How do I get gCentroid to work at the pole? - r

Question

I am struggling with gCentroid, because it doesn't seem -- to me -- to give the 'right' answer near a pole of the Earth.
For instance:
library(rgeos)
gCentroid(SpatialPoints(coords=data.frame(longitude=c(-135,-45,45,135),latitute=c(80,80,80,80)),proj4string = CRS('EPSG:4326')))
does not give me the North Pole, it gives:
> SpatialPoints:
> x y
> 1 0 80
> Coordinate Reference System (CRS) arguments: +proj=longlat +datum=WGS84 +no_defs
How do I get gCentroid to work on the surface of the Earth?

Answer 1

The GEOS library is limited to planar geometry operations; this can bring issues in edge cases / the poles being a notorious example.
For the centroid via GEOS to work as intended you need to transform your coordinates from WGS84 to a coordinate reference system appropriate to polar regions; for Arctic regions I suggest EPSG:3995.
library(sp)
library(dplyr)
library(rgeos)
points_sp <- SpatialPoints(coords=data.frame(longitude=c(-135,-45,45,135),latitute=c(80,80,80,80)),proj4string = CRS('EPSG:4326'))
points_updated <- points_sp %>%
spTransform(CRS("EPSG:3995")) # a projected CRS apropriate for Arctic regions
centroid <- gCentroid(points_updated) %>%
spTransform(CRS("EPSG:4326")) # back to safety of WGS84!
centroid # looks better now...
# SpatialPoints:
# x y
# 1 0 90
# Coordinate Reference System (CRS) arguments: +proj=longlat +datum=WGS84 +no_defs
Also note that your workflow - while not wrong in principle - is a bit dated, and the {rgeos} package is approaching its end of life.
It may be good time to give a strong consideration to {sf} package, which is newer, actively developed and can, via interface to s2 library from Google, handle spherical geometry operations.
For an example of {sf} based workflow consider this code; the result (centroid = North Pole) is equivalent to the sp / rgeos one.
library(sf)
points_sf <- points_sp %>% # declared earlier
st_as_sf()
centroid_sf <- points_sf %>%
st_union() %>% # unite featrues / from 4 points >> 1 multipoint
st_centroid()
centroid_sf # the North Pole in a slightly different (sf vs sp) format
# Geometry set for 1 feature
# Geometry type: POINT
# Dimension: XY
# Bounding box: xmin: 0 ymin: 90 xmax: 0 ymax: 90
# Geodetic CRS: WGS 84 (with axis order normalized for visualization)
# POINT (0 90)