How to do ray plane intersection?

Pontus Magnusson picture Pontus Magnusson · Jun 1, 2014 · Viewed 39.9k times · Source

How do I calculate the intersection between a ray and a plane?

Code

This produces the wrong results.

float denom = normal.dot(ray.direction);

if (denom > 0)
{
    float t = -((center - ray.origin).dot(normal)) / denom;

    if (t >= 0)
    {
        rec.tHit = t;
        rec.anyHit = true;
        computeSurfaceHitFields(ray, rec);
        return true;
    }
}

Parameters

ray represents the ray object.
ray.direction is the direction vector.
ray.origin is the origin vector.
rec represents the result object.
rec.tHit is the value of the hit.
rec.anyHit is a boolean.

My function has access to the plane:
center and normal defines the plane

Answer

Trillian picture Trillian · Jun 1, 2014

As wonce commented, you want to also allow the denominator to be negative, otherwise you will miss intersections with the front face of your plane. However, you still want a test to avoid a division by zero, which would indicate the ray being parallel to the plane. You also have a superfluous negation in your computation of t. Overall, it should look like this:

float denom = normal.dot(ray.direction);
if (abs(denom) > 0.0001f) // your favorite epsilon
{
    float t = (center - ray.origin).dot(normal) / denom;
    if (t >= 0) return true; // you might want to allow an epsilon here too
}
return false;