---
title: "Combining repulsion and nudging"
subtitle: "Packages 'ggrepel' and 'ggpp' working as a team"
author: "Pedro J. Aphalo"
date: "`r Sys.Date()`"
output: 
  rmarkdown::html_vignette:
    toc: yes
vignette: >
  %\VignetteIndexEntry{Combining repulsion and nudging}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  markdown: 
    wrap: 72
---

```{r, include=FALSE, echo=FALSE}
library(knitr)
opts_chunk$set(fig.align = 'center', 
               fig.show = 'hold', fig.width = 7, fig.height = 4)
options(warnPartialMatchArgs = FALSE,
        tibble.print.max = 4,
        tibble.print.min = 4,
        dplyr.summarise.inform = FALSE)
```

## Introduction

The very popular R package 'ggrepel' does a great job at avoiding
overlaps among data labels and between them and observations plotted as
points. A difficulty that stems from the use of an algorithm based on
random displacements is that the final location of the data labels can
become more disordered than necessary. In addition when including smooth
regression lines the data labels may partly occlude the fitted line
and/or the confidence band.

Package 'ggpp' defines new position functions that save the starting
position like `position_nudge_repel()` does but come in multiple
flavors. Their use together with repulsive geometries from 'ggrepel'
makes it possible to give to the data labels an initial "push" in a
non-random direction. This helps a lot, much more than what I expect
initially, in obtaining a more orderly displacement by repulsion of the
data labels away from a cloud of observations or a line.

Another problem sometimes encountered when using position functions is
that combinations of pairs of displacements would be required. 'ggpp'
does define such new position functions which can also be used together
with the repulsive geometries from package 'ggrepel'.

Because of the naming convention used, the new position functions remain
fully compatible with all geometries that have a formal parameter
`position`. However, most examples below use geometries from packages
'ggrepel' or 'ggpp' to create a plot layer containing data labels.

## Preliminaries

As we will use text and labels on the plotting area we change the
default theme to an uncluttered one.

```{r, message = FALSE}
library(dplyr)
library(lubridate)
library(ggplot2)
library(ggpp)
library(grid)
# Is a compatible version of 'ggrepel' installed?
eval_ggrepel <- requireNamespace("ggrepel", quietly = TRUE) &&
  packageVersion("ggrepel") >= "0.9.2"
if (eval_ggrepel) library(ggrepel)

old_theme <- theme_set(theme_bw())
```

## Position functions and nudging

Nudging shifts deterministically the *x* and/or *y* coordinates of an
observation. This takes place early enough for the limits of the
corresponding scales be set based on the displaced positions. In
'ggplot2', position functions and consequently also geometries by
default apply no nudging.

Function `position_nudge()` from package 'ggplot2' applies the nudge, to
*x* and/or *y* data coordinates based directly on the values passed to
its parameters `x` and `y`. Passing arguments to the `nudge_x` and/or
`nudge_y` parameters of a geometry has the same effect, as these values
are passed to `position_nudge()` within the geometry's code. Geometries
also have a `position` parameter to which we can pass an expression
based on a *position function* which opens the door to more elaborate
approaches to nudging, as well as allowing other changes in coordinates
such as stacking.

We use `geom_point_s()` to exemplify what nudging does. The
black dots are the original positions and the red ones the nudged
positions, with the arrows of length 0.5 along _x_, showing the displacement
and its direction.

```{r}
ggplot(data.frame(x = 1:10, y = rnorm(10)), aes(x, y)) +
  geom_point() +
  geom_point_s(nudge_x = 0.5, colour = "red")
```

Function `position_nudge_keep()` keeps a copy of the original position making it
possible for geometries like `geom_point_s()` to draw connecting segments or
arrows.

Package 'ggpp' provides several new position functions to facilitate nudging.
All of them keep the original positions to allow links to be drawn. Some of
them, just simplify some use cases, e.g., `position_nudge_to()`, which accepts
the desired nudged coordinates directly, instead of as a displacement away from
the initial position. This allows to push data labels away from observations
into a row or column.

Other new position functions compute the nudge for individual observations based
on different criteria. For example by nudging away from a focal point, a line or
a curve. The focal point or line can be either supplied directly or fitted to
the observations. In `position_nudge_center()` and `position_nudge_line()`
described below, this reference alters only the direction (angle) along which
nudge is applied but not the extent of the shift. Advanced nudging works very
well, but only for some patterns of observations and may require manual
adjustment of positions, repulsion is more generally applicable but like
jittering is aleatory. Combining nudging and repulsion we can make repulsion
more predictable with little loss of its applicability.

