Provably good sampling and meshing of surfaces

Graphical Models

Volumn 67, Issue 5, 2005, Pages 405-451

  Boissonnat, Jean Daniel ^a   Oudot, Steve ^a  

^a INRIA   (France)

Author keywords

sampling; Mesh refinement; Restricted Delaunay triangulation; Surface approximation; Surface mesh generation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; SAMPLING; TOPOLOGY;

Ε-SAMPLING; MESH REFINEMENT; RESTRICTED DELAUNAY TRIANGULATION; SURFACE APPROXIMATION; SURFACE MESH GENERATION;

SURFACE TREATMENT;

GRAPHICAL METHOD;

EID: 24944582018     PISSN: 15240703     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.gmod.2005.01.004     Document Type: Conference Paper

References (34)

1. Anders Adamson, Marc Alexa, Approximating and Intersecting Surfaces from Points, in: Proc. 1st Annu. Sympos. on Geometry Processing, 2003, pp. 230-239.
2. Marc Alexa, Johannes Behr, Daniel Cohen-Or, Shachar Fleishman, David Levin and Claudio T. Silva, Point Set Surfaces, in: Proc. 12th IEEE Visualization, 2001.
3. N. Amenta, and M. Bern Surface reconstruction by voronoi filtering Discrete Comput. Geom. 22 1999 481 504
4. N. Amenta, S. Choi, T.K. Dey, and N. Leekha A simple algorithm for homeomorphic surface reconstruction Int. J. Comput. Geom. Appl. 12 1-2 2002 125 141
5. N. Amenta, T.J. Peters, and A.C. Russell Computational topology: ambient isotopic approximation of 2-manifolds Theor. Comput. Sci. 305 1-3 2003 3 15
6. P. Bhattacharya, Efficient neighbor finding algorithms in quadtree and octree, Master's thesis, Indian Institute of Technology, Kampur, 2001.
7. J.-D. Boissonnat, and F. Cazals Natural neighbour coordinates of points on a surface Comp. Geom. Theory Appl. 2001 155 174
8. J.-D. Boissonnat, and F. Cazals Smooth surface reconstruction via natural neighbour interpolation of distance functions Comp. Geom. Theory Appl. 1 2002 185 203
9. J.-D. Boissonnat, D. Cohen-Steiner, G. Vegter, Isotopic implicit surface meshing, in: Proc. 36th Annu. Sympos. on Theory of Computation, 2004, pp. 301-309.
10. J.-D. Boissonnat, S. Oudot, Provably good surface sampling and approximation, in: Proc. 1st Annu. Sympos. on Geometry Processing, 2003, pp. 9-19.
11. E. Brieskorn, and H. Knörrer Plane algebraic curves 1986 Birkhaüser Basel Boston Stuttgart
12. F. Chazal, A. Lieutier, The "λ-medial axis." Graphical Models, 2005, doi:10.1016/j.gmod.2005.01.002.
13. Y.-S. Chen, W.-H. Hsu, Parallel thinning algorithm for binary digital patterns, in: Handbook of Pattern Recognition and Computer Vision, World Scientific, 1993, pp. 458-461.
14. S-W. Cheng, T.K. Dey, E.A. Ramos, T. Ray. Sampling and meshing a surface with guaranteed topology and geometry, in: Proc. 20th Annu. Sympos. on Comput. Geom., 2004, pp. 280-289.
15. H.-L. Cheng, T.K. Dey, H. Edelsbrunner, and J. Sullivan Dynamic skin triangulation Discrete Comput. Geom. 25 4 2001 525 568
16. E.V. Chernyaev, Marching cubes 33: construction of topologically correct isosurfaces, Technical report CERN CN 95-17, 1995.
17. L.P. Chew, Guaranteed-Quality Mesh Generation for Curved Surfaces, in: Proc. 9th Annu. ACM Sympos. Comput. Geom., 1993, pp. 274-280.
18. D. Cohen-Steiner, J.-M. Morvan, Restricted delaunay triangulations and normal cycle, in: Proc. 19th Annu. ACM Sympos. Comput. Geom., 2003.
19. T.K. Dey, S. Goswami, Tight cocone: a water tight surface reconstructor, in: Proc. 8th ACM Sympos. Solid Modeling Appl., 2003, pp 127-134.
20. T.K. Dey, S. Goswami, Provable surface reconstruction from noisy samples, in: Proc. 20th Annu. Sympos. Comput. Geom., 2004, pp. 330-339.
21. M.P. Do Carmo Differential geometry of curves and surfaces 1976 Prentice Hall London p. 142
22. H. Edelsbrunner, and N.R. Shah Triangulating topological spaces Int. J. Comput. Geom. Appl. 7 4 1997 365 378
23. H. Edelsbrunner Geometry and topology for mesh generation 2001 Cambridge University Press pp. 39-43
24. J. Erickson Nice point sets can have nasty Delaunay triangulations Discrete Comput. Geom. 30 l 2003 109 132
25. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, W. Stuetzle, Mesh optimization, Proc. SIGGRAPH, 1993, pp. 19-26.
26. W.E. Lorensen, H.E. Cline, Marching cubes: a high-resolution 3d surface construction algorithm, in: Proc. SIGGRAPH, 1987.
27. B. Mederos, L. Velho, L.H. de Figueiredo, Moving least squares multiresolution surface approximation, in: Proc. SIBGRAPI, 2003.
28. J.-M. Morvan, B. Thibert, On the approximation of the area of a surface. INRIA RR-4375, 2002.
29. S. PLantinga, G. Vegter, Isotopic approximation of implicit curves and surfaces, in: Proc. 2nd Sympos. on Geometry Processing, 2004, pp. 251-260.
30. J. Ruppert A delaunay refinement algorithm for quality 2-dimensional mesh generation J. Algorithms 1995
31. P. Trébuchet, Vers une résolution stable et rapide des équations algébriques, Doctoral thesis, University of Paris 6, 2002. Available from: < http://www.inria.fr/rrrt/tu-1067.html >.
32. http://www.cgal.org/index.html.
33. http://www-sop.inria.fr/galaad/logiciels/synaps/index.html.
34. http://www-sop.inria.fr/epidaure/personnel/Herve.Delingette/yav++.html.