International Conference on Theory and Application of Diagrams

Diagrams 2014: Diagrammatic Representation and Inference pp 123-137 | Cite as

The Impact of Shape on the Perception of Euler Diagrams

  • Andrew Blake
  • Gem Stapleton
  • Peter Rodgers
  • Liz Cheek
  • John Howse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8578)


Euler diagrams are often used for visualizing data collected into sets. However, there is a significant lack of guidance regarding graphical choices for Euler diagram layout. To address this deficiency, this paper asks the question ‘does the shape of a closed curve affect a user’s comprehension of an Euler diagram?’ By empirical study, we establish that curve shape does indeed impact on understandability. Our analysis of performance data indicates that circles perform best, followed by squares, with ellipses and rectangles jointly performing worst. We conclude that, where possible, circles should be used to draw effective Euler diagrams. Further, the ability to discriminate curves from zones and the symmetry of the curve shapes is argued to be important. We utilize perceptual theory to explain these results. As a consequence of this research, improved diagram layout decisions can be made for Euler diagrams whether they are manually or automatically drawn.


euler diagram shape visualization perceptual organisation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Architectural Association, London (April 2013),
  2. 2.
    Benoy, F., Rodgers, P.: Evaluating the comprehension of Euler diagrams. In: 11th International Conference on Information Visualization, pp. 771–778. IEEE (2007)Google Scholar
  3. 3.
    Bertin, J.: Semiology of Graphics: Diagrams, Networks, Maps. University of Wisconsin Press (1983)Google Scholar
  4. 4.
    Blake, A., Stapleton, G., Rodgers, P., Cheek, L., Howse, J.: Does the orientation of an Euler diagram affect user comprehension? In: 18th International Conference on Distributed Multimedia Systems, International Workshop on Visual Languages and Computing, pp. 185–190. Knowledge Systems Institute (2012)Google Scholar
  5. 5.
    DeChiara, R., Erra, U., Scarano, V.: A system for virtual directories using Euler diagrams. Proceedings of Euler Diagrams. Electronic Notes in Theoretical Computer Science 134, 33–53 (2005)CrossRefGoogle Scholar
  6. 6.
    Duncan, J., Humphreys, G.: Visual search and stimulus similarity. Psychological Review 96, 433–458 (1989)CrossRefGoogle Scholar
  7. 7.
    Farrell, G., Sousa, W.: Repeat victimization and hot spots: The overlap and its implication for crime control and problem-oriented policing. Crime Prevention Studies 12, 221–240 (2001)Google Scholar
  8. 8.
    Gurr, C.: Effective diagrammatic communication: Syntactic, semantic and pragmatic issues. Journal of Visual Languages and Computing 10(4), 317–342 (1999)CrossRefGoogle Scholar
  9. 9.
    Healey, C., Enns, J.: Attention and visual memory in visualization and computer graphics. IEEE Transactions on Visualisation and Computer Graphics 18, 1170–1188 (2011)CrossRefGoogle Scholar
  10. 10.
    Ip, E.: Visualizing multiple regression. Journal of Statistics Education 9(1) (2001)Google Scholar
  11. 11.
    Isenberg, P., Bezerianos, A., Dragicevic, P., Fekete, J.: A study on dual-scale data charts. IEEE Transactions on Visualization and Computer Graphics, 2469–2478 (2011)CrossRefGoogle Scholar
  12. 12.
    Kestler, H.: Vennmaster: Area-proportional Euler diagrams for functional GO analysis of microarrays. BMC Bioinformatics 9(1)(67) (2008)CrossRefGoogle Scholar
  13. 13.
    Koffka, K.: Principles of Gestalt Pschology. Lund Humphries (1935)Google Scholar
  14. 14.
    Micallef, L., Rodgers, P.: Drawing Area-Proportional Venn-3 Diagrams Using Ellipses. Tech. Rep. TR-3-11, School of Computing, University of Kent, Canterbury, UK (2011),
  15. 15.
    Purchase, H.: Which aesthetic has the greatest effect on human understanding? In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 248–261. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  16. 16.
    Purchase, H.: Experimental Human Computer Interaction: A Practical Guide with Visual Examples. Cambridge University Press (2012)Google Scholar
  17. 17.
    Riche, N., Dwyer, T.: Untangling Euler diagrams. IEEE Transactions on Visualisation and Computer Graphics 16, 1090–1097 (2010)CrossRefGoogle Scholar
  18. 18.
    Rodgers, P., Zhang, L., Purchase, H.: Wellformedness properties in Euler diagrams: Which should be used? IEEE Transactions on Visualization and Computer Graphics 18(7), 1089–1100 (2012)CrossRefGoogle Scholar
  19. 19.
    Rodgers, P., Stapleton, G., Howse, J., Zhang, L.: Euler graph transformations for Euler diagram layout. In: Visual Languages and Human-Centric Computing (VL/HCC), pp. 111–118. IEEE (2010)Google Scholar
  20. 20.
    Simonetto, P., Auber, D.: Visualise undrawable Euler diagrams. In: 12th International Conference on Information Visualization, pp. 594–599. IEEE (2008)Google Scholar
  21. 21.
    Simonetto, P., Auber, D., Archambault, D.: Fully automatic visualisation of overlapping sets. Computer Graphics Forum 28(3) (2009)CrossRefGoogle Scholar
  22. 22.
    Stapleton, G., et al.: Automatically drawing Euler diagrams with circles. Journal of Visual Languages and Computing 12, 163–193 (2012)CrossRefGoogle Scholar
  23. 23.
    Stapleton, G., et al.: Inductively generating Euler diagrams. IEEE Transactions of Visualization and Computer Graphics 17(1), 88–100 (2009)CrossRefGoogle Scholar
  24. 24.
    Thièvre, J., Viaud, M., Verroust-Blondet, A.: Using Euler diagrams in traditional library environments. In: Euler Diagrams. ENTCS, vol. 134, pp. 189–202. ENTCS (2005)Google Scholar
  25. 25.
    Wagemans, J., Elder, J., Kubovy, M., Palmer, S., Peterson, M., Singh, M.: A century of gestalt psychology in visual perception: I. perceptual grouping and figure-ground organisation. Computer Vision, Graphics, and Image Processing 31, 156–177 (1985)CrossRefGoogle Scholar
  26. 26.
    Wilkinson, L.: Exact and approximate area-proportional circular Venn and Euler diagrams. IEEE Transactions on Visualisation and Computer Graphics 18, 321–330 (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Andrew Blake
    • 1
  • Gem Stapleton
    • 1
  • Peter Rodgers
    • 2
  • Liz Cheek
    • 1
  • John Howse
    • 1
  1. 1.University of BrightonUK
  2. 2.University of KentUK

Personalised recommendations