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.
翻译:$\ textit{polygonal cury} $\ textit{ polygonal curound} 是一个以 $_p_0, p_1,\ ldots, p_m $为线性内插的线条段集合 。 这些曲线可以从以$\ mathbb{R ⁇ n$为方向的曲线取样点中获得 。 在应用中, 这个点的样本可以使用于 \ textit{ equigront}, 相继点之间的距离相等 。 我们为多边形曲线点的间隔提供了一种高效的计算方法, 并显示此方法的迭接会与等边多边形曲线相交汇 。