orientation.log edit page

the logarithmic map that translates a orientation into a tangent vector.

Therefore it converts a given orientation, relative to a reference orientation, into its corresponding tangent vector in the tangent space at the reference.

Hence, the log-function computes the relative orientation. This can also be interpreted as misorientation vector between two orientations, which is measured in the tangent space.

The misorientation vector can also be seen as the projection of an orientation onto the tangential space of the orientation space centered at the orientation ori_ref. The inverse mapping from the tangential space onto the orientation space is the exponential map exp.

The pair is reduced by symmetry first, exactly as angle does it, so that the result describes the two crystals and not the representatives they happen to be stored as. In particular norm(log(ori,ori_ref)) is angle(ori,ori_ref). Pass 'noSymmetry' to take the logarithm of the rotations as they are.

Syntax

v = log(ori)
v = log(ori,ori_ref,SO3TangentSpace.rightVector)

Input

ori,ori_ref orientation

Output

v SO3TangentVector, spinTensor

Example

compute misorientation vector in crystal coordinates

cs = crystalSymmetry('432');
mori = orientation.KurdjumovSachs(cs,cs)
v = log(mori,SO3TangentSpace.rightVector)
round(Miller(v,mori.CS))
mori = misorientation (432 → 432)
 
 (111) || (011)   [101̅] || [111̅]
 
 
v = SO3TangentVector (crystal)
 intern symmetries: 432 → 432
 TagentSpace: rightVector
      x     y     z
  0.133 0.133 0.724
 
ans = Miller (432)
  h  k  l
  2  2 11

See also

orientation.logm quaternion.log vector3d.exp Miller.exp

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.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.