  Creating comprehensible visualizations of highly overlapping set-typed data
is a challenging task due to its complexity. To facilitate insights into set
connectivity and to leverage semantic relations between intersections, we
propose a fast two-step layout technique for Euler diagrams that are both
well-matched and well-formed. Our method conforms to established form
guidelines for Euler diagrams regarding semantics, aesthetics, and readability.
First, we establish an initial ordering of the data, which we then use to
incrementally create a planar, connected, and monotone dual graph
representation. In the next step, the graph is transformed into a circular
layout that maintains the semantics and yields simple Euler diagrams with
smooth curves. When the data cannot be represented by simple diagrams, our
algorithm always falls back to a solution that is not well-formed but still
well-matched, whereas previous methods often fail to produce expected results.
We show the usefulness of our method for visualizing set-typed data using
examples from text analysis and infographics. Furthermore, we discuss the
characteristics of our approach and evaluate our method against
state-of-the-art methods.
