Opinion about 3D fitting process

Dear all,

actually i'm dealing with a problem involving a fitting of 3D points. Even if I know that there aren't general rules to choose the type of fitting or the degree of a polynomial, i have a couple of questions:

• I have to create a function to describe a compressor efficiency map (somethng like the figure below), where the contour represent the efficiency and on the x-axis there is the mass flow and on the y-axis the compression ratio.

I do have a number of points which I know the three parameter, what could help me in the decision of the fitting method is that:

1) I will always work in the range where I do have the points, never outside,

2) the z-axis level (efficiency) changes from a minimum of 0.2 to a maximum of 0.85.

In these cases do you have any suggestion on the way to set the fitting process?

• If for example iI work with a polynomial fitting in the report I can read ''x is normalized by mean 298.1 and std 156.6'', std I think is the standard deviation, do I have to use it in the equation proposed by the fitting process?
• If I choose an interpolant method, it will be used only for graphicas porpouses, since in the results box of the Curve Fitting Tool I can't find any information that could be useful for my pourposes.

Thank you for the attention and excuse me if I'm not clear at all.

Niccolò.