define rotations by homochoric coordinates
Description
The inverse of homochoric. A homochoric vector points along the rotational axis and has length
\[ \rho = \left(\frac{3}{4}\left(\omega - \sin\omega\right)\right)^{1/3} \]
for the rotational angle \(\omega\), so the rotation group is mapped onto a ball of radius \((3\pi/4)^{1/3}\). Recovering \(\omega\) from \(\rho\) has no closed form and is done by a Newton iteration started at the small angle limit \(\omega \approx 2\rho\), which is exact up to \(O(\rho^5)\).
Syntax
rot = rotation.byHomochoric(v)
rot = rotation.byHomochoric([x y z])Input
| v | homochoric vector3d |
Output
| rot | rotation |
See also
quaternion.homochoric quaternion.cubochoric rotation.byRodrigues
Citing this page.
This page is part of the documentation of
MTEX, a free and open
source MATLAB toolbox for analyzing and modeling crystallographic textures.
It was written by The MTEX Developers and is published at
https://mtex-toolbox.github.io/rotation.byHomochoric.html.
If you use MTEX, or reuse text or figures from this page, in your research,
please cite
F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63
BibTeX
@article{bachmann2010mtex,
author = {F. Bachmann and R. Hielscher and H. Schaeben},
title = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
journal = {Solid State Phenomena},
volume = {160},
pages = {63-68},
year = {2010},
doi = {10.4028/www.scientific.net/SSP.160.63},
url = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.