Haptic display of rigid body contact using generalized penetration depth

Rigid body contact with multiple regions is common in virtual environments. The traditional penalty based haptic display treats translational penetration depth at each contact region independently, and hence causes the undesired effect of visual interpenetration since it does not guarantee all geometrical constraints simultaneously. It may also introduce force discontinuity due to the singularity of penetration depth. To overcome these artifacts, we present a method based on the concept of generalized penetration depth (GPD), which considers both translation and rotation to separate two overlapping objects. The method could be viewed as an extension of the classic god-object method from Euclidean space to configuration space in which GPD is defined. We demonstrate the method for 3-DoF rigid bodies using pre-computed contact space. For 6-DoF rigid bodies where pre-computation is not feasible, we propose an efficient method to approximate the local contact space based on continuous collision detection and quadratic programming.