Approximations for the distribution of microflake normals

Scenes in computer animation can have extreme complexity, especially when high resolution objects are placed in the distance and occupy only a few pixels. A useful technique for level of detail in these cases is to use a sparse voxel octree containing both hard surfaces and a participating medium consisting of microflakes. In this paper, we discuss three different methods for approximating the distribution of normals of the microflakes, which is needed to compute extinction, inscattering of attenuated direct illumination, and multiple scattering in the participating medium. Specifically, we consider (a) k means approximation with k weighted representatives, (b) expansion in spherical harmonics, and (c) the distribution of the normals of a specific ellipsoid. We compare their image quality, data size, and computation time.