bool SkDCubic::ComplexBreak(const SkPoint pointsPtr[4], SkScalar* t) {
SkScalar d[3];
SkCubicType cubicType = SkClassifyCubic(pointsPtr, d);
if (cubicType == kLoop_SkCubicType) {
// crib code from gpu path utils that finds t values where loop self-intersects
// use it to find mid of t values which should be a friendly place to chop
SkScalar tempSqrt = SkScalarSqrt(4.f * d[0] * d[2] - 3.f * d[1] * d[1]);
SkScalar ls = d[1] - tempSqrt;
SkScalar lt = 2.f * d[0];
SkScalar ms = d[1] + tempSqrt;
SkScalar mt = 2.f * d[0];
if (roughly_between(0, ls, lt) && roughly_between(0, ms, mt)) {
ls = ls / lt;
ms = ms / mt;
SkASSERT(roughly_between(0, ls, 1) && roughly_between(0, ms, 1));
*t = (ls + ms) / 2;
SkASSERT(roughly_between(0, *t, 1));
return *t > 0 && *t < 1;
}
} else if (kSerpentine_SkCubicType == cubicType || kCusp_SkCubicType == cubicType) {
SkDCubic cubic;
cubic.set(pointsPtr);
double inflectionTs[2];
int infTCount = cubic.findInflections(inflectionTs);
if (infTCount == 2) {
double maxCurvature[3];
int roots = cubic.findMaxCurvature(maxCurvature);
#if DEBUG_CUBIC_SPLIT
SkDebugf("%s\n", __FUNCTION__);
cubic.dump();
for (int index = 0; index < infTCount; ++index) {
SkDebugf("inflectionsTs[%d]=%1.9g ", index, inflectionTs[index]);
SkDPoint pt = cubic.ptAtT(inflectionTs[index]);
SkDVector dPt = cubic.dxdyAtT(inflectionTs[index]);
SkDLine perp = {{pt - dPt, pt + dPt}};
perp.dump();
}
for (int index = 0; index < roots; ++index) {
SkDebugf("maxCurvature[%d]=%1.9g ", index, maxCurvature[index]);
SkDPoint pt = cubic.ptAtT(maxCurvature[index]);
SkDVector dPt = cubic.dxdyAtT(maxCurvature[index]);
SkDLine perp = {{pt - dPt, pt + dPt}};
perp.dump();
}
#endif
for (int index = 0; index < roots; ++index) {
if (between(inflectionTs[0], maxCurvature[index], inflectionTs[1])) {
*t = maxCurvature[index];
return *t > 0 && *t < 1;
}
}
} else if (infTCount == 1) {
*t = inflectionTs[0];
return *t > 0 && *t < 1;
}
}
return false;
}
// determine that slop required after quad/quad finds a candidate intersection
// use the cross of the tangents plus the distance from 1 or 0 as knobs
DEF_TEST(PathOpsCubicQuadSlop, reporter) {
// create a random non-selfintersecting cubic
// break it into quadratics
// offset the quadratic, measuring the slop required to find the intersection
if (!gPathOpCubicQuadSlopVerbose) { // takes a while to run -- so exclude it by default
return;
}
int results[101];
sk_bzero(results, sizeof(results));
double minCross[101];
sk_bzero(minCross, sizeof(minCross));
double maxCross[101];
sk_bzero(maxCross, sizeof(maxCross));
double sumCross[101];
sk_bzero(sumCross, sizeof(sumCross));
int foundOne = 0;
int slopCount = 1;
SkRandom ran;
for (int index = 0; index < 10000000; ++index) {
if (index % 1000 == 999) SkDebugf(".");
SkDCubic cubic = {{
{ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)},
{ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)},
{ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)},
{ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)}
}};
SkIntersections i;
if (i.intersect(cubic)) {
continue;
}
SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts;
cubic.toQuadraticTs(cubic.calcPrecision(), &ts);
double tStart = 0;
int tsCount = ts.count();
for (int i1 = 0; i1 <= tsCount; ++i1) {
const double tEnd = i1 < tsCount ? ts[i1] : 1;
