An efficient space partitioning technique based on linear kd-trees for collision culling

We present an efficient “broad phase” algorithm for selecting candidate collision pairs in N-body simulation. As our technique is derived from kd-trees, we first introduce some background kdtree concepts and their geometrical interpretation. Then we cover the construction of a linear kd-tree and its use in N-body simulation. We finally study its time and memory complexity, and compare the performance of an implementation with that of other algorithms (namely Sweep and Prune and Delaunay triangulation). Preliminary tests show that the linear kd-tree performs more than fifty times faster than the other methods on conventional computers, for highly dynamic simulations with a few thousand elements or more. We also conclude that simulations of several million elements are feasible on a single processor in less than five seconds per time step.