Stratified Sampling of Projected Spherical Caps

Carlos Ureña, Iliyan Georgiev
EGSR 2018

Our method can be used for importance sampling the direct illumination from spherical light sources. In the absence of occlusion in diffuse scenes, solid angle sampling (left) has non-zero variance, while our sampling technique (right) gives the exact illumination solution with a single sample per light source.


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.

Downloads and links

  • paper (PDF, 5.5 MB)
  • citation (BIB)
  • code - a C++ implementation of our two area-preserving projected spherical cap maps

BibTeX reference

    Author = {Carlos Ure\~{n}a and Iliyan Georgiev},
    Journal = {Computer Graphics Forum (Proceedings of EGSR)},
    Number = {4},
    Title = {Stratified Sampling of Projected Spherical Caps},
    Volume = {37},
    Year = {2018}