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Minimizing edge length to connect sparsely sampled unstructured point sets

Title:

Minimizing edge length to connect sparsely sampled unstructured point sets

Ohrhallinger, Stefan, Mudur, Sudhir and Wimmer, Michael (2013) Minimizing edge length to connect sparsely sampled unstructured point sets. Computers & Graphics, 37 (6). pp. 645-658. ISSN 00978493

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Official URL: http://dx.doi.org/10.1016/j.cag.2013.05.016

Abstract

Most methods for interpolating unstructured point clouds handle densely sampled point sets quite well but get into trouble when the point set contains regions with much sparser sampling, a situation often encountered in practice. In this paper, we present a new method that provides a better interpolation of sparsely sampled features.

We pose the surface construction problem as finding the triangle mesh which minimizes the sum of all triangles’ longest edge. Since searching for matching umbrellas among sparsely sampled points to yield a closed manifold shape is a difficult problem, we introduce suitable heuristics. Our algorithm first connects the points by triangles chosen in order of their longest edge and with the requirement that all edges must have at least two incident triangles. This yields a closed non-manifold shape which we call the Boundary Complex. Then we transform it into a manifold triangulation using topological operations. We show that in practice, runtime is linear to that of the Delaunay triangulation of the points. Source code is available online.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Computer Science and Software Engineering
Item Type:Article
Refereed:Yes
Authors:Ohrhallinger, Stefan and Mudur, Sudhir and Wimmer, Michael
Journal or Publication:Computers & Graphics
Date:2013
Digital Object Identifier (DOI):10.1016/j.cag.2013.05.016
Keywords:Surface reconstruction; Point cloud; Boundary complex; Sharp features; Sparse sampling; Energy minimization
ID Code:977887
Deposited By: DANIELLE DENNIE
Deposited On:01 Oct 2013 18:13
Last Modified:18 Jan 2018 17:45

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