The effect of axis rotation on distance estimation

The objective of this paper is to evaluate the usefulness of the weighted lp norm as a distance measure when axis rotation is included to obtain the best fit. We compare the weighted lp and Euclidean norms in an empirical study of 18 major country and city road networks. A substantial improvement in accuracy is obtained with the weighted lp norm for networks with a significant component of rectangular travel. We show that the weighted lp norm, and by inference other multi-parameter distance estimators, are justified in practice provided the reference axes are oriented properly to model the directional bias inherent in the network.