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

Syntax

S2G = equispacedS2Grid(resolution=5*degree)

Nearly equidistant directions.

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

A spherical cap.

S2G = S2Grid(S2G.thetaGrid, S2G.rhoGrid, resolution=5*degree)

From its rings.

Description

The difference to a plain list of vector3d is that the grid knows its rings, so finding the grid points closest to a direction, or within a radius of it, searches the ladders instead of every point. A grid is built by equispacedS2Grid; anything that breaks the rings, an index or an operation, returns a plain vector3d. regularS2Grid and plotS2Grid return a matrix of vector3d, as their layout is the matrix.

Input

`theta`	S1Grid, the ladder of polar angles of the rings
`rho`	a list of S1Grid, the azimuths of every ring

Keywords

keyword	default	description
`frame`		the frame of the directions
`resolution`		the resolution the grid was built with, in radians
`antipodal`		the directions are axes

Output

S2G S2Grid

Members

cat	the list of the operands, MATLAB’s [a, b]
cross	the cross product of two plane normals is a lattice direction and the one of two directions a plane normal, so the indices switch sides
find	the nearest grid point of every direction and its angle, or with eps the sparse matrices of the points within eps and their angles
hasUniformSteps	whether the polar ladder and every ring of more than one point have uniform steps, so that the nearest point is found by arithmetic
nearestStepwise	the nearest point without a search, for equispaced ladders: the ring is the polar angle over the ring step and the point the azimuth over that ring’s step, both rounded the nearest node of a grid with uniform steps, arithmetic on every direction at once: the ring from the polar angle, the node on the ring from the azimuth against the ring’s own first node, step and count
neighbourIndices	the indices of the grid points within eps of one direction
numRings	the number of rings, polar angles, of the grid
plus
polar	the polar angles of the grid points, exact from the rings
refine	the directions with a new one between every three neighbours: the centroids of the Delaunay triangles of the points on the sphere, none below the lowest point, so a cap stays a cap
resolution	the resolution the grid was built with, NaN when none was given
ring	the indices of the points on ring k
rotate	the vectors turned by a rotation, rot * v
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
subGrid	the grid points selected by a mask, or within eps of a centre
subsref
times

MATLAB’s S2Grid_index

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/S2Grid_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.

The class S2Grid