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Computing the Region Areas of Euler Diagrams Drawn with Three Ellipses

Micallef, Luana, Rodgers, Peter (2014) Computing the Region Areas of Euler Diagrams Drawn with Three Ellipses. In: Burton, Jim and Stapleton, Gem and Klein, Karsten, eds. CEUR Workshop Proceedings. Joint Proceedings of the Fourth International Workshop on Euler Diagrams and the First International Workshop on Graph Visualization in Practice co-located with Diagrams 2014. 1244. pp. 1-15. (KAR id:41436)


Ellipses generate accurate area-proportional Euler diagrams for more data than is possible with circles. However, computing the region areas is difficult as ellipses have various degrees of freedom. Numerical methods could be used, but approximation errors are introduced. Current analytic methods are limited to computing the area of only two overlapping ellipses, but area-proportional Euler diagrams in diverse application areas often have three curves. This paper provides an overview of different methods that could be used to compute the region areas of Euler diagrams drawn with ellipses. We also detail two novel analytic algorithms to instantaneously compute the exact region areas of three general overlapping ellipses. One of the algorithms decomposes the region of interest into ellipse segments, while the other uses integral calculus. Both methods perform equally well with respect to accuracy and time.

Item Type: Conference or workshop item (Paper)
Additional information: Invited for submission to a special issue of the Journal of Logic, Language and Information on Euler and Venn diagrams
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
Depositing User: Luana Micallef
Date Deposited: 16 Jun 2014 13:51 UTC
Last Modified: 16 Feb 2021 12:54 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Micallef, Luana.

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Rodgers, Peter.

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