I'm trying to create a pointy "ball" in 3d space using triangles. I want each triangle to pass through a sphere's center, with each point lying on the surface.
I can easily make points on the surface. Currently I'm doing this by creating a direction vector with random values between -1 and 1. Then I normalize the vector and multiply by the radius to get the final point.
My question is, given two of these points, how can I create a third that is (a) at least semi-random, and (b) ensure it creates a triangle coplanar with the sphere's center.
Update: Forgot to mention, the center of the sphere is always located at (0,0,0)