--- _id: '4073' abstract: - lang: eng text: A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. The problem of estimating how many such cuts are always sufficient is addressed. A few related algorithmic and combinatorial geometry problems are considered. article_processing_charge: No author: - first_name: Bernard full_name: Chazelle, Bernard last_name: Chazelle - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Leonidas full_name: Guibas, Leonidas last_name: Guibas - first_name: Richard full_name: Pollack, Richard last_name: Pollack - first_name: Raimund full_name: Seidel, Raimund last_name: Seidel - first_name: Micha full_name: Sharir, Micha last_name: Sharir - first_name: Jack full_name: Snoeyink, Jack last_name: Snoeyink citation: ama: 'Chazelle B, Edelsbrunner H, Guibas L, et al. Counting and cutting cycles of lines and rods in space. In: 31st Annual Symposium on Foundations of Computer Science. IEEE; 1990:242-251. doi:10.1109/FSCS.1990.89543' apa: 'Chazelle, B., Edelsbrunner, H., Guibas, L., Pollack, R., Seidel, R., Sharir, M., & Snoeyink, J. (1990). Counting and cutting cycles of lines and rods in space. In 31st Annual Symposium on Foundations of Computer Science (pp. 242–251). St. Louis, MO, United States of America: IEEE. https://doi.org/10.1109/FSCS.1990.89543' chicago: Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, Richard Pollack, Raimund Seidel, Micha Sharir, and Jack Snoeyink. “Counting and Cutting Cycles of Lines and Rods in Space.” In 31st Annual Symposium on Foundations of Computer Science, 242–51. IEEE, 1990. https://doi.org/10.1109/FSCS.1990.89543. ieee: B. Chazelle et al., “Counting and cutting cycles of lines and rods in space,” in 31st Annual Symposium on Foundations of Computer Science, St. Louis, MO, United States of America, 1990, pp. 242–251. ista: 'Chazelle B, Edelsbrunner H, Guibas L, Pollack R, Seidel R, Sharir M, Snoeyink J. 1990. Counting and cutting cycles of lines and rods in space. 31st Annual Symposium on Foundations of Computer Science. FOCS: Foundations of Computer Science, 242–251.' mla: Chazelle, Bernard, et al. “Counting and Cutting Cycles of Lines and Rods in Space.” 31st Annual Symposium on Foundations of Computer Science, IEEE, 1990, pp. 242–51, doi:10.1109/FSCS.1990.89543. short: B. Chazelle, H. Edelsbrunner, L. Guibas, R. Pollack, R. Seidel, M. Sharir, J. Snoeyink, in:, 31st Annual Symposium on Foundations of Computer Science, IEEE, 1990, pp. 242–251. conference: end_date: 1990-10-24 location: St. Louis, MO, United States of America name: 'FOCS: Foundations of Computer Science' start_date: 1990-10-22 date_created: 2018-12-11T12:06:47Z date_published: 1990-01-01T00:00:00Z date_updated: 2022-02-17T11:07:07Z day: '01' doi: 10.1109/FSCS.1990.89543 extern: '1' language: - iso: eng main_file_link: - url: https://ieeexplore.ieee.org/document/89543 month: '01' oa_version: None page: 242 - 251 publication: 31st Annual Symposium on Foundations of Computer Science publication_identifier: isbn: - 0-8186-2082-X publication_status: published publisher: IEEE publist_id: '2047' quality_controlled: '1' scopus_import: '1' status: public title: Counting and cutting cycles of lines and rods in space type: conference user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 year: '1990' ... --- _id: '4070' abstract: - lang: eng text: Let S be a set of n closed intervals on the x-axis. A ranking assigns to each interval, s, a distinct rank, p(s)∊ [1, 2,…,n]. We say that s can see t if p(s)International Journal of Computer Mathematics. 1990;34(3-4):129-144. doi:10.1080/00207169008803871 apa: Edelsbrunner, H., Overmars, M., Welzl, E., Hartman, I., & Feldman, J. (1990). Ranking intervals under visibility constraints. International Journal of Computer Mathematics. Taylor & Francis. https://doi.org/10.1080/00207169008803871 chicago: Edelsbrunner, Herbert, Mark Overmars, Emo Welzl, Irith Hartman, and Jack Feldman. “Ranking Intervals under Visibility Constraints.” International Journal of Computer Mathematics. Taylor & Francis, 1990. https://doi.org/10.1080/00207169008803871. ieee: H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, and J. Feldman, “Ranking intervals under visibility constraints,” International Journal of Computer Mathematics, vol. 34, no. 3–4. Taylor & Francis, pp. 129–144, 1990. ista: Edelsbrunner H, Overmars M, Welzl E, Hartman I, Feldman J. 1990. Ranking intervals under visibility constraints. International Journal of Computer Mathematics. 