Geodesics on Point Clouds

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

Editors: Mohamed Abd El Aziz

Journal: Mathematical Problems in Engineering

Volume: 2014

Issue: Article ID 860136

DOI: 10.1155/2014/860136


In this paper, 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 hyper-surfaces or point clouds with high genus or high curvature.

Source: Manual

Preferred by: Hongchuan Yu