Particle System Based Geodesic Computation for Implicit Surface

This source preferred by Hongchuan Yu

Authors: Yu, H., Zhang, W. and Zhang, J.J.

Editors: M. J. Daffé

Journal: Pensee Journal

Volume: 75

Issue: 12

Pages: 199-214

ISSN: 0031-4773

In this paper, we present a new approach to computing geodesics on implicit hypersurfaces. Our method consists of three parts, particle based implicit surface sampling, Dijkstra’s 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.

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