/* * Copyright 2015 Google Inc. * * Use of this source code is governed by a BSD-style license that can be * found in the LICENSE file. */ #include "SkIntersections.h" #include "SkPathOpsConic.h" #include "SkPathOpsCurve.h" #include "SkPathOpsLine.h" class LineConicIntersections { public: enum PinTPoint { kPointUninitialized, kPointInitialized }; LineConicIntersections(const SkDConic& c, const SkDLine& l, SkIntersections* i) : fConic(c) , fLine(&l) , fIntersections(i) , fAllowNear(true) { i->setMax(4); // allow short partial coincidence plus discrete intersection } LineConicIntersections(const SkDConic& c) : fConic(c) SkDEBUGPARAMS(fLine(nullptr)) SkDEBUGPARAMS(fIntersections(nullptr)) SkDEBUGPARAMS(fAllowNear(false)) { } void allowNear(bool allow) { fAllowNear = allow; } void checkCoincident() { int last = fIntersections->used() - 1; for (int index = 0; index < last; ) { double conicMidT = ((*fIntersections)[0][index] + (*fIntersections)[0][index + 1]) / 2; SkDPoint conicMidPt = fConic.ptAtT(conicMidT); double t = fLine->nearPoint(conicMidPt, nullptr); if (t < 0) { ++index; continue; } if (fIntersections->isCoincident(index)) { fIntersections->removeOne(index); --last; } else if (fIntersections->isCoincident(index + 1)) { fIntersections->removeOne(index + 1); --last; } else { fIntersections->setCoincident(index++); } fIntersections->setCoincident(index); } } #ifdef SK_DEBUG static bool close_to(double a, double b, const double c[3]) { double max = SkTMax(-SkTMin(SkTMin(c[0], c[1]), c[2]), SkTMax(SkTMax(c[0], c[1]), c[2])); return approximately_zero_when_compared_to(a - b, max); } #endif int horizontalIntersect(double axisIntercept, double roots[2]) { double conicVals[] = { fConic[0].fY, fConic[1].fY, fConic[2].fY }; return this->validT(conicVals, axisIntercept, roots); } int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) { this->addExactHorizontalEndPoints(left, right, axisIntercept); if (fAllowNear) { this->addNearHorizontalEndPoints(left, right, axisIntercept); } double roots[2]; int count = this->horizontalIntersect(axisIntercept, roots); for (int index = 0; index < count; ++index) { double conicT = roots[index]; SkDPoint pt = fConic.ptAtT(conicT); SkDEBUGCODE(double conicVals[] = { fConic[0].fY, fConic[1].fY, fConic[2].fY }); SkOPOBJASSERT(fIntersections, close_to(pt.fY, axisIntercept, conicVals)); double lineT = (pt.fX - left) / (right - left); if (this->pinTs(&conicT, &lineT, &pt, kPointInitialized) && this->uniqueAnswer(conicT, pt)) { fIntersections->insert(conicT, lineT, pt); } } if (flipped) { fIntersections->flip(); } this->checkCoincident(); return fIntersections->used(); } int intersect() { this->addExactEndPoints(); if (fAllowNear) { this->addNearEndPoints(); } double rootVals[2]; int roots = this->intersectRay(rootVals); for (int index = 0; index < roots; ++index) { double conicT = rootVals[index]; double lineT = this->findLineT(conicT); #ifdef SK_DEBUG if (!fIntersections->globalState() || !fIntersections->globalState()->debugSkipAssert()) { SkDEBUGCODE(SkDPoint conicPt = fConic.ptAtT(conicT)); SkDEBUGCODE(SkDPoint linePt = fLine->ptAtT(lineT)); SkASSERT(conicPt.approximatelyDEqual(linePt)); } #endif SkDPoint pt; if (this->pinTs(&conicT, &lineT, &pt, kPointUninitialized) && this->uniqueAnswer(conicT, pt)) { fIntersections->insert(conicT, lineT, pt); } } this->checkCoincident(); return fIntersections->used(); } int intersectRay(double roots[2]) { double adj = (*fLine)[1].fX - (*fLine)[0].fX; double opp = (*fLine)[1].fY - (*fLine)[0].fY; double r[3]; for (int n = 0; n < 3; ++n) { r[n] = (fConic[n].fY - (*fLine)[0].fY) * adj - (fConic[n].fX - (*fLine)[0].fX) * opp; } return