a function on SO(3) through values at orientations, by radial basis functions, by harmonics or as a Bingham distribution; ori.interp(values) calls it

Syntax

SO3F = ori.interp(y)

A sum of kernels, the default.

SO3F = interpSO3(ori, y, halfwidth=10*degree, resolution=7*degree, density=True)

Of a kernel and grid, a density.

SO3F = interpSO3(ori, y, 'harmonic', bandwidth=16)

In harmonic form.

SO3F = interpSO3(ori, y, 'harmonic', regularisation=1e-4, SobolevIndex=2)

Regularised.

SO3F = interpSO3(ori, y, 'bingham')

The Bingham distribution of the weighted orientations.

Description

The method is the flag: no flag gives an SO3FunRBF fitted by interpolateRBF, which takes the other keywords (halfwidth, kernel, resolution, SO3Grid, exact, density, mean, tol, maxIter); ‘harmonic’ an SO3FunHarmonic fitted by least squares, interpolate, which takes bandwidth, weights, tol and maxIter; ‘bingham’ the Bingham distribution fitted to the orientations weighted by the values, calcBinghamODF. Vector values give a vector field.

Input

ori orientation, the nodes
values the values at the nodes, or vectors for a vector field
flags ‘harmonic’ or ‘bingham’

Keywords

keyword default description
regularisation None the weight of the Sobolev penalty of the harmonic fit
SobolevIndex None the Sobolev index s of the penalty of the harmonic fit

Output

SO3F SO3FunRBF, SO3FunHarmonic, SO3FunBingham or a vector field

See also

interpolateRBF, interpolate, calcBinghamODF, SO3FunApproximationTheory, RBFApproximationTheory

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/interpSO3_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.