Area-proportional Euler diagrams representing three sets are commonly used to visualize the results of medical experiments, business data, and information from other applications where statistical results are best shown using interlinking curves. Currently, there is no tool that will reliably visualize exact area-proportional diagrams for up to three sets. Limited success, in terms of diagram accuracy, has been achieved for a small number of cases, such as Venn-2 and Venn-3 where all intersections between the sets must be represented. Euler diagrams do not have to include all intersections and so permit the visualization of cases where some intersections have a zero value. This paper describes a general, implemented, method for visualizing all 40 Euler-3 diagrams in an area-proportional manner. We provide techniques for generating the curves with circles and convex polygons, analyze the drawability of data with these shapes, and give a mechanism for deciding whether such data can be drawn with circles. For the cases where nonconvex curves are necessary, our method draws an appropriate diagram using nonconvex polygons. Thus, we are now always able to automatically visualize data for up to three sets.

Many data sets are visualized effectively with area proportional Venn diagrams, where the area of the regions is in proportion to a defined specification. In particular, Venn diagrams with three intersecting curves are considered useful for visualizing data in many applications, including bioscience, ecology and medicine. To ease the understanding of such diagrams,using restricted dasianicepsila shapes for the curves is considered beneficial. Many research questions on the use of such diagrams are still open. For instance, a general solution to the question of when given area specifications can be represented by Venn3 using convex curves is still unknown.In this paper we study symmetric Venn3 drawn with convex curves and show that there is a symmetric area specification that cannot be represented with such a diagram. In addition, by using symmetric diagrams drawn with polygons, we show that, if area specifications are restricted so that the double intersection areas are no greater than the triple intersection area then the specification can be drawn with convex curves. We also propose a construction that allows the representation of some area specifications when the double intersection areas are greater than the triple intersection area.Finally, we present some open questions on the topic.

In this paper we describe a method to lay out a graph enhanced Euler diagram so that it looks similar to a previously drawn graph enhanced Euler diagram. This task is nontrivial when the underlying structures of the diagrams differ. In particular, if a structural change is made to an existing drawn diagram, our work enables the presentation of the new diagram with minor disruption to the user's mental map. As the new diagram can be generated from an abstract representation, its initial embedding may be very different from that of the original. We have developed comparison measures for Euler diagrams, integrated into a multicriteria optimizer, and applied a force model for associated graphs that attempts to move nodes towards their positions in the original layout. To further enhance the usability of the system, the transition between diagrams can be animated

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. 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.