Composition Algorithms for Cardinal Direction Relations

We present a formal model for qualitative spatial reasoning with cardinal directions that is based on a recent proposal in the literature. We use our formal framework to study the composition operation for the cardinal direction relations of this model. We consider progressively more expressive classes of cardinal direction relations and give composition algorithms for these classes. Finally, when we consider the problem in its generality, we show that the binary relation resulting from the composition of some cardinal direction relations cannot even be expressed using the relations which are currently employed by the related proposal.