Fast Sampling of Implicit Surfaces by Particle Systems

Particle systems, as originally proposed by Witkin and Heckbert, are a powerful way to sample implicit surfaces since they generate almost evenly distributed samples over the surface, thanks to a global minimization of an energy criterion. Nonetheless, due to the computational cost of the relaxation process, the sampling process becomes rather expensive when the number of samples exceeds a few thousands. In this paper, we propose a technique that only relies on a pure geometry processing which enables us to rapidly generate the set of final particles (e.g., half a second to generate 5,000 particles for an analytic implicit surface) with near-optimal positions. Because of its characteristics, the technique does not need the usual split-and-death criterion any more and only about ten relaxation steps are necessary to get a high quality sampling. Either uniform or non-uniform sampling can be performed with our technique