SQ-Map: efficient layered collision detection and haptic rendering.

This paper presents a novel layered and fast framework for real-time collision detection and haptic interaction in virtual environments based on superquadric virtual object modeling. An efficient algorithm is initially proposed for decomposing the complex objects into subobjects suitable for superquadric modeling, based on visual salience and curvature constraints. The distance between the superquadrics and the mesh is then projected onto the superquadric surface, thus generating a distance map (SQ-Map). Approximate collision detection is then performed by computing the analytical equations and distance maps instead of triangle per triangle intersection tests. Collision response is then calculated directly from the superquadric models and realistic smooth force feedback is obtained using analytical formulae and local smoothing on the distance map. Experimental evaluation demonstrates that SQ-Map reduces significantly the computational cost when compared to accurate collision detection methods and does not require the huge amounts of memory demanded by distance field-based methods. Finally, force feedback is calculated directly from the distance map and the superquadric formulae.