General Euler Diagram Generation

Euler diagrams are a natural method of representing set-theoretic data and have been employed in diverse areas such as visualizing statistical data, as a basis for diagrammatic logics and for displaying the results of database search queries. For effective use of Euler diagrams in practical computer based applications, the generation of a diagram as a set of curves from an abstract description is necessary. Various practical methods for Euler diagram generation have been proposed, but in all of these methods the diagrams that can be produced are only for a restricted subset of all possible abstract descriptions. We describe a method for Euler diagram generation, demonstrated by implemented software, and illustrate the advances in methodology via the production of diagrams which were difficult or impossible to draw using previous approaches. To allow the generation of all abstract descriptions we may be required to have some properties of the final diagram that are not considered nice. In particular we permit more than two curves to pass though a single point, permit some curve segments to be drawn concurrently, and permit duplication of curve labels. However, our method attempts to minimize these bad properties according to a chosen prioritization.