Figure 1: Volume visualizations of tetrahedral meshes which have been encoded in a compact texture representation based on tetrahedral strips and are stored in the texture memory of the graphics adapter. The renderings have been computed with a ray casting algorithm for programmable graphics hardware adapted for this mesh representation. ABSTRACTThe use of triangle strips is a common method to compactly store and efficiently render large polygonal meshes. The advantages of triangle stripification also apply to tetrahedral meshes; therefore, tetrahedral strips are an attractive data structure for storing and volume rendering tetrahedral meshes as noted in several publications. However, tetrahedral strips are still not supported by current graphics hardware.In this paper, we present the first system to take advantage of tetrahedral strips in off-the-shelf graphics hardware. This is achieved by encoding tetrahedral strips in texture maps and rendering them with the help of a ray casting algorithm running solely on the graphics chip. Our data structure supports sequential and generalized tetrahedral strips by including a small amount of adjacency information, which allows us to access all face neighbors in constant time.Utilizing these texture-encoded tetrahedral strips, our enhanced graphics-hardware-based volume ray casting algorithm for tetrahedral meshes is capable of handling large data sets. Additional improvements presented in this paper include support for multiple ray traversal steps in one rendering pass and the intrinsic support for non-convex meshes using a rendering technique similar to depth peeling.

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For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions, classical diffusion approximation suffers from non-physical radiative fluxes which leads to a poor match to correct light transport. In particular, this prevents the application of classical diffusion approximation to heterogeneous media, where opaque material is embedded within transparent regions. To address this limitation, we introduce flux-limited diffusion, a technique from the astrophysics domain. This method provides a better approximation to light transport than classical diffusion approximation, particularly when applied to heterogeneous media, and hence broadens the applicability of diffusion-based techniques. We provide an algorithm for flux-limited diffusion, which is validated using the transport theory for a point light source in an infinite homogeneous medium. We further demonstrate that our implementation of flux-limited diffusion produces more accurate renderings of multiple scattering in various heterogeneous datasets than classical diffusion approximation, by comparing both methods to ground truth renderings obtained via volumetric path tracing.Comment: Accepted in Computer Graphics Foru

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