| /* |
| * Copyright 2012 Google Inc. |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| #include "CurveIntersection.h" |
| #include "CurveUtilities.h" |
| #include "CubicIntersection_TestData.h" |
| #include "Intersection_Tests.h" |
| #include "Intersections.h" |
| #include "TestUtilities.h" |
| |
| #define SHOW_ORIGINAL 1 |
| |
| const int firstCubicIntersectionTest = 9; |
| |
| static void standardTestCases() { |
| for (size_t index = firstCubicIntersectionTest; index < tests_count; ++index) { |
| const Cubic& cubic1 = tests[index][0]; |
| const Cubic& cubic2 = tests[index][1]; |
| Cubic reduce1, reduce2; |
| int order1 = reduceOrder(cubic1, reduce1, kReduceOrder_NoQuadraticsAllowed, |
| kReduceOrder_TreatAsFill); |
| int order2 = reduceOrder(cubic2, reduce2, kReduceOrder_NoQuadraticsAllowed, |
| kReduceOrder_TreatAsFill); |
| if (order1 < 4) { |
| printf("%s [%d] cubic1 order=%d\n", __FUNCTION__, (int) index, order1); |
| continue; |
| } |
| if (order2 < 4) { |
| printf("%s [%d] cubic2 order=%d\n", __FUNCTION__, (int) index, order2); |
| continue; |
| } |
| if (implicit_matches(reduce1, reduce2)) { |
| printf("%s [%d] coincident\n", __FUNCTION__, (int) index); |
| continue; |
| } |
| Intersections tIntersections; |
| intersect(reduce1, reduce2, tIntersections); |
| if (!tIntersections.intersected()) { |
| printf("%s [%d] no intersection\n", __FUNCTION__, (int) index); |
| continue; |
| } |
| for (int pt = 0; pt < tIntersections.used(); ++pt) { |
| double tt1 = tIntersections.fT[0][pt]; |
| double tx1, ty1; |
| xy_at_t(cubic1, tt1, tx1, ty1); |
| double tt2 = tIntersections.fT[1][pt]; |
| double tx2, ty2; |
| xy_at_t(cubic2, tt2, tx2, ty2); |
| if (!AlmostEqualUlps(tx1, tx2)) { |
| printf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n", |
| __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2); |
| } |
| if (!AlmostEqualUlps(ty1, ty2)) { |
| printf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n", |
| __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2); |
| } |
| } |
| } |
| } |
| |
| static const Cubic testSet[] = { |
| {{67.426548091427676, 37.993772624988935}, {23.483695892376684, 90.476863174921306}, {35.597065061143162, 79.872482633158796}, {75.38634169631932, 18.244890038969412}}, |
| {{67.4265481, 37.9937726}, {23.4836959, 90.4768632}, {35.5970651, 79.8724826}, {75.3863417, 18.24489}}, |
| |
| {{0, 0}, {0, 1}, {1, 1}, {1, 0}}, |
| {{1, 0}, {0, 0}, {0, 1}, {1, 1}}, |
| |
| {{0,1}, {4,5}, {1,0}, {5,3}}, |
| {{0,1}, {3,5}, {1,0}, {5,4}}, |
| |
| {{0, 1}, {1, 6}, {1, 0}, {1, 0}}, |
| {{0, 1}, {0, 1}, {1, 0}, {6, 1}}, |
| |
| {{0,1}, {3,4}, {1,0}, {5,1}}, |
| {{0,1}, {1,5}, {1,0}, {4,3}}, |
| |
| {{0,1}, {1,2}, {1,0}, {6,1}}, |
| {{0,1}, {1,6}, {1,0}, {2,1}}, |
| |
| {{0,1}, {0,5}, {1,0}, {4,0}}, |
| {{0,1}, {0,4}, {1,0}, {5,0}}, |
| |
| {{0,1}, {3,4}, {1,0}, {3,0}}, |
| {{0,1}, {0,3}, {1,0}, {4,3}}, |
| |
| {{0, 0}, {1, 2}, {3, 4}, {4, 4}}, |
| {{0, 0}, {1, 2}, {3, 4}, {4, 4}}, |
| {{4, 4}, {3, 4}, {1, 2}, {0, 0}}, |
| |
| {{0,1}, {2,3}, {1,0}, {1,0}}, |
| {{0,1}, {0,1}, {1,0}, {3,2}}, |
| |
| {{0,2}, {0,1}, {1,0}, {1,0}}, |
| {{0,1}, {0,1}, {2,0}, {1,0}}, |
| |
| {{0, 1}, {0, 2}, {1, 0}, {1, 0}}, |
| {{0, 1}, {0, 1}, {1, 0}, {2, 0}}, |
| |
| {{0, 1}, {1, 6}, {1, 0}, {2, 0}}, |
| {{0, 1}, {0, 2}, {1, 0}, {6, 1}}, |
| |
| {{0, 1}, {5, 6}, {1, 0}, {1, 0}}, |
| {{0, 1}, {0, 1}, {1, 0}, {6, 5}}, |
| |
| {{95.837747722788592, 45.025976907939643}, {16.564570095652982, 0.72959763963222402}, {63.209855865319199, 68.047528419665767}, {57.640240647662544, 59.524565264361243}}, |
