A Time Efficient Delaunay Refinement Algorithm

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 15, Issue , 2004, Pages 393-402

  Miller, Gary L ^a  

^a Carnegie Mellon University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DELAUNAY REFINEMENT CODE; MESHING PROBLEMS; PLANAR STRAIGHT LINE GRAPHS (PSLG); QUADTREE METHODS;

ALGORITHMS; COMPUTATIONAL GEOMETRY; GRAPH THEORY; MATHEMATICAL TECHNIQUES; PROBLEM SOLVING; THEOREM PROVING;

ASPECT RATIO;

EID: 1842435239     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (23)

1. [Bar02] Jernej Barbic. Quadratic example for delaunay refinement. 2002.
2. [BE92] Marshall Wayne Bern and David Eppstein. Mesh generation and optimal triangulation. In Ding-Zhu Du and Frank Kwang-Ming Hwang, editors, Computing in Euclidean Geometry, number 1 in Lecture Notes Series on Computing, pages 23-90. World Scientific, 1992.
3. [BEG94] Marshall Bern, David Eppstein, and John Gilbert. Provably good mesh generation. J. Comput. System Sci., 48(3):384-409, 1994. 31st Annual Symposium on Foundations of Computer Science (FOCS) (St. Louis, MO, 1990).
4. [BET99] Marshall W. Bern, David Eppstein, and Shang-Hua Teng. Parallel construction of quadtrees and quality triangulations. International Journal of Computational Geometry and Applications, 9(6):517-532, 1999.
5. [BOG01] Charles Boivin and Carl F. Ollivier-Gooch. Guaranteed-quality simplicial mesh generation with cell size and grading control. Engineering with Computers, 17(3):269-286, 2001.
6. [Che87] P. Chew. Constrained Delauany triangulation. In in Proc. ACM Symposium on Comp. Geometry, pages 213-222, 1987.
7. [Che89] L. Paul Chew. Guaranteed-quality triangular meshes. Technical Report 89-983, Computer Science Department, Cornell University, 1989.
8. [CLRS01] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. MIT-press and MCGraw-Hill, 2 edition, 2001.
9. [dBvKOS00] Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf. Computational geometry. Springer-Verlag, Berlin, revised edition, 2000. Algorithms and applications.
10. [Ede01] H. Edelsbrunner, Geometry and Topology of Mesh Generation. Cambridge Univ. Press, England, 2001.
11. [Kad01] Clemens Kadow. A fully incremental Delaunay refinement algorithm. Posterpresentation 10th International Meshing Roundtable, October 2001.
12. [KM92] T. C. Kau and David M. Mount. Incremental construction and dynamic maintenance of constrained delaunay triangulations. In Proc. 4th Canad. Conf. Computational Geometry, pages 170-175, 1992.
13. [MPW02] Gary L. Miller, Steven E. Pav, and Noel J. Walkington. A finer analysis of the Delaunay Refinement Algorithm. in preparation, november 2002.
14. [Rup95] Jim Ruppert. A Delaunay refinement algorithm for quality 2-dimensional mesh generation. J. Algorithms, 18(3):548-585, 1995. Fourth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (Austin, TX, 1993).
15. [Sei88] R. Seidel. Constrained Delauany triangulation and voronoi diagrams with obstacles. Technical Report Rep 260, IIG-TU Graz, 1988.
16. [She95] J. R. Shewchuck. Triangle: A two-dimensional quality mesh generator and Delaunay triangulator. 1995.
17. [She96] Jonathan Richard Shewchuk. Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In Ming C. Lin and Dinesh Manocha, editors, Applied Computational Geometry: Towards Geometric Engineering, volume 1148 of Lecture Notes in Computer Science, pages 203-222. Springer-Verlag, May 1996. From the First ACM Workshop on Applied Computational Geometry.
18. [She97] Jonathan Richard Shewchuk. Delaunay Refinement Mesh Generation, PhD thesis, School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1997. Available as Technical Report CMU-CS-97-137.
19. [She00] Jonathan Richard Shewchuk. Mesh generation for domains with small angles. In Proceedings of the Sixteenth Annual Symposium on Computational Geometry (Hong Kong, 2000), pages 1-10 (electronic), New York, 2000. ACM.
20. [She02a] Jonathan Richard Shewchuk. Delaunay refinement algorithms for triangular mesh generation. Computational Geometry: Theory and Applications, 22(1-3):21-74, May 2002.
21. [She02b] Jonathan Richard Shewchuk. Delaunay refinement algorithms for triangular mesh generation. Comput. Geom., 22(1-3):21-74, 2002. 16th ACM Symposium on Computational Geometry (Hong Kong, 2000).
22. [STÜ02] Daniel Spielman, Shang-Hua Teng, and Alper Üngör. Parallel delaunay refinement:algorithms and analyses, In Proceedings, 11th International Meshing Roundtable, pages 205-218. Sandia National Laboratories, September 15-18 2002.
23. [WS87] C. Wang and L. Schubert. An optimal algorithm for constructing the Delauany triangulation of a set of line segments. In in Proc. ACM Symposium on Comp. Geometry, pages 223-232, 1987.