Iterative Respacing of Polygonal Curves

TL;DR

This paper introduces an efficient iterative method for respacing points on polygonal curves to achieve equilateral spacing, with proven convergence to an equilateral polygonal shape.

Contribution

The paper presents a novel, computationally efficient algorithm for respacing polygonal curves and proves its convergence to an equilateral configuration.

Findings

The method converges to an equilateral polygonal curve.

The algorithm is computationally efficient.

It is applicable to sampling points from curves in f3nf3n.

Abstract

A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in $\mathbb{R}^n$. In applications it can be useful for this sample of points to be close to \textit{equilateral}, with equal distance between consecutive points. We present a computationally efficient method for respacing the points of a polygonal curve and show that iteration of this method converges to an equilateral polygonal curve.