[{"acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","year":"2023","_id":"13270","page":"1059-1089","date_updated":"2024-01-29T11:16:16Z","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."}],"month":"07","oa_version":"Published Version","type":"journal_article","volume":70,"date_created":"2023-07-23T22:01:14Z","file_date_updated":"2024-01-29T11:15:22Z","status":"public","external_id":{"arxiv":["2107.04112"],"isi":["001023742800003"]},"intvolume":"        70","citation":{"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>","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.","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>.","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>.","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.","short":"F.R. Brunck, Discrete and Computational Geometry 70 (2023) 1059–1089."},"oa":1,"publication_status":"published","has_accepted_license":"1","ddc":["510"],"date_published":"2023-07-05T00:00:00Z","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"UlWa"}],"publication":"Discrete and Computational Geometry","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","author":[{"first_name":"Florestan R","last_name":"Brunck","id":"6ab6e556-f394-11eb-9cf6-9dfb78f00d8d","full_name":"Brunck, Florestan R"}],"file":[{"file_size":1466020,"relation":"main_file","content_type":"application/pdf","creator":"dernst","file_name":"2023_DiscreteComputGeometry_Brunck.pdf","success":1,"date_created":"2024-01-29T11:15:22Z","access_level":"open_access","file_id":"14897","date_updated":"2024-01-29T11:15:22Z","checksum":"865e68daafdd4edcfc280172ec50f5ea"}],"day":"05","arxiv":1,"title":"Iterated medial triangle subdivision in surfaces of constant curvature","isi":1,"language":[{"iso":"eng"}],"issue":"3","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"doi":"10.1007/s00454-023-00500-5","quality_controlled":"1"}]