experimental/Intersection/QuadraticIntersection_Test.cpp - Issue 867213004: remove prototype pathops code

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Issue 867213004: remove prototype pathops code (Closed) Base URL: https://skia.googlesource.com/skia.git@master

Patch Set: Created 5 years, 10 months ago

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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 "Intersection_Tests.h"

10 #include "Intersections.h"

11 #include "LineIntersection.h"

12 #include "QuadraticIntersection_TestData.h"

13 #include "QuadraticUtilities.h"

14 #include "TestUtilities.h"

15

16 const int firstQuadIntersectionTest = 9;

17

18 static void standardTestCases() {

19 for (size_t index = firstQuadIntersectionTest; index < quadraticTests_count; ++index) {

20 const Quadratic& quad1 = quadraticTests[index][0];

21 const Quadratic& quad2 = quadraticTests[index][1];

22 Quadratic reduce1, reduce2;

23 int order1 = reduceOrder(quad1, reduce1, kReduceOrder_TreatAsFill);

24 int order2 = reduceOrder(quad2, reduce2, kReduceOrder_TreatAsFill);

25 if (order1 < 3) {

26 printf("[%d] quad1 order=%d\n", (int) index, order1);

27 }

28 if (order2 < 3) {

29 printf("[%d] quad2 order=%d\n", (int) index, order2);

30 }

31 if (order1 == 3 && order2 == 3) {

32 Intersections intersections;

33 intersect2(reduce1, reduce2, intersections);

34 if (intersections.intersected()) {

35 for (int pt = 0; pt < intersections.used(); ++pt) {

36 double tt1 = intersections.fT[0][pt];

37 double tx1, ty1;

38 xy_at_t(quad1, tt1, tx1, ty1);

39 double tt2 = intersections.fT[1][pt];

40 double tx2, ty2;

41 xy_at_t(quad2, tt2, tx2, ty2);

42 if (!approximately_equal(tx1, tx2)) {

43 printf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",

44 __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx 2, ty2);

45 }

46 if (!approximately_equal(ty1, ty2)) {

47 printf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n",

48 __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx 2, ty2);

49 }

50 }

51 }

52 }

53 }

54 }

55

56 static const Quadratic testSet[] = {

57 {{3.0774019473063863, 3.35198509346713}, {3.0757503498668397, 3.327320623945933} , {3.0744102085015879, 3.3025879417907196}},

58 {{3.053913680774329, 3.3310471586283938}, {3.0758730889691694, 3.327346607037015 2}, {3.0975671980059394, 3.3235031316554351}},

