Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets

Verroust, Anne; Viaud, Marie-Luce

doi:10.1007/978-3-540-25931-2_13

Cited by 47 publications

(57 citation statements)

References 7 publications

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“…Moreover, algorithms for automatically producing Euler diagrams, given the information to be visualized, are sought and a number of them now exist for the 2D case, including [3,7,8,14,16,17,19,24,25]. These algorithms require a description of a required diagram, d, to be provided which typically comprises precisely the descriptions of the zones in d.…”

Section: The Drawability Problemmentioning

confidence: 99%

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On the drawability of 3D Venn and Euler diagrams

Flower

Rodgers

2014

Journal of Visual Languages & Computing

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abstract3D Euler diagrams visually represent the set-theoretic notions of intersection, containment and disjointness by using closed, orientable surfaces. In previous work, we introduced 3D Venn and Euler diagrams and formally defined them. In this paper, we consider the drawability of data sets using 3D Venn and Euler diagrams. The specific contributions are as follows. First, we demonstrate that there is more choice of layout when drawing 3D Euler diagrams than when drawing 2D Euler diagrams. These choices impact the topological adjacency properties of the diagrams and having more choice is helpful for some Euler diagram drawing algorithms. To illustrate this, we consider the well-known class of Venn-3 diagrams in detail. We then proceed to consider drawability questions centered around which data sets can be visualized when the diagrams are required to possess certain properties. We show that any diagram description can be drawn with 3D Euler diagrams that have unique labels. We then go on to define a set of necessary and sufficient conditions for wellformed drawability in 3D.

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Section: The Drawability Problemmentioning

confidence: 99%

“…If we want to enforce the unique labels property then we must allow the curves used in the Euler diagrams to be non-simple (i.e. they must be allowed to self-intersect) [9,24]. However, using either non-unique labels or self-intersecting curves brings with it usability weaknesses.…”

Section: Comparison: Everything Is Drawablementioning

confidence: 99%

On the drawability of 3D Venn and Euler diagrams

Flower

Rodgers

2014

Journal of Visual Languages & Computing

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“…For example, in [2] some well-formedness conditions are relaxed and the term Euler-like diagrams is adopted for variations such as allowing "holes". In [16] it is shown that all abstract diagrams for at most eight sets are drawable using such Euler-like diagrams. Recently, a methodology for generating general Euler diagrams has been developed [11], ensuring the production of a diagram, with a heuristic approach to repairing possible breaks in well-formedness.…”

Section: Coloured Euler Diagramsmentioning

confidence: 99%

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

Bottoni

Fish

2010

Diagrammatic Representation and Inference

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Abstract. Euler diagrams are a popular method for visualising sets and their relationships, exploited for resource management and visual logic specification, for example. We add the notion of colouring, provide a formal description of the extended system and demonstrate how coloured Euler diagrams provide adequate visualisations for concepts in the new bio-inspired model of Reaction Systems and for polyarchies, visualising multiple intersecting hierarchies.

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“…Thus, for example, contours are not allowed 'to be tangential to' or 'to run along' one another -they must cross transversely. Other authors have made different choices as to which topological features are allowed [9,19,29,44].…”

Section: Concrete Spider Diagramsmentioning

confidence: 99%

Spider Diagrams

Howse¹,

Taylor²

2005

LMS J. Comput. Math.

127

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The use of diagrams in mathematics has traditionally been restricted to guiding intuition and communication. With rare exceptions such as Peirce's α and β systems, purely diagrammatic formal reasoning has not been in the mathematician's or logician's toolkit. This paper develops a purely diagrammatic reasoning system of 'spider diagrams'that builds on Euler, Venn and Peirce diagrams. The system is known to be expressively equivalent to first-order monadic logic with equality. Two levels of diagrammatic syntax have been developed: an 'abstract' syntax that captures the structure of diagrams, and a 'concrete' syntax that captures topological properties of drawn diagrams. A number of simple diagrammatic transformation rules are given, and the resulting reasoning system is shown to be sound and complete.

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Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets

Cited by 47 publications

References 7 publications

On the drawability of 3D Venn and Euler diagrams

On the drawability of 3D Venn and Euler diagrams

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

Spider Diagrams

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