Changing Euler Diagram Properties by Edge Transformation of Euler Dual Graphs

Euler diagrams form the basis of several visual modelling notations, including statecharts and constraint diagrams. Recently, various techniques for automated Euler diagram drawing have been proposed, contributing to the Euler diagram generation problem: given an abstract description, draw an Euler diagram with that description and which possesses certain properties. A common generation method is to find a dual graph from which an Euler diagram is subsequently created. In this paper we define transformations of the dual graph that allow us to alter the properties that the generated diagram possesses. In addition, because the dual graph of a previously generated diagram can be found, our transformations can be used to take such a diagram and produce a new diagram with the same abstract description, but with different properties. As a result, we can produce a variety of different diagrams for any given abstract description, allowing us to choose an Euler diagram that conforms to the properties that a user prefers.