Check if point is in spatial object which consists of multiple polygons/holes

Question

I have a SpatialPolygonsDataFrame with 11589 objects of class "polygons". 10699 of those objects consists of exactly 1 polygon, however the rest of those objects consists of multiple polygons (2 to 22).

If an object of consists of multiple polygons, three scenarios are possible:

1. Sometimes, those additional polygons describe a "hole" in the geographic ara describe by the first polygon in the object of class "polygons".
2. Sometimes, those additional polygons describe additional geographic areas, i.e. the shape of the region is quite complex and described by putting together multiple parts.
3. Sometimes, it might be a mix of both, 1) and 2).

Stackoverflow helped me to plot such an spatial object properly (Plot spatial area defined by multiple polygons).

However, I am still not able to answer how to determine whether a point (defined by longitude/latitude) is in a polygon.

Below is my code. I tried to apply the function point.in.polygon in the sp package, but found no way how it could handle such an object which consists of multiple polygons/holes.

# Load packages
# ---------------------------------------------------------------------------
library(maptools)
library(rgdal)
library(rgeos)
library(ggplot2)
library(sp) 


# Get data
# ---------------------------------------------------------------------------
# Download shape information from the internet
URL <- "http://www.geodatenzentrum.de/auftrag1/archiv/vektor/vg250_ebenen/2012/vg250_2012-01-01.utm32s.shape.ebenen.zip"
td <- tempdir()
setwd(td)
temp <- tempfile(fileext = ".zip")
download.file(URL, temp)
unzip(temp)

# Get shape file
shp <- file.path(tempdir(),"vg250_0101.utm32s.shape.ebenen/vg250_ebenen/vg250_gem.shp")

# Read in shape file
map <- readShapeSpatial(shp, proj4string = CRS("+init=epsg:25832"))

# Transform the geocoding from UTM to Longitude/Latitude
map <- spTransform(map, CRS("+proj=longlat +datum=WGS84"))


# Pick an geographic area which consists of multiple polygons
# ---------------------------------------------------------------------------
# Output a frequency table of areas with N polygons 
nPolys <- sapply(map@polygons, function(x)length(x@Polygons))

# Get geographic area with the most polygons
polygon.with.max.polygons <- which(nPolys==max(nPolys))

# Get shape for the geographic area with the most polygons
Poly.coords <- map[which(nPolys==max(nPolys)),]


# Plot
# ---------------------------------------------------------------------------
# Plot region without Google maps (ggplot2) 
plot(Poly.coords,  col="lightgreen")


# Find if a point is in a polygon 
# ---------------------------------------------------------------------------
# Define points 
points_of_interest <- data.frame(long=c(10.5,10.51,10.15,10.4), 
                     lat =c(51.85,51.72,51.81,51.7),
                     id  =c("A","B","C","D"), stringsAsFactors=F)

# Plot points
points(points_of_interest$long, points_of_interest$lat, pch=19)

Answer 1

You can do this simply with gContains(...) in the rgeos package.

gContains(sp1,sp2)

returns a logical depending on whether sp2 is contained within sp1. The only nuance is that sp2 has to be a SpatialPoints object, and it has to have the same projection as sp1. To do that, you would do something like this:

point <- data.frame(lon=10.2, lat=51.7)
sp2   <- SpatialPoints(point,proj4string=CRS(proj4string(sp1)))
gContains(sp1,sp2)

Here is a working example based on the answer to your previous question.

library(rgdal)   # for readOGR(...)
library(rgeos)   # for gContains(...)
library(ggplot2)

setwd("< directory with all your files >")
map <- readOGR(dsn=".", layer="vg250_gem", p4s="+init=epsg:25832")
map <- spTransform(map, CRS("+proj=longlat +datum=WGS84"))

nPolys <- sapply(map@polygons, function(x)length(x@Polygons))
region <- map[which(nPolys==max(nPolys)),]

region.df <- fortify(region)
points <- data.frame(long=c(10.5,10.51,10.15,10.4), 
                     lat =c(51.85,51.72,51.81,51.7),
                     id  =c("A","B","C","D"), stringsAsFactors=F)

ggplot(region.df, aes(x=long,y=lat,group=group))+
  geom_polygon(fill="lightgreen")+
  geom_path(colour="grey50")+
  geom_point(data=points,aes(x=long,y=lat,group=NULL, color=id), size=4)+
  coord_fixed()

Here, point A is in the main polygon, point B is in a lake (hole), point C is on an island, and point D is completely outside the region. So this code checks all of the points using gContains(...)

sapply(1:4,function(i)
  list(id=points[i,]$id,
       gContains(region,SpatialPoints(points[i,1:2],proj4string=CRS(proj4string(region))))))
#    [,1] [,2]  [,3] [,4] 
# id "A"  "B"   "C"  "D"  
#    TRUE FALSE TRUE FALSE