A Closed-Form Solution to Single Scattering for General Phase Functions and Light Distributions

Due to the intricate nature of the equation governing light transport in participating media, accurately and efficiently simulating radiative energy transfer remains very challenging in spite of its broad range of applications. As an alternative to traditional numerical estimation methods such as ray-marching and volume-slicing, a few analytical approaches to solving single scattering have been proposed but current techniques are limited to the assumption of isotropy, rely on simplifying approximations and/or require substantial numerical precomputation and storage. In this paper, we present the very first closed-form solution to the air-light integral in homogeneous media for general 1-D anisotropic phase functions and punctual light sources. By addressing an open problem in the overall light transport literature, this novel theoretical result enables the analytical computation of exact solutions to complex scattering phenomena while achieving semi-interactive performance on graphics hardware for several common scattering modes.