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A New Perspective on Drawing Venn Diagrams for Data Visualization

Bálint Csanády

TL;DR

VennFan addresses the readability challenges of high-arity Venn diagrams by replacing exponential amplitude decay with tunable decays and shaping, then projecting trig-based boundaries onto the unit disk in polar coordinates. It presents both sine- and cosine-based variants, connects the cosine form to Edwards' cogwheel construction, and introduces a label placement heuristic to maximize readability. Empirically, VennFan yields more balanced region areas than Edwards' cogwheels and remains readable up to around $n \sim 8$ with reasonable parameter choices, aided by an accessible Python implementation. This provides a practical, flexible framework for visualizing overlaps among many sets in domains like biology and annotated time-series data.

Abstract

We introduce VennFan, a method for generating $n$-set Venn diagrams based on the polar coordinate projection of trigonometric boundaries, resulting in Venn diagrams that resemble a set of fan blades. Unlike most classical constructions, our method emphasizes readability and customizability by using shaped sinusoids and amplitude scaling. We describe both sine- and cosine-based variants of VennFan and propose an automatic label placement heuristic tailored to these fan-like layouts. VennFan is available as a Python package (https://pypi.org/project/vennfan/).

A New Perspective on Drawing Venn Diagrams for Data Visualization

TL;DR

VennFan addresses the readability challenges of high-arity Venn diagrams by replacing exponential amplitude decay with tunable decays and shaping, then projecting trig-based boundaries onto the unit disk in polar coordinates. It presents both sine- and cosine-based variants, connects the cosine form to Edwards' cogwheel construction, and introduces a label placement heuristic to maximize readability. Empirically, VennFan yields more balanced region areas than Edwards' cogwheels and remains readable up to around with reasonable parameter choices, aided by an accessible Python implementation. This provides a practical, flexible framework for visualizing overlaps among many sets in domains like biology and annotated time-series data.

Abstract

We introduce VennFan, a method for generating -set Venn diagrams based on the polar coordinate projection of trigonometric boundaries, resulting in Venn diagrams that resemble a set of fan blades. Unlike most classical constructions, our method emphasizes readability and customizability by using shaped sinusoids and amplitude scaling. We describe both sine- and cosine-based variants of VennFan and propose an automatic label placement heuristic tailored to these fan-like layouts. VennFan is available as a Python package (https://pypi.org/project/vennfan/).
Paper Structure (9 sections, 7 equations, 19 figures)

This paper contains 9 sections, 7 equations, 19 figures.

Table of Contents

  1. Introduction
  2. Background
  3. The VennFan Construction
  4. Empirical Properties
  5. Theoretical Remarks
  6. Label placement
  7. Conclusions
  8. Recreating Edwards' Cogwheel Diagrams
  9. Additional VennFan diagrams

Figures (19)

  • Figure 1: Ellipsoidal Venn diagrams for $2 \le n \le 5$.
  • Figure 2: VennFan diagrams of overlaps between six different seizure annotators in EEG data.
  • Figure 3: Nice and simple Venn diagrams for $n=6$.
  • Figure 4: Examples of trigonometric (Smith) and cogwheel (Edwards) diagrams.
  • Figure 5: Linear decay on the sinusoidal Smith diagram.
  • ...and 14 more figures