Stochastic Iteration for Non-diffuse Global Illumination

Abstract

This paper presents a single-pass, view-dependent method to solve the rendering equation, using a stochastic iterational scheme where the transport operator is selected randomly in each iteration. The requirements of convergence are given for the general case. To demonstrate the basic idea, a very simple,continuous random transport operator is examined, which gives back the light tracing algorithm incorporating Russian roulette. Then, a new mixed continuous and finite-element based iteration method is proposed, which uses ray-bundles to transfer the radiance in a single random direction. The resulting algorithm is fast, it provides initial results in seconds and accurate solutions in minutes and does not suffer from the error accumulation problem and the high memory demand of other finite-element and hierarchical approaches.