Euler3 Applet: Exact 3 Set Area-Proportional Euler Diagrams with Circles and Convex Curves

Version 1.0

  Euler 3 Applet Screenshot
The download link: the applet. Left click the link and choose 'Save Target As...' or similar, depending on browser. Hopefully double clicking the saved file will result in the applet running. Otherwise here is a discussion on running .jar files.
This applet requires Java.
If you don't have 1.6 or greater installed, download Java.

This Euler3 applet draws an Euler diagram with 3 curves, where the areas of the regions are proportional to the input populations. It attempts to use circles (approximated by regular polygons), if this is not possible it then attempts to use convex polygons, finally it resorts to non-convex polygons.

The results of this applet are free for any use.

If you do use the results of this applet, we encourage you to reference the paper that describes how it works:
Peter Rodgers, Gem Stapleton, Jean Flower and John Howse. Drawing Area-Proportional Euler Diagrams Representing Up To Three Sets. IEEE Transactions on Visualization and Computer Graphics, 20 (1). pp. 56-69, 2014.


The applet draws Euler Diagrams with 3 curves. It makes each of the regions proportional to the population assigned to it.

To draw a diagram with your own data, simply type in the data for the zones in the 'population' column, and click the 'Draw Diagram' button, you should map the 3 set names of your data to A, B and C. The population values can be any you like, the program will scale them so that the diagram fits in the applet. Regions with very small values in proportion to the largest (less than 0.5% of the largest) may appear slightly bigger (they are increased to 0.5% of the largest). Zero or empty regions will not appear in the diagram.

You can create an unlabelled diagram by choosing the 'No Labels' option. The display of the curves and shading can be altered by the 'Colour', 'Shading' and 'Dashed' options. When curves run together, 'Concurrent Separation' separates them slightly so the different lines are not completely on top of one another. The 'Approximate Circles' and 'Unimproved' options are not very useful, except in relation to understanding the various constructions.

Downloading: You can get an SVG (Scalable Vector Graphics) version of the diagram by downloading the applet: left click this link and choose 'Save Target As...' or similar, depending on browser. Once saved to your hard disk, double click the Euler4Applet.jar file and (assuming your java installation is set up suitably), the applet will appear. If not, there is a discussion on running .jar files here. Diagrams can be accessed via the 'Save as SVG File' button. Inkscape is an effective, free svg editor.

The source is also bundled into the .jar. You can access this is, for example, in Windows, by changing the extension of the downloaded applet from .jar to .zip and double clicking the resultant file in Windows File Manager.

Related Work

Ideas used to generate this software were developed by:
Peter Rodgers, University of Kent, UK; Jean Flower, Gem Stapleton and John Howse, University of Brighton, UK
Contact: Peter Rodgers, University of Kent, UK (email)