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Geometric structures in computational geometry

  • Herbert Edelsbrunner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)

Keywords

Line Segment Voronoi Diagram Computational Geometry Combinatorial Complexity Vertical Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [BO79]
    J. L. Bentley and T. A. Ottmann. Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput. C-28 (1979), 643–647.Google Scholar
  2. [CE88]
    B. Chazelle and H. Edelsbrunner. An optimal algorithm for intersecting line segments in the plane. Manuscript, 1988.Google Scholar
  3. [CEG88]
    K. L. Clarkson, H. Edelsbrunner, L. J. Guibas, M. Sharir and E. Welzl. Combinatorial complexity bounds for arrangements. Manuscript, 1988.Google Scholar
  4. [Cla87]
    K. L. Clarkson. New applications of random sampling in computational geometry. Discrete Comput. Geom. 2 (1987), 195–222.Google Scholar
  5. [Cla88]
    K. L. Clarkson. Applications of random sampling in computational geometry, II. In “Proc. 4th Ann. ACM Sympos. Comput. Geom. 1988”, to appear.Google Scholar
  6. [Ede87]
    H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, Heidelberg, Germany, 1987.Google Scholar
  7. [EGS87]
    H. Edelsbrunner, L. J. Guibas, and M. Sharir. The upper envelope of piecewise linear functions: algorithms and applications. Discrete Comput. Geom., to appear.Google Scholar
  8. [EGS88]
    H. Edelsbrunner, L. J. Guibas, and M. Sharir. The complexity of many faces in arrangements of lines and of segments. In “Proc. 4th Ann. ACM Sympos. Comput. Geom. 1988”, to appear.Google Scholar
  9. [EM88]
    H. Edelsbrunner and E. P. Mücke. Simulation of Simplicity: a technique to cope with degenerate cases in geometric algorithms. In “Proc. 4th Ann. ACM Sympos. Comput. Geom. 1988”, to appear.Google Scholar
  10. [EOS86]
    H. Edelsbrunner, J. O'Rourke, and R. Seidel. Constructing arrangements of lines and hyperplanes with applications. SIAM J. Comput. 15 (1986), 341–363.Google Scholar
  11. [Erd46]
    P. Erdös. On sets of distances of n points. Amer. Math. Monthly 53 (1946), 248–250.Google Scholar
  12. [Erd60]
    P. Erdös. On sets of distances of n points in Euclidean space. Magyar Tud. Akad. Mat. Kutaló Int. Kozl. 5, (1960), 165–169.Google Scholar
  13. [Gru67]
    B. Grünbaum. Convex Polytopes. John Wiley & Sons, London, England, 1967.Google Scholar
  14. [GOS88]
    L. J. Guibas, M. H. Overmars, and M. Sharir. Intersections, connectivity, and related problems for arrangements of line segments. In preparation.Google Scholar
  15. [HS86]
    S. Hart and M. Sharir. Nonlinearity of Davenport-Schinzel sequences and of generalized path compression schemes. Combinatorica 6 (1986), 151–177.Google Scholar
  16. [HW87]
    D. Haussler and E. Welzl. ɛ-nets and simplex range queries. Discrete Comput. Geom. 2 (1987), 127–151.Google Scholar
  17. [PS88]
    J. Pach and M. Sharir. The upper envelope on piecewise linear functions and the boundary of a region enclosed by convex plates: combinatorial analysis. Discrete Comput. Geom., to appear.Google Scholar
  18. [PSS88]
    R. Pollack, M. Sharir, and S. Sifrony. Separating two simple polygons by a sequence of translations. Discrete Comput. Geom. 3 (1988), 123–136.Google Scholar
  19. [SH76]
    M. I. Shamos and D. Hoey. Geometric intersection problems. In “Proc. 17th Ann. ACM Sympos. Found. Comput. Sci. 1976”, 208–215.Google Scholar
  20. [SST84]
    J. Spencer, E. Szemerédi and W. T. Trotter, Jr. Unit distances in the Euclidean plane. In Graph Theory and Combinatorics, 293–303, Academic Press, London, 1984.Google Scholar
  21. [WS88]
    A. Wiernik and M. Sharir. Planar realization of nonlinear Davenport-Schinzel sequences by segments. Discrete Comput. Geom. 3 (1988), 15–47.Google Scholar
  22. [Zas75]
    Th. Zaslavsky. Facing up to Arrangements: Face-count Formulas for Partitions of Space by Hyperplanes. Memoirs Amer. Math. Soc. 154, 1975.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Herbert Edelsbrunner
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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