Meshless parameterization and surface reconstruction

Abstract This paper proposes a method called meshless parameterization , for parameterizing and triangulating “single patch” unorganized point sets. The points are mapped into a planar parameter domain by solving a sparse linear system. By making a standard triangulation of the parameter points, we obtain a corresponding triangulation of the original data set.

[1]  L. Schumaker,et al.  Surface Fitting and Multiresolution Methods , 1997 .

[2]  Michael S. Floater,et al.  Parametric Tilings and Scattered Data Approximation , 1998, Int. J. Shape Model..

[3]  Gábor Renner,et al.  Curve and surface design: H. Hagen (Ed.) SIAM, USA (1992), 219 pp, ISBN 089871-281-5 , 1993, Comput. Aided Des..

[4]  Tony DeRose,et al.  Surface reconstruction from unorganized points , 1992, SIGGRAPH.

[5]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[6]  Anne Verroust-Blondet,et al.  Interactive texture mapping , 1993, SIGGRAPH.

[7]  David P. Dobkin,et al.  MAPS: multiresolution adaptive parameterization of surfaces , 1998, SIGGRAPH.

[8]  Chandrajit L. Bajaj,et al.  Automatic reconstruction of surfaces and scalar fields from 3D scans , 1995, SIGGRAPH.

[9]  K. Hormann,et al.  MIPS: An Efficient Global Parametrization Method , 2000 .

[10]  Marshall W. Bern,et al.  A new Voronoi-based surface reconstruction algorithm , 1998, SIGGRAPH.

[11]  Bruno Lévy,et al.  Non-distorted texture mapping for sheared triangulated meshes , 1998, SIGGRAPH.

[12]  Ralph R. Martin,et al.  Reverse engineering of geometric models - an introduction , 1997, Comput. Aided Des..

[13]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[14]  Michael S. Floater,et al.  Parametrization and smooth approximation of surface triangulations , 1997, Comput. Aided Geom. Des..

[15]  Guido Brunnett,et al.  Polyhedral Reconstruction of 3D Objects by Tetrahedra Removal , 1997 .

[16]  Jean-Daniel Boissonnat,et al.  Geometric structures for three-dimensional shape representation , 1984, TOGS.

[17]  Weiyin Ma,et al.  Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces , 1995, Comput. Aided Des..