Is this a single valued function of x and y? Or x and z, y and z? No.
Is this a function over some contiguous convex region in some plane, thus of any two of those variables?
None of the above. So you cannot interpolate it using interp2. You cannot interpolate using griddata. You cannot use scatteredInterpolant.
However, you would have created it is using a parametric form, probably as a function of r and theta. You would create z as a function of r and theta, then compute x and y coordintes the same way. If you want to interpolate it, then you need to interpolate as a function of THOSE variables.