1 /* 2 * Copyright 2012 Google Inc. 3 * 4 * Use of this source code is governed by a BSD-style license that can be 5 * found in the LICENSE file. 6 */ 7 #include "CurveIntersection.h" 8 #include "CurveUtilities.h" 9 #include "CubicIntersection_TestData.h" 10 #include "Intersection_Tests.h" 11 #include "Intersections.h" 12 #include "TestUtilities.h" 13 14 #define SHOW_ORIGINAL 1 15 16 const int firstCubicIntersectionTest = 9; 17 18 static void standardTestCases() { 19 for (size_t index = firstCubicIntersectionTest; index < tests_count; ++index) { 20 const Cubic& cubic1 = tests[index][0]; 21 const Cubic& cubic2 = tests[index][1]; 22 Cubic reduce1, reduce2; 23 int order1 = reduceOrder(cubic1, reduce1, kReduceOrder_NoQuadraticsAllowed, 24 kReduceOrder_TreatAsFill); 25 int order2 = reduceOrder(cubic2, reduce2, kReduceOrder_NoQuadraticsAllowed, 26 kReduceOrder_TreatAsFill); 27 if (order1 < 4) { 28 printf("%s [%d] cubic1 order=%d\n", __FUNCTION__, (int) index, order1); 29 continue; 30 } 31 if (order2 < 4) { 32 printf("%s [%d] cubic2 order=%d\n", __FUNCTION__, (int) index, order2); 33 continue; 34 } 35 if (implicit_matches(reduce1, reduce2)) { 36 printf("%s [%d] coincident\n", __FUNCTION__, (int) index); 37 continue; 38 } 39 Intersections tIntersections; 40 intersect(reduce1, reduce2, tIntersections); 41 if (!tIntersections.intersected()) { 42 printf("%s [%d] no intersection\n", __FUNCTION__, (int) index); 43 continue; 44 } 45 for (int pt = 0; pt < tIntersections.used(); ++pt) { 46 double tt1 = tIntersections.fT[0][pt]; 47 double tx1, ty1; 48 xy_at_t(cubic1, tt1, tx1, ty1); 49 double tt2 = tIntersections.fT[1][pt]; 50 double tx2, ty2; 51 xy_at_t(cubic2, tt2, tx2, ty2); 52 if (!AlmostEqualUlps(tx1, tx2)) { 53 printf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n", 54 __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2); 55 } 56 if (!AlmostEqualUlps(ty1, ty2)) { 57 printf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n", 58 __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2); 59 } 60 } 61 } 62 } 63 64 static const Cubic testSet[] = { 65 {{67.426548091427676, 37.993772624988935}, {23.483695892376684, 90.476863174921306}, {35.597065061143162, 79.872482633158796}, {75.38634169631932, 18.244890038969412}}, 66 {{67.4265481, 37.9937726}, {23.4836959, 90.4768632}, {35.5970651, 79.8724826}, {75.3863417, 18.24489}}, 67 68 {{0, 0}, {0, 1}, {1, 1}, {1, 0}}, 69 {{1, 0}, {0, 0}, {0, 1}, {1, 1}}, 70 71 {{0,1}, {4,5}, {1,0}, {5,3}}, 72 {{0,1}, {3,5}, {1,0}, {5,4}}, 73 74 {{0, 1}, {1, 6}, {1, 0}, {1, 0}}, 75 {{0, 1}, {0, 1}, {1, 0}, {6, 1}}, 76 77 {{0,1}, {3,4}, {1,0}, {5,1}}, 78 {{0,1}, {1,5}, {1,0}, {4,3}}, 79 80 {{0,1}, {1,2}, {1,0}, {6,1}}, 81 {{0,1}, {1,6}, {1,0}, {2,1}}, 82 83 {{0,1}, {0,5}, {1,0}, {4,0}}, 84 {{0,1}, {0,4}, {1,0}, {5,0}}, 85 86 {{0,1}, {3,4}, {1,0}, {3,0}}, 87 {{0,1}, {0,3}, {1,0}, {4,3}}, 88 89 {{0, 0}, {1, 2}, {3, 4}, {4, 4}}, 90 {{0, 0}, {1, 2}, {3, 4}, {4, 4}}, 91 {{4, 4}, {3, 4}, {1, 2}, {0, 0}}, 92 93 {{0,1}, {2,3}, {1,0}, {1,0}}, 94 {{0,1}, {0,1}, {1,0}, {3,2}}, 95 96 {{0,2}, {0,1}, {1,0}, {1,0}}, 97 {{0,1}, {0,1}, {2,0}, {1,0}}, 98 99 {{0, 1}, {0, 2}, {1, 0}, {1, 0}}, 100 {{0, 1}, {0, 1}, {1, 0}, {2, 0}}, 101 102 {{0, 1}, {1, 6}, {1, 0}, {2, 0}}, 103 {{0, 1}, {0, 2}, {1, 0}, {6, 1}}, 104 105 {{0, 1}, {5, 6}, {1, 0}, {1, 0}}, 106 {{0, 1}, {0, 1}, {1, 0}, {6, 5}}, 107 108 {{95.837747722788592, 45.025976907939643}, {16.564570095652982, 0.72959763963222402}, {63.209855865319199, 68.047528419665767}, {57.640240647662544, 