Incremental Topological Flipping Works for Regular Triangulations

Algorithmica (New York)

Volumn 15, Issue 3, 1996, Pages 223-241

  Edelsbrunner, H ^a   Shah, N R ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

Flipping; Geometric algorithms; Grid generation; Incremental; Point location; Randomized; Regular and Delaunay triangulations; Topological order

Indexed keywords

EID: 0000670028     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01975867     Document Type: Article

References (28)

1. F. Aurenhammer. Power diagrams: properties, algorithms and applications. SIAM J. Comput., 16 (1987) 78-96.
2. F. Aurenhammer. Voronoi diagrams - a survey of a fundamental geometric data structure. ACM Comput. Surveys, 23 (1991), 345-406.
3. J.-D. Boissonnat and M. Teillaud. On the randomized construction of the Delaunay tree. Theoret. Comput. Sci., 112 (1993), 339-354.
4. H. Bruggesser and P. Mani. Shellable decompositions of cells and spheres. Math. Scand., 29(1971), 197-205.
5. C. Buchta, J. Müller, and R. F. Tichy. Stochastical approximation of convex bodies. Math. Ann., 271 (1985), 225-235.
6. K. Clarkson and P. Shor. Applications of random sampling in computational geometry. Discrete Comput. Geom., 4 (1989), 387-421.
7. B. N. Delaunay. Sur la sphère vide. Izv. Akad. Nauk SSSR Otdel. Mat. Est. Nauk, 7 (1934), 793-800.
8. O. Devillers, S. Meiser, and M. Teillaud. The space of spheres, a geometric tool to unify duality results on Voronoi diagrams. Proc. 4th Canad. Conf. on Computational Geometry, 1992, pp. 263-268.
9. R. A. Dwyer. Higher-dimensional Voronoi diagrams in linear expected time. Discrete Comput. Geom., 6 (1991), 343-367.
10. H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, Heidelberg, 1987.
11. H. Edelsbrunner. An acyclicity theorem for cell complexes in d dimensions. Combinatorica. 10 (1990), 251-260.
12. H. Edelsbrunner, D. G. Kirkpatrick, and R. Seidel. On the shape of a set of points in the plane. IEEE Trans. Inform. Theory, 29 (1983), 551-559.
13. H. Edelsbrunner and E. P. Mücke. Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graphics, 9 (1990), 66-104.
14. H. Edelsbrunner and E. P. Mücke. Three-dimensional alpha shapes. Manuscript, Dept. Comput. Sci., Univ. Illinois at Urbana-Champaign, 1992.
15. L. J. Guibas, D. E. Knuth, and M. Sharir. Randomized incremental construction of Delaunay and Voronoi diagrams. Algorithmica, 7 (1992), 381-413.
16. B. Joe. Three-dimensional triangulations from local transformations. SIAM J. Sci. Statist. Comput., 10 (1989), 718-741.
17. B. Joe. Construction of three-dimensional Delaunay triangulations using local transformations. Comput. Aided Geom. Design, 8 (1991), 123-142.
18. C. L. Lawson. Generation of a triangular grid with applications to contour plotting. Memo 299, Jet Propulsion Laboratory, Pasadena, CA, 1972.
19. 1 surface interpolation. In Mathematical Software III, edited by J. Rice. Academic Press, New York, 1977, pp. 161-194.
20. C. L. Lawson. Properties of n-dimensional triangulations. Comput. Aided Geom. Design, 3 (1986), 231-246.
21. C. Lee. Regular triangulations of convex polytopes. Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift, edited by P. Gritzmann and B. Sturmfels, American Mathematical Society, Providence, RI, 1991, 443-456.
22. K. Melhorn, S. Meiser, and C. Ó'Dúnlaing. On the construction of abstract Voronoi diagrams. Discrete Comput. Geom., 6 (1991), 211-224.
23. F. P. Preparata and M. I. Shamos. Computational Geometry - An Introduction. Springer-Verlag, New York, 1985.
24. J. Radon. Mengen konvexer Körper, die einen gemeinsamen Punkt enthalten. Math. Ann., 83 (1921), 113-115.
25. d. Proc. 7th Ann. Symp. on Computational Geometry, 1991, pp. 357-363.
26. E. Schönhardt. Über die Zerlegung von Dreieckspolyedern in Tetraeder. Math. Ann., 98 (1928), 309-312.
27. R. Seidel. Constructing higher-dimensional convex hulls at logarithmic cost per face. Proc. 18th Ann. ACM Symp. on Theory of Computing, 1986, pp 403-413.
28. G. F. Voronoi. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. J. Reine Angew. Math., 133 (1907), 97-178.