Sorting Jordan sequences in linear time using level-linked search trees
Information and Control
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
Arrangements of curves in the plane—topology, combinatorics, and algorithms
Theoretical Computer Science
Constraint diagrams: visualizing invariants in object-oriented models
Proceedings of the 12th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
Using Animation in Diagrammatic Theorem Proving
DIAGRAMS '02 Proceedings of the Second International Conference on Diagrammatic Representation and Inference
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
A Decidable Constraint Diagram Reasoning System
Journal of Logic and Computation
Which n-Venn Diagrams Can Be Drawn with Convex k-Gons?
Discrete & Computational Geometry
EulerView: a non-hierarchical visualization component
VLHCC '07 Proceedings of the IEEE Symposium on Visual Languages and Human-Centric Computing
Automated Theorem Proving in Euler Diagram Systems
Journal of Automated Reasoning
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
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
A Normal Form for Euler Diagrams with Shading
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
Journal of Visual Languages and Computing
Interactive visual classification with Euler diagrams
VLHCC '09 Proceedings of the 2009 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)
A System for Virtual Directories Using Euler Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
Abstractions of Euler Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
Using Euler Diagrams in Traditional Library Environments
Electronic Notes in Theoretical Computer Science (ENTCS)
The semantics of augmented constraint diagrams
Journal of Visual Languages and Computing
Personalised resource categorisation using euler diagrams
IS-EUD'11 Proceedings of the Third international conference on End-user development
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
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Euler diagrams are an accessible and effective visualisation of data involving simple set-theoretic relationships. Sets are represented by closed curves in the plane and often have wellformedness conditions placed on them in order to enhance comprehensibility. The theoretical underpinning for tool support has usually focussed on the problem of generating an Euler diagram from an abstract model. However, the problem of efficient computation of the abstract model from the concrete diagram has not been addressed before, despite this computation being a necessity for computer interpretations of user drawn diagrams. This may be used, together with automated manipulations of the abstract model, for purposes such as semantic information presentation or diagrammatic theorem proving. Furthermore, in interactive settings, the user may update diagrams ''on-line'' by adding and removing curves, for example, in which case a system requirement is the update of the abstract model (without the necessity of recomputation of the entire abstract model). We define the notion of marked Euler diagrams, together with a method for associating marked points on the diagram with regions in the plane. Utilising these, we provide on-line algorithms which quickly compute the abstract model of a weakly reducible wellformed Euler diagram (constructible as a sequence of additions or removals of curves, keeping a wellformed diagram at each step), and quickly updates both the set of curves in the plane as well as the abstract model according to the on-line operations. Efficiency is demonstrated by comparison with a common, naive algorithm. Furthermore, the methodology enables a straightforward implementation which has subsequently been realised as an application for the user classification domain.