59

60 {{3.39068129,4.44939202}, {3.03659239,3.81843234}, {3.06844529,3.02100922}},

61 {{2.10714698,3.44196686}, {3.12180288,3.38575704}, {3.75968569,3.1281838}},

62

63 {{2.74792918,4.77711896}, {2.82236867,4.23882547}, {2.82848144,3.63729341}},

64 {{2.62772567,3.64823958}, {3.46652495,3.64258364}, {4.1425079,3.48623815}},

65

66 {{1.34375,2.03125}, {2.2734375,2.6640625}, {3.25,3.25}},

67 {{3.96875,4.65625}, {3.3359375,3.7265625}, {2.75,2.75}},

68

69 {{0,1}, {0.324417544,2.27953848}, {0.664376547,2.58940267}},

70 {{1,2}, {0.62109375,2.70703125}, {0.640625,2.546875}},

71

72 {{1,2}, {0.984375,2.3359375}, {1.0625,2.15625}},

73 {{0,1}, {0.983539095,2.30041152}, {1.47325103,2.61316872}},

74

75 {{4.09011926,2.20971038}, {4.74608133,1.9335932}, {5.02469918,2.00694987}},

76 {{2.79472921,1.73568666}, {3.36246373,1.21251209}, {5,2}},

77

78 {{1.80814127,2.41537795}, {2.23475077,2.05922313}, {3.16529668,1.98358763}},

79 {{2.16505631,2.55782454}, {2.40541285,2.02193091}, {2.99836023,1.68247638}},

80

81 {{3, 1.875}, {3.375, 1.54296875}, {3.375, 1.421875}},

82 {{3.375, 1.421875}, {3.3749999999999996, 1.3007812499999998}, {3, 2}},

83

84 {{3.34,8.98}, {2.83363281,9.4265625}, {2.83796875,9.363125}},

85 {{2.83796875,9.363125}, {2.84230469,9.2996875}, {3.17875,9.1725}},

86

87 {{2.7279999999999998, 3.024}, {2.5600000000000005, 2.5600000000000005}, {2.15200 00000000001, 1.8560000000000001}},

88 {{0.66666666666666652, 1.1481481481481481}, {1.3333333333333326, 1.3333333333333 335}, {2.6666666666666665, 2.1851851851851851}},

89

90 {{2.728,3.024}, {2.56,2.56}, {2.152,1.856}},

91 {{0.666666667,1.14814815}, {1.33333333,1.33333333}, {2.66666667,2.18518519}},

92

93 {{0.875,1.5}, {1.03125,1.11022302e-16}, {1,0}},

94 {{0.875,0.859375}, {1.6875,0.73046875}, {2.5,0.625}},

95

96 {{1.64451042,0.0942001592}, {1.53635465,0.00152863961}, {1,0}},

97 {{1.27672209,0.15}, {1.32143477,9.25185854e-17}, {1,0}},

98

99 {{0, 0}, {0.51851851851851849, 1.0185185185185186}, {1.2592592592592591, 1.92592 59259259258}},

100 {{1.2592592592592593, 1.9259259259259265}, {0.51851851851851893, 1.0185185185185 195}, {0, 0}},

101

102 {{1.93281168,2.58856757}, {2.38543691,2.7096125}, {2.51967352,2.34531784}},

103 {{2.51967352,2.34531784}, {2.65263731,2.00639194}, {3.1212119,1.98608967}},

104 {{2.09544533,2.51981963}, {2.33331524,2.25252128}, {2.92003302,2.39442311}},

105

106

107 {{0.924337655,1.94072717}, {1.25185043,1.52836494}, {1.71793901,1.06149951}},

108 {{0.940798831,1.67439357}, {1.25988251,1.39778567}, {1.71791672,1.06650313}},

109

110 {{0.924337655,1.94072717}, {1.39158994,1.32418496}, {2.14967426,0.687365435}},

111 {{0.940798831,1.67439357}, {1.48941875,1.16280321}, {2.47884711,0.60465921}},

112

113 {{1.7465749139282332,1.9930452039527999}, {1.8320006564080331,1.85948134518908 9}, {1.8731035127758437,1.6344055934266613}},

114 {{1.8731035127758437,1.6344055934266613}, {1.89928170345231,1.5006405518943067 }, {1.9223833226085514,1.3495796165215643}},

115 {{1.74657491,1.9930452}, {1.87407679,1.76762853}, {1.92238332,1.34957962}},

116 {{0.60797907,1.68776977}, {1.0447864,1.50810914}, {1.87464474,1.63655092}},

117 {{1.87464474,1.63655092}, {2.70450308,1.76499271}, {4,3}},

118

119 {{1.2071879545809394,0.82163474041730045}, {1.1534203513372994,0.527908700699302 29}, {1.0880000000000001,0.29599999999999982}}, //t=0.63155333662549329,0.800000 00000000004

120 {{0.33333333333333326,0.81481481481481488}, {0.63395173631977997,0.6874413672631 3931}, {1.205684411948591,0.81344322326274499}},

121 {{0.33333333333333326,0.81481481481481488}, {0.63396444791444551,0.6874336836244 4768}, {1.205732763658403,0.81345617746834109}},//t=0.33333333333333331,0.633964 44791444551