59.524565264361243}}, 109 {{51.593891741518817, 38.53849970667553}, {62.34752929878772, 74.924924725166022}, {74.810149322641152, 34.17966562983564}, {29.368398119401373, 94.66719277886078}}, 110 111 {{39.765160968417838, 33.060396198677083}, {5.1922921581157908, 66.854301452103215}, {31.619281802149157, 25.269248720849514}, {81.541621071073038, 70.025341524754353}}, 112 {{46.078911165743556, 48.259962651999651}, {20.24450549867214, 49.403916182650214}, {0.26325131778756683, 24.46489805563581}, {15.915006546264051, 83.515023059917155}}, 113 114 {{65.454505973241524, 93.881892270353575}, {45.867360264932437, 92.723972719499827}, {2.1464054482739447, 74.636369140183717}, {33.774068594804994, 40.770872887582925}}, 115 {{72.963387832494163, 95.659300729473728}, {11.809496633619768, 82.209921247423594}, {13.456139067865974, 57.329313623406605}, {36.060621606214262, 70.867335643091849}}, 116 117 {{32.484981432782945, 75.082940782924624}, {42.467313093350882, 48.131159948246157}, {3.5963115764764657, 43.208665839959245}, {79.442476890721579, 89.709102357602262}}, 118 {{18.98573861410177, 93.308887208490106}, {40.405250173250792, 91.039661826118675}, {8.0467721950480584, 42.100282172719147}, {40.883324221187891, 26.030185504830527}}, 119 120 {{7.5374809128872498, 82.441702896003477}, {22.444346930107265, 22.138854312775123}, {66.76091829629658, 50.753805856571446}, {78.193478508942519, 97.7932997968948}}, 121 {{97.700573130371311, 53.53260215070685}, {87.72443481149358, 84.575876772671876}, {19.215031396232092, 47.032676472809484}, {11.989686410869325, 10.659507480757082}}, 122 123 {{26.192053931854691, 9.8504326817814416}, {10.174241480498686, 98.476562741434464}, {21.177712558385782, 33.814968789841501}, {75.329030899018534, 55.02231980442177}}, 124 {{56.222082700683771, 24.54395039218662}, {95.589995289030483, 81.050822735322086}, {28.180450866082897, 28.837706255185282}, {60.128952916771617, 87.311672180570511}}, 125 126 {{42.449716172390481, 52.379709366885805}, {27.896043159019225, 48.797373636065686}, {92.770268299044233, 89.899302036454571}, {12.102066544863426, 99.43241951960718}}, 127 {{45.77532924980639, 45.958701495993274}, {37.458701356062065, 68.393691335056758}, {37.569326692060258, 27.673713456687381}, {60.674866037757539, 62.47349659096146}}, 128 129 {{67.426548091427676, 37.993772624988935}, {23.483695892376684, 90.476863174921306}, {35.597065061143162, 79.872482633158796}, {75.38634169631932, 18.244890038969412}}, 130 {{61.336508189019057, 82.693132843213675}, {44.639380902349664, 54.074825790745592}, {16.815615499771951, 20.049704667203923}, {41.866884958868326, 56.735503699973002}}, 131 132 {{67.4265481, 37.9937726}, {23.4836959, 90.4768632}, {35.5970651, 79.8724826}, {75.3863417, 18.24489}}, 133 {{61.3365082, 82.6931328}, {44.6393809, 54.0748258}, {16.8156155, 20.0497047}, {41.866885, 56.7355037}}, 134 135 {{18.1312339, 31.6473732}, {95.5711034, 63.5350219}, {92.3283165, 62.0158945}, {18.5656052, 32.1268808}}, 136 {{97.402018, 35.7169972}, {33.1127443, 25.8935163}, {1.13970027, 54.9424981}, {56.4860195, 60.529264}}, 137 }; 138 139 const size_t testSetCount = sizeof(testSet) / sizeof(testSet[0]); 140 141 static const Cubic newTestSet[] = { 142 {{1,3}, {5,6}, {5,3}, {5,4}}, 143 {{3,5}, {4,5}, {3,1}, {6,5}}, 144 145 {{0,5}, {0,5}, {5,4}, {6,4}}, 146 {{4,5}, {4,6}, {5,0}, {5,0}}, 147 148 {{0,4}, {1,3}, {5,4}, {4,2}}, 149 {{4,5}, {2,4}, {4,0}, {3,1}}, 150 151 {{0,2}, {1,5}, {3,2}, {4,1}}, 152 {{2,3}, {1,4}, {2,0}, {5,1}}, 153 154 {{0,2}, {2,3}, {5,1}, {3,2}}, 