Modeling contacts in a physically based simulation

TL;DR: A model for polyhedral contact that may be llsed in a physically based simulation based on a geometric analysis formulated as a static problem in three-dimensional space to resolve certain cases where the normals of a region are indeterminate.

Abstract: In this paper we present a model for polyhedral contact that may be llsed in a physically based simulation. The model is based on a geometric analysis formulated as a static problem in three-dimensional space. The geometric contact analysis 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 behavior of low relative velocity contact is modeled by the addition of kinematic constraints over the areas in contact. The geometric analysis consists mainly of collecting adjacent contact points into separate regions which share the same normals. Since non-convex polyhedra are allowed, the intersection can produce surface areas which have more than one associated normal The geometric modeler can provide this entire set of normals or any small subset which spans the same space, whichever the dynamics modeler requires. When a contact region persists from time step to time step in the simulation, the contact analysis can return the normals for that region from the previous time step rather than recalculating them. This temporal coherence of the normals can resolve certain cases where 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 be already in contact or in close proximity. An efficient and robust implementation of the intersection is achieved by nsing the brep-index data structnre in conjunction with a back-face culling technique based on relative velocities at surface points.