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A Survey of Euler Diagrams
, 2013
"... Euler diagrams visually represent containment, intersection and exclusion using closed curves. They first appeared several hundred years ago, however, there has been a resurgence in Euler diagram research in the twentyfirst century. This was initially driven by their use in visual languages, where ..."
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Euler diagrams visually represent containment, intersection and exclusion using closed curves. They first appeared several hundred years ago, however, there has been a resurgence in Euler diagram research in the twentyfirst century. This was initially driven by their use in visual languages, where they can be used to represent logical expressions diagrammatically. This work lead to the requirement to automatically generate Euler diagrams from an abstract description. The ability to generate diagrams has accelerated their use in information visualization, both in the standard case where multiple grouping of data items inside curves is required and in the areaproportional case where the area of curve intersections is important. As a result, examining the usability of Euler diagrams has become an important aspect of this research. Usability has been investigated by empirical studies, but much research has concentrated on wellformedness, which concerns how curves and other features of the diagram interrelate. This work has revealed the drawability of Euler diagrams under various wellformedness properties and has developed embedding methods that meet these properties. Euler diagram research surveyed in this paper includes theoretical results, generation techniques, transformation methods and the development of automated reasoning systems for Euler diagrams. It also overviews application areas and the ways in which Euler diagrams have been extended.
Euler Graph Transformations for Euler Diagram Layout
 IEEE Symposium on Visual Languages and Human Centric Computing (VL/HCC 2010
, 2010
"... Abstract — Euler diagrams are frequently used for visualizing information about collections of objects and form an important component of various visual languages. Properties possessed by Euler diagrams correlate with their usability, such as whether the diagram has only simple curves or possesses c ..."
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Abstract — Euler diagrams are frequently used for visualizing information about collections of objects and form an important component of various visual languages. Properties possessed by Euler diagrams correlate with their usability, such as whether the diagram has only simple curves or possesses concurrency. Sometimes, every diagram that represents some given information possesses some undesirable properties, and reducing the number of violations of undesirable properties is beneficial. In this paper we show how to count the number of violations from the reduced Euler graph. We then define various transformations on the Euler graph which can reduce the number of violations of a given property, but sometimes at the expense of increasing the number of violations of another property. These transformations can be used to improve the quality of the drawn diagram, which is important for effective information visualization. KeywordsEuler diagrams; Venn diagrams; graph transformations. I.
2010 IEEE Symposium on Visual Languages and HumanCentric Computing Euler Graph Transformations for Euler Diagram Layout
"... Abstract — Euler diagrams are frequently used for visualizing information about collections of objects and form an important component of various visual languages. Properties possessed by Euler diagrams correlate with their usability, such as whether the diagram has only simple curves or possesses c ..."
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Abstract — Euler diagrams are frequently used for visualizing information about collections of objects and form an important component of various visual languages. Properties possessed by Euler diagrams correlate with their usability, such as whether the diagram has only simple curves or possesses concurrency. Sometimes, every diagram that represents some given information possesses some undesirable properties, and reducing the number of violations of undesirable properties is beneficial. In this paper we show how to count the number of violations from the reduced Euler graph. We then define various transformations on the Euler graph which can reduce the number of violations of a given property, but sometimes at the expense of increasing the number of violations of another property. These transformations can be used to improve the quality of the drawn diagram, which is important for effective information visualization. KeywordsEuler diagrams; Venn diagrams; graph transformations. I.
The Online Abstraction Problem for Euler Diagrams
"... Abstract. A Euler diagrams are an accessible and effective visualisation of data involving simple settheoretic relationships. Efficient algorithms to quickly compute the abstract regions of an Euler diagram upon curve addition and removal have been developed, but a strict set of drawing conventions ..."
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Abstract. A Euler diagrams are an accessible and effective visualisation of data involving simple settheoretic relationships. Efficient algorithms to quickly compute the abstract regions of an Euler diagram upon curve addition and removal have been developed, but a strict set of drawing conventions (called wellformedness conditions) were enforced, meaning that some abstract diagrams are not representable as concrete diagrams. We present a variation and extension of the methodology which enables region computations for Euler diagrams under the relaxation of several drawing conventions. We provide complexity analysis and compare with the previous methodology. The algorithms are presented for generic curves, allowing for specialisations such as utilising fixed geometric shapes for curves that often occur in applications. 1