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 that are assumed to have position independent, but not direction independent radiance. The direction dependent radiance function is then computed by random walk using bundles of parallel rays. In a single step of the walk, the radiance transfer is evaluated exploiting the hardware z-buffer of workstations, making the calculation fast. 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 sampling method.
Rendering equation, Importance sampling, Metropolis method, z-buffer,
Monte-Carlo and quasi-Monte Carlo integration.