this->validT(r, 0, roots); } int validT(double r[3], double axisIntercept, double roots[2]) { double A = r[2]; double B = r[1] * fConic.fWeight - axisIntercept * fConic.fWeight + axisIntercept; double C = r[0]; A += C - 2 * B; // A = a + c - 2*(b*w - xCept*w + xCept) B -= C; // B = b*w - w * xCept + xCept - a C -= axisIntercept; return SkDQuad::RootsValidT(A, 2 * B, C, roots); } int verticalIntersect(double axisIntercept, double roots[2]) { double conicVals[] = { fConic[0].fX, fConic[1].fX, fConic[2].fX }; return this->validT(conicVals, axisIntercept, roots); } int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) { this->addExactVerticalEndPoints(top, bottom, axisIntercept); if (fAllowNear) { this->addNearVerticalEndPoints(top, bottom, axisIntercept); } double roots[2]; int count = this->verticalIntersect(axisIntercept, roots); for (int index = 0; index < count; ++index) { double conicT = roots[index]; SkDPoint pt = fConic.ptAtT(conicT); SkDEBUGCODE(double conicVals[] = { fConic[0].fX, fConic[1].fX, fConic[2].fX }); SkOPOBJASSERT(fIntersections, close_to(pt.fX, axisIntercept, conicVals)); double lineT = (pt.fY - top) / (bottom - top); if (this->pinTs(&conicT, &lineT, &pt, kPointInitialized) && this->uniqueAnswer(conicT, pt)) { fIntersections->insert(conicT, lineT, pt); } } if (flipped) { fIntersections->flip(); } this->checkCoincident(); return fIntersections->used(); } protected: // OPTIMIZE: Functions of the form add .. points are indentical to the conic routines. // add endpoints first to get zero and one t values exactly void addExactEndPoints() { for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) { double lineT = fLine->exactPoint(fConic[cIndex]); if (lineT < 0) { continue; } double conicT = (double) (cIndex >> 1); fIntersections->insert(conicT, lineT, fConic[cIndex]); } } void addNearEndPoints() { for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) { double conicT = (double) (cIndex >> 1); if (fIntersections->hasT(conicT)) { continue; } double lineT = fLine->nearPoint(fConic[cIndex], nullptr); if (lineT < 0) { continue; } fIntersections->insert(conicT, lineT, fConic[cIndex]); } this->addLineNearEndPoints(); } void addLineNearEndPoints() { for (int lIndex = 0; lIndex < 2; ++lIndex) { double lineT = (double) lIndex; if (fIntersections->hasOppT(lineT)) { continue; } double conicT = ((SkDCurve*) &fConic)->nearPoint(SkPath::kConic_Verb, (*fLine)[lIndex], (*fLine)[!lIndex]); if (conicT < 0) { continue; } fIntersections->insert(conicT, lineT, (*fLine)[lIndex]); } } void addExactHorizontalEndPoints(double left, double right, double y) { for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) { double lineT = SkDLine::ExactPointH(fConic[cIndex], left, right, y); if (lineT < 0) { continue; } double conicT = (double) (cIndex >> 1); fIntersections->insert(conicT, lineT, fConic[cIndex]); } } void addNearHorizontalEndPoints(double left, double right, double y) { for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) { double conicT = (double) (cIndex >> 1); if (fIntersections->hasT(conicT)) { continue; } double lineT = SkDLine::NearPointH(fConic[cIndex], left, right, y); if (lineT < 0) { continue; } fIntersections->insert(conicT, lineT, fConic[cIndex]); } this->addLineNearEndPoints(); } void addExactVerticalEndPoints(double top, double bottom, double x) { for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) { double lineT = SkDLine::ExactPointV(fConic[cIndex], top, bottom, x); if (lineT < 0) { continue; } double conicT = (double) (cIndex >> 1); fIntersections->insert(conicT, lineT, fConic[cIndex]); } } void addNearVerticalEndPoints(double top, double