These position functions can be used with any geometry but if segments joining
the nudged positions to the original ones are desired, only geometries from
packages 'ggrepel' or 'ggpp' can currently be used. Geometries
`geom_text_repel()` or `geom_label_repel()` from 'ggrepel' should be used when
repulsion is desired. Setting `max.iter = 0` in these functions disables
repulsion but allows the drawing of segments or arrows. Alternatively, several
geometries from 'ggpp' implement the drawing of connecting segments, but none
of them implement repulsion. Please see
the documentation for the different geometries from packages 'ggrepel' and
'ggpp' for the details.

As mentioned above, drawing of segments or arrows is made possible by position
functions storing in `data` both the nudged and original *x* and *y*
coordinates. The joint use of 'ggrepel' and 'ggpp' was made possible by
coordinated development of these packages and agreement on a naming convention
for storing the original position. Keeping both nudged and original positions
increases the size of the data, and consequently also the size of the ggplot
objects. Because of this, the position functions from 'ggpp' allow the keeping 
of the original positions to be disabled when needed.

### Connecting segments and arrows

Function `position_nudge_keep()` is like `ggplot2::position_nudge()` but
keeps (stores) the original *x* and *y* coordinates. It is similar to
function `position_nudge_repel()` but uses a different naming convention
for the coordinates. Both work with `geom_text_repel()` or
`geom_label_repel()` from package 'ggrepel' (\>= 0.9.2), but only
`position_nudge_keep()` can be used interchangeably with
`ggplot2::position_nudge()` with other geometries such as `geom_text()`.

```{r}
set.seed(84532)
df <- data.frame(
  x = rnorm(20),
  y = rnorm(20, 2, 2),
  l = paste("label:", letters[1:20])
)

```

With `position_nudge_keep()` from 'ggpp' used together with
`geom_text_repel()` or `geom_label_repel()` segments between a nudged
and/or repelled label and the original position (here indicated by a
point) are drawn. As shown here, passing `max.iter = 0` disables
repulsion.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y, label = l)) +
  geom_point() +
  geom_text_repel(position = position_nudge_keep(x = 0.3),
                  max.iter = 0)
```

With `position_nudge()` from 'ggplot2' used together with
`geom_text_repel()` or `geom_label_repel()` segments connecting a nudged
and/or repelled label and the original position (here indicated by a
point) are **not** drawn.

`position_nudge_keep()` and all other position functions from 'ggpp', described
below, can be used with all 'ggplot2' geometries but the original position will
be ignored and no connecting segment drawn unless the geometry has been designed
to work together with them. Currently, `geom_text_repel()` and
`geom_label_repel()` from 'ggrepel' and `geom_text_s()`, `geom_label_s()`,
`geom_point_s()`, `geom_plot()`, `geom_table()` and `geom_grob()` from package
'ggpp' draw connecting segments.

### Differences among geometries

The geometries from 'ggrepel' and 'ggpp' can interoperate. However, these
geometries are different in several respects. The simpler geometries from 'ggpp'
add a few features but lack several features compared to `geom_text_repel()` and
`geom_label_repel()`. First of all, the geometries from 'ggpp' do not support
repulsion. Those from 'ggpp' allow aesthetic mappings to be selectively applied
to the different components of the label and/or to segments. However, they do
not support aesthetics affecting the segments. While `geom_text_repel()` and
`geom_label_repel()` support curved connecting segments and arrows, the
geometries from 'ggpp' support only straight segments and arrows.

Another important difference is that the geometries from the two packages use by
default a different approach to justification of the displaced data labels. The
geometries from 'ggpp' by default justify the text or label to the nearest edge
to the original position (thus, away from it). This new justification approach
named `"position"` in 'ggpp' is not yet available in geometries defined in 
'ggrepel'.

```{r}
ggplot(df, aes(x, y, label = l)) +
  geom_point() +
  geom_text_s(position = position_nudge_keep(x = 0.1),
              min.segment.length = 0) +
  expand_limits(x = 2.3)
```

`geom_text_repel()` draws the segment by default from the centre of the
text and trims it to the edge of the text plus the padding. In contrast,
`geom_text_s()` uses justification to avoid the overlap and only the
default justification `"position"` and one of the edges, "left" in this
case, are currently usable as the untrimmed segment otherwise overplots
the text (not shown).

