## 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.