122 {{1.205684411948591,0.81344322326274499}, {1.2057085875611198,0.8134496999932925 3}, {1.205732763658403,0.81345617746834109}},

123

124 {{1.20718795,0.82163474}, {1.15342035,0.527908701}, {1.088,0.296}},

125 {{1.20568441,0.813443223}, {1.20570859,0.8134497}, {1.20573276,0.813456177}},

126

127 {{41.5072916,87.1234036}, {28.2747836,80.9545395}, {23.5780771,69.3344126}},

128 {{72.9633878,95.6593007}, {42.7738746,88.4730382}, {31.1932785,80.2458029}},

129

130 {{31.1663962,54.7302484}, {31.1662882,54.7301074}, {31.1663969,54.7302485}},

131 {{26.0404936,45.4260361}, {27.7887523,33.1863051}, {40.8833242,26.0301855}},

132

133 {{29.9404074,49.1672596}, {44.3131071,45.3915253}, {58.1067559,59.5061814}},

134 {{72.6510251,64.2972928}, {53.6989659,60.1862397}, {35.2053722,44.8391126}},

135

136 {{52.14807018377202, 65.012420045148644}, {44.778669050208237, 66.31556270560437 8}, {51.619118408823567, 63.787827046262684}},

137 {{30.004993234763383, 93.921296668202288}, {53.384822003076991, 60.7321803418027 53}, {58.652998934338584, 43.111073088306185}},

138

139 {{80.897794748143198, 49.236332042718459}, {81.082078218891212, 64.0667499044886 31}, {69.972305057149981, 72.968595519850993}},

140 {{72.503745601281395, 32.952320736577882}, {88.030880716061645, 38.1371948478101 64}, {73.193774825517906, 67.773492479591397}},

141

142 {{67.426548091427676, 37.993772624988935}, {51.129513170665035, 57.5422812345636 46}, {44.594748190899189, 65.644267382683879}},

143 {{61.336508189019057, 82.693132843213675}, {54.825078921449354, 71.6639327992124 32}, {47.727444217558926, 61.4049645128392}},

144

145 {{67.4265481,37.9937726}, {51.1295132,57.5422812}, {44.5947482,65.6442674}},

146 {{61.3365082,82.6931328}, {54.8250789,71.6639328}, {47.7274442,61.4049645}},

147

148 {{53.774852327053594, 53.318060789841951}, {45.787877803416805, 51.3934920262849 81}, {46.703936967162392, 53.06860709822206}},

149 {{46.703936967162392, 53.06860709822206}, {47.619996130907957, 54.74372217015916 }, {53.020051653535361, 48.633140968832024}},

150

151 {{50.934805397717923, 51.52391952648901}, {56.803308902971423, 44.24623461062759 6}, {69.776888596721406, 40.166645096692555}},

152 {{50.230212796400401, 38.386469101526998}, {49.855620812184917, 38.8189903921536 09}, {56.356567496227363, 47.229909093319407}},

153

154 {{36.148792695174222, 70.336952793070424}, {36.141613037691357, 70.7116547398700 85}, {36.154708826402597, 71.088492662905836}},

155 {{35.216235592661825, 70.580199617313212}, {36.244476835123969, 71.0108977873040 74}, {37.230244263238326, 71.423156953613102}},

156

157 // this pair is nearly coincident, and causes the quartic code to produce bad

158 // data. Mathematica doesn't think they touch. Graphically, I can't tell.

