On overlays and minimization diagrams

Proceedings of the Annual Symposium on Computational Geometry

Volumn 2006, Issue , 2006, Pages 395-401

  Koltun, Vladlen ^a   Sharir, Micha ^b,c  

^a Stanford University   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

Arrangements; Hyperplanes; Lower envelopes; Minimization diagrams; Overlays; Power diagrams; Voronoi diagrams

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; OPTIMIZATION; THEOREM PROVING;

ARRANGEMENTS; HYPERPLANES; LOWER ENVELOPES; MINIMIZATION DIAGRAMS; OVERLAYS; POWER DIAGRAMS; VORONOI DIAGRAMS;

COMPUTATIONAL GEOMETRY;

EID: 33748049445     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1137856.1137914     Document Type: Conference Paper

References (22)

1. P. K. Agarwal, B. Aronov, S. Hax-Peled, and M. Sharir. Approximation and exact algorithms for minimum-width annuli and shells. Discrete Comput. Geom., 24(4):687-705, 2000.
2. P. K. Agarwal, B. Aronov, and M. Sharir. Computing envelopes in four dimensions with applications. SIAM J. Comput., 26:1714-1732, 1997.
3. P. K. Agarwal, B. Aronov, and M. Sharir. Exact and approximation algorithms for minimum-width cylindrical shells. Discrete Comput. Geom., 26:307-320, 2001.
4. P. K. Agarwal, O. Schwarzkopf, and M. Sharir. The overlay of lower envelopes and its applications. Discrete Comput. Geom., 15:1-13, 1996.
5. P. K. Agarwal and M. Sharir. Arrangements and their applications. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 49-119. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
6. S. Basu, R. Pollack, and M.-F. Roy. Algorithms in Real Algebraic Geometry. Springer Verlag, Berlin, 2003.
7. P. J. Besl and N. D. McKay, A method for registration of 3-d shapes. IEEE Trans. Pattern Anal. Mach. Intell., 14(2):239-256, 1992.
8. T. M. Chan. Approximating the diameter, width, smallest enclosing cylinder and minimum-width annulus. Internat. J. Comput. Geom. Appl., 12(2):67-85, 2002.
9. B. Chazelle. An optimal convex hull algorithm in any fixed dimension, Discrete Comput. Geom., 10:377-409, 1993.
10. K. L. Clarkson. A randomized algorithm for closest-point queries. SIAM J. Comput., 17:830-847, 1988.
11. C. A. Duncan, M. T. Goodrich, and E. A. Ramos. Efficient approximation and optimization algorithms for computational metrology. In Proc. 8th ACM-SIAM Annu. Sympos. Discrete Algo., pages 121-130, 1997.
12. H. Ebara, N. Fukuyama, H. Nakano, and Y. Nakanishi. Roundness algorithms using the Voronoi diagrams. In Abstracts 1st Canad. Conf. Comput. Geom., page 41, 1989.
13. H. Edelsbrunner. The upper envelope of piecewise linear functions: Tight complexity bounds in higher dimensions. Discrete Comput. Geom., 4:337-343, 1989.
14. H. Edelsbrunner and R. Seidel, Voronoi diagrams and arrangements. Discrete Comput. Geom., 1:25-44, 1986.
15. E. Ezra and M. Sharir, Bounds for the ICP algorithm. These proceedings, 2005.
16. L. J. Guibas, D. Halperin, J. Matoušek, and M. Sharir. On vertical decomposition of arrangements of hyperplanes in four dimensions. Discrete Comput. Geom., 14:113-122, 1995.
17. V. Koltun and M. Sharir. The partition technique for overlays of envelopes. SIAM J. Comput., 32:841-863, 2003.
18. V. Koltun and C. Wenk. Matching polyhedral terrains using overlays of envelopes. Algorithmica, 41:159-183, 2005.
19. P. McMullen. The maximal number of faces of a convex polytope. Mathematika, 17:179-184, 1970.
20. M. Sharir. Almost tight upper bounds for lower envelopes in higher dimensions. Discrete Comput Geom., 12:327-345, 1994.
21. M. Shaxir and P. K. Agarwal. Davenport-Schinzel Sequences and Their Geometric Applications. Cambridge University Press, New York, 1995.
22. G. M. Ziegler, Lectures on Polytopes, volume 152 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. Revised edition 1998.