# Some Results for Drawing Area Proportional Venn3 With Convex Curves

Rodgers, Peter, Flower, Jean, Stapleton, Gem, Howse, John (2009) Some Results for Drawing Area Proportional Venn3 With Convex Curves. In: 13th International Conference Information Visualisation (IV09). . pp. 667-672. IEEE ISBN 978-0-7695-3733-7. (doi:10.1109/IV.2009.93) (KAR id:24129)

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## 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.

Item Type: Conference or workshop item (UNSPECIFIED) 10.1109/IV.2009.93 Venn diagrams; diagram layout; data visualization; shape; environmental factors; reflection Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming, Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing Peter Rodgers 29 Mar 2010 12:16 UTC 16 Feb 2021 12:34 UTC https://kar.kent.ac.uk/id/eprint/24129 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-4100-3596
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