Triangulation of uniform particle systems: its application to the implicit surface texturing

Particle systems, as originally presented by Witkin and Heckbert [32], offer air elegant solution to sample implicit surfaces of arbitrary genus, while providing an extremely regular distribution of samples over the surface. In this paper, we present an efficient technique that uses particle systems to rapidly generate a triangular mesh over an implicit surface, where each triangle is almost equilateral. The major advantage of such a triangulation is that it minimizes the deformations between the mesh and the underlying implicit surface. We exploit this property by using few triangular texture samples mapped in a non-periodic fashion as presented by Neyret and Cani [16]. The result is a pattern-based texturing method that maps homogeneous non-periodic textures to arbitrary implicit surfaces, with almost no deformation.