Dynamic interaction between deformable surfaces and nonsmooth objects

In this paper, we introduce new techniques that enhance the computational performance for the interactions between sharp objects and deformable surfaces. The new formulation is based on a time-domain predictor-corrector model. For this purpose, we define a new kind of (pi, beta, I)-surface. The partitioning of a deformable surface into a finite set of (pi, beta, I)-surfaces allows us to prune a large number of noncolliding feature pairs. This leads to a significant performance improvement in the collision detection process. The intrinsic collision detection is performed in the time domain. Although it is more expensive compared to the static interference test, it avoids portions of the surfaces passing through each other in a single time step. In order to resolve all the possible collision events at a given time, a penetration-free motion space is constructed for each colliding particle. By keeping the velocity of each particle inside the motion space, we guarantee that the current colliding feature pairs will not penetrate each other in the subsequent motion. A static analysis approach is adopted to handle friction by considering the forces acting on the particles and their velocities. In our formulation, we further reduce the computational complexity by eliminating the need to compute repulsive forces.