closestPointToPoint method

Vector3 closestPointToPoint(Vector3 p, Vector3 target)

Implementation

Vector3 closestPointToPoint(Vector3 p, Vector3 target) {
  final a = this.a, b = this.b, c = this.c;
  double v, w;

  // algorithm thanks to Real-Time Collision Detection by Christer Ericson,
  // published by Morgan Kaufmann Publishers, (c) 2005 Elsevier Inc.,
  // under the accompanying license; see chapter 5.1.5 for detailed explanation.
  // basically, we're distinguishing which of the voronoi regions of the triangle
  // the point lies in with the minimum amount of redundant computation.

  _vab.sub2(b, a);
  _vac.sub2(c, a);
  _vap.sub2(p, a);
  final d1 = _vab.dot(_vap);
  final d2 = _vac.dot(_vap);
  if (d1 <= 0 && d2 <= 0) {
    // vertex region of A; barycentric coords (1, 0, 0)
    return target.setFrom(a);
  }

  _vbp.sub2(p, b);
  final d3 = _vab.dot(_vbp);
  final d4 = _vac.dot(_vbp);
  if (d3 >= 0 && d4 <= d3) {
    // vertex region of B; barycentric coords (0, 1, 0)
    return target.setFrom(b);
  }

  final vc = d1 * d4 - d3 * d2;
  if (vc <= 0 && d1 >= 0 && d3 <= 0) {
    v = d1 / (d1 - d3);
    // edge region of AB; barycentric coords (1-v, v, 0)
    return target.setFrom(a).addScaled(_vab, v);
  }

  _vcp.sub2(p, c);
  final d5 = _vab.dot(_vcp);
  final d6 = _vac.dot(_vcp);
  if (d6 >= 0 && d5 <= d6) {
    // vertex region of C; barycentric coords (0, 0, 1)
    return target.setFrom(c);
  }

  final vb = d5 * d2 - d1 * d6;
  if (vb <= 0 && d2 >= 0 && d6 <= 0) {
    w = d2 / (d2 - d6);
    // edge region of AC; barycentric coords (1-w, 0, w)
    return target.setFrom(a).addScaled(_vac, w);
  }

  final va = d3 * d6 - d5 * d4;
  if (va <= 0 && (d4 - d3) >= 0 && (d5 - d6) >= 0) {
    _vbc.sub2(c, b);
    w = (d4 - d3) / ((d4 - d3) + (d5 - d6));
    // edge region of BC; barycentric coords (0, 1-w, w)
    return target.setFrom(b).addScaled(_vbc, w); // edge region of BC

  }

  // face region
  final denom = 1 / (va + vb + vc);
  // u = va * denom
  v = vb * denom;
  w = vc * denom;

  return target.setFrom(a).addScaled(_vab, v).addScaled(_vac, w);
}