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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?

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    Just a fleeting though, perhaps this could be considered as the (possibly overdetermined) *method of lines* solution of a PDE, and then one could run an inverse method approach to reconstruct the original surface.2012-11-02
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    The equations in the sets are determined experimentally themselves and don't represent differential equations, if that helps.2012-11-02

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