--- _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' ... --- _id: '3467' abstract: - lang: eng text: The effects of mast cell degranulating peptide (MCDP), a toxin from the honey bee, and of dendrotoxin (DTX), a toxin from the green mamba snake, were studied in voltage-clamped experiments with myelinated nerve fibres of Xenopus. MCDP and DTX blocked part of the K+ current. About 20% of the K+ current, however, was resistant to the toxins even in high concentrations. In Ringer solution half-maximal block was reached with concentrations of 33 nM MCDP and 11 nM DTX. In high-K+ solution the potency of both toxins was lower. β-Bungarotoxin (β-BuTX), another snake toxin, also blocked part of the K+ current, but was less potent than MCDP and DTX. Tail currents in high-K+ solution were analysed and three K+ current components were separated according to Dubois (1981b). Both MCDP and DTX selectively blocked a fast deactivating, slowly inactivating K+ current component which steeply activates between E = -60 mV and E = -40 mV (component f1). In concentrations around 100 nM, MCDP and DTX blocked neither the slow K+ current (component s) nor the fast deactivating, rapidly inactivating K+ current which activates between E = -40 mV and E = 20 mV (component f2). Similar results could be derived from K+ outward currents in Ringer solution. In high-K+, IC50 of MCDP for component f1 was 99 nM, whereas it was 7.6 μM for f2. Corresponding values for DTX are 68 nM and 1.8 μM. Binding studies with nerve fibre membranes of Xenopus reveal high-affinity binding sites for 125I-labelled DTX )K(D) = 22 pM in Ringer solution and 81 pM in high-K+ solution). 125I-labelled DTX can be displaced from its sites completely by unlabelled DTX, toxin I (black mamba toxin), MCDP, and partially by β-BuTX. Immunocytochemical staining demonstrates that binding sites for DTX are present in nodal and paranodal regions of the axonal membrane. The axonal membrane of motor and sensory nerve fibres is equipped with three types of well-characterized K+ channels and constitutes so far the best preparation to study MCDP- and DTX-sensitive K+ channels with electrophysiological and biochemical methods. acknowledgement: "We thank Professor E. Habermann for critical reading of the manuscript and E. Schmidt and J. Schafer for technical assistance. Financial support by the Deutsche Forschungsgemeinschaft (Vo 188/13-1 and SFB 249) is gratefully acknowledged.\r\n" article_processing_charge: No article_type: original author: - first_name: Michael full_name: Bräu, Michael last_name: Bräu - first_name: Florian full_name: Dreyer, Florian last_name: Dreyer - first_name: Peter M full_name: Jonas, Peter M id: 353C1B58-F248-11E8-B48F-1D18A9856A87 last_name: Jonas orcid: 0000-0001-5001-4804 - first_name: Holger full_name: Repp, Holger last_name: Repp - first_name: Werner full_name: Vogel, Werner last_name: Vogel citation: ama: 'Bräu M, Dreyer F, Jonas PM, Repp H, Vogel W. A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments. Journal of Physiology. 1990;420:365-385. doi:10.1113/jphysiol.1990.sp017918' apa: 'Bräu, M., Dreyer, F., Jonas, P. M., Repp, H., & Vogel, W. (1990). A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments. Journal of Physiology. Wiley-Blackwell. https://doi.org/10.1113/jphysiol.1990.sp017918' chicago: 'Bräu, Michael, Florian Dreyer, Peter M Jonas, Holger Repp, and Werner Vogel. “A K+ Channel in Xenopus Nerve Fibres Selectively Blocked by Bee and Snake Toxins: Binding and Voltage-Clamp Experiments.” Journal of Physiology. Wiley-Blackwell, 1990. https://doi.org/10.1113/jphysiol.1990.sp017918.' ieee: 'M. Bräu, F. Dreyer, P. M. Jonas, H. Repp, and W. Vogel, “A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments,” Journal of Physiology, vol. 420. Wiley-Blackwell, pp. 365–385, 1990.' ista: 'Bräu M, Dreyer F, Jonas PM, Repp H, Vogel W. 1990. A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments. Journal of Physiology. 