bottom, double x) { for (int cIndex = 0; cIndex < SkDConic::kPointCount; cIndex += SkDConic::kPointLast) { double conicT = (double) (cIndex >> 1); if (fIntersections->hasT(conicT)) { continue; } double lineT = SkDLine::NearPointV(fConic[cIndex], top, bottom, x); if (lineT < 0) { continue; } fIntersections->insert(conicT, lineT, fConic[cIndex]); } this->addLineNearEndPoints(); } double findLineT(double t) { SkDPoint xy = fConic.ptAtT(t); double dx = (*fLine)[1].fX - (*fLine)[0].fX; double dy = (*fLine)[1].fY - (*fLine)[0].fY; if (fabs(dx) > fabs(dy)) { return (xy.fX - (*fLine)[0].fX) / dx; } return (xy.fY - (*fLine)[0].fY) / dy; } bool pinTs(double* conicT, double* lineT, SkDPoint* pt, PinTPoint ptSet) { if (!approximately_one_or_less_double(*lineT)) { return false; } if (!approximately_zero_or_more_double(*lineT)) { return false; } double qT = *conicT = SkPinT(*conicT); double lT = *lineT = SkPinT(*lineT); if (lT == 0 || lT == 1 || (ptSet == kPointUninitialized && qT != 0 && qT != 1)) { *pt = (*fLine).ptAtT(lT); } else if (ptSet == kPointUninitialized) { *pt = fConic.ptAtT(qT); } SkPoint gridPt = pt->asSkPoint(); if (SkDPoint::ApproximatelyEqual(gridPt, (*fLine)[0].asSkPoint())) { *pt = (*fLine)[0]; *lineT = 0; } else if (SkDPoint::ApproximatelyEqual(gridPt, (*fLine)[1].asSkPoint())) { *pt = (*fLine)[1]; *lineT = 1; } if (fIntersections->used() > 0 && approximately_equal((*fIntersections)[1][0], *lineT)) { return false; } if (gridPt == fConic[0].asSkPoint()) { *pt = fConic[0]; *conicT = 0; } else if (gridPt == fConic[2].asSkPoint()) { *pt = fConic[2]; *conicT = 1; } return true; } bool uniqueAnswer(double conicT, const SkDPoint& pt) { for (int inner = 0; inner < fIntersections->used(); ++inner) { if (fIntersections->pt(inner) != pt) { continue; } double existingConicT = (*fIntersections)[0][inner]; if (conicT == existingConicT) { return false; } // check if midway on conic is also same point. If so, discard this double conicMidT = (existingConicT + conicT) / 2; SkDPoint conicMidPt = fConic.ptAtT(conicMidT); if (conicMidPt.approximatelyEqual(pt)) { return false; } } #if ONE_OFF_DEBUG SkDPoint qPt = fConic.ptAtT(conicT); SkDebugf("%s pt=(%1.9g,%1.9g) cPt=(%1.9g,%1.9g)\n", __FUNCTION__, pt.fX, pt.fY, qPt.fX, qPt.fY); #endif return true; } private: const SkDConic& fConic; const SkDLine* fLine; SkIntersections* fIntersections; bool fAllowNear; }; int SkIntersections::horizontal(const SkDConic& conic, double left, double right, double y, bool flipped) { SkDLine line = {{{ left, y }, { right, y }}}; LineConicIntersections c(conic, line, this); return c.horizontalIntersect(y, left, right, flipped); } int SkIntersections::vertical(const SkDConic& conic, double top, double bottom, double x, bool flipped) { SkDLine line = {{{ x, top }, { x, bottom }}}; LineConicIntersections c(conic, line, this); return c.verticalIntersect(x, top, bottom, flipped); } int SkIntersections::intersect(const SkDConic& conic, const SkDLine& line) { LineConicIntersections c(conic, line, this); c.allowNear(fAllowNear); return c.intersect(); } int SkIntersections::intersectRay(const SkDConic& conic, const SkDLine& line) { LineConicIntersections c(conic, line, this); fUsed = c.intersectRay(fT[0]); for (int index = 0; index < fUsed; ++index) { fPt[index] = conic.ptAtT(fT[0][index]); } return fUsed; } int SkIntersections::HorizontalIntercept(const SkDConic& conic, SkScalar y, double* roots) { LineConicIntersections c(conic); return c.horizontalIntersect(y, roots); } int SkIntersections::VerticalIntercept(const SkDConic& conic, SkScalar x, double* roots) { LineConicIntersections c(conic); return c.verticalIntersect(x, roots); }