Plot points outside grid as arrows pointing to data with ggplot2 in R

Question

I am generating maps with world-scale data, and then zooming in to certain regions. On the zoomed-in view, I would like to show that there are other data points outside the bounding box, by putting arrowheads that point from the center of the box to where the data point is in the outside world.

Note: I do not need it to be a "great circle" path, just XY vectors in Mercator projection, because I imagine this will be useful for "normal" plots as well.

As an example, here is the world map showing the extent of the data:

And here is the zoomed in view, with magenta arrows manually added to show what I would like to generate.

Below is the code and data I am using to generate these two basic plots. What I need is a way to generate the arrowheads.

require(ggplot2)

te = structure(list(lat = c(33.7399, 32.8571, 50.2214, 36.96263, 33.5835, 
33.54557, 47.76147, 48, 59.40289, 35.93411, 32.87962, 38.3241, 
50.03844, 37.44, 50.07774, 50.26668, 36.5944), lng = c(-118.37608, 
-117.25746, -5.3865, -122.00809, -117.86159, -117.79805, -124.45055, 
-126, -146.35157, -122.931472, -117.25285, -123.07331, -5.26339, 
25.4, -5.709894, -3.86828, -121.96201)), .Names = c("lat", "lng"
), class = "data.frame", row.names = c(NA, -17L))

all_states = map_data("world")

# world version:
wp = ggplot() + 
      geom_polygon(data = all_states, aes(x = long, y = lat, group = group), colour = "gray",
                   fill = "gray") +
      coord_cartesian(ylim = c(0, 80), xlim = c(-155, 45)) + 
      geom_point(data = te, aes(x = lng, y = lat), color = "blue", size = 5,alpha = 0.6)

print(wp)

#states plot
sp = ggplot() +
      geom_polygon(data = all_states, aes(x = long, y = lat, group = group), colour = "gray", fill = "gray") +
      coord_cartesian(ylim = c(30, 52), xlim = c(-128, -114)) + 
      geom_point(data = te, aes(x = lng, y = lat), color = "blue", size = 5, alpha = 0.6) 

print(sp)

Yon

you could add a geom_segment layer, they provide optional arrow heads and with sufficiently small distance it's the only thing visible. – Duester

Look at this blog post, it might give you some ideas. – Urine

Thanks for the comments. It is not generating the arrow that I am worried about, but figuring out how to plot them in the right location and orientation. Worst-case scenario I will have to make a function that checks for points outside the bounding box, then calculates vectors for them, solves for the x.y of where that line intersects the side of the box, and then plot rotated triangles at those points. But I was hoping there was a library or feature that might already do this..! – Yon

Do you need the arrows to point across the 180 degree longitude line, or to always point in the direction on a flat projected map? – Incarcerate

I guess the shortest distance? I see your point, but typically in my data set, they would not cross 180, so flat projected map is acceptable. They don't have to be a great circle or anything. Just straight line mercator. – Yon

The tricky bit might be that ggplot only decides on the bounding box when it plots things, so you don't know where the edge coordinates are until you've added the arrows, and to add the arrows in the right place you need the edge coordinates... Its a catch-22... I have an idea... – Incarcerate

I am manually defining the bounding box in all anticipated cases. Those could/should probably be broken out as variables in the example code to make this more clear. – Yon

@claus-wilke do you happen to have an easy way to do this? – Yon

Answer 1

This solution uses sp and rgeos packages to manipulate spatial data, the main crux being intersecting lines and a box polygon to get the edge points for arrows. Then if you draw arrows with geom_segment and zero width, the line is invisible and only the arrow head remains.

This function computes the line-box intersections:

boxint <- function(xlim, ylim, xp, yp){
    ## build box as SpatialPolygons
    box = cbind(xlim[c(1,2,2,1,1)],
        ylim[c(1,1,2,2,1)])
    box <- sp::SpatialPolygons(list(sp::Polygons(list(sp::Polygon(box)),ID=1)))

    ## get centre of box
    x0=mean(xlim)
    y0=mean(ylim)

    ## construct line segments to points
    sl = sp::SpatialLines(
        lapply(1:length(xp),
               function(i){
                   sp::Lines(list(sp::Line(cbind(c(x0,xp[i]),c(y0,yp[i])))),ID=i)
               }
               )
        )
    ## intersect lines segments with boxes to make points
    pts = rgeos::gIntersection(sl, as(box, "SpatialLines"))
    as.data.frame(sp::coordinates(pts), row.names=1:length(xp))
}

