We present a novel six-degree-of-freedom haptic rendering algorithm using incremental and localized contact computations. It uses an incremental approach for contact and force computations and takes advantage of spatial and temporal coherence between successive frames. As part of a preprocess, we decompose the surface of each polyhedron into convex pieces and construct bounding volume hierarchies to perform fast proximity queries. Once the objects have intersected, we compute the penetration depth (PD) in the neighborhood of the contact between each pair of decomposed convex pieces using a new incremental algorithm. Moreover, we cluster different contacts based on their spatial proximity to speed up the force computation. We have implemented this algorithm and applied it to complex contact scenarios consisting of multiple contacts. We demonstrate its effectiveness on electronic prototyping of complex mechanical structures and virtual exploration of a digestive system.

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