## 2D polynomial fitting with SVD

version 1.4.0.0 (2.47 KB) by
Fits a polynomial f(x,y) to best fit the data points z using SVD.

Updated 14 Jul 2011

Use coeffs = fit2dPolySVD(x, y, z, order) to fit a polynomial of x and y so that it provides a best fit to the data z.
Uses SVD which is robust even if the data is degenerate. Will always produce a least-squares best fit to the data even if the data is overspecified or underspecified.
x, y, z are column vectors specifying the points to be fitted.
The three vectors must be the same length.
Order is the order of the polynomial to fit.
Coeffs returns the coefficients of the polynomial. These are in increasing power of y for each increasing power of x, e.g. for order 2:
zbar = coeffs(1) + coeffs(2).*y + coeffs(3).*y^2 + coeffs(4).*x + coeffs(5).*x.*y + coeffs(6).*x^2

Use eval2dPoly(x,y,coeffs) to evaluate the polynomial at any (x,y) points.

If the data is underspecified then the LOWER order coefficients will come out as zero, the solution being a fit using higher orders; use a lower order fit for a more obvious solution in this case.

### Cite As

Richard Whitehead (2021). 2D polynomial fitting with SVD (https://www.mathworks.com/matlabcentral/fileexchange/31636-2d-polynomial-fitting-with-svd), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2011a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux