Günter Rote, Moritz Rüber, and Morteza Saghafian:

Grid peeling of parabolas

In: 40th International Symposium on Computational Geometry (SoCG 2024), Athens, June 2024. Editors: Wolfgang Mulzer and Jeff M. Phillips, Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2024, Vol. 293, pp. 76:1–76:18. doi:10.4230/LIPIcs.SOCG.2024.76, arXiv:2402.15787 [cs.CG].  →BibTeX

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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Last update: June 6, 2024.