An analysis of Shewchuk's Delaunay refinement algorithm

Proceedings of the 18th International Meshing Roundtable, IMR 2009

Volumn , Issue , 2009, Pages 499-518

  Si, Hang ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DELAUNAY REFINEMENTS; EDGE LENGTH; PAIRWISE DISTANCES; SIMPLE SCHEMES; TIME AND SPACE COMPLEXITY; VERTEX DEGREE;

ALGORITHMS;

EID: 84878166343     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-642-04319-2_29     Document Type: Conference Paper

References (25)

1. Bern, M., Eppstein, D., Gilbert, J.R.: Provably good mesh generation. Journal of Computer and System Sciences 48(3), 384-409 (1994)
2. Cheng, S.-W., Dey, T., Edelsbrunner, H., Facello, M.A., Teng, S.-H.: Sliver exudation. J. Assoc. Comput. Mach. 47, 883-904 (2000)
3. Cheng, S.-W., Dey, T.K., Levine, J.A.: A practical Delaunay meshing algorithm for a large class of domains. In: Proc. 16th International Meshing Roundtable, pp. 477-494 (2007)
4. Cheng, S.-W., Dey, T.K., Ramos, E.A., Ray, T.: Quality meshing for polyhedra with small angles. International Journal on Computational Geometry and Applications 15, 421-461 (2005)
5. Cheng, S.-W., Poon, S.-H.: Three-dimensional Delaunay mesh generation. Discrete and Computational Geometry 36, 419-456 (2006)
6. Chew, P.L.: Guaranteed-quality triangular meshes. Technical Report TR 89-983, Dept. of Comp. Sci., Cornell University (1989)
7. Delaunay, B.N.: Sur la sphère vide. Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk 7, 793-800 (1934)
8. Erickson, J.: Nice point sets can have nasty Delaunay triangulations. Discrete and Computational Geometry 30(1), 109-132 (2003)
9. Gabriel, K.R., Sokal, R.R.: A new statistical approach to geographic analysis. Systematic Zoology 18(3), 259-278 (1969)
10. Hudson, B., Miller, G.L., Phillips, T.: Sparse voronoi refinement. In: Proc. 15th International Meshing Roundtable, pp. 339-356 (2006)
11. Hudson, B., Miller, G.L., Phillips, T., Sheehy, D.: Size complexity of volume meshes vs. surface meshes. In: 20th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1041-1047 (2009)
12. Miller, G.L., Phillips, T., Sheehy, D.: Linear-size meshes. In: 20th Canadian Conference on Computational Geometry (2008)
13. Miller, G.L., Talmor, D., Teng, S.-H., Walkington, N.J., Wang, H.: Control volume meshes using sphere packing: Generation, refinement and coarsening. In: Proc. 5th International Meshing Roundtable (1996)
14. Mitchell, S.A., Vavasis, S.A.: Quality mesh generation in higher dimensions. SIAM Journal on Computing 29, 1334-1370 (2000)
15. Oudot, S., Rineau, L., Yvinec, M.: Meshing volumes bounded by smooth surfaces. In: Proc. 14th International Meshing Roundtable, pp. 203-220 (2005)
16. Pav, S.E.: Delaunay Refinement Algorithm. PhD thesis, Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania (2003)
17. Pav, S.E., Walkington, N.J.: Robust three dimensional Delaunay refinement. In: Proc. 13th International Meshing Roundtable (2004)
18. Ruppert, J.: A Delaunay refinement algorithm for quality 2-dimensional mesh generation. Journal of Algorithms 18(3), 548-585 (1995)
19. Shewchuk, J.R.: Delaunay Refinement Mesh Generation. PhD thesis, Department of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania (1997)
20. Shewchuk, J.R.: Pyramid (2006) (Unpublished)
21. Shewchuk, J.R.: Triangle (2006), http://www.cs.cmu.edu/~quake/triangle. html
22. Si, H.: TetGen (2007), http://tetgen.berlios.de
23. Si, H.: Adaptive tetrahedral mesh generation by constrained delaunay refinement. International Journal for Numerical Methods in Engineering 75(7), 856-880 (2008)
24. Si, H.: Three dimensional boundary conforming Delaunay mesh generation. PhD thesis, Institute für Mathematik, Technische Universität Berlin (2008)
25. Talmor, D.: Well-spaced points for numerical methods. PhD thesis, Dept. of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania (1997)