Incidences between points and circles in three and higher dimensions

Discrete and Computational Geometry

Volumn 33, Issue 2, 2005, Pages 185-206

  Aronov, Boris ^a   Koltun, Vladlen ^b   Sharir, Micha ^c,d  

^a POLYTECHNIC UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

^d NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 12944331236     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-004-1111-9     Document Type: Article

References (22)

1. P.K. Agarwal, E. Nevo, J. Pach, R. Pinchasi, M. Shari, and S. Smorodinsky, Lenses in arrangements of pseudo-circles and their applications, J. ACM 51 (2004), 139-186.
2. P. Agarwal and M. Sharir, On the number of congruent simplices in a point set, Discrete Comput. Geom. 28 (2002), 123-150.
3. T. Akutsu, H. Tamaki, and T. Tokuyama, Distribution of distances and triangles in a point set and algorithms for computing the largest common point set, Discrete Comput. Geom. 20 (1998), 307-331.
4. B. Aronov, V. Koltun, and M. Sharir, Incidences between points and circles in three and higher dimensions, Proc. 18th ACM Symp. on Computational Geometry (2002), pp. 116-122.
5. B. Aronov, J. Pach, M. Sharir, and G. Tardos, Distinct distances in higher dimensions, Combin. Probab. Comput. 13 (2004), 283-293.
6. B. Aronov and M. Sharir, Cutting circles into pseudo-segments and improved bounds on incidences, Discrete Comput. Geom. 28 (2002), 475-490.
7. T.M. Chan, On levels in arrangements of curves, Discrete Comput. Geom. 29 (2003), 375-393.
8. B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, and J. Stolfi, Lines in space: combinatorics and algorithms, Algorithmica 15 (1996), 428-447.
9. B. Chazelle and J. Friedman, A deterministic view of random sampling and its use in geometry, Combinatorica 10 (1990), 229-249.
10. K. Clarkson, H. Edelsbrunner, L. Guibas, M. Sharir, and E. Welzl, Combinatorial complexity bounds for arrangements of curves and spheres, Discrete Comput. Geom. 5 (1990), 99-160.
11. T. Dey, Improved bounds for planar k-sets and related problems, Discrete Comput. Geom. 19 (1998), 373-382.
12. H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer-Verlag, Heidelberg, 1987.
13. S. Feldman and M. Sharir, An improved bound for joints in arrangements of lines in space, Discrete Comput. Geom., DOI: 10.1007/s00454-004-1093-7.
14. J. Matoušek, Lectures on Discrete Geometry, Graduate Texts in Mathematics, Springer-Verlag, Berlin, 2002.
15. J. Pach and P.K. Agarwal, Combinatorial Geometry, Wiley-Interscience, New York, 1995.
16. J. Pach and M. Sharir, On the number of incidences between points and curves, Combin. Probab. Comput. 7 (1998), 121-127.
17. J. Pach and M. Sharir. Geometric incidences, in Towards a Theory of Geometric Graphs (J. Pach, ed.), pp. 185-223, Contemporary Mathematics, vol. 342, American Mathematical Society, Providence, RI, 2004.
18. M. Sharir and E. Welzl, Point-line incidences in space, Combin. Probab. Comput., 13 (2004), 203-220.
19. D.M.Y. Sommerville, Analytic Geometry of Three Dimensions, Cambridge University Press, Cambridge, 1934.
20. J. Spencer, E. Szemerédi, and W.T. Trotter, Unit distances in the Euclidean plane, in Graph Theory and Combinatoncs (B. Bollobás, ed.), Academic Press, New York, 1984, pp. 293-303.
21. L. Székely, Crossing numbers and hard Erdos problems in discrete geometry, Combin. Probab. Comput. 6 (1997), 353-358.
22. E. Szemerédi and W.T. Trotter, Extremal problems in discrete geometry, Combinatorica 3 (1983), 381-392.