Inductively generating Euler diagrams

Stapleton, Gem, Rodgers, Peter, Howse, John and Zhang, Leishi (2011) Inductively generating Euler diagrams IEEE Transactions on Visualization and Computer Graphics, 17 (1). pp. 88-100. ISSN 1077-2626

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Euler diagrams have a wide variety of uses, from information visualization to logical reasoning. In all of their application areas, the ability to automatically layout Euler diagrams brings considerable benefits. In this paper, we present a novel approach to Euler diagram generation. We develop certain graphs associated with Euler diagrams in order to allow curves to be added by finding cycles in these graphs. This permits us to build Euler diagrams inductively, adding one curve at a time. Our technique is adaptable, allowing the easy specification, and enforcement, of sets of wellformednesss conditions; we present a series of results that identify properties of cycles that correspond to the wellformedness conditions. This improves upon other contributions towards the automated generation of Euler diagrams which implicitly assume some fixed set of wellformedness conditions must hold. In addition, unlike most of these other generation methods, our technique allows any abstract description to be drawn as an Euler diagram. To establish the utility of the approach, a prototype implementation has been developed.

Item Type: Journal article
Uncontrolled Keywords: Information visualization; diagram layout; diagram generation; Euler diagrams; Venn diagrams
Subjects: G000 Computing and Mathematical Sciences
DOI (a stable link to the resource): 10.1109/TVCG.2010.28
Faculties: Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Visual Modelling
Depositing User: Converis
Date Deposited: 11 Mar 2011 09:28
Last Modified: 20 Apr 2015 15:51

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