Drawing Area-Proportional Euler Diagrams Representing Up To Three Sets

Rodgers, Peter, Stapleton, Gem, Flower, Jean, Howse, John (2014) Drawing Area-Proportional Euler Diagrams Representing Up To Three Sets. IEEE Transactions on Visualization and Computer Graphics, 20 (1). pp. 56-69. ISSN 1077-2626. (doi:10.1109/TVCG.2013.104) (KAR id:34969)

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Abstract

Area-proportional Euler diagrams representing three sets are commonly used to visualize the results of medical experiments, business data, and information from other applications where statistical results are best shown using interlinking curves. Currently, there is no tool that will reliably visualize exact area-proportional diagrams for up to three sets. Limited success, in terms of diagram accuracy, has been achieved for a small number of cases, such as Venn-2 and Venn-3 where all intersections between the sets must be represented. Euler diagrams do not have to include all intersections and so permit the visualization of cases where some intersections have a zero value. This paper describes a general, implemented, method for visualizing all 40 Euler-3 diagrams in an area-proportional manner. We provide techniques for generating the curves with circles and convex polygons, analyze the drawability of data with these shapes, and give a mechanism for deciding whether such data can be drawn with circles. For the cases where non-convex curves are necessary, our method draws an appropriate diagram using non-convex polygons. Thus, we are now always able to automatically visualize data for up to three sets.

Item Type: Article 10.1109/TVCG.2013.104 Venn Diagrams; Euler Diagrams Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer scienceQ Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming, Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing Peter Rodgers 18 Aug 2013 15:17 UTC 09 Dec 2022 04:57 UTC https://kar.kent.ac.uk/id/eprint/34969 (The current URI for this page, for reference purposes)

University of Kent Author Information

Rodgers, Peter.

Creator's ORCID: https://orcid.org/0000-0002-4100-3596