Inductively generating Euler diagrams

Stapleton, Gem and Rodgers, Peter and 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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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.

Item Type: Article
Research Areas: A. > School of Science and Technology > Computer Science
Item ID: 11234
Useful Links:
Depositing User: Teddy ~
Date Deposited: 10 Jul 2013 10:12
Last Modified: 13 Oct 2016 14:27
URI: http://eprints.mdx.ac.uk/id/eprint/11234

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