How to draw connecting routes on map with R and great circles

This post explains how to draw connection lines between several localizations on a map, using R. The method proposed here relies on the use of the gcIntermediate function from the geosphere package. Instead of making straight lines, it offers to draw the shortest routes, using great circles. A special care is given for situations where cities are very far from each other and where the shortest connection thus passes behind the map.

First we need to load 3 libraries. Maps allows to draw the background map, and geosphere provides the gcintermediate function.

library(tidyverse)
library(maps)
library(geosphere)

1- Draw an empty map

This is easily done using the ‘maps’ package. You can see plenty of other maps made with R in the map section of the R graph gallery.

par(mar=c(0,0,0,0))
map('world',col="#f2f2f2", fill=TRUE, bg="white", lwd=0.05,mar=rep(0,4),border=0, ylim=c(-80,80) )

2- Add 3 cities

First we create a data frame with the coordinates of Buenos Aires, Melbourne and Paris

Buenos_aires=c(-58,-34)
Paris=c(2,49)
Melbourne=c(145,-38)
data=rbind(Buenos_aires, Paris, Melbourne) %>% as.data.frame()
colnames(data)=c("long","lat")

Then add it to the map using the ‘points’ function:

points(x=data$long, y=data$lat, col="slateblue", cex=3, pch=20)

4- Show connection between them

Now we can connect cities drawing the shortest route between them. This is done using great circles, what gives a better visualization than using straight lines. This technique has been proposed by Nathan Yau on FlowingData

# Connection between Buenos Aires and Paris
inter <- gcIntermediate(Paris,  Buenos_aires, n=50, addStartEnd=TRUE, breakAtDateLine=F)             
lines(inter, col="slateblue", lwd=2)

# Between Paris and Melbourne
inter <- gcIntermediate(Melbourne,  Paris, n=50, addStartEnd=TRUE, breakAtDateLine=F)             
lines(inter, col="slateblue", lwd=2)

5 – Correcting gcIntermediate

If we use the same method between Melbourne and Buenos Aires, we get this disappointing result:

What happens is that gcintermediate follows the shortest path, which means it will go East from Australia until the date line, break the line and come back heading East from the pacific to South America. Because we do not want to see the horizontal line, we need to plot this connection in 2 times.

To do so we can use the following function, which breaks the line in 2 sections when the distance between 2 points is longer than 180 degrees.

plot_my_connection=function( dep_lon, dep_lat, arr_lon, arr_lat, ...){
	inter <- gcIntermediate(c(dep_lon, dep_lat), c(arr_lon, arr_lat), n=50, addStartEnd=TRUE, breakAtDateLine=F)             
	inter=data.frame(inter)
	diff_of_lon=abs(dep_lon) + abs(arr_lon)
	if(diff_of_lon > 180){
		lines(subset(inter, lon>=0), ...)
		lines(subset(inter, lon<0), ...)
	}else{
		lines(inter, ...)
		}
	}

Let’s try it!

map('world',col="#f2f2f2", fill=TRUE, bg="white", lwd=0.05,mar=rep(0,4),border=0, ylim=c(-80,80) )
points(x=data$long, y=data$lat, col="slateblue", cex=3, pch=20)

plot_my_connection(Paris[1], Paris[2], Melbourne[1], Melbourne[2], col="slateblue", lwd=2)
plot_my_connection(Buenos_aires[1], Buenos_aires[2], Melbourne[1], Melbourne[2], col="slateblue", lwd=2)
plot_my_connection(Buenos_aires[1], Buenos_aires[2], Paris[1], Paris[2], col="slateblue", lwd=2)

6 – Apply it to several pairs of cities

Let’s consider 8 cities:

data=rbind(
	Buenos_aires=c(-58,-34),
	Paris=c(2,49),
	Melbourne=c(145,-38),
	Saint.Petersburg=c(30.32, 59.93),
	Abidjan=c(-4.03, 5.33),
	Montreal=c(-73.57, 45.52),
	Nairobi=c(36.82, -1.29),
	Salvador=c(-38.5, -12.97)
	)  %>% as.data.frame()
colnames(data)=c("long","lat")

We can generate all pairs of coordinates

all_pairs=cbind(t(combn(data$long, 2)), t(combn(data$lat, 2))) %>% as.data.frame()
colnames(all_pairs)=c("long1","long2","lat1","lat2")

And plot every connections:

# background map
par(mar=c(0,0,0,0))
map('world',col="#f2f2f2", fill=TRUE, bg="white", lwd=0.05,mar=rep(0,4),border=0, ylim=c(-80,80) )

# add every connections:
for(i in 1:nrow(all_pairs)){
	plot_my_connection(all_pairs$long1[i], all_pairs$lat1[i], all_pairs$long2[i], all_pairs$lat2[i], col="skyblue", lwd=1)
	}

# add points and names of cities
points(x=data$long, y=data$lat, col="slateblue", cex=2, pch=20)
text(rownames(data), x=data$long, y=data$lat,  col="slateblue", cex=1, pos=4)

7 – An alternative using the greatCircle function

This is the method proposed by the Simply Statistics Blog to draw a twitter connection map. The idea is to calculate the whole great circle, and keep only the part that stays in front of the map, never going behind it.

# A function that keeps the good part of the great circle, by Jeff Leek:
getGreatCircle = function(userLL,relationLL){
  tmpCircle = greatCircle(userLL,relationLL, n=200)
  start = which.min(abs(tmpCircle[,1] - data.frame(userLL)[1,1]))
  end = which.min(abs(tmpCircle[,1] - relationLL[1]))
  greatC = tmpCircle[start:end,]
  return(greatC)
}

# map 3 connections:
map('world',col="#f2f2f2", fill=TRUE, bg="white", lwd=0.05,mar=rep(0,4),border=0, ylim=c(-80,80) )
great=getGreatCircle(Paris, Melbourne)
lines(great, col="skyblue", lwd=2)
great=getGreatCircle(Buenos_aires, Melbourne)
lines(great, col="skyblue", lwd=2)
great=getGreatCircle(Paris, Buenos_aires)
lines(great, col="skyblue", lwd=2)
points(x=data$long, y=data$lat, col="slateblue", cex=3, pch=20)
text(rownames(data), x=data$long, y=data$lat,  col="slateblue", cex=1, pos=4)

Note that the R graph gallery proposes lot of other examples of maps made with R. You can follow the gallery on Twitter or on Facebook to be aware or recent updates.