How do I find the polygon nearest to a point in R?

Question

I have a spatial points data frame and a spatial polygons data frame. For example, my polygons would be a polygon for each block in Manhattan. And the points are people, which are scattered all over, sometimes falling in the middle of a street, which is not part of a polygon.

I know how to check if a point is contained inside a polygon, but how could I assign points to their closest polygon?

## Make some example  data
set.seed(1)
library(raster)
library(rgdal)
library(rgeos)
p <- shapefile(system.file("external/lux.shp", package="raster"))
p2 <- as(1.5*extent(p), "SpatialPolygons")
proj4string(p2) <- proj4string(p)
pts <- spsample(p2-p, n=10, type="random")

## Plot to visualize
plot(pts, pch=16, cex=.5,col="red")
plot(p, col=colorRampPalette(blues9)(12), add=TRUE)

Answer 1

Here's an answer that uses an approach based on that described by mdsumner in this excellent answer from a few years back.

One important note (added as an EDIT on 2/8/2015): rgeos, which is here used to compute distances, expects that the geometries on which it operates will be projected in planar coordinates. For these example data, that means that they should be first transformed into UTM coordinates (or some other planar projection). If you make the mistake of leaving the data in their original lat-long coordinates, the computed distances will be incorrect, as they will have treated degrees of latitude and longitude as having equal lengths.

library(rgeos)

##  First project data into a planar coordinate system (here UTM zone 32)
utmStr <- "+proj=utm +zone=%d +datum=NAD83 +units=m +no_defs +ellps=GRS80"
crs <- CRS(sprintf(utmStr, 32))
pUTM <- spTransform(p, crs)
ptsUTM <- spTransform(pts, crs)

## Set up containers for results
n <- length(ptsUTM)
nearestCanton <- character(n)
distToNearestCanton <- numeric(n)

## For each point, find name of nearest polygon (in this case, Belgian cantons)
for (i in seq_along(nearestCanton)) {
    gDists <- gDistance(ptsUTM[i,], pUTM, byid=TRUE)
    nearestCanton[i] <- pUTM$NAME_2[which.min(gDists)]
    distToNearestCanton[i] <- min(gDists)
}

## Check that it worked
data.frame(nearestCanton, distToNearestCanton)
#       nearestCanton distToNearestCanton
# 1             Wiltz           15342.222
# 2        Echternach            7470.728
# 3            Remich           20520.800
# 4          Clervaux            6658.167
# 5        Echternach           22177.771
# 6          Clervaux           26388.388
# 7           Redange            8135.764
# 8            Remich            2199.394
# 9  Esch-sur-Alzette           11776.534
# 10           Remich           14998.204

plot(pts, pch=16, col="red")
text(pts, 1:10, pos=3)
plot(p, add=TRUE)
text(p, p$NAME_2, cex=0.7)