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Graph."],"published-print":{"date-parts":[[2013,7,21]]},"abstract":"<jats:p>The highest fidelity images to date of complex materials like cloth use extremely high-resolution volumetric models. However, rendering such complex volumetric media is expensive, with brute-force path tracing often the only viable solution. Fortunately, common volumetric materials (fabrics, finished wood, synthesized solid textures) are structured, with repeated patterns approximated by tiling a small number of exemplar blocks. In this paper, we introduce a precomputation-based rendering approach for such volumetric media with repeated structures based on a modular transfer formulation. We model each exemplar block as a voxel grid and precompute voxel-to-voxel, patch-to-patch, and patch-to-voxel flux transfer matrices. At render time, when blocks are tiled to produce a high-resolution volume, we accurately compute low-order scattering, with modular flux transfer used to approximate higher-order scattering. We achieve speedups of up to 12\u00d7 over path tracing on extremely complex volumes, with minimal loss of quality. 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