---
_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
arxiv: 1
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.
    <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>
  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.
  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>.
  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'
...