Area-preserving parameterizations for spherical ellipses

TL;DR

This paper introduces new area-preserving mappings from a square to spherical ellipses, enabling low-variance sampling of disk-shaped light sources for improved rendering quality.

Contribution

The authors develop two novel area-preserving mappings for spherical ellipses, enhancing stratified sampling efficiency in rendering applications.

Findings

Lower variance in sampling compared to previous methods

Effective integration into production rendering pipelines

Demonstrated improved rendering quality

Abstract

We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area-preserving mappings from the unit square $[0,1]^2$ to a spherical ellipse (i.e. the projection of the disk onto the unit sphere). These mappings allow for low-variance stratified sampling of direct illumination from disk-shaped light sources. We discuss how to efficiently incorporate our methods into a production renderer and demonstrate the quality of our maps, showing significantly lower variance than previous work.