{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:20:40Z","timestamp":1760242840079,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2016,8,27]],"date-time":"2016-08-27T00:00:00Z","timestamp":1472256000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/ijgi5090152","type":"journal-article","created":{"date-parts":[[2016,8,29]],"date-time":"2016-08-29T10:18:38Z","timestamp":1472465918000},"page":"152","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Algebraic and Geometric Characterizations of Double-Cross Matrices of Polylines"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5774-0948","authenticated-orcid":false,"given":"Bart","family":"Kuijpers","sequence":"first","affiliation":[{"name":"Databases and Theoretical Computer Science Research Group, Hasselt University and Transnational University of Limburg, Agoralaan, Building D, 3590 Diepenbeek, Belgium"}]},{"given":"Bart","family":"Moelans","sequence":"additional","affiliation":[{"name":"Databases and Theoretical Computer Science Research Group, Hasselt University and Transnational University of Limburg, Agoralaan, Building D, 3590 Diepenbeek, Belgium"}]}],"member":"1968","published-online":{"date-parts":[[2016,8,27]]},"reference":[{"key":"ref_1","unstructured":"G\u00fcting, R.H., and Schneider, M. 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