| {{51.593891741518817, 38.53849970667553}, {62.34752929878772, 74.924924725166022}, {74.810149322641152, 34.17966562983564}, {29.368398119401373, 94.66719277886078}}, |
| |
| {{39.765160968417838, 33.060396198677083}, {5.1922921581157908, 66.854301452103215}, {31.619281802149157, 25.269248720849514}, {81.541621071073038, 70.025341524754353}}, |
| {{46.078911165743556, 48.259962651999651}, {20.24450549867214, 49.403916182650214}, {0.26325131778756683, 24.46489805563581}, {15.915006546264051, 83.515023059917155}}, |
| |
| {{65.454505973241524, 93.881892270353575}, {45.867360264932437, 92.723972719499827}, {2.1464054482739447, 74.636369140183717}, {33.774068594804994, 40.770872887582925}}, |
| {{72.963387832494163, 95.659300729473728}, {11.809496633619768, 82.209921247423594}, {13.456139067865974, 57.329313623406605}, {36.060621606214262, 70.867335643091849}}, |
| |
| {{32.484981432782945, 75.082940782924624}, {42.467313093350882, 48.131159948246157}, {3.5963115764764657, 43.208665839959245}, {79.442476890721579, 89.709102357602262}}, |
| {{18.98573861410177, 93.308887208490106}, {40.405250173250792, 91.039661826118675}, {8.0467721950480584, 42.100282172719147}, {40.883324221187891, 26.030185504830527}}, |
| |
| {{7.5374809128872498, 82.441702896003477}, {22.444346930107265, 22.138854312775123}, {66.76091829629658, 50.753805856571446}, {78.193478508942519, 97.7932997968948}}, |
| {{97.700573130371311, 53.53260215070685}, {87.72443481149358, 84.575876772671876}, {19.215031396232092, 47.032676472809484}, {11.989686410869325, 10.659507480757082}}, |
| |
| {{26.192053931854691, 9.8504326817814416}, {10.174241480498686, 98.476562741434464}, {21.177712558385782, 33.814968789841501}, {75.329030899018534, 55.02231980442177}}, |
| {{56.222082700683771, 24.54395039218662}, {95.589995289030483, 81.050822735322086}, {28.180450866082897, 28.837706255185282}, {60.128952916771617, 87.311672180570511}}, |
| |
| {{42.449716172390481, 52.379709366885805}, {27.896043159019225, 48.797373636065686}, {92.770268299044233, 89.899302036454571}, {12.102066544863426, 99.43241951960718}}, |
| {{45.77532924980639, 45.958701495993274}, {37.458701356062065, 68.393691335056758}, {37.569326692060258, 27.673713456687381}, {60.674866037757539, 62.47349659096146}}, |
| |
| {{67.426548091427676, 37.993772624988935}, {23.483695892376684, 90.476863174921306}, {35.597065061143162, 79.872482633158796}, {75.38634169631932, 18.244890038969412}}, |
| {{61.336508189019057, 82.693132843213675}, {44.639380902349664, 54.074825790745592}, {16.815615499771951, 20.049704667203923}, {41.866884958868326, 56.735503699973002}}, |
| |
| {{67.4265481, 37.9937726}, {23.4836959, 90.4768632}, {35.5970651, 79.8724826}, {75.3863417, 18.24489}}, |
| {{61.3365082, 82.6931328}, {44.6393809, 54.0748258}, {16.8156155, 20.0497047}, {41.866885, 56.7355037}}, |
| |
| {{18.1312339, 31.6473732}, {95.5711034, 63.5350219}, {92.3283165, 62.0158945}, {18.5656052, 32.1268808}}, |
| {{97.402018, 35.7169972}, {33.1127443, 25.8935163}, {1.13970027, 54.9424981}, {56.4860195, 60.529264}}, |
| }; |
| |
| const size_t testSetCount = sizeof(testSet) / sizeof(testSet[0]); |
| |
| static const Cubic newTestSet[] = { |
| {{1,3}, {5,6}, {5,3}, {5,4}}, |
| {{3,5}, {4,5}, {3,1}, {6,5}}, |
| |
| {{0,5}, {0,5}, {5,4}, {6,4}}, |
| {{4,5}, {4,6}, {5,0}, {5,0}}, |
| |
| {{0,4}, {1,3}, {5,4}, {4,2}}, |
| {{4,5}, {2,4}, {4,0}, {3,1}}, |
| |
| {{0,2}, {1,5}, {3,2}, {4,1}}, |
| {{2,3}, {1,4}, {2,0}, {5,1}}, |
| |