34(3–4), 129–144. mla: Edelsbrunner, Herbert, et al. “Ranking Intervals under Visibility Constraints.” International Journal of Computer Mathematics, vol. 34, no. 3–4, Taylor & Francis, 1990, pp. 129–44, doi:10.1080/00207169008803871. short: H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, J. Feldman, International Journal of Computer Mathematics 34 (1990) 129–144. date_created: 2018-12-11T12:06:46Z date_published: 1990-01-01T00:00:00Z date_updated: 2022-02-21T13:19:52Z day: '01' doi: 10.1080/00207169008803871 extern: '1' intvolume: ' 34' issue: 3-4 language: - iso: eng main_file_link: - url: https://www.tandfonline.com/doi/abs/10.1080/00207169008803871 month: '01' oa_version: None page: 129 - 144 publication: International Journal of Computer Mathematics publication_identifier: eissn: - 1029-0265 issn: - 0020-7160 publication_status: published publisher: Taylor & Francis publist_id: '2051' quality_controlled: '1' scopus_import: '1' status: public title: Ranking intervals under visibility constraints type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 34 year: '1990' ... --- _id: '4071' abstract: - lang: eng text: We show that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time O(n2 log n) and space O(n). In the same amount of time and space we can also handle the constrained case where edges are prescribed. The algorithm iteratively improves an arbitrary initial triangulation and is fairly easy to implement. 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 - first_name: Tiow full_name: Tan, Tiow last_name: Tan - first_name: Roman full_name: Waupotitsch, Roman last_name: Waupotitsch citation: ama: 'Edelsbrunner H, Tan T, Waupotitsch R. An O(n^2log n) time algorithm for the MinMax angle triangulation. In: Proceedings of the 6th Annual Symposium on Computational Geometry. ACM; 1990:44-52. doi:10.1145/98524.98535' apa: 'Edelsbrunner, H., Tan, T., & Waupotitsch, R. (1990). An O(n^2log n) time algorithm for the MinMax angle triangulation. In Proceedings of the 6th annual symposium on Computational geometry (pp. 44–52). Berkley, CA, United States: ACM. https://doi.org/10.1145/98524.98535' chicago: Edelsbrunner, Herbert, Tiow Tan, and Roman Waupotitsch. “An O(N^2log n) Time Algorithm for the MinMax Angle Triangulation.” In Proceedings of the 6th Annual Symposium on Computational Geometry, 44–52. ACM, 1990. https://doi.org/10.1145/98524.98535. ieee: H. Edelsbrunner, T. Tan, and R. Waupotitsch, “An O(n^2log n) time algorithm for the MinMax angle triangulation,” in Proceedings of the 6th annual symposium on Computational geometry, Berkley, CA, United States, 1990, pp. 44–52. ista: 'Edelsbrunner H, Tan T, Waupotitsch R. 1990. An O(n^2log n) time algorithm for the MinMax angle triangulation. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 44–52.' mla: Edelsbrunner, Herbert, et al. “An O(N^2log n) Time Algorithm for the MinMax Angle Triangulation.” Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 44–52, doi:10.1145/98524.98535. short: H. Edelsbrunner, T. Tan, R. Waupotitsch, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 44–52. conference: end_date: 1990-06-09 location: Berkley, CA, United States name: 'SCG: Symposium on Computational Geometry' start_date: 1990-06-07 date_created: 2018-12-11T12:06:46Z date_published: 1990-01-01T00:00:00Z date_updated: 2022-02-22T08:56:42Z day: '01' doi: 10.1145/98524.98535 extern: '1' language: - iso: eng main_file_link: - url: https://dl.acm.org/doi/10.1145/98524.98535 month: '01' oa_version: None page: 44 - 52 publication: Proceedings of the 6th annual symposium on Computational geometry publication_identifier: isbn: - 978-0-89791-362-1 publication_status: published publisher: ACM publist_id: '2052' quality_controlled: '1' status: public title: An O(n^2log n) time algorithm for the MinMax angle triangulation type: conference user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 year: '1990' ... --- _id: '4068' abstract: - lang: eng text: "LetS be a collection ofn convex, closed, and pairwise nonintersecting sets in the Euclidean plane labeled from 1 ton. A pair of permutations\r\n(i1i2in−1in)(inin−1i2i1) \r\nis called ageometric permutation of S if there is a line that intersects all sets ofS in this order. We prove thatS can realize at most 2n–2 geometric permutations. This upper bound is tight." acknowledgement: Research of the first author was supported by Amoco Foundation for Faculty Development in Computer Science Grant No. 1-6-44862. Work on this paper by the second author was supported by Office of Naval Research Grant No. N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation and the IBM Corporation. article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Micha full_name: Sharir, Micha last_name: Sharir citation: ama: Edelsbrunner H, Sharir M. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. Discrete & Computational Geometry. 1990;5(1):35-42. doi:10.1007/BF02187778 apa: Edelsbrunner, H., & Sharir, M. (1990). The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02187778 chicago: Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” Discrete & Computational Geometry. Springer, 1990. https://doi.org/10.1007/BF02187778. ieee: H. Edelsbrunner and M. Sharir, “The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2,” Discrete & Computational Geometry, vol. 5, no. 1. Springer, pp. 35–42, 1990. ista: Edelsbrunner H, Sharir M. 1990. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. Discrete & Computational Geometry. 5(1), 35–42. mla: Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” Discrete & Computational Geometry, vol. 5, no. 1, Springer, 1990, pp. 35–42, doi:10.1007/BF02187778. short: H. Edelsbrunner, M. Sharir, Discrete & Computational Geometry 5 (1990) 35–42. date_created: 2018-12-11T12:06:45Z date_published: 1990-01-01T00:00:00Z date_updated: 2022-02-22T14:50:34Z day: '01' doi: 10.1007/BF02187778 extern: '1' intvolume: ' 5' issue: '1' language: - iso: eng main_file_link: - url: https://link.springer.com/article/10.1007/BF02187778 month: '01' oa_version: None page: 35 - 42 publication: Discrete & Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer publist_id: '2057' quality_controlled: '1' status: public title: The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2 type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 5 year: '1990' ... --- _id: '4069' 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. acknowledgement: Research reported in this paper was supported by the National Science Foundation under grant CCR-8714565. article_processing_charge: No article_type: original 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. Combinatorica. 1990;10(3):251-260. doi:10.1007/BF02122779 apa: Edelsbrunner, H. (1990). An acyclicity theorem for cell complexes in d dimension. Combinatorica. Springer. https://doi.org/10.1007/BF02122779 chicago: Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” Combinatorica. Springer, 1990. https://doi.org/10.1007/BF02122779. ieee: H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,” Combinatorica, vol. 10, no. 3. Springer, pp. 251–260, 1990. ista: Edelsbrunner H. 1990. An acyclicity theorem for cell complexes in d dimension. Combinatorica. 10(3), 251–260. mla: Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” Combinatorica, vol. 10, no. 3, Springer, 1990, pp. 251–60, doi:10.1007/BF02122779. short: H. Edelsbrunner, Combinatorica 10 (1990) 251–260. date_created: 2018-12-11T12:06:45Z date_published: 1990-09-01T00:00:00Z date_updated: 2022-02-21T11:08:30Z day: '01' doi: 10.1007/BF02122779 extern: '1' intvolume: ' 10' issue: '3' language: - iso: eng main_file_link: - url: https://link.springer.com/article/10.1007/BF02122779 month: '09' oa_version: None page: 251 - 260 publication: Combinatorica publication_identifier: eissn: - 1439-6912 issn: - 0209-9683 publication_status: published publisher: Springer publist_id: '2050' quality_controlled: '1' scopus_import: '1' status: public title: An acyclicity theorem for cell complexes in d dimension type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 10 year: '1990' ...