```{r}
ggplot(df, aes(x, y, label = l)) +
  geom_point() +
  geom_text_s(position = position_nudge_keep(x = 0.1),
              min.segment.length = 0,
              hjust = "left") +
  expand_limits(x = 2.3)
```

---

Each approach has advantages and disadvantages. The main difference is that with
`geom_text_s()` and `geom_label_s()` shorter nudging displacements may be needed
than with `geom_text_repel()` and `geom_label_repel()` when using their
respective default justification approaches.

---

A usually more problematic example is the labeling of loadings in PCA
and similar biplots.

```{r, eval=eval_ggrepel}
## Example data frame where each species' principal components have been computed.
df1 <- data.frame(
  Species = paste("Species",1:5),
  PC1     = c(-4, -3.5, 1, 2, 3),
  PC2     = c(-1, -1, 0, -0.5, 0.7)) 

ggplot(df1, aes(x=PC1, y = PC2, label = Species, colour = Species)) +
  geom_hline(aes(yintercept = 0), linewidth = .2) +
  geom_vline(aes(xintercept = 0), linewidth = .2) +
  geom_segment(aes(x = 0, y = 0, xend = PC1, yend = PC2), 
               arrow = arrow(length = unit(0.1, "inches"))) +
  geom_label_repel(position = position_nudge_center(x = 0.2, y = 0.01,
                                                    center_x = 0, center_y = 0),
                   label.size = NA,
                   label.padding = 0.1,
                   fill = rgb(red = 1, green = 1, blue = 1, alpha = 0.75)) +
  xlim(-5, 5) +
  ylim(-2, 2) +
  # Stadard settings for displaying biplots
  coord_fixed() +
  theme(legend.position = "none")
```

The use of `position_nudge_center()` together with repulsion, shown above,
results a much better plot than using only repulsion.

```{r}
ggplot(df1, aes(x=PC1, y = PC2, label = Species, colour = Species)) +
  geom_hline(aes(yintercept = 0), linewidth = .2) +
  geom_vline(aes(xintercept = 0), linewidth = .2) +
  geom_segment(aes(x = 0, y = 0, xend = PC1, yend = PC2), 
               arrow = arrow(length = unit(0.1, "inches"))) +
  geom_label_repel(label.size = NA,
                   label.padding = 0.1,
                   fill = rgb(red = 1, green = 1, blue = 1, alpha = 0.75)) +
  xlim(-5, 5) +
  ylim(-2, 2) +
  # Stadard settings for displaying biplots
  coord_fixed() +
  theme(legend.position = "none")
```

The use of `position_nudge_center()` together with repulsion, shown above,
results a much better plot than using only nudging. In this case, the default
justification to the center needs to be overidden.

```{r}
ggplot(df1, aes(x=PC1, y = PC2, label = Species, colour = Species)) +
  geom_hline(aes(yintercept = 0), linewidth = .2) +
  geom_vline(aes(xintercept = 0), linewidth = .2) +
  geom_segment(aes(x = 0, y = 0, xend = PC1, yend = PC2), 
               arrow = arrow(length = unit(0.1, "inches"))) +
  geom_label(position = position_nudge_center(x = 0.2, y = 0.01,
                                              center_x = 0, center_y = 0),
             label.size = 0,
             vjust = "outward", hjust = "outward",
             fill = rgb(red = 1, green = 1, blue = 1, alpha = 0.75)) +
  xlim(-5, 5) +
  ylim(-2, 2) +
  # Stadard settings for displaying biplots
  coord_fixed() +
  theme(legend.position = "none")
```

Of course, nudging and justification could be manually adjusted for each label,
but here we are concerned with approaches that avoid manual tweaking.

### Aligned data labels

Function `position_nudge_to()` nudges to a given position instead of
using the same shift for each observation. It can be used to align labels
for points that are not themselves aligned.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y, label = ifelse(x < 0.5, "", l) )) +
  geom_point() +
  geom_text_repel(position = 
                    position_nudge_to(x = 2.3),
                  min.segment.length = 0,
                  segment.color = "red",
                  arrow = arrow(length = unit(0.015, "npc")),
                  direction = "y") +
  expand_limits(x = 3)
```

