Concentric Circles like a grid, centered at origin

Question

I would like to include a sequence of concentric circles as a grid in a plot of points. The goal is to give the viewer an idea of which points in the plot have approximately

Answer 1

How about this with ggplot2 and grid:

require(ggplot2)
require(grid)

x<-(runif(100)-0.5)*4
y<-(runif(100)-0.5)*4

circ_rads<-seq(0.25,2,0.25)

qplot(x,y)+
  lapply(circ_rads,FUN=function(x)annotation_custom(circleGrob(gp=gpar(fill="transparent",color="black")),-x,x,-x,x))+
  geom_text(aes(x=0,y=circ_rads+0.1,label=circ_rads)) + coord_fixed(ratio = 1) 

Answer 2

set.seed(1)
xy <- data.frame(x=rnorm(100),y=rnorm(100))
rmax = sqrt(max(xy$x)^2+max(xy$y)^2)
theta=seq(from=0,by=.01,to=2*pi)
ncirc=10

dat.circ = do.call(rbind,
  lapply(seq_len(ncirc),function(n){
  r <- n*rmax/ncirc
  data.frame(x=r*sin(theta),y=r*cos(theta),r=round(r,2))
}))

rr <- unique(dat.circ$r)

dat.text=data.frame(x=rr*cos(30),y=rr*sin(30),label=rr)

library(ggplot2)

ggplot(xy,aes(x,y))+
   geom_point() +
   geom_path(data=dat.circ,alpha=.2,aes(group=factor(r))) +
   geom_text(data=dat.text,aes(label=rr),vjust=-1)