Assuming a spherical surface with unknown origin (and perhaps radius), you can run an optimization algorithm to estimate the model parameters (origin, etc.) and subtract the location of the points on the surface of the sphere from your data. That would give you, roughly, a plane-like view of your data at a distance equal to the radius of the sphere.
A better planar view might be to actually project the data into an r-theta-z plane, but this would require a more complicated algorithm.
% "Unknown" model parameters.
x0 = 45;
y0 = 30;
z0 = -198;
r = 200.0;
% Construct the data surface
[X,Y] = meshgrid(0:1:100, 0:1:60);
Z = sqrt((r+randn(size(X))).^2 - (X-x0).^2 - (Y-y0).^2) + z0;
surf(X,Y,Z)
% Estimate model parameters x0, y0, z0, and r.
% You can remove "r" from the estimation if it is already known.
P0 = [30, 30, -30, 10];
options = optimset('MaxFunEvals', 2000);
P = fminsearch(@(p) fcn(p,X,Y,Z), P0, options)
% Project into the plane at distance r.
x0 = P(1);
y0 = P(2);
z0 = P(3);
r = P(4);
Zplane = Z - sqrt(r^2 - (X-x0).^2 - (Y-y0).^2) - z0;
surf(X,Y,Zplane)
function cost = fcn(p, X, Y, Z)
x0 = p(1);
y0 = p(2);
z0 = p(3);
r = p(4);
z = sqrt(r^2 - (X-x0).^2 - (Y-y0).^2) + z0;
cost = norm(z-Z, 2); % Least squares cost.
end
