### 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 dasianicepsila 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.

Original language | English |
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Title of host publication | Proceedings of the 13th International Conference on Information Visualisation, IV 2009 |

Place of Publication | New York, NY, USA |

Publisher | IEEE |

Pages | 667-672 |

Number of pages | 6 |

ISBN (Print) | 9780769537337 |

DOIs | |

Publication status | Published - 4 Aug 2009 |

Event | Proceedings of the 13th International Conference on Information Visualisation, IV 2009 - Barcelona, Spain, 15-17 July, 2009 Duration: 4 Aug 2009 → … |

### Publication series

Name | International Conference Information Visualization |
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### Conference

Conference | Proceedings of the 13th International Conference on Information Visualisation, IV 2009 |
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Period | 4/08/09 → … |

### Keywords

- Venn diagrams
- diagram layout

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## Cite this

Rodgers, P., Flower, J., Stapleton, G., & Howse, J. (2009). Some results for drawing area-proportional Venn3 with convex curves. In

*Proceedings of the 13th International Conference on Information Visualisation, IV 2009*(pp. 667-672). (International Conference Information Visualization). IEEE. https://doi.org/10.1109/IV.2009.93