Interpolate from periodic closed curve data in R

Question

Let us consider few points from a closed curve f(x): [0,2*pi] -> (0, +Inf), as follows

x <- c(0.0000000, 0.6283185, 1.2566371, 1.8849556, 2.5132741, 
3.1415927,3.7699112, 4.3982297, 5.0265482, 5.6548668, 6.2769021)

and

f <- c(7.156246, 2.634750, 4.012373, 5.734145, 6.812517,
6.072547,5.821391, 6.331051,4.900359, 5.825402, 7.176812)

Then how to interpolate values of the function f at some given points (2.3,10) in R?

Here people have done similar work using scipy function of Python. How to do it in R?