159 // it may not be so bad to pretend that they don't touch, if I can detect that

160 {{369.848602,145.680267}, {382.360413,121.298294}, {406.207703,121.298294}},

161 {{369.850525,145.675964}, {382.362915,121.29287}, {406.211273,121.29287}},

162

163 {{33.567436351153468, 62.336347586395924}, {35.200980274619084, 65.0385614601444 79}, {36.479571811084995, 67.632178905412445}},

164 {{41.349524945572696, 67.886658677862641}, {39.125562529359087, 67.4297727351492 14}, {35.600314083992416, 66.705372160552685}},

165

166 {{67.25299631583178, 21.109080184767524}, {43.617595267398613, 33.65803416857752 9}, {33.38371819435676, 44.214192553988745}},

167 {{40.476838859398541, 39.543209911285999}, {36.701186108431131, 34.8817994016458 }, {30.102144288878023, 26.739063172945315}},

168

169 {{25.367434474345036, 50.4712103169743}, {17.865013304933097, 37.356741010559439 }, {16.818988838905465, 37.682915484123129}},

170 {{16.818988838905465, 37.682915484123129}, {15.772964372877833, 38.0090899576868 11}, {20.624104547604965, 41.825131596683121}},

171

172 {{26.440225044088567, 79.695009812848298}, {26.085525979582247, 83.7179283541347 84}, {27.075079976297072, 84.820633667838905}},

173 {{27.075079976297072, 84.820633667838905}, {28.276546859574015, 85.9885741840290 34}, {25.649263209500006, 87.166762066617025}},

174

175 {{34.879150914024962, 83.862726601601125}, {35.095810134304429, 83.6934732101695 43}, {35.359284111931586, 83.488069234177502}},

176 {{54.503204203015471, 76.094098492518242}, {51.366889541918894, 71.6098560612991 55}, {46.53086955445437, 69.949863036494207}},

177

178 {{0, 0}, {1, 0}, {0, 3}},

179 {{1, 0}, {0, 1}, {1, 1}},

180 {{369.961151,137.980698}, {383.970093,121.298294}, {406.213287,121.298294}},

181 {{353.2948,194.351074}, {353.2948,173.767563}, {364.167572,160.819855}},

182 {{360.416077,166.795715}, {370.126831,147.872162}, {388.635406,147.872162}},

183 {{406.236359,121.254936}, {409.445679,121.254936}, {412.975952,121.789818}},

184 {{406.235992,121.254936}, {425.705902,121.254936}, {439.71994,137.087616}},

185

186 {{369.8543701171875, 145.66734313964844}, {382.36788940429688, 121.2820358276367 2}, {406.21844482421875, 121.28203582763672}},

187 {{369.96469116210938, 137.96672058105469}, {383.97555541992188, 121.282035827636 72}, {406.2218017578125, 121.28203582763672}},

188

189 {{369.962311, 137.976044}, {383.971893, 121.29287}, {406.216125, 121.29287}} ,

190

191 {{400.121704, 149.468719}, {391.949493, 161.037186}, {391.949493, 181.202423 }},

192 {{391.946747, 181.839218}, {391.946747, 155.62442}, {406.115479, 138.855438} },

193 {{360.048828125, 229.2578125}, {360.048828125, 224.4140625}, {362.607421875, 221.3671875}},

194 {{362.607421875, 221.3671875}, {365.166015625, 218.3203125}, {369.228515625, 218.3203125}},

195 {{8, 8}, {10, 10}, {8, -10}},

196 {{8, 8}, {12, 12}, {14, 4}},

197 {{8, 8}, {9, 9}, {10, 8}}

198 };

199

200 const size_t testSetCount = sizeof(testSet) / sizeof(testSet[0]);

201

202 static void oneOffTest1(size_t outer, size_t inner) {

203 const Quadratic& quad1 = testSet[outer];

204 const Quadratic& quad2 = testSet[inner];

205 Intersections intersections2;

206 intersect2(quad1, quad2, intersections2);

207 if (intersections2.fUnsortable) {

208 SkASSERT(0);

209 return;

210 }

211 for (int pt = 0; pt < intersections2.used(); ++pt) {

212 double tt1 = intersections2.fT[0][pt];

213 double tx1, ty1;

214 xy_at_t(quad1, tt1, tx1, ty1);

215 int pt2 = intersections2.fFlip ? intersections2.used() - pt - 1 : pt;

216 double tt2 = intersections2.fT[1][pt2];

