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Collision detection is frequently a bottleneck in computer assisted design, computer animation or simulation applications. So a lot of research has been done and the literature is rich. But this is a hard problem and most of the proposed optimisations only concern convex polyhedrons.
Recent work by Gottshalk & al. propose a very fast technique to detect collisions between non convex polyhedrons. The algorithm uses a pre-computed hierarchy of oriented bounding boxes. Oriented means that bounding boxes are not aligned to an axis which allows one to better fit the object geometry.
This technique is really very efficient, but it requires pre-computation. In our context of deformable objects, the pre-computed data structure needs to be updated or re-computed after each simulation time step.
Thus, we can’t use a collision detection algorithm which uses pre-computation.