S2FunHarmonic.S2FunHarmonic edit page

a class representing a function on the sphere by its harmonic series

The function is stored by its coefficients fhat with respect to the spherical harmonics, ordered degree by degree. This is the default representation in MTEX, since convolution, rotation and quadrature are cheap on it.

Syntax

sF = S2FunHarmonic(fhat)
sF = S2FunHarmonic(fun)
sF = S2FunHarmonic(psi)
sF = S2FunHarmonic(fun,'bandwidth',N)

Input

`fhat`	`harmonic coefficients, ordered by degree`
`fun`	`S2Fun or @function_handle to be approximated`
`psi`	`S2Kernel`

Output

`sF`	`S2FunHarmonic`

Options

`bandwidth`	`maximum harmonic degree`
`antipodal`	`the function fulfills f(v) = f(-v)`

Class Properties

`fhat`	`harmonic coefficients`
`bandwidth`	`maximum harmonic degree`
`antipodal`	`f(v) = f(-v)`
`isReal`	`the function takes only real values`

Example

sF = S2FunHarmonic.quadrature(@(v) dot(v,vector3d.Z).^2)

sF = S2FunHarmonic (y↓→x)
  bandwidth: 128
  antipodal: true

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/S2FunHarmonic.S2FunHarmonic.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.

S2FunHarmonic.S2FunHarmonic