Approximation of the normal vector field and the area of a smooth surface

Discrete and Computational Geometry

Volumn 32, Issue 3, 2004, Pages 383-400

  Morvan, Jean Marie ^a,b   Thibert, Boris ^b  

^a INRIA   (France)

^b UNIVERSITÉ LYON 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4744370353     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-004-1096-4     Document Type: Article

References (15)

1. N. Amenta, M. Bern, Surface reconstruction by Voronoi filtering, Discrete Comput. Geom. 22 (1999), 481-504.
2. N. Amenta, M. Bern, M. Kamvysselis, A new Voronoi-based surface reconstruction algorithm, Proc. Siggraph '98 (1998), pp. 415-421.
3. N. Amenta, S. Choi, T.K. Dey, N. Leekha, A simple algorithm for homeomorphic surface reconstruction, Proc. 16th Ann. Symp. on Computational Geometry (2000), pp. 213-222.
4. M. Berger, B. Gostiaux, Géométrie différentielle: variétés, courbes et surfaces, seconde édition, Presses Universitaires de France, Paris, 1992.
5. J.D. Boissonnat, Diagrammes de Voronoï, Triangulations et surfaces, cours de DEA, novembre 2001.
6. J.D. Boissonnat, F. Cazals, Smooth surface reconstruction via natural neighbor interpolation of distance functions, In Proc. 16th Ann. Symp. on Computational Geometry (2000), pp. 223-232.
7. L.P. Chew, Guaranteed-quality mesh generation for curved surfaces, Proc. 9th Ann. Computational Geometry (1993), pp. 274-280.
8. M. P. Do Carmo, Differential Geometry of Curves and Surfaces (translated from the Portuguese), Prentice-Hall, Englewood Cliffs, NJ, 1976.
9. H. Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418-491.
10. J. Fu, Convergence of curvatures in secant approximations, J. Differential Geom. 37 (1993), 177-190.
11. A. Haraux, How to differentiate the projection on a convex set in Hilbert space. Some applications to variational inequalities, J. Math. Soc. Japan 29(4) (1977), 615-631.
12. J. Milnor, Morse Theory, Princeton University Press, Princeton, NJ, 1963.
13. F. Morgan, Geometric Measure Theory, Academic Press, New York, 1987.
14. J.M. Morvan, B. Thibert, On the approximation of a smooth surface with a triangulated mesh, Comput. Geom. Theory Appl. 23(3) (2002), 337-352.
15. M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. III, second edition, Publish or Perish, Wilmington, DE, 1979.