20 5b4a 5d29 200a int_rad * [J]) .\n+000169a0: 2020 2020 2020 2020 2020 7468 656e 2072 then r\n+000169b0: 6f74 6174 6528 6469 7374 616c 5f31 5f72 otate(distal_1_r\n+000169c0: 6f74 2c20 5b49 5d29 200a 2020 2020 2020 ot, [I]) . \n+000169d0: 2020 2020 7468 656e 2074 7261 6e73 6c61 then transla\n+000169e0: 7465 2828 6469 7374 616c 5f6c 656e 202b te((distal_len +\n+000169f0: 206a 6f69 6e74 5f67 6170 202a 206a 6f69 joint_gap * joi\n+00016a00: 6e74 5f72 6164 2920 2a20 5b4a 5d29 207d nt_rad) * [J]) }\n+00016a10: 0a20 2020 2020 207b 7365 676d 656e 747d . {segment}\n+00016a20: 0a20 2020 2070 7574 207b 2072 6f74 6174 . put { rotat\n+00016a30: 6528 6469 7374 616c 5f31 5f72 6f74 202f e(distal_1_rot /\n+00016a40: 2032 2c20 5b49 5d29 0a20 2020 2020 2020 2, [I]). \n+00016a50: 2020 2074 6865 6e20 7472 616e 736c 6174 then translat\n+00016a60: 6528 2864 6973 7461 6c5f 6c65 6e20 2b20 e((distal_len + \n+00016a70: 6a6f 696e 745f 6761 7020 2a20 6a6f 696e joint_gap * join\n+00016a80: 745f 7261 6429 202a 205b 4a5d 2920 7d20 t_rad) * [J]) } \n+00016a90: 0a20 2020 2020 207b 6a6f 696e 745f 7370 . {joint_sp\n+00016aa0: 6865 7265 7d0a 2020 2020 7075 7420 7b20 here}. put { \n+00016ab0: 7363 616c 6528 205b 4a5d 202b 2070 726f scale( [J] + pro\n+00016ac0: 7869 6d61 6c5f 6469 7374 616c 5f72 6174 ximal_distal_rat\n+00016ad0: 696f 202a 2028 5b49 5d2b 5b4b 5d29 2029 io * ([I]+[K]) )\n+00016ae0: 207d 0a20 2020 2020 207b 7365 676d 656e }. {segmen\n+00016af0: 747d 0a20 207d 2020 0a54 6865 2069 6465 t}. } .The ide\n+00016b00: 6e74 6966 6965 7273 2068 6572 6520 6172 ntifiers here ar\n+00016b10: 6520 666f 7220 7369 7a65 2061 6e64 206c e for size and l\n+00016b20: 6f63 6174 696f 6e20 636f 6e73 7461 6e74 ocation constant\n+00016b30: 732e 2020 5468 6520 6578 6365 7074 696f s. The exceptio\n+00016b40: 6e0a 6973 20e2 8098 6469 7374 616c 5f72 n.is ...distal_r\n+00016b50: 6f74 5f31 e280 992e 2020 5468 6973 2072 ot_1.... This r\n+00016b60: 6f74 6174 696f 6e20 7061 7261 6d65 7465 otation paramete\n+00016b70: 7220 6d6f 6465 6c73 2074 6865 2066 6c65 r models the fle\n+00016b80: 7869 6e67 206f 6620 7468 650a 6669 6e67 xing of the.fing\n+00016b90: 6572 2074 6970 2e20 2054 6865 2066 6972 er tip. The fir\n+00016ba0: 7374 20e2 8098 7075 74e2 8099 206d 616b st ...put... mak\n+00016bb0: 6573 2061 2063 6f70 7920 6f66 2074 6865 es a copy of the\n+00016bc0: 2066 696e 6765 7220 7365 676d 656e 7420 finger segment \n+00016bd0: 7468 6174 2069 730a 7472 616e 736c 6174 that is.translat\n+00016be0: 6564 2075 7077 6172 6420 6a75 7374 2066 ed upward just f\n+00016bf0: 6172 2065 6e6f 7567 6820 746f 206d 616b ar enough to mak\n+00016c00: 6520 726f 6f6d 2066 6f72 2074 6865 2073 e room for the s\n+00016c10: 7068 6572 6963 616c 206a 6f69 6e74 2e0a pherical joint..\n+00016c20: 5468 656e 2069 7420 6170 706c 6965 7320 Then it applies \n+00016c30: 7468 6520 6469 7374 616c 2072 6f74 6174 the distal rotat\n+00016c40: 696f 6e2e 2020 4669 6e61 6c6c 7920 6974 ion. Finally it\n+00016c50: 2074 7261 6e73 6c61 7465 7320 7468 6520 translates the \n+00016c60: 7768 6f6c 650a 6173 7365 6d62 6c79 2075 whole.assembly u\n+00016c70: 7077 6172 6420 6167 6169 6e20 746f 206d pward again to m\n+00016c80: 616b 6520 726f 6f6d 2066 6f72 2074 6865 ake room for the\n+00016c90: 206d 6964 646c 6520 7068 6c61 6e67 6573 middle phlanges\n+00016ca0: 2028 7468 6520 6e65 7874 0a62 6f6e 6520 (the next.bone \n+00016cb0: 746f 7761 7264 2074 6865 2070 616c 6d29 toward the palm)\n+00016cc0: 2e20 2054 6865 2073 6563 6f6e 6420 e280 . The second ..\n+00016cd0: 9870 7574 e280 9920 706f 7369 7469 6f6e .put... position\n+00016ce0: 7320 7468 6520 7370 6865 7265 2e20 2054 s the sphere. T\n+00016cf0: 6865 7265 2069 730a 6120 726f 7461 7469 here is.a rotati\n+00016d00: 6f6e 2074 6f20 706c 6163 6520 7468 6520 on to place the \n+00016d10: 6772 6964 206f 6e20 7468 6520 7370 6865 grid on the sphe\n+00016d20: 7265 2073 7572 6661 6365 2061 7420 616e re surface at an\n+00016d30: 206e 6963 6520 616e 676c 652c 0a74 6865 nice angle,.the\n+00016d40: 6e20 6120 7472 616e 736c 6174 696f 6e20 n a translation \n+00016d50: 746f 2074 6865 2062 6173 6520 6f66 2074 to the base of t\n+00016d60: 6865 2064 6973 7461 6c20 7068 6c61 6e67 he distal phlang\n+00016d70: 6573 2c20 7768 6963 6820 6973 2061 6c73 es, which is als\n+00016d80: 6f0a 6365 6e74 6572 206f 6620 6974 7320 o.center of its \n+00016d90: 726f 7461 7469 6f6e 2e20 2046 696e 616c rotation. Final\n+00016da0: 6c79 2c20 7468 6520 6c61 7374 20e2 8098 ly, the last ...\n+00016db0: 7075 74e2 8099 2070 6f73 6974 696f 6e73 put... positions\n+00016dc0: 2074 6865 206d 6964 646c 650a 7365 676d the middle.segm\n+00016dd0: 656e 7420 6974 7365 6c66 2e0a 0a20 2020 ent itself... \n+00016de0: 5468 6520 6d69 6464 6c65 206a 6f69 6e74 The middle joint\n+00016df0: 2069 7320 7468 6520 6e65 7874 206f 6e65 is the next one\n+00016e00: 2064 6f77 6e2c 2077 6974 6820 726f 7461 down, with rota\n+00016e10: 7469 6f6e 2061 6e67 6c65 0ae2 8098 6d69 tion angle....mi\n+00016e20: 6464 6c65 5f72 6f74 5f31 e280 992e 2020 ddle_rot_1.... \n+00016e30: 5768 656e 2074 6869 7320 616e 676c 6520 When this angle \n+00016e40: 6368 616e 6765 732c 2077 6520 6e65 6564 changes, we need\n+00016e50: 2061 6c6c 2074 6865 206f 626a 6563 7473 all the objects\n+00016e60: 2069 6e0a e280 9864 6973 7461 6c5f 31e2 in....distal_1.\n+00016e70: 8099 2074 6f20 726f 7461 7465 2061 7320 .. to rotate as \n+00016e80: 6120 756e 6974 2e20 2054 6869 7320 6973 a unit. This is\n+00016e90: 2074 6865 2072 6561 736f 6e69 6e67 2062 the reasoning b\n+00016ea0: 6568 696e 6420 7468 6520 6e65 7874 0a64 ehind the next.d\n+00016eb0: 6566 696e 6974 696f 6e2e 0a20 2064 6566 efinition.. def\n+00016ec0: 2066 696e 6765 725f 3120 7b0a 2020 2020 finger_1 {. \n+00016ed0: 7075 7420 7b20 7472 616e 736c 6174 6528 put { translate(\n+00016ee0: 6a6f 696e 745f 6761 7020 2a20 6a6f 696e joint_gap * join\n+00016ef0: 745f 7261 6420 2a20 5b4a 5d29 0a20 2020 t_rad * [J]). \n+00016f00: 2020 2020 2020 2074 6865 6e20 726f 7461 then rota\n+00016f10: 7465 286d 6964 646c 655f 315f 726f 742c te(middle_1_rot,\n+00016f20: 205b 495d 290a 2020 2020 2020 2020 2020 [I]). \n+00016f30: 7468 656e 2074 7261 6e73 6c61 7465 2828 then translate((\n+00016f40: 6d69 6464 6c65 5f72 6174 696f 202a 2064 middle_ratio * d\n+00016f50: 6973 7461 6c5f 6c65 6e20 2b20 0a20 2020 istal_len + . \n 00016f60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00016f70: 2020 2020 2020 2020 206a 6f69 6e74 5f67 joint_g\n-00016f80: 6170 202a 206a 6f69 6e74 5f72 6164 2920 ap * joint_rad) \n-00016f90: 2a20 5b4a 5d29 207d 0a20 2020 2020 207b * [J]) }. {\n-00016fa0: 6469 7374 616c 5f31 7d0a 2020 2020 7075 distal_1}. pu\n-00016fb0: 7420 7b20 7363 616c 6528 7072 6f78 696d t { scale(proxim\n-00016fc0: 616c 5f64 6973 7461 6c5f 7261 7469 6f29 al_distal_ratio)\n-00016fd0: 0a20 2020 2020 2020 2020 2074 6865 6e20 . then \n-00016fe0: 726f 7461 7465 286d 6964 646c 655f 315f rotate(middle_1_\n-00016ff0: 726f 7420 2f20 322c 205b 495d 290a 2020 rot / 2, [I]). \n-00017000: 2020 2020 2020 2020 7468 656e 2074 7261 then tra\n-00017010: 6e73 6c61 7465 2828 6d69 6464 6c65 5f72 nslate((middle_r\n-00017020: 6174 696f 202a 2064 6973 7461 6c5f 6c65 atio * distal_le\n-00017030: 6e20 2b20 0a20 2020 2020 2020 2020 2020 n + . \n-00017040: 2020 2020 2020 2020 2020 2020 2020 206a j\n-00017050: 6f69 6e74 5f67 6170 202a 206a 6f69 6e74 oint_gap * joint\n-00017060: 5f72 6164 2920 2a20 5b4a 5d29 207d 200a _rad) * [J]) } .\n-00017070: 2020 2020 2020 7b6a 6f69 6e74 5f73 7068 {joint_sph\n-00017080: 6572 657d 0a20 2020 2070 7574 207b 2073 ere}. put { s\n-00017090: 6361 6c65 2820 6d69 6464 6c65 5f72 6174 cale( middle_rat\n-000170a0: 696f 202a 205b 4a5d 202b 200a 2020 2020 io * [J] + . \n-000170b0: 2020 2020 2020 2020 2020 2020 2070 726f pro\n-000170c0: 7869 6d61 6c5f 6469 7374 616c 5f72 6174 ximal_distal_rat\n-000170d0: 696f 5e32 202a 2028 5b49 5d2b 5b4b 5d29 io^2 * ([I]+[K])\n-000170e0: 2029 207d 0a20 2020 2020 207b 7365 676d ) }. {segm\n-000170f0: 656e 747d 0a20 207d 0a54 6869 7320 6c6f ent}. }.This lo\n-00017100: 6f6b 7320 7665 7279 2073 696d 696c 6172 oks very similar\n-00017110: 2074 6f20 7468 6520 7072 6576 696f 7573 to the previous\n-00017120: 2064 6566 696e 6974 696f 6e2c 2061 6e64 definition, and\n-00017130: 2069 7420 6973 2e20 2054 6865 0a69 6d70 it is. The.imp\n-00017140: 6f72 7461 6e74 2064 6966 6665 7265 6e63 ortant differenc\n-00017150: 6520 6973 2074 6861 7420 7261 7468 6572 e is that rather\n-00017160: 2074 6861 6e20 706f 7369 7469 6f6e 696e than positionin\n-00017170: 6720 616e 6420 726f 7461 7469 6e67 2061 g and rotating a\n-00017180: 0a73 696e 676c 6520 7365 676d 656e 742c .single segment,\n-00017190: 2077 6520 706f 7369 7469 6f6e 2061 6e64 we position and\n-000171a0: 2072 6f74 6174 6520 7468 6520 656e 7469 rotate the enti\n-000171b0: 7265 2022 6173 7365 6d62 6c79 2220 6465 re \"assembly\" de\n-000171c0: 6669 6e65 6420 6173 0ae2 8098 6469 7374 fined as....dist\n-000171d0: 616c 5f31 e280 992e 2020 5468 6520 7265 al_1.... The re\n-000171e0: 7374 2069 7320 6a75 7374 2061 7269 7468 st is just arith\n-000171f0: 6d65 7469 6320 746f 2063 6f6d 7075 7465 metic to compute\n-00017200: 2073 697a 6573 2061 6e64 2070 6f73 6974 sizes and posit\n-00017210: 696f 6e73 0a74 6861 7420 6c6f 6f6b 206e ions.that look n\n-00017220: 6963 652e 2020 5468 6520 6c61 7374 20e2 ice. The last .\n-00017230: 8098 7075 74e2 8099 2070 6c61 6365 7320 ..put... places \n-00017240: 616e 2061 7070 726f 7072 6961 7465 6c79 an appropriately\n-00017250: 2073 6861 7065 6420 7365 676d 656e 740a shaped segment.\n-00017260: 7468 6174 2069 7320 7468 6520 5f70 726f that is the _pro\n-00017270: 7869 6d61 6c20 7068 6c61 6e67 6573 5f2c ximal phlanges_,\n-00017280: 2074 6865 2062 6f6e 6520 7468 6174 206a the bone that j\n-00017290: 6f69 6e73 2074 6865 2070 616c 6d20 6f66 oins the palm of\n-000172a0: 2074 6865 0a68 616e 642e 2020 5468 6973 the.hand. This\n-000172b0: 2063 6f6d 706c 6574 6573 2074 6865 2066 completes the f\n-000172c0: 696e 6765 7220 6974 7365 6c66 2e0a 0a20 inger itself... \n-000172d0: 2020 416c 6c20 7468 6520 6f74 6865 7220 All the other \n-000172e0: 6669 6e67 6572 7320 6172 6520 6465 7363 fingers are desc\n-000172f0: 7269 6265 6420 6964 656e 7469 6361 6c6c ribed identicall\n-00017300: 7920 746f 2074 6869 7320 6f6e 652e 2020 y to this one. \n-00017310: 5765 0a61 6363 6f75 6e74 2066 6f72 2074 We.account for t\n-00017320: 6865 2066 6163 7420 7468 6174 2072 6561 he fact that rea\n-00017330: 6c20 6669 6e67 6572 7320 6172 6520 6469 l fingers are di\n-00017340: 6666 6572 656e 7420 7369 7a65 7320 696e fferent sizes in\n-00017350: 2074 6865 206e 6578 740a 7374 6570 2c20 the next.step, \n-00017360: 7768 6963 6820 6973 2074 6f20 6275 696c which is to buil\n-00017370: 6420 7468 6520 656e 7469 7265 2068 616e d the entire han\n-00017380: 642e 0a0a 2020 2054 6865 20e2 8098 6861 d... The ...ha\n-00017390: 6e64 e280 9920 6465 6669 6e69 7469 6f6e nd... definition\n-000173a0: 2074 6861 7420 666f 6c6c 6f77 7320 696e that follows in\n-000173b0: 636c 7564 6573 2061 2073 6563 7469 6f6e cludes a section\n-000173c0: 2066 6f72 2065 6163 680a 6669 6e67 6572 for each.finger\n-000173d0: 2e20 2057 6527 6c6c 2063 6f6e 7469 6e75 . We'll continu\n-000173e0: 6520 7769 7468 2066 696e 6765 7220 3120 e with finger 1 \n-000173f0: 616e 6420 6f6d 6974 2061 6c6c 2074 6865 and omit all the\n-00017400: 206f 7468 6572 732e 2020 284f 6620 6e6f others. (Of no\n-00017410: 7465 0a69 7320 7468 6174 2074 6865 2074 te.is that the t\n-00017420: 6875 6d62 206e 6565 6473 2073 6c69 6768 humb needs sligh\n-00017430: 746c 7920 7370 6563 6961 6c20 7472 6561 tly special trea\n-00017440: 746d 656e 742d 2d61 6e20 6578 7472 6120 tment--an extra \n-00017450: 726f 7461 7469 6f6e 2074 6f0a 6163 636f rotation to.acco\n-00017460: 756e 7420 666f 7220 6974 7320 6f70 706f unt for its oppo\n-00017470: 7369 6e67 2061 6e67 6c65 2e20 2054 6869 sing angle. Thi\n-00017480: 7320 6973 2063 6c65 6172 2069 6e20 7468 s is clear in th\n-00017490: 6520 6675 6c6c 2073 6f75 7263 6520 636f e full source co\n-000174a0: 6465 2e29 0a4e 6f74 2073 7572 7072 6973 de.).Not surpris\n-000174b0: 696e 676c 792c 2074 6865 20e2 8098 6861 ingly, the ...ha\n-000174c0: 6e64 e280 9920 6465 6669 6e69 7469 6f6e nd... definition\n-000174d0: 206c 6f6f 6b73 2076 6572 7920 6d75 6368 looks very much\n-000174e0: 206c 696b 6520 7468 650a 7072 6576 696f like the.previo\n-000174f0: 7573 2074 776f 2e20 2049 7420 7368 6f75 us two. It shou\n-00017500: 6c64 2062 6520 6e6f 2073 7572 7072 6973 ld be no surpris\n-00017510: 6520 7468 6174 2077 6865 6e20 7468 6520 e that when the \n-00017520: 726f 7461 7469 6f6e 2070 6172 616d 6574 rotation paramet\n-00017530: 6572 0ae2 8098 6d65 7461 5f31 5f72 6f74 er....meta_1_rot\n-00017540: e280 9920 6368 616e 6765 732c 2074 6865 ... changes, the\n-00017550: 2065 6e74 6972 6520 6669 6e67 6572 2072 entire finger r\n-00017560: 6f74 6174 6573 2120 2054 6865 7265 2069 otates! There i\n-00017570: 7320 616e 2061 6464 6974 696f 6e61 6c0a s an additional.\n-00017580: 726f 7461 7469 6f6e 2074 6861 7420 616c rotation that al\n-00017590: 6c6f 7773 2074 6865 2066 696e 6765 7273 lows the fingers\n-000175a0: 2074 6f20 7370 7265 6164 206c 6174 6572 to spread later\n-000175b0: 616c 6c79 2e20 2057 6520 7361 7920 7468 ally. We say th\n-000175c0: 6573 650a 6a6f 696e 7473 206f 6620 7468 ese.joints of th\n-000175d0: 6520 7072 6f78 696d 616c 2070 686c 616e e proximal phlan\n-000175e0: 6765 7320 6861 7665 2074 776f 205f 6465 ges have two _de\n-000175f0: 6772 6565 7320 6f66 2066 7265 6564 6f6d grees of freedom\n-00017600: 5f2e 2020 5468 650a 6a6f 696e 7473 2068 _. The.joints h\n-00017610: 6967 6865 7220 6f6e 2074 6865 2066 696e igher on the fin\n-00017620: 6765 7220 6861 7665 206f 6e6c 7920 6f6e ger have only on\n-00017630: 652e 2020 4669 6e61 6c6c 792c 2065 6163 e. Finally, eac\n-00017640: 6820 6669 6e67 6572 2069 730a 7363 616c h finger is.scal\n-00017650: 6564 2062 7920 6120 6661 6374 6f72 2074 ed by a factor t\n-00017660: 6f20 6c65 6e64 2069 7420 7072 6f70 6f72 o lend it propor\n-00017670: 7469 6f6e 2e0a 2020 6465 6620 6861 6e64 tion.. def hand\n-00017680: 207b 0a20 2020 2025 2066 696e 6765 7220 {. % finger \n-00017690: 3120 5b61 6c6c 206f 7468 6572 2066 696e 1 [all other fin\n-000176a0: 6765 7273 206f 6d69 7474 6564 5d0a 2020 gers omitted]. \n-000176b0: 2020 6465 6620 7363 616c 655f 3120 2e38 def scale_1 .8\n-000176c0: 350a 2020 2020 7075 7420 7b20 7363 616c 5. put { scal\n-000176d0: 6528 7363 616c 655f 3129 200a 2020 2020 e(scale_1) . \n-000176e0: 2020 2020 2020 7468 656e 2074 7261 6e73 then trans\n-000176f0: 6c61 7465 2828 6a6f 696e 745f 6761 7020 late((joint_gap \n-00017700: 2a20 6a6f 696e 745f 7261 6429 202a 205b * joint_rad) * [\n-00017710: 4a5d 290a 0920 2074 6865 6e20 726f 7461 J]).. then rota\n-00017720: 7465 286d 6574 615f 315f 726f 742c 205b te(meta_1_rot, [\n-00017730: 495d 290a 2020 2020 2020 2020 2020 7468 I]). th\n-00017740: 656e 2072 6f74 6174 6528 2d73 7072 6561 en rotate(-sprea\n-00017750: 645f 726f 742c 205b 4b5d 290a 2020 2020 d_rot, [K]). \n-00017760: 2020 2020 2020 7468 656e 2074 7261 6e73 then trans\n-00017770: 6c61 7465 2828 7072 6f78 696d 616c 5f31 late((proximal_1\n-00017780: 5f6c 6f63 2920 2d20 284f 2929 207d 200a _loc) - (O)) } .\n-00017790: 2020 2020 2020 7b66 696e 6765 725f 317d {finger_1}\n-000177a0: 0a20 2020 2070 7574 207b 2073 6361 6c65 . put { scale\n-000177b0: 2873 6361 6c65 5f31 202a 2070 726f 7869 (scale_1 * proxi\n-000177c0: 6d61 6c5f 6469 7374 616c 5f72 6174 696f mal_distal_ratio\n-000177d0: 5e32 290a 2020 2020 2020 2020 2020 7468 ^2). th\n-000177e0: 656e 2072 6f74 6174 6528 6d65 7461 5f31 en rotate(meta_1\n-000177f0: 5f72 6f74 202f 2032 2c20 5b49 5d29 0a20 _rot / 2, [I]). \n-00017800: 2020 2020 2020 2020 2074 6865 6e20 726f then ro\n-00017810: 7461 7465 282d 7370 7265 6164 5f72 6f74 tate(-spread_rot\n-00017820: 2c20 5b4b 5d29 0a20 2020 2020 2020 2020 , [K]). \n-00017830: 2074 6865 6e20 7472 616e 736c 6174 6528 then translate(\n-00017840: 2870 726f 7869 6d61 6c5f 315f 6c6f 6329 (proximal_1_loc)\n-00017850: 202d 2028 4f29 2920 7d20 0a20 2020 2020 - (O)) } . \n-00017860: 207b 6a6f 696e 745f 7370 6865 7265 7d0a {joint_sphere}.\n-00017870: 0a20 2020 2025 2070 616c 6d0a 2020 2020 . % palm. \n-00017880: 7377 6565 7020 7b20 312c 2072 6f74 6174 sweep { 1, rotat\n-00017890: 6528 362c 2028 302c 3135 2c30 292c 205b e(6, (0,15,0), [\n-000178a0: 495d 2920 7d0a 2020 2020 2020 7075 7420 I]) }. put \n-000178b0: 7b20 726f 7461 7465 282d 332c 2028 302c { rotate(-3, (0,\n-000178c0: 3135 2c30 292c 205b 495d 2920 7d20 7b0a 15,0), [I]) } {.\n-000178d0: 2020 2020 2020 2020 706f 6c79 676f 6e28 polygon(\n-000178e0: 7072 6f78 696d 616c 5f31 5f6c 6f63 2928 proximal_1_loc)(\n-000178f0: 7072 6f78 696d 616c 5f32 5f6c 6f63 290a proximal_2_loc).\n-00017900: 2020 2020 2020 2020 2020 2020 2020 2028 (\n-00017910: 7072 6f78 696d 616c 5f33 5f6c 6f63 2928 proximal_3_loc)(\n-00017920: 7072 6f78 696d 616c 5f34 5f6c 6f63 290a proximal_4_loc).\n-00017930: 2020 2020 2020 2020 2020 2020 2020 2028 (\n-00017940: 6835 2928 6836 2928 6836 6129 2868 3929 h5)(h6)(h6a)(h9)\n-00017950: 2868 3130 290a 2020 2020 2020 2020 706f (h10). po\n-00017960: 6c79 676f 6e28 6836 6129 2868 3729 2868 lygon(h6a)(h7)(h\n-00017970: 3829 2868 3929 0a20 2020 7d20 207d 0a54 8)(h9). } }.T\n-00017980: 6865 206c 6173 7420 7365 6374 696f 6e20 he last section \n-00017990: 6f66 2074 6865 2064 6566 696e 6974 696f of the definitio\n-000179a0: 6e20 6372 6561 7465 7320 7468 6520 706f n creates the po\n-000179b0: 6c79 746f 7065 2066 6f72 2074 6865 2070 lytope for the p\n-000179c0: 616c 6d20 6f66 0a74 6865 2068 616e 6420 alm of.the hand \n-000179d0: 6279 20e2 8098 7377 6565 70e2 8099 696e by ...sweep...in\n-000179e0: 6720 6120 3130 2d73 6964 6564 2070 6f6c g a 10-sided pol\n-000179f0: 7967 6f6e 2074 6872 6f75 6768 2061 2076 ygon through a v\n-00017a00: 6572 7920 7368 6f72 7420 6172 630a 2839 ery short arc.(9\n-00017a10: 2064 6567 7265 6573 292e 2020 5468 6973 degrees). This\n-00017a20: 2070 726f 7669 6465 7320 6120 7765 6467 provides a wedg\n-00017a30: 652d 7368 6170 6564 2070 726f 6669 6c65 e-shaped profile\n-00017a40: 2077 6865 6e20 7669 6577 6564 2066 726f when viewed fro\n-00017a50: 6d20 7468 650a 7369 6465 2e20 2054 6865 m the.side. The\n-00017a60: 2074 6869 636b 2065 6e64 206f 6620 7468 thick end of th\n-00017a70: 6520 7765 6467 6520 6973 2074 6865 2077 e wedge is the w\n-00017a80: 7269 7374 2e20 2042 6563 6175 7365 2074 rist. Because t\n-00017a90: 6865 2070 6f6c 7967 6f6e 2069 730a 636f he polygon is.co\n-00017aa0: 6e63 6176 652c 2069 7420 6973 2073 706c ncave, it is spl\n-00017ab0: 6974 2069 6e74 6f20 696e 746f 2074 776f it into into two\n-00017ac0: 2063 6f6e 7665 7820 7368 6170 6573 2077 convex shapes w\n-00017ad0: 6974 6820 6e69 6e65 2061 6e64 2066 6f75 ith nine and fou\n-00017ae0: 720a 7665 7274 6963 6573 2e0a 0a20 2020 r.vertices... \n-00017af0: 5765 2063 616e 206e 6f77 2068 6176 6520 We can now have \n-00017b00: 6675 6e20 706f 7369 7469 6f6e 696e 6720 fun positioning \n-00017b10: 7468 6520 6861 6e64 2062 7920 6164 6a75 the hand by adju\n-00017b20: 7374 696e 6720 7468 6520 7661 7269 6f75 sting the variou\n-00017b30: 730a 726f 7461 7469 6f6e 2061 6e67 6c65 s.rotation angle\n-00017b40: 732e 2020 5468 6520 636f 6d70 6c65 7465 s. The complete\n-00017b50: 2073 6f75 7263 6520 696e 636c 7564 6573 source includes\n-00017b60: 2064 6566 696e 6974 696f 6e73 2077 6974 definitions wit\n-00017b70: 680a 616c 7465 726e 6174 6976 6573 2074 h.alternatives t\n-00017b80: 6861 7420 696e 636c 7564 6520 7468 6520 hat include the \n-00017b90: 666f 6c6c 6f77 696e 6720 7669 6577 7320 following views \n-00017ba0: 616e 6420 6d6f 7265 2e0a 0a00 085b 696d and more.....[im\n-00017bb0: 6167 6520 7372 633d 2265 7832 3130 2e70 age src=\"ex210.p\n-00017bc0: 6e67 2220 7465 7874 3d22 496d 6167 6520 ng\" text=\"Image \n-00017bd0: 6578 3231 3020 6f6d 6974 7465 6420 696e ex210 omitted in\n-00017be0: 2074 6578 7420 7665 7273 696f 6e20 6f66 text version of\n-00017bf0: 2074 6869 7320 646f 6375 6d65 6e74 2e22 this document.\"\n-00017c00: 0008 5d00 085b 696d 6167 6520 7372 633d ..]..[image src=\n-00017c10: 2265 7832 3230 2e70 6e67 2220 7465 7874 \"ex220.png\" text\n-00017c20: 3d22 496d 6167 6520 6578 3232 3020 6f6d =\"Image ex220 om\n-00017c30: 6974 7465 6420 696e 2074 6578 7420 7665 itted in text ve\n-00017c40: 7273 696f 6e20 6f66 2074 6869 7320 646f rsion of this do\n-00017c50: 6375 6d65 6e74 2e22 0008 5d00 085b 696d cument.\"..]..[im\n-00017c60: 6167 6520 7372 633d 2265 7832 3330 2e70 age src=\"ex230.p\n-00017c70: 6e67 2220 7465 7874 3d22 496d 6167 6520 ng\" text=\"Image \n-00017c80: 6578 3233 3020 6f6d 6974 7465 6420 696e ex230 omitted in\n-00017c90: 2074 6578 7420 7665 7273 696f 6e20 6f66 text version of\n-00017ca0: 2074 6869 7320 646f 6375 6d65 6e74 2e22 this document.\"\n-00017cb0: 0008 5d00 085b 696d 6167 6520 7372 633d ..]..[image src=\n-00017cc0: 2265 7832 3430 2e70 6e67 2220 7465 7874 \"ex240.png\" text\n-00017cd0: 3d22 496d 6167 6520 6578 3234 3020 6f6d =\"Image ex240 om\n-00017ce0: 6974 7465 6420 696e 2074 6578 7420 7665 itted in text ve\n-00017cf0: 7273 696f 6e20 6f66 2074 6869 7320 646f rsion of this do\n-00017d00: 6375 6d65 6e74 2e22 0008 5d0a 0a1f 0a46 cument.\"..]....F\n-00017d10: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n-00017d20: 2c20 204e 6f64 653a 2043 6176 6561 7473 , Node: Caveats\n-00017d30: 2c20 2050 7265 763a 2041 2068 6965 7261 , Prev: A hiera\n-00017d40: 7263 6869 6361 6c20 6d6f 6465 6c2c 2020 rchical model, \n-00017d50: 5570 3a20 4275 696c 6469 6e67 2061 2064 Up: Building a d\n-00017d60: 7261 7769 6e67 0a0a 342e 3420 4361 7665 rawing..4.4 Cave\n-00017d70: 6174 730a 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a ats.===========.\n-00017d80: 0ae2 8098 536b 6574 6368 e280 9920 6973 ....Sketch... is\n-00017d90: 2061 2066 6169 726c 7920 706f 7765 7266 a fairly powerf\n-00017da0: 756c 2074 6f6f 6c20 666f 7220 6472 6177 ul tool for draw\n-00017db0: 696e 672c 2062 7574 2c20 6a75 7374 2061 ing, but, just a\n-00017dc0: 7320 7769 7468 2054 6558 2c0a 7468 6520 s with TeX,.the \n-00017dd0: 706f 7765 7220 746f 2063 7265 6174 6520 power to create \n-00017de0: 6265 6175 7469 6675 6c20 7265 7375 6c74 beautiful result\n-00017df0: 7320 636f 6d65 7320 616c 6f6e 6720 7769 s comes along wi\n-00017e00: 7468 2074 6865 2070 6f77 6572 2074 6f20 th the power to \n-00017e10: 6d61 6b65 0a6d 6973 7461 6b65 732e 2020 make.mistakes. \n-00017e20: 5468 6520 666f 6c6c 6f77 696e 6720 6172 The following ar\n-00017e30: 6520 736f 6d65 2070 6f69 6e74 7320 7768 e some points wh\n-00017e40: 6572 6520 6361 7265 2069 7320 6e65 6365 ere care is nece\n-00017e50: 7373 6172 7920 616e 640a 7768 6572 6520 ssary and.where \n-00017e60: 7468 6520 6375 7272 656e 7420 7665 7273 the current vers\n-00017e70: 696f 6e20 6f66 20e2 8098 736b 6574 6368 ion of ...sketch\n-00017e80: e280 9920 6973 206c 696d 6974 6564 206f ... is limited o\n-00017e90: 7220 6861 7320 6b6e 6f77 6e20 6275 6773 r has known bugs\n-00017ea0: 2e0a 0a2a 204d 656e 753a 0a0a 2a20 4c69 ...* Menu:..* Li\n-00017eb0: 6d69 7473 206f 6e20 6572 726f 7220 6465 mits on error de\n-00017ec0: 7465 6374 696f 6e3a 3a20 2020 5768 6174 tection:: What\n-00017ed0: 2073 6b65 7463 6820 646f 6573 6e27 7420 sketch doesn't \n-00017ee0: 646f 2e0a 2a20 436c 6970 7069 6e67 3a3a do..* Clipping::\n+00016f70: 2020 2020 2020 206a 6f69 6e74 5f67 6170 joint_gap\n+00016f80: 202a 206a 6f69 6e74 5f72 6164 2920 2a20 * joint_rad) * \n+00016f90: 5b4a 5d29 207d 0a20 2020 2020 207b 6469 [J]) }. {di\n+00016fa0: 7374 616c 5f31 7d0a 2020 2020 7075 7420 stal_1}. put \n+00016fb0: 7b20 7363 616c 6528 7072 6f78 696d 616c { scale(proximal\n+00016fc0: 5f64 6973 7461 6c5f 7261 7469 6f29 0a20 _distal_ratio). \n+00016fd0: 2020 2020 2020 2020 2074 6865 6e20 726f then ro\n+00016fe0: 7461 7465 286d 6964 646c 655f 315f 726f tate(middle_1_ro\n+00016ff0: 7420 2f20 322c 205b 495d 290a 2020 2020 t / 2, [I]). \n+00017000: 2020 2020 2020 7468 656e 2074 7261 6e73 then trans\n+00017010: 6c61 7465 2828 6d69 6464 6c65 5f72 6174 late((middle_rat\n+00017020: 696f 202a 2064 6973 7461 6c5f 6c65 6e20 io * distal_len \n+00017030: 2b20 0a20 2020 2020 2020 2020 2020 2020 + . \n+00017040: 2020 2020 2020 2020 2020 2020 206a 6f69 joi\n+00017050: 6e74 5f67 6170 202a 206a 6f69 6e74 5f72 nt_gap * joint_r\n+00017060: 6164 2920 2a20 5b4a 5d29 207d 200a 2020 ad) * [J]) } . \n+00017070: 2020 2020 7b6a 6f69 6e74 5f73 7068 6572 {joint_spher\n+00017080: 657d 0a20 2020 2070 7574 207b 2073 6361 e}. put { sca\n+00017090: 6c65 2820 6d69 6464 6c65 5f72 6174 696f le( middle_ratio\n+000170a0: 202a 205b 4a5d 202b 200a 2020 2020 2020 * [J] + . \n+000170b0: 2020 2020 2020 2020 2020 2070 726f 7869 proxi\n+000170c0: 6d61 6c5f 6469 7374 616c 5f72 6174 696f mal_distal_ratio\n+000170d0: 5e32 202a 2028 5b49 5d2b 5b4b 5d29 2029 ^2 * ([I]+[K]) )\n+000170e0: 207d 0a20 2020 2020 207b 7365 676d 656e }. {segmen\n+000170f0: 747d 0a20 207d 0a54 6869 7320 6c6f 6f6b t}. }.This look\n+00017100: 7320 7665 7279 2073 696d 696c 6172 2074 s very similar t\n+00017110: 6f20 7468 6520 7072 6576 696f 7573 2064 o the previous d\n+00017120: 6566 696e 6974 696f 6e2c 2061 6e64 2069 efinition, and i\n+00017130: 7420 6973 2e20 2054 6865 0a69 6d70 6f72 t is. The.impor\n+00017140: 7461 6e74 2064 6966 6665 7265 6e63 6520 tant difference \n+00017150: 6973 2074 6861 7420 7261 7468 6572 2074 is that rather t\n+00017160: 6861 6e20 706f 7369 7469 6f6e 696e 6720 han positioning \n+00017170: 616e 6420 726f 7461 7469 6e67 2061 0a73 and rotating a.s\n+00017180: 696e 676c 6520 7365 676d 656e 742c 2077 ingle segment, w\n+00017190: 6520 706f 7369 7469 6f6e 2061 6e64 2072 e position and r\n+000171a0: 6f74 6174 6520 7468 6520 656e 7469 7265 otate the entire\n+000171b0: 2022 6173 7365 6d62 6c79 2220 6465 6669 \"assembly\" defi\n+000171c0: 6e65 6420 6173 0ae2 8098 6469 7374 616c ned as....distal\n+000171d0: 5f31 e280 992e 2020 5468 6520 7265 7374 _1.... The rest\n+000171e0: 2069 7320 6a75 7374 2061 7269 7468 6d65 is just arithme\n+000171f0: 7469 6320 746f 2063 6f6d 7075 7465 2073 tic to compute s\n+00017200: 697a 6573 2061 6e64 2070 6f73 6974 696f izes and positio\n+00017210: 6e73 0a74 6861 7420 6c6f 6f6b 206e 6963 ns.that look nic\n+00017220: 652e 2020 5468 6520 6c61 7374 20e2 8098 e. The last ...\n+00017230: 7075 74e2 8099 2070 6c61 6365 7320 616e put... places an\n+00017240: 2061 7070 726f 7072 6961 7465 6c79 2073 appropriately s\n+00017250: 6861 7065 6420 7365 676d 656e 740a 7468 haped segment.th\n+00017260: 6174 2069 7320 7468 6520 5f70 726f 7869 at is the _proxi\n+00017270: 6d61 6c20 7068 6c61 6e67 6573 5f2c 2074 mal phlanges_, t\n+00017280: 6865 2062 6f6e 6520 7468 6174 206a 6f69 he bone that joi\n+00017290: 6e73 2074 6865 2070 616c 6d20 6f66 2074 ns the palm of t\n+000172a0: 6865 0a68 616e 642e 2020 5468 6973 2063 he.hand. This c\n+000172b0: 6f6d 706c 6574 6573 2074 6865 2066 696e ompletes the fin\n+000172c0: 6765 7220 6974 7365 6c66 2e0a 0a20 2020 ger itself... \n+000172d0: 416c 6c20 7468 6520 6f74 6865 7220 6669 All the other fi\n+000172e0: 6e67 6572 7320 6172 6520 6465 7363 7269 ngers are descri\n+000172f0: 6265 6420 6964 656e 7469 6361 6c6c 7920 bed identically \n+00017300: 746f 2074 6869 7320 6f6e 652e 2020 5765 to this one. We\n+00017310: 0a61 6363 6f75 6e74 2066 6f72 2074 6865 .account for the\n+00017320: 2066 6163 7420 7468 6174 2072 6561 6c20 fact that real \n+00017330: 6669 6e67 6572 7320 6172 6520 6469 6666 fingers are diff\n+00017340: 6572 656e 7420 7369 7a65 7320 696e 2074 erent sizes in t\n+00017350: 6865 206e 6578 740a 7374 6570 2c20 7768 he next.step, wh\n+00017360: 6963 6820 6973 2074 6f20 6275 696c 6420 ich is to build \n+00017370: 7468 6520 656e 7469 7265 2068 616e 642e the entire hand.\n+00017380: 0a0a 2020 2054 6865 20e2 8098 6861 6e64 .. The ...hand\n+00017390: e280 9920 6465 6669 6e69 7469 6f6e 2074 ... definition t\n+000173a0: 6861 7420 666f 6c6c 6f77 7320 696e 636c hat follows incl\n+000173b0: 7564 6573 2061 2073 6563 7469 6f6e 2066 udes a section f\n+000173c0: 6f72 2065 6163 680a 6669 6e67 6572 2e20 or each.finger. \n+000173d0: 2057 6527 6c6c 2063 6f6e 7469 6e75 6520 We'll continue \n+000173e0: 7769 7468 2066 696e 6765 7220 3120 616e with finger 1 an\n+000173f0: 6420 6f6d 6974 2061 6c6c 2074 6865 206f d omit all the o\n+00017400: 7468 6572 732e 2020 284f 6620 6e6f 7465 thers. (Of note\n+00017410: 0a69 7320 7468 6174 2074 6865 2074 6875 .is that the thu\n+00017420: 6d62 206e 6565 6473 2073 6c69 6768 746c mb needs slightl\n+00017430: 7920 7370 6563 6961 6c20 7472 6561 746d y special treatm\n+00017440: 656e 742d 2d61 6e20 6578 7472 6120 726f ent--an extra ro\n+00017450: 7461 7469 6f6e 2074 6f0a 6163 636f 756e tation to.accoun\n+00017460: 7420 666f 7220 6974 7320 6f70 706f 7369 t for its opposi\n+00017470: 6e67 2061 6e67 6c65 2e20 2054 6869 7320 ng angle. This \n+00017480: 6973 2063 6c65 6172 2069 6e20 7468 6520 is clear in the \n+00017490: 6675 6c6c 2073 6f75 7263 6520 636f 6465 full source code\n+000174a0: 2e29 0a4e 6f74 2073 7572 7072 6973 696e .).Not surprisin\n+000174b0: 676c 792c 2074 6865 20e2 8098 6861 6e64 gly, the ...hand\n+000174c0: e280 9920 6465 6669 6e69 7469 6f6e 206c ... definition l\n+000174d0: 6f6f 6b73 2076 6572 7920 6d75 6368 206c ooks very much l\n+000174e0: 696b 6520 7468 650a 7072 6576 696f 7573 ike the.previous\n+000174f0: 2074 776f 2e20 2049 7420 7368 6f75 6c64 two. It should\n+00017500: 2062 6520 6e6f 2073 7572 7072 6973 6520 be no surprise \n+00017510: 7468 6174 2077 6865 6e20 7468 6520 726f that when the ro\n+00017520: 7461 7469 6f6e 2070 6172 616d 6574 6572 tation parameter\n+00017530: 0ae2 8098 6d65 7461 5f31 5f72 6f74 e280 ....meta_1_rot..\n+00017540: 9920 6368 616e 6765 732c 2074 6865 2065 . changes, the e\n+00017550: 6e74 6972 6520 6669 6e67 6572 2072 6f74 ntire finger rot\n+00017560: 6174 6573 2120 2054 6865 7265 2069 7320 ates! There is \n+00017570: 616e 2061 6464 6974 696f 6e61 6c0a 726f an additional.ro\n+00017580: 7461 7469 6f6e 2074 6861 7420 616c 6c6f tation that allo\n+00017590: 7773 2074 6865 2066 696e 6765 7273 2074 ws the fingers t\n+000175a0: 6f20 7370 7265 6164 206c 6174 6572 616c o spread lateral\n+000175b0: 6c79 2e20 2057 6520 7361 7920 7468 6573 ly. We say thes\n+000175c0: 650a 6a6f 696e 7473 206f 6620 7468 6520 e.joints of the \n+000175d0: 7072 6f78 696d 616c 2070 686c 616e 6765 proximal phlange\n+000175e0: 7320 6861 7665 2074 776f 205f 6465 6772 s have two _degr\n+000175f0: 6565 7320 6f66 2066 7265 6564 6f6d 5f2e ees of freedom_.\n+00017600: 2020 5468 650a 6a6f 696e 7473 2068 6967 The.joints hig\n+00017610: 6865 7220 6f6e 2074 6865 2066 696e 6765 her on the finge\n+00017620: 7220 6861 7665 206f 6e6c 7920 6f6e 652e r have only one.\n+00017630: 2020 4669 6e61 6c6c 792c 2065 6163 6820 Finally, each \n+00017640: 6669 6e67 6572 2069 730a 7363 616c 6564 finger is.scaled\n+00017650: 2062 7920 6120 6661 6374 6f72 2074 6f20 by a factor to \n+00017660: 6c65 6e64 2069 7420 7072 6f70 6f72 7469 lend it proporti\n+00017670: 6f6e 2e0a 2020 6465 6620 6861 6e64 207b on.. def hand {\n+00017680: 0a20 2020 2025 2066 696e 6765 7220 3120 . % finger 1 \n+00017690: 5b61 6c6c 206f 7468 6572 2066 696e 6765 [all other finge\n+000176a0: 7273 206f 6d69 7474 6564 5d0a 2020 2020 rs omitted]. \n+000176b0: 6465 6620 7363 616c 655f 3120 2e38 350a def scale_1 .85.\n+000176c0: 2020 2020 7075 7420 7b20 7363 616c 6528 put { scale(\n+000176d0: 7363 616c 655f 3129 200a 2020 2020 2020 scale_1) . \n+000176e0: 2020 2020 7468 656e 2074 7261 6e73 6c61 then transla\n+000176f0: 7465 2828 6a6f 696e 745f 6761 7020 2a20 te((joint_gap * \n+00017700: 6a6f 696e 745f 7261 6429 202a 205b 4a5d joint_rad) * [J]\n+00017710: 290a 0920 2074 6865 6e20 726f 7461 7465 ).. then rotate\n+00017720: 286d 6574 615f 315f 726f 742c 205b 495d (meta_1_rot, [I]\n+00017730: 290a 2020 2020 2020 2020 2020 7468 656e ). then\n+00017740: 2072 6f74 6174 6528 2d73 7072 6561 645f rotate(-spread_\n+00017750: 726f 742c 205b 4b5d 290a 2020 2020 2020 rot, [K]). \n+00017760: 2020 2020 7468 656e 2074 7261 6e73 6c61 then transla\n+00017770: 7465 2828 7072 6f78 696d 616c 5f31 5f6c te((proximal_1_l\n+00017780: 6f63 2920 2d20 284f 2929 207d 200a 2020 oc) - (O)) } . \n+00017790: 2020 2020 7b66 696e 6765 725f 317d 0a20 {finger_1}. \n+000177a0: 2020 2070 7574 207b 2073 6361 6c65 2873 put { scale(s\n+000177b0: 6361 6c65 5f31 202a 2070 726f 7869 6d61 cale_1 * proxima\n+000177c0: 6c5f 6469 7374 616c 5f72 6174 696f 5e32 l_distal_ratio^2\n+000177d0: 290a 2020 2020 2020 2020 2020 7468 656e ). then\n+000177e0: 2072 6f74 6174 6528 6d65 7461 5f31 5f72 rotate(meta_1_r\n+000177f0: 6f74 202f 2032 2c20 5b49 5d29 0a20 2020 ot / 2, [I]). \n+00017800: 2020 2020 2020 2074 6865 6e20 726f 7461 then rota\n+00017810: 7465 282d 7370 7265 6164 5f72 6f74 2c20 te(-spread_rot, \n+00017820: 5b4b 5d29 0a20 2020 2020 2020 2020 2074 [K]). t\n+00017830: 6865 6e20 7472 616e 736c 6174 6528 2870 hen translate((p\n+00017840: 726f 7869 6d61 6c5f 315f 6c6f 6329 202d roximal_1_loc) -\n+00017850: 2028 4f29 2920 7d20 0a20 2020 2020 207b (O)) } . {\n+00017860: 6a6f 696e 745f 7370 6865 7265 7d0a 0a20 joint_sphere}.. \n+00017870: 2020 2025 2070 616c 6d0a 2020 2020 7377 % palm. sw\n+00017880: 6565 7020 7b20 312c 2072 6f74 6174 6528 eep { 1, rotate(\n+00017890: 362c 2028 302c 3135 2c30 292c 205b 495d 6, (0,15,0), [I]\n+000178a0: 2920 7d0a 2020 2020 2020 7075 7420 7b20 ) }. put { \n+000178b0: 726f 7461 7465 282d 332c 2028 302c 3135 rotate(-3, (0,15\n+000178c0: 2c30 292c 205b 495d 2920 7d20 7b0a 2020 ,0), [I]) } {. \n+000178d0: 2020 2020 2020 706f 6c79 676f 6e28 7072 polygon(pr\n+000178e0: 6f78 696d 616c 5f31 5f6c 6f63 2928 7072 oximal_1_loc)(pr\n+000178f0: 6f78 696d 616c 5f32 5f6c 6f63 290a 2020 oximal_2_loc). \n+00017900: 2020 2020 2020 2020 2020 2020 2028 7072 (pr\n+00017910: 6f78 696d 616c 5f33 5f6c 6f63 2928 7072 oximal_3_loc)(pr\n+00017920: 6f78 696d 616c 5f34 5f6c 6f63 290a 2020 oximal_4_loc). \n+00017930: 2020 2020 2020 2020 2020 2020 2028 6835 (h5\n+00017940: 2928 6836 2928 6836 6129 2868 3929 2868 )(h6)(h6a)(h9)(h\n+00017950: 3130 290a 2020 2020 2020 2020 706f 6c79 10). poly\n+00017960: 676f 6e28 6836 6129 2868 3729 2868 3829 gon(h6a)(h7)(h8)\n+00017970: 2868 3929 0a20 2020 7d20 207d 0a54 6865 (h9). } }.The\n+00017980: 206c 6173 7420 7365 6374 696f 6e20 6f66 last section of\n+00017990: 2074 6865 2064 6566 696e 6974 696f 6e20 the definition \n+000179a0: 6372 6561 7465 7320 7468 6520 706f 6c79 creates the poly\n+000179b0: 746f 7065 2066 6f72 2074 6865 2070 616c tope for the pal\n+000179c0: 6d20 6f66 0a74 6865 2068 616e 6420 6279 m of.the hand by\n+000179d0: 20e2 8098 7377 6565 70e2 8099 696e 6720 ...sweep...ing \n+000179e0: 6120 3130 2d73 6964 6564 2070 6f6c 7967 a 10-sided polyg\n+000179f0: 6f6e 2074 6872 6f75 6768 2061 2076 6572 on through a ver\n+00017a00: 7920 7368 6f72 7420 6172 630a 2839 2064 y short arc.(9 d\n+00017a10: 6567 7265 6573 292e 2020 5468 6973 2070 egrees). This p\n+00017a20: 726f 7669 6465 7320 6120 7765 6467 652d rovides a wedge-\n+00017a30: 7368 6170 6564 2070 726f 6669 6c65 2077 shaped profile w\n+00017a40: 6865 6e20 7669 6577 6564 2066 726f 6d20 hen viewed from \n+00017a50: 7468 650a 7369 6465 2e20 2054 6865 2074 the.side. The t\n+00017a60: 6869 636b 2065 6e64 206f 6620 7468 6520 hick end of the \n+00017a70: 7765 6467 6520 6973 2074 6865 2077 7269 wedge is the wri\n+00017a80: 7374 2e20 2042 6563 6175 7365 2074 6865 st. Because the\n+00017a90: 2070 6f6c 7967 6f6e 2069 730a 636f 6e63 polygon is.conc\n+00017aa0: 6176 652c 2069 7420 6973 2073 706c 6974 ave, it is split\n+00017ab0: 2069 6e74 6f20 696e 746f 2074 776f 2063 into into two c\n+00017ac0: 6f6e 7665 7820 7368 6170 6573 2077 6974 onvex shapes wit\n+00017ad0: 6820 6e69 6e65 2061 6e64 2066 6f75 720a h nine and four.\n+00017ae0: 7665 7274 6963 6573 2e0a 0a20 2020 5765 vertices... We\n+00017af0: 2063 616e 206e 6f77 2068 6176 6520 6675 can now have fu\n+00017b00: 6e20 706f 7369 7469 6f6e 696e 6720 7468 n positioning th\n+00017b10: 6520 6861 6e64 2062 7920 6164 6a75 7374 e hand by adjust\n+00017b20: 696e 6720 7468 6520 7661 7269 6f75 730a ing the various.\n+00017b30: 726f 7461 7469 6f6e 2061 6e67 6c65 732e rotation angles.\n+00017b40: 2020 5468 6520 636f 6d70 6c65 7465 2073 The complete s\n+00017b50: 6f75 7263 6520 696e 636c 7564 6573 2064 ource includes d\n+00017b60: 6566 696e 6974 696f 6e73 2077 6974 680a efinitions with.\n+00017b70: 616c 7465 726e 6174 6976 6573 2074 6861 alternatives tha\n+00017b80: 7420 696e 636c 7564 6520 7468 6520 666f t include the fo\n+00017b90: 6c6c 6f77 696e 6720 7669 6577 7320 616e llowing views an\n+00017ba0: 6420 6d6f 7265 2e0a 0a00 085b 696d 6167 d more.....[imag\n+00017bb0: 6520 7372 633d 2265 7832 3130 2e70 6e67 e src=\"ex210.png\n+00017bc0: 2220 7465 7874 3d22 496d 6167 6520 6578 \" text=\"Image ex\n+00017bd0: 3231 3020 6f6d 6974 7465 6420 696e 2074 210 omitted in t\n+00017be0: 6578 7420 7665 7273 696f 6e20 6f66 2074 ext version of t\n+00017bf0: 6869 7320 646f 6375 6d65 6e74 2e22 0008 his document.\"..\n+00017c00: 5d00 085b 696d 6167 6520 7372 633d 2265 ]..[image src=\"e\n+00017c10: 7832 3230 2e70 6e67 2220 7465 7874 3d22 x220.png\" text=\"\n+00017c20: 496d 6167 6520 6578 3232 3020 6f6d 6974 Image ex220 omit\n+00017c30: 7465 6420 696e 2074 6578 7420 7665 7273 ted in text vers\n+00017c40: 696f 6e20 6f66 2074 6869 7320 646f 6375 ion of this docu\n+00017c50: 6d65 6e74 2e22 0008 5d00 085b 696d 6167 ment.\"..]..[imag\n+00017c60: 6520 7372 633d 2265 7832 3330 2e70 6e67 e src=\"ex230.png\n+00017c70: 2220 7465 7874 3d22 496d 6167 6520 6578 \" text=\"Image ex\n+00017c80: 3233 3020 6f6d 6974 7465 6420 696e 2074 230 omitted in t\n+00017c90: 6578 7420 7665 7273 696f 6e20 6f66 2074 ext version of t\n+00017ca0: 6869 7320 646f 6375 6d65 6e74 2e22 0008 his document.\"..\n+00017cb0: 5d00 085b 696d 6167 6520 7372 633d 2265 ]..[image src=\"e\n+00017cc0: 7832 3430 2e70 6e67 2220 7465 7874 3d22 x240.png\" text=\"\n+00017cd0: 496d 6167 6520 6578 3234 3020 6f6d 6974 Image ex240 omit\n+00017ce0: 7465 6420 696e 2074 6578 7420 7665 7273 ted in text vers\n+00017cf0: 696f 6e20 6f66 2074 6869 7320 646f 6375 ion of this docu\n+00017d00: 6d65 6e74 2e22 0008 5d0a 0a1f 0a46 696c ment.\"..]....Fil\n+00017d10: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n+00017d20: 204e 6f64 653a 2043 6176 6561 7473 2c20 Node: Caveats, \n+00017d30: 2050 7265 763a 2041 2068 6965 7261 7263 Prev: A hierarc\n+00017d40: 6869 6361 6c20 6d6f 6465 6c2c 2020 5570 hical model, Up\n+00017d50: 3a20 4275 696c 6469 6e67 2061 2064 7261 : Building a dra\n+00017d60: 7769 6e67 0a0a 342e 3420 4361 7665 6174 wing..4.4 Caveat\n+00017d70: 730a 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a 0ae2 s.===========...\n+00017d80: 8098 536b 6574 6368 e280 9920 6973 2061 ..Sketch... is a\n+00017d90: 2066 6169 726c 7920 706f 7765 7266 756c fairly powerful\n+00017da0: 2074 6f6f 6c20 666f 7220 6472 6177 696e tool for drawin\n+00017db0: 672c 2062 7574 2c20 6a75 7374 2061 7320 g, but, just as \n+00017dc0: 7769 7468 2054 6558 2c0a 7468 6520 706f with TeX,.the po\n+00017dd0: 7765 7220 746f 2063 7265 6174 6520 6265 wer to create be\n+00017de0: 6175 7469 6675 6c20 7265 7375 6c74 7320 autiful results \n+00017df0: 636f 6d65 7320 616c 6f6e 6720 7769 7468 comes along with\n+00017e00: 2074 6865 2070 6f77 6572 2074 6f20 6d61 the power to ma\n+00017e10: 6b65 0a6d 6973 7461 6b65 732e 2020 5468 ke.mistakes. Th\n+00017e20: 6520 666f 6c6c 6f77 696e 6720 6172 6520 e following are \n+00017e30: 736f 6d65 2070 6f69 6e74 7320 7768 6572 some points wher\n+00017e40: 6520 6361 7265 2069 7320 6e65 6365 7373 e care is necess\n+00017e50: 6172 7920 616e 640a 7768 6572 6520 7468 ary and.where th\n+00017e60: 6520 6375 7272 656e 7420 7665 7273 696f e current versio\n+00017e70: 6e20 6f66 20e2 8098 736b 6574 6368 e280 n of ...sketch..\n+00017e80: 9920 6973 206c 696d 6974 6564 206f 7220 . is limited or \n+00017e90: 6861 7320 6b6e 6f77 6e20 6275 6773 2e0a has known bugs..\n+00017ea0: 0a2a 204d 656e 753a 0a0a 2a20 4c69 6d69 .* Menu:..* Limi\n+00017eb0: 7473 206f 6e20 6572 726f 7220 6465 7465 ts on error dete\n+00017ec0: 6374 696f 6e3a 3a20 2020 5768 6174 2073 ction:: What s\n+00017ed0: 6b65 7463 6820 646f 6573 6e27 7420 646f ketch doesn't do\n+00017ee0: 2e0a 2a20 436c 6970 7069 6e67 3a3a 2020 ..* Clipping:: \n 00017ef0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00017f00: 2020 2020 4e6f 2063 6c69 7070 696e 6720 No clipping \n-00017f10: 6174 2070 7265 7365 6e74 2e0a 2a20 4869 at present..* Hi\n-00017f20: 6464 656e 2073 7572 6661 6365 2072 656d dden surface rem\n-00017f30: 6f76 616c 3a3a 2020 2020 2020 496d 7065 oval:: Impe\n-00017f40: 7266 6563 7469 6f6e 7320 746f 2066 6978 rfections to fix\n-00017f50: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n-00017f60: 682e 696e 666f 2c20 204e 6f64 653a 204c h.info, Node: L\n-00017f70: 696d 6974 7320 6f6e 2065 7272 6f72 2064 imits on error d\n-00017f80: 6574 6563 7469 6f6e 2c20 204e 6578 743a etection, Next:\n-00017f90: 2043 6c69 7070 696e 672c 2020 5072 6576 Clipping, Prev\n-00017fa0: 3a20 4361 7665 6174 732c 2020 5570 3a20 : Caveats, Up: \n-00017fb0: 4361 7665 6174 730a 0a34 2e34 2e31 204c Caveats..4.4.1 L\n-00017fc0: 696d 6974 7320 6f6e 20e2 8098 736b 6574 imits on ...sket\n-00017fd0: 6368 e280 9920 6572 726f 7220 6465 7465 ch... error dete\n-00017fe0: 6374 696f 6e0a 2d2d 2d2d 2d2d 2d2d 2d2d ction.----------\n+00017f00: 2020 4e6f 2063 6c69 7070 696e 6720 6174 No clipping at\n+00017f10: 2070 7265 7365 6e74 2e0a 2a20 4869 6464 present..* Hidd\n+00017f20: 656e 2073 7572 6661 6365 2072 656d 6f76 en surface remov\n+00017f30: 616c 3a3a 2020 2020 2020 496d 7065 7266 al:: Imperf\n+00017f40: 6563 7469 6f6e 7320 746f 2066 6978 2e0a ections to fix..\n+00017f50: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n+00017f60: 696e 666f 2c20 204e 6f64 653a 204c 696d info, Node: Lim\n+00017f70: 6974 7320 6f6e 2065 7272 6f72 2064 6574 its on error det\n+00017f80: 6563 7469 6f6e 2c20 204e 6578 743a 2043 ection, Next: C\n+00017f90: 6c69 7070 696e 672c 2020 5072 6576 3a20 lipping, Prev: \n+00017fa0: 4361 7665 6174 732c 2020 5570 3a20 4361 Caveats, Up: Ca\n+00017fb0: 7665 6174 730a 0a34 2e34 2e31 204c 696d veats..4.4.1 Lim\n+00017fc0: 6974 7320 6f6e 20e2 8098 736b 6574 6368 its on ...sketch\n+00017fd0: e280 9920 6572 726f 7220 6465 7465 6374 ... error detect\n+00017fe0: 696f 6e0a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ion.------------\n 00017ff0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-00018000: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a --------------..\n-00018010: e280 9853 6b65 7463 68e2 8099 2063 6174 ...Sketch... cat\n-00018020: 6368 6573 206d 616e 7920 6b69 6e64 7320 ches many kinds \n-00018030: 6f66 2065 7272 6f72 732c 2062 7574 206e of errors, but n\n-00018040: 6f74 2061 6c6c 2e20 2046 6f72 2065 7861 ot all. For exa\n-00018050: 6d70 6c65 2c0a 6f70 7469 6f6e 7320 7468 mple,.options th\n-00018060: 6174 2073 6b65 7463 6820 646f 6573 206e at sketch does n\n-00018070: 6f74 2072 6563 6f67 6e69 7a65 2c20 6576 ot recognize, ev\n-00018080: 656e 2069 6e63 6f72 7265 6374 206f 6e65 en incorrect one\n-00018090: 732c 2061 7265 2071 7569 6574 6c79 0a63 s, are quietly.c\n-000180a0: 6f70 6965 6420 746f 20e2 8098 5053 5472 opied to ...PSTr\n-000180b0: 6963 6b73 e280 9920 636f 6d6d 616e 6473 icks... commands\n-000180c0: 2069 6e20 7468 6520 6f75 7470 7574 2e20 in the output. \n-000180d0: 2049 7420 6973 2061 6c73 6f20 756e 666f It is also unfo\n-000180e0: 7274 756e 6174 656c 790a 6561 7379 2074 rtunately.easy t\n-000180f0: 6f20 7072 6f64 7563 6520 e280 9873 6b65 o produce ...ske\n-00018100: 7463 68e2 8099 2069 6e70 7574 7320 7468 tch... inputs th\n-00018110: 6174 206c 6561 6420 746f 206e 6f20 7069 at lead to no pi\n-00018120: 6374 7572 6520 6174 2061 6c6c 2028 696d cture at all (im\n-00018130: 7072 6f70 6572 0a76 6572 7465 7820 6f72 proper.vertex or\n-00018140: 6465 7269 6e67 2063 6175 7365 7320 6576 dering causes ev\n-00018150: 6572 7974 6869 6e67 2074 6f20 6265 2063 erything to be c\n-00018160: 756c 6c65 6429 2c20 746f 2070 6963 7475 ulled), to pictu\n-00018170: 7265 7320 7468 6174 2061 7265 0a74 6f6f res that are.too\n-00018180: 2062 6967 206f 7220 746f 6f20 736d 616c big or too smal\n-00018190: 6c20 666f 7220 e280 9850 5354 7269 636b l for ...PSTrick\n-000181a0: 73e2 8099 2074 6f20 6472 6177 2028 6475 s... to draw (du\n-000181b0: 6520 746f 206c 696d 6974 7320 6f66 2054 e to limits of T\n-000181c0: 6558 206d 6174 6829 2c0a 616e 6420 7069 eX math),.and pi\n-000181d0: 6374 7572 6573 2074 6861 7420 6c6f 6f6b ctures that look\n-000181e0: 206e 6f74 6869 6e67 206c 696b 6520 7768 nothing like wh\n-000181f0: 6174 2077 6173 2069 6e74 656e 6465 642e at was intended.\n-00018200: 2020 4120 7069 6374 7572 6520 7769 7468 A picture with\n-00018210: 0a6f 6e65 206f 6620 7468 6573 6520 7072 .one of these pr\n-00018220: 6f62 6c65 6d73 2063 616e 2062 6520 6469 oblems can be di\n-00018230: 6666 6963 756c 7420 746f 2022 6465 6275 fficult to \"debu\n-00018240: 672e 2220 2057 6520 6f66 6665 7220 7468 g.\" We offer th\n-00018250: 650a 666f 6c6c 6f77 696e 6720 7375 6767 e.following sugg\n-00018260: 6573 7469 6f6e 732e 0a20 2020 e280 a220 estions.. ... \n-00018270: 466f 6c6c 6f77 2074 6865 2073 7567 6765 Follow the sugge\n-00018280: 7374 6564 2069 6e63 7265 6d65 6e74 616c sted incremental\n-00018290: 2064 6576 656c 6f70 6d65 6e74 206d 6574 development met\n-000182a0: 686f 6420 6465 7363 7269 6265 6420 696e hod described in\n-000182b0: 0a20 2020 2020 2a6e 6f74 6520 4f76 6572 . *note Over\n-000182c0: 7669 6577 3a3a 2e0a 2020 20e2 80a2 2041 view::.. ... A\n-000182d0: 6c77 6179 7320 6d61 696e 7461 696e 206f lways maintain o\n-000182e0: 6e65 206f 7220 7477 6f20 6261 636b 2d76 ne or two back-v\n-000182f0: 6572 7369 6f6e 7320 6f66 2061 2064 7261 ersions of a dra\n-00018300: 7769 6e67 2073 6f20 7468 6174 2069 7420 wing so that it \n-00018310: 6973 0a20 2020 2020 6561 7379 2074 6f20 is. easy to \n-00018320: 6661 6c6c 2062 6163 6b20 746f 2061 206b fall back to a k\n-00018330: 6e6f 776e 2d67 6f6f 6420 696e 6372 656d nown-good increm\n-00018340: 656e 742e 0a20 2020 e280 a220 5768 656e ent.. ... When\n-00018350: 2075 7369 6e67 20e2 8098 7065 7273 7065 using ...perspe\n-00018360: 6374 6976 65e2 8099 2c20 656e 7375 7265 ctive..., ensure\n-00018370: 2061 6c6c 2066 696e 616c 6c79 2074 7261 all finally tra\n-00018380: 6e73 666f 726d 6564 206f 626a 6563 7473 nsformed objects\n-00018390: 0a20 2020 2020 7361 7469 7366 7920 7a3c . satisfy z<\n-000183a0: 3020 616e 642c 2069 6e20 6661 6374 2c20 0 and, in fact, \n-000183b0: 646f 206e 6f74 2063 6f6d 6520 7665 7279 do not come very\n-000183c0: 2063 6c6f 7365 2074 6f20 7468 6520 6f72 close to the or\n-000183d0: 6967 696e 2061 740a 2020 2020 2061 6c6c igin at. all\n-000183e0: 2e0a 2020 20e2 80a2 2054 656d 706f 7261 .. ... Tempora\n-000183f0: 7269 6c79 2075 7365 20e2 8098 6375 6c6c rily use ...cull\n-00018400: 3d66 616c 7365 e280 9920 746f 2073 6565 =false... to see\n-00018410: 2077 6865 7265 2076 6572 7465 7820 6f72 where vertex or\n-00018420: 6465 7269 6e67 2070 726f 626c 656d 730a dering problems.\n-00018430: 2020 2020 206c 6965 2e0a 2020 20e2 80a2 lie.. ...\n-00018440: 2055 7365 2074 656d 706f 7261 7279 2063 Use temporary c\n-00018450: 6861 6e67 6573 206f 6620 636f 6c6f 7220 hanges of color \n-00018460: 6f66 206f 6e65 206f 7220 6d6f 7265 206f of one or more o\n-00018470: 626a 6563 7473 2074 6f20 656e 7375 7265 bjects to ensure\n-00018480: 0a20 2020 2020 7468 6174 2079 6f75 7220 . that your \n-00018490: 756e 6465 7273 7461 6e64 696e 6720 6f66 understanding of\n-000184a0: 2074 6865 2073 6365 6e65 2067 656f 6d65 the scene geome\n-000184b0: 7472 7920 6973 2063 6f72 7265 6374 2e0a try is correct..\n-000184c0: 2020 20e2 80a2 2049 6620 e280 9850 5354 ... If ...PST\n-000184d0: 7269 636b 73e2 8099 2063 6f6d 706c 6169 ricks... complai\n-000184e0: 6e73 2061 626f 7574 2073 6f6d 6574 6869 ns about somethi\n-000184f0: 6e67 2c20 696e 7370 6563 7420 7468 6520 ng, inspect the \n-00018500: 6f75 7470 7574 0a20 2020 2020 6469 7265 output. dire\n-00018510: 6374 6c79 2066 6f72 2063 6c75 6573 2e0a ctly for clues..\n-00018520: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n-00018530: 696e 666f 2c20 204e 6f64 653a 2043 6c69 info, Node: Cli\n-00018540: 7070 696e 672c 2020 4e65 7874 3a20 4869 pping, Next: Hi\n-00018550: 6464 656e 2073 7572 6661 6365 2072 656d dden surface rem\n-00018560: 6f76 616c 2c20 2050 7265 763a 204c 696d oval, Prev: Lim\n-00018570: 6974 7320 6f6e 2065 7272 6f72 2064 6574 its on error det\n-00018580: 6563 7469 6f6e 2c20 2055 703a 2043 6176 ection, Up: Cav\n-00018590: 6561 7473 0a0a 342e 342e 3220 436c 6970 eats..4.4.2 Clip\n-000185a0: 7069 6e67 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d ping.-----------\n-000185b0: 2d2d 2d0a 0a54 6865 2063 7572 7265 6e74 ---..The current\n-000185c0: 2076 6572 7369 6f6e 206f 6620 e280 9873 version of ...s\n-000185d0: 6b65 7463 68e2 8099 2068 6173 206e 6f20 ketch... has no \n-000185e0: 636c 6970 7069 6e67 206f 7065 7261 7469 clipping operati\n-000185f0: 6f6e 732e 2020 5468 6520 656e 7469 7265 ons. The entire\n-00018600: 0a73 6365 6e65 2069 7320 616c 7761 7973 .scene is always\n-00018610: 2064 7261 776e 2e20 2054 6869 7320 6d65 drawn. This me\n-00018620: 616e 7320 7468 6174 2077 6865 6e20 6120 ans that when a \n-00018630: 7065 7273 7065 6374 6976 6520 7472 616e perspective tran\n-00018640: 7366 6f72 6d20 6973 0a65 6d70 6c6f 7965 sform is.employe\n-00018650: 642c 2069 7420 6973 2074 6865 2075 7365 d, it is the use\n-00018660: 7227 7320 7265 7370 6f6e 7369 6269 6c69 r's responsibili\n-00018670: 7479 2074 6f20 6d61 6b65 2073 7572 6520 ty to make sure \n-00018680: 7468 6520 656e 7469 7265 2073 6365 6e65 the entire scene\n-00018690: 0a72 656d 6169 6e73 2069 6e20 6672 6f6e .remains in fron\n-000186a0: 7420 6f66 2074 6865 2076 6965 7765 722c t of the viewer,\n-000186b0: 2074 6865 2072 6567 696f 6e20 7a3c 302e the region z<0.\n-000186c0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n-000186d0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4869 .info, Node: Hi\n-000186e0: 6464 656e 2073 7572 6661 6365 2072 656d dden surface rem\n-000186f0: 6f76 616c 2c20 2050 7265 763a 2043 6c69 oval, Prev: Cli\n-00018700: 7070 696e 672c 2020 5570 3a20 4361 7665 pping, Up: Cave\n-00018710: 6174 730a 0a34 2e34 2e33 2048 6964 6465 ats..4.4.3 Hidde\n-00018720: 6e20 7375 7266 6163 6520 7265 6d6f 7661 n surface remova\n-00018730: 6c20 616e 6420 706f 6c79 676f 6e20 7370 l and polygon sp\n-00018740: 6c69 7474 696e 670a 2d2d 2d2d 2d2d 2d2d litting.--------\n+00018000: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a e280 ------------....