Hierarchical Spherical Distance Fields for Collision Detection

Authors:
Christoph Funfzig;Torsten Ullrich;Dieter W. Fellner
Affiliations:
Braunschweig University of Technology, Germany;Graz University of Technology, Austria;Graz University of Technology, Austria
Venue:
IEEE Computer Graphics and Applications
Year:
2006

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Abstract

This article presents a fast collision detection technique for all types of rigid bodies demonstrated with polygon soups. During the preprocessing step, a spherical sampling of the model is performed and then stored in a wavelet-like representation. This representation is space-efficient and allows the on-the-fly generation of spherical shell bounding volumes. In contrast to the commonly used filter banks, this construction uses the max-plus algebra. This guarantees that each low-resolution version of a bounding volume encloses all versions of higher resolution. The technique is scalable in the information it gives in collision determination. If it reports a single triangle per spherical shell then the collision time only depends on the sampling density and the extent of spherical shells, used as bounding volumes, but not on the primitives' count of the model. Due to this fact, it's possible to estimate the time bounds for the collision test tightly. For bounding volume hierarchies known worst-case time bounds are not tight, as the bounding volumes can overlap in space. As an intermediate approach it's possible to report a single triangle per layer of each model. For surface models this information together with surface neighborhood is often sufficient for collision response. If we check all triangle pairs inside a spherical shell for intersection, then the approach is most general and works well in situations with few collisions, which are the most relevant in practice.