Grid Peeling of Parabolas

Rote, Günter; Rüber, Moritz; Saghafian, Morteza

doi:10.4230/LIPIcs.SoCG.2024.76

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LIPIcs.SoCG.2024.76.pdf

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Document Identifiers

DOI: 10.4230/LIPIcs.SoCG.2024.76
URN: urn:nbn:de:0030-drops-200213

Author Details

Günter Rote

Institut für Informatik, Freie Universität Berlin, Germany

Moritz Rüber

Freie Universität Berlin, Germany

Morteza Saghafian

Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria

Acknowledgements

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.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.SoCG.2024.76

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.

Subject Classification

ACM Subject Classification

Mathematics of computing → Discretization

Keywords

grid polygons
curvature flow

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