Determining the cut of any given polygon and pyramid

Question

I am trying to implement in C++ a function that determines the cut of any given polygon and pyramid.

This has actually turned out to be far simpler than I had first imagined.

Firstly for each edge of the pyramid, test line-plane intersection (the given polygon is a plane, made up of 3 points). This will result in the new vertices at the cutting plane.

Secondly, since the polygon is not an infinite plane one needs to test for line-line intersection between the polygon edges (three) and each of the edges.

Answer 1

Indeed, this is not a simple problem. For simplicity, let's assume that there are no parallel line segments.

First determine the plane where your convex polygon is in. Then detemerine the intersection of that plane with the pyramid. This results in a second convex polygon.

Now you should find the intersection of the two convex polygons. How this can be done, you can find here.