| {{0,2}, {2,3}, {5,1}, {3,2}}, |
| {{1,5}, {2,3}, {2,0}, {3,2}}, |
| |
| {{2,6}, {4,5}, {1,0}, {6,1}}, |
| {{0,1}, {1,6}, {6,2}, {5,4}}, |
| |
| {{0,1}, {1,2}, {6,5}, {5,4}}, |
| {{5,6}, {4,5}, {1,0}, {2,1}}, |
| |
| {{2.5119999999999996, 1.5710000000000002}, {2.6399999999999983, 1.6599999999999997}, {2.8000000000000007, 1.8000000000000003}, {3, 2}}, |
| {{2.4181876227114887, 1.9849772580462195}, {2.8269904869227211, 2.009330650246834}, {3.2004679292461624, 1.9942047174679169}, {3.4986199496818058, 2.0035994597094731}}, |
| |
| {{2,3}, {1,4}, {1,0}, {6,0}}, |
| {{0,1}, {0,6}, {3,2}, {4,1}}, |
| |
| {{0,2}, {1,5}, {1,0}, {6,1}}, |
| {{0,1}, {1,6}, {2,0}, {5,1}}, |
| |
| {{0,1}, {1,5}, {2,1}, {4,0}}, |
| {{1,2}, {0,4}, {1,0}, {5,1}}, |
| |
| {{0,1}, {3,5}, {2,1}, {3,1}}, |
| {{1,2}, {1,3}, {1,0}, {5,3}}, |
| |
| {{0,1}, {2,5}, {6,0}, {5,3}}, |
| {{0,6}, {3,5}, {1,0}, {5,2}}, |
| |
| {{0,1}, {3,6}, {1,0}, {5,2}}, |
| {{0,1}, {2,5}, {1,0}, {6,3}}, |
| |
| {{1,2},{5,6},{1,0},{1,0}}, |
| {{0,1},{0,1},{2,1},{6,5}}, |
| |
| {{0,6},{1,2},{1,0},{1,0}}, |
| {{0,1},{0,1},{6,0},{2,1}}, |
| |
| {{0,2},{0,1},{3,0},{1,0}}, |
| {{0,3},{0,1},{2,0},{1,0}}, |
| }; |
| |
| const size_t newTestSetCount = sizeof(newTestSet) / sizeof(newTestSet[0]); |
| |
| #if 0 |
| static void oneOff(const Cubic& cubic1, const Cubic& cubic2) { |
| SkTDArray<Quadratic> quads1; |
| cubic_to_quadratics(cubic1, calcPrecision(cubic1), quads1); |
| #if SHOW_ORIGINAL |
| SkDebugf("computed quadratics given\n"); |
| SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}, {%1.9g,%1.9g}},\n", |
| cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y, |
| cubic1[2].x, cubic1[2].y, cubic1[3].x, cubic1[3].y)); |
| SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}, {%1.9g,%1.9g}},\n", |
| cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y, |
| cubic2[2].x, cubic2[2].y, cubic2[3].x, cubic2[3].y)); |
| #endif |
| #if ONE_OFF_DEBUG |
| SkDebugf("computed quadratics set 1\n"); |
| for (int index = 0; index < quads1.count(); ++index) { |
| const Quadratic& q = quads1[index]; |
| SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y, |
| q[1].x, q[1].y, q[2].x, q[2].y); |
| } |
| #endif |
| SkTDArray<Quadratic> quads2; |
| cubic_to_quadratics(cubic2, calcPrecision(cubic2), quads2); |
| #if ONE_OFF_DEBUG |
| SkDebugf("computed quadratics set 2\n"); |
| for (int index = 0; index < quads2.count(); ++index) { |
| const Quadratic& q = quads2[index]; |
| SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y, |
| q[1].x, q[1].y, q[2].x, q[2].y); |
| } |
| #endif |
| Intersections intersections2, intersections3; |
| intersect2(cubic1, cubic2, intersections2); |
| intersect3(cubic1, cubic2, intersections3); |
| int pt1, pt2, pt3; |
| bool found; |
| double tt1, tt2, last = -1; |
| _Point xy1, xy2; |
| for (pt1 = 0; pt1 < intersections2.used(); ++pt1) { |
| tt1 = intersections2.fT[0][pt1]; |
| SkASSERT(!approximately_equal(last, tt1)); |
| last = tt1; |
| xy_at_t(cubic1, tt1, xy1.x, xy1.y); |
| pt2 = intersections2.fFlip ? intersections2.used() - pt1 - 1 : pt1; |
| tt2 = intersections2.fT[1][pt2]; |
| xy_at_t(cubic2, tt2, xy2.x, xy2.y); |
| #if ONE_OFF_DEBUG |
| SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n", |
| __FUNCTION__, tt1, xy1.x, xy1.y, intersections2.fPt[pt1].x, |
| intersections2.fPt[pt1].y, xy2.x, xy2.y, tt2); |
| #endif |
| SkASSERT(xy1.approximatelyEqual(xy2)); |
| #if SK_DEBUG |
| found = false; |
| for (pt3 = 0; pt3 < intersections3.used(); ++pt3) { |
| if (roughly_equal(tt1, intersections3.fT[0][pt3])) { |
