[{"volume":70,"issue":"3","license":"https://creativecommons.org/licenses/by/4.0/","file":[{"file_size":1466020,"date_updated":"2024-01-29T11:15:22Z","creator":"dernst","file_name":"2023_DiscreteComputGeometry_Brunck.pdf","date_created":"2024-01-29T11:15:22Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"14897","checksum":"865e68daafdd4edcfc280172ec50f5ea"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publication_status":"published","month":"07","intvolume":" 70","scopus_import":"1","oa_version":"Published Version","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."}],"file_date_updated":"2024-01-29T11:15:22Z","department":[{"_id":"UlWa"}],"ddc":["510"],"date_updated":"2024-01-29T11:16:16Z","status":"public","type":"journal_article","article_type":"original","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)"},"_id":"13270","doi":"10.1007/s00454-023-00500-5","date_published":"2023-07-05T00:00:00Z","date_created":"2023-07-23T22:01:14Z","page":"1059-1089","day":"05","publication":"Discrete and Computational Geometry","has_accepted_license":"1","isi":1,"year":"2023","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","title":"Iterated medial triangle subdivision in surfaces of constant curvature","author":[{"first_name":"Florestan R","id":"6ab6e556-f394-11eb-9cf6-9dfb78f00d8d","last_name":"Brunck","full_name":"Brunck, Florestan R"}],"external_id":{"isi":["001023742800003"],"arxiv":["2107.04112"]},"article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00500-5.","ieee":"F. R. Brunck, “Iterated medial triangle subdivision in surfaces of constant curvature,” Discrete and Computational Geometry, vol. 70, no. 3. Springer Nature, pp. 1059–1089, 2023.","short":"F.R. Brunck, Discrete and Computational Geometry 70 (2023) 1059–1089.","apa":"Brunck, F. R. (2023). Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00500-5","ama":"Brunck FR. Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. 2023;70(3):1059-1089. doi:10.1007/s00454-023-00500-5","mla":"Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” Discrete and Computational Geometry, vol. 70, no. 3, Springer Nature, 2023, pp. 1059–89, doi:10.1007/s00454-023-00500-5."}}]