217 double tx2, ty2;

218 xy_at_t(quad2, tt2, tx2, ty2);

219 if (!AlmostEqualUlps(tx1, tx2)) {

220 SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",

221 __FUNCTION__, (int)outer, (int)inner, tt1, tx1, ty1, tt2, tx2, t y2);

222 SkASSERT(0);

223 }

224 if (!AlmostEqualUlps(ty1, ty2)) {

225 SkDebugf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n",

226 __FUNCTION__, (int)outer, (int)inner, tt1, tx1, ty1, tt2, tx2, t y2);

227 SkASSERT(0);

228 }

229 #if ONE_OFF_DEBUG

230 SkDebugf("%s [%d][%d] t1=%1.9g (%1.9g, %1.9g) t2=%1.9g\n", __FUNCTION__,

231 outer, inner, tt1, tx1, ty1, tt2);

232 #endif

233 }

234 }

235

236 void QuadraticIntersection_OneOffTest() {

237 oneOffTest1(0, 1);

238 oneOffTest1(1, 0);

239 }

240

241 static void oneOffTests() {

242 for (size_t outer = 0; outer < testSetCount - 1; ++outer) {

243 for (size_t inner = outer + 1; inner < testSetCount; ++inner) {

244 oneOffTest1(outer, inner);

245 }

246 }

247 }

248

249 static const Quadratic coincidentTestSet[] = {

250 {{369.850525, 145.675964}, {382.362915, 121.29287}, {406.211273, 121.29287}} ,

251 {{369.850525, 145.675964}, {382.362915, 121.29287}, {406.211273, 121.29287}} ,

252 {{8, 8}, {10, 10}, {8, -10}},

253 {{8, -10}, {10, 10}, {8, 8}},

254 };

255

256 const size_t coincidentTestSetCount = sizeof(coincidentTestSet) / sizeof(coincid entTestSet[0]);

257

258 static void coincidentTest() {

259 for (size_t testIndex = 0; testIndex < coincidentTestSetCount - 1; testIndex += 2) {

260 const Quadratic& quad1 = coincidentTestSet[testIndex];

261 const Quadratic& quad2 = coincidentTestSet[testIndex + 1];

262 Intersections intersections2;

263 intersect2(quad1, quad2, intersections2);

264 SkASSERT(intersections2.coincidentUsed() == 2);

265 SkASSERT(intersections2.used() == 2);

266 for (int pt = 0; pt < intersections2.coincidentUsed(); ++pt) {

267 SkDEBUGCODE(double tt1 = intersections2.fT[0][pt]);

268 SkDEBUGCODE(double tt2 = intersections2.fT[1][pt]);

269 SkASSERT(approximately_equal(1, tt1) \|\| approximately_zero(tt1));

270 SkASSERT(approximately_equal(1, tt2) \|\| approximately_zero(tt2));

271 }

272 }

273 }

274

275 void QuadraticIntersection_Test() {

276 oneOffTests();

277 coincidentTest();

278 standardTestCases();

279 }

280

281 static int floatSign(double x) {

282 return x < 0 ? -1 : x > 0 ? 1 : 0;

283 }

284

285 static const Quadratic pointFinderTestSet[] = {

286 //>=0.633974464 0.633974 846 <=

287 {{1.2071879545809394,0.82163474041730045}, {1.1534203513372994,0.527908700699302 29}, {1.0880000000000001,0.29599999999999982}}, //t=0.63155333662549329,0.800000 00000000004

288 {{1.2071879545809394,0.82163474041730045}, {1.2065040319428038,0.817667532591199 95}, {1.2058123269101506,0.81370135061854221}}, //t=0.63155333662549329,0.633904 9773632347

289 {{1.2058123269101506,0.81370135061854221}, {1.152376363978022,0.5244097415381026 }, {1.0880000000000001,0.29599999999999982}}, //t=0.6339049773632347, 0.800000 00000000004

