A new triangulation algorithm from 3D unorganized dense point cloud

This paper presents an algorithm for triangular mesh generation from unorganized points based on 3D Delaunay tetrahedralization and mesh-growing method. This algorithm requires the point density to meet the well-sampled condition in smooth regions and dense sampling in sections of a great curvature and two close opposite surfaces. The principle of the algorithm is as follows. It begins with 3D Delaunay tetrahedralization of all sampling points. Then extract part of triangles belonging to the surface as the seed facets according to the rough separation characteristics which based on the angle formed by the circumscribing balls of incident tetrahedrons. Finally, the algorithm grows the seed facets from front triangles to all triangles of the surface. This paper shows several experimental results which explain this approach is general and applicable to various object topologies.

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

[2]  Chiew-Lan Tai,et al.  A mesh reconstruction algorithm driven by an intrinsic property of a point cloud , 2004, Comput. Aided Des..

[3]  Benjamin B. Kimia,et al.  Surface Reconstruction from Point Clouds by Transforming the Medial Scaffold , 2007, Sixth International Conference on 3-D Digital Imaging and Modeling (3DIM 2007).

[4]  Jong-Hwa Kim,et al.  A Surface Reconstruction Algorithm Using Weighted Alpha Shapes , 2005, FSKD.

[5]  Luca Di Angelo,et al.  A new mesh-growing algorithm for fast surface reconstruction , 2011, Comput. Aided Des..

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

[7]  Tamal K. Dey,et al.  Tight cocone: a water-tight surface reconstructor , 2003, SM '03.

[8]  Rex A. Dwyer.  A faster divide-and-conquer algorithm for constructing delaunay triangulations , 1987, Algorithmica.

[9]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[10]  Tamal K. Dey,et al.  Provable surface reconstruction from noisy samples , 2006, Comput. Geom..

[11]  Zhou Ru.  Algorithmic Research on Surface Reconstruction from Dense Scattered Points , 2001 .

[12]  Gabriel Taubin,et al.  The ball-pivoting algorithm for surface reconstruction , 1999, IEEE Transactions on Visualization and Computer Graphics.

[13]  Tamal K. Dey,et al.  Delaunay based shape reconstruction from large data , 2001, Proceedings IEEE 2001 Symposium on Parallel and Large-Data Visualization and Graphics (Cat. No.01EX520).

[14]  David Eppstein,et al.  The Crust and the beta-Skeleton: Combinatorial Curve Reconstruction , 1998, Graph. Model. Image Process..

[15]  Luo Sheng,et al.  A New Mesh Growing Surface Reconstruction Algorithm , 2009, 2009 First International Workshop on Education Technology and Computer Science.

[16]  Chia-Hsiang Menq,et al.  Combinatorial manifold mesh reconstruction and optimization from unorganized points with arbitrary topology , 2002, Comput. Aided Des..

[17]  L. Di Angelo,et al.  A fast algorithm for manifold reconstruction of surfaces , 2011 .

[18]  Kurt E. Brassel,et al.  A Procedure to Generate Thiessen Polygons , 2010 .

[19]  Afra Zomorodian,et al.  Conformal alpha shapes , 2005, Proceedings Eurographics/IEEE VGTC Symposium Point-Based Graphics, 2005..

[20]  D. T. Lee,et al.  Two algorithms for constructing a Delaunay triangulation , 1980, International Journal of Computer & Information Sciences.

[21]  Hsi-Yung Feng,et al.  Reconstruction of 2D polygonal curves and 3D triangular surfaces via clustering of Delaunay circles/spheres , 2011, Comput. Aided Des..

[22]  Xiaokun Li,et al.  On surface reconstruction: A priority driven approach , 2009, Comput. Aided Des..

[23]  Sunghee Choi,et al.  A Simple Algorithm for Homeomorphic Surface Reconstruction , 2002, Int. J. Comput. Geom. Appl..

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