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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;
}
SkDPoint SkDConic::top(double startT, double endT) const {
SkDConic sub = subDivide(startT, endT);
SkDPoint topPt = sub[0];
if (topPt.fY > sub[2].fY || (topPt.fY == sub[2].fY && topPt.fX > sub[2].fX)) {
topPt = sub[2];
}
if (!between(sub[0].fY, sub[1].fY, sub[2].fY)) {
double extremeT;
if (FindExtrema(&sub[0].fY, sub.fWeight, &extremeT)) {
extremeT = startT + (endT - startT) * extremeT;
SkDPoint test = ptAtT(extremeT);
if (topPt.fY > test.fY || (topPt.fY == test.fY && topPt.fX > test.fX)) {
topPt = test;
}
}
}
return topPt;
}
/* 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];
}
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