How many sample points are needed when re-constructing linear combination of 2D polynomials defined over unit circle ?

I have a set of first 25 Zernike polynomials. I am not using 1st since it is piston; so I have these 24 two-dim ANALYTICAL functions expressed in X-Y Cartesian co-ordinate system. All are defined over unit circle, as they are orthogonal over unit circle. The problem which I am describing here is relevant to other 2D surfaces also apart from Zernike Polynomials.

Suppose that origin (0,0) of the XY co-ordinate system and the centre of the unit circle are same.

Next, I take linear combination of these 24 polynomials to build a 2D wavefront shape. I use 24 random input coefficients in this combination.

Upto this point, everything is analytical part which can be done on paper.

Now comes the discretization!

I know that when you want to re-construct a signal (1Dim/2Dim), your sampling frequency should be at least twice the maximum frequency present in the signal (Nyquist-Shanon principle).

Now my question is first how to find out this maximum sampling frequency in my case. I can not use MATLAB fft2() since it means already I have samples taken across the wavefront!!

Second thing: Suppose somehow I got these sampling frequency numbers. There will be 2 maximum frequencies: 1 along X and 1 along Y axis. Then how many sample points should I take from -1 to +1 along both X & Y axes? (Radius of unit circle is 1).

Any help will be appreciated.

Thanks