History-free Collision Response for Deformable Surfaces

Abstract: Continuous collision detection (CCD) and response methods are widely adopted in dynamics simulation of deformable models. They are history-based, as their success is strictly based on an assumption of a collision-free state at the start of each time interval. On the other hand, in many applications surfaces have normals defined to designate their orientation (i.e. front- and back-face), yet CCD methods are totally blind to such orientation identification (thus are orientation-free). We notice that if such information is utilized, many penetrations can be untangled. In this paper we present a history-free method for separation of two penetrating meshes, where at least one of them has clarified surface orientation. This method first computes all edge-face (E-F) intersections with discrete collision detection (DCD), and then builds a number of penetration stencils. On response, the stencil vertices are relocated into a penetration-free state, via a global displacement minimizer. Our method is very effective for handling penetration between two meshes, being it an initial configuration or in the middle of physics simulation. The major limitation is that it is not applicable to self-collision within one mesh at the time being.