A method of SO3Kernel.

the kernel at the cosine argument t (the angle on S1), or at a rotation or direction, or between two of them; MATLAB’s eval

Syntax

v = psi.eval(t)

At the cosines t, cos(omega/2) on SO(3), cos(theta) on S2.

v = psi(t)

The same.

v = psi.eval(rot)

At the angles of rotations, or the polar angles of directions.

v = psi.eval(rot1, rot2)

At the angles between two rotations or two directions.

Description

A kernel on SO(3) is a function of the cosine of half the rotation angle, one on the sphere of the cosine of the polar angle, one on the circle of the angle itself. Rotations or directions are reduced to that argument first: |a| of a rotation, the dot product of two; the z coordinate of a direction, the cosine between two.

Input

psi SO3Kernel, S2Kernel or S1Kernel
t ndarray of arguments, or rotation (SO3Kernel), or vector3d (S2Kernel)

Keywords

keyword default description
other None a second rotation or direction: the kernel at the angle between t and it

Output

v ndarray, the values

See also

SO3Kernel.grad, SO3Kernel.calcFourier

MATLAB’s SO3Kernel.eval

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/SO3Kernel.eval_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.