Question

I’m having a hard time following the ray-plane intersection described in the following page.

SIGGRAPH Ray-Plane Intersection

Here is my understanding.

The plane is described as Ax + By + Cz + D = 0

or

The Vector ( A, B, C, D ), Where A, B, C define a normal plan. If A, B, and C define a unit normal, then the distance from the origin [0, 0, 0] to the plan is D.

My question is shouldn’t D be a vector? Since it represents the distants between two points. I guess I just don’t understand how you can represent the distance between to points as a non vector.

Any help is much appreciated.

Answer 1

Distance between two points is ALWAYS a scalar, a single number. Think of the vectors as points in space, right? So, when you say distance between two vectors, you are finding the distance between those two points which is a number. Distance between two vectors is the magnitude of the difference vector of the two vectors. So, you subtract the 2 vectors, get the difference vector and find its magnitude. That is your distance which is a SCALAR and NOT a vector.