Concentric Circles like a grid, centered at origin - r

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 the same magnitude.
I created a hack to do this:
add_circle_grid <- function(g,ncirc = 10){
gb <- ggplot_build(g)
xl <- gb$panel$ranges[[1]]$x.range
yl <- gb$panel$ranges[[1]]$y.range
rmax = sqrt(max(xl)^2+max(yl)^2)
theta=seq(from=0,by=.01,to=2*pi)
for(n in 1:ncirc){
r <- n*rmax/ncirc
circle <- data.frame(x=r*sin(theta),y=r*cos(theta))
g<- g+geom_path(data=circle,aes(x=x,y=y),alpha=.2)
}
return(g+xlim(xl)+ylim(yl))
}
xy<-data.frame(x=rnorm(100),y=rnorm(100))
ggplot(xy,aes(x,y))+geom_point()
ggg<-add_circle_grid(ggplot(xy,aes(x,y))+geom_point())
print(ggg)
But I was wondering if there is a more ggplot way to do this. I also considered using polar coordinates but it does not allow me to set x- and y-limits in the same way.
Finally, I wouldn't mind little text labels indicating the radius of each circle.
EDIT
Perhaps this is asking too much but there are two other things that I would like.
The axis limits should stay the same (which can be done via ggplot_build)
Can this work with facets? As far as I can tell you would need to somehow figure out the facets if I want to add the circles dynamically.

Answer 1

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)

Answer 2

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)