A method of rotation.

the rotation best mapping the list u onto the list v, by Horn’s quaternion method or Kabsch’s matrix method

Syntax

rot = rotation.fit(u, v)

Rot * u is nearest v.

rot = rotation.fit(u, v, weights=w)

Some pairs counting more.

rot = rotation.fit(u, v, method='kabsch')

By the singular value decomposition.

Description

The rotation maximising the weighted sum of <rot u_i, v_i> over the unit vectors: Horn’s method takes the largest eigenvector of a 4 x 4 matrix, Kabsch’s the singular value decomposition of the cross covariance; both give the same rotation. MATLAB’s call is rotation.fit(r, l) with l = rot * r, the same order. MATLAB’s handling of antipodal vectors is not ported: the vectors are taken with their sign.

Input

u, v vector3d, lists of one length

Keywords

keyword	default	description
`weights`	`None`	one weight per pair
`method`	`'horn'`	‘horn’ or ‘kabsch’

Output

rot rotation

References

W. Kabsch, A solution for the best rotation to relate two sets of vectors, Acta Cryst. A32 (1976) 922
B. K. P. Horn, Closed-form solution of absolute orientation using unit quaternions, Journal of the Optical Society of America A 4 (1987) 629

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.fit_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.

rotation.fit