Drawing Area Proportional Venn and Euler Diagrams

Abstract:

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.

Stirling Chow, Department of Computer Science, University of Victoria, Canada.
Frank Ruskey, Department of Computer Science, University of Victoria, Canada.

• The postscript file is ??? bytes, the dvi file is ??? bytes, the pdf file is 281KB.
• Presented at the 11th International Symposium on Graph Drawing, Perugia, Italy.
• Appears in Lecture Notes in Computer Science, LNCS 2912 (2003) 466-477.
• Stirling's powerpoint slides for the talk in Perugia (coming soon).
• Stirling's Java implementation of the 2-set and 3-set drawing algorithms (coming soon).
• Selected papers which refer to this one:
  • Tom Quick, Chrystopher Nehaniv, Kerstin Dautenhahn and Graham Roberts, Sensorimotor Information flow in Genetic Regulatory Network driven control systems, Artificial Life X, MIT Press, 2006.
  • Gem Stapleton and Aidan Delaney, Evaluating and Generalizing Constraint Diagrams, Journal of Visual Languages and Computing, 19 (2008) 499-521.
  • Jens Bleiholder, Karsten Draba, and Felix Naumann, FuSem: exploring different semantics of data fusion, Proceedings of the 33rd international conference on Very large data bases, pp. 1350-1353, Vienna, 2007.
  • Simon Barquera, et. al., Dyslipidemias and obesity in Mexico, Salud Publica de Mexico, vol. 49, suplemnto 3 de 2007, S338-S347.
  • B. Greber, H. Lehrach, and J. Adjaye, Silencing of core transcription factors in human EC cells highlights the importance of autocrine FGF signaling for self-renewal, BMC Developmental Biology, 2007, 7:46, 15 pages.
  • B. Wieland, M. Wittwer, G. Regula, T.M. Wassenaar, A.P. Burnens, J. Keller, K.D.C. Stärk,
    Phenon cluster analysis as a method to investigate epidemiological relatedness between sources of Campylobacter jejuni, Journal of Applied Microbiology 100-2 (2006) 316-324.
  • Paul H. Artes and Balwantray C. Chauhan, Longitudinal changes in the visual field and optic disk glaucoma, Progress in Retinal and Eye Research, 24 (2005) 333-354.
  • Paul Mutton, Peter Rodgers, and Jean Flower, Drawing Graphs in Euler Diagrams, Diagrams 2004, Cambridge, UK, March 22-24, pp. 66-81, 2004.
  • Peter Rodgers, Paul Mutton, Jean Flower, Dynamic Euler Diagram Drawing, 2004 IEEE Symposium on Visual Languages - Human Centric Computing (VLHCC'04), pp. 147-156, 2004.