Inductively Generating Euler Diagrams

Stapleton, Gem; Rodgers, Peter; Howse, John; Zhang, Leishi

doi:10.1109/tvcg.2010.28

Cited by 42 publications

(45 citation statements)

References 23 publications

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“…Riche and Dwyer [20] describe a method that prioritizes the containment of sets and splits sets in the diagram, when required, connecting them with edges. Stapleton et al [27] present a method for inductively adding curves to a diagram and preserving wellformedness properties in the drawing. We demonstrate our technique operating on the output of many of these algorithms [9,17,20,21,25].…”

Section: Euler Diagram Drawingmentioning

confidence: 99%

A Simple Approach for Boundary Improvement of Euler Diagrams

Simonetto

Archambault

Scheidegger

2016

IEEE Trans. Visual. Comput. Graphics

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Abstract-General methods for drawing Euler diagrams tend to generate irregular polygons. Yet, empirical evidence indicates that smoother contours make these diagrams easier to read. In this paper, we present a simple method to smooth the boundaries of any Euler diagram drawing. When refining the diagram, the method must ensure that set elements remain inside their appropriate boundaries and that no region is removed or created in the diagram. Our approach uses a force system that improves the diagram while at the same time ensuring its topological structure does not change. We demonstrate the effectiveness of the approach through case studies and quantitative evaluations.

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Section: Euler Diagram Drawingmentioning

confidence: 99%

A Simple Approach for Boundary Improvement of Euler Diagrams

Simonetto

Archambault

Scheidegger

2016

IEEE Trans. Visual. Comput. Graphics

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“…An understanding of the range of topologically different diagrams with a given description is important for researchers developing inductive drawing algorithms [4,19,[21][22][23]. These inductive (or incremental) approaches add one contour at a time to a drawing, building up the diagram until all of the contours are present.…”

Section: Diagram Equivalencesmentioning

confidence: 99%

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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“…Reflecting the importance of understanding such data there have been a large number of techniques proposed for visualizing it such as [1,10,16,25,28,29,32,33,39]. Most of these techniques represent the sets using Euler diagrams.…”

Section: Introductionmentioning

confidence: 99%

The impact of topological and graphical choices on the perception of Euler diagrams

Blake

Rodgers

Howse

2016

Information Sciences

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This paper establishes the impact of topological and graphical properties on the comprehension of Euler diagrams. To-date, various studies have examined the impact of individual properties of Euler diagrams, such as curve shape and orientation. This has allowed us to establish guides for using these properties such as 'draw Euler diagrams with circles' and 'draw Euler diagrams without regard to orientation'. However, until the work described here, questions still remain, for example 'do these guides, when combined, make a significant difference to real-world Euler diagrams?', and if so, 'should they be used by those visualizing set data with Euler diagrams?' To answer these questions an empirical study was conducted to compare Euler diagrams that have been drawn by others for their real-world data, against versions that adhere to all of the guides in combination. The study establishes that both the accuracy and the speed with which information is derived from Euler diagrams is significantly improved when Euler diagrams adhere, where possible, to all the guides. The improvement is considerable when using the guided diagrams, with on average, the error rate being more than halved from 21.4% to 10.3%, and a 9 second improvement in the average time taken, from 34.2 seconds to 24.9 seconds. As Euler diagrams are regularly used to visualize information in a multitude of areas, ranging from crime control to social network analysis, our results indicate that applying the guides to these diagrams will improve the ability of users to accurately and quickly extract information.

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Inductively Generating Euler Diagrams

Cited by 42 publications

References 23 publications

A Simple Approach for Boundary Improvement of Euler Diagrams

A Simple Approach for Boundary Improvement of Euler Diagrams

On the drawability of 3D Venn and Euler diagrams

The impact of topological and graphical choices on the perception of Euler diagrams

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