420, 365–385.' mla: 'Bräu, Michael, et al. “A K+ Channel in Xenopus Nerve Fibres Selectively Blocked by Bee and Snake Toxins: Binding and Voltage-Clamp Experiments.” Journal of Physiology, vol. 420, Wiley-Blackwell, 1990, pp. 365–85, doi:10.1113/jphysiol.1990.sp017918.' short: M. Bräu, F. Dreyer, P.M. Jonas, H. Repp, W. Vogel, Journal of Physiology 420 (1990) 365–385. date_created: 2018-12-11T12:03:29Z date_published: 1990-01-01T00:00:00Z date_updated: 2022-02-23T16:10:03Z day: '01' doi: 10.1113/jphysiol.1990.sp017918 extern: '1' external_id: pmid: - '2324990' intvolume: ' 420' language: - iso: eng main_file_link: - open_access: '1' url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1190055/ month: '01' oa: 1 oa_version: None page: 365 - 385 pmid: 1 publication: Journal of Physiology publication_identifier: eissn: - 1469-7793 issn: - 0022-3751 publication_status: published publisher: Wiley-Blackwell publist_id: '2920' quality_controlled: '1' scopus_import: '1' status: public title: 'A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments' type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 420 year: '1990' ... --- _id: '3565' abstract: - lang: eng text: We investigate the complexity of determining the shape and presentation (i.e. position with orientation) of convex polytopes in multi-dimensional Euclidean space using a variety of probe models. acknowledgement: "NSF Grant MCS-83-03926 and DCR-85-05517\r\nAmoco Foundation Faculty Development in Computer Science\r\nNSF Grant DCR-84-01633 and DCR-84-01898" article_processing_charge: No author: - first_name: David full_name: Dobkin, David last_name: Dobkin - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Chee full_name: Yap, Chee last_name: Yap citation: ama: 'Dobkin D, Edelsbrunner H, Yap C. Probing convex polytopes. In: Cox I, Wilfong G, eds. Autonomous Robot Vehicles. Springer; 1990:328-341. doi:10.1007/978-1-4613-8997-2_25' apa: Dobkin, D., Edelsbrunner, H., & Yap, C. (1990). Probing convex polytopes. In I. Cox & G. Wilfong (Eds.), Autonomous Robot Vehicles (pp. 328–341). Springer. https://doi.org/10.1007/978-1-4613-8997-2_25 chicago: Dobkin, David, Herbert Edelsbrunner, and Chee Yap. “Probing Convex Polytopes.” In Autonomous Robot Vehicles, edited by Ingemar Cox and Gordon Wilfong, 328–41. Springer, 1990. https://doi.org/10.1007/978-1-4613-8997-2_25. ieee: D. Dobkin, H. Edelsbrunner, and C. Yap, “Probing convex polytopes,” in Autonomous Robot Vehicles, I. Cox and G. Wilfong, Eds. Springer, 1990, pp. 328–341. ista: 'Dobkin D, Edelsbrunner H, Yap C. 1990.Probing convex polytopes. In: Autonomous Robot Vehicles. , 328–341.' mla: Dobkin, David, et al. “Probing Convex Polytopes.” Autonomous Robot Vehicles, edited by Ingemar Cox and Gordon Wilfong, Springer, 1990, pp. 328–41, doi:10.1007/978-1-4613-8997-2_25. short: D. Dobkin, H. Edelsbrunner, C. Yap, in:, I. Cox, G. Wilfong (Eds.), Autonomous Robot Vehicles, Springer, 1990, pp. 328–341. date_created: 2018-12-11T12:03:59Z date_published: 1990-01-01T00:00:00Z date_updated: 2022-02-23T15:41:07Z day: '01' doi: 10.1007/978-1-4613-8997-2_25 editor: - first_name: Ingemar full_name: Cox, Ingemar last_name: Cox - first_name: Gordon full_name: Wilfong, Gordon last_name: Wilfong extern: '1' language: - iso: eng main_file_link: - url: https://link.springer.com/chapter/10.1007/978-1-4613-8997-2_25 month: '01' oa_version: None page: 328 - 341 publication: Autonomous Robot Vehicles publication_identifier: isbn: - 978-1-4613-8997-2 publication_status: published publisher: Springer publist_id: '2820' quality_controlled: '1' status: public title: Probing convex polytopes type: book_chapter user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 year: '1990' ... --- _id: '4064' abstract: - lang: eng text: Given a set of data points pi = (xi, yi ) for 1 ≤ i ≤ n, the least median of squares regression line is a line y = ax + b for which the median of the squared residuals is a minimum over all choices of a and b. An algorithm is described that computes such a line in O(n 2) time and O(n) memory space, thus improving previous upper bounds on the problem. This algorithm is an application of a general method built on top of the topological sweep of line arrangements. 