By providing two values for nudging with opposite sign, we can add labels
alternating between sides. We use here `geom_text_s()` but other geometries
could have been used as well. How the data labels been closer together repulsion
would have been needed in addition to nudging.

```{r}
size_from_area <- function(x) {sqrt(max(0, x) / pi)}

df2 <- data.frame(b = exp(seq(2, 4, length.out = 10)))

ggplot(df2, aes(1, b, size = b)) + 
  geom_text_s(aes(label = round(b,2)),
              position = position_nudge_to(x = c(1.1, 0.9)),
              box.padding = 0.5) +
  geom_point() +
  scale_size_area() +
  xlim(0, 2) +
  theme(legend.position = "none")
```

It is also useful when labeling curves than end at different positions along
the *x* axis. In this example we avoid overlaps with repulsion along the _y_
axis. The data set used in this example is dynamic, so we use nudging to a
position that is dynamicaly computed from the data.

```{r, eval=eval_ggrepel}
keep <- c("Israel", "United States", "European Union", "China", "South Africa", "Qatar",
          "Argentina", "Chile", "Brazil", "Ukraine", "Indonesia", "Bangladesh")

data <- read.csv("https://raw.githubusercontent.com/owid/covid-19-data/master/public/data/vaccinations/vaccinations.csv")
data$date <- ymd(data$date)

data %>%
  filter(location %in% keep) %>%
  select(location, date, total_vaccinations_per_hundred) %>%
  arrange(location, date) %>%
  filter(!is.na(total_vaccinations_per_hundred)) %>%
  mutate(location = factor(location),
         location = reorder(location, total_vaccinations_per_hundred)) %>%
  group_by(location) %>% # max(date) depends on the location!
  mutate(label = if_else(date == max(date), 
                         as.character(location), 
                         "")) -> owid

ggplot(owid,
       aes(x = date, 
           y = total_vaccinations_per_hundred,
           color = location)) +
  geom_line() +
  geom_text_repel(aes(label = label),
                  size = 3,
                  position = position_nudge_to(x = max(owid$date) + days(30)),
                  segment.color = 'grey',
                  point.size = 0,
                  box.padding = 0.1,
                  point.padding = 0.1,
                  hjust = "left",
                  direction = "y") + 
  scale_x_date(expand = expansion(mult = c(0.05, 0.2))) +
  labs(title = "Cumulative COVID-19 vaccination doses administered per 100 people",
       y = "",
       x = "Date (year-month)") +
  theme_bw() +
  theme(legend.position = "none")
```

In the call to `position_nudge_to()` we passed a vector of length one as
argument for `y`, but both `x` and `y` also accept longer vectors. In other
words, this position function makes it possible manual positioning of text and
labels.

In the next example we decrease the forces used for repulsion and the
padding so that the labels remain close together. In this way, we can
label the observations on the rug of a combined point and rug plot.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y, label = round(x, 2))) +
  geom_point(size = 3) +
  geom_text_repel(position = position_nudge_to(y = -2.7), 
            size = 3,
            angle = 90,
            hjust = 0,
            box.padding = 0.05,
            min.segment.length = Inf,
            direction = "x",
            force = 0.1,
            force_pull = 0.1) +
  geom_rug(sides = "b", length = unit(0.02, "npc"))
```

### Clouds of observations

In many cases data are distributed as a cloud with decreasing density towards
edges. In some other cases, even with evely distributed observations, a certain
partly systematic pattern of displacement of data labels is visually more
attractive than a fully random one. In both cases, combining nudging and
repulsion is usually an effective approach.

We start with an examples showing a specific nudging pattern, and only later we
combine them with repulsion. Function `position_nudge_center()` can nudge
radially away from a focal point if both `x` and `y` are passed as arguments, or
towards opposite sides of a vertical or horizontal *virtual* boundary line if
only one of `x` or `y` is passed an argument. By default, the "center" is the
centroid computed using `mean()`, but other functions or numeric values can be
passed to override it. When data are sparse, such nudging may be effective in
avoiding label overlaps, and in achieving a visually pleasing positioning.

By default, split is away or towards the `mean()`. Here we allow
repulsion to separate the labels (compare with the previous plot).

