# 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.

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## Abstract

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) Invited for submission to a special issue of the Journal of Logic, Language and Information on Euler and Venn diagrams Q Science > Q Science (General)Q Science > QA Mathematics (inc Computing science) Faculties > Sciences > School of Computing > Computational Intelligence Group L. Micallef 16 Jun 2014 13:51 UTC 23 Jan 2020 04:08 UTC https://kar.kent.ac.uk/id/eprint/41436 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-4100-3596