1 research outputs found
-Method for Multiple Scattering in Participating Media
Rendering highly scattering participating media using brute force path
tracing is a challenge. The diffusion approximation reduces the problem to
solving a simple linear partial differential equation. Flux-limited diffusion
introduces non-linearities to improve the accuracy of the solution, especially
in low optical depth media, but introduces several ad-hoc assumptions. Both
methods are based on a spherical harmonics expansion of the radiance field that
is truncated after the first order. In this paper, we investigate the open
question of whether going to higher spherical harmonic orders provides a viable
improvement to these two approaches. Increasing the order introduces a set of
complex coupled partial differential equations (the -equations), whose
growing number make them difficult to work with at higher orders. We thus use a
computer algebra framework for representing and manipulating the underlying
mathematical equations, and use it to derive the real-valued -equations
for arbitrary orders. We further present a staggered-grid -solver and
generate its stencil code directly from the expression tree of the
-equations. Finally, we discuss how our method compares to prior work for
various standard problems.Comment: Proceedings of Eurographics Symposium on Rendering 201