#set up the grid
x<-y<-seq(-2.5,2.5,by=0.01)
#calculate x^2+y^2
sumsq<-function(x,y) x^2+y^2
#evaluate matrix z 
#for given x and y
z<-outer(x,y,"sumsq")
#evaluate bivariate standard normal distribution function
f<-exp(-z/2)/(2*pi)

#draw a filled contour plot with 8 levels
filled.contour(x,y,z,nlevels=8, asp=1) ###Roughly matches my 3-d wooden model
#draw a filled contour plot with 20 levels
filled.contour(x,y,z,nlevels=20, asp=1)
#draw a filled contour plot with 100 levels
filled.contour(x,y,z,nlevels=100, asp=1)



### The origin in the graph is actually at (-0.86,0), and the
### point with apparent coordinates, (1,0), is at (-0.1,0). 
### I want to draw white circles out from the nominal origin to
### remove the shading from outside the circle of radius 2.5. 
### To do this, I can take the previous points and change x to 
### xp = x*0.76 - 0.86.
### Bit it's depends on the dimension of the window! Ach!!
###Here's code to do this.

for (i in seq(2.5,4,by=0.005)) {
for (j in seq(0,2*pi,by=0.005)) {
xw<-i*cos(j)
yw<-i*sin(j)
if (max(abs(xw),abs(yw))<2.5) 
points(xw*0.76-0.86,yw,col="white")}}
lines(c(-2.5,2.5)*0.76-0.73,c(2.5,2.5))
lines(c(-2.5,2.5)*0.76-0.73,c(-2.5,-2.5))
lines(c(-2.53,-2.53)*0.77-0.73,c(-2.49,2.49),col="white",lwd=5)