Representing plane intersections as a system of linear equations

When you are watching a digitally-rendered battle onscreen in the latest blockbuster movie, you don’t always think about the “camera” moving about that scene. In the real-world, cameras have a field of view that dictates how much of the world about them they can see. Virtual cameras have a similar concept (called the viewing frustum) whereby they can only show so much of the digital scene. Everything else gets chopped off, so to speak. Because rendering a digital scene is a laborious task, computer scientists are very interested in making it go faster. Understandably, they only want to spend time drawing pixels that you’ll see in the final picture and forget about everything else (outside the field of view, or occluded (hidden) behind something else).

Our friends in the digital graphics world make heavy use of planes everyday, and being able to test for plane-plane intersection is extremely important.

In this post, I’ll try to break down what a plane is in understandable terms, how we can create one given a triangle, and how we would go about testing for the intersection between two of them.