---
_id: '4085'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
citation:
  ama: 'Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. In:
    <i>Proceedings of the 5th Annual Symposium on Computational Geometry</i>. ACM;
    1989:145-151. doi:<a href="https://doi.org/10.1145/73833.73850">10.1145/73833.73850</a>'
  apa: 'Edelsbrunner, H. (1989). An acyclicity theorem for cell complexes in d dimension.
    In <i>Proceedings of the 5th annual symposium on Computational geometry</i> (pp.
    145–151). Saarbruchen, Germany: ACM. <a href="https://doi.org/10.1145/73833.73850">https://doi.org/10.1145/73833.73850</a>'
  chicago: Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.”
    In <i>Proceedings of the 5th Annual Symposium on Computational Geometry</i>, 145–51.
    ACM, 1989. <a href="https://doi.org/10.1145/73833.73850">https://doi.org/10.1145/73833.73850</a>.
  ieee: H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,”
    in <i>Proceedings of the 5th annual symposium on Computational geometry</i>, Saarbruchen,
    Germany, 1989, pp. 145–151.
  ista: '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.'
  mla: Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.”
    <i>Proceedings of the 5th Annual Symposium on Computational Geometry</i>, ACM,
    1989, pp. 145–51, doi:<a href="https://doi.org/10.1145/73833.73850">10.1145/73833.73850</a>.
  short: H. Edelsbrunner, in:, Proceedings of the 5th Annual Symposium on Computational
    Geometry, ACM, 1989, pp. 145–151.
conference:
  end_date: 1989-06-07
  location: Saarbruchen, Germany
  name: 'SCG: Symposium on Computational Geometry'
  start_date: 1989-06-05
date_created: 2018-12-11T12:06:51Z
date_published: 1989-06-01T00:00:00Z
date_updated: 2022-02-10T10:56:49Z
day: '01'
doi: 10.1145/73833.73850
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://dl.acm.org/doi/10.1145/73833.73850
month: '06'
oa_version: None
page: 145 - 151
publication: Proceedings of the 5th annual symposium on Computational geometry
publication_identifier:
  isbn:
  - 978-0-89791-318-8
publication_status: published
publisher: ACM
publist_id: '2033'
quality_controlled: '1'
scopus_import: '1'
status: public
title: An acyclicity theorem for cell complexes in d dimension
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1989'
...