SO3VectorFieldHarmonic.interpolate edit page

Approximate a vector field on the rotation group (SO(3)) in its harmonic representation from some given orientations with corresponding tangent vectors and maybe some noise.

We compute this vector field componentwise, i.e. we compute three SO3FunHarmonics individually by interpolation. So, see SO3FunHarmonic.interpolate for further information.

Syntax

SO3VF = SO3VectorFieldHarmonic.interpolate(nodes,y)
SO3VF = SO3VectorFieldHarmonic.interpolate(nodes,y,'bandwidth',48)
SO3VF = SO3VectorFieldHarmonic.interpolate(nodes,y,'weights','equal')
SO3VF = SO3VectorFieldHarmonic.interpolate(nodes,y,'bandwidth',48,'weights',W,'tol',1e-6,'maxit',200)
SO3VF = SO3VectorFieldHarmonic.interpolate(nodes,y,'regularization',0) % no regularization
SO3VF = SO3VectorFieldHarmonic.interpolate(nodes,y,'regularization',1e-4,'SobolevIndex',2)

Input

nodes rotation, orientation
y vector3d, spinTensor, SO3TangentVector

Output

SO3VF SO3VectorFieldHarmonic

Options

bandwidth maximal harmonic degree (Be careful by setting the bandwidth by yourself, since it may yields undersampling)
weights corresponding to the nodes (default: Voronoi weights, 'equal': all nodes are weighted similar, numeric array W: specific weights for every node)
tol tolerance as termination condition for lsqr
maxit maximum number of iterations as termination condition for lsqr
regularization the energy functional of the lsqr solver is regularized by the Sobolev norm of SO3F with regularization parameter lambda (default: 1e-4)(0: no regularization)
SobolevIndex for regularization (default = 2)

See also

rotation.interp SO3FunHarmonic.interpolate

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/SO3VectorFieldHarmonic.interpolate.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.