\n+00018010: 9853 6b65 7463 68e2 8099 2063 6174 6368 .Sketch... catch\n+00018020: 6573 206d 616e 7920 6b69 6e64 7320 6f66 es many kinds of\n+00018030: 2065 7272 6f72 732c 2062 7574 206e 6f74 errors, but not\n+00018040: 2061 6c6c 2e20 2046 6f72 2065 7861 6d70 all. For examp\n+00018050: 6c65 2c0a 6f70 7469 6f6e 7320 7468 6174 le,.options that\n+00018060: 2073 6b65 7463 6820 646f 6573 206e 6f74 sketch does not\n+00018070: 2072 6563 6f67 6e69 7a65 2c20 6576 656e recognize, even\n+00018080: 2069 6e63 6f72 7265 6374 206f 6e65 732c incorrect ones,\n+00018090: 2061 7265 2071 7569 6574 6c79 0a63 6f70 are quietly.cop\n+000180a0: 6965 6420 746f 20e2 8098 5053 5472 6963 ied to ...PSTric\n+000180b0: 6b73 e280 9920 636f 6d6d 616e 6473 2069 ks... commands i\n+000180c0: 6e20 7468 6520 6f75 7470 7574 2e20 2049 n the output. I\n+000180d0: 7420 6973 2061 6c73 6f20 756e 666f 7274 t is also unfort\n+000180e0: 756e 6174 656c 790a 6561 7379 2074 6f20 unately.easy to \n+000180f0: 7072 6f64 7563 6520 e280 9873 6b65 7463 produce ...sketc\n+00018100: 68e2 8099 2069 6e70 7574 7320 7468 6174 h... inputs that\n+00018110: 206c 6561 6420 746f 206e 6f20 7069 6374 lead to no pict\n+00018120: 7572 6520 6174 2061 6c6c 2028 696d 7072 ure at all (impr\n+00018130: 6f70 6572 0a76 6572 7465 7820 6f72 6465 oper.vertex orde\n+00018140: 7269 6e67 2063 6175 7365 7320 6576 6572 ring causes ever\n+00018150: 7974 6869 6e67 2074 6f20 6265 2063 756c ything to be cul\n+00018160: 6c65 6429 2c20 746f 2070 6963 7475 7265 led), to picture\n+00018170: 7320 7468 6174 2061 7265 0a74 6f6f 2062 s that are.too b\n+00018180: 6967 206f 7220 746f 6f20 736d 616c 6c20 ig or too small \n+00018190: 666f 7220 e280 9850 5354 7269 636b 73e2 for ...PSTricks.\n+000181a0: 8099 2074 6f20 6472 6177 2028 6475 6520 .. to draw (due \n+000181b0: 746f 206c 696d 6974 7320 6f66 2054 6558 to limits of TeX\n+000181c0: 206d 6174 6829 2c0a 616e 6420 7069 6374 math),.and pict\n+000181d0: 7572 6573 2074 6861 7420 6c6f 6f6b 206e ures that look n\n+000181e0: 6f74 6869 6e67 206c 696b 6520 7768 6174 othing like what\n+000181f0: 2077 6173 2069 6e74 656e 6465 642e 2020 was intended. \n+00018200: 4120 7069 6374 7572 6520 7769 7468 0a6f A picture with.o\n+00018210: 6e65 206f 6620 7468 6573 6520 7072 6f62 ne of these prob\n+00018220: 6c65 6d73 2063 616e 2062 6520 6469 6666 lems can be diff\n+00018230: 6963 756c 7420 746f 2022 6465 6275 672e icult to \"debug.\n+00018240: 2220 2057 6520 6f66 6665 7220 7468 650a \" We offer the.\n+00018250: 666f 6c6c 6f77 696e 6720 7375 6767 6573 following sugges\n+00018260: 7469 6f6e 732e 0a20 2020 e280 a220 466f tions.. ... Fo\n+00018270: 6c6c 6f77 2074 6865 2073 7567 6765 7374 llow the suggest\n+00018280: 6564 2069 6e63 7265 6d65 6e74 616c 2064 ed incremental d\n+00018290: 6576 656c 6f70 6d65 6e74 206d 6574 686f evelopment metho\n+000182a0: 6420 6465 7363 7269 6265 6420 696e 0a20 d described in. \n+000182b0: 2020 2020 2a6e 6f74 6520 4f76 6572 7669 *note Overvi\n+000182c0: 6577 3a3a 2e0a 2020 20e2 80a2 2041 6c77 ew::.. ... Alw\n+000182d0: 6179 7320 6d61 696e 7461 696e 206f 6e65 ays maintain one\n+000182e0: 206f 7220 7477 6f20 6261 636b 2d76 6572 or two back-ver\n+000182f0: 7369 6f6e 7320 6f66 2061 2064 7261 7769 sions of a drawi\n+00018300: 6e67 2073 6f20 7468 6174 2069 7420 6973 ng so that it is\n+00018310: 0a20 2020 2020 6561 7379 2074 6f20 6661 . easy to fa\n+00018320: 6c6c 2062 6163 6b20 746f 2061 206b 6e6f ll back to a kno\n+00018330: 776e 2d67 6f6f 6420 696e 6372 656d 656e wn-good incremen\n+00018340: 742e 0a20 2020 e280 a220 5768 656e 2075 t.. ... When u\n+00018350: 7369 6e67 20e2 8098 7065 7273 7065 6374 sing ...perspect\n+00018360: 6976 65e2 8099 2c20 656e 7375 7265 2061 ive..., ensure a\n+00018370: 6c6c 2066 696e 616c 6c79 2074 7261 6e73 ll finally trans\n+00018380: 666f 726d 6564 206f 626a 6563 7473 0a20 formed objects. \n+00018390: 2020 2020 7361 7469 7366 7920 7a3c 3020 satisfy z<0 \n+000183a0: 616e 642c 2069 6e20 6661 6374 2c20 646f and, in fact, do\n+000183b0: 206e 6f74 2063 6f6d 6520 7665 7279 2063 not come very c\n+000183c0: 6c6f 7365 2074 6f20 7468 6520 6f72 6967 lose to the orig\n+000183d0: 696e 2061 740a 2020 2020 2061 6c6c 2e0a in at. all..\n+000183e0: 2020 20e2 80a2 2054 656d 706f 7261 7269 ... Temporari\n+000183f0: 6c79 2075 7365 20e2 8098 6375 6c6c 3d66 ly use ...cull=f\n+00018400: 616c 7365 e280 9920 746f 2073 6565 2077 alse... to see w\n+00018410: 6865 7265 2076 6572 7465 7820 6f72 6465 here vertex orde\n+00018420: 7269 6e67 2070 726f 626c 656d 730a 2020 ring problems. \n+00018430: 2020 206c 6965 2e0a 2020 20e2 80a2 2055 lie.. ... U\n+00018440: 7365 2074 656d 706f 7261 7279 2063 6861 se temporary cha\n+00018450: 6e67 6573 206f 6620 636f 6c6f 7220 6f66 nges of color of\n+00018460: 206f 6e65 206f 7220 6d6f 7265 206f 626a one or more obj\n+00018470: 6563 7473 2074 6f20 656e 7375 7265 0a20 ects to ensure. \n+00018480: 2020 2020 7468 6174 2079 6f75 7220 756e that your un\n+00018490: 6465 7273 7461 6e64 696e 6720 6f66 2074 derstanding of t\n+000184a0: 6865 2073 6365 6e65 2067 656f 6d65 7472 he scene geometr\n+000184b0: 7920 6973 2063 6f72 7265 6374 2e0a 2020 y is correct.. \n+000184c0: 20e2 80a2 2049 6620 e280 9850 5354 7269 ... If ...PSTri\n+000184d0: 636b 73e2 8099 2063 6f6d 706c 6169 6e73 cks... complains\n+000184e0: 2061 626f 7574 2073 6f6d 6574 6869 6e67 about something\n+000184f0: 2c20 696e 7370 6563 7420 7468 6520 6f75 , inspect the ou\n+00018500: 7470 7574 0a20 2020 2020 6469 7265 6374 tput. direct\n+00018510: 6c79 2066 6f72 2063 6c75 6573 2e0a 0a1f ly for clues....\n+00018520: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+00018530: 666f 2c20 204e 6f64 653a 2043 6c69 7070 fo, Node: Clipp\n+00018540: 696e 672c 2020 4e65 7874 3a20 4869 6464 ing, Next: Hidd\n+00018550: 656e 2073 7572 6661 6365 2072 656d 6f76 en surface remov\n+00018560: 616c 2c20 2050 7265 763a 204c 696d 6974 al, Prev: Limit\n+00018570: 7320 6f6e 2065 7272 6f72 2064 6574 6563 s on error detec\n+00018580: 7469 6f6e 2c20 2055 703a 2043 6176 6561 tion, Up: Cavea\n+00018590: 7473 0a0a 342e 342e 3220 436c 6970 7069 ts..4.4.2 Clippi\n+000185a0: 6e67 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ng.-------------\n+000185b0: 2d0a 0a54 6865 2063 7572 7265 6e74 2076 -..The current v\n+000185c0: 6572 7369 6f6e 206f 6620 e280 9873 6b65 ersion of ...ske\n+000185d0: 7463 68e2 8099 2068 6173 206e 6f20 636c tch... has no cl\n+000185e0: 6970 7069 6e67 206f 7065 7261 7469 6f6e ipping operation\n+000185f0: 732e 2020 5468 6520 656e 7469 7265 0a73 s. The entire.s\n+00018600: 6365 6e65 2069 7320 616c 7761 7973 2064 cene is always d\n+00018610: 7261 776e 2e20 2054 6869 7320 6d65 616e rawn. This mean\n+00018620: 7320 7468 6174 2077 6865 6e20 6120 7065 s that when a pe\n+00018630: 7273 7065 6374 6976 6520 7472 616e 7366 rspective transf\n+00018640: 6f72 6d20 6973 0a65 6d70 6c6f 7965 642c orm is.employed,\n+00018650: 2069 7420 6973 2074 6865 2075 7365 7227 it is the user'\n+00018660: 7320 7265 7370 6f6e 7369 6269 6c69 7479 s responsibility\n+00018670: 2074 6f20 6d61 6b65 2073 7572 6520 7468 to make sure th\n+00018680: 6520 656e 7469 7265 2073 6365 6e65 0a72 e entire scene.r\n+00018690: 656d 6169 6e73 2069 6e20 6672 6f6e 7420 emains in front \n+000186a0: 6f66 2074 6865 2076 6965 7765 722c 2074 of the viewer, t\n+000186b0: 6865 2072 6567 696f 6e20 7a3c 302e 0a0a he region z<0...\n+000186c0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+000186d0: 6e66 6f2c 2020 4e6f 6465 3a20 4869 6464 nfo, Node: Hidd\n+000186e0: 656e 2073 7572 6661 6365 2072 656d 6f76 en surface remov\n+000186f0: 616c 2c20 2050 7265 763a 2043 6c69 7070 al, Prev: Clipp\n+00018700: 696e 672c 2020 5570 3a20 4361 7665 6174 ing, Up: Caveat\n+00018710: 730a 0a34 2e34 2e33 2048 6964 6465 6e20 s..4.4.3 Hidden \n+00018720: 7375 7266 6163 6520 7265 6d6f 7661 6c20 surface removal \n+00018730: 616e 6420 706f 6c79 676f 6e20 7370 6c69 and polygon spli\n+00018740: 7474 696e 670a 2d2d 2d2d 2d2d 2d2d 2d2d tting.----------\n 00018750: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 00018760: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-00018770: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a e280 9853 ----------.....S\n-00018780: 6b65 7463 68e2 8099 2075 7365 7320 7468 ketch... uses th\n-00018790: 6520 e280 9c64 6570 7468 2073 6f72 7420 e ...depth sort \n-000187a0: 616c 676f 7269 7468 6de2 809d 2066 6f72 algorithm... for\n-000187b0: 2068 6964 6465 6e20 7375 7266 6163 6520 hidden surface \n-000187c0: 7265 6d6f 7661 6c2e 0a54 6869 7320 6973 removal..This is\n-000187d0: 2061 2076 6572 7920 6f6c 6420 7465 6368 a very old tech\n-000187e0: 6e69 7175 6520 6475 6520 746f 204e 6577 nique due to New\n-000187f0: 656c 6c2e 2831 2920 2049 7420 6973 2067 ell.(1) It is g\n-00018800: 656e 6572 616c 6c79 2072 6567 6172 6465 enerally regarde\n-00018810: 640a 6173 2074 6f6f 2073 6c6f 7720 666f d.as too slow fo\n-00018820: 7220 7265 616c 2074 696d 6520 6772 6170 r real time grap\n-00018830: 6869 6373 2c20 6275 7420 6974 2069 7320 hics, but it is \n-00018840: 6964 6561 6c20 666f 7220 6f75 7220 7075 ideal for our pu\n-00018850: 7270 6f73 650a 7768 6572 6520 7370 6565 rpose.where spee\n-00018860: 6420 6973 206e 6f74 2076 6572 7920 696d d is not very im\n-00018870: 706f 7274 616e 742e 2832 290a 0a20 2020 portant.(2).. \n-00018880: 5468 6520 6465 7074 6820 736f 7274 2061 The depth sort a\n-00018890: 6c67 6f72 6974 686d 206d 6572 656c 7920 lgorithm merely \n-000188a0: 736f 7274 7320 6f62 6a65 6374 7320 6f6e sorts objects on\n-000188b0: 2061 206b 6579 206f 6620 696e 6372 6561 a key of increa\n-000188c0: 7369 6e67 0a7a 2d63 6f6f 7264 696e 6174 sing.z-coordinat\n-000188d0: 652c 2065 7175 6976 616c 656e 7420 746f e, equivalent to\n-000188e0: 2064 6563 7265 6173 696e 6720 6465 7074 decreasing dept\n-000188f0: 682e 2020 4f62 6a65 6374 7320 6172 6520 h. Objects are \n-00018900: 7468 656e 2064 7261 776e 2069 6e0a 7468 then drawn in.th\n-00018910: 6520 736f 7274 6564 2073 6571 7565 6e63 e sorted sequenc\n-00018920: 6520 736f 2074 6861 7420 7468 6f73 6520 e so that those \n-00018930: 6174 2074 6865 2072 6561 7220 6f66 2074 at the rear of t\n-00018940: 6865 2073 6365 6e65 2061 7265 0a6f 7665 he scene are.ove\n-00018950: 7277 7269 7474 656e 2062 7920 7468 6f73 rwritten by thos\n-00018960: 6520 636c 6f73 6572 2074 6f20 7468 6520 e closer to the \n-00018970: 7669 6577 6572 2e20 2053 696e 6365 2074 viewer. Since t\n-00018980: 6869 7320 6973 2061 6c73 6f20 686f 7720 his is also how \n-00018990: 6f69 6c0a 7061 696e 7465 7273 2070 7261 oil.painters pra\n-000189a0: 6374 6963 6520 7468 6569 7220 6172 742c ctice their art,\n-000189b0: 2064 6570 7468 2073 6f72 7420 6973 2073 depth sort is s\n-000189c0: 6f6d 6574 696d 6573 2063 616c 6c65 6420 ometimes called \n-000189d0: 2274 6865 0a70 6169 6e74 6572 2773 2061 \"the.painter's a\n-000189e0: 6c67 6f72 6974 686d 2e22 0a0a 2020 2049 lgorithm.\".. I\n-000189f0: 6e20 736f 6d65 2063 6173 6573 2069 7420 n some cases it \n-00018a00: 6973 2069 6d70 6f73 7369 626c 6520 746f is impossible to\n-00018a10: 2073 7472 6963 746c 7920 6f72 6465 7220 strictly order \n-00018a20: 706f 6c79 676f 6e73 2061 6363 6f72 6469 polygons accordi\n-00018a30: 6e67 0a74 6f20 6465 7074 682e 2020 4d6f ng.to depth. Mo\n-00018a40: 7265 6f76 6572 2c20 6576 656e 2069 6620 reover, even if \n-00018a50: 6120 636f 7272 6563 7420 6465 7074 6820 a correct depth \n-00018a60: 6f72 6465 7269 6e67 2065 7869 7374 732c ordering exists,\n-00018a70: 2074 6865 0a63 6f6d 7075 7461 7469 6f6e the.computation\n-00018a80: 206e 6565 6465 6420 746f 2066 696e 6420 needed to find \n-00018a90: 6974 206d 6179 2062 6520 746f 6f20 636f it may be too co\n-00018aa0: 6d70 6c65 7820 616e 6420 736c 6f77 2e20 mplex and slow. \n-00018ab0: 2049 6e20 7468 6573 650a 6361 7365 732c In these.cases,\n-00018ac0: 20e2 8098 736b 6574 6368 e280 9920 7370 ...sketch... sp\n-00018ad0: 6c69 7473 206f 6e65 206f 7220 6d6f 7265 lits one or more\n-00018ae0: 2070 6f6c 7967 6f6e 7320 696e 746f 2070 polygons into p\n-00018af0: 6965 6365 732e 2020 5468 650a 6578 7065 ieces. The.expe\n-00018b00: 6374 6174 696f 6e20 6973 2074 6861 7420 ctation is that \n-00018b10: 7468 6520 6e65 772c 2073 6d61 6c6c 6572 the new, smaller\n-00018b20: 2070 6f6c 7967 6f6e 7320 7769 6c6c 2062 polygons will b\n-00018b30: 6520 7369 6d70 6c65 7220 746f 206f 7264 e simpler to ord\n-00018b40: 6572 2e0a e280 9853 6b65 7463 68e2 8099 er.....Sketch...\n-00018b50: 2075 7365 7320 6120 4253 5020 2862 696e uses a BSP (bin\n-00018b60: 6172 7920 7370 6163 6520 7061 7274 6974 ary space partit\n-00018b70: 696f 6e29 2074 6f20 6861 6e64 6c65 2074 ion) to handle t\n-00018b80: 6865 2073 706c 6974 7469 6e67 0a6f 7065 he splitting.ope\n-00018b90: 7261 7469 6f6e 2e0a 0a2a 204d 656e 753a ration...* Menu:\n-00018ba0: 0a0a 2a20 5374 6174 6973 7469 6373 3a3a ..* Statistics::\n+00018770: 2d2d 2d2d 2d2d 2d2d 0a0a e280 9853 6b65 --------.....Ske\n+00018780: 7463 68e2 8099 2075 7365 7320 7468 6520 tch... uses the \n+00018790: e280 9c64 6570 7468 2073 6f72 7420 616c ...depth sort al\n+000187a0: 676f 7269 7468 6de2 809d 2066 6f72 2068 gorithm... for h\n+000187b0: 6964 6465 6e20 7375 7266 6163 6520 7265 idden surface re\n+000187c0: 6d6f 7661 6c2e 0a54 6869 7320 6973 2061 moval..This is a\n+000187d0: 2076 6572 7920 6f6c 6420 7465 6368 6e69 very old techni\n+000187e0: 7175 6520 6475 6520 746f 204e 6577 656c que due to Newel\n+000187f0: 6c2e 2831 2920 2049 7420 6973 2067 656e l.(1) It is gen\n+00018800: 6572 616c 6c79 2072 6567 6172 6465 640a erally regarded.\n+00018810: 6173 2074 6f6f 2073 6c6f 7720 666f 7220 as too slow for \n+00018820: 7265 616c 2074 696d 6520 6772 6170 6869 real time graphi\n+00018830: 6373 2c20 6275 7420 6974 2069 7320 6964 cs, but it is id\n+00018840: 6561 6c20 666f 7220 6f75 7220 7075 7270 eal for our purp\n+00018850: 6f73 650a 7768 6572 6520 7370 6565 6420 ose.where speed \n+00018860: 6973 206e 6f74 2076 6572 7920 696d 706f is not very impo\n+00018870: 7274 616e 742e 2832 290a 0a20 2020 5468 rtant.(2).. Th\n+00018880: 6520 6465 7074 6820 736f 7274 2061 6c67 e depth sort alg\n+00018890: 6f72 6974 686d 206d 6572 656c 7920 736f orithm merely so\n+000188a0: 7274 7320 6f62 6a65 6374 7320 6f6e 2061 rts objects on a\n+000188b0: 206b 6579 206f 6620 696e 6372 6561 7369 key of increasi\n+000188c0: 6e67 0a7a 2d63 6f6f 7264 696e 6174 652c ng.z-coordinate,\n+000188d0: 2065 7175 6976 616c 656e 7420 746f 2064 equivalent to d\n+000188e0: 6563 7265 6173 696e 6720 6465 7074 682e ecreasing depth.\n+000188f0: 2020 4f62 6a65 6374 7320 6172 6520 7468 Objects are th\n+00018900: 656e 2064 7261 776e 2069 6e0a 7468 6520 en drawn in.the \n+00018910: 736f 7274 6564 2073 6571 7565 6e63 6520 sorted sequence \n+00018920: 736f 2074 6861 7420 7468 6f73 6520 6174 so that those at\n+00018930: 2074 6865 2072 6561 7220 6f66 2074 6865 the rear of the\n+00018940: 2073 6365 6e65 2061 7265 0a6f 7665 7277 scene are.overw\n+00018950: 7269 7474 656e 2062 7920 7468 6f73 6520 ritten by those \n+00018960: 636c 6f73 6572 2074 6f20 7468 6520 7669 closer to the vi\n+00018970: 6577 6572 2e20 2053 696e 6365 2074 6869 ewer. Since thi\n+00018980: 7320 6973 2061 6c73 6f20 686f 7720 6f69 s is also how oi\n+00018990: 6c0a 7061 696e 7465 7273 2070 7261 6374 l.painters pract\n+000189a0: 6963 6520 7468 6569 7220 6172 742c 2064 ice their art, d\n+000189b0: 6570 7468 2073 6f72 7420 6973 2073 6f6d epth sort is som\n+000189c0: 6574 696d 6573 2063 616c 6c65 6420 2274 etimes called \"t\n+000189d0: 6865 0a70 6169 6e74 6572 2773 2061 6c67 he.painter's alg\n+000189e0: 6f72 6974 686d 2e22 0a0a 2020 2049 6e20 orithm.\".. In \n+000189f0: 736f 6d65 2063 6173 6573 2069 7420 6973 some cases it is\n+00018a00: 2069 6d70 6f73 7369 626c 6520 746f 2073 impossible to s\n+00018a10: 7472 6963 746c 7920 6f72 6465 7220 706f trictly order po\n+00018a20: 6c79 676f 6e73 2061 6363 6f72 6469 6e67 lygons according\n+00018a30: 0a74 6f20 6465 7074 682e 2020 4d6f 7265 .to depth. More\n+00018a40: 6f76 6572 2c20 6576 656e 2069 6620 6120 over, even if a \n+00018a50: 636f 7272 6563 7420 6465 7074 6820 6f72 correct depth or\n+00018a60: 6465 7269 6e67 2065 7869 7374 732c 2074 dering exists, t\n+00018a70: 6865 0a63 6f6d 7075 7461 7469 6f6e 206e he.computation n\n+00018a80: 6565 6465 6420 746f 2066 696e 6420 6974 eeded to find it\n+00018a90: 206d 6179 2062 6520 746f 6f20 636f 6d70 may be too comp\n+00018aa0: 6c65 7820 616e 6420 736c 6f77 2e20 2049 lex and slow. I\n+00018ab0: 6e20 7468 6573 650a 6361 7365 732c 20e2 n these.cases, .\n+00018ac0: 8098 736b 6574 6368 e280 9920 7370 6c69 ..sketch... spli\n+00018ad0: 7473 206f 6e65 206f 7220 6d6f 7265 2070 ts one or more p\n+00018ae0: 6f6c 7967 6f6e 7320 696e 746f 2070 6965 olygons into pie\n+00018af0: 6365 732e 2020 5468 650a 6578 7065 6374 ces. The.expect\n+00018b00: 6174 696f 6e20 6973 2074 6861 7420 7468 ation is that th\n+00018b10: 6520 6e65 772c 2073 6d61 6c6c 6572 2070 e new, smaller p\n+00018b20: 6f6c 7967 6f6e 7320 7769 6c6c 2062 6520 olygons will be \n+00018b30: 7369 6d70 6c65 7220 746f 206f 7264 6572 simpler to order\n+00018b40: 2e0a e280 9853 6b65 7463 68e2 8099 2075 .....Sketch... u\n+00018b50: 7365 7320 6120 4253 5020 2862 696e 6172 ses a BSP (binar\n+00018b60: 7920 7370 6163 6520 7061 7274 6974 696f y space partitio\n+00018b70: 6e29 2074 6f20 6861 6e64 6c65 2074 6865 n) to handle the\n+00018b80: 2073 706c 6974 7469 6e67 0a6f 7065 7261 splitting.opera\n+00018b90: 7469 6f6e 2e0a 0a2a 204d 656e 753a 0a0a tion...* Menu:..\n+00018ba0: 2a20 5374 6174 6973 7469 6373 3a3a 2020 * Statistics:: \n 00018bb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00018bc0: 2020 5065 7266 6f72 6d61 6e63 6520 6e75 Performance nu\n-00018bd0: 6d62 6572 7320 6f6e 2064 6570 7468 2073 mbers on depth s\n-00018be0: 6f72 742e 0a2a 2042 7567 7320 616e 6420 ort..* Bugs and \n-00018bf0: 616e 6f6d 616c 6965 733a 3a20 2020 2020 anomalies:: \n-00018c00: 2020 2020 2049 6d70 6572 6665 6374 696f Imperfectio\n-00018c10: 6e73 2069 6e20 7468 6973 2069 6d70 6c65 ns in this imple\n-00018c20: 6d65 6e74 6174 696f 6e2e 0a0a 2020 202d mentation... -\n-00018c30: 2d2d 2d2d 2d2d 2d2d 2d20 466f 6f74 6e6f --------- Footno\n-00018c40: 7465 7320 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a tes ----------..\n-00018c50: 2020 2028 3129 204e 6577 656c 6c2c 204d (1) Newell, M\n-00018c60: 2e45 2e2c 2052 2e47 2e20 4e65 7765 6c6c .E., R.G. Newell\n-00018c70: 2c20 616e 6420 542e 4c2e 2053 616e 6368 , and T.L. Sanch\n-00018c80: 612c 2041 2073 6f6c 7574 696f 6e20 746f a, A solution to\n-00018c90: 2074 6865 0a68 6964 6465 6e20 7375 7266 the.hidden surf\n-00018ca0: 6163 6520 7072 6f62 6c65 6d2e 2020 5072 ace problem. Pr\n-00018cb0: 6f63 6565 6469 6e67 7320 6f66 2074 6865 oceedings of the\n-00018cc0: 2041 434d 2061 6e6e 7561 6c20 636f 6e66 ACM annual conf\n-00018cd0: 6572 656e 6365 202d 0a56 6f6c 756d 6520 erence -.Volume \n-00018ce0: 312c 2070 6167 6520 3434 332d 3435 302c 1, page 443-450,\n-00018cf0: 2041 434d 2050 7265 7373 2c20 3139 3732 ACM Press, 1972\n-00018d00: 2e0a 0a20 2020 2832 2920 5765 2068 6176 ... (2) We hav\n-00018d10: 6520 7275 6e20 e280 9873 6b65 7463 68e2 e run ...sketch.\n-00018d20: 8099 206f 6e20 7468 6520 6661 6d6f 7573 .. on the famous\n-00018d30: 2053 7461 6e66 6f72 6420 4275 6e6e 792c Stanford Bunny,\n-00018d40: 2077 6869 6368 2063 6f6e 7369 7374 730a which consists.\n-00018d50: 6f66 206e 6561 726c 7920 3730 2c30 3030 of nearly 70,000\n-00018d60: 2074 7269 616e 676c 6573 2e20 2052 756e triangles. Run\n-00018d70: 2074 696d 6520 7761 7320 6162 6f75 7420 time was about \n-00018d80: 3620 7365 636f 6e64 732e 2020 4d6f 7374 6 seconds. Most\n-00018d90: 206f 6620 7468 6973 0a77 6173 2073 7065 of this.was spe\n-00018da0: 6e74 2077 7269 7469 6e67 2074 6865 206f nt writing the o\n-00018db0: 7574 7075 7420 6669 6c65 2072 6174 6865 utput file rathe\n-00018dc0: 7220 7468 616e 2069 6e20 7468 6520 6869 r than in the hi\n-00018dd0: 6464 656e 2073 7572 6661 6365 0a61 6c67 dden surface.alg\n-00018de0: 6f72 6974 686d 2e20 204c 6154 6558 2074 orithm. LaTeX t\n-00018df0: 6f6f 6b20 6d75 6368 206c 6f6e 6765 7220 ook much longer \n-00018e00: 746f 2070 726f 6365 7373 2074 6865 2072 to process the r\n-00018e10: 6573 756c 7469 6e67 20e2 8098 5053 5472 esulting ...PSTr\n-00018e20: 6963 6b73 e280 990a 636f 6465 2e20 2054 icks....code. T\n-00018e30: 6865 206f 6276 696f 7573 2063 6f6e 636c he obvious concl\n-00018e40: 7573 696f 6e20 6973 2074 6861 7420 7468 usion is that th\n-00018e50: 6520 7370 6565 6420 6f66 2074 6865 2064 e speed of the d\n-00018e60: 6570 7468 2073 6f72 740a 616c 676f 7269 epth sort.algori\n-00018e70: 7468 6d20 6973 206e 6f74 2061 2077 6f72 thm is not a wor\n-00018e80: 7279 2e0a 0a1f 0a46 696c 653a 2073 6b65 ry.....File: ske\n-00018e90: 7463 682e 696e 666f 2c20 204e 6f64 653a tch.info, Node:\n-00018ea0: 2053 7461 7469 7374 6963 732c 2020 4e65 Statistics, Ne\n-00018eb0: 7874 3a20 4275 6773 2061 6e64 2061 6e6f xt: Bugs and ano\n-00018ec0: 6d61 6c69 6573 2c20 2050 7265 763a 2048 malies, Prev: H\n-00018ed0: 6964 6465 6e20 7375 7266 6163 6520 7265 idden surface re\n-00018ee0: 6d6f 7661 6c2c 2020 5570 3a20 4869 6464 moval, Up: Hidd\n-00018ef0: 656e 2073 7572 6661 6365 2072 656d 6f76 en surface remov\n-00018f00: 616c 0a0a 342e 342e 332e 3120 5374 6174 al..4.4.3.1 Stat\n-00018f10: 6973 7469 6373 0a2e 2e2e 2e2e 2e2e 2e2e istics..........\n-00018f20: 2e2e 2e2e 2e2e 2e2e 2e0a 0a46 6f72 2074 ...........For t\n-00018f30: 6865 2063 7572 696f 7573 2c20 e280 9873 he curious, ...s\n-00018f40: 6b65 7463 68e2 8099 2077 7269 7465 7320 ketch... writes \n-00018f50: 6f6e 6520 6c69 6e65 206f 6620 6465 7074 one line of dept\n-00018f60: 6820 736f 7274 2073 7461 7469 7374 6963 h sort statistic\n-00018f70: 732e 0a48 6572 6520 6973 2061 6e20 6578 s..Here is an ex\n-00018f80: 616d 706c 6520 666f 7220 6120 6c61 7267 ample for a larg\n-00018f90: 6520 636f 6c6c 6563 7469 6f6e 206f 6620 e collection of \n-00018fa0: 7472 6961 6e67 6c65 732e 0a20 2072 656d triangles.. rem\n-00018fb0: 6172 6b2c 206e 6f64 653d 3334 3832 3420 ark, node=34824 \n-00018fc0: 7072 6f62 653d 3538 312e 3920 7377 6170 probe=581.9 swap\n-00018fd0: 3d35 2073 706c 6974 3d32 2028 696e 3d34 =5 split=2 (in=4\n-00018fe0: 206f 7574 3d36 2920 6f6c 733d 3234 3835 out=6) ols=2485\n-00018ff0: 312f 300a 4974 206d 6561 6e73 2074 6861 1/0.It means tha\n-00019000: 7420 3334 2c38 3234 206f 626a 6563 7473 t 34,824 objects\n-00019010: 2077 6572 6520 6465 7074 6820 736f 7274 were depth sort\n-00019020: 6564 2061 6674 6572 2063 756c 6c69 6e67 ed after culling\n-00019030: 2e20 2046 6f72 2065 6163 682c 0a61 6e20 . For each,.an \n-00019040: 6176 6572 6167 6520 6f66 2035 3831 2e39 average of 581.9\n-00019050: 206f 7468 6572 7320 6861 6420 746f 2062 others had to b\n-00019060: 6520 6368 6563 6b65 6420 746f 2065 6e73 e checked to ens\n-00019070: 7572 6520 7468 6174 2074 6865 2069 6e69 ure that the ini\n-00019080: 7469 616c 2c0a 6170 7072 6f78 696d 6174 tial,.approximat\n-00019090: 6520 6f72 6465 7269 6e67 2077 6173 2063 e ordering was c\n-000190a0: 6f72 7265 6374 2e20 2041 6d6f 6e67 2061 orrect. Among a\n-000190b0: 6c6c 2074 6865 7365 2063 6865 636b 732c ll these checks,\n-000190c0: 206f 6e6c 7920 350a 7265 7375 6c74 6564 only 5.resulted\n-000190d0: 2069 6e20 7377 6170 7320 746f 2072 656f in swaps to reo\n-000190e0: 7264 6572 2074 6865 2069 6e69 7469 616c rder the initial\n-000190f0: 2073 6f72 742e 2020 496e 2074 776f 2063 sort. In two c\n-00019100: 6173 6573 2c20 6120 636f 7272 6563 740a ases, a correct.\n-00019110: 6f72 6465 7269 6e67 2063 6f75 6c64 206e ordering could n\n-00019120: 6f74 2062 6520 6465 7465 726d 696e 6564 ot be determined\n-00019130: 2c20 736f 2062 696e 6172 7920 7370 6163 , so binary spac\n-00019140: 6520 7061 7274 6974 696f 6e73 2077 6572 e partitions wer\n-00019150: 650a 636f 6e73 7472 7563 7465 6420 666f e.constructed fo\n-00019160: 7220 7370 6c69 7474 696e 672e 2020 4120 r splitting. A \n-00019170: 746f 7461 6c20 6f66 2034 206f 626a 6563 total of 4 objec\n-00019180: 7473 2028 7472 6961 6e67 6c65 7320 696e ts (triangles in\n-00019190: 2074 6869 730a 6361 7365 2920 7765 7265 this.case) were\n-000191a0: 2069 6e73 6572 7465 6420 696e 2074 6865 inserted in the\n-000191b0: 2070 6172 7469 7469 6f6e 732c 2061 6e64 partitions, and\n-000191c0: 2036 2070 6f6c 7967 6f6e 7320 7765 7265 6 polygons were\n-000191d0: 2070 726f 6475 6365 642e 0a46 696e 616c produced..Final\n-000191e0: 6c79 2c20 3234 2c38 3531 2022 6c61 7374 ly, 24,851 \"last\n-000191f0: 2072 6573 6f72 7422 2070 6f6c 7967 6f6e resort\" polygon\n-00019200: 206f 7665 726c 6170 2063 6865 636b 7320 overlap checks \n-00019210: 7765 7265 2070 6572 666f 726d 6564 0a61 were performed.a\n-00019220: 6674 6572 2073 696d 706c 6572 2c20 6661 fter simpler, fa\n-00019230: 7374 6572 2063 6865 636b 7320 6661 696c ster checks fail\n-00019240: 6564 2074 6f20 7969 656c 6420 636f 6e63 ed to yield conc\n-00019250: 6c75 7369 7665 2072 6573 756c 7473 2e20 lusive results. \n-00019260: 2054 6865 0a66 696e 616c 202f 3020 6973 The.final /0 is\n-00019270: 2066 6f72 206c 696e 652d 706f 6c79 676f for line-polygo\n-00019280: 6e20 6f76 6572 6c61 7020 6368 6563 6b73 n overlap checks\n-00019290: 2e20 2046 6f72 2063 6f6d 7061 7269 736f . For compariso\n-000192a0: 6e2c 2074 6865 0a73 7461 7469 7374 6963 n, the.statistic\n-000192b0: 7320 666f 7220 7468 6520 6c61 7374 2066 s for the last f\n-000192c0: 6967 7572 6520 696e 202a 6e6f 7465 204f igure in *note O\n-000192d0: 7665 7276 6965 773a 3a20 666f 6c6c 6f77 verview:: follow\n-000192e0: 2e0a 2020 7265 6d61 726b 2c20 6e6f 6465 .. remark, node\n-000192f0: 3d32 3720 7072 6f62 653d 3134 2e36 2073 =27 probe=14.6 s\n-00019300: 7761 703d 3336 2073 706c 6974 3d31 3520 wap=36 split=15 \n-00019310: 2869 6e3d 3330 206f 7574 3d34 3529 206f (in=30 out=45) o\n-00019320: 6c73 3d30 2f36 390a 4e6f 7465 2074 6861 ls=0/69.Note tha\n-00019330: 7420 7468 6572 6520 7761 7320 7072 6f70 t there was prop\n-00019340: 6f72 7469 6f6e 616c 6c79 206d 7563 6820 ortionally much \n-00019350: 6d6f 7265 2073 7761 7070 696e 6720 616e more swapping an\n-00019360: 6420 7370 6c69 7474 696e 670a 6163 7469 d splitting.acti\n-00019370: 7669 7479 2069 6e20 7468 6973 2068 6967 vity in this hig\n-00019380: 686c 7920 636f 6e6e 6563 7465 6420 7363 hly connected sc\n-00019390: 656e 652e 0a0a 1f0a 4669 6c65 3a20 736b ene.....File: sk\n-000193a0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-000193b0: 3a20 4275 6773 2061 6e64 2061 6e6f 6d61 : Bugs and anoma\n-000193c0: 6c69 6573 2c20 2050 7265 763a 2053 7461 lies, Prev: Sta\n-000193d0: 7469 7374 6963 732c 2020 5570 3a20 4869 tistics, Up: Hi\n-000193e0: 6464 656e 2073 7572 6661 6365 2072 656d dden surface rem\n-000193f0: 6f76 616c 0a0a 342e 342e 332e 3220 4275 oval..4.4.3.2 Bu\n-00019400: 6773 2061 6e64 2061 6e6f 6d61 6c69 6573 gs and anomalies\n-00019410: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-00019420: 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a50 6f6c .............Pol\n-00019430: 7967 6f6e 2061 6e64 206c 696e 6520 7370 ygon and line sp\n-00019440: 6c69 7474 696e 6720 6361 6e20 626f 7468 litting can both\n-00019450: 2063 6175 7365 2061 6e6f 6d61 6c69 6573 cause anomalies\n-00019460: 2069 6e20 7468 6520 6f75 7470 7574 2e0a in the output..\n-00019470: e280 9850 5354 7269 636b 73e2 8099 2064 ...PSTricks... d\n-00019480: 6173 6820 7061 7474 6572 6e73 2c20 7370 ash patterns, sp\n-00019490: 6563 6966 6965 6420 7769 7468 20e2 8098 ecified with ...\n-000194a0: 6c69 6e65 7374 796c 653d 6461 7368 6564 linestyle=dashed\n-000194b0: e280 992c 2063 616e 2062 650a 6469 7372 ..., can be.disr\n-000194c0: 7570 7465 6420 6279 2073 706c 6974 7469 upted by splitti\n-000194d0: 6e67 2e20 2054 6869 7320 6f63 6375 7273 ng. This occurs\n-000194e0: 2077 6865 6e20 7468 6520 6465 7074 6820 when the depth \n-000194f0: 736f 7274 2067 6976 6573 2075 7020 746f sort gives up to\n-00019500: 6f0a 6561 726c 7920 616e 6420 7370 6c69 o.early and spli\n-00019510: 7473 2061 206c 696e 6520 7768 6572 6520 ts a line where \n-00019520: 6974 2069 7320 6e6f 7420 7265 616c 6c79 it is not really\n-00019530: 206e 6563 6573 7361 7279 2e20 2041 2077 necessary. A w\n-00019540: 6f72 6b61 726f 756e 640a 6973 2074 6f20 orkaround.is to \n-00019550: 7573 6520 6772 6179 206f 7220 6669 6e65 use gray or fine\n-00019560: 6c79 2064 6f74 7465 6420 6c69 6e65 7320 ly dotted lines \n-00019570: 696e 7374 6561 642e 2020 4966 2079 6f75 instead. If you\n-00019580: 7220 6472 6177 696e 6720 6973 0a73 6d61 r drawing is.sma\n-00019590: 6c6c 2c20 796f 7520 6361 6e20 616c 736f ll, you can also\n-000195a0: 2065 6469 7420 7468 6520 e280 9873 6b65 edit the ...ske\n-000195b0: 7463 68e2 8099 206f 7574 7075 7420 6279 tch... output by\n-000195c0: 2068 616e 6420 746f 206d 6572 6765 2074 hand to merge t\n-000195d0: 6865 2070 6965 6365 730a 6f66 2074 6865 he pieces.of the\n-000195e0: 206f 6666 656e 6469 6e67 206c 696e 652e offending line.\n-000195f0: 0a0a 2020 2041 6e6f 7468 6572 2061 6e6f .. Another ano\n-00019600: 6d61 6c79 2069 7320 7469 6e79 2028 6f72 maly is tiny (or\n-00019610: 2069 6e20 6465 6765 6e65 7261 7465 2063 in degenerate c\n-00019620: 6173 6573 206e 6f74 2d73 6f2d 7469 6e79 ases not-so-tiny\n-00019630: 2920 6e6f 7463 6865 730a 696e 2074 6865 ) notches.in the\n-00019640: 206c 696e 6573 2074 6861 7420 626f 7264 lines that bord\n-00019650: 6572 2073 706c 6974 2070 6f6c 7967 6f6e er split polygon\n-00019660: 732e 2020 5468 6573 6520 6465 7269 7665 s. These derive\n-00019670: 2066 726f 6d20 7468 6520 7761 7920 6561 from the way ea\n-00019680: 6368 0a70 6f6c 7967 6f6e 2069 7320 7061 ch.polygon is pa\n-00019690: 696e 7465 643a 2066 6972 7374 2c20 616c inted: first, al\n-000196a0: 6c20 7069 7865 6c73 2077 6974 6869 6e20 l pixels within \n-000196b0: 7468 6520 626f 756e 6461 7279 2061 7265 the boundary are\n-000196c0: 20e2 809c 6669 6c6c 6564 e280 9d0a 7769 ...filled....wi\n-000196d0: 7468 2063 6f6c 6f72 2028 7065 7268 6170 th color (perhap\n-000196e0: 7320 7768 6974 6529 2c20 7468 656e 2074 s white), then t\n-000196f0: 6865 2073 616d 6520 626f 756e 6461 7279 he same boundary\n-00019700: 2069 7320 e280 9c73 7472 6f6b 6564 e280 is ...stroked..\n-00019710: 9d20 2861 0a50 6f73 7473 6372 6970 7420 . (a.Postscript \n-00019720: 7465 726d 2920 7769 7468 2061 206c 696e term) with a lin\n-00019730: 652e 2020 5468 6520 7265 7375 6c74 2069 e. The result i\n-00019740: 7320 7468 6174 2068 616c 6620 7468 6520 s that half the \n-00019750: 6c69 6e65 206c 6965 730a 696e 7369 6465 line lies.inside\n-00019760: 2074 6865 2062 6f75 6e64 6172 7920 616e the boundary an\n-00019770: 6420 6861 6c66 206f 7574 7369 6465 2c20 d half outside, \n-00019780: 7768 696c 6520 7468 6520 5061 696e 7465 while the Painte\n-00019790: 7227 7320 616c 676f 7269 7468 6d0a 6173 r's algorithm.as\n-000197a0: 7375 6d65 7320 7468 6520 706f 6c79 676f sumes the polygo\n-000197b0: 6e20 6c69 6573 2065 6e74 6972 656c 7920 n lies entirely \n-000197c0: 7769 7468 696e 2069 7473 2062 6f75 6e64 within its bound\n-000197d0: 6172 792e 2020 5468 6520 6e6f 7463 6865 ary. The notche\n-000197e0: 7320 6172 650a 6475 6520 746f 206f 6e65 s are.due to one\n-000197f0: 2070 6f6c 7967 6f6e 2066 696c 6c20 6f70 polygon fill op\n-00019800: 6572 6174 696f 6e20 6f76 6572 7772 6974 eration overwrit\n-00019810: 696e 6720 7468 6520 616c 7265 6164 792d ing the already-\n-00019820: 6472 6177 6e20 696e 7369 6465 0a6f 6620 drawn inside.of \n-00019830: 7468 6520 626f 7264 6572 206f 6620 616e the border of an\n-00019840: 6f74 6865 7220 706f 6c79 676f 6e2e 2831 other polygon.(1\n-00019850: 2920 204f 6e65 2077 6f72 6b61 726f 756e ) One workaroun\n-00019860: 6420 6973 2074 6f20 6d61 6b65 2062 6f72 d is to make bor\n-00019870: 6465 720a 6c69 6e65 7320 7665 7279 2074 der.lines very t\n-00019880: 6869 6e2e 2020 496e 2066 6163 7420 e280 hin. In fact ..\n-00019890: 986c 696e 6577 6964 7468 3d30 7074 e280 .linewidth=0pt..\n-000198a0: 9920 6973 2067 7561 7261 6e74 6565 6420 . is guaranteed \n-000198b0: 746f 2065 6c69 6d69 6e61 7465 0a74 6869 to eliminate.thi\n-000198c0: 7320 7072 6f62 6c65 6d2c 2074 686f 7567 s problem, thoug\n-000198d0: 6820 7468 6973 2072 6573 756c 7473 2069 h this results i\n-000198e0: 6e20 7468 6520 7468 696e 6e65 7374 206c n the thinnest l\n-000198f0: 696e 6520 796f 7572 206f 7574 7075 740a ine your output.\n-00019900: 6465 7669 6365 2063 616e 2064 7261 772c device can draw,\n-00019910: 2077 6869 6368 2069 7320 7573 7561 6c6c which is usuall\n-00019920: 7920 746f 6f20 7468 696e 2e20 2059 6f75 y too thin. You\n-00019930: 206d 6967 6874 2067 6574 206c 7563 6b79 might get lucky\n-00019940: 2062 790a 6d65 7265 6c79 2072 656f 7264 by.merely reord\n-00019950: 6572 696e 6720 7468 696e 6773 2069 6e20 ering things in \n-00019960: 7468 6520 696e 7075 7420 6669 6c65 2c20 the input file, \n-00019970: 7768 6963 6820 6973 206c 696b 656c 7920 which is likely \n-00019980: 746f 206d 6f76 6520 7468 650a 7370 6c69 to move the.spli\n-00019990: 7473 2074 6f20 6469 6666 6572 656e 7420 ts to different \n-000199a0: 706c 6163 6573 2e20 2054 6865 206f 6e6c places. The onl\n-000199b0: 7920 7375 7265 2d66 6972 6520 736f 6c75 y sure-fire solu\n-000199c0: 7469 6f6e 2069 7320 7072 6574 7479 0a74 tion is pretty.t\n-000199d0: 6572 7269 626c 653a 2063 7573 746f 6d20 errible: custom \n-000199e0: 6669 7420 e280 9873 7065 6369 616c e280 fit ...special..\n-000199f0: 9920 6f76 6572 6c61 7920 6c69 6e65 7320 . overlay lines \n-00019a00: 2877 6974 6820 e280 985c 7073 6c69 6e65 (with ...\\psline\n-00019a10: e280 9929 2074 6f20 636f 7665 720a 7468 ...) to cover.th\n-00019a20: 6520 6e6f 7463 6865 732e 0a0a 2020 2050 e notches... P\n-00019a30: 6f6c 7967 6f6e 2073 706c 6974 7469 6e67 olygon splitting\n-00019a40: 2061 6c73 6f20 6272 6561 6b73 20e2 8098 also breaks ...\n-00019a50: 5053 5472 6963 6b73 e280 9920 6861 7463 PSTricks... hatc\n-00019a60: 6820 7061 7474 6572 6e73 2e20 2054 6865 h patterns. The\n-00019a70: 206f 6e6c 790a 6b6e 6f77 6e20 776f 726b only.known work\n-00019a80: 6172 6f75 6e64 2069 7320 746f 2073 7562 around is to sub\n-00019a90: 7374 6974 7574 6520 6120 736f 6c69 6420 stitute a solid \n-00019aa0: 6669 6c6c 2066 6f72 2074 6865 2068 6174 fill for the hat\n-00019ab0: 6368 2e0a 0a20 2020 2d2d 2d2d 2d2d 2d2d ch... --------\n-00019ac0: 2d2d 2046 6f6f 746e 6f74 6573 202d 2d2d -- Footnotes ---\n-00019ad0: 2d2d 2d2d 2d2d 2d0a 0a20 2020 2831 2920 -------.. (1) \n-00019ae0: 4920 6b6e 6f77 2068 6f77 2074 6f20 6669 I know how to fi\n-00019af0: 7820 7468 6973 2070 726f 626c 656d 2c20 x this problem, \n-00019b00: 6275 7420 4920 646f 6e27 7420 6c69 6b65 but I don't like\n-00019b10: 206d 7920 736f 6c75 7469 6f6e 2c20 616e my solution, an\n-00019b20: 640a 4927 6d20 696e 7465 7265 7374 6564 d.I'm interested\n-00019b30: 2069 6e20 796f 7572 732e 0a0a 1f0a 4669 in yours.....Fi\n-00019b40: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n-00019b50: 2020 4e6f 6465 3a20 436f 6d6d 616e 6420 Node: Command \n-00019b60: 6c69 6e65 2c20 204e 6578 743a 2049 6e73 line, Next: Ins\n-00019b70: 7461 6c6c 696e 6720 736b 6574 6368 2c20 talling sketch, \n-00019b80: 2050 7265 763a 2042 7569 6c64 696e 6720 Prev: Building \n-00019b90: 6120 6472 6177 696e 672c 2020 5570 3a20 a drawing, Up: \n-00019ba0: 546f 700a 0a35 2043 6f6d 6d61 6e64 206c Top..5 Command l\n-00019bb0: 696e 650a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a ine.************\n-00019bc0: 2a2a 0a0a 2a53 796e 6f70 7369 733a 2a0a **..*Synopsis:*.\n-00019bd0: 2020 2020 2073 6b65 7463 6820 5b2d 685d sketch [-h]\n-00019be0: 5b2d 5620 782e 795d 5b2d 765d 5b2d 625d [-V x.y][-v][-b]\n-00019bf0: 5b2d 645d 5b74 2064 6f63 746d 705d 5b2d [-d][t doctmp][-\n-00019c00: 545b 757c 655d 5b70 5b50 7c54 5d5b 4c7c T[u|e][p[P|T][L|\n-00019c10: 435d 5d5d 5b2d 6f20 6f75 7470 7574 2e74 C]]][-o output.t\n-00019c20: 6578 5d0a 2020 2020 2020 205b 2d44 2054 ex]. [-D T\n-00019c30: 4147 202e 2e2e 5d20 696e 7075 7431 2e73 AG ...] input1.s\n-00019c40: 6b20 5b2d 5520 5441 4720 2e2e 2e5d 2069 k [-U TAG ...] i\n-00019c50: 6e70 7574 322e 736b 202e 2e2e 0a0a 2a44 nput2.sk .....*D\n-00019c60: 6573 6372 6970 7469 6f6e 2a20 5072 6f63 escription* Proc\n-00019c70: 6573 7365 7320 7468 6520 e280 9873 6b65 esses the ...ske\n-00019c80: 7463 68e2 8099 2069 6e70 7574 2066 696c tch... input fil\n-00019c90: 6573 2069 6e20 6f72 6465 7220 746f 2070 es in order to p\n-00019ca0: 726f 6475 6365 0ae2 8098 5053 5472 6963 roduce....PSTric\n-00019cb0: 6b73 e280 9920 6f75 7470 7574 2063 6f64 ks... output cod\n-00019cc0: 6520 7375 6974 6162 6c65 2066 6f72 2069 e suitable for i\n-00019cd0: 6e63 6c75 7369 6f6e 2069 6e20 6120 5465 nclusion in a Te\n-00019ce0: 5820 6f72 204c 6154 6558 0a64 6f63 756d X or LaTeX.docum\n-00019cf0: 656e 742e 0a0a 2a4f 7074 696f 6e73 3a2a ent...*Options:*\n-00019d00: 0ae2 8098 2d68 e280 990a 2020 2020 2050 ....-h.... P\n-00019d10: 7269 6e74 2061 2073 686f 7274 2063 6174 rint a short cat\n-00019d20: 616c 6f67 206f 6620 6f70 7469 6f6e 732e alog of options.\n-00019d30: 0ae2 8098 2d56 e280 990a 2020 2020 2053 ....-V.... S\n-00019d40: 6574 2074 6865 20e2 8098 5053 5472 6963 et the ...PSTric\n-00019d50: 6b73 e280 9920 7665 7273 696f 6e20 6173 ks... version as\n-00019d60: 7375 6d65 6420 666f 7220 6f75 7470 7574 sumed for output\n-00019d70: 2070 7572 706f 7365 7320 746f 20e2 8098 purposes to ...\n-00019d80: 782e 79e2 8099 2c0a 2020 2020 2066 6f72 x.y...,. for\n-00019d90: 2065 7861 6d70 6c65 2031 2e31 392e 2020 example 1.19. \n-00019da0: 5573 7561 6c6c 7920 6e65 6564 6564 206f Usually needed o\n-00019db0: 6e6c 7920 6966 2079 6f75 7220 e280 9850 nly if your ...P\n-00019dc0: 5354 7269 636b 73e2 8099 2069 7320 6f6c STricks... is ol\n-00019dd0: 640a 2020 2020 2063 6f6d 7061 7265 6420 d. compared \n-00019de0: 746f 2079 6f75 7220 e280 9873 6b65 7463 to your ...sketc\n-00019df0: 68e2 8099 2e20 2055 7365 20e2 8098 2d76 h.... Use ...-v\n-00019e00: e280 9920 746f 2073 6565 2077 6861 7420 ... to see what \n-00019e10: e280 9873 6b65 7463 68e2 8099 2061 7373 ...sketch... ass\n-00019e20: 756d 6573 0a20 2020 2020 6279 2064 6566 umes. by def\n-00019e30: 6175 6c74 2e0a e280 982d 76e2 8099 0a20 ault.....-v.... \n-00019e40: 2020 2020 5072 696e 7420 7665 7273 696f Print versio\n-00019e50: 6e20 696e 666f 726d 6174 696f 6e20 746f n information to\n-00019e60: 2073 7461 6e64 6172 6420 6f75 7470 7574 standard output\n-00019e70: 2c20 696e 636c 7564 696e 6720 7468 6520 , including the \n-00019e80: 7665 7273 696f 6e0a 2020 2020 206f 6620 version. of \n-00019e90: e280 9850 5354 7269 636b 73e2 8099 2061 ...PSTricks... a\n-00019ea0: 7373 756d 6564 2066 6f72 206f 7574 7075 ssumed for outpu\n-00019eb0: 7420 2863 616e 2062 6520 6368 616e 6765 t (can be change\n-00019ec0: 6420 7769 7468 20e2 8098 2d56 e280 9920 d with ...-V... \n-00019ed0: 6162 6f76 6529 2e0a e280 982d 62e2 8099 above).....-b...\n-00019ee0: 0a20 2020 2020 5573 6520 6120 4253 5020 . Use a BSP \n-00019ef0: 282a 4e6f 7465 2048 6964 6465 6e20 7375 (*Note Hidden su\n-00019f00: 7266 6163 6520 7265 6d6f 7661 6c3a 3a2e rface removal::.\n-00019f10: 2920 2066 6f72 205f 616c 6c5f 2068 6964 ) for _all_ hid\n-00019f20: 6465 6e0a 2020 2020 2073 7572 6661 6365 den. surface\n-00019f30: 2072 656d 6f76 616c 2072 6174 6865 7220 removal rather \n-00019f40: 7468 616e 2074 6865 2064 6566 6175 6c74 than the default\n-00019f50: 2c20 7768 6963 6820 6973 2074 6865 2064 , which is the d\n-00019f60: 6570 7468 2073 6f72 740a 2020 2020 2061 epth sort. a\n-00019f70: 6c67 6f72 6974 686d 2077 6974 6820 4253 lgorithm with BS\n-00019f80: 5073 2075 7365 6420 6f6e 6c79 2066 6f72 Ps used only for\n-00019f90: 2063 7963 6c65 2072 6573 6f6c 7574 696f cycle resolutio\n-00019fa0: 6e2e 2020 5468 6973 206d 6179 0a20 2020 n. This may. \n-00019fb0: 2020 7072 6f64 7563 6520 636f 7272 6563 produce correc\n-00019fc0: 7420 6f75 7470 7574 2069 6e20 6365 7274 t output in cert\n-00019fd0: 6169 6e20 6465 6765 6e65 7261 7465 2063 ain degenerate c\n-00019fe0: 6173 6573 2077 6865 7265 2074 6865 2064 ases where the d\n-00019ff0: 6570 7468 0a20 2020 2020 736f 7274 2063 epth. sort c\n-0001a000: 616e 6e6f 742c 2062 7574 2069 7420 616c annot, but it al\n-0001a010: 736f 206c 6561 6473 2074 6f20 6d61 6e79 so leads to many\n-0001a020: 2067 7261 7475 6974 6f75 7320 7370 6c69 gratuitous spli\n-0001a030: 7473 2c20 6865 6e63 650a 2020 2020 206d ts, hence. m\n-0001a040: 6f72 6520 616e 6f6d 616c 6965 7320 2a6e ore anomalies *n\n-0001a050: 6f74 6520 4275 6773 2061 6e64 2061 6e6f ote Bugs and ano\n-0001a060: 6d61 6c69 6573 3a3a 2061 6e64 2062 6967 malies:: and big\n-0001a070: 206f 7574 7075 7420 6669 6c65 732e 0ae2 output files...\n-0001a080: 8098 2d64 e280 990a 2020 2020 2052 756e ..-d.... Run\n-0001a090: 20e2 8098 736b 6574 6368 e280 9927 7320 ...sketch...'s \n-0001a0a0: 7061 7273 6572 2069 6e20 6465 6275 6767 parser in debugg\n-0001a0b0: 696e 6720 6d6f 6465 2e20 2054 6869 7320 ing mode. This \n-0001a0c0: 6973 2070 7269 6d61 7269 6c79 2066 6f72 is primarily for\n-0001a0d0: 0a20 2020 2020 6465 7665 6c6f 706d 656e . developmen\n-0001a0e0: 742e 0ae2 8098 2d74 e280 990a 2020 2020 t.....-t.... \n-0001a0f0: 2055 7365 2063 6f6e 7465 6e74 7320 6f66 Use contents of\n-0001a100: 2066 696c 6520 e280 9864 6f63 746d 70e2 file ...doctmp.\n-0001a110: 8099 2061 7320 6120 646f 6375 6d65 6e74 .. as a document\n-0001a120: 2074 656d 706c 6174 6520 696e 2077 6869 template in whi\n-0001a130: 6368 2074 6f0a 2020 2020 2065 6e63 6c6f ch to. enclo\n-0001a140: 7365 20e2 8098 5053 5472 6963 6b73 e280 se ...PSTricks..\n-0001a150: 9920 6f75 7470 7574 2063 6f64 652e 2020 . output code. \n-0001a160: 5468 6520 636f 6465 2069 7320 696e 7365 The code is inse\n-0001a170: 7274 6564 2069 6e20 706c 6163 6520 6f66 rted in place of\n-0001a180: 0a20 2020 2020 7468 6520 6669 7273 7420 . the first \n-0001a190: 696e 7374 616e 6365 206f 6620 7468 6520 instance of the \n-0001a1a0: 6573 6361 7065 2073 7472 696e 6720 2525 escape string %%\n-0001a1b0: 534b 4554 4348 5f4f 5554 5055 5425 252e SKETCH_OUTPUT%%.\n-0001a1c0: 0ae2 8098 2d54 e280 990a 2020 2020 2043 ....-T.... C\n-0001a1d0: 6175 7365 7320 e280 9850 5354 7269 636b auses ...PSTrick\n-0001a1e0: 73e2 8099 206f 7574 7075 7420 746f 2062 s... output to b\n-0001a1f0: 6520 656e 636c 6f73 6564 2069 6e20 6465 e enclosed in de\n-0001a200: 6661 756c 7420 5553 2064 6f63 756d 656e fault US documen\n-0001a210: 740a 2020 2020 2074 656d 706c 6174 6520 t. template \n-0001a220: 7465 7874 2e20 204f 7074 696f 6e20 e280 text. Option ..\n-0001a230: 982d 5475 e280 9920 6973 2061 2073 796e .-Tu... is a syn\n-0001a240: 6f6e 796d 2e20 204f 7074 696f 6e20 e280 onym. Option ..\n-0001a250: 982d 5465 e280 9920 6361 7573 6573 2074 .-Te... causes t\n-0001a260: 6865 0a20 2020 2020 4575 726f 2073 7461 he. Euro sta\n-0001a270: 6e64 6172 6420 646f 6375 6d65 6e74 2074 ndard document t\n-0001a280: 656d 706c 6174 6520 746f 2062 6520 7573 emplate to be us\n-0001a290: 6564 2e20 2041 20e2 8098 70e2 8099 2061 ed. A ...p... a\n-0001a2a0: 7070 656e 6465 6420 746f 2061 6e79 0a20 ppended to any. \n-0001a2b0: 2020 2020 6f66 2074 6865 7365 206f 7074 of these opt\n-0001a2c0: 696f 6e73 2063 6175 7365 7320 7468 6520 ions causes the \n-0001a2d0: 7265 7370 6563 7469 7665 2064 6566 6175 respective defau\n-0001a2e0: 6c74 20e2 8098 5053 5472 6963 6b73 e280 lt ...PSTricks..\n-0001a2f0: 9920 646f 6375 6d65 6e74 0a20 2020 2020 . document. \n-0001a300: 7465 6d70 6c61 7465 2074 6f20 6265 2070 template to be p\n-0001a310: 7269 6e74 6564 2074 6f20 7374 616e 6461 rinted to standa\n-0001a320: 7264 206f 7574 7075 742e 2020 416e 2061 rd output. An a\n-0001a330: 7070 656e 6465 6420 e280 9850 e280 9920 ppended ...P... \n-0001a340: 6973 2061 0a20 2020 2020 7379 6e6f 6e79 is a. synony\n-0001a350: 6d2e 2020 416e 2061 7070 656e 6465 6420 m. An appended \n-0001a360: e280 9854 e280 9920 6361 7573 6573 2074 ...T... causes t\n-0001a370: 6865 2074 6865 20e2 8098 5469 6b5a 2f50 he the ...TikZ/P\n-0001a380: 4746 e280 9920 7465 6d70 6c61 7465 2074 GF... template t\n-0001a390: 6f20 6265 0a20 2020 2020 7072 696e 7465 o be. printe\n-0001a3a0: 642e 2020 416e 2061 7070 656e 6465 6420 d. An appended \n-0001a3b0: e280 984c e280 9920 7072 696e 7473 2074 ...L... prints t\n-0001a3c0: 6865 204c 6154 6558 2076 6572 7369 6f6e he LaTeX version\n-0001a3d0: 206f 6620 7468 6520 646f 6375 6d65 6e74 of the document\n-0001a3e0: 0a20 2020 2020 7465 6d70 6c61 7465 2c20 . template, \n-0001a3f0: 6120 7379 6e6f 6e79 6d20 666f 7220 7468 a synonym for th\n-0001a400: 6520 6465 6661 756c 742e 2020 4120 e280 e default. A ..\n-0001a410: 9843 e280 9920 7072 696e 7473 2074 6865 .C... prints the\n-0001a420: 20e2 8098 436f 6e54 6558 74e2 8099 0a20 ...ConTeXt.... \n-0001a430: 2020 2020 7465 6d70 6c61 7465 2e0a e280 template....\n-0001a440: 982d 6fe2 8099 0a20 2020 2020 5573 6520 .-o.... Use \n-0001a450: e280 986f 7574 7075 742e 7465 78e2 8099 ...output.tex...\n-0001a460: 2061 7320 7468 6520 6f75 7470 7574 2066 as the output f\n-0001a470: 696c 652e 2020 5468 6520 6465 6661 756c ile. The defaul\n-0001a480: 7420 6973 2073 7461 6e64 6172 640a 2020 t is standard. \n-0001a490: 2020 206f 7574 7075 742e 0ae2 8098 2d44 output.....-D\n-0001a4a0: e280 990a 2020 2020 2044 6566 696e 6520 .... Define \n-0001a4b0: 6120 7461 6720 666f 7220 7075 7270 6f73 a tag for purpos\n-0001a4c0: 6573 206f 6620 7365 6c65 6374 696e 6720 es of selecting \n-0001a4d0: 6465 6669 6e69 7469 6f6e 2061 6c74 6572 definition alter\n-0001a4e0: 6e61 7469 7665 732e 0a20 2020 2020 2a4e natives.. *N\n-0001a4f0: 6f74 6520 4465 6669 6e69 7469 6f6e 733a ote Definitions:\n-0001a500: 3a2e 2020 5468 6520 6465 6669 6e69 7469 :. The definiti\n-0001a510: 6f6e 2061 7070 6c69 6573 2066 6f72 2061 on applies for a\n-0001a520: 6c6c 2069 6e70 7574 2066 696c 6573 0a20 ll input files. \n-0001a530: 2020 2020 7468 6174 2066 6f6c 6c6f 7720 that follow \n-0001a540: 756e 6c65 7373 2074 6865 2074 6167 2069 unless the tag i\n-0001a550: 7320 756e 6465 6669 6e65 6420 7769 7468 s undefined with\n-0001a560: 20e2 8098 2d55 e280 992e 0ae2 8098 696e ...-U........in\n-0001a570: 7075 7469 2e73 6be2 8099 0a20 2020 2020 puti.sk.... \n-0001a580: 496e 7075 7420 6669 6c65 732c 2072 6561 Input files, rea\n-0001a590: 6420 696e 2074 6865 2073 6571 7565 6e63 d in the sequenc\n-0001a5a0: 6520 7468 6579 2061 7265 2067 6976 656e e they are given\n-0001a5b0: 2e0a e280 982d 55e2 8099 0a20 2020 2020 .....-U.... \n-0001a5c0: 556e 2d64 6566 696e 6520 6120 7461 6720 Un-define a tag \n-0001a5d0: 666f 7220 7075 7270 6f73 6573 206f 6620 for purposes of \n-0001a5e0: 7365 6c65 6374 696e 6720 6465 6669 6e69 selecting defini\n-0001a5f0: 7469 6f6e 2061 6c74 6572 6e61 7469 7665 tion alternative\n-0001a600: 732e 0a0a 1f0a 4669 6c65 3a20 736b 6574 s.....File: sket\n-0001a610: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n-0001a620: 496e 7374 616c 6c69 6e67 2073 6b65 7463 Installing sketc\n-0001a630: 682c 2020 4e65 7874 3a20 496e 6465 7820 h, Next: Index \n-0001a640: 6f66 2073 796e 7461 782c 2020 5072 6576 of syntax, Prev\n-0001a650: 3a20 436f 6d6d 616e 6420 6c69 6e65 2c20 : Command line, \n-0001a660: 2055 703a 2054 6f70 0a0a 3620 4275 696c Up: Top..6 Buil\n-0001a670: 6469 6e67 2061 6e64 2069 6e73 7461 6c6c ding and install\n-0001a680: 696e 6720 e280 9873 6b65 7463 68e2 8099 ing ...sketch...\n-0001a690: 0a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a .***************\n+00018bc0: 5065 7266 6f72 6d61 6e63 6520 6e75 6d62 Performance numb\n+00018bd0: 6572 7320 6f6e 2064 6570 7468 2073 6f72 ers on depth sor\n+00018be0: 742e 0a2a 2042 7567 7320 616e 6420 616e t..* Bugs and an\n+00018bf0: 6f6d 616c 6965 733a 3a20 2020 2020 2020 omalies:: \n+00018c00: 2020 2049 6d70 6572 6665 6374 696f 6e73 Imperfections\n+00018c10: 2069 6e20 7468 6973 2069 6d70 6c65 6d65 in this impleme\n+00018c20: 6e74 6174 696f 6e2e 0a0a 2020 202d 2d2d ntation... ---\n+00018c30: 2d2d 2d2d 2d2d 2d20 466f 6f74 6e6f 7465 ------- Footnote\n+00018c40: 7320 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2020 s ----------.. \n+00018c50: 2028 3129 204e 6577 656c 6c2c 204d 2e45 (1) Newell, M.E\n+00018c60: 2e2c 2052 2e47 2e20 4e65 7765 6c6c 2c20 ., R.G. Newell, \n+00018c70: 616e 6420 542e 4c2e 2053 616e 6368 612c and T.L. Sancha,\n+00018c80: 2041 2073 6f6c 7574 696f 6e20 746f 2074 A solution to t\n+00018c90: 6865 0a68 6964 6465 6e20 7375 7266 6163 he.hidden surfac\n+00018ca0: 6520 7072 6f62 6c65 6d2e 2020 5072 6f63 e problem. Proc\n+00018cb0: 6565 6469 6e67 7320 6f66 2074 6865 2041 eedings of the A\n+00018cc0: 434d 2061 6e6e 7561 6c20 636f 6e66 6572 CM annual confer\n+00018cd0: 656e 6365 202d 0a56 6f6c 756d 6520 312c ence -.Volume 1,\n+00018ce0: 2070 6167 6520 3434 332d 3435 302c 2041 page 443-450, A\n+00018cf0: 434d 2050 7265 7373 2c20 3139 3732 2e0a CM Press, 1972..\n+00018d00: 0a20 2020 2832 2920 5765 2068 6176 6520 . (2) We have \n+00018d10: 7275 6e20 e280 9873 6b65 7463 68e2 8099 run ...sketch...\n+00018d20: 206f 6e20 7468 6520 6661 6d6f 7573 2053 on the famous S\n+00018d30: 7461 6e66 6f72 6420 4275 6e6e 792c 2077 tanford Bunny, w\n+00018d40: 6869 6368 2063 6f6e 7369 7374 730a 6f66 hich consists.of\n+00018d50: 206e 6561 726c 7920 3730 2c30 3030 2074 nearly 70,000 t\n+00018d60: 7269 616e 676c 6573 2e20 2052 756e 2074 riangles. Run t\n+00018d70: 696d 6520 7761 7320 6162 6f75 7420 3620 ime was about 6 \n+00018d80: 7365 636f 6e64 732e 2020 4d6f 7374 206f seconds. Most o\n+00018d90: 6620 7468 6973 0a77 6173 2073 7065 6e74 f this.was spent\n+00018da0: 2077 7269 7469 6e67 2074 6865 206f 7574 writing the out\n+00018db0: 7075 7420 6669 6c65 2072 6174 6865 7220 put file rather \n+00018dc0: 7468 616e 2069 6e20 7468 6520 6869 6464 than in the hidd\n+00018dd0: 656e 2073 7572 6661 6365 0a61 6c67 6f72 en surface.algor\n+00018de0: 6974 686d 2e20 204c 6154 6558 2074 6f6f ithm. LaTeX too\n+00018df0: 6b20 6d75 6368 206c 6f6e 6765 7220 746f k much longer to\n+00018e00: 2070 726f 6365 7373 2074 6865 2072 6573 process the res\n+00018e10: 756c 7469 6e67 20e2 8098 5053 5472 6963 ulting ...PSTric\n+00018e20: 6b73 e280 990a 636f 6465 2e20 2054 6865 ks....code. The\n+00018e30: 206f 6276 696f 7573 2063 6f6e 636c 7573 obvious conclus\n+00018e40: 696f 6e20 6973 2074 6861 7420 7468 6520 ion is that the \n+00018e50: 7370 6565 6420 6f66 2074 6865 2064 6570 speed of the dep\n+00018e60: 7468 2073 6f72 740a 616c 676f 7269 7468 th sort.algorith\n+00018e70: 6d20 6973 206e 6f74 2061 2077 6f72 7279 m is not a worry\n+00018e80: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n+00018e90: 682e 696e 666f 2c20 204e 6f64 653a 2053 h.info, Node: S\n+00018ea0: 7461 7469 7374 6963 732c 2020 4e65 7874 tatistics, Next\n+00018eb0: 3a20 4275 6773 2061 6e64 2061 6e6f 6d61 : Bugs and anoma\n+00018ec0: 6c69 6573 2c20 2050 7265 763a 2048 6964 lies, Prev: Hid\n+00018ed0: 6465 6e20 7375 7266 6163 6520 7265 6d6f den surface remo\n+00018ee0: 7661 6c2c 2020 5570 3a20 4869 6464 656e val, Up: Hidden\n+00018ef0: 2073 7572 6661 6365 2072 656d 6f76 616c surface removal\n+00018f00: 0a0a 342e 342e 332e 3120 5374 6174 6973 ..4.4.3.1 Statis\n+00018f10: 7469 6373 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e tics............\n+00018f20: 2e2e 2e2e 2e2e 2e0a 0a46 6f72 2074 6865 .........For the\n+00018f30: 2063 7572 696f 7573 2c20 e280 9873 6b65 curious, ...ske\n+00018f40: 7463 68e2 8099 2077 7269 7465 7320 6f6e tch... writes on\n+00018f50: 6520 6c69 6e65 206f 6620 6465 7074 6820 e line of depth \n+00018f60: 736f 7274 2073 7461 7469 7374 6963 732e sort statistics.\n+00018f70: 0a48 6572 6520 6973 2061 6e20 6578 616d .Here is an exam\n+00018f80: 706c 6520 666f 7220 6120 6c61 7267 6520 ple for a large \n+00018f90: 636f 6c6c 6563 7469 6f6e 206f 6620 7472 collection of tr\n+00018fa0: 6961 6e67 6c65 732e 0a20 2072 656d 6172 iangles.. remar\n+00018fb0: 6b2c 206e 6f64 653d 3334 3832 3420 7072 k, node=34824 pr\n+00018fc0: 6f62 653d 3538 312e 3920 7377 6170 3d35 obe=581.9 swap=5\n+00018fd0: 2073 706c 6974 3d32 2028 696e 3d34 206f split=2 (in=4 o\n+00018fe0: 7574 3d36 2920 6f6c 733d 3234 3835 312f ut=6) ols=24851/\n+00018ff0: 300a 4974 206d 6561 6e73 2074 6861 7420 0.It means that \n+00019000: 3334 2c38 3234 206f 626a 6563 7473 2077 34,824 objects w\n+00019010: 6572 6520 6465 7074 6820 736f 7274 6564 ere depth sorted\n+00019020: 2061 6674 6572 2063 756c 6c69 6e67 2e20 after culling. \n+00019030: 2046 6f72 2065 6163 682c 0a61 6e20 6176 For each,.an av\n+00019040: 6572 6167 6520 6f66 2035 3831 2e39 206f erage of 581.9 o\n+00019050: 7468 6572 7320 6861 6420 746f 2062 6520 thers had to be \n+00019060: 6368 6563 6b65 6420 746f 2065 6e73 7572 checked to ensur\n+00019070: 6520 7468 6174 2074 6865 2069 6e69 7469 e that the initi\n+00019080: 616c 2c0a 6170 7072 6f78 696d 6174 6520 al,.approximate \n+00019090: 6f72 6465 7269 6e67 2077 6173 2063 6f72 ordering was cor\n+000190a0: 7265 6374 2e20 2041 6d6f 6e67 2061 6c6c rect. Among all\n+000190b0: 2074 6865 7365 2063 6865 636b 732c 206f these checks, o\n+000190c0: 6e6c 7920 350a 7265 7375 6c74 6564 2069 nly 5.resulted i\n+000190d0: 6e20 7377 6170 7320 746f 2072 656f 7264 n swaps to reord\n+000190e0: 6572 2074 6865 2069 6e69 7469 616c 2073 er the initial s\n+000190f0: 6f72 742e 2020 496e 2074 776f 2063 6173 ort. In two cas\n+00019100: 6573 2c20 6120 636f 7272 6563 740a 6f72 es, a correct.or\n+00019110: 6465 7269 6e67 2063 6f75 6c64 206e 6f74 dering could not\n+00019120: 2062 6520 6465 7465 726d 696e 6564 2c20 be determined, \n+00019130: 736f 2062 696e 6172 7920 7370 6163 6520 so binary space \n+00019140: 7061 7274 6974 696f 6e73 2077 6572 650a partitions were.