  We introduce an orientation-preserving landmark-based distance for continuous
curves, which can be viewed as an alternative to the \Frechet or Dynamic Time
Warping distances. This measure retains many of the properties of those
measures, and we prove some relations, but can be interpreted as a Euclidean
distance in a particular vector space. Hence it is significantly easier to use,
faster for general nearest neighbor queries, and allows easier access to
classification results than those measures. It is based on the \emph{signed}
distance function to the curves or other objects from a fixed set of landmark
points. We also prove new stability properties with respect to the choice of
landmark points, and along the way introduce a concept called signed local
feature size (slfs) which parameterizes these notions. Slfs explains the
complexity of shapes such as non-closed curves where the notion of local
orientation is in dispute -- but is more general than the well-known concept of
(unsigned) local feature size, and is for instance infinite for closed simple
curves. Altogether, this work provides a novel, simple, and powerful method for
oriented shape similarity and analysis.