290 //>=0.633974083 0.633975 227 <=

291 {{0.33333333333333326,0.81481481481481488}, {0.63395173631977997,0.6874413672631 3931}, {1.205684411948591,0.81344322326274499}},//t=0.33333333333333331,0.633951 73631977986

292 {{0.33333333333333326,0.81481481481481488}, {0.63396444791444551,0.6874336836244 4768}, {1.205732763658403,0.81345617746834109}},//t=0.33333333333333331,0.633964 44791444551

293 {{1.205684411948591,0.81344322326274499}, {1.2057085875611198,0.8134496999932925 3}, {1.205732763658403,0.81345617746834109}}, //t=0.63395173631977986,0.633964 44791444551

294 {{1.205732763658403,0.81345617746834109}, {1.267928895828891,0.83008534558465619 }, {1.3333333333333333,0.85185185185185175}}, //t=0.63396444791444551,0.666666 66666666663

295 };

296

297 static void pointFinder(const Quadratic& q1, const Quadratic& q2) {

298 for (int index = 0; index < 3; ++index) {

299 double t = nearestT(q1, q2[index]);

300 _Point onQuad;

301 xy_at_t(q1, t, onQuad.x, onQuad.y);

302 SkDebugf("%s t=%1.9g (%1.9g,%1.9g) dist=%1.9g\n", __FUNCTION__, t, onQua d.x, onQuad.y,

303 onQuad.distance(q2[index]));

304 double left[3];

305 left[0] = is_left((const _Line&) q1[0], q2[index]);

306 left[1] = is_left((const _Line&) q1[1], q2[index]);

307 _Line diag = {q1[0], q1[2]};

308 left[2] = is_left(diag, q2[index]);

309 SkDebugf("%s left=(%d, %d, %d) inHull=%s\n", __FUNCTION__, floatSign(lef t[0]),

310 floatSign(left[1]), floatSign(left[2]),

311 point_in_hull(q1, q2[index]) ? "true" : "false");

312 }

313 SkDebugf("\n");

314 }

315

316 static void hullIntersect(const Quadratic& q1, const Quadratic& q2) {

317 SkDebugf("%s", __FUNCTION__);

318 Intersections ts;

319 for (int i1 = 0; i1 < 3; ++i1) {

320 _Line l1 = {q1[i1], q1[(i1 + 1) % 3]};

321 for (int i2 = 0; i2 < 3; ++i2) {

322 _Line l2 = {q2[i2], q2[(i2 + 1) % 3]};

323 if (intersect(l1, l2, ts)) {

324 SkDebugf(" [%d,%d]", i1, i2);

325 }

326 }

327 }

328 SkDebugf("\n");

329 }

330

331 void QuadraticIntersection_PointFinder() {

332 pointFinder(pointFinderTestSet[0], pointFinderTestSet[4]);

333 pointFinder(pointFinderTestSet[4], pointFinderTestSet[0]);

334 pointFinder(pointFinderTestSet[0], pointFinderTestSet[6]);

335 pointFinder(pointFinderTestSet[6], pointFinderTestSet[0]);

336 hullIntersect(pointFinderTestSet[0], pointFinderTestSet[4]);

337 hullIntersect(pointFinderTestSet[0], pointFinderTestSet[6]);

338 }

339

340 static void intersectionFinder(int test1, int test2) {

341 const Quadratic& quad1 = testSet[test1];

342 const Quadratic& quad2 = testSet[test2];

343

344 double t1Seed = 0.5;

345 double t2Seed = 0.8;

346 double t1Step = 0.1;

347 double t2Step = 0.1;

348 _Point t1[3], t2[3];

349 bool toggle = true;

350 do {

351 xy_at_t(quad1, t1Seed - t1Step, t1[0].x, t1[0].y);

352 xy_at_t(quad1, t1Seed, t1[1].x, t1[1].y);

353 xy_at_t(quad1, t1Seed + t1Step, t1[2].x, t1[2].y);

