Embedding Wellformed Euler Diagrams

Rodgers, Peter; Zhang, Leishi; Fish, Andrew

doi:10.1109/iv.2008.57

Cited by 11 publications

(15 citation statements)

References 15 publications

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“…Several researchers have worked on axiomatic solutions for Euler diagrams [16,37,38,46] and area-proportional Euler diagrams [36]. In [47] Rodgers and Stapleton build Euler diagrams inductively, by adding one curve at a time based on a dual graph of the diagram.…”

Section: Axiomatic Approachesmentioning

confidence: 99%

Exact and Approximate Area-Proportional Circular Venn and Euler Diagrams

Wilkinson

2012

IEEE Trans. Visual. Comput. Graphics

127

114

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Abstract-Scientists conducting microarray and other experiments use circular Venn and Euler diagrams to analyze and illustrate their results. As one solution to this problem, this article introduces a statistical model for fitting area-proportional Venn and Euler diagrams to observed data. The statistical model outlined in this report includes a statistical loss function and a minimization procedure that enables formal estimation of the Venn/Euler area-proportional model for the first time. A significance test of the null hypothesis is computed for the solution. Residuals from the model are available for inspection. As a result, this algorithm can be used for both exploration and inference on real datasets.

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Section: Axiomatic Approachesmentioning

confidence: 99%

Exact and Approximate Area-Proportional Circular Venn and Euler Diagrams

Wilkinson

2012

IEEE Trans. Visual. Comput. Graphics

127

114

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“…Rodgers et al introduce a method for drawing a subclass of Euler diagrams [22] and then extend this research to work on any input instance [21]. In these approaches, the dual graph of the Euler diagram is transformed into a planar graph for drawing.…”

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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“…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%

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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Embedding Wellformed Euler Diagrams

Abstract: Abstract

Cited by 11 publications

References 15 publications

Exact and Approximate Area-Proportional Circular Venn and Euler Diagrams

Exact and Approximate Area-Proportional Circular Venn and Euler Diagrams

A Simple Approach for Boundary Improvement of Euler Diagrams

On the drawability of 3D Venn and Euler diagrams

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