From b954ba5024717aea8a1be6d0657d576e3d7ccb33 Mon Sep 17 00:00:00 2001 From: Almar Klein Date: Wed, 20 Apr 2016 02:41:09 +0200 Subject: [PATCH] add extra materials related to lewiner mc algorithm --- skimage/measure/mc_meta/LookUpTable.h | 2322 +++++++++++++++++++++ skimage/measure/mc_meta/MarchingCubes.cpp | 1302 ++++++++++++ skimage/measure/mc_meta/createluts.py | 175 ++ skimage/measure/mc_meta/visual_test.py | 64 + 4 files changed, 3863 insertions(+) create mode 100644 skimage/measure/mc_meta/LookUpTable.h create mode 100644 skimage/measure/mc_meta/MarchingCubes.cpp create mode 100644 skimage/measure/mc_meta/createluts.py create mode 100644 skimage/measure/mc_meta/visual_test.py diff --git a/skimage/measure/mc_meta/LookUpTable.h b/skimage/measure/mc_meta/LookUpTable.h new file mode 100644 index 00000000..55293469 --- /dev/null +++ b/skimage/measure/mc_meta/LookUpTable.h @@ -0,0 +1,2322 @@ +/** + * @file LookUpTable.h + * @author Thomas Lewiner + * @author Math Dept, PUC-Rio + * @version 0.2 + * @date 12/08/2002 + * + * @brief LookUpTable for the MarchingCubes 33 Algorithm + */ +//________________________________________________ + + + +#ifndef _LOOKUPTABLE_H_ +#define _LOOKUPTABLE_H_ + + + + + +//_____________________________________________________________________________ +/** + * \brief case mapping + * For each of the possible vertex states listed in this table there is a + * specific triangulation of the edge intersection points. The table lists + * all of them in the form of 0-5 edge triples with the list terminated by + * the invalid value -1. For example: case[3] list the 2 triangles + * formed when cube[0] and cube[1] are inside of the surface, but the rest of + * the cube is not. + * + * Cube description: + * 7 ________ 6 _____6__ ________ + * /| /| 7/| /| /| /| + * / | / | / | /5 | / 6 / | + * 4 /_______ / | /__4____ / 10 /_______3/ | + * | | |5 | | 11 | | | | | 2 | + * | 3|__|_____|2 | |__|__2__| | 4 |__|_____| + * | / | / 8 3/ 9 / | / | / + * | / | / | / | /1 | / 5 / + * |/_______|/ |/___0___|/ |/_1_____|/ + * 0 1 0 1 + */ +//----------------------------------------------------------------------------- +static const char cases[256][2] = { +/* 0: */ { 0, -1 }, +/* 1: 0, */ { 1, 0 }, +/* 2: 1, */ { 1, 1 }, +/* 3: 0, 1, */ { 2, 0 }, +/* 4: 2, */ { 1, 2 }, +/* 5: 0, 2, */ { 3, 0 }, +/* 6: 1, 2, */ { 2, 3 }, +/* 7: 0, 1, 2, */ { 5, 0 }, +/* 8: 3, */ { 1, 3 }, +/* 9: 0, 3, */ { 2, 1 }, +/* 10: 1, 3, */ { 3, 3 }, +/* 11: 0, 1, 3, */ { 5, 1 }, +/* 12: 2, 3, */ { 2, 5 }, +/* 13: 0, 2, 3, */ { 5, 4 }, +/* 14: 1, 2, 3, */ { 5, 9 }, +/* 15: 0, 1, 2, 3, */ { 8, 0 }, +/* 16: 4, */ { 1, 4 }, +/* 17: 0, 4, */ { 2, 2 }, +/* 18: 1, 4, */ { 3, 4 }, +/* 19: 0, 1, 4, */ { 5, 2 }, +/* 20: 2, 4, */ { 4, 2 }, +/* 21: 0, 2, 4, */ { 6, 2 }, +/* 22: 1, 2, 4, */ { 6, 9 }, +/* 23: 0, 1, 2, 4, */ { 11, 0 }, +/* 24: 3, 4, */ { 3, 8 }, +/* 25: 0, 3, 4, */ { 5, 5 }, +/* 26: 1, 3, 4, */ { 7, 3 }, +/* 27: 0, 1, 3, 4, */ { 9, 1 }, +/* 28: 2, 3, 4, */ { 6, 16 }, +/* 29: 0, 2, 3, 4, */ { 14, 3 }, +/* 30: 1, 2, 3, 4, */ { 12, 12 }, +/* 31: 0, 1, 2, 3, 4, */ { 5, 24 }, +/* 32: 5, */ { 1, 5 }, +/* 33: 0, 5, */ { 3, 1 }, +/* 34: 1, 5, */ { 2, 4 }, +/* 35: 0, 1, 5, */ { 5, 3 }, +/* 36: 2, 5, */ { 3, 6 }, +/* 37: 0, 2, 5, */ { 7, 0 }, +/* 38: 1, 2, 5, */ { 5, 10 }, +/* 39: 0, 1, 2, 5, */ { 9, 0 }, +/* 40: 3, 5, */ { 4, 3 }, +/* 41: 0, 3, 5, */ { 6, 4 }, +/* 42: 1, 3, 5, */ { 6, 11 }, +/* 43: 0, 1, 3, 5, */ { 14, 1 }, +/* 44: 2, 3, 5, */ { 6, 17 }, +/* 45: 0, 2, 3, 5, */ { 12, 4 }, +/* 46: 1, 2, 3, 5, */ { 11, 6 }, +/* 47: 0, 1, 2, 3, 5, */ { 5, 25 }, +/* 48: 4, 5, */ { 2, 8 }, +/* 49: 0, 4, 5, */ { 5, 7 }, +/* 50: 1, 4, 5, */ { 5, 12 }, +/* 51: 0, 1, 4, 5, */ { 8, 1 }, +/* 52: 2, 4, 5, */ { 6, 18 }, +/* 53: 0, 2, 4, 5, */ { 12, 5 }, +/* 54: 1, 2, 4, 5, */ { 14, 7 }, +/* 55: 0, 1, 2, 4, 5, */ { 5, 28 }, +/* 56: 3, 4, 5, */ { 6, 21 }, +/* 57: 0, 3, 4, 5, */ { 11, 4 }, +/* 58: 1, 3, 4, 5, */ { 12, 15 }, +/* 59: 0, 1, 3, 4, 5, */ { 5, 30 }, +/* 60: 2, 3, 4, 5, */ { 10, 5 }, +/* 61: 0, 2, 3, 4, 5, */ { 6, 32 }, +/* 62: 1, 2, 3, 4, 5, */ { 6, 39 }, +/* 63: 0, 1, 2, 3, 4, 5, */ { 2, 12 }, +/* 64: 6, */ { 1, 6 }, +/* 65: 0, 6, */ { 4, 0 }, +/* 66: 1, 6, */ { 3, 5 }, +/* 67: 0, 1, 6, */ { 6, 0 }, +/* 68: 2, 6, */ { 2, 6 }, +/* 69: 0, 2, 6, */ { 6, 3 }, +/* 70: 1, 2, 6, */ { 5, 11 }, +/* 71: 0, 1, 2, 6, */ { 14, 0 }, +/* 72: 3, 6, */ { 3, 9 }, +/* 73: 0, 3, 6, */ { 6, 5 }, +/* 74: 1, 3, 6, */ { 7, 4 }, +/* 75: 0, 1, 3, 6, */ { 12, 1 }, +/* 76: 2, 3, 6, */ { 5, 14 }, +/* 77: 0, 2, 3, 6, */ { 11, 3 }, +/* 78: 1, 2, 3, 6, */ { 9, 4 }, +/* 79: 0, 1, 2, 3, 6, */ { 5, 26 }, +/* 80: 4, 6, */ { 3, 10 }, +/* 81: 0, 4, 6, */ { 6, 6 }, +/* 82: 1, 4, 6, */ { 7, 5 }, +/* 83: 0, 1, 4, 6, */ { 12, 2 }, +/* 84: 2, 4, 6, */ { 6, 19 }, +/* 85: 0, 2, 4, 6, */ { 10, 1 }, +/* 86: 1, 2, 4, 6, */ { 12, 13 }, +/* 87: 0, 1, 2, 4, 6, */ { 6, 24 }, +/* 88: 3, 4, 6, */ { 7, 7 }, +/* 89: 0, 3, 4, 6, */ { 12, 9 }, +/* 90: 1, 3, 4, 6, */ { 13, 1 }, +/* 91: 0, 1, 3, 4, 6, */ { 7, 9 }, +/* 92: 2, 3, 4, 6, */ { 12, 20 }, +/* 93: 0, 2, 3, 4, 6, */ { 6, 33 }, +/* 94: 1, 2, 3, 4, 6, */ { 7, 13 }, +/* 95: 0, 1, 2, 3, 4, 6, */ { 3, 12 }, +/* 96: 5, 6, */ { 2, 10 }, +/* 97: 0, 5, 6, */ { 6, 7 }, +/* 98: 1, 5, 6, */ { 5, 13 }, +/* 99: 0, 1, 5, 6, */ { 11, 2 }, +/* 100: 2, 5, 6, */ { 5, 16 }, +/* 101: 0, 2, 5, 6, */ { 12, 7 }, +/* 102: 1, 2, 5, 6, */ { 8, 3 }, +/* 103: 0, 1, 2, 5, 6, */ { 5, 29 }, +/* 104: 3, 5, 6, */ { 6, 22 }, +/* 105: 0, 3, 5, 6, */ { 10, 2 }, +/* 106: 1, 3, 5, 6, */ { 12, 17 }, +/* 107: 0, 1, 3, 5, 6, */ { 6, 27 }, +/* 108: 2, 3, 5, 6, */ { 14, 9 }, +/* 109: 0, 2, 3, 5, 6, */ { 6, 34 }, +/* 110: 1, 2, 3, 5, 6, */ { 5, 39 }, +/* 111: 0, 1, 2, 3, 5, 6, */ { 2, 14 }, +/* 112: 4, 5, 6, */ { 5, 20 }, +/* 113: 0, 4, 5, 6, */ { 14, 5 }, +/* 114: 1, 4, 5, 6, */ { 9, 5 }, +/* 115: 0, 1, 4, 5, 6, */ { 5, 32 }, +/* 116: 2, 4, 5, 6, */ { 11, 10 }, +/* 117: 0, 2, 4, 5, 6, */ { 6, 35 }, +/* 118: 1, 2, 4, 5, 6, */ { 5, 41 }, +/* 119: 0, 1, 2, 4, 5, 6, */ { 2, 16 }, +/* 120: 3, 4, 5, 6, */ { 12, 23 }, +/* 121: 0, 3, 4, 5, 6, */ { 6, 37 }, +/* 122: 1, 3, 4, 5, 6, */ { 7, 14 }, +/* 123: 0, 1, 3, 4, 5, 6, */ { 3, 16 }, +/* 124: 2, 3, 4, 5, 6, */ { 6, 46 }, +/* 125: 0, 2, 3, 4, 5, 6, */ { 4, 6 }, +/* 126: 1, 2, 3, 4, 5, 6, */ { 3, 21 }, +/* 127: 0, 1, 2, 3, 4, 5, 6, */ { 1, 8 }, +/* 128: 7, */ { 1, 7 }, +/* 129: 0, 7, */ { 3, 2 }, +/* 130: 1, 7, */ { 4, 1 }, +/* 131: 0, 1, 7, */ { 6, 1 }, +/* 132: 2, 7, */ { 3, 7 }, +/* 133: 0, 2, 7, */ { 7, 1 }, +/* 134: 1, 2, 7, */ { 6, 10 }, +/* 135: 0, 1, 2, 7, */ { 12, 0 }, +/* 136: 3, 7, */ { 2, 7 }, +/* 137: 0, 3, 7, */ { 5, 6 }, +/* 138: 1, 3, 7, */ { 6, 12 }, +/* 139: 0, 1, 3, 7, */ { 11, 1 }, +/* 140: 2, 3, 7, */ { 5, 15 }, +/* 141: 0, 2, 3, 7, */ { 9, 2 }, +/* 142: 1, 2, 3, 7, */ { 14, 6 }, +/* 143: 0, 1, 2, 3, 7, */ { 5, 27 }, +/* 144: 4, 7, */ { 2, 9 }, +/* 145: 0, 4, 7, */ { 5, 8 }, +/* 146: 1, 4, 7, */ { 6, 13 }, +/* 147: 0, 1, 4, 7, */ { 14, 2 }, +/* 148: 2, 4, 7, */ { 6, 20 }, +/* 149: 0, 2, 4, 7, */ { 12, 6 }, +/* 150: 1, 2, 4, 7, */ { 10, 3 }, +/* 151: 0, 1, 2, 4, 7, */ { 6, 25 }, +/* 152: 3, 4, 7, */ { 5, 18 }, +/* 153: 0, 3, 4, 7, */ { 8, 2 }, +/* 154: 1, 3, 4, 7, */ { 12, 16 }, +/* 155: 0, 1, 3, 4, 7, */ { 5, 31 }, +/* 156: 2, 3, 4, 7, */ { 11, 9 }, +/* 157: 0, 2, 3, 4, 7, */ { 5, 34 }, +/* 158: 1, 2, 3, 4, 7, */ { 6, 40 }, +/* 159: 0, 1, 2, 3, 4, 7, */ { 2, 13 }, +/* 160: 5, 7, */ { 3, 11 }, +/* 161: 0, 5, 7, */ { 7, 2 }, +/* 162: 1, 5, 7, */ { 6, 14 }, +/* 163: 0, 1, 5, 7, */ { 12, 3 }, +/* 164: 2, 5, 7, */ { 7, 6 }, +/* 165: 0, 2, 5, 7, */ { 13, 0 }, +/* 166: 1, 2, 5, 7, */ { 12, 14 }, +/* 167: 0, 1, 2, 5, 7, */ { 7, 8 }, +/* 168: 3, 5, 7, */ { 6, 23 }, +/* 169: 0, 3, 5, 7, */ { 12, 10 }, +/* 170: 1, 3, 5, 7, */ { 10, 4 }, +/* 171: 0, 1, 3, 5, 7, */ { 6, 28 }, +/* 172: 2, 3, 5, 7, */ { 12, 21 }, +/* 173: 0, 2, 3, 5, 7, */ { 7, 10 }, +/* 174: 1, 2, 3, 5, 7, */ { 6, 41 }, +/* 175: 0, 1, 2, 3, 5, 7, */ { 3, 13 }, +/* 176: 4, 5, 7, */ { 5, 21 }, +/* 177: 0, 4, 5, 7, */ { 9, 3 }, +/* 178: 1, 4, 5, 7, */ { 11, 8 }, +/* 179: 0, 1, 4, 5, 7, */ { 5, 33 }, +/* 180: 2, 4, 5, 7, */ { 12, 22 }, +/* 181: 0, 2, 4, 5, 7, */ { 7, 11 }, +/* 182: 1, 2, 4, 5, 7, */ { 6, 42 }, +/* 183: 0, 1, 2, 4, 5, 7, */ { 3, 14 }, +/* 184: 3, 4, 5, 7, */ { 14, 11 }, +/* 185: 0, 3, 4, 5, 7, */ { 5, 36 }, +/* 186: 1, 3, 4, 5, 7, */ { 6, 44 }, +/* 187: 0, 1, 3, 4, 5, 7, */ { 2, 17 }, +/* 188: 2, 3, 4, 5, 7, */ { 6, 47 }, +/* 189: 0, 2, 3, 4, 5, 7, */ { 3, 18 }, +/* 190: 1, 2, 3, 4, 5, 7, */ { 4, 7 }, +/* 191: 0, 1, 2, 3, 4, 5, 7, */ { 1, 9 }, +/* 192: 6, 7, */ { 2, 11 }, +/* 193: 0, 6, 7, */ { 6, 8 }, +/* 194: 1, 6, 7, */ { 6, 15 }, +/* 195: 0, 1, 6, 7, */ { 10, 0 }, +/* 196: 2, 6, 7, */ { 5, 17 }, +/* 197: 0, 2, 6, 7, */ { 12, 8 }, +/* 198: 1, 2, 6, 7, */ { 11, 7 }, +/* 199: 0, 1, 2, 6, 7, */ { 6, 26 }, +/* 200: 3, 6, 7, */ { 5, 19 }, +/* 201: 0, 3, 6, 7, */ { 14, 4 }, +/* 202: 1, 3, 6, 7, */ { 12, 18 }, +/* 203: 0, 1, 3, 6, 7, */ { 6, 29 }, +/* 204: 2, 3, 6, 7, */ { 8, 4 }, +/* 205: 0, 2, 3, 6, 7, */ { 5, 35 }, +/* 206: 1, 2, 3, 6, 7, */ { 5, 40 }, +/* 207: 0, 1, 2, 3, 6, 7, */ { 2, 15 }, +/* 208: 4, 6, 7, */ { 5, 22 }, +/* 209: 0, 4, 6, 7, */ { 11, 5 }, +/* 210: 1, 4, 6, 7, */ { 12, 19 }, +/* 211: 0, 1, 4, 6, 7, */ { 6, 30 }, +/* 212: 2, 4, 6, 7, */ { 14, 10 }, +/* 213: 0, 2, 4, 6, 7, */ { 6, 36 }, +/* 214: 1, 2, 4, 6, 7, */ { 6, 43 }, +/* 215: 0, 1, 2, 4, 6, 7, */ { 4, 4 }, +/* 216: 3, 4, 6, 7, */ { 9, 7 }, +/* 217: 0, 3, 4, 6, 7, */ { 5, 37 }, +/* 218: 1, 3, 4, 6, 7, */ { 7, 15 }, +/* 219: 0, 1, 3, 4, 6, 7, */ { 3, 17 }, +/* 220: 2, 3, 4, 6, 7, */ { 5, 44 }, +/* 221: 0, 2, 3, 4, 6, 7, */ { 2, 19 }, +/* 222: 1, 2, 3, 4, 6, 7, */ { 3, 22 }, +/* 223: 0, 1, 2, 3, 4, 6, 7, */ { 1, 10 }, +/* 224: 5, 6, 7, */ { 5, 23 }, +/* 225: 0, 5, 6, 7, */ { 12, 11 }, +/* 226: 1, 5, 6, 7, */ { 14, 8 }, +/* 227: 0, 1, 5, 6, 7, */ { 6, 31 }, +/* 228: 2, 5, 6, 7, */ { 9, 6 }, +/* 229: 0, 2, 5, 6, 7, */ { 7, 12 }, +/* 230: 1, 2, 5, 6, 7, */ { 5, 42 }, +/* 231: 0, 1, 2, 5, 6, 7, */ { 3, 15 }, +/* 232: 3, 5, 6, 7, */ { 11, 11 }, +/* 233: 0, 3, 5, 6, 7, */ { 6, 38 }, +/* 234: 1, 3, 5, 6, 7, */ { 6, 45 }, +/* 235: 0, 1, 3, 5, 6, 7, */ { 4, 5 }, +/* 236: 2, 3, 5, 6, 7, */ { 5, 45 }, +/* 237: 0, 2, 3, 5, 6, 7, */ { 3, 19 }, +/* 238: 1, 2, 3, 5, 6, 7, */ { 2, 21 }, +/* 239: 0, 1, 2, 3, 5, 6, 7, */ { 1, 11 }, +/* 240: 4, 5, 6, 7, */ { 8, 5 }, +/* 241: 0, 4, 5, 6, 7, */ { 5, 38 }, +/* 242: 1, 4, 5, 6, 7, */ { 5, 43 }, +/* 243: 0, 1, 4, 5, 6, 7, */ { 2, 18 }, +/* 244: 2, 4, 5, 6, 7, */ { 5, 46 }, +/* 245: 0, 2, 4, 5, 6, 7, */ { 3, 20 }, +/* 246: 1, 2, 4, 5, 6, 7, */ { 2, 22 }, +/* 247: 0, 1, 2, 4, 5, 6, 7, */ { 1, 12 }, +/* 248: 3, 4, 5, 6, 7, */ { 5, 47 }, +/* 249: 0, 3, 4, 5, 6, 7, */ { 2, 20 }, +/* 250: 1, 3, 4, 5, 6, 7, */ { 3, 23 }, +/* 251: 0, 1, 3, 4, 5, 6, 7, */ { 1, 13 }, +/* 252: 2, 3, 4, 5, 6, 7, */ { 2, 23 }, +/* 253: 0, 2, 3, 4, 5, 6, 7, */ { 1, 14 }, +/* 254: 1, 2, 3, 4, 5, 6, 7, */ { 1, 15 }, +/* 255: 0, 1, 2, 3, 4, 5, 6, 7, */ { 0, -1 } +}; +//_____________________________________________________________________________ + + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 1 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling1[16][3] = { +/* 1: 0, */ { 0, 8, 3 }, +/* 2: 1, */ { 0, 1, 9 }, +/* 4: 2, */ { 1, 2, 10 }, +/* 8: 3, */ { 3, 11, 2 }, +/* 16: 4, */ { 4, 7, 8 }, +/* 32: 5, */ { 9, 5, 4 }, +/* 64: 6, */ { 10, 6, 5 }, +/* 128: 7, */ { 7, 6, 11 }, +/* 127: 0, 1, 2, 3, 4, 5, 6, */ { 7, 11, 6 }, +/* 191: 0, 1, 2, 3, 4, 5, 7, */ { 10, 5, 6 }, +/* 223: 0, 1, 2, 3, 4, 6, 7, */ { 9, 4, 5 }, +/* 239: 0, 1, 2, 3, 5, 6, 7, */ { 4, 8, 7 }, +/* 247: 0, 1, 2, 4, 5, 6, 7, */ { 3, 2, 11 }, +/* 251: 0, 1, 3, 4, 5, 6, 7, */ { 1, 10, 2 }, +/* 253: 0, 2, 3, 4, 5, 6, 7, */ { 0, 9, 1 }, +/* 254: 1, 2, 3, 4, 5, 6, 7, */ { 0, 3, 8 } +}; +//_____________________________________________________________________________ + + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling2[24][6] = { +/* 3: 0, 1, */ { 1, 8, 3, 9, 8, 1 }, +/* 9: 0, 3, */ { 0, 11, 2, 8, 11, 0 }, +/* 17: 0, 4, */ { 4, 3, 0, 7, 3, 4 }, +/* 6: 1, 2, */ { 9, 2, 10, 0, 2, 9 }, +/* 34: 1, 5, */ { 0, 5, 4, 1, 5, 0 }, +/* 12: 2, 3, */ { 3, 10, 1, 11, 10, 3 }, +/* 68: 2, 6, */ { 1, 6, 5, 2, 6, 1 }, +/* 136: 3, 7, */ { 7, 2, 3, 6, 2, 7 }, +/* 48: 4, 5, */ { 9, 7, 8, 5, 7, 9 }, +/* 144: 4, 7, */ { 6, 8, 4, 11, 8, 6 }, +/* 96: 5, 6, */ { 10, 4, 9, 6, 4, 10 }, +/* 192: 6, 7, */ { 11, 5, 10, 7, 5, 11 }, +/* 63: 0, 1, 2, 3, 4, 5, */ { 11, 10, 5, 7, 11, 5 }, +/* 159: 0, 1, 2, 3, 4, 7, */ { 10, 9, 4, 6, 10, 4 }, +/* 111: 0, 1, 2, 3, 5, 6, */ { 6, 4, 8, 11, 6, 8 }, +/* 207: 0, 1, 2, 3, 6, 7, */ { 9, 8, 7, 5, 9, 7 }, +/* 119: 0, 1, 2, 4, 5, 6, */ { 7, 3, 2, 6, 7, 2 }, +/* 187: 0, 1, 3, 4, 5, 7, */ { 1, 5, 6, 2, 1, 6 }, +/* 243: 0, 1, 4, 5, 6, 7, */ { 3, 1, 10, 11, 3, 10 }, +/* 221: 0, 2, 3, 4, 6, 7, */ { 0, 4, 5, 1, 0, 5 }, +/* 249: 0, 3, 4, 5, 6, 7, */ { 9, 10, 2, 0, 9, 2 }, +/* 238: 1, 2, 3, 5, 6, 7, */ { 4, 0, 3, 7, 4, 3 }, +/* 246: 1, 2, 4, 5, 6, 7, */ { 0, 2, 11, 8, 0, 11 }, +/* 252: 2, 3, 4, 5, 6, 7, */ { 1, 3, 8, 9, 1, 8 } +}; +//_____________________________________________________________________________ + +//_____________________________________________________________________________ +/** + * \brief test table for case 3 + * One face to test + * When the test on the specified face is positive : 4 first triangles + * When the test on the specified face is negative : 2 last triangles + * + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char test3[24] = { +/* 5: 0, 2, */ 5, +/* 33: 0, 5, */ 1, +/* 129: 0, 7, */ 4, +/* 10: 1, 3, */ 5, +/* 18: 1, 4, */ 1, +/* 66: 1, 6, */ 2, +/* 36: 2, 5, */ 2, +/* 132: 2, 7, */ 3, +/* 24: 3, 4, */ 4, +/* 72: 3, 6, */ 3, +/* 80: 4, 6, */ 6, +/* 160: 5, 7, */ 6, +/* 95: 0, 1, 2, 3, 4, 6, */ -6, +/* 175: 0, 1, 2, 3, 5, 7, */ -6, +/* 183: 0, 1, 2, 4, 5, 7, */ -3, +/* 231: 0, 1, 2, 5, 6, 7, */ -4, +/* 123: 0, 1, 3, 4, 5, 6, */ -3, +/* 219: 0, 1, 3, 4, 6, 7, */ -2, +/* 189: 0, 2, 3, 4, 5, 7, */ -2, +/* 237: 0, 2, 3, 5, 6, 7, */ -1, +/* 245: 0, 2, 4, 5, 6, 7, */ -5, +/* 126: 1, 2, 3, 4, 5, 6, */ -4, +/* 222: 1, 2, 3, 4, 6, 7, */ -1, +/* 250: 1, 3, 4, 5, 6, 7, */ -5 +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 3.1 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling3_1[24][6] = { +/* 5: 0, 2, */ { 0, 8, 3, 1, 2, 10 }, +/* 33: 0, 5, */ { 9, 5, 4, 0, 8, 3 }, +/* 129: 0, 7, */ { 3, 0, 8, 11, 7, 6 }, +/* 10: 1, 3, */ { 1, 9, 0, 2, 3, 11 }, +/* 18: 1, 4, */ { 0, 1, 9, 8, 4, 7 }, +/* 66: 1, 6, */ { 9, 0, 1, 5, 10, 6 }, +/* 36: 2, 5, */ { 1, 2, 10, 9, 5, 4 }, +/* 132: 2, 7, */ { 10, 1, 2, 6, 11, 7 }, +/* 24: 3, 4, */ { 8, 4, 7, 3, 11, 2 }, +/* 72: 3, 6, */ { 2, 3, 11, 10, 6, 5 }, +/* 80: 4, 6, */ { 5, 10, 6, 4, 7, 8 }, +/* 160: 5, 7, */ { 4, 9, 5, 7, 6, 11 }, +/* 95: 0, 1, 2, 3, 4, 6, */ { 5, 9, 4, 11, 6, 7 }, +/* 175: 0, 1, 2, 3, 5, 7, */ { 6, 10, 5, 8, 7, 4 }, +/* 183: 0, 1, 2, 4, 5, 7, */ { 11, 3, 2, 5, 6, 10 }, +/* 231: 0, 1, 2, 5, 6, 7, */ { 7, 4, 8, 2, 11, 3 }, +/* 123: 0, 1, 3, 4, 5, 6, */ { 2, 1, 10, 7, 11, 6 }, +/* 219: 0, 1, 3, 4, 6, 7, */ { 10, 2, 1, 4, 5, 9 }, +/* 189: 0, 2, 3, 4, 5, 7, */ { 1, 0, 9, 6, 10, 5 }, +/* 237: 0, 2, 3, 5, 6, 7, */ { 9, 1, 0, 7, 4, 8 }, +/* 245: 0, 2, 4, 5, 6, 7, */ { 0, 9, 1, 11, 3, 2 }, +/* 126: 1, 2, 3, 4, 5, 6, */ { 8, 0, 3, 6, 7, 11 }, +/* 222: 1, 2, 3, 4, 6, 7, */ { 4, 5, 9, 3, 8, 0 }, +/* 250: 1, 3, 4, 5, 6, 7, */ { 3, 8, 0, 10, 2, 1 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 3.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling3_2[24][12] = { +/* 5: 0, 2, */ { 10, 3, 2, 10, 8, 3, 10, 1, 0, 8, 10, 0 }, +/* 33: 0, 5, */ { 3, 4, 8, 3, 5, 4, 3, 0, 9, 5, 3, 9 }, +/* 129: 0, 7, */ { 6, 8, 7, 6, 0, 8, 6, 11, 3, 0, 6, 3 }, +/* 10: 1, 3, */ { 11, 0, 3, 11, 9, 0, 11, 2, 1, 9, 11, 1 }, +/* 18: 1, 4, */ { 7, 9, 4, 7, 1, 9, 7, 8, 0, 1, 7, 0 }, +/* 66: 1, 6, */ { 6, 1, 10, 6, 0, 1, 9, 0, 6, 9, 6, 5 }, +/* 36: 2, 5, */ { 4, 10, 5, 4, 2, 10, 4, 9, 1, 2, 4, 1 }, +/* 132: 2, 7, */ { 7, 2, 11, 7, 1, 2, 7, 6, 10, 1, 7, 10 }, +/* 24: 3, 4, */ { 2, 7, 11, 2, 4, 7, 2, 3, 8, 4, 2, 8 }, +/* 72: 3, 6, */ { 5, 11, 6, 5, 3, 11, 5, 10, 2, 3, 5, 2 }, +/* 80: 4, 6, */ { 8, 6, 7, 8, 10, 6, 8, 4, 5, 10, 8, 5 }, +/* 160: 5, 7, */ { 11, 5, 6, 11, 9, 5, 11, 7, 4, 9, 11, 4 }, +/* 95: 0, 1, 2, 3, 4, 6, */ { 6, 5, 11, 5, 9, 11, 4, 7, 11, 4, 11, 9 }, +/* 175: 0, 1, 2, 3, 5, 7, */ { 7, 6, 8, 6, 10, 8, 5, 4, 8, 5, 8, 10 }, +/* 183: 0, 1, 2, 4, 5, 7, */ { 6, 11, 5, 11, 3, 5, 2, 10, 5, 2, 5, 3 }, +/* 231: 0, 1, 2, 5, 6, 7, */ { 11, 7, 2, 7, 4, 2, 8, 3, 2, 8, 2, 4 }, +/* 123: 0, 1, 3, 4, 5, 6, */ { 11, 2, 7, 2, 1, 7, 10, 6, 7, 10, 7, 1 }, +/* 219: 0, 1, 3, 4, 6, 7, */ { 5, 10, 4, 10, 2, 4, 1, 9, 4, 1, 4, 2 }, +/* 189: 0, 2, 3, 4, 5, 7, */ { 10, 1, 6, 1, 0, 6, 6, 0, 9, 5, 6, 9 }, +/* 237: 0, 2, 3, 5, 6, 7, */ { 4, 9, 7, 9, 1, 7, 0, 8, 7, 0, 7, 1 }, +/* 245: 0, 2, 4, 5, 6, 7, */ { 3, 0, 11, 0, 9, 11, 1, 2, 11, 1, 11, 9 }, +/* 126: 1, 2, 3, 4, 5, 6, */ { 7, 8, 6, 8, 0, 6, 3, 11, 6, 3, 6, 0 }, +/* 222: 1, 2, 3, 4, 6, 7, */ { 8, 4, 3, 4, 5, 3, 9, 0, 3, 9, 3, 5 }, +/* 250: 1, 3, 4, 5, 6, 7, */ { 2, 3, 10, 3, 8, 10, 0, 1, 10, 0, 10, 8 } +}; +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +/** + * \brief test table for case 4 + * Interior to test + * When the test on the interior is negative : 2 first triangles + * When the test on the interior is positive : 6 last triangles + * + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char test4[8] = { +/* 65: 0, 6, */ 7, +/* 130: 1, 7, */ 7, +/* 20: 2, 4, */ 7, +/* 40: 3, 5, */ 7, +/* 215: 0, 1, 2, 4, 6, 7, */ -7, +/* 235: 0, 1, 3, 5, 6, 7, */ -7, +/* 125: 0, 2, 3, 4, 5, 6, */ -7, +/* 190: 1, 2, 3, 4, 5, 7, */ -7 +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 4.1 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling4_1[8][6] = { +/* 65: 0, 6, */ { 0, 8, 3, 5, 10, 6 }, +/* 130: 1, 7, */ { 0, 1, 9, 11, 7, 6 }, +/* 20: 2, 4, */ { 1, 2, 10, 8, 4, 7 }, +/* 40: 3, 5, */ { 9, 5, 4, 2, 3, 11 }, +/* 215: 0, 1, 2, 4, 6, 7, */ { 4, 5, 9, 11, 3, 2 }, +/* 235: 0, 1, 3, 5, 6, 7, */ { 10, 2, 1, 7, 4, 8 }, +/* 125: 0, 2, 3, 4, 5, 6, */ { 9, 1, 0, 6, 7, 11 }, +/* 190: 1, 2, 3, 4, 5, 7, */ { 3, 8, 0, 6, 10, 5 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 4.