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 /* * 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 "SkLineParameters.h" #include "SkPathOpsConic.h" #include "SkPathOpsCubic.h" #include "SkPathOpsQuad.h" // cribbed from the float version in SkGeometry.cpp static void conic_deriv_coeff(const double src[], SkScalar w, double coeff[3]) { const double P20 = src[4] - src[0]; const double P10 = src[2] - src[0]; const double wP10 = w * P10; coeff[0] = w * P20 - P20; coeff[1] = P20 - 2 * wP10; coeff[2] = wP10; } static double conic_eval_tan(const double coord[], SkScalar w, double t) { double coeff[3]; conic_deriv_coeff(coord, w, coeff); return t * (t * coeff[0] + coeff[1]) + coeff[2]; } int SkDConic::FindExtrema(const double src[], SkScalar w, double t[1]) { double coeff[3]; conic_deriv_coeff(src, w, coeff); double tValues[2]; int roots = SkDQuad::RootsValidT(coeff[0], coeff[1], coeff[2], tValues); SkASSERT(0 == roots || 1 == roots); if (1 == roots) { t[0] = tValues[0]; return 1; } return 0; } SkDVector SkDConic::dxdyAtT(double t) const { SkDVector result = { conic_eval_tan(&fPts[0].fX, fWeight, t), conic_eval_tan(&fPts[0].fY, fWeight, t) }; return result; } static double conic_eval_numerator(const double src[], SkScalar w, double t) { SkASSERT(src); SkASSERT(t >= 0 && t <= 1); double src2w = src[2] * w; double C = src[0]; double A = src[4] - 2 * src2w + C; double B = 2 * (src2w - C); return (A * t + B) * t + C; } static double conic_eval_denominator(SkScalar w, double t) { double B = 2 * (w - 1); double C = 1; double A = -B; return (A * t + B) * t + C; } bool SkDConic::hullIntersects(const SkDCubic& cubic, bool* isLinear) const { return cubic.hullIntersects(*this, isLinear); } SkDPoint SkDConic::ptAtT(double t) const { double denominator = conic_eval_denominator(fWeight, t); SkDPoint result = { conic_eval_numerator(&fPts[0].fX, fWeight, t) / denominator, conic_eval_numerator(&fPts[0].fY, fWeight, t) / denominator }; return result; } /* see quad subdivide for rationale */ SkDConic SkDConic::subDivide(double t1, double t2) const { double ax = conic_eval_numerator(&fPts[0].fX, fWeight, t1); double ay = conic_eval_numerator(&fPts[0].fY, fWeight, t1); double az = conic_eval_denominator(fWeight, t1); double midT = (t1 + t2) / 2; double dx = conic_eval_numerator(&fPts[0].fX, fWeight, midT); double dy = conic_eval_numerator(&fPts[0].fY, fWeight, midT); double dz = conic_eval_denominator(fWeight, midT); double cx = conic_eval_numerator(&fPts[0].fX, fWeight, t2); double cy = conic_eval_numerator(&fPts[0].fY, fWeight, t2); double cz = conic_eval_denominator(fWeight, t2); double bx = 2 * dx - (ax + cx) / 2; double by = 2 * dy - (ay + cy) / 2; double bz = 2 * dz - (az + cz) / 2; double dt = t2 - t1; double dt_1 = 1 - dt; SkScalar w = SkDoubleToScalar((1 + dt * (fWeight - 1)) / sqrt(dt * dt + 2 * dt * dt_1 * fWeight + dt_1 * dt_1)); SkDConic dst = {{{{ax / az, ay / az}, {bx / bz, by / bz}, {cx / cz, cy / cz}}}, w }; return dst; } SkDPoint SkDConic::subDivide(const SkDPoint& a, const SkDPoint& c, double t1, double t2, SkScalar* weight) const { SkDConic chopped = this->subDivide(t1, t2); *weight = chopped.fWeight; return chopped[1]; }