const double EPSILON = 0.000001;
bool line_intercepts_triangle(const Ray& r, const Triangle& t){
  // Normals for the triangle's edges.
  Vector e1(t.b, t.a), // Normal from vertex 1 to vertex 0
         e2(t.c, t.a); // Normal from vertex 2 to vertex 0

  // pvec = the cross product of the ray's direction and the v2-v0 normal
  Vector pvec;
  pvec.cross(r.d, e2);

  // Determinant
  double det = e1.dot_product(pvec);

  // If the determinant is 0, the ray is on the same plane as the triangle
  // Determinant == 0, modified for floating point imprecision
  if (det > -EPSILON && det < EPSILON)
    return false;

  // Inverse determinant
  double inv_det = 1.0 / det;

  // Distance from vertex 0 to the origin of the ray
  Vector tvec(r.o, t.a);

  // Calculate U value, and ensure it is valid
  double u = tvec.dot_product(pvec) * inv_det;
  if (u < 0.0 || u > 1.0)
    return false;

  // ??
  Vector qvec = tvec;
  qvec.cross(e1);

  // Calculate V value, and ensure it is valid
  double v = r.d.dot_product(qvec) * inv_det;
  if (v < 0.0 || u + v > 1.0)
    return false;

  return true;
}