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling4_2[8][18] = { +/* 65: 0, 6, */ { 8, 5, 0, 5, 8, 6, 3, 6, 8, 6, 3, 10, 0, 10, 3, 10, 0, 5 }, +/* 130: 1, 7, */ { 9, 6, 1, 6, 9, 7, 0, 7, 9, 7, 0, 11, 1, 11, 0, 11, 1, 6 }, +/* 20: 2, 4, */ { 10, 7, 2, 7, 10, 4, 1, 4, 10, 4, 1, 8, 2, 8, 1, 8, 2, 7 }, +/* 40: 3, 5, */ { 11, 4, 3, 4, 11, 5, 2, 5, 11, 5, 2, 9, 3, 9, 2, 9, 3, 4 }, +/* 215: 0, 1, 2, 4, 6, 7, */ { 3, 4, 11, 5, 11, 4, 11, 5, 2, 9, 2, 5, 2, 9, 3, 4, 3, 9 }, +/* 235: 0, 1, 3, 5, 6, 7, */ { 2, 7, 10, 4, 10, 7, 10, 4, 1, 8, 1, 4, 1, 8, 2, 7, 2, 8 }, +/* 125: 0, 2, 3, 4, 5, 6, */ { 1, 6, 9, 7, 9, 6, 9, 7, 0, 11, 0, 7, 0, 11, 1, 6, 1, 11 }, +/* 190: 1, 2, 3, 4, 5, 7, */ { 0, 5, 8, 6, 8, 5, 8, 6, 3, 10, 3, 6, 3, 10, 0, 5, 0, 10 } +}; +//_____________________________________________________________________________ + + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 5 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling5[48][9] = { +/* 7: 0, 1, 2, */ { 2, 8, 3, 2, 10, 8, 10, 9, 8 }, +/* 11: 0, 1, 3, */ { 1, 11, 2, 1, 9, 11, 9, 8, 11 }, +/* 19: 0, 1, 4, */ { 4, 1, 9, 4, 7, 1, 7, 3, 1 }, +/* 35: 0, 1, 5, */ { 8, 5, 4, 8, 3, 5, 3, 1, 5 }, +/* 13: 0, 2, 3, */ { 0, 10, 1, 0, 8, 10, 8, 11, 10 }, +/* 25: 0, 3, 4, */ { 11, 4, 7, 11, 2, 4, 2, 0, 4 }, +/* 137: 0, 3, 7, */ { 7, 0, 8, 7, 6, 0, 6, 2, 0 }, +/* 49: 0, 4, 5, */ { 9, 3, 0, 9, 5, 3, 5, 7, 3 }, +/* 145: 0, 4, 7, */ { 3, 6, 11, 3, 0, 6, 0, 4, 6 }, +/* 14: 1, 2, 3, */ { 3, 9, 0, 3, 11, 9, 11, 10, 9 }, +/* 38: 1, 2, 5, */ { 5, 2, 10, 5, 4, 2, 4, 0, 2 }, +/* 70: 1, 2, 6, */ { 9, 6, 5, 9, 0, 6, 0, 2, 6 }, +/* 50: 1, 4, 5, */ { 0, 7, 8, 0, 1, 7, 1, 5, 7 }, +/* 98: 1, 5, 6, */ { 10, 0, 1, 10, 6, 0, 6, 4, 0 }, +/* 76: 2, 3, 6, */ { 6, 3, 11, 6, 5, 3, 5, 1, 3 }, +/* 140: 2, 3, 7, */ { 10, 7, 6, 10, 1, 7, 1, 3, 7 }, +/* 100: 2, 5, 6, */ { 1, 4, 9, 1, 2, 4, 2, 6, 4 }, +/* 196: 2, 6, 7, */ { 11, 1, 2, 11, 7, 1, 7, 5, 1 }, +/* 152: 3, 4, 7, */ { 8, 2, 3, 8, 4, 2, 4, 6, 2 }, +/* 200: 3, 6, 7, */ { 2, 5, 10, 2, 3, 5, 3, 7, 5 }, +/* 112: 4, 5, 6, */ { 7, 10, 6, 7, 8, 10, 8, 9, 10 }, +/* 176: 4, 5, 7, */ { 6, 9, 5, 6, 11, 9, 11, 8, 9 }, +/* 208: 4, 6, 7, */ { 5, 8, 4, 5, 10, 8, 10, 11, 8 }, +/* 224: 5, 6, 7, */ { 4, 11, 7, 4, 9, 11, 9, 10, 11 }, +/* 31: 0, 1, 2, 3, 4, */ { 4, 7, 11, 4, 11, 9, 9, 11, 10 }, +/* 47: 0, 1, 2, 3, 5, */ { 5, 4, 8, 5, 8, 10, 10, 8, 11 }, +/* 79: 0, 1, 2, 3, 6, */ { 6, 5, 9, 6, 9, 11, 11, 9, 8 }, +/* 143: 0, 1, 2, 3, 7, */ { 7, 6, 10, 7, 10, 8, 8, 10, 9 }, +/* 55: 0, 1, 2, 4, 5, */ { 2, 10, 5, 2, 5, 3, 3, 5, 7 }, +/* 103: 0, 1, 2, 5, 6, */ { 8, 3, 2, 8, 2, 4, 4, 2, 6 }, +/* 59: 0, 1, 3, 4, 5, */ { 11, 2, 1, 11, 1, 7, 7, 1, 5 }, +/* 155: 0, 1, 3, 4, 7, */ { 1, 9, 4, 1, 4, 2, 2, 4, 6 }, +/* 115: 0, 1, 4, 5, 6, */ { 10, 6, 7, 10, 7, 1, 1, 7, 3 }, +/* 179: 0, 1, 4, 5, 7, */ { 6, 11, 3, 6, 3, 5, 5, 3, 1 }, +/* 157: 0, 2, 3, 4, 7, */ { 10, 1, 0, 10, 0, 6, 6, 0, 4 }, +/* 205: 0, 2, 3, 6, 7, */ { 0, 8, 7, 0, 7, 1, 1, 7, 5 }, +/* 185: 0, 3, 4, 5, 7, */ { 9, 5, 6, 9, 6, 0, 0, 6, 2 }, +/* 217: 0, 3, 4, 6, 7, */ { 5, 10, 2, 5, 2, 4, 4, 2, 0 }, +/* 241: 0, 4, 5, 6, 7, */ { 3, 0, 9, 3, 9, 11, 11, 9, 10 }, +/* 110: 1, 2, 3, 5, 6, */ { 3, 11, 6, 3, 6, 0, 0, 6, 4 }, +/* 206: 1, 2, 3, 6, 7, */ { 9, 0, 3, 9, 3, 5, 5, 3, 7 }, +/* 118: 1, 2, 4, 5, 6, */ { 7, 8, 0, 7, 0, 6, 6, 0, 2 }, +/* 230: 1, 2, 5, 6, 7, */ { 11, 7, 4, 11, 4, 2, 2, 4, 0 }, +/* 242: 1, 4, 5, 6, 7, */ { 0, 1, 10, 0, 10, 8, 8, 10, 11 }, +/* 220: 2, 3, 4, 6, 7, */ { 8, 4, 5, 8, 5, 3, 3, 5, 1 }, +/* 236: 2, 3, 5, 6, 7, */ { 4, 9, 1, 4, 1, 7, 7, 1, 3 }, +/* 244: 2, 4, 5, 6, 7, */ { 1, 2, 11, 1, 11, 9, 9, 11, 8 }, +/* 248: 3, 4, 5, 6, 7, */ { 2, 3, 8, 2, 8, 10, 10, 8, 9 } +}; +//_____________________________________________________________________________ + + +//_____________________________________________________________________________ +/** + * \brief test table for case 6 + * 1 face to test + eventually the interior + * When the test on the specified face is positive : 5 first triangles + * When the test on the specified face is negative : + * - if the test on the interior is negative : 3 middle triangles + * - if the test on the interior is positive : 8 last triangles + * The support edge for the interior test is marked as the 3rd column. + * + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char test6[48][3] = { +/* 67: 0, 1, 6, */ { 2, 7, 10 }, +/* 131: 0, 1, 7, */ { 4, 7, 11 }, +/* 21: 0, 2, 4, */ { 5, 7, 1 }, +/* 69: 0, 2, 6, */ { 5, 7, 3 }, +/* 41: 0, 3, 5, */ { 1, 7, 9 }, +/* 73: 0, 3, 6, */ { 3, 7, 10 }, +/* 81: 0, 4, 6, */ { 6, 7, 5 }, +/* 97: 0, 5, 6, */ { 1, 7, 8 }, +/* 193: 0, 6, 7, */ { 4, 7, 8 }, +/* 22: 1, 2, 4, */ { 1, 7, 8 }, +/* 134: 1, 2, 7, */ { 3, 7, 11 }, +/* 42: 1, 3, 5, */ { 5, 7, 2 }, +/* 138: 1, 3, 7, */ { 5, 7, 0 }, +/* 146: 1, 4, 7, */ { 1, 7, 9 }, +/* 162: 1, 5, 7, */ { 6, 7, 6 }, +/* 194: 1, 6, 7, */ { 2, 7, 9 }, +/* 28: 2, 3, 4, */ { 4, 7, 8 }, +/* 44: 2, 3, 5, */ { 2, 7, 9 }, +/* 52: 2, 4, 5, */ { 2, 7, 10 }, +/* 84: 2, 4, 6, */ { 6, 7, 7 }, +/* 148: 2, 4, 7, */ { 3, 7, 10 }, +/* 56: 3, 4, 5, */ { 4, 7, 11 }, +/* 104: 3, 5, 6, */ { 3, 7, 11 }, +/* 168: 3, 5, 7, */ { 6, 7, 4 }, +/* 87: 0, 1, 2, 4, 6, */ { -6, -7, 4 }, +/* 151: 0, 1, 2, 4, 7, */ { -3, -7, 11 }, +/* 199: 0, 1, 2, 6, 7, */ { -4, -7, 11 }, +/* 107: 0, 1, 3, 5, 6, */ { -3, -7, 10 }, +/* 171: 0, 1, 3, 5, 7, */ { -6, -7, 7 }, +/* 203: 0, 1, 3, 6, 7, */ { -2, -7, 10 }, +/* 211: 0, 1, 4, 6, 7, */ { -2, -7, 9 }, +/* 227: 0, 1, 5, 6, 7, */ { -4, -7, 8 }, +/* 61: 0, 2, 3, 4, 5, */ { -2, -7, 9 }, +/* 93: 0, 2, 3, 4, 6, */ { -6, -7, 6 }, +/* 109: 0, 2, 3, 5, 6, */ { -1, -7, 9 }, +/* 117: 0, 2, 4, 5, 6, */ { -5, -7, 0 }, +/* 213: 0, 2, 4, 6, 7, */ { -5, -7, 2 }, +/* 121: 0, 3, 4, 5, 6, */ { -3, -7, 11 }, +/* 233: 0, 3, 5, 6, 7, */ { -1, -7, 8 }, +/* 62: 1, 2, 3, 4, 5, */ { -4, -7, 8 }, +/* 158: 1, 2, 3, 4, 7, */ { -1, -7, 8 }, +/* 174: 1, 2, 3, 5, 7, */ { -6, -7, 5 }, +/* 182: 1, 2, 4, 5, 7, */ { -3, -7, 10 }, +/* 214: 1, 2, 4, 6, 7, */ { -1, -7, 9 }, +/* 186: 1, 3, 4, 5, 7, */ { -5, -7, 3 }, +/* 234: 1, 3, 5, 6, 7, */ { -5, -7, 1 }, +/* 124: 2, 3, 4, 5, 6, */ { -4, -7, 11 }, +/* 188: 2, 3, 4, 5, 7, */ { -2, -7, 10 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 6.1.1 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling6_1_1[48][9] = { +/* 67: 0, 1, 6, */ { 6, 5, 10, 3, 1, 8, 9, 8, 1 }, +/* 131: 0, 1, 7, */ { 11, 7, 6, 9, 3, 1, 3, 9, 8 }, +/* 21: 0, 2, 4, */ { 1, 2, 10, 7, 0, 4, 0, 7, 3 }, +/* 69: 0, 2, 6, */ { 3, 0, 8, 5, 2, 6, 2, 5, 1 }, +/* 41: 0, 3, 5, */ { 5, 4, 9, 2, 0, 11, 8, 11, 0 }, +/* 73: 0, 3, 6, */ { 10, 6, 5, 8, 2, 0, 2, 8, 11 }, +/* 81: 0, 4, 6, */ { 10, 6, 5, 0, 4, 3, 7, 3, 4 }, +/* 97: 0, 5, 6, */ { 3, 0, 8, 6, 4, 10, 9, 10, 4 }, +/* 193: 0, 6, 7, */ { 8, 3, 0, 10, 7, 5, 7, 10, 11 }, +/* 22: 1, 2, 4, */ { 8, 4, 7, 10, 0, 2, 0, 10, 9 }, +/* 134: 1, 2, 7, */ { 7, 6, 11, 0, 2, 9, 10, 9, 2 }, +/* 42: 1, 3, 5, */ { 2, 3, 11, 4, 1, 5, 1, 4, 0 }, +/* 138: 1, 3, 7, */ { 0, 1, 9, 6, 3, 7, 3, 6, 2 }, +/* 146: 1, 4, 7, */ { 9, 0, 1, 11, 4, 6, 4, 11, 8 }, +/* 162: 1, 5, 7, */ { 11, 7, 6, 1, 5, 0, 4, 0, 5 }, +/* 194: 1, 6, 7, */ { 0, 1, 9, 7, 5, 11, 10, 11, 5 }, +/* 28: 2, 3, 4, */ { 4, 7, 8, 1, 3, 10, 11, 10, 3 }, +/* 44: 2, 3, 5, */ { 9, 5, 4, 11, 1, 3, 1, 11, 10 }, +/* 52: 2, 4, 5, */ { 10, 1, 2, 8, 5, 7, 5, 8, 9 }, +/* 84: 2, 4, 6, */ { 8, 4, 7, 2, 6, 1, 5, 1, 6 }, +/* 148: 2, 4, 7, */ { 1, 2, 10, 4, 6, 8, 11, 8, 6 }, +/* 56: 3, 4, 5, */ { 2, 3, 11, 5, 7, 9, 8, 9, 7 }, +/* 104: 3, 5, 6, */ { 11, 2, 3, 9, 6, 4, 6, 9, 10 }, +/* 168: 3, 5, 7, */ { 9, 5, 4, 3, 7, 2, 6, 2, 7 }, +/* 87: 0, 1, 2, 4, 6, */ { 4, 5, 9, 2, 7, 3, 7, 2, 6 }, +/* 151: 0, 1, 2, 4, 7, */ { 3, 2, 11, 4, 6, 9, 10, 9, 6 }, +/* 199: 0, 1, 2, 6, 7, */ { 11, 3, 2, 9, 7, 5, 7, 9, 8 }, +/* 107: 0, 1, 3, 5, 6, */ { 10, 2, 1, 8, 6, 4, 6, 8, 11 }, +/* 171: 0, 1, 3, 5, 7, */ { 7, 4, 8, 1, 6, 2, 6, 1, 5 }, +/* 203: 0, 1, 3, 6, 7, */ { 2, 1, 10, 7, 5, 8, 9, 8, 5 }, +/* 211: 0, 1, 4, 6, 7, */ { 4, 5, 9, 3, 1, 11, 10, 11, 1 }, +/* 227: 0, 1, 5, 6, 7, */ { 8, 7, 4, 10, 3, 1, 3, 10, 11 }, +/* 61: 0, 2, 3, 4, 5, */ { 9, 1, 0, 11, 5, 7, 5, 11, 10 }, +/* 93: 0, 2, 3, 4, 6, */ { 6, 7, 11, 0, 5, 1, 5, 0, 4 }, +/* 109: 0, 2, 3, 5, 6, */ { 1, 0, 9, 6, 4, 11, 8, 11, 4 }, +/* 117: 0, 2, 4, 5, 6, */ { 9, 1, 0, 7, 3, 6, 2, 6, 3 }, +/* 213: 0, 2, 4, 6, 7, */ { 11, 3, 2, 5, 1, 4, 0, 4, 1 }, +/* 121: 0, 3, 4, 5, 6, */ { 11, 6, 7, 9, 2, 0, 2, 9, 10 }, +/* 233: 0, 3, 5, 6, 7, */ { 7, 4, 8, 2, 0, 10, 9, 10, 0 }, +/* 62: 1, 2, 3, 4, 5, */ { 0, 3, 8, 5, 7, 10, 11, 10, 7 }, +/* 158: 1, 2, 3, 4, 7, */ { 8, 0, 3, 10, 4, 6, 4, 10, 9 }, +/* 174: 1, 2, 3, 5, 7, */ { 5, 6, 10, 3, 4, 0, 4, 3, 7 }, +/* 182: 1, 2, 4, 5, 7, */ { 5, 6, 10, 0, 2, 8, 11, 8, 2 }, +/* 214: 1, 2, 4, 6, 7, */ { 9, 4, 5, 11, 0, 2, 0, 11, 8 }, +/* 186: 1, 3, 4, 5, 7, */ { 8, 0, 3, 6, 2, 5, 1, 5, 2 }, +/* 234: 1, 3, 5, 6, 7, */ { 10, 2, 1, 4, 0, 7, 3, 7, 0 }, +/* 124: 2, 3, 4, 5, 6, */ { 6, 7, 11, 1, 3, 9, 8, 9, 3 }, +/* 188: 2, 3, 4, 5, 7, */ { 10, 5, 6, 8, 1, 3, 1, 8, 9 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 6.1.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling6_1_2[48][27] = { + /* 67: 0, 1, 6, */ { 1, 12, 3, 12, 10, 3, 6, 3, 10, 3, 6, 8, 5, 8, 6, 8, 5, 12, 12, 9, 8, 1, 9, 12, 12, 5, 10 }, + /* 131: 0, 1, 7, */ { 1, 12, 3, 1, 11, 12, 11, 1, 6, 9, 6, 1, 6, 9, 7, 12, 7, 9, 9, 8, 12, 12, 8, 3, 11, 7, 12 }, + /* 21: 0, 2, 4, */ { 4, 12, 0, 4, 1, 12, 1, 4, 10, 7, 10, 4, 10, 7, 2, 12, 2, 7, 7, 3, 12, 12, 3, 0, 1, 2, 12 }, + /* 69: 0, 2, 6, */ { 6, 12, 2, 6, 3, 12, 3, 6, 8, 5, 8, 6, 8, 5, 0, 12, 0, 5, 5, 1, 12, 12, 1, 2, 3, 0, 12 }, + /* 41: 0, 3, 5, */ { 0, 12, 2, 12, 9, 2, 5, 2, 9, 2, 5, 11, 4, 11, 5, 11, 4, 12, 12, 8, 11, 0, 8, 12, 12, 4, 9 }, + /* 73: 0, 3, 6, */ { 0, 12, 2, 0, 10, 12, 10, 0, 5, 8, 5, 0, 5, 8, 6, 12, 6, 8, 8, 11, 12, 12, 11, 2, 10, 6, 12 }, + /* 81: 0, 4, 6, */ { 4, 12, 0, 12, 5, 0, 10, 0, 5, 0, 10, 3, 6, 3, 10, 3, 6, 12, 12, 7, 3, 4, 7, 12, 12, 6, 5 }, + /* 97: 0, 5, 6, */ { 4, 12, 6, 12, 8, 6, 3, 6, 8, 6, 3, 10, 0, 10, 3, 10, 0, 12, 12, 9, 10, 4, 9, 12, 12, 0, 8 }, + /* 193: 0, 6, 7, */ { 5, 12, 7, 5, 8, 12, 8, 5, 0, 10, 0, 5, 0, 10, 3, 12, 3, 10, 10, 11, 12, 12, 11, 7, 8, 3, 12 }, + /* 22: 1, 2, 4, */ { 2, 12, 0, 2, 8, 12, 8, 2, 7, 10, 7, 2, 7, 10, 4, 12, 4, 10, 10, 9, 12, 12, 9, 0, 8, 4, 12 }, + /* 134: 1, 2, 7, */ { 2, 12, 0, 12, 11, 0, 7, 0, 11, 0, 7, 9, 6, 9, 7, 9, 6, 12, 12, 10, 9, 2, 10, 12, 12, 6, 11 }, + /* 42: 1, 3, 5, */ { 5, 12, 1, 5, 2, 12, 2, 5, 11, 4, 11, 5, 11, 4, 3, 12, 3, 4, 4, 0, 12, 12, 0, 1, 2, 3, 12 }, + /* 138: 1, 3, 7, */ { 7, 12, 3, 7, 0, 12, 0, 7, 9, 6, 9, 7, 9, 6, 1, 12, 1, 6, 6, 2, 12, 12, 2, 3, 0, 1, 12 }, + /* 146: 1, 4, 7, */ { 6, 12, 4, 6, 9, 12, 9, 6, 1, 11, 1, 6, 1, 11, 0, 12, 0, 11, 11, 8, 12, 12, 8, 4, 9, 0, 12 }, + /* 162: 1, 5, 7, */ { 5, 12, 1, 12, 6, 1, 11, 1, 6, 1, 11, 0, 7, 0, 11, 0, 7, 12, 12, 4, 0, 5, 4, 12, 12, 7, 6 }, + /* 194: 1, 6, 7, */ { 5, 12, 7, 12, 9, 7, 0, 7, 9, 7, 0, 11, 1, 11, 0, 11, 1, 12, 12, 10, 11, 5, 10, 12, 12, 1, 9 }, + /* 28: 2, 3, 4, */ { 3, 12, 1, 12, 8, 1, 4, 1, 8, 1, 4, 10, 7, 10, 4, 10, 7, 12, 12, 11, 10, 3, 11, 12, 12, 7, 8 }, + /* 44: 2, 3, 5, */ { 3, 12, 1, 3, 9, 12, 9, 3, 4, 11, 4, 3, 4, 11, 5, 12, 5, 11, 11, 10, 12, 12, 10, 1, 9, 5, 12 }, + /* 52: 2, 4, 5, */ { 7, 12, 5, 7, 10, 12, 10, 7, 2, 8, 2, 7, 2, 8, 1, 12, 1, 8, 8, 9, 12, 12, 9, 5, 10, 1, 12 }, + /* 84: 2, 4, 6, */ { 6, 12, 2, 12, 7, 2, 8, 2, 7, 2, 8, 1, 4, 1, 8, 1, 4, 12, 12, 5, 1, 6, 5, 12, 12, 4, 7 }, + /* 148: 2, 4, 7, */ { 6, 12, 4, 12, 10, 4, 1, 4, 10, 4, 1, 8, 2, 8, 1, 8, 2, 12, 12, 11, 8, 6, 11, 12, 12, 2, 10 }, + /* 56: 3, 4, 5, */ { 7, 12, 5, 12, 11, 5, 2, 5, 11, 5, 2, 9, 3, 9, 2, 9, 3, 12, 12, 8, 9, 7, 8, 12, 12, 3, 11 }, + /* 104: 3, 5, 6, */ { 4, 12, 6, 4, 11, 12, 11, 4, 3, 9, 3, 4, 3, 9, 2, 12, 2, 9, 9, 10, 12, 12, 10, 6, 11, 2, 12 }, + /* 168: 3, 5, 7, */ { 7, 12, 3, 12, 4, 3, 9, 3, 4, 3, 9, 2, 5, 2, 9, 2, 5, 12, 12, 6, 2, 7, 6, 12, 12, 5, 4 }, + /* 87: 0, 1, 2, 4, 6, */ { 3, 12, 7, 3, 4, 12, 4, 3, 9, 2, 9, 3, 9, 2, 5, 12, 5, 2, 2, 6, 12, 12, 6, 7, 4, 5, 12 }, + /* 151: 0, 1, 2, 4, 7, */ { 6, 12, 4, 12, 11, 4, 3, 4, 11, 4, 3, 9, 2, 9, 3, 9, 2, 12, 12, 10, 9, 6, 10, 12, 12, 2, 11 }, + /* 199: 0, 1, 2, 6, 7, */ { 5, 12, 7, 5, 11, 12, 11, 5, 2, 9, 2, 5, 2, 9, 3, 12, 3, 9, 9, 8, 12, 12, 8, 7, 11, 3, 12 }, + /* 107: 0, 1, 3, 5, 6, */ { 4, 12, 6, 4, 10, 12, 10, 4, 1, 8, 1, 4, 1, 8, 2, 12, 2, 8, 8, 11, 12, 12, 11, 6, 10, 2, 12 }, + /* 171: 0, 1, 3, 5, 7, */ { 2, 12, 6, 2, 7, 12, 7, 2, 8, 1, 8, 2, 8, 1, 4, 12, 4, 1, 1, 5, 12, 12, 5, 6, 7, 4, 12 }, + /* 203: 0, 1, 3, 6, 7, */ { 5, 12, 7, 12, 10, 7, 2, 7, 10, 7, 2, 8, 1, 8, 2, 8, 1, 12, 12, 9, 8, 5, 9, 12, 12, 1, 10 }, + /* 211: 0, 1, 4, 6, 7, */ { 1, 12, 3, 12, 9, 3, 4, 3, 9, 3, 4, 11, 5, 11, 4, 11, 5, 12, 12, 10, 11, 1, 10, 12, 12, 5, 9 }, + /* 227: 0, 1, 5, 6, 7, */ { 1, 12, 3, 1, 8, 12, 8, 1, 4, 10, 4, 1, 4, 10, 7, 12, 7, 10, 10, 11, 12, 12, 11, 3, 8, 7, 12 }, + /* 61: 0, 2, 3, 4, 5, */ { 7, 12, 5, 7, 9, 12, 9, 7, 0, 11, 0, 7, 0, 11, 1, 12, 1, 11, 11, 10, 12, 12, 10, 5, 9, 1, 12 }, + /* 93: 0, 2, 3, 4, 6, */ { 1, 12, 5, 1, 6, 12, 6, 1, 11, 0, 11, 1, 11, 0, 7, 12, 7, 0, 0, 4, 12, 12, 4, 5, 6, 7, 12 }, + /* 109: 0, 2, 3, 5, 6, */ { 4, 12, 6, 12, 9, 6, 1, 6, 9, 6, 1, 11, 0, 11, 1, 11, 0, 12, 12, 8, 11, 4, 8, 12, 12, 0, 9 }, + /* 117: 0, 2, 4, 5, 6, */ { 3, 12, 7, 12, 0, 7, 9, 7, 0, 7, 9, 6, 1, 6, 9, 6, 1, 12, 12, 2, 6, 3, 2, 12, 12, 1, 0 }, + /* 213: 0, 2, 4, 6, 7, */ { 1, 12, 5, 12, 2, 5, 11, 5, 2, 5, 11, 4, 3, 4, 11, 4, 3, 12, 12, 0, 4, 1, 0, 12, 12, 3, 2 }, + /* 121: 0, 3, 4, 5, 6, */ { 0, 12, 2, 0, 11, 12, 11, 0, 7, 9, 7, 0, 7, 9, 6, 12, 6, 9, 9, 10, 12, 12, 10, 2, 11, 6, 12 }, + /* 233: 0, 3, 5, 6, 7, */ { 0, 12, 2, 12, 8, 2, 7, 2, 8, 2, 7, 10, 4, 10, 7, 10, 4, 12, 12, 9, 10, 0, 9, 12, 12, 4, 8 }, + /* 62: 1, 2, 3, 4, 5, */ { 7, 12, 5, 12, 8, 5, 0, 5, 8, 5, 0, 10, 3, 10, 0, 10, 3, 12, 12, 11, 10, 7, 11, 12, 12, 3, 8 }, + /* 158: 1, 2, 3, 4, 7, */ { 6, 12, 4, 6, 8, 12, 8, 6, 3, 10, 3, 6, 3, 10, 0, 12, 0, 10, 10, 9, 12, 12, 9, 4, 8, 0, 12 }, + /* 174: 1, 2, 3, 5, 7, */ { 0, 12, 4, 0, 5, 12, 5, 0, 10, 3, 10, 0, 10, 3, 6, 12, 6, 3, 3, 7, 12, 12, 7, 4, 5, 6, 12 }, + /* 182: 1, 2, 4, 5, 7, */ { 2, 12, 0, 12, 10, 0, 5, 0, 10, 0, 5, 8, 6, 8, 5, 8, 6, 12, 12, 11, 8, 2, 11, 12, 12, 6, 10 }, + /* 214: 1, 2, 4, 6, 7, */ { 2, 12, 0, 2, 9, 12, 9, 2, 5, 11, 5, 2, 5, 11, 4, 12, 4, 11, 11, 8, 12, 12, 8, 0, 9, 4, 12 }, + /* 186: 1, 3, 4, 5, 7, */ { 2, 12, 6, 12, 3, 6, 8, 6, 3, 6, 8, 5, 0, 5, 8, 5, 0, 12, 12, 1, 5, 2, 1, 12, 12, 0, 3 }, + /* 234: 1, 3, 5, 6, 7, */ { 0, 12, 4, 12, 1, 4, 10, 4, 1, 4, 10, 7, 2, 7, 10, 7, 2, 12, 12, 3, 7, 0, 3, 12, 12, 2, 1 }, + /* 124: 2, 3, 4, 5, 6, */ { 3, 12, 1, 12, 11, 1, 6, 1, 11, 1, 6, 9, 7, 9, 6, 9, 7, 12, 12, 8, 9, 3, 8, 12, 12, 7, 11 }, + /* 188: 2, 3, 4, 5, 7, */ { 3, 12, 1, 3, 10, 12, 10, 3, 6, 8, 6, 3, 6, 8, 5, 12, 5, 8, 8, 9, 12, 12, 9, 1, 10, 5, 12 }, +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 6.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling6_2[48][15] = { +/* 67: 0, 1, 6, */ { 1, 10, 3, 6, 3, 10, 3, 6, 8, 5, 8, 6, 8, 5, 9 }, +/* 131: 0, 1, 7, */ { 1, 11, 3, 11, 1, 6, 9, 6, 1, 6, 9, 7, 8, 7, 9 }, +/* 21: 0, 2, 4, */ { 4, 1, 0, 1, 4, 10, 7, 10, 4, 10, 7, 2, 3, 2, 7 }, +/* 69: 0, 2, 6, */ { 6, 3, 2, 3, 6, 8, 5, 8, 6, 8, 5, 0, 1, 0, 5 }, +/* 41: 0, 3, 5, */ { 0, 9, 2, 5, 2, 9, 2, 5, 11, 4, 11, 5, 11, 4, 8 }, +/* 73: 0, 3, 6, */ { 0, 10, 2, 10, 0, 5, 8, 5, 0, 5, 8, 6, 11, 6, 8 }, +/* 81: 0, 4, 6, */ { 4, 5, 0, 10, 0, 5, 0, 10, 3, 6, 3, 10, 3, 6, 7 }, +/* 97: 0, 5, 6, */ { 4, 8, 6, 3, 6, 8, 6, 3, 10, 0, 10, 3, 10, 0, 9 }, +/* 193: 0, 6, 7, */ { 5, 8, 7, 8, 5, 0, 10, 0, 5, 0, 10, 3, 11, 3, 10 }, +/* 22: 1, 2, 4, */ { 2, 8, 0, 8, 2, 7, 10, 7, 2, 7, 10, 4, 9, 4, 10 }, +/* 134: 1, 2, 7, */ { 2, 11, 0, 7, 0, 11, 0, 7, 9, 6, 9, 7, 9, 6, 10 }, +/* 42: 1, 3, 5, */ { 5, 2, 1, 2, 5, 11, 4, 11, 5, 11, 4, 3, 0, 3, 4 }, +/* 138: 1, 3, 7, */ { 7, 0, 3, 0, 7, 9, 6, 9, 7, 9, 6, 1, 2, 1, 6 }, +/* 146: 1, 4, 7, */ { 6, 9, 4, 9, 6, 1, 11, 1, 6, 1, 11, 0, 8, 0, 11 }, +/* 162: 1, 5, 7, */ { 5, 6, 1, 11, 1, 6, 1, 11, 0, 7, 0, 11, 0, 7, 4 }, +/* 194: 1, 6, 7, */ { 5, 9, 7, 0, 7, 9, 7, 0, 11, 1, 11, 0, 11, 1, 10 }, +/* 28: 2, 3, 4, */ { 3, 8, 1, 4, 1, 8, 1, 4, 10, 7, 10, 4, 10, 7, 11 }, +/* 44: 2, 3, 5, */ { 3, 9, 1, 9, 3, 4, 11, 4, 3, 4, 11, 5, 10, 5, 11 }, +/* 52: 2, 4, 5, */ { 7, 10, 5, 10, 7, 2, 8, 2, 7, 2, 8, 1, 9, 1, 8 }, +/* 84: 2, 4, 6, */ { 6, 7, 2, 8, 2, 7, 2, 8, 1, 4, 1, 8, 1, 4, 5 }, +/* 148: 2, 4, 7, */ { 6, 10, 4, 1, 4, 10, 4, 1, 8, 2, 8, 1, 8, 2, 11 }, +/* 56: 3, 4, 5, */ { 7, 11, 5, 2, 5, 11, 5, 2, 9, 3, 9, 2, 9, 3, 8 }, +/* 104: 3, 5, 6, */ { 4, 11, 6, 11, 4, 3, 9, 3, 4, 3, 9, 2, 10, 2, 9 }, +/* 168: 3, 5, 7, */ { 7, 4, 3, 9, 3, 4, 3, 9, 2, 5, 2, 9, 2, 5, 6 }, +/* 87: 0, 1, 2, 4, 6, */ { 3, 4, 7, 4, 3, 9, 2, 9, 3, 9, 2, 5, 6, 5, 2 }, +/* 151: 0, 1, 2, 4, 7, */ { 6, 11, 4, 3, 4, 11, 4, 3, 9, 2, 9, 3, 9, 2, 10 }, +/* 199: 0, 1, 2, 6, 7, */ { 5, 11, 7, 11, 5, 2, 9, 2, 5, 2, 9, 3, 8, 3, 9 }, +/* 107: 0, 1, 3, 5, 6, */ { 4, 10, 6, 10, 4, 1, 8, 1, 4, 1, 8, 2, 11, 2, 8 }, +/* 171: 0, 1, 3, 5, 7, */ { 2, 7, 6, 7, 2, 8, 1, 8, 2, 8, 1, 4, 5, 4, 1 }, +/* 203: 0, 1, 3, 6, 7, */ { 5, 10, 7, 2, 7, 10, 7, 2, 8, 1, 8, 2, 8, 1, 9 }, +/* 211: 0, 1, 4, 6, 7, */ { 1, 9, 3, 4, 3, 9, 3, 4, 11, 5, 11, 4, 11, 5, 10 }, +/* 227: 0, 1, 5, 6, 7, */ { 1, 8, 3, 8, 1, 4, 10, 4, 1, 4, 10, 7, 11, 7, 10 }, +/* 61: 0, 2, 3, 4, 5, */ { 7, 9, 5, 9, 7, 0, 11, 0, 7, 0, 11, 1, 10, 1, 11 }, +/* 93: 0, 2, 3, 4, 6, */ { 1, 6, 5, 6, 1, 11, 0, 11, 1, 11, 0, 7, 4, 7, 0 }, +/* 109: 0, 2, 3, 5, 6, */ { 4, 9, 6, 1, 6, 9, 6, 1, 11, 0, 11, 1, 11, 0, 8 }, +/* 117: 0, 2, 4, 5, 6, */ { 3, 0, 7, 9, 7, 0, 7, 9, 6, 1, 6, 9, 6, 1, 2 }, +/* 213: 0, 2, 4, 6, 7, */ { 1, 2, 5, 11, 5, 2, 5, 11, 4, 3, 4, 11, 4, 3, 0 }, +/* 121: 0, 3, 4, 5, 6, */ { 0, 11, 2, 11, 0, 7, 9, 7, 0, 7, 9, 6, 10, 6, 9 }, +/* 233: 0, 3, 5, 6, 7, */ { 0, 8, 2, 7, 2, 8, 2, 7, 10, 4, 10, 7, 10, 4, 9 }, +/* 62: 1, 2, 3, 4, 5, */ { 7, 8, 5, 0, 5, 8, 5, 0, 10, 3, 10, 0, 10, 3, 11 }, +/* 158: 1, 2, 3, 4, 7, */ { 6, 8, 4, 8, 6, 3, 10, 3, 6, 3, 10, 0, 9, 0, 10 }, +/* 174: 1, 2, 3, 5, 7, */ { 0, 5, 4, 5, 0, 10, 3, 10, 0, 10, 3, 6, 7, 6, 3 }, +/* 182: 1, 2, 4, 5, 7, */ { 2, 10, 0, 5, 0, 10, 0, 5, 8, 6, 8, 5, 8, 6, 11 }, +/* 214: 1, 2, 4, 6, 7, */ { 2, 9, 0, 9, 2, 5, 11, 5, 2, 5, 11, 4, 8, 4, 11 }, +/* 186: 1, 3, 4, 5, 7, */ { 2, 3, 6, 8, 6, 3, 6, 8, 5, 0, 5, 8, 5, 0, 1 }, +/* 234: 1, 3, 5, 6, 7, */ { 0, 1, 4, 10, 4, 1, 4, 10, 7, 2, 7, 10, 7, 2, 3 }, +/* 124: 2, 3, 4, 5, 6, */ { 3, 11, 1, 6, 1, 11, 1, 6, 9, 7, 9, 6, 9, 7, 8 }, +/* 188: 2, 3, 4, 5, 7, */ { 3, 10, 1, 10, 3, 6, 8, 6, 3, 6, 8, 5, 9, 5, 8 } +}; +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +/** + * \brief test table for case 7 + * 3 faces to test + eventually the interior + * When the tests on the 3 specified faces are positive : + * - if the test on the interior is positive : 5 first triangles + * - if the test on the interior is negative : 9 next triangles + * When the tests on the first and the second specified faces are positive : 9 next triangles + * When the tests on the first and the third specified faces are positive : 9 next triangles + * When the tests on the second and the third specified faces are positive : 9 next triangles + * When the test on the first specified face is positive : 5 next triangles + * When the test on the second specified face is positive : 5 next triangles + * When the test on the third specified face is positive : 5 next triangles + * When the tests on the 3 specified faces are negative : 3 last triangles + * The support edge for the interior test is marked as the 5th column. + * + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char test7[16][5] = { +/* 37: 0, 2, 5, */ { 1, 2, 5, 7, 1 }, +/* 133: 0, 2, 7, */ { 3, 4, 5, 7, 3 }, +/* 161: 0, 5, 7, */ { 4, 1, 6, 7, 4 }, +/* 26: 1, 3, 4, */ { 4, 1, 5, 7, 0 }, +/* 74: 1, 3, 6, */ { 2, 3, 5, 7, 2 }, +/* 82: 1, 4, 6, */ { 1, 2, 6, 7, 5 }, +/* 164: 2, 5, 7, */ { 2, 3, 6, 7, 6 }, +/* 88: 3, 4, 6, */ { 3, 4, 6, 7, 7 }, +/* 167: 0, 1, 2, 5, 7, */ { -3, -4, -6, -7, 7 }, +/* 91: 0, 1, 3, 4, 6, */ { -2, -3, -6, -7, 6 }, +/* 173: 0, 2, 3, 5, 7, */ { -1, -2, -6, -7, 5 }, +/* 181: 0, 2, 4, 5, 7, */ { -2, -3, -5, -7, 2 }, +/* 229: 0, 2, 5, 6, 7, */ { -4, -1, -5, -7, 0 }, +/* 94: 1, 2, 3, 4, 6, */ { -4, -1, -6, -7, 4 }, +/* 122: 1, 3, 4, 5, 6, */ { -3, -4, -5, -7, 3 }, +/* 218: 1, 3, 4, 6, 7, */ { -1, -2, -5, -7, 1 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 7.1 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling7_1[16][9] = { +/* 37: 0, 2, 5, */ { 9, 5, 4, 10, 1, 2, 8, 3, 0 }, +/* 133: 0, 2, 7, */ { 11, 7, 6, 8, 3, 0, 10, 1, 2 }, +/* 161: 0, 5, 7, */ { 3, 0, 8, 5, 4, 9, 7, 6, 11 }, +/* 26: 1, 3, 4, */ { 8, 4, 7, 9, 0, 1, 11, 2, 3 }, +/* 74: 1, 3, 6, */ { 10, 6, 5, 11, 2, 3, 9, 0, 1 }, +/* 82: 1, 4, 6, */ { 0, 1, 9, 6, 5, 10, 4, 7, 8 }, +/* 164: 2, 5, 7, */ { 1, 2, 10, 7, 6, 11, 5, 4, 9 }, +/* 88: 3, 4, 6, */ { 2, 3, 11, 4, 7, 8, 6, 5, 10 }, +/* 167: 0, 1, 2, 5, 7, */ { 11, 3, 2, 8, 7, 4, 10, 5, 6 }, +/* 91: 0, 1, 3, 4, 6, */ { 10, 2, 1, 11, 6, 7, 9, 4, 5 }, +/* 173: 0, 2, 3, 5, 7, */ { 9, 1, 0, 10, 5, 6, 8, 7, 4 }, +/* 181: 0, 2, 4, 5, 7, */ { 5, 6, 10, 3, 2, 11, 1, 0, 9 }, +/* 229: 0, 2, 5, 6, 7, */ { 7, 4, 8, 1, 0, 9, 3, 2, 11 }, +/* 94: 1, 2, 3, 4, 6, */ { 8, 0, 3, 9, 4, 5, 11, 6, 7 }, +/* 122: 1, 3, 4, 5, 6, */ { 6, 7, 11, 0, 3, 8, 2, 1, 10 }, +/* 218: 1, 3, 4, 6, 7, */ { 4, 5, 9, 2, 1, 10, 0, 3, 8 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 7.