Stratified Sampling of Projected Spherical Caps

Abstract

We present a method for uniformly sampling points inside the projection of a spherical cap onto a plane through the sphere's center. To achieve this, we devise two novel area-preserving mappings from the unit square to this projection, which is often an ellipse but generally has a more complex shape. Our maps allow for low-variance rendering of direct illumination from finite and infinite (e.g. sun-like) spherical light sources by sampling their projected solid angle in a stratified manner. We discuss the practical implementation of our maps and show significant quality improvement over traditional uniform spherical cap sampling in a production renderer.