Visualisation of sets using boat diagrams: a new form of rotationally symmetrical three-way Venn diagram

Abstract

Venn diagrams are a staple visualisation tool for presentation of data, concepts and sets. We present a novel three-way Venn diagram based on three closed polygonal curves resembling boat shapes, called ‘‘boat diagrams,’’ with two variants. We show that boat diagrams and the traditional three-way circular Venn diagram may be fully described using a size parameter that scales the diagrams, and a separation parameter that modifies their shape and the relative areas of the internal regions (triple-, double-, or non-intersecting). We investigated boat diagrams quantitatively by assessing relative areas of each region as a function of their separation parameter. Relative to each other, and to their analogous circular Venn diagram, boat diagrams behave differently with respect to their regions’ areas. For one variant, evenness across all seven internal regions (or three types of region) can be improved relative to the circular variant. We also compare them to other three-way Venn drawing tools across several criteria. We present two use cases (qualitative and quantitative) of science communication and one use case illustrating how they could be implemented as an educational tool, distinct from circular Venn diagrams. We have implemented an open-access online tool to explore the relative properties of these novel diagrams and export them for use in visualisation.