Angular spline fitting of data

I have a set of x,y points that I would like to fit to a circle. I saw an example of "angular spline fitting" on the matlab page that uses definite x (theta given in radians) and y values. -- https://in.mathworks.com/help/matlab/ref/spline.html#bvjdts5

Can someone please tell me how to do the same for any set of x,y values ? When I make a polar plot of these values, I can see a circle emerging. I want to perform a spline fitting on the same..