# Oriented Straight Line Segment Algebra: Qualitative Spatial Reasoning About Oriented Objects

Reinhard Moratz 1and Dominik L¨ucke 2and Till Mossakowski 2 October 26, 2018 1University of Maine, National Center for Geographic Information and Analysis, Department of Spatial Information Science and Engineering, 348 Boardman Hall, Orono, 04469 Maine, USA.

moratz@spatial.maine.edu 2University of Bremen, Collaborative Research Center on Spatial Cognition (SFB/TR 8),
Department of Mathematics and Informatics, Bibliothekstr. 1, 28359 Bremen, Germany.

till | luecke@informatik.uni-bremen.de

## Abstract

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.

Keywords:
Qualitative Spatial Reasoning, Relation Algebra, Affine Geometry 