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26
General Euler diagram generation.
 In Diagrams,
, 2008
"... Abstract. Euler diagrams are a natural method of representing settheoretic data and have been employed in diverse areas such as visualizing statistical data, as a basis for diagrammatic logics and for displaying the results of database search queries. For effective use of Euler diagrams in practic ..."
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Abstract. Euler diagrams are a natural method of representing settheoretic data and have been employed in diverse areas such as visualizing statistical data, as a basis for diagrammatic logics and for displaying the results of database search queries. For effective use of Euler diagrams in practical computer based applications, the generation of a diagram as a set of curves from an abstract description is necessary. Various practical methods for Euler diagram generation have been proposed, but in all of these methods the diagrams that can be produced are only for a restricted subset of all possible abstract descriptions. We describe a method for Euler diagram generation, demonstrated by implemented software, and illustrate the advances in methodology via the production of diagrams which were difficult or impossible to draw using previous approaches. To allow the generation of all abstract descriptions we may be required to have some properties of the final diagram that are not considered nice. In particular we permit more than two curves to pass though a single point, permit some curve segments to be drawn concurrently, and permit duplication of curve labels. However, our method attempts to minimize these bad properties according to a chosen prioritization.
On the Completeness and Expressiveness of Spider Diagram Systems
 PROC. DIAGRAMS 2000, EDINBURGH, SEPT 2000. LNAI 1889
, 2000
"... Spider diagram systems provide a visual language that extends the popular and intuitive Venn diagrams and Euler circles. Designed to complement objectoriented modelling notations in the specification of large software systems they can be used to reason diagrammatically about sets, their cardinalit ..."
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Cited by 18 (7 self)
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Spider diagram systems provide a visual language that extends the popular and intuitive Venn diagrams and Euler circles. Designed to complement objectoriented modelling notations in the specification of large software systems they can be used to reason diagrammatically about sets, their cardinalities and their relationships with other sets. A set of reasoning rules for a spider diagram system is shown to be sound and complete. We discuss the extension of this result to diagrammatically richer notations and also consider their expressiveness. Finally, we show that for a rich enough system we can diagrammatically express the negation of any diagram.
Inductively Generating Euler Diagrams
"... Abstractâ€”Euler diagrams have a wide variety of uses, from information visualization to logical reasoning. In all of their application areas, the ability to automatically layout Euler diagrams brings considerable benefits. In this paper, we present a novel approach to Euler diagram generation. We dev ..."
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Cited by 17 (10 self)
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Abstractâ€”Euler diagrams have a wide variety of uses, from information visualization to logical reasoning. In all of their application areas, the ability to automatically layout Euler diagrams brings considerable benefits. In this paper, we present a novel approach to Euler diagram generation. We develop certain graphs associated with Euler diagrams in order to allow curves to be added by finding cycles in these graphs. This permits us to build Euler diagrams inductively, adding one curve at a time. Our technique is adaptable, allowing the easy specification, and enforcement, of sets of wellformedness conditions; we present a series of results that identify properties of cycles that correspond to the wellformedness conditions. This improves upon other contributions toward the automated generation of Euler diagrams which implicitly assume some fixed set of wellformedness conditions must hold. In addition, unlike most of these other generation methods, our technique allows any abstract description to be drawn as an Euler diagram. To establish the utility of the approach, a prototype implementation has been developed.
Reasoning with Constraint Diagrams
 School of Computing, Mathematical and Information Sciences
, 2004
"... Constraint diagrams are designed for the formal specification of software systems. However, their applications are broader than this since constraint diagrams are a logic that can be used in any formal setting. This document summarizes the main results presented in my PhD thesis, the focus of which ..."
