Fréchet distance tells how similar two curves are. Now let's say I have two curves A and B, both represented in several discrete coordinate x, y points. And the fréchet distance between A and B is d. What technique can I employ to find another curve that has d/2 fréchet distance from both curves and has a total euclidean distance which is in the range [min(|A|, |B|), max(|A|, |B|)], where |A| is the total euclidean distance of the curve A and |B| is the total euclidean distance of the curve B? I know that there is probably not a single curve, any one curve will be great help for me. Thanks in advance.
Raichel and Har-Peled wrote a paper, The Frechet Distance Revisited and Extended, which explains how to compute various curves. This might implicitly give you the answer.