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Bi-Quadratic Interpolation

 

The bi-quadratic interpolation scheme attempt to represent Z as a function of X and Y using the following relation

 

 

The coefficients are found using linear least squares to minimize the error in representing N points in the vicinity of the point of interest.  By default, N=16.  The Interpolate2D function provides an optional argument to specify N.  If N is less than the number of data points, N points will be selected that are closest to Z in normalized coordinates.