What would be the equation of the following surface?
I have the raw data of X, Y, Z, where X and Y are inputs and Z is the output. Plotting the surface gives the red curve in the below picture:
The surface seems to be a simple function involving trigonometric functions. For example, plotting the equation cos(X)^2 + cos(Y)^2 gives the blue surface and it looks similar to the red graph (but the RMS error is very large).
I have tried introducing variables (a1*cos(X)^2 + a2*cos(Y)^2), where a1 and a2 vary from 0 to 1) but the RMS error is still large.
I also tried the surface fitting functions (MATLAB's fit function) but it's models are limited (unlike the curve fitting models which include Fourier series, sin series, etc).
How can I find the equation which gives the red surface?
Edit for clarity: I am able to use the lsqcurvefit (or any other curve fitting toolbox functions) to find which coefficients to use, but I am not sure what the equation should be. cos(X)^2 + cos(Y)^2, for example, is not the right equation but it does have a similar shape.
If this seems improbabilistic, how can I vary cos(X)^2 + cos(Y)^2 to align the end curves of the surface (where there seems to be highest misalignment)?
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Update 3: Added some surface plots.[X, Y] = meshgrid(-1:0.05:1); %% Polynomial function c = 1; b = 1/2; a = b; Z = c - b*Y.^2 - a*X.^2; % can try higher-order polynomial functions surf(X, Y, Z), grid on title('Quadratic function'), xlabel x, ylabel y, zlabel f(x,y)
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What would be the equation of the following surface?













