DROPS

Document

DOI: 10.4230/LIPIcs.SoCG.2024.76

Grid Peeling of Parabolas

Authors: Günter Rote, Moritz Rüber, and Morteza Saghafian

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract

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.

Cite as

Günter Rote, Moritz Rüber, and Morteza Saghafian. Grid Peeling of Parabolas. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 76:1-76:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{rote_et_al:LIPIcs.SoCG.2024.76,
  author =	{Rote, G\"{u}nter and R\"{u}ber, Moritz and Saghafian, Morteza},
  title =	{{Grid Peeling of Parabolas}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{76:1--76:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.76},
  URN =		{urn:nbn:de:0030-drops-200213},
  doi =		{10.4230/LIPIcs.SoCG.2024.76},
  annote =	{Keywords: grid polygons, curvature flow}
}

Search Results

Documents authored by Rüber, Moritz

Grid Peeling of Parabolas

Abstract

Cite as