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A common task in GIS is comparing the spatial extent of one layer with another. Say you have a load of points, some of which overlay a polygon layer. You are only interested in the points that intersect with the points. What do you do? Also, how can you aggregated-up the values contained in the points to correspond with the polygons. These are complex computational problems. In this post we will see how recent updates to R's sp package make the solution surprisingly intuitive and incredibly terse. All of the data (and more) for this can be downloaded from the tutorial page on GitHub. To make this tutorial reproducible on any computer, we will download each input dataset from within R using download.file.

library(sp)
plot(stations[sample(1:nrow(stations), 500), ])
plot(lnd, add = T, col = "red") # Spatial subsetting (clipping)

As the plot demonstrates, the stations are far more exentsive than polygons of central London. We must therefore clip them. Doing this manually would take much time – we'd have to interrogate the coordinates of each point to see whether or not it falls within one of the polygon boundaries.

Fortunately with have the over function from the sp package to make this operation more terse:

sel <- over(stations, lnd)
stations <- stations[!is.na(sel[, 1]), ]


As if that weren't enough, the developers of sp have integrated spatial subsetting into R's main index system with the square brackets. Because this is a common procedure it is actually possible to perform it with a single line of code:

stations <- stations[lnd, ]
plot(stations) As the figure shows, only stations within the London borroughs are now shown. All that was needed was to place another spatial object in the row index of the points ([lnd, ]) and R automatically understood that a subset based on location should be produced. This line of code is an example of R's 'terseness' - only a single line of code is needed to perform what is in fact quite a complex operation.

The third way to acheive the same result uses the rgeos package. This is more complex and not included in this tutorial (interested readers can see a vignette of this, to accomany the tutorial on RPubs.com/Robinlovelace). The next section demonstrates spatial aggregation, a more advanced version of spatial subsetting.

# Spatial aggregation

As with R's very terse code for spatial subsetting, the base function aggregate (which provides summaries of variables based on some grouping variable) also behaves differently when the inputs are spatial objects.

stations.c <- aggregate(stations, lnd, length)
[email protected][, 1]

##   48 22 43 18 12 13 25 24 12 46 18 20 28 32 38 19 30 25 31  7 10 38 12
##  16 28 17 16 28  4  6 14 26  5


The above code performs a number of steps in just one line:

• aggregate identifies which lnd polygon (borrough) each station is located in and groups them accordingly
• it counts the number of stations in each borrough
• a new spatial object is created and assigned the name stations.c, the count of stations

As shown below, the spatial implementation of aggregate can provide summary statistics of variables. In this case we take the variable NUMBER and find its mean value for the stations in each ward.

stations.m <- aggregate(stations[c("NUMBER")], by = lnd, FUN = mean)


For an optional advanced task, let us analyse and plot the result.

q <- cut(stations.m$NUMBER, breaks = c(quantile(stations.m$NUMBER)), include.lowest = T)
summary(q)

## [1.82e+04,1.94e+04] (1.94e+04,1.99e+04] (1.99e+04,2.05e+04]
##                   9                   8                   8
##  (2.05e+04,2.1e+04]
##                   8

clr <- as.character(factor(q, labels = paste0("grey", seq(20, 80, 20))))
plot(stations.m, col = clr)
legend(legend = paste0("q", 1:4), fill = paste0("grey", seq(20, 80, 20)), "topright") areas <- sapply([email protected], function(x) [email protected])


This results in a simple choropleth map and a new vector containing the area of each borrough. As an additional step, try comparing the mean area of each borrough with the mean value of stations within it: plot(stations.m\$NUMBER, areas).