| found = true; |
| break; |
| } |
| } |
| SkASSERT(found); |
| #endif |
| } |
| last = -1; |
| for (pt3 = 0; pt3 < intersections3.used(); ++pt3) { |
| found = false; |
| double tt3 = intersections3.fT[0][pt3]; |
| SkASSERT(!approximately_equal(last, tt3)); |
| last = tt3; |
| for (pt1 = 0; pt1 < intersections2.used(); ++pt1) { |
| if (approximately_equal(tt3, intersections2.fT[0][pt1])) { |
| found = true; |
| break; |
| } |
| } |
| if (!found) { |
| tt1 = intersections3.fT[0][pt3]; |
| xy_at_t(cubic1, tt1, xy1.x, xy1.y); |
| pt2 = intersections3.fFlip ? intersections3.used() - pt3 - 1 : pt3; |
| tt2 = intersections3.fT[1][pt2]; |
| xy_at_t(cubic2, tt2, xy2.x, xy2.y); |
| #if ONE_OFF_DEBUG |
| SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n", |
| __FUNCTION__, tt1, xy1.x, xy1.y, intersections3.fPt[pt1].x, |
| intersections3.fPt[pt1].y, xy2.x, xy2.y, tt2); |
| #endif |
| SkASSERT(xy1.approximatelyEqual(xy2)); |
| SkDebugf("%s missing in intersect2\n", __FUNCTION__); |
| } |
| } |
| } |
| #endif |
| |
| static void oneOff3(const Cubic& cubic1, const Cubic& cubic2) { |
| #if ONE_OFF_DEBUG |
| SkDebugf("computed quadratics given\n"); |
| SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", |
| cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y, |
| cubic1[2].x, cubic1[2].y, cubic1[3].x, cubic1[3].y); |
| SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", |
| cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y, |
| cubic2[2].x, cubic2[2].y, cubic2[3].x, cubic2[3].y); |
| #endif |
| SkTDArray<Quadratic> quads1; |
| cubic_to_quadratics(cubic1, calcPrecision(cubic1), quads1); |
| #if ONE_OFF_DEBUG |
| SkDebugf("computed quadratics set 1\n"); |
| for (int index = 0; index < quads1.count(); ++index) { |
| const Quadratic& q = quads1[index]; |
| SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y, |
| q[1].x, q[1].y, q[2].x, q[2].y); |
| } |
| #endif |
| SkTDArray<Quadratic> quads2; |
| cubic_to_quadratics(cubic2, calcPrecision(cubic2), quads2); |
| #if ONE_OFF_DEBUG |
| SkDebugf("computed quadratics set 2\n"); |
| for (int index = 0; index < quads2.count(); ++index) { |
| const Quadratic& q = quads2[index]; |
| SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].x, q[0].y, |
| q[1].x, q[1].y, q[2].x, q[2].y); |
| } |
| #endif |
| Intersections intersections3; |
| intersect3(cubic1, cubic2, intersections3); |
| int pt2, pt3; |
| double tt1, tt2, last = -1; |
| _Point xy1, xy2; |
| for (pt3 = 0; pt3 < intersections3.used(); ++pt3) { |
| double tt3 = intersections3.fT[0][pt3]; |
| // SkASSERT(!approximately_equal(last, tt3)); |
| last = tt3; |
| tt1 = intersections3.fT[0][pt3]; |
| xy_at_t(cubic1, tt1, xy1.x, xy1.y); |
| pt2 = intersections3.fFlip ? intersections3.used() - pt3 - 1 : pt3; |
| tt2 = intersections3.fT[1][pt2]; |
| xy_at_t(cubic2, tt2, xy2.x, xy2.y); |
| #if ONE_OFF_DEBUG |
| SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n", |
| __FUNCTION__, tt1, xy1.x, xy1.y, intersections3.fPt[pt3].x, |
| intersections3.fPt[pt3].y, xy2.x, xy2.y, tt2); |
| #endif |
| SkASSERT(xy1.approximatelyEqual(xy2)); |
| } |
| } |
| |
| #if 0 |
| static int fails[][2] = { {0, 23}, // fails in intersect2 recursing |
| {2, 7}, // answers differ, but neither is correct ('3' is closer) |
| {3, 26}, // fails in intersect2 recursing |
| {4, 9}, // fails in intersect2 recursing |
| {4, 10}, // fails in intersect2 recursing |
| {10, 17}, // fails in intersect2 recursing |
| {12, 14}, // loops indefinitely |
