**Abstract:**

The paper introduces a global illumination method that combines 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. Iteration and random walk 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 walkthrough animation in glossy scenes since when the viewpoint changes, only the small Monte-Carlo component needs to be recomputed.

**Keywords:**

Rendering equation, global radiance, Monte-Carlo Carlo integration,
light-tracing, global ray-bundle tracing.