My idea of physically based blue noise generation relies on the interaction of charged particles on a plane, and I found it possible to formulate similar repulsive forces between particles over the sphere using an angular formulation. The sphere-native resultant point set is useful for illumination integration when a Quasi Monte Carlo approach is desired. The following is the abstract of the short paper accepted by Pacific Graphics 2018.
[ Abstract ] We present a physically based method which generates unstructured uniform point set directly on the S2-sphere. Spherical uniform point sets are useful for illumination sampling in Quasi Monte Carlo (QMC) rendering but it is challenging to generate high quality uniform point sets directly. Most methods rely on mapping the low discrepancy unit square point sets to the spherical domain. However, these transformed point sets often exhibit sub-optimal uniformity due to the inability of preserving the low discrepancy properties. Our method is designed specifically for direct generation of uniform point sets in the spherical domain. We name our generated result as Spherical Blue Noise point set because it shares similar point distribution characteristics with the 2D blue noise. Our point sets possess high spatial uniformity without a global structure, and we show that they deliver competitive results for illumination integration in QMC rendering, and general numerical integration on the spherical domain.
The following video is a real-time generation demo of a spherical blue noise point set (see below).