SkDCubic part = cubic.subDivide(tStart, tEnd);
SkDQuad quad = part.toQuad();
SkReduceOrder reducer;
int order = reducer.reduce(quad);
if (order != 3) {
continue;
}
for (int i2 = 0; i2 < 100; ++i2) {
SkDPoint endDisplacement = {ran.nextRangeF(-100, 100), ran.nextRangeF(-100, 100)};
SkDQuad nearby = {{
{quad[0].fX + endDisplacement.fX, quad[0].fY + endDisplacement.fY},
{quad[1].fX + ran.nextRangeF(-100, 100), quad[1].fY + ran.nextRangeF(-100, 100)},
{quad[2].fX - endDisplacement.fX, quad[2].fY - endDisplacement.fY}
}};
order = reducer.reduce(nearby);
if (order != 3) {
continue;
}
SkIntersections locals;
locals.allowNear(false);
locals.intersect(quad, nearby);
if (locals.used() != 1) {
continue;
}
// brute force find actual intersection
SkDLine cubicLine = {{ {0, 0}, {cubic[0].fX, cubic[0].fY } }};
SkIntersections liner;
int i3;
int found = -1;
int foundErr = true;
for (i3 = 1; i3 <= 1000; ++i3) {
cubicLine[0] = cubicLine[1];
cubicLine[1] = cubic.ptAtT(i3 / 1000.);
liner.reset();
liner.allowNear(false);
liner.intersect(nearby, cubicLine);
if (liner.used() == 0) {
continue;
}
if (liner.used() > 1) {
foundErr = true;
break;
}
if (found > 0) {
foundErr = true;
break;
}
foundErr = false;
found = i3;
}
if (foundErr) {
continue;
}
SkDVector dist = liner.pt(0) - locals.pt(0);
SkDVector qV = nearby.dxdyAtT(locals[0][0]);
double cubicT = (found - 1 + liner[1][0]) / 1000.;
SkDVector cV = cubic.dxdyAtT(cubicT);
double qxc = qV.crossCheck(cV);
double qvLen = qV.length();
double cvLen = cV.length();
double maxLen = SkTMax(qvLen, cvLen);
qxc /= maxLen;
double quadT = tStart + (tEnd - tStart) * locals[0][0];
double diffT = fabs(cubicT - quadT);
int diffIdx = (int) (diffT * 100);
results[diffIdx]++;
double absQxc = fabs(qxc);
if (sumCross[diffIdx] == 0) {
minCross[diffIdx] = maxCross[diffIdx] = sumCross[diffIdx] = absQxc;
} else {
minCross[diffIdx] = SkTMin(minCross[diffIdx], absQxc);
maxCross[diffIdx] = SkTMax(maxCross[diffIdx], absQxc);
sumCross[diffIdx] += absQxc;
}
if (diffIdx >= 20) {
#if 01
SkDebugf("cubic={{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}"
" quad={{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}"
" {{{%1.9g,%1.9g}, {%1.9g,%1.9g}}}"
" qT=%1.9g cT=%1.9g dist=%1.9g cross=%1.9g\n",
cubic[0].fX, cubic[0].fY, cubic[1].fX, cubic[1].fY,
cubic[2].fX, cubic[2].fY, cubic[3].fX, cubic[3].fY,
nearby[0].fX, nearby[0].fY, nearby[1].fX, nearby[1].fY,
nearby[2].fX, nearby[2].fY,
liner.pt(0).fX, liner.pt(0).fY,
locals.pt(0).fX, locals.pt(0).fY, quadT, cubicT, dist.length(), qxc);
#else
SkDebugf("qT=%1.9g cT=%1.9g dist=%1.9g cross=%1.9g\n",
quadT, cubicT, dist.length(), qxc);
SkDebugf("<div id=\"slop%d\">\n", ++slopCount);
SkDebugf("{{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}\n"
"{{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}\n"
"{{{%1.9g,%1.9g}, {%1.9g,%1.9g}}}\n",
cubic[0].fX, cubic[0].fY, cubic[1].fX, cubic[1].fY,
cubic[2].fX, cubic[2].fY, cubic[3].fX, cubic[3].fY,
nearby[0].fX, nearby[0].fY, nearby[1].fX, nearby[1].fY,
nearby[2].fX, nearby[2].fY,
liner.pt(0).fX, liner.pt(0).fY,
locals.pt(0).fX, locals.pt(0).fY);
SkDebugf("</div>\n\n");
#endif
}
++foundOne;
}
tStart = tEnd;
}
if (++foundOne >= 100000) {
break;
}
}
#if 01
SkDebugf("slopCount=%d\n", slopCount);
int max = 100;
