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ISPRS Int. J. Geo-Inf. 2016, 5(9), 152; doi:10.3390/ijgi5090152

Algebraic and Geometric Characterizations of Double-Cross Matrices of Polylines

Databases and Theoretical Computer Science Research Group, Hasselt University and Transnational University of Limburg, Agoralaan, Building D, 3590 Diepenbeek, Belgium
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Academic Editor: Wolfgang Kainz
Received: 4 July 2016 / Revised: 7 August 2016 / Accepted: 18 August 2016 / Published: 27 August 2016
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Abstract

We study the double-cross matrix descriptions of polylines in the two-dimensional plane. The double-cross matrix is a qualitative description of polylines in which exact, quantitative information is given up in favour of directional information. First, we give an algebraic characterization of the double-cross matrix of a polyline and derive some properties of double-cross matrices from this characterisation. Next, we give a geometric characterization of double-cross similarity of two polylines, using the technique of local carrier orders of polylines. We also identify the transformations of the plane that leave the double-cross matrix of all polylines in the two-dimensional plane invariant. View Full-Text
Keywords: double-cross matrix; qualitative calculus; polyline; qualitative descriptions of polylines; trajectory and moving object bata double-cross matrix; qualitative calculus; polyline; qualitative descriptions of polylines; trajectory and moving object bata
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MDPI and ACS Style

Kuijpers, B.; Moelans, B. Algebraic and Geometric Characterizations of Double-Cross Matrices of Polylines. ISPRS Int. J. Geo-Inf. 2016, 5, 152.

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