| /* |
| * Copyright 2014 Google Inc. |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| #include "PathOpsTestCommon.h" |
| #include "SkIntersections.h" |
| #include "SkPathOpsCubic.h" |
| #include "SkPathOpsLine.h" |
| #include "SkPathOpsQuad.h" |
| #include "SkRandom.h" |
| #include "SkReduceOrder.h" |
| #include "Test.h" |
| |
| static bool gPathOpsCubicLineIntersectionIdeasVerbose = false; |
| |
| static struct CubicLineFailures { |
| SkDCubic c; |
| double t; |
| SkDPoint p; |
| } cubicLineFailures[] = { |
| {{{{-164.3726806640625, 36.826904296875}, {-189.045166015625, -953.2220458984375}, |
| {926.505859375, -897.36175537109375}, {-139.33489990234375, 204.40771484375}}}, |
| 0.37329583, {107.54935269006289, -632.13736293162208}}, |
| {{{{784.056884765625, -554.8350830078125}, {67.5489501953125, 509.0224609375}, |
| {-447.713134765625, 751.375}, {415.7784423828125, 172.22265625}}}, |
| 0.660005242, {-32.973148967736151, 478.01341797403569}}, |
| {{{{-580.6834716796875, -127.044921875}, {-872.8983154296875, -945.54302978515625}, |
| {260.8092041015625, -909.34991455078125}, {-976.2125244140625, -18.46551513671875}}}, |
| 0.578826774, {-390.17910153915489, -687.21144412296007}}, |
| }; |
| |
| int cubicLineFailuresCount = (int) SK_ARRAY_COUNT(cubicLineFailures); |
| |
| double measuredSteps[] = { |
| 9.15910731e-007, 8.6600277e-007, 7.4122059e-007, 6.92087618e-007, 8.35290245e-007, |
| 3.29763199e-007, 5.07547773e-007, 4.41294224e-007, 0, 0, |
| 3.76879167e-006, 1.06126249e-006, 2.36873967e-006, 1.62421134e-005, 3.09103599e-005, |
| 4.38917976e-005, 0.000112348938, 0.000243149242, 0.000433174114, 0.00170880232, |
| 0.00272619724, 0.00518844604, 0.000352621078, 0.00175960064, 0.027875185, |
| 0.0351329803, 0.103964925, |
| }; |
| |
| /* last output : errors=3121 |
| 9.1796875e-007 8.59375e-007 7.5e-007 6.875e-007 8.4375e-007 |
| 3.125e-007 5e-007 4.375e-007 0 0 |
| 3.75e-006 1.09375e-006 2.1875e-006 1.640625e-005 3.0859375e-005 |
| 4.38964844e-005 0.000112304687 0.000243164063 0.000433181763 0.00170898437 |
| 0.00272619247 0.00518844604 0.000352621078 0.00175960064 0.027875185 |
| 0.0351329803 0.103964925 |
| */ |
| |
| static double binary_search(const SkDCubic& cubic, double step, const SkDPoint& pt, double t, |
| int* iters) { |
| double firstStep = step; |
| do { |
| *iters += 1; |
| SkDPoint cubicAtT = cubic.ptAtT(t); |
| if (cubicAtT.approximatelyEqual(pt)) { |
| break; |
| } |
| double calcX = cubicAtT.fX - pt.fX; |
| double calcY = cubicAtT.fY - pt.fY; |
| double calcDist = calcX * calcX + calcY * calcY; |
| if (step == 0) { |
| SkDebugf("binary search failed: step=%1.9g cubic=", firstStep); |
| cubic.dump(); |
| SkDebugf(" t=%1.9g ", t); |
| pt.dump(); |
| SkDebugf("\n"); |
| return -1; |
| } |
| double lastStep = step; |
| step /= 2; |
| SkDPoint lessPt = cubic.ptAtT(t - lastStep); |
| double lessX = lessPt.fX - pt.fX; |
| double lessY = lessPt.fY - pt.fY; |
| double lessDist = lessX * lessX + lessY * lessY; |
| // use larger x/y difference to choose step |
| if (calcDist > lessDist) { |
| t -= step; |
| t = SkTMax(0., t); |
