---
_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'
...