\n+00019150: 636f 6e73 7472 7563 7465 6420 666f 7220 constructed for \n+00019160: 7370 6c69 7474 696e 672e 2020 4120 746f splitting. A to\n+00019170: 7461 6c20 6f66 2034 206f 626a 6563 7473 tal of 4 objects\n+00019180: 2028 7472 6961 6e67 6c65 7320 696e 2074 (triangles in t\n+00019190: 6869 730a 6361 7365 2920 7765 7265 2069 his.case) were i\n+000191a0: 6e73 6572 7465 6420 696e 2074 6865 2070 nserted in the p\n+000191b0: 6172 7469 7469 6f6e 732c 2061 6e64 2036 artitions, and 6\n+000191c0: 2070 6f6c 7967 6f6e 7320 7765 7265 2070 polygons were p\n+000191d0: 726f 6475 6365 642e 0a46 696e 616c 6c79 roduced..Finally\n+000191e0: 2c20 3234 2c38 3531 2022 6c61 7374 2072 , 24,851 \"last r\n+000191f0: 6573 6f72 7422 2070 6f6c 7967 6f6e 206f esort\" polygon o\n+00019200: 7665 726c 6170 2063 6865 636b 7320 7765 verlap checks we\n+00019210: 7265 2070 6572 666f 726d 6564 0a61 6674 re performed.aft\n+00019220: 6572 2073 696d 706c 6572 2c20 6661 7374 er simpler, fast\n+00019230: 6572 2063 6865 636b 7320 6661 696c 6564 er checks failed\n+00019240: 2074 6f20 7969 656c 6420 636f 6e63 6c75 to yield conclu\n+00019250: 7369 7665 2072 6573 756c 7473 2e20 2054 sive results. T\n+00019260: 6865 0a66 696e 616c 202f 3020 6973 2066 he.final /0 is f\n+00019270: 6f72 206c 696e 652d 706f 6c79 676f 6e20 or line-polygon \n+00019280: 6f76 6572 6c61 7020 6368 6563 6b73 2e20 overlap checks. \n+00019290: 2046 6f72 2063 6f6d 7061 7269 736f 6e2c For comparison,\n+000192a0: 2074 6865 0a73 7461 7469 7374 6963 7320 the.statistics \n+000192b0: 666f 7220 7468 6520 6c61 7374 2066 6967 for the last fig\n+000192c0: 7572 6520 696e 202a 6e6f 7465 204f 7665 ure in *note Ove\n+000192d0: 7276 6965 773a 3a20 666f 6c6c 6f77 2e0a rview:: follow..\n+000192e0: 2020 7265 6d61 726b 2c20 6e6f 6465 3d32 remark, node=2\n+000192f0: 3720 7072 6f62 653d 3134 2e36 2073 7761 7 probe=14.6 swa\n+00019300: 703d 3336 2073 706c 6974 3d31 3520 2869 p=36 split=15 (i\n+00019310: 6e3d 3330 206f 7574 3d34 3529 206f 6c73 n=30 out=45) ols\n+00019320: 3d30 2f36 390a 4e6f 7465 2074 6861 7420 =0/69.Note that \n+00019330: 7468 6572 6520 7761 7320 7072 6f70 6f72 there was propor\n+00019340: 7469 6f6e 616c 6c79 206d 7563 6820 6d6f tionally much mo\n+00019350: 7265 2073 7761 7070 696e 6720 616e 6420 re swapping and \n+00019360: 7370 6c69 7474 696e 670a 6163 7469 7669 splitting.activi\n+00019370: 7479 2069 6e20 7468 6973 2068 6967 686c ty in this highl\n+00019380: 7920 636f 6e6e 6563 7465 6420 7363 656e y connected scen\n+00019390: 652e 0a0a 1f0a 4669 6c65 3a20 736b 6574 e.....File: sket\n+000193a0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n+000193b0: 4275 6773 2061 6e64 2061 6e6f 6d61 6c69 Bugs and anomali\n+000193c0: 6573 2c20 2050 7265 763a 2053 7461 7469 es, Prev: Stati\n+000193d0: 7374 6963 732c 2020 5570 3a20 4869 6464 stics, Up: Hidd\n+000193e0: 656e 2073 7572 6661 6365 2072 656d 6f76 en surface remov\n+000193f0: 616c 0a0a 342e 342e 332e 3220 4275 6773 al..4.4.3.2 Bugs\n+00019400: 2061 6e64 2061 6e6f 6d61 6c69 6573 0a2e and anomalies..\n+00019410: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n+00019420: 2e2e 2e2e 2e2e 2e2e 2e0a 0a50 6f6c 7967 ...........Polyg\n+00019430: 6f6e 2061 6e64 206c 696e 6520 7370 6c69 on and line spli\n+00019440: 7474 696e 6720 6361 6e20 626f 7468 2063 tting can both c\n+00019450: 6175 7365 2061 6e6f 6d61 6c69 6573 2069 ause anomalies i\n+00019460: 6e20 7468 6520 6f75 7470 7574 2e0a e280 n the output....\n+00019470: 9850 5354 7269 636b 73e2 8099 2064 6173 .PSTricks... das\n+00019480: 6820 7061 7474 6572 6e73 2c20 7370 6563 h patterns, spec\n+00019490: 6966 6965 6420 7769 7468 20e2 8098 6c69 ified with ...li\n+000194a0: 6e65 7374 796c 653d 6461 7368 6564 e280 nestyle=dashed..\n+000194b0: 992c 2063 616e 2062 650a 6469 7372 7570 ., can be.disrup\n+000194c0: 7465 6420 6279 2073 706c 6974 7469 6e67 ted by splitting\n+000194d0: 2e20 2054 6869 7320 6f63 6375 7273 2077 . This occurs w\n+000194e0: 6865 6e20 7468 6520 6465 7074 6820 736f hen the depth so\n+000194f0: 7274 2067 6976 6573 2075 7020 746f 6f0a rt gives up too.\n+00019500: 6561 726c 7920 616e 6420 7370 6c69 7473 early and splits\n+00019510: 2061 206c 696e 6520 7768 6572 6520 6974 a line where it\n+00019520: 2069 7320 6e6f 7420 7265 616c 6c79 206e is not really n\n+00019530: 6563 6573 7361 7279 2e20 2041 2077 6f72 ecessary. A wor\n+00019540: 6b61 726f 756e 640a 6973 2074 6f20 7573 karound.is to us\n+00019550: 6520 6772 6179 206f 7220 6669 6e65 6c79 e gray or finely\n+00019560: 2064 6f74 7465 6420 6c69 6e65 7320 696e dotted lines in\n+00019570: 7374 6561 642e 2020 4966 2079 6f75 7220 stead. If your \n+00019580: 6472 6177 696e 6720 6973 0a73 6d61 6c6c drawing is.small\n+00019590: 2c20 796f 7520 6361 6e20 616c 736f 2065 , you can also e\n+000195a0: 6469 7420 7468 6520 e280 9873 6b65 7463 dit the ...sketc\n+000195b0: 68e2 8099 206f 7574 7075 7420 6279 2068 h... output by h\n+000195c0: 616e 6420 746f 206d 6572 6765 2074 6865 and to merge the\n+000195d0: 2070 6965 6365 730a 6f66 2074 6865 206f pieces.of the o\n+000195e0: 6666 656e 6469 6e67 206c 696e 652e 0a0a ffending line...\n+000195f0: 2020 2041 6e6f 7468 6572 2061 6e6f 6d61 Another anoma\n+00019600: 6c79 2069 7320 7469 6e79 2028 6f72 2069 ly is tiny (or i\n+00019610: 6e20 6465 6765 6e65 7261 7465 2063 6173 n degenerate cas\n+00019620: 6573 206e 6f74 2d73 6f2d 7469 6e79 2920 es not-so-tiny) \n+00019630: 6e6f 7463 6865 730a 696e 2074 6865 206c notches.in the l\n+00019640: 696e 6573 2074 6861 7420 626f 7264 6572 ines that border\n+00019650: 2073 706c 6974 2070 6f6c 7967 6f6e 732e split polygons.\n+00019660: 2020 5468 6573 6520 6465 7269 7665 2066 These derive f\n+00019670: 726f 6d20 7468 6520 7761 7920 6561 6368 rom the way each\n+00019680: 0a70 6f6c 7967 6f6e 2069 7320 7061 696e .polygon is pain\n+00019690: 7465 643a 2066 6972 7374 2c20 616c 6c20 ted: first, all \n+000196a0: 7069 7865 6c73 2077 6974 6869 6e20 7468 pixels within th\n+000196b0: 6520 626f 756e 6461 7279 2061 7265 20e2 e boundary are .\n+000196c0: 809c 6669 6c6c 6564 e280 9d0a 7769 7468 ..filled....with\n+000196d0: 2063 6f6c 6f72 2028 7065 7268 6170 7320 color (perhaps \n+000196e0: 7768 6974 6529 2c20 7468 656e 2074 6865 white), then the\n+000196f0: 2073 616d 6520 626f 756e 6461 7279 2069 same boundary i\n+00019700: 7320 e280 9c73 7472 6f6b 6564 e280 9d20 s ...stroked... \n+00019710: 2861 0a50 6f73 7473 6372 6970 7420 7465 (a.Postscript te\n+00019720: 726d 2920 7769 7468 2061 206c 696e 652e rm) with a line.\n+00019730: 2020 5468 6520 7265 7375 6c74 2069 7320 The result is \n+00019740: 7468 6174 2068 616c 6620 7468 6520 6c69 that half the li\n+00019750: 6e65 206c 6965 730a 696e 7369 6465 2074 ne lies.inside t\n+00019760: 6865 2062 6f75 6e64 6172 7920 616e 6420 he boundary and \n+00019770: 6861 6c66 206f 7574 7369 6465 2c20 7768 half outside, wh\n+00019780: 696c 6520 7468 6520 5061 696e 7465 7227 ile the Painter'\n+00019790: 7320 616c 676f 7269 7468 6d0a 6173 7375 s algorithm.assu\n+000197a0: 6d65 7320 7468 6520 706f 6c79 676f 6e20 mes the polygon \n+000197b0: 6c69 6573 2065 6e74 6972 656c 7920 7769 lies entirely wi\n+000197c0: 7468 696e 2069 7473 2062 6f75 6e64 6172 thin its boundar\n+000197d0: 792e 2020 5468 6520 6e6f 7463 6865 7320 y. The notches \n+000197e0: 6172 650a 6475 6520 746f 206f 6e65 2070 are.due to one p\n+000197f0: 6f6c 7967 6f6e 2066 696c 6c20 6f70 6572 olygon fill oper\n+00019800: 6174 696f 6e20 6f76 6572 7772 6974 696e ation overwritin\n+00019810: 6720 7468 6520 616c 7265 6164 792d 6472 g the already-dr\n+00019820: 6177 6e20 696e 7369 6465 0a6f 6620 7468 awn inside.of th\n+00019830: 6520 626f 7264 6572 206f 6620 616e 6f74 e border of anot\n+00019840: 6865 7220 706f 6c79 676f 6e2e 2831 2920 her polygon.(1) \n+00019850: 204f 6e65 2077 6f72 6b61 726f 756e 6420 One workaround \n+00019860: 6973 2074 6f20 6d61 6b65 2062 6f72 6465 is to make borde\n+00019870: 720a 6c69 6e65 7320 7665 7279 2074 6869 r.lines very thi\n+00019880: 6e2e 2020 496e 2066 6163 7420 e280 986c n. In fact ...l\n+00019890: 696e 6577 6964 7468 3d30 7074 e280 9920 inewidth=0pt... \n+000198a0: 6973 2067 7561 7261 6e74 6565 6420 746f is guaranteed to\n+000198b0: 2065 6c69 6d69 6e61 7465 0a74 6869 7320 eliminate.this \n+000198c0: 7072 6f62 6c65 6d2c 2074 686f 7567 6820 problem, though \n+000198d0: 7468 6973 2072 6573 756c 7473 2069 6e20 this results in \n+000198e0: 7468 6520 7468 696e 6e65 7374 206c 696e the thinnest lin\n+000198f0: 6520 796f 7572 206f 7574 7075 740a 6465 e your output.de\n+00019900: 7669 6365 2063 616e 2064 7261 772c 2077 vice can draw, w\n+00019910: 6869 6368 2069 7320 7573 7561 6c6c 7920 hich is usually \n+00019920: 746f 6f20 7468 696e 2e20 2059 6f75 206d too thin. You m\n+00019930: 6967 6874 2067 6574 206c 7563 6b79 2062 ight get lucky b\n+00019940: 790a 6d65 7265 6c79 2072 656f 7264 6572 y.merely reorder\n+00019950: 696e 6720 7468 696e 6773 2069 6e20 7468 ing things in th\n+00019960: 6520 696e 7075 7420 6669 6c65 2c20 7768 e input file, wh\n+00019970: 6963 6820 6973 206c 696b 656c 7920 746f ich is likely to\n+00019980: 206d 6f76 6520 7468 650a 7370 6c69 7473 move the.splits\n+00019990: 2074 6f20 6469 6666 6572 656e 7420 706c to different pl\n+000199a0: 6163 6573 2e20 2054 6865 206f 6e6c 7920 aces. The only \n+000199b0: 7375 7265 2d66 6972 6520 736f 6c75 7469 sure-fire soluti\n+000199c0: 6f6e 2069 7320 7072 6574 7479 0a74 6572 on is pretty.ter\n+000199d0: 7269 626c 653a 2063 7573 746f 6d20 6669 rible: custom fi\n+000199e0: 7420 e280 9873 7065 6369 616c e280 9920 t ...special... \n+000199f0: 6f76 6572 6c61 7920 6c69 6e65 7320 2877 overlay lines (w\n+00019a00: 6974 6820 e280 985c 7073 6c69 6e65 e280 ith ...\\psline..\n+00019a10: 9929 2074 6f20 636f 7665 720a 7468 6520 .) to cover.the \n+00019a20: 6e6f 7463 6865 732e 0a0a 2020 2050 6f6c notches... Pol\n+00019a30: 7967 6f6e 2073 706c 6974 7469 6e67 2061 ygon splitting a\n+00019a40: 6c73 6f20 6272 6561 6b73 20e2 8098 5053 lso breaks ...PS\n+00019a50: 5472 6963 6b73 e280 9920 6861 7463 6820 Tricks... hatch \n+00019a60: 7061 7474 6572 6e73 2e20 2054 6865 206f patterns. The o\n+00019a70: 6e6c 790a 6b6e 6f77 6e20 776f 726b 6172 nly.known workar\n+00019a80: 6f75 6e64 2069 7320 746f 2073 7562 7374 ound is to subst\n+00019a90: 6974 7574 6520 6120 736f 6c69 6420 6669 itute a solid fi\n+00019aa0: 6c6c 2066 6f72 2074 6865 2068 6174 6368 ll for the hatch\n+00019ab0: 2e0a 0a20 2020 2d2d 2d2d 2d2d 2d2d 2d2d ... ----------\n+00019ac0: 2046 6f6f 746e 6f74 6573 202d 2d2d 2d2d Footnotes -----\n+00019ad0: 2d2d 2d2d 2d0a 0a20 2020 2831 2920 4920 -----.. (1) I \n+00019ae0: 6b6e 6f77 2068 6f77 2074 6f20 6669 7820 know how to fix \n+00019af0: 7468 6973 2070 726f 626c 656d 2c20 6275 this problem, bu\n+00019b00: 7420 4920 646f 6e27 7420 6c69 6b65 206d t I don't like m\n+00019b10: 7920 736f 6c75 7469 6f6e 2c20 616e 640a y solution, and.\n+00019b20: 4927 6d20 696e 7465 7265 7374 6564 2069 I'm interested i\n+00019b30: 6e20 796f 7572 732e 0a0a 1f0a 4669 6c65 n yours.....File\n+00019b40: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n+00019b50: 4e6f 6465 3a20 436f 6d6d 616e 6420 6c69 Node: Command li\n+00019b60: 6e65 2c20 204e 6578 743a 2049 6e73 7461 ne, Next: Insta\n+00019b70: 6c6c 696e 6720 736b 6574 6368 2c20 2050 lling sketch, P\n+00019b80: 7265 763a 2042 7569 6c64 696e 6720 6120 rev: Building a \n+00019b90: 6472 6177 696e 672c 2020 5570 3a20 546f drawing, Up: To\n+00019ba0: 700a 0a35 2043 6f6d 6d61 6e64 206c 696e p..5 Command lin\n+00019bb0: 650a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a e.**************\n+00019bc0: 0a0a 2a53 796e 6f70 7369 733a 2a0a 2020 ..*Synopsis:*. \n+00019bd0: 2020 2073 6b65 7463 6820 5b2d 685d 5b2d sketch [-h][-\n+00019be0: 5620 782e 795d 5b2d 765d 5b2d 625d 5b2d V x.y][-v][-b][-\n+00019bf0: 645d 5b74 2064 6f63 746d 705d 5b2d 545b d][t doctmp][-T[\n+00019c00: 757c 655d 5b70 5b50 7c54 5d5b 4c7c 435d u|e][p[P|T][L|C]\n+00019c10: 5d5d 5b2d 6f20 6f75 7470 7574 2e74 6578 ]][-o output.tex\n+00019c20: 5d0a 2020 2020 2020 205b 2d44 2054 4147 ]. [-D TAG\n+00019c30: 202e 2e2e 5d20 696e 7075 7431 2e73 6b20 ...] input1.sk \n+00019c40: 5b2d 5520 5441 4720 2e2e 2e5d 2069 6e70 [-U TAG ...] inp\n+00019c50: 7574 322e 736b 202e 2e2e 0a0a 2a44 6573 ut2.sk .....*Des\n+00019c60: 6372 6970 7469 6f6e 2a20 5072 6f63 6573 cription* Proces\n+00019c70: 7365 7320 7468 6520 e280 9873 6b65 7463 ses the ...sketc\n+00019c80: 68e2 8099 2069 6e70 7574 2066 696c 6573 h... input files\n+00019c90: 2069 6e20 6f72 6465 7220 746f 2070 726f in order to pro\n+00019ca0: 6475 6365 0ae2 8098 5053 5472 6963 6b73 duce....PSTricks\n+00019cb0: e280 9920 6f75 7470 7574 2063 6f64 6520 ... output code \n+00019cc0: 7375 6974 6162 6c65 2066 6f72 2069 6e63 suitable for inc\n+00019cd0: 6c75 7369 6f6e 2069 6e20 6120 5465 5820 lusion in a TeX \n+00019ce0: 6f72 204c 6154 6558 0a64 6f63 756d 656e or LaTeX.documen\n+00019cf0: 742e 0a0a 2a4f 7074 696f 6e73 3a2a 0ae2 t...*Options:*..\n+00019d00: 8098 2d68 e280 990a 2020 2020 2050 7269 ..-h.... Pri\n+00019d10: 6e74 2061 2073 686f 7274 2063 6174 616c nt a short catal\n+00019d20: 6f67 206f 6620 6f70 7469 6f6e 732e 0ae2 og of options...\n+00019d30: 8098 2d56 e280 990a 2020 2020 2053 6574 ..-V.... Set\n+00019d40: 2074 6865 20e2 8098 5053 5472 6963 6b73 the ...PSTricks\n+00019d50: e280 9920 7665 7273 696f 6e20 6173 7375 ... version assu\n+00019d60: 6d65 6420 666f 7220 6f75 7470 7574 2070 med for output p\n+00019d70: 7572 706f 7365 7320 746f 20e2 8098 782e urposes to ...x.\n+00019d80: 79e2 8099 2c0a 2020 2020 2066 6f72 2065 y...,. for e\n+00019d90: 7861 6d70 6c65 2031 2e31 392e 2020 5573 xample 1.19. Us\n+00019da0: 7561 6c6c 7920 6e65 6564 6564 206f 6e6c ually needed onl\n+00019db0: 7920 6966 2079 6f75 7220 e280 9850 5354 y if your ...PST\n+00019dc0: 7269 636b 73e2 8099 2069 7320 6f6c 640a ricks... is old.\n+00019dd0: 2020 2020 2063 6f6d 7061 7265 6420 746f compared to\n+00019de0: 2079 6f75 7220 e280 9873 6b65 7463 68e2 your ...sketch.\n+00019df0: 8099 2e20 2055 7365 20e2 8098 2d76 e280 ... Use ...-v..\n+00019e00: 9920 746f 2073 6565 2077 6861 7420 e280 . to see what ..\n+00019e10: 9873 6b65 7463 68e2 8099 2061 7373 756d .sketch... assum\n+00019e20: 6573 0a20 2020 2020 6279 2064 6566 6175 es. by defau\n+00019e30: 6c74 2e0a e280 982d 76e2 8099 0a20 2020 lt.....-v.... \n+00019e40: 2020 5072 696e 7420 7665 7273 696f 6e20 Print version \n+00019e50: 696e 666f 726d 6174 696f 6e20 746f 2073 information to s\n+00019e60: 7461 6e64 6172 6420 6f75 7470 7574 2c20 tandard output, \n+00019e70: 696e 636c 7564 696e 6720 7468 6520 7665 including the ve\n+00019e80: 7273 696f 6e0a 2020 2020 206f 6620 e280 rsion. of ..\n+00019e90: 9850 5354 7269 636b 73e2 8099 2061 7373 .PSTricks... ass\n+00019ea0: 756d 6564 2066 6f72 206f 7574 7075 7420 umed for output \n+00019eb0: 2863 616e 2062 6520 6368 616e 6765 6420 (can be changed \n+00019ec0: 7769 7468 20e2 8098 2d56 e280 9920 6162 with ...-V... ab\n+00019ed0: 6f76 6529 2e0a e280 982d 62e2 8099 0a20 ove).....-b.... \n+00019ee0: 2020 2020 5573 6520 6120 4253 5020 282a Use a BSP (*\n+00019ef0: 4e6f 7465 2048 6964 6465 6e20 7375 7266 Note Hidden surf\n+00019f00: 6163 6520 7265 6d6f 7661 6c3a 3a2e 2920 ace removal::.) \n+00019f10: 2066 6f72 205f 616c 6c5f 2068 6964 6465 for _all_ hidde\n+00019f20: 6e0a 2020 2020 2073 7572 6661 6365 2072 n. surface r\n+00019f30: 656d 6f76 616c 2072 6174 6865 7220 7468 emoval rather th\n+00019f40: 616e 2074 6865 2064 6566 6175 6c74 2c20 an the default, \n+00019f50: 7768 6963 6820 6973 2074 6865 2064 6570 which is the dep\n+00019f60: 7468 2073 6f72 740a 2020 2020 2061 6c67 th sort. alg\n+00019f70: 6f72 6974 686d 2077 6974 6820 4253 5073 orithm with BSPs\n+00019f80: 2075 7365 6420 6f6e 6c79 2066 6f72 2063 used only for c\n+00019f90: 7963 6c65 2072 6573 6f6c 7574 696f 6e2e ycle resolution.\n+00019fa0: 2020 5468 6973 206d 6179 0a20 2020 2020 This may. \n+00019fb0: 7072 6f64 7563 6520 636f 7272 6563 7420 produce correct \n+00019fc0: 6f75 7470 7574 2069 6e20 6365 7274 6169 output in certai\n+00019fd0: 6e20 6465 6765 6e65 7261 7465 2063 6173 n degenerate cas\n+00019fe0: 6573 2077 6865 7265 2074 6865 2064 6570 es where the dep\n+00019ff0: 7468 0a20 2020 2020 736f 7274 2063 616e th. sort can\n+0001a000: 6e6f 742c 2062 7574 2069 7420 616c 736f not, but it also\n+0001a010: 206c 6561 6473 2074 6f20 6d61 6e79 2067 leads to many g\n+0001a020: 7261 7475 6974 6f75 7320 7370 6c69 7473 ratuitous splits\n+0001a030: 2c20 6865 6e63 650a 2020 2020 206d 6f72 , hence. mor\n+0001a040: 6520 616e 6f6d 616c 6965 7320 2a6e 6f74 e anomalies *not\n+0001a050: 6520 4275 6773 2061 6e64 2061 6e6f 6d61 e Bugs and anoma\n+0001a060: 6c69 6573 3a3a 2061 6e64 2062 6967 206f lies:: and big o\n+0001a070: 7574 7075 7420 6669 6c65 732e 0ae2 8098 utput files.....\n+0001a080: 2d64 e280 990a 2020 2020 2052 756e 20e2 -d.... 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Thi\n+0001b130: 7320 746f 6f6c 2069 7320 6176 6169 6c61 s tool is availa\n+0001b140: 626c 6520 696e 0a62 696e 6172 7920 666f ble in.binary fo\n+0001b150: 726d 2066 6f72 2057 696e 646f 7773 2c20 rm for Windows, \n+0001b160: 616e 6420 6974 2062 7569 6c64 7320 6561 and it builds ea\n+0001b170: 7369 6c79 2077 6974 6820 6120 7369 6d70 sily with a simp\n+0001b180: 6c65 20e2 8098 6d61 6b65 e280 9920 756e le ...make... un\n+0001b190: 6465 720a 6c69 6e75 7820 6f72 2043 7967 der.linux or Cyg\n+0001b1a0: 7769 6e20 696e 7374 616c 6c61 7469 6f6e win installation\n+0001b1b0: 7320 7468 6174 2068 6176 6520 6465 7665 s that have deve\n+0001b1c0: 6c6f 706d 656e 7420 746f 6f6c 7320 696e lopment tools in\n+0001b1d0: 7374 616c 6c65 6420 6f72 0a75 6e64 6572 stalled or.under\n+0001b1e0: 20e2 8098 4d61 6320 4f53 2058 e280 9920 ...Mac OS X... \n+0001b1f0: 7769 7468 20e2 8098 5843 6f64 65e2 8099 with ...XCode...\n+0001b200: 2069 6e73 7461 6c6c 6564 2e0a 0a1f 0a46 installed.....F\n+0001b210: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+0001b220: 2c20 204e 6f64 653a 2049 6e64 6578 206f , Node: Index o\n+0001b230: 6620 7379 6e74 6178 2c20 204e 6578 743a f syntax, Next:\n+0001b240: 2049 6e64 6578 2c20 2050 7265 763a 2049 Index, Prev: I\n+0001b250: 6e73 7461 6c6c 696e 6720 736b 6574 6368 nstalling sketch\n+0001b260: 2c20 2055 703a 2054 6f70 0a0a 496e 6465 , Up: Top..Inde\n+0001b270: 7820 6f66 2073 796e 7461 780a 2a2a 2a2a x of syntax.****\n+0001b280: 2a2a 2a2a 2a2a 2a2a 2a2a 2a0a 0a00 085b ***********....[\n+0001b290: 696e 6465 7800 085d 0a2a 204d 656e 753a index..].* Menu:\n+0001b2a0: 0a0a 2a20 2d2c 206d 696e 7573 206f 7065 ..* -, minus ope\n+0001b2b0: 7261 746f 723a 2020 2020 2020 2020 2020 rator: \n+0001b2c0: 2020 2020 2020 2020 2020 2054 776f 2d6f Two-o\n+0001b2d0: 7065 7261 6e64 2028 6269 6e61 7279 2920 perand (binary) \n+0001b2e0: 666f 726d 732e 0a20 2020 2020 2020 2020 forms.. \n 0001b2f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b300: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b310: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b320: 2020 2020 2020 2020 286c 696e 6520 3135 (line 15\n-0001b330: 290a 2a20 2d2c 2075 6e61 7279 206d 696e ).* -, unary min\n-0001b340: 7573 206f 7065 7261 746f 723a 2020 2020 us operator: \n-0001b350: 2020 2020 2020 2020 2020 2055 6e61 7279 Unary\n-0001b360: 2066 6f72 6d73 2e20 2020 2020 2020 2020 forms. \n-0001b370: 2028 6c69 6e65 2031 3029 0a2a 202e 2c20 (line 10).* ., \n-0001b380: 646f 7420 6f70 6572 6174 6f72 3a20 2020 dot operator: \n+0001b320: 2020 2020 2020 286c 696e 6520 3135 290a (line 15).\n+0001b330: 2a20 2d2c 2075 6e61 7279 206d 696e 7573 * -, unary minus\n+0001b340: 206f 7065 7261 746f 723a 2020 2020 2020 operator: \n+0001b350: 2020 2020 2020 2020 2055 6e61 7279 2066 Unary f\n+0001b360: 6f72 6d73 2e20 2020 2020 2020 2020 2028 orms. (\n+0001b370: 6c69 6e65 2031 3029 0a2a 202e 2c20 646f line 10).* ., do\n+0001b380: 7420 6f70 6572 6174 6f72 3a20 2020 2020 t operator: \n 0001b390: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b3a0: 2020 2020 5477 6f2d 6f70 6572 616e 6420 Two-operand \n-0001b3b0: 2862 696e 6172 7929 2066 6f72 6d73 2e0a (binary) forms..\n+0001b3a0: 2020 5477 6f2d 6f70 6572 616e 6420 2862 Two-operand (b\n+0001b3b0: 696e 6172 7929 2066 6f72 6d73 2e0a 2020 inary) forms.. \n 0001b3c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b3d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b3e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b3f0: 2020 2020 2020 2020 2020 2020 2020 2028 (\n-0001b400: 6c69 6e65 2031 3929 0a2a 202e 2c20 646f line 19).* ., do\n-0001b410: 7420 6f70 6572 6174 6f72 203c 313e 3a20 t operator <1>: \n+0001b3f0: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+0001b400: 6e65 2031 3929 0a2a 202e 2c20 646f 7420 ne 19).* ., dot \n+0001b410: 6f70 6572 6174 6f72 203c 313e 3a20 2020 operator <1>: \n 0001b420: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b430: 2020 5477 6f2d 6f70 6572 616e 6420 2862 Two-operand (b\n-0001b440: 696e 6172 7929 2066 6f72 6d73 2e0a 2020 inary) forms.. \n+0001b430: 5477 6f2d 6f70 6572 616e 6420 2862 696e Two-operand (bin\n+0001b440: 6172 7929 2066 6f72 6d73 2e0a 2020 2020 ary) forms.. \n 0001b450: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b460: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b470: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b480: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-0001b490: 6e65 2036 3129 0a2a 2027 782c 2027 792c ne 61).* 'x, 'y,\n-0001b4a0: 2061 6e64 2027 7a3a 2020 2020 2020 2020 and 'z: \n-0001b4b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b4c0: 4166 6669 6e65 2061 7269 7468 6d65 7469 Affine arithmeti\n-0001b4d0: 632e 2020 2020 286c 696e 6520 3337 290a c. (line 37).\n-0001b4e0: 2a20 2778 2c20 2779 2c20 616e 6420 277a * 'x, 'y, and 'z\n-0001b4f0: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n-0001b500: 2020 2020 2020 2020 2054 776f 2d6f 7065 Two-ope\n-0001b510: 7261 6e64 2028 6269 6e61 7279 2920 666f rand (binary) fo\n-0001b520: 726d 732e 0a20 2020 2020 2020 2020 2020 rms.. \n+0001b480: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+0001b490: 2036 3129 0a2a 2027 782c 2027 792c 2061 61).* 'x, 'y, a\n+0001b4a0: 6e64 2027 7a3a 2020 2020 2020 2020 2020 nd 'z: \n+0001b4b0: 2020 2020 2020 2020 2020 2020 2020 4166 Af\n+0001b4c0: 6669 6e65 2061 7269 7468 6d65 7469 632e fine arithmetic.\n+0001b4d0: 2020 2020 286c 696e 6520 3337 290a 2a20 (line 37).* \n+0001b4e0: 2778 2c20 2779 2c20 616e 6420 277a 203c 'x, 'y, and 'z <\n+0001b4f0: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n+0001b500: 2020 2020 2020 2054 776f 2d6f 7065 7261 Two-opera\n+0001b510: 6e64 2028 6269 6e61 7279 2920 666f 726d nd (binary) form\n+0001b520: 732e 0a20 2020 2020 2020 2020 2020 2020 s.. \n 0001b530: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b540: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b550: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b560: 2020 2020 286c 696e 6520 3431 290a 2a20 (line 41).* \n-0001b570: 2820 292c 2067 726f 7570 696e 673a 2020 ( ), grouping: \n+0001b560: 2020 286c 696e 6520 3431 290a 2a20 2820 (line 41).* ( \n+0001b570: 292c 2067 726f 7570 696e 673a 2020 2020 ), grouping: \n 0001b580: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b590: 2020 2020 2020 2054 776f 2d6f 7065 7261 Two-opera\n-0001b5a0: 6e64 2028 6269 6e61 7279 2920 666f 726d nd (binary) form\n-0001b5b0: 732e 0a20 2020 2020 2020 2020 2020 2020 s.. \n+0001b590: 2020 2020 2054 776f 2d6f 7065 7261 6e64 Two-operand\n+0001b5a0: 2028 6269 6e61 7279 2920 666f 726d 732e (binary) forms.\n+0001b5b0: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n 0001b5c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b5d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b5e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b5f0: 2020 286c 696e 6520 3538 290a 2a20 2866 (line 58).* (f\n-0001b600: 6f6f 292c 2070 6f69 6e74 2072 6566 6572 oo), point refer\n-0001b610: 656e 6365 3a20 2020 2020 2020 2020 2020 ence: \n-0001b620: 2020 2020 2044 7261 7769 6e67 2061 2073 Drawing a s\n-0001b630: 6f6c 6964 2e20 2020 2020 2028 6c69 6e65 olid. (line\n-0001b640: 2032 3429 0a2a 2028 666f 6f29 2c20 706f 24).* (foo), po\n-0001b650: 696e 7420 7265 6665 7265 6e63 6520 3c31 int reference <1\n-0001b660: 3e3a 2020 2020 2020 2020 2020 2020 466f >: Fo\n-0001b670: 726d 7320 6f66 2072 6566 6572 656e 6365 rms of reference\n-0001b680: 732e 2020 286c 696e 6520 3134 290a 2a20 s. (line 14).* \n-0001b690: 5b5b 205d 5b20 5d5b 205d 5b20 5d5d 2c20 [[ ][ ][ ][ ]], \n-0001b6a0: 7472 616e 7366 6f72 6d20 6c69 7465 7261 transform litera\n-0001b6b0: 6c3a 2020 2020 2054 7261 6e73 666f 726d l: Transform\n-0001b6c0: 206c 6974 6572 616c 732e 2020 2028 6c69 literals. (li\n-0001b6d0: 6e65 2034 3729 0a2a 205b 5b20 5d5b 205d ne 47).* [[ ][ ]\n-0001b6e0: 5b20 5d5b 205d 5d2c 2074 7261 6e73 666f [ ][ ]], transfo\n-0001b6f0: 726d 206c 6974 6572 616c 203c 313e 3a20 rm literal <1>: \n-0001b700: 5472 616e 7366 6f72 6d20 6c69 7465 7261 Transform litera\n-0001b710: 6c73 2e20 2020 286c 696e 6520 3533 290a ls. (line 53).\n-0001b720: 2a20 5b5b 666f 6f5d 5d2c 2074 7261 6e73 * [[foo]], trans\n-0001b730: 666f 726d 2072 6566 6572 656e 6365 3a20 form reference: \n-0001b740: 2020 2020 2020 2020 2046 6f72 6d73 206f Forms o\n-0001b750: 6620 7265 6665 7265 6e63 6573 2e20 2028 f references. (\n-0001b760: 6c69 6e65 2031 3629 0a2a 205b 5b66 6f6f line 16).* [[foo\n-0001b770: 5d5d 2c20 7472 616e 7366 6f72 6d20 7265 ]], transform re\n-0001b780: 6665 7265 6e63 6520 3c31 3e3a 2020 2020 ference <1>: \n-0001b790: 2020 4f76 6572 7669 6577 2e20 2020 2020 Overview. \n-0001b7a0: 2020 2020 2020 2020 286c 696e 6520 3335 (line 35\n-0001b7b0: 290a 2a20 5b5b 666f 6f5d 5d2c 2074 7261 ).* [[foo]], tra\n-0001b7c0: 6e73 666f 726d 2072 6566 6572 656e 6365 nsform reference\n-0001b7d0: 203c 323e 3a20 2020 2020 204f 7665 7276 <2>: Overv\n-0001b7e0: 6965 772e 2020 2020 2020 2020 2020 2020 iew. \n-0001b7f0: 2028 6c69 6e65 2033 3529 0a2a 205b 666f (line 35).* [fo\n-0001b800: 6f2c 2e2e 2e2c 6261 725d 2c20 6d75 6c74 o,...,bar], mult\n-0001b810: 6970 6c65 206f 7074 696f 6e73 2072 6566 iple options ref\n-0001b820: 6572 656e 6365 3a20 466f 726d 7320 6f66 erence: Forms of\n-0001b830: 2072 6566 6572 656e 6365 732e 0a20 2020 references.. \n+0001b5f0: 286c 696e 6520 3538 290a 2a20 2866 6f6f (line 58).* (foo\n+0001b600: 292c 2070 6f69 6e74 2072 6566 6572 656e ), point referen\n+0001b610: 6365 3a20 2020 2020 2020 2020 2020 2020 ce: \n+0001b620: 2020 2044 7261 7769 6e67 2061 2073 6f6c Drawing a sol\n+0001b630: 6964 2e20 2020 2020 2028 6c69 6e65 2032 id. (line 2\n+0001b640: 3429 0a2a 2028 666f 6f29 2c20 706f 696e 4).* (foo), poin\n+0001b650: 7420 7265 6665 7265 6e63 6520 3c31 3e3a t reference <1>:\n+0001b660: 2020 2020 2020 2020 2020 2020 466f 726d Form\n+0001b670: 7320 6f66 2072 6566 6572 656e 6365 732e s of references.\n+0001b680: 2020 286c 696e 6520 3134 290a 2a20 5b5b (line 14).* [[\n+0001b690: 205d 5b20 5d5b 205d 5b20 5d5d 2c20 7472 ][ ][ ][ ]], tr\n+0001b6a0: 616e 7366 6f72 6d20 6c69 7465 7261 6c3a ansform literal:\n+0001b6b0: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n+0001b6c0: 6974 6572 616c 732e 2020 2028 6c69 6e65 iterals. (line\n+0001b6d0: 2034 3729 0a2a 205b 5b20 5d5b 205d 5b20 47).* [[ ][ ][ \n+0001b6e0: 5d5b 205d 5d2c 2074 7261 6e73 666f 726d ][ ]], transform\n+0001b6f0: 206c 6974 6572 616c 203c 313e 3a20 5472 literal <1>: Tr\n+0001b700: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n+0001b710: 2e20 2020 286c 696e 6520 3533 290a 2a20 . (line 53).* \n+0001b720: 5b5b 666f 6f5d 5d2c 2074 7261 6e73 666f [[foo]], transfo\n+0001b730: 726d 2072 6566 6572 656e 6365 3a20 2020 rm reference: \n+0001b740: 2020 2020 2020 2046 6f72 6d73 206f 6620 Forms of \n+0001b750: 7265 6665 7265 6e63 6573 2e20 2028 6c69 references. (li\n+0001b760: 6e65 2031 3629 0a2a 205b 5b66 6f6f 5d5d ne 16).* [[foo]]\n+0001b770: 2c20 7472 616e 7366 6f72 6d20 7265 6665 , transform refe\n+0001b780: 7265 6e63 6520 3c31 3e3a 2020 2020 2020 rence <1>: \n+0001b790: 4f76 6572 7669 6577 2e20 2020 2020 2020 Overview. \n+0001b7a0: 2020 2020 2020 286c 696e 6520 3335 290a (line 35).\n+0001b7b0: 2a20 5b5b 666f 6f5d 5d2c 2074 7261 6e73 * [[foo]], trans\n+0001b7c0: 666f 726d 2072 6566 6572 656e 6365 203c form reference <\n+0001b7d0: 323e 3a20 2020 2020 204f 7665 7276 6965 2>: Overvie\n+0001b7e0: 772e 2020 2020 2020 2020 2020 2020 2028 w. (\n+0001b7f0: 6c69 6e65 2033 3529 0a2a 205b 666f 6f2c line 35).* [foo,\n+0001b800: 2e2e 2e2c 6261 725d 2c20 6d75 6c74 6970 ...,bar], multip\n+0001b810: 6c65 206f 7074 696f 6e73 2072 6566 6572 le options refer\n+0001b820: 656e 6365 3a20 466f 726d 7320 6f66 2072 ence: Forms of r\n+0001b830: 6566 6572 656e 6365 732e 0a20 2020 2020 eferences.. \n 0001b840: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b850: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b860: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b870: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-0001b880: 6520 3138 290a 2a20 5b66 6f6f 5d2c 206f e 18).* [foo], o\n-0001b890: 7074 696f 6e73 2072 6566 6572 656e 6365 ptions reference\n-0001b8a0: 3a20 2020 2020 2020 2020 2020 2020 2050 : P\n-0001b8b0: 6f6c 796c 696e 6520 7377 6565 7073 2077 olyline sweeps w\n-0001b8c0: 6974 6820 636c 6f73 7572 652e 0a20 2020 ith closure.. \n+0001b870: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+0001b880: 3138 290a 2a20 5b66 6f6f 5d2c 206f 7074 18).* [foo], opt\n+0001b890: 696f 6e73 2072 6566 6572 656e 6365 3a20 ions reference: \n+0001b8a0: 2020 2020 2020 2020 2020 2020 2050 6f6c Pol\n+0001b8b0: 796c 696e 6520 7377 6565 7073 2077 6974 yline sweeps wit\n+0001b8c0: 6820 636c 6f73 7572 652e 0a20 2020 2020 h closure.. \n 0001b8d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b8e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b8f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b900: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-0001b910: 6520 3234 290a 2a20 5b66 6f6f 5d2c 206f e 24).* [foo], o\n-0001b920: 7074 696f 6e73 2072 6566 6572 656e 6365 ptions reference\n-0001b930: 203c 313e 3a20 2020 2020 2020 2020 2046 <1>: F\n-0001b940: 6f72 6d73 206f 6620 7265 6665 7265 6e63 orms of referenc\n-0001b950: 6573 2e20 2028 6c69 6e65 2031 3829 0a2a es. (line 18).*\n-0001b960: 205b 666f 6f5d 2c20 7665 6374 6f72 2072 [foo], vector r\n-0001b970: 6566 6572 656e 6365 3a20 2020 2020 2020 eference: \n-0001b980: 2020 2020 2020 2020 506f 6c79 6c69 6e65 Polyline\n-0001b990: 2073 7765 6570 732e 2020 2020 2020 286c sweeps. (l\n-0001b9a0: 696e 6520 3230 290a 2a20 5b66 6f6f 5d2c ine 20).* [foo],\n-0001b9b0: 2076 6563 746f 7220 7265 6665 7265 6e63 vector referenc\n-0001b9c0: 6520 3c31 3e3a 2020 2020 2020 2020 2020 e <1>: \n-0001b9d0: 2046 6f72 6d73 206f 6620 7265 6665 7265 Forms of refere\n-0001b9e0: 6e63 6573 2e20 2028 6c69 6e65 2031 3529 nces. 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(line 2\n-0001ba80: 3529 0a2a 207b 207d 2c20 626c 6f63 6b20 5).* { }, block \n-0001ba90: 6472 6177 6162 6c65 203c 323e 3a20 2020 drawable <2>: \n-0001baa0: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n-0001bab0: 7420 626c 6f63 6b73 2e20 2020 2020 2020 t blocks. \n-0001bac0: 2020 286c 696e 6520 2037 290a 2a20 7b20 (line 7).* { \n-0001bad0: 7d2c 2062 6c6f 636b 2064 7261 7761 626c }, block drawabl\n-0001bae0: 6520 3c33 3e3a 2020 2020 2020 2020 2020 e <3>: \n-0001baf0: 2020 2020 2042 6c6f 636b 732e 2020 2020 Blocks. \n-0001bb00: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001bb10: 2020 3629 0a2a 207b 207d 2c20 626c 6f63 6).* { }, bloc\n-0001bb20: 6b20 6472 6177 6162 6c65 203c 343e 3a20 k drawable <4>: \n-0001bb30: 2020 2020 2020 2020 2020 2020 2020 4f76 Ov\n-0001bb40: 6572 7669 6577 2e20 2020 2020 2020 2020 erview. \n-0001bb50: 2020 2020 286c 696e 6520 3337 290a 2a20 (line 37).* \n-0001bb60: 7b66 6f6f 7d2c 2064 7261 7761 626c 6520 {foo}, drawable \n-0001bb70: 7265 6665 7265 6e63 653a 2020 2020 2020 reference: \n-0001bb80: 2020 2020 2020 204f 626a 6563 7420 7472 Object tr\n-0001bb90: 616e 7366 6f72 6d73 2e20 2020 2028 6c69 ansforms. 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(li\n+0001c260: 6e65 2031 3929 0a2a 207c 587c 2c20 6d61 ne 19).* |X|, ma\n+0001c270: 676e 6974 7564 6520 6f70 6572 6174 6f72 gnitude operator\n+0001c280: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001c290: 556e 6172 7920 666f 726d 732e 2020 2020 Unary forms. \n+0001c2a0: 2020 2020 2020 286c 696e 6520 3132 290a (line 12).\n+0001c2b0: 2a20 6163 6f73 3a20 2020 2020 2020 2020 * acos: \n 0001c2c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c2d0: 2020 2020 2020 2020 2020 2055 6e61 7279 Unary\n-0001c2e0: 2066 6f72 6d73 2e20 2020 2020 2020 2020 forms. \n-0001c2f0: 2028 6c69 6e65 2031 3829 0a2a 2061 7272 (line 18).* arr\n-0001c300: 6f77 733a 2020 2020 2020 2020 2020 2020 ows: \n+0001c2d0: 2020 2020 2020 2020 2055 6e61 7279 2066 Unary f\n+0001c2e0: 6f72 6d73 2e20 2020 2020 2020 2020 2028 orms. (\n+0001c2f0: 6c69 6e65 2031 3829 0a2a 2061 7272 6f77 line 18).* arrow\n+0001c300: 733a 2020 2020 2020 2020 2020 2020 2020 s: \n 0001c310: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c320: 2020 2020 4166 6669 6e65 2061 7269 7468 Affine arith\n-0001c330: 6d65 7469 632e 2020 2020 286c 696e 6520 metic. (line \n-0001c340: 3131 290a 2a20 6172 726f 7773 203c 313e 11).* arrows <1>\n-0001c350: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001c360: 2020 2020 2020 2020 2020 2020 2041 6666 Aff\n-0001c370: 696e 6520 6172 6974 686d 6574 6963 2e20 ine arithmetic. \n-0001c380: 2020 2028 6c69 6e65 2032 3829 0a2a 2061 (line 28).* a\n-0001c390: 7272 6f77 7320 3c32 3e3a 2020 2020 2020 rrows <2>: \n+0001c320: 2020 4166 6669 6e65 2061 7269 7468 6d65 Affine arithme\n+0001c330: 7469 632e 2020 2020 286c 696e 6520 3131 tic. (line 11\n+0001c340: 290a 2a20 6172 726f 7773 203c 313e 3a20 ).* arrows <1>: \n+0001c350: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001c360: 2020 2020 2020 2020 2020 2041 6666 696e Affin\n+0001c370: 6520 6172 6974 686d 6574 6963 2e20 2020 e arithmetic. \n+0001c380: 2028 6c69 6e65 2032 3829 0a2a 2061 7272 (line 28).* arr\n+0001c390: 6f77 7320 3c32 3e3a 2020 2020 2020 2020 ows <2>: \n 0001c3a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c3b0: 2020 2020 2020 4f76 6572 7669 6577 2e20 Overview. \n-0001c3c0: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-0001c3d0: 6520 3639 290a 2a20 6172 726f 7773 203c e 69).* arrows <\n-0001c3e0: 333e 3a20 2020 2020 2020 2020 2020 2020 3>: \n-0001c3f0: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-0001c400: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n-0001c410: 6e67 2e20 2028 6c69 6e65 2032 3629 0a2a ng. (line 26).*\n-0001c420: 2061 7272 6f77 7320 3c34 3e3a 2020 2020 arrows <4>: \n+0001c3b0: 2020 2020 4f76 6572 7669 6577 2e20 2020 Overview. \n+0001c3c0: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+0001c3d0: 3639 290a 2a20 6172 726f 7773 203c 333e 69).* arrows <3>\n+0001c3e0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001c3f0: 2020 2020 2020 2020 2020 2020 2041 2074 A t\n+0001c400: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n+0001c410: 2e20 2028 6c69 6e65 2032 3629 0a2a 2061 . (line 26).* a\n+0001c420: 7272 6f77 7320 3c34 3e3a 2020 2020 2020 rrows <4>: \n 0001c430: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c440: 2020 2020 2020 2020 4120 7465 6368 6e69 A techni\n-0001c450: 6361 6c20 6472 6177 696e 672e 2020 286c cal drawing. (l\n-0001c460: 696e 6520 3638 290a 2a20 6173 696e 3a20 ine 68).* asin: \n+0001c440: 2020 2020 2020 4120 7465 6368 6e69 6361 A technica\n+0001c450: 6c20 6472 6177 696e 672e 2020 286c 696e l drawing. (lin\n+0001c460: 6520 3638 290a 2a20 6173 696e 3a20 2020 e 68).* asin: \n 0001c470: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c480: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c490: 2055 6e61 7279 2066 6f72 6d73 2e20 2020 Unary forms. \n-0001c4a0: 2020 2020 2020 2028 6c69 6e65 2031 3729 (line 17)\n-0001c4b0: 0a2a 2061 7461 6e32 3a20 2020 2020 2020 .* atan2: \n+0001c480: 2020 2020 2020 2020 2020 2020 2020 2055 U\n+0001c490: 6e61 7279 2066 6f72 6d73 2e20 2020 2020 nary forms. \n+0001c4a0: 2020 2020 2028 6c69 6e65 2031 3729 0a2a (line 17).*\n+0001c4b0: 2061 7461 6e32 3a20 2020 2020 2020 2020 atan2: \n 0001c4c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c4d0: 2020 2020 2020 2020 2020 556e 6172 7920 Unary \n-0001c4e0: 666f 726d 732e 2020 2020 2020 2020 2020 forms. \n-0001c4f0: 286c 696e 6520 3139 290a 2a20 6361 6d65 (line 19).* came\n-0001c500: 7261 3a20 2020 2020 2020 2020 2020 2020 ra: \n+0001c4d0: 2020 2020 2020 2020 556e 6172 7920 666f Unary fo\n+0001c4e0: 726d 732e 2020 2020 2020 2020 2020 286c rms. (l\n+0001c4f0: 696e 6520 3139 290a 2a20 6361 6d65 7261 ine 19).* camera\n+0001c500: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n 0001c510: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c520: 2020 2043 616d 6572 612e 2020 2020 2020 Camera. \n-0001c530: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-0001c540: 3629 0a2a 2063 6f6e 7465 7874 3a20 2020 6).* context: \n+0001c520: 2043 616d 6572 612e 2020 2020 2020 2020 Camera. \n+0001c530: 2020 2020 2020 2028 6c69 6e65 2020 3629 (line 6)\n+0001c540: 0a2a 2063 6f6e 7465 7874 3a20 2020 2020 .* context: \n 0001c550: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c560: 2020 2020 2020 2020 2020 2020 4c61 6e67 Lang\n-0001c570: 7561 6765 2e20 2020 2020 2020 2020 2020 uage. \n-0001c580: 2020 286c 696e 6520 3137 290a 2a20 636f (line 17).* co\n-0001c590: 733a 2020 2020 2020 2020 2020 2020 2020 s: \n+0001c560: 2020 2020 2020 2020 2020 4c61 6e67 7561 Langua\n+0001c570: 6765 2e20 2020 2020 2020 2020 2020 2020 ge. \n+0001c580: 286c 696e 6520 3137 290a 2a20 636f 733a (line 17).* cos:\n+0001c590: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001c5a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c5b0: 2020 2020 2055 6e61 7279 2066 6f72 6d73 Unary forms\n-0001c5c0: 2e20 2020 2020 2020 2020 2028 6c69 6e65 . (line\n-0001c5d0: 2031 3629 0a2a 2063 756c 6c3a 2020 2020 16).* cull: \n+0001c5b0: 2020 2055 6e61 7279 2066 6f72 6d73 2e20 Unary forms. \n+0001c5c0: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n+0001c5d0: 3629 0a2a 2063 756c 6c3a 2020 2020 2020 6).* cull: \n 0001c5e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c5f0: 2020 2020 2020 2020 2020 2020 2020 4472 Dr\n-0001c600: 6177 696e 6720 6120 736f 6c69 642e 2020 awing a solid. \n-0001c610: 2020 2020 286c 696e 6520 3435 290a 2a20 (line 45).* \n-0001c620: 6375 6c6c 203c 313e 3a20 2020 2020 2020 cull <1>: \n+0001c5f0: 2020 2020 2020 2020 2020 2020 4472 6177 Draw\n+0001c600: 696e 6720 6120 736f 6c69 642e 2020 2020 ing a solid. \n+0001c610: 2020 286c 696e 6520 3435 290a 2a20 6375 (line 45).* cu\n+0001c620: 6c6c 203c 313e 3a20 2020 2020 2020 2020 ll <1>: \n 0001c630: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c640: 2020 2020 2020 2050 6f6c 796c 696e 6520 Polyline \n-0001c650: 7377 6565 7073 2e20 2020 2020 2028 6c69 sweeps. (li\n-0001c660: 6e65 2020 3929 0a2a 2063 756c 6c20 3c32 ne 9).* cull <2\n-0001c670: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001c680: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c690: 5472 616e 7370 6172 656e 6379 2e20 2020 Transparency. \n-0001c6a0: 2020 2020 2020 286c 696e 6520 3135 290a (line 15).\n-0001c6b0: 2a20 6375 6c6c 203c 333e 3a20 2020 2020 * cull <3>: \n+0001c640: 2020 2020 2050 6f6c 796c 696e 6520 7377 Polyline sw\n+0001c650: 6565 7073 2e20 2020 2020 2028 6c69 6e65 eeps. (line\n+0001c660: 2020 3929 0a2a 2063 756c 6c20 3c32 3e3a 9).* cull <2>:\n+0001c670: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001c680: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n+0001c690: 616e 7370 6172 656e 6379 2e20 2020 2020 ansparency. \n+0001c6a0: 2020 2020 286c 696e 6520 3135 290a 2a20 (line 15).* \n+0001c6b0: 6375 6c6c 203c 333e 3a20 2020 2020 2020 cull <3>: \n 0001c6c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c6d0: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n-0001c6e0: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n-0001c6f0: 6c69 6e65 2032 3029 0a2a 2063 756c 6c20 line 20).* cull \n-0001c700: 3c34 3e3a 2020 2020 2020 2020 2020 2020 <4>: \n+0001c6d0: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n+0001c6e0: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n+0001c6f0: 6e65 2032 3029 0a2a 2063 756c 6c20 3c34 ne 20).* cull <4\n+0001c700: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n 0001c710: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c720: 2020 496e 7465 726e 616c 206f 7074 696f Internal optio\n-0001c730: 6e73 2e20 2020 2020 286c 696e 6520 2037 ns. (line 7\n-0001c740: 290a 2a20 6375 6c6c 203c 353e 3a20 2020 ).* cull <5>: \n+0001c720: 496e 7465 726e 616c 206f 7074 696f 6e73 Internal options\n+0001c730: 2e20 2020 2020 286c 696e 6520 2037 290a . (line 7).\n+0001c740: 2a20 6375 6c6c 203c 353e 3a20 2020 2020 * cull <5>: \n 0001c750: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c760: 2020 2020 2020 2020 2020 2047 6c6f 6261 Globa\n-0001c770: 6c20 6f70 7469 6f6e 732e 2020 2020 2020 l options. \n-0001c780: 2028 6c69 6e65 2031 3329 0a2a 2063 7572 (line 13).* cur\n-0001c790: 7665 3a20 2020 2020 2020 2020 2020 2020 ve: \n+0001c760: 2020 2020 2020 2020 2047 6c6f 6261 6c20 Global \n+0001c770: 6f70 7469 6f6e 732e 2020 2020 2020 2028 options. (\n+0001c780: 6c69 6e65 2031 3329 0a2a 2063 7572 7665 line 13).* curve\n+0001c790: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n 0001c7a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c7b0: 2020 2020 4375 7276 6573 2e20 2020 2020 Curves. \n-0001c7c0: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-0001c7d0: 2036 290a 2a20 6465 663a 2020 2020 2020 6).* def: \n+0001c7b0: 2020 4375 7276 6573 2e20 2020 2020 2020 Curves. \n+0001c7c0: 2020 2020 2020 2020 286c 696e 6520 2036 (line 6\n+0001c7d0: 290a 2a20 6465 663a 2020 2020 2020 2020 ).* def: \n 0001c7e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c7f0: 2020 2020 2020 2020 2020 2020 2044 7261 Dra\n-0001c800: 7769 6e67 2061 2073 6f6c 6964 2e20 2020 wing a solid. \n-0001c810: 2020 2028 6c69 6e65 2020 3929 0a2a 2064 (line 9).* d\n-0001c820: 6566 203c 313e 3a20 2020 2020 2020 2020 ef <1>: \n+0001c7f0: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n+0001c800: 6e67 2061 2073 6f6c 6964 2e20 2020 2020 ng a solid. \n+0001c810: 2028 6c69 6e65 2020 3929 0a2a 2064 6566 (line 9).* def\n+0001c820: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n 0001c830: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c840: 2020 2020 2020 4472 6177 696e 6720 6120 Drawing a \n-0001c850: 736f 6c69 642e 2020 2020 2020 286c 696e solid. (lin\n-0001c860: 6520 3232 290a 2a20 6465 6620 3c32 3e3a e 22).* def <2>:\n+0001c840: 2020 2020 4472 6177 696e 6720 6120 736f Drawing a so\n+0001c850: 6c69 642e 2020 2020 2020 286c 696e 6520 lid. (line \n+0001c860: 3232 290a 2a20 6465 6620 3c32 3e3a 2020 22).* def <2>: \n 0001c870: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c880: 2020 2020 2020 2020 2020 2020 2020 204f O\n-0001c890: 626a 6563 7420 7472 616e 7366 6f72 6d73 bject transforms\n-0001c8a0: 2e20 2020 2028 6c69 6e65 2031 3029 0a2a . (line 10).*\n-0001c8b0: 2064 6566 203c 333e 3a20 2020 2020 2020 def <3>: \n+0001c880: 2020 2020 2020 2020 2020 2020 204f 626a Obj\n+0001c890: 6563 7420 7472 616e 7366 6f72 6d73 2e20 ect transforms. \n+0001c8a0: 2020 2028 6c69 6e65 2031 3029 0a2a 2064 (line 10).* d\n+0001c8b0: 6566 203c 333e 3a20 2020 2020 2020 2020 ef <3>: \n 0001c8c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c8d0: 2020 2020 2020 2020 506f 696e 7420 7377 Point sw\n-0001c8e0: 6565 7073 2e20 2020 2020 2020 2020 286c eeps. (l\n-0001c8f0: 696e 6520 3139 290a 2a20 6465 6620 3c34 ine 19).* def <4\n-0001c900: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001c910: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c920: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n-0001c930: 2e20 2020 2020 2028 6c69 6e65 2020 3929 . (line 9)\n-0001c940: 0a2a 2064 6566 203c 353e 3a20 2020 2020 .* def <5>: \n+0001c8d0: 2020 2020 2020 506f 696e 7420 7377 6565 Point swee\n+0001c8e0: 7073 2e20 2020 2020 2020 2020 286c 696e ps. (lin\n+0001c8f0: 6520 3139 290a 2a20 6465 6620 3c34 3e3a e 19).* def <4>:\n+0001c900: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001c910: 2020 2020 2020 2020 2020 2020 2020 2050 P\n+0001c920: 6f6c 796c 696e 6520 7377 6565 7073 2e20 olyline sweeps. \n+0001c930: 2020 2020 2028 6c69 6e65 2020 3929 0a2a (line 9).*\n+0001c940: 2064 6566 203c 353e 3a20 2020 2020 2020 def <5>: \n 0001c950: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c960: 2020 2020 2020 2020 2020 4e65 7374 6564 Nested\n-0001c970: 2073 7765 6570 732e 2020 2020 2020 2020 sweeps. \n-0001c980: 286c 696e 6520 2038 290a 2a20 6465 6620 (line 8).* def \n-0001c990: 3c36 3e3a 2020 2020 2020 2020 2020 2020 <6>: \n+0001c960: 2020 2020 2020 2020 4e65 7374 6564 2073 Nested s\n+0001c970: 7765 6570 732e 2020 2020 2020 2020 286c weeps. (l\n+0001c980: 696e 6520 2038 290a 2a20 6465 6620 3c36 ine 8).* def <6\n+0001c990: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n 0001c9a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c9b0: 2020 2050 6f6c 796c 696e 6520 7377 6565 Polyline swee\n-0001c9c0: 7073 2077 6974 6820 636c 6f73 7572 652e ps with closure.\n-0001c9d0: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n+0001c9b0: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n+0001c9c0: 2077 6974 6820 636c 6f73 7572 652e 0a20 with closure.. \n+0001c9d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001c9e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001c9f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ca00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ca10: 286c 696e 6520 3130 290a 2a20 6465 6620 (line 10).* def \n-0001ca20: 3c37 3e3a 2020 2020 2020 2020 2020 2020 <7>: \n+0001ca00: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+0001ca10: 696e 6520 3130 290a 2a20 6465 6620 3c37 ine 10).* def <7\n+0001ca20: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n 0001ca30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ca40: 2020 2041 6666 696e 6520 6172 6974 686d Affine arithm\n-0001ca50: 6574 6963 2e20 2020 2028 6c69 6e65 2031 etic. (line 1\n-0001ca60: 3129 0a2a 2064 6566 203c 383e 3a20 2020 1).* def <8>: \n+0001ca40: 2041 6666 696e 6520 6172 6974 686d 6574 Affine arithmet\n+0001ca50: 6963 2e20 2020 2028 6c69 6e65 2031 3129 ic. (line 11)\n+0001ca60: 0a2a 2064 6566 203c 383e 3a20 2020 2020 .* def <8>: \n 0001ca70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ca80: 2020 2020 2020 2020 2020 2020 4f76 6572 Over\n-0001ca90: 7669 6577 2e20 2020 2020 2020 2020 2020 view. \n-0001caa0: 2020 286c 696e 6520 3132 290a 2a20 6465 (line 12).* de\n-0001cab0: 6620 3c39 3e3a 2020 2020 2020 2020 2020 f <9>: \n+0001ca80: 2020 2020 2020 2020 2020 4f76 6572 7669 Overvi\n+0001ca90: 6577 2e20 2020 2020 2020 2020 2020 2020 ew. \n+0001caa0: 286c 696e 6520 3132 290a 2a20 6465 6620 (line 12).* def \n+0001cab0: 3c39 3e3a 2020 2020 2020 2020 2020 2020 <9>: \n 0001cac0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cad0: 2020 2020 204f 7665 7276 6965 772e 2020 Overview. \n-0001cae0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001caf0: 2033 3729 0a2a 2064 6566 203c 3130 3e3a 37).* def <10>:\n+0001cad0: 2020 204f 7665 7276 6965 772e 2020 2020 Overview. \n+0001cae0: 2020 2020 2020 2020 2028 6c69 6e65 2033 (line 3\n+0001caf0: 3729 0a2a 2064 6566 203c 3130 3e3a 2020 7).* def <10>: \n 0001cb00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cb10: 2020 2020 2020 2020 2020 2020 2020 4f76 Ov\n-0001cb20: 6572 7669 6577 2e20 2020 2020 2020 2020 erview. \n-0001cb30: 2020 2020 286c 696e 6520 3639 290a 2a20 (line 69).* \n-0001cb40: 6465 6620 3c31 313e 3a20 2020 2020 2020 def <11>: \n+0001cb10: 2020 2020 2020 2020 2020 2020 4f76 6572 Over\n+0001cb20: 7669 6577 2e20 2020 2020 2020 2020 2020 view. \n+0001cb30: 2020 286c 696e 6520 3639 290a 2a20 6465 (line 69).* de\n+0001cb40: 6620 3c31 313e 3a20 2020 2020 2020 2020 f <11>: \n 0001cb50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cb60: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n-0001cb70: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n-0001cb80: 6e65 2031 3429 0a2a 2064 6566 203c 3132 ne 14).* def <12\n-0001cb90: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001cba0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cbb0: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n-0001cbc0: 696e 672e 2020 286c 696e 6520 3236 290a ing. (line 26).\n-0001cbd0: 2a20 6465 6620 3c31 333e 3a20 2020 2020 * def <13>: \n+0001cb60: 2020 2020 2041 2074 6563 686e 6963 616c A technical\n+0001cb70: 2064 7261 7769 6e67 2e20 2028 6c69 6e65 drawing. (line\n+0001cb80: 2031 3429 0a2a 2064 6566 203c 3132 3e3a 14).* def <12>:\n+0001cb90: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001cba0: 2020 2020 2020 2020 2020 2020 2020 4120 A \n+0001cbb0: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n+0001cbc0: 672e 2020 286c 696e 6520 3236 290a 2a20 g. (line 26).* \n+0001cbd0: 6465 6620 3c31 333e 3a20 2020 2020 2020 def <13>: \n 0001cbe0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cbf0: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n-0001cc00: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n-0001cc10: 6c69 6e65 2034 3129 0a2a 2064 6566 203c line 41).* def <\n-0001cc20: 3134 3e3a 2020 2020 2020 2020 2020 2020 14>: \n+0001cbf0: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n+0001cc00: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n+0001cc10: 6e65 2034 3129 0a2a 2064 6566 203c 3134 ne 41).* def <14\n+0001cc20: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n 0001cc30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cc40: 2020 4120 7465 6368 6e69 6361 6c20 6472 A technical dr\n-0001cc50: 6177 696e 672e 2020 286c 696e 6520 3638 awing. (line 68\n-0001cc60: 290a 2a20 6465 6620 3c31 353e 3a20 2020 ).* def <15>: \n+0001cc40: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n+0001cc50: 696e 672e 2020 286c 696e 6520 3638 290a ing. (line 68).\n+0001cc60: 2a20 6465 6620 3c31 353e 3a20 2020 2020 * def <15>: \n 0001cc70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cc80: 2020 2020 2020 2020 2020 2041 2074 6563 A tec\n-0001cc90: 686e 6963 616c 2064 7261 7769 6e67 2e20 hnical drawing. \n-0001cca0: 2028 6c69 6e65 2039 3529 0a2a 2064 6566 (line 95).* def\n-0001ccb0: 203c 3136 3e3a 2020 2020 2020 2020 2020 <16>: \n+0001cc80: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n+0001cc90: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n+0001cca0: 6c69 6e65 2039 3529 0a2a 2064 6566 203c line 95).