Exact and Approximate Area-Proportional Circular Venn and Euler Diagrams

Wilkinson, Leland

doi:10.1109/tvcg.2011.56

Cited by 129 publications

(117 citation statements)

References 44 publications

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“…As the algorithm we propose in this work improves diagrams that represent sets as polygons, we focus on these methods for set visualization in this section. However, it is important to note that other approaches exist for visualizing sets and their intersections that are based on circles [13,26,33], ellipses [16], and approaches that are not based on closed curves at all [1,2,15,23].…”

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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“…The spatial relationships utilize containment, disjointness and overlapping, although other spatial relationships, such as alignment, are not of semantic importance. They often use curves with specific shapes, like circles [Wilkinson 2012] or regular polygons [Kestler et al 2008], because of their aesthetically pleasing nature. Graphs are incorporated into Euler diagrams to represent connected individuals or items within the sets, allowing the visualization of more complex information.…”

Section: Visual Languages: Applications and Propertiesmentioning

confidence: 99%

Combining Sketching and Traditional Diagram Editing Tools

Plimmer

Delaney

Rodgers

2015

ACM Trans. Intell. Syst. Technol.

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The least cognitively demanding way to create a diagram is to draw it with a pen. Yet there is also a need for more formal visualizations, that is diagrams created using both traditional keyboard and mouse interaction. Our objective is to allow the creation of diagrams using traditional and stylus-based input. Having two diagram creation interfaces requires that changes to a diagram should be automatically rendered in the other visualization. Because sketches are imprecise, there is always the possibility that conversion between visualizations results in a lack of syntactic consistency between the two visualizations. We propose methods for converting diagrams between forms, checking them for equivalence and rectifying inconsistencies. As a result of our theoretical contributions, we present an intelligent software system allowing users to create and edit diagrams in sketch or formal mode. Our proof of concept tool supports diagrams with connected and spatial syntactic elements. Two user studies show that this approach is viable and participants found the software easy to use. We conclude that supporting such diagram creation is now possible in practice.

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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%

“…[12],S i m o n e t t o et al [17],Stapletonetal. [19] and Wilkinson [25]. In addition, the impact that various properties have on user understanding has been studied empirically [5,13].T os u m m a r i z ek e y findings from this existing work: it is known that drawing wellformed 2D Euler diagrams is important for usability, we have necessary and sufficient conditions for wellformed drawability, some sets can only be visualized with nonwellformed diagrams, and a variety of methods for automatically drawing Euler diagrams in 2D exist.…”

Section: Introductionmentioning

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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Exact and Approximate Area-Proportional Circular Venn and Euler Diagrams

Cited by 129 publications

References 44 publications

A Simple Approach for Boundary Improvement of Euler Diagrams

A Simple Approach for Boundary Improvement of Euler Diagrams

Combining Sketching and Traditional Diagram Editing Tools

On the drawability of 3D Venn and Euler diagrams

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