| {12, 21}, // fails in intersect2 recursing |
| {13, 21}, // fails in intersect2 recursing |
| {14, 21}, // fails in intersect2 recursing |
| {17, 25}, // fails in intersect2 recursing |
| {23, 25}, // fails in intersect2 recursing |
| }; |
| |
| static int failCount = sizeof(fails) / sizeof(fails[0]); |
| #endif |
| |
| static void oneOff(int outer, int inner) { |
| const Cubic& cubic1 = testSet[outer]; |
| const Cubic& cubic2 = testSet[inner]; |
| #if 0 |
| bool failing = false; |
| for (int i = 0; i < failCount; ++i) { |
| if ((fails[i][0] == outer && fails[i][1] == inner) |
| || (fails[i][1] == outer && fails[i][0] == inner)) { |
| failing = true; |
| break; |
| } |
| } |
| if (!failing) { |
| oneOff(cubic1, cubic2); |
| } else { |
| #endif |
| oneOff3(cubic1, cubic2); |
| // } |
| } |
| |
| void CubicIntersection_OneOffTest() { |
| oneOff(0, 1); |
| } |
| |
| static void newOneOff(int outer, int inner) { |
| const Cubic& cubic1 = newTestSet[outer]; |
| const Cubic& cubic2 = newTestSet[inner]; |
| oneOff3(cubic1, cubic2); |
| } |
| |
| void CubicIntersection_NewOneOffTest() { |
| newOneOff(0, 1); |
| } |
| |
| static void oneOffTests() { |
| for (size_t outer = 0; outer < testSetCount - 1; ++outer) { |
| for (size_t inner = outer + 1; inner < testSetCount; ++inner) { |
| oneOff(outer, inner); |
| } |
| } |
| } |
| |
| void CubicIntersection_OneOffTests() { |
| oneOffTests(); |
| } |
| |
| #define DEBUG_CRASH 0 |
| |
| class CubicChopper { |
| public: |
| |
| // only finds one intersection |
| CubicChopper(const Cubic& c1, const Cubic& c2) |
| : cubic1(c1) |
| , cubic2(c2) |
| , depth(0) { |
| } |
| |
| bool intersect(double minT1, double maxT1, double minT2, double maxT2) { |
| Cubic sub1, sub2; |
| // FIXME: carry last subdivide and reduceOrder result with cubic |
| sub_divide(cubic1, minT1, maxT1, sub1); |
| sub_divide(cubic2, minT2, maxT2, sub2); |
| Intersections i; |
| intersect3(sub1, sub2, i); |
| if (i.used() == 0) { |
| return false; |
| } |
| double x1, y1, x2, y2; |
| t1 = minT1 + i.fT[0][0] * (maxT1 - minT1); |
| t2 = minT2 + i.fT[1][0] * (maxT2 - minT2); |
| xy_at_t(cubic1, t1, x1, y1); |
| xy_at_t(cubic2, t2, x2, y2); |
| if (AlmostEqualUlps(x1, x2) && AlmostEqualUlps(y1, y2)) { |
| return true; |
| } |
| double half1 = (minT1 + maxT1) / 2; |
| double half2 = (minT2 + maxT2) / 2; |
| ++depth; |
| bool result; |
| if (depth & 1) { |
| result = intersect(minT1, half1, minT2, maxT2) || intersect(half1, maxT1, minT2, maxT2) |
| || intersect(minT1, maxT1, minT2, half2) || intersect(minT1, maxT1, half2, maxT2); |
| } else { |
| result = intersect(minT1, maxT1, minT2, half2) || intersect(minT1, maxT1, half2, maxT2) |
| || intersect(minT1, half1, minT2, maxT2) || intersect(half1, maxT1, minT2, maxT2); |
| } |
| --depth; |
| return result; |
| } |
| |
| const Cubic& cubic1; |
| const Cubic& cubic2; |
| double t1; |
| double t2; |
| int depth; |
| }; |
| |
| #define TRY_OLD 0 // old way fails on test == 1 |
| |
| void CubicIntersection_RandTestOld() { |
| srand(0); |
| const int tests = 1000000; // 10000000; |
| double largestFactor = DBL_MAX; |
| for (int test = 0; test < tests; ++test) { |
| Cubic cubic1, cubic2; |
| for (int i = 0; i < 4; ++i) { |
| cubic1[i].x = (double) rand() / RAND_MAX * 100; |
| cubic1[i].y = (double) rand() / RAND_MAX * 100; |
| cubic2[i].x = (double) rand() / RAND_MAX * 100; |
| cubic2[i].y = (double) rand() / RAND_MAX * 100; |
| } |
| if (test == 2513) { // the pair crosses three times, but the quadratic approximation |
