Euler diagram generation

Abstract

Euler diagrams form the basis of many diagrammatic notations used to represent set theoretic relationships in a wide range of contexts including: file system information, statistical data representation, object-oriented modeling, logical specification and reasoning systems, and database search queries. An abstract Euler diagram is a formal abstract description of the information that is to be displayed as a concrete (or drawn) Euler diagram. If the abstract diagram can be visualized, whilst satisfying certain desirable visual properties (called well-formedness conditions), then we say the diagram is drawable. We solve the drawability problem for a given set of well-formedness conditions, identifying the properties which classify a diagram as drawable or undrawable. Furthermore, we present a high level algorithm which enables the generation of a concrete diagram from an abstract diagram, whenever it is drawable.