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it is known that if we have a curvilinear coordinate system in ℝ^{2}like [itex]x=x(u,v)[/itex], [itex]y=y(u,v)[/itex], and we keep one coordinate fixed, say [itex]v=\lambda [/itex], we obtain a family of one-dimensional curves [itex]C_{\lambda}(u)=\left( x(u,\lambda),y(u,\lambda) \right)[/itex]. The analogous argument holds for the other coordinateu. These family of curves are sometimes calledcoordinate lines, orlevel curves.

My question is: if I am given two family of curves [itex]C_v(u)[/itex] and [itex]C_u(v)[/itex] is it possible to obtain the system of curvilinear coordinates [itex]x(u,v)[/itex], [itex]y(u,v)[/itex] that generated them?

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# How to obtain a 2D-coordinate system from two family of curves?

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