3d data interpolation

[WERT]

I have a set of 3d raw data. Is there a VI that will simply interpolate a "z" value based on the raw data if both the "x" and "y" are inputted. Currently I am fitting a 3rd order polynomial to the data and using this to solve my problem. The main problem with this is that I don't know how well the polynomial fits my data. If it outputted an r^2 value than i would be happy.

[altenbach]

Do the x,y values form an equally spaced regular grid or are the points randomly placed.

Do you need to interpolate in one direction, e.g. along each plane with constant x, or do you need to form a solid surface, potentially calculating Z for any fractional x and y.

Do you know anything about the data? Is there a theoretical model that you can fit to it? This would be the most reasonable approach in general.

If you simply need to interpolate without any theoretical model, you could do a 2D spline. Since a spline goes through all the data points, chisquare will be zero.

Or are you looking for a solution that does some smoothing of your data?

[WERT]

The x,y values form a relativly linear surface that twists in the z direction.

The data is taken from a valve calibration. The pressure is measured for each position of the valve. However there is a 3rd variable in the system. This means that the pressure required is dependent on valve position and the 3rd variable. This third variable causes small changes in the other two.
What I am trying to do is calculate my valve position for a known pressure and 3rd variable.

The data doesn't need to be smoothed.