# calculate {minimal} distance between polygons in R

I have calculated the surface area of species distributions (merging polygons from shapefiles), but since this area can be comprised of quite distanced polygons, I would like to calculate some measure of dispersion. What I have done so far is to retrieved the centroids of each polygon, calculated the distance between those and used these to calculate the coefficient of variation, as in the dummy example below;

``````require(sp)
require(ggplot2)
require(mapdata)
require(gridExtra)
require(scales)
require(rgeos)
require(spatstat)

# Create the coordinates for 3 squares
ls.coords <- list()
ls.coords <- list()
ls.coords[] <- c(15.7, 42.3, # a list of coordinates
16.7, 42.3,
16.7, 41.6,
15.7, 41.6,
15.7, 42.3)

ls.coords[] <- ls.coords[]+0.5 # use simple offset

ls.coords[] <- c(13.8, 45.4, # a list of coordinates
15.6, 45.4,
15.6, 43.7,
13.8, 43.7,
13.8, 45.4)

# Prepare lists to receive the sp objects and data frames
ls.polys <- list()
ls.sp.polys <- list()

for (ii in seq_along(ls.coords)) {
crs.args <- "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"
my.rows <- length(ls.coords[[ii]])/2
# create matrix of pairs
my.coords <- matrix(ls.coords[[ii]],nrow = my.rows,ncol = 2,byrow = TRUE)
# now build sp objects from scratch...
poly = Polygon(my.coords)
# layer by layer...
polys = Polygons(list(poly),1)
spolys = SpatialPolygons(list(polys))
# projection is important
proj4string(spolys) <- crs.args
# Now save sp objects for later use
ls.sp.polys[[ii]] <- spolys
# Then create data frames for ggplot()
poly.df <- fortify(spolys)
poly.df\$id <- ii
ls.polys[[ii]] <- poly.df
}

# Convert the list of polygons to a list of owins
w <- lapply(ls.sp.polys, as.owin)
# Calculate the centroids and get the output to a matrix
centroid <- lapply(w, centroid.owin)
centroid <- lapply(centroid, rbind)
centroid <- lapply(centroid, function(x) rbind(unlist(x)))
centroid <- do.call('rbind', centroid)

# Create a new df and use fortify for ggplot
centroid_df <- fortify(as.data.frame(centroid))
# Add a group column
centroid_df\$V3 <- rownames(centroid_df)

ggplot(data = italy, aes(x = long, y = lat, group = group)) +
geom_polygon(fill = "grey50") +
# Constrain the scale to 'zoom in'
coord_cartesian(xlim = c(13, 19), ylim = c(41, 46)) +
geom_polygon(data = ls.polys[], aes(x = long, y = lat, group = group), fill = alpha("red", 0.3)) +
geom_polygon(data = ls.polys[], aes(x = long, y = lat, group = group), fill = alpha("green", 0.3)) +
geom_polygon(data = ls.polys[], aes(x = long, y = lat, group = group), fill = alpha("lightblue", 0.8)) +
coord_equal() +
# Plot the centroids
geom_point(data=centroid_points, aes(x = V1, y = V2, group = V3))

# Calculate the centroid distances using spDists {sp}
centroid_dists <- spDists(x=centroid, y=centroid, longlat=TRUE)

centroid_dists

[,1]      [,2]     [,3]
[1,]   0.00000  69.16756 313.2383
[2,]  69.16756   0.00000 283.7120
[3,] 313.23834 283.71202   0.0000

# Calculate the coefficient of variation as a measure of polygon dispersion
cv <- sd(centroid_dist)/mean(centroid_dist)
 0.9835782
``````

Plot of the three polygons and their centroids Im not sure if this approach is very useful since in quite many cases, some of the polygons (as the blue one in the above example) are quite large compared to the rest, thus increasing the distance even further. E.g. the centroid of Australia have almost the same distance to it's western boarders as to Papau.

What I would like to get is some input on alternative approches. E.g. how or with what function can I calculate the distance between polygons? I have tested to convert the SpatialPolygon dataframe above to PointPatterns (ppp) `{spatstat}`to be able to run `nndist() {spatstat}` to calculate the distance between all points. But since I am dealing with quite large areas (many polygons and large ones), the matrix gets huge and Im not sure how to continue to get to the minimal distance between the polygons.

