--- _id: '1578' abstract: - lang: eng text: We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations. acknowledgement: "The research of the second author is partially supported by NSF under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n" author: - first_name: Thanhtung full_name: Cao, Thanhtung last_name: Cao - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Tiowseng full_name: Tan, Tiowseng last_name: Tan citation: ama: Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 2015;48(7):507-519. doi:10.1016/j.comgeo.2015.04.001 apa: Cao, T., Edelsbrunner, H., & Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2015.04.001 chicago: Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.04.001. ieee: T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct digital Voronoi diagrams,” Computational Geometry, vol. 48, no. 7. Elsevier, pp. 507–519, 2015. ista: Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519. mla: Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry, vol. 48, no. 7, Elsevier, 2015, pp. 507–19, doi:10.1016/j.comgeo.2015.04.001. short: T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519. date_created: 2018-12-11T11:52:49Z date_published: 2015-08-01T00:00:00Z date_updated: 2021-01-12T06:51:43Z day: '01' department: - _id: HeEd doi: 10.1016/j.comgeo.2015.04.001 intvolume: ' 48' issue: '7' language: - iso: eng month: '08' oa_version: None page: 507 - 519 publication: Computational Geometry publication_status: published publisher: Elsevier publist_id: '5593' quality_controlled: '1' scopus_import: 1 status: public title: Triangulations from topologically correct digital Voronoi diagrams type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1584' abstract: - lang: eng text: We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004' apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004' chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004.' ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 5. Elsevier, pp. 429–442, 2015.' ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(5), 429–442.' mla: 'Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier, 2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004.' short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.' date_created: 2018-12-11T11:52:51Z date_published: 2015-07-01T00:00:00Z date_updated: 2023-02-23T10:05:22Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2015.01.004 file: - access_level: open_access checksum: 5b33719a86f7f4c8e5dc62c1b6893f49 content_type: application/pdf creator: system date_created: 2018-12-12T10:17:36Z date_updated: 2020-07-14T12:45:03Z file_id: '5292' file_name: IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf file_size: 508379 relation: main_file file_date_updated: 2020-07-14T12:45:03Z has_accepted_license: '1' intvolume: ' 48' issue: '5' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 429 - 442 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5587' pubrep_id: '475' quality_controlled: '1' related_material: record: - id: '1582' relation: other status: public scopus_import: 1 status: public title: 'Reprint of: Weighted straight skeletons in the plane' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1582' abstract: - lang: eng text: We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133. doi:10.1016/j.comgeo.2014.08.006' apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006' chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006.' ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 2. Elsevier, pp. 120–133, 2015.' ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(2), 120–133.' mla: 'Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33, doi:10.1016/j.comgeo.2014.08.006.' short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.' date_created: 2018-12-11T11:52:51Z date_published: 2015-02-01T00:00:00Z date_updated: 2023-02-23T10:05:27Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2014.08.006 file: - access_level: open_access checksum: c1ef67f6ec925e12f73a96b8fe285ab4 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:28Z date_updated: 2020-07-14T12:45:02Z file_id: '5215' file_name: IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf file_size: 505987 relation: main_file file_date_updated: 2020-07-14T12:45:02Z has_accepted_license: '1' intvolume: ' 48' issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 120 - 133 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5589' pubrep_id: '474' quality_controlled: '1' related_material: record: - id: '1584' relation: other status: public scopus_import: 1 status: public title: Weighted straight skeletons in the plane tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1583' abstract: - lang: eng text: We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021 apa: Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021 chicago: Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021. ieee: T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” Information Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015. ista: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 115(2), 243–247. mla: Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021. short: T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247. date_created: 2018-12-11T11:52:51Z date_published: 2015-02-01T00:00:00Z date_updated: 2021-01-12T06:51:45Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.ipl.2014.09.021 file: - access_level: open_access checksum: 2779a648610c9b5c86d0b51a62816d23 content_type: application/pdf creator: system date_created: 2018-12-12T10:18:45Z date_updated: 2020-07-14T12:45:03Z file_id: '5367' file_name: IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf file_size: 270137 relation: main_file file_date_updated: 2020-07-14T12:45:03Z has_accepted_license: '1' intvolume: ' 115' issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 243 - 247 publication: Information Processing Letters publication_status: published publisher: Elsevier publist_id: '5588' pubrep_id: '473' quality_controlled: '1' scopus_import: 1 status: public title: A simple algorithm for computing positively weighted straight skeletons of monotone polygons tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 115 year: '2015' ... --- _id: '1590' abstract: - lang: eng text: 'The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Thomas full_name: Hackl, Thomas last_name: Hackl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber citation: ama: 'Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28' apa: 'Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., & Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28' chicago: Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28. ieee: O. Aichholzer et al., “Representing directed trees as straight skeletons,” in Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–347. ista: 'Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 335–347.' mla: Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:10.1007/978-3-319-27261-0_28. short: O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347. conference: end_date: 2015-09-26 location: Los Angeles, CA, United States name: 'GD: International Symposium on Graph Drawing' start_date: 2015-09-24 date_created: 2018-12-11T11:52:54Z date_published: 2015-11-27T00:00:00Z date_updated: 2022-01-28T09:10:37Z day: '27' department: - _id: HeEd doi: 10.1007/978-3-319-27261-0_28 intvolume: ' 9411' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1508.01076 month: '11' oa: 1 oa_version: Preprint page: 335 - 347 publication: Graph Drawing and Network Visualization publication_identifier: eisbn: - 978-3-319-27261-0 isbn: - 978-3-319-27260-3 publication_status: published publisher: Springer Nature publist_id: '5581' quality_controlled: '1' scopus_import: '1' status: public title: Representing directed trees as straight skeletons type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9411 year: '2015' ...