proper rotations represented by unit quaternions, with opposite signs identified.

Syntax

rot = rotation(a, b, c, d)
rot = rotation(q)
rot = rotation(cs)

Description

Numeric coefficients and general quaternions are normalised on construction. A point group or reference frame supplies its proper rotational parts. Improper orthogonal transforms cannot be converted to a rotation; use orthogonalTransform to retain parity.

For vector3d data, rot*v rotates each vector. The product rot1*rot2 applies rot2 first, then rot1. Array shapes broadcast, while the trailing four coefficients are internal to each element.

Keywords

keyword default description
dtype None floating-point type of the stored coefficients

Properties

a, b, c, d unit quaternion coefficients, with opposite signs representing the same rotation
data coefficient array of shape rot.shape + (4,)
phi1, Phi, phi2 Bunge Euler angles in radians
shape shape of the rotation array

See also

rotation.byEuler, rotation.byAxisAngle, rotation.byMatrix, quaternion

Used on

CrystalSymmetries, MTEXvsBungeConvention, EBSDKAM, RotationDefinition, RotationImproper, SO3FunConvolution, SO3FunOperations, SO3FunVectorValued

MATLAB’s rotation.rotation

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/rotation.rotation_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.