the kernel of the inclination of a boundary plane about its trace, the one calcGBND convolves with

Syntax

Psi, psi = calcGBNDKernel()

The kernel of halfwidth 10 degree.

Psi, psi = calcGBNDKernel(5*degree, nonneg=True)

A nonnegative kernel of another halfwidth.

Psi, psi = calcGBNDKernel(S2DeLaValleePoussinKernel(halfwidth=10*degree))

The kernel for a given density kernel.

Description

A trace in a section leaves the inclination of the plane open. Psi is a function of the cosine t between a normal and the trace, and psi(v) = Psi(v.z) sin(angle(v, x)) is the spherical function it is applied as, for a trace along z in a section with normal x. Both are normalised so that a uniform distribution of planes gives one.

By default Psi solves the integral equation that makes the density of the normals the de la Vallee Poussin kernel of the halfwidth, or the S2Kernel given in its place; that solution may be negative. nonneg takes a Gaussian in t instead, bump the indicator of |t| < arcsin(halfwidth), MATLAB’s bound.

Keywords

keyword default description
halfwidth 10*degree the halfwidth of the kernel, or an S2Kernel, the density of the normals the kernel of the inclination is to give
nonneg False a nonnegative kernel, a Gaussian in the cosine to the trace
bump False a bump kernel, one within the halfwidth and zero outside

Output

Psi S2Kernel, or S2KernelHandle with nonneg or bump, the kernel of the inclination
psi S2FunHarmonic, the spherical function of a trace along z, antipodal

See also

calcGBND, S2DeLaValleePoussinKernel

MATLAB’s calcGBNDKernel

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/calcGBNDKernel_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.