nearly equidistant orientations covering one fundamental region of the frame pair

Syntax

S3G = equispacedSO3Grid(CS, SS, points=1000)

About this many points.

S3G = equispacedSO3Grid(CS, resolution=5*degree)

Of a given resolution.

S3G = equispacedSO3Grid(CS, maxAngle=20*degree)

Only a ball about the identity.

S3G = equispacedSO3Grid(CS, maxAngle=20*degree, center=ori)

A ball about an orientation.

Description

An equispaced grid of the images of z at the resolution, with a ladder of the third Euler angle at each, kept where it lies in the fundamental region of the crystal and the specimen symmetry. The SO3Grid knows its structure, which makes its searches fast (find, radius); the last four grids are kept, so that asking for the same grid again costs nothing. With maxAngle only the ball about the centre is kept; a ball about the identity smaller than the fundamental region is a localOrientationGrid, an orientation.

Input

`CS`	crystalFrame
`SS`	specimenFrame, by default the default specimen frame

Keywords

keyword	default	description
`resolution`	`5*degree`	the spacing of the grid, in radians
`points`	`None`	the approximate number of points, which sets the resolution instead
`maxAngle`	`180*degree`	the radius of the ball to fill
`center`	`None`	orientation, the centre of the ball, by default the identity

Output

S3G SO3Grid, or orientation for a small ball

Used on

OrientationGrid, ODFExport, RBFApproximationTheory, SO3FunApproximationTheory, SO3FunVectorField, SO3FunVectorValued

MATLAB’s equispacedSO3Grid

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/equispacedSO3Grid_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.

equispacedSO3Grid