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Cited by 14 (3 self)
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Constraint diagrams are designed for the formal specification of software systems. However, their applications are broader than this since constraint diagrams are a logic that can be used in any formal setting. This document summarizes the main results presented in my PhD thesis, the focus of which is on a fragment of the constraint diagram language, called spider diagrams, and constraint diagrams themselves. In the thesis, sound and complete systems of spider diagrams and constraint diagrams are presented and the expressiveness of the spider diagram language is established. 1
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
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Generating Euler Diagrams from Existing Layouts
, 2008
"... Euler diagrams have a wide variety of uses, from information visualization to logical reasoning. In the case of software engineering, they form the basis of a number of notations, such as state charts and constraint diagrams. In all of their application areas, the ability to automatically layout Eu ..."
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Cited by 9 (5 self)
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Euler diagrams have a wide variety of uses, from information visualization to logical reasoning. In the case of software engineering, they form the basis of a number of notations, such as state charts and constraint diagrams. In all of their application areas, the ability to automatically layout Euler diagrams brings considerable benefits. There have been several recent contributions towards the automatic generation and layout of Euler diagrams, all of which start from an abstract description of the diagram and produce a collection of closed curves embedded in the plane. In this paper, we are concerned with producing layouts by modifying existing ones. This type of layout approach is particularly useful in domains where we require an updated, or modified, diagram such as in a logical reasoning context. We provide two methods to add a curve to an Euler diagram in order to create a new diagram. The first method is guaranteed to produce layouts that meet specified wellformedness conditions that are typically chosen by others who produced generation algorithms; these conditions are thought to correlate well accurate user interpretation. We also overview a second method that can be used to produce a layout of any abstract description.
Formal Issues in Languages Based on Closed Curves
"... Three important questions arise when using visual languages: for any given piece of information can we draw a diagram representing that information, can we reliably interpret the diagrams and can we reason diagrammatically about that information? The desirable answer to all three questions is yes, b ..."
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Cited by 7 (4 self)
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Three important questions arise when using visual languages: for any given piece of information can we draw a diagram representing that information, can we reliably interpret the diagrams and can we reason diagrammatically about that information? The desirable answer to all three questions is yes, but these desires are often conflicting; for example, wellformedness conditions can be enforced to assist diagram interpretation but this can result in drawability problems. In this paper, we focus on visual languages based on closed curves, which are used in numerous computing applications. Many such languages effectively use spatial properties such as containment and disjointness. We consider the consequences of enforcing various wellformedness conditions, such as simplicity and connectedness of minimal regions, in relation to the above questions. We suggest refinements of the conditions in order to find a balance between the conflicting desires.
Changing Euler Diagram Properties by Edge Transformation of Euler Dual Graphs
 VL/HCC 2009
"... Euler diagrams form the basis of several visual modelling notations, including statecharts and constraint diagrams. Recently, various techniques for automated Euler diagram drawing have been proposed, contributing to the Euler diagram generation problem: given an abstract description, draw an Euler ..."
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Cited by 5 (4 self)
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Euler diagrams form the basis of several visual modelling notations, including statecharts and constraint diagrams. Recently, various techniques for automated Euler diagram drawing have been proposed, contributing to the Euler diagram generation problem: given an abstract description, draw an Euler diagram with that description and which possesses certain properties. A common generation method is to find a dual graph from which an Euler diagram is subsequently created. In this paper we define transformations of the dual graph that allow us to alter the properties that the generated diagram possesses. In addition, because the dual graph of a previously generated diagram can be found, our transformations can be used to take such a diagram description, but with different properties. As a result, we can produce a variety of different diagrams for any given abstract description, allowing us to choose an Euler diagram that conforms to the properties that a user prefers. 1
Formal Concept Analysis applications to Requirements Engineering and Design
, 2004
"... I declare that the work presented in this thesis is, to the best of my knowledge and belief, original and my own work, except as acknowledged in the text, and that the material has not been submitted, either in whole or in part, for a degree at this or any other university. Thomas Tilley, B.Sc.(Math ..."
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Cited by 5 (1 self)
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I declare that the work presented in this thesis is, to the best of my knowledge and belief, original and my own work, except as acknowledged in the text, and that the material has not been submitted, either in whole or in part, for a degree at this or any other university. Thomas Tilley, B.Sc.(Maths & Comp. Sc.), B.Info.Tech.(Hons)