* def <\n+0001ccb0: 3136 3e3a 2020 2020 2020 2020 2020 2020 16>: \n 0001ccc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ccd0: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n-0001cce0: 616c 206d 6f64 656c 2e20 286c 696e 6520 al model. (line \n-0001ccf0: 3130 290a 2a20 6465 6620 3c31 373e 3a20 10).* def <17>: \n+0001ccd0: 2020 4120 6869 6572 6172 6368 6963 616c A hierarchical\n+0001cce0: 206d 6f64 656c 2e20 286c 696e 6520 3130 model. (line 10\n+0001ccf0: 290a 2a20 6465 6620 3c31 373e 3a20 2020 ).* def <17>: \n 0001cd00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cd10: 2020 2020 2020 2020 2020 2020 2041 2068 A h\n-0001cd20: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n-0001cd30: 6c2e 2028 6c69 6e65 2032 3329 0a2a 2064 l. (line 23).* d\n-0001cd40: 6566 203c 3138 3e3a 2020 2020 2020 2020 ef <18>: \n+0001cd10: 2020 2020 2020 2020 2020 2041 2068 6965 A hie\n+0001cd20: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e rarchical model.\n+0001cd30: 2028 6c69 6e65 2032 3329 0a2a 2064 6566 (line 23).* def\n+0001cd40: 203c 3138 3e3a 2020 2020 2020 2020 2020 <18>: \n 0001cd50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cd60: 2020 2020 2020 4120 6869 6572 6172 6368 A hierarch\n-0001cd70: 6963 616c 206d 6f64 656c 2e20 286c 696e ical model. (lin\n-0001cd80: 6520 3332 290a 2a20 646f 7473 3a20 2020 e 32).* dots: \n+0001cd60: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n+0001cd70: 616c 206d 6f64 656c 2e20 286c 696e 6520 al model. (line \n+0001cd80: 3332 290a 2a20 646f 7473 3a20 2020 2020 32).* dots: \n 0001cd90: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cda0: 2020 2020 2020 2020 2020 2020 2020 2044 D\n-0001cdb0: 6f74 732e 2020 2020 2020 2020 2020 2020 ots. \n-0001cdc0: 2020 2020 2028 6c69 6e65 2020 3629 0a2a (line 6).*\n-0001cdd0: 2066 696c 6c20 6f70 6163 6974 793a 2020 fill opacity: \n+0001cda0: 2020 2020 2020 2020 2020 2020 2044 6f74 Dot\n+0001cdb0: 732e 2020 2020 2020 2020 2020 2020 2020 s. \n+0001cdc0: 2020 2028 6c69 6e65 2020 3629 0a2a 2066 (line 6).* f\n+0001cdd0: 696c 6c20 6f70 6163 6974 793a 2020 2020 ill opacity: \n 0001cde0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cdf0: 2020 2020 2020 2020 5472 616e 7370 6172 Transpar\n-0001ce00: 656e 6379 2e20 2020 2020 2020 2020 286c ency. (l\n-0001ce10: 696e 6520 3130 290a 2a20 6669 6c6c 2073 ine 10).* fill s\n-0001ce20: 7479 6c65 3a20 2020 2020 2020 2020 2020 tyle: \n-0001ce30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ce40: 2054 696b 5a2f 5047 4620 7573 6572 2d64 TikZ/PGF user-d\n-0001ce50: 6566 696e 6564 2073 7479 6c65 732e 0a20 efined styles.. \n+0001cdf0: 2020 2020 2020 5472 616e 7370 6172 656e Transparen\n+0001ce00: 6379 2e20 2020 2020 2020 2020 286c 696e cy. (lin\n+0001ce10: 6520 3130 290a 2a20 6669 6c6c 2073 7479 e 10).* fill sty\n+0001ce20: 6c65 3a20 2020 2020 2020 2020 2020 2020 le: \n+0001ce30: 2020 2020 2020 2020 2020 2020 2020 2054 T\n+0001ce40: 696b 5a2f 5047 4620 7573 6572 2d64 6566 ikZ/PGF user-def\n+0001ce50: 696e 6564 2073 7479 6c65 732e 0a20 2020 ined styles.. \n 0001ce60: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001ce70: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001ce80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ce90: 2020 2020 2020 2020 2020 2020 2020 286c (l\n-0001cea0: 696e 6520 3235 290a 2a20 6669 6c6c 636f ine 25).* fillco\n-0001ceb0: 6c6f 723a 2020 2020 2020 2020 2020 2020 lor: \n-0001cec0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ced0: 204f 626a 6563 7420 7472 616e 7366 6f72 Object transfor\n-0001cee0: 6d73 2e20 2020 2028 6c69 6e65 2031 3029 ms. (line 10)\n-0001cef0: 0a2a 2066 696c 6c63 6f6c 6f72 203c 313e .* fillcolor <1>\n-0001cf00: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001cf10: 2020 2020 2020 2020 2020 506f 6c79 6c69 Polyli\n-0001cf20: 6e65 2073 7765 6570 7320 7769 7468 2063 ne sweeps with c\n-0001cf30: 6c6f 7375 7265 2e0a 2020 2020 2020 2020 losure.. \n+0001ce90: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+0001cea0: 6520 3235 290a 2a20 6669 6c6c 636f 6c6f e 25).* fillcolo\n+0001ceb0: 723a 2020 2020 2020 2020 2020 2020 2020 r: \n+0001cec0: 2020 2020 2020 2020 2020 2020 2020 204f O\n+0001ced0: 626a 6563 7420 7472 616e 7366 6f72 6d73 bject transforms\n+0001cee0: 2e20 2020 2028 6c69 6e65 2031 3029 0a2a . (line 10).*\n+0001cef0: 2066 696c 6c63 6f6c 6f72 203c 313e 3a20 fillcolor <1>: \n+0001cf00: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001cf10: 2020 2020 2020 2020 506f 6c79 6c69 6e65 Polyline\n+0001cf20: 2073 7765 6570 7320 7769 7468 2063 6c6f sweeps with clo\n+0001cf30: 7375 7265 2e0a 2020 2020 2020 2020 2020 sure.. \n 0001cf40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001cf50: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001cf60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cf70: 2020 2020 2020 2028 6c69 6e65 2031 3029 (line 10)\n-0001cf80: 0a2a 2066 696c 6c63 6f6c 6f72 203c 323e .* fillcolor <2>\n-0001cf90: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001cfa0: 2020 2020 2020 2020 2020 4f76 6572 7669 Overvi\n-0001cfb0: 6577 2e20 2020 2020 2020 2020 2020 2020 ew. \n-0001cfc0: 286c 696e 6520 3337 290a 2a20 6672 616d (line 37).* fram\n-0001cfd0: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n+0001cf70: 2020 2020 2028 6c69 6e65 2031 3029 0a2a (line 10).*\n+0001cf80: 2066 696c 6c63 6f6c 6f72 203c 323e 3a20 fillcolor <2>: \n+0001cf90: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001cfa0: 2020 2020 2020 2020 4f76 6572 7669 6577 Overview\n+0001cfb0: 2e20 2020 2020 2020 2020 2020 2020 286c . (l\n+0001cfc0: 696e 6520 3337 290a 2a20 6672 616d 653a ine 37).* frame:\n+0001cfd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001cfe0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cff0: 2020 2046 7261 6d65 2e20 2020 2020 2020 Frame. \n-0001d000: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-0001d010: 3629 0a2a 2066 7261 6d65 7365 703a 2020 6).* framesep: \n+0001cff0: 2046 7261 6d65 2e20 2020 2020 2020 2020 Frame. \n+0001d000: 2020 2020 2020 2028 6c69 6e65 2020 3629 (line 6)\n+0001d010: 0a2a 2066 7261 6d65 7365 703a 2020 2020 .* framesep: \n 0001d020: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d030: 2020 2020 2020 2020 2020 2020 4672 616d Fram\n-0001d040: 652e 2020 2020 2020 2020 2020 2020 2020 e. \n-0001d050: 2020 286c 696e 6520 3131 290a 2a20 676c (line 11).* gl\n-0001d060: 6f62 616c 3a20 2020 2020 2020 2020 2020 obal: \n+0001d030: 2020 2020 2020 2020 2020 4672 616d 652e Frame.\n+0001d040: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001d050: 286c 696e 6520 3131 290a 2a20 676c 6f62 (line 11).* glob\n+0001d060: 616c 3a20 2020 2020 2020 2020 2020 2020 al: \n 0001d070: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d080: 2020 2020 2047 6c6f 6261 6c20 656e 7669 Global envi\n-0001d090: 726f 6e6d 656e 742e 2020 2028 6c69 6e65 ronment. (line\n-0001d0a0: 2031 3229 0a2a 2069 6e70 7574 3a20 2020 12).* input: \n+0001d080: 2020 2047 6c6f 6261 6c20 656e 7669 726f Global enviro\n+0001d090: 6e6d 656e 742e 2020 2028 6c69 6e65 2031 nment. (line 1\n+0001d0a0: 3229 0a2a 2069 6e70 7574 3a20 2020 2020 2).* input: \n 0001d0b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d0c0: 2020 2020 2020 2020 2020 2020 2020 4c61 La\n-0001d0d0: 6e67 7561 6765 2062 6173 6963 732e 2020 nguage basics. \n-0001d0e0: 2020 2020 286c 696e 6520 3139 290a 2a20 (line 19).* \n-0001d0f0: 696e 7665 7273 653a 2020 2020 2020 2020 inverse: \n+0001d0c0: 2020 2020 2020 2020 2020 2020 4c61 6e67 Lang\n+0001d0d0: 7561 6765 2062 6173 6963 732e 2020 2020 uage basics. \n+0001d0e0: 2020 286c 696e 6520 3139 290a 2a20 696e (line 19).* in\n+0001d0f0: 7665 7273 653a 2020 2020 2020 2020 2020 verse: \n 0001d100: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d110: 2020 2020 2020 2055 6e61 7279 2066 6f72 Unary for\n-0001d120: 6d73 2e20 2020 2020 2020 2020 2028 6c69 ms. (li\n-0001d130: 6e65 2032 3129 0a2a 206c 616e 6775 6167 ne 21).* languag\n-0001d140: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n-0001d150: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d160: 4c61 6e67 7561 6765 2e20 2020 2020 2020 Language. \n-0001d170: 2020 2020 2020 286c 696e 6520 2036 290a (line 6).\n-0001d180: 2a20 6c61 7465 783a 2020 2020 2020 2020 * latex: \n+0001d110: 2020 2020 2055 6e61 7279 2066 6f72 6d73 Unary forms\n+0001d120: 2e20 2020 2020 2020 2020 2028 6c69 6e65 . (line\n+0001d130: 2032 3129 0a2a 206c 616e 6775 6167 653a 21).* language:\n+0001d140: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001d150: 2020 2020 2020 2020 2020 2020 2020 4c61 La\n+0001d160: 6e67 7561 6765 2e20 2020 2020 2020 2020 nguage. \n+0001d170: 2020 2020 286c 696e 6520 2036 290a 2a20 (line 6).* \n+0001d180: 6c61 7465 783a 2020 2020 2020 2020 2020 latex: \n 0001d190: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d1a0: 2020 2020 2020 2020 204c 616e 6775 6167 Languag\n-0001d1b0: 652e 2020 2020 2020 2020 2020 2020 2028 e. (\n-0001d1c0: 6c69 6e65 2031 3729 0a2a 206c 6179 3a20 line 17).* lay: \n+0001d1a0: 2020 2020 2020 204c 616e 6775 6167 652e Language.\n+0001d1b0: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+0001d1c0: 6e65 2031 3729 0a2a 206c 6179 3a20 2020 ne 17).* lay: \n 0001d1d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d1e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d1f0: 2020 5370 6563 6961 6c20 6f62 6a65 6374 Special object\n-0001d200: 732e 2020 2020 2020 286c 696e 6520 3438 s. (line 48\n-0001d210: 290a 2a20 6c61 7920 3c31 3e3a 2020 2020 ).* lay <1>: \n+0001d1f0: 5370 6563 6961 6c20 6f62 6a65 6374 732e Special objects.\n+0001d200: 2020 2020 2020 286c 696e 6520 3438 290a (line 48).\n+0001d210: 2a20 6c61 7920 3c31 3e3a 2020 2020 2020 * lay <1>: \n 0001d220: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d230: 2020 2020 2020 2020 2020 2054 696b 5a2f TikZ/\n-0001d240: 5047 4620 7573 6572 2d64 6566 696e 6564 PGF user-defined\n-0001d250: 2073 7479 6c65 732e 0a20 2020 2020 2020 styles.. \n+0001d230: 2020 2020 2020 2020 2054 696b 5a2f 5047 TikZ/PG\n+0001d240: 4620 7573 6572 2d64 6566 696e 6564 2073 F user-defined s\n+0001d250: 7479 6c65 732e 0a20 2020 2020 2020 2020 tyles.. \n 0001d260: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d270: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d280: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d290: 2020 2020 2020 2020 286c 696e 6520 3336 (line 36\n-0001d2a0: 290a 2a20 6c61 7920 3c32 3e3a 2020 2020 ).* lay <2>: \n+0001d290: 2020 2020 2020 286c 696e 6520 3336 290a (line 36).\n+0001d2a0: 2a20 6c61 7920 3c32 3e3a 2020 2020 2020 * lay <2>: \n 0001d2b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d2c0: 2020 2020 2020 2020 2020 2041 2074 6563 A tec\n-0001d2d0: 686e 6963 616c 2064 7261 7769 6e67 2e20 hnical drawing. \n-0001d2e0: 2028 6c69 6e65 2032 3629 0a2a 206c 6179 (line 26).* lay\n-0001d2f0: 203c 333e 3a20 2020 2020 2020 2020 2020 <3>: \n+0001d2c0: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n+0001d2d0: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n+0001d2e0: 6c69 6e65 2032 3629 0a2a 206c 6179 203c line 26).* lay <\n+0001d2f0: 333e 3a20 2020 2020 2020 2020 2020 2020 3>: \n 0001d300: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d310: 2020 2020 4120 7465 6368 6e69 6361 6c20 A technical \n-0001d320: 6472 6177 696e 672e 2020 286c 696e 6520 drawing. (line \n-0001d330: 3236 290a 2a20 6c61 7920 3c34 3e3a 2020 26).* lay <4>: \n+0001d310: 2020 4120 7465 6368 6e69 6361 6c20 6472 A technical dr\n+0001d320: 6177 696e 672e 2020 286c 696e 6520 3236 awing. (line 26\n+0001d330: 290a 2a20 6c61 7920 3c34 3e3a 2020 2020 ).* lay <4>: \n 0001d340: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d350: 2020 2020 2020 2020 2020 2020 2041 2074 A t\n-0001d360: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n-0001d370: 2e20 2028 6c69 6e65 2039 3529 0a2a 206c . (line 95).* l\n-0001d380: 6179 203c 353e 3a20 2020 2020 2020 2020 ay <5>: \n+0001d350: 2020 2020 2020 2020 2020 2041 2074 6563 A tec\n+0001d360: 686e 6963 616c 2064 7261 7769 6e67 2e20 hnical drawing. \n+0001d370: 2028 6c69 6e65 2039 3529 0a2a 206c 6179 (line 95).* lay\n+0001d380: 203c 353e 3a20 2020 2020 2020 2020 2020 <5>: \n 0001d390: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d3a0: 2020 2020 2020 496e 7465 726e 616c 206f Internal o\n-0001d3b0: 7074 696f 6e73 2e20 2020 2020 286c 696e ptions. (lin\n-0001d3c0: 6520 2037 290a 2a20 6c61 7920 3c36 3e3a e 7).* lay <6>:\n+0001d3a0: 2020 2020 496e 7465 726e 616c 206f 7074 Internal opt\n+0001d3b0: 696f 6e73 2e20 2020 2020 286c 696e 6520 ions. (line \n+0001d3c0: 2037 290a 2a20 6c61 7920 3c36 3e3a 2020 7).* lay <6>: \n 0001d3d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d3e0: 2020 2020 2020 2020 2020 2020 2020 2053 S\n-0001d3f0: 7065 6369 616c 732e 2020 2020 2020 2020 pecials. \n-0001d400: 2020 2020 2028 6c69 6e65 2034 3229 0a2a (line 42).*\n-0001d410: 206c 6179 203c 373e 3a20 2020 2020 2020 lay <7>: \n+0001d3e0: 2020 2020 2020 2020 2020 2020 2053 7065 Spe\n+0001d3f0: 6369 616c 732e 2020 2020 2020 2020 2020 cials. \n+0001d400: 2020 2028 6c69 6e65 2034 3229 0a2a 206c (line 42).* l\n+0001d410: 6179 203c 373e 3a20 2020 2020 2020 2020 ay <7>: \n 0001d420: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d430: 2020 2020 2020 2020 476c 6f62 616c 206f Global o\n-0001d440: 7074 696f 6e73 2e20 2020 2020 2020 286c ptions. (l\n-0001d450: 696e 6520 3133 290a 2a20 6c69 6e65 3a20 ine 13).* line: \n+0001d430: 2020 2020 2020 476c 6f62 616c 206f 7074 Global opt\n+0001d440: 696f 6e73 2e20 2020 2020 2020 286c 696e ions. (lin\n+0001d450: 6520 3133 290a 2a20 6c69 6e65 3a20 2020 e 13).* line: \n 0001d460: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d470: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d480: 2044 7261 7769 6e67 206f 7074 696f 6e73 Drawing options\n-0001d490: 2e20 2020 2020 2028 6c69 6e65 2020 3729 . (line 7)\n-0001d4a0: 0a2a 206c 696e 6520 3c31 3e3a 2020 2020 .* line <1>: \n+0001d470: 2020 2020 2020 2020 2020 2020 2020 2044 D\n+0001d480: 7261 7769 6e67 206f 7074 696f 6e73 2e20 rawing options. \n+0001d490: 2020 2020 2028 6c69 6e65 2020 3729 0a2a (line 7).*\n+0001d4a0: 206c 696e 6520 3c31 3e3a 2020 2020 2020 line <1>: \n 0001d4b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d4c0: 2020 2020 2020 2020 2020 4f62 6a65 6374 Object\n-0001d4d0: 2074 7261 6e73 666f 726d 732e 2020 2020 transforms. \n-0001d4e0: 286c 696e 6520 3130 290a 2a20 6c69 6e65 (line 10).* line\n-0001d4f0: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n+0001d4c0: 2020 2020 2020 2020 4f62 6a65 6374 2074 Object t\n+0001d4d0: 7261 6e73 666f 726d 732e 2020 2020 286c ransforms. (l\n+0001d4e0: 696e 6520 3130 290a 2a20 6c69 6e65 203c ine 10).* line <\n+0001d4f0: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n 0001d500: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d510: 2020 2050 6f6c 796c 696e 6520 7377 6565 Polyline swee\n-0001d520: 7073 2077 6974 6820 636c 6f73 7572 652e ps with closure.\n-0001d530: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n+0001d510: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n+0001d520: 2077 6974 6820 636c 6f73 7572 652e 0a20 with closure.. \n+0001d530: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d540: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d550: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d560: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d570: 286c 696e 6520 3130 290a 2a20 6c69 6e65 (line 10).* line\n-0001d580: 203c 333e 3a20 2020 2020 2020 2020 2020 <3>: \n+0001d560: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+0001d570: 696e 6520 3130 290a 2a20 6c69 6e65 203c ine 10).* line <\n+0001d580: 333e 3a20 2020 2020 2020 2020 2020 2020 3>: \n 0001d590: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d5a0: 2020 2041 6666 696e 6520 6172 6974 686d Affine arithm\n-0001d5b0: 6574 6963 2e20 2020 2028 6c69 6e65 2031 etic. (line 1\n-0001d5c0: 3129 0a2a 206c 696e 6520 3c34 3e3a 2020 1).* line <4>: \n+0001d5a0: 2041 6666 696e 6520 6172 6974 686d 6574 Affine arithmet\n+0001d5b0: 6963 2e20 2020 2028 6c69 6e65 2031 3129 ic. (line 11)\n+0001d5c0: 0a2a 206c 696e 6520 3c34 3e3a 2020 2020 .* line <4>: \n 0001d5d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d5e0: 2020 2020 2020 2020 2020 2020 4c69 6e65 Line\n-0001d5f0: 732e 2020 2020 2020 2020 2020 2020 2020 s. \n-0001d600: 2020 286c 696e 6520 2036 290a 2a20 6c69 (line 6).* li\n-0001d610: 6e65 203c 353e 3a20 2020 2020 2020 2020 ne <5>: \n+0001d5e0: 2020 2020 2020 2020 2020 4c69 6e65 732e Lines.\n+0001d5f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001d600: 286c 696e 6520 2036 290a 2a20 6c69 6e65 (line 6).* line\n+0001d610: 203c 353e 3a20 2020 2020 2020 2020 2020 <5>: \n 0001d620: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d630: 2020 2020 2053 7765 7074 2062 6c6f 636b Swept block\n-0001d640: 732e 2020 2020 2020 2020 2028 6c69 6e65 s. (line\n-0001d650: 2020 3729 0a2a 206c 696e 6520 3c36 3e3a 7).* line <6>:\n+0001d630: 2020 2053 7765 7074 2062 6c6f 636b 732e Swept blocks.\n+0001d640: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+0001d650: 3729 0a2a 206c 696e 6520 3c36 3e3a 2020 7).* line <6>: \n 0001d660: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d670: 2020 2020 2020 2020 2020 2020 2020 4f76 Ov\n-0001d680: 6572 7669 6577 2e20 2020 2020 2020 2020 erview. \n-0001d690: 2020 2020 286c 696e 6520 3639 290a 2a20 (line 69).* \n-0001d6a0: 6c69 6e65 203c 373e 3a20 2020 2020 2020 line <7>: \n+0001d670: 2020 2020 2020 2020 2020 2020 4f76 6572 Over\n+0001d680: 7669 6577 2e20 2020 2020 2020 2020 2020 view. \n+0001d690: 2020 286c 696e 6520 3639 290a 2a20 6c69 (line 69).* li\n+0001d6a0: 6e65 203c 373e 3a20 2020 2020 2020 2020 ne <7>: \n 0001d6b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d6c0: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n-0001d6d0: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n-0001d6e0: 6e65 2032 3029 0a2a 206c 696e 6520 3c38 ne 20).* line <8\n-0001d6f0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001d700: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d710: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n-0001d720: 696e 672e 2020 286c 696e 6520 3236 290a ing. (line 26).\n-0001d730: 2a20 6c69 6e65 203c 393e 3a20 2020 2020 * line <9>: \n+0001d6c0: 2020 2020 2041 2074 6563 686e 6963 616c A technical\n+0001d6d0: 2064 7261 7769 6e67 2e20 2028 6c69 6e65 drawing. (line\n+0001d6e0: 2032 3029 0a2a 206c 696e 6520 3c38 3e3a 20).* line <8>:\n+0001d6f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001d700: 2020 2020 2020 2020 2020 2020 2020 4120 A \n+0001d710: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n+0001d720: 672e 2020 286c 696e 6520 3236 290a 2a20 g. (line 26).* \n+0001d730: 6c69 6e65 203c 393e 3a20 2020 2020 2020 line <9>: \n 0001d740: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d750: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n-0001d760: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n-0001d770: 6c69 6e65 2034 3129 0a2a 206c 696e 6520 line 41).* line \n-0001d780: 3c31 303e 3a20 2020 2020 2020 2020 2020 <10>: \n+0001d750: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n+0001d760: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n+0001d770: 6e65 2034 3129 0a2a 206c 696e 6520 3c31 ne 41).* line <1\n+0001d780: 303e 3a20 2020 2020 2020 2020 2020 2020 0>: \n 0001d790: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d7a0: 2020 4120 7465 6368 6e69 6361 6c20 6472 A technical dr\n-0001d7b0: 6177 696e 672e 2020 286c 696e 6520 3638 awing. (line 68\n-0001d7c0: 290a 2a20 6c69 6e65 203c 3131 3e3a 2020 ).* line <11>: \n+0001d7a0: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n+0001d7b0: 696e 672e 2020 286c 696e 6520 3638 290a ing. (line 68).\n+0001d7c0: 2a20 6c69 6e65 203c 3131 3e3a 2020 2020 * line <11>: \n 0001d7d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d7e0: 2020 2020 2020 2020 2020 2041 2068 6965 A hie\n-0001d7f0: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e rarchical model.\n-0001d800: 2028 6c69 6e65 2031 3029 0a2a 206c 696e (line 10).* lin\n-0001d810: 6520 7374 796c 653a 2020 2020 2020 2020 e style: \n+0001d7e0: 2020 2020 2020 2020 2041 2068 6965 7261 A hiera\n+0001d7f0: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028 rchical model. (\n+0001d800: 6c69 6e65 2031 3029 0a2a 206c 696e 6520 line 10).* line \n+0001d810: 7374 796c 653a 2020 2020 2020 2020 2020 style: \n 0001d820: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d830: 2020 2020 5469 6b5a 2f50 4746 2075 7365 TikZ/PGF use\n-0001d840: 722d 6465 6669 6e65 6420 7374 796c 6573 r-defined styles\n-0001d850: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+0001d830: 2020 5469 6b5a 2f50 4746 2075 7365 722d TikZ/PGF user-\n+0001d840: 6465 6669 6e65 6420 7374 796c 6573 2e0a defined styles..\n+0001d850: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d860: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d870: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d880: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d890: 2028 6c69 6e65 2032 3529 0a2a 206c 696e (line 25).* lin\n-0001d8a0: 6563 6f6c 6f72 3a20 2020 2020 2020 2020 ecolor: \n+0001d880: 2020 2020 2020 2020 2020 2020 2020 2028 (\n+0001d890: 6c69 6e65 2032 3529 0a2a 206c 696e 6563 line 25).* linec\n+0001d8a0: 6f6c 6f72 3a20 2020 2020 2020 2020 2020 olor: \n 0001d8b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d8c0: 2020 2020 4f62 6a65 6374 2074 7261 6e73 Object trans\n-0001d8d0: 666f 726d 732e 2020 2020 286c 696e 6520 forms. (line \n-0001d8e0: 3130 290a 2a20 6c69 6e65 636f 6c6f 7220 10).* linecolor \n-0001d8f0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-0001d900: 2020 2020 2020 2020 2020 2020 2046 7261 Fra\n-0001d910: 6d65 2e20 2020 2020 2020 2020 2020 2020 me. \n-0001d920: 2020 2028 6c69 6e65 2031 3029 0a2a 206c (line 10).* l\n-0001d930: 696e 6563 6f6c 6f72 203c 323e 3a20 2020 inecolor <2>: \n+0001d8c0: 2020 4f62 6a65 6374 2074 7261 6e73 666f Object transfo\n+0001d8d0: 726d 732e 2020 2020 286c 696e 6520 3130 rms. (line 10\n+0001d8e0: 290a 2a20 6c69 6e65 636f 6c6f 7220 3c31 ).* linecolor <1\n+0001d8f0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+0001d900: 2020 2020 2020 2020 2020 2046 7261 6d65 Frame\n+0001d910: 2e20 2020 2020 2020 2020 2020 2020 2020 . \n+0001d920: 2028 6c69 6e65 2031 3029 0a2a 206c 696e (line 10).* lin\n+0001d930: 6563 6f6c 6f72 203c 323e 3a20 2020 2020 ecolor <2>: \n 0001d940: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d950: 2020 2020 2020 4f76 6572 7669 6577 2e20 Overview. \n-0001d960: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-0001d970: 6520 3639 290a 2a20 6c69 6e65 7374 796c e 69).* linestyl\n-0001d980: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n-0001d990: 2020 2020 2020 2020 2020 2020 2020 2046 F\n-0001d9a0: 7261 6d65 2e20 2020 2020 2020 2020 2020 rame. \n-0001d9b0: 2020 2020 2028 6c69 6e65 2031 3029 0a2a (line 10).*\n-0001d9c0: 206c 696e 6573 7479 6c65 203c 313e 3a20 linestyle <1>: \n+0001d950: 2020 2020 4f76 6572 7669 6577 2e20 2020 Overview. \n+0001d960: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+0001d970: 3639 290a 2a20 6c69 6e65 7374 796c 653a 69).* linestyle:\n+0001d980: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001d990: 2020 2020 2020 2020 2020 2020 2046 7261 Fra\n+0001d9a0: 6d65 2e20 2020 2020 2020 2020 2020 2020 me. \n+0001d9b0: 2020 2028 6c69 6e65 2031 3029 0a2a 206c (line 10).* l\n+0001d9c0: 696e 6573 7479 6c65 203c 313e 3a20 2020 inestyle <1>: \n 0001d9d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d9e0: 2020 2020 2020 2020 4f76 6572 7669 6577 Overview\n-0001d9f0: 2e20 2020 2020 2020 2020 2020 2020 286c . (l\n-0001da00: 696e 6520 3639 290a 2a20 6c69 6e65 7374 ine 69).* linest\n-0001da10: 796c 6520 3c32 3e3a 2020 2020 2020 2020 yle <2>: \n-0001da20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001da30: 2041 2074 6563 686e 6963 616c 2064 7261 A technical dra\n-0001da40: 7769 6e67 2e20 2028 6c69 6e65 2032 3629 wing. (line 26)\n-0001da50: 0a2a 206c 696e 6573 7479 6c65 203c 333e .* linestyle <3>\n-0001da60: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001da70: 2020 2020 2020 2020 2020 4275 6773 2061 Bugs a\n-0001da80: 6e64 2061 6e6f 6d61 6c69 6573 2e20 2020 nd anomalies. \n-0001da90: 286c 696e 6520 2037 290a 2a20 6c69 6e65 (line 7).* line\n-0001daa0: 7769 6474 683a 2020 2020 2020 2020 2020 width: \n+0001d9e0: 2020 2020 2020 4f76 6572 7669 6577 2e20 Overview. \n+0001d9f0: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+0001da00: 6520 3639 290a 2a20 6c69 6e65 7374 796c e 69).* linestyl\n+0001da10: 6520 3c32 3e3a 2020 2020 2020 2020 2020 e <2>: \n+0001da20: 2020 2020 2020 2020 2020 2020 2020 2041 A\n+0001da30: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n+0001da40: 6e67 2e20 2028 6c69 6e65 2032 3629 0a2a ng. (line 26).*\n+0001da50: 206c 696e 6573 7479 6c65 203c 333e 3a20 linestyle <3>: \n+0001da60: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001da70: 2020 2020 2020 2020 4275 6773 2061 6e64 Bugs and\n+0001da80: 2061 6e6f 6d61 6c69 6573 2e20 2020 286c anomalies. (l\n+0001da90: 696e 6520 2037 290a 2a20 6c69 6e65 7769 ine 7).* linewi\n+0001daa0: 6474 683a 2020 2020 2020 2020 2020 2020 dth: \n 0001dab0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dac0: 2020 2050 6f6c 796c 696e 6520 7377 6565 Polyline swee\n-0001dad0: 7073 2e20 2020 2020 2028 6c69 6e65 2020 ps. (line \n-0001dae0: 3929 0a2a 206c 696e 6577 6964 7468 203c 9).* linewidth <\n-0001daf0: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n-0001db00: 2020 2020 2020 2020 2020 2020 4672 616d Fram\n-0001db10: 652e 2020 2020 2020 2020 2020 2020 2020 e. \n-0001db20: 2020 286c 696e 6520 3130 290a 2a20 6c69 (line 10).* li\n-0001db30: 6e65 7769 6474 6820 3c32 3e3a 2020 2020 newidth <2>: \n+0001dac0: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n+0001dad0: 2e20 2020 2020 2028 6c69 6e65 2020 3929 . (line 9)\n+0001dae0: 0a2a 206c 696e 6577 6964 7468 203c 313e .* linewidth <1>\n+0001daf0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001db00: 2020 2020 2020 2020 2020 4672 616d 652e Frame.\n+0001db10: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001db20: 286c 696e 6520 3130 290a 2a20 6c69 6e65 (line 10).* line\n+0001db30: 7769 6474 6820 3c32 3e3a 2020 2020 2020 width <2>: \n 0001db40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001db50: 2020 2020 204f 7665 7276 6965 772e 2020 Overview. \n-0001db60: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001db70: 2036 3929 0a2a 206c 696e 6577 6964 7468 69).* linewidth\n-0001db80: 203c 333e 3a20 2020 2020 2020 2020 2020 <3>: \n-0001db90: 2020 2020 2020 2020 2020 2020 2020 4120 A \n-0001dba0: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n-0001dbb0: 672e 2020 286c 696e 6520 3236 290a 2a20 g. (line 26).* \n-0001dbc0: 6f70 6163 6974 793a 2020 2020 2020 2020 opacity: \n+0001db50: 2020 204f 7665 7276 6965 772e 2020 2020 Overview. \n+0001db60: 2020 2020 2020 2020 2028 6c69 6e65 2036 (line 6\n+0001db70: 3929 0a2a 206c 696e 6577 6964 7468 203c 9).* linewidth <\n+0001db80: 333e 3a20 2020 2020 2020 2020 2020 2020 3>: \n+0001db90: 2020 2020 2020 2020 2020 2020 4120 7465 A te\n+0001dba0: 6368 6e69 6361 6c20 6472 6177 696e 672e chnical drawing.\n+0001dbb0: 2020 286c 696e 6520 3236 290a 2a20 6f70 (line 26).* op\n+0001dbc0: 6163 6974 793a 2020 2020 2020 2020 2020 acity: \n 0001dbd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dbe0: 2020 2020 2020 2054 7261 6e73 7061 7265 Transpare\n-0001dbf0: 6e63 792e 2020 2020 2020 2020 2028 6c69 ncy. (li\n-0001dc00: 6e65 2031 3029 0a2a 2070 6572 7370 6563 ne 10).* perspec\n-0001dc10: 7469 7665 3a20 2020 2020 2020 2020 2020 tive: \n-0001dc20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dc30: 5472 616e 7366 6f72 6d20 6c69 7465 7261 Transform litera\n-0001dc40: 6c73 2e20 2020 286c 696e 6520 3231 290a ls. (line 21).\n-0001dc50: 2a20 7069 6374 7572 6562 6f78 3a20 2020 * picturebox: \n+0001dbe0: 2020 2020 2054 7261 6e73 7061 7265 6e63 Transparenc\n+0001dbf0: 792e 2020 2020 2020 2020 2028 6c69 6e65 y. (line\n+0001dc00: 2031 3029 0a2a 2070 6572 7370 6563 7469 10).* perspecti\n+0001dc10: 7665 3a20 2020 2020 2020 2020 2020 2020 ve: \n+0001dc20: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n+0001dc30: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n+0001dc40: 2e20 2020 286c 696e 6520 3231 290a 2a20 . (line 21).* \n+0001dc50: 7069 6374 7572 6562 6f78 3a20 2020 2020 picturebox: \n 0001dc60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dc70: 2020 2020 2020 2020 2050 6963 7475 7265 Picture\n-0001dc80: 2062 6f78 2e20 2020 2020 2020 2020 2028 box. (\n-0001dc90: 6c69 6e65 2020 3629 0a2a 2070 6f69 6e74 line 6).* point\n-0001dca0: 206c 6973 743a 2020 2020 2020 2020 2020 list: \n+0001dc70: 2020 2020 2020 2050 6963 7475 7265 2062 Picture b\n+0001dc80: 6f78 2e20 2020 2020 2020 2020 2028 6c69 ox. (li\n+0001dc90: 6e65 2020 3629 0a2a 2070 6f69 6e74 206c ne 6).* point l\n+0001dca0: 6973 743a 2020 2020 2020 2020 2020 2020 ist: \n 0001dcb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dcc0: 2020 496e 7465 726e 616c 206f 7074 696f Internal optio\n-0001dcd0: 6e73 2e20 2020 2020 286c 696e 6520 3234 ns. (line 24\n-0001dce0: 290a 2a20 706f 6c79 676f 6e3a 2020 2020 ).* polygon: \n+0001dcc0: 496e 7465 726e 616c 206f 7074 696f 6e73 Internal options\n+0001dcd0: 2e20 2020 2020 286c 696e 6520 3234 290a . (line 24).\n+0001dce0: 2a20 706f 6c79 676f 6e3a 2020 2020 2020 * polygon: \n 0001dcf0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dd00: 2020 2020 2020 2020 2020 2048 656c 6c6f Hello\n-0001dd10: 2077 6f72 6c64 2e20 2020 2020 2020 2020 world. \n-0001dd20: 2028 6c69 6e65 2033 3829 0a2a 2070 6f6c (line 38).* pol\n-0001dd30: 7967 6f6e 203c 313e 3a20 2020 2020 2020 ygon <1>: \n+0001dd00: 2020 2020 2020 2020 2048 656c 6c6f 2077 Hello w\n+0001dd10: 6f72 6c64 2e20 2020 2020 2020 2020 2028 orld. (\n+0001dd20: 6c69 6e65 2033 3829 0a2a 2070 6f6c 7967 line 38).* polyg\n+0001dd30: 6f6e 203c 313e 3a20 2020 2020 2020 2020 on <1>: \n 0001dd40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dd50: 2020 2020 4472 6177 696e 6720 6120 736f Drawing a so\n-0001dd60: 6c69 642e 2020 2020 2020 286c 696e 6520 lid. (line \n-0001dd70: 2039 290a 2a20 706f 6c79 676f 6e20 3c32 9).* polygon <2\n-0001dd80: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001dd90: 2020 2020 2020 2020 2020 2020 204f 626a Obj\n-0001dda0: 6563 7420 7472 616e 7366 6f72 6d73 2e20 ect transforms. \n-0001ddb0: 2020 2028 6c69 6e65 2031 3029 0a2a 2070 (line 10).* p\n-0001ddc0: 6f6c 7967 6f6e 203c 333e 3a20 2020 2020 olygon <3>: \n+0001dd50: 2020 4472 6177 696e 6720 6120 736f 6c69 Drawing a soli\n+0001dd60: 642e 2020 2020 2020 286c 696e 6520 2039 d. (line 9\n+0001dd70: 290a 2a20 706f 6c79 676f 6e20 3c32 3e3a ).* polygon <2>:\n+0001dd80: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001dd90: 2020 2020 2020 2020 2020 204f 626a 6563 Objec\n+0001dda0: 7420 7472 616e 7366 6f72 6d73 2e20 2020 t transforms. \n+0001ddb0: 2028 6c69 6e65 2031 3029 0a2a 2070 6f6c (line 10).* pol\n+0001ddc0: 7967 6f6e 203c 333e 3a20 2020 2020 2020 ygon <3>: \n 0001ddd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dde0: 2020 2020 2020 4166 6669 6e65 2061 7269 Affine ari\n-0001ddf0: 7468 6d65 7469 632e 2020 2020 286c 696e thmetic. (lin\n-0001de00: 6520 3131 290a 2a20 706f 6c79 676f 6e20 e 11).* polygon \n-0001de10: 3c34 3e3a 2020 2020 2020 2020 2020 2020 <4>: \n-0001de20: 2020 2020 2020 2020 2020 2020 2020 2050 P\n-0001de30: 6f6c 7967 6f6e 732e 2020 2020 2020 2020 olygons. \n-0001de40: 2020 2020 2028 6c69 6e65 2020 3629 0a2a (line 6).*\n-0001de50: 2070 6f6c 7967 6f6e 203c 353e 3a20 2020 polygon <5>: \n+0001dde0: 2020 2020 4166 6669 6e65 2061 7269 7468 Affine arith\n+0001ddf0: 6d65 7469 632e 2020 2020 286c 696e 6520 metic. (line \n+0001de00: 3131 290a 2a20 706f 6c79 676f 6e20 3c34 11).* polygon <4\n+0001de10: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+0001de20: 2020 2020 2020 2020 2020 2020 2050 6f6c Pol\n+0001de30: 7967 6f6e 732e 2020 2020 2020 2020 2020 ygons. \n+0001de40: 2020 2028 6c69 6e65 2020 3629 0a2a 2070 (line 6).* p\n+0001de50: 6f6c 7967 6f6e 203c 353e 3a20 2020 2020 olygon <5>: \n 0001de60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001de70: 2020 2020 2020 2020 5377 6570 7420 626c Swept bl\n-0001de80: 6f63 6b73 2e20 2020 2020 2020 2020 286c ocks. (l\n-0001de90: 696e 6520 2037 290a 2a20 706f 6c79 676f ine 7).* polygo\n-0001dea0: 6e20 3c36 3e3a 2020 2020 2020 2020 2020 n <6>: \n-0001deb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dec0: 204f 7665 7276 6965 772e 2020 2020 2020 Overview. \n-0001ded0: 2020 2020 2020 2028 6c69 6e65 2033 3729 (line 37)\n-0001dee0: 0a2a 2070 726f 6a65 6374 3a20 2020 2020 .* project: \n+0001de70: 2020 2020 2020 5377 6570 7420 626c 6f63 Swept bloc\n+0001de80: 6b73 2e20 2020 2020 2020 2020 286c 696e ks. (lin\n+0001de90: 6520 2037 290a 2a20 706f 6c79 676f 6e20 e 7).* polygon \n+0001dea0: 3c36 3e3a 2020 2020 2020 2020 2020 2020 <6>: \n+0001deb0: 2020 2020 2020 2020 2020 2020 2020 204f O\n+0001dec0: 7665 7276 6965 772e 2020 2020 2020 2020 verview. \n+0001ded0: 2020 2020 2028 6c69 6e65 2033 3729 0a2a (line 37).*\n+0001dee0: 2070 726f 6a65 6374 3a20 2020 2020 2020 project: \n 0001def0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001df00: 2020 2020 2020 2020 2020 5472 616e 7366 Transf\n-0001df10: 6f72 6d20 6c69 7465 7261 6c73 2e20 2020 orm literals. \n-0001df20: 286c 696e 6520 3138 290a 2a20 7072 6f6a (line 18).* proj\n-0001df30: 6563 7420 3c31 3e3a 2020 2020 2020 2020 ect <1>: \n+0001df00: 2020 2020 2020 2020 5472 616e 7366 6f72 Transfor\n+0001df10: 6d20 6c69 7465 7261 6c73 2e20 2020 286c m literals. (l\n+0001df20: 696e 6520 3138 290a 2a20 7072 6f6a 6563 ine 18).* projec\n+0001df30: 7420 3c31 3e3a 2020 2020 2020 2020 2020 t <1>: \n 0001df40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001df50: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n-0001df60: 6572 616c 732e 2020 2028 6c69 6e65 2031 erals. (line 1\n-0001df70: 3929 0a2a 2070 726f 6a65 6374 203c 323e 9).* project <2>\n-0001df80: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001df90: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n-0001dfa0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n-0001dfb0: 2020 286c 696e 6520 3437 290a 2a20 7073 (line 47).* ps\n-0001dfc0: 7472 6963 6b73 3a20 2020 2020 2020 2020 tricks: \n+0001df50: 2054 7261 6e73 666f 726d 206c 6974 6572 Transform liter\n+0001df60: 616c 732e 2020 2028 6c69 6e65 2031 3929 als. (line 19)\n+0001df70: 0a2a 2070 726f 6a65 6374 203c 323e 3a20 .* project <2>: \n+0001df80: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001df90: 2020 2020 2020 2020 2020 5472 616e 7366 Transf\n+0001dfa0: 6f72 6d20 6c69 7465 7261 6c73 2e20 2020 orm literals. \n+0001dfb0: 286c 696e 6520 3437 290a 2a20 7073 7472 (line 47).* pstr\n+0001dfc0: 6963 6b73 3a20 2020 2020 2020 2020 2020 icks: \n 0001dfd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dfe0: 2020 2020 204c 616e 6775 6167 652e 2020 Language. \n-0001dff0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001e000: 2031 3029 0a2a 2070 7574 3a20 2020 2020 10).* put: \n+0001dfe0: 2020 204c 616e 6775 6167 652e 2020 2020 Language. \n+0001dff0: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n+0001e000: 3029 0a2a 2070 7574 3a20 2020 2020 2020 0).* put: \n 0001e010: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e020: 2020 2020 2020 2020 2020 2020 2020 4f62 Ob\n-0001e030: 6a65 6374 2074 7261 6e73 666f 726d 732e ject transforms.\n-0001e040: 2020 2020 286c 696e 6520 3130 290a 2a20 (line 10).* \n-0001e050: 7075 7420 3c31 3e3a 2020 2020 2020 2020 put <1>: \n+0001e020: 2020 2020 2020 2020 2020 2020 4f62 6a65 Obje\n+0001e030: 6374 2074 7261 6e73 666f 726d 732e 2020 ct transforms. \n+0001e040: 2020 286c 696e 6520 3130 290a 2a20 7075 (line 10).* pu\n+0001e050: 7420 3c31 3e3a 2020 2020 2020 2020 2020 t <1>: \n 0001e060: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e070: 2020 2020 2020 204e 6573 7465 6420 7377 Nested sw\n-0001e080: 6565 7073 2e20 2020 2020 2020 2028 6c69 eeps. (li\n-0001e090: 6e65 2032 3529 0a2a 2070 7574 203c 323e ne 25).* put <2>\n-0001e0a0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001e0b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e0c0: 5075 7473 2e20 2020 2020 2020 2020 2020 Puts. \n-0001e0d0: 2020 2020 2020 286c 696e 6520 2036 290a (line 6).\n-0001e0e0: 2a20 7075 7420 3c33 3e3a 2020 2020 2020 * put <3>: \n+0001e070: 2020 2020 204e 6573 7465 6420 7377 6565 Nested swee\n+0001e080: 7073 2e20 2020 2020 2020 2028 6c69 6e65 ps. (line\n+0001e090: 2032 3529 0a2a 2070 7574 203c 323e 3a20 25).* put <2>: \n+0001e0a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e0b0: 2020 2020 2020 2020 2020 2020 2020 5075 Pu\n+0001e0c0: 7473 2e20 2020 2020 2020 2020 2020 2020 ts. \n+0001e0d0: 2020 2020 286c 696e 6520 2036 290a 2a20 (line 6).* \n+0001e0e0: 7075 7420 3c33 3e3a 2020 2020 2020 2020 put <3>: \n 0001e0f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e100: 2020 2020 2020 2020 2041 2068 6965 7261 A hiera\n-0001e110: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028 rchical model. (\n-0001e120: 6c69 6e65 2033 3229 0a2a 2072 6570 6561 line 32).* repea\n-0001e130: 743a 2020 2020 2020 2020 2020 2020 2020 t: \n+0001e100: 2020 2020 2020 2041 2068 6965 7261 7263 A hierarc\n+0001e110: 6869 6361 6c20 6d6f 6465 6c2e 2028 6c69 hical model. (li\n+0001e120: 6e65 2033 3229 0a2a 2072 6570 6561 743a ne 32).* repeat:\n+0001e130: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001e140: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e150: 2020 5265 7065 6174 6564 206f 626a 6563 Repeated objec\n-0001e160: 7473 2e20 2020 2020 286c 696e 6520 2038 ts. (line 8\n-0001e170: 290a 2a20 7265 7065 6174 203c 313e 3a20 ).* repeat <1>: \n+0001e150: 5265 7065 6174 6564 206f 626a 6563 7473 Repeated objects\n+0001e160: 2e20 2020 2020 286c 696e 6520 2038 290a . (line 8).\n+0001e170: 2a20 7265 7065 6174 203c 313e 3a20 2020 * repeat <1>: \n 0001e180: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e190: 2020 2020 2020 2020 2020 204e 6573 7465 Neste\n-0001e1a0: 6420 7377 6565 7073 2e20 2020 2020 2020 d sweeps. \n-0001e1b0: 2028 6c69 6e65 2032 3529 0a2a 2072 6570 (line 25).* rep\n-0001e1c0: 6561 7420 3c32 3e3a 2020 2020 2020 2020 eat <2>: \n+0001e190: 2020 2020 2020 2020 204e 6573 7465 6420 Nested \n+0001e1a0: 7377 6565 7073 2e20 2020 2020 2020 2028 sweeps. (\n+0001e1b0: 6c69 6e65 2032 3529 0a2a 2072 6570 6561 line 25).* repea\n+0001e1c0: 7420 3c32 3e3a 2020 2020 2020 2020 2020 t <2>: \n 0001e1d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e1e0: 2020 2020 506f 6c79 6c69 6e65 2073 7765 Polyline swe\n-0001e1f0: 6570 7320 7769 7468 2063 6c6f 7375 7265 eps with closure\n-0001e200: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+0001e1e0: 2020 506f 6c79 6c69 6e65 2073 7765 6570 Polyline sweep\n+0001e1f0: 7320 7769 7468 2063 6c6f 7375 7265 2e0a s with closure..\n+0001e200: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001e210: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001e220: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e230: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e240: 2028 6c69 6e65 2031 3029 0a2a 2072 6570 (line 10).* rep\n-0001e250: 6561 7420 3c33 3e3a 2020 2020 2020 2020 eat <3>: \n+0001e230: 2020 2020 2020 2020 2020 2020 2020 2028 (\n+0001e240: 6c69 6e65 2031 3029 0a2a 2072 6570 6561 line 10).* repea\n+0001e250: 7420 3c33 3e3a 2020 2020 2020 2020 2020 t <3>: \n 0001e260: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e270: 2020 2020 5265 7065 6174 732e 2020 2020 Repeats. \n-0001e280: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-0001e290: 2036 290a 2a20 7265 7065 6174 203c 343e 6).* repeat <4>\n-0001e2a0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001e2b0: 2020 2020 2020 2020 2020 2020 204f 7665 Ove\n-0001e2c0: 7276 6965 772e 2020 2020 2020 2020 2020 rview. \n-0001e2d0: 2020 2028 6c69 6e65 2035 3729 0a2a 2072 (line 57).* r\n-0001e2e0: 6f74 6174 653a 2020 2020 2020 2020 2020 otate: \n+0001e270: 2020 5265 7065 6174 732e 2020 2020 2020 Repeats. \n+0001e280: 2020 2020 2020 2020 286c 696e 6520 2036 (line 6\n+0001e290: 290a 2a20 7265 7065 6174 203c 343e 3a20 ).* repeat <4>: \n+0001e2a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e2b0: 2020 2020 2020 2020 2020 204f 7665 7276 Overv\n+0001e2c0: 6965 772e 2020 2020 2020 2020 2020 2020 iew. \n+0001e2d0: 2028 6c69 6e65 2035 3729 0a2a 2072 6f74 (line 57).* rot\n+0001e2e0: 6174 653a 2020 2020 2020 2020 2020 2020 ate: \n 0001e2f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e300: 2020 2020 2020 4f62 6a65 6374 2074 7261 Object tra\n-0001e310: 6e73 666f 726d 732e 2020 2020 286c 696e nsforms. (lin\n-0001e320: 6520 3130 290a 2a20 726f 7461 7465 203c e 10).* rotate <\n-0001e330: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n-0001e340: 2020 2020 2020 2020 2020 2020 2020 204f O\n-0001e350: 626a 6563 7420 7472 616e 7366 6f72 6d73 bject transforms\n-0001e360: 2e20 2020 2028 6c69 6e65 2033 3929 0a2a . (line 39).*\n-0001e370: 2072 6f74 6174 6520 3c32 3e3a 2020 2020 rotate <2>: \n+0001e300: 2020 2020 4f62 6a65 6374 2074 7261 6e73 Object trans\n+0001e310: 666f 726d 732e 2020 2020 286c 696e 6520 forms. (line \n+0001e320: 3130 290a 2a20 726f 7461 7465 203c 313e 10).* rotate <1>\n+0001e330: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001e340: 2020 2020 2020 2020 2020 2020 204f 626a Obj\n+0001e350: 6563 7420 7472 616e 7366 6f72 6d73 2e20 ect transforms. \n+0001e360: 2020 2028 6c69 6e65 2033 3929 0a2a 2072 (line 39).* r\n+0001e370: 6f74 6174 6520 3c32 3e3a 2020 2020 2020 otate <2>: \n 0001e380: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e390: 2020 2020 2020 2020 5265 7065 6174 6564 Repeated\n-0001e3a0: 206f 626a 6563 7473 2e20 2020 2020 286c objects. (l\n-0001e3b0: 696e 6520 2038 290a 2a20 726f 7461 7465 ine 8).* rotate\n-0001e3c0: 203c 333e 3a20 2020 2020 2020 2020 2020 <3>: \n-0001e3d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e3e0: 2053 7765 7074 206f 626a 6563 7473 2e20 Swept objects. \n-0001e3f0: 2020 2020 2020 2028 6c69 6e65 2020 3829 (line 8)\n-0001e400: 0a2a 2072 6f74 6174 6520 3c34 3e3a 2020 .* rotate <4>: \n+0001e390: 2020 2020 2020 5265 7065 6174 6564 206f Repeated o\n+0001e3a0: 626a 6563 7473 2e20 2020 2020 286c 696e bjects. (lin\n+0001e3b0: 6520 2038 290a 2a20 726f 7461 7465 203c e 8).* rotate <\n+0001e3c0: 333e 3a20 2020 2020 2020 2020 2020 2020 3>: \n+0001e3d0: 2020 2020 2020 2020 2020 2020 2020 2053 S\n+0001e3e0: 7765 7074 206f 626a 6563 7473 2e20 2020 wept objects. \n+0001e3f0: 2020 2020 2028 6c69 6e65 2020 3829 0a2a (line 8).*\n+0001e400: 2072 6f74 6174 6520 3c34 3e3a 2020 2020 rotate <4>: \n 0001e410: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e420: 2020 2020 2020 2020 2020 506f 696e 7420 Point \n-0001e430: 7377 6565 7073 2e20 2020 2020 2020 2020 sweeps. \n-0001e440: 286c 696e 6520 3139 290a 2a20 726f 7461 (line 19).* rota\n-0001e450: 7465 203c 353e 3a20 2020 2020 2020 2020 te <5>: \n+0001e420: 2020 2020 2020 2020 506f 696e 7420 7377 Point sw\n+0001e430: 6565 7073 2e20 2020 2020 2020 2020 286c eeps. (l\n+0001e440: 696e 6520 3139 290a 2a20 726f 7461 7465 ine 19).* rotate\n+0001e450: 203c 353e 3a20 2020 2020 2020 2020 2020 <5>: \n 0001e460: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e470: 2020 2050 6f6c 796c 696e 6520 7377 6565 Polyline swee\n-0001e480: 7073 2e20 2020 2020 2028 6c69 6e65 2020 ps. (line \n-0001e490: 3929 0a2a 2072 6f74 6174 6520 3c36 3e3a 9).* rotate <6>:\n+0001e470: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n+0001e480: 2e20 2020 2020 2028 6c69 6e65 2020 3929 . (line 9)\n+0001e490: 0a2a 2072 6f74 6174 6520 3c36 3e3a 2020 .* rotate <6>: \n 0001e4a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e4b0: 2020 2020 2020 2020 2020 2020 4e65 7374 Nest\n-0001e4c0: 6564 2073 7765 6570 732e 2020 2020 2020 ed sweeps. \n-0001e4d0: 2020 286c 696e 6520 2038 290a 2a20 726f (line 8).* ro\n-0001e4e0: 7461 7465 203c 373e 3a20 2020 2020 2020 tate <7>: \n+0001e4b0: 2020 2020 2020 2020 2020 4e65 7374 6564 Nested\n+0001e4c0: 2073 7765 6570 732e 2020 2020 2020 2020 sweeps. \n+0001e4d0: 286c 696e 6520 2038 290a 2a20 726f 7461 (line 8).* rota\n+0001e4e0: 7465 203c 373e 3a20 2020 2020 2020 2020 te <7>: \n 0001e4f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e500: 2020 2020 2050 6f6c 796c 696e 6520 7377 Polyline sw\n-0001e510: 6565 7073 2077 6974 6820 636c 6f73 7572 eeps with closur\n-0001e520: 652e 0a20 2020 2020 2020 2020 2020 2020 e.. \n+0001e500: 2020 2050 6f6c 796c 696e 6520 7377 6565 Polyline swee\n+0001e510: 7073 2077 6974 6820 636c 6f73 7572 652e ps with closure.\n+0001e520: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n 0001e530: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001e540: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001e550: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e560: 2020 286c 696e 6520 3130 290a 2a20 726f (line 10).* ro\n-0001e570: 7461 7465 203c 383e 3a20 2020 2020 2020 tate <8>: \n+0001e560: 286c 696e 6520 3130 290a 2a20 726f 7461 (line 10).* rota\n+0001e570: 7465 203c 383e 3a20 2020 2020 2020 2020 te <8>: \n 0001e580: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e590: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n-0001e5a0: 6974 6572 616c 732e 2020 2028 6c69 6e65 iterals. (line\n-0001e5b0: 2031 3029 0a2a 2072 6f74 6174 6520 3c39 10).* rotate <9\n-0001e5c0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001e5d0: 2020 2020 2020 2020 2020 2020 2020 4f76 Ov\n-0001e5e0: 6572 7669 6577 2e20 2020 2020 2020 2020 erview. \n-0001e5f0: 2020 2020 286c 696e 6520 3537 290a 2a20 (line 57).* \n-0001e600: 726f 7461 7465 203c 3130 3e3a 2020 2020 rotate <10>: \n+0001e590: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n+0001e5a0: 6572 616c 732e 2020 2028 6c69 6e65 2031 erals. (line 1\n+0001e5b0: 3029 0a2a 2072 6f74 6174 6520 3c39 3e3a 0).* rotate <9>:\n+0001e5c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e5d0: 2020 2020 2020 2020 2020 2020 4f76 6572 Over\n+0001e5e0: 7669 6577 2e20 2020 2020 2020 2020 2020 view. \n+0001e5f0: 2020 286c 696e 6520 3537 290a 2a20 726f (line 57).* ro\n+0001e600: 7461 7465 203c 3130 3e3a 2020 2020 2020 tate <10>: \n 0001e610: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e620: 2020 2020 2020 204f 7665 7276 6965 772e Overview.\n-0001e630: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-0001e640: 6e65 2036 3929 0a2a 2072 6f74 6174 6520 ne 69).* rotate \n-0001e650: 3c31 313e 3a20 2020 2020 2020 2020 2020 <11>: \n-0001e660: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e670: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n-0001e680: 696e 672e 2020 286c 696e 6520 3134 290a ing. (line 14).\n-0001e690: 2a20 726f 7461 7465 203c 3132 3e3a 2020 * rotate <12>: \n+0001e620: 2020 2020 204f 7665 7276 6965 772e 2020 Overview. \n+0001e630: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+0001e640: 2036 3929 0a2a 2072 6f74 6174 6520 3c31 69).* rotate <1\n+0001e650: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n+0001e660: 2020 2020 2020 2020 2020 2020 2020 4120 A \n+0001e670: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n+0001e680: 672e 2020 286c 696e 6520 3134 290a 2a20 g. (line 14).* \n+0001e690: 726f 7461 7465 203c 3132 3e3a 2020 2020 rotate <12>: \n 0001e6a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e6b0: 2020 2020 2020 2020 2041 2068 6965 7261 A hiera\n-0001e6c0: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028 rchical model. (\n-0001e6d0: 6c69 6e65 2031 3029 0a2a 2072 6f74 6174 line 10).* rotat\n-0001e6e0: 6520 3c31 333e 3a20 2020 2020 2020 2020 e <13>: \n+0001e6b0: 2020 2020 2020 2041 2068 6965 7261 7263 A hierarc\n+0001e6c0: 6869 6361 6c20 6d6f 6465 6c2e 2028 6c69 hical model. (li\n+0001e6d0: 6e65 2031 3029 0a2a 2072 6f74 6174 6520 ne 10).* rotate \n+0001e6e0: 3c31 333e 3a20 2020 2020 2020 2020 2020 <13>: \n 0001e6f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e700: 2020 4120 6869 6572 6172 6368 6963 616c A hierarchical\n-0001e710: 206d 6f64 656c 2e20 286c 696e 6520 3233 model. (line 23\n-0001e720: 290a 2a20 726f 7461 7465 203c 3134 3e3a ).* rotate <14>:\n+0001e700: 4120 6869 6572 6172 6368 6963 616c 206d A hierarchical m\n+0001e710: 6f64 656c 2e20 286c 696e 6520 3233 290a odel. (line 23).\n+0001e720: 2a20 726f 7461 7465 203c 3134 3e3a 2020 * rotate <14>: \n 0001e730: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e740: 2020 2020 2020 2020 2020 2041 2068 6965 A hie\n-0001e750: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e rarchical model.\n-0001e760: 2028 6c69 6e65 2033 3229 0a2a 2073 6361 (line 32).* sca\n-0001e770: 6c65 3a20 2020 2020 2020 2020 2020 2020 le: \n+0001e740: 2020 2020 2020 2020 2041 2068 6965 7261 A hiera\n+0001e750: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028 rchical model. (\n+0001e760: 6c69 6e65 2033 3229 0a2a 2073 6361 6c65 line 32).* scale\n+0001e770: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n 0001e780: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e790: 2020 2020 5472 616e 7366 6f72 6d20 6c69 Transform li\n-0001e7a0: 7465 7261 6c73 2e20 2020 286c 696e 6520 terals. (line \n-0001e7b0: 3136 290a 2a20 7363 616c 6520 3c31 3e3a 16).* scale <1>:\n+0001e790: 2020 5472 616e 7366 6f72 6d20 6c69 7465 Transform lite\n+0001e7a0: 7261 6c73 2e20 2020 286c 696e 6520 3136 rals. (line 16\n+0001e7b0: 290a 2a20 7363 616c 6520 3c31 3e3a 2020 ).* scale <1>: \n 0001e7c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e7d0: 2020 2020 2020 2020 2020 2020 2054 7261 Tra\n-0001e7e0: 6e73 666f 726d 206c 6974 6572 616c 732e nsform literals.\n-0001e7f0: 2020 2028 6c69 6e65 2031 3729 0a2a 2073 (line 17).* s\n-0001e800: 6361 6c65 203c 323e 3a20 2020 2020 2020 cale <2>: \n+0001e7d0: 2020 2020 2020 2020 2020 2054 7261 6e73 Trans\n+0001e7e0: 666f 726d 206c 6974 6572 616c 732e 2020 form literals. \n+0001e7f0: 2028 6c69 6e65 2031 3729 0a2a 2073 6361 (line 17).* sca\n+0001e800: 6c65 203c 323e 3a20 2020 2020 2020 2020 le <2>: \n 0001e810: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e820: 2020 2020 2020 4120 7465 6368 6e69 6361 A technica\n-0001e830: 6c20 6472 6177 696e 672e 2020 286c 696e l drawing. (lin\n-0001e840: 6520 3431 290a 2a20 7363 616c 6520 3c33 e 41).* scale <3\n-0001e850: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001e860: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-0001e870: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n-0001e880: 6e67 2e20 2028 6c69 6e65 2036 3829 0a2a ng. (line 68).*\n-0001e890: 2073 6361 6c65 203c 343e 3a20 2020 2020 scale <4>: \n+0001e820: 2020 2020 4120 7465 6368 6e69 6361 6c20 A technical \n+0001e830: 6472 6177 696e 672e 2020 286c 696e 6520 drawing. (line \n+0001e840: 3431 290a 2a20 7363 616c 6520 3c33 3e3a 41).* scale <3>:\n+0001e850: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e860: 2020 2020 2020 2020 2020 2020 2041 2074 A t\n+0001e870: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n+0001e880: 2e20 2028 6c69 6e65 2036 3829 0a2a 2073 . (line 68).* s\n+0001e890: 6361 6c65 203c 343e 3a20 2020 2020 2020 cale <4>: \n 0001e8a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e8b0: 2020 2020 2020 2020 4120 6869 6572 6172 A hierar\n-0001e8c0: 6368 6963 616c 206d 6f64 656c 2e20 286c chical model. (l\n-0001e8d0: 696e 6520 3332 290a 2a20 7365 743a 2020 ine 32).