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## Labeling Euler diagram overlaps

The purpose of my R package eulerr

is to fit and *visualize* Euler diagrams. Besides the various intricacies

involved in fitting the diagrams, there are many interesting

problems involved in their visualization. One of these is the labeling of the

overlaps.

Naturally, simply positioning the labels at the shapes’ centers

fails more often than not. Nevertheless, this stategy is employed by

**venneuler**, for instance, and the plots usually demand

manual tuning.

```
# an example set combination
s <- c("SE" = 13, "Treat" = 28, "Anti-CCP" = 101, "DAS28" = 91,
"SE&Treat" = 1, "SE&DAS28" = 14, "Treat&Anti-CCP" = 6,
"SE&Anti-CCP&DAS28" = 1)
library(venneuler, quietly = TRUE)
fit_venneuler <- venneuler(s)
plot(fit_venneuler)
```

Up til now, I solved this in **eulerr** by, for each overlap,

filling one of the involved shapes (circles or ellipses) with points

and then numerically optimizing the location of the point using a

Nelder–Mead optimizer. However, given that the solution to

finding the distance between a point and an ellipse—at least one that

is rotated—itself requires a numerical solution (Eberly 2013), this procedure

turned out to be quite inefficient.

## The promise of polygons

R has powerful functionality for plotting in general, but lacks

capabilities for drawing ellipses using curves. High-resolution

polygons are thankfully a readily available remedy for this and have

since several version back been used also in **eulerr**.

The upside of using polygons, however, are that they are usually

much easier, even if sometimes inefficient,

to work with. For instance, they make constructing separate shapes

for each overlap a breeze using the polyclip package (Johnson and Baddeley 2018).

And because basically all shapes in digital maps are polygons,

there happens to exist a multitude of other useful tools to deal with

a wide variety of tasks related to polygons. One of these turned out

to be precisely what I needed: polylabel (Mapbox 2018) from the Mapbox suite.

Because the details of the library

have already been explained elsewhere

I will spare you the details, but briefly put it uses quadtree

binning to divide the polygon into square bins, pruning away dead-ends.

It is inefficient and will, according to the authors, find

a point that is “guaranteed to be a global optimum within the given precision”.

Because it appeared to be such a valuable tool for R users, I decided

to create a wrapper for the c++ header for polylabel and

bundle it as a package for R users.

```
# install.packages("polylabelr")
library(polylabelr)
# a concave polygon with a hole
x <- c(0, 6, 3, 9, 10, 12, 4, 0, NA, 2, 5, 3)
y <- c(0, 0, 1, 3, 1, 5, 3, 0, NA, 1, 2, 2)
# locate the pole of inaccessibility
p <- poi(x, y, precision = 0.01)
plot.new()
plot.window(range(x, na.rm = TRUE), range(y, na.rm = TRUE), asp = 1)
polypath(x, y, col = "grey90", rule = "evenodd")
points(p, cex = 2, pch = 16)
```

The package is availabe on cran,

the source code is located at https://github.com/jolars/polylabelr and

is documented at https://jolars.github.io/polylabelr/.

## Euler diagrams

To come back around to where we started at, **polylabelr** has now been

employed in the development branch

of **eulerr** where it is used to quickly and appropriately

figure out locations for the labels of the diagram.

```
library(eulerr)
plot(euler(s))
```

## References

Eberly, David. 2013. “Distance from a Point to an Ellipse, an Ellipsoid, or a Hyperellipsoid.” *Geometric Tools*. https://www.geometrictools.com/Documentation/DistancePointEllipseEllipsoid.pdf.

Johnson, Angus, and Adrian Baddeley. 2018. “polyclip: Polygon Clipping.” https://CRAN.R-project.org/package=polyclip.

Mapbox. 2018. “A Fast Algorithm for Finding the Pole of Inaccessibility of a Polygon (in JavaScript and C++): Mapbox/Polylabel.” Mapbox.

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