Document Type

Technical Report

Publication Date


Technical Report Number



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 accommodates correlations by disentangling the concepts of the free-flight distribution and transmittance, which are equivalent when scatterers are statistically independent, but become distinct when correlations are present. 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 energy conservation, reciprocity, and bidirectional rendering algorithms, all in the presence of surfaces and correlated media.

Original Citation

Original posted in March 2018; "Revision 1" (metadata revision 2) posted on April 4, 2018.