On the drawability of 3D Venn and Euler diagrams

Flower, Jean; Rodgers, Peter

doi:10.1016/j.jvlc.2013.08.009

Cited by 8 publications

(9 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The description of the internal structure of the RDH, and more in particular of the various types of complementarities, crucially relies on the idea that smaller diagrams occur inside bigger diagrams. These notions of subdiagram or diagram embedding/nesting have been studied for other types of diagrams as well, more in particular Euler diagrams [7], Venn diagrams [8], spider diagrams [9] or algebra diagrams [10]. The analysis proposed in the present paper is very much in line with the visual grammar or visual syntax approach developed by Engelhardt [11, p. 104] in that "various syntactic principles can be identified in graphics of different types, and the nature of visual representation allows for visual nesting and recursion [...] any object may contain a set of (sub-)objects within the space that it occupies.…”

Section: Introductionmentioning

confidence: 99%

Logical and Geometrical Complementarities between Aristotelian Diagrams

Smessaert

Demey

2014

Diagrammatic Representation and Inference

View full text Add to dashboard Cite

Abstract. This paper concerns the Aristotelian relations of contradiction, contrariety, subcontrariety and subalternation between 14 contingent formulae, which can get a 2D or 3D visual representation by means of Aristotelian diagrams. The overall 3D diagram representing these Aristotelian relations is the rhombic dodecahedron (RDH), a polyhedron consisting of 14 vertices and 12 rhombic faces (Section 2). The ultimate aim is to study the various complementarities between Aristotelian diagrams inside the RDH. The crucial notions are therefore those of subdiagram and of nesting or embedding smaller diagrams into bigger ones. Three types of Aristotelian squares are characterised in terms of which types of contradictory diagonals they contain (Section 3). Secondly, any Aristotelian hexagon contains 3 squares (Section 4), and any Aristotelian octagon contains 4 hexagons (Section 5), so that different types of bigger diagrams can be distinguished in terms of which types of subdiagrams they contain. In a final part, the logical complementarities between 6 and 8 formulae are related to the geometrical complementarities between the 3D embeddings of hexagons and octagons inside the RDH (Section 6).

show abstract

Section: Introductionmentioning

confidence: 99%

Logical and Geometrical Complementarities between Aristotelian Diagrams

Smessaert

Demey

2014

Diagrammatic Representation and Inference

View full text Add to dashboard Cite

show abstract

“…Examples from each of the major categories are shown in Figure 2. [32]). These were designed for use as 'fake' items in the decision task (described below).…”

Section: The Npv Corpusmentioning

confidence: 99%

“…Euler and Venn diagrams[32]). duality diagrams[7]), and even diagrams that visualize single formulas (e.g.…”

mentioning

confidence: 99%

Diagrammatic Representation and Inference

Dwyer¹,

Purchase²,

Delaney³

2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

“…Automatic drawing of Venn and Euler diagrams is also problematic. [29,12,36] In response to these limitations, alternative set visualization techniques have been proposed.…”

Section: Introductionmentioning

confidence: 99%

A comparison of linear and mosaic diagrams for set visualization

Luz

Masoodian

2018

Information Visualization

View full text Add to dashboard Cite

Linear diagrams have been shown to compare favourably to better known forms of set visualization, such as Venn and Euler diagrams, in supporting non-interactive assessment of set relationships. Recent studies that compared several variants of linear diagrams have demonstrated that users perform best at tasks involving identification of intersections, disjointness and subsets when using a horizontally drawn linear diagram with thin lines representing sets and employing vertical lines as guide lines. The essential visual task the user needs to perform in order to interpret this kind of diagram is vertical alignment of parallel lines and detection of overlaps. Space-filling mosaic diagrams which support this same visual task have been used in other applications, such as the visualization of schedules of activities, where they have been shown to be superior to linear Gantt charts. In this article, we present an experimental comparison of linear and mosaic diagrams for visualization of set relationships, in terms of accuracy, time-to-answer and subjective ratings of perceived task difficulty. The findings show that the two visualizations are largely similar with respect to these measures, suggesting that the choice of one or the other may be solely guided by other visual design considerations. Mosaic diagrams might be more suitable, for instance, in cases where miniature diagrams representing overviews of relations in different collections of sets are required, such as in small-multiples displays.

show abstract

On the drawability of 3D Venn and Euler diagrams

Cited by 8 publications

References 21 publications

Logical and Geometrical Complementarities between Aristotelian Diagrams

Logical and Geometrical Complementarities between Aristotelian Diagrams

Diagrammatic Representation and Inference

A comparison of linear and mosaic diagrams for set visualization

Contact Info

Product

Resources

About