An integrating approach to meshing scattered point data

In this paper, we propose a new method for approximating an unorganized set of points scattered over a piecewise smooth surface by a triangle mesh. The method is based on the Garland-Heckbert local quadric error minimization strategy. First an adaptive spherical cover and auxiliary points corresponding to the cover elements are generated. Then the intersections between the spheres of the cover are analyzed and the auxiliary points are connected. Finally the resulting mesh is cleaned from non-manifold parts. The method allows us to control the approximation accuracy, process noisy data, and reconstruct sharp edges and corners. Further, the vast majority of the triangles of the generated mesh have their aspect ratios close to optimal. Thus our approach integrates the mesh reconstruction, smoothing, decimation, feature restoration, and remeshing stages together.

[1]  Marc Levoy,et al.  Zippered polygon meshes from range images , 1994, SIGGRAPH.

[2]  Tao Ju,et al.  Robust repair of polygonal models , 2004, ACM Trans. Graph..

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

[4]  Jean-Daniel Boissonnat,et al.  A coordinate system associated with points scattered on a surface , 2004, Comput. Aided Des..

[5]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  K. Ueno.  An Introduction to Algebraic Geometry , 1997 .

[7]  Hans-Peter Seidel,et al.  3D scattered data approximation with adaptive compactly supported radial basis functions , 2004, Proceedings Shape Modeling Applications, 2004..

[8]  Sunghee Choi,et al.  The power crust , 2001, SMA '01.

[9]  James F. O'Brien,et al.  Interpolating and approximating implicit surfaces from polygon soup , 2004, SIGGRAPH Courses.

[10]  Marco Attene,et al.  Edge-Sharpener: Recovering Sharp Features in Triangulations of non-adaptively re-meshed surfaces , 2003, Symposium on Geometry Processing.

[11]  Gabriel Taubin,et al.  A signal processing approach to fair surface design , 1995, SIGGRAPH.

[12]  Herbert Edelsbrunner,et al.  The union of balls and its dual shape , 1993, SCG '93.

[13]  Reinhard Klette,et al.  Computer vision - three-dimensional data from images , 1998 .

[14]  Marc Levoy,et al.  A volumetric method for building complex models from range images , 1996, SIGGRAPH.

[15]  Tim Weyrich,et al.  Post-processing of Scanned 3D Surface Data , 2004, PBG.

[16]  Michael Garland,et al.  Optimal triangulation and quadric-based surface simplification , 1999, Comput. Geom..

[17]  Greg Turk,et al.  Re-tiling polygonal surfaces , 1992, SIGGRAPH.

[18]  Joachim Giesen,et al.  Surface reconstruction using umbrella filters , 2002, Comput. Geom..

[19]  Richard K. Beatson,et al.  Reconstruction and representation of 3D objects with radial basis functions , 2001, SIGGRAPH.

[20]  Marco Attene,et al.  Automatic Surface Reconstruction from Point Sets in Space , 2000, Comput. Graph. Forum.

[21]  Martin Isenburg,et al.  Isotropic surface remeshing , 2003, 2003 Shape Modeling International..

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

[23]  Hans-Peter Seidel,et al.  Multi-level partition of unity implicits , 2003, ACM Trans. Graph..

[24]  Stefan Gumhold,et al.  Feature Extraction From Point Clouds , 2001, IMR.

[25]  Mathieu Desbrun,et al.  Removing excess topology from isosurfaces , 2004, TOGS.

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

[27]  Craig Gotsman,et al.  Explicit Surface Remeshing , 2003, Symposium on Geometry Processing.

[28]  Mark Meyer,et al.  Implicit fairing of irregular meshes using diffusion and curvature flow , 1999, SIGGRAPH.

[29]  André Guéziec,et al.  Locally Toleranced Surface Simplification , 1999, IEEE Trans. Vis. Comput. Graph..

[30]  Franz Lemmermeyer,et al.  Introduction to Algebraic Geometry , 2005 .

[31]  Michael Garland,et al.  Surface simplification using quadric error metrics , 1997, SIGGRAPH.

[32]  David Mumford,et al.  Filtering, Segmentation and Depth , 1993, Lecture Notes in Computer Science.

[33]  Hans-Peter Seidel,et al.  Using growing cell structures for surface reconstruction , 2003, 2003 Shape Modeling International..

[34]  Pierre Alliez,et al.  Anisotropic polygonal remeshing , 2003, ACM Trans. Graph..

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

[36]  Daniel Cohen-Or,et al.  Bilateral mesh denoising , 2003 .

[37]  Tamal K. Dey,et al.  Provable surface reconstruction from noisy samples , 2004, SCG '04.

[38]  Jean-Daniel Boissonnat,et al.  Smooth surface reconstruction via natural neighbour interpolation of distance functions , 2000, SCG '00.

[39]  Leif Kobbelt,et al.  Optimized Sub‐Sampling of Point Sets for Surface Splatting , 2004, Comput. Graph. Forum.

[40]  Luiz Velho,et al.  Smooth Surface Reconstruction from Noisy Clouds , 2004, J. Braz. Comput. Soc..

[41]  David Cohen-Steiner,et al.  A greedy Delaunay-based surface reconstruction algorithm , 2004, The Visual Computer.

[42]  Frédo Durand,et al.  Non-iterative, feature-preserving mesh smoothing , 2003, ACM Trans. Graph..

[43]  Peter Liepa,et al.  Filling Holes in Meshes , 2003, Symposium on Geometry Processing.