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Generating Euler Diagrams from Existing Layouts

By Gem Stapleton, John Howse, Peter Rodgers and Leishi Zhang

Abstract

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 wellformednesss conditions; we present a series of results that identify properties of cycles that correspond to the wellformedness conditions. This improves upon other contributions towards 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

Topics: QA76
Publisher: Electronic Communications of the EASST
Year: 2008
OAI identifier: oai:kar.kent.ac.uk:24020

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Citations

  1. (2003). A System for Virtual Directories Using Euler Diagrams.
  2. (2008). Abstract Euler Diagram Isomorphism. accepted for Visual Languages and Computing, Knowledge Systems Institute,
  3. (2007). Automated Theorem Proving in Euler Diagrams Systems. Journal of Automated Reasoning, doi
  4. (2005). Collaborative Knowledge Capture in Ontologies. doi
  5. (2006). Defining Health/Illness: Societal and/or Clinical Medicine?
  6. (2003). Drawing Area-Proportional Venn and Euler Diagrams. doi
  7. (2004). Ensuring the Drawability of Euler Diagrams for up to Eight Sets. doi
  8. (2008). Euler Diagram Decomposition. accepted for Diagrams doi
  9. (2004). Failure Mode Modular De-Composition Using Spider Diagrams. doi
  10. (2008). General Euler Diagram Generation, accepted for Diagrams doi
  11. (2005). Generalized Venn Diagrams: A New Method for Visualizing Complex Genetic Set Relations. doi
  12. (2007). Generating and Drawing Area-Proportional Euler and Venn Diagrams. doi
  13. (2002). Generating Euler Diagrams. doi
  14. (2000). JVenn: A Visual Reasoning System with Diagrams and Sentences. doi
  15. (1995). Layout Adjustment and the Mental Map, doi
  16. (2003). Layout metrics for Euler Diagrams. doi
  17. (2004). Nesting in Euler diagrams: syntax, semantics and construction. Software and Systems Modelling 3:55–67, doi
  18. (2006). oj. Defining Health/Illness: Societal and/or Clinical Medicine?
  19. (2005). Precise Visual Modelling. doi
  20. (2007). Properties of Euler Diagrams. doi
  21. (1994). The Logical Status of Diagrams. doi
  22. (2005). Towards a General Solution to Drawing Area-Proportional Euler Diagrams. doi
  23. (2002). Towards a Visual Editing Environment for the Languages of the Semantic Web.
  24. (2004). Using DAG Transformations to Verify Euler/Venn Homogeneous and Euler/Venn FOL Heterogeneous Rules of Inference. doi
  25. (2004). Using Euler Diagrams in Traditional Library Environments. Euler Diagrams doi
  26. (1999). Visualization of Formal Specifications. doi

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