Timeline for "Derived" polyhedra and polytopes
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2013 at 13:35 | comment | added | Joseph O'Rourke | @Olga: Good question! That will not be an easy experiment for me because I am relying on the convex hull in 3D for each successive polyhedron. But conceptually it is possible, and perhaps would untangle to a convex shape just as in 2D. | |
| Nov 28, 2013 at 8:18 | comment | added | Olga | Did you try "polyhedra" with intersecting faces as in the example for a polygon? Could you provide a picture just to see what happens? Is the obtained polyhedron going "back to normal"? | |
| Nov 26, 2013 at 13:23 | answer | added | Joseph O'Rourke | timeline score: 3 | |
| Nov 25, 2013 at 5:23 | answer | added | Gjergji Zaimi | timeline score: 16 | |
| Nov 24, 2013 at 16:41 | comment | added | Joseph O'Rourke | @AllenKnutson: Excellent point! These are quite analogous to Subdivision surfaces. | |
| Nov 24, 2013 at 15:47 | comment | added | Allen Knutson | It's not so far off from talks I've seen by Tony DeRose of Pixar, where the limit mesh is used as a model in animation. Old papers are at homes.cs.washington.edu/~derose/papers.html , and probably one can watch a talk on the MSRI website, msri.org/general_events/20258 | |
| Nov 24, 2013 at 14:24 | comment | added | Lev Borisov | It is an interesting setup, maybe some people in probability have looked at it. There is certainly some discontinuity in the process, even if you look at centroids, because the new polytope will depend discontinuously on the original one. Still, there is probably some finite dimensional space of limiting shapes with probability 1, at least locally. | |
| Nov 24, 2013 at 14:00 | comment | added | Joseph O'Rourke | @LevBorisov: Good point, Lev. I am just using one, random order. Probably using the centroid is the cleanest rule. | |
| Nov 24, 2013 at 13:14 | comment | added | Lev Borisov | How do you order the points of the triangles? Do you use all six orders? | |
| Nov 24, 2013 at 12:13 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Cite correction; clarification.
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| Nov 24, 2013 at 2:53 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |