Collision detection for volumetric objects

We propose a probability model for the handling of complicated interactions between volumetric objects. In our model each volume is associated with a "probability map" that assigns a "surface crossing" probability to each space point according to local volume properties. The interaction between two volumes is then described by finding the intersecting regions between the volumes, and calculating the "collision probabilities" at each intersecting point from the surface crossing probabilities. To enable fast and efficient calculations, we introduce the concept of a distance map and develop two hierarchical collision detection algorithms, taking advantage of the uniform structure of volumetric datasets.