distance]{} has received significant attention. Here we focus on approaches that restrict the allowed matchings. Efrat [*et al.*]{} [@Efrat2002] introduced Fréchet-like metrics, the geodesic width and link width, to restrict to matchings suitable for curve morphing. Their method is suitable only for non-intersecting polylines. Moreover, geodesic width and link width do not resolve the problem illustrated in Fig. \[fig:badmatch\]: both matchings also have minimal geodesic width and minimal link width. Maheshwari [*et al.*]{} [@Maheshwari2011] studied a restriction by “speed limits”, which may exclude all [Fréchet matching]{}s and may cause undesirable effects near “outliers” (see Fig. \[fig:speedcounter\]). Buchin [*et al.*]{} [@Buchin2010] describe a framework for restricting [Fréchet matching]{}s, which they illustrate by restricting slope and path length. The former corresponds to speed limits. We briefly discuss the latter at the end of Section \[sec:algorithm\].

Preliminaries {#sec:prelims}
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[**Curves.**]{} Let $P$ be a polygonal curve with $m$ edges, defined by vertices $p_0, \ldots, p_m$. We treat a curve as a continuous map $P : [0,m] \rightarrow \mathbb{R}^d$. In this map, $P(i)$ equals $p_i$ for integer $i$. Furthermore, $P(i+\lambda)$ is a parameterization of the $(i+1)$st edge, that is, $P(i+\lambda) = (1-\lambda) \cdot p_i + \lambda \cdot p_{i+1}$, for integer $i$ and $0 < 