The paper presents a single-pass, view-dependent method to solve the general rendering equation, using a combined finite element and random walk approach. Applying finite element techniques, the surfaces are decomposed into planar patches on which the radiance is assumed to be combined from finite number of unknown directional radiance functions by predefined positional basis functions. The directional radiance functions are then computed by random walk using bundles of parallel rays. To compute the radiance transfer in a single direction, several global visibility methods are considered, including the global versions of the painter's, z-buffer, Weiler-Atherton's and planar graph based algorithms. The method requires no preprocessing except for handling point lightsources, for which a first-shot technique is proposed. The proposed method is particularly efficient for scenes including not very specular materials illuminated by large area lightsources or sky-light. In order to increase the speed for difficult lighting situations, walks can be selected according to their importance. The importance can be explored adaptively by the Metropolis and VEGAS sampling techniques.
Rendering equation, global radiance, Monte-Carlo and quasi-Monte Carlo
integration, Importance sampling, Metropolis method, z-buffer.