# An acyclicity theorem for cell complexes in d dimension

Edelsbrunner H. 1989. An acyclicity theorem for cell complexes in d dimension. Proceedings of the 5th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 145–151.

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Author

Abstract

Let C be a cell complex in d-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope in d + 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 of C with respect to any fixed viewpoint x is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry.

Publishing Year

Date Published

1989-06-01

Proceedings Title

Proceedings of the 5th annual symposium on Computational geometry

Page

145 - 151

Conference

SCG: Symposium on Computational Geometry

Conference Location

Saarbruchen, Germany

Conference Date

1989-06-05 – 1989-06-07

ISBN

IST-REx-ID

### Cite this

Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. In:

*Proceedings of the 5th Annual Symposium on Computational Geometry*. ACM; 1989:145-151. doi:10.1145/73833.73850Edelsbrunner, H. (1989). An acyclicity theorem for cell complexes in d dimension. In

*Proceedings of the 5th annual symposium on Computational geometry*(pp. 145–151). Saarbruchen, Germany: ACM. https://doi.org/10.1145/73833.73850Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” In

*Proceedings of the 5th Annual Symposium on Computational Geometry*, 145–51. ACM, 1989. https://doi.org/10.1145/73833.73850.H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,” in

*Proceedings of the 5th annual symposium on Computational geometry*, Saarbruchen, Germany, 1989, pp. 145–151.Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.”

*Proceedings of the 5th Annual Symposium on Computational Geometry*, ACM, 1989, pp. 145–51, doi:10.1145/73833.73850.