László Szirmay-Kalos , Milán Magdics , and Mateu Sbert 
 Department of Control Engineering and Information Technology, Budapest University of Technology and Economics,
 Tianjin University; University of Girona
Rendering inhomogeneous participating media requires a lot of volume samples since the extinction coefficient needs to be integrated along light paths. Ray marching makes small steps, which is time consuming and leads to biased algorithms. Woodcock-like approaches use analytic sampling and a random rejection scheme guaranteeing that the expectations will be the same as in the original model. These models and the application of control variates for the extinction have been successful to compute transmittance and single scattering but were not fully exploited in multiple scattering simulation. Our paper attacks the multiple scattering problem in heterogeneous media and modifies the light--medium interaction model to allow the use of simple analytic formulae while preserving the correct expected values. The model transformation reduces the variance of the estimates with the help of Rao-Blackwellization and control variates applied both for the extinction coefficient and the incident radiance. Based on the transformed model, efficient Monte Carlo rendering algorithms are obtained.
Keywords: Participating media, multiple scattering, free path sampling, Woodcock tracking, Monte Carlo method, Volumetric global illumination.