Reprojecting Vectors in R

library(rgdal)
library(mapdata)
library(ggplot2)
library(raster)

x<-runif(100, -180, 180)
y<-runif(100,-90, -83)

https://en.wikipedia.org/wiki/ISO_3166-1

d <- data.frame(lon=x, lat=y)
ant<-getData(name="GADM", country="ATA", level=0)
ant_df<-fortify(ant)

ggplot() + 
  geom_polygon(data=ant_df, aes(x=long,y=lat,group=group), fill="grey")+
  geom_point(data=d, aes(x=lon, y=lat), colour="black" )+
  coord_equal()+
  theme_bw()

http://spatialreference.org

coordinates(d) <- c("lon", "lat")
proj4string(d) <- CRS("+init=epsg:4326") # WGS 84 UTM 35S
CRS.new <- CRS("+init=epsg:3031")
d_new<- spTransform(d, CRS.new)
ant_new<- spTransform(ant, CRS.new)

ant_new_df<-fortify(ant_new)
d_df<-data.frame(d_new)

ggplot() + 
  geom_polygon(data=ant_new_df, aes(x=long,y=lat,group=group), fill="grey")+
  geom_point(data=d_df, aes(x=lon, y=lat), colour="black")+
  coord_equal()+
  theme_bw()