The Stochastic Ray Method for Radiosity

This paper solves the system of radiosity equations with a stochastic numerical approach. Due to the high complexity of the problem for highly complex scenes, a stochastic variation of Jacobi iteration is developed which converges stochastically to the correct solution. The new method, called the Stochastic Ray Method, is a significant improvement of Stochastic Radiosity. A large number of independent rays is chosen stochastically by importance sampling of the patches according to their power after the previous iteration step. They all carry an equal amount of power into random directions, thereby representing together the total energy interreflection of the entire environment in a stochastic manner. Assuming a correctly distributed initial solution, which can be reached easily, the iteration process converges quickly and reduces the error in the result faster than other stochastic radiosity approaches. The new algorithm can easily be extended to treat various phenomena which are normally rather costly to incorporate in radiosity environments, perfect specular reflection and specular transmittance, non-diffuse self-emission and point light sources.