Best way to test if some point on a line if in front of another point on the same line in 3D

Question

I have a line in 3D defined by point P0 and direction vector D. For given input point P on a line defined as above, I want to test if P is in front of point P0. The code will be used in GLSL fragment shader.

So far, my best solution is following GLSL function:

bool IsInFront(vec3 P, vec3 P0, vec3 D)
{
  float d = length(P - P0);
  vec3 Pp = P0 + d * D;
  return (length(Pp - P) < 1.0E-4);
}

Explanation is simple. d is distance between P and P0, and there are only two possible positions on a line where a point with distance d from point P0 can be on a line: in front, or behind point P0. Then I just check if positive point is same as input P.

However, this code uses precision 1.0E-4, and recalculation of input point P. Is there a faster and numerically more stable way to do this?

Regards

Answer 1

I think I found an answer by myself.

bool IsInFront(vec3 P, vec3 P0, vec3 D)
{
  vec3 D2 = P - P0;
  float c = dot(D, D2);
  return (c > 0.0);
}

In this solution, D2 is unnormalized vector from P0 to P which is either in same or opposite direction compared to D. c is cosine similarity between D and D2 multiplied by length of vector D2. It is either length of vector D2, or negated length of vector D2 depending on it's orientation.

Answer 2

Not sure if its relevant (Not 100% sure what your actually asking, but ill attempt my advice anyway) but use a raycast, this will then have a function that allows you to measure the "ray's" distance between the player and an object, or 2 objects if you prefer.