Updating and constructing constrained Delaunay and constrained regular triangulations by flips

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2003, Pages 181-190

  Shewchuk, Jonathan Richard ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bistellar flip; Constrained Delaunay triangulation

Indexed keywords

ALGORITHMS; ASPECT RATIO; CONSTRAINT THEORY; PROBLEM SOLVING;

CONSTRAINED REGULAR TRIANGULATIONS;

COMPUTATIONAL GEOMETRY;

EID: 0038038276     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/777819.777821     Document Type: Conference Paper

References (25)

1. Oswin Aichholzer, Franz Aurenhammer, and Hannes Krasser. Pseudo-Triangulations from Surfaces and a Novel Type of Edge Flip. Manuscript, 2003.
2. Siu-Wing Cheng, Tamal K. Dey, Herbert Edelsbrunner, Michael A. Facello, and Shang-Hua Teng. Sliver Exudation. Journal of the ACM 47(5):883-904, September 2000.
3. L. Paul Chew. Constrained Delaunay Triangulations. Algorithmica 4(1):97-108, 1989.
4. _. Guaranteed-Quality Triangular Meshes. Technical Report TR-89-983, Department of Computer Science, Cornell University, 1989.
5. Kenneth L. Clarkson and Peter W. Shor. Applications of Random Sampling in Computational Geometry, II. Discrete & Computational Geometry 4(1):387-421, 1989.
6. Jesús A. de Loera, Francisco Santos, and Jorge Urrutia. The Number of Geometric Bistellar Neighbors of a Triangulation. Discrete & Computational Geometry 21(1):131-142, 1999.
7. Boris N. Delaunay. Sur la Sphère Vide. Izvestia Akademia Nauk SSSR, VII Seria, Otdelenie Matematicheskii I Estestvennyka Nauk 7:793-800, 1934.
8. Herbert Edelsbrunner and Ernst Peter Mücke. Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms. ACM Transactions on Graphics 9(1):66-104, 1990.
9. Herbert Edelsbrunner and Raimund Seidel. Voronoi Diagrams and Arrangements. Discrete & Computational Geometry 1:25-44, 1986.
10. Herbert Edelsbrunner and N. R. Shah. Incremental Topological Flipping Works for Regular Triangulations. Algorithmica 15(3):223-241, March 1996.
11. Leonidas J. Guibas. Kinetic Data Structures - A State of the An Report. Proceedings of the Third Workshop on Algorithmic Foundations of Robotics (Houston, Texas), pages 191-209, 1998.
12. Barry Joe. Three-Dimensional Triangulations from Local Transformations. SIAM Journal on Scientific and Statistical Computing 10:718-741, 1989.
13. _. Construction of κ-Dimensional Delaunay Triangulations using Local Transformations. SIAM Journal on Scientific Computing 14(6): 1415-1436, November 1993.
14. 1 Surface Interpolation. Mathematical Software III (John R. Rice, editor), pages 161-194. Academic Press, New York, 1977.
15. _. Properties of n-Dimensional Triangulations. Computer Aided Geometric Design 3:231-246, 1986.
16. Der-Tsai Lee and A. K. Lin. Generalized Delaunay Triangulations for Planar Graphs. Discrete & Computational Geometry 1:201-217, 1986.
17. Gary L. Miller, Dafna Talmor, Shang-Hua Teng, Noel Walkington, and Han Wang. Control Volume Meshes using Sphere Packing: Generation, Refinement and Coarsening. Fifth International Meshing Roundtable (Pittsburgh, Pennsylvania), pages 47-61, October 1996.
18. Johann Radon. Mengen Konvexer Körper, die Einen Gemeinschaftlichen Punkt Enthalten. Mathematische Annalen 83:113-115, 1921.
19. Raimund Seidel. The Upper Bound Theorem for Polytopes: An Easy Proof of Its Asymptotic Version. Computational Geometry: Theory and Applications 5:115-116, 1985.
20. _. Constrained Delaunay Triangulations and Voronoi Diagrams with Obstacles. 1978-1988 Ten Years IIG (H. S. Poingratz and W. Schinnerl, editors), pages 178-191. Institute for Information Processing, Graz University of Technology, 1988.
21. Jonathan Richard Shewchuk. A Condition Guaranteeing the Existence of Higher-Dimensional Constrained Delaunay Triangulations. Proceedings of the Fourteenth Annual Symposium on Computational Geometry (Minneapolis, Minnesota), pages 76-85. Association for Computing Machinery, June 1998.
22. _. Mesh Generation for Domains with Small Angles. Proceedings of the Sixteenth Annual Symposium on Computational Geometry (Hong Kong), pages 1-10. Association for Computing Machinery, June 2000.
23. _. Sweep Algorithms for Constructing Higher-Dimensional Constrained Delaunay Triangulations. Proceedings of the Sixteenth Annual Symposium on Computational Geometry (Hong Kong), pages 350-359. Association for Computing Machinery, June 2000.
24. _. Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery. Eleventh International Meshing Roundtable (Ithaca, New York), pages 193-204. Sandia National Laboratories, September 2002.
25. _. What is a Good Linear Element? Interpolation, Conditioning, and Quality Measures. Eleventh International Meshing Roundtable (Ithaca, New York), pages 115-126. Sandia National Laboratories, September 2002.