Let G be a connected graph with n vertices embedded in a metric space with metric δ. The stretch factor of G is the maximum over all pairs of distinct vertices u, v ∈ G of the ratio δG(u, v)/δ(u, v), where δG(u, v) is the metric distance in G between u and v. We consider the plane equipped with a weighted fixed orientation metric, i.e. a metric that measures the distance between a pair of point...