Kinetic Collision Detection for Low-Density Scenes in the Black-Box Model

We present an efficient method for collision detection in the black-box KDS model for a set S of n objects in the plane. In this model we receive the object locations at regular time steps and we know a bound dmax on the maximum displacement of any object within one time step. Our method maintains, in O((λ+k)n) time per time step, a compressed quadtree on the bounding-box vertices of the objects; here λ denotes the density of S and k denotes the maximum number of objects that can intersect any disk of radius dmax. Collisions can then be detected by testingO((λ+k)n) pairs of objects for intersection.