Function getDistancePointToTriangle

src/utilities/geometry/Geometry.cpp:301–378

}

double getDistancePointToTriangle(const Point3d& point, const std::vector<Point3d>& triangle) {
  if (triangle.size() != 3) {
    return 0;
  }

  //Distance Between Point and Triangle in 3D
  //David Eberly
  //Geometric Tools, LLC
  //http://www.geometrictools.com/

  //T(s; t) = B+sE0+tE1

  const Point3d& B = triangle[0];
  const Vector3d E0 = triangle[1] - triangle[0];
  const Vector3d E1 = triangle[2] - triangle[0];
  const Vector3d BminusP = B - point;

  const double b = E0.dot(E1);

  if (std::abs(b) > 1.0 - 1.0E-12) {
    // triangle is collinear
    return 0;
  }

  const double a = E0.dot(E0);
  const double c = E1.dot(E1);
  const double d = E0.dot(BminusP);
  const double e = E1.dot(BminusP);
  // const double f = BminusP.dot(BminusP); // unused

  const double det = a * c - b * b;
  const double s = b * e - c * d;
  const double t = b * d - a * e;

  Point3d closestPoint;

  if (s + t <= det) {
    if (s < 0) {
      if (t < 0) {
        //region 4, closest to point triangle[0]
        return getDistance(point, triangle[0]);
      } else {
        //region 3, closest to line triangle[0] to triangle[2]
        std::vector<Point3d> line;
        line.push_back(triangle[0]);
        line.push_back(triangle[2]);
        return getDistancePointToLineSegment(point, line);
      }
    } else if (t < 0) {
      //region 5, closest to line triangle[0] to triangle[1]
      std::vector<Point3d> line;
      line.push_back(triangle[0]);
      line.push_back(triangle[1]);
      return getDistancePointToLineSegment(point, line);
    } else {
      //region 0, closest point is inside triangle
      const double invDet = 1.0 / det;
      closestPoint = B + invDet * s * E0 + invDet * t * E1;