Logic and Visual Information
DIAGRAMS '02 Proceedings of the Second International Conference on Diagrammatic Representation and Inference
Visualization of Formal Specifications
APSEC '99 Proceedings of the Sixth Asia Pacific Software Engineering Conference
VENNFS: A Venn-Diagram File Manager
IV '03 Proceedings of the Seventh International Conference on Information Visualization
Collaborative knowledge capture in ontologies
Proceedings of the 3rd international conference on Knowledge capture
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
Visualise Undrawable Euler Diagrams
IV '08 Proceedings of the 2008 12th International Conference Information Visualisation
Towards a General Solution to Drawing Area-Proportional Euler Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
A System for Virtual Directories Using Euler Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
Using Euler Diagrams in Traditional Library Environments
Electronic Notes in Theoretical Computer Science (ENTCS)
A general method for drawing area-proportional Euler diagrams
Journal of Visual Languages and Computing
Automatically drawing Euler diagrams with circles
Journal of Visual Languages and Computing
Hi-index | 5.23 |
Euler diagrams are used in a wide variety of areas for representing information about relationships between collections of objects. Recently, several 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, sometimes called well-formedness conditions. We present the first fully formalized, general framework that permits the embedding of Euler diagrams that possess any collection of the six typically considered well-formedness conditions. Our method first converts the abstract description into a vertex-labelled graph. An Euler diagram can then be formed, essentially by finding a dual graph of such a graph. However, we cannot use an arbitrary plane embedding of the vertex-labelled graph for this purpose. We identify specific embeddings that allow the construction of appropriate duals. From these embeddings, we can also identify precisely which properties the drawn Euler diagram will possess and 'measure' the number of times that each well-formedness condition is broken. We prove that every abstract description can be embedded using our method. Moreover, we identify exactly which (large) class of Euler diagrams can be generated.