Iterative Respacing of Polygonal Curves

Abstract

A $\text{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0,p_1,\dots ,p_m\}$. 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.

For accompanying Mathematica implementation see: https://drive.google.com/drive/folders/1lLu-5O-cs1wA1T47KhsQd83qfgFa9xew?usp=sharing