I have also looked at the function `gDistance {rgeos}`, but I think it only works on projected data which can be a problem for me since my areas can cross several `EPSG areas`. The same problem would arise for the function `crossdist {spatstat}`.

Any pointers would be very much appreciated. Thanks!

• Would you consider using `postgres/postgis` in addition to `R`? I have used a workflow where I perform the majority of my work in `R`, but store the data in a database that I access using `sqldf`. This enables you to use all of the `postgis` functions (of which distance between polygons is straightfoward) – djq Jan 21 '14 at 14:46
• @djq: Thanks for commenting. Yeah, I would definitely give it a go :) I started out building a database in `postgres` but stopped when I didn't know (didn't look) how to connect the workflow/geostats between the database and `R`... – jO. Jan 21 '14 at 14:53

## 1 Answer

You can do this analysis in the "spdep" package. In the relevant neighbor functions, if you use "longlat=TRUE", the function calculates great circle distance and returns kilometers as the distance unit. In the below example you could coerce the resulting distance list object ("dist.list") to a matrix or data.frame however, it is quite efficient calculating summary statistics using lapply.

``````require(sp)
require(spdep)

# Create SpatialPolygonsDataFrame for 3 squares
poly1 <- Polygons(list(Polygon(matrix(c(15.7,42.3,16.7,42.3,16.7,41.6,15.7,41.6,15.7,42.3),
nrow=5, ncol=2, byrow=TRUE))),"1")
poly2 <- Polygons(list(Polygon(matrix(c(15.7,42.3,16.7,42.3,16.7,41.6,15.7,41.6,15.7,42.3)+0.5,
nrow=5, ncol=2, byrow=TRUE))),"2")
poly3 <- Polygons(list(Polygon(matrix(c(13.8, 45.4, 15.6, 45.4,15.6, 43.7,13.8, 43.7,13.8, 45.4),
nrow=5, ncol=2, byrow=TRUE))),"3")
spolys = SpatialPolygons(list(poly1,poly2,poly3),1:3)
spolys <- SpatialPolygonsDataFrame(spolys, data.frame(ID=sapply(slot(spolys, "polygons"),
function(x) slot(x, "ID"))) )
proj4string(spolys) <- "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"

# Centroid coordinates (not used but provided for example)
coords <- coordinates(spolys)

# Create K Nearest Neighbor list
skNN.nb <- knn2nb(knearneigh(coordinates(spolys), longlat=TRUE),
row.names=spolys@data\$ID)

# Calculate maximum distance for all linkages
maxDist <- max(unlist(nbdists(skNN.nb, coordinates(spolys), longlat=TRUE)))

# Create spdep distance object
sDist <- dnearneigh(coordinates(spolys), 0, maxDist^2, row.names=spolys@data\$ID)
summary(sDist, coordinates(spolys), longlat=TRUE)

# Plot neighbor linkages
plot(spolys, border="grey")
plot(sDist, coordinates(spolys), add=TRUE)

# Create neighbor distance list
( dist.list <- nbdists(sDist, coordinates(spolys), longlat=TRUE) )

# Minimum distance
( dist.min <- lapply(dist.list, FUN=min) )

# Distance coefficient of variation
( dist.cv <- lapply(dist.list, FUN=function(x) { sd(x) / mean(x) } ) )
``````
• Thanks for commenting and the insight into the `spdeb` package. Just for clarification, this approach yields the same output as in my example, right? – jO. Jan 21 '14 at 20:02
• Just in case you didn't see my above comment – jO. Jan 28 '14 at 16:34
• Although the response provides useful code for calculating distances between centroids it does not deal with the central point of the OP which is how to find the distance between the two nearest points of the polygon borders. – csfowler Jul 15 '16 at 15:30
• A huge cop out and bad form for SE, but I can't do the full work up right now. My own search for an answer to this question seems to indicate that the gDistance function from library rgeos will do what the OP intended: find the shortest distance between the edges. If, in my haste to meet a tight deadline I have misinterpreted OP or Jeffrey Evans my sincere apologies. – csfowler Jul 15 '16 at 15:46