Geodesics on Point Clouds
Authors: Yu, H., Zhang, J.J. and Jiao, Z.
Editors: Mohamed Abd El Aziz
Journal: Mathematical Problems in Engineering
Issue: Article ID 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.
Preferred by: Hongchuan Yu