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling7_2[16][3][15] = { +/* 37: 0, 2, 5, */ { + /* 1,0 */ { 1, 2, 10, 3, 4, 8, 4, 3, 5, 0, 5, 3, 5, 0, 9 }, + /* 0,1 */ { 3, 0, 8, 9, 1, 4, 2, 4, 1, 4, 2, 5, 10, 5, 2 }, + /* 1,1 */ { 9, 5, 4, 0, 10, 1, 10, 0, 8, 10, 8, 2, 3, 2, 8 } +}, +/* 133: 0, 2, 7, */ { + /* 1,0 */ { 3, 0, 8, 1, 6, 10, 6, 1, 7, 2, 7, 1, 7, 2, 11 }, + /* 0,1 */ { 1, 2, 10, 11, 3, 6, 0, 6, 3, 6, 0, 7, 8, 7, 0 }, + /* 1,1 */ { 11, 7, 6, 2, 8, 3, 8, 2, 10, 8, 10, 0, 1, 0, 10 } +}, +/* 161: 0, 5, 7, */ { + /* 1,0 */ { 9, 5, 4, 11, 3, 6, 0, 6, 3, 6, 0, 7, 8, 7, 0 }, + /* 0,1 */ { 11, 7, 6, 3, 4, 8, 4, 3, 5, 0, 5, 3, 5, 0, 9 }, + /* 1,1 */ { 3, 0, 8, 4, 9, 7, 11, 7, 9, 5, 11, 9, 11, 5, 6 } +}, +/* 26: 1, 3, 4, */ { + /* 1,0 */ { 0, 1, 9, 2, 7, 11, 7, 2, 4, 3, 4, 2, 4, 3, 8 }, + /* 0,1 */ { 2, 3, 11, 8, 0, 7, 1, 7, 0, 7, 1, 4, 9, 4, 1 }, + /* 1,1 */ { 8, 4, 7, 3, 9, 0, 9, 3, 11, 9, 11, 1, 2, 1, 11 } +}, +/* 74: 1, 3, 6, */ { + /* 1,0 */ { 2, 3, 11, 0, 5, 9, 5, 0, 6, 1, 6, 0, 6, 1, 10 }, + /* 0,1 */ { 0, 1, 9, 10, 2, 5, 3, 5, 2, 5, 3, 6, 11, 6, 3 }, + /* 1,1 */ { 6, 5, 10, 1, 11, 2, 11, 1, 9, 11, 9, 3, 0, 3, 9 } +}, +/* 82: 1, 4, 6, */ { + /* 1,0 */ { 6, 5, 10, 8, 0, 7, 1, 7, 0, 7, 1, 4, 9, 4, 1 }, + /* 0,1 */ { 8, 4, 7, 0, 5, 9, 5, 0, 6, 1, 6, 0, 6, 1, 10 }, + /* 1,1 */ { 0, 1, 9, 5, 10, 4, 8, 4, 10, 6, 8, 10, 8, 6, 7 } +}, +/* 164: 2, 5, 7, */ { + /* 1,0 */ { 11, 7, 6, 9, 1, 4, 2, 4, 1, 4, 2, 5, 10, 5, 2 }, + /* 0,1 */ { 9, 5, 4, 1, 6, 10, 6, 1, 7, 2, 7, 1, 7, 2, 11 }, + /* 1,1 */ { 1, 2, 10, 6, 11, 5, 9, 5, 11, 7, 9, 11, 9, 7, 4 } +}, +/* 88: 3, 4, 6, */ { + /* 1,0 */ { 8, 4, 7, 10, 2, 5, 3, 5, 2, 5, 3, 6, 11, 6, 3 }, + /* 0,1 */ { 6, 5, 10, 2, 7, 11, 7, 2, 4, 3, 4, 2, 4, 3, 8 }, + /* 1,1 */ { 2, 3, 11, 7, 8, 6, 10, 6, 8, 4, 10, 8, 10, 4, 5 } +}, +/* 167: 0, 1, 2, 5, 7, */ { + /* 1,0 */ { 7, 4, 8, 5, 2, 10, 2, 5, 3, 6, 3, 5, 3, 6, 11 }, + /* 0,1 */ { 10, 5, 6, 11, 7, 2, 4, 2, 7, 2, 4, 3, 8, 3, 4 }, + /* 1,1 */ { 11, 3, 2, 6, 8, 7, 8, 6, 10, 8, 10, 4, 5, 4, 10 } +}, +/* 91: 0, 1, 3, 4, 6, */ { + /* 1,0 */ { 6, 7, 11, 4, 1, 9, 1, 4, 2, 5, 2, 4, 2, 5, 10 }, + /* 0,1 */ { 4, 5, 9, 10, 6, 1, 7, 1, 6, 1, 7, 2, 11, 2, 7 }, + /* 1,1 */ { 10, 2, 1, 5, 11, 6, 11, 5, 9, 11, 9, 7, 4, 7, 9 } +}, +/* 173: 0, 2, 3, 5, 7, */ { + /* 1,0 */ { 10, 5, 6, 7, 0, 8, 0, 7, 1, 4, 1, 7, 1, 4, 9 }, + /* 0,1 */ { 7, 4, 8, 9, 5, 0, 6, 0, 5, 0, 6, 1, 10, 1, 6 }, + /* 1,1 */ { 9, 1, 0, 4, 10, 5, 10, 4, 8, 10, 8, 6, 7, 6, 8 } +}, +/* 181: 0, 2, 4, 5, 7, */ { + /* 1,0 */ { 11, 3, 2, 9, 5, 0, 6, 0, 5, 0, 6, 1, 10, 1, 6 }, + /* 0,1 */ { 9, 1, 0, 5, 2, 10, 2, 5, 3, 6, 3, 5, 3, 6, 11 }, + /* 1,1 */ { 10, 5, 6, 2, 11, 1, 9, 1, 11, 3, 9, 11, 9, 3, 0 } +}, +/* 229: 0, 2, 5, 6, 7, */ { + /* 1,0 */ { 9, 1, 0, 11, 7, 2, 4, 2, 7, 2, 4, 3, 8, 3, 4 }, + /* 0,1 */ { 11, 3, 2, 7, 0, 8, 0, 7, 1, 4, 1, 7, 1, 4, 9 }, + /* 1,1 */ { 7, 4, 8, 0, 9, 3, 11, 3, 9, 1, 11, 9, 11, 1, 2 } +}, +/* 94: 1, 2, 3, 4, 6, */ { + /* 1,0 */ { 4, 5, 9, 6, 3, 11, 3, 6, 0, 7, 0, 6, 0, 7, 8 }, + /* 0,1 */ { 6, 7, 11, 8, 4, 3, 5, 3, 4, 3, 5, 0, 9, 0, 5 }, + /* 1,1 */ { 8, 0, 3, 7, 9, 4, 9, 7, 11, 9, 11, 5, 6, 5, 11 } +}, +/* 122: 1, 3, 4, 5, 6, */ { + /* 1,0 */ { 8, 0, 3, 10, 6, 1, 7, 1, 6, 1, 7, 2, 11, 2, 7 }, + /* 0,1 */ { 10, 2, 1, 6, 3, 11, 3, 6, 0, 7, 0, 6, 0, 7, 8 }, + /* 1,1 */ { 6, 7, 11, 3, 8, 2, 10, 2, 8, 0, 10, 8, 10, 0, 1 } +}, +/* 218: 1, 3, 4, 6, 7, */ { + /* 1,0 */ { 10, 2, 1, 8, 4, 3, 5, 3, 4, 3, 5, 0, 9, 0, 5 }, + /* 0,1 */ { 8, 0, 3, 4, 1, 9, 1, 4, 2, 5, 2, 4, 2, 5, 10 }, + /* 1,1 */ { 4, 5, 9, 1, 10, 0, 8, 0, 10, 2, 8, 10, 8, 2, 3 } } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 7.3 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling7_3[16][3][27] = { +/* 37: 0, 2, 5, */ { + /* 1,0 */ { 12, 2, 10, 12, 10, 5, 12, 5, 4, 12, 4, 8, 12, 8, 3, 12, 3, 0, 12, 0, 9, 12, 9, 1, 12, 1, 2 }, + /* 0,1 */ { 12, 5, 4, 12, 4, 8, 12, 8, 3, 12, 3, 2, 12, 2, 10, 12, 10, 1, 12, 1, 0, 12, 0, 9, 12, 9, 5 }, + /* 1,1 */ { 5, 4, 12, 10, 5, 12, 2, 10, 12, 3, 2, 12, 8, 3, 12, 0, 8, 12, 1, 0, 12, 9, 1, 12, 4, 9, 12 } +}, +/* 133: 0, 2, 7, */ { + /* 1,0 */ { 12, 0, 8, 12, 8, 7, 12, 7, 6, 12, 6, 10, 12, 10, 1, 12, 1, 2, 12, 2, 11, 12, 11, 3, 12, 3, 0 }, + /* 0,1 */ { 12, 7, 6, 12, 6, 10, 12, 10, 1, 12, 1, 0, 12, 0, 8, 12, 8, 3, 12, 3, 2, 12, 2, 11, 12, 11, 7 }, + /* 1,1 */ { 7, 6, 12, 8, 7, 12, 0, 8, 12, 1, 0, 12, 10, 1, 12, 2, 10, 12, 3, 2, 12, 11, 3, 12, 6, 11, 12 } +}, +/* 161: 0, 5, 7, */ { + /* 1,0 */ { 9, 5, 12, 0, 9, 12, 3, 0, 12, 11, 3, 12, 6, 11, 12, 7, 6, 12, 8, 7, 12, 4, 8, 12, 5, 4, 12 }, + /* 0,1 */ { 3, 0, 12, 11, 3, 12, 6, 11, 12, 5, 6, 12, 9, 5, 12, 4, 9, 12, 7, 4, 12, 8, 7, 12, 0, 8, 12 }, + /* 1,1 */ { 12, 3, 0, 12, 0, 9, 12, 9, 5, 12, 5, 6, 12, 6, 11, 12, 11, 7, 12, 7, 4, 12, 4, 8, 12, 8, 3 } +}, +/* 26: 1, 3, 4, */ { + /* 1,0 */ { 12, 1, 9, 12, 9, 4, 12, 4, 7, 12, 7, 11, 12, 11, 2, 12, 2, 3, 12, 3, 8, 12, 8, 0, 12, 0, 1 }, + /* 0,1 */ { 12, 4, 7, 12, 7, 11, 12, 11, 2, 12, 2, 1, 12, 1, 9, 12, 9, 0, 12, 0, 3, 12, 3, 8, 12, 8, 4 }, + /* 1,1 */ { 4, 7, 12, 9, 4, 12, 1, 9, 12, 2, 1, 12, 11, 2, 12, 3, 11, 12, 0, 3, 12, 8, 0, 12, 7, 8, 12 } +}, +/* 74: 1, 3, 6, */ { + /* 1,0 */ { 12, 3, 11, 12, 11, 6, 12, 6, 5, 12, 5, 9, 12, 9, 0, 12, 0, 1, 12, 1, 10, 12, 10, 2, 12, 2, 3 }, + /* 0,1 */ { 12, 6, 5, 12, 5, 9, 12, 9, 0, 12, 0, 3, 12, 3, 11, 12, 11, 2, 12, 2, 1, 12, 1, 10, 12, 10, 6 }, + /* 1,1 */ { 6, 5, 12, 11, 6, 12, 3, 11, 12, 0, 3, 12, 9, 0, 12, 1, 9, 12, 2, 1, 12, 10, 2, 12, 5, 10, 12 } +}, +/* 82: 1, 4, 6, */ { + /* 1,0 */ { 10, 6, 12, 1, 10, 12, 0, 1, 12, 8, 0, 12, 7, 8, 12, 4, 7, 12, 9, 4, 12, 5, 9, 12, 6, 5, 12 }, + /* 0,1 */ { 0, 1, 12, 8, 0, 12, 7, 8, 12, 6, 7, 12, 10, 6, 12, 5, 10, 12, 4, 5, 12, 9, 4, 12, 1, 9, 12 }, + /* 1,1 */ { 12, 0, 1, 12, 1, 10, 12, 10, 6, 12, 6, 7, 12, 7, 8, 12, 8, 4, 12, 4, 5, 12, 5, 9, 12, 9, 0 } +}, +/* 164: 2, 5, 7, */ { + /* 1,0 */ { 11, 7, 12, 2, 11, 12, 1, 2, 12, 9, 1, 12, 4, 9, 12, 5, 4, 12, 10, 5, 12, 6, 10, 12, 7, 6, 12 }, + /* 0,1 */ { 1, 2, 12, 9, 1, 12, 4, 9, 12, 7, 4, 12, 11, 7, 12, 6, 11, 12, 5, 6, 12, 10, 5, 12, 2, 10, 12 }, + /* 1,1 */ { 12, 1, 2, 12, 2, 11, 12, 11, 7, 12, 7, 4, 12, 4, 9, 12, 9, 5, 12, 5, 6, 12, 6, 10, 12, 10, 1 } +}, +/* 88: 3, 4, 6, */ { + /* 1,0 */ { 8, 4, 12, 3, 8, 12, 2, 3, 12, 10, 2, 12, 5, 10, 12, 6, 5, 12, 11, 6, 12, 7, 11, 12, 4, 7, 12 }, + /* 0,1 */ { 2, 3, 12, 10, 2, 12, 5, 10, 12, 4, 5, 12, 8, 4, 12, 7, 8, 12, 6, 7, 12, 11, 6, 12, 3, 11, 12 }, + /* 1,1 */ { 12, 2, 3, 12, 3, 8, 12, 8, 4, 12, 4, 5, 12, 5, 10, 12, 10, 6, 12, 6, 7, 12, 7, 11, 12, 11, 2 } +}, +/* 167: 0, 1, 2, 5, 7, */ { + /* 1,0 */ { 12, 4, 8, 12, 8, 3, 12, 3, 2, 12, 2, 10, 12, 10, 5, 12, 5, 6, 12, 6, 11, 12, 11, 7, 12, 7, 4 }, + /* 0,1 */ { 12, 3, 2, 12, 2, 10, 12, 10, 5, 12, 5, 4, 12, 4, 8, 12, 8, 7, 12, 7, 6, 12, 6, 11, 12, 11, 3 }, + /* 1,1 */ { 3, 2, 12, 8, 3, 12, 4, 8, 12, 5, 4, 12, 10, 5, 12, 6, 10, 12, 7, 6, 12, 11, 7, 12, 2, 11, 12 } +}, +/* 91: 0, 1, 3, 4, 6, */ { + /* 1,0 */ { 12, 7, 11, 12, 11, 2, 12, 2, 1, 12, 1, 9, 12, 9, 4, 12, 4, 5, 12, 5, 10, 12, 10, 6, 12, 6, 7 }, + /* 0,1 */ { 12, 2, 1, 12, 1, 9, 12, 9, 4, 12, 4, 7, 12, 7, 11, 12, 11, 6, 12, 6, 5, 12, 5, 10, 12, 10, 2 }, + /* 1,1 */ { 2, 1, 12, 11, 2, 12, 7, 11, 12, 4, 7, 12, 9, 4, 12, 5, 9, 12, 6, 5, 12, 10, 6, 12, 1, 10, 12 } +}, +/* 173: 0, 2, 3, 5, 7, */ { + /* 1,0 */ { 12, 6, 10, 12, 10, 1, 12, 1, 0, 12, 0, 8, 12, 8, 7, 12, 7, 4, 12, 4, 9, 12, 9, 5, 12, 5, 6 }, + /* 0,1 */ { 12, 1, 0, 12, 0, 8, 12, 8, 7, 12, 7, 6, 12, 6, 10, 12, 10, 5, 12, 5, 4, 12, 4, 9, 12, 9, 1 }, + /* 1,1 */ { 1, 0, 12, 10, 1, 12, 6, 10, 12, 7, 6, 12, 8, 7, 12, 4, 8, 12, 5, 4, 12, 9, 5, 12, 0, 9, 12 } +}, +/* 181: 0, 2, 4, 5, 7, */ { + /* 1,0 */ { 11, 3, 12, 6, 11, 12, 5, 6, 12, 9, 5, 12, 0, 9, 12, 1, 0, 12, 10, 1, 12, 2, 10, 12, 3, 2, 12 }, + /* 0,1 */ { 5, 6, 12, 9, 5, 12, 0, 9, 12, 3, 0, 12, 11, 3, 12, 2, 11, 12, 1, 2, 12, 10, 1, 12, 6, 10, 12 }, + /* 1,1 */ { 12, 5, 6, 12, 6, 11, 12, 11, 3, 12, 3, 0, 12, 0, 9, 12, 9, 1, 12, 1, 2, 12, 2, 10, 12, 10, 5 } +}, +/* 229: 0, 2, 5, 6, 7, */ { + /* 1,0 */ { 9, 1, 12, 4, 9, 12, 7, 4, 12, 11, 7, 12, 2, 11, 12, 3, 2, 12, 8, 3, 12, 0, 8, 12, 1, 0, 12 }, + /* 0,1 */ { 7, 4, 12, 11, 7, 12, 2, 11, 12, 1, 2, 12, 9, 1, 12, 0, 9, 12, 3, 0, 12, 8, 3, 12, 4, 8, 12 }, + /* 1,1 */ { 12, 7, 4, 12, 4, 9, 12, 9, 1, 12, 1, 2, 12, 2, 11, 12, 11, 3, 12, 3, 0, 12, 0, 8, 12, 8, 7 } +}, +/* 94: 1, 2, 3, 4, 6, */ { + /* 1,0 */ { 12, 5, 9, 12, 9, 0, 12, 0, 3, 12, 3, 11, 12, 11, 6, 12, 6, 7, 12, 7, 8, 12, 8, 4, 12, 4, 5 }, + /* 0,1 */ { 12, 0, 3, 12, 3, 11, 12, 11, 6, 12, 6, 5, 12, 5, 9, 12, 9, 4, 12, 4, 7, 12, 7, 8, 12, 8, 0 }, + /* 1,1 */ { 0, 3, 12, 9, 0, 12, 5, 9, 12, 6, 5, 12, 11, 6, 12, 7, 11, 12, 4, 7, 12, 8, 4, 12, 3, 8, 12 } +}, +/* 122: 1, 3, 4, 5, 6, */ { + /* 1,0 */ { 8, 0, 12, 7, 8, 12, 6, 7, 12, 10, 6, 12, 1, 10, 12, 2, 1, 12, 11, 2, 12, 3, 11, 12, 0, 3, 12 }, + /* 0,1 */ { 6, 7, 12, 10, 6, 12, 1, 10, 12, 0, 1, 12, 8, 0, 12, 3, 8, 12, 2, 3, 12, 11, 2, 12, 7, 11, 12 }, + /* 1,1 */ { 12, 6, 7, 12, 7, 8, 12, 8, 0, 12, 0, 1, 12, 1, 10, 12, 10, 2, 12, 2, 3, 12, 3, 11, 12, 11, 6 } +}, +/* 218: 1, 3, 4, 6, 7, */ { + /* 1,0 */ { 10, 2, 12, 5, 10, 12, 4, 5, 12, 8, 4, 12, 3, 8, 12, 0, 3, 12, 9, 0, 12, 1, 9, 12, 2, 1, 12 }, + /* 0,1 */ { 4, 5, 12, 8, 4, 12, 3, 8, 12, 2, 3, 12, 10, 2, 12, 1, 10, 12, 0, 1, 12, 9, 0, 12, 5, 9, 12 }, + /* 1,1 */ { 12, 4, 5, 12, 5, 10, 12, 10, 2, 12, 2, 3, 12, 3, 8, 12, 8, 0, 12, 0, 1, 12, 1, 9, 12, 9, 4 } } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 7.4.1 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling7_4_1[16][15] = { +/* 37: 0, 2, 5, */ { 3, 4, 8, 4, 3, 10, 2, 10, 3, 4, 10, 5, 9, 1, 0 }, +/* 133: 0, 2, 7, */ { 1, 6, 10, 6, 1, 8, 0, 8, 1, 6, 8, 7, 11, 3, 2 }, +/* 161: 0, 5, 7, */ { 11, 3, 6, 9, 6, 3, 6, 9, 5, 0, 9, 3, 7, 4, 8 }, +/* 26: 1, 3, 4, */ { 2, 7, 11, 7, 2, 9, 1, 9, 2, 7, 9, 4, 8, 0, 3 }, +/* 74: 1, 3, 6, */ { 0, 5, 9, 5, 0, 11, 3, 11, 0, 5, 11, 6, 10, 2, 1 }, +/* 82: 1, 4, 6, */ { 8, 0, 7, 10, 7, 0, 7, 10, 6, 1, 10, 0, 4, 5, 9 }, +/* 164: 2, 5, 7, */ { 9, 1, 4, 11, 4, 1, 4, 11, 7, 2, 11, 1, 5, 6, 10 }, +/* 88: 3, 4, 6, */ { 10, 2, 5, 8, 5, 2, 5, 8, 4, 3, 8, 2, 6, 7, 11 }, +/* 167: 0, 1, 2, 5, 7, */ { 5, 2, 10, 2, 5, 8, 4, 8, 5, 2, 8, 3, 11, 7, 6 }, +/* 91: 0, 1, 3, 4, 6, */ { 4, 1, 9, 1, 4, 11, 7, 11, 4, 1, 11, 2, 10, 6, 5 }, +/* 173: 0, 2, 3, 5, 7, */ { 7, 0, 8, 0, 7, 10, 6, 10, 7, 0, 10, 1, 9, 5, 4 }, +/* 181: 0, 2, 4, 5, 7, */ { 9, 5, 0, 11, 0, 5, 0, 11, 3, 6, 11, 5, 1, 2, 10 }, +/* 229: 0, 2, 5, 6, 7, */ { 11, 7, 2, 9, 2, 7, 2, 9, 1, 4, 9, 7, 3, 0, 8 }, +/* 94: 1, 2, 3, 4, 6, */ { 6, 3, 11, 3, 6, 9, 5, 9, 6, 3, 9, 0, 8, 4, 7 }, +/* 122: 1, 3, 4, 5, 6, */ { 10, 6, 1, 8, 1, 6, 1, 8, 0, 7, 8, 6, 2, 3, 11 }, +/* 218: 1, 3, 4, 6, 7, */ { 8, 4, 3, 10, 3, 4, 3, 10, 2, 5, 10, 4, 0, 1, 9 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 7.4.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling7_4_2[16][27] = { +/* 37: 0, 2, 5, */ { 9, 4, 8, 4, 9, 5, 10, 5, 9, 1, 10, 9, 10, 1, 2, 0, 2, 1, 2, 0, 3, 8, 3, 0, 9, 8, 0 }, +/* 133: 0, 2, 7, */ { 11, 6, 10, 6, 11, 7, 8, 7, 11, 3, 8, 11, 8, 3, 0, 2, 0, 3, 0, 2, 1, 10, 1, 2, 11, 10, 2 }, +/* 161: 0, 5, 7, */ { 11, 3, 8, 0, 8, 3, 8, 0, 9, 8, 9, 4, 5, 4, 9, 4, 5, 7, 6, 7, 5, 7, 6, 11, 7, 11, 8 }, +/* 26: 1, 3, 4, */ { 8, 7, 11, 7, 8, 4, 9, 4, 8, 0, 9, 8, 9, 0, 1, 3, 1, 0, 1, 3, 2, 11, 2, 3, 8, 11, 3 }, +/* 74: 1, 3, 6, */ { 10, 5, 9, 5, 10, 6, 11, 6, 10, 2, 11, 10, 11, 2, 3, 1, 3, 2, 3, 1, 0, 9, 0, 1, 10, 9, 1 }, +/* 82: 1, 4, 6, */ { 8, 0, 9, 1, 9, 0, 9, 1, 10, 9, 10, 5, 6, 5, 10, 5, 6, 4, 7, 4, 6, 4, 7, 8, 4, 8, 9 }, +/* 164: 2, 5, 7, */ { 9, 1, 10, 2, 10, 1, 10, 2, 11, 10, 11, 6, 7, 6, 11, 6, 7, 5, 4, 5, 7, 5, 4, 9, 5, 9, 10 }, +/* 88: 3, 4, 6, */ { 10, 2, 11, 3, 11, 2, 11, 3, 8, 11, 8, 7, 4, 7, 8, 7, 4, 6, 5, 6, 4, 6, 5, 10, 6, 10, 11 }, +/* 167: 0, 1, 2, 5, 7, */ { 11, 2, 10, 2, 11, 3, 8, 3, 11, 7, 8, 11, 8, 7, 4, 6, 4, 7, 4, 6, 5, 10, 5, 6, 11, 10, 6 }, +/* 91: 0, 1, 3, 4, 6, */ { 10, 1, 9, 1, 10, 2, 11, 2, 10, 6, 11, 10, 11, 6, 7, 5, 7, 6, 7, 5, 4, 9, 4, 5, 10, 9, 5 }, +/* 173: 0, 2, 3, 5, 7, */ { 9, 0, 8, 0, 9, 1, 10, 1, 9, 5, 10, 9, 10, 5, 6, 4, 6, 5, 6, 4, 7, 8, 7, 4, 9, 8, 4 }, +/* 181: 0, 2, 4, 5, 7, */ { 9, 5, 10, 6, 10, 5, 10, 6, 11, 10, 11, 2, 3, 2, 11, 2, 3, 1, 0, 1, 3, 1, 0, 9, 1, 9, 10 }, +/* 229: 0, 2, 5, 6, 7, */ { 11, 7, 8, 4, 8, 7, 8, 4, 9, 8, 9, 0, 1, 0, 9, 0, 1, 3, 2, 3, 1, 3, 2, 11, 3, 11, 8 }, +/* 94: 1, 2, 3, 4, 6, */ { 8, 3, 11, 3, 8, 0, 9, 0, 8, 4, 9, 8, 9, 4, 5, 7, 5, 4, 5, 7, 6, 11, 6, 7, 8, 11, 7 }, +/* 122: 1, 3, 4, 5, 6, */ { 10, 6, 11, 7, 11, 6, 11, 7, 8, 11, 8, 3, 0, 3, 8, 3, 0, 2, 1, 2, 0, 2, 1, 10, 2, 10, 11 }, +/* 218: 1, 3, 4, 6, 7, */ { 8, 4, 9, 5, 9, 4, 9, 5, 10, 9, 10, 1, 2, 1, 10, 1, 2, 0, 3, 0, 2, 0, 3, 8, 0, 8, 9 } +}; +//_____________________________________________________________________________ + + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 8 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling8[6][6] = { +/* 15: 0, 1, 2, 3, */ { 9, 8, 10, 10, 8, 11 }, +/* 51: 0, 1, 4, 5, */ { 1, 5, 3, 3, 5, 7 }, +/* 153: 0, 3, 4, 7, */ { 0, 4, 2, 4, 6, 2 }, +/* 102: 1, 2, 5, 6, */ { 0, 2, 4, 4, 2, 6 }, +/* 204: 2, 3, 6, 7, */ { 1, 3, 5, 3, 7, 5 }, +/* 240: 4, 5, 6, 7, */ { 9, 10, 8, 10, 11, 8 } +}; +//_____________________________________________________________________________ + + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 9 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling9[8][12] = { +/* 39: 0, 1, 2, 5, */ { 2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8 }, +/* 27: 0, 1, 3, 4, */ { 4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1 }, +/* 141: 0, 2, 3, 7, */ { 10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8 }, +/* 177: 0, 4, 5, 7, */ { 3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5 }, +/* 78: 1, 2, 3, 6, */ { 3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9 }, +/* 114: 1, 4, 5, 6, */ { 10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0 }, +/* 228: 2, 5, 6, 7, */ { 4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2 }, +/* 216: 3, 4, 6, 7, */ { 2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4 } +}; +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +/** + * \brief test table for case 10 + * 2 faces to test + eventually the interior + * When the tests on both specified faces are positive : 4 middle triangles (1) + * When the test on the first specified face is positive : 8 first triangles + * When the test on the second specified face is positive : 8 next triangles + * When the tests on both specified faces are negative : + * - if the test on the interior is negative : 4 middle triangles + * - if the test on the interior is positive : 8 last triangles + * + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char test10[6][3] = { +/* 195: 0, 1, 6, 7, */ { 2, 4, 7 }, +/* 85: 0, 2, 4, 6, */ { 5, 6, 7 }, +/* 105: 0, 3, 5, 6, */ { 1, 3, 7 }, +/* 150: 1, 2, 4, 7, */ { 1, 3, 7 }, +/* 170: 1, 3, 5, 7, */ { 5, 6, 7 }, +/* 60: 2, 3, 4, 5, */ { 2, 4, 7 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 10.1.1 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling10_1_1[6][12] = { +/* 195: 0, 1, 6, 7, */ { 5, 10, 7, 11, 7, 10, 8, 1, 9, 1, 8, 3 }, +/* 85: 0, 2, 4, 6, */ { 1, 2, 5, 6, 5, 2, 4, 3, 0, 3, 4, 7 }, +/* 105: 0, 3, 5, 6, */ { 11, 0, 8, 0, 11, 2, 4, 9, 6, 10, 6, 9 }, +/* 150: 1, 2, 4, 7, */ { 9, 0, 10, 2, 10, 0, 6, 8, 4, 8, 6, 11 }, +/* 170: 1, 3, 5, 7, */ { 7, 2, 3, 2, 7, 6, 0, 1, 4, 5, 4, 1 }, +/* 60: 2, 3, 4, 5, */ { 7, 9, 5, 9, 7, 8, 10, 1, 11, 3, 11, 1 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 10.1.1 inverted + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling10_1_1_[6][12] = { +/* 195: 0, 1, 6, 7, */ { 5, 9, 7, 8, 7, 9, 11, 1, 10, 1, 11, 3 }, +/* 85: 0, 2, 4, 6, */ { 3, 2, 7, 6, 7, 2, 4, 1, 0, 1, 4, 5 }, +/* 105: 0, 3, 5, 6, */ { 10, 0, 9, 0, 10, 2, 4, 8, 6, 11, 6, 8 }, +/* 150: 1, 2, 4, 7, */ { 8, 0, 11, 2, 11, 0, 6, 9, 4, 9, 6, 10 }, +/* 170: 1, 3, 5, 7, */ { 5, 2, 1, 2, 5, 6, 0, 3, 4, 7, 4, 3 }, +/* 60: 2, 3, 4, 5, */ { 7, 10, 5, 10, 7, 11, 9, 1, 8, 3, 8, 1 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 10.1.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling10_1_2[6][24] = { +/* 195: 0, 1, 6, 7, */ { 3, 11, 7, 3, 7, 8, 9, 8, 7, 5, 9, 7, 9, 5, 10, 9, 10, 1, 3, 1, 10, 11, 3, 10 }, +/* 85: 0, 2, 4, 6, */ { 7, 6, 5, 7, 5, 4, 0, 4, 5, 1, 0, 5, 0, 1, 2, 0, 2, 3, 7, 3, 2, 6, 7, 2 }, +/* 105: 0, 3, 5, 6, */ { 11, 2, 10, 6, 11, 10, 11, 6, 4, 11, 4, 8, 0, 8, 4, 9, 0, 4, 0, 9, 10, 0, 10, 2 }, +/* 150: 1, 2, 4, 7, */ { 11, 2, 10, 11, 10, 6, 4, 6, 10, 9, 4, 10, 4, 9, 0, 4, 0, 8, 11, 8, 0, 2, 11, 0 }, +/* 170: 1, 3, 5, 7, */ { 7, 6, 5, 4, 7, 5, 7, 4, 0, 7, 0, 3, 2, 3, 0, 1, 2, 0, 2, 1, 5, 2, 5, 6 }, +/* 60: 2, 3, 4, 5, */ { 7, 8, 3, 11, 7, 3, 7, 11, 10, 7, 10, 5, 9, 5, 10, 1, 9, 10, 9, 1, 3, 9, 3, 8 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 10.