Abstract: Extending the frontier of visual computing, real-time physically-based interactions and haptic (touch-enabled) rendering have the potential to increase the quality of man-machine communication. By accommodating the sense of touch and introducing realistic modeling of physical elements, haptic interfaces provide an attractive augmentation to visual display and enhance the level of immersion in a virtual environment. One of the major research challenges in haptics is to display intricate interaction between two 3D objects of high geometric complexity at the desired force update rates.