while (results[max] == 0) {
--max;
}
for (int i = 0; i <= max; ++i) {
if (i > 0 && i % 10 == 0) {
SkDebugf("\n");
}
SkDebugf("%d ", results[i]);
}
SkDebugf("min\n");
for (int i = 0; i <= max; ++i) {
if (i > 0 && i % 10 == 0) {
SkDebugf("\n");
}
SkDebugf("%1.9g ", minCross[i]);
}
SkDebugf("max\n");
for (int i = 0; i <= max; ++i) {
if (i > 0 && i % 10 == 0) {
SkDebugf("\n");
}
SkDebugf("%1.9g ", maxCross[i]);
}
SkDebugf("avg\n");
for (int i = 0; i <= max; ++i) {
if (i > 0 && i % 10 == 0) {
SkDebugf("\n");
}
SkDebugf("%1.9g ", sumCross[i] / results[i]);
}
#else
for (int i = 1; i < slopCount; ++i) {
SkDebugf(" slop%d,\n", i);
}
#endif
SkDebugf("\n");
}
int SkDCubic::ComplexBreak(const SkPoint pointsPtr[4], SkScalar* t) {
SkDCubic cubic;
cubic.set(pointsPtr);
if (cubic.monotonicInX() && cubic.monotonicInY()) {
return 0;
}
SkScalar d[3];
SkCubicType cubicType = SkClassifyCubic(pointsPtr, d);
switch (cubicType) {
case kLoop_SkCubicType: {
// crib code from gpu path utils that finds t values where loop self-intersects
// use it to find mid of t values which should be a friendly place to chop
SkScalar tempSqrt = SkScalarSqrt(4.f * d[0] * d[2] - 3.f * d[1] * d[1]);
SkScalar ls = d[1] - tempSqrt;
SkScalar lt = 2.f * d[0];
SkScalar ms = d[1] + tempSqrt;
SkScalar mt = 2.f * d[0];
if (roughly_between(0, ls, lt) && roughly_between(0, ms, mt)) {
ls = ls / lt;
ms = ms / mt;
SkASSERT(roughly_between(0, ls, 1) && roughly_between(0, ms, 1));
t[0] = (ls + ms) / 2;
SkASSERT(roughly_between(0, *t, 1));
return (int) (t[0] > 0 && t[0] < 1);
}
}
// fall through if no t value found
case kSerpentine_SkCubicType:
case kCusp_SkCubicType: {
double inflectionTs[2];
int infTCount = cubic.findInflections(inflectionTs);
double maxCurvature[3];
int roots = cubic.findMaxCurvature(maxCurvature);
#if DEBUG_CUBIC_SPLIT
SkDebugf("%s\n", __FUNCTION__);
cubic.dump();
for (int index = 0; index < infTCount; ++index) {
SkDebugf("inflectionsTs[%d]=%1.9g ", index, inflectionTs[index]);
SkDPoint pt = cubic.ptAtT(inflectionTs[index]);
SkDVector dPt = cubic.dxdyAtT(inflectionTs[index]);
SkDLine perp = {{pt - dPt, pt + dPt}};
perp.dump();
}
for (int index = 0; index < roots; ++index) {
SkDebugf("maxCurvature[%d]=%1.9g ", index, maxCurvature[index]);
SkDPoint pt = cubic.ptAtT(maxCurvature[index]);
SkDVector dPt = cubic.dxdyAtT(maxCurvature[index]);
SkDLine perp = {{pt - dPt, pt + dPt}};
perp.dump();
}
#endif
if (infTCount == 2) {
for (int index = 0; index < roots; ++index) {
if (between(inflectionTs[0], maxCurvature[index], inflectionTs[1])) {
t[0] = maxCurvature[index];
return (int) (t[0] > 0 && t[0] < 1);
}
}
} else {
int resultCount = 0;
// FIXME: constant found through experimentation -- maybe there's a better way....
double precision = cubic.calcPrecision() * 2;
for (int index = 0; index < roots; ++index) {
double testT = maxCurvature[index];
if (0 >= testT || testT >= 1) {
continue;
}
// don't call dxdyAtT since we want (0,0) results
SkDVector dPt = { derivative_at_t(&cubic.fPts[0].fX, testT),
derivative_at_t(&cubic.fPts[0].fY, testT) };
double dPtLen = dPt.length();
if (dPtLen < precision) {
t[resultCount++] = testT;
}
}
if (!resultCount && infTCount == 1) {
t[0] = inflectionTs[0];
resultCount = (int) (t[0] > 0 && t[0] < 1);
}
return resultCount;
}
}
default:
;
}
return 0;
}
