Adaptive Algorithms for Collision Detection and Ray Tracing of Deformable Meshes

Many applications in computer graphics and visualization are directly dependent on accurate and fast intersection queries. To prevent bodies passing directly through each other, the simulation system must be able to track touching or intersecting geometric primitives. In real-time graphics simulations, in which hundreds of thousands of geometric primitives are involved, highly efficient collision detection algorithms are needed. The efficient handling of deformable models constitutes a particular challenge to the simulation system, since the possibilities of precomputing efficient data structures are decreased dramatically. The same type of problem arises in interactive ray tracing, where a huge number of geometric intersections must be determined in just a fraction of a second.For these reasons, new efficient collision detection and ray tracing methods for deformable meshes are suggested in this thesis. The proposed solutions are based on bounding volume hierarchies which allow the models they represent to be deformed at every time step of the simulation. Different update methods to efficiently refit the bounding volumes in the hierarchies as the models deform are presented. The models considered are represented by polygon meshes that are either deformed by arbitrary vertex repositioning or by mesh morphing. The update methods postpone updates in the hierarchies until they are absolutely needed in order to avoid unnecessary updating work. The results from the experiments performed indicate that significant speed-ups can be achieved by using these new methods in comparison with approaches suggested previously. The thesis also shows that mesh morphing constitutes a specific example of a restricted type of deformation that allows particularly efficient hierarchical data structures, with expected sub-linear collision queries in the number of geometric primitives of the meshes.