a projection of the sphere to the plane, restricted to a region and a hemisphere

Syntax

sphericalProjection(sR, pC, antipodal=False, upper=True)

proj.project(v)

The plane coordinates, NaN outside the region.

proj.iproject(x, y)

The direction drawn at a point of the plane.

Description

Fields: sR, the region shown; pC, the plotting convention; antipodal, whether v and -v are one point; upper, whether the chart shows the hemisphere out of the screen; symmetric, whether the data carry the symmetry of the frame, as a function does.

Input

sR sphericalRegion to display; None selects the whole sphere before hemisphere restriction
pC plottingConvention defining screen axes; None uses the current default
antipodal identify opposite directions; default False
upper show the hemisphere pointing out of the screen; False selects the opposite hemisphere

Members

boundary the boundary of the region as plane curves, one (x, y) pair per arc
bounds the bounding box of the drawn region, from its boundary, as (xmin, xmax, ymin, ymax)
chartRegion the region as seen in the frame of the convention, folded into the upper hemisphere
extent the radius of the whole hemisphere, the natural extent of a chart
frame the frame of the region shown
grid a grid regular in the polar angles of the chart, one strip of polar angles per azimuth so that the cells follow the boundary: the directions, in the frame of the region, and their plane coordinates, all nTheta x nRho
gridLines the meridians and small circles of the convention at a spacing, clipped to the region: plane curves with NaN where they leave it
iproject the direction drawn at the plane point (x, y)
isPlain whether the chart draws the polar angles as plain coordinates, False here
labels the labels: the Miller indices at the corners of the sector of a crystal frame, or at its axes when it has no sector
polarAngle the polar angle drawn at the plane radius r, the inverse of radius
polarIn the polar coordinates of directions in the frame of the convention, folded into the hemisphere of the chart
project the plane coordinates (x, y) of directions, NaN outside the region
projectUnchecked the plane coordinates of directions known to lie in the chart
radius the plane radius r(theta) a polar angle is drawn at, 2 sin(theta / 2) for the equal area chart
withRegion the same chart showing another region, for an outline drawn behind the data

MATLAB’s sphericalProjection_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/sphericalProjection_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.