| continue; // only sees one -- should be OK to ignore the other two? |
| } |
| if (test == 12932) { // this exposes a weakness when one cubic touches the other but |
| continue; // does not touch the quad approximation. Captured in qc.htm as cubic15 |
| } |
| #if DEBUG_CRASH |
| char str[1024]; |
| sprintf(str, "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n" |
| "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n", |
| cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y, cubic1[2].x, cubic1[2].y, |
| cubic1[3].x, cubic1[3].y, |
| cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y, cubic2[2].x, cubic2[2].y, |
| cubic2[3].x, cubic2[3].y); |
| #endif |
| _Rect rect1, rect2; |
| rect1.setBounds(cubic1); |
| rect2.setBounds(cubic2); |
| bool boundsIntersect = rect1.left <= rect2.right && rect2.left <= rect2.right |
| && rect1.top <= rect2.bottom && rect2.top <= rect1.bottom; |
| Intersections i1, i2; |
| #if TRY_OLD |
| bool oldIntersects = intersect(cubic1, cubic2, i1); |
| #else |
| bool oldIntersects = false; |
| #endif |
| if (test == -1) { |
| SkDebugf("ready...\n"); |
| } |
| bool newIntersects = intersect3(cubic1, cubic2, i2); |
| if (!boundsIntersect && (oldIntersects || newIntersects)) { |
| #if DEBUG_CRASH |
| SkDebugf("%s %d unexpected intersection boundsIntersect=%d oldIntersects=%d" |
| " newIntersects=%d\n%s %s\n", __FUNCTION__, test, boundsIntersect, |
| oldIntersects, newIntersects, __FUNCTION__, str); |
| #endif |
| SkASSERT(0); |
| } |
| if (oldIntersects && !newIntersects) { |
| #if DEBUG_CRASH |
| SkDebugf("%s %d missing intersection oldIntersects=%d newIntersects=%d\n%s %s\n", |
| __FUNCTION__, test, oldIntersects, newIntersects, __FUNCTION__, str); |
| #endif |
| SkASSERT(0); |
| } |
| if (!oldIntersects && !newIntersects) { |
| continue; |
| } |
| if (i2.used() > 1) { |
| continue; |
| // just look at single intercepts for simplicity |
| } |
| Intersections self1, self2; // self-intersect checks |
| if (intersect(cubic1, self1)) { |
| continue; |
| } |
| if (intersect(cubic2, self2)) { |
| continue; |
| } |
| // binary search for range necessary to enclose real intersection |
| CubicChopper c(cubic1, cubic2); |
| bool result = c.intersect(0, 1, 0, 1); |
| if (!result) { |
| // FIXME: a failure here probably means that a core routine used by CubicChopper is failing |
| continue; |
| } |
| double delta1 = fabs(c.t1 - i2.fT[0][0]); |
| double delta2 = fabs(c.t2 - i2.fT[1][0]); |
| double calc1 = calcPrecision(cubic1); |
| double calc2 = calcPrecision(cubic2); |
| double factor1 = calc1 / delta1; |
| double factor2 = calc2 / delta2; |
| SkDebugf("%s %d calc1=%1.9g delta1=%1.9g factor1=%1.9g calc2=%1.9g delta2=%1.9g" |
| " factor2=%1.9g\n", __FUNCTION__, test, |
| calc1, delta1, factor1, calc2, delta2, factor2); |
| if (factor1 < largestFactor) { |
| SkDebugf("WE HAVE A WINNER! %1.9g\n", factor1); |
| #if DEBUG_CRASH |
| SkDebugf("%s\n", str); |
| #endif |
| oneOff3(cubic1, cubic2); |
| largestFactor = factor1; |
| } |
| if (factor2 < largestFactor) { |
| SkDebugf("WE HAVE A WINNER! %1.9g\n", factor2); |
| #if DEBUG_CRASH |
| SkDebugf("%s\n", str); |
| #endif |
| oneOff3(cubic1, cubic2); |
| largestFactor = factor2; |
| } |
| } |
| } |
| |
| void CubicIntersection_RandTest() { |
| srand(0); |
| const int tests = 10000000; |
| for (int test = 0; test < tests; ++test) { |
| Cubic cubic1, cubic2; |
| for (int i = 0; i < 4; ++i) { |
| cubic1[i].x = (double) rand() / RAND_MAX * 100; |
| cubic1[i].y = (double) rand() / RAND_MAX * 100; |