354 xy_at_t(quad2, t2Seed - t2Step, t2[0].x, t2[0].y);

355 xy_at_t(quad2, t2Seed, t2[1].x, t2[1].y);

356 xy_at_t(quad2, t2Seed + t2Step, t2[2].x, t2[2].y);

357 double dist[3][3];

358 dist[1][1] = t1[1].distance(t2[1]);

359 int best_i = 1, best_j = 1;

360 for (int i = 0; i < 3; ++i) {

361 for (int j = 0; j < 3; ++j) {

362 if (i == 1 && j == 1) {

363 continue;

364 }

365 dist[i][j] = t1[i].distance(t2[j]);

366 if (dist[best_i][best_j] > dist[i][j]) {

367 best_i = i;

368 best_j = j;

369 }

370 }

371 }

372 if (best_i == 0) {

373 t1Seed -= t1Step;

374 } else if (best_i == 2) {

375 t1Seed += t1Step;

376 }

377 if (best_j == 0) {

378 t2Seed -= t2Step;

379 } else if (best_j == 2) {

380 t2Seed += t2Step;

381 }

382 if (best_i == 1 && best_j == 1) {

383 if ((toggle ^= true)) {

384 t1Step /= 2;

385 } else {

386 t2Step /= 2;

387 }

388 }

389 } while (!t1[1].approximatelyEqual(t2[1]));

390 t1Step = t2Step = 0.1;

391 double t10 = t1Seed - t1Step * 2;

392 double t12 = t1Seed + t1Step * 2;

393 double t20 = t2Seed - t2Step * 2;

394 double t22 = t2Seed + t2Step * 2;

395 _Point test;

396 while (!approximately_zero(t1Step)) {

397 xy_at_t(quad1, t10, test.x, test.y);

398 t10 += t1[1].approximatelyEqual(test) ? -t1Step : t1Step;

399 t1Step /= 2;

400 }

401 t1Step = 0.1;

402 while (!approximately_zero(t1Step)) {

403 xy_at_t(quad1, t12, test.x, test.y);

404 t12 -= t1[1].approximatelyEqual(test) ? -t1Step : t1Step;

405 t1Step /= 2;

406 }

407 while (!approximately_zero(t2Step)) {

408 xy_at_t(quad2, t20, test.x, test.y);

409 t20 += t2[1].approximatelyEqual(test) ? -t2Step : t2Step;

410 t2Step /= 2;

411 }

412 t2Step = 0.1;

413 while (!approximately_zero(t2Step)) {

414 xy_at_t(quad2, t22, test.x, test.y);

415 t22 -= t2[1].approximatelyEqual(test) ? -t2Step : t2Step;

416 t2Step /= 2;

417 }

418 #if ONE_OFF_DEBUG

419 SkDebugf("%s t1=(%1.9g<%1.9g<%1.9g) t2=(%1.9g<%1.9g<%1.9g)\n", __FUNCTION__,

420 t10, t1Seed, t12, t20, t2Seed, t22);

421 _Point p10 = xy_at_t(quad1, t10);

422 _Point p1Seed = xy_at_t(quad1, t1Seed);

423 _Point p12 = xy_at_t(quad1, t12);

424 SkDebugf("%s p1=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__,

425 p10.x, p10.y, p1Seed.x, p1Seed.y, p12.x, p12.y);

426 _Point p20 = xy_at_t(quad2, t20);

427 _Point p2Seed = xy_at_t(quad2, t2Seed);

428 _Point p22 = xy_at_t(quad2, t22);

429 SkDebugf("%s p2=(%1.9g,%1.9g)<(%1.9g,%1.9g)<(%1.9g,%1.9g)\n", __FUNCTION__,

430 p20.x, p20.y, p2Seed.x, p2Seed.y, p22.x, p22.y);

431 #endif

432 }

433

434 void QuadraticIntersection_IntersectionFinder() {

435 intersectionFinder(0, 1);

436 }

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