Grids and triangulations for sampling directions and rotations, and for finding nearby samples.
| Class or function | Description |
|---|---|
| S1Grid | a sorted list of angles on an interval [min, max], periodic or not, the nearest neighbour and radius search of the tensor product grids S2Grid and SO3Grid |
| S2Grid | a grid on the sphere with ring structure, a ladder of polar angles theta and one azimuth grid per ring, whose nearest and radius searches use that structure |
| S2Triangulation | the Delaunay triangulation of directions on the sphere, their convex hull: the triangles T, counterclockwise from outside, and the triangle opposite each vertex |
| SO3Grid | the equispaced grid of orientations over one fundamental region of its frame pair, MATLAB’s SO3Grid: an S2 grid of the images of z with a ladder of gamma per node, so a search costs three binary searches |
| fibonacciS2Grid | the spherical Fibonacci grid: N = 2n + 1 points along a spiral, z linear in the index and the azimuth advancing by the golden angle |
| quadratureS2Grid | nodes and surface-area weights for integrating functions on the unit sphere |
| fibonacciSO3Grid | a low discrepancy grid of orientations from a super-Fibonacci spiral, restricted to the fundamental region of the frame pair |
| quadratureSO3Grid | the quadrature grid on SO(3) of a bandwidth: the nodes and weights that integrate every harmonic function up to that degree exactly |
| HEALPixS2Grid | the HEALPix nodes of the sphere as a list of directions |
| SO3FibonacciGrid | the super-Fibonacci grid of orientations, a low-discrepancy quaternion spiral trimmed to one fundamental region of the frame pair, searched through the quaternion k-d tree |
| equispacedS2Grid | an equispaced spherical grid, nearly equidistant directions on rings of constant polar angle |
| regularS2Grid | a regular spherical grid, the tensor product of a ladder of polar angles and a ladder of azimuths, the layout of pole figure files |
| equispacedSO3Grid | nearly equidistant orientations covering one fundamental region of the frame pair |
| regularSO3Grid | the regular raster of Euler angles over the Euler box of the frames, as the ODF sections show it |
| superfibonacciSO3Grid | a super-Fibonacci grid of orientations covering one fundamental region of the frame pair, its resolution the mean spacing of nearest neighbours |
| localOrientationGrid | an equispaced grid of orientations in a ball about a centre |
| localS2Grid | an equispaced grid of directions in a spherical cap about a centre |
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/geometryGrids_index_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.