# Area-preserving parameterizations for spherical ellipses

arXiv: https://arxiv.org/abs/1805.09048 · HTML: https://mlsanity.com/paper/1805.09048/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 1 of 1)

- [A Learned Radiance-Field Representation for Complex Luminaires](https://mlsanity.com/paper/2207.05009/) (2022)

## Abstract (arXiv)

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.