Coloured Euler Diagrams: A Tool for Visualizing Dynamic Systems and Structured Information

Bottoni, Paolo; Fish, Andrew

doi:10.1007/978-3-642-14600-8_8

Cited by 8 publications

(2 citation statements)

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“…ED-based representations are also used for set-based information visualisation, where the representation of elements or items effectively yields a SD, although with different semantics (e.g. [3,9,51]). In such applications, one often visualises sequences of diagrams representing some set-based data changes.…”

Section: Discussionmentioning

confidence: 99%

Spider Graphs: a graph transformation system for spider diagrams

2013

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The use of diagrammatic logic as a reasoning mechanism to produce inferences on subsets of some universe could provide a way to overcome the current limitations of visual modelling methods, which have to be integrated with textual languages to express complex constraints. On the other hand, graph transformations are becoming widespread as a way to express formal semantics for visual modelling languages, so that a mechanisation of diagrammatic logic based on graph transformation would facilitate language integration, based on a common underlying machinery. In this paper, we propose such a mechanisation for spider diagrams (SDs), an established language for reasoning with diagrams modelling relations between sets and constraints on their cardinalities. The concrete syntax of SDs extends that of Euler diagrams that use closed curves and the enclosed regions to represent sets and their intersections. The language is augmented with reasoning rules, i.e. syntactic transformation rules corresponding to logical inference rules. However, these rules are typically defined in procedural terms, so that a completely formal specification and an adequate mechanisation of them has not been achieved yet. We propose an abstract syntax for SDs in terms of typed graphs and define the corresponding language of Spider Graphs (SGs), expressing reasoning rules for SDs as graph transformation units. This enables a direct realisation of the reasoning system via graph transformation tools without resorting to ad hoc implementations, and we provide an implementation in AGG. Techniques for static analysis become available to reason on proof strategies and on possible optimisations. © 2013 Springer-Verlag Berlin Heidelberg

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Section: Discussionmentioning

confidence: 99%

Spider Graphs: a graph transformation system for spider diagrams

2013

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“…Whilst many Euler diagram visualizations make liberal use of colour for either curves or regions, the concept has been formalized to provide extra dimensions for representing domain features [12].…”

Section: Extending Euler Diagramsmentioning

confidence: 99%

A survey of Euler diagrams

Rodgers

2014

Journal of Visual Languages & Computing

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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 twenty-first 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 area-proportional 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.

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