Qualitative Reasoning about Relative Direction on Adjustable Levels of Granularity

An important issue in Qualitative Spatial Reasoning is the representation of relative direction. In this paper we present simple geometric rules that enable reasoning about relative direction between oriented points. This framework, the Oriented Point Algebra OPRA_m, has a scalable granularity m. We develop a simple algorithm for computing the OPRA_m composition tables and prove its correctness. Using a composition table, algebraic closure for a set of OPRA statements is sufficient to solve spatial navigation tasks. And it turns out that scalable granularity is useful in these navigation tasks.