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling10_2[6][24] = { +/* 195: 0, 1, 6, 7, */ { 12, 5, 9, 12, 9, 8, 12, 8, 3, 12, 3, 1, 12, 1, 10, 12, 10, 11, 12, 11, 7, 12, 7, 5 }, +/* 85: 0, 2, 4, 6, */ { 12, 1, 0, 12, 0, 4, 12, 4, 7, 12, 7, 3, 12, 3, 2, 12, 2, 6, 12, 6, 5, 12, 5, 1 }, +/* 105: 0, 3, 5, 6, */ { 4, 8, 12, 6, 4, 12, 10, 6, 12, 9, 10, 12, 0, 9, 12, 2, 0, 12, 11, 2, 12, 8, 11, 12 }, +/* 150: 1, 2, 4, 7, */ { 12, 9, 4, 12, 4, 6, 12, 6, 11, 12, 11, 8, 12, 8, 0, 12, 0, 2, 12, 2, 10, 12, 10, 9 }, +/* 170: 1, 3, 5, 7, */ { 0, 3, 12, 4, 0, 12, 5, 4, 12, 1, 5, 12, 2, 1, 12, 6, 2, 12, 7, 6, 12, 3, 7, 12 }, +/* 60: 2, 3, 4, 5, */ { 10, 5, 12, 11, 10, 12, 3, 11, 12, 1, 3, 12, 9, 1, 12, 8, 9, 12, 7, 8, 12, 5, 7, 12 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 10.2 inverted + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling10_2_[6][24] = { +/* 195: 0, 1, 6, 7, */ { 8, 7, 12, 9, 8, 12, 1, 9, 12, 3, 1, 12, 11, 3, 12, 10, 11, 12, 5, 10, 12, 7, 5, 12 }, +/* 85: 0, 2, 4, 6, */ { 4, 5, 12, 0, 4, 12, 3, 0, 12, 7, 3, 12, 6, 7, 12, 2, 6, 12, 1, 2, 12, 5, 1, 12 }, +/* 105: 0, 3, 5, 6, */ { 12, 11, 6, 12, 6, 4, 12, 4, 9, 12, 9, 10, 12, 10, 2, 12, 2, 0, 12, 0, 8, 12, 8, 11 }, +/* 150: 1, 2, 4, 7, */ { 6, 10, 12, 4, 6, 12, 8, 4, 12, 11, 8, 12, 2, 11, 12, 0, 2, 12, 9, 0, 12, 10, 9, 12 }, +/* 170: 1, 3, 5, 7, */ { 12, 7, 4, 12, 4, 0, 12, 0, 1, 12, 1, 5, 12, 5, 6, 12, 6, 2, 12, 2, 3, 12, 3, 7 }, +/* 60: 2, 3, 4, 5, */ { 12, 7, 11, 12, 11, 10, 12, 10, 1, 12, 1, 3, 12, 3, 8, 12, 8, 9, 12, 9, 5, 12, 5, 7 } +}; +//_____________________________________________________________________________ + + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 11 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling11[12][12] = { +/* 23: 0, 1, 2, 4, */ { 2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4 }, +/* 139: 0, 1, 3, 7, */ { 1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6 }, +/* 99: 0, 1, 5, 6, */ { 8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10 }, +/* 77: 0, 2, 3, 6, */ { 0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6 }, +/* 57: 0, 3, 4, 5, */ { 9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11 }, +/* 209: 0, 4, 6, 7, */ { 5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0 }, +/* 46: 1, 2, 3, 5, */ { 5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3 }, +/* 198: 1, 2, 6, 7, */ { 9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7 }, +/* 178: 1, 4, 5, 7, */ { 0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11 }, +/* 156: 2, 3, 4, 7, */ { 8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1 }, +/* 116: 2, 4, 5, 6, */ { 1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7 }, +/* 232: 3, 5, 6, 7, */ { 2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9 } +}; +//_____________________________________________________________________________ + + +//_____________________________________________________________________________ +/** + * \brief test table for case 12 + * 2 faces to test + eventually the interior + * When the tests on both specified faces are positive : 4 middle triangles (1) + * When the test on the first specified face is positive : 8 first triangles + * When the test on the second specified face is positive : 8 next triangles + * When the tests on both specified faces are negative : + * - if the test on the interior is negative : 4 middle triangles + * - if the test on the interior is positive : 8 last triangles + * The support edge for the interior test is marked as the 4th column. + * + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char test12[24][4] = { +/* 135: 0, 1, 2, 7, */ { 4, 3, 7, 11 }, +/* 75: 0, 1, 3, 6, */ { 3, 2, 7, 10 }, +/* 83: 0, 1, 4, 6, */ { 2, 6, 7, 5 }, +/* 163: 0, 1, 5, 7, */ { 6, 4, 7, 7 }, +/* 45: 0, 2, 3, 5, */ { 2, 1, 7, 9 }, +/* 53: 0, 2, 4, 5, */ { 5, 2, 7, 1 }, +/* 149: 0, 2, 4, 7, */ { 5, 3, 7, 2 }, +/* 101: 0, 2, 5, 6, */ { 5, 1, 7, 0 }, +/* 197: 0, 2, 6, 7, */ { 5, 4, 7, 3 }, +/* 89: 0, 3, 4, 6, */ { 6, 3, 7, 6 }, +/* 169: 0, 3, 5, 7, */ { 1, 6, 7, 4 }, +/* 225: 0, 5, 6, 7, */ { 1, 4, 7, 8 }, +/* 30: 1, 2, 3, 4, */ { 4, 1, 7, 8 }, +/* 86: 1, 2, 4, 6, */ { 6, 1, 7, 4 }, +/* 166: 1, 2, 5, 7, */ { 3, 6, 7, 6 }, +/* 58: 1, 3, 4, 5, */ { 4, 5, 7, 3 }, +/* 154: 1, 3, 4, 7, */ { 1, 5, 7, 0 }, +/* 106: 1, 3, 5, 6, */ { 3, 5, 7, 2 }, +/* 202: 1, 3, 6, 7, */ { 2, 5, 7, 1 }, +/* 210: 1, 4, 6, 7, */ { 1, 2, 7, 9 }, +/* 92: 2, 3, 4, 6, */ { 4, 6, 7, 7 }, +/* 172: 2, 3, 5, 7, */ { 6, 2, 7, 5 }, +/* 180: 2, 4, 5, 7, */ { 2, 3, 7, 10 }, +/* 120: 3, 4, 5, 6, */ { 3, 4, 7, 11 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 12.1.1 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling12_1_1[24][12] = { +/* 135: 0, 1, 2, 7, */ { 7, 6, 11, 10, 3, 2, 3, 10, 8, 9, 8, 10 }, +/* 75: 0, 1, 3, 6, */ { 6, 5, 10, 9, 2, 1, 2, 9, 11, 8, 11, 9 }, +/* 83: 0, 1, 4, 6, */ { 10, 6, 5, 7, 9, 4, 9, 7, 1, 3, 1, 7 }, +/* 163: 0, 1, 5, 7, */ { 7, 6, 11, 4, 8, 5, 3, 5, 8, 5, 3, 1 }, +/* 45: 0, 2, 3, 5, */ { 5, 4, 9, 8, 1, 0, 1, 8, 10, 11, 10, 8 }, +/* 53: 0, 2, 4, 5, */ { 1, 2, 10, 0, 9, 3, 5, 3, 9, 3, 5, 7 }, +/* 149: 0, 2, 4, 7, */ { 10, 1, 2, 0, 11, 3, 11, 0, 6, 4, 6, 0 }, +/* 101: 0, 2, 5, 6, */ { 8, 3, 0, 2, 9, 1, 9, 2, 4, 6, 4, 2 }, +/* 197: 0, 2, 6, 7, */ { 3, 0, 8, 2, 11, 1, 7, 1, 11, 1, 7, 5 }, +/* 89: 0, 3, 4, 6, */ { 6, 5, 10, 7, 11, 4, 2, 4, 11, 4, 2, 0 }, +/* 169: 0, 3, 5, 7, */ { 9, 5, 4, 6, 8, 7, 8, 6, 0, 2, 0, 6 }, +/* 225: 0, 5, 6, 7, */ { 8, 3, 0, 7, 4, 11, 9, 11, 4, 11, 9, 10 }, +/* 30: 1, 2, 3, 4, */ { 4, 7, 8, 11, 0, 3, 0, 11, 9, 10, 9, 11 }, +/* 86: 1, 2, 4, 6, */ { 4, 7, 8, 5, 9, 6, 0, 6, 9, 6, 0, 2 }, +/* 166: 1, 2, 5, 7, */ { 11, 7, 6, 4, 10, 5, 10, 4, 2, 0, 2, 4 }, +/* 58: 1, 3, 4, 5, */ { 11, 2, 3, 1, 8, 0, 8, 1, 7, 5, 7, 1 }, +/* 154: 1, 3, 4, 7, */ { 0, 1, 9, 3, 8, 2, 4, 2, 8, 2, 4, 6 }, +/* 106: 1, 3, 5, 6, */ { 2, 3, 11, 1, 10, 0, 6, 0, 10, 0, 6, 4 }, +/* 202: 1, 3, 6, 7, */ { 9, 0, 1, 3, 10, 2, 10, 3, 5, 7, 5, 3 }, +/* 210: 1, 4, 6, 7, */ { 9, 0, 1, 4, 5, 8, 10, 8, 5, 8, 10, 11 }, +/* 92: 2, 3, 4, 6, */ { 8, 4, 7, 5, 11, 6, 11, 5, 3, 1, 3, 5 }, +/* 172: 2, 3, 5, 7, */ { 5, 4, 9, 6, 10, 7, 1, 7, 10, 7, 1, 3 }, +/* 180: 2, 4, 5, 7, */ { 10, 1, 2, 5, 6, 9, 11, 9, 6, 9, 11, 8 }, +/* 120: 3, 4, 5, 6, */ { 11, 2, 3, 6, 7, 10, 8, 10, 7, 10, 8, 9 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 12.1.1 inverted + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling12_1_1_[24][12] = { +/* 135: 0, 1, 2, 7, */ { 3, 2, 11, 10, 7, 6, 7, 10, 8, 9, 8, 10 }, +/* 75: 0, 1, 3, 6, */ { 2, 1, 10, 9, 6, 5, 6, 9, 11, 8, 11, 9 }, +/* 83: 0, 1, 4, 6, */ { 9, 4, 5, 7, 10, 6, 10, 7, 1, 3, 1, 7 }, +/* 163: 0, 1, 5, 7, */ { 7, 4, 8, 6, 11, 5, 3, 5, 11, 5, 3, 1 }, +/* 45: 0, 2, 3, 5, */ { 1, 0, 9, 8, 5, 4, 5, 8, 10, 11, 10, 8 }, +/* 53: 0, 2, 4, 5, */ { 1, 0, 9, 2, 10, 3, 5, 3, 10, 3, 5, 7 }, +/* 149: 0, 2, 4, 7, */ { 11, 3, 2, 0, 10, 1, 10, 0, 6, 4, 6, 0 }, +/* 101: 0, 2, 5, 6, */ { 9, 1, 0, 2, 8, 3, 8, 2, 4, 6, 4, 2 }, +/* 197: 0, 2, 6, 7, */ { 3, 2, 11, 0, 8, 1, 7, 1, 8, 1, 7, 5 }, +/* 89: 0, 3, 4, 6, */ { 6, 7, 11, 5, 10, 4, 2, 4, 10, 4, 2, 0 }, +/* 169: 0, 3, 5, 7, */ { 8, 7, 4, 6, 9, 5, 9, 6, 0, 2, 0, 6 }, +/* 225: 0, 5, 6, 7, */ { 8, 7, 4, 3, 0, 11, 9, 11, 0, 11, 9, 10 }, +/* 30: 1, 2, 3, 4, */ { 0, 3, 8, 11, 4, 7, 4, 11, 9, 10, 9, 11 }, +/* 86: 1, 2, 4, 6, */ { 4, 5, 9, 7, 8, 6, 0, 6, 8, 6, 0, 2 }, +/* 166: 1, 2, 5, 7, */ { 10, 5, 6, 4, 11, 7, 11, 4, 2, 0, 2, 4 }, +/* 58: 1, 3, 4, 5, */ { 8, 0, 3, 1, 11, 2, 11, 1, 7, 5, 7, 1 }, +/* 154: 1, 3, 4, 7, */ { 0, 3, 8, 1, 9, 2, 4, 2, 9, 2, 4, 6 }, +/* 106: 1, 3, 5, 6, */ { 2, 1, 10, 3, 11, 0, 6, 0, 11, 0, 6, 4 }, +/* 202: 1, 3, 6, 7, */ { 10, 2, 1, 3, 9, 0, 9, 3, 5, 7, 5, 3 }, +/* 210: 1, 4, 6, 7, */ { 9, 4, 5, 0, 1, 8, 10, 8, 1, 8, 10, 11 }, +/* 92: 2, 3, 4, 6, */ { 11, 6, 7, 5, 8, 4, 8, 5, 3, 1, 3, 5 }, +/* 172: 2, 3, 5, 7, */ { 5, 6, 10, 4, 9, 7, 1, 7, 9, 7, 1, 3 }, +/* 180: 2, 4, 5, 7, */ { 10, 5, 6, 1, 2, 9, 11, 9, 2, 9, 11, 8 }, +/* 120: 3, 4, 5, 6, */ { 11, 6, 7, 2, 3, 10, 8, 10, 3, 10, 8, 9 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 12.1.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling12_1_2[24][24] = { +/* 135: 0, 1, 2, 7, */ { 7, 3, 11, 3, 7, 8, 9, 8, 7, 6, 9, 7, 9, 6, 10, 2, 10, 6, 11, 2, 6, 2, 11, 3 }, +/* 75: 0, 1, 3, 6, */ { 6, 2, 10, 2, 6, 11, 8, 11, 6, 5, 8, 6, 8, 5, 9, 1, 9, 5, 10, 1, 5, 1, 10, 2 }, +/* 83: 0, 1, 4, 6, */ { 10, 9, 5, 9, 10, 1, 3, 1, 10, 6, 3, 10, 3, 6, 7, 4, 7, 6, 5, 4, 6, 4, 5, 9 }, +/* 163: 0, 1, 5, 7, */ { 7, 8, 11, 3, 11, 8, 11, 3, 1, 11, 1, 6, 5, 6, 1, 6, 5, 4, 6, 4, 7, 8, 7, 4 }, +/* 45: 0, 2, 3, 5, */ { 5, 1, 9, 1, 5, 10, 11, 10, 5, 4, 11, 5, 11, 4, 8, 0, 8, 4, 9, 0, 4, 0, 9, 1 }, +/* 53: 0, 2, 4, 5, */ { 1, 9, 10, 5, 10, 9, 10, 5, 7, 10, 7, 2, 3, 2, 7, 2, 3, 0, 2, 0, 1, 9, 1, 0 }, +/* 149: 0, 2, 4, 7, */ { 10, 11, 2, 11, 10, 6, 4, 6, 10, 1, 4, 10, 4, 1, 0, 3, 0, 1, 2, 3, 1, 3, 2, 11 }, +/* 101: 0, 2, 5, 6, */ { 8, 9, 0, 9, 8, 4, 6, 4, 8, 3, 6, 8, 6, 3, 2, 1, 2, 3, 0, 1, 3, 1, 0, 9 }, +/* 197: 0, 2, 6, 7, */ { 3, 11, 8, 7, 8, 11, 8, 7, 5, 8, 5, 0, 1, 0, 5, 0, 1, 2, 0, 2, 3, 11, 3, 2 }, +/* 89: 0, 3, 4, 6, */ { 6, 11, 10, 2, 10, 11, 10, 2, 0, 10, 0, 5, 4, 5, 0, 5, 4, 7, 5, 7, 6, 11, 6, 7 }, +/* 169: 0, 3, 5, 7, */ { 9, 8, 4, 8, 9, 0, 2, 0, 9, 5, 2, 9, 2, 5, 6, 7, 6, 5, 4, 7, 5, 7, 4, 8 }, +/* 225: 0, 5, 6, 7, */ { 8, 4, 0, 9, 0, 4, 0, 9, 10, 0, 10, 3, 11, 3, 10, 3, 11, 7, 3, 7, 8, 4, 8, 7 }, +/* 30: 1, 2, 3, 4, */ { 4, 0, 8, 0, 4, 9, 10, 9, 4, 7, 10, 4, 10, 7, 11, 3, 11, 7, 8, 3, 7, 3, 8, 0 }, +/* 86: 1, 2, 4, 6, */ { 4, 9, 8, 0, 8, 9, 8, 0, 2, 8, 2, 7, 6, 7, 2, 7, 6, 5, 7, 5, 4, 9, 4, 5 }, +/* 166: 1, 2, 5, 7, */ { 11, 10, 6, 10, 11, 2, 0, 2, 11, 7, 0, 11, 0, 7, 4, 5, 4, 7, 6, 5, 7, 5, 6, 10 }, +/* 58: 1, 3, 4, 5, */ { 11, 8, 3, 8, 11, 7, 5, 7, 11, 2, 5, 11, 5, 2, 1, 0, 1, 2, 3, 0, 2, 0, 3, 8 }, +/* 154: 1, 3, 4, 7, */ { 0, 8, 9, 4, 9, 8, 9, 4, 6, 9, 6, 1, 2, 1, 6, 1, 2, 3, 1, 3, 0, 8, 0, 3 }, +/* 106: 1, 3, 5, 6, */ { 2, 10, 11, 6, 11, 10, 11, 6, 4, 11, 4, 3, 0, 3, 4, 3, 0, 1, 3, 1, 2, 10, 2, 1 }, +/* 202: 1, 3, 6, 7, */ { 9, 10, 1, 10, 9, 5, 7, 5, 9, 0, 7, 9, 7, 0, 3, 2, 3, 0, 1, 2, 0, 2, 1, 10 }, +/* 210: 1, 4, 6, 7, */ { 9, 5, 1, 10, 1, 5, 1, 10, 11, 1, 11, 0, 8, 0, 11, 0, 8, 4, 0, 4, 9, 5, 9, 4 }, +/* 92: 2, 3, 4, 6, */ { 8, 11, 7, 11, 8, 3, 1, 3, 8, 4, 1, 8, 1, 4, 5, 6, 5, 4, 7, 6, 4, 6, 7, 11 }, +/* 172: 2, 3, 5, 7, */ { 5, 10, 9, 1, 9, 10, 9, 1, 3, 9, 3, 4, 7, 4, 3, 4, 7, 6, 4, 6, 5, 10, 5, 6 }, +/* 180: 2, 4, 5, 7, */ { 10, 6, 2, 11, 2, 6, 2, 11, 8, 2, 8, 1, 9, 1, 8, 1, 9, 5, 1, 5, 10, 6, 10, 5 }, +/* 120: 3, 4, 5, 6, */ { 11, 7, 3, 8, 3, 7, 3, 8, 9, 3, 9, 2, 10, 2, 9, 2, 10, 6, 2, 6, 11, 7, 11, 6 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 12.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling12_2[24][24] = { +/* 135: 0, 1, 2, 7, */ { 9, 8, 12, 10, 9, 12, 2, 10, 12, 3, 2, 12, 11, 3, 12, 6, 11, 12, 7, 6, 12, 8, 7, 12 }, +/* 75: 0, 1, 3, 6, */ { 8, 11, 12, 9, 8, 12, 1, 9, 12, 2, 1, 12, 10, 2, 12, 5, 10, 12, 6, 5, 12, 11, 6, 12 }, +/* 83: 0, 1, 4, 6, */ { 3, 1, 12, 7, 3, 12, 4, 7, 12, 9, 4, 12, 5, 9, 12, 6, 5, 12, 10, 6, 12, 1, 10, 12 }, +/* 163: 0, 1, 5, 7, */ { 12, 3, 1, 12, 1, 5, 12, 5, 6, 12, 6, 11, 12, 11, 7, 12, 7, 4, 12, 4, 8, 12, 8, 3 }, +/* 45: 0, 2, 3, 5, */ { 11, 10, 12, 8, 11, 12, 0, 8, 12, 1, 0, 12, 9, 1, 12, 4, 9, 12, 5, 4, 12, 10, 5, 12 }, +/* 53: 0, 2, 4, 5, */ { 12, 5, 7, 12, 7, 3, 12, 3, 2, 12, 2, 10, 12, 10, 1, 12, 1, 0, 12, 0, 9, 12, 9, 5 }, +/* 149: 0, 2, 4, 7, */ { 4, 6, 12, 0, 4, 12, 1, 0, 12, 10, 1, 12, 2, 10, 12, 3, 2, 12, 11, 3, 12, 6, 11, 12 }, +/* 101: 0, 2, 5, 6, */ { 6, 4, 12, 2, 6, 12, 3, 2, 12, 8, 3, 12, 0, 8, 12, 1, 0, 12, 9, 1, 12, 4, 9, 12 }, +/* 197: 0, 2, 6, 7, */ { 12, 7, 5, 12, 5, 1, 12, 1, 0, 12, 0, 8, 12, 8, 3, 12, 3, 2, 12, 2, 11, 12, 11, 7 }, +/* 89: 0, 3, 4, 6, */ { 12, 2, 0, 12, 0, 4, 12, 4, 5, 12, 5, 10, 12, 10, 6, 12, 6, 7, 12, 7, 11, 12, 11, 2 }, +/* 169: 0, 3, 5, 7, */ { 2, 0, 12, 6, 2, 12, 7, 6, 12, 8, 7, 12, 4, 8, 12, 5, 4, 12, 9, 5, 12, 0, 9, 12 }, +/* 225: 0, 5, 6, 7, */ { 12, 9, 10, 12, 10, 11, 12, 11, 7, 12, 7, 4, 12, 4, 8, 12, 8, 3, 12, 3, 0, 12, 0, 9 }, +/* 30: 1, 2, 3, 4, */ { 10, 9, 12, 11, 10, 12, 7, 11, 12, 4, 7, 12, 8, 4, 12, 3, 8, 12, 0, 3, 12, 9, 0, 12 }, +/* 86: 1, 2, 4, 6, */ { 12, 0, 2, 12, 2, 6, 12, 6, 7, 12, 7, 8, 12, 8, 4, 12, 4, 5, 12, 5, 9, 12, 9, 0 }, +/* 166: 1, 2, 5, 7, */ { 0, 2, 12, 4, 0, 12, 5, 4, 12, 10, 5, 12, 6, 10, 12, 7, 6, 12, 11, 7, 12, 2, 11, 12 }, +/* 58: 1, 3, 4, 5, */ { 5, 7, 12, 1, 5, 12, 0, 1, 12, 8, 0, 12, 3, 8, 12, 2, 3, 12, 11, 2, 12, 7, 11, 12 }, +/* 154: 1, 3, 4, 7, */ { 12, 4, 6, 12, 6, 2, 12, 2, 3, 12, 3, 8, 12, 8, 0, 12, 0, 1, 12, 1, 9, 12, 9, 4 }, +/* 106: 1, 3, 5, 6, */ { 12, 6, 4, 12, 4, 0, 12, 0, 1, 12, 1, 10, 12, 10, 2, 12, 2, 3, 12, 3, 11, 12, 11, 6 }, +/* 202: 1, 3, 6, 7, */ { 7, 5, 12, 3, 7, 12, 2, 3, 12, 10, 2, 12, 1, 10, 12, 0, 1, 12, 9, 0, 12, 5, 9, 12 }, +/* 210: 1, 4, 6, 7, */ { 12, 10, 11, 12, 11, 8, 12, 8, 0, 12, 0, 1, 12, 1, 9, 12, 9, 4, 12, 4, 5, 12, 5, 10 }, +/* 92: 2, 3, 4, 6, */ { 1, 3, 12, 5, 1, 12, 6, 5, 12, 11, 6, 12, 7, 11, 12, 4, 7, 12, 8, 4, 12, 3, 8, 12 }, +/* 172: 2, 3, 5, 7, */ { 12, 1, 3, 12, 3, 7, 12, 7, 4, 12, 4, 9, 12, 9, 5, 12, 5, 6, 12, 6, 10, 12, 10, 1 }, +/* 180: 2, 4, 5, 7, */ { 12, 11, 8, 12, 8, 9, 12, 9, 1, 12, 1, 2, 12, 2, 10, 12, 10, 5, 12, 5, 6, 12, 6, 11 }, +/* 120: 3, 4, 5, 6, */ { 12, 8, 9, 12, 9, 10, 12, 10, 2, 12, 2, 3, 12, 3, 11, 12, 11, 6, 12, 6, 7, 12, 7, 8 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 12.2 inverted + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling12_2_[24][24] = { +/* 135: 0, 1, 2, 7, */ { 12, 2, 11, 12, 11, 7, 12, 7, 6, 12, 6, 10, 12, 10, 9, 12, 9, 8, 12, 8, 3, 12, 3, 2 }, +/* 75: 0, 1, 3, 6, */ { 12, 1, 10, 12, 10, 6, 12, 6, 5, 12, 5, 9, 12, 9, 8, 12, 8, 11, 12, 11, 2, 12, 2, 1 }, +/* 83: 0, 1, 4, 6, */ { 12, 4, 5, 12, 5, 10, 12, 10, 6, 12, 6, 7, 12, 7, 3, 12, 3, 1, 12, 1, 9, 12, 9, 4 }, +/* 163: 0, 1, 5, 7, */ { 7, 6, 12, 8, 7, 12, 4, 8, 12, 5, 4, 12, 1, 5, 12, 3, 1, 12, 11, 3, 12, 6, 11, 12 }, +/* 45: 0, 2, 3, 5, */ { 12, 0, 9, 12, 9, 5, 12, 5, 4, 12, 4, 8, 12, 8, 11, 12, 11, 10, 12, 10, 1, 12, 1, 0 }, +/* 53: 0, 2, 4, 5, */ { 1, 2, 12, 9, 1, 12, 0, 9, 12, 3, 0, 12, 7, 3, 12, 5, 7, 12, 10, 5, 12, 2, 10, 12 }, +/* 149: 0, 2, 4, 7, */ { 12, 1, 2, 12, 2, 11, 12, 11, 3, 12, 3, 0, 12, 0, 4, 12, 4, 6, 12, 6, 10, 12, 10, 1 }, +/* 101: 0, 2, 5, 6, */ { 12, 3, 0, 12, 0, 9, 12, 9, 1, 12, 1, 2, 12, 2, 6, 12, 6, 4, 12, 4, 8, 12, 8, 3 }, +/* 197: 0, 2, 6, 7, */ { 3, 0, 12, 11, 3, 12, 2, 11, 12, 1, 2, 12, 5, 1, 12, 7, 5, 12, 8, 7, 12, 0, 8, 12 }, +/* 89: 0, 3, 4, 6, */ { 6, 5, 12, 11, 6, 12, 7, 11, 12, 4, 7, 12, 0, 4, 12, 2, 0, 12, 10, 2, 12, 5, 10, 12 }, +/* 169: 0, 3, 5, 7, */ { 12, 7, 4, 12, 4, 9, 12, 9, 5, 12, 5, 6, 12, 6, 2, 12, 2, 0, 12, 0, 8, 12, 8, 7 }, +/* 225: 0, 5, 6, 7, */ { 8, 7, 12, 0, 8, 12, 3, 0, 12, 11, 3, 12, 10, 11, 12, 9, 10, 12, 4, 9, 12, 7, 4, 12 }, +/* 30: 1, 2, 3, 4, */ { 12, 7, 8, 12, 8, 0, 12, 0, 3, 12, 3, 11, 12, 11, 10, 12, 10, 9, 12, 9, 4, 12, 4, 7 }, +/* 86: 1, 2, 4, 6, */ { 4, 7, 12, 9, 4, 12, 5, 9, 12, 6, 5, 12, 2, 6, 12, 0, 2, 12, 8, 0, 12, 7, 8, 12 }, +/* 166: 1, 2, 5, 7, */ { 12, 5, 6, 12, 6, 11, 12, 11, 7, 12, 7, 4, 12, 4, 0, 12, 0, 2, 12, 2, 10, 12, 10, 5 }, +/* 58: 1, 3, 4, 5, */ { 12, 0, 3, 12, 3, 11, 12, 11, 2, 12, 2, 1, 12, 1, 5, 12, 5, 7, 12, 7, 8, 12, 8, 0 }, +/* 154: 1, 3, 4, 7, */ { 0, 3, 12, 9, 0, 12, 1, 9, 12, 2, 1, 12, 6, 2, 12, 4, 6, 12, 8, 4, 12, 3, 8, 12 }, +/* 106: 1, 3, 5, 6, */ { 2, 1, 12, 11, 2, 12, 3, 11, 12, 0, 3, 12, 4, 0, 12, 6, 4, 12, 10, 6, 12, 1, 10, 12 }, +/* 202: 1, 3, 6, 7, */ { 12, 2, 1, 12, 1, 9, 12, 9, 0, 12, 0, 3, 12, 3, 7, 12, 7, 5, 12, 5, 10, 12, 10, 2 }, +/* 210: 1, 4, 6, 7, */ { 9, 0, 12, 5, 9, 12, 4, 5, 12, 8, 4, 12, 11, 8, 12, 10, 11, 12, 1, 10, 12, 0, 1, 12 }, +/* 92: 2, 3, 4, 6, */ { 12, 6, 7, 12, 7, 8, 12, 8, 4, 12, 4, 5, 12, 5, 1, 12, 1, 3, 12, 3, 11, 12, 11, 6 }, +/* 172: 2, 3, 5, 7, */ { 5, 4, 12, 10, 5, 12, 6, 10, 12, 7, 6, 12, 3, 7, 12, 1, 3, 12, 9, 1, 12, 4, 9, 12 }, +/* 180: 2, 4, 5, 7, */ { 10, 1, 12, 6, 10, 12, 5, 6, 12, 9, 5, 12, 8, 9, 12, 11, 8, 12, 2, 11, 12, 1, 2, 12 }, +/* 120: 3, 4, 5, 6, */ { 11, 2, 12, 7, 11, 12, 6, 7, 12, 10, 6, 12, 9, 10, 12, 8, 9, 12, 3, 8, 12, 2, 3, 12 } +}; +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +/** + * \brief test table for case 13 + * All faces are to be tested + * + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13: face test */ +static const char test13[2][7] = { +/* 165: 0, 2, 5, 7, */ { 1,2,3,4,5,6,7 }, +/* 90: 1, 3, 4, 6, */ { 2,3,4,1,5,6,7 }, +}; + + + +//_____________________________________________________________________________ +/** + * \brief subconfiguration table for case 13 + * Hard-coded tests for the subconfiguration determination + * + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13: sub configs */ +static const char subconfig13[64] = { +/* 0: 0,0,0,0,0,0 */ 0, +/* 1: 1,0,0,0,0,0 */ 1, +/* 2: 0,1,0,0,0,0 */ 2, +/* 3: 1,1,0,0,0,0 */ 7, +/* 4: 0,0,1,0,0,0 */ 3, +/* 5: 1,0,1,0,0,0 */ -1, +/* 6: 0,1,1,0,0,0 */ 11, +/* 7: 1,1,1,0,0,0 */ -1, +/* 8: 0,0,0,1,0,0 */ 4, +/* 9: 1,0,0,1,0,0 */ 8, +/* 10: 0,1,0,1,0,0 */ -1, +/* 11: 1,1,0,1,0,0 */ -1, +/* 12: 0,0,1,1,0,0 */ 14, +/* 13: 1,0,1,1,0,0 */ -1, +/* 14: 0,1,1,1,0,0 */ -1, +/* 15: 1,1,1,1,0,0 */ -1, +/* 16: 0,0,0,0,1,0 */ 5, +/* 17: 1,0,0,0,1,0 */ 9, +/* 18: 0,1,0,0,1,0 */ 12, +/* 19: 1,1,0,0,1,0 */ 23, +/* 20: 0,0,1,0,1,0 */ 15, +/* 21: 1,0,1,0,1,0 */ -1, +/* 22: 0,1,1,0,1,0 */ 21, +/* 23: 1,1,1,0,1,0 */ 38, +/* 24: 0,0,0,1,1,0 */ 17, +/* 25: 1,0,0,1,1,0 */ 20, +/* 26: 0,1,0,1,1,0 */ -1, +/* 27: 1,1,0,1,1,0 */ 36, +/* 28: 0,0,1,1,1,0 */ 26, +/* 29: 1,0,1,1,1,0 */ 33, +/* 30: 0,1,1,1,1,0 */ 30, +/* 31: 1,1,1,1,1,0 */ 44, +/* 32: 0,0,0,0,0,1 */ 6, +/* 33: 1,0,0,0,0,1 */ 10, +/* 34: 0,1,0,0,0,1 */ 13, +/* 35: 1,1,0,0,0,1 */ 19, +/* 36: 0,0,1,0,0,1 */ 16, +/* 37: 1,0,1,0,0,1 */ -1, +/* 38: 0,1,1,0,0,1 */ 25, +/* 39: 1,1,1,0,0,1 */ 37, +/* 40: 0,0,0,1,0,1 */ 18, +/* 41: 1,0,0,1,0,1 */ 24, +/* 42: 0,1,0,1,0,1 */ -1, +/* 43: 1,1,0,1,0,1 */ 35, +/* 44: 0,0,1,1,0,1 */ 22, +/* 45: 1,0,1,1,0,1 */ 32, +/* 46: 0,1,1,1,0,1 */ 29, +/* 47: 1,1,1,1,0,1 */ 43, +/* 48: 0,0,0,0,1,1 */ -1, +/* 49: 1,0,0,0,1,1 */ -1, +/* 50: 0,1,0,0,1,1 */ -1, +/* 51: 1,1,0,0,1,1 */ 34, +/* 52: 0,0,1,0,1,1 */ -1, +/* 53: 1,0,1,0,1,1 */ -1, +/* 54: 0,1,1,0,1,1 */ 28, +/* 55: 1,1,1,0,1,1 */ 42, +/* 56: 0,0,0,1,1,1 */ -1, +/* 57: 1,0,0,1,1,1 */ 31, +/* 58: 0,1,0,1,1,1 */ -1, +/* 59: 1,1,0,1,1,1 */ 41, +/* 60: 0,0,1,1,1,1 */ 27, +/* 61: 1,0,1,1,1,1 */ 40, +/* 62: 0,1,1,1,1,1 */ 39, +/* 63: 1,1,1,1,1,1 */ 45, +}; + + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 13.1 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13.1 */ +static const char tiling13_1[2][12] = { +/* 165: 0, 2, 5, 7, */ { 11, 7, 6, 1, 2, 10, 8, 3, 0, 9, 5, 4 }, +/* 90: 1, 3, 4, 6, */ { 8, 4, 7, 2, 3, 11, 9, 0, 1, 10, 6, 5 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 13.1 inverted + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13.1 */ +static const char tiling13_1_[2][12] = { +/* 165: 0, 2, 5, 7, */ { 7, 4, 8, 11, 3, 2, 1, 0, 9, 5, 6, 10 }, +/* 90: 1, 3, 4, 6, */ { 6, 7, 11, 10, 2, 1, 0, 3, 8, 4, 5, 9 } +}; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 13.