A graph-theoretic model for simultaneous collisions in virtual environments

In a virtual environment as well as in practice, collisions between complex surfaces and/or articulated bodies may occur simultaneously at multiple points of interference. Previous solutions to the collision response problem have been formulated based on pairwise rigid body dynamic interactions. These give only a local view of the dynamic response of each body. We present a new solution to the global interactions and dynamic response between multiple structures in a three-dimensional environment. This is based on a graph-theoretical framework that allows a systematic formulation of the equations of motion, gives a global view of all the interactions in a system, and suggests other approaches to the computation of dynamic response of a system.