1 /* 2 * Copyright 2014 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 "PathOpsTestCommon.h" 8 #include "SkIntersections.h" 9 #include "SkPathOpsCubic.h" 10 #include "SkPathOpsLine.h" 11 #include "SkPathOpsQuad.h" 12 #include "SkRandom.h" 13 #include "SkReduceOrder.h" 14 #include "Test.h" 15 16 static bool gPathOpsCubicLineIntersectionIdeasVerbose = false; 17 18 static struct CubicLineFailures { 19 SkDCubic c; 20 double t; 21 SkDPoint p; 22 } cubicLineFailures[] = { 23 {{{{-164.3726806640625, 36.826904296875}, {-189.045166015625, -953.2220458984375}, 24 {926.505859375, -897.36175537109375}, {-139.33489990234375, 204.40771484375}}}, 25 0.37329583, {107.54935269006289, -632.13736293162208}}, 26 {{{{784.056884765625, -554.8350830078125}, {67.5489501953125, 509.0224609375}, 27 {-447.713134765625, 751.375}, {415.7784423828125, 172.22265625}}}, 28 0.660005242, {-32.973148967736151, 478.01341797403569}}, 29 {{{{-580.6834716796875, -127.044921875}, {-872.8983154296875, -945.54302978515625}, 30 {260.8092041015625, -909.34991455078125}, {-976.2125244140625, -18.46551513671875}}}, 31 0.578826774, {-390.17910153915489, -687.21144412296007}}, 32 }; 33 34 int cubicLineFailuresCount = (int) SK_ARRAY_COUNT(cubicLineFailures); 35 36 double measuredSteps[] = { 37 9.15910731e-007, 8.6600277e-007, 7.4122059e-007, 6.92087618e-007, 8.35290245e-007, 38 3.29763199e-007, 5.07547773e-007, 4.41294224e-007, 0, 0, 39 3.76879167e-006, 1.06126249e-006, 2.36873967e-006, 1.62421134e-005, 3.09103599e-005, 40 4.38917976e-005, 0.000112348938, 0.000243149242, 0.000433174114, 0.00170880232, 41 0.00272619724, 0.00518844604, 0.000352621078, 0.00175960064, 0.027875185, 42 0.0351329803, 0.103964925, 43 }; 44 45 /* last output : errors=3121 46 9.1796875e-007 8.59375e-007 7.5e-007 6.875e-007 8.4375e-007 47 3.125e-007 5e-007 4.375e-007 0 0 48 3.75e-006 1.09375e-006 2.1875e-006 1.640625e-005 3.0859375e-005 49 4.38964844e-005 0.000112304687 0.000243164063 0.000433181763 0.00170898437 50 0.00272619247 0.00518844604 0.000352621078 0.00175960064 0.027875185 51 0.0351329803 0.103964925 52 */ 53 54 static double binary_search(const SkDCubic& cubic, double step, const SkDPoint& pt, double t, 55 int* iters) { 56 double firstStep = step; 57 do { 58 *iters += 1; 59 SkDPoint cubicAtT = cubic.ptAtT(t); 60 if (cubicAtT.approximatelyEqual(pt)) { 61 break; 62 } 63 double calcX = cubicAtT.fX - pt.fX; 64 double calcY = cubicAtT.fY - pt.fY; 65 double calcDist = calcX * calcX + calcY * calcY; 66 if (step == 0) { 67 SkDebugf("binary search failed: step=%1.9g cubic=", firstStep); 68 cubic.dump(); 69 SkDebugf(" t=%1.9g ", t); 70 pt.dump(); 71 SkDebugf("\n"); 72 return -1; 73 } 74 double lastStep = step; 75 step /= 2; 76 SkDPoint lessPt = cubic.ptAtT(t - lastStep); 77 double lessX = lessPt.fX - pt.fX; 78 double lessY = lessPt.fY - pt.fY; 79 double lessDist = lessX * lessX + lessY * lessY; 80 // use larger x/y difference to choose step 81 if (calcDist > lessDist) { 82 t -= step; 83 t = SkTMax(0., t); 84 } else { 85 SkDPoint morePt = cubic.ptAtT(t + lastStep); 86 double