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13.2 */ +static const char tiling13_2[2][6][18] = { +/* 165: 0, 2, 5, 7, */ { + /* 1 */ { 1, 2, 10, 11, 7, 6, 3, 4, 8, 4, 3, 5, 0, 5, 3, 5, 0, 9 }, + /* 2 */ { 8, 3, 0, 11, 7, 6, 9, 1, 4, 2, 4, 1, 4, 2, 5, 10, 5, 2 }, + /* 3 */ { 9, 5, 4, 8, 3, 0, 1, 6, 10, 6, 1, 7, 2, 7, 1, 7, 2, 11 }, + /* 4 */ { 9, 5, 4, 1, 2, 10, 11, 3, 6, 0, 6, 3, 6, 0, 7, 8, 7, 0 }, + /* 5 */ { 9, 5, 4, 11, 7, 6, 0, 10, 1, 10, 0, 8, 10, 8, 2, 3, 2, 8 }, + /* 6 */ { 1, 2, 10, 3, 0, 8, 4, 9, 7, 11, 7, 9, 5, 11, 9, 11, 5, 6 } +}, +/* 90: 1, 3, 4, 6, */ { + /* 1 */ { 2, 3, 11, 8, 4, 7, 0, 5, 9, 5, 0, 6, 1, 6, 0, 6, 1, 10 }, + /* 2 */ { 9, 0, 1, 8, 4, 7, 10, 2, 5, 3, 5, 2, 5, 3, 6, 11, 6, 3 }, + /* 3 */ { 6, 5, 10, 9, 0, 1, 2, 7, 11, 7, 2, 4, 3, 4, 2, 4, 3, 8 }, + /* 4 */ { 6, 5, 10, 2, 3, 11, 8, 0, 7, 1, 7, 0, 7, 1, 4, 9, 4, 1 }, + /* 5 */ { 6, 5, 10, 8, 4, 7, 1, 11, 2, 11, 1, 9, 11, 9, 3, 0, 3, 9 }, + /* 6 */ { 2, 3, 11, 0, 1, 9, 5, 10, 4, 8, 4, 10, 6, 8, 10, 8, 6, 7 } +} }; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 13.2 inverted + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13.2 */ +static const char tiling13_2_[2][6][18] = { +/* 165: 0, 2, 5, 7, */ { + /* 1 */ { 10, 5, 6, 11, 3, 2, 7, 0, 8, 0, 7, 1, 4, 1, 7, 1, 4, 9 }, + /* 2 */ { 11, 3, 2, 7, 4, 8, 9, 5, 0, 6, 0, 5, 0, 6, 1, 10, 1, 6 }, + /* 3 */ { 1, 0, 9, 7, 4, 8, 5, 2, 10, 2, 5, 3, 6, 3, 5, 3, 6, 11 }, + /* 4 */ { 10, 5, 6, 1, 0, 9, 11, 7, 2, 4, 2, 7, 2, 4, 3, 8, 3, 4 }, + /* 5 */ { 10, 5, 6, 7, 4, 8, 2, 11, 1, 9, 1, 11, 3, 9, 11, 9, 3, 0 }, + /* 6 */ { 11, 3, 2, 9, 1, 0, 4, 10, 5, 10, 4, 8, 10, 8, 6, 7, 6, 8 } +}, +/* 90: 1, 3, 4, 6, */ { + /* 1 */ { 6, 7, 11, 8, 0, 3, 4, 1, 9, 1, 4, 2, 5, 2, 4, 2, 5, 10 }, + /* 2 */ { 8, 0, 3, 4, 5, 9, 10, 6, 1, 7, 1, 6, 1, 7, 2, 11, 2, 7 }, + /* 3 */ { 2, 1, 10, 4, 5, 9, 6, 3, 11, 3, 6, 0, 7, 0, 6, 0, 7, 8 }, + /* 4 */ { 6, 7, 11, 2, 1, 10, 8, 4, 3, 5, 3, 4, 3, 5, 0, 9, 0, 5 }, + /* 5 */ { 6, 7, 11, 4, 5, 9, 3, 8, 2, 10, 2, 8, 0, 10, 8, 10, 0, 1 }, + /* 6 */ { 8, 0, 3, 10, 2, 1, 5, 11, 6, 11, 5, 9, 11, 9, 7, 4, 7, 9 } +} }; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 13.3 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13.3 */ +static const char tiling13_3[2][12][30] = { +/* 165: 0, 2, 5, 7, */ { + /* 1,2 */ { 11, 7, 6, 12, 2, 10, 12, 10, 5, 12, 5, 4, 12, 4, 8, 12, 8, 3, 12, 3, 0, 12, 0, 9, 12, 9, 1, 12, 1, 2 }, + /* 1,4 */ { 1, 2, 10, 9, 5, 12, 0, 9, 12, 3, 0, 12, 11, 3, 12, 6, 11, 12, 7, 6, 12, 8, 7, 12, 4, 8, 12, 5, 4, 12 }, + /* 1,5 */ { 11, 7, 6, 12, 5, 4, 12, 4, 8, 12, 8, 3, 12, 3, 2, 12, 2, 10, 12, 10, 1, 12, 1, 0, 12, 0, 9, 12, 9, 5 }, + /* 1,6 */ { 1, 2, 10, 12, 3, 0, 12, 0, 9, 12, 9, 5, 12, 5, 6, 12, 6, 11, 12, 11, 7, 12, 7, 4, 12, 4, 8, 12, 8, 3 }, + /* 2,3 */ { 8, 3, 0, 11, 7, 12, 2, 11, 12, 1, 2, 12, 9, 1, 12, 4, 9, 12, 5, 4, 12, 10, 5, 12, 6, 10, 12, 7, 6, 12 }, + /* 2,5 */ { 11, 7, 6, 5, 4, 12, 10, 5, 12, 2, 10, 12, 3, 2, 12, 8, 3, 12, 0, 8, 12, 1, 0, 12, 9, 1, 12, 4, 9, 12 }, + /* 2,6 */ { 8, 3, 0, 1, 2, 12, 9, 1, 12, 4, 9, 12, 7, 4, 12, 11, 7, 12, 6, 11, 12, 5, 6, 12, 10, 5, 12, 2, 10, 12 }, + /* 3,4 */ { 9, 5, 4, 12, 0, 8, 12, 8, 7, 12, 7, 6, 12, 6, 10, 12, 10, 1, 12, 1, 2, 12, 2, 11, 12, 11, 3, 12, 3, 0 }, + /* 3,5 */ { 9, 5, 4, 12, 7, 6, 12, 6, 10, 12, 10, 1, 12, 1, 0, 12, 0, 8, 12, 8, 3, 12, 3, 2, 12, 2, 11, 12, 11, 7 }, + /* 3,6 */ { 8, 3, 0, 12, 1, 2, 12, 2, 11, 12, 11, 7, 12, 7, 4, 12, 4, 9, 12, 9, 5, 12, 5, 6, 12, 6, 10, 12, 10, 1 }, + /* 4,5 */ { 9, 5, 4, 7, 6, 12, 8, 7, 12, 0, 8, 12, 1, 0, 12, 10, 1, 12, 2, 10, 12, 3, 2, 12, 11, 3, 12, 6, 11, 12 }, + /* 4,6 */ { 1, 2, 10, 3, 0, 12, 11, 3, 12, 6, 11, 12, 5, 6, 12, 9, 5, 12, 4, 9, 12, 7, 4, 12, 8, 7, 12, 0, 8, 12 } +}, +/* 90: 1, 3, 4, 6, */ { + /* 1,2 */ { 8, 4, 7, 12, 3, 11, 12, 11, 6, 12, 6, 5, 12, 5, 9, 12, 9, 0, 12, 0, 1, 12, 1, 10, 12, 10, 2, 12, 2, 3 }, + /* 1,4 */ { 2, 3, 11, 10, 6, 12, 1, 10, 12, 0, 1, 12, 8, 0, 12, 7, 8, 12, 4, 7, 12, 9, 4, 12, 5, 9, 12, 6, 5, 12 }, + /* 1,5 */ { 8, 4, 7, 12, 6, 5, 12, 5, 9, 12, 9, 0, 12, 0, 3, 12, 3, 11, 12, 11, 2, 12, 2, 1, 12, 1, 10, 12, 10, 6 }, + /* 1,6 */ { 2, 3, 11, 12, 0, 1, 12, 1, 10, 12, 10, 6, 12, 6, 7, 12, 7, 8, 12, 8, 4, 12, 4, 5, 12, 5, 9, 12, 9, 0 }, + /* 2,3 */ { 0, 1, 9, 8, 4, 12, 3, 8, 12, 2, 3, 12, 10, 2, 12, 5, 10, 12, 6, 5, 12, 11, 6, 12, 7, 11, 12, 4, 7, 12 }, + /* 2,5 */ { 8, 4, 7, 6, 5, 12, 11, 6, 12, 3, 11, 12, 0, 3, 12, 9, 0, 12, 1, 9, 12, 2, 1, 12, 10, 2, 12, 5, 10, 12 }, + /* 2,6 */ { 9, 0, 1, 2, 3, 12, 10, 2, 12, 5, 10, 12, 4, 5, 12, 8, 4, 12, 7, 8, 12, 6, 7, 12, 11, 6, 12, 3, 11, 12 }, + /* 3,4 */ { 6, 5, 10, 12, 1, 9, 12, 9, 4, 12, 4, 7, 12, 7, 11, 12, 11, 2, 12, 2, 3, 12, 3, 8, 12, 8, 0, 12, 0, 1 }, + /* 3,5 */ { 6, 5, 10, 12, 4, 7, 12, 7, 11, 12, 11, 2, 12, 2, 1, 12, 1, 9, 12, 9, 0, 12, 0, 3, 12, 3, 8, 12, 8, 4 }, + /* 3,6 */ { 9, 0, 1, 12, 2, 3, 12, 3, 8, 12, 8, 4, 12, 4, 5, 12, 5, 10, 12, 10, 6, 12, 6, 7, 12, 7, 11, 12, 11, 2 }, + /* 4,5 */ { 6, 5, 10, 4, 7, 12, 9, 4, 12, 1, 9, 12, 2, 1, 12, 11, 2, 12, 3, 11, 12, 0, 3, 12, 8, 0, 12, 7, 8, 12 }, + /* 4,6 */ { 2, 3, 11, 0, 1, 12, 8, 0, 12, 7, 8, 12, 6, 7, 12, 10, 6, 12, 5, 10, 12, 4, 5, 12, 9, 4, 12, 1, 9, 12 } +} }; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 13.3, inverted + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13.3 */ +static const char tiling13_3_[2][12][30] = { +/* 165: 0, 2, 5, 7, */ { + /* 1,2 */ { 3, 2, 11, 8, 7, 12, 0, 8, 12, 1, 0, 12, 10, 1, 12, 6, 10, 12, 5, 6, 12, 9, 5, 12, 4, 9, 12, 7, 4, 12 }, + /* 1,4 */ { 5, 6, 10, 12, 2, 11, 12, 11, 7, 12, 7, 4, 12, 4, 9, 12, 9, 1, 12, 1, 0, 12, 0, 8, 12, 8, 3, 12, 3, 2 }, + /* 1,5 */ { 10, 5, 6, 12, 7, 4, 12, 4, 9, 12, 9, 1, 12, 1, 2, 12, 2, 11, 12, 11, 3, 12, 3, 0, 12, 0, 8, 12, 8, 7 }, + /* 1,6 */ { 11, 3, 2, 12, 1, 0, 12, 0, 8, 12, 8, 7, 12, 7, 6, 12, 6, 10, 12, 10, 5, 12, 5, 4, 12, 4, 9, 12, 9, 1 }, + /* 2,3 */ { 7, 4, 8, 11, 3, 12, 6, 11, 12, 5, 6, 12, 9, 5, 12, 0, 9, 12, 1, 0, 12, 10, 1, 12, 2, 10, 12, 3, 2, 12 }, + /* 2,5 */ { 7, 4, 8, 5, 6, 12, 9, 5, 12, 0, 9, 12, 3, 0, 12, 11, 3, 12, 2, 11, 12, 1, 2, 12, 10, 1, 12, 6, 10, 12 }, + /* 2,6 */ { 11, 3, 2, 1, 0, 12, 10, 1, 12, 6, 10, 12, 7, 6, 12, 8, 7, 12, 4, 8, 12, 5, 4, 12, 9, 5, 12, 0, 9, 12 }, + /* 3,4 */ { 1, 0, 9, 12, 4, 8, 12, 8, 3, 12, 3, 2, 12, 2, 10, 12, 10, 5, 12, 5, 6, 12, 6, 11, 12, 11, 7, 12, 7, 4 }, + /* 3,5 */ { 7, 4, 8, 12, 5, 6, 12, 6, 11, 12, 11, 3, 12, 3, 0, 12, 0, 9, 12, 9, 1, 12, 1, 2, 12, 2, 10, 12, 10, 5 }, + /* 3,6 */ { 1, 0, 9, 12, 3, 2, 12, 2, 10, 12, 10, 5, 12, 5, 4, 12, 4, 8, 12, 8, 7, 12, 7, 6, 12, 6, 11, 12, 11, 3 }, + /* 4,5 */ { 10, 5, 6, 7, 4, 12, 11, 7, 12, 2, 11, 12, 1, 2, 12, 9, 1, 12, 0, 9, 12, 3, 0, 12, 8, 3, 12, 4, 8, 12 }, + /* 4,6 */ { 9, 1, 0, 3, 2, 12, 8, 3, 12, 4, 8, 12, 5, 4, 12, 10, 5, 12, 6, 10, 12, 7, 6, 12, 11, 7, 12, 2, 11, 12 } +}, +/* 90: 1, 3, 4, 6, */ { + /* 1,2 */ { 0, 3, 8, 9, 4, 12, 1, 9, 12, 2, 1, 12, 11, 2, 12, 7, 11, 12, 6, 7, 12, 10, 6, 12, 5, 10, 12, 4, 5, 12 }, + /* 1,4 */ { 11, 6, 7, 12, 3, 8, 12, 8, 4, 12, 4, 5, 12, 5, 10, 12, 10, 2, 12, 2, 1, 12, 1, 9, 12, 9, 0, 12, 0, 3 }, + /* 1,5 */ { 6, 7, 11, 12, 4, 5, 12, 5, 10, 12, 10, 2, 12, 2, 3, 12, 3, 8, 12, 8, 0, 12, 0, 1, 12, 1, 9, 12, 9, 4 }, + /* 1,6 */ { 8, 0, 3, 12, 2, 1, 12, 1, 9, 12, 9, 4, 12, 4, 7, 12, 7, 11, 12, 11, 6, 12, 6, 5, 12, 5, 10, 12, 10, 2 }, + /* 2,3 */ { 4, 5, 9, 8, 0, 12, 7, 8, 12, 6, 7, 12, 10, 6, 12, 1, 10, 12, 2, 1, 12, 11, 2, 12, 3, 11, 12, 0, 3, 12 }, + /* 2,5 */ { 4, 5, 9, 6, 7, 12, 10, 6, 12, 1, 10, 12, 0, 1, 12, 8, 0, 12, 3, 8, 12, 2, 3, 12, 11, 2, 12, 7, 11, 12 }, + /* 2,6 */ { 8, 0, 3, 2, 1, 12, 11, 2, 12, 7, 11, 12, 4, 7, 12, 9, 4, 12, 5, 9, 12, 6, 5, 12, 10, 6, 12, 1, 10, 12 }, + /* 3,4 */ { 2, 1, 10, 12, 5, 9, 12, 9, 0, 12, 0, 3, 12, 3, 11, 12, 11, 6, 12, 6, 7, 12, 7, 8, 12, 8, 4, 12, 4, 5 }, + /* 3,5 */ { 4, 5, 9, 12, 6, 7, 12, 7, 8, 12, 8, 0, 12, 0, 1, 12, 1, 10, 12, 10, 2, 12, 2, 3, 12, 3, 11, 12, 11, 6 }, + /* 3,6 */ { 2, 1, 10, 12, 0, 3, 12, 3, 11, 12, 11, 6, 12, 6, 5, 12, 5, 9, 12, 9, 4, 12, 4, 7, 12, 7, 8, 12, 8, 0 }, + /* 4,5 */ { 6, 7, 11, 4, 5, 12, 8, 4, 12, 3, 8, 12, 2, 3, 12, 10, 2, 12, 1, 10, 12, 0, 1, 12, 9, 0, 12, 5, 9, 12 }, + /* 4,6 */ { 10, 2, 1, 0, 3, 12, 9, 0, 12, 5, 9, 12, 6, 5, 12, 11, 6, 12, 7, 11, 12, 4, 7, 12, 8, 4, 12, 3, 8, 12 } +} }; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 13.4 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13.4 */ +static const char tiling13_4[2][4][36] = { +/* 165: 0, 2, 5, 7, */ { +/* 1,2,6 */ { 12, 2, 10, 12, 10, 5, 12, 5, 6, 12, 6, 11, 12, 11, 7, 12, 7, 4, 12, 4, 8, 12, 8, 3, 12, 3, 0, 12, 0, 9, 12, 9, 1, 12, 1, 2 }, +/* 1,4,5 */ { 11, 3, 12, 6, 11, 12, 7, 6, 12, 8, 7, 12, 4, 8, 12, 5, 4, 12, 9, 5, 12, 0, 9, 12, 1, 0, 12, 10, 1, 12, 2, 10, 12, 3, 2, 12 }, +/* 2,3,5 */ { 9, 1, 12, 4, 9, 12, 5, 4, 12, 10, 5, 12, 6, 10, 12, 7, 6, 12, 11, 7, 12, 2, 11, 12, 3, 2, 12, 8, 3, 12, 0, 8, 12, 1, 0, 12 }, +/* 3,4,6 */ { 12, 0, 8, 12, 8, 7, 12, 7, 4, 12, 4, 9, 12, 9, 5, 12, 5, 6, 12, 6, 10, 12, 10, 1, 12, 1, 2, 12, 2, 11, 12, 11, 3, 12, 3, 0 } +}, +/* 90: 1, 3, 4, 6, */ { +/* 1,2,6 */ { 12, 3, 11, 12, 11, 6, 12, 6, 7, 12, 7, 8, 12, 8, 4, 12, 4, 5, 12, 5, 9, 12, 9, 0, 12, 0, 1, 12, 1, 10, 12, 10, 2, 12, 2, 3 }, +/* 1,4,5 */ { 8, 0, 12, 7, 8, 12, 4, 7, 12, 9, 4, 12, 5, 9, 12, 6, 5, 12, 10, 6, 12, 1, 10, 12, 2, 1, 12, 11, 2, 12, 3, 11, 12, 0, 3, 12 }, +/* 2,3,5 */ { 10, 2, 12, 5, 10, 12, 6, 5, 12, 11, 6, 12, 7, 11, 12, 4, 7, 12, 8, 4, 12, 3, 8, 12, 0, 3, 12, 9, 0, 12, 1, 9, 12, 2, 1, 12 }, +/* 3,4,6 */ { 12, 1, 9, 12, 9, 4, 12, 4, 5, 12, 5, 10, 12, 10, 6, 12, 6, 7, 12, 7, 11, 12, 11, 2, 12, 2, 3, 12, 3, 8, 12, 8, 0, 12, 0, 1 } +} }; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 13.5.1 + * The support edge for the interior test is marked as the 1st column. + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13.5.1 */ +static const char tiling13_5_1[2][4][18] = { +/* 165: 0, 2, 5, 7, */ { +/* 1,2,5 */ { 7, 6, 11, 1, 0, 9, 10, 3, 2, 3, 10, 5, 3, 5, 8, 4, 8, 5 }, +/* 1,4,6 */ { 1, 2, 10, 7, 4, 8, 3, 0, 11, 6, 11, 0, 9, 6, 0, 6, 9, 5 }, +/* 2,3,6 */ { 3, 0, 8, 5, 6, 10, 1, 2, 9, 4, 9, 2, 11, 4, 2, 4, 11, 7 }, +/* 3,4,5 */ { 5, 4, 9, 3, 2, 11, 8, 1, 0, 1, 8, 7, 1, 7, 10, 6, 10, 7 } +}, +/* 90: 1, 3, 4, 6, */ { +/* 1,2,5 */ { 4, 7, 8, 2, 1, 10, 11, 0, 3, 0, 11, 6, 0, 6, 9, 5, 9, 6 }, +/* 1,4,6 */ { 2, 3, 11, 4, 5, 9, 0, 1, 8, 7, 8, 1, 10, 7, 1, 7, 10, 6 }, +/* 2,3,6 */ { 0, 1, 9, 6, 7, 11, 2, 3, 10, 5, 10, 3, 8, 5, 3, 5, 8, 4 }, +/* 3,4,5 */ { 6, 5, 10, 0, 3, 8, 9, 2, 1, 2, 9, 4, 2, 4, 11, 7, 11, 4 } +} }; + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 13.5.2 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +/* 13.5.2 */ +static const char tiling13_5_2[2][4][30] = { +/* 165: 0, 2, 5, 7, */ { +/* 1,2,5 */ { 1, 0, 9, 7, 4, 8, 7, 8, 3, 7, 3, 11, 2, 11, 3, 11, 2, 10, 11, 10, 6, 5, 6, 10, 6, 5, 7, 4, 7, 5 }, +/* 1,4,6 */ { 7, 4, 8, 11, 3, 2, 6, 11, 2, 10, 6, 2, 6, 10, 5, 9, 5, 10, 1, 9, 10, 9, 1, 0, 2, 0, 1, 0, 2, 3 }, +/* 2,3,6 */ { 5, 6, 10, 9, 1, 0, 4, 9, 0, 8, 4, 0, 4, 8, 7, 11, 7, 8, 3, 11, 8, 11, 3, 2, 0, 2, 3, 2, 0, 1 }, +/* 3,4,5 */ { 3, 2, 11, 5, 6, 10, 5, 10, 1, 5, 1, 9, 0, 9, 1, 9, 0, 8, 9, 8, 4, 4, 8, 7, 4, 7, 5, 6, 5, 7 } +}, +/* 90: 1, 3, 4, 6, */ { +/* 1,2,5 */ { 2, 1, 10, 4, 5, 9, 4, 9, 0, 4, 0, 8, 3, 8, 0, 8, 3, 11, 8, 11, 7, 6, 7, 11, 7, 6, 4, 5, 4, 6 }, +/* 1,4,6 */ { 4, 5, 9, 8, 0, 3, 7, 8, 3, 11, 7, 3, 7, 11, 6, 10, 6, 11, 2, 10, 11, 10, 2, 1, 3, 1, 2, 1, 3, 0 }, +/* 2,3,6 */ { 6, 7, 11, 10, 2, 1, 5, 10, 1, 9, 5, 1, 5, 9, 4, 8, 4, 9, 0, 8, 9, 8, 0, 3, 1, 3, 0, 3, 1, 2 }, +/* 3,4,5 */ { 0, 3, 8, 6, 7, 11, 6, 11, 2, 6, 2, 10, 1, 10, 2, 10, 1, 9, 10, 9, 5, 5, 9, 4, 5, 4, 6, 7, 6, 4 } +} }; +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +/** + * \brief tiling table for case 14 + * For each of the case above, the specific triangulation of the edge + * intersection points is given. + * When a case is ambiguous, there is an auxiliary table that contains + * the face number to test and the tiling table contains the specific + * triangulations depending on the results + * A minus sign means to invert the result of the test. + */ +//----------------------------------------------------------------------------- +static const char tiling14[12][12] = { +/* 71: 0, 1, 2, 6, */ { 5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8 }, +/* 43: 0, 1, 3, 5, */ { 2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5 }, +/* 147: 0, 1, 4, 7, */ { 9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6 }, +/* 29: 0, 2, 3, 4, */ { 1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4 }, +/* 201: 0, 3, 6, 7, */ { 8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5 }, +/* 113: 0, 4, 5, 6, */ { 0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10 }, +/* 142: 1, 2, 3, 7, */ { 0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7 }, +/* 54: 1, 2, 4, 5, */ { 8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2 }, +/* 226: 1, 5, 6, 7, */ { 1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11 }, +/* 108: 2, 3, 5, 6, */ { 9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3 }, +/* 212: 2, 4, 6, 7, */ { 2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8 }, +/* 184: 3, 4, 5, 7, */ { 5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2 } +}; +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +/** + * \brief original Marching Cubes implementation + * For each of the possible vertex states listed in this table there is a + * specific triangulation of the edge intersection points. The table lists + * all of them in the form of 0-5 edge triples with the list terminated by + * the invalid value -1. For example: casesClassic[3] list the 2 triangles + * formed when cube[0] and cube[1] are inside of the surface, but the rest of + * the cube is not. + */ +//----------------------------------------------------------------------------- +static const char casesClassic[256][16] = { +/* 0: */ { -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 1: 0, */ { 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 2: 1, */ { 0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 3: 0, 1, */ { 1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 4: 2, */ { 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 5: 0, 2, */ { 0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 6: 1, 2, */ { 9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 7: 0, 1, 2, */ { 2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1 }, +/* 8: 3, */ { 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 9: 0, 3, */ { 0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 10: 1, 3, */ { 1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 11: 0, 1, 3, */ { 1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1 }, +/* 12: 2, 3, */ { 3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 13: 0, 2, 3, */ { 0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1 }, +/* 14: 1, 2, 3, */ { 3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1 }, +/* 15: 0, 1, 2, 3, */ { 9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 16: 4, */ { 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 17: 0, 4, */ { 4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 18: 1, 4, */ { 0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 19: 0, 1, 4, */ { 4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1 }, +/* 20: 2, 4, */ { 1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 21: 0, 2, 4, */ { 3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1 }, +/* 22: 1, 2, 4, */ { 9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1 }, +/* 23: 0, 1, 2, 4, */ { 2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1 }, +/* 24: 3, 4, */ { 8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 25: 0, 3, 4, */ { 11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1 }, +/* 26: 1, 3, 4, */ { 9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1 }, +/* 27: 0, 1, 3, 4, */ { 4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1 }, +/* 28: 2, 3, 4, */ { 3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1 }, +/* 29: 0, 2, 3, 4, */ { 1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1 }, +/* 30: 1, 2, 3, 4, */ { 4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1 }, +/* 31: 0, 1, 2, 3, 4, */ { 4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1 }, +/* 32: 5, */ { 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 33: 0, 5, */ { 9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 34: 1, 5, */ { 0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 35: 0, 1, 5, */ { 8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1 }, +/* 36: 2, 5, */ { 1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 37: 0, 2, 5, */ { 3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1 }, +/* 38: 1, 2, 5, */ { 5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1 }, +/* 39: 0, 1, 2, 5, */ { 2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1 }, +/* 40: 3, 5, */ { 9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 41: 0, 3, 5, */ { 0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1 }, +/* 42: 1, 3, 5, */ { 0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1 }, +/* 43: 0, 1, 3, 5, */ { 2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1 }, +/* 44: 2, 3, 5, */ { 10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1 }, +/* 45: 0, 2, 3, 5, */ { 4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1 }, +/* 46: 1, 2, 3, 5, */ { 5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1 }, +/* 47: 0, 1, 2, 3, 5, */ { 5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1 }, +/* 48: 4, 5, */ { 9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 49: 0, 4, 5, */ { 9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1 }, +/* 50: 1, 4, 5, */ { 0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1 }, +/* 51: 0, 1, 4, 5, */ { 1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 52: 2, 4, 5, */ { 9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1 }, +/* 53: 0, 2, 4, 5, */ { 10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1 }, +/* 54: 1, 2, 4, 5, */ { 8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1 }, +/* 55: 0, 1, 2, 4, 5, */ { 2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1 }, +/* 56: 3, 4, 5, */ { 7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1 }, +/* 57: 0, 3, 4, 5, */ { 9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1 }, +/* 58: 1, 3, 4, 5, */ { 2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1 }, +/* 59: 0, 1, 3, 4, 5, */ { 11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1 }, +/* 60: 2, 3, 4, 5, */ { 9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1 }, +/* 61: 0, 2, 3, 4, 5, */ { 5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1 }, +/* 62: 1, 2, 3, 4, 5, */ { 11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1 }, +/* 63: 0, 1, 2, 3, 4, 5, */ { 11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 64: 6, */ { 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 65: 0, 6, */ { 0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 66: 1, 6, */ { 9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 67: 0, 1, 6, */ { 1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1 }, +/* 68: 2, 6, */ { 1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 69: 0, 2, 6, */ { 1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1 }, +/* 70: 1, 2, 6, */ { 9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1 }, +/* 71: 0, 1, 2, 6, */ { 5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1 }, +/* 72: 3, 6, */ { 2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 73: 0, 3, 6, */ { 11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1 }, +/* 74: 1, 3, 6, */ { 0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1 }, +/* 75: 0, 1, 3, 6, */ { 5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1 }, +/* 76: 2, 3, 6, */ { 6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1 }, +/* 77: 0, 2, 3, 6, */ { 0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1 }, +/* 78: 1, 2, 3, 6, */ { 3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1 }, +/* 79: 0, 1, 2, 3, 6, */ { 6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1 }, +/* 80: 4, 6, */ { 5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 81: 0, 4, 6, */ { 4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1 }, +/* 82: 1, 4, 6, */ { 1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1 }, +/* 83: 0, 1, 4, 6, */ { 10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1 }, +/* 84: 2, 4, 6, */ { 6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1 }, +/* 85: 0, 2, 4, 6, */ { 1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1 }, +/* 86: 1, 2, 4, 6, */ { 8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1 }, +/* 87: 0, 1, 2, 4, 6, */ { 7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1 }, +/* 88: 3, 4, 6, */ { 3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1 }, +/* 89: 0, 3, 4, 6, */ { 5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1 }, +/* 90: 1, 3, 4, 6, */ { 0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1 }, +/* 91: 0, 1, 3, 4, 6, */ { 9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1 }, +/* 92: 2, 3, 4, 6, */ { 8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1 }, +/* 93: 0, 2, 3, 4, 6, */ { 5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1 }, +/* 94: 1, 2, 3, 4, 6, */ { 0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1 }, +/* 95: 0, 1, 2, 3, 4, 6, */ { 6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1 }, +/* 96: 5, 6, */ { 10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 97: 0, 5, 6, */ { 4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1 }, +/* 98: 1, 5, 6, */ { 10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1 }, +/* 99: 0, 1, 5, 6, */ { 8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1 }, +/* 100: 2, 5, 6, */ { 1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1 }, +/* 101: 0, 2, 5, 6, */ { 3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1 }, +/* 102: 1, 2, 5, 6, */ { 0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 103: 0, 1, 2, 5, 6, */ { 8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1 }, +/* 104: 3, 5, 6, */ { 10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1 }, +/* 105: 0, 3, 5, 6, */ { 0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1 }, +/* 106: 1, 3, 5, 6, */ { 3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1 }, +/* 107: 0, 1, 3, 5, 6, */ { 6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1 }, +/* 108: 2, 3, 5, 6, */ { 9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1 }, +/* 109: 0, 2, 3, 5, 6, */ { 8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1 }, +/* 110: 1, 2, 3, 5, 6, */ { 3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1 }, +/* 111: 0, 1, 2, 3, 5, 6, */ { 6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 112: 4, 5, 6, */ { 7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1 }, +/* 113: 0, 4, 5, 6, */ { 0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1 }, +/* 114: 1, 4, 5, 6, */ { 10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1 }, +/* 115: 0, 1, 4, 5, 6, */ { 10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1 }, +/* 116: 2, 4, 5, 6, */ { 1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1 }, +/* 117: 0, 2, 4, 5, 6, */ { 2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1 }, +/* 118: 1, 2, 4, 5, 6, */ { 7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1 }, +/* 119: 0, 1, 2, 4, 5, 6, */ { 7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 120: 3, 4, 5, 6, */ { 2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1 }, +/* 121: 0, 3, 4, 5, 6, */ { 2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1 }, +/* 122: 1, 3, 4, 5, 6, */ { 1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1 }, +/* 123: 0, 1, 3, 4, 5, 6, */ { 11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1 }, +/* 124: 2, 3, 4, 5, 6, */ { 8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1 }, +/* 125: 0, 2, 3, 4, 5, 6, */ { 0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 126: 1, 2, 3, 4, 5, 6, */ { 7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1 }, +/* 127: 0, 1, 2, 3, 4, 5, 6, */ { 7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 128: 7, */ { 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 129: 0, 7, */ { 3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 130: 1, 7, */ { 0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 131: 0, 1, 7, */ { 8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1 }, +/* 132: 2, 7, */ { 10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 133: 0, 2, 7, */ { 1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1 }, +/* 134: 1, 2, 7, */ { 2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1 }, +/* 135: 0, 1, 2, 7, */ { 6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1 }, +/* 136: 3, 7, */ { 7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 137: 0, 3, 7, */ { 7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1 }, +/* 138: 1, 3, 7, */ { 2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1 }, +/* 139: 0, 1, 3, 7, */ { 1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1 }, +/* 140: 2, 3, 7, */ { 10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1 }, +/* 141: 0, 2, 3, 7, */ { 10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1 }, +/* 142: 1, 2, 3, 7, */ { 0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1 }, +/* 143: 0, 1, 2, 3, 7, */ { 7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1 }, +/* 144: 4, 7, */ { 6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 145: 0, 4, 7, */ { 3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1 }, +/* 146: 1, 4, 7, */ { 8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1 }, +/* 147: 0, 1, 4, 7, */ { 9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1 }, +/* 148: 2, 4, 7, */ { 6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1 }, +/* 149: 0, 2, 4, 7, */ { 1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1 }, +/* 150: 1, 2, 4, 7, */ { 4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1 }, +/* 151: 0, 1, 2, 4, 7, */ { 10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1 }, +/* 152: 3, 4, 7, */ { 8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1 }, +/* 153: 0, 3, 4, 7, */ { 0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 154: 1, 3, 4, 7, */ { 1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1 }, +/* 155: 0, 1, 3, 4, 7, */ { 1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1 }, +/* 156: 2, 3, 4, 7, */ { 8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1 }, +/* 157: 0, 2, 3, 4, 7, */ { 10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1 }, +/* 158: 1, 2, 3, 4, 7, */ { 4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1 }, +/* 159: 0, 1, 2, 3, 4, 7, */ { 10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 160: 5, 7, */ { 4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 161: 0, 5, 7, */ { 0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1 }, +/* 162: 1, 5, 7, */ { 5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1 }, +/* 163: 0, 1, 5, 7, */ { 11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1 }, +/* 164: 2, 5, 7, */ { 9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1 }, +/* 165: 0, 2, 5, 7, */ { 6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1 }, +/* 166: 1, 2, 5, 7, */ { 7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1 }, +/* 167: 0, 1, 2, 5, 7, */ { 3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1 }, +/* 168: 3, 5, 7, */ { 7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1 }, +/* 169: 0, 3, 5, 7, */ { 9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1 }, +/* 170: 1, 3, 5, 7, */ { 3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1 }, +/* 171: 0, 1, 3, 5, 7, */ { 6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1 }, +/* 172: 2, 3, 5, 7, */ { 9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1 }, +/* 173: 0, 2, 3, 5, 7, */ { 1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1 }, +/* 174: 1, 2, 3, 5, 7, */ { 4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1 }, +/* 175: 0, 1, 2, 3, 5, 7, */ { 7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1 }, +/* 176: 4, 5, 7, */ { 6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1 }, +/* 177: 0, 4, 5, 7, */ { 3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1 }, +/* 178: 1, 4, 5, 7, */ { 0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1 }, +/* 179: 0, 1, 4, 5, 7, */ { 6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1 }, +/* 180: 2, 4, 5, 7, */ { 1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1 }, +/* 181: 0, 2, 4, 5, 7, */ { 0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1 }, +/* 182: 1, 2, 4, 5, 7, */ { 11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1 }, +/* 183: 0, 1, 2, 4, 5, 7, */ { 6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1 }, +/* 184: 3, 4, 5, 7, */ { 5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1 }, +/* 185: 0, 3, 4, 5, 7, */ { 9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1 }, +/* 186: 1, 3, 4, 5, 7, */ { 1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1 }, +/* 187: 0, 1, 3, 4, 5, 7, */ { 1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 188: 2, 3, 4, 5, 7, */ { 1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1 }, +/* 189: 0, 2, 3, 4, 5, 7, */ { 10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1 }, +/* 190: 1, 2, 3, 4, 5, 7, */ { 0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 191: 0, 1, 2, 3, 4, 5, 7, */ { 10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 192: 6, 7, */ { 11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 193: 0, 6, 7, */ { 11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1 }, +/* 194: 1, 6, 7, */ { 5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1 }, +/* 195: 0, 1, 6, 7, */ { 10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1 }, +/* 196: 2, 6, 7, */ { 11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1 }, +/* 197: 0, 2, 6, 7, */ { 0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1 }, +/* 198: 1, 2, 6, 7, */ { 9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1 }, +/* 199: 0, 1, 2, 6, 7, */ { 7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1 }, +/* 200: 3, 6, 7, */ { 2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1 }, +/* 201: 0, 3, 6, 7, */ { 8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1 }, +/* 202: 1, 3, 6, 7, */ { 9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1 }, +/* 203: 0, 1, 3, 6, 7, */ { 9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1 }, +/* 204: 2, 3, 6, 7, */ { 1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 205: 0, 2, 3, 6, 7, */ { 0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1 }, +/* 206: 1, 2, 3, 6, 7, */ { 9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1 }, +/* 207: 0, 1, 2, 3, 6, 7, */ { 9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 208: 4, 6, 7, */ { 5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1 }, +/* 209: 0, 4, 6, 7, */ { 5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1 }, +/* 210: 1, 4, 6, 7, */ { 0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1 }, +/* 211: 0, 1, 4, 6, 7, */ { 10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1 }, +/* 212: 2, 4, 6, 7, */ { 2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1 }, +/* 213: 0, 2, 4, 6, 7, */ { 0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1 }, +/* 214: 1, 2, 4, 6, 7, */ { 0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1 }, +/* 215: 0, 1, 2, 4, 6, 7, */ { 9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 216: 3, 4, 6, 7, */ { 2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1 }, +/* 217: 0, 3, 4, 6, 7, */ { 5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1 }, +/* 218: 1, 3, 4, 6, 7, */ { 3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1 }, +/* 219: 0, 1, 3, 4, 6, 7, */ { 5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1 }, +/* 220: 2, 3, 4, 6, 7, */ { 8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1 }, +/* 221: 0, 2, 3, 4, 6, 7, */ { 0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 222: 1, 2, 3, 4, 6, 7, */ { 8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1 }, +/* 223: 0, 1, 2, 3, 4, 6, 7, */ { 9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 224: 5, 6, 7, */ { 4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1 }, +/* 225: 0, 5, 6, 7, */ { 0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1 }, +/* 226: 1, 5, 6, 7, */ { 1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1 }, +/* 227: 0, 1, 5, 6, 7, */ { 3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1 }, +/* 228: 2, 5, 6, 7, */ { 4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1 }, +/* 229: 0, 2, 5, 6, 7, */ { 9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1 }, +/* 230: 1, 2, 5, 6, 7, */ { 11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1 }, +/* 231: 0, 1, 2, 5, 6, 7, */ { 11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1 }, +/* 232: 3, 5, 6, 7, */ { 2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1 }, +/* 233: 0, 3, 5, 6, 7, */ { 9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1 }, +/* 234: 1, 3, 5, 6, 7, */ { 3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1 }, +/* 235: 0, 1, 3, 5, 6, 7, */ { 1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 236: 2, 3, 5, 6, 7, */ { 4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1 }, +/* 237: 0, 2, 3, 5, 6, 7, */ { 4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1 }, +/* 238: 1, 2, 3, 5, 6, 7, */ { 4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 239: 0, 1, 2, 3, 5, 6, 7, */ { 4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 240: 4, 5, 6, 7, */ { 9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 241: 0, 4, 5, 6, 7, */ { 3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1 }, +/* 242: 1, 4, 5, 6, 7, */ { 0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1 }, +/* 243: 0, 1, 4, 5, 6, 7, */ { 3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 244: 2, 4, 5, 6, 7, */ { 1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1 }, +/* 245: 0, 2, 4, 5, 6, 7, */ { 3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1 }, +/* 246: 1, 2, 4, 5, 6, 7, */ { 0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 247: 0, 1, 2, 4, 5, 6, 7, */ { 3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 248: 3, 4, 5, 6, 7, */ { 2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1 }, +/* 249: 0, 3, 4, 5, 6, 7, */ { 9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 250: 1, 3, 4, 5, 6, 7, */ { 2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1 }, +/* 251: 0, 1, 3, 4, 5, 6, 7, */ { 1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 252: 2, 3, 4, 5, 6, 7, */ { 1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 253: 0, 2, 3, 4, 5, 6, 7, */ { 0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 254: 1, 2, 3, 4, 5, 6, 7, */ { 0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, +/* 255: 0, 1, 2, 3, 4, 5, 6, 7, */ { -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 } +}; +//_____________________________________________________________________________ + + + +#endif // _LOOKUPTABLE_H_ diff --git a/skimage/measure/mc_meta/MarchingCubes.cpp b/skimage/measure/mc_meta/MarchingCubes.cpp new file mode 100644 index 00000000..d9012f04 --- /dev/null +++ b/skimage/measure/mc_meta/MarchingCubes.cpp @@ -0,0 +1,1302 @@ +/** + * @file MarchingCubes.cpp + * @author Thomas Lewiner + * @author Math Dept, PUC-Rio + * @version 0.2 + * @date 12/08/2002 + * + * @brief MarchingCubes Algorithm + */ +//________________________________________________ + + +#if !defined(WIN32) || defined(__CYGWIN__) +#pragma implementation +#endif // WIN32 + +#include +#include +#include +#include +#include +#include "MarchingCubes.h" +#include "ply.h" +#include "LookUpTable.h" + +// step size of the arrays of vertices and triangles +#define ALLOC_SIZE 65536 + +//_____________________________________________________________________________ +// print cube for debug +void MarchingCubes::print_cube() { printf( "\t%f %f %f %f %f %f %f %f\n", _cube[0], _cube[1], _cube[2], _cube[3], _cube[4], _cube[5], _cube[6], _cube[7]) ; } +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// Constructor +MarchingCubes::MarchingCubes( const int size_x /*= -1*/, const int size_y /*= -1*/, const int size_z /*= -1*/ ) : +//----------------------------------------------------------------------------- + _originalMC(false), + _ext_data (false), + _size_x (size_x), + _size_y (size_y), + _size_z (size_z), + _data ((real *)NULL), + _x_verts (( int *)NULL), + _y_verts (( int *)NULL), + _z_verts (( int *)NULL), + _nverts (0), + _ntrigs (0), + _Nverts (0), + _Ntrigs (0), + _vertices (( Vertex *)NULL), + _triangles ((Triangle*)NULL) +{} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// Destructor +MarchingCubes::~MarchingCubes() +//----------------------------------------------------------------------------- +{ + clean_all() ; +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// main algorithm +void MarchingCubes::run( real iso ) +//----------------------------------------------------------------------------- +{ + clock_t time = clock() ; + + compute_intersection_points( iso ) ; + + for( _k = 0 ; _k < _size_z-1 ; _k++ ) + for( _j = 0 ; _j < _size_y-1 ; _j++ ) + for( _i = 0 ; _i < _size_x-1 ; _i++ ) + { + _lut_entry = 0 ; + for( int p = 0 ; p < 8 ; ++p ) + { + _cube[p] = get_data( _i+((p^(p>>1))&1), _j+((p>>1)&1), _k+((p>>2)&1) ) - iso ; + if( fabs( _cube[p] ) < FLT_EPSILON ) _cube[p] = FLT_EPSILON ; + if( _cube[p] > 0 ) _lut_entry += 1 << p ; + } +/* + if( ( _cube[0] = get_data( _i , _j , _k ) ) > 0 ) _lut_entry += 1 ; + if( ( _cube[1] = get_data(_i+1, _j , _k ) ) > 0 ) _lut_entry += 2 ; + if( ( _cube[2] = get_data(_i+1,_j+1, _k ) ) > 0 ) _lut_entry += 4 ; + if( ( _cube[3] = get_data( _i ,_j+1, _k ) ) > 0 ) _lut_entry += 8 ; + if( ( _cube[4] = get_data( _i , _j ,_k+1) ) > 0 ) _lut_entry += 16 ; + if( ( _cube[5] = get_data(_i+1, _j ,_k+1) ) > 0 ) _lut_entry += 32 ; + if( ( _cube[6] = get_data(_i+1,_j+1,_k+1) ) > 0 ) _lut_entry += 64 ; + if( ( _cube[7] = get_data( _i ,_j+1,_k+1) ) > 0 ) _lut_entry += 128 ; +*/ + process_cube( ) ; + } + + printf("Marching Cubes ran in %lf secs.\n", (double)(clock() - time)/CLOCKS_PER_SEC) ; +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// init temporary structures (must set sizes before call) +void MarchingCubes::init_temps() +//----------------------------------------------------------------------------- +{ + if( !_ext_data ) + _data = new real [_size_x * _size_y * _size_z] ; + _x_verts = new int [_size_x * _size_y * _size_z] ; + _y_verts = new int [_size_x * _size_y * _size_z] ; + _z_verts = new int [_size_x * _size_y * _size_z] ; + + memset( _x_verts, -1, _size_x * _size_y * _size_z * sizeof( int ) ) ; + memset( _y_verts, -1, _size_x * _size_y * _size_z * sizeof( int ) ) ; + memset( _z_verts, -1, _size_x * _size_y * _size_z * sizeof( int ) ) ; +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// init all structures (must set sizes before call) +void MarchingCubes::init_all () +//----------------------------------------------------------------------------- +{ + init_temps() ; + + _nverts = _ntrigs = 0 ; + _Nverts = _Ntrigs = ALLOC_SIZE ; + _vertices = new Vertex [_Nverts] ; + _triangles = new Triangle[_Ntrigs] ; +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// clean temporary structures +void MarchingCubes::clean_temps() +//----------------------------------------------------------------------------- +{ + if( !_ext_data ) + delete [] _data; + delete [] _x_verts; + delete [] _y_verts; + delete [] _z_verts; + + if( !