123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287 |
- /*
- * 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 "include/utils/SkRandom.h"
- #include "src/pathops/SkIntersections.h"
- #include "src/pathops/SkPathOpsCubic.h"
- #include "src/pathops/SkPathOpsLine.h"
- #include "src/pathops/SkPathOpsQuad.h"
- #include "src/pathops/SkReduceOrder.h"
- #include "tests/PathOpsTestCommon.h"
- #include "tests/Test.h"
- static bool gPathOpsCubicLineIntersectionIdeasVerbose = false;
- static struct CubicLineFailures {
- CubicPts 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)};
- CubicPts cuPts = {{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);
- SkDCubic cubic;
- cubic.debugSet(cuPts.fPts);
- 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]);
- }
- SkASSERT_RELEASE(smallest < 0);
- SkASSERT_RELEASE(smallest >= -1);
- largeBits = 0;
- } else {
- frexp(largest, &largeBits);
- SkASSERT_RELEASE(largeBits >= 0);
- SkASSERT_RELEASE(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;
- SkASSERT_RELEASE(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 CubicPts& c = failure.c;
- SkDCubic cubic;
- cubic.debugSet(c.fPts);
- 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);
- SkASSERT_RELEASE(valid == 1);
- SkASSERT_RELEASE(realRoots != 1);
- double t = validRoots[0];
- SkDPoint calcPt = cubic.ptAtT(t);
- SkASSERT_RELEASE(!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);
- SkASSERT_RELEASE(newT >= 0);
- }
- }
- DEF_TEST(PathOpsCubicLineOneFailure, reporter) {
- return; // disable for now
- const CubicLineFailures& failure = cubicLineFailures[1];
- double newT = testOneFailure(failure);
- SkASSERT_RELEASE(newT >= 0);
- }
|