A new duality result concerning Voronoi diagrams

  • F. Aurenhammer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 226)


Voronoi Diagram Convex Polyhedron Power Diagram White Edge Triangle Incident 
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  1. [Al]
    Aurenhammer, F. Power diagrams — properties, algorithms and applications. To appear in SIAM J. Comp.Google Scholar
  2. [A2]
    Aurenhammer, F. A criterion for the affine equivalence of cell complexes in E d and convex polyhedra in E d+1. Rep. 205, IIG, Tech. Univ. of Graz, Austria (1985).Google Scholar
  3. [B]
    Brown, K.Q. Voronoi diagrams from convex hulls. Inf. Proc. Lett. 9 (1979), 223–228.Google Scholar
  4. [CE]
    Chazelle, B., Edelsbrunner, H. An improved algorithm for constructing k th-order Voronoi diagrams. Proc. ACM Symp. on Computational Geometry (1985), 228–234.Google Scholar
  5. [E]
    Edelsbrunner, H. Constructing edge-skeletons in three dimensions with applications to power diagrams and dissecting three-dimensional point-sets. Rep. 140, IIG, Tech. Univ. of Graz, Austria (1984).Google Scholar
  6. [EOS]
    Edelsbrunner, H., O'Rourke, J., Seidel, R. Constructing arrangements of lines and hyperplanes with applications. Proc. 24th Ann. IEEE Symp. Found. Comput. Sci. (1983), 83–91.Google Scholar
  7. [L]
    Lee, D.T. On k-nearest neighbor Voronoi diagrams in the plane. IEEE Trans. Comput. C-31 (1982), 478–487.Google Scholar
  8. [PH]
    Preparata, F.P., Hong, S.J. Convex hulls of finite sets of points in two and three dimensions. Comm. ACM (1977), 87–93.Google Scholar
  9. [S]
    Seidel, R. A convex hull algorithm optimal for point-sets in even dimensions. M.S. Thesis, Rep. 81-14, Dep. Comp. Sci., Univ. of British Columbia, Vanc. (1981).Google Scholar
  10. [SH]
    Shamos, M.I., Hoey, D. Closest-point problems. Proc. 16th. Ann. IEEE Symp. Found. Comput. Sci. (1975), 151–162.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • F. Aurenhammer
    • 1
  1. 1.Institutes for Information ProcessingTU Graz and Austrian Computer SocietyGrazAustria

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