Drawing Euler Diagrams with Circles: The Theory of Piercings

Zhang, Leishi; Howse, John; Rodgers, Peter

doi:10.1109/tvcg.2010.119

Cited by 28 publications

(74 citation statements)

References 32 publications

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“…This will involve solving challenging problems, such as identifying what constitutes an effective diagram (as shown in this paper, there are different diagrams that convey the same information) and how to automatically draw chosen diagrams from abstract descriptions of them. This functionality could build on recent advances in automated Euler diagram drawing [15,18,19], although the layout problem for concept diagrams is more challenging. In addition, we want to allow ontology creators to be able to specify the axioms directly with concept diagrams, which may require a sketch recognition engine to be devised; this could also build on recent work that recognizes sketches of Euler diagrams [20].…”

Section: Resultsmentioning

confidence: 99%

Visualizing Ontologies: A Case Study

Howse

Stapleton

Taylor

et al. 2011

The Semantic Web – ISWC 2011

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Abstract. Concept diagrams were introduced for precisely specifying ontologies in a manner more readily accessible to developers and other stakeholders than symbolic notations. In this paper, we present a case study on the use of concept diagrams in visually specifying the Semantic Sensor Networks (SSN) ontology. The SSN ontology was originally developed by an Incubator Group of the W3C. In the ontology, a sensor is a physical object that implements sensing and an observation is observed by a single sensor. These, and other, roles and concepts are captured visually, but precisely, by concept diagrams. We consider the lessons learnt from developing this visual model and show how to convert description logic axioms into concept diagrams. We also demonstrate how to merge simple concept diagram axioms into more complex axioms, whilst ensuring that diagrams remain relatively uncluttered.

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Section: Resultsmentioning

confidence: 99%

Visualizing Ontologies: A Case Study

Howse

Stapleton

Taylor

et al. 2011

The Semantic Web – ISWC 2011

Self Cite

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“…The most common methods for visualizing overlapping sets are based on Euler diagrams (or variants, such as Venn diagrams), which employ overlapping closed curves to represent overlapping sets [Collins et al 2009;Riche and Dwyer 2010;Rodgers et al 2008;Set Visualiser 2014;Simonetto et al 2009;Stapleton et al 2011;Stapleton et al 2009]. An example Euler diagram can be seen in Fig.…”

Section: Frenchmentioning

confidence: 99%

Visualizing Sets with Linear Diagrams

Rodgers

Chapman

2015

ACM Trans. Comput.-Hum. Interact.

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This paper presents the first design principles that optimize the visualization of sets using linear diagrams. These principles are justified through empirical studies that evaluate the impact of graphical features on task performance. Linear diagrams represent sets using straight line segments, with line overlaps corresponding to set intersections. This work builds on recent empirical research which establishes that linear diagrams can be superior to prominent set visualization techniques, namely Euler and Venn diagrams. We address the problem of how to best visualize overlapping sets using linear diagrams. To solve the problem, we investigate which graphical features of linear diagrams significantly impact user task performance. To this end, we conducted seven crowd-sourced empirical studies involving a total of 1760 participants. These studies allowed us to identify the following design principles, which significantly aid task performance: use a minimal number of line segments, use guide-lines where overlaps start and end, and draw lines that are thin as opposed to thick bars. We also evaluated the following graphical properties which did not significantly impact task performance: colour, orientation, and set-order. The results are brought to life through a freely available software implementation that automatically draws linear diagrams with user-controlled graphical choices. An important consequence of our research is that users are now able to create effective visualizations of sets automatically, thus improving human-computer interaction.

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“…A major theme of Euler diagrams research has been on establishing when a diagram exists as a visualization of information, often under some additional constraints including being wellformed [7],orbeingdrawablewithcircles [22]. 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].…”

Section: The Drawability Problemmentioning

confidence: 99%

“…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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Drawing Euler Diagrams with Circles: The Theory of Piercings

Cited by 28 publications

References 32 publications

Visualizing Ontologies: A Case Study

Visualizing Ontologies: A Case Study

Visualizing Sets with Linear Diagrams

On the drawability of 3D Venn and Euler diagrams

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