Computer Graphics Forum (Proceedings of Eurographics Symposium on Rendering 2024)
Abstract
Explicit sampling of and connecting to light sources is often essential for reducing variance in Monte Carlo rendering. In dense,
forward-scattering participating media, its benefit declines, as significant transport happens over longer multiple-scattering
paths around the straight connection to the light. Sampling these paths is challenging, as their contribution is shaped by the
product of reciprocal squared distance terms and the phase functions. Previous work demonstrates that sampling several of
these terms jointly is crucial. However, these methods are tied to low-order scattering or struggle with highly-peaked phase
functions.
We present a method for sampling a bridge: a subpath of arbitrary vertex count connecting two vertices. Its probability density
is proportional to all phase functions at inner vertices and reciprocal squared distance terms. To achieve this, we importance
sample the phase functions first, and subsequently all distances at once. For the latter, we sample an independent, preliminary
distance for each edge of the bridge, and afterwards scale the bridge such that it matches the connection distance. The scale
factor can be marginalized out analytically to obtain the probability density of the bridge. This approach leads to a simple
algorithm and can construct bridges of any vertex count. For the case of one or two inserted vertices, we also show an alternative
without scaling or marginalization.
For practical path sampling, we present a method to sample the number of bridge vertices whose distribution depends on
the connection distance, the phase function, and the collision coefficient. While our importance sampling treats media as
homogeneous we demonstrate its effectiveness on heterogeneous media.
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Bibtex
@article{2024_bridges,
author = {Vincent Schüßler and Johannes Hanika and Carsten Dachsbacher},
title = {{Bridge Sampling for Connections via Multiple Scattering Events}},
journal = {Computer Graphics Forum (Proceedings of Eurographics Symposium on Rendering)},
volume = 43,
number = 4,
year = 2024,
publisher = {The Eurographics Association and John Wiley \& Sons Ltd.},
doi = {10.1111/cgf.15160}
}
