How to draw circles around polygon/spider chart, without plotting libraries

Without using ggplot2 or other plotting libraries, I would need to draw circles around a polygon/star chart vertices, i.e. each circle with a radius equal to the respective polygon radius. You can see an example here:

d1 <- 1:4
names(d1) <- LETTERS[1:4]
stars(matrix(d1,nrow=1),axes=TRUE, scale=FALSE,radius=TRUE, frame.plot=TRUE,labels = dimnames(d1)[[1]])
grid()[enter image description here][1]

I understand I should combine the stars() with the symbols(), polygon() functions or par(...) graphics, but honestly, I am new to these kind of plotting techniques and very lost on how to combine functions and arguments

Solution

I don't know of any functions in base R that do circles for you, but you can concoct them manually.

center <- c(x=2.1, y=2.1) # probably a better way
half <- seq(0, pi, length.out = 51)
for (D in d1) {
  Xs <- D * cos(half); Ys <- D * sin(half)
  lines(center["x"] + Xs, center["y"] + Ys, col = "gray", xpd = NA)
  lines(center["x"] + Xs, center["y"] - Ys, col = "gray", xpd = NA)
}

Notes:

I don't know off-hand how the center-point should be calculated, I chose that point using locator(1); not being familiar with stars, there may be a better way to determine this programmatically and more accurately;
The first lines(.) draws the upper semi-circle; the second draws the lower.
The xpd=NA is to preclude clipping due to the drawing margin. It may not be necessary in your "real" data. See ?par for more details on this.
Though it may be difficult to detect here, the gray circles are drawn on top of the stars plot, which might be an aesthetic compromise. The only way around that is to plot the circles first. To do this, draw the first semicircle first with plot(..., type="l") and then add the remainder as expected, and only then run stars(..., add=TRUE).