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