eulerr: Area-Proportional Euler Diagrams with Ellipses

Sammanfattning: Euler diagrams are common and intuitive visualizations for data involving sets and relationships thereof. Compared to Venn diagrams, Euler diagrams do not require all set relationships to be present and may therefore be area-proportional also with subset or disjoint relationships in the input. Most Euler diagrams use circles, but circles do not always support accurate diagrams. A promising alternative for Euler diagrams is ellipses, which enable accurate diagrams for a wider range of set combinations. Ellipses, however, have not yet been implemented for more than three sets or three-set diagrams where there are disjoint or subset relationships. The aim of this thesis is to present a method and software for elliptical Euler diagrams for any number of sets. In this thesis, we provide and outline an R-based implementation called eulerr. It fits Euler diagrams using numerical optimization and exact-area algorithms through two steps: first, an initial layout is formed using the sets' pairwise relationships; second, this layout is finalized taking all the sets' intersections into account. Finally, we compare eulerr with other software implementations of Euler diagrams and show that the package is overall both more consistent and accurate as well as faster for up to seven sets compared to the other R-packages. eulerr perfectly reproduces samples of circular Euler diagrams as well as three-set diagrams with ellipses, but performs suboptimally with elliptical diagrams of more than three sets. eulerr also outperforms the other software tested in this thesis in fitting Euler diagrams to set configurations that might lack exact solutions provided that we use ellipses; eulerr's circular diagrams, meanwhile, fit better on all accounts save for the diagError metric in the case of three-set diagrams.