How to interpolate the outline of 2d grid points

I have data at x and y coordinates that represent a shape, say like a circle. I want to interpolate, somehow, to find values at query points along the outline, where the x and y values might not be strictly monotonic. What is the best function to do that? Thanks

Answer 1

[Walter Roberson]

Some shapes can be made monotonic in theta (angle) with the origin at the centroid of the object.

[Mark]

Thanks for the help Walter. Is there a particular function or option in a function you are referring to? Or is it a mathematical manipulation of something like interp1?