Fast Surface Particle Repulsion

A fast algorithm for simulating particle repulsion on surfa ces is described. Particles are distributed across a surface and made to repel. Calculating pairwise repulsion between n particles costs O(n 2 ) in general, but if the energy potential drops off very rapidly, repulsion can b e simulated in O(n) time. This is accomplished using a simple grid data structure with spherical range quer ies. Particles change in number and position, necessitating a dynamic data structure. The method is used to accelerate repulsion in an algorithm for uniformly sampling implicit surfaces during interactive surface des ign. Although this method is straightforward, it is quite effective: speedups of 160 times were realized for sim ulations with 10,000 particles. We also give references to related work outside the field of computer graphics.