Para fins de reprodução, considere os seguintes dados:

library(rgdal)
library(ggplot2)
library(rgeos)

download.file("http://spatialanalysis.co.uk/wp-content/uploads/2010/09/London_Sport.zip", 

destfile = "London_Sport.zip")
unzip("London_Sport.zip")

projection="+proj=merc"

london_shape = readOGR("./", layer="london_sport")

# Create random points
set.seed(1)
points = data.frame(long=rnorm(10000, mean=-0.1, sd=0.1), lat=rnorm(10000, mean=51.5, sd=0.1))
points = SpatialPoints(points, proj4string=CRS("+proj=latlon"))

# Transform data to our projection
london = spTransform(london_shape, CRS(projection))
points = spTransform(points, CRS(projection))

# Keeps only points inside London
intersection = gIntersects(points, london, byid = T)
outside = apply(intersection == FALSE, MARGIN = 2, all)
points = points[which(!outside), ]

# Blank theme
new_theme_empty <- theme_bw()
new_theme_empty$line <- element_blank()
new_theme_empty$rect <- element_blank()
new_theme_empty$strip.text <- element_blank()
new_theme_empty$axis.text <- element_blank()
new_theme_empty$plot.title <- element_blank()
new_theme_empty$axis.title <- element_blank()
new_theme_empty$plot.margin <- structure(c(0, 0, -1, -1), unit = "lines", valid.unit = 3L, class = "unit")

# Prepare data to ggplot
london = fortify(london)
points = as.data.frame(points)

Quero traçar um mapa de densidade dos pontos. Eu posso fazer isso usandostat_bin2d:

ggplot() + 
  geom_polygon(data=london, aes(x=long,y=lat,group=group), fill="black") +
  stat_bin2d(data=points, aes(x=long,y=lat), bins=40) +
  geom_path(data=london, aes(x=long,y=lat,group=id), colour='white') +
  coord_equal() +
  new_theme_empty

Mas isso resulta em algumas partes dos quadrados de densidade a serem plotados fora de Londres:

Como plotar o mapa de densidade somente dentro de Londres?