File:Spin 180,60.svg
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Summary
[edit]DescriptionSpin 180,60.svg |
English: Products of two versors (Spin(3) elements) in both orders acting on a 2-sphere shown in w:stereographic projection. The versor f induces a 180° rotation (violet), but is represented with a 90° great arc (π/2 length, black). Such versors are termed right versors. The versor g induces a 60° rotation (yellow), but is represented with a 30° great arc (π/6 length, shown as two straight upwards black arrows). Two products of versors form two spherical triangles (green fill). Note that direction of 180° arrows is important: reversing them would result in same SO(3) elements, but in opposite versors represented with 90° great arcs in opposite direction (clockwise). The rotation of the g f product is shown in red, of f g is shown in azure; one can follow some compositions of violet and yellow arrows in different orders. Note that the right yellow circle has arrows spaced by 30° (one g rotation corresponds to two intervals between arrows).
At the upper left corner there is a depiction of the same sphere in orthographic projection and a schema of the stereographic projection is present. Near side of the sphere corresponds to the lower side of the image and is seen upside-down (the main image shows the sphere from inside, whereas the orthographic projection shows its exterior view). |
Date | |
Source | Own work, got some fragments from File:SO(3) 60-90-60.svg (the same author) and private drafts with a similar form. |
Author | Incnis Mrsi |
Other versions | see Category: Group actions |
SVG development InfoField | This trigonometry was created with a text editor. |
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[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
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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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 14:24, 8 October 2016 | 800 × 896 (13 KB) | Incnis Mrsi (talk | contribs) | converted from <g><title>…</title><element …/></g> to <element …><title>…</title></element>, other tweaks | |
22:17, 2 October 2016 | 800 × 896 (11 KB) | Incnis Mrsi (talk | contribs) | fixed broken «id=» | ||
22:15, 2 October 2016 | 800 × 896 (11 KB) | Incnis Mrsi (talk | contribs) | final «title=» fixes | ||
22:01, 2 October 2016 | 800 × 896 (11 KB) | Incnis Mrsi (talk | contribs) | «title=» fixes (?) | ||
21:44, 2 October 2016 | 800 × 896 (11 KB) | Incnis Mrsi (talk | contribs) | «id=» fixes, added «title=» | ||
14:15, 31 January 2014 | 800 × 896 (11 KB) | Incnis Mrsi (talk | contribs) | =={{int:filedesc}}== {{Information |Description={{en|1=Products of two versors (Spin(3) elements) in both orders acting on a 2-sphere shown in w:stereographic projection. The versor ''f'' induces a 180° rotation (vi... |
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Width | 800 |
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Height | 896 |