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Issue No.07 - July (2011 vol.17)
pp: 956-969
Adam Arbree , Autodesk® Corporation, San Francisco
Bruce Walter , Cornell University, Ithaca
Kavita Bala , Cornell University, Ithaca
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 with two key elements: the diffusive source boundary condition (DSBC)—an accurate model of the reduced intensity (RI) source—and its associated render query function. Second, we solve this formulation accurately and efficiently using the FE method. With these contributions, 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 match path traced references, that required hours.
INDEX TERMS
Three-dimensional graphics and realism, color, shading, shadowing, texture, miscellaneous, subsurface scattering, partial differential equations, finite element methods.
CITATION
Adam Arbree, Bruce Walter, Kavita Bala, "Heterogeneous Subsurface Scattering Using the Finite Element Method", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 7, pp. 956-969, July 2011, doi:10.1109/TVCG.2010.117
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