An Analysis of Quasi-Monte Carlo Integration Applied to the Transillumination Radiosity Method

Abstract

This paper presents an enhanced transillumination radiosity method that can provide accurate solutions at relatively low computational cost. The proposed algorithm breaks down the double integral of the gathered power to an area integral that is computed analytically and to a directional integral that is evaluated by quasi-Monte Carlo techniques. Since the analytical integration results in a continuous function of finite variation, the quasi-Monte Carlo integration that follows the analytical integration will be efficient and its error can be bounded by the Koksma-Hlawka inequality. The paper also analyses the requirements of the convergence, presents theoretical error bounds and proposes error reduction techniques. The theoretical bounds are compared with simulation results.