b2c82c99f8
git-svn-id: http://skia.googlecode.com/svn/trunk@14636 2bbb7eff-a529-9590-31e7-b0007b416f81
284 lines
9.8 KiB
C++
284 lines
9.8 KiB
C++
/*
|
|
* 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);
|
|
}
|