Robust particle systems for curvature dependent sampling of implicit surfaces

Recent research on point-based surface representations suggests that point sets may be a viable alternative to parametric surface representations 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. The state of the art in surface sampling particle systems, however, presents some shortcomings. First, most of these systems have many parameters that interact with some 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.