Bringing closed polygonal curves in the plane to normal form via local moves
type: Item
instance of: scholarly article
title: Bringing closed polygonal curves in the plane to normal form via local moves
zbMATH Open document ID: 1401.52032
DOI: 10.1134/S0001434618030124
author: D. Kharzeev
published in: Mathematical Notes
publication date: 2018-07-23T00:00:00Z
review text: The key-concept in this paper is introduced as follows: a closed polygonal plane curve with \(n\) vertices is in normal form if: (1) it is a regular polygon; (2) its sides are of equal length and it is inscribed in a circle going around it several times; (3) its sides are of equal length, and it is inscribed in a ``figure eight'' curve and self-intersects only at the curve's double point. The authors prove that given a closed polygonal plane curve there is a regular homotopy that transforms it into normal form. Two algorithms performing this transformation via local moves are constructed: in case of closed polygonal curves with equal edges, and in case of closed polygonal plane curves with arbitrary edges. The problem and the algorithms are related to modeling the motion of a biological entity on a flat surface.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 52C30
zbMATH DE Number: 6909354
zbMATH Keywords: regular closed polygonal curve
zbMATH Keywords: regular homotopy
zbMATH Keywords: normal form of a polygonal curve
zbMATH Keywords: local moves
zbMATH Keywords: winding number of a plane curve
zbMATH Keywords: Euler functional
zbMATH Keywords: gradient descent
MaRDI profile type: Publication
cites work: Q5676551
cites work: Euler elasticae in the plane and the Whitney-Graustein theorem
cites work: On the normal form of knots
cites work: Closed Euler elasticae
full work available at URL: s0001434618030124
OpenAlex ID: W2799418335
description: scientific article; zbMATH DE number 6909354