An acyclicity theorem for cell complexes ind dimension


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.

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Research reported in this paper was supported by the National Science Foundation under grant CCR-8714565

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Edelsbrunner, H. An acyclicity theorem for cell complexes ind dimension. Combinatorica 10, 251–260 (1990).

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AMS subject classification (1980)

  • 52 A 45
  • 05 B 45
  • 05 B 30