[{"date_published":"2023-07-05T00:00:00Z","publisher":"Springer Nature","quality_controlled":"1","volume":70,"page":"1059-1089","department":[{"_id":"UlWa"}],"publication_status":"published","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"abstract":[{"lang":"eng","text":"Consider a geodesic triangle on a surface of constant curvature and subdivide it recursively into four triangles by joining the midpoints of its edges. We show the existence of a uniform δ>0\r\n such that, at any step of the subdivision, all the triangle angles lie in the interval (δ,π−δ)\r\n. Additionally, we exhibit stabilising behaviours for both angles and lengths as this subdivision progresses."}],"external_id":{"isi":["001023742800003"],"arxiv":["2107.04112"]},"_id":"13270","article_type":"original","file_date_updated":"2024-01-29T11:15:22Z","doi":"10.1007/s00454-023-00500-5","year":"2023","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","date_created":"2023-07-23T22:01:14Z","citation":{"apa":"Brunck, F. R. (2023). Iterated medial triangle subdivision in surfaces of constant curvature. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-023-00500-5\">https://doi.org/10.1007/s00454-023-00500-5</a>","ista":"Brunck FR. 2023. Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. 70(3), 1059–1089.","chicago":"Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-023-00500-5\">https://doi.org/10.1007/s00454-023-00500-5</a>.","mla":"Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” <i>Discrete and Computational Geometry</i>, vol. 70, no. 3, Springer Nature, 2023, pp. 1059–89, doi:<a href=\"https://doi.org/10.1007/s00454-023-00500-5\">10.1007/s00454-023-00500-5</a>.","short":"F.R. Brunck, Discrete and Computational Geometry 70 (2023) 1059–1089.","ama":"Brunck FR. Iterated medial triangle subdivision in surfaces of constant curvature. <i>Discrete and Computational Geometry</i>. 2023;70(3):1059-1089. doi:<a href=\"https://doi.org/10.1007/s00454-023-00500-5\">10.1007/s00454-023-00500-5</a>","ieee":"F. R. Brunck, “Iterated medial triangle subdivision in surfaces of constant curvature,” <i>Discrete and Computational Geometry</i>, vol. 70, no. 3. Springer Nature, pp. 1059–1089, 2023."},"type":"journal_article","status":"public","arxiv":1,"author":[{"first_name":"Florestan R","full_name":"Brunck, Florestan R","last_name":"Brunck","id":"6ab6e556-f394-11eb-9cf6-9dfb78f00d8d"}],"month":"07","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"file":[{"date_updated":"2024-01-29T11:15:22Z","date_created":"2024-01-29T11:15:22Z","file_name":"2023_DiscreteComputGeometry_Brunck.pdf","checksum":"865e68daafdd4edcfc280172ec50f5ea","file_id":"14897","success":1,"access_level":"open_access","relation":"main_file","file_size":1466020,"content_type":"application/pdf","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"05","oa_version":"Published Version","language":[{"iso":"eng"}],"publication":"Discrete and Computational Geometry","issue":"3","article_processing_charge":"Yes (via OA deal)","oa":1,"date_updated":"2024-01-29T11:16:16Z","title":"Iterated medial triangle subdivision in surfaces of constant curvature","isi":1,"scopus_import":"1","has_accepted_license":"1","intvolume":"        70"}]