Abstract
In this chapter, we present our novel geometric data structure, the Inner Sphere Trees. It is the first data structure that is able to compute the penetration volume between a pair of colliding objects at haptic rates. This new contact information guarantees physically-plausible and continuous forces and torques for a stable collision response that is essential for stable haptic rendering. Moreover, we propose a new clustering-based algorithm for creating bounding volume hierarchies and a time-critical traversal scheme for time-budgeted collision detection scenarios.
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