a region on the sphere bounded by small circles: all directions v with dot(v, N_i) >= alpha_i for every normal N_i

Syntax

sR = sphericalRegion()

The whole sphere.

sR = sphericalRegion(N)

The intersection of the hemispheres about N.

sR = sphericalRegion(N, alpha)

The intersection of the caps dot(v, N_i) >= alpha_i.

sR = sphericalRegion(N, antipodal=True)

A region of axes, v or -v inside.

sR = sphericalRegion('upper')

The hemisphere about z, ‘lower’ about -z.

sR = sphericalRegion(N, frame=cs)

A region given in a reference frame.

sR = sphericalRegion.byVertices(V)

The polygon through the vertices.

Description

An alpha of 0 makes the boundary a great circle, a positive alpha a cap smaller than a hemisphere. The fundamental sectors of the point groups are spherical regions: fundamentalSector, dirichletSector. sR.checkInside(v) tests directions, sR.volume() gives the fraction of the sphere the region covers.

Input

N vector3d, the normals of the bounding circles, or ‘upper’ or ‘lower’
alpha array, the cosines of the bounding circles, one for all or one per normal; by default 0

Keywords

keyword default description
frame None the referenceFrame the region is given in
antipodal False a region of axes: a direction is inside when v or -v is

Output

sR sphericalRegion

See also

fundamentalSector, dirichletSector, sphericalRegion.checkInside, VectorGrids, FundamentalSector

MATLAB’s sphericalRegion.sphericalRegion

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/sphericalRegion.sphericalRegion_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.