Adaptive deformations with fast tight bounds

Simulation of deformations and collision detection are two highly intertwined problems that are often treated separately. This is especially true in existing elegant adaptive simulation techniques, where standard collision detection algorithms cannot leverage the adaptively selected degrees of freedom. We propose a seamless integration of multigrid algorithms and collision detection that identifies boundary conditions while inherently exploiting adaptivity. We realize this integration through multiscale bounding hierarchies, a novel unified hierarchical representation, together with an adaptive multigrid algorithm for irregular meshes and an adaptivity-aware hierarchical collision detection algorithm. Our solution produces detailed deformations with adapted computational cost, but it also enables robust interactive simulation of self-colliding deformable objects with high-resolution surfaces.