Find the inverse of a system of two polynomials

Hi,

I have a system of two polynomials that map a 2D position X,Y to a target 2D position X', Y'. The polynomials are of order 2 and have a set of coefficients, represented in the coefficient matrix A of size (2,12).

X'=                X-(A(1,1)+A(1,2)*2*(X-A(1,11))./A(1,12)+A(1,3)*(2*(X-A(1,11))./A(1,12).^2)+A(1,4)*(2*(X-A(1,11))./A(1,12).^3)... 
                   +A(1,5)*2*(Y-A(2,11))./A(2,12)+A(1,6)*(2*(Y-A(2,11))./A(2,12).^2)+A(1,7)*(2*(Y-A(2,11))./A(2,12).^3)... 
                   +A(1,8)*2*(X-A(1,11))./A(1,12).*2*(Y-A(2,11))./A(2,12)+A(1,9)*(2*(X-A(1,11))./A(1,12).^2).*2*(Y-A(2,11))./A(2,12)+A(1,10)*(2*(Y-A(2,11))./A(2,12).^2).*2*(X-A(1,11))./A(1,12)) 

Y'=                Y-(A(2,1)+A(2,2)*2*(X-A(1,11))./A(1,12)+A(2,3)*(2*(X-A(1,11))./A(1,12).^2)+A(2,4)*(2*(X-A(1,11))./A(1,12).^3)... 
                   +A(2,5)*2*(Y-A(2,11))./A(2,12)+A(2,6)*(2*(Y-A(2,11))./A(2,12).^2)+A(2,7)*(2*(Y-A(2,11))./A(2,12).^3)... 
                   +A(2,8)*2*(X-A(1,11))./A(1,12).*2*(Y-A(2,11))./A(2,12)+A(2,9)*(2*(X-A(1,11))./A(1,12).^2).*2*(Y-A(2,11))./A(2,12)+A(2,10)*(2*(Y-A(2,11))./A(2,12).^2).*2*(X-A(1,11))./A(1,12))

I wonder if you can help me find a solution for the inverse?

Thanks

Answer 1

[Torsten]

You may try MATLAB's 'solve' command.

If this does not work, insert numerical values for the coefficients and use fsolve.

In both cases, you will have to find the roots of the system

X' - above right-hand-side of first equation = 0

Y' - above right-hand side of second equation = 0

Best wishes

Torsten.