A Kinematic Model for Collision Response

Over the course of several years, an informal poll by Dave Forsey of commercial animators revealed that the single most useful tool to add to a computer animation system would be a way to control the simple act of pressing one object into another. This ability would drastically increase the range and style of animations that could be created within a production environment. This thesis presents a simple, fast, geometric approach to controlling the nature, extent and timing of the surface deformations arising from the interpenetration of kinematically controlled animated objects. Rather than using dynamic simulations, which are di cult to con gure, code, and control, the algorithm presented here is based upon the idea that collision response is a matter of moving speci c points on the surface towards speci c goal points at a certain rate. This is an operation similar to manipulating chains of rigid bodies using inverse kinematics. This formulation is easily extendable to free-form surface modeling where generally only one point, or possibly more, is manipulated interactively at a time. We use a multi-resolution approach to deformations to provide control over the response of the surface using a small number of parameters. Each of the parameters determine how a level in the multi-resolution representation of the surface reacts to the interpenetration. The deformations are calculated in time and space proportional to the number of points used to de ne the surface.