* set: \n+0001e8b0: 2020 2020 2020 4120 6869 6572 6172 6368 A hierarch\n+0001e8c0: 6963 616c 206d 6f64 656c 2e20 286c 696e ical model. (lin\n+0001e8d0: 6520 3332 290a 2a20 7365 743a 2020 2020 e 32).* set: \n 0001e8e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e8f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e900: 2047 6c6f 6261 6c20 6f70 7469 6f6e 732e Global options.\n-0001e910: 2020 2020 2020 2028 6c69 6e65 2020 3629 (line 6)\n-0001e920: 0a2a 2073 696e 3a20 2020 2020 2020 2020 .* sin: \n+0001e8f0: 2020 2020 2020 2020 2020 2020 2020 2047 G\n+0001e900: 6c6f 6261 6c20 6f70 7469 6f6e 732e 2020 lobal options. \n+0001e910: 2020 2020 2028 6c69 6e65 2020 3629 0a2a (line 6).*\n+0001e920: 2073 696e 3a20 2020 2020 2020 2020 2020 sin: \n 0001e930: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e940: 2020 2020 2020 2020 2020 556e 6172 7920 Unary \n-0001e950: 666f 726d 732e 2020 2020 2020 2020 2020 forms. \n-0001e960: 286c 696e 6520 3135 290a 2a20 7370 6563 (line 15).* spec\n-0001e970: 6961 6c3a 2020 2020 2020 2020 2020 2020 ial: \n+0001e940: 2020 2020 2020 2020 556e 6172 7920 666f Unary fo\n+0001e950: 726d 732e 2020 2020 2020 2020 2020 286c rms. (l\n+0001e960: 696e 6520 3135 290a 2a20 7370 6563 6961 ine 15).* specia\n+0001e970: 6c3a 2020 2020 2020 2020 2020 2020 2020 l: \n 0001e980: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e990: 2020 2053 7065 6369 616c 206f 626a 6563 Special objec\n-0001e9a0: 7473 2e20 2020 2020 2028 6c69 6e65 2020 ts. (line \n-0001e9b0: 3629 0a2a 2073 7065 6369 616c 203c 313e 6).* special <1>\n-0001e9c0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001e9d0: 2020 2020 2020 2020 2020 2020 5370 6563 Spec\n-0001e9e0: 6961 6c73 2e20 2020 2020 2020 2020 2020 ials. \n-0001e9f0: 2020 286c 696e 6520 2036 290a 2a20 7370 (line 6).* sp\n-0001ea00: 6563 6961 6c20 3c32 3e3a 2020 2020 2020 ecial <2>: \n+0001e990: 2053 7065 6369 616c 206f 626a 6563 7473 Special objects\n+0001e9a0: 2e20 2020 2020 2028 6c69 6e65 2020 3629 . (line 6)\n+0001e9b0: 0a2a 2073 7065 6369 616c 203c 313e 3a20 .* special <1>: \n+0001e9c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e9d0: 2020 2020 2020 2020 2020 5370 6563 6961 Specia\n+0001e9e0: 6c73 2e20 2020 2020 2020 2020 2020 2020 ls. \n+0001e9f0: 286c 696e 6520 2036 290a 2a20 7370 6563 (line 6).* spec\n+0001ea00: 6961 6c20 3c32 3e3a 2020 2020 2020 2020 ial <2>: \n 0001ea10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ea20: 2020 2020 204f 7665 7276 6965 772e 2020 Overview. \n-0001ea30: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001ea40: 2036 3929 0a2a 2073 7065 6369 616c 203c 69).* special <\n-0001ea50: 333e 3a20 2020 2020 2020 2020 2020 2020 3>: \n-0001ea60: 2020 2020 2020 2020 2020 2020 2020 4120 A \n-0001ea70: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n-0001ea80: 672e 2020 286c 696e 6520 3236 290a 2a20 g. (line 26).* \n-0001ea90: 7370 6563 6961 6c20 3c34 3e3a 2020 2020 special <4>: \n+0001ea20: 2020 204f 7665 7276 6965 772e 2020 2020 Overview. \n+0001ea30: 2020 2020 2020 2020 2028 6c69 6e65 2036 (line 6\n+0001ea40: 3929 0a2a 2073 7065 6369 616c 203c 333e 9).* special <3>\n+0001ea50: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001ea60: 2020 2020 2020 2020 2020 2020 4120 7465 A te\n+0001ea70: 6368 6e69 6361 6c20 6472 6177 696e 672e chnical drawing.\n+0001ea80: 2020 286c 696e 6520 3236 290a 2a20 7370 (line 26).* sp\n+0001ea90: 6563 6961 6c20 3c34 3e3a 2020 2020 2020 ecial <4>: \n 0001eaa0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eab0: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n-0001eac0: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n-0001ead0: 6e65 2034 3129 0a2a 2073 7065 6369 616c ne 41).* special\n-0001eae0: 203c 353e 3a20 2020 2020 2020 2020 2020 <5>: \n-0001eaf0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eb00: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n-0001eb10: 696e 672e 2020 286c 696e 6520 3638 290a ing. (line 68).\n-0001eb20: 2a20 7370 6563 6961 6c20 3c36 3e3a 2020 * special <6>: \n+0001eab0: 2020 2020 2041 2074 6563 686e 6963 616c A technical\n+0001eac0: 2064 7261 7769 6e67 2e20 2028 6c69 6e65 drawing. (line\n+0001ead0: 2034 3129 0a2a 2073 7065 6369 616c 203c 41).* special <\n+0001eae0: 353e 3a20 2020 2020 2020 2020 2020 2020 5>: \n+0001eaf0: 2020 2020 2020 2020 2020 2020 2020 4120 A \n+0001eb00: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n+0001eb10: 672e 2020 286c 696e 6520 3638 290a 2a20 g. (line 68).* \n+0001eb20: 7370 6563 6961 6c20 3c36 3e3a 2020 2020 special <6>: \n 0001eb30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eb40: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n-0001eb50: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n-0001eb60: 6c69 6e65 2039 3529 0a2a 2073 706c 6974 line 95).* split\n-0001eb70: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001eb40: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n+0001eb50: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n+0001eb60: 6e65 2039 3529 0a2a 2073 706c 6974 3a20 ne 95).* split: \n+0001eb70: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001eb80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eb90: 2020 496e 7465 726e 616c 206f 7074 696f Internal optio\n-0001eba0: 6e73 2e20 2020 2020 286c 696e 6520 2037 ns. (line 7\n-0001ebb0: 290a 2a20 7370 6c69 7420 3c31 3e3a 2020 ).* split <1>: \n+0001eb90: 496e 7465 726e 616c 206f 7074 696f 6e73 Internal options\n+0001eba0: 2e20 2020 2020 286c 696e 6520 2037 290a . (line 7).\n+0001ebb0: 2a20 7370 6c69 7420 3c31 3e3a 2020 2020 * split <1>: \n 0001ebc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ebd0: 2020 2020 2020 2020 2020 2047 6c6f 6261 Globa\n-0001ebe0: 6c20 6f70 7469 6f6e 732e 2020 2020 2020 l options. \n-0001ebf0: 2028 6c69 6e65 2031 3329 0a2a 2073 7172 (line 13).* sqr\n-0001ec00: 743a 2020 2020 2020 2020 2020 2020 2020 t: \n+0001ebd0: 2020 2020 2020 2020 2047 6c6f 6261 6c20 Global \n+0001ebe0: 6f70 7469 6f6e 732e 2020 2020 2020 2028 options. (\n+0001ebf0: 6c69 6e65 2031 3329 0a2a 2073 7172 743a line 13).* sqrt:\n+0001ec00: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001ec10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ec20: 2020 2020 556e 6172 7920 666f 726d 732e Unary forms.\n-0001ec30: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-0001ec40: 3134 290a 2a20 7377 6565 703a 2020 2020 14).* sweep: \n+0001ec20: 2020 556e 6172 7920 666f 726d 732e 2020 Unary forms. \n+0001ec30: 2020 2020 2020 2020 286c 696e 6520 3134 (line 14\n+0001ec40: 290a 2a20 7377 6565 703a 2020 2020 2020 ).* sweep: \n 0001ec50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ec60: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n-0001ec70: 7074 206f 626a 6563 7473 2e20 2020 2020 pt objects. \n-0001ec80: 2020 2028 6c69 6e65 2020 3829 0a2a 2073 (line 8).* s\n-0001ec90: 7765 6570 203c 313e 3a20 2020 2020 2020 weep <1>: \n+0001ec60: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n+0001ec70: 206f 626a 6563 7473 2e20 2020 2020 2020 objects. \n+0001ec80: 2028 6c69 6e65 2020 3829 0a2a 2073 7765 (line 8).* swe\n+0001ec90: 6570 203c 313e 3a20 2020 2020 2020 2020 ep <1>: \n 0001eca0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ecb0: 2020 2020 2020 506f 696e 7420 7377 6565 Point swee\n-0001ecc0: 7073 2e20 2020 2020 2020 2020 286c 696e ps. (lin\n-0001ecd0: 6520 3139 290a 2a20 7377 6565 7020 3c32 e 19).* sweep <2\n-0001ece0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001ecf0: 2020 2020 2020 2020 2020 2020 2020 2050 P\n-0001ed00: 6f6c 796c 696e 6520 7377 6565 7073 2e20 olyline sweeps. \n-0001ed10: 2020 2020 2028 6c69 6e65 2020 3929 0a2a (line 9).*\n-0001ed20: 2073 7765 6570 203c 333e 3a20 2020 2020 sweep <3>: \n+0001ecb0: 2020 2020 506f 696e 7420 7377 6565 7073 Point sweeps\n+0001ecc0: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n+0001ecd0: 3139 290a 2a20 7377 6565 7020 3c32 3e3a 19).* sweep <2>:\n+0001ece0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001ecf0: 2020 2020 2020 2020 2020 2020 2050 6f6c Pol\n+0001ed00: 796c 696e 6520 7377 6565 7073 2e20 2020 yline sweeps. \n+0001ed10: 2020 2028 6c69 6e65 2020 3929 0a2a 2073 (line 9).* s\n+0001ed20: 7765 6570 203c 333e 3a20 2020 2020 2020 weep <3>: \n 0001ed30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ed40: 2020 2020 2020 2020 4e65 7374 6564 2073 Nested s\n-0001ed50: 7765 6570 732e 2020 2020 2020 2020 286c weeps. (l\n-0001ed60: 696e 6520 2038 290a 2a20 7377 6565 7020 ine 8).* sweep \n-0001ed70: 3c34 3e3a 2020 2020 2020 2020 2020 2020 <4>: \n-0001ed80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ed90: 204e 6573 7465 6420 7377 6565 7073 2e20 Nested sweeps. \n-0001eda0: 2020 2020 2020 2028 6c69 6e65 2032 3229 (line 22)\n-0001edb0: 0a2a 2073 7765 6570 203c 353e 3a20 2020 .* sweep <5>: \n+0001ed40: 2020 2020 2020 4e65 7374 6564 2073 7765 Nested swe\n+0001ed50: 6570 732e 2020 2020 2020 2020 286c 696e eps. (lin\n+0001ed60: 6520 2038 290a 2a20 7377 6565 7020 3c34 e 8).* sweep <4\n+0001ed70: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+0001ed80: 2020 2020 2020 2020 2020 2020 2020 204e N\n+0001ed90: 6573 7465 6420 7377 6565 7073 2e20 2020 ested sweeps. \n+0001eda0: 2020 2020 2028 6c69 6e65 2032 3229 0a2a (line 22).*\n+0001edb0: 2073 7765 6570 203c 353e 3a20 2020 2020 sweep <5>: \n 0001edc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001edd0: 2020 2020 2020 2020 2020 506f 6c79 6c69 Polyli\n-0001ede0: 6e65 2073 7765 6570 7320 7769 7468 2063 ne sweeps with c\n-0001edf0: 6c6f 7375 7265 2e0a 2020 2020 2020 2020 losure.. \n+0001edd0: 2020 2020 2020 2020 506f 6c79 6c69 6e65 Polyline\n+0001ede0: 2073 7765 6570 7320 7769 7468 2063 6c6f sweeps with clo\n+0001edf0: 7375 7265 2e0a 2020 2020 2020 2020 2020 sure.. \n 0001ee00: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001ee10: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001ee20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ee30: 2020 2020 2020 2028 6c69 6e65 2031 3029 (line 10)\n-0001ee40: 0a2a 2073 7765 6570 203c 363e 3a20 2020 .* sweep <6>: \n+0001ee30: 2020 2020 2028 6c69 6e65 2031 3029 0a2a (line 10).*\n+0001ee40: 2073 7765 6570 203c 363e 3a20 2020 2020 sweep <6>: \n 0001ee50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ee60: 2020 2020 2020 2020 2020 5377 6565 7073 Sweeps\n-0001ee70: 2e20 2020 2020 2020 2020 2020 2020 2020 . \n-0001ee80: 286c 696e 6520 2036 290a 2a20 7377 6565 (line 6).* swee\n-0001ee90: 7020 3c37 3e3a 2020 2020 2020 2020 2020 p <7>: \n+0001ee60: 2020 2020 2020 2020 5377 6565 7073 2e20 Sweeps. \n+0001ee70: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+0001ee80: 696e 6520 2036 290a 2a20 7377 6565 7020 ine 6).* sweep \n+0001ee90: 3c37 3e3a 2020 2020 2020 2020 2020 2020 <7>: \n 0001eea0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eeb0: 2020 2041 2074 6563 686e 6963 616c 2064 A technical d\n-0001eec0: 7261 7769 6e67 2e20 2028 6c69 6e65 2032 rawing. (line 2\n-0001eed0: 3029 0a2a 2073 7765 6570 203c 383e 3a20 0).* sweep <8>: \n+0001eeb0: 2041 2074 6563 686e 6963 616c 2064 7261 A technical dra\n+0001eec0: 7769 6e67 2e20 2028 6c69 6e65 2032 3029 wing. (line 20)\n+0001eed0: 0a2a 2073 7765 6570 203c 383e 3a20 2020 .* sweep <8>: \n 0001eee0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eef0: 2020 2020 2020 2020 2020 2020 4120 6869 A hi\n-0001ef00: 6572 6172 6368 6963 616c 206d 6f64 656c erarchical model\n-0001ef10: 2e20 286c 696e 6520 3130 290a 2a20 7377 . (line 10).* sw\n-0001ef20: 6565 7020 3c39 3e3a 2020 2020 2020 2020 eep <9>: \n+0001eef0: 2020 2020 2020 2020 2020 4120 6869 6572 A hier\n+0001ef00: 6172 6368 6963 616c 206d 6f64 656c 2e20 archical model. \n+0001ef10: 286c 696e 6520 3130 290a 2a20 7377 6565 (line 10).* swee\n+0001ef20: 7020 3c39 3e3a 2020 2020 2020 2020 2020 p <9>: \n 0001ef30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ef40: 2020 2020 2041 2068 6965 7261 7263 6869 A hierarchi\n-0001ef50: 6361 6c20 6d6f 6465 6c2e 2028 6c69 6e65 cal model. (line\n-0001ef60: 2032 3329 0a2a 2074 6865 6e3a 2020 2020 23).* then: \n+0001ef40: 2020 2041 2068 6965 7261 7263 6869 6361 A hierarchica\n+0001ef50: 6c20 6d6f 6465 6c2e 2028 6c69 6e65 2032 l model. (line 2\n+0001ef60: 3329 0a2a 2074 6865 6e3a 2020 2020 2020 3).* then: \n 0001ef70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ef80: 2020 2020 2020 2020 2020 2020 2020 4f62 Ob\n-0001ef90: 6a65 6374 2074 7261 6e73 666f 726d 732e ject transforms.\n-0001efa0: 2020 2020 286c 696e 6520 3130 290a 2a20 (line 10).* \n-0001efb0: 7468 656e 203c 313e 3a20 2020 2020 2020 then <1>: \n+0001ef80: 2020 2020 2020 2020 2020 2020 4f62 6a65 Obje\n+0001ef90: 6374 2074 7261 6e73 666f 726d 732e 2020 ct transforms. \n+0001efa0: 2020 286c 696e 6520 3130 290a 2a20 7468 (line 10).* th\n+0001efb0: 656e 203c 313e 3a20 2020 2020 2020 2020 en <1>: \n 0001efc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001efd0: 2020 2020 2020 2050 6f6c 796c 696e 6520 Polyline \n-0001efe0: 7377 6565 7073 2077 6974 6820 636c 6f73 sweeps with clos\n-0001eff0: 7572 652e 0a20 2020 2020 2020 2020 2020 ure.. \n+0001efd0: 2020 2020 2050 6f6c 796c 696e 6520 7377 Polyline sw\n+0001efe0: 6565 7073 2077 6974 6820 636c 6f73 7572 eeps with closur\n+0001eff0: 652e 0a20 2020 2020 2020 2020 2020 2020 e.. \n 0001f000: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f010: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f020: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f030: 2020 2020 286c 696e 6520 3130 290a 2a20 (line 10).* \n-0001f040: 7468 656e 203c 323e 3a20 2020 2020 2020 then <2>: \n+0001f030: 2020 286c 696e 6520 3130 290a 2a20 7468 (line 10).* th\n+0001f040: 656e 203c 323e 3a20 2020 2020 2020 2020 en <2>: \n 0001f050: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f060: 2020 2020 2020 2054 776f 2d6f 7065 7261 Two-opera\n-0001f070: 6e64 2028 6269 6e61 7279 2920 666f 726d nd (binary) form\n-0001f080: 732e 0a20 2020 2020 2020 2020 2020 2020 s.. \n+0001f060: 2020 2020 2054 776f 2d6f 7065 7261 6e64 Two-operand\n+0001f070: 2028 6269 6e61 7279 2920 666f 726d 732e (binary) forms.\n+0001f080: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n 0001f090: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f0a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f0b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f0c0: 2020 286c 696e 6520 3336 290a 2a20 7468 (line 36).* th\n-0001f0d0: 656e 203c 333e 3a20 2020 2020 2020 2020 en <3>: \n+0001f0c0: 286c 696e 6520 3336 290a 2a20 7468 656e (line 36).* then\n+0001f0d0: 203c 333e 3a20 2020 2020 2020 2020 2020 <3>: \n 0001f0e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f0f0: 2020 2020 2054 776f 2d6f 7065 7261 6e64 Two-operand\n-0001f100: 2028 6269 6e61 7279 2920 666f 726d 732e (binary) forms.\n-0001f110: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n+0001f0f0: 2020 2054 776f 2d6f 7065 7261 6e64 2028 Two-operand (\n+0001f100: 6269 6e61 7279 2920 666f 726d 732e 0a20 binary) forms.. \n+0001f110: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f120: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f130: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f140: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f150: 286c 696e 6520 3633 290a 2a20 7469 6b7a (line 63).* tikz\n-0001f160: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001f140: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+0001f150: 696e 6520 3633 290a 2a20 7469 6b7a 3a20 ine 63).* tikz: \n+0001f160: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f170: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f180: 2020 204c 616e 6775 6167 652e 2020 2020 Language. \n-0001f190: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n-0001f1a0: 3029 0a2a 2074 7261 6e73 6c61 7465 3a20 0).* translate: \n+0001f180: 204c 616e 6775 6167 652e 2020 2020 2020 Language. \n+0001f190: 2020 2020 2020 2028 6c69 6e65 2031 3029 (line 10)\n+0001f1a0: 0a2a 2074 7261 6e73 6c61 7465 3a20 2020 .* translate: \n 0001f1b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f1c0: 2020 2020 2020 2020 2020 2020 4f62 6a65 Obje\n-0001f1d0: 6374 2074 7261 6e73 666f 726d 732e 2020 ct transforms. \n-0001f1e0: 2020 286c 696e 6520 3130 290a 2a20 7472 (line 10).* tr\n-0001f1f0: 616e 736c 6174 6520 3c31 3e3a 2020 2020 anslate <1>: \n+0001f1c0: 2020 2020 2020 2020 2020 4f62 6a65 6374 Object\n+0001f1d0: 2074 7261 6e73 666f 726d 732e 2020 2020 transforms. \n+0001f1e0: 286c 696e 6520 3130 290a 2a20 7472 616e (line 10).* tran\n+0001f1f0: 736c 6174 6520 3c31 3e3a 2020 2020 2020 slate <1>: \n 0001f200: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f210: 2020 2020 204f 626a 6563 7420 7472 616e Object tran\n-0001f220: 7366 6f72 6d73 2e20 2020 2028 6c69 6e65 sforms. (line\n-0001f230: 2034 3729 0a2a 2074 7261 6e73 6c61 7465 47).* translate\n-0001f240: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n-0001f250: 2020 2020 2020 2020 2020 2020 2020 5265 Re\n-0001f260: 7065 6174 6564 206f 626a 6563 7473 2e20 peated objects. \n-0001f270: 2020 2020 286c 696e 6520 2038 290a 2a20 (line 8).* \n-0001f280: 7472 616e 736c 6174 6520 3c33 3e3a 2020 translate <3>: \n+0001f210: 2020 204f 626a 6563 7420 7472 616e 7366 Object transf\n+0001f220: 6f72 6d73 2e20 2020 2028 6c69 6e65 2034 orms. (line 4\n+0001f230: 3729 0a2a 2074 7261 6e73 6c61 7465 203c 7).* translate <\n+0001f240: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n+0001f250: 2020 2020 2020 2020 2020 2020 5265 7065 Repe\n+0001f260: 6174 6564 206f 626a 6563 7473 2e20 2020 ated objects. \n+0001f270: 2020 286c 696e 6520 2038 290a 2a20 7472 (line 8).* tr\n+0001f280: 616e 736c 6174 6520 3c33 3e3a 2020 2020 anslate <3>: \n 0001f290: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f2a0: 2020 2020 2020 2050 6f6c 796c 696e 6520 Polyline \n-0001f2b0: 7377 6565 7073 2e20 2020 2020 2028 6c69 sweeps. (li\n-0001f2c0: 6e65 2020 3929 0a2a 2074 7261 6e73 6c61 ne 9).* transla\n-0001f2d0: 7465 203c 343e 3a20 2020 2020 2020 2020 te <4>: \n-0001f2e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f2f0: 506f 6c79 6c69 6e65 2073 7765 6570 7320 Polyline sweeps \n-0001f300: 7769 7468 2063 6c6f 7375 7265 2e0a 2020 with closure.. \n+0001f2a0: 2020 2020 2050 6f6c 796c 696e 6520 7377 Polyline sw\n+0001f2b0: 6565 7073 2e20 2020 2020 2028 6c69 6e65 eeps. (line\n+0001f2c0: 2020 3929 0a2a 2074 7261 6e73 6c61 7465 9).* translate\n+0001f2d0: 203c 343e 3a20 2020 2020 2020 2020 2020 <4>: \n+0001f2e0: 2020 2020 2020 2020 2020 2020 2020 506f Po\n+0001f2f0: 6c79 6c69 6e65 2073 7765 6570 7320 7769 lyline sweeps wi\n+0001f300: 7468 2063 6c6f 7375 7265 2e0a 2020 2020 th closure.. \n 0001f310: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f320: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f330: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f340: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-0001f350: 6e65 2031 3029 0a2a 2074 7261 6e73 6c61 ne 10).* transla\n-0001f360: 7465 203c 353e 3a20 2020 2020 2020 2020 te <5>: \n-0001f370: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f380: 5472 616e 7366 6f72 6d20 6c69 7465 7261 Transform litera\n-0001f390: 6c73 2e20 2020 286c 696e 6520 3135 290a ls. (line 15).\n-0001f3a0: 2a20 7472 616e 736c 6174 6520 3c36 3e3a * translate <6>:\n+0001f340: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+0001f350: 2031 3029 0a2a 2074 7261 6e73 6c61 7465 10).* translate\n+0001f360: 203c 353e 3a20 2020 2020 2020 2020 2020 <5>: \n+0001f370: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n+0001f380: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n+0001f390: 2e20 2020 286c 696e 6520 3135 290a 2a20 . (line 15).* \n+0001f3a0: 7472 616e 736c 6174 6520 3c36 3e3a 2020 translate <6>: \n 0001f3b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f3c0: 2020 2020 2020 2020 204f 7665 7276 6965 Overvie\n-0001f3d0: 772e 2020 2020 2020 2020 2020 2020 2028 w. (\n-0001f3e0: 6c69 6e65 2035 3729 0a2a 2074 7261 6e73 line 57).* trans\n-0001f3f0: 6c61 7465 203c 373e 3a20 2020 2020 2020 late <7>: \n+0001f3c0: 2020 2020 2020 204f 7665 7276 6965 772e Overview.\n+0001f3d0: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+0001f3e0: 6e65 2035 3729 0a2a 2074 7261 6e73 6c61 ne 57).* transla\n+0001f3f0: 7465 203c 373e 3a20 2020 2020 2020 2020 te <7>: \n 0001f400: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f410: 2020 4f76 6572 7669 6577 2e20 2020 2020 Overview. \n-0001f420: 2020 2020 2020 2020 286c 696e 6520 3639 (line 69\n-0001f430: 290a 2a20 7472 616e 736c 6174 6520 3c38 ).* translate <8\n-0001f440: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001f450: 2020 2020 2020 2020 2020 2041 2068 6965 A hie\n-0001f460: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e rarchical model.\n-0001f470: 2028 6c69 6e65 2033 3229 0a2a 2074 7261 (line 32).* tra\n-0001f480: 6e73 7061 6c70 6861 3a20 2020 2020 2020 nspalpha: \n+0001f410: 4f76 6572 7669 6577 2e20 2020 2020 2020 Overview. \n+0001f420: 2020 2020 2020 286c 696e 6520 3639 290a (line 69).\n+0001f430: 2a20 7472 616e 736c 6174 6520 3c38 3e3a * translate <8>:\n+0001f440: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001f450: 2020 2020 2020 2020 2041 2068 6965 7261 A hiera\n+0001f460: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028 rchical model. (\n+0001f470: 6c69 6e65 2033 3229 0a2a 2074 7261 6e73 line 32).* trans\n+0001f480: 7061 6c70 6861 3a20 2020 2020 2020 2020 palpha: \n 0001f490: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f4a0: 2020 2020 5472 616e 7370 6172 656e 6379 Transparency\n-0001f4b0: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n-0001f4c0: 3130 290a 2a20 756e 6974 3a20 2020 2020 10).* unit: \n+0001f4a0: 2020 5472 616e 7370 6172 656e 6379 2e20 Transparency. \n+0001f4b0: 2020 2020 2020 2020 286c 696e 6520 3130 (line 10\n+0001f4c0: 290a 2a20 756e 6974 3a20 2020 2020 2020 ).* unit: \n 0001f4d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f4e0: 2020 2020 2020 2020 2020 2020 2055 6e61 Una\n-0001f4f0: 7279 2066 6f72 6d73 2e20 2020 2020 2020 ry forms. \n-0001f500: 2020 2028 6c69 6e65 2031 3329 0a2a 2075 (line 13).* u\n-0001f510: 6e69 7420 3c31 3e3a 2020 2020 2020 2020 nit <1>: \n+0001f4e0: 2020 2020 2020 2020 2020 2055 6e61 7279 Unary\n+0001f4f0: 2066 6f72 6d73 2e20 2020 2020 2020 2020 forms. \n+0001f500: 2028 6c69 6e65 2031 3329 0a2a 2075 6e69 (line 13).* uni\n+0001f510: 7420 3c31 3e3a 2020 2020 2020 2020 2020 t <1>: \n 0001f520: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f530: 2020 2020 2020 4120 7465 6368 6e69 6361 A technica\n-0001f540: 6c20 6472 6177 696e 672e 2020 286c 696e l drawing. (lin\n-0001f550: 6520 3431 290a 2a20 7669 6577 3a20 2020 e 41).* view: \n+0001f530: 2020 2020 4120 7465 6368 6e69 6361 6c20 A technical \n+0001f540: 6472 6177 696e 672e 2020 286c 696e 6520 drawing. (line \n+0001f550: 3431 290a 2a20 7669 6577 3a20 2020 2020 41).* view: \n 0001f560: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f570: 2020 2020 2020 2020 2020 2020 2020 2054 T\n-0001f580: 7261 6e73 666f 726d 206c 6974 6572 616c ransform literal\n-0001f590: 732e 2020 2028 6c69 6e65 2032 3529 0a2a s. (line 25).*\n-0001f5a0: 2076 6965 7720 3c31 3e3a 2020 2020 2020 view <1>: \n+0001f570: 2020 2020 2020 2020 2020 2020 2054 7261 Tra\n+0001f580: 6e73 666f 726d 206c 6974 6572 616c 732e nsform literals.\n+0001f590: 2020 2028 6c69 6e65 2032 3529 0a2a 2076 (line 25).* v\n+0001f5a0: 6965 7720 3c31 3e3a 2020 2020 2020 2020 iew <1>: \n 0001f5b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f5c0: 2020 2020 2020 2020 5472 616e 7366 6f72 Transfor\n-0001f5d0: 6d20 6c69 7465 7261 6c73 2e20 2020 286c m literals. (l\n-0001f5e0: 696e 6520 3335 290a 0a1f 0a46 696c 653a ine 35)....File:\n-0001f5f0: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-0001f600: 6f64 653a 2049 6e64 6578 2c20 2050 7265 ode: Index, Pre\n-0001f610: 763a 2049 6e64 6578 206f 6620 7379 6e74 v: Index of synt\n-0001f620: 6178 2c20 2055 703a 2054 6f70 0a0a 496e ax, Up: Top..In\n-0001f630: 6465 7820 6f66 2063 6f6e 6365 7074 730a dex of concepts.\n-0001f640: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a ****************\n-0001f650: 2a0a 0a00 085b 696e 6465 7800 085d 0a2a *....[index..].*\n-0001f660: 204d 656e 753a 0a0a 2a20 6166 6669 6e65 Menu:..* affine\n-0001f670: 2061 7269 7468 6d65 7469 633a 2020 2020 arithmetic: \n-0001f680: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f690: 2041 6666 696e 6520 6172 6974 686d 6574 Affine arithmet\n-0001f6a0: 6963 2e20 2020 286c 696e 6520 2020 3829 ic. (line 8)\n-0001f6b0: 0a2a 2061 6666 696e 6520 6172 6974 686d .* affine arithm\n-0001f6c0: 6574 6963 203c 313e 3a20 2020 2020 2020 etic <1>: \n-0001f6d0: 2020 2020 2020 2020 2020 4120 7465 6368 A tech\n-0001f6e0: 6e69 6361 6c20 6472 6177 696e 672e 2028 nical drawing. (\n-0001f6f0: 6c69 6e65 2020 3430 290a 2a20 616c 7465 line 40).* alte\n-0001f700: 726e 6174 6976 6573 2c20 6465 6669 6e69 rnatives, defini\n-0001f710: 7469 6f6e 3a20 2020 2020 2020 2020 2020 tion: \n-0001f720: 2020 2046 6f72 6d73 206f 6620 6465 6669 Forms of defi\n-0001f730: 6e69 7469 6f6e 732e 0a20 2020 2020 2020 nitions.. \n+0001f5c0: 2020 2020 2020 5472 616e 7366 6f72 6d20 Transform \n+0001f5d0: 6c69 7465 7261 6c73 2e20 2020 286c 696e literals. (lin\n+0001f5e0: 6520 3335 290a 0a1f 0a46 696c 653a 2073 e 35)....File: s\n+0001f5f0: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+0001f600: 653a 2049 6e64 6578 2c20 2050 7265 763a e: Index, Prev:\n+0001f610: 2049 6e64 6578 206f 6620 7379 6e74 6178 Index of syntax\n+0001f620: 2c20 2055 703a 2054 6f70 0a0a 496e 6465 , Up: Top..Inde\n+0001f630: 7820 6f66 2063 6f6e 6365 7074 730a 2a2a x of concepts.**\n+0001f640: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a0a ***************.\n+0001f650: 0a00 085b 696e 6465 7800 085d 0a2a 204d ...[index..].* M\n+0001f660: 656e 753a 0a0a 2a20 6166 6669 6e65 2061 enu:..* affine a\n+0001f670: 7269 7468 6d65 7469 633a 2020 2020 2020 rithmetic: \n+0001f680: 2020 2020 2020 2020 2020 2020 2020 2041 A\n+0001f690: 6666 696e 6520 6172 6974 686d 6574 6963 ffine arithmetic\n+0001f6a0: 2e20 2020 286c 696e 6520 2020 3829 0a2a . (line 8).*\n+0001f6b0: 2061 6666 696e 6520 6172 6974 686d 6574 affine arithmet\n+0001f6c0: 6963 203c 313e 3a20 2020 2020 2020 2020 ic <1>: \n+0001f6d0: 2020 2020 2020 2020 4120 7465 6368 6e69 A techni\n+0001f6e0: 6361 6c20 6472 6177 696e 672e 2028 6c69 cal drawing. (li\n+0001f6f0: 6e65 2020 3430 290a 2a20 616c 7465 726e ne 40).* altern\n+0001f700: 6174 6976 6573 2c20 6465 6669 6e69 7469 atives, definiti\n+0001f710: 6f6e 3a20 2020 2020 2020 2020 2020 2020 on: \n+0001f720: 2046 6f72 6d73 206f 6620 6465 6669 6e69 Forms of defini\n+0001f730: 7469 6f6e 732e 0a20 2020 2020 2020 2020 tions.. \n 0001f740: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f750: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f760: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f770: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n-0001f780: 290a 2a20 6172 6775 6d65 6e74 2c20 7370 ).* argument, sp\n-0001f790: 6563 6961 6c3a 2020 2020 2020 2020 2020 ecial: \n-0001f7a0: 2020 2020 2020 2020 2020 2053 7065 6369 Speci\n-0001f7b0: 616c 206f 626a 6563 7473 2e20 2020 2020 al objects. \n-0001f7c0: 286c 696e 6520 2032 3529 0a2a 2061 7267 (line 25).* arg\n-0001f7d0: 756d 656e 742c 2073 7065 6369 616c 203c ument, special <\n-0001f7e0: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n-0001f7f0: 2020 2020 5370 6563 6961 6c73 2e20 2020 Specials. \n-0001f800: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-0001f810: 3130 290a 2a20 6173 736f 6369 6174 6976 10).* associativ\n-0001f820: 6974 792c 206f 7065 7261 746f 723a 2020 ity, operator: \n-0001f830: 2020 2020 2020 2020 2020 2020 2054 776f Two\n-0001f840: 2d6f 7065 7261 6e64 2028 6269 6e61 7279 -operand (binary\n-0001f850: 2920 666f 726d 732e 0a20 2020 2020 2020 ) forms.. \n+0001f770: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n+0001f780: 2a20 6172 6775 6d65 6e74 2c20 7370 6563 * argument, spec\n+0001f790: 6961 6c3a 2020 2020 2020 2020 2020 2020 ial: \n+0001f7a0: 2020 2020 2020 2020 2053 7065 6369 616c Special\n+0001f7b0: 206f 626a 6563 7473 2e20 2020 2020 286c objects. (l\n+0001f7c0: 696e 6520 2032 3529 0a2a 2061 7267 756d ine 25).* argum\n+0001f7d0: 656e 742c 2073 7065 6369 616c 203c 313e ent, special <1>\n+0001f7e0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001f7f0: 2020 5370 6563 6961 6c73 2e20 2020 2020 Specials. \n+0001f800: 2020 2020 2020 2028 6c69 6e65 2020 3130 (line 10\n+0001f810: 290a 2a20 6173 736f 6369 6174 6976 6974 ).* associativit\n+0001f820: 792c 206f 7065 7261 746f 723a 2020 2020 y, operator: \n+0001f830: 2020 2020 2020 2020 2020 2054 776f 2d6f Two-o\n+0001f840: 7065 7261 6e64 2028 6269 6e61 7279 2920 perand (binary) \n+0001f850: 666f 726d 732e 0a20 2020 2020 2020 2020 forms.. \n 0001f860: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f870: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f880: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f890: 2020 2020 2020 2028 6c69 6e65 2020 3538 (line 58\n-0001f8a0: 290a 2a20 6178 6973 2c20 726f 7461 7469 ).* axis, rotati\n-0001f8b0: 6f6e 3a20 2020 2020 2020 2020 2020 2020 on: \n-0001f8c0: 2020 2020 2020 2020 2020 204f 626a 6563 Objec\n-0001f8d0: 7420 7472 616e 7366 6f72 6d73 2e20 2020 t transforms. \n-0001f8e0: 286c 696e 6520 2034 3029 0a2a 2062 6163 (line 40).* bac\n-0001f8f0: 6b20 6661 6365 3a20 2020 2020 2020 2020 k face: \n+0001f890: 2020 2020 2028 6c69 6e65 2020 3538 290a (line 58).\n+0001f8a0: 2a20 6178 6973 2c20 726f 7461 7469 6f6e * axis, rotation\n+0001f8b0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001f8c0: 2020 2020 2020 2020 204f 626a 6563 7420 Object \n+0001f8d0: 7472 616e 7366 6f72 6d73 2e20 2020 286c transforms. (l\n+0001f8e0: 696e 6520 2034 3029 0a2a 2062 6163 6b20 ine 40).* back \n+0001f8f0: 6661 6365 3a20 2020 2020 2020 2020 2020 face: \n 0001f900: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f910: 2020 2020 4472 6177 696e 6720 6120 736f Drawing a so\n-0001f920: 6c69 642e 2020 2020 2028 6c69 6e65 2020 lid. (line \n-0001f930: 3335 290a 2a20 6261 7365 6c69 6e65 2066 35).* baseline f\n-0001f940: 7261 6374 696f 6e3a 2020 2020 2020 2020 raction: \n-0001f950: 2020 2020 2020 2020 2020 2020 2050 6963 Pic\n-0001f960: 7475 7265 2062 6f78 2e20 2020 2020 2020 ture box. \n-0001f970: 2020 286c 696e 6520 2031 3029 0a2a 2062 (line 10).* b\n-0001f980: 696e 6172 7920 666f 726d 3a20 2020 2020 inary form: \n+0001f910: 2020 4472 6177 696e 6720 6120 736f 6c69 Drawing a soli\n+0001f920: 642e 2020 2020 2028 6c69 6e65 2020 3335 d. (line 35\n+0001f930: 290a 2a20 6261 7365 6c69 6e65 2066 7261 ).* baseline fra\n+0001f940: 6374 696f 6e3a 2020 2020 2020 2020 2020 ction: \n+0001f950: 2020 2020 2020 2020 2020 2050 6963 7475 Pictu\n+0001f960: 7265 2062 6f78 2e20 2020 2020 2020 2020 re box. \n+0001f970: 286c 696e 6520 2031 3029 0a2a 2062 696e (line 10).* bin\n+0001f980: 6172 7920 666f 726d 3a20 2020 2020 2020 ary form: \n 0001f990: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f9a0: 2020 2020 2020 5477 6f2d 6f70 6572 616e Two-operan\n-0001f9b0: 6420 2862 696e 6172 7929 2066 6f72 6d73 d (binary) forms\n-0001f9c0: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+0001f9a0: 2020 2020 5477 6f2d 6f70 6572 616e 6420 Two-operand \n+0001f9b0: 2862 696e 6172 7929 2066 6f72 6d73 2e0a (binary) forms..\n+0001f9c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f9d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f9e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f9f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fa00: 286c 696e 6520 2020 3629 0a2a 2062 696e (line 6).* bin\n-0001fa10: 6172 7920 7370 6163 6520 7061 7274 6974 ary space partit\n-0001fa20: 696f 6e3a 2020 2020 2020 2020 2020 2020 ion: \n-0001fa30: 2020 2020 4869 6464 656e 2073 7572 6661 Hidden surfa\n-0001fa40: 6365 2072 656d 6f76 616c 2e0a 2020 2020 ce removal.. \n+0001f9f0: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+0001fa00: 696e 6520 2020 3629 0a2a 2062 696e 6172 ine 6).* binar\n+0001fa10: 7920 7370 6163 6520 7061 7274 6974 696f y space partitio\n+0001fa20: 6e3a 2020 2020 2020 2020 2020 2020 2020 n: \n+0001fa30: 2020 4869 6464 656e 2073 7572 6661 6365 Hidden surface\n+0001fa40: 2072 656d 6f76 616c 2e0a 2020 2020 2020 removal.. \n 0001fa50: 2020 2020 2020 2020 2020 2020 2020 2020 \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 286c 696e 6520 (line \n-0001fa90: 2032 3329 0a2a 2062 696e 6172 7920 7370 23).* binary sp\n-0001faa0: 6163 6520 7061 7274 6974 696f 6e20 3c31 ace partition <1\n-0001fab0: 3e3a 2020 2020 2020 2020 2020 2020 5374 >: St\n-0001fac0: 6174 6973 7469 6373 2e20 2020 2020 2020 atistics. \n-0001fad0: 2020 2028 6c69 6e65 2020 3133 290a 2a20 (line 13).* \n-0001fae0: 6269 6e61 7279 2073 7061 6365 2070 6172 binary space par\n-0001faf0: 7469 7469 6f6e 203c 323e 3a20 2020 2020 tition <2>: \n-0001fb00: 2020 2020 2020 2043 6f6d 6d61 6e64 206c Command l\n-0001fb10: 696e 652e 2020 2020 2020 2020 286c 696e ine. (lin\n-0001fb20: 6520 2032 3629 0a2a 2062 6c6f 636b 3a20 e 26).* block: \n+0001fa80: 2020 2020 2020 2020 286c 696e 6520 2032 (line 2\n+0001fa90: 3329 0a2a 2062 696e 6172 7920 7370 6163 3).* binary spac\n+0001faa0: 6520 7061 7274 6974 696f 6e20 3c31 3e3a e partition <1>:\n+0001fab0: 2020 2020 2020 2020 2020 2020 5374 6174 Stat\n+0001fac0: 6973 7469 6373 2e20 2020 2020 2020 2020 istics. \n+0001fad0: 2028 6c69 6e65 2020 3133 290a 2a20 6269 (line 13).* bi\n+0001fae0: 6e61 7279 2073 7061 6365 2070 6172 7469 nary space parti\n+0001faf0: 7469 6f6e 203c 323e 3a20 2020 2020 2020 tion <2>: \n+0001fb00: 2020 2020 2043 6f6d 6d61 6e64 206c 696e Command lin\n+0001fb10: 652e 2020 2020 2020 2020 286c 696e 6520 e. (line \n+0001fb20: 2032 3629 0a2a 2062 6c6f 636b 3a20 2020 26).* block: \n 0001fb30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fb40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fb50: 4f62 6a65 6374 2074 7261 6e73 666f 726d Object transform\n-0001fb60: 732e 2020 2028 6c69 6e65 2020 3234 290a s. (line 24).\n-0001fb70: 2a20 626c 6f63 6b20 3c31 3e3a 2020 2020 * block <1>: \n+0001fb40: 2020 2020 2020 2020 2020 2020 2020 4f62 Ob\n+0001fb50: 6a65 6374 2074 7261 6e73 666f 726d 732e ject transforms.\n+0001fb60: 2020 2028 6c69 6e65 2020 3234 290a 2a20 (line 24).* \n+0001fb70: 626c 6f63 6b20 3c31 3e3a 2020 2020 2020 block <1>: \n 0001fb80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fb90: 2020 2020 2020 2020 2053 7765 7074 2062 Swept b\n-0001fba0: 6c6f 636b 732e 2020 2020 2020 2020 286c locks. (l\n-0001fbb0: 696e 6520 2020 3729 0a2a 2062 6c6f 636b ine 7).* block\n-0001fbc0: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n+0001fb90: 2020 2020 2020 2053 7765 7074 2062 6c6f Swept blo\n+0001fba0: 636b 732e 2020 2020 2020 2020 286c 696e cks. (lin\n+0001fbb0: 6520 2020 3729 0a2a 2062 6c6f 636b 203c e 7).* block <\n+0001fbc0: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n 0001fbd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fbe0: 2020 426c 6f63 6b73 2e20 2020 2020 2020 Blocks. \n-0001fbf0: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n-0001fc00: 290a 2a20 626c 6f63 6b20 7377 6565 703a ).* block sweep:\n+0001fbe0: 426c 6f63 6b73 2e20 2020 2020 2020 2020 Blocks. \n+0001fbf0: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n+0001fc00: 2a20 626c 6f63 6b20 7377 6565 703a 2020 * block sweep: \n 0001fc10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fc20: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n-0001fc30: 2062 6c6f 636b 732e 2020 2020 2020 2020 blocks. \n-0001fc40: 286c 696e 6520 2020 3629 0a2a 2062 6f64 (line 6).* bod\n-0001fc50: 7920 706f 6c79 676f 6e3a 2020 2020 2020 y polygon: \n+0001fc20: 2020 2020 2020 2020 2053 7765 7074 2062 Swept b\n+0001fc30: 6c6f 636b 732e 2020 2020 2020 2020 286c locks. (l\n+0001fc40: 696e 6520 2020 3629 0a2a 2062 6f64 7920 ine 6).* body \n+0001fc50: 706f 6c79 676f 6e3a 2020 2020 2020 2020 polygon: \n 0001fc60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fc70: 2020 2020 496e 7465 726e 616c 206f 7074 Internal opt\n-0001fc80: 696f 6e73 2e20 2020 2028 6c69 6e65 2020 ions. (line \n-0001fc90: 3136 290a 2a20 626f 6479 2070 6f6c 7967 16).* body polyg\n-0001fca0: 6f6e 203c 313e 3a20 2020 2020 2020 2020 on <1>: \n-0001fcb0: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n-0001fcc0: 7074 206c 696e 6573 2e20 2020 2020 2020 pt lines. \n-0001fcd0: 2020 286c 696e 6520 2031 3029 0a2a 2062 (line 10).* b\n-0001fce0: 6f64 7920 706f 6c79 676f 6e20 3c32 3e3a ody polygon <2>:\n+0001fc70: 2020 496e 7465 726e 616c 206f 7074 696f Internal optio\n+0001fc80: 6e73 2e20 2020 2028 6c69 6e65 2020 3136 ns. (line 16\n+0001fc90: 290a 2a20 626f 6479 2070 6f6c 7967 6f6e ).* body polygon\n+0001fca0: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+0001fcb0: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n+0001fcc0: 206c 696e 6573 2e20 2020 2020 2020 2020 lines. \n+0001fcd0: 286c 696e 6520 2031 3029 0a2a 2062 6f64 (line 10).* bod\n+0001fce0: 7920 706f 6c79 676f 6e20 3c32 3e3a 2020 y polygon <2>: \n 0001fcf0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fd00: 2020 2020 2020 5377 6570 7420 706f 6c79 Swept poly\n-0001fd10: 676f 6e73 2e20 2020 2020 2028 6c69 6e65 gons. (line\n-0001fd20: 2020 2039 290a 2a20 626f 756e 6469 6e67 9).* bounding\n-0001fd30: 2062 6f78 3a20 2020 2020 2020 2020 2020 box: \n-0001fd40: 2020 2020 2020 2020 2020 2020 2020 2050 P\n-0001fd50: 6963 7475 7265 2062 6f78 2e20 2020 2020 icture box. \n-0001fd60: 2020 2020 286c 696e 6520 2031 3529 0a2a (line 15).*\n-0001fd70: 2042 5350 2c20 6269 6e61 7279 2073 7061 BSP, binary spa\n-0001fd80: 6365 2070 6172 7469 7469 6f6e 3a20 2020 ce partition: \n-0001fd90: 2020 2020 2020 2020 4869 6464 656e 2073 Hidden s\n-0001fda0: 7572 6661 6365 2072 656d 6f76 616c 2e0a urface removal..\n+0001fd00: 2020 2020 5377 6570 7420 706f 6c79 676f Swept polygo\n+0001fd10: 6e73 2e20 2020 2020 2028 6c69 6e65 2020 ns. (line \n+0001fd20: 2039 290a 2a20 626f 756e 6469 6e67 2062 9).* bounding b\n+0001fd30: 6f78 3a20 2020 2020 2020 2020 2020 2020 ox: \n+0001fd40: 2020 2020 2020 2020 2020 2020 2050 6963 Pic\n+0001fd50: 7475 7265 2062 6f78 2e20 2020 2020 2020 ture box. \n+0001fd60: 2020 286c 696e 6520 2031 3529 0a2a 2042 (line 15).* B\n+0001fd70: 5350 2c20 6269 6e61 7279 2073 7061 6365 SP, binary space\n+0001fd80: 2070 6172 7469 7469 6f6e 3a20 2020 2020 partition: \n+0001fd90: 2020 2020 2020 4869 6464 656e 2073 7572 Hidden sur\n+0001fda0: 6661 6365 2072 656d 6f76 616c 2e0a 2020 face removal.. \n 0001fdb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001fdc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001fdd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fde0: 2020 2020 2020 2020 2020 2020 2020 286c (l\n-0001fdf0: 696e 6520 2032 3329 0a2a 2042 5350 2c20 ine 23).* BSP, \n-0001fe00: 6269 6e61 7279 2073 7061 6365 2070 6172 binary space par\n-0001fe10: 7469 7469 6f6e 203c 313e 3a20 2020 2020 tition <1>: \n-0001fe20: 2020 436f 6d6d 616e 6420 6c69 6e65 2e20 Command line. \n-0001fe30: 2020 2020 2020 2028 6c69 6e65 2020 3236 (line 26\n-0001fe40: 290a 2a20 6361 6d65 7261 3a20 2020 2020 ).* camera: \n+0001fde0: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+0001fdf0: 6520 2032 3329 0a2a 2042 5350 2c20 6269 e 23).* BSP, bi\n+0001fe00: 6e61 7279 2073 7061 6365 2070 6172 7469 nary space parti\n+0001fe10: 7469 6f6e 203c 313e 3a20 2020 2020 2020 tion <1>: \n+0001fe20: 436f 6d6d 616e 6420 6c69 6e65 2e20 2020 Command line. \n+0001fe30: 2020 2020 2028 6c69 6e65 2020 3236 290a (line 26).\n+0001fe40: 2a20 6361 6d65 7261 3a20 2020 2020 2020 * camera: \n 0001fe50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fe60: 2020 2020 2020 2020 2020 2043 616d 6572 Camer\n-0001fe70: 612e 2020 2020 2020 2020 2020 2020 2020 a. \n-0001fe80: 286c 696e 6520 2020 3629 0a2a 2063 656e (line 6).* cen\n-0001fe90: 7465 7220 6f66 2072 6f74 6174 696f 6e3a ter of rotation:\n+0001fe60: 2020 2020 2020 2020 2043 616d 6572 612e Camera.\n+0001fe70: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+0001fe80: 696e 6520 2020 3629 0a2a 2063 656e 7465 ine 6).* cente\n+0001fe90: 7220 6f66 2072 6f74 6174 696f 6e3a 2020 r of rotation: \n 0001fea0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001feb0: 2020 2020 4f62 6a65 6374 2074 7261 6e73 Object trans\n-0001fec0: 666f 726d 732e 2020 2028 6c69 6e65 2020 forms. (line \n-0001fed0: 2038 290a 2a20 6365 6e74 6572 206f 6620 8).* center of \n-0001fee0: 726f 7461 7469 6f6e 203c 313e 3a20 2020 rotation <1>: \n-0001fef0: 2020 2020 2020 2020 2020 2020 204e 6573 Nes\n-0001ff00: 7465 6420 7377 6565 7073 2e20 2020 2020 ted sweeps. \n-0001ff10: 2020 286c 696e 6520 2020 3629 0a2a 2063 (line 6).* c\n-0001ff20: 656e 7472 6f69 643a 2020 2020 2020 2020 entroid: \n+0001feb0: 2020 4f62 6a65 6374 2074 7261 6e73 666f Object transfo\n+0001fec0: 726d 732e 2020 2028 6c69 6e65 2020 2038 rms. (line 8\n+0001fed0: 290a 2a20 6365 6e74 6572 206f 6620 726f ).* center of ro\n+0001fee0: 7461 7469 6f6e 203c 313e 3a20 2020 2020 tation <1>: \n+0001fef0: 2020 2020 2020 2020 2020 204e 6573 7465 Neste\n+0001ff00: 6420 7377 6565 7073 2e20 2020 2020 2020 d sweeps. \n+0001ff10: 286c 696e 6520 2020 3629 0a2a 2063 656e (line 6).* cen\n+0001ff20: 7472 6f69 643a 2020 2020 2020 2020 2020 troid: \n 0001ff30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ff40: 2020 2020 2020 4120 7465 6368 6e69 6361 A technica\n-0001ff50: 6c20 6472 6177 696e 672e 2028 6c69 6e65 l drawing. (line\n-0001ff60: 2020 3634 290a 2a20 6365 6e74 726f 6964 64).* centroid\n-0001ff70: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n-0001ff80: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-0001ff90: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n-0001ffa0: 6e67 2e20 286c 696e 6520 3130 3229 0a2a ng. (line 102).*\n-0001ffb0: 2063 6c69 7070 696e 673a 2020 2020 2020 clipping: \n+0001ff40: 2020 2020 4120 7465 6368 6e69 6361 6c20 A technical \n+0001ff50: 6472 6177 696e 672e 2028 6c69 6e65 2020 drawing. (line \n+0001ff60: 3634 290a 2a20 6365 6e74 726f 6964 203c 64).* centroid <\n+0001ff70: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n+0001ff80: 2020 2020 2020 2020 2020 2020 2041 2074 A t\n+0001ff90: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n+0001ffa0: 2e20 286c 696e 6520 3130 3229 0a2a 2063 . (line 102).* c\n+0001ffb0: 6c69 7070 696e 673a 2020 2020 2020 2020 lipping: \n 0001ffc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ffd0: 2020 2020 2020 2020 5069 6374 7572 6520 Picture \n-0001ffe0: 626f 782e 2020 2020 2020 2020 2028 6c69 box. (li\n-0001fff0: 6e65 2020 3137 290a 2a20 636c 6970 7069 ne 17).* clippi\n-00020000: 6e67 203c 313e 3a20 2020 2020 2020 2020 ng <1>: \n-00020010: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020020: 2043 6c69 7070 696e 672e 2020 2020 2020 Clipping. \n-00020030: 2020 2020 2020 286c 696e 6520 2020 3629 (line 6)\n-00020040: 0a2a 2063 6c6f 7375 7265 2074 6167 2c20 .* closure tag, \n-00020050: 3c3e 3a20 2020 2020 2020 2020 2020 2020 <>: \n-00020060: 2020 2020 2020 2020 2020 506f 696e 7420 Point \n-00020070: 7377 6565 7073 2e20 2020 2020 2020 2028 sweeps. (\n-00020080: 6c69 6e65 2020 3138 290a 2a20 636c 6f73 line 18).* clos\n-00020090: 7572 6520 7461 672c 203c 3e20 3c31 3e3a ure tag, <> <1>:\n+0001ffd0: 2020 2020 2020 5069 6374 7572 6520 626f Picture bo\n+0001ffe0: 782e 2020 2020 2020 2020 2028 6c69 6e65 x. (line\n+0001fff0: 2020 3137 290a 2a20 636c 6970 7069 6e67 17).* clipping\n+00020000: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+00020010: 2020 2020 2020 2020 2020 2020 2020 2043 C\n+00020020: 6c69 7070 696e 672e 2020 2020 2020 2020 lipping. \n+00020030: 2020 2020 286c 696e 6520 2020 3629 0a2a (line 6).*\n+00020040: 2063 6c6f 7375 7265 2074 6167 2c20 3c3e closure tag, <>\n+00020050: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00020060: 2020 2020 2020 2020 506f 696e 7420 7377 Point sw\n+00020070: 6565 7073 2e20 2020 2020 2020 2028 6c69 eeps. (li\n+00020080: 6e65 2020 3138 290a 2a20 636c 6f73 7572 ne 18).* closur\n+00020090: 6520 7461 672c 203c 3e20 3c31 3e3a 2020 e tag, <> <1>: \n 000200a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000200b0: 2020 2050 6f6c 796c 696e 6520 7377 6565 Polyline swee\n-000200c0: 7073 2077 6974 6820 636c 6f73 7572 652e ps with closure.\n-000200d0: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n+000200b0: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n+000200c0: 2077 6974 6820 636c 6f73 7572 652e 0a20 with closure.. \n+000200d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000200e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000200f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020100: 2020 2020 2020 2020 2020 2020 2020 2028 (\n-00020110: 6c69 6e65 2020 2036 290a 2a20 636c 6f73 line 6).* clos\n-00020120: 7572 6520 7461 672c 203c 3e20 3c32 3e3a ure tag, <> <2>:\n+00020100: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+00020110: 6e65 2020 2036 290a 2a20 636c 6f73 7572 ne 6).* closur\n+00020120: 6520 7461 672c 203c 3e20 3c32 3e3a 2020 e tag, <> <2>: \n 00020130: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020140: 2020 2053 7765 6570 732e 2020 2020 2020 Sweeps. \n-00020150: 2020 2020 2020 2020 286c 696e 6520 2031 (line 1\n-00020160: 3929 0a2a 2063 6c6f 7375 7265 2074 6167 9).* closure tag\n-00020170: 2c20 3c3e 203c 333e 3a20 2020 2020 2020 , <> <3>: \n-00020180: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n-00020190: 7420 706f 696e 7473 2e20 2020 2020 2020 t points. \n-000201a0: 2028 6c69 6e65 2020 2036 290a 2a20 636c (line 6).* cl\n-000201b0: 6f73 7572 6520 7461 672c 203c 3e20 3c34 osure tag, <> <4\n-000201c0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-000201d0: 2020 2020 2053 7765 7074 2070 6f69 6e74 Swept point\n-000201e0: 732e 2020 2020 2020 2020 286c 696e 6520 s. (line \n-000201f0: 2031 3329 0a2a 2063 6c6f 7375 7265 2074 13).* closure t\n-00020200: 6167 2c20 3c3e 203c 353e 3a20 2020 2020 ag, <> <5>: \n-00020210: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n-00020220: 6570 7420 6c69 6e65 732e 2020 2020 2020 ept lines. \n-00020230: 2020 2028 6c69 6e65 2020 2036 290a 2a20 (line 6).* \n-00020240: 636c 6f73 7572 6520 7461 672c 203c 3e20 closure tag, <> \n-00020250: 3c36 3e3a 2020 2020 2020 2020 2020 2020 <6>: \n-00020260: 2020 2020 2020 2053 7765 7074 206c 696e Swept lin\n-00020270: 6573 2e20 2020 2020 2020 2020 286c 696e es. (lin\n-00020280: 6520 2032 3829 0a2a 2063 6c6f 7375 7265 e 28).* closure\n-00020290: 2074 6167 2c20 3c3e 203c 373e 3a20 2020 tag, <> <7>: \n-000202a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000202b0: 5377 6565 7020 6661 6365 2073 706c 6974 Sweep face split\n-000202c0: 7469 6e67 2e0a 2020 2020 2020 2020 2020 ting.. \n+00020140: 2053 7765 6570 732e 2020 2020 2020 2020 Sweeps. \n+00020150: 2020 2020 2020 286c 696e 6520 2031 3929 (line 19)\n+00020160: 0a2a 2063 6c6f 7375 7265 2074 6167 2c20 .* closure tag, \n+00020170: 3c3e 203c 333e 3a20 2020 2020 2020 2020 <> <3>: \n+00020180: 2020 2020 2020 2020 2020 5377 6570 7420 Swept \n+00020190: 706f 696e 7473 2e20 2020 2020 2020 2028 points. (\n+000201a0: 6c69 6e65 2020 2036 290a 2a20 636c 6f73 line 6).* clos\n+000201b0: 7572 6520 7461 672c 203c 3e20 3c34 3e3a ure tag, <> <4>:\n+000201c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000201d0: 2020 2053 7765 7074 2070 6f69 6e74 732e Swept points.\n+000201e0: 2020 2020 2020 2020 286c 696e 6520 2031 (line 1\n+000201f0: 3329 0a2a 2063 6c6f 7375 7265 2074 6167 3).* closure tag\n+00020200: 2c20 3c3e 203c 353e 3a20 2020 2020 2020 , <> <5>: \n+00020210: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n+00020220: 7420 6c69 6e65 732e 2020 2020 2020 2020 t lines. \n+00020230: 2028 6c69 6e65 2020 2036 290a 2a20 636c (line 6).* cl\n+00020240: 6f73 7572 6520 7461 672c 203c 3e20 3c36 osure tag, <> <6\n+00020250: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00020260: 2020 2020 2053 7765 7074 206c 696e 6573 Swept lines\n+00020270: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n+00020280: 2032 3829 0a2a 2063 6c6f 7375 7265 2074 28).* closure t\n+00020290: 6167 2c20 3c3e 203c 373e 3a20 2020 2020 ag, <> <7>: \n+000202a0: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n+000202b0: 6565 7020 6661 6365 2073 706c 6974 7469 eep face splitti\n+000202c0: 6e67 2e0a 2020 2020 2020 2020 2020 2020 ng.. \n 000202d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000202e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000202f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020300: 2020 2020 286c 696e 6520 2031 3129 0a2a (line 11).*\n-00020310: 2063 6f6d 6d61 6e64 206c 696e 6520 6f70 command line op\n-00020320: 7469 6f6e 3a20 2020 2020 2020 2020 2020 tion: \n-00020330: 2020 2020 2020 2020 4865 6c6c 6f20 776f Hello wo\n-00020340: 726c 642e 2020 2020 2020 2020 2028 6c69 rld. (li\n-00020350: 6e65 2020 3330 290a 2a20 636f 6d6d 616e ne 30).* comman\n-00020360: 6420 6c69 6e65 206f 7074 696f 6e73 3a20 d line options: \n-00020370: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020380: 2043 6f6d 6d61 6e64 206c 696e 652e 2020 Command line. \n-00020390: 2020 2020 2020 286c 696e 6520 2031 3429 (line 14)\n-000203a0: 0a2a 2063 6f6d 6d61 6e64 206c 696e 652c .* command line,\n-000203b0: 2073 6b65 7463 683a 2020 2020 2020 2020 sketch: \n-000203c0: 2020 2020 2020 2020 2020 4865 6c6c 6f20 Hello \n-000203d0: 776f 726c 642e 2020 2020 2020 2020 2028 world. (\n-000203e0: 6c69 6e65 2020 2039 290a 2a20 636f 6d6d line 9).* comm\n-000203f0: 616e 6420 6c69 6e65 2c20 736b 6574 6368 and line, sketch\n-00020400: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n-00020410: 2020 2043 6f6d 6d61 6e64 206c 696e 652e Command line.\n-00020420: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n-00020430: 3629 0a2a 2063 6f6d 6d65 6e74 733a 2020 6).* comments: \n+00020300: 2020 286c 696e 6520 2031 3129 0a2a 2063 (line 11).* c\n+00020310: 6f6d 6d61 6e64 206c 696e 6520 6f70 7469 ommand line opti\n+00020320: 6f6e 3a20 2020 2020 2020 2020 2020 2020 on: \n+00020330: 2020 2020 2020 4865 6c6c 6f20 776f 726c Hello worl\n+00020340: 642e 2020 2020 2020 2020 2028 6c69 6e65 d. (line\n+00020350: 2020 3330 290a 2a20 636f 6d6d 616e 6420 30).* command \n+00020360: 6c69 6e65 206f 7074 696f 6e73 3a20 2020 line options: \n+00020370: 2020 2020 2020 2020 2020 2020 2020 2043 C\n+00020380: 6f6d 6d61 6e64 206c 696e 652e 2020 2020 ommand line. \n+00020390: 2020 2020 286c 696e 6520 2031 3429 0a2a (line 14).*\n+000203a0: 2063 6f6d 6d61 6e64 206c 696e 652c 2073 command line, s\n+000203b0: 6b65 7463 683a 2020 2020 2020 2020 2020 ketch: \n+000203c0: 2020 2020 2020 2020 4865 6c6c 6f20 776f Hello wo\n+000203d0: 726c 642e 2020 2020 2020 2020 2028 6c69 rld. (li\n+000203e0: 6e65 2020 2039 290a 2a20 636f 6d6d 616e ne 9).* comman\n+000203f0: 6420 6c69 6e65 2c20 736b 6574 6368 203c d line, sketch <\n+00020400: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n+00020410: 2043 6f6d 6d61 6e64 206c 696e 652e 2020 Command line. \n+00020420: 2020 2020 2020 286c 696e 6520 2020 3629 (line 6)\n+00020430: 0a2a 2063 6f6d 6d65 6e74 733a 2020 2020 .* comments: \n 00020440: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020450: 2020 2020 2020 2020 2020 2020 4472 6177 Draw\n-00020460: 696e 6720 6120 736f 6c69 642e 2020 2020 ing a solid. \n-00020470: 2028 6c69 6e65 2020 3238 290a 2a20 636f (line 28).* co\n-00020480: 6d6d 656e 7473 203c 313e 3a20 2020 2020 mments <1>: \n+00020450: 2020 2020 2020 2020 2020 4472 6177 696e Drawin\n+00020460: 6720 6120 736f 6c69 642e 2020 2020 2028 g a solid. (\n+00020470: 6c69 6e65 2020 3238 290a 2a20 636f 6d6d line 28).