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