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

Syntax

S1G = S1Grid(np.arange(0, 360, 10)*degree, 0, 2*np.pi, periodic=True)

The angles of a circle.

S1G = S1Grid(points, 0, 1)

Angles on an interval.

S1G = S1Grid(points)

The interval from the smallest to the largest point.

Description

The points are sorted. Its use is the fast search: S1G.nearest(x), S1G.neighbours(x, eps) within a radius and S1G.dist(x, y), binary searches, plain arithmetic on an equispaced ladder; on a periodic grid min and max are identified and the distance wraps around the period max - min. MATLAB’s option ‘matrix’, one grid per column of points, is not taken.

Input

`points`	array of angles, in radians
`min`	the start of the interval, by default the smallest point
`max`	the end of the interval, by default the largest point

Keywords

keyword	default	description
`periodic`		identify min and max: the grid lies on a circle of length max - min

Output

S1G S1Grid

Members

dist	the periodic distance of two angles
double	the coordinates of the images of an embedding in their orthonormal basis, one row per orientation, e.double()
fold	an angle moved into [min, min + period)
ladderIndex	the index of the nearest point of an equispaced ladder, arithmetic
max	the maximum of a function on SO(3) or the sphere, the value and the position, numLocal local maxima from a grid refined down to the accuracy
min	the minimum of a function on SO(3) or the sphere, the value and the position, numLocal local minima
nearest	the index of the nearest point, for any array of angles
neighbours	the indices of the points within eps of one angle, in order
period	the length max - min of a periodic grid, zero for one that is not periodic
plot	plot(x, …) draws x as its kind is drawn
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
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
subGrid	the points selected by a mask, the range kept

MATLAB’s S1Grid_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/S1Grid_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 S1Grid