**Abstract:**

The hemicube is a classical tool to transfer the power in diffuse radiosity algorithms. The main advantage of the hemicube based light transfer is that the visible patches can easily be identified by the graphics hardware. This paper extends the hemicube approach to solve the non-diffuse global illumination problem. In order to get rid of the quadratic complexity of classical radiosity algorithms and to allow specular surfaces without storing directional finite-elements, the original iteration is replaced by stochastic iteration. Unlike classical iteration where all patches should be selected to gather the radiosity or to shoot their unshot radiosity, stochastic iteration can exploit that a randomly selected patch may represent its neighbors as well, thus accurate results can be obtained even if just a fraction of patches are selected at all. Since stochastic iteration requires just a random approximation of the patch radiance, it can use just a single variable per patch even if the general, non-diffuse problem is attacked. The final result will be computed in the image space as the average of these random radiance approximations. Random selection, however, may introduce noise that is particularly significant where the source and receiver patches are close. We also propose a solution strategy to eliminate these artifacts. The paper also discusses further improvements by applying constant radiance step and by the randomization of the hemicube.

**Keywords:**

Stochastic iteration, hemicube, biased Monte-Carlo methods.