Generalized Projection Matrices

TL;DR

This paper introduces a unified generalized projection matrix that encompasses both perspective and orthographic projections, simplifying their integration in computer graphics rendering.

Contribution

It presents a novel mathematical formulation that unifies perspective and orthographic projection matrices into a single generalized form.

Findings

Unified projection matrix can represent both types seamlessly.

Simplifies rendering pipeline by reducing the need for separate projection matrices.

Potentially improves computational efficiency in graphics applications.

Abstract

Projection matrices are necessary for a large portion of rendering computer graphics. There are primarily two different types of projection matrices -- perspective and orthographic -- which are used frequently, and are traditionally treated as mutually incompatible with each other in how they are defined. Here, we bridge the gap between the two different forms of projection matrices to present a single generalized projection matrix that can represent both.