Drawing Euler diagrams with circles and ellipses

Abstract

The use of Euler diagrams as a basis for visual languages is commonplace and they are often used for visualizing information. The ability to automatically draw these diagrams is, therefore, likely to be of widespread practical use. The Euler diagram drawing problem is recognized as challenging, but the potential pay-off from the derivation of a comprehensive solution, that produces usable and effective diagrams, is significant. Previous research on automated Euler diagram drawing has used various different approaches, each of which had their own problems, including: (a) failure to draw a diagram in all cases, (b) poor diagram layout, and (c) inability to ensure that certain wellformedness properties of the drawn diagrams hold. In this paper, we present a novel approach to Euler diagram drawing that draws diagrams with circles, ellipses and curves in general. This new approach will draw a diagram in all cases, avoiding bad layout where possible (by the use of `nice' geometric shapes) and can enforce wellformedness properties as chosen by the user.