Fast and Accurate Distance, Penetration, and Collision Queries Using Point-Sphere Trees and Distance Fields

Collision detection, force computation, and proximity queries are fundamental in interactive gaming, assembly simulations, or virtual prototyping. However, many available methods have to find a trade-off between the accuracy and the high computational speed required by haptics (1 kHz). [McNeely et al. 2006] presented the Voxmap-Pointshell (VPS) Algorithm, which enabled more reliable six-DoF haptic rendering between complex geometries than other approaches based on polygonal data structures. For each colliding object pair, this approach uses (i) a voxelmap or voxelized representation of one object and (ii) a pointshell or point-sampled representation of the other object (see Figure 2). In each cycle, the penetration of the points in the voxelized object is computed, which yields the collision force. [Barbic and James 2008] extended the VPS Algorithm to support deformable objects. This approach builds hierarchical data structures and distance fields that are updated during simulation as the objects deform. We present a haptic rendering algorithm for rigid bodies based on the VPS Algorithm which also uses hierarchies and distance fields. Yet, our data structures are optimized for fast and accurate collision and proximity queries rather than for deformation simulations