Heterogeneous Subsurface Scattering Using the Finite Element Method

Adam Arbree, Bruce Walter, Kavita Bala

Transactions on Visualization and Computer Graphics

Abstract: Materials with visually important heterogeneous subsurface scattering, including marble, skin, leaves, and minerals, are common in the real world. However, general, accurate and efficient rendering of these materials is an open problem. In this paper, we describe a finite element (FE) solution of the heterogeneous diffusion equation (DE) that solves this problem. Our algorithm is the first to use the FE method to solve the difficult problem of heterogeneous subsurface rendering. To create our algorithm, we make two contributions. First, we correct previous work and derive an accurate and complete heterogeneous diffusion formulation. This formulation has two key elements: an accurate model of the reduced intensity (RI) source, the diffusive source boundary condition (DSBC), and its associated render query function. Second, we solve this formulation accurately and efficiently using the FE method. Using there results, we can render subsurface scattering with a simple four step algorithm. To demonstrate that our algorithm is simultaneously general, accurate and efficient, we test its performance on a series of difficult scenes. For a wide range of materials and geometry, it produces, in minutes, images that nearly match path traced references, that required hours.

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