a low discrepancy grid of orientations from a super-Fibonacci spiral, restricted to the fundamental region of the frame pair; MATLAB’s fibonacciSO3Grid

Syntax

S3G = fibonacciSO3Grid(cs)

5 degree resolution.

S3G = fibonacciSO3Grid(cs, ss, points=10000)

About 10000 nodes in the region.

S3G = fibonacciSO3Grid(cs, ss, resolution=2.5*degree)

A finer grid.

S3G = fibonacciSO3Grid(cs, cs, antipodal=True)

Misorientations with antipodal symmetry.

Description

The nodes are the super-Fibonacci spiral of Alexa with round(8 pi^2 / resolution^3) nodes over SO(3), one node per resolution^3 of its volume, trimmed to the fundamental region. Unlike a lattice the number of nodes is free; points sets the resolution from the volume fraction of the fundamental region. To cover a ball around one orientation take localOrientationGrid.

Input

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

Keywords

keyword	default	description
`resolution`	`5*degree`	the node spacing, in radians
`points`	`None`	the approximate number of nodes in the fundamental region, instead of the resolution
`antipodal`	`False`	the fundamental region with the antipodal symmetry of misorientations, half the region

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/fibonacciSO3Grid_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.

fibonacciSO3Grid