Timeline for Curvature flows for PL closed curves in the plane?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 2, 2017 at 12:43 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Broken link fixed.
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| Sep 17, 2013 at 22:42 | comment | added | Ryan Budney | If you look at their proof they choose "struts" and there's more than one choice, generally. So say you were to write a computer algorithm to perform the motion described in the CDR paper, you would have to choose the struts (as the DE isn't defined without a choice of struts, the the DE depends on the choice). So if you vary the initial conditions (perturb the initial polygon a little) the motion your computer program performs would not always vary continuously with the input polygon. | |
| Sep 17, 2013 at 22:33 | comment | added | Joseph O'Rourke | I confess I do not understand the difference, as CDR operates on any collection of closed and open polygons simultaneously, and follows a differential equation, not unlike Gage-Hamilton. But we are speaking different languages and perhaps I cannot help further. | |
| Sep 17, 2013 at 21:00 | comment | added | Ryan Budney | Unfortunately the Connelly, Demaine and Rote paper takes as input to the motion more information than just the polygon -- they make a choice of "struts". So their motion does not make sense as a continuous function on the space of all polygons, and in that regard it's not analogous to the Gage-Hamilton result. Do you know if anyone has done work that does not involve making choices -- something that defines dynamics on the space of all polygons (as a space)? Connelly-Demaine-Rote basically just show that the polygon space is connected. I want a flow that gives contractibility. | |
| Sep 17, 2013 at 0:52 | comment | added | Joseph O'Rourke | @RyanBudney: I added a linkage reference. Hope that helps! | |
| Sep 17, 2013 at 0:51 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Added linkage references.
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| Sep 17, 2013 at 0:18 | comment | added | Ryan Budney | Yes, exactly, I'm looking for a "linkage" version of the papers you cite. | |
| Sep 17, 2013 at 0:16 | comment | added | Joseph O'Rourke | Ah, interesting question! There is work on morphings of arbitrary polygons to convex polygons, while all edges remain fixed in length, so it is a reconfiguration of a closed linkage. Perhaps this is what you mean? | |
| Sep 16, 2013 at 23:37 | comment | added | Ryan Budney | Thanks. Have you seen an analysis of any flows that keep the edge lengths constant? | |
| Sep 16, 2013 at 23:25 | history | answered | Joseph O'Rourke | CC BY-SA 3.0 |