##https://twitter.com/geospacedman/status/1047194503424200705

library(graticule)

## Loading required package: sp

r <- 1/(pi/2)
g <- graticule(seq(-180, 180, 5), c(-90, 0), 
               proj = sprintf("+proj=aeqd +lat_0=-90 +a=%f +b=%f", r, r), 
               tiles = TRUE)

## Loading required namespace: rgeos

plot(g, axes = TRUE, col = hsv(h = seq(0, 1, length = nrow(g)), s = 0.75))
abline(h = c(-1, 1), v= c(-1, 1))

nvert <- 72
ang <- 2 * pi/nvert
angles <- seq(0, 2 * pi - ang, by = ang)
rad <- 1
xx <- cos(angles) * rad + 0
yy <- sin(angles) * rad + 0

## brute force with high quality triangulation
xy <- cbind(c(0, xx), c(0, yy))
plot(g, axes = TRUE, col = hsv(h = seq(0, 1, length = nrow(g)), s = 0.75), border = NA)
abline(h = c(-1, 1), v= c(-1, 1))

library(RTriangle)
tri <- RTriangle::triangulate(RTriangle::pslg(P = xy), D = TRUE)
#plot(xy)
apply(tri$T, 1, function(i) polygon(xy[i, ], , lty = 2))

## NULL