---
title: "Venn diagrams with eulerr"
author: "Johan Larsson"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Venn diagrams with eulerr}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.show = "hold",
  fig.width = 3.2,
  fig.aling = "center"
)
```

Venn diagrams are specialized Euler diagrams. Unlike Euler diagrams,
they require that all intersections are represented. In most
implementations---including **eulerr**'s---they are also not
area-proportional. 

The first requirement is often prohibitive in terms of interpretability since
we often waste a considerable amount of space on the diagram's canvas with
intersections that just as well might be represented by their absence.
An area-proportional Euler diagram is often much more intuitive and,
for relatively sparse inputs, much easier to interpret. The property
of being area-proportional may sometimes, however, be treacherous, at least
if the viewer isn't advised of the diagram's faults. 

In such instances, it is often better to give up on area-proportionality 
and use a Venn diagram. It might not be as easy on the eye, but at least
will be interpreted correctly.

**eulerr** only supports diagrams for up to 5 sets. Part of the reason is
practical. **eulerr** is built around ellipses and ellipses are only
good for Venn diagrams with at most 5 sets. The other part of the
reason has to do with usability. A five-set diagram is already 
stretching it in terms of what we can reasonably expect the viewer to
be able to decipher. And despite the hilarity of [banana-shaped six-set Venn diagrams](https://www.nature.com/articles/nature11241/figures/4), monstrosities like that are better left in the dark.

## Examples of Venn and Euler diagrams

We will now look at some Venn diagrams and their respective Euler diagrams.

```{r two}
library(eulerr)
set.seed(1)

s2 <- c(A = 1, B = 2)

plot(venn(s2))
plot(euler(s2), quantities = TRUE)
```

```{r three}
plot(venn(fruits[, 1:3]))
plot(euler(fruits[, 1:3], shape = "ellipse"), quantities = TRUE)
```

```{r four}
s4 <- list(a = c(1, 2, 3),
           b = c(1, 2),
           c = c(1, 4),
           e = c(5))
plot(venn(s4))
plot(euler(s4, shape = "ellipse"), quantities = TRUE)
```

```{r five}
plot(venn(organisms))
plot(euler(organisms, shape = "ellipse"), quantities = TRUE)
```

As you can see in the last plot, there are cases where Euler
diagrams can be misleading. Despite the algorithm attempting its best
to make the diagram area-proportional, the constraints imposed by the 
geometry of the ellipses prevent a perfect fit. This is probably
a case where a Venn diagram makes for a good alternative. In the author's
opinion, the opposite is true for the rest.