I have a grid (a map) of $(x_i,y_j)$ with some functional value defined at the grid points $f_{ij}=f(x_i,y_j)$. In this map, I would like to do interpolation so that i can calculate value of $f$ at some points in polar coordinates. I have read about multidimensional interpolation in the numerical recipes but they only discuss the interpolation on a rectangular grids not in polar coordinates. What I actually need is to determine the value of $f$ at some $(r,\varphi)$ polar coordinates.
One idea that i have is to determine the cartesian coordinates for the given $(r,\varphi)$ and use e.g. bilinear interpolation on the cartesian grid for the corresponding $(x(r,\varphi),y(r,\varphi))$ points. But i am not sure, if this is the correct approach.
I have found some topics on here but i cannot say they were very helpful. Can someone comment on how to approach this or point me to some literature?