orientations defined by Euler angles

Syntax

ori = orientation.byEuler(phi1, Phi, phi2, cs, ss)

Bunge’s convention.

ori = orientation.byEuler(alpha, beta, gamma, 'ZYZ', cs, ss)

Matthies’ convention.

ori = orientation.byEuler(phi1, Phi, phi2, 'Kocks', cs, ss)

Kocks’ convention.

ori = orientation.byEuler([phi1, Phi, phi2], cs)

The angles as one triple, or an array of triples.

Description

The angles are in radians, arrays of them broadcast against each other. Without a convention the preference EulerAngleConvention decides, Bunge’s ZXZ by default. The convention and the frames follow the angles, in any order.

Input

`a`	the first angle, phi1 or alpha; or an array whose last axis holds the three angles
`b`	the second angle, Phi or beta
`c`	the third angle, phi2 or gamma
`args`	the convention, ‘Bunge’ or ‘ZXZ’, ‘Matthies’, ‘ZYZ’ or ‘ABG’, ‘Roe’, ‘Kocks’, ‘Canova’, ‘nfft’; the crystal frame cs and the specimen frame ss, or a second crystal frame for a misorientation

Keywords

keyword	default	description
`antipodal`	`False`	a misorientation with grain exchange

Output

ori orientation

Example

Construct a Bunge orientation from angles in degrees. Applying it to a crystal direction expresses that direction in specimen coordinates; the rotated cube shows the same transformation.

import numpy as np
import matplotlib.pyplot as plt
from mtex import crystalFrame, orientation, Miller, crystalShape, degree, plot

cs = crystalFrame('m-3m')
ori = orientation.byEuler(45*degree, 30*degree, 60*degree, cs)
h = Miller(0, 0, 1, cs, 'uvw')
r = ori * h
print('Specimen direction:', np.round(r.normalize().data, 3))
plot(ori * crystalShape.cube(cs), faceAlpha=0.4, colored=True)
plt.show()

Specimen direction: [ 0.354 -0.354  0.866]

Example output for orientation.byEuler

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.byEuler_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.byEuler