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I am trying to do a 2D interpolation between two curves as you can see from the attached picture. enter image description here

where $a$ is a varrying paramter. $f_{a_1}$ and $f_{a_2}$ are known, or at least I can perform interpolation along them. The desired point is $(x_{des},y_{a_{des}}(x_{des}))$. Hence, I think I will have to do three interpolations as follows:

  1. Interpolate along $f_{a_1} $
  2. Interpolate along $f_{a_2}$
  3. Interpolate between the results to get $f_{a_{des}}$

However, I am not trusting the outcome. Does any one have a suggestion? thanks in advance.

user2536125
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  • Are those blue and red curves given as a set of points? – Misery Oct 20 '13 at 11:01
  • @Misery , yes, they are given as a set of points – user2536125 Oct 20 '13 at 11:11
  • I would suggest using kernel interpolation (estimation) treating all points (for both curves) as one set. See Wiki and this free e-book – Misery Oct 20 '13 at 11:14
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    It is not clear what makes $x_{des}, y_{des}$ special in your sketch. If you are just looking for something in between two functions, you could take the average of their $y$-values. Apparently you need something more sophisticated than that, but since the objective is unstated, it's impossible to tell what would meet it. – Post No Bulls Nov 29 '13 at 03:05

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