Robust Particle Systems for Curvature Dependent Sampling of Implicit Surfaces

by
Miriah Meyer

Advised by
Ross Whitaker

Recent research on point-based surface representations suggests that they may be a viable alternative to parametric surfaces in applications where the topological constraints of a parameterization are unwieldy or inefficient. Particle systems offer a mechanism for controlling point samples and distributing them according to needs of the application.Furthermore, particle systems can serve as a surface representation in their own right, or to augment implicit functions, allowing for both efficient rendering and control of implicit function parameters. Particles rest on the surface of interest and repel one another in order to achieve a homogeneous covering. For deformation, the motions of the particles give rise to updates of the parameters of the underlying implicit function. The state of the art in particle systems, however, presents some short comings. First, most of these systems have many parameters that interact with some numerical complexity, making it difficult for users to tune the system to meet specific requirements. Furthermore, these systems do not lend themselves to spatially adaptive sampling schemes, which are essential for efficient, accurate representations of complex surfaces. In this paper we present a new class of energy functions for distributing particles on implicit surfaces and a corresponding set of numerical techniques. These techniques provide stable, scalable, efficient, and controllable mechanisms for distributing particles that sample implicit surfaces within a locally adaptive framework.