Drawing Area-Proportional Venn and Euler Diagrams

  • Stirling Chow
  • Frank Ruskey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)


We consider the problem of drawing Venn diagrams for which each region’s area is proportional to some weight (e.g., population or percentage) assigned to that region. These area-proportional Venn diagrams have an enhanced ability over traditional Venn diagrams to visually convey information about data sets with interacting characteristics. We develop algorithms for drawing area-proportional Venn diagrams for any population distribution over two characteristics using circles and over three characteristics using rectangles and near-rectangular polygons; modifications of these algorithms are then presented for drawing the more general Euler diagrams. We present results concerning which population distributions can be drawn using specific shapes. A program to aid further investigation of area-proportional Venn diagrams is also described.


  1. 1.
    Battista, G.D., Eades, P., Tomassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall, Englewood Cliffs (1999)zbMATHGoogle Scholar
  2. 2.
    Burden, R.L., Faires, J.D.: Numerical Analysis: 4th edn. PWS Publishing Co. (1988)Google Scholar
  3. 3.
    Card, S.K., Mackinlay, J.D., Shneiderman, B.: Readings in Information Visualization: Using Vision to Think. Morgan Kaufmann Publishers, San Francisco (1999)Google Scholar
  4. 4.
    Edwards, A.W.F.: Venn diagrams for many sets. New Scientist 7, 51–56 (1989)Google Scholar
  5. 5.
    Euler, L.: Lettres a Une Princesse d’Allemagne, vol. 2, 1761. Letters no. 102–108Google Scholar
  6. 6.
    Flower, J., Howse, J.: Generating Euler diagrams. In: Proceedings of Diagrams 2002, April 2002, pp. 61–75. Springer, Heidelberg (2002)Google Scholar
  7. 7.
    (Yossi) Gil, J., Kent, S., Howse, J.: Formalizing spider diagrams. In: Proceedings of the IEEE Symposium on Visual Languages, September 1999, pp. 130–137. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  8. 8.
    (Yossi) Gil, J., Kent, S., Howse, J., Taylor, J.: Projections in Venn-Euler diagrams. In: Proceedings of the IEEE Symposium on Visual Languages, September 2000, pp. 119–126. IEEE Computer Society Press, Los Alamitos (2000)Google Scholar
  9. 9.
    Knopp, K.: Theory of Functions, Parts I and II, Two Volumes Bound as One, vol. 1. Dover, New York (1996)Google Scholar
  10. 10.
    Ruskey, F.: A survey of Venn diagrams. Electronic Journal of Combinatorics 4 (1997) (update 2001). DS#5Google Scholar
  11. 11.
    Venn, J.: On the diagrammatic and mechanical representation of propositions and reasonings. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 9, 1–18 (1880)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Stirling Chow
    • 1
  • Frank Ruskey
    • 1
  1. 1.Department of Computer ScienceUniversity of VictoriaCanada

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