Unifying Continuous Random-Walk and

Finite-Element Based Iteration Type

Global Illumination Algorithms

Szirmay-Kalos László
Department of Control Engineering and Information Technology, Technical University of Budapest,
Budapest, Muegyetem rkp. 11, H-1111, HUNGARY


The paper introduces a method that can combine continuous and finite-element approaches, preserving the speed of finite-element based iteration and the accuracy of continuous random walks.
The basic idea is to decompose the radiance function to a finite-element component that is only a rough estimate and to a difference component that is obtained by Monte-Carlo techniques. The classical iteration using finite-elements and random walks are handled uniformly in the framework of stochastic iteration. This uniform treatment allows the finite-element component to be built up adaptively aiming at minimizing the Monte-Carlo component. The method is also suited for interactive walkthroughs and view-animation since when the viewpoint changes, only the small Monte-Carlo component needs to be recomputed. With this approach quite complex scenes consisting of tens of thousands of surface elements can be rendered in about a minute, and when the solution is available, we can walk in the scene


Non-diffuse global illumination, stochastic iteration, Monte-Carlo quadrature, global methods, finite-element techniques, random-walk

7 seconds, first-shot
20 seconds, first-shot + 10 iterations
45 seconds, first-shot + 30 iterations
7 seconds, first-shot
20 seconds, first-shot+10 iterations
46 seconds, first-shot+30 iterations