Smooth surface reconstruction via natural neighbour interpolation of distance functions

Computational Geometry: Theory and Applications

Volumn 22, Issue 1-3, 2002, Pages 185-203

  Boissonnat, Jean Daniel ^a   Gazais, Frédéric ^a  

^a INRIA   (France)

Author keywords

Delaunay triangulation; Natural neighbour interpolation; Reconstruction; Smooth surface; Voronoi diagram

Indexed keywords

EID: 31244436824     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-7721(01)00048-7     Document Type: Article

References (33)

1. N. Amenta, M. Bern, Surface reconstruction by Voronoi filtering, Discrete Comput. Geom. 22 (4) (1999) 481-504.
2. N. Amenta, M. Bern, M. Kamvysselis, A new Voronoi-based surface reconstruction algorithm, in: Proc. SIGGRAPH'98, Computer Graphics Proceedings, Annual Conference Series, 1998, pp. 41215.
3. D. Attali, r-regular shape reconstruction from unorganized points, Computational Geometry: Theory and Applications 10 (1998) 239-247.
4. C. Bajaj, F. Bernardini, G. Xu, Automatic reconstruction of surface and scalar fields from 3d scans, Comput. Graph. 11 (1995) 109-118, Proc. SIGGRAPH'95.
5. F. Bernardini, C. Bajaj, J. Chen, D. Schikore, Triangulation-based object reconstruction methods, in: Proc. 13th Annual ACM Symp. Comput. Geom., 1997, pp. 481-484.
6. F. Bernardini, C.L. Bajaj, Sampling and reconstructing manifolds using alpha-shapes, in: Proc. 9th Canad. Conf. Comput. Geom., 1997, pp. 193-198.
7. F. Bernardini, J. Mittleman, H. Rushmeir, C. Suva, G. Taubin, The ball-pivoting algorithm for surface reconstruction, IEEE Transactions on Visualization and Computer Graphics 5 (4) (1999) 349-359.
8. J. Bloomenthal (Ed.), Introduction to Implicit Surfaces, Vol. 391, Morgan Kaufmann, San Mateo, CA, 1997.
9. J.-D. Boissonnat, Geometric structures for three-dimensional shape representation, ACM Trans. Graph. 3 (4) (1984)266-286.
10. J.-D. Boissonnat, F. Cazals, Natural neighbor coordinates of points on a surface, Computational Geometry: Theory and Applications 19 (2001) 155-173.
11. J.L. Brown, Systems of coordinates associated with points scattered in the plane, Computer-Aided Design 14 (1997)547-559.
12. J.W. Bruce, P.J. Giblin, Curves and Singularities, 2nd edn., Cambridge University Press, New York, 1992.
13. L.P. Chew, Guaranteed-quality mesh generation for curved surfaces, in: Proc. 9th Annual ACM Symp. Comput. Geom., 1993, pp. 274-280.
14. B. Curless, M. Levoy, A volumetric method for building complex models from range images, in: Proc. SIGGRAPH'96,1996, pp. 303-312.
15. O. Devillers, Improved incremental randomized Delaunay triangulation, in: Proc. 14th Annual ACM Symp. Comput. Geom., 1998, pp. 106-115.
16. T.K. Dey, K. Mehlhorn, E.R. Ramos, Curve reconstruction: Connecting dots with good reason, in: Proc. 15th Annual ACM Symp. Comput. Geom., 1999, pp. 197-206.
17. H. Edelsbrunner, D.G. Kirkpatrick, R. Seidel, On the shape of a set of points in the plane, IEEE Trans. Inform. Theory IT-29 (1983) 551-559.
18. H. Edelsbrunner, E.P. Mücke, Three-dimensional alpha shapes, ACM Trans. Graph. 13 (1) (1994) 43-72.
19. A. Fomenko, T. Kunii, Topological Modeling for Visualization, Springer, Berlin, 1997.
20. J. Giesen, Curve reconstruction, the traveling salesman problem and Menger's theorem on length, in: Proc. 15th Annual ACM Symp. Comput. Geom., 1999, pp. 207-216.
21. M. Gopi, S. Krishnan, C. Suva, Surface reconstruction based on lower dimensional localized Delaunay triangulation, in: Proc. Eurographics 2000, Vol. 19, 2000, pp. C467-C478.
22. H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jin, J. McDonald, J. Schweitzer, W. Stuetzle, Piecewise smooth surface reconstruction, in: Proc. SIGGRAPH'94, 1994, pp. 295-302.
23. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, W. Stuetzle, Surface reconstruction from unorganized points, Comput. Graphics 26 (2) (1992) 71-78, Proc. SIGGRAPH'92.
24. D. Levin, Mesh-independent surface interpolation, in: Proc. 4th International Conference on Curves and Surfaces, Saint-Malo, France, 1999, p. 46.
25. M. Melkemi, A-shapes and their derivatives, in: Proc. 13th Annual ACM Symp. Comput. Geom., 1997, pp. 367-369.
26. S.J. Owen, An implementation of natural neighbor interpolation in three dimensions, Master's Thesis, Brigham Young University, Provo, UT, 1992.
27. B. Piper, Properties of local coordinates based on Dirichlet tesselations, Computing 8 (1993) 227-239.
28. J.A. Sethian, Level Set Methods, Cambridge University Press, Cambridge, 1996.
29. E. Sherbrooke, N. Patrikalakis, F.-E. Woher, Differential and topological properties of medial axis transforms, Graphical Models and Image Processing 58 (6) (1996) 574-592.
30. R. Sibson, A vector identity for the Dirichlet tesselation, Math. Proc. Cambridge Philos. Soc. 87 (1980) 151-155.
31. R. Sibson, A brief description of natural neighbour interpolation, in: V. Barnet (Ed.), Interpreting Multivariate Data, Wiley, Chichester, 1981, pp. 21-36.
32. D.F. Watson, Contouring: A Guide to the Analysis and Display of Spatial Data, Pergamon, Oxford, 1992.
33. H.-K. Zhao, S. Osher, B. Merriman, M. Kang, Implicit, nonparametric shape reconstruction from unorganized points using a variational level set method, Cam Report 98-7, UCLA, Los Angeles, CA, 1998, http://www.ma th.ucla.edu/applied/cam/index.html.