orthogonal transforms, a rotation and a parity as a fifth coordinate, -1 for an improper one, the rotation followed by the inversion
Syntax
orthogonalTransform(rot)
orthogonalTransform(rot, True)
The improper transform -rot.
orthogonalTransform(cs)
The elements of a point group.
Input
rot |
rotation, quaternion coordinates, or a referenceFrame or symmetry supplying its elements; None selects identity |
improper |
whether to apply inversion after the rotation; default False |
dtype |
floating-point type of the stored coordinates |
Members
| a | the coefficient a of the rotational part |
| angle | the rotational angle of the rotational part, or the angle between the rotational parts of two |
| axis | the rotational axis of the rotational part |
| b | the coefficient b of the rotational part |
| byAxisAngle | the proper transforms rotating by omega about the axis v |
| byEuler | proper orthogonal transforms defined by Euler angles |
| byMatrix | an orthogonal matrix of either sign |
| c | the coefficient c of the rotational part |
| d | the coefficient d of the rotational part |
| dot | the inner product of the rotational parts up to sign, zero between transforms of different parity |
| Euler | the Euler angles of the rotational part, in the convention named or the session’s |
| i | whether the transform is improper, MATLAB’s rot.i |
| id | the identity transform |
| inv | the inverse transform, the inverse rotation with the same parity |
| inversion | the inversion -I |
| isclose | equal within the angular tolerance tol and of one parity, MATLAB’s eq |
| isImproper | whether the transform is improper, its determinant -1 |
| matrix | the orthogonal matrices, the rotation matrix times the parity |
| parity | the parity, 1 for a proper and -1 for an improper transform |
| rot | the rotational part, a rotation |
| unique | the disjoint list of orthogonal transforms, those equal up to a tolerance taken as one |
Used on
CrystalSymmetries, RotationImproper
source
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/orthogonalTransform_index_py.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.