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