Timeline for Approximating Jordan curves
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2018 at 23:46 | comment | added | Pietro Majer | Are you really interested in curve parametrized on intervals? the situation would be simpler for closed curves $\gamma:\mathbb{S}^1\to\mathbb{R}^2$. For curves defined on $[0,1]$ e.g. property 1 may fail just because $\gamma_2$ ends a bit earlier, or because they diverge a bit near the endpoint. | |
| Jan 7, 2013 at 1:18 | comment | added | Joseph O'Rourke | The Fréchet distance might be an appropriate measure? Informally it is the shortest leash that allow a master walking on one curve to walk a dog who follows the other curve. en.wikipedia.org/wiki/Fr%C3%A9chet_distance | |
| Jan 6, 2013 at 14:00 | history | edited | Hans-Peter Stricker |
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| Jan 6, 2013 at 1:48 | answer | added | Kevin R. Vixie | timeline score: 7 | |
| Jan 6, 2013 at 0:51 | comment | added | Mariano Suárez-Álvarez | Well, what I meant is: if $\gamma_2$ can be expressed in that way (and it seems it can) then express your intution in terms of conditions on $f$. So, yes, you would have to impose conditions on $f$! | |
| Jan 6, 2013 at 0:34 | comment | added | Hans-Peter Stricker | But you would have to impose some restrictions on $f(t)$. It must not get arbitrarily large to comply with the conditions, does it? But basically you are right, I have thought about this, too. | |
| Jan 6, 2013 at 0:34 | comment | added | Mariano Suárez-Álvarez | This looks like it would be easier to be made sense of if you tried to express it in terms of the function $f$ such that $\gamma_2(t)=\gamma_1(t)+f(t)\textbf{n}(t)$ with $\textbf n$ the normal vector to $\gamma_1$ (for some reparametrization of $\gamma_2$; this can be done, I think, because of your second condition) | |
| Jan 5, 2013 at 23:50 | history | asked | Hans-Peter Stricker | CC BY-SA 3.0 |