155 {{1,5}, {2,3}, {2,0}, {3,2}}, 156 157 {{2,6}, {4,5}, {1,0}, {6,1}}, 158 {{0,1}, {1,6}, {6,2}, {5,4}}, 159 160 {{0,1}, {1,2}, {6,5}, {5,4}}, 161 {{5,6}, {4,5}, {1,0}, {2,1}}, 162 163 {{2.5119999999999996, 1.5710000000000002}, {2.6399999999999983, 1.6599999999999997}, {2.8000000000000007, 1.8000000000000003}, {3, 2}}, 164 {{2.4181876227114887, 1.9849772580462195}, {2.8269904869227211, 2.009330650246834}, {3.2004679292461624, 1.9942047174679169}, {3.4986199496818058, 2.0035994597094731}}, 165 166 {{2,3}, {1,4}, {1,0}, {6,0}}, 167 {{0,1}, {0,6}, {3,2}, {4,1}}, 168 169 {{0,2}, {1,5}, {1,0}, {6,1}}, 170 {{0,1}, {1,6}, {2,0}, {5,1}}, 171 172 {{0,1}, {1,5}, {2,1}, {4,0}}, 173 {{1,2}, {0,4}, {1,0}, {5,1}}, 174 175 {{0,1}, {3,5}, {2,1}, {3,1}}, 176 {{1,2}, {1,3}, {1,0}, {5,3}}, 177 178 {{0,1}, {2,5}, {6,0}, {5,3}}, 179 {{0,6}, {3,5}, {1,0}, {5,2}}, 180 181 {{0,1}, {3,6}, {1,0}, {5,2}}, 182 {{0,1}, {2,5}, {1,0}, {6,3}}, 183 184 {{1,2},{5,6},{1,0},{1,0}}, 185 {{0,1},{0,1},{2,1},{6,5}}, 186 187 {{0,6},{1,2},{1,0},{1,0}}, 188 {{0,1},{0,1},{6,0},{2,1}}, 189 190 {{0,2},{0,1},{3,0},{1,0}}, 191 {{0,3},{0,1},{2,0},{1,0}}, 192 }; 193 194 const size_t newTestSetCount = sizeof(newTestSet) / sizeof(newTestSet[0]); 195 196 #if 0 197 static void oneOff(const Cubic& cubic1, const Cubic& cubic2) { 198 SkTDArray<Quadratic> quads1; 199 cubic_to_quadratics(cubic1, calcPrecision(cubic1), quads1); 200 #if SHOW_ORIGINAL 201 SkDebugf("computed quadratics given\n"); 202 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}, {%1.9g,%1.9g}},\n", 203 cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y, 204 cubic1[2].x, cubic1[2].y, cubic1[3].x, cubic1[3].y)); 205 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}, {%1.9g,%1.9g}},\n", 206 cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y, 207 cubic2[2].x, cubic2[2].y, cubic2[3].x, cubic2[3].y)); 208 #endif 209 #if ONE_OFF_DEBUG 210 SkDebugf("computed quadratics set 1\n"); 211 for (int index = 0; index < quads1.count(); ++index) { 212 const Quadratic& q = quads1[index]; 213 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y, 214 q[1].x, q[1].y, q[2].x, q[2].y); 215 } 216 #endif 217 SkTDArray<Quadratic> quads2; 218 cubic_to_quadratics(cubic2, calcPrecision(cubic2), quads2); 219 #if ONE_OFF_DEBUG 220 SkDebugf("computed quadratics set 2\n"); 221 for (int index = 0; index < quads2.count(); ++index) { 222 const Quadratic& q = quads2[index]; 223 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y, 224 q[1].x, q[1].y, q[2].x, q[2].y); 225 } 226 #endif 227 Intersections intersections2, intersections3; 228 intersect2(cubic1, cubic2, intersections2); 229 intersect3(cubic1, cubic2, intersections3); 230 int pt1, pt2, pt3; 231 bool found; 232 double tt1, tt2, last = -1; 233 _Point xy1, xy2; 234 for (pt1 = 0; pt1 < intersections2.used(); ++pt1) { 235 tt1 = intersections2.fT[0][pt1]; 236 SkASSERT(!approximately_equal(last, tt1)); 237 last = tt1; 238 xy_at_t(cubic1, tt1, xy1.x, xy1.y); 239 pt2 = intersections2.fFlip ? intersections2.used() - pt1 - 1 : pt1; 240 tt2 = intersections2.fT[1][pt2]; 241 xy_at_t(cubic2, tt2, xy2.x, xy2.y); 242 #if ONE_OFF_DEBUG 243 SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n", 244 __FUNCTION__, tt1, xy1.x, xy1.y, intersections2.fPt[pt1].x, 245 intersections2.fPt[pt1].y, xy2.x, xy2.y, tt2); 246 #endif 247 SkASSERT(xy1.approximatelyEqual(xy2)); 248 #ifdef SK_DEBUG 249 found = false; 250 for (pt3 = 0; pt3 < intersections3.used(); ++pt3) { 251 if (roughly_equal(tt1, intersections3.fT[0][pt3])) { 