Size of this preview: 315 × 432 pixels.
Original file (315 × 432 pixels, file size: 285 KB, MIME type: image/gif, looped, 62 frames)
This is a file from the Wikimedia Commons. Information from its description page there is shown below.
Commons is a freely licensed media file repository. You can help.
Commons is a freely licensed media file repository. You can help.
Summary
| Description |
English: This is an animation of a typical geodesic in the Heisenberg group, parameterized by arc-length. |
| Date | |
| Source | Created in mathematica, using equation 2.23 of Capogna et al "Introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem" |
| Author | Slawekb |
- Other information
Mathematica source:
R[f_] := {Re[f1], Im[f1], f2}
\[Gamma][c_, \[Phi]_][s_] =
R[{E^(I \[Phi]) (1 - E^(-I c s))/c, (c s - Sin[c s])/(2 c^2)}] //
ComplexExpand
u[S_] := ParametricPlot3D[{\[Gamma][1, 0][s]1 t, \[Gamma][1, 0][
s][2] t, 0}, {s, 0, S}, {t, 0, 1}, Mesh -> False]
v[S_] := ParametricPlot3D[\[Gamma][1, 0][s], {s, 0, S}]
PlotTab =
Table[Show[u[S], v[S],
PlotRange -> {{0, 2}, {-1, 1}, {0, \[Pi]}}], {S, 0.1, 2 \[Pi],
0.1}];
Export["heis.gif", PlotTab]
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
|
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 16:12, 3 May 2016 | | 315 × 432 (285 KB) | Slawekb | Uploading a self-made file using File Upload Wizard |
File usage
The following 2 pages use this file:
Global file usage
The following other wikis use this file:
- Usage on ca.wikipedia.org
- Usage on gl.wikipedia.org
- Usage on pt.wikipedia.org
- Usage on www.wikidata.org
