Computing the Region Areas of Euler Diagrams Drawn with Three Ellipses

Micallef, Luana and Rodgers, Peter (2014) Computing the Region Areas of Euler Diagrams Drawn with Three Ellipses. In: 4th International Workshop on Euler Diagrams, CEUR-WS. org, July 28, 2014, Melbourne, Australia. (Full text available)

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http://ceur-ws.org/Vol-1244/

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)
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: Faculties > Sciences > School of Computing > Computational Intelligence Group
Depositing User: L. Micallef
Date Deposited: 16 Jun 2014 13:51 UTC
Last Modified: 17 Jan 2017 12:12 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/41436 (The current URI for this page, for reference purposes)
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