barycentric coordinates triangle
// Compute barycentric coordinates (u, v, w) for
// point p with respect to triangle (a, b, c)
void Barycentric(Point p, Point a, Point b, Point c, float &u, float &v, float &w)
{
Vector v0 = b - a, v1 = c - a, v2 = p - a;
float d00 = Dot(v0, v0);
float d01 = Dot(v0, v1);
float d11 = Dot(v1, v1);
float d20 = Dot(v2, v0);
float d21 = Dot(v2, v1);
float denom = d00 * d11 - d01 * d01;
v = (d11 * d20 - d01 * d21) / denom;
w = (d00 * d21 - d01 * d20) / denom;
u = 1.0f - v - w;
}
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