| } else { |
| SkDPoint morePt = cubic.ptAtT(t + lastStep); |
| double moreX = morePt.fX - pt.fX; |
| double moreY = morePt.fY - pt.fY; |
| double moreDist = moreX * moreX + moreY * moreY; |
| if (calcDist <= moreDist) { |
| continue; |
| } |
| t += step; |
| t = SkTMin(1., t); |
| } |
| } while (true); |
| return t; |
| } |
| |
| #if 0 |
| static bool r2check(double A, double B, double C, double D, double* R2MinusQ3Ptr) { |
| if (approximately_zero(A) |
| && approximately_zero_when_compared_to(A, B) |
| && approximately_zero_when_compared_to(A, C) |
| && approximately_zero_when_compared_to(A, D)) { // we're just a quadratic |
| return false; |
| } |
| if (approximately_zero_when_compared_to(D, A) |
| && approximately_zero_when_compared_to(D, B) |
| && approximately_zero_when_compared_to(D, C)) { // 0 is one root |
| return false; |
| } |
| if (approximately_zero(A + B + C + D)) { // 1 is one root |
| return false; |
| } |
| double a, b, c; |
| { |
| double invA = 1 / A; |
| a = B * invA; |
| b = C * invA; |
| c = D * invA; |
| } |
| double a2 = a * a; |
| double Q = (a2 - b * 3) / 9; |
| double R = (2 * a2 * a - 9 * a * b + 27 * c) / 54; |
| double R2 = R * R; |
| double Q3 = Q * Q * Q; |
| double R2MinusQ3 = R2 - Q3; |
| *R2MinusQ3Ptr = R2MinusQ3; |
| return true; |
| } |
| #endif |
| |
| /* What is the relationship between the accuracy of the root in range and the magnitude of all |
| roots? To find out, create a bunch of cubics, and measure */ |
| |
| DEF_TEST(PathOpsCubicLineRoots, reporter) { |
| if (!gPathOpsCubicLineIntersectionIdeasVerbose) { // slow; exclude it by default |
| return; |
| } |
| SkRandom ran; |
| double worstStep[256] = {0}; |
| int errors = 0; |
| int iters = 0; |
| double smallestR2 = 0; |
| double largestR2 = 0; |
| for (int index = 0; index < 1000000000; ++index) { |
| SkDPoint origin = {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)}; |
| SkDCubic cubic = {{origin, |
| {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)}, |
| {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)}, |
| {ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)} |
| }}; |
| // construct a line at a known intersection |
| double t = ran.nextRangeF(0, 1); |
| SkDPoint pt = cubic.ptAtT(t); |
| // skip answers with no intersections (although note the bug!) or two, or more |
| // see if the line / cubic has a fun range of roots |
| double A, B, C, D; |
| SkDCubic::Coefficients(&cubic[0].fY, &A, &B, &C, &D); |
| D -= pt.fY; |
| double allRoots[3] = {0}, validRoots[3] = {0}; |
| int realRoots = SkDCubic::RootsReal(A, B, C, D, allRoots); |
| int valid = SkDQuad::AddValidTs(allRoots, realRoots, validRoots); |
| if (valid != 1) { |
| continue; |
| } |
| if (realRoots == 1) { |
| continue; |
| } |
| t = validRoots[0]; |
| SkDPoint calcPt = cubic.ptAtT(t); |
| if (calcPt.approximatelyEqual(pt)) { |
| continue; |
| } |
| #if 0 |
| double R2MinusQ3; |
| if (r2check(A, B, C, D, &R2MinusQ3)) { |
| smallestR2 = SkTMin(smallestR2, R2MinusQ3); |
| largestR2 = SkTMax(largestR2, R2MinusQ3); |
| } |
| #endif |
| double largest = SkTMax(fabs(allRoots[0]), fabs(allRoots[1])); |
