Syntax

SO3F = SO3FunCBF(h, r)

The fibre h

r, a 10 degree kernel.

SO3F = SO3FunCBF(h, r, weights, psi)

Several fibres, weighted, the kernel psi.

SO3F = SO3FunCBF(f, halfwidth=10*degree)

From a fibre f.

Description

The function of the orientation g is sum_i w_i psi(g h_i . r_i), every fibre taken with all its symmetrically equivalent fibres; it is constant along each fibre. The crystal frame is that of h, the specimen frame that of r or SS. The weights default to equal ones giving a mean of one. fibreODF builds one with the weights normalised.

Input

`h`	Miller or vector3d, the crystal directions, or a fibre
`r`	vector3d, the specimen directions, one per crystal direction
`weights`	one weight per fibre; by default a mean of one
`psi`	S2Kernel; by default the de la Vallee Poussin kernel

Keywords

keyword	default	description
`SS`		the specimen frame, when r has none
`halfwidth`		the halfwidth of the default kernel, 10 degree unless given

Output

SO3F SO3FunCBF

Members

abs	the absolute value of the function, pointwise, as a function handle
bandwidth	the harmonic bandwidth of the S2 kernel
calcError	the distance between two orientation density functions, or the error of an ODF against pole figures
conv	the convolution with a kernel psi, through the harmonic expansion
discreteSample	a random sample of n orientations drawn from an orientation density, of directions from a density on the sphere, of numbers from a density on an interval, or n random members of a list
eval	the values at rotations or orientations, the kernel sum over the fibres and their symmetric equivalents
exp	the exponential of the function, pointwise, as a function handle
frameA	the frame the orientations map from, the crystal frame
frameB	the frame the orientations map to, the specimen or a second crystal frame
grad	the gradient of a fibre ODF at orientations, or without them the vector field of the gradients of its harmonic expansion, as MATLAB’s grad
log	the logarithm of the function, pointwise, as a function handle
mean	the mean of the function over SO(3), the sum of the weights times the kernel’s mean
norm	the L2 norm of the function, from its harmonic expansion
radon	the Radon transform of a fibre ODF: the pole figure of a crystal direction, the inverse pole figure of a specimen direction, or the pole density of both
rotate	the function rotated by r on the left, the specimen side, or with side=’right’ on the crystal side
SO3FunCBF	a fibre ODF: a sum over fibres h \|\| r of a kernel on the sphere of the angle between g h and r
sqrt	the square root of the function, pointwise, as a function handle
textureIndex	the texture index of a function on SO(3) or on the sphere, the squared L2 norm of its harmonic expansion
times
uminus

Used on

SO3FunDefinition

MATLAB’s SO3FunCBF_index

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/SO3FunCBF_index_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.

The class SO3FunCBF