An Analytical Solution to Single Scattering in Homogeneous Participating Media

Despite their numerous applications, efficiently rendering participating media remains a challenging task due to the intricacy of the radiative transport equation. As they provide a generic means of solving a wide variety of problems, numerical methods are most often used to solve the air-light integral even under simplifying assumptions. In this paper, we present a novel analytical approach to single scattering from isotropic point light sources in homogeneous media. We derive the first closed-form solution to the air-light integral in isotropic media and extend this formulation to anisotropic phase functions. The technique relies neither on pre-computation nor on storage, and we provide a practical implementation allowing for an explicit control on the accuracy of the solutions. Finally, we demonstrate its quantitative and qualitative benefits over both previous numerical and analytical approaches.