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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);
// In extreme cases, the number of roots returned can be 2. Pathops
// will fail later on, so there's no advantage to plumbing in an error
// return here.
// 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)
};
if (result.fX == 0 && result.fY == 0) {
if (zero_or_one(t)) {
result = fPts[2] - fPts[0];
} else {
// incomplete
SkDebugf("!k");
}
}
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 {
if (t == 0) {
return fPts[0];
}
if (t == 1) {
return fPts[2];
}
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 point rationale */
/* w rationale : the mid point between t1 and t2 could be determined from the computed a/b/c
values if the computed w was known. Since we know the mid point at (t1+t2)/2, we'll assume
that it is the same as the point on the new curve t==(0+1)/2.
d / dz == conic_poly(dst, unknownW, .5) / conic_weight(unknownW, .5);
conic_poly(dst, unknownW, .5)
= a / 4 + (b * unknownW) / 2 + c / 4
= (a + c) / 4 + (bx * unknownW) / 2
conic_weight(unknownW, .5)
= unknownW / 2 + 1 / 2
d / dz == ((a + c) / 2 + b * unknownW) / (unknownW + 1)
d / dz * (unknownW + 1) == (a + c) / 2 + b * unknownW
unknownW = ((a + c) / 2 - d / dz) / (d / dz - b)
Thus, w is the ratio of the distance from the mid of end points to the on-curve point, and the
distance of the on-curve point to the control point.
*/
SkDConic SkDConic::subDivide(double t1, double t2) const {
double ax, ay, az;
if (t1 == 0) {
ax = fPts[0].fX;
ay = fPts[0].fY;
az = 1;
} else if (t1 != 1) {
ax = conic_eval_numerator(&fPts[0].fX, fWeight, t1);
ay = conic_eval_numerator(&fPts[0].fY, fWeight, t1);
az = conic_eval_denominator(fWeight, t1);
} else {
ax = fPts[2].fX;
ay = fPts[2].fY;
az = 1;
}
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, cy, cz;
if (t2 == 1) {
cx = fPts[2].fX;
cy = fPts[2].fY;
cz = 1;
} else if (t2 != 0) {
cx = conic_eval_numerator(&fPts[0].fX, fWeight, t2);
cy = conic_eval_numerator(&fPts[0].fY, fWeight, t2);
cz = conic_eval_denominator(fWeight, t2);
} else {
cx = fPts[0].fX;
cy = fPts[0].fY;
cz = 1;
}
double bx = 2 * dx - (ax + cx) / 2;
double by = 2 * dy - (ay + cy) / 2;
double bz = 2 * dz - (az + cz) / 2;
SkDConic dst = {{{{ax / az, ay / az}, {bx / bz, by / bz}, {cx / cz, cy / cz}}
SkDEBUGPARAMS(fPts.fDebugGlobalState) },
SkDoubleToScalar(bz / sqrt(az * cz)) };
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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