Inductively generating Euler diagrams


Stapleton, G., Rodgers, P., Howse, J. and Zhang, L. 2011. Inductively generating Euler diagrams. IEEE Transactions on Visualization and Computer Graphics. 17 (1), pp. 88-100.
TitleInductively generating Euler diagrams
AuthorsStapleton, G., Rodgers, P., Howse, J. and Zhang, L.

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.

PublisherInstitute of Electrical and Electronics Engineers (IEEE)
JournalIEEE Transactions on Visualization and Computer Graphics
Publication dates
PrintJan 2011
Publication process dates
Deposited10 Jul 2013
Output statusPublished
Digital Object Identifier (DOI)
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