---
_id: '17145'
abstract:
- lang: eng
  text: Grid peeling is the process of repeatedly removing the convex hull vertices
    of the grid points that lie inside a given convex curve. It has been conjectured
    that, for a more and more refined grid, grid peeling converges to a continuous
    process, the affine curve-shortening flow, which deforms the curve based on the
    curvature. We prove this conjecture for one class of curves, parabolas with a
    vertical axis, and we determine the value of the constant factor in the formula
    that relates the two processes.
acknowledgement: Part of this work was done while G.R. enjoyed the hospitality of
  the Institute of Science and Technology Austria (ISTA) as a visiting professor during
  his sabbatical in the winter semester 2022/23.
alternative_title:
- LIPIcs
article_number: '76'
article_processing_charge: No
arxiv: 1
author:
- first_name: Günter
  full_name: Rote, Günter
  last_name: Rote
- first_name: Moritz
  full_name: Rüber, Moritz
  last_name: Rüber
- first_name: Morteza
  full_name: Saghafian, Morteza
  id: f86f7148-b140-11ec-9577-95435b8df824
  last_name: Saghafian
citation:
  ama: 'Rote G, Rüber M, Saghafian M. Grid peeling of parabolas. In: <i>40th International
    Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum
    für Informatik; 2024. doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2024.76">10.4230/LIPIcs.SoCG.2024.76</a>'
  apa: 'Rote, G., Rüber, M., &#38; Saghafian, M. (2024). Grid peeling of parabolas.
    In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens,
    Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2024.76">https://doi.org/10.4230/LIPIcs.SoCG.2024.76</a>'
  chicago: Rote, Günter, Moritz Rüber, and Morteza Saghafian. “Grid Peeling of Parabolas.”
    In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss
    Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2024.76">https://doi.org/10.4230/LIPIcs.SoCG.2024.76</a>.
  ieee: G. Rote, M. Rüber, and M. Saghafian, “Grid peeling of parabolas,” in <i>40th
    International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol.
    293.
  ista: 'Rote G, Rüber M, Saghafian M. 2024. Grid peeling of parabolas. 40th International
    Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry,
    LIPIcs, vol. 293, 76.'
  mla: Rote, Günter, et al. “Grid Peeling of Parabolas.” <i>40th International Symposium
    on Computational Geometry</i>, vol. 293, 76, Schloss Dagstuhl - Leibniz-Zentrum
    für Informatik, 2024, doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2024.76">10.4230/LIPIcs.SoCG.2024.76</a>.
  short: G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational
    Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
conference:
  end_date: 2024-06-14
  location: Athens, Greece
  name: 'SoCG: Symposium on Computational Geometry'
  start_date: 2024-06-11
date_created: 2024-06-16T22:01:06Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2024-06-17T08:41:56Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2024.76
external_id:
  arxiv:
  - '2402.15787'
file:
- access_level: open_access
  checksum: fbad1de06383a6b7e8a1cb3e8c7205ce
  content_type: application/pdf
  creator: dernst
  date_created: 2024-06-17T08:40:04Z
  date_updated: 2024-06-17T08:40:04Z
  file_id: '17151'
  file_name: 2024_LIPICS_Rote.pdf
  file_size: 1430896
  relation: main_file
  success: 1
file_date_updated: 2024-06-17T08:40:04Z
has_accepted_license: '1'
intvolume: '       293'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: 40th International Symposium on Computational Geometry
publication_identifier:
  isbn:
  - '9783959773164'
  issn:
  - 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Grid peeling of parabolas
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: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 293
year: '2024'
...