// calcuate barycentric coordinates (u,v,w) for point p with respect to triangle (a,b,c)
// use 3d PVector to store u,v,w
// https://en.wikipedia.org/wiki/Barycentric_coordinate_system

PVector getBaryCentric(PVector p, PVector a, PVector b, PVector c) {
  PVector v0 = PVector.sub(b, a);
  PVector v1 = PVector.sub(c, a);
  PVector v2 = PVector.sub(p, a);
  float den = v0.x * v1.y - v1.x * v0.y;
  float v = (v2.x * v1.y - v1.x * v2.y) / den;
  float w = (v0.x * v2.y - v2.x * v0.y) / den;
  float u = 1.0f - v - w;
  return new PVector(u, v, w);
}