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Some Results for Drawing Area Proportional Venn3 With Convex Curves

By Peter Rodgers, Jean Flower, Gem Stapleton and John Howse

Abstract

Many data sets are visualized effectively with area proportional Venn diagrams, where the area of the regions is in proportion to a defined specification. In particular, Venn diagrams with three intersecting curves are considered useful for visualizing data in many applications, including bioscience, ecology and medicine. To ease the understanding of such diagrams, using restricted nice shapes for the curves is considered beneficial. Many research questions on the use of such diagrams are still open. For instance, a general solution to the question of when given area specifications can be represented by Venn3 using convex curves is still unknown. In this paper we study symmetric Venn3 drawn with convex curves and show that there is a symmetric area specification that cannot be represented with such a diagram. In addition, by using symmetric diagrams drawn with polygons, we show that, if area specifications are restricted so that the double intersection areas are no greater than the triple intersection area then the specification can be drawn with convex curves. We also propose a construction that allows the representation of some area specifications when the double intersection areas are greater than the triple intersection area. Finally, we present some open questions on the topic

Topics: QA76
Publisher: IEEE
Year: 2009
OAI identifier: oai:kar.kent.ac.uk:24129

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Citations

  1. (2008). Agentbased visualization of streaming text.
  2. (2000). Drawing Venn Triangles.
  3. (2008). Generating and Drawing Area-Proportional Venn and Euler Diagrams. PhD Thesis. doi
  4. (2005). Constructing Area-proportional Venn and Euler Diagrams with Three Circles.
  5. (2003). Drawing Area-Proportional Venn and Euler Diagrams. Graph Drawing doi
  6. (2007). Multi-scale study of bird species distribution and of their response to vegetation change: a Mediterranean example. Landscape Ecol doi
  7. (2008). BioVenn – a web application for the comparison and visualization of biological lists using area-proportional Venn diagrams. doi
  8. (2006). Chronic kidney disease care delivered by US family medicine and internal medicine trainees: results from an online survey.
  9. (2005). Generalized Venn Diagrams: A new method of visualizing complex genetic set relations. doi
  10. (2005). A Survey of Venn Diagrams. Electronic J. Combinatorics Dynamical Survey DS5,
  11. On the Diagrammatic and Mechanical Representation of Propositions and Reasonings. The London, Edinburgh, and Dublin Philosophical Magazine and doi

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