Semantics of collinearity among regions

Authors:
Roland Billen;Eliseo Clementini
Affiliations:
Dept. of Geography and Geomatics, University of Glasgow, Glasgow, Scotland, UK;Dept. of Electrical Engineering, University of L’Aquila, Poggio di Roio (AQ), Italy
Venue:
OTM'05 Proceedings of the 2005 OTM Confederated international conference on On the Move to Meaningful Internet Systems
Year:
2005

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Abstract

Collinearity is a basic arrangement of regions in the plane. We investigate the semantics of collinearity in various possible meanings for three regions and we combine these concepts to obtain definitions for four and more regions. The aim of the paper is to support the formalization of projective properties for modelling geographic information and qualitative spatial reasoning. Exploring the semantics of collinearity will enable us to shed light on elementary projective properties from which all the others can be inferred. Collinearity is also used to find a qualitative classification of the arrangement of many regions in the plane.