General Euler Diagram Generation

  • Peter Rodgers
  • Leishi Zhang
  • Andrew Fish
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5223)


Euler diagrams are a natural method of representing set-theoretic 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.


Euler Diagrams Venn Diagrams 


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  1. 1.
    Chow, S.: Generating and Drawing Area-Proportional Venn and Euler Diagrams. Ph.D Thesis. University of Victoria, Canada (2008)Google Scholar
  2. 2.
    Chow, S., Ruskey, F.: Drawing area-proportional Venn and Euler diagrams. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 466–477. Springer, Heidelberg (2004)Google Scholar
  3. 3.
    DeChiara, R., Erra, U., Scarano, V.: VennFS: A Venn diagram file manager. In: Proc. IV 2003, pp. 120–126. IEEE Computer Society, Los Alamitos (2003)Google Scholar
  4. 4.
    Eades, P.: A Heuristic for Graph Drawing. Congressus Numerantium 22, 149–160 (1984)MathSciNetGoogle Scholar
  5. 5.
    Euler, L.: Lettres à une Princesse d’Allemagne, vol 2, Letters No. 102–108 (1761)Google Scholar
  6. 6.
    Flower, J., Fish, A., Howse, J.: Euler Diagram Generation. Journal of Visual Languages and Computing (2008)Google Scholar
  7. 7.
    Flower, J., Howse, J.: Generating Euler Diagrams. In: Hegarty, M., Meyer, B., Narayanan, N.H. (eds.) Diagrams 2002. LNCS (LNAI), vol. 2317, pp. 61–75. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Flower, J., Howse, J., Taylor, J.: Nesting in Euler diagrams: syntax, semantics and construction. Journal of Software and Systems Modeling, 55–67 (2003)Google Scholar
  9. 9.
    Flower, J., Rodgers, P., Mutton, P.: Layout Metrics for Euler Diagrams. In: Proc. IEEE Information Visualization (IV 2003), pp. 272–280 (2003)Google Scholar
  10. 10.
    Gurr, C.: Effective diagrammatic communication: Syntactic, semantic and pragmatic issues. Journal of Visual Languages and Computing 10(4), 317–342 (1999)CrossRefGoogle Scholar
  11. 11.
    Hayes, P., Eskridge, T., Saavedra, R., Reichherzer, T., Mehrotra, M., Bobrovnikoff, D.: Collaborative knowledge capture in ontologies. In: Proc. of 3rd International Conference on Knowledge Capture, pp. 99–106 (2005)Google Scholar
  12. 12.
    Howse, J., Stapleton, G., Taylor, J.: Spider diagrams. LMS J. Computation and Mathematics 8, 145–194 (2005)MATHMathSciNetGoogle Scholar
  13. 13.
    Kestler, H.A., Müller, A., Gress, T.M., Buchholz, M.: Generalized Venn diagrams: a new method of visualizing complex genetic set relations. Bioinformatics 21(8) (2005)Google Scholar
  14. 14.
    Kim, S.-K., Carrington, D.: Visualization of formal specifications. In: Proc. APSEC, pp. 102–109 (1999)Google Scholar
  15. 15.
    Rodgers, P.J., Zhang, L., Fish, A.: Embedding Wellformed Euler Diagrams. In: Proc. Information Visualization (IV 2008) (to appear, 2008)Google Scholar
  16. 16.
    Ruskey, F.: A Survey of Venn Diagrams. The Electronic Journal of Combinatorics (March 2001)Google Scholar
  17. 17.
    Shimojima, A.: Inferential and expressive capacities of graphical representations: Survey and some generalizations. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 18–21. Springer, Heidelberg (2004)Google Scholar
  18. 18.
    Tavel, P.: Modeling and Simulation Design. AK Peters Ltd. (2007)Google Scholar
  19. 19.
    Verroust, A., Viaud, M.-L.: Ensuring the drawability of Euler diagrams for up to eight sets. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 128–141. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Peter Rodgers
    • 1
  • Leishi Zhang
    • 1
  • Andrew Fish
    • 2
  1. 1.Computing LaboratoryUniversity of KentUK
  2. 2.Computing Mathematical & Information SciencesBrighton University of BrightonUK

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