NVenn: Generalized, quasi-proportional Venn and Euler diagrams

Abstract

Motivation: Venn and Euler diagrams are extensively used for the visualization of relationships between experiments and datasets. However, representing more than three datasets while keeping the proportions of each region is still not feasible with existing tools. Results: We present an algorithm to render all the regions of a generalized n-dimensional Venn diagram, while keeping the area of each region approximately proportional to the number of elements included. In addition, missing regions in Euler diagrams lead to simplified representations. The algorithm generates an n-dimensional Venn diagram and inserts circles of given areas in each region. Then, the diagram is rearranged with a dynamic, self-correcting simulation in which each set border is contracted until it contacts the circles inside. This algorithm is implemented in a C++tool (nVenn) with or without a web interface. The web interface also provides the ability to analyze the regions of the diagram.