T. Mossakowski and R. Moratz, 2012, Qualitative Reasoning about Relative Direction of Oriented Points. Artificial Intelligence Journal, Volumes 180-181, pages 34-45.
An important issue in qualitative spatial reasoning is the representation of relative directions. In this paper we present simple geometric rules that enable reasoning about the relative direction between oriented points. This framework, the oriented point algebra OPRAm, has a scalable granularity m. We develop a simple algorithm for computing the OPRAm composition tables and prove its correctness. Using a composition table, algebraic closure for a set of OPRAm statements is very useful to solve spatial navigation tasks. It turns out that scalable granularity is useful in these navigation tasks.