Layout Metrics for Euler Diagrams

An alternative term for these diagrams is “Euler-Venn diagrams” but they are often inaccurately called “Venn diagrams”. Venn diagrams often look similar, but must contain all possible intersections of contours. In contrast, Euler diagrams contain any desired combination of intersections between the contours. Visualizations of Venn diagrams are often created by taking advantage of the symmetries present in a Venn structure [12]. We present an aesthetics based method for drawing Euler diagrams. Aesthetic layout metrics have been found to be useful in graph drawing algorithms, which use metrics motivated by aesthetic principles that aid user understanding of diagrams. We have taken a similar approach to Euler diagram drawing, and have defined a set of suitable metrics to be used within a hill climbing multicriteria optimiser to produce “good” drawings. There are added difficulties when drawing Euler diagrams as they are made up of contours whose structural properties of intersection and containment must be preserved under any layout improvements. In this paper we describe our Java implementation of a pair of hill climbing variants to find good drawings, a set of metrics that measure aesthetics for good diagram layout, and issues concerning the choice of weightings for a useful combination of the metrics.