Drawing euler diagrams with circles
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
A general method for drawing area-proportional Euler diagrams
Journal of Visual Languages and Computing
Automatically drawing Euler diagrams with circles
Journal of Visual Languages and Computing
A Diagrammatic Inference System with Euler Circles
Journal of Logic, Language and Information
Visual analysis of set relations in a graph
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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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 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.