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: Diane full_name: Souvaine, Diane last_name: Souvaine citation: ama: Edelsbrunner H, Souvaine D. Computing least median of squares regression lines and guided topological sweep. Journal of the American Statistical Association. 1990;85(409):115-119. doi:10.1080/01621459.1990.10475313 apa: Edelsbrunner, H., & Souvaine, D. (1990). Computing least median of squares regression lines and guided topological sweep. Journal of the American Statistical Association. American Statistical Association. https://doi.org/10.1080/01621459.1990.10475313 chicago: Edelsbrunner, Herbert, and Diane Souvaine. “Computing Least Median of Squares Regression Lines and Guided Topological Sweep.” Journal of the American Statistical Association. American Statistical Association, 1990. https://doi.org/10.1080/01621459.1990.10475313. ieee: H. Edelsbrunner and D. Souvaine, “Computing least median of squares regression lines and guided topological sweep,” Journal of the American Statistical Association, vol. 85, no. 409. American Statistical Association, pp. 115–119, 1990. ista: Edelsbrunner H, Souvaine D. 1990. Computing least median of squares regression lines and guided topological sweep. Journal of the American Statistical Association. 85(409), 115–119. mla: Edelsbrunner, Herbert, and Diane Souvaine. “Computing Least Median of Squares Regression Lines and Guided Topological Sweep.” Journal of the American Statistical Association, vol. 85, no. 409, American Statistical Association, 1990, pp. 115–19, doi:10.1080/01621459.1990.10475313. short: H. Edelsbrunner, D. Souvaine, Journal of the American Statistical Association 85 (1990) 115–119. date_created: 2018-12-11T12:06:43Z date_published: 1990-01-01T00:00:00Z date_updated: 2022-02-22T15:10:54Z day: '01' doi: 10.1080/01621459.1990.10475313 extern: '1' intvolume: ' 85' issue: '409' language: - iso: eng main_file_link: - url: https://www.tandfonline.com/doi/abs/10.1080/01621459.1990.10475313 month: '01' oa_version: None page: 115 - 119 publication: Journal of the American Statistical Association publication_identifier: eissn: - 1537-274X issn: - 0003-1291 publication_status: published publisher: American Statistical Association publist_id: '2059' quality_controlled: '1' scopus_import: '1' status: public title: Computing least median of squares regression lines and guided topological sweep type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 85 year: '1990' ... --- _id: '4063' abstract: - lang: eng text: This paper describes a general-purpose programming technique, called Simulation of Simplicity, that can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task of providing a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software. acknowledgement: 'Research of both authors was supported by Amoco Foundation Faculty Development grant CS 1-6-44862. It was partially carried out while both authors were with the Institutes for Information Processing at the Technical University of Graz, Austria. The first author also acknowledges support 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 - first_name: Ernst full_name: Mücke, Ernst last_name: Mücke citation: ama: 'Edelsbrunner H, Mücke E. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics. 1990;9(1):66-104. doi:10.1145/77635.77639' apa: 'Edelsbrunner, H., & Mücke, E. (1990). Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics. ACM. https://doi.org/10.1145/77635.77639' chicago: 'Edelsbrunner, Herbert, and Ernst Mücke. “Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms.” ACM Transactions on Graphics. ACM, 1990. https://doi.org/10.1145/77635.77639.' ieee: 'H. Edelsbrunner and E. Mücke, “Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms,” ACM Transactions on Graphics, vol. 9, no. 1. ACM, pp. 66–104, 1990.' ista: 'Edelsbrunner H, Mücke E. 1990. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics. 9(1), 66–104.' mla: 'Edelsbrunner, Herbert, and Ernst Mücke. “Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms.” ACM Transactions on Graphics, vol. 9, no. 1, ACM, 1990, pp. 66–104, doi:10.1145/77635.77639.' short: H. Edelsbrunner, E. Mücke, ACM Transactions on Graphics 9 (1990) 66–104. date_created: 2018-12-11T12:06:43Z date_published: 1990-01-01T00:00:00Z date_updated: 2022-02-22T14:58:39Z day: '01' doi: 10.1145/77635.77639 extern: '1' intvolume: ' 9' issue: '1' language: - iso: eng main_file_link: - url: https://dl.acm.org/doi/10.1145/77635.77639 month: '01' oa_version: None page: 66 - 104 publication: ACM Transactions on Graphics publication_identifier: eissn: - 1557-7368 issn: - 0730-0301 publication_status: published publisher: ACM publist_id: '2058' quality_controlled: '1' scopus_import: '1' status: public title: 'Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms' type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 9 year: '1990' ... --- _id: '4060' abstract: - lang: eng text: This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are co-planar, It also presents an algorithm that in O(n log n) time constructs a tetrahedrization of a set of n points consisting of at most 3n-11 tetrahedra. acknowledgement: Research of the first author is supported by Amoco Fnd. Fac. Dec. Comput. Sci. 1-6-44862, the second author is supported by NSF Grant ECS 84-10902, and research of the third author is supported in part by ONR Grant N00014-85K0570 and by NSF Grant DMS 8504322. 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: Franco full_name: Preparata, Franco last_name: Preparata - first_name: Douglas full_name: West, Douglas last_name: West citation: ama: Edelsbrunner H, Preparata F, West D. Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. 1990;10(3-4):335-347. doi:10.1016/S0747-7171(08)80068-5 apa: Edelsbrunner, H., Preparata, F., & West, D. (1990). Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. Elsevier. https://doi.org/10.1016/S0747-7171(08)80068-5 chicago: Edelsbrunner, Herbert, Franco Preparata, and Douglas West. “Tetrahedrizing Point Sets in Three Dimensions.” Journal of Symbolic Computation. Elsevier, 1990. https://doi.org/10.1016/S0747-7171(08)80068-5. ieee: H. Edelsbrunner, F. Preparata, and D. West, “Tetrahedrizing point sets in three dimensions,” Journal of Symbolic Computation, vol. 10, no. 3–4. Elsevier, pp. 335–347, 1990. ista: Edelsbrunner H, Preparata F, West D. 1990. Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. 10(3–4), 335–347. mla: Edelsbrunner, Herbert, et al. “Tetrahedrizing Point Sets in Three Dimensions.” Journal of Symbolic Computation, vol. 10, no. 3–4, Elsevier, 1990, pp. 335–47, doi:10.1016/S0747-7171(08)80068-5. short: H. Edelsbrunner, F. Preparata, D. West, Journal of Symbolic Computation 10 (1990) 335–347. date_created: 2018-12-11T12:06:42Z date_published: 1990-01-01T00:00:00Z date_updated: 2022-02-23T10:10:35Z day: '01' doi: 10.1016/S0747-7171(08)80068-5 extern: '1' intvolume: ' 10' issue: 3-4 language: - iso: eng main_file_link: - open_access: '1' url: https://www.sciencedirect.com/science/article/pii/S0747717108800685?via%3Dihub month: '01' oa: 1 oa_version: Published Version page: 335 - 347 publication: Journal of Symbolic Computation publication_identifier: eissn: - 1095-855X issn: - 0747-7171 publication_status: published publisher: Elsevier publist_id: '2061' quality_controlled: '1' scopus_import: '1' status: public title: Tetrahedrizing point sets in three dimensions type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 10 year: '1990' ...