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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.

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  • $\begingroup$ Perhaps you can interpolate the two curves. $\endgroup$ – Yuval Filmus Aug 22 '17 at 10:40
  • $\begingroup$ Can you give a simple example how interpolation would be like? $\endgroup$ – besabestin Aug 22 '17 at 10:46
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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.

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