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EDIT (David White): This is really a comment to Gerhard's answer, not an answer in and of itself.

Thank you for your input Gerhard. A small clarification: what is desired is not two surfaces f3 $f_3$ and f4, $f_4$, but just one function that would undergo directional distortion and that would be some interpolation of f1 $f_1$ and f2 $f_2$ (to ensure tangentiality as f1 $f_1$ grows closer to f2) $f_2$).

Regarding the straw model. Are you using some discrete description (particles)? Where each point would undergo a different displacement u? $u$? If so, we can generate a surface f3 $f_3$ but we loose the closed-form formula for it, am I correct?

Thanks again,

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Thank you for your input Gerhard. A small clarification : what is desired is not two surfaces f3 and f4, but just one function that would undergo directional distortion and that would be some interpolation of f1 and f2 (to ensure tangentiality as f1 grows closer to f2)

Regarding the straw model. Are you using some discrete description (particles)? Where each point would undergo a different displacement u? If so, we can generate a surface f3 but we loose the closed-form formula for it, am I correct?

Thanks again,