Geodesics on point clouds
type: Item
instance of: scholarly article
title: Geodesics on point clouds
zbMATH Open document ID: 1407.53037
DOI: 10.1155/2014/860136
author: Xianqiang Yang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 86A30
zbMATH DE Number: 7017455
Wikidata QID: Q59070123
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/860136
OpenAlex ID: W2067763469
cites work: Q4247633
cites work: Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces
cites work: The Discrete Geodesic Problem
cites work: SHORTEST PATHS ON A POLYHEDRON, Part I: COMPUTING SHORTEST PATHS
cites work: Q4251963
cites work: Introduction to algorithms
cites work: An optimal algorithm for approximate nearest neighbor searching fixed dimensions
cites work: Geodesic active contours
cites work: Q5287558
description: scientific article; zbMATH DE number 7017455