citation from wikipedia:
It is possible for two curves to have small Hausdorff distance but large Fréchet distance
Can anybody give me an example where this occurs?
(sub-question: is it even true?)
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What does "Fréchet distance" mean? (You might also clarify the meaning of Hausdorff distance, just in case. A link to Wikipedia usually suffices) – Giuseppe Negro Apr 22 '14 at 10:52
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http://en.wikipedia.org/wiki/Hausdorff_distance – Riko Apr 22 '14 at 10:53
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http://en.wikipedia.org/wiki/Frechet_distance – Riko Apr 22 '14 at 10:53
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I have finally found such an example. The weak Fréchet distance is shown on the picture below, the Fréchet distance (not the weak one) is even larger (actually about half the horizontal length of the figure).
Riko
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1The Fréchet distance in this example is actually about half the horizontal length of the figure, because the point on $f$ can only move forwards while the point on $g$ goes back and forth between the left and right extremes. – Apr 24 '14 at 19:12
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@Rahul Yes, you are right, I forgot to mention that it is actually the weak Fréchet distance shown on the picture, I will clarify it – Riko Apr 24 '14 at 20:39