Voronoi-Delaunay duality and Delaunay meshes

Proceedings - SPM 2007: ACM Symposium on Solid and Physical Modeling

Volumn , Issue , 2007, Pages 415-420

  Dyer, Ramsay ^a   Zhang, Hao ^a   Möller, Torsten ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Delaunay mesh; Delaunay triangulation (DT); Intrinsic DT; Restricted DT; Voronoi diagram

Indexed keywords

MATHEMATICAL MODELS; SURFACES;

DELAUNAY MESH; DELAUNAY TRIANGULATION (DT); INTRINSIC DT; VORONOI DIAGRAMS;

TRIANGULATION;

EID: 35348891433     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1236246.1236306     Document Type: Conference Paper

References (18)

1. ALEKSANDROV, A. D., AND ZALGALLER, V. A. 1967. Intrinsic Geometry of Surfaces, vol. 15 of Transactions of mathematical monographs. AMS.
2. AMENTA, N., AND BERN, M. W. 1998. Surface Reconstruction by Voronoi Filtering. In Symp. Comp. Geom., 39-48.
3. AMENTA, N., CHOI, S., DEY, T. K., AND LEEKHA, N. 2000. A Simple Algorithm for Homeomorphic Surface Reconstruction. In Symp. Comp. Geom., 213-222.
4. BOBENKO, A. I., AND SPRINGBORN, B. A. 2005. A discrete Laplace-Beltrami operator for simplicial surfaces. arXiv:math.DG/ 0503219 vl.
5. CHEW, L. P. 1993. Guaranteed-quality mesh generation for curved surfaces. In Symp. Comp. Geom, 274-280.
6. DE BERG, M., VAN KREVELD, M., OVERMARS, M., AND SCHWARZKOPF, O. 1998. Computational Geometry. Algorithms and Applications. Springer-Verlag.
7. DESBRUN, M., MEYER, M., AND ALLIEZ, P. 2002. Intrinsic parameterizations of surface meshes. In Proceedings of Eurographics, 209-218.
8. DO CARMO, M. P. 1976. Differential Geometry of Curves and Surfaces. Prentice-Hall.
9. DYER, R., ZHANG, H., AND MÖLLER, T. 2007. On VoronoiDelaunay duality and Delaunay meshes. Tech. Rep. TR 2007-04, Simon Fraser University.
10. EDELSBRUNNER, H., AND SHAH, N. R. 1994. Triangulating topological spaces. In Symp. Comp. Geom., 285-292.
11. FISHER, M., SPRINGBORN, B., BOBENKO, A. I., AND SCHRÖDER, P. 2006. An algorithm for the construction of intrinsic Delaunay triangulations with applications to digital geometry processing. In SIGGRAPH '06 Courses, 69-74.
12. FLOATER, M. S. 1998. Parametric tilings and scattered data approximation. Int. J. of Shape Modeling 4, 165-182.
13. LEIBON, G., AND LETSCHER, D. 2000. Delaunay Triangulations and Voronoi Diagrams for Riemannian Manifolds. In Proc. 16th Symposium on Comp. Geom., 341-349.
14. MEYER, M., DESBRUN, M., SCHRÖDER, P., AND BARR, A. H. 2003. Discrete Differential-Geometry Operators for Triangulated 2-Manifolds. In Visualization and Mathematics III. Springer-Verlag, 35-57.
15. ONISHI, K., AND ITOH, J. 2003. Estimation of the necessary number of points in Riemannian Voronoi diagram. In Proc. 15th Canadian Conf. Comput. Geom., 19-24.
16. PEYRÉ, G., AND COHEN, L. 2003. Geodesic Remeshing Using Front Propagation. In Proceedings VLSM, 33-40.
17. SHEWCHUK, J. R. 1997. Delaunay Refinement Mesh Generation. PhD thesis, School of Computer Science, Carnegie Mellon University. Technical Report CMU-CS-97-137.
18. TURK, G. 1991. Generating textures on arbitrary surfaces using reaction-diffusion. In ACM SIGGRAPH, 289-298.