polar coordinates of a region (MATLAB @sphericalRegion/polarCoordinates), which is what a colour key is built on: the radius is one at the centre and zero on the boundary, taken along the great circle through the centre, and the azimuth is measured about the centre from a reference direction and then equalised, so that a wide part of the sector takes as much of the turn as a narrow one and the vertices sit at equal angles

Syntax

r, rho = polarCoordinates(sR, h, regionCenter(sR))

The radius and the equalised azimuth.

r, rho = polarCoordinates(sR, h, regionCenter(sR), equalise=False)

The plain azimuth about the centre.

r, rho = polarCoordinates(sR, h, regionCenter(sR), ref=xvector)

The reference direction for rho = 0.

Description

The azimuth starts at the pole of the plotting convention seen from the centre; only where the centre is that pole does the reference direction take over. A centre at a vertex or on the boundary of the region spreads the part of the turn the region covers over the whole turn.

Input

sR sphericalRegion
v vector3d, the directions
center vector3d or (3,) array, the centre of the coordinates

Keywords

keyword default description
ref None the direction rho = 0 points to where the centre is the pole; x by default
equalise True reparametrise the azimuth by the distance to the boundary

Output

r array, one at the centre and zero on the boundary
rho array, the azimuth about the centre in [0, 2 pi)

See also

regionCenter, HSVDirectionKey, sectorFolds

MATLAB’s sphericalRegion.polarCoordinates

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.polarCoordinates_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.