General Euler Diagram Generation

Abstract

Abstract. 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.

Visualizing Ontologies: A Case Study

“…This will involve solving challenging problems, such as identifying what constitutes an effective diagram (as shown in this paper, there are different diagrams that convey the same information) and how to automatically draw chosen diagrams from abstract descriptions of them. This functionality could build on recent advances in automated Euler diagram drawing [15,18,19], although the layout problem for concept diagrams is more challenging. In addition, we want to allow ontology creators to be able to specify the axioms directly with concept diagrams, which may require a sketch recognition engine to be devised; this could also build on recent work that recognizes sketches of Euler diagrams [20].…”

Coloured Euler Diagrams: A Tool for Visualizing Dynamic Systems and Structured Information

“…In [16] it is shown that all abstract diagrams for at most eight sets are drawable using such Euler-like diagrams. Recently, a methodology for generating general Euler diagrams has been developed [11], ensuring the production of a diagram, with a heuristic approach to repairing possible breaks in well-formedness.…”

On the drawability of 3D Venn and Euler diagrams

“…Since that first work, a number of methods have been devised to automatically draw 2D Euler diagrams under varying sets of wellformedness properties, including research by Chow and Ruskey [3], Kestler et al [8],R o d g e r se ta l . [12],S i m o n e t t o et al [17],Stapletonetal. [19] and Wilkinson [25].…”