Bounding ellipsoids for ray-fractal intersection

Recently published papers have shown that, with appropriate intersection algorithms, the rendering of many procedural objects is possible with all the advantages offered by the ray-tracing techniques. In the case of stochastic surfaces, the intersection can be computed by a recursive subdivision technique. The efficiency of this algorithm depends essentially on the bounding volume whose size and shape are directly related to the stochastic characteristics of these surfaces. After a brief review of the rendering of stochastic surfaces and the bounding volume selection problem, two types of bounding volume are studied, describing how their intersection with a ray can be computed and how their size can be derived from the stochastic characteristics. The efficiency then, of these bounding volumes are compared.