```{r}
ggplot(df, aes(x, y, label = l)) +
  geom_vline(xintercept = 0, linetype = "dashed") +
  geom_point() +
  geom_point_s(position = 
                    position_nudge_center(x = 0.3, center_x = 0),
               colour = "red")
```

In this second example we use repulsion and add data labels instead of displaced 
points. In all cases nudging shifts the coordinates giving a new *x* and/or *y* position
that expands the limits of the corresponding scales to include the nudged
coordinate values, but not necessarily the whole of justified text or labels.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y, label = l)) +
  geom_vline(xintercept = 0, linetype = "dashed") +
  geom_point() +
  geom_text_repel(position = 
                    position_nudge_center(x = 0.3, center_x = 0),
                  min.segment.length = 0)
```

We set a different split point as a constant value.

```{r}
ggplot(df, aes(x, y)) +
  geom_vline(xintercept = 1, linetype = "dashed") +
  geom_point() +
  geom_point_s(position = 
                    position_nudge_center(x = 0.3, center_x = 1),
               colour = "red")
```

We set a different split point as the value computed by a function
function, by name.

```{r}
ggplot(df, aes(x, y)) +
  geom_vline(xintercept = median(df$x), linetype = "dashed") +
  geom_point() +
  geom_point_s(position = 
                    position_nudge_center(x = 0.3, center_x = median),
               colour = "red")
```

We set a different split point as the value computed by an anonymous
function. Here we split on the first quartile along *x* and _y_ = 2.

```{r}
ggplot(df, aes(x, y)) +
  geom_point() +
  geom_point_s(position = 
                    position_nudge_center(x = 0.3, y = 0.3,
                                          center_x = function(x) {
                                            quantile(x, 
                                                     probs = 1/4, 
                                                     names = FALSE)
                                          },
                                          center_y = 2,
                                          direction = "split"),
               colour = "red")
```

The labels can be rotated as long as the geometry used supports this.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y, label = l)) +
  geom_point() +
  geom_text_repel(angle = 90,
                  position = 
                    position_nudge_center(y = 0.1,
                                          direction = "split"))
```

By requesting nudging along *x* and *y* and setting `direction = "split"`
nudging is applied according to the quadrants centred on the centroid of the
data.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y)) +
  stat_centroid(shape = "+", size = 5, colour = "red") +
  geom_point() +
  geom_point_s(position = 
                    position_nudge_center(x = 0.2,
                                          y = 0.3,
                                          direction = "split"),
               colour = "red")
```


```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y, label = l)) +
  geom_point() +
  geom_text_repel(position = 
                    position_nudge_center(x = 0.1,
                                          y = 0.15,
                                          direction = "split"))
```

With `direction = "radial"`, the distance nudged away from the center is
the same for all labels.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y)) +
  stat_centroid(shape = "+", size = 5, colour = "red") +
  geom_point() +
  geom_point_s(position = 
                    position_nudge_center(x = 0.25,
                                          y = 0.4,
                                          direction = "radial"),
               colour = "red")
```


```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y, label = l)) +
  geom_point() +
  geom_text_repel(position = 
                    position_nudge_center(x = 0.25,
                                          y = 0.4,
                                          direction = "radial"),
                  min.segment.length = 0)
```

As shown above for `direction = "split"` we can set the coordinates of
the center also with `direction = "radial"`.

We can also set the justification of the text labels although repulsion
usually works best with labels justified at the centre, which is the
default in `geom_text_repel()`.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y, label = l)) +
  geom_point() +
  geom_text_repel(position = 
                    position_nudge_center(x = 0.125,
                                          y = 0.25,
                                          center_x = 0,
                                          center_y = 0,
                                          direction = "radial"),
                  min.segment.length = 0,
                  hjust = "outward", vjust = "outward") +
  expand_limits(x = c(-2.7, +2.3))
```

