an equispaced spherical grid, nearly equidistant directions on rings of constant polar angle

Syntax

S2G = equispacedS2Grid(resolution=5*degree)

The sphere at 5 degree.

S2G = equispacedS2Grid(points=1000)

About 1000 points.

S2G = equispacedS2Grid(resolution=5*degree, antipodal=True)

Axes, the upper hemisphere.

S2G = equispacedS2Grid(resolution=5*degree, maxTheta=70*degree)

A spherical cap.

S2G = equispacedS2Grid(cs, resolution=5*degree)

The fundamental sector of a frame.

Description

The rings lie resolution apart in the polar angle, each holding sin(theta) times the equator count of azimuths, the odd rings offset by half a step. With a number of points the resolution is chosen to give about that many. A frame restricts the grid to its fundamental sector, of the Laue group for axes; a sphericalRegion to that region.

Python has no ‘identified’ hemisphere and no restrict2MinMax, and center is the flag of a point at the pole, not MATLAB’s centre direction.

Input

args a crystalFrame or specimenFrame, whose fundamental sector the grid covers, or a sphericalRegion

Keywords

keyword	default	description
`resolution`	`2.5*degree`	the spacing of the rings and of the points on a ring, in radians
`points`	`None`	the number of points instead of the resolution
`minTheta`	`0.0`	the smallest polar angle
`maxTheta`	`None`	the largest polar angle; by default pi, or pi/2 for axes and the upper hemisphere
`minRho`	`0.0`	the smallest azimuth
`maxRho`	`360*degree`	the largest azimuth
`antipodal`	`False`	the directions are axes, the grid covers the upper hemisphere
`hemisphere`	`'complete'`	‘complete’, ‘upper’ or ‘lower’
`center`	`True`	the first ring is the pole; False starts half a step from it, MATLAB’s ‘no_center’
`rhoPeriod`	`360*degree`	the period of the azimuths, of the searches on a ring
`region`	`None`	a sphericalRegion the grid is restricted to
`frame`	`None`	the frame of the directions; by default that of the frame or region given

Output

S2G S2Grid

Used on

Grain_dispersion_axes, ColorMaps, PlotTypes, PoleFigure2ODFGhostCorrection, PoleFigureRefinement, PoleFigureSantaFe, RotationRepresentations, SO3FunConvolution, S2FunAxisField, S2FunRadon, S2FunVectorField, S2FunVectorValued

MATLAB’s equispacedS2Grid

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/equispacedS2Grid_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.

equispacedS2Grid