Euler diagram generation

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

“…Let ∆ ⊂ Z + denote the set of prime numbers and DIV (x) the set of prime integer divisors of x for x ∈ Z. We assume that ∅ ∈ S for all set systems; this corresponds to the requirement that the "outside zone" is present in the diagrams, so the term set system becomes synonymous with the abstract diagram from [6]. Definition 1.…”

“…Commonly, somewhat restrictive set-ups are adopted, typically consisting of the well-formed diagrams of [6], where a decision procedure is provided to indicate if there is a well-formed concrete diagram realising an abstract diagram and if so to produce a drawing of it. The well-formedness conditions are concrete level constraints imposed on the system, with the intention of reducing human comprehension errors, and so there is validity in trying to preserve them; the conditions for [6] are: curves are simple (i.e.…”

“…The well-formedness conditions are concrete level constraints imposed on the system, with the intention of reducing human comprehension errors, and so there is validity in trying to preserve them; the conditions for [6] are: curves are simple (i.e. no self-intersection); curves only intersect at a finite number of points (i.e.…”

“…any abstract model has a visualisation), we cannot use uniquely labelled simple closed curves, as in [6]. Instead, we use unions of simple closed curves (or more precisely, the region bounded by them) to represent the sets of a set system, with labels determining the association.…”

General Euler Diagram Generation

“…Although Euler himself [5] did not formally define the diagrams he was using, his illustrations do not break any of wellformedness conditions given in Figure 1. In [7] the first Euler diagram generation algorithm was presented and further formalized in [6]. This work guaranteed the production of an Euler diagram that meets all of the wellformedness conditions in Fig.…”