--- _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: Proceedings of the 5th Annual Symposium on Computational Geometry. ACM; 1989:145-151. doi:10.1145/73833.73850' apa: 'Edelsbrunner, 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/10.1145/73833.73850' chicago: Edelsbrunner, 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. ieee: 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. 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.” Proceedings of the 5th Annual Symposium on Computational Geometry, ACM, 1989, pp. 145–51, doi:10.1145/73833.73850. 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' ...