Modelling contacts in a physically based simulation

Abstract

The paper presents a model of polyhedral contact that can be used in a physically based simulation. The model is based on a geometric analysis formulated as a static problem in 3D space. The geometric analysis of contact between a pair of objects determines the set of surface areas which are in contact and their associated normals. From these areas and normals, the dynamics simulator can formulate equations that model the physical consequences of the contact. For areas that come into contact with high relative velocity, these equations model the collision impulse force. The pushing and sliding behaviour of low-relative-velocity contact is modelled by the addition of kinematic contrraints over the areas in contact. The geometric analysis consists mainly of collecting adjacent contact points into separate regions which share the same normals. Since nonconvex polyhedra are allowed, the intersection can be produce surface areas which have more than one associated normal. The geometric modeller can provide this entire set of normals, or any small subset which spans the same space, whichever the dynamics modeller requires. When a contact region persists from the time to step in the simulation, the contact analysis can return the normals for that region from the previous time step, rather than recalculate them. This temporal coherence of the normals can resolve certain cases in which the normals of a region are indeterminate. The interpretation of the contact requires a full set-theoretic intersection of the two objects. The objects in question are assumed to already be in contact or in close proximity. An efficient and robust implementation of the intersection is achieved by using the Brep-Index data structure in conjunction with a back-face culling technique based on relative velocities at surface points.