| cubic2[i].x = (double) rand() / RAND_MAX * 100; |
| cubic2[i].y = (double) rand() / RAND_MAX * 100; |
| } |
| #if DEBUG_CRASH |
| char str[1024]; |
| sprintf(str, "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n" |
| "{{%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}, {%1.9g, %1.9g}},\n", |
| cubic1[0].x, cubic1[0].y, cubic1[1].x, cubic1[1].y, cubic1[2].x, cubic1[2].y, |
| cubic1[3].x, cubic1[3].y, |
| cubic2[0].x, cubic2[0].y, cubic2[1].x, cubic2[1].y, cubic2[2].x, cubic2[2].y, |
| cubic2[3].x, cubic2[3].y); |
| #endif |
| _Rect rect1, rect2; |
| rect1.setBounds(cubic1); |
| rect2.setBounds(cubic2); |
| bool boundsIntersect = rect1.left <= rect2.right && rect2.left <= rect2.right |
| && rect1.top <= rect2.bottom && rect2.top <= rect1.bottom; |
| if (test == -1) { |
| SkDebugf("ready...\n"); |
| } |
| Intersections intersections2; |
| bool newIntersects = intersect3(cubic1, cubic2, intersections2); |
| if (!boundsIntersect && newIntersects) { |
| #if DEBUG_CRASH |
| SkDebugf("%s %d unexpected intersection boundsIntersect=%d " |
| " newIntersects=%d\n%s %s\n", __FUNCTION__, test, boundsIntersect, |
| newIntersects, __FUNCTION__, str); |
| #endif |
| SkASSERT(0); |
| } |
| for (int pt = 0; pt < intersections2.used(); ++pt) { |
| double tt1 = intersections2.fT[0][pt]; |
| _Point xy1, xy2; |
| xy_at_t(cubic1, tt1, xy1.x, xy1.y); |
| int pt2 = intersections2.fFlip ? intersections2.used() - pt - 1 : pt; |
| double tt2 = intersections2.fT[1][pt2]; |
| xy_at_t(cubic2, tt2, xy2.x, xy2.y); |
| #if 0 |
| SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n", __FUNCTION__, |
| tt1, xy1.x, xy1.y, xy2.x, xy2.y, tt2); |
| #endif |
| SkASSERT(xy1.approximatelyEqual(xy2)); |
| } |
| } |
| } |
| |
| static void intersectionFinder(int index0, int index1, double t1Seed, double t2Seed, |
| double t1Step, double t2Step) { |
| const Cubic& cubic1 = newTestSet[index0]; |
| const Cubic& cubic2 = newTestSet[index1]; |
| _Point t1[3], t2[3]; |
| bool toggle = true; |
| do { |
| xy_at_t(cubic1, t1Seed - t1Step, t1[0].x, t1[0].y); |
| xy_at_t(cubic1, t1Seed, t1[1].x, t1[1].y); |
| xy_at_t(cubic1, t1Seed + t1Step, t1[2].x, t1[2].y); |
| xy_at_t(cubic2, t2Seed - t2Step, t2[0].x, t2[0].y); |
| xy_at_t(cubic2, t2Seed, t2[1].x, t2[1].y); |
| xy_at_t(cubic2, t2Seed + t2Step, t2[2].x, t2[2].y); |
| double dist[3][3]; |
| dist[1][1] = t1[1].distance(t2[1]); |
| int best_i = 1, best_j = 1; |
| for (int i = 0; i < 3; ++i) { |
| for (int j = 0; j < 3; ++j) { |
| if (i == 1 && j == 1) { |
| continue; |
| } |
| dist[i][j] = t1[i].distance(t2[j]); |
| if (dist[best_i][best_j] > dist[i][j]) { |
| best_i = i; |
| best_j = j; |
| } |
| } |
| } |
| if (best_i == 0) { |
| t1Seed -= t1Step; |
| } else if (best_i == 2) { |
| t1Seed += t1Step; |
| } |
| if (best_j == 0) { |
| t2Seed -= t2Step; |
| } else if (best_j == 2) { |
| t2Seed += t2Step; |
| } |
| if (best_i == 1 && best_j == 1) { |
| if ((toggle ^= true)) { |
| t1Step /= 2; |
| } else { |
| t2Step /= 2; |
| } |
| } |
| } while (!t1[1].approximatelyEqual(t2[1])); |
| t1Step = t2Step = 0.1; |
| double t10 = t1Seed - t1Step * 2; |
| double t12 = t1Seed + t1Step * 2; |
| double t20 = t2Seed - t2Step * 2; |
| double t22 = t2Seed + t2Step * 2; |
| _Point test; |
| while (!approximately_zero(t1Step)) { |
| xy_at_t(cubic1, t10, test.x, test.y); |
| t10 += t1[1].approximatelyEqual(test) ? -t1Step : t1Step; |
| t1Step /= 2; |
| } |
| t1Step = 0.1; |
| while (!approximately_zero(t1Step)) { |
| xy_at_t(cubic1, t12, test.x, test.y); |
