As a follow-up to my article on Model Matrix Rotations, I’m continuing my exploration of the OpenGL rendering pipeline’s mathematical foundations. This new article examines projection matrices, one of the final computational steps before rasterization transforms 3D geometry into the 2D pixels we see on screen.

The article provides mathematical derivations for both orthographic and perspective projection matrices, demonstrating how arbitrary view volumes in camera space are transformed into the canonical unit cube through clip space coordinates.

If you’re interested in how coordinate spaces work in 3D graphics, particularly in OpenGL, this article should be worth your time.