  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.
