Geodesics on point clouds

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Authors: Yu, H., Zhang, J.J. and Jiao, Z.

Journal: Mathematical Problems in Engineering

Volume: 2014

eISSN: 1563-5147

ISSN: 1024-123X

DOI: 10.1155/2014/860136

We present a novel framework to compute geodesics on implicit surfaces and point clouds. Our framework consists of three parts, particle based approximate geodesics on implicit surfaces, Cartesian grid based approximate geodesics on point clouds, and geodesic correction. The first two parts can effectively generate approximate geodesics on implicit surfaces and point clouds, respectively. By introducing the geodesic curvature flow, the third part produces smooth and accurate geodesic solutions. Differing from most of the existing methods, our algorithms can converge to a given tolerance. The presented computational framework is suitable for arbitrary implicit hypersurfaces or point clouds with high genus or high curvature. © 2014 Hongchuan Yu et al.

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