Timeline for Could somebody suggest a way to determine if a parallelogram contains another parallelogram?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| S Jun 14, 2021 at 14:56 | history | suggested | Igor Sikora | CC BY-SA 4.0 |
Corrected spelling
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| Jun 14, 2021 at 8:33 | review | Suggested edits | |||
| S Jun 14, 2021 at 14:56 | |||||
| Jun 14, 2021 at 8:12 | answer | added | Karl Fabian | timeline score: 4 | |
| Jun 4, 2021 at 12:04 | comment | added | user44143 | @syk, it would help for the post to state explicitly how the algorithm should respond in these examples: 1) Is the parallelogram at $(0,0)$ with basis vectors $2i$ and $4j$ contained in the parallelogram at $(1,0)$ with basis vectors $3i$ and $5j$? 2) Is the parallelogram at $(0,0)$ with basis vectors $2i$ and $4j$ contained in the parallelogram at $(0,0)$ with basis vectors $5i$ and $3j$? | |
| Jun 4, 2021 at 7:38 | comment | added | syk | @SamHopkins You're right if they share the same origin, but in my case, the parallelotopes can have arbitrary location and shape. Please refer to my previous answer above. | |
| Jun 4, 2021 at 7:00 | history | edited | YCor |
edited tags; edited tags; edited tags
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| Jun 4, 2021 at 6:42 | comment | added | syk | @MattF. In my algorithm, I use a generator that has a vertex $x_0$ as a reference point of the parallelotope and n linearly independent vectors $v_k (\forall{k=1,..,n})$as bases. ( $P=\{x_0,v_1,v_2, .. , v_n\}$ for $n$-dim.). In this way, I can operate a parallelotope at the $n$-dimensional space using an affine transform in $n+1$ linear calculation. | |
| Jun 4, 2021 at 6:42 | history | edited | syk | CC BY-SA 4.0 |
added 18 characters in body
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| Jun 3, 2021 at 17:55 | review | Close votes | |||
| Jun 8, 2021 at 3:08 | |||||
| Jun 3, 2021 at 14:26 | comment | added | Neil Strickland | This question is somewhat related: mathoverflow.net/questions/279021 | |
| Jun 3, 2021 at 13:58 | review | First posts | |||
| Jun 3, 2021 at 17:33 | |||||
| Jun 3, 2021 at 13:55 | comment | added | Sam Hopkins | Are the parallelotopes based at the origin? Here's a guess, which might not be right. An $n$-dimensional parallelotope (based at the origin) is generated (i.e., as a zonotope) by $n$ linearly independent vectors. Say you have one set of vectors $\{v_1,\ldots,v_n\}$ corresponding to one parallelotope, and another $\{w_1,\ldots,w_n\}$ corresponding to another. Maybe it's the case that we have a containment of parallelotopes if and only if $\{w_1,\ldots,w_n\}$ is contained in the simplex generated by $\{v_1,\ldots,v_n\}$ and the origin. | |
| Jun 3, 2021 at 13:50 | history | asked | syk | CC BY-SA 4.0 |