// from http://blog.gludion.com/2009/08/distance-to-quadratic-bezier-curve.html
// (currently only used by testing)
double SkDQuad::nearestT(const SkDPoint& pt) const {
SkDVector pos = fPts[0] - pt;
// search points P of bezier curve with PM.(dP / dt) = 0
// a calculus leads to a 3d degree equation :
SkDVector A = fPts[1] - fPts[0];
SkDVector B = fPts[2] - fPts[1];
B -= A;
double a = B.dot(B);
double b = 3 * A.dot(B);
double c = 2 * A.dot(A) + pos.dot(B);
double d = pos.dot(A);
double ts[3];
int roots = SkDCubic::RootsValidT(a, b, c, d, ts);
double d0 = pt.distanceSquared(fPts[0]);
double d2 = pt.distanceSquared(fPts[2]);
double distMin = SkTMin(d0, d2);
int bestIndex = -1;
for (int index = 0; index < roots; ++index) {
SkDPoint onQuad = ptAtT(ts[index]);
double dist = pt.distanceSquared(onQuad);
if (distMin > dist) {
distMin = dist;
bestIndex = index;
}
}
if (bestIndex >= 0) {
return ts[bestIndex];
}
return d0 < d2 ? 0 : 1;
}
bool SkDCubic::controlsContainedByEnds() const {
SkDVector startTan = fPts[1] - fPts[0];
if (startTan.fX == 0 && startTan.fY == 0) {
startTan = fPts[2] - fPts[0];
}
SkDVector endTan = fPts[2] - fPts[3];
if (endTan.fX == 0 && endTan.fY == 0) {
endTan = fPts[1] - fPts[3];
}
if (startTan.dot(endTan) >= 0) {
return false;
}
SkDLine startEdge = {{fPts[0], fPts[0]}};
startEdge[1].fX -= startTan.fY;
startEdge[1].fY += startTan.fX;
SkDLine endEdge = {{fPts[3], fPts[3]}};
endEdge[1].fX -= endTan.fY;
endEdge[1].fY += endTan.fX;
double leftStart1 = startEdge.isLeft(fPts[1]);
if (leftStart1 * startEdge.isLeft(fPts[2]) < 0) {
return false;
}
double leftEnd1 = endEdge.isLeft(fPts[1]);
if (leftEnd1 * endEdge.isLeft(fPts[2]) < 0) {
return false;
}
return leftStart1 * leftEnd1 >= 0;
}