/*
* 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);
}