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Issue No.01 - January (2011 vol.17)
pp: 88-100
Gem Stapleton , University of Brighton, Brighton, UK
Peter Rodgers , University of Kent, Canterbury, UK
John Howse , University of Brighton, Brighton, UK
Leishi Zhang , University of Kent, Canterbury, UK
ABSTRACT
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 well-formedness conditions; we present a series of results that identify properties of cycles that correspond to the well-formedness conditions. This improves upon other contributions toward the automated generation of Euler diagrams which implicitly assume some fixed set of well-formedness 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.
INDEX TERMS
Information visualization, diagram layout, diagram generation, Euler diagrams, Venn diagrams.
CITATION
Gem Stapleton, Peter Rodgers, John Howse, Leishi Zhang, "Inductively Generating Euler Diagrams", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 1, pp. 88-100, January 2011, doi:10.1109/TVCG.2010.28
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