Tight bounding volumes for subdivision surfaces

We first demonstrate how to compute exact limit points and tangents for surfaces generated by an arbitrary, stationary subdivision scheme. We then describe how to construct simple bounding volumes for the patches of a subdivision surface and present a simple numerical technique to compute guaranteed bounds for the ranges of the basis functions being associated with the subdivision scheme. Merging the local bounding volumes allows us to generate envelope meshes which tightly enclose the limit surface and which have the same structure as the initial control mesh. The prominent applications for these envelope meshes are the efficient ray tracing of subdivision surfaces as well as efficient collision detection.