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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.

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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)

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@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}
}

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Grid Peeling of Parabolas

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