Preprocessing for Accelerating Convergence of Repulsive-Particle Systems for Sampling Implicit Surfaces

Recently repulsive-particle systems have been used as convenient tools for homogeneously distributing particles over an implicit surface. However, the death- and-split scheme of particles makes the convergence of the systems much slow, if the system includes a large number of particles. To avoid the use of the death-and- split scheme, we propose a novel preprocessing technique to tune an initial state of the particle systems. The preprocessing can make initial particle density either uniform or non-uniform. Then an excellent initial state is realized for the particle systems, and the death-and-split scheme becomes unnecessary. Therefore our preprocessing accelerates convergence of the particle systems noticeably keeping the number of particles constant. It also leads to uniform inter-particle distances in the final convergent state. Moreover our preprocessing is fast, easy to implement, and enables the particle systems to handle several hundreds of thousand particles.