Timeline for Intersection of two Jordan curves lying in the rectangle
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 11, 2021 at 18:28 | comment | added | Sam Nead | Re: invariant. I was going to colour various things, and use that to get a labelling a la Sperner. Your invariant is simpler. | |
| Jan 11, 2021 at 18:26 | comment | added | Sam Nead | Re: slopes - good point. I should have said "make them piecewise linear but generic with respect to the vertical projection". I've added a simpler version of that to the answer. Thank you! | |
| Jan 11, 2021 at 18:25 | history | edited | Sam Nead | CC BY-SA 4.0 |
added 156 characters in body
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| Jan 11, 2021 at 13:50 | comment | added | Pietro Majer | This is nice; I'd also arrange the slopes of $\alpha$ and $\beta$ never to be vertical, so that the intersection of $\alpha\cup \beta$ with $\ell_t$ is always finite and suitably continuous. I guess the invariant you mean is more subtle than as described in the quoted link; may be you mean "the parity of the cardinality of the set of pairs $(a,b)\in (\alpha\cup \beta)\cap\ell_t$ s.that $a$ is above $b$" (that is $a_2>b_2$), which is indeed locally constant (yet changes from $t=0$ to $t=1$). | |
| Jan 11, 2021 at 12:50 | history | answered | Sam Nead | CC BY-SA 4.0 |