moreX = morePt.fX - pt.fX; 87 double moreY = morePt.fY - pt.fY; 88 double moreDist = moreX * moreX + moreY * moreY; 89 if (calcDist <= moreDist) { 90 continue; 91 } 92 t += step; 93 t = SkTMin(1., t); 94 } 95 } while (true); 96 return t; 97 } 98 99 #if 0 100 static bool r2check(double A, double B, double C, double D, double* R2MinusQ3Ptr) { 101 if (approximately_zero(A) 102 && approximately_zero_when_compared_to(A, B) 103 && approximately_zero_when_compared_to(A, C) 104 && approximately_zero_when_compared_to(A, D)) { // we're just a quadratic 105 return false; 106 } 107 if (approximately_zero_when_compared_to(D, A) 108 && approximately_zero_when_compared_to(D, B) 109 && approximately_zero_when_compared_to(D, C)) { // 0 is one root 110 return false; 111 } 112 if (approximately_zero(A + B + C + D)) { // 1 is one root 113 return false; 114 } 115 double a, b, c; 116 { 117 double invA = 1 / A; 118 a = B * invA; 119 b = C * invA; 120 c = D * invA; 121 } 122 double a2 = a * a; 123 double Q = (a2 - b * 3) / 9; 124 double R = (2 * a2 * a - 9 * a * b + 27 * c) / 54; 125 double R2 = R * R; 126 double Q3 = Q * Q * Q; 127 double R2MinusQ3 = R2 - Q3; 128 *R2MinusQ3Ptr = R2MinusQ3; 129 return true; 130 } 131 #endif 132 133 /* What is the relationship between the accuracy of the root in range and the magnitude of all 134 roots? To find out, create a bunch of cubics, and measure */ 135 136 DEF_TEST(PathOpsCubicLineRoots, reporter) { 137 if (!gPathOpsCubicLineIntersectionIdeasVerbose) { // slow; exclude it by default 138 return; 139 } 140 SkRandom ran; 141 double worstStep[256] = {0}; 142 int errors = 0; 143 int iters = 0; 144 double smallestR2 = 0; 145 double largestR2 = 0; 146 for (int index = 0; index < 1000000000; ++index) { 147 SkDPoint origin = {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)}; 148 SkDCubic cubic = {{origin, 149 {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)}, 150 {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)}, 151 {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)} 152 }}; 153 // construct a line at a known intersection 154 double t = ran.nextRangeF(0, 1); 155 SkDPoint pt = cubic.ptAtT(t); 156 // skip answers with no intersections (although note the bug!) or two, or more 157 // see if the line / cubic has a fun range of roots 158 double A, B, C, D; 159 SkDCubic::Coefficients(&cubic[0].fY, &A, &B, &C, &D); 160 D -= pt.fY; 161 double allRoots[3] = {0}, validRoots[3] = {0}; 162 int realRoots = SkDCubic::RootsReal(A, B, C, D, allRoots); 163 int valid = SkDQuad::AddValidTs(allRoots, realRoots, validRoots); 164 if (valid != 1) { 165 continue; 166 } 167 if (realRoots == 1) { 168 continue; 169 } 170 t = validRoots[0]; 171 SkDPoint calcPt = cubic.ptAtT(t); 172 if (calcPt.approximatelyEqual(pt)) { 173 continue; 174 } 175 #if 0 176 double R2MinusQ3; 177 if (r2check(A, B, C, D, &R2MinusQ3)) { 178 smallestR2 = SkTMin(smallestR2, R2MinusQ3); 179 largestR2 = SkTMax(largestR2, R2MinusQ3); 180 } 181 #endif 182 double largest = SkTMax(fabs(allRoots[0]), fabs(allRoots[1])); 183 if (realRoots == 3) { 184 largest = SkTMax(largest, fabs(allRoots[2])); 185 } 186 int largeBits; 187 if (largest <= 1) { 188 #if 0 189 SkDebugf("realRoots=%d (%1.9g, %1.9g, %1.9g) valid=%d (%1.9g, %1.9g, %1.9g)\n", 190 realRoots, allRoots[0], allRoots[1], allRoots[2], valid, validRoots[0], 191 validRoots[1], validRoots[2]); 192 #endif 193 double smallest = SkTMin(allRoots[0], allRoots[1]); 194 if (realRoots == 3) { 195 smallest = SkTMin(smallest, allRoots[2]); 196 } 197 SK_ALWAYSBREAK(smallest < 0); 198 SK_ALWAYSBREAK(smallest >= -1); 199 largeBits = 0; 200 } else { 201 frexp(largest, &largeBits); 202 SK_ALWAYSBREAK(largeBits >= 0); 203 SK_ALWAYSBREAK(largeBits < 256); 204 } 205 double step = 1e-6; 206 if (largeBits > 21) { 207 step = 1e-1; 208 } else if (largeBits > 18) { 209 step = 1e-2; 210 } else if (largeBits > 15) { 211 step = 1e-3; 212 } else if (largeBits > 12) { 213 step = 1e-4; 214 } else if (largeBits > 9) { 215 step = 1e-5; 216 } 217 double diff; 218 do { 219 double newT = binary_search(cubic, step, pt, t, &iters); 220 if (newT >= 0) { 221 diff = fabs(t - newT); 222 break; 223 } 224 step *= 1.5; 225 SK_ALWAYSBREAK(step < 1); 226 } while (true); 227 worstStep[largeBits] = SkTMax(worstStep[largeBits], diff); 228 #if 0 229 { 230 cubic.dump(); 231 SkDebugf("\n"); 232 SkDLine line = {{{pt.fX - 1, pt.fY}, {pt.fX + 1, pt.fY}}}; 233 line.dump(); 234 SkDebugf("\n"); 235 } 236 #endif 237 ++errors; 238 } 239 SkDebugf("errors=%d avgIter=%1.9g", errors, (double) iters / errors); 240 SkDebugf(" steps: "); 241 int worstLimit = SK_ARRAY_COUNT(worstStep); 242 while (worstStep[--worstLimit] == 0) ; 243 for (int idx2 = 0; idx2 <= worstLimit; ++idx2) { 244 SkDebugf("%1.9g ", worstStep[idx2]); 245 } 246 SkDebugf("\n"); 247 SkDebugf("smallestR2=%1.9g largestR2=%1.9g\n", smallestR2, largestR2); 248 } 249 250 static double testOneFailure(const CubicLineFailures& failure) { 251 const SkDCubic& cubic = failure.c; 252 const SkDPoint& pt = failure.p; 253 double A, B, C, D; 254 SkDCubic::Coefficients(&cubic[0].fY, &A, &B, &C, &D); 255 D -= pt.fY; 256 double allRoots[3] = {0}, validRoots[3] = {0}; 257 int realRoots = SkDCubic::RootsReal(A, B, C, D, allRoots); 258 int valid = SkDQuad::AddValidTs(allRoots, realRoots, validRoots); 259 SK_ALWAYSBREAK(valid == 1); 260 SK_ALWAYSBREAK(realRoots != 1); 261 double t = validRoots[0]; 262 SkDPoint calcPt = cubic.ptAtT(t); 263 SK_ALWAYSBREAK(!calcPt.approximatelyEqual(pt)); 264 int iters = 0; 265 double newT = binary_search(cubic, 0.1, pt, t, &iters); 266 return newT; 267 } 268 269 DEF_TEST(PathOpsCubicLineFailures, reporter) { 270 return; // disable for now 271 for (int index = 0; index < cubicLineFailuresCount; ++index) { 272 const CubicLineFailures& failure = cubicLineFailures[index]; 273 double newT = testOneFailure(failure); 274 SK_ALWAYSBREAK(newT >= 0); 275 } 276 } 277 278 DEF_TEST(PathOpsCubicLineOneFailure, reporter) { 279 return; // disable for now 280 const CubicLineFailures& failure = cubicLineFailures[1]; 281 double newT = testOneFailure(failure); 282 SK_ALWAYSBREAK(newT >= 0); 283 } 284