* comm\n+00020480: 656e 7473 203c 313e 3a20 2020 2020 2020 ents <1>: \n 00020490: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000204a0: 2020 2020 204c 616e 6775 6167 6520 6261 Language ba\n-000204b0: 7369 6373 2e20 2020 2020 286c 696e 6520 sics. (line \n-000204c0: 2031 3829 0a2a 2063 6f6e 7374 7275 6374 18).* construct\n-000204d0: 6f72 3a20 2020 2020 2020 2020 2020 2020 or: \n-000204e0: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n-000204f0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-00020500: 2e20 2028 6c69 6e65 2020 2036 290a 2a20 . (line 6).* \n-00020510: 636f 6f72 6469 6e61 7465 2073 7973 7465 coordinate syste\n-00020520: 6d2c 2072 6967 6874 2d68 616e 6465 643a m, right-handed:\n-00020530: 2020 2020 2020 2049 6e74 726f 6475 6374 Introduct\n-00020540: 696f 6e20 6279 2065 7861 6d70 6c65 2e0a ion by example..\n+000204a0: 2020 204c 616e 6775 6167 6520 6261 7369 Language basi\n+000204b0: 6373 2e20 2020 2020 286c 696e 6520 2031 cs. (line 1\n+000204c0: 3829 0a2a 2063 6f6e 7374 7275 6374 6f72 8).* constructor\n+000204d0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+000204e0: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n+000204f0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n+00020500: 2028 6c69 6e65 2020 2036 290a 2a20 636f (line 6).* co\n+00020510: 6f72 6469 6e61 7465 2073 7973 7465 6d2c ordinate system,\n+00020520: 2072 6967 6874 2d68 616e 6465 643a 2020 right-handed: \n+00020530: 2020 2020 2049 6e74 726f 6475 6374 696f Introductio\n+00020540: 6e20 6279 2065 7861 6d70 6c65 2e0a 2020 n by example.. \n 00020550: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020560: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020570: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020580: 2020 2020 2020 2020 2020 2020 2020 286c (l\n-00020590: 696e 6520 2031 3129 0a2a 2063 6f75 6e74 ine 11).* count\n-000205a0: 6572 2d63 6c6f 636b 7769 7365 2070 6f6c er-clockwise pol\n-000205b0: 7967 6f6e 2076 6572 7465 7820 6f72 6465 ygon vertex orde\n-000205c0: 723a 2048 656c 6c6f 2077 6f72 6c64 2e20 r: Hello world. \n-000205d0: 2020 2020 2020 2028 6c69 6e65 2020 3339 (line 39\n-000205e0: 290a 2a20 6375 6c6c 696e 673a 2020 2020 ).* culling: \n+00020580: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+00020590: 6520 2031 3129 0a2a 2063 6f75 6e74 6572 e 11).* counter\n+000205a0: 2d63 6c6f 636b 7769 7365 2070 6f6c 7967 -clockwise polyg\n+000205b0: 6f6e 2076 6572 7465 7820 6f72 6465 723a on vertex order:\n+000205c0: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020 Hello world. \n+000205d0: 2020 2020 2028 6c69 6e65 2020 3339 290a (line 39).\n+000205e0: 2a20 6375 6c6c 696e 673a 2020 2020 2020 * culling: \n 000205f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020600: 2020 2020 2020 2020 2020 2048 656c 6c6f Hello\n-00020610: 2077 6f72 6c64 2e20 2020 2020 2020 2020 world. \n-00020620: 286c 696e 6520 2034 3329 0a2a 2063 756c (line 43).* cul\n-00020630: 6c69 6e67 203c 313e 3a20 2020 2020 2020 ling <1>: \n+00020600: 2020 2020 2020 2020 2048 656c 6c6f 2077 Hello w\n+00020610: 6f72 6c64 2e20 2020 2020 2020 2020 286c orld. 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(line 35\n+00020670: 290a 2a20 6375 6c6c 696e 6720 3c32 3e3a ).* culling <2>:\n+00020680: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00020690: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n+000206a0: 6e67 2061 2073 6f6c 6964 2e20 2020 2020 ng a solid. \n+000206b0: 286c 696e 6520 2034 3129 0a2a 2063 756c (line 41).* cul\n+000206c0: 6c69 6e67 203c 333e 3a20 2020 2020 2020 ling <3>: \n 000206d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000206e0: 2020 2020 2020 5377 6570 7420 6c69 6e65 Swept line\n-000206f0: 732e 2020 2020 2020 2020 2028 6c69 6e65 s. (line\n-00020700: 2020 3136 290a 2a20 6465 636c 6172 6174 16).* declarat\n-00020710: 6976 6520 6c61 6e67 7561 6765 3a20 2020 ive language: \n-00020720: 2020 2020 2020 2020 2020 2020 2020 204c L\n-00020730: 616e 6775 6167 6520 6261 7369 6373 2e20 anguage basics. \n-00020740: 2020 2020 286c 696e 6520 2020 3829 0a2a (line 8).*\n-00020750: 2064 6566 696e 6974 696f 6e3a 2020 2020 definition: \n+000206e0: 2020 2020 5377 6570 7420 6c69 6e65 732e Swept lines.\n+000206f0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00020700: 3136 290a 2a20 6465 636c 6172 6174 6976 16).* declarativ\n+00020710: 6520 6c61 6e67 7561 6765 3a20 2020 2020 e language: \n+00020720: 2020 2020 2020 2020 2020 2020 204c 616e Lan\n+00020730: 6775 6167 6520 6261 7369 6373 2e20 2020 guage basics. \n+00020740: 2020 286c 696e 6520 2020 3829 0a2a 2064 (line 8).* d\n+00020750: 6566 696e 6974 696f 6e3a 2020 2020 2020 efinition: \n 00020760: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020770: 2020 2020 2020 2020 4472 6177 696e 6720 Drawing \n-00020780: 6120 736f 6c69 642e 2020 2020 2028 6c69 a solid. (li\n-00020790: 6e65 2020 3232 290a 2a20 6465 6669 6e69 ne 22).* defini\n-000207a0: 7469 6f6e 203c 313e 3a20 2020 2020 2020 tion <1>: \n-000207b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000207c0: 2044 6566 696e 6974 696f 6e73 2e20 2020 Definitions. \n-000207d0: 2020 2020 2020 286c 696e 6520 2020 3629 (line 6)\n-000207e0: 0a2a 2064 6566 696e 6974 696f 6e20 7769 .* definition wi\n-000207f0: 7468 2061 6c74 6572 6e61 7469 7665 733a th alternatives:\n-00020800: 2020 2020 2020 2020 2020 466f 726d 7320 Forms \n-00020810: 6f66 2064 6566 696e 6974 696f 6e73 2e0a of definitions..\n+00020770: 2020 2020 2020 4472 6177 696e 6720 6120 Drawing a \n+00020780: 736f 6c69 642e 2020 2020 2028 6c69 6e65 solid. (line\n+00020790: 2020 3232 290a 2a20 6465 6669 6e69 7469 22).* definiti\n+000207a0: 6f6e 203c 313e 3a20 2020 2020 2020 2020 on <1>: \n+000207b0: 2020 2020 2020 2020 2020 2020 2020 2044 D\n+000207c0: 6566 696e 6974 696f 6e73 2e20 2020 2020 efinitions. \n+000207d0: 2020 2020 286c 696e 6520 2020 3629 0a2a (line 6).*\n+000207e0: 2064 6566 696e 6974 696f 6e20 7769 7468 definition with\n+000207f0: 2061 6c74 6572 6e61 7469 7665 733a 2020 alternatives: \n+00020800: 2020 2020 2020 2020 466f 726d 7320 6f66 Forms of\n+00020810: 2064 6566 696e 6974 696f 6e73 2e0a 2020 definitions.. \n 00020820: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020830: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020840: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020850: 2020 2020 2020 2020 2020 2020 2020 286c (l\n-00020860: 696e 6520 2020 3629 0a2a 2064 6566 696e ine 6).* defin\n-00020870: 6974 696f 6e2c 2064 7261 7761 626c 653a ition, drawable:\n+00020850: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+00020860: 6520 2020 3629 0a2a 2064 6566 696e 6974 e 6).* definit\n+00020870: 696f 6e2c 2064 7261 7761 626c 653a 2020 ion, drawable: \n 00020880: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020890: 2020 4f62 6a65 6374 2074 7261 6e73 666f Object transfo\n-000208a0: 726d 732e 2020 2028 6c69 6e65 2020 3237 rms. (line 27\n-000208b0: 290a 2a20 6465 6669 6e69 7469 6f6e 2c20 ).* definition, \n-000208c0: 6f70 7469 6f6e 733a 2020 2020 2020 2020 options: \n-000208d0: 2020 2020 2020 2020 2020 2050 6f6c 796c Polyl\n-000208e0: 696e 6520 7377 6565 7073 2077 6974 6820 ine sweeps with \n-000208f0: 636c 6f73 7572 652e 0a20 2020 2020 2020 closure.. \n+00020890: 4f62 6a65 6374 2074 7261 6e73 666f 726d Object transform\n+000208a0: 732e 2020 2028 6c69 6e65 2020 3237 290a s. (line 27).\n+000208b0: 2a20 6465 6669 6e69 7469 6f6e 2c20 6f70 * definition, op\n+000208c0: 7469 6f6e 733a 2020 2020 2020 2020 2020 tions: \n+000208d0: 2020 2020 2020 2020 2050 6f6c 796c 696e Polylin\n+000208e0: 6520 7377 6565 7073 2077 6974 6820 636c e sweeps with cl\n+000208f0: 6f73 7572 652e 0a20 2020 2020 2020 2020 osure.. \n 00020900: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020910: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020920: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020930: 2020 2020 2020 2028 6c69 6e65 2020 3233 (line 23\n-00020940: 290a 2a20 6465 6669 6e69 7469 6f6e 2c20 ).* definition, \n-00020950: 706f 696e 743a 2020 2020 2020 2020 2020 point: \n-00020960: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n-00020970: 6e67 2061 2073 6f6c 6964 2e20 2020 2020 ng a solid. \n-00020980: 286c 696e 6520 2032 3329 0a2a 2064 6566 (line 23).* def\n-00020990: 696e 6974 696f 6e2c 2073 6361 6c61 723a inition, scalar:\n+00020930: 2020 2020 2028 6c69 6e65 2020 3233 290a (line 23).\n+00020940: 2a20 6465 6669 6e69 7469 6f6e 2c20 706f * definition, po\n+00020950: 696e 743a 2020 2020 2020 2020 2020 2020 int: \n+00020960: 2020 2020 2020 2020 2044 7261 7769 6e67 Drawing\n+00020970: 2061 2073 6f6c 6964 2e20 2020 2020 286c a solid. (l\n+00020980: 696e 6520 2032 3329 0a2a 2064 6566 696e ine 23).* defin\n+00020990: 6974 696f 6e2c 2073 6361 6c61 723a 2020 ition, scalar: \n 000209a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000209b0: 2020 2020 5377 6570 7420 6f62 6a65 6374 Swept object\n-000209c0: 732e 2020 2020 2020 2028 6c69 6e65 2020 s. (line \n-000209d0: 3133 290a 2a20 6465 6669 6e69 7469 6f6e 13).* definition\n-000209e0: 2c20 7369 6d70 6c65 3a20 2020 2020 2020 , simple: \n-000209f0: 2020 2020 2020 2020 2020 2020 2046 6f72 For\n-00020a00: 6d73 206f 6620 6465 6669 6e69 7469 6f6e ms of definition\n-00020a10: 732e 0a20 2020 2020 2020 2020 2020 2020 s.. \n+000209b0: 2020 5377 6570 7420 6f62 6a65 6374 732e Swept objects.\n+000209c0: 2020 2020 2020 2028 6c69 6e65 2020 3133 (line 13\n+000209d0: 290a 2a20 6465 6669 6e69 7469 6f6e 2c20 ).* definition, \n+000209e0: 7369 6d70 6c65 3a20 2020 2020 2020 2020 simple: \n+000209f0: 2020 2020 2020 2020 2020 2046 6f72 6d73 Forms\n+00020a00: 206f 6620 6465 6669 6e69 7469 6f6e 732e of definitions.\n+00020a10: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n 00020a20: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020a30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020a40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020a50: 2028 6c69 6e65 2020 2036 290a 2a20 6465 (line 6).* de\n-00020a60: 6669 6e69 7469 6f6e 2c20 7461 673a 2020 finition, tag: \n+00020a40: 2020 2020 2020 2020 2020 2020 2020 2028 (\n+00020a50: 6c69 6e65 2020 2036 290a 2a20 6465 6669 line 6).* defi\n+00020a60: 6e69 7469 6f6e 2c20 7461 673a 2020 2020 nition, tag: \n 00020a70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020a80: 2020 2020 2044 6566 696e 6974 696f 6e73 Definitions\n-00020a90: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n-00020aa0: 2031 3829 0a2a 2064 6566 696e 6974 696f 18).* definitio\n-00020ab0: 6e2c 2074 6167 203c 313e 3a20 2020 2020 n, tag <1>: \n-00020ac0: 2020 2020 2020 2020 2020 2020 2020 466f Fo\n-00020ad0: 726d 7320 6f66 2064 6566 696e 6974 696f rms of definitio\n-00020ae0: 6e73 2e0a 2020 2020 2020 2020 2020 2020 ns.. \n+00020a80: 2020 2044 6566 696e 6974 696f 6e73 2e20 Definitions. \n+00020a90: 2020 2020 2020 2020 286c 696e 6520 2031 (line 1\n+00020aa0: 3829 0a2a 2064 6566 696e 6974 696f 6e2c 8).* definition,\n+00020ab0: 2074 6167 203c 313e 3a20 2020 2020 2020 tag <1>: \n+00020ac0: 2020 2020 2020 2020 2020 2020 466f 726d Form\n+00020ad0: 7320 6f66 2064 6566 696e 6974 696f 6e73 s of definitions\n+00020ae0: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n 00020af0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020b00: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020b10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020b20: 2020 286c 696e 6520 2020 3729 0a2a 2064 (line 7).* d\n-00020b30: 6566 696e 6974 696f 6e2c 2074 6167 203c efinition, tag <\n-00020b40: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n-00020b50: 2020 2020 2020 436f 6d6d 616e 6420 6c69 Command li\n-00020b60: 6e65 2e20 2020 2020 2020 2028 6c69 6e65 ne. (line\n-00020b70: 2020 3533 290a 2a20 6465 6669 6e69 7469 53).* definiti\n-00020b80: 6f6e 2c20 7472 616e 7366 6f72 6d3a 2020 on, transform: \n-00020b90: 2020 2020 2020 2020 2020 2020 2020 204f O\n-00020ba0: 7665 7276 6965 772e 2020 2020 2020 2020 verview. \n-00020bb0: 2020 2020 286c 696e 6520 2033 3529 0a2a (line 35).*\n-00020bc0: 2064 6566 696e 6974 696f 6e2c 2076 6563 definition, vec\n-00020bd0: 746f 723a 2020 2020 2020 2020 2020 2020 tor: \n-00020be0: 2020 2020 2020 2020 506f 6c79 6c69 6e65 Polyline\n-00020bf0: 2073 7765 6570 732e 2020 2020 2028 6c69 sweeps. (li\n-00020c00: 6e65 2020 3139 290a 2a20 6465 7074 6820 ne 19).* depth \n-00020c10: 736f 7274 3a20 2020 2020 2020 2020 2020 sort: \n-00020c20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020c30: 2049 6e74 6572 6e61 6c20 6f70 7469 6f6e Internal option\n-00020c40: 732e 2020 2020 286c 696e 6520 2031 3329 s. (line 13)\n-00020c50: 0a2a 2064 6570 7468 2073 6f72 7420 3c31 .* depth sort <1\n-00020c60: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-00020c70: 2020 2020 2020 2020 2020 4869 6464 656e Hidden\n-00020c80: 2073 7572 6661 6365 2072 656d 6f76 616c surface removal\n-00020c90: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+00020b20: 286c 696e 6520 2020 3729 0a2a 2064 6566 (line 7).* def\n+00020b30: 696e 6974 696f 6e2c 2074 6167 203c 323e inition, tag <2>\n+00020b40: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00020b50: 2020 2020 436f 6d6d 616e 6420 6c69 6e65 Command line\n+00020b60: 2e20 2020 2020 2020 2028 6c69 6e65 2020 . (line \n+00020b70: 3533 290a 2a20 6465 6669 6e69 7469 6f6e 53).* definition\n+00020b80: 2c20 7472 616e 7366 6f72 6d3a 2020 2020 , transform: \n+00020b90: 2020 2020 2020 2020 2020 2020 204f 7665 Ove\n+00020ba0: 7276 6965 772e 2020 2020 2020 2020 2020 rview. \n+00020bb0: 2020 286c 696e 6520 2033 3529 0a2a 2064 (line 35).* d\n+00020bc0: 6566 696e 6974 696f 6e2c 2076 6563 746f efinition, vecto\n+00020bd0: 723a 2020 2020 2020 2020 2020 2020 2020 r: \n+00020be0: 2020 2020 2020 506f 6c79 6c69 6e65 2073 Polyline s\n+00020bf0: 7765 6570 732e 2020 2020 2028 6c69 6e65 weeps. (line\n+00020c00: 2020 3139 290a 2a20 6465 7074 6820 736f 19).* depth so\n+00020c10: 7274 3a20 2020 2020 2020 2020 2020 2020 rt: \n+00020c20: 2020 2020 2020 2020 2020 2020 2020 2049 I\n+00020c30: 6e74 6572 6e61 6c20 6f70 7469 6f6e 732e nternal options.\n+00020c40: 2020 2020 286c 696e 6520 2031 3329 0a2a (line 13).*\n+00020c50: 2064 6570 7468 2073 6f72 7420 3c31 3e3a depth sort <1>:\n+00020c60: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00020c70: 2020 2020 2020 2020 4869 6464 656e 2073 Hidden s\n+00020c80: 7572 6661 6365 2072 656d 6f76 616c 2e0a urface removal..\n+00020c90: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020ca0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020cb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020cc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020cd0: 286c 696e 6520 2020 3629 0a2a 2064 6570 (line 6).* dep\n-00020ce0: 7468 2073 6f72 7420 3c32 3e3a 2020 2020 th sort <2>: \n+00020cc0: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+00020cd0: 696e 6520 2020 3629 0a2a 2064 6570 7468 ine 6).* depth\n+00020ce0: 2073 6f72 7420 3c32 3e3a 2020 2020 2020 sort <2>: \n 00020cf0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020d00: 2020 2020 4275 6773 2061 6e64 2061 6e6f Bugs and ano\n-00020d10: 6d61 6c69 6573 2e20 2028 6c69 6e65 2020 malies. (line \n-00020d20: 2038 290a 2a20 6469 7265 6374 2074 7261 8).* direct tra\n-00020d30: 6e73 666f 726d 3a20 2020 2020 2020 2020 nsform: \n-00020d40: 2020 2020 2020 2020 2020 2020 2054 7261 Tra\n-00020d50: 6e73 666f 726d 206c 6974 6572 616c 732e nsform literals.\n-00020d60: 2020 286c 696e 6520 2034 3729 0a2a 2064 (line 47).* d\n-00020d70: 6972 6563 7420 7472 616e 7366 6f72 6d20 irect transform \n-00020d80: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-00020d90: 2020 2020 2020 5472 616e 7366 6f72 6d20 Transform \n-00020da0: 6c69 7465 7261 6c73 2e20 2028 6c69 6e65 literals. (line\n-00020db0: 2020 3533 290a 2a20 646f 6375 6d65 6e74 53).* document\n-00020dc0: 2074 656d 706c 6174 653a 2020 2020 2020 template: \n-00020dd0: 2020 2020 2020 2020 2020 2020 2020 2048 H\n-00020de0: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020 ello world. \n-00020df0: 2020 2020 286c 696e 6520 2033 3229 0a2a (line 32).*\n-00020e00: 2064 6f63 756d 656e 7420 7465 6d70 6c61 document templa\n-00020e10: 7465 203c 313e 3a20 2020 2020 2020 2020 te <1>: \n-00020e20: 2020 2020 2020 2020 436f 6d6d 616e 6420 Command \n-00020e30: 6c69 6e65 2e20 2020 2020 2020 2028 6c69 line. (li\n-00020e40: 6e65 2020 3336 290a 2a20 6472 6177 6162 ne 36).* drawab\n-00020e50: 6c65 3a20 2020 2020 2020 2020 2020 2020 le: \n-00020e60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020e70: 204f 626a 6563 7420 7472 616e 7366 6f72 Object transfor\n-00020e80: 6d73 2e20 2020 286c 696e 6520 2032 3729 ms. (line 27)\n-00020e90: 0a2a 2064 7261 7761 626c 6520 3c31 3e3a .* drawable <1>:\n+00020d00: 2020 4275 6773 2061 6e64 2061 6e6f 6d61 Bugs and anoma\n+00020d10: 6c69 6573 2e20 2028 6c69 6e65 2020 2038 lies. (line 8\n+00020d20: 290a 2a20 6469 7265 6374 2074 7261 6e73 ).* direct trans\n+00020d30: 666f 726d 3a20 2020 2020 2020 2020 2020 form: \n+00020d40: 2020 2020 2020 2020 2020 2054 7261 6e73 Trans\n+00020d50: 666f 726d 206c 6974 6572 616c 732e 2020 form literals. \n+00020d60: 286c 696e 6520 2034 3729 0a2a 2064 6972 (line 47).* dir\n+00020d70: 6563 7420 7472 616e 7366 6f72 6d20 3c31 ect transform <1\n+00020d80: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00020d90: 2020 2020 5472 616e 7366 6f72 6d20 6c69 Transform li\n+00020da0: 7465 7261 6c73 2e20 2028 6c69 6e65 2020 terals. (line \n+00020db0: 3533 290a 2a20 646f 6375 6d65 6e74 2074 53).* document t\n+00020dc0: 656d 706c 6174 653a 2020 2020 2020 2020 emplate: \n+00020dd0: 2020 2020 2020 2020 2020 2020 2048 656c Hel\n+00020de0: 6c6f 2077 6f72 6c64 2e20 2020 2020 2020 lo world. \n+00020df0: 2020 286c 696e 6520 2033 3229 0a2a 2064 (line 32).* d\n+00020e00: 6f63 756d 656e 7420 7465 6d70 6c61 7465 ocument template\n+00020e10: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+00020e20: 2020 2020 2020 436f 6d6d 616e 6420 6c69 Command li\n+00020e30: 6e65 2e20 2020 2020 2020 2028 6c69 6e65 ne. (line\n+00020e40: 2020 3336 290a 2a20 6472 6177 6162 6c65 36).* drawable\n+00020e50: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00020e60: 2020 2020 2020 2020 2020 2020 2020 204f O\n+00020e70: 626a 6563 7420 7472 616e 7366 6f72 6d73 bject transforms\n+00020e80: 2e20 2020 286c 696e 6520 2032 3729 0a2a . (line 27).*\n+00020e90: 2064 7261 7761 626c 6520 3c31 3e3a 2020 drawable <1>: \n 00020ea0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020eb0: 2020 2020 2020 2020 2020 4472 6177 6162 Drawab\n-00020ec0: 6c65 732e 2020 2020 2020 2020 2020 2028 les. (\n-00020ed0: 6c69 6e65 2020 2036 290a 2a20 6472 6177 line 6).* draw\n-00020ee0: 6162 6c65 2064 6566 696e 6974 696f 6e3a able definition:\n+00020eb0: 2020 2020 2020 2020 4472 6177 6162 6c65 Drawable\n+00020ec0: 732e 2020 2020 2020 2020 2020 2028 6c69 s. (li\n+00020ed0: 6e65 2020 2036 290a 2a20 6472 6177 6162 ne 6).* drawab\n+00020ee0: 6c65 2064 6566 696e 6974 696f 6e3a 2020 le definition: \n 00020ef0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020f00: 2020 204f 626a 6563 7420 7472 616e 7366 Object transf\n-00020f10: 6f72 6d73 2e20 2020 286c 696e 6520 2032 orms. (line 2\n-00020f20: 3729 0a2a 2064 7261 7761 626c 6520 7265 7).* drawable re\n-00020f30: 6665 7265 6e63 653a 2020 2020 2020 2020 ference: \n-00020f40: 2020 2020 2020 2020 2020 2020 466f 726d Form\n-00020f50: 7320 6f66 2072 6566 6572 656e 6365 732e s of references.\n-00020f60: 2028 6c69 6e65 2020 3137 290a 2a20 656e (line 17).* en\n-00020f70: 6420 706f 6c79 676f 6e3a 2020 2020 2020 d polygon: \n+00020f00: 204f 626a 6563 7420 7472 616e 7366 6f72 Object transfor\n+00020f10: 6d73 2e20 2020 286c 696e 6520 2032 3729 ms. (line 27)\n+00020f20: 0a2a 2064 7261 7761 626c 6520 7265 6665 .* drawable refe\n+00020f30: 7265 6e63 653a 2020 2020 2020 2020 2020 rence: \n+00020f40: 2020 2020 2020 2020 2020 466f 726d 7320 Forms \n+00020f50: 6f66 2072 6566 6572 656e 6365 732e 2028 of references. (\n+00020f60: 6c69 6e65 2020 3137 290a 2a20 656e 6420 line 17).* end \n+00020f70: 706f 6c79 676f 6e3a 2020 2020 2020 2020 polygon: \n 00020f80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020f90: 2020 2020 2053 7765 7074 206c 696e 6573 Swept lines\n-00020fa0: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n-00020fb0: 2033 3829 0a2a 2065 6e64 2070 6f6c 7967 38).* end polyg\n-00020fc0: 6f6e 203c 313e 3a20 2020 2020 2020 2020 on <1>: \n-00020fd0: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n-00020fe0: 6570 7420 706f 6c79 676f 6e73 2e20 2020 ept polygons. \n-00020ff0: 2020 2028 6c69 6e65 2020 3135 290a 2a20 (line 15).* \n-00021000: 6661 6365 733a 2020 2020 2020 2020 2020 faces: \n+00020f90: 2020 2053 7765 7074 206c 696e 6573 2e20 Swept lines. \n+00020fa0: 2020 2020 2020 2020 286c 696e 6520 2033 (line 3\n+00020fb0: 3829 0a2a 2065 6e64 2070 6f6c 7967 6f6e 8).* end polygon\n+00020fc0: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+00020fd0: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n+00020fe0: 7420 706f 6c79 676f 6e73 2e20 2020 2020 t polygons. \n+00020ff0: 2028 6c69 6e65 2020 3135 290a 2a20 6661 (line 15).* fa\n+00021000: 6365 733a 2020 2020 2020 2020 2020 2020 ces: \n 00021010: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021020: 2020 2020 2020 2044 7261 7769 6e67 2061 Drawing a\n-00021030: 2073 6f6c 6964 2e20 2020 2020 286c 696e solid. (lin\n-00021040: 6520 2020 3729 0a2a 2066 6163 6573 203c e 7).* faces <\n-00021050: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n-00021060: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021070: 506f 6c79 6c69 6e65 2073 7765 6570 732e Polyline sweeps.\n-00021080: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n-00021090: 2a20 6669 6c65 2c20 696e 636c 7564 653a * file, include:\n+00021020: 2020 2020 2044 7261 7769 6e67 2061 2073 Drawing a s\n+00021030: 6f6c 6964 2e20 2020 2020 286c 696e 6520 olid. (line \n+00021040: 2020 3729 0a2a 2066 6163 6573 203c 313e 7).* faces <1>\n+00021050: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00021060: 2020 2020 2020 2020 2020 2020 2020 506f Po\n+00021070: 6c79 6c69 6e65 2073 7765 6570 732e 2020 lyline sweeps. \n+00021080: 2020 2028 6c69 6e65 2020 2036 290a 2a20 (line 6).* \n+00021090: 6669 6c65 2c20 696e 636c 7564 653a 2020 file, include: \n 000210a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000210b0: 2020 2020 2020 2020 204c 616e 6775 6167 Languag\n-000210c0: 6520 6261 7369 6373 2e20 2020 2020 286c e basics. (l\n-000210d0: 696e 6520 2031 3929 0a2a 2066 696c 652c ine 19).* file,\n-000210e0: 2069 6e70 7574 3a20 2020 2020 2020 2020 input: \n+000210b0: 2020 2020 2020 204c 616e 6775 6167 6520 Language \n+000210c0: 6261 7369 6373 2e20 2020 2020 286c 696e basics. (lin\n+000210d0: 6520 2031 3929 0a2a 2066 696c 652c 2069 e 19).* file, i\n+000210e0: 6e70 7574 3a20 2020 2020 2020 2020 2020 nput: \n 000210f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021100: 2020 4c61 6e67 7561 6765 2062 6173 6963 Language basic\n-00021110: 732e 2020 2020 2028 6c69 6e65 2020 2036 s. (line 6\n-00021120: 290a 2a20 6672 616d 6520 626f 783a 2020 ).* frame box: \n+00021100: 4c61 6e67 7561 6765 2062 6173 6963 732e Language basics.\n+00021110: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n+00021120: 2a20 6672 616d 6520 626f 783a 2020 2020 * frame box: \n 00021130: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021140: 2020 2020 2020 2020 2020 2046 7261 6d65 Frame\n-00021150: 2e20 2020 2020 2020 2020 2020 2020 2020 . \n-00021160: 286c 696e 6520 2020 3629 0a2a 2067 6c6f (line 6).* glo\n-00021170: 6261 6c20 6f70 7469 6f6e 733a 2020 2020 bal options: \n+00021140: 2020 2020 2020 2020 2046 7261 6d65 2e20 Frame. \n+00021150: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+00021160: 696e 6520 2020 3629 0a2a 2067 6c6f 6261 ine 6).* globa\n+00021170: 6c20 6f70 7469 6f6e 733a 2020 2020 2020 l options: \n 00021180: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021190: 2020 2020 4472 6177 696e 6720 6f70 7469 Drawing opti\n-000211a0: 6f6e 732e 2020 2020 2028 6c69 6e65 2020 ons. (line \n-000211b0: 3138 290a 2a20 676c 6f62 616c 206f 7074 18).* global opt\n-000211c0: 696f 6e73 203c 313e 3a20 2020 2020 2020 ions <1>: \n-000211d0: 2020 2020 2020 2020 2020 2020 2047 6c6f Glo\n-000211e0: 6261 6c20 6f70 7469 6f6e 732e 2020 2020 bal options. \n-000211f0: 2020 286c 696e 6520 2020 3629 0a2a 2068 (line 6).* h\n-00021200: 656c 6978 3a20 2020 2020 2020 2020 2020 elix: \n+00021190: 2020 4472 6177 696e 6720 6f70 7469 6f6e Drawing option\n+000211a0: 732e 2020 2020 2028 6c69 6e65 2020 3138 s. (line 18\n+000211b0: 290a 2a20 676c 6f62 616c 206f 7074 696f ).* global optio\n+000211c0: 6e73 203c 313e 3a20 2020 2020 2020 2020 ns <1>: \n+000211d0: 2020 2020 2020 2020 2020 2047 6c6f 6261 Globa\n+000211e0: 6c20 6f70 7469 6f6e 732e 2020 2020 2020 l options. \n+000211f0: 286c 696e 6520 2020 3629 0a2a 2068 656c (line 6).* hel\n+00021200: 6978 3a20 2020 2020 2020 2020 2020 2020 ix: \n 00021210: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021220: 2020 2020 2020 4472 6177 696e 6720 6120 Drawing a \n-00021230: 736f 6c69 642e 2020 2020 2028 6c69 6e65 solid. (line\n-00021240: 2020 3437 290a 2a20 6865 6c69 7820 3c31 47).* helix <1\n-00021250: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-00021260: 2020 2020 2020 2020 2020 2020 2020 2050 P\n-00021270: 6f6c 796c 696e 6520 7377 6565 7073 2e20 olyline sweeps. \n-00021280: 2020 2020 286c 696e 6520 2031 3529 0a2a (line 15).*\n-00021290: 2068 656c 6c6f 2077 6f72 6c64 3a20 2020 hello world: \n+00021220: 2020 2020 4472 6177 696e 6720 6120 736f Drawing a so\n+00021230: 6c69 642e 2020 2020 2028 6c69 6e65 2020 lid. (line \n+00021240: 3437 290a 2a20 6865 6c69 7820 3c31 3e3a 47).* helix <1>:\n+00021250: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00021260: 2020 2020 2020 2020 2020 2020 2050 6f6c Pol\n+00021270: 796c 696e 6520 7377 6565 7073 2e20 2020 yline sweeps. \n+00021280: 2020 286c 696e 6520 2031 3529 0a2a 2068 (line 15).* h\n+00021290: 656c 6c6f 2077 6f72 6c64 3a20 2020 2020 ello world: \n 000212a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000212b0: 2020 2020 2020 2020 4865 6c6c 6f20 776f Hello wo\n-000212c0: 726c 642e 2020 2020 2020 2020 2028 6c69 rld. (li\n-000212d0: 6e65 2020 2037 290a 2a20 6869 6464 656e ne 7).* hidden\n-000212e0: 2073 7572 6661 6365 2061 6c67 6f72 6974 surface algorit\n-000212f0: 686d 3a20 2020 2020 2020 2020 2020 2020 hm: \n-00021300: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020 Hello world. \n-00021310: 2020 2020 2020 286c 696e 6520 2031 3929 (line 19)\n-00021320: 0a2a 2068 6964 6465 6e20 7375 7266 6163 .* hidden surfac\n-00021330: 6520 616c 676f 7269 7468 6d20 3c31 3e3a e algorithm <1>:\n-00021340: 2020 2020 2020 2020 2020 5370 6563 6961 Specia\n-00021350: 6c20 6f62 6a65 6374 732e 2020 2020 2028 l objects. (\n-00021360: 6c69 6e65 2020 3438 290a 2a20 6869 6464 line 48).* hidd\n-00021370: 656e 2073 7572 6661 6365 2061 6c67 6f72 en surface algor\n-00021380: 6974 686d 203c 323e 3a20 2020 2020 2020 ithm <2>: \n-00021390: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n-000213a0: 6572 616c 732e 2020 286c 696e 6520 2032 erals. (line 2\n-000213b0: 3429 0a2a 2068 6964 6465 6e20 7375 7266 4).* hidden surf\n-000213c0: 6163 6520 616c 676f 7269 7468 6d20 3c33 ace algorithm <3\n-000213d0: 3e3a 2020 2020 2020 2020 2020 4120 7465 >: A te\n-000213e0: 6368 6e69 6361 6c20 6472 6177 696e 672e chnical drawing.\n-000213f0: 2028 6c69 6e65 2020 3235 290a 2a20 6869 (line 25).* hi\n-00021400: 6464 656e 2073 7572 6661 6365 2061 6c67 dden surface alg\n-00021410: 6f72 6974 686d 203c 343e 3a20 2020 2020 orithm <4>: \n-00021420: 2020 2020 2048 6964 6465 6e20 7375 7266 Hidden surf\n-00021430: 6163 6520 7265 6d6f 7661 6c2e 0a20 2020 ace removal.. \n+000212b0: 2020 2020 2020 4865 6c6c 6f20 776f 726c Hello worl\n+000212c0: 642e 2020 2020 2020 2020 2028 6c69 6e65 d. 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(line \n+00021550: 2020 3729 0a2a 2069 6e63 6c75 6465 2066 7).* include f\n+00021560: 696c 653a 2020 2020 2020 2020 2020 2020 ile: \n+00021570: 2020 2020 2020 2020 2020 2020 2020 4c61 La\n+00021580: 6e67 7561 6765 2062 6173 6963 732e 2020 nguage basics. \n+00021590: 2020 2028 6c69 6e65 2020 3139 290a 2a20 (line 19).* \n+000215a0: 696e 7075 7420 6669 6c65 3a20 2020 2020 input file: \n 000215b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000215c0: 2020 2020 2020 2020 204c 616e 6775 6167 Languag\n-000215d0: 6520 6261 7369 6373 2e20 2020 2020 286c e basics. (l\n-000215e0: 696e 6520 2020 3629 0a2a 2069 6e74 6572 ine 6).* inter\n-000215f0: 6e61 6c20 6f70 7469 6f6e 3a20 2020 2020 nal option: \n+000215c0: 2020 2020 2020 204c 616e 6775 6167 6520 Language \n+000215d0: 6261 7369 6373 2e20 2020 2020 286c 696e basics. 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(line 8\n-00021870: 290a 2a20 6c65 7869 6361 6c20 7363 6f70 ).* lexical scop\n-00021880: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n-00021890: 2020 2020 2020 2020 2020 204f 626a 6563 Objec\n-000218a0: 7420 7472 616e 7366 6f72 6d73 2e20 2020 t transforms. \n-000218b0: 286c 696e 6520 2032 3629 0a2a 206c 6578 (line 26).* lex\n-000218c0: 6963 616c 2073 636f 7065 203c 313e 3a20 ical scope <1>: \n+00021770: 2020 2020 2053 7065 6369 616c 206f 626a Special obj\n+00021780: 6563 7473 2e20 2020 2020 286c 696e 6520 ects. 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(line\n-00021990: 2020 2036 290a 2a20 6c69 6e65 2073 7765 6).* line swe\n-000219a0: 6570 203c 323e 3a20 2020 2020 2020 2020 ep <2>: \n-000219b0: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-000219c0: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n-000219d0: 6e67 2e20 286c 696e 6520 2032 3029 0a2a ng. (line 20).*\n-000219e0: 206c 6974 6572 616c 2c20 706f 696e 743a literal, point:\n+00021970: 2020 2020 5377 6570 7420 6c69 6e65 732e Swept lines.\n+00021980: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00021990: 2036 290a 2a20 6c69 6e65 2073 7765 6570 6).* line sweep\n+000219a0: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n+000219b0: 2020 2020 2020 2020 2020 2020 2041 2074 A t\n+000219c0: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n+000219d0: 2e20 286c 696e 6520 2032 3029 0a2a 206c . (line 20).* l\n+000219e0: 6974 6572 616c 2c20 706f 696e 743a 2020 iteral, point: \n 000219f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021a00: 2020 2020 2020 2020 506f 696e 7420 616e Point an\n-00021a10: 6420 7665 6374 6f72 206c 6974 6572 616c d vector literal\n-00021a20: 732e 0a20 2020 2020 2020 2020 2020 2020 s.. \n+00021a00: 2020 2020 2020 506f 696e 7420 616e 6420 Point and \n+00021a10: 7665 6374 6f72 206c 6974 6572 616c 732e vector literals.\n+00021a20: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n 00021a30: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021a40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021a50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021a60: 2028 6c69 6e65 2020 2036 290a 2a20 6c69 (line 6).* li\n-00021a70: 7465 7261 6c2c 2073 6361 6c61 723a 2020 teral, scalar: \n+00021a50: 2020 2020 2020 2020 2020 2020 2020 2028 (\n+00021a60: 6c69 6e65 2020 2036 290a 2a20 6c69 7465 line 6).* lite\n+00021a70: 7261 6c2c 2073 6361 6c61 723a 2020 2020 ral, scalar: \n 00021a80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021a90: 2020 2020 2053 6361 6c61 7220 6c69 7465 Scalar lite\n-00021aa0: 7261 6c73 2e20 2020 2020 286c 696e 6520 rals. (line \n-00021ab0: 2020 3629 0a2a 206c 6974 6572 616c 2c20 6).* literal, \n-00021ac0: 7472 616e 7366 6f72 6d3a 2020 2020 2020 transform: \n-00021ad0: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n-00021ae0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-00021af0: 2e20 2028 6c69 6e65 2020 2036 290a 2a20 . (line 6).* \n-00021b00: 6c69 7465 7261 6c2c 2076 6563 746f 723a literal, vector:\n+00021a90: 2020 2053 6361 6c61 7220 6c69 7465 7261 Scalar litera\n+00021aa0: 6c73 2e20 2020 2020 286c 696e 6520 2020 ls. (line \n+00021ab0: 3629 0a2a 206c 6974 6572 616c 2c20 7472 6).* literal, tr\n+00021ac0: 616e 7366 6f72 6d3a 2020 2020 2020 2020 ansform: \n+00021ad0: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n+00021ae0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n+00021af0: 2028 6c69 6e65 2020 2036 290a 2a20 6c69 (line 6).* li\n+00021b00: 7465 7261 6c2c 2076 6563 746f 723a 2020 teral, vector: \n 00021b10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021b20: 2020 2020 2020 2050 6f69 6e74 2061 6e64 Point and\n-00021b30: 2076 6563 746f 7220 6c69 7465 7261 6c73 vector literals\n-00021b40: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+00021b20: 2020 2020 2050 6f69 6e74 2061 6e64 2076 Point and v\n+00021b30: 6563 746f 7220 6c69 7465 7261 6c73 2e0a ector literals..\n+00021b40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021b50: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021b60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021b70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021b80: 286c 696e 6520 2020 3629 0a2a 206e 6573 (line 6).* nes\n-00021b90: 7469 6e67 2c20 7377 6570 7420 6f62 6a65 ting, swept obje\n-00021ba0: 6374 3a20 2020 2020 2020 2020 2020 2020 ct: \n-00021bb0: 2020 2020 4e65 7374 6564 2073 7765 6570 Nested sweep\n-00021bc0: 732e 2020 2020 2020 2028 6c69 6e65 2020 s. (line \n-00021bd0: 3232 290a 2a20 6f6e 652d 6f70 6572 616e 22).* one-operan\n-00021be0: 6420 666f 726d 3a20 2020 2020 2020 2020 d form: \n-00021bf0: 2020 2020 2020 2020 2020 2020 2055 6e61 Una\n-00021c00: 7279 2066 6f72 6d73 2e20 2020 2020 2020 ry forms. \n-00021c10: 2020 286c 696e 6520 2020 3629 0a2a 206f (line 6).* o\n-00021c20: 7065 7261 746f 7220 6173 736f 6369 6174 perator associat\n-00021c30: 6976 6974 793a 2020 2020 2020 2020 2020 ivity: \n-00021c40: 2020 2020 2020 5477 6f2d 6f70 6572 616e Two-operan\n-00021c50: 6420 2862 696e 6172 7929 2066 6f72 6d73 d (binary) forms\n-00021c60: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+00021b70: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+00021b80: 696e 6520 2020 3629 0a2a 206e 6573 7469 ine 6).* nesti\n+00021b90: 6e67 2c20 7377 6570 7420 6f62 6a65 6374 ng, swept object\n+00021ba0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00021bb0: 2020 4e65 7374 6564 2073 7765 6570 732e Nested sweeps.\n+00021bc0: 2020 2020 2020 2028 6c69 6e65 2020 3232 (line 22\n+00021bd0: 290a 2a20 6f6e 652d 6f70 6572 616e 6420 ).* one-operand \n+00021be0: 666f 726d 3a20 2020 2020 2020 2020 2020 form: \n+00021bf0: 2020 2020 2020 2020 2020 2055 6e61 7279 Unary\n+00021c00: 2066 6f72 6d73 2e20 2020 2020 2020 2020 forms. \n+00021c10: 286c 696e 6520 2020 3629 0a2a 206f 7065 (line 6).* ope\n+00021c20: 7261 746f 7220 6173 736f 6369 6174 6976 rator associativ\n+00021c30: 6974 793a 2020 2020 2020 2020 2020 2020 ity: \n+00021c40: 2020 2020 5477 6f2d 6f70 6572 616e 6420 Two-operand \n+00021c50: 2862 696e 6172 7929 2066 6f72 6d73 2e0a (binary) forms..\n+00021c60: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021c70: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021c80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021c90: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021ca0: 286c 696e 6520 2035 3829 0a2a 206f 7065 (line 58).* ope\n-00021cb0: 7261 746f 7220 7072 6563 6564 656e 6365 rator precedence\n-00021cc0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00021cd0: 2020 2020 5477 6f2d 6f70 6572 616e 6420 Two-operand \n-00021ce0: 2862 696e 6172 7929 2066 6f72 6d73 2e0a (binary) forms..\n+00021c90: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+00021ca0: 696e 6520 2035 3829 0a2a 206f 7065 7261 ine 58).* opera\n+00021cb0: 746f 7220 7072 6563 6564 656e 6365 3a20 tor precedence: \n+00021cc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00021cd0: 2020 5477 6f2d 6f70 6572 616e 6420 2862 Two-operand (b\n+00021ce0: 696e 6172 7929 2066 6f72 6d73 2e0a 2020 inary) forms.. \n 00021cf0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021d00: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021d10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021d20: 2020 2020 2020 2020 2020 2020 2020 286c (l\n-00021d30: 696e 6520 2034 3529 0a2a 206f 7074 696f ine 45).* optio\n-00021d40: 6e3a 2020 2020 2020 2020 2020 2020 2020 n: \n+00021d20: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+00021d30: 6520 2034 3529 0a2a 206f 7074 696f 6e3a e 45).* option:\n+00021d40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021d50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021d60: 2020 4472 6177 696e 6720 6f70 7469 6f6e Drawing option\n-00021d70: 732e 2020 2020 2028 6c69 6e65 2020 2036 s. (line 6\n-00021d80: 290a 2a20 6f70 7469 6f6e 2c20 636f 6d6d ).* option, comm\n-00021d90: 616e 6420 6c69 6e65 3a20 2020 2020 2020 and line: \n-00021da0: 2020 2020 2020 2020 2020 2048 656c 6c6f Hello\n-00021db0: 2077 6f72 6c64 2e20 2020 2020 2020 2020 world. \n-00021dc0: 286c 696e 6520 2033 3029 0a2a 206f 7074 (line 30).* opt\n-00021dd0: 696f 6e2c 2069 6e74 6572 6e61 6c3a 2020 ion, internal: \n+00021d60: 4472 6177 696e 6720 6f70 7469 6f6e 732e Drawing options.\n+00021d70: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n+00021d80: 2a20 6f70 7469 6f6e 2c20 636f 6d6d 616e * option, comman\n+00021d90: 6420 6c69 6e65 3a20 2020 2020 2020 2020 d line: \n+00021da0: 2020 2020 2020 2020 2048 656c 6c6f 2077 Hello w\n+00021db0: 6f72 6c64 2e20 2020 2020 2020 2020 286c orld. (l\n+00021dc0: 696e 6520 2033 3029 0a2a 206f 7074 696f ine 30).* optio\n+00021dd0: 6e2c 2069 6e74 6572 6e61 6c3a 2020 2020 n, internal: \n 00021de0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021df0: 2020 2020 5370 6563 6961 6c20 6f62 6a65 Special obje\n-00021e00: 6374 732e 2020 2020 2028 6c69 6e65 2020 cts. (line \n-00021e10: 3437 290a 2a20 6f70 7469 6f6e 733a 2020 47).* options: \n+00021df0: 2020 5370 6563 6961 6c20 6f62 6a65 6374 Special object\n+00021e00: 732e 2020 2020 2028 6c69 6e65 2020 3437 s. (line 47\n+00021e10: 290a 2a20 6f70 7469 6f6e 733a 2020 2020 ).* options: \n 00021e20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021e30: 2020 2020 2020 2020 2020 2020 204f 7074 Opt\n-00021e40: 696f 6e73 2e20 2020 2020 2020 2020 2020 ions. \n-00021e50: 2020 286c 696e 6520 2020 3629 0a2a 206f (line 6).* o\n-00021e60: 7074 696f 6e73 2064 6566 696e 6974 696f ptions definitio\n-00021e70: 6e3a 2020 2020 2020 2020 2020 2020 2020 n: \n-00021e80: 2020 2020 2020 506f 6c79 6c69 6e65 2073 Polyline s\n-00021e90: 7765 6570 7320 7769 7468 2063 6c6f 7375 weeps with closu\n-00021ea0: 7265 2e0a 2020 2020 2020 2020 2020 2020 re.. \n+00021e30: 2020 2020 2020 2020 2020 204f 7074 696f Optio\n+00021e40: 6e73 2e20 2020 2020 2020 2020 2020 2020 ns. \n+00021e50: 286c 696e 6520 2020 3629 0a2a 206f 7074 (line 6).* opt\n+00021e60: 696f 6e73 2064 6566 696e 6974 696f 6e3a ions definition:\n+00021e70: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00021e80: 2020 2020 506f 6c79 6c69 6e65 2073 7765 Polyline swe\n+00021e90: 6570 7320 7769 7468 2063 6c6f 7375 7265 eps with closure\n+00021ea0: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n 00021eb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021ec0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021ed0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021ee0: 2020 286c 696e 6520 2032 3329 0a2a 206f (line 23).* o\n-00021ef0: 7074 696f 6e73 206d 756c 7469 706c 6520 ptions multiple \n-00021f00: 7265 6665 7265 6e63 653a 2020 2020 2020 reference: \n-00021f10: 2020 2020 2020 466f 726d 7320 6f66 2072 Forms of r\n-00021f20: 6566 6572 656e 6365 732e 2028 6c69 6e65 eferences. (line\n-00021f30: 2020 3138 290a 2a20 6f70 7469 6f6e 7320 18).* options \n-00021f40: 7265 6665 7265 6e63 653a 2020 2020 2020 reference: \n-00021f50: 2020 2020 2020 2020 2020 2020 2020 2046 F\n-00021f60: 6f72 6d73 206f 6620 7265 6665 7265 6e63 orms of referenc\n-00021f70: 6573 2e20 286c 696e 6520 2031 3829 0a2a es. (line 18).*\n-00021f80: 206f 7074 696f 6e73 2c20 636f 6d6d 616e options, comman\n-00021f90: 6420 6c69 6e65 3a20 2020 2020 2020 2020 d line: \n-00021fa0: 2020 2020 2020 2020 436f 6d6d 616e 6420 Command \n-00021fb0: 6c69 6e65 2e20 2020 2020 2020 2028 6c69 line. (li\n-00021fc0: 6e65 2020 3134 290a 2a20 6f70 7469 6f6e ne 14).* option\n-00021fd0: 732c 2067 6c6f 6261 6c3a 2020 2020 2020 s, global: \n-00021fe0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021ff0: 2044 7261 7769 6e67 206f 7074 696f 6e73 Drawing options\n-00022000: 2e20 2020 2020 286c 696e 6520 2031 3829 . (line 18)\n-00022010: 0a2a 206f 7074 696f 6e73 2c20 676c 6f62 .* options, glob\n-00022020: 616c 203c 313e 3a20 2020 2020 2020 2020 al <1>: \n-00022030: 2020 2020 2020 2020 2020 476c 6f62 616c Global\n-00022040: 206f 7074 696f 6e73 2e20 2020 2020 2028 options. (\n-00022050: 6c69 6e65 2020 2036 290a 2a20 6f70 7469 line 6).* opti\n-00022060: 6f6e 732c 2069 6e74 6572 6e61 6c3a 2020 ons, internal: \n+00021ee0: 286c 696e 6520 2032 3329 0a2a 206f 7074 (line 23).* opt\n+00021ef0: 696f 6e73 206d 756c 7469 706c 6520 7265 ions multiple re\n+00021f00: 6665 7265 6e63 653a 2020 2020 2020 2020 ference: \n+00021f10: 2020 2020 466f 726d 7320 6f66 2072 6566 Forms of ref\n+00021f20: 6572 656e 6365 732e 2028 6c69 6e65 2020 erences. (line \n+00021f30: 3138 290a 2a20 6f70 7469 6f6e 7320 7265 18).* options re\n+00021f40: 6665 7265 6e63 653a 2020 2020 2020 2020 ference: \n+00021f50: 2020 2020 2020 2020 2020 2020 2046 6f72 For\n+00021f60: 6d73 206f 6620 7265 6665 7265 6e63 6573 ms of references\n+00021f70: 2e20 286c 696e 6520 2031 3829 0a2a 206f . (line 18).* o\n+00021f80: 7074 696f 6e73 2c20 636f 6d6d 616e 6420 ptions, command \n+00021f90: 6c69 6e65 3a20 2020 2020 2020 2020 2020 line: \n+00021fa0: 2020 2020 2020 436f 6d6d 616e 6420 6c69 Command li\n+00021fb0: 6e65 2e20 2020 2020 2020 2028 6c69 6e65 ne. (line\n+00021fc0: 2020 3134 290a 2a20 6f70 7469 6f6e 732c 14).* options,\n+00021fd0: 2067 6c6f 6261 6c3a 2020 2020 2020 2020 global: \n+00021fe0: 2020 2020 2020 2020 2020 2020 2020 2044 D\n+00021ff0: 7261 7769 6e67 206f 7074 696f 6e73 2e20 rawing options. \n+00022000: 2020 2020 286c 696e 6520 2031 3829 0a2a (line 18).*\n+00022010: 206f 7074 696f 6e73 2c20 676c 6f62 616c options, global\n+00022020: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+00022030: 2020 2020 2020 2020 476c 6f62 616c 206f Global o\n+00022040: 7074 696f 6e73 2e20 2020 2020 2028 6c69 ptions. (li\n+00022050: 6e65 2020 2036 290a 2a20 6f70 7469 6f6e ne 6).* option\n+00022060: 732c 2069 6e74 6572 6e61 6c3a 2020 2020 s, internal: \n 00022070: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022080: 2020 2049 6e74 6572 6e61 6c20 6f70 7469 Internal opti\n-00022090: 6f6e 732e 2020 2020 286c 696e 6520 2020 ons. (line \n-000220a0: 3629 0a2a 206f 7074 696f 6e73 2c20 696e 6).* options, in\n-000220b0: 7465 726e 616c 203c 313e 3a20 2020 2020 ternal <1>: \n-000220c0: 2020 2020 2020 2020 2020 2020 476c 6f62 Glob\n-000220d0: 616c 206f 7074 696f 6e73 2e20 2020 2020 al options. \n-000220e0: 2028 6c69 6e65 2020 3132 290a 2a20 6f70 (line 12).* op\n-000220f0: 7469 6f6e 732c 2073 7765 6570 3a20 2020 tions, sweep: \n+00022080: 2049 6e74 6572 6e61 6c20 6f70 7469 6f6e Internal option\n+00022090: 732e 2020 2020 286c 696e 6520 2020 3629 s. (line 6)\n+000220a0: 0a2a 206f 7074 696f 6e73 2c20 696e 7465 .* options, inte\n+000220b0: 726e 616c 203c 313e 3a20 2020 2020 2020 rnal <1>: \n+000220c0: 2020 2020 2020 2020 2020 476c 6f62 616c Global\n+000220d0: 206f 7074 696f 6e73 2e20 2020 2020 2028 options. (\n+000220e0: 6c69 6e65 2020 3132 290a 2a20 6f70 7469 line 12).* opti\n+000220f0: 6f6e 732c 2073 7765 6570 3a20 2020 2020 ons, sweep: \n 00022100: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022110: 2020 2020 2050 6f6c 796c 696e 6520 7377 Polyline sw\n-00022120: 6565 7073 2e20 2020 2020 286c 696e 6520 eeps. (line \n-00022130: 2031 3629 0a2a 206f 7074 696f 6e73 2c20 16).* options, \n-00022140: 7377 6565 7020 3c31 3e3a 2020 2020 2020 sweep <1>: \n-00022150: 2020 2020 2020 2020 2020 2020 2020 506f Po\n-00022160: 6c79 676f 6e20 7377 6565 7073 2e20 2020 lygon sweeps. \n-00022170: 2020 2028 6c69 6e65 2020 2039 290a 2a20 (line 9).* \n-00022180: 6f70 7469 6f6e 732c 2073 7765 6570 203c options, sweep <\n-00022190: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n-000221a0: 2020 2020 2020 2053 7765 7074 2070 6f69 Swept poi\n-000221b0: 6e74 732e 2020 2020 2020 2020 286c 696e nts. (lin\n-000221c0: 6520 2032 3129 0a2a 206f 7074 696f 6e73 e 21).* options\n-000221d0: 2c20 7377 6565 7020 3c33 3e3a 2020 2020 , sweep <3>: \n-000221e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000221f0: 5377 6570 7420 6c69 6e65 732e 2020 2020 Swept lines. \n-00022200: 2020 2020 2028 6c69 6e65 2020 3235 290a (line 25).\n-00022210: 2a20 6f70 7469 6f6e 732c 2073 7765 6570 * options, sweep\n-00022220: 203c 343e 3a20 2020 2020 2020 2020 2020 <4>: \n-00022230: 2020 2020 2020 2020 2053 7765 7074 206c Swept l\n-00022240: 696e 6573 2e20 2020 2020 2020 2020 286c ines. (l\n-00022250: 696e 6520 2034 3829 0a2a 206f 7074 696f ine 48).* optio\n-00022260: 6e73 2c20 7377 6570 7420 6f62 6a65 6374 ns, swept object\n-00022270: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00022280: 2020 506f 6c79 676f 6e20 7377 6565 7073 Polygon sweeps\n-00022290: 2e20 2020 2020 2028 6c69 6e65 2020 2038 . (line 8\n-000222a0: 290a 2a20 6f70 7469 6f6e 732c 2073 7765 ).* options, swe\n-000222b0: 7074 206f 626a 6563 7420 3c31 3e3a 2020 pt object <1>: \n-000222c0: 2020 2020 2020 2020 2020 2050 6f6c 796c Polyl\n-000222d0: 696e 6520 7377 6565 7073 2077 6974 6820 ine sweeps with \n-000222e0: 636c 6f73 7572 652e 0a20 2020 2020 2020 closure.. \n+00022110: 2020 2050 6f6c 796c 696e 6520 7377 6565 Polyline swee\n+00022120: 7073 2e20 2020 2020 286c 696e 6520 2031 ps. (line 1\n+00022130: 3629 0a2a 206f 7074 696f 6e73 2c20 7377 6).* options, sw\n+00022140: 6565 7020 3c31 3e3a 2020 2020 2020 2020 eep <1>: \n+00022150: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n+00022160: 676f 6e20 7377 6565 7073 2e20 2020 2020 gon sweeps. \n+00022170: 2028 6c69 6e65 2020 2039 290a 2a20 6f70 (line 9).* op\n+00022180: 7469 6f6e 732c 2073 7765 6570 203c 323e tions, sweep <2>\n+00022190: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+000221a0: 2020 2020 2053 7765 7074 2070 6f69 6e74 Swept point\n+000221b0: 732e 2020 2020 2020 2020 286c 696e 6520 s. (line \n+000221c0: 2032 3129 0a2a 206f 7074 696f 6e73 2c20 21).* options, \n+000221d0: 7377 6565 7020 3c33 3e3a 2020 2020 2020 sweep <3>: \n+000221e0: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n+000221f0: 6570 7420 6c69 6e65 732e 2020 2020 2020 ept lines. \n+00022200: 2020 2028 6c69 6e65 2020 3235 290a 2a20 (line 25).* \n+00022210: 6f70 7469 6f6e 732c 2073 7765 6570 203c options, sweep <\n+00022220: 343e 3a20 2020 2020 2020 2020 2020 2020 4>: \n+00022230: 2020 2020 2020 2053 7765 7074 206c 696e Swept lin\n+00022240: 6573 2e20 2020 2020 2020 2020 286c 696e es. (lin\n+00022250: 6520 2034 3829 0a2a 206f 7074 696f 6e73 e 48).* options\n+00022260: 2c20 7377 6570 7420 6f62 6a65 6374 3a20 , swept object: \n+00022270: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00022280: 506f 6c79 676f 6e20 7377 6565 7073 2e20 Polygon sweeps. \n+00022290: 2020 2020 2028 6c69 6e65 2020 2038 290a (line 8).\n+000222a0: 2a20 6f70 7469 6f6e 732c 2073 7765 7074 * options, swept\n+000222b0: 206f 626a 6563 7420 3c31 3e3a 2020 2020 object <1>: \n+000222c0: 2020 2020 2020 2020 2050 6f6c 796c 696e Polylin\n+000222d0: 6520 7377 6565 7073 2077 6974 6820 636c e sweeps with cl\n+000222e0: 6f73 7572 652e 0a20 2020 2020 2020 2020 osure.. \n 000222f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022300: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022310: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022320: 2020 2020 2020 2028 6c69 6e65 2020 3232 (line 22\n-00022330: 290a 2a20 6f70 7469 6f6e 732c 2073 7765 ).* options, swe\n-00022340: 7074 206f 626a 6563 7420 3c32 3e3a 2020 pt object <2>: \n-00022350: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n-00022360: 206c 696e 6573 2e20 2020 2020 2020 2020 lines. \n-00022370: 286c 696e 6520 2032 3629 0a2a 206f 7074 (line 26).* opt\n-00022380: 696f 6e73 2c20 7377 6570 7420 6f62 6a65 ions, swept obje\n-00022390: 6374 203c 333e 3a20 2020 2020 2020 2020 ct <3>: \n-000223a0: 2020 2020 5377 6570 7420 6c69 6e65 732e Swept lines.\n-000223b0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-000223c0: 3438 290a 2a20 6f72 6465 722c 2070 6f6c 48).* order, pol\n-000223d0: 7967 6f6e 2076 6572 7465 783a 2020 2020 ygon vertex: \n-000223e0: 2020 2020 2020 2020 2020 2020 2048 656c Hel\n-000223f0: 6c6f 2077 6f72 6c64 2e20 2020 2020 2020 lo world. \n-00022400: 2020 286c 696e 6520 2033 3929 0a2a 206f (line 39).* o\n-00022410: 7264 6572 2c20 706f 6c79 676f 6e20 7665 rder, polygon ve\n-00022420: 7274 6578 203c 313e 3a20 2020 2020 2020 rtex <1>: \n-00022430: 2020 2020 2020 5377 6570 7420 6c69 6e65 Swept line\n-00022440: 732e 2020 2020 2020 2020 2028 6c69 6e65 s. (line\n-00022450: 2020 3134 290a 2a20 6f72 6465 722c 2070 14).* order, p\n-00022460: 6f6c 7967 6f6e 2076 6572 7465 7820 3c32 olygon vertex <2\n-00022470: 3e3a 2020 2020 2020 2020 2020 2020 2053 >: S\n-00022480: 7765 7074 206c 696e 6573 2e20 2020 2020 wept lines. \n-00022490: 2020 2020 286c 696e 6520 2034 3029 0a2a (line 40).*\n-000224a0: 206f 7264 6572 2c20 706f 6c79 676f 6e20 order, polygon \n-000224b0: 7665 7274 6578 203c 333e 3a20 2020 2020 vertex <3>: \n-000224c0: 2020 2020 2020 2020 5377 6570 7420 706f Swept po\n-000224d0: 6c79 676f 6e73 2e20 2020 2020 2028 6c69 lygons. (li\n-000224e0: 6e65 2020 3139 290a 2a20 6f72 6465 722c ne 19).* order,\n-000224f0: 2070 6f6c 7967 6f6e 2076 6572 7465 7820 polygon vertex \n-00022500: 3c34 3e3a 2020 2020 2020 2020 2020 2020 <4>: \n-00022510: 204f 7665 7276 6965 772e 2020 2020 2020 Overview. \n-00022520: 2020 2020 2020 286c 696e 6520 2033 3729 (line 37)\n-00022530: 0a2a 206f 7264 6572 2c20 706f 6c79 676f .* order, polygo\n-00022540: 6e20 7665 7274 6578 203c 353e 3a20 2020 n vertex <5>: \n-00022550: 2020 2020 2020 2020 2020 4f76 6572 7669 Overvi\n-00022560: 6577 2e20 2020 2020 2020 2020 2020 2028 ew. (\n-00022570: 6c69 6e65 2020 3535 290a 2a20 6f75 7470 line 55).* outp\n-00022580: 7574 206c 616e 6775 6167 653a 2020 2020 ut language: \n+00022320: 2020 2020 2028 6c69 6e65 2020 3232 290a (line 22).\n+00022330: 2a20 6f70 7469 6f6e 732c 2073 7765 7074 * options, swept\n+00022340: 206f 626a 6563 7420 3c32 3e3a 2020 2020 object <2>: \n+00022350: 2020 2020 2020 2020 2053 7765 7074 206c Swept l\n+00022360: 696e 6573 2e20 2020 2020 2020 2020 286c ines. (l\n+00022370: 696e 6520 2032 3629 0a2a 206f 7074 696f ine 26).* optio\n+00022380: 6e73 2c20 7377 6570 7420 6f62 6a65 6374 ns, swept object\n+00022390: 203c 333e 3a20 2020 2020 2020 2020 2020 <3>: \n+000223a0: 2020 5377 6570 7420 6c69 6e65 732e 2020 Swept lines. \n+000223b0: 2020 2020 2020 2028 6c69 6e65 2020 3438 (line 48\n+000223c0: 290a 2a20 6f72 6465 722c 2070 6f6c 7967 ).* order, polyg\n+000223d0: 6f6e 2076 6572 7465 783a 2020 2020 2020 on vertex: \n+000223e0: 2020 2020 2020 2020 2020 2048 656c 6c6f Hello\n+000223f0: 2077 6f72 6c64 2e20 2020 2020 2020 2020 world. \n+00022400: 286c 696e 6520 2033 3929 0a2a 206f 7264 (line 39).* ord\n+00022410: 6572 2c20 706f 6c79 676f 6e20 7665 7274 er, polygon vert\n+00022420: 6578 203c 313e 3a20 2020 2020 2020 2020 ex <1>: \n+00022430: 2020 2020 5377 6570 7420 6c69 6e65 732e Swept lines.\n+00022440: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00022450: 3134 290a 2a20 6f72 6465 722c 2070 6f6c 14).