Heterogeneous Subsurface Scattering Using the Finite Element Method

Abstract

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.

A practical analytic model for the radiosity of translucent scenes

“…Dipole diffusion model [Jensen et al 2001] for highly scattering materials is easy to implement, much faster than MonteCarlo simulations and has been widely used in computer graphics. Later works extended this diffusion model to support multilayer translucent materials [Donner and Jensen 2005], heterogeneous translucent materials [Wang et al 2008a;Arbree et al 2011], anisotropic diffusion [Jakob et al 2010]. To accelerate the rendering speed of translucent objects, hierarchical methods [Jensen and Buhler 2002;Arbree et al 2008] have been proposed to support large scenes with complex illumination.…”

“…Again, measurements such as those from the DISCO system [Goesele et al 2004], or numerical evaluations [Wang et al 2008a;Arbree et al 2011], can be incorporated. We present a simple heuristic in the next section to generate plausible renderings by combining the scattering properties of multiple homogeneous materials.…”

TransCut: Interactive Rendering of Translucent Cutouts

“…While existing algorithms for heterogeneous translucent materials offer fast [1] or even real-time [7] rendering performance, none of them can efficiently handle dynamic object fracturing and cutting operations. The finite element method of Arbree et al [1] produces excellent visual results but is unsuitable for interactive applications due to the high cost of numerical integration.…”

“…The finite element method of Arbree et al [1] produces excellent visual results but is unsuitable for interactive applications due to the high cost of numerical integration. In the real-time finite difference (FD) method of Wang et al [7], the nonregular meshes that often result from cutting or fracturing operations lead to much degradation in rendering quality.…”

“…The solver is derived from a direct discretization of the divergence operator based on finite elements/volumes. While producing results comparable to the state-of-art method of Arbree et al [1], the discrete divergence-based solver moreover takes advantage of analytic formulas for linear finite elements to efficiently construct the linear system matrix for solving the diffusion equation. In this way, it avoids the time-consuming numerical integration used in Arbree et al [1] and obtains significantly faster performance.…”