So I have two sets of equations:
$\mathcal{A}$ = \begin{equation} \{ f(y_{0},x), \, f(y_{1},x) , \;... \;, f(y_{n},x) \} \end{equation}
$\mathcal{B}$ = \begin{equation} \{ g(y,x_{0}), \, g(y,x_{1}) , \;... \;, g(y,x_{n}) \} \end{equation}
And I created a surface out of these equations in a plot. I know I can find an equation for this surface by fitting the plot data to known surfaces, but that is not what I want.
I want to be able to directly derive an equation for the surface from just these equations. Is this possible? How can I do this?