| if (realRoots == 3) { |
| largest = SkTMax(largest, fabs(allRoots[2])); |
| } |
| int largeBits; |
| if (largest <= 1) { |
| #if 0 |
| SkDebugf("realRoots=%d (%1.9g, %1.9g, %1.9g) valid=%d (%1.9g, %1.9g, %1.9g)\n", |
| realRoots, allRoots[0], allRoots[1], allRoots[2], valid, validRoots[0], |
| validRoots[1], validRoots[2]); |
| #endif |
| double smallest = SkTMin(allRoots[0], allRoots[1]); |
| if (realRoots == 3) { |
| smallest = SkTMin(smallest, allRoots[2]); |
| } |
| SK_ALWAYSBREAK(smallest < 0); |
| SK_ALWAYSBREAK(smallest >= -1); |
| largeBits = 0; |
| } else { |
| frexp(largest, &largeBits); |
| SK_ALWAYSBREAK(largeBits >= 0); |
| SK_ALWAYSBREAK(largeBits < 256); |
| } |
| double step = 1e-6; |
| if (largeBits > 21) { |
| step = 1e-1; |
| } else if (largeBits > 18) { |
| step = 1e-2; |
| } else if (largeBits > 15) { |
| step = 1e-3; |
| } else if (largeBits > 12) { |
| step = 1e-4; |
| } else if (largeBits > 9) { |
| step = 1e-5; |
| } |
| double diff; |
| do { |
| double newT = binary_search(cubic, step, pt, t, &iters); |
| if (newT >= 0) { |
| diff = fabs(t - newT); |
| break; |
| } |
| step *= 1.5; |
| SK_ALWAYSBREAK(step < 1); |
| } while (true); |
| worstStep[largeBits] = SkTMax(worstStep[largeBits], diff); |
| #if 0 |
| { |
| cubic.dump(); |
| SkDebugf("\n"); |
| SkDLine line = {{{pt.fX - 1, pt.fY}, {pt.fX + 1, pt.fY}}}; |
| line.dump(); |
| SkDebugf("\n"); |
| } |
| #endif |
| ++errors; |
| } |
| SkDebugf("errors=%d avgIter=%1.9g", errors, (double) iters / errors); |
| SkDebugf(" steps: "); |
| int worstLimit = SK_ARRAY_COUNT(worstStep); |
| while (worstStep[--worstLimit] == 0) ; |
| for (int idx2 = 0; idx2 <= worstLimit; ++idx2) { |
| SkDebugf("%1.9g ", worstStep[idx2]); |
| } |
| SkDebugf("\n"); |
| SkDebugf("smallestR2=%1.9g largestR2=%1.9g\n", smallestR2, largestR2); |
| } |
| |
| static double testOneFailure(const CubicLineFailures& failure) { |
| const SkDCubic& cubic = failure.c; |
| const SkDPoint& pt = failure.p; |
| double A, B, C, D; |
| SkDCubic::Coefficients(&cubic[0].fY, &A, &B, &C, &D); |
| D -= pt.fY; |
| double allRoots[3] = {0}, validRoots[3] = {0}; |
| int realRoots = SkDCubic::RootsReal(A, B, C, D, allRoots); |
| int valid = SkDQuad::AddValidTs(allRoots, realRoots, validRoots); |
| SK_ALWAYSBREAK(valid == 1); |
| SK_ALWAYSBREAK(realRoots != 1); |
| double t = validRoots[0]; |
| SkDPoint calcPt = cubic.ptAtT(t); |
| SK_ALWAYSBREAK(!calcPt.approximatelyEqual(pt)); |
| int iters = 0; |
| double newT = binary_search(cubic, 0.1, pt, t, &iters); |
| return newT; |
| } |
| |
| DEF_TEST(PathOpsCubicLineFailures, reporter) { |
| return; // disable for now |
| for (int index = 0; index < cubicLineFailuresCount; ++index) { |
| const CubicLineFailures& failure = cubicLineFailures[index]; |
| double newT = testOneFailure(failure); |
| SK_ALWAYSBREAK(newT >= 0); |
| } |
| } |
| |
| DEF_TEST(PathOpsCubicLineOneFailure, reporter) { |
| return; // disable for now |
| const CubicLineFailures& failure = cubicLineFailures[1]; |
| double newT = testOneFailure(failure); |
| SK_ALWAYSBREAK(newT >= 0); |
| } |
