a super-Fibonacci grid of orientations covering one fundamental region of the frame pair, its resolution the mean spacing of nearest neighbours

Syntax

S3G = superfibonacciSO3Grid(cs)

About 5 degree spacing.

S3G = superfibonacciSO3Grid(cs, ss, points=1000)

About 1000 nodes in the region.

S3G = superfibonacciSO3Grid(cs, resolution=2.5*degree)

A finer grid.

Description

The nodes are the super-Fibonacci spiral of Alexa, a low discrepancy sequence of quaternions, trimmed to the fundamental region. The length of the spiral is set from the resolution, taken as the mean distance to the nearest neighbour; with points it is set from the fraction of SO(3) the region fills, which is measured on a probe spiral, so that any pair of symmetries calibrates itself. fibonacciSO3Grid is MATLAB’s form, one node per resolution^3 of the volume.

Input

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

Keywords

keyword	default	description
`resolution`	`5*degree`	the mean distance to the nearest node, in radians
`points`	`None`	the approximate number of nodes in the fundamental region, instead of the resolution

Output

S3G SO3FibonacciGrid, orientations from CS to SS

References

M. Alexa, Super-Fibonacci spirals: fast, low-discrepancy sampling of SO(3), CVPR 2022, 8291-8300

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/superfibonacciSO3Grid_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.

superfibonacciSO3Grid