A method of orientation.

the logarithm of an orientation, the tangent vector at a reference pointing to it

Syntax

v = log(ori)

At the identity.

v = log(ori, oriRef)

At oriRef, in specimen coordinates.

v = log(ori, oriRef, side='right')

At oriRef, in crystal coordinates.

v = log(mori, 'right')

The misorientation vector in crystal coordinates.

Description

The tangent vector v at oriRef with exp(v) = ori, the misorientation vector of ori relative to oriRef. The pair is reduced by symmetry first, as angle does it, so that the vector describes the two crystals and not their stored representatives: norm(log(ori, oriRef)) is angle(ori, oriRef). With side ‘left’ the vector is ori * inv(oriRef) taken to the tangent space, a specimen direction; with ‘right’ it is inv(oriRef) * ori, a crystal direction.

Input

ori orientation
ref orientation, the reference, by default the identity between the frames of ori; or ‘left’ or ‘right’, the side

Keywords

keyword default description
side 'left' ‘left’, the vector in specimen coordinates, or ‘right’, in crystal coordinates, MATLAB’s SO3TangentSpace.leftVector and rightVector
symmetry True reduce the pair by symmetry first; False takes the rotations as stored, MATLAB’s ‘noSymmetry’

Output

v SO3TangentVector at the reference, its norm the angle in radians

See also

SO3TangentVector.exp, orientation.angle, orientation.axis, RotationTangentSpace

MATLAB’s orientation.log

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/orientation.log_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.