I am trying to do a 2D interpolation between two curves as you can see from the attached picture.
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:
- Interpolate along $f_{a_1} $
- Interpolate along $f_{a_2}$
- 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.