_ext_data ) + _data = (real*)NULL ; + _x_verts = (int*)NULL ; + _y_verts = (int*)NULL ; + _z_verts = (int*)NULL ; +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// clean all structures +void MarchingCubes::clean_all() +//----------------------------------------------------------------------------- +{ + clean_temps() ; + delete [] _vertices ; + delete [] _triangles ; + _vertices = (Vertex *)NULL ; + _triangles = (Triangle *)NULL ; + _nverts = _ntrigs = 0 ; + _Nverts = _Ntrigs = 0 ; + + _size_x = _size_y = _size_z = -1 ; +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +//_____________________________________________________________________________ + + +//_____________________________________________________________________________ +// Compute the intersection points +void MarchingCubes::compute_intersection_points( real iso ) +//----------------------------------------------------------------------------- +{ + for( _k = 0 ; _k < _size_z ; _k++ ) + for( _j = 0 ; _j < _size_y ; _j++ ) + for( _i = 0 ; _i < _size_x ; _i++ ) + { + _cube[0] = get_data( _i, _j, _k ) - iso ; + if( _i < _size_x - 1 ) _cube[1] = get_data(_i+1, _j , _k ) - iso ; + else _cube[1] = _cube[0] ; + + if( _j < _size_y - 1 ) _cube[3] = get_data( _i ,_j+1, _k ) - iso ; + else _cube[3] = _cube[0] ; + + if( _k < _size_z - 1 ) _cube[4] = get_data( _i , _j ,_k+1) - iso ; + else _cube[4] = _cube[0] ; + + if( fabs( _cube[0] ) < FLT_EPSILON ) _cube[0] = FLT_EPSILON ; + if( fabs( _cube[1] ) < FLT_EPSILON ) _cube[1] = FLT_EPSILON ; + if( fabs( _cube[3] ) < FLT_EPSILON ) _cube[3] = FLT_EPSILON ; + if( fabs( _cube[4] ) < FLT_EPSILON ) _cube[4] = FLT_EPSILON ; + + if( _cube[0] < 0 ) + { + if( _cube[1] > 0 ) set_x_vert( add_x_vertex( ), _i,_j,_k ) ; + if( _cube[3] > 0 ) set_y_vert( add_y_vertex( ), _i,_j,_k ) ; + if( _cube[4] > 0 ) set_z_vert( add_z_vertex( ), _i,_j,_k ) ; + } + else + { + if( _cube[1] < 0 ) set_x_vert( add_x_vertex( ), _i,_j,_k ) ; + if( _cube[3] < 0 ) set_y_vert( add_y_vertex( ), _i,_j,_k ) ; + if( _cube[4] < 0 ) set_z_vert( add_z_vertex( ), _i,_j,_k ) ; + } + } +} +//_____________________________________________________________________________ + + + + + +//_____________________________________________________________________________ +// Test a face +// if face>0 return true if the face contains a part of the surface +bool MarchingCubes::test_face( schar face ) +//----------------------------------------------------------------------------- +{ + real A,B,C,D ; + + switch( face ) + { + case -1 : case 1 : A = _cube[0] ; B = _cube[4] ; C = _cube[5] ; D = _cube[1] ; break ; + case -2 : case 2 : A = _cube[1] ; B = _cube[5] ; C = _cube[6] ; D = _cube[2] ; break ; + case -3 : case 3 : A = _cube[2] ; B = _cube[6] ; C = _cube[7] ; D = _cube[3] ; break ; + case -4 : case 4 : A = _cube[3] ; B = _cube[7] ; C = _cube[4] ; D = _cube[0] ; break ; + case -5 : case 5 : A = _cube[0] ; B = _cube[3] ; C = _cube[2] ; D = _cube[1] ; break ; + case -6 : case 6 : A = _cube[4] ; B = _cube[7] ; C = _cube[6] ; D = _cube[5] ; break ; + default : printf( "Invalid face code %d\n", face ) ; print_cube() ; A = B = C = D = 0 ; + }; + + if( fabs( A*C - B*D ) < FLT_EPSILON ) + return face >= 0 ; + return face * A * ( A*C - B*D ) >= 0 ; // face and A invert signs +} +//_____________________________________________________________________________ + + + + + +//_____________________________________________________________________________ +// Test the interior of a cube +// if s == 7, return true if the interior is empty +// if s ==-7, return false if the interior is empty +bool MarchingCubes::test_interior( schar s ) +//----------------------------------------------------------------------------- +{ + real t, At=0, Bt=0, Ct=0, Dt=0, a, b ; + char test = 0 ; + char edge = -1 ; // reference edge of the triangulation + + switch( _case ) + { + case 4 : + case 10 : + a = ( _cube[4] - _cube[0] ) * ( _cube[6] - _cube[2] ) - ( _cube[7] - _cube[3] ) * ( _cube[5] - _cube[1] ) ; + b = _cube[2] * ( _cube[4] - _cube[0] ) + _cube[0] * ( _cube[6] - _cube[2] ) + - _cube[1] * ( _cube[7] - _cube[3] ) - _cube[3] * ( _cube[5] - _cube[1] ) ; + t = - b / (2*a) ; + if( t<0 || t>1 ) return s>0 ; + + At = _cube[0] + ( _cube[4] - _cube[0] ) * t ; + Bt = _cube[3] + ( _cube[7] - _cube[3] ) * t ; + Ct = _cube[2] + ( _cube[6] - _cube[2] ) * t ; + Dt = _cube[1] + ( _cube[5] - _cube[1] ) * t ; + break ; + + case 6 : + case 7 : + case 12 : + case 13 : + switch( _case ) + { + case 6 : edge = test6 [_config][2] ; break ; + case 7 : edge = test7 [_config][4] ; break ; + case 12 : edge = test12[_config][3] ; break ; + case 13 : edge = tiling13_5_1[_config][_subconfig][0] ; break ; + } + switch( edge ) + { + case 0 : + t = _cube[0] / ( _cube[0] - _cube[1] ) ; + At = 0 ; + Bt = _cube[3] + ( _cube[2] - _cube[3] ) * t ; + Ct = _cube[7] + ( _cube[6] - _cube[7] ) * t ; + Dt = _cube[4] + ( _cube[5] - _cube[4] ) * t ; + break ; + case 1 : + t = _cube[1] / ( _cube[1] - _cube[2] ) ; + At = 0 ; + Bt = _cube[0] + ( _cube[3] - _cube[0] ) * t ; + Ct = _cube[4] + ( _cube[7] - _cube[4] ) * t ; + Dt = _cube[5] + ( _cube[6] - _cube[5] ) * t ; + break ; + case 2 : + t = _cube[2] / ( _cube[2] - _cube[3] ) ; + At = 0 ; + Bt = _cube[1] + ( _cube[0] - _cube[1] ) * t ; + Ct = _cube[5] + ( _cube[4] - _cube[5] ) * t ; + Dt = _cube[6] + ( _cube[7] - _cube[6] ) * t ; + break ; + case 3 : + t = _cube[3] / ( _cube[3] - _cube[0] ) ; + At = 0 ; + Bt = _cube[2] + ( _cube[1] - _cube[2] ) * t ; + Ct = _cube[6] + ( _cube[5] - _cube[6] ) * t ; + Dt = _cube[7] + ( _cube[4] - _cube[7] ) * t ; + break ; + case 4 : + t = _cube[4] / ( _cube[4] - _cube[5] ) ; + At = 0 ; + Bt = _cube[7] + ( _cube[6] - _cube[7] ) * t ; + Ct = _cube[3] + ( _cube[2] - _cube[3] ) * t ; + Dt = _cube[0] + ( _cube[1] - _cube[0] ) * t ; + break ; + case 5 : + t = _cube[5] / ( _cube[5] - _cube[6] ) ; + At = 0 ; + Bt = _cube[4] + ( _cube[7] - _cube[4] ) * t ; + Ct = _cube[0] + ( _cube[3] - _cube[0] ) * t ; + Dt = _cube[1] + ( _cube[2] - _cube[1] ) * t ; + break ; + case 6 : + t = _cube[6] / ( _cube[6] - _cube[7] ) ; + At = 0 ; + Bt = _cube[5] + ( _cube[4] - _cube[5] ) * t ; + Ct = _cube[1] + ( _cube[0] - _cube[1] ) * t ; + Dt = _cube[2] + ( _cube[3] - _cube[2] ) * t ; + break ; + case 7 : + t = _cube[7] / ( _cube[7] - _cube[4] ) ; + At = 0 ; + Bt = _cube[6] + ( _cube[5] - _cube[6] ) * t ; + Ct = _cube[2] + ( _cube[1] - _cube[2] ) * t ; + Dt = _cube[3] + ( _cube[0] - _cube[3] ) * t ; + break ; + case 8 : + t = _cube[0] / ( _cube[0] - _cube[4] ) ; + At = 0 ; + Bt = _cube[3] + ( _cube[7] - _cube[3] ) * t ; + Ct = _cube[2] + ( _cube[6] - _cube[2] ) * t ; + Dt = _cube[1] + ( _cube[5] - _cube[1] ) * t ; + break ; + case 9 : + t = _cube[1] / ( _cube[1] - _cube[5] ) ; + At = 0 ; + Bt = _cube[0] + ( _cube[4] - _cube[0] ) * t ; + Ct = _cube[3] + ( _cube[7] - _cube[3] ) * t ; + Dt = _cube[2] + ( _cube[6] - _cube[2] ) * t ; + break ; + case 10 : + t = _cube[2] / ( _cube[2] - _cube[6] ) ; + At = 0 ; + Bt = _cube[1] + ( _cube[5] - _cube[1] ) * t ; + Ct = _cube[0] + ( _cube[4] - _cube[0] ) * t ; + Dt = _cube[3] + ( _cube[7] - _cube[3] ) * t ; + break ; + case 11 : + t = _cube[3] / ( _cube[3] - _cube[7] ) ; + At = 0 ; + Bt = _cube[2] + ( _cube[6] - _cube[2] ) * t ; + Ct = _cube[1] + ( _cube[5] - _cube[1] ) * t ; + Dt = _cube[0] + ( _cube[4] - _cube[0] ) * t ; + break ; + default : printf( "Invalid edge %d\n", edge ) ; print_cube() ; break ; + } + break ; + + default : printf( "Invalid ambiguous case %d\n", _case ) ; print_cube() ; break ; + } + + if( At >= 0 ) test ++ ; + if( Bt >= 0 ) test += 2 ; + if( Ct >= 0 ) test += 4 ; + if( Dt >= 0 ) test += 8 ; + switch( test ) + { + case 0 : return s>0 ; + case 1 : return s>0 ; + case 2 : return s>0 ; + case 3 : return s>0 ; + case 4 : return s>0 ; + case 5 : if( At * Ct - Bt * Dt < FLT_EPSILON ) return s>0 ; break ; + case 6 : return s>0 ; + case 7 : return s<0 ; + case 8 : return s>0 ; + case 9 : return s>0 ; + case 10 : if( At * Ct - Bt * Dt >= FLT_EPSILON ) return s>0 ; break ; + case 11 : return s<0 ; + case 12 : return s>0 ; + case 13 : return s<0 ; + case 14 : return s<0 ; + case 15 : return s<0 ; + } + + return s<0 ; +} +//_____________________________________________________________________________ + + + + +//_____________________________________________________________________________ +// Process a unit cube +void MarchingCubes::process_cube( ) +//----------------------------------------------------------------------------- +{ + if( _originalMC ) + { + char nt = 0 ; + while( casesClassic[_lut_entry][3*nt] != -1 ) nt++ ; + add_triangle( casesClassic[_lut_entry], nt ) ; + return ; + } + + int v12 = -1 ; + _case = cases[_lut_entry][0] ; + _config = cases[_lut_entry][1] ; + _subconfig = 0 ; + + switch( _case ) + { + case 0 : + break ; + + case 1 : + add_triangle( tiling1[_config], 1 ) ; + break ; + + case 2 : + add_triangle( tiling2[_config], 2 ) ; + break ; + + case 3 : + if( test_face( test3[_config]) ) + add_triangle( tiling3_2[_config], 4 ) ; // 3.2 + else + add_triangle( tiling3_1[_config], 2 ) ; // 3.1 + break ; + + case 4 : + if( test_interior( test4[_config]) ) + add_triangle( tiling4_1[_config], 2 ) ; // 4.1.1 + else + add_triangle( tiling4_2[_config], 6 ) ; // 4.1.2 + break ; + + case 5 : + add_triangle( tiling5[_config], 3 ) ; + break ; + + case 6 : + if( test_face( test6[_config][0]) ) + add_triangle( tiling6_2[_config], 5 ) ; // 6.2 + else + { + if( test_interior( test6[_config][1]) ) + add_triangle( tiling6_1_1[_config], 3 ) ; // 6.1.1 + else + { + v12 = add_c_vertex() ; + add_triangle( tiling6_1_2[_config], 9 , v12) ; // 6.1.2 + } + } + break ; + + case 7 : + if( test_face( test7[_config][0] ) ) _subconfig += 1 ; + if( test_face( test7[_config][1] ) ) _subconfig += 2 ; + if( test_face( test7[_config][2] ) ) _subconfig += 4 ; + switch( _subconfig ) + { + case 0 : + add_triangle( tiling7_1[_config], 3 ) ; break ; + case 1 : + add_triangle( tiling7_2[_config][0], 5 ) ; break ; + case 2 : + add_triangle( tiling7_2[_config][1], 5 ) ; break ; + case 3 : + v12 = add_c_vertex() ; + add_triangle( tiling7_3[_config][0], 9, v12 ) ; break ; + case 4 : + add_triangle( tiling7_2[_config][2], 5 ) ; break ; + case 5 : + v12 = add_c_vertex() ; + add_triangle( tiling7_3[_config][1], 9, v12 ) ; break ; + case 6 : + v12 = add_c_vertex() ; + add_triangle( tiling7_3[_config][2], 9, v12 ) ; break ; + case 7 : + if( test_interior( test7[_config][3]) ) + add_triangle( tiling7_4_2[_config], 9 ) ; + else + add_triangle( tiling7_4_1[_config], 5 ) ; + break ; + }; + break ; + + case 8 : + add_triangle( tiling8[_config], 2 ) ; + break ; + + case 9 : + add_triangle( tiling9[_config], 4 ) ; + break ; + + case 10 : + if( test_face( test10[_config][0]) ) + { + if( test_face( test10[_config][1]) ) + add_triangle( tiling10_1_1_[_config], 4 ) ; // 10.1.1 + else + { + v12 = add_c_vertex() ; + add_triangle( tiling10_2[_config], 8, v12 ) ; // 10.2 + } + } + else + { + if( test_face( test10[_config][1]) ) + { + v12 = add_c_vertex() ; + add_triangle( tiling10_2_[_config], 8, v12 ) ; // 10.2 + } + else + { + if( test_interior( test10[_config][2]) ) + add_triangle( tiling10_1_1[_config], 4 ) ; // 10.1.1 + else + add_triangle( tiling10_1_2[_config], 8 ) ; // 10.1.2 + } + } + break ; + + case 11 : + add_triangle( tiling11[_config], 4 ) ; + break ; + + case 12 : + if( test_face( test12[_config][0]) ) + { + if( test_face( test12[_config][1]) ) + add_triangle( tiling12_1_1_[_config], 4 ) ; // 12.1.1 + else + { + v12 = add_c_vertex() ; + add_triangle( tiling12_2[_config], 8, v12 ) ; // 12.2 + } + } + else + { + if( test_face( test12[_config][1]) ) + { + v12 = add_c_vertex() ; + add_triangle( tiling12_2_[_config], 8, v12 ) ; // 12.2 + } + else + { + if( test_interior( test12[_config][2]) ) + add_triangle( tiling12_1_1[_config], 4 ) ; // 12.1.1 + else + add_triangle( tiling12_1_2[_config], 8 ) ; // 12.1.2 + } + } + break ; + + case 13 : + if( test_face( test13[_config][0] ) ) _subconfig += 1 ; + if( test_face( test13[_config][1] ) ) _subconfig += 2 ; + if( test_face( test13[_config][2] ) ) _subconfig += 4 ; + if( test_face( test13[_config][3] ) ) _subconfig += 8 ; + if( test_face( test13[_config][4] ) ) _subconfig += 16 ; + if( test_face( test13[_config][5] ) ) _subconfig += 32 ; + switch( subconfig13[_subconfig] ) + { + case 0 :/* 13.1 */ + add_triangle( tiling13_1[_config], 4 ) ; break ; + + case 1 :/* 13.2 */ + add_triangle( tiling13_2[_config][0], 6 ) ; break ; + case 2 :/* 13.2 */ + add_triangle( tiling13_2[_config][1], 6 ) ; break ; + case 3 :/* 13.2 */ + add_triangle( tiling13_2[_config][2], 6 ) ; break ; + case 4 :/* 13.2 */ + add_triangle( tiling13_2[_config][3], 6 ) ; break ; + case 5 :/* 13.2 */ + add_triangle( tiling13_2[_config][4], 6 ) ; break ; + case 6 :/* 13.2 */ + add_triangle( tiling13_2[_config][5], 6 ) ; break ; + + case 7 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][0], 10, v12 ) ; break ; + case 8 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][1], 10, v12 ) ; break ; + case 9 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][2], 10, v12 ) ; break ; + case 10 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][3], 10, v12 ) ; break ; + case 11 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][4], 10, v12 ) ; break ; + case 12 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][5], 10, v12 ) ; break ; + case 13 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][6], 10, v12 ) ; break ; + case 14 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][7], 10, v12 ) ; break ; + case 15 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][8], 10, v12 ) ; break ; + case 16 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][9], 10, v12 ) ; break ; + case 17 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][10], 10, v12 ) ; break ; + case 18 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3[_config][11], 10, v12 ) ; break ; + + case 19 :/* 13.4 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_4[_config][0], 12, v12 ) ; break ; + case 20 :/* 13.4 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_4[_config][1], 12, v12 ) ; break ; + case 21 :/* 13.4 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_4[_config][2], 12, v12 ) ; break ; + case 22 :/* 13.4 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_4[_config][3], 12, v12 ) ; break ; + + case 23 :/* 13.5 */ + _subconfig = 0 ; + if( test_interior( test13[_config][6] ) ) + add_triangle( tiling13_5_1[_config][0], 6 ) ; + else + add_triangle( tiling13_5_2[_config][0], 10 ) ; + break ; + case 24 :/* 13.5 */ + _subconfig = 1 ; + if( test_interior( test13[_config][6] ) ) + add_triangle( tiling13_5_1[_config][1], 6 ) ; + else + add_triangle( tiling13_5_2[_config][1], 10 ) ; + break ; + case 25 :/* 13.5 */ + _subconfig = 2 ; + if( test_interior( test13[_config][6] ) ) + add_triangle( tiling13_5_1[_config][2], 6 ) ; + else + add_triangle( tiling13_5_2[_config][2], 10 ) ; + break ; + case 26 :/* 13.5 */ + _subconfig = 3 ; + if( test_interior( test13[_config][6] ) ) + add_triangle( tiling13_5_1[_config][3], 6 ) ; + else + add_triangle( tiling13_5_2[_config][3], 10 ) ; + break ; + + case 27 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][0], 10, v12 ) ; break ; + case 28 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][1], 10, v12 ) ; break ; + case 29 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][2], 10, v12 ) ; break ; + case 30 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][3], 10, v12 ) ; break ; + case 31 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][4], 10, v12 ) ; break ; + case 32 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][5], 10, v12 ) ; break ; + case 33 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][6], 10, v12 ) ; break ; + case 34 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][7], 10, v12 ) ; break ; + case 35 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][8], 10, v12 ) ; break ; + case 36 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][9], 10, v12 ) ; break ; + case 37 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][10], 10, v12 ) ; break ; + case 38 :/* 13.3 */ + v12 = add_c_vertex() ; + add_triangle( tiling13_3_[_config][11], 10, v12 ) ; break ; + + case 39 :/* 13.2 */ + add_triangle( tiling13_2_[_config][0], 6 ) ; break ; + case 40 :/* 13.2 */ + add_triangle( tiling13_2_[_config][1], 6 ) ; break ; + case 41 :/* 13.2 */ + add_triangle( tiling13_2_[_config][2], 6 ) ; break ; + case 42 :/* 13.2 */ + add_triangle( tiling13_2_[_config][3], 6 ) ; break ; + case 43 :/* 13.2 */ + add_triangle( tiling13_2_[_config][4], 6 ) ; break ; + case 44 :/* 13.2 */ + add_triangle( tiling13_2_[_config][5], 6 ) ; break ; + + case 45 :/* 13.1 */ + add_triangle( tiling13_1_[_config], 4 ) ; break ; + + default : + printf("Marching Cubes: Impossible case 13?\n" ) ; print_cube() ; + } + break ; + + case 14 : + add_triangle( tiling14[_config], 4 ) ; + break ; + }; +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// Adding triangles +void MarchingCubes::add_triangle( const char* trig, char n, int v12 ) +//----------------------------------------------------------------------------- +{ + int tv[3] ; + + for( int t = 0 ; t < 3*n ; t++ ) + { + switch( trig[t] ) + { + case 0 : tv[ t % 3 ] = get_x_vert( _i , _j , _k ) ; break ; + case 1 : tv[ t % 3 ] = get_y_vert(_i+1, _j , _k ) ; break ; + case 2 : tv[ t % 3 ] = get_x_vert( _i ,_j+1, _k ) ; break ; + case 3 : tv[ t % 3 ] = get_y_vert( _i , _j , _k ) ; break ; + case 4 : tv[ t % 3 ] = get_x_vert( _i , _j ,_k+1) ; break ; + case 5 : tv[ t % 3 ] = get_y_vert(_i+1, _j ,_k+1) ; break ; + case 6 : tv[ t % 3 ] = get_x_vert( _i ,_j+1,_k+1) ; break ; + case 7 : tv[ t % 3 ] = get_y_vert( _i , _j ,_k+1) ; break ; + case 8 : tv[ t % 3 ] = get_z_vert( _i , _j , _k ) ; break ; + case 9 : tv[ t % 3 ] = get_z_vert(_i+1, _j , _k ) ; break ; + case 10 : tv[ t % 3 ] = get_z_vert(_i+1,_j+1, _k ) ; break ; + case 11 : tv[ t % 3 ] = get_z_vert( _i ,_j+1, _k ) ; break ; + case 12 : tv[ t % 3 ] = v12 ; break ; + default : break ; + } + + if( tv[t%3] == -1 ) + { + printf("Marching Cubes: invalid triangle %d\n", _ntrigs+1) ; + print_cube() ; + } + + if( t%3 == 2 ) + { + if( _ntrigs >= _Ntrigs ) + { + Triangle *temp = _triangles ; + _triangles = new Triangle[ 2*_Ntrigs ] ; + memcpy( _triangles, temp, _Ntrigs*sizeof(Triangle) ) ; + delete[] temp ; + printf("%d allocated triangles\n", _Ntrigs) ; + _Ntrigs *= 2 ; + } + + Triangle *T = _triangles + _ntrigs++ ; + T->v1 = tv[0] ; + T->v2 = tv[1] ; + T->v3 = tv[2] ; + } + } +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// Calculating gradient + +real MarchingCubes::get_x_grad( const int i, const int j, const int k ) const +//----------------------------------------------------------------------------- +{ + if( i > 0 ) + { + if ( i < _size_x - 1 ) + return ( get_data( i+1, j, k ) - get_data( i-1, j, k ) ) / 2 ; + else + return get_data( i, j, k ) - get_data( i-1, j, k ) ; + } + else + return get_data( i+1, j, k ) - get_data( i, j, k ) ; +} +//----------------------------------------------------------------------------- + +real MarchingCubes::get_y_grad( const int i, const int j, const int k ) const +//----------------------------------------------------------------------------- +{ + if( j > 0 ) + { + if ( j < _size_y - 1 ) + return ( get_data( i, j+1, k ) - get_data( i, j-1, k ) ) / 2 ; + else + return get_data( i, j, k ) - get_data( i, j-1, k ) ; + } + else + return get_data( i, j+1, k ) - get_data( i, j, k ) ; +} +//----------------------------------------------------------------------------- + +real MarchingCubes::get_z_grad( const int i, const int j, const int k ) const +//----------------------------------------------------------------------------- +{ + if( k > 0 ) + { + if ( k < _size_z - 1 ) + return ( get_data( i, j, k+1 ) - get_data( i, j, k-1 ) ) / 2 ; + else + return get_data( i, j, k ) - get_data( i, j, k-1 ) ; + } + else + return get_data( i, j, k+1 ) - get_data( i, j, k ) ; +} +//_____________________________________________________________________________ + + +//_____________________________________________________________________________ +// Adding vertices + +void MarchingCubes::test_vertex_addition() +{ + if( _nverts >= _Nverts ) + { + Vertex *temp = _vertices ; + _vertices = new Vertex[ _Nverts*2 ] ; + memcpy( _vertices, temp, _Nverts*sizeof(Vertex) ) ; + delete[] temp ; + printf("%d allocated vertices\n", _Nverts) ; + _Nverts *= 2 ; + } +} + + +int MarchingCubes::add_x_vertex( ) +//----------------------------------------------------------------------------- +{ + test_vertex_addition() ; + Vertex *vert = _vertices + _nverts++ ; + + real u = ( _cube[0] ) / ( _cube[0] - _cube[1] ) ; + + vert->x = (real)_i+u; + vert->y = (real) _j ; + vert->z = (real) _k ; + + vert->nx = (1-u)*get_x_grad(_i,_j,_k) + u*get_x_grad(_i+1,_j,_k) ; + vert->ny = (1-u)*get_y_grad(_i,_j,_k) + u*get_y_grad(_i+1,_j,_k) ; + vert->nz = (1-u)*get_z_grad(_i,_j,_k) + u*get_z_grad(_i+1,_j,_k) ; + + u = (real) sqrt( vert->nx * vert->nx + vert->ny * vert->ny +vert->nz * vert->nz ) ; + if( u > 0 ) + { + vert->nx /= u ; + vert->ny /= u ; + vert->nz /= u ; + } + + + return _nverts-1 ; +} +//----------------------------------------------------------------------------- + +int MarchingCubes::add_y_vertex( ) +//----------------------------------------------------------------------------- +{ + test_vertex_addition() ; + Vertex *vert = _vertices + _nverts++ ; + + real u = ( _cube[0] ) / ( _cube[0] - _cube[3] ) ; + + vert->x = (real) _i ; + vert->y = (real)_j+u; + vert->z = (real) _k ; + + vert->nx = (1-u)*get_x_grad(_i,_j,_k) + u*get_x_grad(_i,_j+1,_k) ; + vert->ny = (1-u)*get_y_grad(_i,_j,_k) + u*get_y_grad(_i,_j+1,_k) ; + vert->nz = (1-u)*get_z_grad(_i,_j,_k) + u*get_z_grad(_i,_j+1,_k) ; + + u = (real) sqrt( vert->nx * vert->nx + vert->ny * vert->ny +vert->nz * vert->nz ) ; + if( u > 0 ) + { + vert->nx /= u ; + vert->ny /= u ; + vert->nz /= u ; + } + + return _nverts-1 ; +} +//----------------------------------------------------------------------------- + +int MarchingCubes::add_z_vertex( ) +//----------------------------------------------------------------------------- +{ + test_vertex_addition() ; + Vertex *vert = _vertices + _nverts++ ; + + real u = ( _cube[0] ) / ( _cube[0] - _cube[4] ) ; + + vert->x = (real) _i ; + vert->y = (real) _j ; + vert->z = (real)_k+u; + + vert->nx = (1-u)*get_x_grad(_i,_j,_k) + u*get_x_grad(_i,_j,_k+1) ; + vert->ny = (1-u)*get_y_grad(_i,_j,_k) + u*get_y_grad(_i,_j,_k+1) ; + vert->nz = (1-u)*get_z_grad(_i,_j,_k) + u*get_z_grad(_i,_j,_k+1) ; + + u = (real) sqrt( vert->nx * vert->nx + vert->ny * vert->ny +vert->nz * vert->nz ) ; + if( u > 0 ) + { + vert->nx /= u ; + vert->ny /= u ; + vert->nz /= u ; + } + + return _nverts-1 ; +} + + +int MarchingCubes::add_c_vertex( ) +//----------------------------------------------------------------------------- +{ + test_vertex_addition() ; + Vertex *vert = _vertices + _nverts++ ; + + real u = 0 ; + int vid ; + + vert->x = vert->y = vert->z = vert->nx = vert->ny = vert->nz = 0 ; + + // Computes the average of the intersection points of the cube + vid = get_x_vert( _i , _j , _k ) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_y_vert(_i+1, _j , _k ) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_x_vert( _i ,_j+1, _k ) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_y_vert( _i , _j , _k ) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_x_vert( _i , _j ,_k+1) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_y_vert(_i+1, _j ,_k+1) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_x_vert( _i ,_j+1,_k+1) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_y_vert( _i , _j ,_k+1) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_z_vert( _i , _j , _k ) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_z_vert(_i+1, _j , _k ) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_z_vert(_i+1,_j+1, _k ) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + vid = get_z_vert( _i ,_j+1, _k ) ; + if( vid != -1 ) { ++u ; const Vertex &v = _vertices[vid] ; vert->x += v.x ; vert->y += v.y ; vert->z += v.z ; vert->nx += v.nx ; vert->ny += v.ny ; vert->nz += v.nz ; } + + vert->x /= u ; + vert->y /= u ; + vert->z /= u ; + + u = (real) sqrt( vert->nx * vert->nx + vert->ny * vert->ny +vert->nz * vert->nz ) ; + if( u > 0 ) + { + vert->nx /= u ; + vert->ny /= u ; + vert->nz /= u ; + } + + return _nverts-1 ; +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +//_____________________________________________________________________________ + + + + +//_____________________________________________________________________________ +// Grid exportation +void MarchingCubes::writeISO(const char *fn ) +//----------------------------------------------------------------------------- +{ + unsigned char buf[sizeof(float)] ; + + FILE *fp = fopen( fn, "wb" ) ; + + // header + * (int*) buf = _size_x ; + fwrite(buf, sizeof(float), 1, fp); + * (int*) buf = _size_y ; + fwrite(buf, sizeof(float), 1, fp); + * (int*) buf = _size_z ; + fwrite(buf, sizeof(float), 1, fp); + + * (float*) buf = -1.0f ; + fwrite(buf, sizeof(float), 1, fp); + * (float*) buf = 1.0f ; + fwrite(buf, sizeof(float), 1, fp); + * (float*) buf = -1.0f ; + fwrite(buf, sizeof(float), 1, fp); + * (float*) buf = 1.0f ; + fwrite(buf, sizeof(float), 1, fp); + * (float*) buf = -1.0f ; + fwrite(buf, sizeof(float), 1, fp); + * (float*) buf = 1.0f ; + fwrite(buf, sizeof(float), 1, fp); + + for( int i = 0 ; i < _size_x ; i++ ) + { + for( int j = 0 ; j < _size_y ; j++ ) + { + for( int k = 0 ; k < _size_z ; k++ ) + { + * (float*) buf = (float)get_data( i,j,k ) ; + fwrite(buf, sizeof(float), 1, fp); + } + } + } + + fclose(fp) ; +} +//_____________________________________________________________________________ + + + + + +//_____________________________________________________________________________ +// PLY exportation +void MarchingCubes::writePLY(const char *fn, bool bin ) +//----------------------------------------------------------------------------- +{ + + typedef struct PlyFace { + unsigned char nverts; /* number of Vertex indices in list */ + int *verts; /* Vertex index list */ + } PlyFace; + + + PlyProperty vert_props[] = { /* list of property information for a PlyVertex */ + {"x", Float32, Float32, offsetof( Vertex,x ), 0, 0, 0, 0}, + {"y", Float32, Float32, offsetof( Vertex,y ), 0, 0, 0, 0}, + {"z", Float32, Float32, offsetof( Vertex,z ), 0, 0, 0, 0}, + {"nx", Float32, Float32, offsetof( Vertex,nx ), 0, 0, 0, 0}, + {"ny", Float32, Float32, offsetof( Vertex,ny ), 0, 0, 0, 0}, + {"nz", Float32, Float32, offsetof( Vertex,nz ), 0, 0, 0, 0} + }; + + PlyProperty face_props[] = { /* list of property information for a PlyFace */ + {"vertex_indices", Int32, Int32, offsetof( PlyFace,verts ), + 1, Uint8, Uint8, offsetof( PlyFace,nverts )}, + }; + + + PlyFile *ply; + FILE *fp = fopen( fn, "w" ); + + int i ; + PlyFace face ; + int verts[3] ; + char *elem_names[] = { "vertex", "face" }; + printf("Marching Cubes::writePLY(%s)...", fn ) ; + ply = write_ply ( fp, 2, elem_names, bin? PLY_BINARY_LE : PLY_ASCII ); + + /* describe what properties go into the PlyVertex elements */ + describe_element_ply ( ply, "vertex", _nverts ); + describe_property_ply ( ply, &vert_props[0] ); + describe_property_ply ( ply, &vert_props[1] ); + describe_property_ply ( ply, &vert_props[2] ); + describe_property_ply ( ply, &vert_props[3] ); + describe_property_ply ( ply, &vert_props[4] ); + describe_property_ply ( ply, &vert_props[5] ); + + /* describe PlyFace properties (just list of PlyVertex indices) */ + describe_element_ply ( ply, "face", _ntrigs ); + describe_property_ply ( ply, &face_props[0] ); + + header_complete_ply ( ply ); + + /* set up and write the PlyVertex elements */ + put_element_setup_ply ( ply, "vertex" ); + for ( i = 0; i < _nverts; i++ ) + put_element_ply ( ply, ( void * ) &(_vertices[i]) ); + printf(" %d vertices written\n", _nverts ) ; + + /* set up and write the PlyFace elements */ + put_element_setup_ply ( ply, "face" ); + face.nverts = 3 ; + face.verts = verts ; + for ( i = 0; i < _ntrigs; i++ ) + { + face.verts[0] = _triangles[i].v1 ; + face.verts[1] = _triangles[i].v2 ; + face.verts[2] = _triangles[i].v3 ; + put_element_ply ( ply, ( void * ) &face ); + } + printf(" %d triangles written\n", _ntrigs ) ; + + close_ply ( ply ); + free_ply ( ply ); + fclose( fp ) ; +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// PLY importation +void MarchingCubes::readPLY(const char *fn ) +//----------------------------------------------------------------------------- +{ + typedef struct PlyFace { + unsigned char nverts; /* number of Vertex indices in list */ + int *verts; /* Vertex index list */ + } PlyFace; + + + PlyProperty vert_props[] = { /* list of property information for a PlyVertex */ + {"x", Float32, Float32, offsetof( Vertex,x ), 0, 0, 0, 0}, + {"y", Float32, Float32, offsetof( Vertex,y ), 0, 0, 0, 0}, + {"z", Float32, Float32, offsetof( Vertex,z ), 0, 0, 0, 0}, + {"nx", Float32, Float32, offsetof( Vertex,nx ), 0, 0, 0, 0}, + {"ny", Float32, Float32, offsetof( Vertex,ny ), 0, 0, 0, 0}, + {"nz", Float32, Float32, offsetof( Vertex,nz ), 0, 0, 0, 0} + }; + + PlyProperty face_props[] = { /* list of property information for a PlyFace */ + {"vertex_indices", Int32, Int32, offsetof( PlyFace,verts ), + 1, Uint8, Uint8, offsetof( PlyFace,nverts )}, + }; + + + FILE *fp = fopen( fn, "r" ); + if( !fp ) return ; + PlyFile *ply = read_ply ( fp ); + printf("Marching Cubes::readPLY(%s)...", fn ) ; + + //----------------------------------------------------------------------------- + + // gets the number of faces and vertices + for ( int i = 0; i < ply->num_elem_types; ++i ) + { + int elem_count ; + char *elem_name = setup_element_read_ply ( ply, i, &elem_count ); + if ( equal_strings ( "vertex", elem_name ) ) + _Nverts = _nverts = elem_count; + if ( equal_strings ( "face", elem_name ) ) + _Ntrigs = _ntrigs = elem_count; + } + delete [] _vertices ; + _vertices = new Vertex [_Nverts] ; + delete [] _triangles ; + _triangles = new Triangle[_Ntrigs] ; + + //----------------------------------------------------------------------------- + + /* examine each element type that is in the file (PlyVertex, PlyFace) */ + + for ( int i = 0; i < ply->num_elem_types; ++i ) + { + /* prepare to read the i'th list of elements */ + int elem_count ; + char *elem_name = setup_element_read_ply ( ply, i, &elem_count ); + + //----------------------------------------------------------------------------- + if ( equal_strings ( "vertex", elem_name ) ) + { + /* set up for getting PlyVertex elements */ + setup_property_ply ( ply, &vert_props[0] ); + setup_property_ply ( ply, &vert_props[1] ); + setup_property_ply ( ply, &vert_props[2] ); + setup_property_ply ( ply, &vert_props[3] ); + setup_property_ply ( ply, &vert_props[4] ); + setup_property_ply ( ply, &vert_props[5] ); + + for ( int j = 0; j < _nverts; ++j ) + { + get_element_ply ( ply, ( void * ) (_vertices + j) ); + } + printf(" %d vertices read\n", _nverts ) ; + } + + //----------------------------------------------------------------------------- + else if ( equal_strings ( "face", elem_name ) ) + { + /* set up for getting PlyFace elements */ + /* (all we need are PlyVertex indices) */ + + setup_property_ply ( ply, &face_props[0] ) ; + PlyFace face ; + for ( int j = 0; j < _ntrigs; ++j ) + { + get_element_ply ( ply, ( void * ) &face ); + if( face.nverts != 3 ) + { + printf( "not a triangulated surface: polygon %d has %d sides\n", j, face.nverts ) ; + return ; + } + + _triangles[j].v1 = face.verts[0] ; + _triangles[j].v2 = face.verts[1] ; + _triangles[j].v3 = face.verts[2] ; + + free( face.verts ) ; + } + printf(" %d triangles read\n", _ntrigs ) ; + } + //----------------------------------------------------------------------------- + + //----------------------------------------------------------------------------- + else /* all non-PlyVertex and non-PlyFace elements are grabbed here */ + get_other_element_ply ( ply ); + //----------------------------------------------------------------------------- + } + + close_ply ( ply ); + free_ply ( ply ); + +// fit_to_bbox() ; + fclose( fp ) ; +} +//_____________________________________________________________________________ + + + +//_____________________________________________________________________________ +// Open Inventor / VRML 1.0 ascii exportation +void MarchingCubes::writeIV(const char *fn ) +//----------------------------------------------------------------------------- +{ + FILE *fp = fopen( fn, "w" ) ; + int i ; + + printf("Marching Cubes::exportIV(%s)...", fn) ; + + fprintf( fp, "#Inventor V2.1 ascii \n\nSeparator { \n ShapeHints {\n vertexOrdering COUNTERCLOCKWISE\n shapeType UNKNOWN_SHAPE_TYPE\n creaseAngle 0.0\n }\n Coordinate3 { \n point [ \n" ) ; + for ( i = 0; i < _nverts; i++ ) + fprintf( fp, " %f %f %f,\n", _vertices[i].x, _vertices[i].y, _vertices[i].z ) ; + printf(" %d vertices written\n", _nverts ) ; + + fprintf( fp, "\n ] \n} \nNormal { \nvector [ \n" ) ; + for ( i = 0; i < _nverts; i++ ) + fprintf( fp, " %f %f %f,\n", _vertices[i].nx, _vertices[i].ny, _vertices[i].nz ) ; + + fprintf( fp, "\n ] \n} \nIndexedFaceSet { \ncoordIndex [ \n" ) ; + for ( i = 0; i < _ntrigs; i++ ) + fprintf( fp, "%d, %d, %d, -1,\n", _triangles[i].v1, _triangles[i].v2, _triangles[i].v3 ) ; + + fprintf( fp, " ] \n } \n } \n" ) ; + fclose( fp ) ; + printf(" %d triangles written\n", _ntrigs ) ; +} +//_____________________________________________________________________________ diff --git a/skimage/measure/mc_meta/createluts.py b/skimage/measure/mc_meta/createluts.py new file mode 100644 index 00000000..c6be213c --- /dev/null +++ b/skimage/measure/mc_meta/createluts.py @@ -0,0 +1,175 @@ +# -*- coding: utf-8 -*- +# Copyright (C) 2012, Almar Klein + +""" Create lookup tables for the marching cubes algorithm, by parsing +the file "LookUpTable.h". This prints a text to the stdout wich +can then be copied to luts.py. + +The luts are tuples of shape and base64 encoded bytes. + +""" + +import numpy as np +import sys +import base64 + +# Get base64 encode/decode functions +PY3 = sys.version_info[0] == 3 +if PY3: + base64encode = base64.encodebytes + base64decode = base64.decodebytes +else: + base64encode = base64.encodestring + base64decode = base64.decodestring + +def create_luts(fname): + + # Get the lines in the C header file + text = open(fname,'rb').read().decode('utf-8') + lines1 = [line.rstrip() for line in text.splitlines()] + + # Init lines for Python + lines2 = [] + + # Get classic table + more_lines, ii = get_table(lines1, 'static const char casesClassic', 0) + lines2.extend(more_lines) + + # Get cases table + more_lines, ii = get_table(lines1, 'static const char cases', 0) + lines2.extend(more_lines) + + # Get tiling tables + ii = 0 + for casenr in range(99): + # Get table + more_lines, ii = get_table(lines1, 'static const char tiling', ii+1) + if ii < 0: + break + else: + lines2.extend(more_lines) + + # Get test tables + ii = 0 + for casenr in range(99): + # Get table + more_lines, ii = get_table(lines1, 'static const char test', ii+1) + if ii < 0: + break + else: + lines2.extend(more_lines) + + # Get subconfig tables + ii = 0 + for casenr in range(99): + # Get table + more_lines, ii = get_table(lines1, 'static const char subconfig', ii+1) + if ii < 0: + break + else: + lines2.extend(more_lines) + + return '\n'.join(lines2) + + +def get_table(lines1, needle, i): + + # Try to find the start + ii = search_line(lines1, needle, i) + if ii < 0: + return [], -1 + + # Init result + lines2 = [] + + # Get size and name + front, dummu, back = lines1[ii].partition('[') + name = front.split(' ')[-1].upper() + size = int(back.split(']',1)[0]) + cdes = lines1[ii].rstrip(' {=') + + # Write name + lines2.append('%s = np.array([' % name) + + # Get elements + for i in range(ii+1, ii+1+9999999): + line1 = lines1[i] + front, dummy, back = line1.partition('*/') + if not back: + front, back = back, front + line2 = ' ' + line2 += back.strip().replace('{', '[').replace('}',']').replace(';','') + line2 += front.replace('/*',' #').rstrip() + lines2.append(line2) + if line1.endswith('};'): + break + + # Close and return + lines2.append(" , 'int8')") + lines2.append('') + #return lines2, ii+size + + # Execute code and get array as base64 text + code = '\n'.join(lines2) + code = code.split('=',1)[1] + array = eval(code) + array64 = base64encode(array.tostring()).decode('utf-8') + # Reverse: bytes = base64decode(text.encode('utf-8')) + text = '%s = %s, """\n%s"""' % (name, str(array.shape), array64) + + # Build actual lines + lines2 = [] + #lines2.append( '# %s -> %s %s' % (cdes, str(array.dtype), str(array.shape)) ) + lines2.append( '#' + cdes) + lines2.append(text) + lines2.append('') + return lines2, ii+size + + +def search_line(lines, refline, start=0): + for i, line in enumerate(lines[start:]): + if line.startswith(refline): + return i + start + return -1 + + + +def getLutNames(prefix): + aa = [] + for a in dir(luts): + if a.startswith(prefix): aa.append(a) + + def sortkey(x): + fullnr = x.split(prefix)[1] + nr, us, subnr = fullnr.partition('_') + if len(nr) == 1: + nr = '0'+nr + return nr + us + subnr + + return [a for a in sorted(aa, key=sortkey)] + + + +if __name__ == '__main__': + import os + fname = os.path.join(os.getcwd(), 'LookUpTable.h') + + if True: + with open(os.path.join(os.getcwd(), 'mcluts.py'), 'w') as f: + f.write('# -*- coding: utf-8 -*-\n') + f.write('# Copyright (C) 2012, Almar Klein\n# Copyright (C) 2002, Thomas Lewiner\n\n') + f.write('# This file was auto-generated from LookUpTable.h by createluts.py.\n\n') + f.write(create_luts(fname)) + + else: + for prefix in ['TILING', 'TEST']: + tmp = ['luts.'+a for a in getLutNames(prefix)] + print(', '.join(tmp)) + print('') + for name in getLutNames(prefix): + print('self.%s = Lut(%s)' % (name, name)) + print('') + for name in getLutNames(prefix): + print('cdef Lut %s' % name) + print('') + print('') diff --git a/skimage/measure/mc_meta/visual_test.py b/skimage/measure/mc_meta/visual_test.py new file mode 100644 index 00000000..ae8c0bfb --- /dev/null +++ b/skimage/measure/mc_meta/visual_test.py @@ -0,0 +1,64 @@ +""" +Script to show the results of the two marching cubes algorithms on different +data. +""" + +import time + +import numpy as np +import visvis as vv + +from skimage.measure import marching_cubes, marching_cubes_lewiner + + +# Create test volume +SELECT = 1 + +if SELECT == 1: + # Medical data + vol = vv.volread('stent') + isovalue = 800 + +elif SELECT == 2: + # Blocky data + vol = vv.aVolume(20, 128) # Different every time + isovalue = 0.2 + +elif SELECT == 3: + # Generate two donuts + n = 48 + a, b = 2.5/n, -1.25 + isovalue = 0.0 + # + vol = np.empty((n,n,n), 'float32') + for iz in range(vol.shape[0]): + for iy in range(vol.shape[1]): + for ix in range(vol.shape[2]): + z, y, x = float(iz)*a+b, float(iy)*a+b, float(ix)*a+b + vol[iz,iy,ix] = ( ( + (8*x)**2 + (8*y-2)**2 + (8*z)**2 + 16 - 1.85*1.85 ) * ( (8*x)**2 + + (8*y-2)**2 + (8*z)**2 + 16 - 1.85*1.85 ) - 64 * ( (8*x)**2 + (8*y-2)**2 ) + ) * ( ( (8*x)**2 + ((8*y-2)+4)*((8*y-2)+4) + (8*z)**2 + 16 - 1.85*1.85 ) + * ( (8*x)**2 + ((8*y-2)+4)*((8*y-2)+4) + (8*z)**2 + 16 - 1.85*1.85 ) - + 64 * ( ((8*y-2)+4)*((8*y-2)+4) + (8*z)**2 + ) ) + 1025 + # Uncommenting the line below will yield different results for classic MC + #vol = -vol + +# Get surface meshes +t0 = time.time() +vertices1, faces1, *_ = marching_cubes_lewiner(vol, isovalue, use_classic=False) +print('finding surface lewiner took %1.0f ms' % (1000*(time.time()-t0)) ) + +t0 = time.time() +vertices2, faces2, *_ = marching_cubes(vol, isovalue) +print('finding surface classic took %1.0f ms' % (1000*(time.time()-t0)) ) + +# Show +vv.figure(1); vv.clf() +a1 = vv.subplot(121); vv.mesh(np.fliplr(vertices1), faces1) +a2 = vv.subplot(122); vv.mesh(np.fliplr(vertices2), faces2) +a1.camera = a2.camera + + +vv.use().Run()