Nudging along one axis, here *x*, and setting the repulsion `direction`
along the other axis, here *y*, tends to give a pleasant arrangement of
labels.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y, label = l)) +
  geom_point() +
  geom_text_repel(position = 
                    position_nudge_center(x = 0.2,
                                          center_x = 0,
                                          direction = "split"),
                  aes(hjust = "outward"),
                  direction = "y",
                  min.segment.length = 0) +
  expand_limits(x = c(-3, 3))
```


When some regions have a high density of observations we may wish to only
label those in the lower density regions. To automate this, we can use
statistics `stat_dens2d_labels()` or `stat_dens1d_labels()` that replace
the labels with `""` but retain all rows in data so that repulsion away
from all points is achieved. In contrast, `stat_dens2d_filter()` or 
`stat_dens1d_filter()` subset `data` using identical criteria.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, y, label = l)) +
  geom_point() +
  stat_dens2d_labels(geom = "text_repel",
                     keep.fraction = 1/3,
                     position = 
                       position_nudge_center(x = 0.2,
                                             center_x = 0,
                                             direction = "split"),
                     aes(hjust = ifelse(x < 0, 1, 0)),
                     direction = "y",
                     min.segment.length = 0) +
  stat_dens2d_filter(geom = "point",
                     keep.fraction = 1/3,
                     shape = "circle open", size = 3) +
  expand_limits(x = c(-3, 3))
```

We create a set of example data with a denser distribution.

```{r}
random_string <- function(len = 3) {
paste(sample(letters, len, replace = TRUE), collapse = "")
}

# Make random data.
set.seed(1001)
d <- tibble::tibble(
  x = rnorm(100),
  y = rnorm(100),
  group = rep(c("A", "B"), c(50, 50)),
  lab = replicate(100, { random_string() })
)
```


```{r, eval=eval_ggrepel}
ggplot(data = d, aes(x, y, label = lab, colour = group)) +
  geom_point() +
  stat_dens2d_labels(geom = "text_repel", 
                     keep.fraction = 0.45)
```

With `geom_label_repel` one usually needs to use a smaller value for
`keep.fracton`, or a smaller `size`, as labels use more space on the
plot than the test alone.

Additional arguments can be used to change the angle and position of the
text, but may give unexpected output when labels are long as the
repulsion algorithm "sees" always a rectangular bounding box that is not
rotated. With short labels or angles that are multiples of 90 degrees,
there is no such problem. Please, see the documentation for
`ggrepel::geom_text_repel` and `ggrepel::geom_label_repel` for the
various ways in which both repulsion and formatting of the labels can be
adjusted.

Using `NA` as argument to `label.fill` makes the observations with
labels set to `NA` *incomplete*, and such rows in data are skipped when
rendering the plot, before the repulsion algorithm is active. This can
lead to overlap between text and points corresponding to unlabelled
observations. Whether points are occluded depends on the order of layers
and transparency, the occlusion can remain easily unnoticed with
`geom_label` and `geom_label_repel`. We keep `geom_point` as the topmost
layer to ensure that all observations are visible.

```{r, eval=eval_ggrepel}
ggplot(data = d, aes(x, y, label = lab, colour = group)) +
  stat_dens2d_labels(geom = "label_repel", 
                     keep.fraction = 0.2, 
                     label.fill = NA) +
    geom_point()
```

The 1D versions work similarly but assess the density along only one of
_x_ or _y_. In other respects than `orientation` and the parameters passed
internally to `stats::density()` the examples given earlier for
`stat_dens2d_labels()` also apply `stat_dens1d_labels()`.

An example for a plot based on an enhancement suggested in an issue raised at
GitHub by Michael Schubert, made possible by parameter `keep.these` added for
this and similar use cases.

```{r}
library(ggplot2)
library(ggpp)
library(ggrepel)
syms = c(letters[1:5], LETTERS[1:5], 0:9)
labs = do.call(paste0, expand.grid(syms, syms))
dset = data.frame(x=rnorm(1e3), y=rnorm(1e3), label=sample(labs, 1e3, replace=TRUE))
```

```{r}
ggplot(dset, aes(x=x, y=y, label = label)) +
  geom_point(colour = "grey85") +
  stat_dens2d_filter(geom = "text_repel",
                     position = position_nudge_centre(x = 0.1, 
                                                      y = 0.1, 
                                                      direction = "radial"),
                     keep.number = 50,
                     keep.these = c("aA", "bB", "cC"),
                     min.segment.length = 0) +
  theme_bw()
```

### Lines, curves and observations along them

Function `position_nudge_line()` nudges away from a line, which can be a
user supplied straight line as well as a smooth spline or a polynomial
fitted to the observations themselves. The nudging is away and
perpendicular to the local slope of the straight or curved line. It
relies on the same assumptions as linear regression, assuming that *x*
values are not subject to error. This in most cases prevents labels from
overlapping a curve fitted to the data, even if not exactly based on the
same model fit. When observations are sparse, this may be enough to
obtain a nice arrangement of data labels, otherwise, it can be used in
combination with repulsive geometries. 

```{r}
set.seed(16532)
df <- data.frame(
  x = -10:10,
  y = (-10:10)^2,
  yy = (-10:10)^2 + rnorm(21, 0, 4),
  yyy = (-10:10) + rnorm(21, 0, 4),
  l = letters[1:21]
)
```

