A characterization of first-order topological properties of planar spatial data

Authors:
Michael Benedikt;Bart Kuijpers;Christof Löding;Jan Van den Bussche;Thomas Wilke
Affiliations:
Bell Laboratories, Murray Hill, New Jersey;Hasselt University, Diepenbeek, Belgium, and Transnationale Universiteit Limburg;RWTH Aachen, Aachen Germany;Hasselt University, Diepenbeek, Belgium, and Transnationale Universiteit Limburg;University of Kiel, Kiel, Germany
Venue:
Journal of the ACM (JACM)
Year:
2006

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Abstract

Planar spatial datasets can be modeled by closed semi-algebraic sets in the plane. We establish a characterization of the topological properties of such datasets expressible in the relational calculus with real polynomial constraints. The characterization is in the form of a query language that can only point that can only talk about points in the set and the “cones” around these points.