/* see quad subdivide for rationale */
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;
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::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;
}
