Results 1 
5 of
5
A Survey of Euler Diagrams
, 2013
"... Euler diagrams visually represent containment, intersection and exclusion using closed curves. They first appeared several hundred years ago, however, there has been a resurgence in Euler diagram research in the twentyfirst century. This was initially driven by their use in visual languages, where ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
Euler diagrams visually represent containment, intersection and exclusion using closed curves. They first appeared several hundred years ago, however, there has been a resurgence in Euler diagram research in the twentyfirst century. This was initially driven by their use in visual languages, where they can be used to represent logical expressions diagrammatically. This work lead to the requirement to automatically generate Euler diagrams from an abstract description. The ability to generate diagrams has accelerated their use in information visualization, both in the standard case where multiple grouping of data items inside curves is required and in the areaproportional case where the area of curve intersections is important. As a result, examining the usability of Euler diagrams has become an important aspect of this research. Usability has been investigated by empirical studies, but much research has concentrated on wellformedness, which concerns how curves and other features of the diagram interrelate. This work has revealed the drawability of Euler diagrams under various wellformedness properties and has developed embedding methods that meet these properties. Euler diagram research surveyed in this paper includes theoretical results, generation techniques, transformation methods and the development of automated reasoning systems for Euler diagrams. It also overviews application areas and the ways in which Euler diagrams have been extended.
Euler Graph Transformations for Euler Diagram Layout
 IEEE Symposium on Visual Languages and Human Centric Computing (VL/HCC 2010
, 2010
"... Abstract — Euler diagrams are frequently used for visualizing information about collections of objects and form an important component of various visual languages. Properties possessed by Euler diagrams correlate with their usability, such as whether the diagram has only simple curves or possesses c ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
(Show Context)
Abstract — Euler diagrams are frequently used for visualizing information about collections of objects and form an important component of various visual languages. Properties possessed by Euler diagrams correlate with their usability, such as whether the diagram has only simple curves or possesses concurrency. Sometimes, every diagram that represents some given information possesses some undesirable properties, and reducing the number of violations of undesirable properties is beneficial. In this paper we show how to count the number of violations from the reduced Euler graph. We then define various transformations on the Euler graph which can reduce the number of violations of a given property, but sometimes at the expense of increasing the number of violations of another property. These transformations can be used to improve the quality of the drawn diagram, which is important for effective information visualization. KeywordsEuler diagrams; Venn diagrams; graph transformations. I.
Drawing Euler Diagrams with Circles and Ellipses
 IEEE SYMPOSIUM ON VISUAL LANGUAGES AND HUMANCENTRIC COMPUTING
, 2011
"... The use of Euler diagrams as a basis for visual languages is commonplace and they are often used for visualizing information. The ability to automatically draw these diagrams is, therefore, likely to be of widespread practical use. The Euler diagram drawing problem is recognized as challenging, but ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
The use of Euler diagrams as a basis for visual languages is commonplace and they are often used for visualizing information. The ability to automatically draw these diagrams is, therefore, likely to be of widespread practical use. The Euler diagram drawing problem is recognized as challenging, but the potential payoff from the derivation of a comprehensive solution, that produces usable and effective diagrams, is significant. Previous research on automated Euler diagram drawing has used various different approaches, each of which had their own problems, including: (a) failure to draw a diagram in all cases, (b) poor diagram layout, and (c) inability to ensure that certain wellformedness properties of the drawn diagrams hold. In this paper, we present a novel approach to Euler diagram drawing that draws diagrams with circles, ellipses and curves in general. This new approach will draw a diagram in all cases, avoiding bad layout where possible (by the use of ‘nice ’ geometric shapes) and can enforce wellformedness properties as chosen by the user.
Properties of Some Euler Graphs Constructed from Euler Diagram
"... Abstract: This article reflects some theoretical results related with Euler Graph obtained from a special pattern of Euler Diagrams. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract: This article reflects some theoretical results related with Euler Graph obtained from a special pattern of Euler Diagrams.
2010 IEEE Symposium on Visual Languages and HumanCentric Computing Euler Graph Transformations for Euler Diagram Layout
"... Abstract — Euler diagrams are frequently used for visualizing information about collections of objects and form an important component of various visual languages. Properties possessed by Euler diagrams correlate with their usability, such as whether the diagram has only simple curves or possesses c ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract — Euler diagrams are frequently used for visualizing information about collections of objects and form an important component of various visual languages. Properties possessed by Euler diagrams correlate with their usability, such as whether the diagram has only simple curves or possesses concurrency. Sometimes, every diagram that represents some given information possesses some undesirable properties, and reducing the number of violations of undesirable properties is beneficial. In this paper we show how to count the number of violations from the reduced Euler graph. We then define various transformations on the Euler graph which can reduce the number of violations of a given property, but sometimes at the expense of increasing the number of violations of another property. These transformations can be used to improve the quality of the drawn diagram, which is important for effective information visualization. KeywordsEuler diagrams; Venn diagrams; graph transformations. I.