How to Bound the Outer Area of Voronoi Polygons and Intersect with Map Data
My end goal in asking this question was to write a script where I can arbitrarily change the number of kmeans
clusters and quickly visualize the results with voronoi
polygons that cover my desired area region.
I haven't quite accomplished this yet, but I have made enough progress that I figured posting what I have may lead to a quicker solution.
# Create Input Data.Frameinput <- as.data.frame(cbind(x$long, x$lat))colnames(input) <- c("long", "lat")# Set Seed and Run Clustering Procedureset.seed(123)km <- kmeans(input, 35)# Format Output for Plottingcenters <- as.data.frame(cbind(km$centers[,1], km$centers[,2]))colnames(centers) <- c("long", "lat")cent.id <- cbind(ID = 1:dim(centers)[1], centers)# Create Spatial Points Data Frame for Calculating Voronoi Polygonscoords <- centers[,1:2]vor_pts <- SpatialPointsDataFrame(coords, centers, proj4string = CRS("+proj=longlat +datum=WGS84"))
I also found the below.function while searching for a solution online.
# Function to Extract Voronoi Polygons SPdf_to_vpoly <- function(sp) { # tile.list extracts the polygon data from the deldir computation vor_desc <- tile.list(deldir(sp@coords[,1], sp@coords[,2])) lapply(1:length(vor_desc), function(i) { # tile.list gets us the points for the polygons but we # still have to close them, hence the need for the rbind tmp <- cbind(vor_desc[[i]]$x, vor_desc[[i]]$y) tmp <- rbind(tmp, tmp[1,]) # Now we can make the polygons Polygons(list(Polygon(tmp)), ID = i) }) -> vor_polygons # Hopefully the caller passed in good metadata sp_dat <- sp@data # This way the IDs should match up with the data & voronoi polys rownames(sp_dat) <- sapply(slot(SpatialPolygons(vor_polygons), 'polygons'), slot, 'ID') SpatialPolygonsDataFrame(SpatialPolygons(vor_polygons), data = sp_dat)}
With the above function defined polygons can be extracted accordingly
vor <- SPdf_to_vpoly(vor_pts)vor_df <- fortify(vor)
In order to get the voronoi
polygons to fit nicely with a US map I downloaded cb_2014_us_state_20m from the Census
website and ran the following:
# US Map Plot to Intersect with Voronoi Polygons - download from census link and place in working directoryus.shp <- readOGR(dsn = ".", layer = "cb_2014_us_state_20m")state.abb <- state.abb[!state.abb %in% c("HI", "AK")]Low48 <- us.shp[us.shp@data$STUSPS %in% state.abb,]# Define Area Polygons and Projections and Calculate IntersectionLow48.poly <- as(Low48, "SpatialPolygons")vor.poly <- as(vor, "SpatialPolygons")proj4string(vor.poly) <- proj4string(Low48.poly)intersect <- gIntersection(vor.poly, Low48.poly, byid = T)# Convert to Data Frames to Plot with ggplotLow48_df <- fortify(Low48.poly)int_df <- fortify(intersect)
From here I could visualize my results using ggplot
like before:
# Plot ResultsStateMap <- ggplot() + geom_polygon(data = Low48_df, aes(x = long, y = lat, group = group), col = "white")StateMap + geom_polygon(data = int_df, aes(x = long, y = lat, group = group, fill = id), alpha = .4) + geom_point(data = input, aes(x = long, y = lat), col = factor(km$cluster)) + geom_label(data = centers, aes(x = long, y = lat, label = row.names(centers)), alpha =.2) + scale_fill_hue(guide = 'none') + coord_map("albers", lat0 = 30, lat1 = 40)
Summary of Updates
The overlapping voronoi
polygons still aren't a perfect fit (I'm guessing due to a lack of input data in the pacific northwest) although I'd imagine that should be a simple fix and I'll try to update that as soon as possible. Also if I alter the number of kmeans centroids
in the beginning of my function and then re-run everything the polygons don't look very nice at all which is not what I was originally hoping for. I'll continue to update with improvements.