A method of SO3FunHarmonic.

the gradient, a harmonic vector field on SO(3), left or with side=’right’ right; with x its values at the orientations x

Syntax

G = SO3F.grad()

The gradient, an SO3VectorFieldHarmonic.

g = SO3F.grad(ori)

Its values at orientations, tangent vectors.

g = SO3F.grad(ori, side='right')

The right tangent vectors, in the crystal frame.

ori_new = exp(5*degree*normalize(g))

5 degree along the gradient from ori.

Description

The left gradient gives its tangent vectors in the specimen frame, the right one in the crystal frame; MATLAB passes SO3TangentSpace.rightVector for the right. The tangent vectors carry their orientations, so exp takes no second argument as MATLAB’s exp(v, rot).

Input

SO3F SO3FunHarmonic
x orientation, where to evaluate the gradient

Keywords

keyword default description
side 'left' ‘left’ or ‘right’, the tangent space

Output

G SO3VectorFieldHarmonic
g SO3TangentVector, the values at x

See also

SO3VectorFieldHarmonic, orientation.exp, SO3FunRBF.grad, SO3FunCBF.grad

MATLAB’s SO3FunHarmonic.grad

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/SO3FunHarmonic.grad_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.