// Stolen from: http://stackoverflow.com/questions/849211/shortest-distance-between-a-point-and-a-line-segment
// Return minimum distance point on line segment vw minimizing the distance to point p
PD nearestPointOnLineSegment(PD v, PD w, PD p) {
if(epsEq(v, w))
return v; // v == w case. Avoid division by zero.
double l2 = distSquared(v, w);
// Consider the line extending the segment, parameterized as v + t (w - v).
// We find projection of point p onto the line.
// It falls where t = [(p-v) . (w-v)] / |w-v|^2
// We clamp t from [0,1] to handle points outside the segment vw.
PD wv = w-v;
double t = clamp01(dotProduct(p-v, wv) / l2);
PD projection = v + (wv * t); // Projection falls on the segment
return projection;
}
double epsEq(PD a, PD b) {
return epsEq(a.XX, b.XX) && epsEq(a.YY, b.YY);
}
static int epsLteF(const float a, const float b)
{
return b > a || epsEq(a, b); // Not necessarily great numerically
}