Hierarchical spatial hashing for real-time collision detection

We present a new, efficient and easy to use collision detection scheme for real-time collision detection between highly deformable tetrahedral models. Tetrahedral models are a common representation of volumetric meshes which are often used in physically based simulations, e.g. in virtual surgery. In a deformable models environment collision detection usually is a performance bottleneck since the data structures used for efficient intersection tests need to be rebuilt or modified frequently. Our approach minimizes the time needed for building a collision detection data structure. We employ an infinite hierarchical spatial grid in which for each single tetrahedron in the scene a well fitting grid cell size is computed. A hash function is used to project occupied grid cells into a finite ID hash table. Only primitives mapped to the same hash index indicate a possible collision and need to be checked for intersections. This results in a high performance collision detection algorithm which does not depend on user defined parameters and thus flexibly adapts to any scene setup.