Generating Euler Diagrams from Existing Layouts

Abstract

Euler diagrams have a wide variety of uses, from information visualiza- tion to logical reasoning. In the case of software engineeri ng, they form the basis of a number of notations, such as state charts and constraint diagrams. In all of their application areas, the ability to automatically layout Eul er diagrams brings consid- erable benefits. There have been several recent contributio ns towards the automatic generation and layout of Euler diagrams, all of which start from an abstract de- scription of the diagram and produce a collection of closed curves embedded in the plane. In this paper, we are concerned with producing layouts by modifying exist- ing ones. This type of layout approach is particularly useful in domains where we require an updated, or modified, diagram such as in a logical r easoning context. We provide two methods to add a curve to an Euler diagram in order to create a new diagram. The first method is guaranteed to produce layouts th at meet specified well- formedness conditions that are typically chosen by others who produced generation algorithms; these conditions are thought to correlate well accurate user interpreta- tion. We also overview a second method that can be used to produce a layout of any abstract description.