问题
TL;DR
What is the best way in R to handle SpatialPolygons intersecting/overlapping the anti meridian at +/-180° of latitude and cut them into two sections along that meridian?
Preface
This is going to be a long one, but only because I'm going to include a lot of code and figures for illustration. I'll show you what my goal is and how I normally achieve that and then demonstrate how it all breaks together in a literal edge case. As the title suggests, I already found one possible solution to my problem, so I'll include that too. But it is not 100% clean and I'd like to see if somebody can come up with something more elegant. In any case I think this is an interesting problem, as only a couple of days ago I wouldn't have have suspected in my wildest dreams that this could even be an issue in 2019.
Regular work flow in R
First, create an example data set that works
library(sp)
library(rgdal)
library(rgeos)
library(dismo)
library(maptools) # this is just for plotting a simple world map in the background
data("wrld_simpl")
# create a set of locations
locations <- SpatialPoints(coords=cbind(c(50,0,0,0), c(10, 30, 50, 70)), proj4string = CRS("+proj=longlat +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0"))
plot(wrld_simpl, border="grey50")
points(locations, pch=19, col="blue")
Looks like this: Then, I use circles() from the dismo package to create circular buffers around those locations. I use this function, because it takes into account that the Earth is not flat:
buffr <- circles(p = locations, d = 1500000, lonlat=TRUE, dissolve=FALSE)
plot(wrld_simpl, border="grey50")
plot(buffr, add=TRUE, border="red", lwd=2)
points(locations, pch=19, col="blue")
That looks like this:
Then, merge the single buffers into one big (multi-) polygon:
buffr <- buffr@polygons # extract the SpatialPolygons object from the "CirclesRange" object
buffr <- gUnaryUnion(buffr) # merge
plot(wrld_simpl, border="grey50")
plot(buffr, add=TRUE, border="red", lwd=2)
points(locations, pch=19, col="blue")
This is exactly what I need:
The problem
Now observe what happens when we introduce locations that so are close to the anti-meridian (+/-180° of longitude) that the buffer has to cross that line:
locations <- SpatialPoints(coords=cbind(c(50,0,0,0, 175, -170), c(10, 30, 50, 70,0,-10)), proj4string = CRS("+proj=longlat +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0"))
buffr <- circles(p = locations, d = 1500000, lonlat=TRUE, dissolve=FALSE)
plot(wrld_simpl, border="grey50")
plot(buffr, add=TRUE, border="red", lwd=2)
points(locations, pch=19, col="blue")
The circles() command does manage to create polygon segments on the other side of the antimeridian (if dissolve=FALSE):
but the polygon crosses the entire globe instead of wrapping around properly (intersecting with 0° instead of 180°). That leads to self-intersections and
buffr <- gUnaryUnion(buffr@polygons)
will fail with
Error in gUnaryUnion(buffr@polygons) : TopologyException: Input geom 0 is invalid: Self-intersection at or near point 170.08604674698876 12.562175561621103 at 170.08604674698876 12.562175561621103
The quick and slightly dirty solution
First, we need to detect whether a polygon crosses the anti meridian. However, none of them actually intersects +/-180°. Instead, I'm using two pseudo anti meridians that lie close to the real one, but far enough to the east and west to probably intersect the polygons in question. If a polygon intersects both of them, it must also cross the anti meridian.
antimeridian <- SpatialLines(list(Lines(slinelist=list(Line(coords=cbind(c(179,179), c(90,-90)))), ID="1"),
Lines(slinelist=list(Line(coords=cbind(c(-179,-179), c(90,-90)))), ID="2")),
proj4string = CRS("+proj=longlat +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0"))
intrscts <- gIntersects(antimeridian, buffr, byid = TRUE)
any(intrscts[,1] & intrscts[,2])
intrscts <- which(intrscts[,1] & intrscts[,2])
buffr.bad <- buffr[intrscts,]
buffr.good <- buffr[-intrscts,]
plot(wrld_simpl)
plot(buffr.good, border="blue", add=TRUE)
plot(buffr.bad, border="red", add=TRUE)
After having detected and separated the "bad" polygons I simply split them into two separate sections by looking at the longitudinal coordinates. Every coordinate pair that has a negative value there goes into the new western polygon, positive ones into the eastern one. Then I just merge it all back together, do my gUnaryUnion and have pretty much what I need:
buffr.fixed <- buffr.good
for(i in 1:length(buffr.bad)){
thispoly <- buffr.bad[i,] # select first problematic polygon
crds <- thispoly@polygons[[1]]@Polygons[[1]]@coords # extract coordinates
crds.west <- subset(crds, crds[,1] < 0) # western half of the polygon
crds.east<- subset(crds, crds[,1] > 0)
# turn into Spatial*, merge back together, re-add original crs
sppol.east <- SpatialPolygons(list(Polygons(list(Polygon(crds.east)), paste0("east_", i))))
sppol.west <- SpatialPolygons(list(Polygons(list(Polygon(crds.west)), paste0("west_", i))))
sppol <- spRbind(sppol.east, sppol.west)
proj4string(sppol) <- proj4string(thispoly)
buffr.fixed <- spRbind(buffr.fixed, sppol)
}
buffr.final <- gUnaryUnion(buffr.fixed)
plot(wrld_simpl, border="grey50")
points(locations, pch=19, col="blue")
plot(buffr.final, add=TRUE, border="red", lwd=2)
The final outcome:
The actual question
So, this solution works for me for my current use case, but it has some issues:
- It will probably break completely as soon as one of the buffers crosses both the anti- and the prime-meridian (which is not so unlikely if the original point locations lie close to the poles).
- it is not quite exact, as the two polygon sections are not cut at +/-180° but at the highest negative/positive values of latitude that were present in the original polygon.
- I find it hard to believe that there is no "proper" way of doing this.
So the question all this boils down to is: Is there a better way of doing this?
While I was trying to figure this out, I came across the nowrapRecenter() and nowrapSpatialPolygons() functions from the maptools package, which at first sight looked like they do exactly what I want. Upon closer inspection, they are aimed at pretty much the opposite use case (centering a map on the anti meridian and thus cutting polygons along the prime meridian). I played around with them, but failed to make them work for me – in fact, they only managed to make things worse.
Thanks for you attention!
回答1:
You're right, it's the current year and there is a solution for your problem. The sf-package has the function st_wrap_dateline(), which is exactly what you need.
library(dismo)
library(sf)
locations <- SpatialPoints(coords=cbind(c(50,0,0,0, 175, -170), c(10, 30, 50, 70,0,-10)), proj4string = CRS("+proj=longlat +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0"))
buffr <- circles(p = locations, d = 1500000, lonlat=TRUE, dissolve=FALSE)
buffr2 <- as(buffr@polygons, Class = "sf") %>%
st_wrap_dateline(options = c("WRAPDATELINE=YES")) %>%
st_union()
plot(wrld_simpl, border="grey50")
plot(buffr2, add=TRUE, border="red", lwd=2)
points(locations, pch=19, col="blue")
st_wrap_dateline converts the polygons which cross the international date line, or "antimeridian", into MULTIPOLYGON. And that's about it.
Does that solve your problem? At least it shortens the way quite a bit, to get where you are now. ^^
来源：https://stackoverflow.com/questions/55162548/is-there-a-better-way-for-handling-spatialpolygons-that-cross-the-antimeridian