The first, simple example shows that `position_nudge_line()` has shifted
the direction of the nudging based on the alignment of the observations
along a line. One could, of course, have in this case passed suitable
values as arguments to *x* and *y* using `position_nudge()` from package
'ggplot2'. However, `position_nudge_line()` will work without change
with curves or with observations not exactly falling on a line.

In the plots that follow the original positions are shown in black and
the nudged ones in red, with an arrow showing the displacement introduced
by nudging.

```{r}
ggplot(df, aes(x, 2 * x, label = l)) +
  geom_point() +
  geom_abline(intercept = 0, slope = 2, linetype = "dotted") +
  geom_point_s(position = position_nudge_line(x = -1, y = -2),
               colour = "red")
```

With observations with variation in *y*, a linear model fit may
need to be used. In this case fitted twice, once in `stat_smooth()` and
once in `position_nudge_line()`.

```{r}
ggplot(subset(df, x >= 0), aes(x, yyy)) +
  geom_point() +
  stat_smooth(method = "lm", formula = y ~ x) +
  geom_point_s(position = position_nudge_line(x = 0, y = 1.2,
                                              method = "lm",
                                              direction = "split"),
               colour = "red")
```

With lower variation in *y*, we can pass to `line_nudge` a multiplier to
keep labels outside of the confidence band.

```{r}
ggplot(subset(df, x >= 0), aes(y, yy)) +
  geom_point() +
  stat_smooth(method = "lm", formula = y ~ x) +
  geom_point_s(position = position_nudge_line(method = "lm",
                                              x = 1.5, y = 3, 
                                              line_nudge = 2.75,
                                              direction = "split"),
               colour = "red")
```

If we want the nudging based on an arbitrary straight line not computed
from `data`, we can pass the intercept and slope in a numeric vector of
length two as an argument to parameter `abline`.

```{r}
ggplot(subset(df, x >= 0), aes(y, yy)) +
  geom_point() +
  geom_abline(intercept = 0, slope = 1, linetype = "dotted") +
  geom_point_s(position = position_nudge_line(abline = c(0, 1),
                                              x = 3, y = 6, 
                                              direction = "split"),
               colour = "red")
```

More frequently observations follow curves rather than straight lines. If
observations follow exactly a simple curve nudging away from the curve with
`position_nudge_line()` can be very effective. In this case, the interpretation
of values passed as arguments to parameters `x` and `y` of the position function
differs from that in `position_nudge()`: positive values correspond to above and inside the curve and negative ones, the
opposite direction.

The next plot shows the effect of nudging with the original positions
as black dots and the nudged positions as red dots.

```{r}
ggplot(df, aes(x, y)) +
  geom_point() +
  geom_line(linetype = "dotted") +
  geom_point_s(position = position_nudge_line(x = 0.6, y = 6),
               colour = "red")
```

Negative values passed as arguments to `x` and `y` correspond to labels
below and outside the curve.

```{r}
ggplot(df, aes(x, y)) +
  geom_point() +
  geom_line(linetype = "dotted") +
  geom_point_s(position = position_nudge_line(x = -0.6, y = -6),
               colour = "red")
```

When the observations include random variation along *y*, it is
important that the smoother used for the line added to a plot and that
passed to `position_nudge_line()` are similar. By default
`stat_smooth()` uses `"loess"` and `position_nudge_line()` with method
`"spline"`, `smooth.sline()`, which are a good enough match.

```{r}
ggplot(df, aes(x, yy)) +
  geom_point() +
  stat_smooth(method = "loess", formula = y ~ x) +
  geom_point_s(position = position_nudge_line(x = 0.6, y = 6,
                                              direction = "split"),
               colour = "red")
```

