We address the challenge of efficiently rendering massive assemblies of grains within a forward path-tracing framework. Previous approaches exist for accelerating high-order scattering for a limited, and static, set of granular materials, often requiring scene-dependent precomputation. We significantly expand the admissible regime of granular materials by considering heterogeneous and dynamic granular mixtures with spatially varying grain concentrations, pack rates, and sizes. Our method supports both procedurally generated grain assemblies and dynamic assemblies authored in off-the-shelf particle simulation tools. The key to our speedup lies in two complementary aggregate scattering approximations which we introduced to jointly accelerate construction of short and long light paths. For low-order scattering, we accelerate path construction using novel grain scattering distribution functions (GSDF) which aggregate intra-grain light transport while retaining important grain-level structure. For highorder scattering, we extend prior work on shell transport functions (STF) to support dynamic, heterogeneous mixtures of grains with varying sizes. We do this without a scene-dependent precomputation and show how this can also be used to accelerate light transport in arbitrary continuous heterogeneous media. Our multi-scale rendering automatically minimizes the usage of explicit path tracing to only the first grain along a light path, or can avoid it completely, when appropriate, by switching to our aggregate transport approximations. We demonstrate our technique on animated scenes containing heterogeneous mixtures of various types of grains that could not previously be rendered efficiently. We also compare to previous work on a simpler class of granular assemblies, reporting significant computation savings, often yielding higher accuracy results.
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