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Meshless quadrangulation by global parameterization

E. R. Li 1 Bruno Lévy 2 Xiaopeng Zhang 1 Wu-Jun Che 1 Weiming Dong 1, 2 Jean-Claude Paul 1, 3, 4 
2 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
4 CAD - Computer Aided Design
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
Abstract : Point cloud is a basic description of discrete shape information. Parameterization of unorganized points is important for shape analysis and shape reconstruction of natural objects. In this paper we present a new algorithm for global parameterization of an unorganized point cloud and its application to the meshing of the cloud. Our method is guided by principal directions so as to preserve the intrinsic geometric properties. After initial estimation of principal directions, we develop a kNN(k-nearest neighbor) graph-based method to get a smooth direction field. Then the point cloud is cut to be topologically equivalent to a disk. The global parameterization is computed and its gradients align well with the guided direction field. A mixed integer solver is used to guarantee a seamless parameterization across the cut lines. The resultant parameterization can be used to triangulate and quadrangulate the point cloud simultaneously in a fully automatic manner, where the shape of the data is of any genus.
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Submitted on : Monday, December 10, 2012 - 2:48:38 PM
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E. R. Li, Bruno Lévy, Xiaopeng Zhang, Wu-Jun Che, Weiming Dong, et al.. Meshless quadrangulation by global parameterization. Computers and Graphics, 2011, 35 (5), pp.992-1000. ⟨10.1016/j.cag.2011.05.003⟩. ⟨hal-00763290⟩



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