Particle system based geodesic computation for implicit surfaces

Abstract

In this paper, we present a new approach to computing geodesics on implicit hyper-surfaces. Our method consists of three parts, particle based implicit surface sampling, Dijkstras algorithm based geodesic computation and geodesic correction. In the first part, we have developed a curvature dependent mechanism for particle distribution by introducing a curvature term in the formulation. Differing from most previous methods, whereby the computed geodesics lie only on the surface mesh, our algorithm is able to compute geodesics on the surface. This is achieved with the introduction of geodesic curvature flow, significantly improving the accuracy for geodesic computation. The presented algorithm is suitable for arbitrary implicit hyper-surfaces of high genus or high curvature.