We can use other geometries, or rather we need to use a repulsive
geometry when the label text is long or the labels are crowded near the
line. Combining repulsion and computed nudging is effective.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, yy)) +
  geom_point() +
  stat_smooth(method = "loess", formula = y ~ x) +
  geom_label_repel(aes(y = yy, label = paste("point", l)),
                   position = position_nudge_line(x = 0.6, 
                                                  y = 8,
                                                  direction = "split"),
                   box.padding = 0.3,
                   min.segment.length = 0)
```

We can see by comparing the plot above with that below, that combining
nudging away from a line with repulsion results in a more pleasant
positioning of the data labels.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, yy)) +
  geom_point() +
  stat_smooth(method = "loess", formula = y ~ x) +
  geom_label_repel(aes(y = yy, label = paste("point", l)),
                  box.padding = 0.5,
                  min.segment.length = 0)
```

Nudging alone, as shown next, results in overlaps and clipping.

```{r}
ggplot(df, aes(x, yy)) +
  geom_point() +
  stat_smooth(method = "loess", formula = y ~ x) +
  geom_label_s(aes(y = yy, label = paste("point", l)),
               position = position_nudge_line(x = 0.6, 
                                              y = 8,
                                              direction = "split"),
               box.padding = 0,
               min.segment.length = 0)
```

While `box.padding` in `geom_text_repel()` controls the separation among data 
labels as well as between data labels and points, in `geom_label_s()` it 
controls only the distance between the end of the segment and the data label.

---

When fitting a polynomial, `"lm"` should be the argument passed to
`method` and a model formula preferably based on `poly()`, setting
`raw = TRUE`, as argument to `formula`.

*Currently no other methods are implemented in* `position_nudge_line()`.

---

In the case of data labels that are small, a single character in the next
example, we also benefit from nudging if they are near a fitted line. 
Nudging plus repulsion, shown next, will be compared to
alternatives. In this case we assume no linking segments are desired as
there is enough space for the data labels to remain near the observations.

```{r}
ggplot(df, aes(x, yy)) +
  geom_point() +
  stat_smooth(method = "lm", 
              formula = y ~ poly(x, 2, raw = TRUE)) +
  geom_text_repel(aes(y = yy, label = l),
                  position = position_nudge_line(method = "lm",
                                                 formula = y ~ poly(x, 2, raw = TRUE),
                                                 x = 0.5, 
                                                 y = 5,
                                                 direction = "split"),
                  box.padding = 0.25,
                  min.segment.length = Inf)
```

Using nudging alone there is little difference, but there is always the posibility of
overlaps, so using nudging plus repulsion as above is safer. 

```{r}
ggplot(df, aes(x, yy)) +
  geom_point() +
  stat_smooth(method = "lm", 
              formula = y ~ poly(x, 2, raw = TRUE)) +
  geom_text(aes(y = yy, label = l),
            position = position_nudge_line(method = "lm",
                                           formula = y ~ poly(x, 2, raw = TRUE),
                                           x = 0.5, 
                                           y = 5,
                                           direction = "split"))
```

Repulsion without nudging as shown below is unsatisfactory in this case, i.e.,
adding nudging displaces the data labels in the desired direction. Compare the
plot below using no nudging with the one above.

```{r, eval=eval_ggrepel}
ggplot(df, aes(x, yy)) +
  geom_point() +
  stat_smooth(method = "lm", 
              formula = y ~ poly(x, 2, raw = TRUE)) +
  geom_text_repel(aes(y = yy, label = l),
                  box.padding = 0.25,
                  min.segment.length = Inf)
```

## Combined position functions

Using `position_stacknudge()` together `geom_label_repel()` makes it
possible to use repulsion for labeling sections of stacked column plots.

```{r, eval=eval_ggrepel}
df <- tibble::tribble(
  ~y, ~x, ~grp,
  "a", 1,  "some long name",
  "a", 2,  "other name",
  "b", 1,  "some name",
  "b", 3,  "another name",
  "b", -1, "some long name"
)

ggplot(data = df, aes(x, y, group = grp)) +
  geom_col(aes(fill = grp), width=0.5) +
  geom_vline(xintercept = 0) +
  geom_label_repel(aes(label = grp),
                   position = position_stacknudge(vjust = 0.5, y = 0.4),
                   label.size = NA)
```

## Acknowledgements

I warmly thank Kamil Slowikowski for agreeing to make changes in
'ggrepel' that make the use of 'ggrepel' together with 'ggpp' possible
and smooth. This document shows some use examples, but surely new ones
will be found by users of R and 'ggplot2'.
