Using Hierarchical Simplicial Meshes to Render Atmospheric Effects

A fundamental element of computer graphics is producing realistic visualizations of various natural phenomena. An important problem in this area is that of rendering scenes containing atmospheric effects, which arise from the absorbtion and scattering of light due to small particles such as dust and smoke. Generating photorealistic renderings through ray-tracing is computationally very demanding because of the time needed to perform numerical integration along the length of each ray to determine the opacity and color of the gaseous media. We present a new data structure and algorithm for efficiently rendering atmospheric effects. Our approach is based on adaptively sampling a sparse set of the rays. Each ray is modeled as a point in a 4-dimensional space, and the results of the numerical integrations for these rays are computed accurately and stored in a 4-dimensional spatial index. The results for arbitrary rays are then computed through relatively inexpensive linear interpolations between neighboring sampled rays. In order for the interpolations to be continuous, it is important that the spatial index be based on a cell complex. This precludes the use of well-known structures such as kd-trees and octrees. Our spatial index is a recently discovered pointerless data structure, called a simplex decomposition tree, which is based on a hierarchical simplicial decomposition of space. In addition to presenting the data structure, we discuss a number of issues in the efficient application of this tree for rendering. We present empirical evidence that our approach can produce renderings of high quality significantly faster than simple ray-tracing. Given the centrality of sampling and reconstruction in computer graphics, this data structure is likely to be useful other applications in this field.