* order, pol\n+00022460: 7967 6f6e 2076 6572 7465 7820 3c32 3e3a ygon vertex <2>:\n+00022470: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n+00022480: 7074 206c 696e 6573 2e20 2020 2020 2020 pt lines. \n+00022490: 2020 286c 696e 6520 2034 3029 0a2a 206f (line 40).* o\n+000224a0: 7264 6572 2c20 706f 6c79 676f 6e20 7665 rder, polygon ve\n+000224b0: 7274 6578 203c 333e 3a20 2020 2020 2020 rtex <3>: \n+000224c0: 2020 2020 2020 5377 6570 7420 706f 6c79 Swept poly\n+000224d0: 676f 6e73 2e20 2020 2020 2028 6c69 6e65 gons. (line\n+000224e0: 2020 3139 290a 2a20 6f72 6465 722c 2070 19).* order, p\n+000224f0: 6f6c 7967 6f6e 2076 6572 7465 7820 3c34 olygon vertex <4\n+00022500: 3e3a 2020 2020 2020 2020 2020 2020 204f >: O\n+00022510: 7665 7276 6965 772e 2020 2020 2020 2020 verview. \n+00022520: 2020 2020 286c 696e 6520 2033 3729 0a2a (line 37).*\n+00022530: 206f 7264 6572 2c20 706f 6c79 676f 6e20 order, polygon \n+00022540: 7665 7274 6578 203c 353e 3a20 2020 2020 vertex <5>: \n+00022550: 2020 2020 2020 2020 4f76 6572 7669 6577 Overview\n+00022560: 2e20 2020 2020 2020 2020 2020 2028 6c69 . (li\n+00022570: 6e65 2020 3535 290a 2a20 6f75 7470 7574 ne 55).* output\n+00022580: 206c 616e 6775 6167 653a 2020 2020 2020 language: \n 00022590: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000225a0: 2020 204c 616e 6775 6167 652e 2020 2020 Language. \n-000225b0: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n-000225c0: 3629 0a2a 206f 7574 7369 6465 206f 6620 6).* outside of \n-000225d0: 6120 706f 6c79 676f 6e3a 2020 2020 2020 a polygon: \n-000225e0: 2020 2020 2020 2020 2020 2020 4865 6c6c Hell\n-000225f0: 6f20 776f 726c 642e 2020 2020 2020 2020 o world. \n-00022600: 2028 6c69 6e65 2020 3337 290a 2a20 7061 (line 37).* pa\n-00022610: 7261 6c6c 656c 2070 726f 6a65 6374 696f rallel projectio\n-00022620: 6e3a 2020 2020 2020 2020 2020 2020 2020 n: \n-00022630: 2020 2020 2048 656c 6c6f 2077 6f72 6c64 Hello world\n-00022640: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n-00022650: 2032 3629 0a2a 2070 6172 616c 6c65 6c20 26).* parallel \n-00022660: 7072 6f6a 6563 7469 6f6e 203c 313e 3a20 projection <1>: \n-00022670: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n-00022680: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-00022690: 2e20 2028 6c69 6e65 2020 3138 290a 2a20 . (line 18).* \n-000226a0: 7061 7261 6c6c 656c 2070 726f 6a65 6374 parallel project\n-000226b0: 696f 6e20 3c32 3e3a 2020 2020 2020 2020 ion <2>: \n-000226c0: 2020 2020 2020 2050 6963 7475 7265 2062 Picture b\n-000226d0: 6f78 2e20 2020 2020 2020 2020 286c 696e ox. (lin\n-000226e0: 6520 2031 3529 0a2a 2070 6172 656e 7468 e 15).* parenth\n-000226f0: 6573 6573 3a20 2020 2020 2020 2020 2020 eses: \n-00022700: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022710: 5477 6f2d 6f70 6572 616e 6420 2862 696e Two-operand (bin\n-00022720: 6172 7929 2066 6f72 6d73 2e0a 2020 2020 ary) forms.. \n+000225a0: 204c 616e 6775 6167 652e 2020 2020 2020 Language. \n+000225b0: 2020 2020 2020 286c 696e 6520 2020 3629 (line 6)\n+000225c0: 0a2a 206f 7574 7369 6465 206f 6620 6120 .* outside of a \n+000225d0: 706f 6c79 676f 6e3a 2020 2020 2020 2020 polygon: \n+000225e0: 2020 2020 2020 2020 2020 4865 6c6c 6f20 Hello \n+000225f0: 776f 726c 642e 2020 2020 2020 2020 2028 world. (\n+00022600: 6c69 6e65 2020 3337 290a 2a20 7061 7261 line 37).* para\n+00022610: 6c6c 656c 2070 726f 6a65 6374 696f 6e3a llel projection:\n+00022620: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00022630: 2020 2048 656c 6c6f 2077 6f72 6c64 2e20 Hello world. \n+00022640: 2020 2020 2020 2020 286c 696e 6520 2032 (line 2\n+00022650: 3629 0a2a 2070 6172 616c 6c65 6c20 7072 6).* parallel pr\n+00022660: 6f6a 6563 7469 6f6e 203c 313e 3a20 2020 ojection <1>: \n+00022670: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n+00022680: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n+00022690: 2028 6c69 6e65 2020 3138 290a 2a20 7061 (line 18).* pa\n+000226a0: 7261 6c6c 656c 2070 726f 6a65 6374 696f rallel projectio\n+000226b0: 6e20 3c32 3e3a 2020 2020 2020 2020 2020 n <2>: \n+000226c0: 2020 2020 2050 6963 7475 7265 2062 6f78 Picture box\n+000226d0: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n+000226e0: 2031 3529 0a2a 2070 6172 656e 7468 6573 15).* parenthes\n+000226f0: 6573 3a20 2020 2020 2020 2020 2020 2020 es: \n+00022700: 2020 2020 2020 2020 2020 2020 2020 5477 Tw\n+00022710: 6f2d 6f70 6572 616e 6420 2862 696e 6172 o-operand (binar\n+00022720: 7929 2066 6f72 6d73 2e0a 2020 2020 2020 y) forms.. \n 00022730: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022740: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022750: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022760: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-00022770: 2035 3829 0a2a 2070 6572 7370 6563 7469 58).* perspecti\n-00022780: 7665 2070 726f 6a65 6374 696f 6e3a 2020 ve projection: \n-00022790: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n-000227a0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-000227b0: 2e20 2028 6c69 6e65 2020 3139 290a 2a20 . (line 19).* \n-000227c0: 7065 7273 7065 6374 6976 6520 7072 6f6a perspective proj\n-000227d0: 6563 7469 6f6e 203c 313e 3a20 2020 2020 ection <1>: \n-000227e0: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n-000227f0: 206c 6974 6572 616c 732e 2020 286c 696e literals. (lin\n-00022800: 6520 2032 3129 0a2a 2070 6572 7370 6563 e 21).* perspec\n-00022810: 7469 7665 2070 726f 6a65 6374 696f 6e20 tive projection \n-00022820: 3c32 3e3a 2020 2020 2020 2020 2020 2020 <2>: \n-00022830: 4f76 6572 7669 6577 2e20 2020 2020 2020 Overview. \n-00022840: 2020 2020 2028 6c69 6e65 2020 2037 290a (line 7).\n-00022850: 2a20 7069 6374 7572 6520 626f 783a 2020 * picture box: \n+00022760: 2020 2020 2020 2020 286c 696e 6520 2035 (line 5\n+00022770: 3829 0a2a 2070 6572 7370 6563 7469 7665 8).* perspective\n+00022780: 2070 726f 6a65 6374 696f 6e3a 2020 2020 projection: \n+00022790: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n+000227a0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n+000227b0: 2028 6c69 6e65 2020 3139 290a 2a20 7065 (line 19).* pe\n+000227c0: 7273 7065 6374 6976 6520 7072 6f6a 6563 rspective projec\n+000227d0: 7469 6f6e 203c 313e 3a20 2020 2020 2020 tion <1>: \n+000227e0: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n+000227f0: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n+00022800: 2032 3129 0a2a 2070 6572 7370 6563 7469 21).* perspecti\n+00022810: 7665 2070 726f 6a65 6374 696f 6e20 3c32 ve projection <2\n+00022820: 3e3a 2020 2020 2020 2020 2020 2020 4f76 >: Ov\n+00022830: 6572 7669 6577 2e20 2020 2020 2020 2020 erview. \n+00022840: 2020 2028 6c69 6e65 2020 2037 290a 2a20 (line 7).* \n+00022850: 7069 6374 7572 6520 626f 783a 2020 2020 picture box: \n 00022860: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022870: 2020 2020 2020 2020 2050 6963 7475 7265 Picture\n-00022880: 2062 6f78 2e20 2020 2020 2020 2020 286c box. (l\n-00022890: 696e 6520 2020 3629 0a2a 2070 6c61 6e61 ine 6).* plana\n-000228a0: 7269 7479 206f 6620 706f 6c79 676f 6e73 rity of polygons\n-000228b0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-000228c0: 2020 506f 6c79 676f 6e73 2e20 2020 2020 Polygons. \n-000228d0: 2020 2020 2020 2028 6c69 6e65 2020 3130 (line 10\n-000228e0: 290a 2a20 706c 616e 6172 6974 7920 6f66 ).* planarity of\n-000228f0: 2070 6f6c 7967 6f6e 7320 3c31 3e3a 2020 polygons <1>: \n-00022900: 2020 2020 2020 2020 2020 2053 7765 6570 Sweep\n-00022910: 2066 6163 6520 7370 6c69 7474 696e 672e face splitting.\n-00022920: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n+00022870: 2020 2020 2020 2050 6963 7475 7265 2062 Picture b\n+00022880: 6f78 2e20 2020 2020 2020 2020 286c 696e ox. (lin\n+00022890: 6520 2020 3629 0a2a 2070 6c61 6e61 7269 e 6).* planari\n+000228a0: 7479 206f 6620 706f 6c79 676f 6e73 3a20 ty of polygons: \n+000228b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000228c0: 506f 6c79 676f 6e73 2e20 2020 2020 2020 Polygons. \n+000228d0: 2020 2020 2028 6c69 6e65 2020 3130 290a (line 10).\n+000228e0: 2a20 706c 616e 6172 6974 7920 6f66 2070 * planarity of p\n+000228f0: 6f6c 7967 6f6e 7320 3c31 3e3a 2020 2020 olygons <1>: \n+00022900: 2020 2020 2020 2020 2053 7765 6570 2066 Sweep f\n+00022910: 6163 6520 7370 6c69 7474 696e 672e 0a20 ace splitting.. \n+00022920: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022930: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022940: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022950: 2020 2020 2020 2020 2020 2020 2020 2028 (\n-00022960: 6c69 6e65 2020 2037 290a 2a20 706f 696e line 7).* poin\n-00022970: 7420 6465 6669 6e69 7469 6f6e 3a20 2020 t definition: \n+00022950: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+00022960: 6e65 2020 2037 290a 2a20 706f 696e 7420 ne 7).* point \n+00022970: 6465 6669 6e69 7469 6f6e 3a20 2020 2020 definition: \n 00022980: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022990: 2020 2044 7261 7769 6e67 2061 2073 6f6c Drawing a sol\n-000229a0: 6964 2e20 2020 2020 286c 696e 6520 2032 id. (line 2\n-000229b0: 3329 0a2a 2070 6f69 6e74 206c 6973 743a 3).* point list:\n+00022990: 2044 7261 7769 6e67 2061 2073 6f6c 6964 Drawing a solid\n+000229a0: 2e20 2020 2020 286c 696e 6520 2032 3329 . (line 23)\n+000229b0: 0a2a 2070 6f69 6e74 206c 6973 743a 2020 .* point list: \n 000229c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000229d0: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n-000229e0: 7420 706f 696e 7473 2e20 2020 2020 2020 t points. \n-000229f0: 2028 6c69 6e65 2020 2039 290a 2a20 706f (line 9).* po\n-00022a00: 696e 7420 6c69 7465 7261 6c3a 2020 2020 int literal: \n+000229d0: 2020 2020 2020 2020 2020 5377 6570 7420 Swept \n+000229e0: 706f 696e 7473 2e20 2020 2020 2020 2028 points. (\n+000229f0: 6c69 6e65 2020 2039 290a 2a20 706f 696e line 9).* poin\n+00022a00: 7420 6c69 7465 7261 6c3a 2020 2020 2020 t literal: \n 00022a10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022a20: 2020 2020 2050 6f69 6e74 2061 6e64 2076 Point and v\n-00022a30: 6563 746f 7220 6c69 7465 7261 6c73 2e0a ector literals..\n+00022a20: 2020 2050 6f69 6e74 2061 6e64 2076 6563 Point and vec\n+00022a30: 746f 7220 6c69 7465 7261 6c73 2e0a 2020 tor literals.. \n 00022a40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022a50: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022a60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022a70: 2020 2020 2020 2020 2020 2020 2020 286c (l\n-00022a80: 696e 6520 2020 3629 0a2a 2070 6f69 6e74 ine 6).* point\n-00022a90: 2072 6566 6572 656e 6365 3a20 2020 2020 reference: \n+00022a70: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+00022a80: 6520 2020 3629 0a2a 2070 6f69 6e74 2072 e 6).* point r\n+00022a90: 6566 6572 656e 6365 3a20 2020 2020 2020 eference: \n 00022aa0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022ab0: 2020 466f 726d 7320 6f66 2072 6566 6572 Forms of refer\n-00022ac0: 656e 6365 732e 2028 6c69 6e65 2020 3134 ences. (line 14\n-00022ad0: 290a 2a20 706f 696e 7420 7377 6565 703a ).* point sweep:\n+00022ab0: 466f 726d 7320 6f66 2072 6566 6572 656e Forms of referen\n+00022ac0: 6365 732e 2028 6c69 6e65 2020 3134 290a ces. (line 14).\n+00022ad0: 2a20 706f 696e 7420 7377 6565 703a 2020 * point sweep: \n 00022ae0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022af0: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n-00022b00: 206f 626a 6563 7473 2e20 2020 2020 2020 objects. \n-00022b10: 286c 696e 6520 2031 3129 0a2a 2070 6f69 (line 11).* poi\n-00022b20: 6e74 2073 7765 6570 203c 313e 3a20 2020 nt sweep <1>: \n+00022af0: 2020 2020 2020 2020 2053 7765 7074 206f Swept o\n+00022b00: 626a 6563 7473 2e20 2020 2020 2020 286c bjects. (l\n+00022b10: 696e 6520 2031 3129 0a2a 2070 6f69 6e74 ine 11).* point\n+00022b20: 2073 7765 6570 203c 313e 3a20 2020 2020 sweep <1>: \n 00022b30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022b40: 2020 2020 5377 6570 7420 706f 696e 7473 Swept points\n-00022b50: 2e20 2020 2020 2020 2028 6c69 6e65 2020 . (line \n-00022b60: 2036 290a 2a20 706f 6c79 676f 6e20 7377 6).* polygon sw\n-00022b70: 6565 703a 2020 2020 2020 2020 2020 2020 eep: \n-00022b80: 2020 2020 2020 2020 2020 2020 2050 6f6c Pol\n-00022b90: 7967 6f6e 2073 7765 6570 732e 2020 2020 ygon sweeps. \n-00022ba0: 2020 286c 696e 6520 2020 3629 0a2a 2070 (line 6).* p\n-00022bb0: 6f6c 7967 6f6e 2073 7765 6570 203c 313e olygon sweep <1>\n-00022bc0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00022bd0: 2020 2020 2020 5377 6570 7420 706f 6c79 Swept poly\n-00022be0: 676f 6e73 2e20 2020 2020 2028 6c69 6e65 gons. (line\n-00022bf0: 2020 2036 290a 2a20 706f 6c79 676f 6e20 6).* polygon \n-00022c00: 7377 6565 7020 3c32 3e3a 2020 2020 2020 sweep <2>: \n-00022c10: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-00022c20: 2068 6965 7261 7263 6869 6361 6c20 6d6f hierarchical mo\n-00022c30: 6465 6c2e 0a20 2020 2020 2020 2020 2020 del.. \n+00022b40: 2020 5377 6570 7420 706f 696e 7473 2e20 Swept points. \n+00022b50: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n+00022b60: 290a 2a20 706f 6c79 676f 6e20 7377 6565 ).* polygon swee\n+00022b70: 703a 2020 2020 2020 2020 2020 2020 2020 p: \n+00022b80: 2020 2020 2020 2020 2020 2050 6f6c 7967 Polyg\n+00022b90: 6f6e 2073 7765 6570 732e 2020 2020 2020 on sweeps. \n+00022ba0: 286c 696e 6520 2020 3629 0a2a 2070 6f6c (line 6).* pol\n+00022bb0: 7967 6f6e 2073 7765 6570 203c 313e 3a20 ygon sweep <1>: \n+00022bc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00022bd0: 2020 2020 5377 6570 7420 706f 6c79 676f Swept polygo\n+00022be0: 6e73 2e20 2020 2020 2028 6c69 6e65 2020 ns. (line \n+00022bf0: 2036 290a 2a20 706f 6c79 676f 6e20 7377 6).* polygon sw\n+00022c00: 6565 7020 3c32 3e3a 2020 2020 2020 2020 eep <2>: \n+00022c10: 2020 2020 2020 2020 2020 2020 2041 2068 A h\n+00022c20: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n+00022c30: 6c2e 0a20 2020 2020 2020 2020 2020 2020 l.. \n 00022c40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022c50: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022c60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022c70: 2020 2028 6c69 6e65 2031 3232 290a 2a20 (line 122).* \n-00022c80: 706f 6c79 676f 6e20 7665 7274 6578 206f polygon vertex o\n-00022c90: 7264 6572 3a20 2020 2020 2020 2020 2020 rder: \n-00022ca0: 2020 2020 2020 2048 656c 6c6f 2077 6f72 Hello wor\n-00022cb0: 6c64 2e20 2020 2020 2020 2020 286c 696e ld. (lin\n-00022cc0: 6520 2033 3929 0a2a 2070 6f6c 7967 6f6e e 39).* polygon\n-00022cd0: 2076 6572 7465 7820 6f72 6465 7220 3c31 vertex order <1\n-00022ce0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-00022cf0: 5377 6570 7420 6c69 6e65 732e 2020 2020 Swept lines. \n-00022d00: 2020 2020 2028 6c69 6e65 2020 3134 290a (line 14).\n-00022d10: 2a20 706f 6c79 676f 6e20 7665 7274 6578 * polygon vertex\n-00022d20: 206f 7264 6572 203c 323e 3a20 2020 2020 order <2>: \n-00022d30: 2020 2020 2020 2020 2053 7765 7074 206c Swept l\n-00022d40: 696e 6573 2e20 2020 2020 2020 2020 286c ines. (l\n-00022d50: 696e 6520 2034 3029 0a2a 2070 6f6c 7967 ine 40).* polyg\n-00022d60: 6f6e 2076 6572 7465 7820 6f72 6465 7220 on vertex order \n-00022d70: 3c33 3e3a 2020 2020 2020 2020 2020 2020 <3>: \n-00022d80: 2020 5377 6570 7420 706f 6c79 676f 6e73 Swept polygons\n-00022d90: 2e20 2020 2020 2028 6c69 6e65 2020 3139 . (line 19\n-00022da0: 290a 2a20 706f 6c79 676f 6e20 7665 7274 ).* polygon vert\n-00022db0: 6578 206f 7264 6572 203c 343e 3a20 2020 ex order <4>: \n-00022dc0: 2020 2020 2020 2020 2020 204f 7665 7276 Overv\n-00022dd0: 6965 772e 2020 2020 2020 2020 2020 2020 iew. \n-00022de0: 286c 696e 6520 2033 3729 0a2a 2070 6f6c (line 37).* pol\n-00022df0: 7967 6f6e 2076 6572 7465 7820 6f72 6465 ygon vertex orde\n-00022e00: 7220 3c35 3e3a 2020 2020 2020 2020 2020 r <5>: \n-00022e10: 2020 2020 4f76 6572 7669 6577 2e20 2020 Overview. \n-00022e20: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00022e30: 3535 290a 2a20 706f 6c79 676f 6e2c 2062 55).* polygon, b\n-00022e40: 6f64 793a 2020 2020 2020 2020 2020 2020 ody: \n-00022e50: 2020 2020 2020 2020 2020 2020 2049 6e74 Int\n-00022e60: 6572 6e61 6c20 6f70 7469 6f6e 732e 2020 ernal options. \n-00022e70: 2020 286c 696e 6520 2031 3629 0a2a 2070 (line 16).* p\n-00022e80: 6f6c 7967 6f6e 2c20 626f 6479 203c 313e olygon, body <1>\n-00022e90: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00022ea0: 2020 2020 2020 5377 6570 7420 6c69 6e65 Swept line\n-00022eb0: 732e 2020 2020 2020 2020 2028 6c69 6e65 s. (line\n-00022ec0: 2020 3130 290a 2a20 706f 6c79 676f 6e2c 10).* polygon,\n-00022ed0: 2062 6f64 7920 3c32 3e3a 2020 2020 2020 body <2>: \n-00022ee0: 2020 2020 2020 2020 2020 2020 2020 2053 S\n-00022ef0: 7765 7074 2070 6f6c 7967 6f6e 732e 2020 wept polygons. \n-00022f00: 2020 2020 286c 696e 6520 2020 3929 0a2a (line 9).*\n-00022f10: 2070 6f6c 7967 6f6e 2c20 656e 643a 2020 polygon, end: \n+00022c70: 2028 6c69 6e65 2031 3232 290a 2a20 706f (line 122).* po\n+00022c80: 6c79 676f 6e20 7665 7274 6578 206f 7264 lygon vertex ord\n+00022c90: 6572 3a20 2020 2020 2020 2020 2020 2020 er: \n+00022ca0: 2020 2020 2048 656c 6c6f 2077 6f72 6c64 Hello world\n+00022cb0: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n+00022cc0: 2033 3929 0a2a 2070 6f6c 7967 6f6e 2076 39).* polygon v\n+00022cd0: 6572 7465 7820 6f72 6465 7220 3c31 3e3a ertex order <1>:\n+00022ce0: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n+00022cf0: 6570 7420 6c69 6e65 732e 2020 2020 2020 ept lines. \n+00022d00: 2020 2028 6c69 6e65 2020 3134 290a 2a20 (line 14).* \n+00022d10: 706f 6c79 676f 6e20 7665 7274 6578 206f polygon vertex o\n+00022d20: 7264 6572 203c 323e 3a20 2020 2020 2020 rder <2>: \n+00022d30: 2020 2020 2020 2053 7765 7074 206c 696e Swept lin\n+00022d40: 6573 2e20 2020 2020 2020 2020 286c 696e es. (lin\n+00022d50: 6520 2034 3029 0a2a 2070 6f6c 7967 6f6e e 40).* polygon\n+00022d60: 2076 6572 7465 7820 6f72 6465 7220 3c33 vertex order <3\n+00022d70: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00022d80: 5377 6570 7420 706f 6c79 676f 6e73 2e20 Swept polygons. \n+00022d90: 2020 2020 2028 6c69 6e65 2020 3139 290a (line 19).\n+00022da0: 2a20 706f 6c79 676f 6e20 7665 7274 6578 * polygon vertex\n+00022db0: 206f 7264 6572 203c 343e 3a20 2020 2020 order <4>: \n+00022dc0: 2020 2020 2020 2020 204f 7665 7276 6965 Overvie\n+00022dd0: 772e 2020 2020 2020 2020 2020 2020 286c w. (l\n+00022de0: 696e 6520 2033 3729 0a2a 2070 6f6c 7967 ine 37).* polyg\n+00022df0: 6f6e 2076 6572 7465 7820 6f72 6465 7220 on vertex order \n+00022e00: 3c35 3e3a 2020 2020 2020 2020 2020 2020 <5>: \n+00022e10: 2020 4f76 6572 7669 6577 2e20 2020 2020 Overview. \n+00022e20: 2020 2020 2020 2028 6c69 6e65 2020 3535 (line 55\n+00022e30: 290a 2a20 706f 6c79 676f 6e2c 2062 6f64 ).* polygon, bod\n+00022e40: 793a 2020 2020 2020 2020 2020 2020 2020 y: \n+00022e50: 2020 2020 2020 2020 2020 2049 6e74 6572 Inter\n+00022e60: 6e61 6c20 6f70 7469 6f6e 732e 2020 2020 nal options. \n+00022e70: 286c 696e 6520 2031 3629 0a2a 2070 6f6c (line 16).* pol\n+00022e80: 7967 6f6e 2c20 626f 6479 203c 313e 3a20 ygon, body <1>: \n+00022e90: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00022ea0: 2020 2020 5377 6570 7420 6c69 6e65 732e Swept lines.\n+00022eb0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00022ec0: 3130 290a 2a20 706f 6c79 676f 6e2c 2062 10).* polygon, b\n+00022ed0: 6f64 7920 3c32 3e3a 2020 2020 2020 2020 ody <2>: \n+00022ee0: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n+00022ef0: 7074 2070 6f6c 7967 6f6e 732e 2020 2020 pt polygons. \n+00022f00: 2020 286c 696e 6520 2020 3929 0a2a 2070 (line 9).* p\n+00022f10: 6f6c 7967 6f6e 2c20 656e 643a 2020 2020 olygon, end: \n 00022f20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022f30: 2020 2020 2020 2020 5377 6570 7420 6c69 Swept li\n-00022f40: 6e65 732e 2020 2020 2020 2020 2028 6c69 nes. (li\n-00022f50: 6e65 2020 3338 290a 2a20 706f 6c79 676f ne 38).* polygo\n-00022f60: 6e2c 2065 6e64 203c 313e 3a20 2020 2020 n, end <1>: \n-00022f70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022f80: 2053 7765 7074 2070 6f6c 7967 6f6e 732e Swept polygons.\n-00022f90: 2020 2020 2020 286c 696e 6520 2031 3529 (line 15)\n-00022fa0: 0a2a 2070 6f6c 7967 6f6e 2c20 6f75 7473 .* polygon, outs\n-00022fb0: 6964 6520 6f66 3a20 2020 2020 2020 2020 ide of: \n-00022fc0: 2020 2020 2020 2020 2020 4865 6c6c 6f20 Hello \n-00022fd0: 776f 726c 642e 2020 2020 2020 2020 2028 world. (\n-00022fe0: 6c69 6e65 2020 3337 290a 2a20 706f 6c79 line 37).* poly\n-00022ff0: 676f 6e2c 2070 6c61 6e61 723a 2020 2020 gon, planar: \n+00022f30: 2020 2020 2020 5377 6570 7420 6c69 6e65 Swept line\n+00022f40: 732e 2020 2020 2020 2020 2028 6c69 6e65 s. (line\n+00022f50: 2020 3338 290a 2a20 706f 6c79 676f 6e2c 38).* polygon,\n+00022f60: 2065 6e64 203c 313e 3a20 2020 2020 2020 end <1>: \n+00022f70: 2020 2020 2020 2020 2020 2020 2020 2053 S\n+00022f80: 7765 7074 2070 6f6c 7967 6f6e 732e 2020 wept polygons. \n+00022f90: 2020 2020 286c 696e 6520 2031 3529 0a2a (line 15).*\n+00022fa0: 2070 6f6c 7967 6f6e 2c20 6f75 7473 6964 polygon, outsid\n+00022fb0: 6520 6f66 3a20 2020 2020 2020 2020 2020 e of: \n+00022fc0: 2020 2020 2020 2020 4865 6c6c 6f20 776f Hello wo\n+00022fd0: 726c 642e 2020 2020 2020 2020 2028 6c69 rld. (li\n+00022fe0: 6e65 2020 3337 290a 2a20 706f 6c79 676f ne 37).* polygo\n+00022ff0: 6e2c 2070 6c61 6e61 723a 2020 2020 2020 n, planar: \n 00023000: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023010: 2020 2050 6f6c 7967 6f6e 732e 2020 2020 Polygons. \n-00023020: 2020 2020 2020 2020 286c 696e 6520 2031 (line 1\n-00023030: 3029 0a2a 2070 6f6c 7967 6f6e 2c20 706c 0).* polygon, pl\n-00023040: 616e 6172 203c 313e 3a20 2020 2020 2020 anar <1>: \n-00023050: 2020 2020 2020 2020 2020 2020 5377 6565 Swee\n-00023060: 7020 6661 6365 2073 706c 6974 7469 6e67 p face splitting\n-00023070: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+00023010: 2050 6f6c 7967 6f6e 732e 2020 2020 2020 Polygons. \n+00023020: 2020 2020 2020 286c 696e 6520 2031 3029 (line 10)\n+00023030: 0a2a 2070 6f6c 7967 6f6e 2c20 706c 616e .* polygon, plan\n+00023040: 6172 203c 313e 3a20 2020 2020 2020 2020 ar <1>: \n+00023050: 2020 2020 2020 2020 2020 5377 6565 7020 Sweep \n+00023060: 6661 6365 2073 706c 6974 7469 6e67 2e0a face splitting..\n+00023070: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023080: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023090: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000230a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000230b0: 286c 696e 6520 2020 3729 0a2a 2070 7265 (line 7).* pre\n-000230c0: 6365 6465 6e63 652c 206f 7065 7261 746f cedence, operato\n-000230d0: 723a 2020 2020 2020 2020 2020 2020 2020 r: \n-000230e0: 2020 2020 5477 6f2d 6f70 6572 616e 6420 Two-operand \n-000230f0: 2862 696e 6172 7929 2066 6f72 6d73 2e0a (binary) forms..\n+000230a0: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+000230b0: 696e 6520 2020 3729 0a2a 2070 7265 6365 ine 7).* prece\n+000230c0: 6465 6e63 652c 206f 7065 7261 746f 723a dence, operator:\n+000230d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000230e0: 2020 5477 6f2d 6f70 6572 616e 6420 2862 Two-operand (b\n+000230f0: 696e 6172 7929 2066 6f72 6d73 2e0a 2020 inary) forms.. \n 00023100: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023110: 2020 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 286c (l\n-00023140: 696e 6520 2034 3529 0a2a 2070 726f 6772 ine 45).* progr\n-00023150: 616d 2c20 6865 6c6c 6f20 776f 726c 643a am, hello world:\n+00023130: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+00023140: 6520 2034 3529 0a2a 2070 726f 6772 616d e 45).* program\n+00023150: 2c20 6865 6c6c 6f20 776f 726c 643a 2020 , hello world: \n 00023160: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023170: 2020 4865 6c6c 6f20 776f 726c 642e 2020 Hello world. \n-00023180: 2020 2020 2020 2028 6c69 6e65 2020 2037 (line 7\n-00023190: 290a 2a20 7072 6f6a 6563 7469 6f6e 2c20 ).* projection, \n-000231a0: 7061 7261 6c6c 656c 3a20 2020 2020 2020 parallel: \n-000231b0: 2020 2020 2020 2020 2020 2048 656c 6c6f Hello\n-000231c0: 2077 6f72 6c64 2e20 2020 2020 2020 2020 world. \n-000231d0: 286c 696e 6520 2032 3629 0a2a 2070 726f (line 26).* pro\n-000231e0: 6a65 6374 696f 6e2c 2070 6172 616c 6c65 jection, paralle\n-000231f0: 6c20 3c31 3e3a 2020 2020 2020 2020 2020 l <1>: \n-00023200: 2020 2020 5472 616e 7366 6f72 6d20 6c69 Transform li\n-00023210: 7465 7261 6c73 2e20 2028 6c69 6e65 2020 terals. (line \n-00023220: 3138 290a 2a20 7072 6f6a 6563 7469 6f6e 18).* projection\n-00023230: 2c20 7061 7261 6c6c 656c 203c 323e 3a20 , parallel <2>: \n-00023240: 2020 2020 2020 2020 2020 2020 2050 6963 Pic\n-00023250: 7475 7265 2062 6f78 2e20 2020 2020 2020 ture box. \n-00023260: 2020 286c 696e 6520 2031 3529 0a2a 2070 (line 15).* p\n-00023270: 726f 6a65 6374 696f 6e2c 2070 6572 7370 rojection, persp\n-00023280: 6563 7469 7665 3a20 2020 2020 2020 2020 ective: \n-00023290: 2020 2020 2020 5472 616e 7366 6f72 6d20 Transform \n-000232a0: 6c69 7465 7261 6c73 2e20 2028 6c69 6e65 literals. (line\n-000232b0: 2020 3139 290a 2a20 7072 6f6a 6563 7469 19).* projecti\n-000232c0: 6f6e 2c20 7065 7273 7065 6374 6976 6520 on, perspective \n-000232d0: 3c31 3e3a 2020 2020 2020 2020 2020 2054 <1>: T\n-000232e0: 7261 6e73 666f 726d 206c 6974 6572 616c ransform literal\n-000232f0: 732e 2020 286c 696e 6520 2032 3129 0a2a s. (line 21).*\n-00023300: 2070 726f 6a65 6374 696f 6e2c 2070 6572 projection, per\n-00023310: 7370 6563 7469 7665 203c 323e 3a20 2020 spective <2>: \n-00023320: 2020 2020 2020 2020 4f76 6572 7669 6577 Overview\n-00023330: 2e20 2020 2020 2020 2020 2020 2028 6c69 . (li\n-00023340: 6e65 2020 2037 290a 2a20 7073 6575 646f ne 7).* pseudo\n-00023350: 2d6f 7074 696f 6e73 3a20 2020 2020 2020 -options: \n-00023360: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023370: 2054 696b 5a2f 5047 4620 7573 6572 2d64 TikZ/PGF user-d\n-00023380: 6566 696e 6564 2073 7479 6c65 732e 0a20 efined styles.. \n+00023170: 4865 6c6c 6f20 776f 726c 642e 2020 2020 Hello world. \n+00023180: 2020 2020 2028 6c69 6e65 2020 2037 290a (line 7).\n+00023190: 2a20 7072 6f6a 6563 7469 6f6e 2c20 7061 * projection, pa\n+000231a0: 7261 6c6c 656c 3a20 2020 2020 2020 2020 rallel: \n+000231b0: 2020 2020 2020 2020 2048 656c 6c6f 2077 Hello w\n+000231c0: 6f72 6c64 2e20 2020 2020 2020 2020 286c orld. (l\n+000231d0: 696e 6520 2032 3629 0a2a 2070 726f 6a65 ine 26).* proje\n+000231e0: 6374 696f 6e2c 2070 6172 616c 6c65 6c20 ction, parallel \n+000231f0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n+00023200: 2020 5472 616e 7366 6f72 6d20 6c69 7465 Transform lite\n+00023210: 7261 6c73 2e20 2028 6c69 6e65 2020 3138 rals. (line 18\n+00023220: 290a 2a20 7072 6f6a 6563 7469 6f6e 2c20 ).* projection, \n+00023230: 7061 7261 6c6c 656c 203c 323e 3a20 2020 parallel <2>: \n+00023240: 2020 2020 2020 2020 2020 2050 6963 7475 Pictu\n+00023250: 7265 2062 6f78 2e20 2020 2020 2020 2020 re box. \n+00023260: 286c 696e 6520 2031 3529 0a2a 2070 726f (line 15).* pro\n+00023270: 6a65 6374 696f 6e2c 2070 6572 7370 6563 jection, perspec\n+00023280: 7469 7665 3a20 2020 2020 2020 2020 2020 tive: \n+00023290: 2020 2020 5472 616e 7366 6f72 6d20 6c69 Transform li\n+000232a0: 7465 7261 6c73 2e20 2028 6c69 6e65 2020 terals. (line \n+000232b0: 3139 290a 2a20 7072 6f6a 6563 7469 6f6e 19).* projection\n+000232c0: 2c20 7065 7273 7065 6374 6976 6520 3c31 , perspective <1\n+000232d0: 3e3a 2020 2020 2020 2020 2020 2054 7261 >: Tra\n+000232e0: 6e73 666f 726d 206c 6974 6572 616c 732e nsform literals.\n+000232f0: 2020 286c 696e 6520 2032 3129 0a2a 2070 (line 21).* p\n+00023300: 726f 6a65 6374 696f 6e2c 2070 6572 7370 rojection, persp\n+00023310: 6563 7469 7665 203c 323e 3a20 2020 2020 ective <2>: \n+00023320: 2020 2020 2020 4f76 6572 7669 6577 2e20 Overview. \n+00023330: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+00023340: 2020 2037 290a 2a20 7073 6575 646f 2d6f 7).* pseudo-o\n+00023350: 7074 696f 6e73 3a20 2020 2020 2020 2020 ptions: \n+00023360: 2020 2020 2020 2020 2020 2020 2020 2054 T\n+00023370: 696b 5a2f 5047 4620 7573 6572 2d64 6566 ikZ/PGF user-def\n+00023380: 696e 6564 2073 7479 6c65 732e 0a20 2020 ined styles.. \n 00023390: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000233a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000233b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000233c0: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-000233d0: 6e65 2020 3235 290a 2a20 7073 6672 616d ne 25).* psfram\n-000233e0: 6562 6f78 3a20 2020 2020 2020 2020 2020 ebox: \n-000233f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023400: 2046 7261 6d65 2e20 2020 2020 2020 2020 Frame. \n-00023410: 2020 2020 2020 286c 696e 6520 2020 3829 (line 8)\n-00023420: 0a2a 2070 7370 6963 7475 7265 3a20 2020 .* pspicture: \n+000233c0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+000233d0: 2020 3235 290a 2a20 7073 6672 616d 6562 25).* psframeb\n+000233e0: 6f78 3a20 2020 2020 2020 2020 2020 2020 ox: \n+000233f0: 2020 2020 2020 2020 2020 2020 2020 2046 F\n+00023400: 7261 6d65 2e20 2020 2020 2020 2020 2020 rame. \n+00023410: 2020 2020 286c 696e 6520 2020 3829 0a2a (line 8).*\n+00023420: 2070 7370 6963 7475 7265 3a20 2020 2020 pspicture: \n 00023430: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023440: 2020 2020 2020 2020 2020 5069 6374 7572 Pictur\n-00023450: 6520 626f 782e 2020 2020 2020 2020 2028 e box. (\n-00023460: 6c69 6e65 2020 3130 290a 2a20 5053 5472 line 10).* PSTr\n-00023470: 6963 6b73 3a20 2020 2020 2020 2020 2020 icks: \n+00023440: 2020 2020 2020 2020 5069 6374 7572 6520 Picture \n+00023450: 626f 782e 2020 2020 2020 2020 2028 6c69 box. (li\n+00023460: 6e65 2020 3130 290a 2a20 5053 5472 6963 ne 10).* PSTric\n+00023470: 6b73 3a20 2020 2020 2020 2020 2020 2020 ks: \n 00023480: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023490: 2020 2041 626f 7574 2073 6b65 7463 682e About sketch.\n-000234a0: 2020 2020 2020 2020 286c 696e 6520 2032 (line 2\n-000234b0: 3129 0a2a 2071 756f 7469 6e67 2c20 7370 1).* quoting, sp\n-000234c0: 6563 6961 6c3a 2020 2020 2020 2020 2020 ecial: \n-000234d0: 2020 2020 2020 2020 2020 2020 5370 6563 Spec\n-000234e0: 6961 6c20 6f62 6a65 6374 732e 2020 2020 ial objects. \n-000234f0: 2028 6c69 6e65 2020 3230 290a 2a20 7175 (line 20).* qu\n-00023500: 6f74 696e 672c 2073 7065 6369 616c 203c oting, special <\n-00023510: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n-00023520: 2020 2020 2053 7065 6369 616c 732e 2020 Specials. \n-00023530: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-00023540: 2020 3829 0a2a 2072 6566 6572 656e 6365 8).* reference\n-00023550: 2c20 6472 6177 6162 6c65 3a20 2020 2020 , drawable: \n-00023560: 2020 2020 2020 2020 2020 2020 2020 4f62 Ob\n-00023570: 6a65 6374 2074 7261 6e73 666f 726d 732e ject transforms.\n-00023580: 2020 2028 6c69 6e65 2020 3333 290a 2a20 (line 33).* \n-00023590: 7265 6665 7265 6e63 652c 2064 7261 7761 reference, drawa\n-000235a0: 626c 6520 3c31 3e3a 2020 2020 2020 2020 ble <1>: \n-000235b0: 2020 2020 2020 2046 6f72 6d73 206f 6620 Forms of \n-000235c0: 7265 6665 7265 6e63 6573 2e20 286c 696e references. (lin\n-000235d0: 6520 2031 3729 0a2a 2072 6566 6572 656e e 17).* referen\n-000235e0: 6365 2c20 6472 6177 6162 6c65 203c 323e ce, drawable <2>\n-000235f0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00023600: 4f76 6572 7669 6577 2e20 2020 2020 2020 Overview. \n-00023610: 2020 2020 2028 6c69 6e65 2020 3437 290a (line 47).\n-00023620: 2a20 7265 6665 7265 6e63 652c 2064 7261 * reference, dra\n-00023630: 7761 626c 6520 3c33 3e3a 2020 2020 2020 wable <3>: \n-00023640: 2020 2020 2020 2020 204f 7665 7276 6965 Overvie\n-00023650: 772e 2020 2020 2020 2020 2020 2020 286c w. (l\n-00023660: 696e 6520 2035 3729 0a2a 2072 6566 6572 ine 57).* refer\n-00023670: 656e 6365 2c20 6d75 6c74 6970 6c65 206f ence, multiple o\n-00023680: 7074 696f 6e73 3a20 2020 2020 2020 2020 ptions: \n-00023690: 2020 466f 726d 7320 6f66 2072 6566 6572 Forms of refer\n-000236a0: 656e 6365 732e 2028 6c69 6e65 2020 3138 ences. (line 18\n-000236b0: 290a 2a20 7265 6665 7265 6e63 652c 206f ).* reference, o\n-000236c0: 7074 696f 6e73 3a20 2020 2020 2020 2020 ptions: \n-000236d0: 2020 2020 2020 2020 2020 2050 6f6c 796c Polyl\n-000236e0: 696e 6520 7377 6565 7073 2077 6974 6820 ine sweeps with \n-000236f0: 636c 6f73 7572 652e 0a20 2020 2020 2020 closure.. \n+00023490: 2041 626f 7574 2073 6b65 7463 682e 2020 About sketch. \n+000234a0: 2020 2020 2020 286c 696e 6520 2032 3129 (line 21)\n+000234b0: 0a2a 2071 756f 7469 6e67 2c20 7370 6563 .* quoting, spec\n+000234c0: 6961 6c3a 2020 2020 2020 2020 2020 2020 ial: \n+000234d0: 2020 2020 2020 2020 2020 5370 6563 6961 Specia\n+000234e0: 6c20 6f62 6a65 6374 732e 2020 2020 2028 l objects. (\n+000234f0: 6c69 6e65 2020 3230 290a 2a20 7175 6f74 line 20).* quot\n+00023500: 696e 672c 2073 7065 6369 616c 203c 313e ing, special <1>\n+00023510: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00023520: 2020 2053 7065 6369 616c 732e 2020 2020 Specials. \n+00023530: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n+00023540: 3829 0a2a 2072 6566 6572 656e 6365 2c20 8).* reference, \n+00023550: 6472 6177 6162 6c65 3a20 2020 2020 2020 drawable: \n+00023560: 2020 2020 2020 2020 2020 2020 4f62 6a65 Obje\n+00023570: 6374 2074 7261 6e73 666f 726d 732e 2020 ct transforms. \n+00023580: 2028 6c69 6e65 2020 3333 290a 2a20 7265 (line 33).* re\n+00023590: 6665 7265 6e63 652c 2064 7261 7761 626c ference, drawabl\n+000235a0: 6520 3c31 3e3a 2020 2020 2020 2020 2020 e <1>: \n+000235b0: 2020 2020 2046 6f72 6d73 206f 6620 7265 Forms of re\n+000235c0: 6665 7265 6e63 6573 2e20 286c 696e 6520 ferences. (line \n+000235d0: 2031 3729 0a2a 2072 6566 6572 656e 6365 17).* reference\n+000235e0: 2c20 6472 6177 6162 6c65 203c 323e 3a20 , drawable <2>: \n+000235f0: 2020 2020 2020 2020 2020 2020 2020 4f76 Ov\n+00023600: 6572 7669 6577 2e20 2020 2020 2020 2020 erview. \n+00023610: 2020 2028 6c69 6e65 2020 3437 290a 2a20 (line 47).* \n+00023620: 7265 6665 7265 6e63 652c 2064 7261 7761 reference, drawa\n+00023630: 626c 6520 3c33 3e3a 2020 2020 2020 2020 ble <3>: \n+00023640: 2020 2020 2020 204f 7665 7276 6965 772e Overview.\n+00023650: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+00023660: 6520 2035 3729 0a2a 2072 6566 6572 656e e 57).* referen\n+00023670: 6365 2c20 6d75 6c74 6970 6c65 206f 7074 ce, multiple opt\n+00023680: 696f 6e73 3a20 2020 2020 2020 2020 2020 ions: \n+00023690: 466f 726d 7320 6f66 2072 6566 6572 656e Forms of referen\n+000236a0: 6365 732e 2028 6c69 6e65 2020 3138 290a ces. (line 18).\n+000236b0: 2a20 7265 6665 7265 6e63 652c 206f 7074 * reference, opt\n+000236c0: 696f 6e73 3a20 2020 2020 2020 2020 2020 ions: \n+000236d0: 2020 2020 2020 2020 2050 6f6c 796c 696e Polylin\n+000236e0: 6520 7377 6565 7073 2077 6974 6820 636c e sweeps with cl\n+000236f0: 6f73 7572 652e 0a20 2020 2020 2020 2020 osure.. \n 00023700: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023710: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023720: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023730: 2020 2020 2020 2028 6c69 6e65 2020 3234 (line 24\n-00023740: 290a 2a20 7265 6665 7265 6e63 652c 206f ).* reference, o\n-00023750: 7074 696f 6e73 203c 313e 3a20 2020 2020 ptions <1>: \n-00023760: 2020 2020 2020 2020 2020 2046 6f72 6d73 Forms\n-00023770: 206f 6620 7265 6665 7265 6e63 6573 2e20 of references. \n-00023780: 286c 696e 6520 2031 3829 0a2a 2072 6566 (line 18).* ref\n-00023790: 6572 656e 6365 2c20 706f 696e 743a 2020 erence, point: \n+00023730: 2020 2020 2028 6c69 6e65 2020 3234 290a (line 24).\n+00023740: 2a20 7265 6665 7265 6e63 652c 206f 7074 * reference, opt\n+00023750: 696f 6e73 203c 313e 3a20 2020 2020 2020 ions <1>: \n+00023760: 2020 2020 2020 2020 2046 6f72 6d73 206f Forms o\n+00023770: 6620 7265 6665 7265 6e63 6573 2e20 286c f references. (l\n+00023780: 696e 6520 2031 3829 0a2a 2072 6566 6572 ine 18).* refer\n+00023790: 656e 6365 2c20 706f 696e 743a 2020 2020 ence, point: \n 000237a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000237b0: 2020 2020 4472 6177 696e 6720 6120 736f Drawing a so\n-000237c0: 6c69 642e 2020 2020 2028 6c69 6e65 2020 lid. (line \n-000237d0: 3233 290a 2a20 7265 6665 7265 6e63 652c 23).* reference,\n-000237e0: 2070 6f69 6e74 203c 313e 3a20 2020 2020 point <1>: \n-000237f0: 2020 2020 2020 2020 2020 2020 2046 6f72 For\n-00023800: 6d73 206f 6620 7265 6665 7265 6e63 6573 ms of references\n-00023810: 2e20 286c 696e 6520 2031 3429 0a2a 2072 . (line 14).* r\n-00023820: 6566 6572 656e 6365 2c20 7363 616c 6172 eference, scalar\n-00023830: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00023840: 2020 2020 2020 5377 6570 7420 6f62 6a65 Swept obje\n-00023850: 6374 732e 2020 2020 2020 2028 6c69 6e65 cts. (line\n-00023860: 2020 3133 290a 2a20 7265 6665 7265 6e63 13).* referenc\n-00023870: 652c 2073 6361 6c61 7220 3c31 3e3a 2020 e, scalar <1>: \n-00023880: 2020 2020 2020 2020 2020 2020 2020 2046 F\n-00023890: 6f72 6d73 206f 6620 7265 6665 7265 6e63 orms of referenc\n-000238a0: 6573 2e20 286c 696e 6520 2031 3329 0a2a es. (line 13).*\n-000238b0: 2072 6566 6572 656e 6365 2c20 7461 673a reference, tag:\n+000237b0: 2020 4472 6177 696e 6720 6120 736f 6c69 Drawing a soli\n+000237c0: 642e 2020 2020 2028 6c69 6e65 2020 3233 d. (line 23\n+000237d0: 290a 2a20 7265 6665 7265 6e63 652c 2070 ).* reference, p\n+000237e0: 6f69 6e74 203c 313e 3a20 2020 2020 2020 oint <1>: \n+000237f0: 2020 2020 2020 2020 2020 2046 6f72 6d73 Forms\n+00023800: 206f 6620 7265 6665 7265 6e63 6573 2e20 of references. \n+00023810: 286c 696e 6520 2031 3429 0a2a 2072 6566 (line 14).* ref\n+00023820: 6572 656e 6365 2c20 7363 616c 6172 3a20 erence, scalar: \n+00023830: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00023840: 2020 2020 5377 6570 7420 6f62 6a65 6374 Swept object\n+00023850: 732e 2020 2020 2020 2028 6c69 6e65 2020 s. (line \n+00023860: 3133 290a 2a20 7265 6665 7265 6e63 652c 13).* reference,\n+00023870: 2073 6361 6c61 7220 3c31 3e3a 2020 2020 scalar <1>: \n+00023880: 2020 2020 2020 2020 2020 2020 2046 6f72 For\n+00023890: 6d73 206f 6620 7265 6665 7265 6e63 6573 ms of references\n+000238a0: 2e20 286c 696e 6520 2031 3329 0a2a 2072 . (line 13).* r\n+000238b0: 6566 6572 656e 6365 2c20 7461 673a 2020 eference, tag: \n 000238c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000238d0: 2020 2020 2020 2020 466f 726d 7320 6f66 Forms of\n-000238e0: 2064 6566 696e 6974 696f 6e73 2e0a 2020 definitions.. \n+000238d0: 2020 2020 2020 466f 726d 7320 6f66 2064 Forms of d\n+000238e0: 6566 696e 6974 696f 6e73 2e0a 2020 2020 efinitions.. \n 000238f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023900: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023910: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023920: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-00023930: 6520 2032 3029 0a2a 2072 6566 6572 656e e 20).* referen\n-00023940: 6365 2c20 7461 6720 3c31 3e3a 2020 2020 ce, tag <1>: \n-00023950: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023960: 466f 726d 7320 6f66 2072 6566 6572 656e Forms of referen\n-00023970: 6365 732e 2028 6c69 6e65 2020 3139 290a ces. (line 19).\n-00023980: 2a20 7265 6665 7265 6e63 652c 2074 7261 * reference, tra\n-00023990: 6e73 666f 726d 3a20 2020 2020 2020 2020 nsform: \n-000239a0: 2020 2020 2020 2020 2046 6f72 6d73 206f Forms o\n-000239b0: 6620 7265 6665 7265 6e63 6573 2e20 286c f references. (l\n-000239c0: 696e 6520 2031 3629 0a2a 2072 6566 6572 ine 16).* refer\n-000239d0: 656e 6365 2c20 7472 616e 7366 6f72 6d20 ence, transform \n-000239e0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-000239f0: 2020 4f76 6572 7669 6577 2e20 2020 2020 Overview. \n-00023a00: 2020 2020 2020 2028 6c69 6e65 2020 3335 (line 35\n-00023a10: 290a 2a20 7265 6665 7265 6e63 652c 2076 ).* reference, v\n-00023a20: 6563 746f 723a 2020 2020 2020 2020 2020 ector: \n-00023a30: 2020 2020 2020 2020 2020 2050 6f6c 796c Polyl\n-00023a40: 696e 6520 7377 6565 7073 2e20 2020 2020 ine sweeps. \n-00023a50: 286c 696e 6520 2032 3029 0a2a 2072 6566 (line 20).* ref\n-00023a60: 6572 656e 6365 2c20 7665 6374 6f72 203c erence, vector <\n-00023a70: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n-00023a80: 2020 2020 466f 726d 7320 6f66 2072 6566 Forms of ref\n-00023a90: 6572 656e 6365 732e 2028 6c69 6e65 2020 erences. (line \n-00023aa0: 3135 290a 2a20 7265 7065 6174 6564 206f 15).* repeated o\n-00023ab0: 626a 6563 743a 2020 2020 2020 2020 2020 bject: \n-00023ac0: 2020 2020 2020 2020 2020 2020 2052 6570 Rep\n-00023ad0: 6561 7473 2e20 2020 2020 2020 2020 2020 eats. \n-00023ae0: 2020 286c 696e 6520 2020 3629 0a2a 2072 (line 6).* r\n-00023af0: 6573 6572 7665 6420 776f 7264 733a 2020 eserved words: \n+00023920: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+00023930: 2032 3029 0a2a 2072 6566 6572 656e 6365 20).* reference\n+00023940: 2c20 7461 6720 3c31 3e3a 2020 2020 2020 , tag <1>: \n+00023950: 2020 2020 2020 2020 2020 2020 2020 466f Fo\n+00023960: 726d 7320 6f66 2072 6566 6572 656e 6365 rms of reference\n+00023970: 732e 2028 6c69 6e65 2020 3139 290a 2a20 s. (line 19).* \n+00023980: 7265 6665 7265 6e63 652c 2074 7261 6e73 reference, trans\n+00023990: 666f 726d 3a20 2020 2020 2020 2020 2020 form: \n+000239a0: 2020 2020 2020 2046 6f72 6d73 206f 6620 Forms of \n+000239b0: 7265 6665 7265 6e63 6573 2e20 286c 696e references. (lin\n+000239c0: 6520 2031 3629 0a2a 2072 6566 6572 656e e 16).* referen\n+000239d0: 6365 2c20 7472 616e 7366 6f72 6d20 3c31 ce, transform <1\n+000239e0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+000239f0: 4f76 6572 7669 6577 2e20 2020 2020 2020 Overview. \n+00023a00: 2020 2020 2028 6c69 6e65 2020 3335 290a (line 35).\n+00023a10: 2a20 7265 6665 7265 6e63 652c 2076 6563 * reference, vec\n+00023a20: 746f 723a 2020 2020 2020 2020 2020 2020 tor: \n+00023a30: 2020 2020 2020 2020 2050 6f6c 796c 696e Polylin\n+00023a40: 6520 7377 6565 7073 2e20 2020 2020 286c e sweeps. (l\n+00023a50: 696e 6520 2032 3029 0a2a 2072 6566 6572 ine 20).* refer\n+00023a60: 656e 6365 2c20 7665 6374 6f72 203c 313e ence, vector <1>\n+00023a70: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00023a80: 2020 466f 726d 7320 6f66 2072 6566 6572 Forms of refer\n+00023a90: 656e 6365 732e 2028 6c69 6e65 2020 3135 ences. (line 15\n+00023aa0: 290a 2a20 7265 7065 6174 6564 206f 626a ).* repeated obj\n+00023ab0: 6563 743a 2020 2020 2020 2020 2020 2020 ect: \n+00023ac0: 2020 2020 2020 2020 2020 2052 6570 6561 Repea\n+00023ad0: 7473 2e20 2020 2020 2020 2020 2020 2020 ts. \n+00023ae0: 286c 696e 6520 2020 3629 0a2a 2072 6573 (line 6).* res\n+00023af0: 6572 7665 6420 776f 7264 733a 2020 2020 erved words: \n 00023b00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023b10: 2020 2020 2020 4b65 7920 616e 6420 7265 Key and re\n-00023b20: 7365 7276 6564 2077 6f72 6473 2e0a 2020 served words.. \n+00023b10: 2020 2020 4b65 7920 616e 6420 7265 7365 Key and rese\n+00023b20: 7276 6564 2077 6f72 6473 2e0a 2020 2020 rved words.. \n 00023b30: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023b40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023b50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023b60: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-00023b70: 6520 2031 3129 0a2a 2072 6967 6874 2068 e 11).* right h\n-00023b80: 616e 6420 7275 6c65 3a20 2020 2020 2020 and rule: \n-00023b90: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023ba0: 4f62 6a65 6374 2074 7261 6e73 666f 726d Object transform\n-00023bb0: 732e 2020 2028 6c69 6e65 2020 3431 290a s. (line 41).\n-00023bc0: 2a20 7269 6768 742d 6861 6e64 2063 6f6f * right-hand coo\n-00023bd0: 7264 696e 6174 6520 7379 7374 656d 3a20 rdinate system: \n-00023be0: 2020 2020 2020 2020 2049 6e74 726f 6475 Introdu\n-00023bf0: 6374 696f 6e20 6279 2065 7861 6d70 6c65 ction by example\n-00023c00: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+00023b60: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+00023b70: 2031 3129 0a2a 2072 6967 6874 2068 616e 11).* right han\n+00023b80: 6420 7275 6c65 3a20 2020 2020 2020 2020 d rule: \n+00023b90: 2020 2020 2020 2020 2020 2020 2020 4f62 Ob\n+00023ba0: 6a65 6374 2074 7261 6e73 666f 726d 732e ject transforms.\n+00023bb0: 2020 2028 6c69 6e65 2020 3431 290a 2a20 (line 41).* \n+00023bc0: 7269 6768 742d 6861 6e64 2063 6f6f 7264 right-hand coord\n+00023bd0: 696e 6174 6520 7379 7374 656d 3a20 2020 inate system: \n+00023be0: 2020 2020 2020 2049 6e74 726f 6475 6374 Introduct\n+00023bf0: 696f 6e20 6279 2065 7861 6d70 6c65 2e0a ion by example..\n+00023c00: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023c10: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023c20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023c30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023c40: 286c 696e 6520 2031 3129 0a2a 2072 6f74 (line 11).* rot\n-00023c50: 6174 696f 6e3a 2020 2020 2020 2020 2020 ation: \n+00023c30: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+00023c40: 696e 6520 2031 3129 0a2a 2072 6f74 6174 ine 11).* rotat\n+00023c50: 696f 6e3a 2020 2020 2020 2020 2020 2020 ion: \n 00023c60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023c70: 2020 2020 4f62 6a65 6374 2074 7261 6e73 Object trans\n-00023c80: 666f 726d 732e 2020 2028 6c69 6e65 2020 forms. (line \n-00023c90: 3339 290a 2a20 726f 7461 7469 6f6e 2074 39).* rotation t\n-00023ca0: 7261 6e73 666f 726d 3a20 2020 2020 2020 ransform: \n-00023cb0: 2020 2020 2020 2020 2020 2020 2054 7261 Tra\n-00023cc0: 6e73 666f 726d 206c 6974 6572 616c 732e nsform literals.\n-00023cd0: 2020 286c 696e 6520 2031 3029 0a2a 2072 (line 10).* r\n-00023ce0: 6f74 6174 696f 6e20 7472 616e 7366 6f72 otation transfor\n-00023cf0: 6d20 3c31 3e3a 2020 2020 2020 2020 2020 m <1>: \n-00023d00: 2020 2020 2020 4120 6869 6572 6172 6368 A hierarch\n-00023d10: 6963 616c 206d 6f64 656c 2e0a 2020 2020 ical model.. \n+00023c70: 2020 4f62 6a65 6374 2074 7261 6e73 666f Object transfo\n+00023c80: 726d 732e 2020 2028 6c69 6e65 2020 3339 rms. (line 39\n+00023c90: 290a 2a20 726f 7461 7469 6f6e 2074 7261 ).* rotation tra\n+00023ca0: 6e73 666f 726d 3a20 2020 2020 2020 2020 nsform: \n+00023cb0: 2020 2020 2020 2020 2020 2054 7261 6e73 Trans\n+00023cc0: 666f 726d 206c 6974 6572 616c 732e 2020 form literals. \n+00023cd0: 286c 696e 6520 2031 3029 0a2a 2072 6f74 (line 10).* rot\n+00023ce0: 6174 696f 6e20 7472 616e 7366 6f72 6d20 ation transform \n+00023cf0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n+00023d00: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n+00023d10: 616c 206d 6f64 656c 2e0a 2020 2020 2020 al model.. \n 00023d20: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023d30: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023d40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023d50: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-00023d60: 2034 3829 0a2a 2072 6f74 6174 696f 6e20 48).* rotation \n-00023d70: 7472 616e 7366 6f72 6d20 3c32 3e3a 2020 transform <2>: \n-00023d80: 2020 2020 2020 2020 2020 2020 2020 4120 A \n-00023d90: 6869 6572 6172 6368 6963 616c 206d 6f64 hierarchical mod\n-00023da0: 656c 2e0a 2020 2020 2020 2020 2020 2020 el.. \n+00023d50: 2020 2020 2020 2020 286c 696e 6520 2034 (line 4\n+00023d60: 3829 0a2a 2072 6f74 6174 696f 6e20 7472 8).* rotation tr\n+00023d70: 616e 7366 6f72 6d20 3c32 3e3a 2020 2020 ansform <2>: \n+00023d80: 2020 2020 2020 2020 2020 2020 4120 6869 A hi\n+00023d90: 6572 6172 6368 6963 616c 206d 6f64 656c erarchical model\n+00023da0: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n 00023db0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023dc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023dd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023de0: 2020 286c 696e 6520 2035 3829 0a2a 2072 (line 58).* r\n-00023df0: 6f74 6174 696f 6e20 7472 616e 7366 6f72 otation transfor\n-00023e00: 6d20 3c33 3e3a 2020 2020 2020 2020 2020 m <3>: \n-00023e10: 2020 2020 2020 4120 6869 6572 6172 6368 A hierarch\n-00023e20: 6963 616c 206d 6f64 656c 2e0a 2020 2020 ical model.. \n+00023de0: 286c 696e 6520 2035 3829 0a2a 2072 6f74 (line 58).* rot\n+00023df0: 6174 696f 6e20 7472 616e 7366 6f72 6d20 ation transform \n+00023e00: 3c33 3e3a 2020 2020 2020 2020 2020 2020 <3>: \n+00023e10: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n+00023e20: 616c 206d 6f64 656c 2e0a 2020 2020 2020 al model.. \n 00023e30: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023e40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023e50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023e60: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-00023e70: 2037 3829 0a2a 2072 6f74 6174 696f 6e20 78).* rotation \n-00023e80: 7472 616e 7366 6f72 6d20 3c34 3e3a 2020 transform <4>: \n-00023e90: 2020 2020 2020 2020 2020 2020 2020 4120 A \n-00023ea0: 6869 6572 6172 6368 6963 616c 206d 6f64 hierarchical mod\n-00023eb0: 656c 2e0a 2020 2020 2020 2020 2020 2020 el.. \n+00023e60: 2020 2020 2020 2020 286c 696e 6520 2037 (line 7\n+00023e70: 3829 0a2a 2072 6f74 6174 696f 6e20 7472 8).* rotation tr\n+00023e80: 616e 7366 6f72 6d20 3c34 3e3a 2020 2020 ansform <4>: \n+00023e90: 2020 2020 2020 2020 2020 2020 4120 6869 A hi\n+00023ea0: 6572 6172 6368 6963 616c 206d 6f64 656c erarchical model\n+00023eb0: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \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 286c 696e 6520 2039 3329 0a2a 2072 (line 93).* r\n-00023f00: 6f74 6174 696f 6e2c 2063 656e 7465 7220 otation, center \n-00023f10: 6f66 3a20 2020 2020 2020 2020 2020 2020 of: \n-00023f20: 2020 2020 2020 4f62 6a65 6374 2074 7261 Object tra\n-00023f30: 6e73 666f 726d 732e 2020 2028 6c69 6e65 nsforms. (line\n-00023f40: 2020 2038 290a 2a20 726f 7461 7469 6f6e 8).* rotation\n-00023f50: 2c20 6365 6e74 6572 206f 6620 3c31 3e3a , center of <1>:\n-00023f60: 2020 2020 2020 2020 2020 2020 2020 204e N\n-00023f70: 6573 7465 6420 7377 6565 7073 2e20 2020 ested sweeps. \n-00023f80: 2020 2020 286c 696e 6520 2020 3629 0a2a (line 6).*\n-00023f90: 2072 756e 6e69 6e67 2073 6b65 7463 683a running sketch:\n+00023ef0: 286c 696e 6520 2039 3329 0a2a 2072 6f74 (line 93).* rot\n+00023f00: 6174 696f 6e2c 2063 656e 7465 7220 6f66 ation, center of\n+00023f10: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00023f20: 2020 2020 4f62 6a65 6374 2074 7261 6e73 Object trans\n+00023f30: 666f 726d 732e 2020 2028 6c69 6e65 2020 forms. (line \n+00023f40: 2038 290a 2a20 726f 7461 7469 6f6e 2c20 8).* rotation, \n+00023f50: 6365 6e74 6572 206f 6620 3c31 3e3a 2020 center of <1>: \n+00023f60: 2020 2020 2020 2020 2020 2020 204e 6573 Nes\n+00023f70: 7465 6420 7377 6565 7073 2e20 2020 2020 ted sweeps. \n+00023f80: 2020 286c 696e 6520 2020 3629 0a2a 2072 (line 6).* r\n+00023f90: 756e 6e69 6e67 2073 6b65 7463 683a 2020 unning sketch: \n 00023fa0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023fb0: 2020 2020 2020 2020 4865 6c6c 6f20 776f Hello wo\n-00023fc0: 726c 642e 2020 2020 2020 2020 2028 6c69 rld. (li\n-00023fd0: 6e65 2020 2039 290a 2a20 7363 616c 6172 ne 9).* scalar\n-00023fe0: 2064 6566 696e 6974 696f 6e3a 2020 2020 definition: \n-00023ff0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024000: 2053 7765 7074 206f 626a 6563 7473 2e20 Swept objects. \n-00024010: 2020 2020 2020 286c 696e 6520 2031 3329 (line 13)\n-00024020: 0a2a 2073 6361 6c61 7220 6c69 7465 7261 .* scalar litera\n-00024030: 6c3a 2020 2020 2020 2020 2020 2020 2020 l: \n-00024040: 2020 2020 2020 2020 2020 5363 616c 6172 Scalar\n-00024050: 206c 6974 6572 616c 732e 2020 2020 2028 literals. (\n-00024060: 6c69 6e65 2020 2036 290a 2a20 7363 616c line 6).