How to do ray plane intersection?

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;

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);
}