int SkOpSegment::debugInflections(int tStart, int tEnd) const {
if (fVerb != SkPath::kCubic_Verb) {
return false;
}
SkDCubic dst = SkDCubic::SubDivide(fPts, fTs[tStart].fT, fTs[tEnd].fT);
double inflections[2];
return dst.findInflections(inflections);
}
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;
}
void CubicPathToSimple(const SkPath& cubicPath, SkPath* simplePath) {
simplePath->reset();
SkDCubic cubic;
SkPath::RawIter iter(cubicPath);
uint8_t verb;
SkPoint pts[4];
while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
switch (verb) {
case SkPath::kMove_Verb:
simplePath->moveTo(pts[0].fX, pts[0].fY);
continue;
case SkPath::kLine_Verb:
simplePath->lineTo(pts[1].fX, pts[1].fY);
break;
case SkPath::kQuad_Verb:
simplePath->quadTo(pts[1].fX, pts[1].fY, pts[2].fX, pts[2].fY);
break;
case SkPath::kCubic_Verb: {
cubic.set(pts);
double tInflects[2];
int inflections = cubic.findInflections(tInflects);
if (inflections > 1 && tInflects[0] > tInflects[1]) {
SkTSwap(tInflects[0], tInflects[1]);
}
double lo = 0;
for (int index = 0; index <= inflections; ++index) {
double hi = index < inflections ? tInflects[index] : 1;
SkDCubic part = cubic.subDivide(lo, hi);
SkPoint cPts[3];
cPts[0] = part[1].asSkPoint();
cPts[1] = part[2].asSkPoint();
cPts[2] = part[3].asSkPoint();
simplePath->cubicTo(cPts[0].fX, cPts[0].fY, cPts[1].fX, cPts[1].fY,
cPts[2].fX, cPts[2].fY);
lo = hi;
}
break;
}
case SkPath::kClose_Verb:
simplePath->close();
break;
default:
SkDEBUGFAIL("bad verb");
return;
}
}
}
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;
}
