Shaded area under two curves using R

Question

I wrote the following code in R

x=seq(-7,10,length=200)
y1=dnorm(x,mean=0,sd=1)
plot(x,y1,type="l",lwd=2,col="red")
y2=dnorm(x,mean=3,sd=2)
lines(x,y2,type="l",lwd=2,col="blue")

How can I shade the area under both curves (known as the overlap between the two curves).

I will highly appreciate any suggestions.

Answer 1

Oh, well, @SachaEpskamp beat me to it, but here is my much less elegant solution.

shade_under_curve <- function(fun, xmin, xmax, length=100){
  xvals <- seq(xmin, xmax, length=length)
  dvals <- match.fun(fun)(xvals)
  polygon(c(xvals,rev(xvals)),c(rep(0,length),rev(dvals)),col="gray")
}


y1 <- function(x)sapply(x, function(xt)dnorm(xt,mean=0,sd=1))
y2 <- function(x)sapply(x, function(xt)dnorm(xt,mean=3,sd=2))

my.fun <- function(x){sapply(x, function(xt)min(y1(xt), y2(xt)))}

Edit to include initial plot:

plot(y1, -10, 10, col="red")
curve(y2, add=TRUE, col="blue")
shade_under_curve(my.fun, -10, 10, length=1000)

Answer 2

Add the following line:

polygon(x,pmin(y1,y2),col="gray")

This basically works exactly like the pen tool in photoshop, where the first vector, x are the x-coordinates and the second vector, pmin(y1,y2) are the y coordinates. pmin gives you a vector with the minimal values of two vectors elementwise, which corresponds to the y coordinates of the top of the overlap.

EDIT:

I prefer using curve() (as Andrie suggested), which can be used to plot a function. You can save it's coordinates while plotting too and us it in exactly the same way:

fun1 <- curve(dnorm(x,mean=0,sd=1),type="l",lwd=2,col="red")
fun2 <- curve(dnorm(x,mean=3,sd=2),type="l",lwd=2,col="blue",add=TRUE)
polygon(fun1$x,pmin(fun1$y,fun2$y),col="gray")