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“Meshless Quadrangulation by Global Parametrization”
Er Li, Bruno Lévy, Xiaopeng Zhang, Wujun Che, Weiming Dong and Jean-Claude Paul
Computer and Graphics

Abstract: Point cloud is a basic description of discrete shape information. Parametrization of unorganized points is important for shape analysis and shape reconstruction of natural objects. In this paper we present a new algorithm for global parametrization of unorganized point clouds and its application to the meshing of point cloud data. Our method is guided by principal directions so as to preserve these intrinsic geometric properties. After an 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 parametrization is computed and its gradient align well with the guided direction field. A mixed-integer solver is used to guarantee a seamless parametrization across the cut border. Our parametrization result can be used to triangulate and quadrangulate the point cloud simultaneously and in a fully automatic manner, where the data can be with any genus.

BibTex reference

   TITLE      = "Meshless Quadrangulation by Global Parametrization",
   AUTHOR     = "Er Li and Bruno Lévy and Xiaopeng Zhang and Wujun Che and Weim
                   ing Dong and Jean-Claude Paul",
   JOURNAL    = "Computer and Graphics",