rvoronoideldir
Find elements that share a common Voronoi boundary
I am trying to find the 'nearest neighbors' for the Voronoi graph elements, in other words, the elements which share a common boundary. Is there an implemented way to do it in R. I tried follow the example from here (https://flowingdata.com/2016/04/12/voronoi-diagram-and-delaunay-triangulation-in-r/) and use the deldir package which helps with estabishing the boundaries:
set.seed(369)
x <- rnorm(50, 0, 1.5)
y <- rnorm(50, 0, 1)
library(deldir)
dta <- deldir(x, y)
plot(x, y, type = "n", asp=1)
points(x, y, pch = 20, col = "red", cex = 0.75)
plot(dta, wlines = "tess", wpoints = "none", number = FALSE, add = TRUE, lty = 1)
How can I find the common boundary neighbours? I there a way to find second degree neighbours (elements that don't share a boundary, but do share a common neighbour)?
Solution
Some helpers:
library(sp)
library(rgeos)
library(deldir)
library(hrbrthemes)
library(ggplot2)
We can turn the deldir object into polygons with this function:
voroni_to_polys <- function(dd) {
vor_desc <- tile.list(dd) # tile.list extracts the polygon data from the deldir computation
# ^^ gets us the points for the polygons but we still have to close them, hence the need for the rbind
lapply(1:(length(vor_desc)), function(i) {
tmp <- cbind(vor_desc[[i]]$x, vor_desc[[i]]$y)
tmp <- rbind(tmp, tmp[1,])
Polygons(list(Polygon(tmp)), ID=i) # now we can make the Polygon(s)
}) -> vor_polygons
# dummy data frame that makes IDs easier
xdf <- data.frame(id=sapply(slot(SpatialPolygons(vor_polygons), 'polygons'), slot, 'ID'))
rownames(xdf) <- xdf$id
SpatialPolygonsDataFrame(SpatialPolygons(vor_polygons), data=xdf)
}
Your data:
set.seed(369)
data.frame(
x = rnorm(50, 0, 1.5),
y = rnorm(50, 0, 1)
) -> pts_df
dta <- deldir(pts_df$x, pts_df$y)
Make the polygons:
vpoly <- voroni_to_polys(dta)
We'll need this to show the ID #'s in the centroid position:
centers <- gCentroid(vpoly, byid=TRUE)
centers <- as.data.frame(centers)
centers$id <- 1:nrow(centers)
plot_df <- fortify(vpoly)
Plot it for a visual reference:
ggplot() +
geom_polygon(data=plot_df, aes(long, lat, group=group), color="#2b2b2b", fill="white") +
geom_point(data=pts_df, aes(x, y), color="red") +
geom_text(data=centers, aes(x, y, label=id), color="black", size=2) +
theme_ipsum(grid="")
Use gTouches() for ones that touch:
gTouches(vpoly, byid=TRUE)
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## 50 FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
You should be able to turn this into node pairs and use n-away graph algorithms for the second part of your question. Or, open a new question.
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