| OLD | NEW |
|---|
| (Empty) |
| 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_NoQuadraticsAllow
ed, | |
| 24 kReduceOrder_TreatAsFill); | |
| 25 int order2 = reduceOrder(cubic2, reduce2, kReduceOrder_NoQuadraticsAllow
ed, | |
| 26 kReduceOrder_TreatAsFill); | |
| 27 if (order1 < 4) { | |
| 28 printf("%s [%d] cubic1 order=%d\n", __FUNCTION__, (int) index, order
1); | |
| 29 continue; | |
| 30 } | |
| 31 if (order2 < 4) { | |
| 32 printf("%s [%d] cubic2 order=%d\n", __FUNCTION__, (int) index, order
2); | |
| 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, 90.4768631749213
06}, {35.597065061143162, 79.872482633158796}, {75.38634169631932, 18.2448900389
69412}}, | |
| 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, 0.72959763963222
402}, {63.209855865319199, 68.047528419665767}, {57.640240647662544, 59.52456526
4361243}}, | |
| 109 {{51.593891741518817, 38.53849970667553}, {62.34752929878772, 74.924924725166022
}, {74.810149322641152, 34.17966562983564}, {29.368398119401373, 94.667192778860
78}}, | |
| 110 | |
| 111 {{39.765160968417838, 33.060396198677083}, {5.1922921581157908, 66.8543014521032
15}, {31.619281802149157, 25.269248720849514}, {81.541621071073038, 70.025341524
754353}}, | |
| 112 {{46.078911165743556, 48.259962651999651}, {20.24450549867214, 49.40391618265021
4}, {0.26325131778756683, 24.46489805563581}, {15.915006546264051, 83.5150230599
17155}}, | |
| 113 | |
| 114 {{65.454505973241524, 93.881892270353575}, {45.867360264932437, 92.7239727194998
27}, {2.1464054482739447, 74.636369140183717}, {33.774068594804994, 40.770872887
582925}}, | |
| 115 {{72.963387832494163, 95.659300729473728}, {11.809496633619768, 82.2099212474235
94}, {13.456139067865974, 57.329313623406605}, {36.060621606214262, 70.867335643
091849}}, | |
| 116 | |
| 117 {{32.484981432782945, 75.082940782924624}, {42.467313093350882, 48.1311599482461
57}, {3.5963115764764657, 43.208665839959245}, {79.442476890721579, 89.709102357
602262}}, | |
| 118 {{18.98573861410177, 93.308887208490106}, {40.405250173250792, 91.03966182611867
5}, {8.0467721950480584, 42.100282172719147}, {40.883324221187891, 26.0301855048
30527}}, | |
| 119 | |
| 120 {{7.5374809128872498, 82.441702896003477}, {22.444346930107265, 22.1388543127751
23}, {66.76091829629658, 50.753805856571446}, {78.193478508942519, 97.7932997968
948}}, | |
| 121 {{97.700573130371311, 53.53260215070685}, {87.72443481149358, 84.575876772671876
}, {19.215031396232092, 47.032676472809484}, {11.989686410869325, 10.65950748075
7082}}, | |
| 122 | |
| 123 {{26.192053931854691, 9.8504326817814416}, {10.174241480498686, 98.4765627414344
64}, {21.177712558385782, 33.814968789841501}, {75.329030899018534, 55.022319804
42177}}, | |
| 124 {{56.222082700683771, 24.54395039218662}, {95.589995289030483, 81.05082273532208
6}, {28.180450866082897, 28.837706255185282}, {60.128952916771617, 87.3116721805
70511}}, | |
| 125 | |
| 126 {{42.449716172390481, 52.379709366885805}, {27.896043159019225, 48.7973736360656
86}, {92.770268299044233, 89.899302036454571}, {12.102066544863426, 99.432419519
60718}}, | |
| 127 {{45.77532924980639, 45.958701495993274}, {37.458701356062065, 68.39369133505675
8}, {37.569326692060258, 27.673713456687381}, {60.674866037757539, 62.4734965909
6146}}, | |
| 128 | |
| 129 {{67.426548091427676, 37.993772624988935}, {23.483695892376684, 90.4768631749213
06}, {35.597065061143162, 79.872482633158796}, {75.38634169631932, 18.2448900389
69412}}, | |
| 130 {{61.336508189019057, 82.693132843213675}, {44.639380902349664, 54.0748257907455
92}, {16.815615499771951, 20.049704667203923}, {41.866884958868326, 56.735503699
973002}}, | |
| 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}, {5
6.4860195, 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, 1.65999999999999
97}, {2.8000000000000007, 1.8000000000000003}, {3, 2}}, | |
| 164 {{2.4181876227114887, 1.9849772580462195}, {2.8269904869227211, 2.00933065024683
4}, {3.2004679292461624, 1.9942047174679169}, {3.4986199496818058, 2.00359945970
94731}}, | |
| 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) t
2=%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 a
pproximation | |
| 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 t
he other but | |
| 476 continue; // does not touch the quad approximation. Captured in qc.h
tm 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 oldInters
ects=%d" | |
| 505 " newIntersects=%d\n%s %s\n", __FUNCTION__, test, boundsInte
rsect, | |
| 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 delta
2=%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, boundsInte
rsect, | |
| 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", __F
UNCTION__, | |
| 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 t2S
eed, | |
| 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[i
dx2]).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 } | |
| OLD | NEW |
|---|
Chromium Code Reviews
Issue 867213004:
remove prototype pathops code (Closed)
Base URL: https://skia.googlesource.com/skia.git@master