Combinatorica

, Volume 10, Issue 3, pp 251–260 | Cite as

An acyclicity theorem for cell complexes ind dimension

  • H. Edelsbrunner
Article

Abstract

LetC be a cell complex ind-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope ind+ 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in_front/behind relation defined for the faces ofC with respect to any fixed viewpointx is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry.

AMS subject classification (1980)

52 A 45 05 B 45 05 B 30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    F. Aurenhammer: Power diagrams: properties, algorithms, and applications,SIAM J. Comput.,16 (1987), 78–96.Google Scholar
  2. [2]
    B. Chazelle: How to search in history,Inform. Control,64 (1985), 77–99.Google Scholar
  3. [3]
    B. Delaunay: Sur la sphére vide,Izv. Akad. Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk,7 (1934), 793–800.Google Scholar
  4. [4]
    H. Edelsbrunner:Algorithms in Combinatorial Geometry, Springer-Verlag, Heidelberg, Germany,1987.Google Scholar
  5. [5]
    H. Edelsbrunner, D. G. Kirkpatrick, andR. Seidel: On the shape of a set of points in the plane,IEEE Trans. Inform. Theory,IT-29 (1983), 551–559.Google Scholar
  6. [6]
    L. De Floriani, B. Falcidieno, C. Pienovi, andG. Nagy:On sorting triangles in a Delaunay tessellation, Techn. Rept., Istituto per la Matematica Applicata, Consiglio Nazionale delle Richerche, Genove, Italy,1988.Google Scholar
  7. [7]
    J. D. Foley, andA. van Dam:Fundamentals of Interactive Computer Graphics, Addison-Wesley, Reading, Massachusetts,1982.Google Scholar
  8. [8]
    H. Fuchs, Z. M. Kedem, andB. Naylor: On visible surface generation by a priori structures,Comput. Graphics,14 (1980), 124–133.Google Scholar
  9. [9]
    G. Voronoi: Sur quelques propriétés des formes quadratiques parfaites,J. Reine Angew. Math.,133 (1907), 212–287.Google Scholar

Copyright information

© Akadémiai Kiadó 1990

Authors and Affiliations

  • H. Edelsbrunner
    • 1
  1. 1.Dep. of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations