English

Grid Peeling of Parabolas

Computational Geometry 2024-02-27 v1 Numerical Analysis Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2402.15787,
  title  = {Grid Peeling of Parabolas},
  author = {Günter Rote and Moritz Rüber and Morteza Saghafian},
  journal= {arXiv preprint arXiv:2402.15787},
  year   = {2024}
}
R2 v1 2026-06-28T14:59:02.331Z