| t12 -= t1[1].approximatelyEqual(test) ? -t1Step : t1Step; |
| t1Step /= 2; |
| } |
| while (!approximately_zero(t2Step)) { |
| xy_at_t(cubic2, t20, test.x, test.y); |
| t20 += t2[1].approximatelyEqual(test) ? -t2Step : t2Step; |
| t2Step /= 2; |
| } |
| t2Step = 0.1; |
| while (!approximately_zero(t2Step)) { |
| xy_at_t(cubic2, t22, test.x, test.y); |
| t22 -= t2[1].approximatelyEqual(test) ? -t2Step : t2Step; |
| t2Step /= 2; |
| } |
| #if ONE_OFF_DEBUG |
| SkDebugf("%s t1=(%1.9g<%1.9g<%1.9g) t2=(%1.9g<%1.9g<%1.9g)\n", __FUNCTION__, |
| t10, t1Seed, t12, t20, t2Seed, t22); |
| _Point p10 = xy_at_t(cubic1, t10); |
| _Point p1Seed = xy_at_t(cubic1, t1Seed); |
| _Point p12 = xy_at_t(cubic1, t12); |
| SkDebugf("%s p1=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__, |
| p10.x, p10.y, p1Seed.x, p1Seed.y, p12.x, p12.y); |
| _Point p20 = xy_at_t(cubic2, t20); |
| _Point p2Seed = xy_at_t(cubic2, t2Seed); |
| _Point p22 = xy_at_t(cubic2, t22); |
| SkDebugf("%s p2=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__, |
| p20.x, p20.y, p2Seed.x, p2Seed.y, p22.x, p22.y); |
| #endif |
| } |
| |
| void CubicIntersection_IntersectionFinder() { |
| |
| // double t1Seed = 0.87; |
| // double t2Seed = 0.87; |
| double t1Step = 0.000001; |
| double t2Step = 0.000001; |
| intersectionFinder(0, 1, 0.855895664, 0.864850875, t1Step, t2Step); |
| intersectionFinder(0, 1, 0.865207906, 0.865207887, t1Step, t2Step); |
| intersectionFinder(0, 1, 0.865213351, 0.865208087, t1Step, t2Step); |
| } |
| |
| static void coincidentTest() { |
| #if 0 |
| Cubic cubic1 = {{0, 1}, {0, 2}, {1, 0}, {1, 0}}; |
| Cubic cubic2 = {{0, 1}, {0, 2}, {1, 0}, {6, 1}}; |
| #endif |
| } |
| |
| void CubicIntersection_SelfTest() { |
| const Cubic selfSet[] = { |
| {{0,2}, {2,3}, {5,1}, {3,2}}, |
| {{0,2}, {3,5}, {5,0}, {4,2}}, |
| {{3.34,8.98}, {1.95,10.27}, {3.76,7.65}, {4.96,10.64}}, |
| {{3.13,2.74}, {1.08,4.62}, {3.71,0.94}, {2.01,3.81}}, |
| {{6.71,3.14}, {7.99,2.75}, {8.27,1.96}, {6.35,3.57}}, |
| {{12.81,7.27}, {7.22,6.98}, {12.49,8.97}, {11.42,6.18}}, |
| }; |
| size_t selfSetCount = sizeof(selfSet) / sizeof(selfSet[0]); |
| size_t firstFail = 1; |
| for (size_t index = firstFail; index < selfSetCount; ++index) { |
| const Cubic& cubic = selfSet[index]; |
| #if ONE_OFF_DEBUG |
| int idx2; |
| double max[3]; |
| int ts = find_cubic_max_curvature(cubic, max); |
| for (idx2 = 0; idx2 < ts; ++idx2) { |
| SkDebugf("%s max[%d]=%1.9g (%1.9g, %1.9g)\n", __FUNCTION__, idx2, |
| max[idx2], xy_at_t(cubic, max[idx2]).x, xy_at_t(cubic, max[idx2]).y); |
| } |
| SkTDArray<double> ts1; |
| SkTDArray<Quadratic> quads1; |
| cubic_to_quadratics(cubic, calcPrecision(cubic), ts1); |
| for (idx2 = 0; idx2 < ts1.count(); ++idx2) { |
| SkDebugf("%s t[%d]=%1.9g\n", __FUNCTION__, idx2, ts1[idx2]); |
| } |
| cubic_to_quadratics(cubic, calcPrecision(cubic), quads1); |
| for (idx2 = 0; idx2 < quads1.count(); ++idx2) { |
| const Quadratic& q = quads1[idx2]; |
| SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", |
| q[0].x, q[0].y, q[1].x, q[1].y, q[2].x, q[2].y); |
| } |
| SkDebugf("\n"); |
| #endif |
| Intersections i; |
| SkDEBUGCODE(int result = ) intersect(cubic, i); |
| SkASSERT(result == 1); |
| SkASSERT(i.used() == 1); |
| SkASSERT(!approximately_equal(i.fT[0][0], i.fT[1][0])); |
| _Point pt1 = xy_at_t(cubic, i.fT[0][0]); |
| _Point pt2 = xy_at_t(cubic, i.fT[1][0]); |
| SkASSERT(pt1.approximatelyEqual(pt2)); |
| } |
| } |
| |
| void CubicIntersection_Test() { |
| oneOffTests(); |
| coincidentTest(); |
| standardTestCases(); |
| } |
