Drawing Area-Proportional Euler Diagrams Representing Up To Three Sets

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 non-convex curves are necessary, our method draws an appropriate diagram using non-convex polygons. Thus, we are now always able to automatically visualize data for up to three sets

A General Method for Drawing Area-Proportional Euler Diagrams

Area-proportional Euler diagrams have many applications, for example they are often used for visualizing data in medical and biological domains. There have been a number of recent research efforts to automatically draw Euler diagrams when the areas of the regions are not considered, leading to a range of different drawing techniques. By contrast, substantially less progress has been made on the problem of automatically drawing area-proportional Euler diagrams, although some partial results have been derived. In this paper, we considerably advance the state-of-the-art in area-proportional Euler diagram drawing by presenting the first method that is capable of generating such a diagram given any area-proportional specification. Moreover, our drawing method is sufficiently flexible that it allows one to specify which of the typically enforced wellformedness conditions should be possessed by the to-be-drawn Euler diagram

Generating Effective Euler Diagrams

Euler diagrams are used for visualizing categorized data,with applications including crime control, bioinformatics, classification systems and education. Various properties of Euler diagrams have been empirically shown to aid, or hinder, their comprehension by users. Therefore, a key goal is to automatically generate Euler diagrams that possess beneficial layout features whilst avoiding those that are a hindrance.The automated layout techniques that currently exist sometimes produce diagrams with undesirable features. In this paper we present a novel approach, called iCurves, for generating Euler diagrams alongside a prototype implementation. We evaluate iCurves against existing techniques based on the aforementioned layout properties. This evaluation suggests that, particularly when the number of zones is high, iCurves can outperform other automated techniques in terms of effectiveness for users, as indicated by the layout properties of the produced Euler diagrams

Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams

In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations and their cardinalities. The data sets are represented by closed curves and the data set relationships are depicted by the overlaps between these curves. Both the sets and their intersections are easily visible as the closed curves are preattentively processed and form common regions that have a strong perceptual grouping effect. Besides set relations such as intersection, containment and disjointness, the cardinality of the sets and their intersections can also be depicted in the same diagram (referred to as area-proportional) through the size of the curves and their overlaps. Size is a preattentive feature and so similarities, differences and trends are easily identified. Thus, such diagrams facilitate data analysis and reasoning about the sets. However, drawing these diagrams manually is difficult, often impossible, and current automatic drawing methods do not always produce appropriate diagrams. This dissertation presents novel automatic drawing methods for different types of Euler diagrams and a user study of how such diagrams can help probabilistic judgement. The main drawing algorithms are: eulerForce, which uses a force-directed approach to lay out Euler diagrams; eulerAPE, which draws area-proportional Venn diagrams with ellipses. The user study evaluated the effectiveness of area- proportional Euler diagrams, glyph representations, Euler diagrams with glyphs and text+visualization formats for Bayesian reasoning, and a method eulerGlyphs was devised to automatically and accurately draw the assessed visualizations for any Bayesian problem. Additionally, analytic algorithms that instantaneously compute the overlapping areas of three general intersecting ellipses are provided, together with an evaluation of the effectiveness of ellipses in drawing accurate area-proportional Venn diagrams for 3-set data and the characteristics of the data that can be depicted accurately with ellipses