How to do ray plane intersection?

Question

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

Code

This produces the wrong results.

float denom = normal.dot(ray.direction         


        

Answer 1

First consider the math of the ray-plane intersection:

In general one intersects the parametric form of the ray, with the implicit form of the geometry.

So given a ray of the form x = a * t + a0, y = b * t + b0, z = c * t + c0;

and a plane of the form: A x * B y * C z + D = 0;

now substitute the x, y and z ray equations into the plane equation and you will get a polynomial in t. you then solve that polynomial for the real values of t. With those values of t you can back substitute into the ray equation to get the real values of x, y and z. Here it is in Maxima:

Note that the answer looks like the quotient of two dot products! The normal to a plane is the first three coefficients of the plane equation A, B, and C. You still need D to uniquely determine the plane. Then you code that up in the language of your choice like so:

Point3D intersectRayPlane(Ray ray, Plane plane)
{
    Point3D point3D;

    //  Do the dot products and find t > epsilon that provides intersection.


    return (point3D);
}