And this returns the geom with arrows:

wherelse <- function(xlim, ylim, points){
    ## get points outside bounding box
    outsides = points[!(
        points$lng>=xlim[1] &
            points$lng <= xlim[2] &
                points$lat >= ylim[1] &
                    points$lat <= ylim[2]),]
    npts = nrow(outsides)
    ## get centre point of box
    x = rep(mean(xlim),npts)
    y = rep(mean(ylim),npts)

    ## compute box-point intersections
    pts = boxint(xlim, ylim, outsides$lng, outsides$lat)
    pts$x0=x
    pts$y0=y
    ## create arrow segments as invisible lines with visible arrowheads
    ggplot2::geom_segment(data=pts, aes(x=x0,y=y0,xend=x,yend=y),
       lwd=0, arrow=grid::arrow(length=unit(0.5,"cm"),
       type="closed"),col="magenta")
}

So your example, the basic plot is:

sp = ggplot() + 
  geom_polygon(
   data=all_states, 
    aes(x=long, y=lat, group = group),colour="gray",fill="gray" ) + 
    coord_cartesian(ylim=c(30, 52), xlim=c(-128,-114)) + 
    geom_point(data=te,aes(x=lng,y=lat),color="blue",size=5,alpha=0.6)

and then add the arrows with:

sp + wherelse(c(-128,-114), c(30,52), te)

Not sure if there's an option to draw arrows exactly like you want them though!

Incarcerate

Re-visiting this years later, I even like the name of your function :^) Thanks. – Yon

Answer 2

Here is my attempt. This is the closest I got. I used gcIntermediate() for calculating the shortest distance between the center point of your US map and the data points which stay outside of the bbox. Hence, the arrow positions may not be something you want. My hope is that somebody else would deliver a better solution based on this attempt.

I first arranged your df (i.e., te) with the center point in the US zoomed map. I then chose data points which are not in the bbox of the US map. Then, add two columns to indicate the center point of the US map. Rename two columns and calculate the shortest distance with gcIntermediate.

library(dplyr)
library(ggplot2)
library(geosphere)

filter(te, !between(lng, -128, -114) | !between(lat, 30, 52)) %>%
mutate(start_long = (-128 - 114) / 2,
       start_lat = (30 + 52) / 2) %>%
rename(end_lat = lat, end_long = lng) %>%
do(fortify(as(gcIntermediate(.[,c("start_long", "start_lat")],
                             .[,c("end_long", "end_lat")],
                             100,
                             breakAtDateLine = FALSE,
                             addStartEnd = TRUE,
                             sp = TRUE), "SpatialLinesDataFrame"))) -> foo

foo contains 100 data points to draw respective line. I chose data points which stay close to the bbox boundary. I was specifically looking for two data points for each line so that I could use geom_segment() later. I admit that I played with the filter condition a bit. In the end, I did not subset data using lat in this case.

filter(foo, between(long, -128, -126.5) | between(long, -115.5, -114)) %>%
group_by(group) %>%
slice(c(1,n())) -> mydf

In the next step, I rearranged the data frame based on this link

mutate(mydf, end_long = lag(long), end_lat = lag(lat)) %>%
slice(n()) -> mydf2

Finally I drew the map with arrows. I hope this will provide some kind of base for you. I also hope that other SO users will provide better solutions.

ggplot() +
geom_polygon(data = all_states, aes(x = long, y = lat, group = group),
             colour = "gray", fill = "gray" ) +
coord_cartesian(ylim = c(30, 52), xlim = c(-128,-114)) +
geom_point(data = te, aes(x = lng,y = lat), color = "blue", size = 5,alpha = 0.6) +
geom_segment(data = mydf2, aes(x = end_long, xend = long,
                               y = end_lat, yend = lat, group = group),
                               arrow = arrow(length = unit(0.2, "cm"), ends = "last"))

Galoot

Thanks jazzurro. I like aspects of your solution and only wish that it calculated the point of intersection with the border, rather than using the closest one from among 100 points. – Yon

@Yon Thanks for your comment. I wanted to help you with things that I know. You got a very helpful answer in the end. I a very happy for you! – Galoot