252 found = true; 253 break; 254 } 255 } 256 SkASSERT(found); 257 #endif 258 } 259 last = -1; 260 for (pt3 = 0; pt3 < intersections3.used(); ++pt3) { 261 found = false; 262 double tt3 = intersections3.fT[0][pt3]; 263 SkASSERT(!approximately_equal(last, tt3)); 264 last = tt3; 265 for (pt1 = 0; pt1 < intersections2.used(); ++pt1) { 266 if (approximately_equal(tt3, intersections2.fT[0][pt1])) { 267 found = true; 268 break; 269 } 270 } 271 if (!found) { 272 tt1 = intersections3.fT[0][pt3]; 273 xy_at_t(cubic1, tt1, xy1.x, xy1.y); 274 pt2 = intersections3.fFlip ? intersections3.used() - pt3 - 1 : pt3; 275 tt2 = intersections3.fT[1][pt2]; 276 xy_at_t(cubic2, tt2, xy2.x, xy2.y); 277 #if ONE_OFF_DEBUG 278 SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n", 279 __FUNCTION__, tt1, xy1.x, xy1.y, intersections3.fPt[pt1].x, 280 intersections3.fPt[pt1].y, xy2.x, xy2.y, tt2); 281 #endif 282 SkASSERT(xy1.approximatelyEqual(xy2)); 283 SkDebugf("%s missing in intersect2\n", __FUNCTION__); 284 } 285 } 286 } 287 #endif 288 289 static void oneOff3(const Cubic& cubic1, const Cubic& cubic2) { 290 #if ONE_OFF_DEBUG 291 SkDebugf("computed quadratics given\n"); 292 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", 293 cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y, 294 cubic1[2].x, cubic1[2].y, cubic1[3].x, cubic1[3].y); 295 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", 296 cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y, 297 cubic2[2].x, cubic2[2].y, cubic2[3].x, cubic2[3].y); 298 #endif 299 SkTDArray<Quadratic> quads1; 300 cubic_to_quadratics(cubic1, calcPrecision(cubic1), quads1); 301 #if ONE_OFF_DEBUG 302 SkDebugf("computed quadratics set 1\n"); 303 for (int index = 0; index < quads1.count(); ++index) { 304 const Quadratic& q = quads1[index]; 305 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y, 306 q[1].x, q[1].y, q[2].x, q[2].y); 307 } 308 #endif 309 SkTDArray<Quadratic> quads2; 310 cubic_to_quadratics(cubic2, calcPrecision(cubic2), quads2); 311 #if ONE_OFF_DEBUG 312 SkDebugf("computed quadratics set 2\n"); 313 for (int index = 0; index < quads2.count(); ++index) { 314 const Quadratic& q = quads2[index]; 315 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y, 316 q[1].x, q[1].y, q[2].x, q[2].y); 317 } 318 #endif 319 Intersections intersections3; 320 intersect3(cubic1, cubic2, intersections3); 321 int pt2, pt3; 322 double tt1, tt2, last = -1; 323 _Point xy1, xy2; 324 for (pt3 = 0; pt3 < intersections3.used(); ++pt3) { 325 double tt3 = intersections3.fT[0][pt3]; 326 // SkASSERT(!approximately_equal(last, tt3)); 327 last = tt3; 328 tt1 = intersections3.fT[0][pt3]; 329 xy_at_t(cubic1, tt1, xy1.x, xy1.y); 330 pt2 = intersections3.fFlip ? intersections3.used() - pt3 - 1 : pt3; 331 tt2 = intersections3.fT[1][pt2]; 332 xy_at_t(cubic2, tt2, xy2.x, xy2.y); 333 #if ONE_OFF_DEBUG 334 SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n", 335 __FUNCTION__, tt1, xy1.x, xy1.y, intersections3.fPt[pt3].x, 336 intersections3.fPt[pt3].y, xy2.x, xy2.y, tt2); 337 #endif 338 SkASSERT(xy1.approximatelyEqual(xy2)); 339 } 340 } 341 342 #if 0 343 static int fails[][2] = { {0, 23}, // fails in intersect2 recursing 344 {2, 7}, // answers differ, but neither is correct ('3' is closer) 345 {3, 26}, // fails in intersect2 recursing 346 {4, 9}, // fails in intersect2 recursing 347 {4, 10}, // fails in intersect2 recursing 348 {10, 17}, // fails in intersect2 recursing 349 {12, 14}, // loops indefinitely 350 {12, 21}, // fails in intersect2 