An analytical approach to single scattering for anisotropic media and light distributions

Despite their numerous applications, efficiently rendering participating media remains a challenging task due to the intricacy of the radiative transport equation. While numerical techniques remain the method of choice for addressing complex problems, a closed-form solution to the air-light integral in optically thin isotropic media was recently derived. In this paper, we extend this work and present a novel analytical approach to single scattering from point light sources in homogeneous media. We propose a combined formulation of the air-light integral which allows both anisotropic phase functions and light distributions to be adequately handled. The technique relies neither on precomputation nor on storage, and we provide a robust and efficient implementation allowing for an explicit control on the accuracy of the results. Finally, the performance characteristics of the method on graphics hardware are evaluated and demonstrate its suitability to real-time applications.