How to get Voronoi diagram around polygons - r

Question

I would like to generate a Voronoi diagram around 2D polygons. This question is somehow similar to this one here addressed for Python.
Is straightforward how this works for points, below is an example with sf::st_voronoi() function:
library(sf)
#> Linking to GEOS 3.8.0, GDAL 3.0.4, PROJ 6.3.1
p <- rbind(c(3.2,4),
c(3,4.6),
c(3.8,4.4),
c(3.5,3.8),
c(3.4,3.6),
c(3.9,4.5))
plot(p, pch = 16)
p %>% st_multipoint() %>% st_voronoi() %>% plot(col = NA, add = TRUE)
Created on 2020-05-28 by the reprex package (v0.3.0)
But when I try the same function for some generated polygons, I do not get the results I would like:
library(sf)
#> Linking to GEOS 3.8.0, GDAL 3.0.4, PROJ 6.3.1
p1 <- rbind(c(0,0), c(1,0), c(3,2), c(2,4), c(1,4), c(0,0))
p2 <- rbind(c(3,0), c(4,0), c(4,1), c(3,1), c(3,0))
pol <- st_multipolygon(list(list(p1), list(p2)))
plot(st_voronoi(pol), col = NA, lwd = 2, lty = 3)
plot(pol, col = rgb(1,0,0, alpha = 0.3), add = TRUE)
Created on 2020-05-28 by the reprex package (v0.3.0)
It seems that the Voronoi grid is based on the vertices of the polygons, which makes sense. However, I would like to get a Voronoi grid surrounding the red polygons and not intersecting them, that is, to treat a polygon as a point. Note that, getting the centroids of the polygons (e.g. with sf::st_centroid) and then generating a Voronoi grid is a path I tried, but the Voronoi grid will still intersect the polygons.

Answer 1

Here is my attempt. This is mostly relying on sf but I use smoothr::densify() to add vertices to straight edges of polygons (since the voronoi polygons are initially built around the polygon vertices), and I rely on a function from data.table to combine sf objects. There are probably ways to make this more efficient.
You would probably also want to simplify input polygons, although that is not needed in this test case.
The one really unresolved issue is for when two polygons share a boundary. The polygon-based voronoi should just follow that boundary, but currently does not.
library(sf)
# additionally requires:
## smoothr to densify polygons
## data.table to combine results
## poly = input sf polygons
## clip = polygon to be used as an extent for the output
## max_distance = argument for smoothr::densify, what max distance to have between vertices of a polygon. For breaking up long edges. In map units.
polyVoronoi <- function(poly, clip = NULL, max_distance = NULL) {
# add vertices to polygons to have voronoi polygons along straight edges of polygon
if (!is.null(max_distance)) {
poly <- smoothr::densify(poly, max_distance = max_distance)
}
# generate voronoi polygons for all vertices
vv <- st_voronoi(st_combine(poly))
vv <- st_collection_extract(vv, 'POLYGON')
# deal with geom validity issues
if (!all(st_is_valid(vv))) {
for (i in 1:length(vv)) {
vv[i] <- st_make_valid(vv[i])
if (!all(st_is_valid(vv[i]))) stop()
}
}
# determine which voronoi polygons intersect with input polygons
ii <- st_intersects(poly, vv)
# union/dissolve voronoi polygons that belong to the same inputs
resList <- vector('list', length(ii))
for (i in 1:length(ii)) {
xx <- vv[ii[[i]]]
xx <- st_combine(xx)
if (!all(st_is_valid(xx))) {
xx <- st_make_valid(xx)
}
resList[[i]] <- st_union(xx)
}
res <- st_as_sf(data.table::rbindlist(lapply(resList, st_as_sf)))
res <- res[1:nrow(res),]
res <- st_geometry(res)
if (!is.null(clip)) {
res <- st_intersection(res, clip)
}
return(res)
}
Example using built in dataset from sf
nc = st_read(system.file("shape/nc.shp", package="sf"))
# project to North America Albers Equal Area
nc <- st_transform(nc, crs = "+proj=aea +lat_1=20 +lat_2=60 +lat_0=40 +lon_0=-96 +x_0=0 +y_0=0 +ellps=GRS80 +datum=NAD83 +units=m +no_defs")
poly = st_geometry(nc)
# sample just a few polygons
poly <- poly[sample(1:length(poly), 12)]
# define bounds that we want for the output
e <- st_buffer(st_make_grid(poly, n = 1), 50000)
vv <- polyVoronoi(poly, clip = e, max_distance = 10000)
plot(vv, border = 'blue')
plot(poly, add = TRUE)
As you can see, there is a problem when polygons are in contact, and I haven't resolved this yet. Suggestions welcome!