I have an old datagram with the values of some coefficients which have been retrieved experimental way.
I want to transform this pictorial representation to the form: $$z=f(x,y)$$ I believe it can be represented by a polynomial function with degree 5 for the variable $x$ and degree 2 for the variable $y$. The common polynomial form of the function should look like:
$$z = a_0x^5y^2+a_1x^4y^2+a_2x^3y^2+a_3x^2y^2+a_4xy^2+a_5y^2 + a_6x^5y+a_7x^4y+a_8x^3y+a_9x^2y+a_{10}xy+a_{11}y + a_{12}x^5+a_{13}x^4+a_{14}x^3+a_{15}x^2+a_{16}x+a_{17}$$
Where can I find the methodology for the constants $a_0...a_{17}$ retrieval?
Clarification:
To be clear, this datagram is actually a nomogram and the process of calculation is represented in the scheme below:
From the value of independent variable $x$, one starts the ray to the intersection with the line, defined by the value of independent variable $y$. The projection of the point of intersection to the axis $z$ is a final value.