Benedikt Bitterli

A radiative transfer framework
for non-exponential media

Benedikt Bitterli   Srinath Ravichandran   Thomas Müller   Magnus Wrenninge
Jan Novák   Steve Marschner   Wojciech Jarosz

In ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia), 2018

A radiative transfer framework for non-exponential media

We show a cloud rendered with a traditional exponential transmittance (left) and with a non-exponential, long-tailed transmittance curve (right). The non-exponential transmittance leads to both deeper light penetration as well as a softer appearance near the surface, allowing for a richer appearance.


We develop a new theory of volumetric light transport for media with non-exponential free-flight distributions. Recent insights from atmospheric sciences and neutron transport demonstrate that such distributions arise in the presence of correlated scatterers, which are naturally produced by processes such as cloud condensation and fractal-pattern formation. Our theory formulates a non-exponential path integral as the result of averaging stochastic classical media, and we introduce practical models to solve the resulting averaging problem efficiently. Our theory results in a generalized path integral which allows us to handle non-exponential media using the full range of Monte Carlo rendering algorithms while enriching the range of achievable appearance. We propose parametric models for controlling the statistical correlations by leveraging work on stochastic processes, and we develop a method to combine such unresolved correlations (and the resulting non-exponential free-flight behavior) with explicitly modeled macroscopic heterogeneity. This provides a powerful authoring approach where artists can freely design the shape of the attenuation profile separately from the macroscopic heterogeneous density, while our theory provides a physically consistent interpretation in terms of a path space integral. We address important considerations for graphics including reciprocity and bidirectional rendering algorithms, all in the presence of surfaces and correlated media.




Presentation Video (contains narration)