Oriented Straight Line Segment Algebra: Qualitative Spatial Reasoning
  about Oriented Objects
  Nearly 15 years ago, a set of qualitative spatial relations between oriented
straight line segments (dipoles) was suggested by Schlieder. This work received
substantial interest amongst the qualitative spatial reasoning community.
However, it turned out to be difficult to establish a sound constraint calculus
based on these relations. In this paper, we present the results of a new
investigation into dipole constraint calculi which uses algebraic methods to
derive sound results on the composition of relations and other properties of
dipole calculi. Our results are based on a condensed semantics of the dipole
relations.
  In contrast to the points that are normally used, dipoles are extended and
have an intrinsic direction. Both features are important properties of natural
objects. This allows for a straightforward representation of prototypical
reasoning tasks for spatial agents. As an example, we show how to generate
survey knowledge from local observations in a street network. The example
illustrates the fast constraint-based reasoning capabilities of the dipole
calculus. We integrate our results into two reasoning tools which are publicly
available.
