A Multi-Scale Singularity Bounding Volume Hierarchy

Abstract

A scale space approach is taken for building Bounding Volume Hierarchies (BVHs) for collision detection. A spherical bounding volume is generated at each node of the BVH using estimates of the mass distribution. Traditional top-down methods approximates the surface of an object in a coarse to fine manner, by recursively increasing resolution by some factor, e.g. 2. The method presented in this article analyzes the mass distribution of a solid object using a well founded scale-space based on the Diffusion Equation: the Gaussian Scale-Space. In the Gaussian scale-space, the deep structure of extremal mass points is naturally binary, and the linking process is therefore simple. The main contribution of this article is a novel approach for constructing BVHs using Multi-Scale Singularity Trees (MSSTs) for collision detection. The BVH-building algorithm extends the field with a new method based on volumetric shape rather than statistics of the surface geometry or geometrical constructs such as medial surfaces.