* scal\n-00024070: 6172 2072 6566 6572 656e 6365 3a20 2020 ar reference: \n+00023fb0: 2020 2020 2020 4865 6c6c 6f20 776f 726c Hello worl\n+00023fc0: 642e 2020 2020 2020 2020 2028 6c69 6e65 d. (line\n+00023fd0: 2020 2039 290a 2a20 7363 616c 6172 2064 9).* scalar d\n+00023fe0: 6566 696e 6974 696f 6e3a 2020 2020 2020 efinition: \n+00023ff0: 2020 2020 2020 2020 2020 2020 2020 2053 S\n+00024000: 7765 7074 206f 626a 6563 7473 2e20 2020 wept objects. \n+00024010: 2020 2020 286c 696e 6520 2031 3329 0a2a (line 13).*\n+00024020: 2073 6361 6c61 7220 6c69 7465 7261 6c3a scalar literal:\n+00024030: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00024040: 2020 2020 2020 2020 5363 616c 6172 206c Scalar l\n+00024050: 6974 6572 616c 732e 2020 2020 2028 6c69 iterals. (li\n+00024060: 6e65 2020 2036 290a 2a20 7363 616c 6172 ne 6).* scalar\n+00024070: 2072 6566 6572 656e 6365 3a20 2020 2020 reference: \n 00024080: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024090: 2020 2046 6f72 6d73 206f 6620 7265 6665 Forms of refe\n-000240a0: 7265 6e63 6573 2e20 286c 696e 6520 2031 rences. (line 1\n-000240b0: 3329 0a2a 2073 6361 6c65 2074 7261 6e73 3).* scale trans\n-000240c0: 666f 726d 3a20 2020 2020 2020 2020 2020 form: \n-000240d0: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n-000240e0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n-000240f0: 2028 6c69 6e65 2020 3136 290a 2a20 7363 (line 16).* sc\n-00024100: 616c 6520 7472 616e 7366 6f72 6d20 3c31 ale transform <1\n-00024110: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-00024120: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n-00024130: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n-00024140: 2031 3729 0a2a 2073 6365 6e65 2064 6573 17).* scene des\n-00024150: 6372 6970 7469 6f6e 206c 616e 6775 6167 cription languag\n-00024160: 653a 2020 2020 2020 2020 2020 2020 4c61 e: La\n-00024170: 6e67 7561 6765 2062 6173 6963 732e 2020 nguage basics. \n-00024180: 2020 2028 6c69 6e65 2020 2038 290a 2a20 (line 8).* \n-00024190: 7363 656e 6520 6465 7363 7269 7074 696f scene descriptio\n-000241a0: 6e20 6c61 6e67 7561 6765 203c 313e 3a20 n language <1>: \n-000241b0: 2020 2020 2020 2042 7569 6c64 696e 6720 Building \n-000241c0: 6120 6472 6177 696e 672e 2020 286c 696e a drawing. (lin\n-000241d0: 6520 2020 3729 0a2a 2073 636f 7065 2c20 e 7).* scope, \n-000241e0: 6964 656e 7469 6669 6572 3a20 2020 2020 identifier: \n-000241f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024200: 4f62 6a65 6374 2074 7261 6e73 666f 726d Object transform\n-00024210: 732e 2020 2028 6c69 6e65 2020 3236 290a s. (line 26).\n-00024220: 2a20 7363 6f70 652c 2069 6465 6e74 6966 * scope, identif\n-00024230: 6965 7220 3c31 3e3a 2020 2020 2020 2020 ier <1>: \n-00024240: 2020 2020 2020 2020 2042 6c6f 636b 732e Blocks.\n-00024250: 2020 2020 2020 2020 2020 2020 2020 286c (l\n-00024260: 696e 6520 2031 3329 0a2a 2073 696d 706c ine 13).* simpl\n-00024270: 6520 6465 6669 6e69 7469 6f6e 3a20 2020 e definition: \n+00024090: 2046 6f72 6d73 206f 6620 7265 6665 7265 Forms of refere\n+000240a0: 6e63 6573 2e20 286c 696e 6520 2031 3329 nces. (line 13)\n+000240b0: 0a2a 2073 6361 6c65 2074 7261 6e73 666f .* scale transfo\n+000240c0: 726d 3a20 2020 2020 2020 2020 2020 2020 rm: \n+000240d0: 2020 2020 2020 2020 2020 5472 616e 7366 Transf\n+000240e0: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028 orm literals. (\n+000240f0: 6c69 6e65 2020 3136 290a 2a20 7363 616c line 16).* scal\n+00024100: 6520 7472 616e 7366 6f72 6d20 3c31 3e3a e transform <1>:\n+00024110: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00024120: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n+00024130: 6572 616c 732e 2020 286c 696e 6520 2031 erals. (line 1\n+00024140: 3729 0a2a 2073 6365 6e65 2064 6573 6372 7).* scene descr\n+00024150: 6970 7469 6f6e 206c 616e 6775 6167 653a iption language:\n+00024160: 2020 2020 2020 2020 2020 2020 4c61 6e67 Lang\n+00024170: 7561 6765 2062 6173 6963 732e 2020 2020 uage basics. \n+00024180: 2028 6c69 6e65 2020 2038 290a 2a20 7363 (line 8).* sc\n+00024190: 656e 6520 6465 7363 7269 7074 696f 6e20 ene description \n+000241a0: 6c61 6e67 7561 6765 203c 313e 3a20 2020 language <1>: \n+000241b0: 2020 2020 2042 7569 6c64 696e 6720 6120 Building a \n+000241c0: 6472 6177 696e 672e 2020 286c 696e 6520 drawing. (line \n+000241d0: 2020 3729 0a2a 2073 636f 7065 2c20 6964 7).* scope, id\n+000241e0: 656e 7469 6669 6572 3a20 2020 2020 2020 entifier: \n+000241f0: 2020 2020 2020 2020 2020 2020 2020 4f62 Ob\n+00024200: 6a65 6374 2074 7261 6e73 666f 726d 732e ject transforms.\n+00024210: 2020 2028 6c69 6e65 2020 3236 290a 2a20 (line 26).* \n+00024220: 7363 6f70 652c 2069 6465 6e74 6966 6965 scope, identifie\n+00024230: 7220 3c31 3e3a 2020 2020 2020 2020 2020 r <1>: \n+00024240: 2020 2020 2020 2042 6c6f 636b 732e 2020 Blocks. \n+00024250: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+00024260: 6520 2031 3329 0a2a 2073 696d 706c 6520 e 13).* simple \n+00024270: 6465 6669 6e69 7469 6f6e 3a20 2020 2020 definition: \n 00024280: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024290: 2020 466f 726d 7320 6f66 2064 6566 696e Forms of defin\n-000242a0: 6974 696f 6e73 2e0a 2020 2020 2020 2020 itions.. \n+00024290: 466f 726d 7320 6f66 2064 6566 696e 6974 Forms of definit\n+000242a0: 696f 6e73 2e0a 2020 2020 2020 2020 2020 ions.. \n 000242b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000242c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000242d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000242e0: 2020 2020 2020 286c 696e 6520 2020 3629 (line 6)\n-000242f0: 0a2a 2073 6f6c 6964 3a20 2020 2020 2020 .* solid: \n+000242e0: 2020 2020 286c 696e 6520 2020 3629 0a2a (line 6).*\n+000242f0: 2073 6f6c 6964 3a20 2020 2020 2020 2020 solid: \n 00024300: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024310: 2020 2020 2020 2020 2020 4472 6177 696e Drawin\n-00024320: 6720 6120 736f 6c69 642e 2020 2020 2028 g a solid. (\n-00024330: 6c69 6e65 2020 2036 290a 2a20 7370 6563 line 6).* spec\n-00024340: 6961 6c20 6172 6775 6d65 6e74 2073 7562 ial argument sub\n-00024350: 7374 6974 7574 696f 6e3a 2020 2020 2020 stitution: \n-00024360: 2020 2053 7065 6369 616c 206f 626a 6563 Special objec\n-00024370: 7473 2e20 2020 2020 286c 696e 6520 2032 ts. (line 2\n-00024380: 3829 0a2a 2073 7065 6369 616c 2061 7267 8).* special arg\n-00024390: 756d 656e 7420 7375 6273 7469 7475 7469 ument substituti\n-000243a0: 6f6e 203c 313e 3a20 2020 2020 5370 6563 on <1>: Spec\n-000243b0: 6961 6c73 2e20 2020 2020 2020 2020 2020 ials. \n-000243c0: 2028 6c69 6e65 2020 3130 290a 2a20 7370 (line 10).* sp\n-000243d0: 6563 6961 6c20 6f62 6a65 6374 3a20 2020 ecial object: \n+00024310: 2020 2020 2020 2020 4472 6177 696e 6720 Drawing \n+00024320: 6120 736f 6c69 642e 2020 2020 2028 6c69 a solid. (li\n+00024330: 6e65 2020 2036 290a 2a20 7370 6563 6961 ne 6).* specia\n+00024340: 6c20 6172 6775 6d65 6e74 2073 7562 7374 l argument subst\n+00024350: 6974 7574 696f 6e3a 2020 2020 2020 2020 itution: \n+00024360: 2053 7065 6369 616c 206f 626a 6563 7473 Special objects\n+00024370: 2e20 2020 2020 286c 696e 6520 2032 3829 . (line 28)\n+00024380: 0a2a 2073 7065 6369 616c 2061 7267 756d .* special argum\n+00024390: 656e 7420 7375 6273 7469 7475 7469 6f6e ent substitution\n+000243a0: 203c 313e 3a20 2020 2020 5370 6563 6961 <1>: Specia\n+000243b0: 6c73 2e20 2020 2020 2020 2020 2020 2028 ls. (\n+000243c0: 6c69 6e65 2020 3130 290a 2a20 7370 6563 line 10).* spec\n+000243d0: 6961 6c20 6f62 6a65 6374 3a20 2020 2020 ial object: \n 000243e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000243f0: 2020 2020 2053 7065 6369 616c 206f 626a Special obj\n-00024400: 6563 7473 2e20 2020 2020 286c 696e 6520 ects. (line \n-00024410: 2020 3629 0a2a 2073 7065 6369 616c 206f 6).* special o\n-00024420: 626a 6563 7473 3a20 2020 2020 2020 2020 bjects: \n-00024430: 2020 2020 2020 2020 2020 2020 2020 4120 A \n-00024440: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n-00024450: 672e 2028 6c69 6e65 2020 3338 290a 2a20 g. (line 38).* \n-00024460: 7370 6c69 7474 696e 672c 206c 696e 6520 splitting, line \n-00024470: 616e 6420 7375 7266 6163 653a 2020 2020 and surface: \n-00024480: 2020 2020 2020 2048 656c 6c6f 2077 6f72 Hello wor\n-00024490: 6c64 2e20 2020 2020 2020 2020 286c 696e ld. (lin\n-000244a0: 6520 2031 3929 0a2a 2073 706c 6974 7469 e 19).* splitti\n-000244b0: 6e67 2c20 6c69 6e65 2061 6e64 2073 7572 ng, line and sur\n-000244c0: 6661 6365 203c 313e 3a20 2020 2020 2020 face <1>: \n-000244d0: 4869 6464 656e 2073 7572 6661 6365 2072 Hidden surface r\n-000244e0: 656d 6f76 616c 2e0a 2020 2020 2020 2020 emoval.. \n+000243f0: 2020 2053 7065 6369 616c 206f 626a 6563 Special objec\n+00024400: 7473 2e20 2020 2020 286c 696e 6520 2020 ts. (line \n+00024410: 3629 0a2a 2073 7065 6369 616c 206f 626a 6).* special obj\n+00024420: 6563 7473 3a20 2020 2020 2020 2020 2020 ects: \n+00024430: 2020 2020 2020 2020 2020 2020 4120 7465 A te\n+00024440: 6368 6e69 6361 6c20 6472 6177 696e 672e chnical drawing.\n+00024450: 2028 6c69 6e65 2020 3338 290a 2a20 7370 (line 38).* sp\n+00024460: 6c69 7474 696e 672c 206c 696e 6520 616e litting, line an\n+00024470: 6420 7375 7266 6163 653a 2020 2020 2020 d surface: \n+00024480: 2020 2020 2048 656c 6c6f 2077 6f72 6c64 Hello world\n+00024490: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n+000244a0: 2031 3929 0a2a 2073 706c 6974 7469 6e67 19).* splitting\n+000244b0: 2c20 6c69 6e65 2061 6e64 2073 7572 6661 , line and surfa\n+000244c0: 6365 203c 313e 3a20 2020 2020 2020 4869 ce <1>: Hi\n+000244d0: 6464 656e 2073 7572 6661 6365 2072 656d dden surface rem\n+000244e0: 6f76 616c 2e0a 2020 2020 2020 2020 2020 oval.. \n 000244f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024500: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024510: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024520: 2020 2020 2020 286c 696e 6520 2032 3129 (line 21)\n-00024530: 0a2a 2073 7562 7374 6974 7574 696f 6e2c .* substitution,\n-00024540: 2073 7065 6369 616c 3a20 2020 2020 2020 special: \n-00024550: 2020 2020 2020 2020 2020 5370 6563 6961 Specia\n-00024560: 6c20 6f62 6a65 6374 732e 2020 2020 2028 l objects. (\n-00024570: 6c69 6e65 2020 3238 290a 2a20 7375 7266 line 28).* surf\n-00024580: 6163 653a 2020 2020 2020 2020 2020 2020 ace: \n+00024520: 2020 2020 286c 696e 6520 2032 3129 0a2a (line 21).*\n+00024530: 2073 7562 7374 6974 7574 696f 6e2c 2073 substitution, s\n+00024540: 7065 6369 616c 3a20 2020 2020 2020 2020 pecial: \n+00024550: 2020 2020 2020 2020 5370 6563 6961 6c20 Special \n+00024560: 6f62 6a65 6374 732e 2020 2020 2028 6c69 objects. (li\n+00024570: 6e65 2020 3238 290a 2a20 7375 7266 6163 ne 28).* surfac\n+00024580: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n 00024590: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000245a0: 2020 2050 6f6c 796c 696e 6520 7377 6565 Polyline swee\n-000245b0: 7073 2e20 2020 2020 286c 696e 6520 2020 ps. (line \n-000245c0: 3629 0a2a 2073 7765 6570 3a20 2020 2020 6).* sweep: \n+000245a0: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n+000245b0: 2e20 2020 2020 286c 696e 6520 2020 3629 . (line 6)\n+000245c0: 0a2a 2073 7765 6570 3a20 2020 2020 2020 .* sweep: \n 000245d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000245e0: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n-000245f0: 7420 6f62 6a65 6374 732e 2020 2020 2020 t objects. \n-00024600: 2028 6c69 6e65 2020 2036 290a 2a20 7377 (line 6).* sw\n-00024610: 6570 7420 626f 636b 3a20 2020 2020 2020 ept bock: \n+000245e0: 2020 2020 2020 2020 2020 5377 6570 7420 Swept \n+000245f0: 6f62 6a65 6374 732e 2020 2020 2020 2028 objects. (\n+00024600: 6c69 6e65 2020 2036 290a 2a20 7377 6570 line 6).* swep\n+00024610: 7420 626f 636b 3a20 2020 2020 2020 2020 t bock: \n 00024620: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024630: 2020 2020 2053 7765 7074 2062 6c6f 636b Swept block\n-00024640: 732e 2020 2020 2020 2020 286c 696e 6520 s. (line \n-00024650: 2020 3629 0a2a 2073 7765 7074 206c 696e 6).* swept lin\n-00024660: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n-00024670: 2020 2020 2020 2020 2020 2020 2020 506f Po\n-00024680: 6c79 6c69 6e65 2073 7765 6570 732e 2020 lyline sweeps. \n-00024690: 2020 2028 6c69 6e65 2020 2036 290a 2a20 (line 6).* \n-000246a0: 7377 6570 7420 6c69 6e65 203c 313e 3a20 swept line <1>: \n+00024630: 2020 2053 7765 7074 2062 6c6f 636b 732e Swept blocks.\n+00024640: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n+00024650: 3629 0a2a 2073 7765 7074 206c 696e 653a 6).* swept line:\n+00024660: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00024670: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n+00024680: 6c69 6e65 2073 7765 6570 732e 2020 2020 line sweeps. \n+00024690: 2028 6c69 6e65 2020 2036 290a 2a20 7377 (line 6).* sw\n+000246a0: 6570 7420 6c69 6e65 203c 313e 3a20 2020 ept line <1>: \n 000246b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000246c0: 2020 2020 2020 2053 7765 7074 206c 696e Swept lin\n-000246d0: 6573 2e20 2020 2020 2020 2020 286c 696e es. (lin\n-000246e0: 6520 2020 3629 0a2a 2073 7765 7074 206c e 6).* swept l\n-000246f0: 696e 6520 3c32 3e3a 2020 2020 2020 2020 ine <2>: \n-00024700: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024710: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n-00024720: 696e 672e 2028 6c69 6e65 2020 3230 290a ing. (line 20).\n-00024730: 2a20 7377 6570 7420 6f62 6a65 6374 3a20 * swept object: \n+000246c0: 2020 2020 2053 7765 7074 206c 696e 6573 Swept lines\n+000246d0: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n+000246e0: 2020 3629 0a2a 2073 7765 7074 206c 696e 6).* swept lin\n+000246f0: 6520 3c32 3e3a 2020 2020 2020 2020 2020 e <2>: \n+00024700: 2020 2020 2020 2020 2020 2020 2020 4120 A \n+00024710: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n+00024720: 672e 2028 6c69 6e65 2020 3230 290a 2a20 g. (line 20).* \n+00024730: 7377 6570 7420 6f62 6a65 6374 3a20 2020 swept object: \n 00024740: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024750: 2020 2020 2020 2020 2053 7765 7074 206f Swept o\n-00024760: 626a 6563 7473 2e20 2020 2020 2020 286c bjects. (l\n-00024770: 696e 6520 2020 3629 0a2a 2073 7765 7074 ine 6).* swept\n-00024780: 206f 626a 6563 7420 3c31 3e3a 2020 2020 object <1>: \n+00024750: 2020 2020 2020 2053 7765 7074 206f 626a Swept obj\n+00024760: 6563 7473 2e20 2020 2020 2020 286c 696e ects. (lin\n+00024770: 6520 2020 3629 0a2a 2073 7765 7074 206f e 6).* swept o\n+00024780: 626a 6563 7420 3c31 3e3a 2020 2020 2020 bject <1>: \n 00024790: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000247a0: 2020 5377 6565 7073 2e20 2020 2020 2020 Sweeps. \n-000247b0: 2020 2020 2020 2028 6c69 6e65 2020 2039 (line 9\n-000247c0: 290a 2a20 7377 6570 7420 706f 696e 743a ).* swept point:\n+000247a0: 5377 6565 7073 2e20 2020 2020 2020 2020 Sweeps. \n+000247b0: 2020 2020 2028 6c69 6e65 2020 2039 290a (line 9).\n+000247c0: 2a20 7377 6570 7420 706f 696e 743a 2020 * swept point: \n 000247d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000247e0: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n-000247f0: 206f 626a 6563 7473 2e20 2020 2020 2020 objects. \n-00024800: 286c 696e 6520 2031 3129 0a2a 2073 7765 (line 11).* swe\n-00024810: 7074 2070 6f69 6e74 203c 313e 3a20 2020 pt point <1>: \n+000247e0: 2020 2020 2020 2020 2053 7765 7074 206f Swept o\n+000247f0: 626a 6563 7473 2e20 2020 2020 2020 286c bjects. (l\n+00024800: 696e 6520 2031 3129 0a2a 2073 7765 7074 ine 11).* swept\n+00024810: 2070 6f69 6e74 203c 313e 3a20 2020 2020 point <1>: \n 00024820: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024830: 2020 2020 5377 6570 7420 706f 696e 7473 Swept points\n-00024840: 2e20 2020 2020 2020 2028 6c69 6e65 2020 . (line \n-00024850: 2036 290a 2a20 7377 6570 7420 706f 6c79 6).* swept poly\n-00024860: 676f 6e3a 2020 2020 2020 2020 2020 2020 gon: \n-00024870: 2020 2020 2020 2020 2020 2020 2050 6f6c Pol\n-00024880: 7967 6f6e 2073 7765 6570 732e 2020 2020 ygon sweeps. \n-00024890: 2020 286c 696e 6520 2020 3629 0a2a 2073 (line 6).* s\n-000248a0: 7765 7074 2070 6f6c 7967 6f6e 203c 313e wept polygon <1>\n-000248b0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-000248c0: 2020 2020 2020 4120 6869 6572 6172 6368 A hierarch\n-000248d0: 6963 616c 206d 6f64 656c 2e0a 2020 2020 ical model.. \n+00024830: 2020 5377 6570 7420 706f 696e 7473 2e20 Swept points. \n+00024840: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n+00024850: 290a 2a20 7377 6570 7420 706f 6c79 676f ).* swept polygo\n+00024860: 6e3a 2020 2020 2020 2020 2020 2020 2020 n: \n+00024870: 2020 2020 2020 2020 2020 2050 6f6c 7967 Polyg\n+00024880: 6f6e 2073 7765 6570 732e 2020 2020 2020 on sweeps. \n+00024890: 286c 696e 6520 2020 3629 0a2a 2073 7765 (line 6).* swe\n+000248a0: 7074 2070 6f6c 7967 6f6e 203c 313e 3a20 pt polygon <1>: \n+000248b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000248c0: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n+000248d0: 616c 206d 6f64 656c 2e0a 2020 2020 2020 al model.. \n 000248e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000248f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024900: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024910: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-00024920: 3132 3229 0a2a 2074 6167 2064 6566 696e 122).* tag defin\n-00024930: 6974 696f 6e3a 2020 2020 2020 2020 2020 ition: \n-00024940: 2020 2020 2020 2020 2020 2020 2020 4465 De\n-00024950: 6669 6e69 7469 6f6e 732e 2020 2020 2020 finitions. \n-00024960: 2020 2028 6c69 6e65 2020 3138 290a 2a20 (line 18).* \n-00024970: 7461 6720 6465 6669 6e69 7469 6f6e 203c tag definition <\n-00024980: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n-00024990: 2020 2020 2020 2046 6f72 6d73 206f 6620 Forms of \n-000249a0: 6465 6669 6e69 7469 6f6e 732e 0a20 2020 definitions.. \n+00024910: 2020 2020 2020 2020 286c 696e 6520 3132 (line 12\n+00024920: 3229 0a2a 2074 6167 2064 6566 696e 6974 2).* tag definit\n+00024930: 696f 6e3a 2020 2020 2020 2020 2020 2020 ion: \n+00024940: 2020 2020 2020 2020 2020 2020 4465 6669 Defi\n+00024950: 6e69 7469 6f6e 732e 2020 2020 2020 2020 nitions. \n+00024960: 2028 6c69 6e65 2020 3138 290a 2a20 7461 (line 18).* ta\n+00024970: 6720 6465 6669 6e69 7469 6f6e 203c 313e g definition <1>\n+00024980: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00024990: 2020 2020 2046 6f72 6d73 206f 6620 6465 Forms of de\n+000249a0: 6669 6e69 7469 6f6e 732e 0a20 2020 2020 finitions.. \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 2020 2020 2020 2020 \n-000249e0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-000249f0: 2020 2037 290a 2a20 7461 6720 6465 6669 7).* tag defi\n-00024a00: 6e69 7469 6f6e 203c 323e 3a20 2020 2020 nition <2>: \n-00024a10: 2020 2020 2020 2020 2020 2020 2020 2043 C\n-00024a20: 6f6d 6d61 6e64 206c 696e 652e 2020 2020 ommand line. \n-00024a30: 2020 2020 286c 696e 6520 2035 3329 0a2a (line 53).*\n-00024a40: 2074 6167 2072 6566 6572 656e 6365 3a20 tag reference: \n+000249e0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+000249f0: 2037 290a 2a20 7461 6720 6465 6669 6e69 7).* tag defini\n+00024a00: 7469 6f6e 203c 323e 3a20 2020 2020 2020 tion <2>: \n+00024a10: 2020 2020 2020 2020 2020 2020 2043 6f6d Com\n+00024a20: 6d61 6e64 206c 696e 652e 2020 2020 2020 mand line. \n+00024a30: 2020 286c 696e 6520 2035 3329 0a2a 2074 (line 53).* t\n+00024a40: 6167 2072 6566 6572 656e 6365 3a20 2020 ag reference: \n 00024a50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024a60: 2020 2020 2020 2020 466f 726d 7320 6f66 Forms of\n-00024a70: 2064 6566 696e 6974 696f 6e73 2e0a 2020 definitions.. \n+00024a60: 2020 2020 2020 466f 726d 7320 6f66 2064 Forms of d\n+00024a70: 6566 696e 6974 696f 6e73 2e0a 2020 2020 efinitions.. \n 00024a80: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024a90: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024aa0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024ab0: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-00024ac0: 6520 2032 3029 0a2a 2074 6167 2072 6566 e 20).* tag ref\n-00024ad0: 6572 656e 6365 203c 313e 3a20 2020 2020 erence <1>: \n-00024ae0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024af0: 466f 726d 7320 6f66 2072 6566 6572 656e Forms of referen\n-00024b00: 6365 732e 2028 6c69 6e65 2020 3139 290a ces. (line 19).\n-00024b10: 2a20 7465 6d70 6c61 7465 2c20 646f 6375 * template, docu\n-00024b20: 6d65 6e74 3a20 2020 2020 2020 2020 2020 ment: \n-00024b30: 2020 2020 2020 2020 2048 656c 6c6f 2077 Hello w\n-00024b40: 6f72 6c64 2e20 2020 2020 2020 2020 286c orld. (l\n-00024b50: 696e 6520 2033 3229 0a2a 2074 656d 706c ine 32).* templ\n-00024b60: 6174 652c 2064 6f63 756d 656e 7420 3c31 ate, document <1\n-00024b70: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-00024b80: 2020 436f 6d6d 616e 6420 6c69 6e65 2e20 Command line. \n-00024b90: 2020 2020 2020 2028 6c69 6e65 2020 3336 (line 36\n-00024ba0: 290a 2a20 7465 7472 6168 6564 726f 6e3a ).* tetrahedron:\n+00024ab0: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+00024ac0: 2032 3029 0a2a 2074 6167 2072 6566 6572 20).* tag refer\n+00024ad0: 656e 6365 203c 313e 3a20 2020 2020 2020 ence <1>: \n+00024ae0: 2020 2020 2020 2020 2020 2020 2020 466f Fo\n+00024af0: 726d 7320 6f66 2072 6566 6572 656e 6365 rms of reference\n+00024b00: 732e 2028 6c69 6e65 2020 3139 290a 2a20 s. (line 19).* \n+00024b10: 7465 6d70 6c61 7465 2c20 646f 6375 6d65 template, docume\n+00024b20: 6e74 3a20 2020 2020 2020 2020 2020 2020 nt: \n+00024b30: 2020 2020 2020 2048 656c 6c6f 2077 6f72 Hello wor\n+00024b40: 6c64 2e20 2020 2020 2020 2020 286c 696e ld. (lin\n+00024b50: 6520 2033 3229 0a2a 2074 656d 706c 6174 e 32).* templat\n+00024b60: 652c 2064 6f63 756d 656e 7420 3c31 3e3a e, document <1>:\n+00024b70: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00024b80: 436f 6d6d 616e 6420 6c69 6e65 2e20 2020 Command line. \n+00024b90: 2020 2020 2028 6c69 6e65 2020 3336 290a (line 36).\n+00024ba0: 2a20 7465 7472 6168 6564 726f 6e3a 2020 * tetrahedron: \n 00024bb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024bc0: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n-00024bd0: 6e67 2061 2073 6f6c 6964 2e20 2020 2020 ng a solid. \n-00024be0: 286c 696e 6520 2020 3929 0a2a 2074 6963 (line 9).* tic\n-00024bf0: 6b20 6f70 6572 6174 6f72 2028 2729 3a20 k operator ('): \n+00024bc0: 2020 2020 2020 2020 2044 7261 7769 6e67 Drawing\n+00024bd0: 2061 2073 6f6c 6964 2e20 2020 2020 286c a solid. (l\n+00024be0: 696e 6520 2020 3929 0a2a 2074 6963 6b20 ine 9).* tick \n+00024bf0: 6f70 6572 6174 6f72 2028 2729 3a20 2020 operator ('): \n 00024c00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024c10: 2020 2020 4166 6669 6e65 2061 7269 7468 Affine arith\n-00024c20: 6d65 7469 632e 2020 2028 6c69 6e65 2020 metic. (line \n-00024c30: 3337 290a 2a20 7469 636b 206f 7065 7261 37).* tick opera\n-00024c40: 746f 7220 2827 2920 3c31 3e3a 2020 2020 tor (') <1>: \n-00024c50: 2020 2020 2020 2020 2020 2020 2054 776f Two\n-00024c60: 2d6f 7065 7261 6e64 2028 6269 6e61 7279 -operand (binary\n-00024c70: 2920 666f 726d 732e 0a20 2020 2020 2020 ) forms.. \n+00024c10: 2020 4166 6669 6e65 2061 7269 7468 6d65 Affine arithme\n+00024c20: 7469 632e 2020 2028 6c69 6e65 2020 3337 tic. (line 37\n+00024c30: 290a 2a20 7469 636b 206f 7065 7261 746f ).* tick operato\n+00024c40: 7220 2827 2920 3c31 3e3a 2020 2020 2020 r (') <1>: \n+00024c50: 2020 2020 2020 2020 2020 2054 776f 2d6f Two-o\n+00024c60: 7065 7261 6e64 2028 6269 6e61 7279 2920 perand (binary) \n+00024c70: 666f 726d 732e 0a20 2020 2020 2020 2020 forms.. \n 00024c80: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024c90: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024ca0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024cb0: 2020 2020 2020 2028 6c69 6e65 2020 3431 (line 41\n-00024cc0: 290a 2a20 5469 6b5a 2f50 4746 3a20 2020 ).* TikZ/PGF: \n+00024cb0: 2020 2020 2028 6c69 6e65 2020 3431 290a (line 41).\n+00024cc0: 2a20 5469 6b5a 2f50 4746 3a20 2020 2020 * TikZ/PGF: \n 00024cd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024ce0: 2020 2020 2020 2020 2020 2041 626f 7574 About\n-00024cf0: 2073 6b65 7463 682e 2020 2020 2020 2020 sketch. \n-00024d00: 286c 696e 6520 2032 3229 0a2a 2074 6f72 (line 22).* tor\n-00024d10: 6f69 643a 2020 2020 2020 2020 2020 2020 oid: \n+00024ce0: 2020 2020 2020 2020 2041 626f 7574 2073 About s\n+00024cf0: 6b65 7463 682e 2020 2020 2020 2020 286c ketch. (l\n+00024d00: 696e 6520 2032 3229 0a2a 2074 6f72 6f69 ine 22).* toroi\n+00024d10: 643a 2020 2020 2020 2020 2020 2020 2020 d: \n 00024d20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024d30: 2020 2020 4e65 7374 6564 2073 7765 6570 Nested sweep\n-00024d40: 732e 2020 2020 2020 2028 6c69 6e65 2020 s. (line \n-00024d50: 2038 290a 2a20 7472 616e 7366 6f72 6d3a 8).* transform:\n+00024d30: 2020 4e65 7374 6564 2073 7765 6570 732e Nested sweeps.\n+00024d40: 2020 2020 2020 2028 6c69 6e65 2020 2038 (line 8\n+00024d50: 290a 2a20 7472 616e 7366 6f72 6d3a 2020 ).* transform: \n 00024d60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024d70: 2020 2020 2020 2020 2020 2020 204f 626a Obj\n-00024d80: 6563 7420 7472 616e 7366 6f72 6d73 2e20 ect transforms. \n-00024d90: 2020 286c 696e 6520 2020 3629 0a2a 2074 (line 6).* t\n-00024da0: 7261 6e73 666f 726d 203c 313e 3a20 2020 ransform <1>: \n+00024d70: 2020 2020 2020 2020 2020 204f 626a 6563 Objec\n+00024d80: 7420 7472 616e 7366 6f72 6d73 2e20 2020 t transforms. \n+00024d90: 286c 696e 6520 2020 3629 0a2a 2074 7261 (line 6).* tra\n+00024da0: 6e73 666f 726d 203c 313e 3a20 2020 2020 nsform <1>: \n 00024db0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024dc0: 2020 2020 2020 5477 6f2d 6f70 6572 616e Two-operan\n-00024dd0: 6420 2862 696e 6172 7929 2066 6f72 6d73 d (binary) forms\n-00024de0: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+00024dc0: 2020 2020 5477 6f2d 6f70 6572 616e 6420 Two-operand \n+00024dd0: 2862 696e 6172 7929 2066 6f72 6d73 2e0a (binary) forms..\n+00024de0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024df0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024e00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024e10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024e20: 286c 696e 6520 2032 3829 0a2a 2074 7261 (line 28).* tra\n-00024e30: 6e73 666f 726d 203c 323e 3a20 2020 2020 nsform <2>: \n+00024e10: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+00024e20: 696e 6520 2032 3829 0a2a 2074 7261 6e73 ine 28).* trans\n+00024e30: 666f 726d 203c 323e 3a20 2020 2020 2020 form <2>: \n 00024e40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024e50: 2020 2020 5377 6565 7073 2e20 2020 2020 Sweeps. \n-00024e60: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00024e70: 3131 290a 2a20 7472 616e 7366 6f72 6d20 11).* transform \n-00024e80: 3c33 3e3a 2020 2020 2020 2020 2020 2020 <3>: \n-00024e90: 2020 2020 2020 2020 2020 2020 2052 6570 Rep\n-00024ea0: 6561 7473 2e20 2020 2020 2020 2020 2020 eats. \n-00024eb0: 2020 286c 696e 6520 2020 3929 0a2a 2074 (line 9).* t\n-00024ec0: 7261 6e73 666f 726d 203c 343e 3a20 2020 ransform <4>: \n+00024e50: 2020 5377 6565 7073 2e20 2020 2020 2020 Sweeps. \n+00024e60: 2020 2020 2020 2028 6c69 6e65 2020 3131 (line 11\n+00024e70: 290a 2a20 7472 616e 7366 6f72 6d20 3c33 ).* transform <3\n+00024e80: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00024e90: 2020 2020 2020 2020 2020 2052 6570 6561 Repea\n+00024ea0: 7473 2e20 2020 2020 2020 2020 2020 2020 ts. \n+00024eb0: 286c 696e 6520 2020 3929 0a2a 2074 7261 (line 9).* tra\n+00024ec0: 6e73 666f 726d 203c 343e 3a20 2020 2020 nsform <4>: \n 00024ed0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024ee0: 2020 2020 2020 4f76 6572 7669 6577 2e20 Overview. \n-00024ef0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00024f00: 2020 2037 290a 2a20 7472 616e 7366 6f72 7).* transfor\n-00024f10: 6d20 6465 6669 6e69 7469 6f6e 3a20 2020 m definition: \n-00024f20: 2020 2020 2020 2020 2020 2020 2020 204f O\n-00024f30: 7665 7276 6965 772e 2020 2020 2020 2020 verview. \n-00024f40: 2020 2020 286c 696e 6520 2033 3529 0a2a (line 35).*\n-00024f50: 2074 7261 6e73 666f 726d 206c 6974 6572 transform liter\n-00024f60: 616c 3a20 2020 2020 2020 2020 2020 2020 al: \n-00024f70: 2020 2020 2020 2020 5472 616e 7366 6f72 Transfor\n-00024f80: 6d20 6c69 7465 7261 6c73 2e20 2028 6c69 m literals. (li\n-00024f90: 6e65 2020 2036 290a 2a20 7472 616e 7366 ne 6).* transf\n-00024fa0: 6f72 6d20 7265 6665 7265 6e63 653a 2020 orm reference: \n-00024fb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024fc0: 2046 6f72 6d73 206f 6620 7265 6665 7265 Forms of refere\n-00024fd0: 6e63 6573 2e20 286c 696e 6520 2031 3629 nces. (line 16)\n-00024fe0: 0a2a 2074 7261 6e73 666f 726d 2072 6566 .* transform ref\n-00024ff0: 6572 656e 6365 203c 313e 3a20 2020 2020 erence <1>: \n-00025000: 2020 2020 2020 2020 2020 4f76 6572 7669 Overvi\n-00025010: 6577 2e20 2020 2020 2020 2020 2020 2028 ew. (\n-00025020: 6c69 6e65 2020 3335 290a 2a20 7472 616e line 35).* tran\n-00025030: 7366 6f72 6d2c 2064 6972 6563 743a 2020 sform, direct: \n+00024ee0: 2020 2020 4f76 6572 7669 6577 2e20 2020 Overview. \n+00024ef0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00024f00: 2037 290a 2a20 7472 616e 7366 6f72 6d20 7).* transform \n+00024f10: 6465 6669 6e69 7469 6f6e 3a20 2020 2020 definition: \n+00024f20: 2020 2020 2020 2020 2020 2020 204f 7665 Ove\n+00024f30: 7276 6965 772e 2020 2020 2020 2020 2020 rview. \n+00024f40: 2020 286c 696e 6520 2033 3529 0a2a 2074 (line 35).* t\n+00024f50: 7261 6e73 666f 726d 206c 6974 6572 616c ransform literal\n+00024f60: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00024f70: 2020 2020 2020 5472 616e 7366 6f72 6d20 Transform \n+00024f80: 6c69 7465 7261 6c73 2e20 2028 6c69 6e65 literals. (line\n+00024f90: 2020 2036 290a 2a20 7472 616e 7366 6f72 6).* transfor\n+00024fa0: 6d20 7265 6665 7265 6e63 653a 2020 2020 m reference: \n+00024fb0: 2020 2020 2020 2020 2020 2020 2020 2046 F\n+00024fc0: 6f72 6d73 206f 6620 7265 6665 7265 6e63 orms of referenc\n+00024fd0: 6573 2e20 286c 696e 6520 2031 3629 0a2a es. (line 16).*\n+00024fe0: 2074 7261 6e73 666f 726d 2072 6566 6572 transform refer\n+00024ff0: 656e 6365 203c 313e 3a20 2020 2020 2020 ence <1>: \n+00025000: 2020 2020 2020 2020 4f76 6572 7669 6577 Overview\n+00025010: 2e20 2020 2020 2020 2020 2020 2028 6c69 . (li\n+00025020: 6e65 2020 3335 290a 2a20 7472 616e 7366 ne 35).* transf\n+00025030: 6f72 6d2c 2064 6972 6563 743a 2020 2020 orm, direct: \n 00025040: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025050: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n-00025060: 6572 616c 732e 2020 286c 696e 6520 2034 erals. (line 4\n-00025070: 3729 0a2a 2074 7261 6e73 666f 726d 2c20 7).* transform, \n-00025080: 6469 7265 6374 203c 313e 3a20 2020 2020 direct <1>: \n-00025090: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n-000250a0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n-000250b0: 2028 6c69 6e65 2020 3533 290a 2a20 7472 (line 53).* tr\n-000250c0: 616e 7366 6f72 6d2c 2072 6f74 6174 696f ansform, rotatio\n-000250d0: 6e3a 2020 2020 2020 2020 2020 2020 2020 n: \n-000250e0: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n-000250f0: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n-00025100: 2031 3029 0a2a 2074 7261 6e73 666f 726d 10).* transform\n-00025110: 2c20 726f 7461 7469 6f6e 203c 313e 3a20 , rotation <1>: \n-00025120: 2020 2020 2020 2020 2020 2020 2020 4120 A \n-00025130: 6869 6572 6172 6368 6963 616c 206d 6f64 hierarchical mod\n-00025140: 656c 2e0a 2020 2020 2020 2020 2020 2020 el.. \n+00025050: 2054 7261 6e73 666f 726d 206c 6974 6572 Transform liter\n+00025060: 616c 732e 2020 286c 696e 6520 2034 3729 als. (line 47)\n+00025070: 0a2a 2074 7261 6e73 666f 726d 2c20 6469 .* transform, di\n+00025080: 7265 6374 203c 313e 3a20 2020 2020 2020 rect <1>: \n+00025090: 2020 2020 2020 2020 2020 5472 616e 7366 Transf\n+000250a0: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028 orm literals. (\n+000250b0: 6c69 6e65 2020 3533 290a 2a20 7472 616e line 53).* tran\n+000250c0: 7366 6f72 6d2c 2072 6f74 6174 696f 6e3a sform, rotation:\n+000250d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000250e0: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n+000250f0: 6572 616c 732e 2020 286c 696e 6520 2031 erals. (line 1\n+00025100: 3029 0a2a 2074 7261 6e73 666f 726d 2c20 0).* transform, \n+00025110: 726f 7461 7469 6f6e 203c 313e 3a20 2020 rotation <1>: \n+00025120: 2020 2020 2020 2020 2020 2020 4120 6869 A hi\n+00025130: 6572 6172 6368 6963 616c 206d 6f64 656c erarchical model\n+00025140: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n 00025150: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025160: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025170: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025180: 2020 286c 696e 6520 2034 3829 0a2a 2074 (line 48).* t\n-00025190: 7261 6e73 666f 726d 2c20 726f 7461 7469 ransform, rotati\n-000251a0: 6f6e 203c 323e 3a20 2020 2020 2020 2020 on <2>: \n-000251b0: 2020 2020 2020 4120 6869 6572 6172 6368 A hierarch\n-000251c0: 6963 616c 206d 6f64 656c 2e0a 2020 2020 ical model.. \n+00025180: 286c 696e 6520 2034 3829 0a2a 2074 7261 (line 48).* tra\n+00025190: 6e73 666f 726d 2c20 726f 7461 7469 6f6e nsform, rotation\n+000251a0: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n+000251b0: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n+000251c0: 616c 206d 6f64 656c 2e0a 2020 2020 2020 al model.. \n 000251d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000251e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000251f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025200: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-00025210: 2035 3829 0a2a 2074 7261 6e73 666f 726d 58).* transform\n-00025220: 2c20 726f 7461 7469 6f6e 203c 333e 3a20 , rotation <3>: \n-00025230: 2020 2020 2020 2020 2020 2020 2020 4120 A \n-00025240: 6869 6572 6172 6368 6963 616c 206d 6f64 hierarchical mod\n-00025250: 656c 2e0a 2020 2020 2020 2020 2020 2020 el.. \n+00025200: 2020 2020 2020 2020 286c 696e 6520 2035 (line 5\n+00025210: 3829 0a2a 2074 7261 6e73 666f 726d 2c20 8).* transform, \n+00025220: 726f 7461 7469 6f6e 203c 333e 3a20 2020 rotation <3>: \n+00025230: 2020 2020 2020 2020 2020 2020 4120 6869 A hi\n+00025240: 6572 6172 6368 6963 616c 206d 6f64 656c erarchical model\n+00025250: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n 00025260: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025270: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025280: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025290: 2020 286c 696e 6520 2037 3829 0a2a 2074 (line 78).* t\n-000252a0: 7261 6e73 666f 726d 2c20 726f 7461 7469 ransform, rotati\n-000252b0: 6f6e 203c 343e 3a20 2020 2020 2020 2020 on <4>: \n-000252c0: 2020 2020 2020 4120 6869 6572 6172 6368 A hierarch\n-000252d0: 6963 616c 206d 6f64 656c 2e0a 2020 2020 ical model.. \n+00025290: 286c 696e 6520 2037 3829 0a2a 2074 7261 (line 78).* tra\n+000252a0: 6e73 666f 726d 2c20 726f 7461 7469 6f6e nsform, rotation\n+000252b0: 203c 343e 3a20 2020 2020 2020 2020 2020 <4>: \n+000252c0: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n+000252d0: 616c 206d 6f64 656c 2e0a 2020 2020 2020 al model.. \n 000252e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000252f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025300: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025310: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-00025320: 2039 3329 0a2a 2074 7261 6e73 666f 726d 93).* transform\n-00025330: 2c20 7363 616c 653a 2020 2020 2020 2020 , scale: \n-00025340: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n-00025350: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-00025360: 2e20 2028 6c69 6e65 2020 3136 290a 2a20 . (line 16).* \n-00025370: 7472 616e 7366 6f72 6d2c 2073 6361 6c65 transform, scale\n-00025380: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n-00025390: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n-000253a0: 206c 6974 6572 616c 732e 2020 286c 696e literals. (lin\n-000253b0: 6520 2031 3729 0a2a 2074 7261 6e73 666f e 17).* transfo\n-000253c0: 726d 2c20 7472 616e 736c 6174 696f 6e3a rm, translation:\n-000253d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000253e0: 4f62 6a65 6374 2074 7261 6e73 666f 726d Object transform\n-000253f0: 732e 2020 2028 6c69 6e65 2020 3437 290a s. (line 47).\n-00025400: 2a20 7472 616e 7366 6f72 6d2c 2074 7261 * transform, tra\n-00025410: 6e73 6c61 7469 6f6e 203c 313e 3a20 2020 nslation <1>: \n-00025420: 2020 2020 2020 2020 2054 7261 6e73 666f Transfo\n-00025430: 726d 206c 6974 6572 616c 732e 2020 286c rm literals. (l\n-00025440: 696e 6520 2031 3529 0a2a 2074 7261 6e73 ine 15).* trans\n-00025450: 666f 726d 2c20 7472 616e 736c 6174 696f form, translatio\n-00025460: 6e20 3c32 3e3a 2020 2020 2020 2020 2020 n <2>: \n-00025470: 2020 4120 6869 6572 6172 6368 6963 616c A hierarchical\n-00025480: 206d 6f64 656c 2e0a 2020 2020 2020 2020 model.. \n+00025310: 2020 2020 2020 2020 286c 696e 6520 2039 (line 9\n+00025320: 3329 0a2a 2074 7261 6e73 666f 726d 2c20 3).* transform, \n+00025330: 7363 616c 653a 2020 2020 2020 2020 2020 scale: \n+00025340: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n+00025350: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n+00025360: 2028 6c69 6e65 2020 3136 290a 2a20 7472 (line 16).* tr\n+00025370: 616e 7366 6f72 6d2c 2073 6361 6c65 203c ansform, scale <\n+00025380: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n+00025390: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n+000253a0: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n+000253b0: 2031 3729 0a2a 2074 7261 6e73 666f 726d 17).* transform\n+000253c0: 2c20 7472 616e 736c 6174 696f 6e3a 2020 , translation: \n+000253d0: 2020 2020 2020 2020 2020 2020 2020 4f62 Ob\n+000253e0: 6a65 6374 2074 7261 6e73 666f 726d 732e ject transforms.\n+000253f0: 2020 2028 6c69 6e65 2020 3437 290a 2a20 (line 47).* \n+00025400: 7472 616e 7366 6f72 6d2c 2074 7261 6e73 transform, trans\n+00025410: 6c61 7469 6f6e 203c 313e 3a20 2020 2020 lation <1>: \n+00025420: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n+00025430: 206c 6974 6572 616c 732e 2020 286c 696e literals. (lin\n+00025440: 6520 2031 3529 0a2a 2074 7261 6e73 666f e 15).* transfo\n+00025450: 726d 2c20 7472 616e 736c 6174 696f 6e20 rm, translation \n+00025460: 3c32 3e3a 2020 2020 2020 2020 2020 2020 <2>: \n+00025470: 4120 6869 6572 6172 6368 6963 616c 206d A hierarchical m\n+00025480: 6f64 656c 2e0a 2020 2020 2020 2020 2020 odel.. \n 00025490: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000254a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000254b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000254c0: 2020 2020 2020 286c 696e 6520 2034 3729 (line 47)\n-000254d0: 0a2a 2074 7261 6e73 666f 726d 2c20 7669 .* transform, vi\n-000254e0: 6577 3a20 2020 2020 2020 2020 2020 2020 ew: \n-000254f0: 2020 2020 2020 2020 2020 5472 616e 7366 Transf\n-00025500: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028 orm literals. (\n-00025510: 6c69 6e65 2020 3235 290a 2a20 7472 616e line 25).* tran\n-00025520: 7366 6f72 6d2c 2076 6965 7720 3c31 3e3a sform, view <1>:\n+000254c0: 2020 2020 286c 696e 6520 2034 3729 0a2a (line 47).*\n+000254d0: 2074 7261 6e73 666f 726d 2c20 7669 6577 transform, view\n+000254e0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+000254f0: 2020 2020 2020 2020 5472 616e 7366 6f72 Transfor\n+00025500: 6d20 6c69 7465 7261 6c73 2e20 2028 6c69 m literals. (li\n+00025510: 6e65 2020 3235 290a 2a20 7472 616e 7366 ne 25).* transf\n+00025520: 6f72 6d2c 2076 6965 7720 3c31 3e3a 2020 orm, view <1>: \n 00025530: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025540: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n-00025550: 6572 616c 732e 2020 286c 696e 6520 2033 erals. (line 3\n-00025560: 3529 0a2a 2074 7261 6e73 6c61 7469 6f6e 5).* translation\n-00025570: 2074 7261 6e73 666f 726d 3a20 2020 2020 transform: \n-00025580: 2020 2020 2020 2020 2020 2020 4f62 6a65 Obje\n-00025590: 6374 2074 7261 6e73 666f 726d 732e 2020 ct transforms. \n-000255a0: 2028 6c69 6e65 2020 3437 290a 2a20 7472 (line 47).* tr\n-000255b0: 616e 736c 6174 696f 6e20 7472 616e 7366 anslation transf\n-000255c0: 6f72 6d20 3c31 3e3a 2020 2020 2020 2020 orm <1>: \n-000255d0: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n-000255e0: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n-000255f0: 2031 3529 0a2a 2074 7261 6e73 6c61 7469 15).* translati\n-00025600: 6f6e 2074 7261 6e73 666f 726d 203c 323e on transform <2>\n-00025610: 3a20 2020 2020 2020 2020 2020 2020 4120 : A \n-00025620: 6869 6572 6172 6368 6963 616c 206d 6f64 hierarchical mod\n-00025630: 656c 2e0a 2020 2020 2020 2020 2020 2020 el.. \n+00025540: 2054 7261 6e73 666f 726d 206c 6974 6572 Transform liter\n+00025550: 616c 732e 2020 286c 696e 6520 2033 3529 als. (line 35)\n+00025560: 0a2a 2074 7261 6e73 6c61 7469 6f6e 2074 .* translation t\n+00025570: 7261 6e73 666f 726d 3a20 2020 2020 2020 ransform: \n+00025580: 2020 2020 2020 2020 2020 4f62 6a65 6374 Object\n+00025590: 2074 7261 6e73 666f 726d 732e 2020 2028 transforms. (\n+000255a0: 6c69 6e65 2020 3437 290a 2a20 7472 616e line 47).* tran\n+000255b0: 736c 6174 696f 6e20 7472 616e 7366 6f72 slation transfor\n+000255c0: 6d20 3c31 3e3a 2020 2020 2020 2020 2020 m <1>: \n+000255d0: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n+000255e0: 6572 616c 732e 2020 286c 696e 6520 2031 erals. (line 1\n+000255f0: 3529 0a2a 2074 7261 6e73 6c61 7469 6f6e 5).* translation\n+00025600: 2074 7261 6e73 666f 726d 203c 323e 3a20 transform <2>: \n+00025610: 2020 2020 2020 2020 2020 2020 4120 6869 A hi\n+00025620: 6572 6172 6368 6963 616c 206d 6f64 656c erarchical model\n+00025630: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n 00025640: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025650: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025660: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025670: 2020 286c 696e 6520 2034 3729 0a2a 2074 (line 47).* t\n-00025680: 7261 6e73 7061 7265 6e63 793a 2020 2020 ransparency: \n+00025670: 286c 696e 6520 2034 3729 0a2a 2074 7261 (line 47).* tra\n+00025680: 6e73 7061 7265 6e63 793a 2020 2020 2020 nsparency: \n 00025690: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000256a0: 2020 2020 2020 5472 616e 7370 6172 656e Transparen\n-000256b0: 6379 2e20 2020 2020 2020 2028 6c69 6e65 cy. (line\n-000256c0: 2020 2036 290a 2a20 7477 6f2d 6f70 6572 6).* two-oper\n-000256d0: 616e 6420 666f 726d 3a20 2020 2020 2020 and form: \n-000256e0: 2020 2020 2020 2020 2020 2020 2020 2054 T\n-000256f0: 776f 2d6f 7065 7261 6e64 2028 6269 6e61 wo-operand (bina\n-00025700: 7279 2920 666f 726d 732e 0a20 2020 2020 ry) forms.. \n+000256a0: 2020 2020 5472 616e 7370 6172 656e 6379 Transparency\n+000256b0: 2e20 2020 2020 2020 2028 6c69 6e65 2020 . (line \n+000256c0: 2036 290a 2a20 7477 6f2d 6f70 6572 616e 6).* two-operan\n+000256d0: 6420 666f 726d 3a20 2020 2020 2020 2020 d form: \n+000256e0: 2020 2020 2020 2020 2020 2020 2054 776f Two\n+000256f0: 2d6f 7065 7261 6e64 2028 6269 6e61 7279 -operand (binary\n+00025700: 2920 666f 726d 732e 0a20 2020 2020 2020 ) forms.. \n 00025710: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025720: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025730: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025740: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00025750: 2036 290a 2a20 756e 6172 7920 666f 726d 6).* unary form\n-00025760: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00025770: 2020 2020 2020 2020 2020 2020 2055 6e61 Una\n-00025780: 7279 2066 6f72 6d73 2e20 2020 2020 2020 ry forms. \n-00025790: 2020 286c 696e 6520 2020 3629 0a2a 2076 (line 6).* v\n-000257a0: 6563 746f 723a 2020 2020 2020 2020 2020 ector: \n+00025740: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n+00025750: 290a 2a20 756e 6172 7920 666f 726d 3a20 ).* unary form: \n+00025760: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00025770: 2020 2020 2020 2020 2020 2055 6e61 7279 Unary\n+00025780: 2066 6f72 6d73 2e20 2020 2020 2020 2020 forms. \n+00025790: 286c 696e 6520 2020 3629 0a2a 2076 6563 (line 6).* vec\n+000257a0: 746f 723a 2020 2020 2020 2020 2020 2020 tor: \n 000257b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000257c0: 2020 2020 2020 4f62 6a65 6374 2074 7261 Object tra\n-000257d0: 6e73 666f 726d 732e 2020 2028 6c69 6e65 nsforms. 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sketch -V option for backward compatibility.\n \\psset{linejoin=1}\n@@ -337,15 +337,15 @@\n reference to special arg %d cannot accept a point\n reference to special arg %d cannot accept a vector\n reference to special arg %d: out of range [1-%d]\n bad tick option character in #%d'%c (try #{%d}'%c)\n unknown special arg from flatten\n use of '#' not as special arg (try ##)\n can't open document template '%s%' for input\n-%% Sketch output, version 0.3 (build 7d, Fri Nov 27 12:42:07 2026)\n+%% Sketch output, version 0.3 (build 7d, Sun Oct 26 08:25:52 2025)\n %% Output language: %s\n document template with no escape '%s' has been ignored\n more than one escape in document template; all but first ignored\n operands of + (types %s and %s) cannot be added\n operands of - (types %s and %s) cannot be subtracted\n operands of * (types %s and %s) cannot be multiplied\n operands of 'then' (types %s and %s) cannot be multiplied\n"}, {"source1": "readelf --wide --decompress --hex-dump=.rodata {}", "source2": "readelf --wide --decompress --hex-dump=.rodata {}", "unified_diff": "@@ -322,16 +322,16 @@\n 0x0001c3f0 202d5470 2c202725 63270000 00000000 -Tp, '%c'......\n 0x0001c400 756e7265 636f676e 697a6564 206d6f64 unrecognized mod\n 0x0001c410 69666965 72206f66 206f7074 696f6e20 ifier of option \n 0x0001c420 272d5425 63270000 6d697373 696e6720 '-T%c'..missing \n 0x0001c430 50535472 69636b73 206f7220 54696b5a PSTricks or TikZ\n 0x0001c440 20766572 73696f6e 20616674 6572202d version after -\n 0x0001c450 56000000 00000000 302e3320 28627569 V.......0.3 (bui\n- 0x0001c460 6c642037 642c2046 7269204e 6f762032 ld 7d, Fri Nov 2\n- 0x0001c470 37203132 3a34323a 30372032 30323629 7 12:42:07 2026)\n+ 0x0001c460 6c642037 642c2053 756e204f 63742032 ld 7d, Sun Oct 2\n+ 0x0001c470 36203038 3a32353a 35322032 30323529 6 08:25:52 2025)\n 0x0001c480 00000000 00000000 25252061 7373756d ........%% assum\n 0x0001c490 65732050 53547269 636b7320 76657273 es PSTricks vers\n 0x0001c4a0 696f6e20 25730a00 25252075 7365202d ion %s..%% use -\n 0x0001c4b0 5620746f 2073656c 65637420 6561726c V to select earl\n 0x0001c4c0 69657220 76657273 696f6e73 0a000000 ier versions....\n 0x0001c4d0 61647661 6e63655f 746f5f6e 6578745f advance_to_next_\n 0x0001c4e0 66696c65 5f6e616d 653a2075 6e657870 file_name: unexp\n@@ -396,16 +396,16 @@\n 0x0001c890 73207370 65636961 6c206172 67202874 s special arg (t\n 0x0001c8a0 72792023 23290000 63616e27 74206f70 ry ##)..can't op\n 0x0001c8b0 656e2064 6f63756d 656e7420 74656d70 en document temp\n 0x0001c8c0 6c617465 20272573 25272066 6f722069 late '%s%' for i\n 0x0001c8d0 6e707574 0a000000 25252053 6b657463 nput....%% Sketc\n 0x0001c8e0 68206f75 74707574 2c207665 7273696f h output, versio\n 0x0001c8f0 6e20302e 33202862 75696c64 2037642c n 0.3 (build 7d,\n- 0x0001c900 20467269 204e6f76 20323720 31323a34 Fri Nov 27 12:4\n- 0x0001c910 323a3037 20323032 36290a25 25204f75 2:07 2026).%% Ou\n+ 0x0001c900 2053756e 204f6374 20323620 30383a32 Sun Oct 26 08:2\n+ 0x0001c910 353a3532 20323032 35290a25 25204f75 5:52 2025).%% Ou\n 0x0001c920 74707574 206c616e 67756167 653a2025 tput language: %\n 0x0001c930 730a0000 00000000 646f6375 6d656e74 s.......document\n 0x0001c940 2074656d 706c6174 65207769 7468206e template with n\n 0x0001c950 6f206573 63617065 20272573 27206861 o escape '%s' ha\n 0x0001c960 73206265 656e2069 676e6f72 65640000 s been ignored..\n 0x0001c970 6d6f7265 20746861 6e206f6e 65206573 more than one es\n 0x0001c980 63617065 20696e20 646f6375 6d656e74 cape in document\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 63366364 31633165 39663937 64333231 c6cd1c1e9f97d321\n- 0x00000010 32336535 34393637 35376331 64343339 23e5496757c1d439\n- 0x00000020 62663763 38622e64 65627567 00000000 bf7c8b.debug....\n- 0x00000030 4c76e3eb Lv..\n+ 0x00000000 62363564 62643166 35386632 30613133 b65dbd1f58f20a13\n+ 0x00000010 63633537 39356130 62646262 36333061 cc5795a0bdbb630a\n+ 0x00000020 61383633 65322e64 65627567 00000000 a863e2.debug....\n+ 0x00000030 c094388e ..8.\n \n"}]}]}]}]}, {"source1": "sketch-dbgsym_0.3.7-13_amd64.deb", "source2": "sketch-dbgsym_0.3.7-13_amd64.deb", "unified_diff": null, "details": [{"source1": "control.tar.xz", "source2": "control.tar.xz", "unified_diff": null, "details": [{"source1": "control.tar", "source2": "control.tar", "unified_diff": null, "details": [{"source1": "./control", "source2": "./control", "unified_diff": "@@ -5,8 +5,8 @@\n Architecture: amd64\n Maintainer: Debian Science Maintainers \n Installed-Size: 276\n Depends: sketch (= 1:0.3.7-13)\n Section: debug\n Priority: optional\n Description: debug symbols for sketch\n-Build-Ids: e0c6cd1c1e9f97d32123e5496757c1d439bf7c8b\n+Build-Ids: 94b65dbd1f58f20a13cc5795a0bdbb630aa863e2\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/e0/c6cd1c1e9f97d32123e5496757c1d439bf7c8b.debug\n+usr/lib/debug/.build-id/94/b65dbd1f58f20a13cc5795a0bdbb630aa863e2.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 2025-10-25 10:55:00.000000 ./\n drwxr-xr-x 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/\n drwxr-xr-x 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/lib/\n drwxr-xr-x 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/lib/debug/\n drwxr-xr-x 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/lib/debug/.build-id/\n-drwxr-xr-x 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/lib/debug/.build-id/e0/\n--rw-r--r-- 0 root (0) root (0) 272120 2025-10-25 10:55:00.000000 ./usr/lib/debug/.build-id/e0/c6cd1c1e9f97d32123e5496757c1d439bf7c8b.debug\n+drwxr-xr-x 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/lib/debug/.build-id/94/\n+-rw-r--r-- 0 root (0) root (0) 272120 2025-10-25 10:55:00.000000 ./usr/lib/debug/.build-id/94/b65dbd1f58f20a13cc5795a0bdbb630aa863e2.debug\n drwxr-xr-x 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/share/\n drwxr-xr-x 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/share/doc/\n lrwxrwxrwx 0 root (0) root (0) 0 2025-10-25 10:55:00.000000 ./usr/share/doc/sketch-dbgsym -> sketch\n"}, {"source1": "./usr/lib/debug/.build-id/e0/c6cd1c1e9f97d32123e5496757c1d439bf7c8b.debug", "source2": "./usr/lib/debug/.build-id/94/b65dbd1f58f20a13cc5795a0bdbb630aa863e2.debug", "comments": ["File has been modified after NT_GNU_BUILD_ID has been applied.", "Files 99% 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": "@@ -1,12 +1,12 @@\n \n Displaying notes found in: .note.gnu.property\n Owner Data size \tDescription\n GNU 0x00000010\tNT_GNU_PROPERTY_TYPE_0\t Properties: x86 ISA needed: x86-64-baseline\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: e0c6cd1c1e9f97d32123e5496757c1d439bf7c8b\n+ GNU 0x00000014\tNT_GNU_BUILD_ID (unique build ID bitstring)\t Build ID: 94b65dbd1f58f20a13cc5795a0bdbb630aa863e2\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"}]}]}]}]}]}