recursing 351 {13, 21}, // fails in intersect2 recursing 352 {14, 21}, // fails in intersect2 recursing 353 {17, 25}, // fails in intersect2 recursing 354 {23, 25}, // fails in intersect2 recursing 355 }; 356 357 static int failCount = sizeof(fails) / sizeof(fails[0]); 358 #endif 359 360 static void oneOff(int outer, int inner) { 361 const Cubic& cubic1 = testSet[outer]; 362 const Cubic& cubic2 = testSet[inner]; 363 #if 0 364 bool failing = false; 365 for (int i = 0; i < failCount; ++i) { 366 if ((fails[i][0] == outer && fails[i][1] == inner) 367 || (fails[i][1] == outer && fails[i][0] == inner)) { 368 failing = true; 369 break; 370 } 371 } 372 if (!failing) { 373 oneOff(cubic1, cubic2); 374 } else { 375 #endif 376 oneOff3(cubic1, cubic2); 377 // } 378 } 379 380 void CubicIntersection_OneOffTest() { 381 oneOff(0, 1); 382 } 383 384 static void newOneOff(int outer, int inner) { 385 const Cubic& cubic1 = newTestSet[outer]; 386 const Cubic& cubic2 = newTestSet[inner]; 387 oneOff3(cubic1, cubic2); 388 } 389 390 void CubicIntersection_NewOneOffTest() { 391 newOneOff(0, 1); 392 } 393 394 static void oneOffTests() { 395 for (size_t outer = 0; outer < testSetCount - 1; ++outer) { 396 for (size_t inner = outer + 1; inner < testSetCount; ++inner) { 397 oneOff(outer, inner); 398 } 399 } 400 } 401 402 void CubicIntersection_OneOffTests() { 403 oneOffTests(); 404 } 405 406 #define DEBUG_CRASH 0 407 408 class CubicChopper { 409 public: 410 411 // only finds one intersection 412 CubicChopper(const Cubic& c1, const Cubic& c2) 413 : cubic1(c1) 414 , cubic2(c2) 415 , depth(0) { 416 } 417 418 bool intersect(double minT1, double maxT1, double minT2, double maxT2) { 419 Cubic sub1, sub2; 420 // FIXME: carry last subdivide and reduceOrder result with cubic 421 sub_divide(cubic1, minT1, maxT1, sub1); 422 sub_divide(cubic2, minT2, maxT2, sub2); 423 Intersections i; 424 intersect3(sub1, sub2, i); 425 if (i.used() == 0) { 426 return false; 427 } 428 double x1, y1, x2, y2; 429 t1 = minT1 + i.fT[0][0] * (maxT1 - minT1); 430 t2 = minT2 + i.fT[1][0] * (maxT2 - minT2); 431 xy_at_t(cubic1, t1, x1, y1); 432 xy_at_t(cubic2, t2, x2, y2); 433 if (AlmostEqualUlps(x1, x2) && AlmostEqualUlps(y1, y2)) { 434 return true; 435 } 436 double half1 = (minT1 + maxT1) / 2; 437 double half2 = (minT2 + maxT2) / 2; 438 ++depth; 439 bool result; 440 if (depth & 1) { 441 result = intersect(minT1, half1, minT2, maxT2) || intersect(half1, maxT1, minT2, maxT2) 442 || intersect(minT1, maxT1, minT2, half2) || intersect(minT1, maxT1, half2, maxT2); 443 } else { 444 result = intersect(minT1, maxT1, minT2, half2) || intersect(minT1, maxT1, half2, maxT2) 445 || intersect(minT1, half1, minT2, maxT2) || intersect(half1, maxT1, minT2, maxT2); 446 } 447 --depth; 448 return result; 449 } 450 451 const Cubic& cubic1; 452 const Cubic& cubic2; 453 double t1; 454 double t2; 455 int depth; 456 }; 457 458 #define TRY_OLD 0 // old way fails on test == 1 459 460 void CubicIntersection_RandTestOld() { 461 srand(0); 462 const int tests = 1000000; // 10000000; 463 double largestFactor = DBL_MAX; 464 for (int test = 0; test < tests; ++test) { 465 Cubic cubic1, cubic2; 466 for (int i = 0; i < 4; ++i) { 467 cubic1[i].x = (double) rand() / RAND_MAX * 100; 468 cubic1[i].y = (double) rand() / RAND_MAX * 100; 469 cubic2[i].x = (double) rand() / RAND_MAX * 100; 470 cubic2[i].y = (double) rand() / RAND_MAX * 100; 471 } 472 if (test == 2513) { // the pair crosses three times, but the quadratic approximation 473 continue; // only sees one -- should be OK to ignore the other two? 474 } 475 if (test == 12932) { // this exposes a weakness when one cubic touches the other but 476 continue; // does not touch the quad approximation. Captured in qc.htm as cubic15 477 } 478 #if DEBUG_CRASH 479 char str[1024]; 480 sprintf(str, "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n" 481 "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n", 482 cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y, cubic1[2].x, cubic1[2].y, 483 cubic1[3].x, cubic1[3].y, 484 cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y, cubic2[2].x, cubic2[2].y, 485 cubic2[3].x, cubic2[3].y); 486 #endif 487 _Rect rect1, rect2; 488 rect1.setBounds(cubic1); 489 rect2.setBounds(cubic2); 490 bool boundsIntersect = rect1.left <= rect2.right && rect2.left <= rect2.right 491 && rect1.top <= rect2.bottom && rect2.top <= rect1.bottom; 492 Intersections i1, i2; 493 #if TRY_OLD 494 bool oldIntersects = intersect(cubic1, cubic2, i1); 495 #else 496 bool oldIntersects = false; 497 #endif 498 if (test == -1) { 499 SkDebugf("ready...\n"); 500 } 501 bool newIntersects = intersect3(cubic1, cubic2, i2); 502 if (!boundsIntersect && (oldIntersects || newIntersects)) { 503 #if DEBUG_CRASH 504 SkDebugf("%s %d unexpected intersection boundsIntersect=%d oldIntersects=%d" 505 " newIntersects=%d\n%s %s\n", __FUNCTION__, test, boundsIntersect, 506 oldIntersects, newIntersects, __FUNCTION__, str); 507 #endif 508 SkASSERT(0); 509 } 510 if (oldIntersects && !newIntersects) { 511 #if DEBUG_CRASH 512 SkDebugf("%s %d missing intersection oldIntersects=%d newIntersects=%d\n%s %s\n", 513 __FUNCTION__, test, oldIntersects, newIntersects, __FUNCTION__, str); 514 #endif 515 SkASSERT(0); 516 } 517 if (!oldIntersects && !newIntersects) { 518 continue; 519 } 520 if (i2.used() > 1) { 521 continue; 522 // just look at single intercepts for simplicity 523 } 524 Intersections self1, self2; // self-intersect checks 525 if (intersect(cubic1, self1)) { 526 continue; 527 } 528 if (intersect(cubic2, self2)) { 529 continue; 530 } 531 // binary search for range necessary to enclose real intersection 532 CubicChopper c(cubic1, cubic2); 533 bool result = c.intersect(0, 1, 0, 1); 534 if (!result) { 535 // FIXME: a failure here probably means that a core routine used by CubicChopper is failing 536 continue; 537 } 538 double delta1 = fabs(c.t1 - i2.fT[0][0]); 539 double delta2 = fabs(c.t2 - i2.fT[1][0]); 540 double calc1 = calcPrecision(cubic1); 541 double calc2 = calcPrecision(cubic2); 542 double factor1 = calc1 / delta1; 543 double factor2 = calc2 / delta2; 544 SkDebugf("%s %d calc1=%1.9g delta1=%1.9g factor1=%1.9g calc2=%1.9g delta2=%1.9g" 545 " factor2=%1.9g\n", __FUNCTION__, test, 546 calc1, delta1, factor1, calc2, delta2, factor2); 547 if (factor1 < largestFactor) { 548 SkDebugf("WE HAVE A WINNER! %1.9g\n", factor1); 549 #if DEBUG_CRASH 550 SkDebugf("%s\n", str); 551 #endif 552 oneOff3(cubic1, cubic2); 553 largestFactor = factor1; 554 } 555 if (factor2 < largestFactor) { 556 SkDebugf("WE HAVE A WINNER! %1.9g\n", factor2); 557 #if DEBUG_CRASH 558 SkDebugf("%s\n", str); 559 #endif 560 oneOff3(cubic1, cubic2); 561 largestFactor = factor2; 562 } 563 } 564 } 565 566 void CubicIntersection_RandTest() { 567 srand(0); 568 const int tests = 10000000; 569 for (int test = 0; test < tests; ++test) { 570 Cubic cubic1, cubic2; 571 for (int i = 0; i < 4; ++i) { 572 cubic1[i].x = (double) rand() / RAND_MAX * 100; 573 cubic1[i].y = (double) rand() / RAND_MAX * 100; 574 cubic2[i].x = (double) rand() / RAND_MAX * 100; 575 cubic2[i].y = (double) rand() / RAND_MAX * 100; 576 } 577 #if DEBUG_CRASH 578 char str[1024]; 579 sprintf(str, "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n" 580 "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n", 581 cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y, cubic1[2].x, cubic1[2].y, 582 cubic1[3].x, cubic1[3].y, 583 cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y, cubic2[2].x, cubic2[2].y, 584 cubic2[3].x, cubic2[3].y); 585 #endif 586 _Rect rect1, rect2; 587 rect1.setBounds(cubic1); 588 rect2.setBounds(cubic2); 589 bool boundsIntersect = rect1.left <= rect2.right && rect2.left <= rect2.right 590 && rect1.top <= rect2.bottom && rect2.top <= rect1.bottom; 591 if (test == -1) { 592 SkDebugf("ready...\n"); 593 } 594 Intersections intersections2; 595 bool newIntersects = intersect3(cubic1, cubic2, intersections2); 596 if (!boundsIntersect && newIntersects) { 597 #if DEBUG_CRASH 598 SkDebugf("%s %d unexpected intersection boundsIntersect=%d " 599 " newIntersects=%d\n%s %s\n", __FUNCTION__, test, boundsIntersect, 600 newIntersects, __FUNCTION__, str); 601 #endif 602 SkASSERT(0); 603 } 604 for (int pt = 0; pt < intersections2.used(); ++pt) { 605 double tt1 = intersections2.fT[0][pt]; 606 _Point xy1, xy2; 607 xy_at_t(cubic1, tt1, xy1.x, xy1.y); 608 int pt2 = intersections2.fFlip ? intersections2.used() - pt - 1 : pt; 609 double tt2 = intersections2.fT[1][pt2]; 610 xy_at_t(cubic2, tt2, xy2.x, xy2.y); 611 #if 0 612 SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n", __FUNCTION__, 613 tt1, xy1.x, xy1.y, xy2.x, xy2.y, tt2); 614 #endif 615 SkASSERT(xy1.approximatelyEqual(xy2)); 616 } 617 } 618 } 619 620 static void intersectionFinder(int index0, int index1, double t1Seed, double t2Seed, 621 double t1Step, double t2Step) { 622 const Cubic& cubic1 = newTestSet[index0]; 623 const Cubic& cubic2 = newTestSet[index1]; 624 _Point t1[3], t2[3]; 625 bool toggle = true; 626 do { 627 xy_at_t(cubic1, t1Seed - t1Step, t1[0].x, t1[0].y); 628 xy_at_t(cubic1, t1Seed, t1[1].x, t1[1].y); 629 xy_at_t(cubic1, t1Seed + t1Step, t1[2].x, t1[2].y); 630 xy_at_t(cubic2, t2Seed - t2Step, t2[0].x, t2[0].y); 631 xy_at_t(cubic2, t2Seed, t2[1].x, t2[1].y); 632 xy_at_t(cubic2, t2Seed + t2Step, t2[2].x, t2[2].y); 633 double dist[3][3]; 634 dist[1][1] = t1[1].distance(t2[1]); 635 int best_i = 1, best_j = 1; 636 for (int i = 0; i < 3; ++i) { 637 for (int j = 0; j < 3; ++j) { 638 if (i == 1 && j == 1) { 639 continue; 640 } 641 dist[i][j] = t1[i].distance(t2[j]); 642 if (dist[best_i][best_j] > dist[i][j]) { 643 best_i = i; 644 best_j = j; 645 } 646 } 647 } 648 if (best_i == 0) { 649 t1Seed -= t1Step; 650 } else if (best_i == 2) { 651 t1Seed += t1Step; 652 } 653 if (best_j == 0) { 654 t2Seed -= t2Step; 655 } else if (best_j == 2) { 656 t2Seed += t2Step; 657 } 658 if (best_i == 1 && best_j == 1) { 659 if ((toggle ^= true)) { 660 t1Step /= 2; 661 } else { 662 t2Step /= 2; 663 } 664 } 665 } while (!t1[1].approximatelyEqual(t2[1])); 666 t1Step = t2Step = 0.1; 667 double t10 = t1Seed - t1Step * 2; 668 double t12 = t1Seed + t1Step * 2; 669 double t20 = t2Seed - t2Step * 2; 670 double t22 = t2Seed + t2Step * 2; 671 _Point test; 672 while (!approximately_zero(t1Step)) { 673 xy_at_t(cubic1, t10, test.x, test.y); 674 t10 += t1[1].approximatelyEqual(test) ? -t1Step : t1Step; 675 t1Step /= 2; 676 } 677 t1Step = 0.1; 678 while (!approximately_zero(t1Step)) { 679 xy_at_t(cubic1, t12, test.x, test.y); 680 t12 -= t1[1].approximatelyEqual(test) ? -t1Step : t1Step; 681 t1Step /= 2; 682 } 683 while (!approximately_zero(t2Step)) { 684 xy_at_t(cubic2, t20, test.x, test.y); 685 t20 += t2[1].approximatelyEqual(test) ? -t2Step : t2Step; 686 t2Step /= 2; 687 } 688 t2Step = 0.1; 689 while (!approximately_zero(t2Step)) { 690 xy_at_t(cubic2, t22, test.x, test.y); 691 t22 -= t2[1].approximatelyEqual(test) ? -t2Step : t2Step; 692 t2Step /= 2; 693 } 694 #if ONE_OFF_DEBUG 695 SkDebugf("%s t1=(%1.9g<%1.9g<%1.9g) t2=(%1.9g<%1.9g<%1.9g)\n", __FUNCTION__, 696 t10, t1Seed, t12, t20, t2Seed, t22); 697 _Point p10 = xy_at_t(cubic1, t10); 698 _Point p1Seed = xy_at_t(cubic1, t1Seed); 699 _Point p12 = xy_at_t(cubic1, t12); 700 SkDebugf("%s p1=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__, 701 p10.x, p10.y, p1Seed.x, p1Seed.y, p12.x, p12.y); 702 _Point p20 = xy_at_t(cubic2, t20); 703 _Point p2Seed = xy_at_t(cubic2, t2Seed); 704 _Point p22 = xy_at_t(cubic2, t22); 705 SkDebugf("%s p2=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__, 706 p20.x, p20.y, p2Seed.x, p2Seed.y, p22.x, p22.y); 707 #endif 708 } 709 710 void CubicIntersection_IntersectionFinder() { 711 712 // double t1Seed = 0.87; 713 // double t2Seed = 0.87; 714 double t1Step = 0.000001; 715 double t2Step = 0.000001; 716 intersectionFinder(0, 1, 0.855895664, 0.864850875, t1Step, t2Step); 717 intersectionFinder(0, 1, 0.865207906, 0.865207887, t1Step, t2Step); 718 intersectionFinder(0, 1, 0.865213351, 0.865208087, t1Step, t2Step); 719 } 720 721 static void coincidentTest() { 722 #if 0 723 Cubic cubic1 = {{0, 1}, {0, 2}, {1, 0}, {1, 0}}; 724 Cubic cubic2 = {{0, 1}, {0, 2}, {1, 0}, {6, 1}}; 725 #endif 726 } 727 728 void CubicIntersection_SelfTest() { 729 const Cubic selfSet[] = { 730 {{0,2}, {2,3}, {5,1}, {3,2}}, 731 {{0,2}, {3,5}, {5,0}, {4,2}}, 732 {{3.34,8.98}, {1.95,10.27}, {3.76,7.65}, {4.96,10.64}}, 733 {{3.13,2.74}, {1.08,4.62}, {3.71,0.94}, {2.01,3.81}}, 734 {{6.71,3.14}, {7.99,2.75}, {8.27,1.96}, {6.35,3.57}}, 735 {{12.81,7.27}, {7.22,6.98}, {12.49,8.97}, {11.42,6.18}}, 736 }; 737 size_t selfSetCount = sizeof(selfSet) / sizeof(selfSet[0]); 738 size_t firstFail = 1; 739 for (size_t index = firstFail; index < selfSetCount; ++index) { 740 const Cubic& cubic = selfSet[index]; 741 #if ONE_OFF_DEBUG 742 int idx2; 743 double max[3]; 744 int ts = find_cubic_max_curvature(cubic, max); 745 for (idx2 = 0; idx2 < ts; ++idx2) { 746 SkDebugf("%s max[%d]=%1.9g (%1.9g, %1.9g)\n", __FUNCTION__, idx2, 747 max[idx2], xy_at_t(cubic, max[idx2]).x, xy_at_t(cubic, max[idx2]).y); 748 } 749 SkTDArray<double> ts1; 750 SkTDArray<Quadratic> quads1; 751 cubic_to_quadratics(cubic, calcPrecision(cubic), ts1); 752 for (idx2 = 0; idx2 < ts1.count(); ++idx2) { 753 SkDebugf("%s t[%d]=%1.9g\n", __FUNCTION__, idx2, ts1[idx2]); 754 } 755 cubic_to_quadratics(cubic, calcPrecision(cubic), quads1); 756 for (idx2 = 0; idx2 < quads1.count(); ++idx2) { 757 const Quadratic& q = quads1[idx2]; 758 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", 759 q[0].x, q[0].y, q[1].x, q[1].y, q[2].x, q[2].y); 760 } 761 SkDebugf("\n"); 762 #endif 763 Intersections i; 764 SkDEBUGCODE(int result = ) intersect(cubic, i); 765 SkASSERT(result == 1); 766 SkASSERT(i.used() == 1); 767 SkASSERT(!approximately_equal(i.fT[0][0], i.fT[1][0])); 768 _Point pt1 = xy_at_t(cubic, i.fT[0][0]); 769 _Point pt2 = xy_at_t(cubic, i.fT[1][0]); 770 SkASSERT(pt1.approximatelyEqual(pt2)); 771 } 772 } 773 774 void CubicIntersection_Test() { 775 oneOffTests(); 776 coincidentTest(); 777 standardTestCases(); 778 } 779
