Timeline for Finding vertices of a polytope?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 13, 2023 at 15:27 | review | Close votes | |||
| Aug 16, 2023 at 8:23 | |||||
| Aug 13, 2023 at 15:22 | answer | added | user1703 | timeline score: 1 | |
| Aug 13, 2023 at 15:06 | comment | added | user1703 | "is exponentially larger ": it can very well turn out that all points that are the intersection of $d$ hyperplanes are indeed vertices of the polytope ! | |
| Aug 13, 2023 at 14:59 | answer | added | Kevin Reid | timeline score: 1 | |
| Aug 13, 2023 at 14:57 | comment | added | user1703 | There is no question ! | |
| Aug 13, 2023 at 4:55 | comment | added | Makogan | @Enigmatisms I perhaps was unclear, you have arbitrarily many of these planes, not just 3 and you are looking for the vertices of the underlying polytope. | |
| Aug 13, 2023 at 2:38 | comment | added | Enigmatisms♦ | So If I understand correctly, you can check the determinant of the 3x3 system before solving for the vertex. If the determinant is 0 (or its absolute value is extremely small), there won't be a good solution for you. | |
| Aug 13, 2023 at 2:29 | comment | added | Enigmatisms♦ | I am not sure what the figure means here. My understanding is that in this figure, the normals of these planes form linear relationship. Since normal is orthogonal to any given line on that plane, so we know the intersection of two planes defines a line of which the direction can be calculated by the cross product of two normals. Since all three normals are on the same plane (due to linear relationship), the intersection lines will be parallel to each other, so the system has no solution thus no vertex. When these lines are exactly the same, then you will have infinite number of solutions. | |
| Aug 12, 2023 at 22:55 | history | asked | Makogan | CC BY-SA 4.0 |