Automatic triangular grid generation on a free-form surface using a particle self-organizing system

Abstract

A novel method for automatic triangular grid generation on a free-form surface based on Coulomb’s law is proposed in this paper, which we refer to as the particle self-organizing system (PSOS). The self-organizing of particles is realized by the interaction between charged particles, which brings about an even layout of particles. After connecting the optimized particles, a uniform triangular grid is generated. First, a moderate number of grid points are randomly arranged on the surface. Second, the grid points are regarded as charged particles with the same charge in the electric field and free to move driven by the Coulomb force. Third, the equilibrium state of the particle system is acquired according to the equivalent electric field intensity of each particle. Finally, the triangular grid is generated by the Delaunay method. According to the different motion space of particles, the particle self-organizing system can be divided into an indirect method and a direct method. The particle motion space of the indirect method is the parameter domain; the grid layout is obtained first and then mapped back to the space surface. The particle motion space of the direct method is the physical space of the surface; a grid is generated directly on the physical domain, and no mapping process is needed. The case studies indicate that both methods can generate a uniform triangular grid quickly, with the direct method having a higher grid quality.