Collision Detection with Glide Rotations

We introduce a framework for collision detection between a pair of rigid polyhedra. Given the initial and final positions and orientations of two objects, the algorithm determines whether the bodies collide, and if so, when and where. All the collisions, including collisions at different times are computed at once. This kind of collision information is useful for handling multiple (nearly) concurrent contact points and for real-time applications such as computer games. The relative motions of the rigid body is limited to glide rotation (i.e., screw motion). This limitation is not always completely accurate, but we give bounds on the error introduced by the assumption. Our implementation uses pixelization to approximate the position and time of the collisions. This allows level-of-detail techniques that provide a tradeoff between accuracy and computational expense. The collision detection algorithms are only approximate, both because of the glide rotation limitation and because of the pixelization. However, they can be made quite robust for rigid bodies so as to always give consistent information about collisions and to avoid sensitivity to roundoff errors.