Precomputed Multiple Scattering for Rapid Light Simulation in Participating Media

International audienceRendering translucent materials is costly: light transport algorithms need to simulate a large number of scattering events inside the material before reaching convergence. The cost is especially high for materials with a large albedo or a small mean-free-path, where higher-order scattering effects dominate. We present a new method for fast computation of global illumination with participating media. Our method uses precomputed multiple scattering effects, stored in two compact tables. These precomputed multiple scattering tables are easy to integrate with any illumination simulation algorithm. We give examples for virtual ray lights (VRL), photon mapping with beams and paths (UPBP), Metropolis Light Transport with Manifold Exploration (MEMLT). The original algorithms are in charge of low-order scattering, combined with multiple scattering computed using our table. Our results show significant improvements in convergence speed and memory costs, with negligible impact on accuracy

Fast hierarchical low-rank view factor matrices for thermal irradiance on planetary surfaces

We present an algorithm for compressing the radiosity view factor model commonly used in radiation heat transfer and computer graphics. We use a format inspired by the hierarchical off-diagonal low rank format, where elements are recursively partitioned using a quadtree or octree and blocks are compressed using a sparse singular value decomposition -- the hierarchical matrix is assembled using dynamic programming. The motivating application is time-dependent thermal modeling on vast planetary surfaces, with a focus on permanently shadowed craters which receive energy through indirect irradiance. In this setting, shape models are comprised of a large number of triangular facets which conform to a rough surface. At each time step, a quadratic number of triangle-to-triangle scattered fluxes must be summed; that is, as the sun moves through the sky, we must solve the same view factor system of equations for a potentially unlimited number of time-varying righthand sides. We first conduct numerical experiments with a synthetic spherical cap-shaped crater, where the equilibrium temperature is analytically available. We also test our implementation with triangle meshes of planetary surfaces derived from digital elevation models recovered by orbiting spacecrafts. Our results indicate that the compressed view factor matrix can be assembled in quadratic time, which is comparable to the time it takes to assemble the full view matrix itself. Memory requirements during assembly are reduced by a large factor. Finally, for a range of compression tolerances, the size of the compressed view factor matrix and the speed of the resulting matrix vector product both scale linearly (as opposed to quadratically for the full matrix), resulting in orders of magnitude savings in processing time and memory space.Comment: 21 pages, 10 figure