Constraint diagrams: visualizing invariants in object-oriented models
Proceedings of the 12th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
Towards the principled design of software engineering diagrams
Proceedings of the 22nd international conference on Software engineering
DIAGRAMS '02 Proceedings of the Second International Conference on Diagrammatic Representation and Inference
VENNFS: A Venn-Diagram File Manager
IV '03 Proceedings of the Seventh International Conference on Information Visualization
Automated Theorem Proving in Euler Diagram Systems
Journal of Automated Reasoning
Evaluating and generalizing constraint diagrams
Journal of Visual Languages and Computing
Generating and drawing area-proportional euler and venn diagrams
Generating and drawing area-proportional euler and venn diagrams
General Euler Diagram Generation
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
A graph theoretic approach to general Euler diagram drawing
Theoretical Computer Science
Using Euler Diagrams in Traditional Library Environments
Electronic Notes in Theoretical Computer Science (ENTCS)
Drawing euler diagrams with circles
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
IEEE Transactions on Visualization and Computer Graphics
Inductively Generating Euler Diagrams
IEEE Transactions on Visualization and Computer Graphics
Drawing Euler Diagrams with Circles: The Theory of Piercings
IEEE Transactions on Visualization and Computer Graphics
Exact and Approximate Area-Proportional Circular Venn and Euler Diagrams
IEEE Transactions on Visualization and Computer Graphics
Fully automatic visualisation of overlapping sets
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
Visualizing and specifying ontologies using diagrammatic logics
AOW '09 Proceedings of the Fifth Australasian Ontology Workshop - Volume 112
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Euler diagrams are used for visualizing categorized data. These categories, together with information about when categories share some datum, can be turned into a succinct diagram description from which an Euler diagram can be generated. Closed curves represent the categories and the relationships between the curves (such as containment) correspond to relationships between the categories (such as subset). A range of automated Euler diagram drawing methods have been proposed but they often produce diagrams that are aesthetically unpleasing, can be computationally complex and most of them cannot draw a diagram for some (often many) given collections of categories. One such method is capable of drawing aesthetically pleasing Euler diagrams, using only circles, and is computationally efficient (being of polynomial time complexity) but it applies to a very restricted subset of collections of categorized data. This paper substantially extends that method so it can always draw an Euler diagram, that is it applies to all collections of categorized data. In particular, we identify a class of diagram descriptions that can be drawn with circles, generalizing previous work. For diagram descriptions outside of this class, we define transformations that can be used to turn them into descriptions inside the 'drawable with circles' class. We demonstrate how such transformations can be done in a general, a process during which many choices must be made. Further, we provide strategies for making particular choices which ensure desirable properties, such as curve containment, are preserved. We have provided a software implementation of the drawing method, which is freely available from www.eulerdiagrams.com/inductivecircles.htm.