Towards a General Solution to Drawing Area-Proportional Euler Diagrams

Chow, Stirling

doi:10.1016/j.entcs.2005.02.017

Cited by 21 publications

(14 citation statements)

References 2 publications

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“…Because the number of intersections is not fixed, drawing Euler diagrams is more complicated than drawing Venn diagrams and the automated generation of Euler diagrams-areaproportional Euler diagrams, especially-is a largely unsolved problem. Building upon the work of Chow and Ruskey (2003, 2005a, 2005b, Chow and Rodgers (2005) had previously developed a technique for generating approximate area-proportional three-set Venn diagrams using circles. However, it is mathematically impossible to construct exact area-proportional three-set Venn (or Euler) diagrams using circles.…”

Section: Venn and Euler Diagramsmentioning

confidence: 99%

Presenting qualitative comparative analysis: Notation, tabular layout, and visualization

Rubinson

2019

Methodological Innovations

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This article reviews approaches to presenting qualitative comparative analysis and set-theoretic research, with an emphasis on graphic presentation. Although visualization is an important aspect of presenting empirical research, techniques for visualizing qualitative comparative analysis remains underdeveloped. This article reviews existing and emerging standards of presenting qualitative comparative analysis and introduces a number of new ones. Techniques are presented for visualizing calibrated data, truth tables, and consistency/coverage solutions, with particular attention given to strategies for presenting superset/subset relationships.

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Section: Venn and Euler Diagramsmentioning

confidence: 99%

Presenting qualitative comparative analysis: Notation, tabular layout, and visualization

Rubinson

2019

Methodological Innovations

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“…It is possible to draw the monotonic class of Euler diagrams with exact area proportions [25] although, of- ten, unnecessary concurrency is present. This builds on work drawing convex intersecting families of simple closed curves [14].…”

Section: P Qmentioning

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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“…Euler diagrams and their extensions have wideranging uses in the area of information visualization, such as [2], [3], [4], [5], [6], [7]. Various methods for automatically generating Euler diagrams have been developed, each concentrating on a particular class of Euler diagrams; for example, see [6], [8], [9], [10], [11], [12], [13]. The generation algorithms developed so far produce Euler diagrams that have certain sets of proper-ties, sometimes called wellformedness conditions; these conditions will be detailed below.…”

Section: Introductionmentioning

confidence: 99%

Inductively Generating Euler Diagrams

Stapleton

Rodgers

Howse

et al. 2011

IEEE Trans. Visual. Comput. Graphics

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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.

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Towards a General Solution to Drawing Area-Proportional Euler Diagrams

Cited by 21 publications

References 2 publications

Presenting qualitative comparative analysis: Notation, tabular layout, and visualization

Presenting qualitative comparative analysis: Notation, tabular layout, and visualization

A survey of Euler diagrams

Inductively Generating Euler Diagrams

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