Timeline for Find a convex hull that contains given points?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2019 at 13:31 | history | edited | Wolfgang | CC BY-SA 4.0 |
minor corrections, fixed Latex
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| Feb 12, 2013 at 18:46 | vote | accept | CommunityBot | ||
| Feb 12, 2013 at 18:42 | vote | accept | CommunityBot | ||
| Feb 12, 2013 at 18:45 | |||||
| Feb 12, 2013 at 10:36 | comment | added | user31317 | Here is an other interesting question. Can you compute that efficiently? | |
| Feb 12, 2013 at 10:29 | comment | added | user31317 | The volume is the absolute value of determinant of matrix $A$ which has as columns the vectors $u_{1},...,u_{n}$. If you change $u_{1}$ with $a_{i} = x_{1}u_{1}+...+x_{n}u_{n}$ (let $|x_{1}|\geq 1$) then the volume of the new parallelepiped will be $|x_{1}||det(A)|$ is that right? I believe you are correct!!! | |
| Feb 12, 2013 at 10:18 | comment | added | user31317 | Observe that $v_{1},...,v_{n}$ are not orthonormal... | |
| Feb 12, 2013 at 10:06 | comment | added | user31317 | @Anton: Can you explain why by exchanging $u_{k}$ and $a_{i}$ the volume is increased? | |
| Feb 12, 2013 at 5:53 | comment | added | Anton Petrunin | @Misha: I do not think you are right; if $|x_i|>1$ once then you can increase the volume. | |
| Feb 11, 2013 at 22:33 | comment | added | Misha | Anton: The last version does not work since some $|x_k|$ could be (much) larger than $1$ and some (much) smaller. It is easy to construct examples with $n=2$ and $m=3$. | |
| Feb 11, 2013 at 19:40 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
added 348 characters in body; added 3 characters in body
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| Feb 10, 2013 at 17:40 | history | answered | Anton Petrunin | CC BY-SA 3.0 |