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Properties of Euler diagrams
 IN PROCEEDINGS OF LAYOUT OF SOFTWARE ENGINEERING DIAGRAMS
, 2007
"... Euler diagrams have numerous application areas, with a large variety of languages based on them. In relation to software engineering, such areas encompass modelling and specification including from a formal perspective. In all of these application areas, it is desirable to provide tools to layout Eu ..."
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Cited by 17 (14 self)
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Euler diagrams have numerous application areas, with a large variety of languages based on them. In relation to software engineering, such areas encompass modelling and specification including from a formal perspective. In all of these application areas, it is desirable to provide tools to layout Euler diagrams, ideally in a nice way. Various notions of ‘niceness ’ can be correlated with certain properties that an Euler diagram may or may not possess. Indeed, the relevant layout algorithms developed to date produce Euler diagrams that have certain sets of properties, sometimes called wellformedness conditions. However, there is not a commonly agreed definition of an Euler diagram and the properties imposed on them are rarely stated precisely. In this paper, we provide a very general definition of an Euler diagram, which can be constrained in varying ways in order to match the variety of definitions that exist in the literature. Indeed, the constraints imposed correspond to properties that the diagrams may possess. A contribution of this paper is to provide formal definitions of these properties and we discuss when these properties may be desirable. Our definition of an Euler diagram and the formalization of these properties provides a general language for the Euler diagram community to utilize. A consequence of using a common language will be better integration of, and more accessible, research results.
Drawing Euler diagrams with circles: The theory of piercings
 IEEE TRANS. ON VISUALISATION AND COMPUTER GRAPHICS
, 2011
"... Euler diagrams are effective tools for visualizing set intersections. They have a large number of application areas ranging from statistical data analysis to software engineering. However, the automated generation of Euler diagrams has never been easy: given an abstract description of a required Eu ..."
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Cited by 11 (7 self)
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Euler diagrams are effective tools for visualizing set intersections. They have a large number of application areas ranging from statistical data analysis to software engineering. However, the automated generation of Euler diagrams has never been easy: given an abstract description of a required Euler diagram, it is computationally expensive to generate the diagram. Moreover, the generated diagrams represent sets by polygons, sometimes with quite irregular shapes that make the diagrams less comprehensible. In this paper, we address these two issues by developing the theory of piercings, where we define single piercing curves and double piercing curves. We prove that if a diagram can be built inductively by successively adding piercing curves under certain constraints, then it can be drawn with circles, which are more esthetically pleasing than arbitrary polygons. The theory of piercings is developed at the abstract level. In addition, we present a Java implementation that, given an inductively pierced abstract description, generates an Euler diagram consisting only of circles within polynomial time.
The expressiveness of spider diagrams augmented with constants.
 Journal of Visual Languages and Computing, available online,
, 2008
"... Abstract ..."
Euler Diagram Transformations
 Graph Transformations & Visual Modelling Techniques, ECEASST
"... Abstract: Euler diagrams are a visual language which are used for purposes such as the presentation of setbased data or as the basis of visual logical languages which can be utilised for software specification and reasoning. Such Euler diagram reasoning systems tend to be defined at an abstract le ..."
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Cited by 4 (1 self)
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Abstract: Euler diagrams are a visual language which are used for purposes such as the presentation of setbased data or as the basis of visual logical languages which can be utilised for software specification and reasoning. Such Euler diagram reasoning systems tend to be defined at an abstract level, and the concrete level is simply a visualisation of an abstract model, thereby capturing some subset of the usual boolean logic. The visualisation process tends to be divorced from the data transformation process thereby affecting the user’s mental map and reducing the effectiveness of the diagrammatic notation. Furthermore, geometric and topological constraints, called wellformedness conditions, are often placed on the concrete diagrams to try to reduce human comprehension errors, and the effects of these conditions are not modelled in these systems. We view Euler diagrams as a type of graph, where the faces that are present are the key features that convey information and we provide transformations at the dual graph level that correspond to transformations of Euler diagrams, both in terms of editing moves and logical reasoning moves. This original approach gives a corre
An Heuristic for the Construction of Intersection Graphs
 13TH INTERNATIONAL CONFERENCE ON INFORMATION VISUALISATION (IV09), BARCELONA: SPAIN
, 2009
"... Most methods for generating Euler diagrams describe the detection of the general structure of the final drawing as the first step. This information is generally encoded using a graph, where nodes are the regions to be represented and edges represent adjacency. A planar drawing of this graph will the ..."
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Most methods for generating Euler diagrams describe the detection of the general structure of the final drawing as the first step. This information is generally encoded using a graph, where nodes are the regions to be represented and edges represent adjacency. A planar drawing of this graph will then indicate how to draw the sets in order to depict all the set intersections. In this paper we present an heuristic to construct this structure, the intersection graph. The final Euler diagram can be constructed by drawing the sets boundaries around the nodes of the intersection graph, either manually or automatically.
Diagrammatic Logics: Past, Present and Future
"... Diagrams have many practical applications and are used in numerous settings. Indeed, it is widely recognized that diagrams are a valuable aid to intuition and help to convey ideas and information in a clear way. Traditionally, however, logicians have viewed diagrams as informal tools and, thus, coul ..."
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Diagrams have many practical applications and are used in numerous settings. Indeed, it is widely recognized that diagrams are a valuable aid to intuition and help to convey ideas and information in a clear way. Traditionally, however, logicians have viewed diagrams as informal tools and, thus, could not be a part of any formal argument; only symbolic logics were seen to fulfil this role. Recently, this perception was overturned in seminal work by Shin. This paper explores the evolution of diagrammatic logics, focusing mainly on those based on the popular and intuitive Euler diagrams. Also discussed are some challenges faced in the area, some of which are specifically related to diagrams. 1.
Journal of Visual Languages Journal of Visual Languages and Comp The expressiveness of spider diagr
"... ogica been soun syntactic elements analogous to constants in first order predicate logic. We extend the spider diagram language to include importance of diagrams in computing systems and statements about certain relationships between sets. Her work is widely regarded as seminal, overturning ..."
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ogica been soun syntactic elements analogous to constants in first order predicate logic. We extend the spider diagram language to include importance of diagrams in computing systems and statements about certain relationships between sets. Her work is widely regarded as seminal, overturning