Thread Subject:

Polynomial surface fitting - least squares

Please i have X,Y,Z coordinate. How can i determine the best surface polynomial coefficients for each X,Y,Z Coordinates value because am confuse.

For example i know that for 2-D case for 1st order as an example:

Xn = a1Xo + a2Yo + a3
Yn = a4Xo + a5Yo + a6

From this i can get a matrix and using the relationship X= (A'*A)\A'*L
where X is the polynomial Coefficient(a1,a2,...a6) to be determned, A is the design matrix, L is the observation (Xn,Yn).

My problem is that, now i have coordinate in 3-D. How can i calculate for the best surface polynomial coefficients for X,Y,Z.