the rotational angle up to symmetry, of the orientation or of the misorientation to other; MATLAB’s orientation.angle

Syntax

omega = angle(ori)

The smallest angle of the equivalents.

omega = angle(ori, symmetry=False)

Ignore the symmetric equivalents.

omega = angle(ori1, ori2)

The misorientation angle between them.

omega = angle(mori, 'max')

The largest angle of the equivalents.

Description

For misorientations with grain exchange, ori1.antipodal or ori2.antipodal, the two argument form is the smaller of the angles to ori2 and to inv(ori2); there is no antipodal option. With a fibre as other it is the angle to the fibre.

Input

ori orientation

Keywords

keyword	default	description
`other`	`None`	orientation, the second one; a fibre; or ‘max’
`symmetry`	`True`	reduce over the symmetric equivalents; False the plain angle of the rotations

Output

omega the angles in radians, of the broadcast shape

Example

Compare the crystallographic misorientation angle with the angle between the stored rotations. A 90-degree rotation about a cubic fourfold axis is a crystal symmetry operation.

from mtex import crystalFrame, orientation, degree, angle

cs = crystalFrame('m-3m')
a = orientation.byEuler(0, 0, 0, cs)
b = orientation.byEuler(90*degree, 0, 0, cs)
print('With cubic symmetry (degrees):', round(float(angle(a, b)/degree), 6))
print('Stored rotations (degrees):', round(float(angle(a, b, symmetry=False)/degree), 6))

angle returns radians. Dividing by degree converts them to degrees. The default searches symmetry-equivalent orientations, so these two stored rotations describe the same cubic orientation.

With cubic symmetry (degrees): 0.0
Stored rotations (degrees): 90.0

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/orientation.angle_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.

orientation.angle