Heterogeneous Subsurface Scattering Using the Finite Element Method
Adam Arbree, Bruce Walter, Kavita Bala
Transactions on Visualization and Computer Graphics
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.