Discretisation of 2 - Sphere (The Class S2Grid)

represents a grid of nodes on the sphere

Class Description

The class S2Grid is used in MTEX to store the set of specimen directions organized in a pole figure. Of central importance is also the plotting method of this class since it is used by almost all other plotting methods in MTEX to perform spherical plots.

Defining a S2Grid

There are various ways to define a S2Grid. Next, you find some examples. For a detailed description of possible specifications look for the documentation of the constructor S2Grid.

% equidistributions
S2G = equispacedS2Grid('points',100,'antipodal');  % specified by number of points
S2G = equispacedS2Grid('RESOLUTION',5*degree,'antipodal');  % specified by resolution

% regular grids
S2G = regularS2Grid('points',[72,19]); % specified by number of theta and rho steps
S2G = regularS2Grid('theta',linspace(0,2*pi,72),...
             'rho',linspace(0,pi/2,19)); % explicitly determine theta and rho values

% restrictes grids
S2G = equispacedS2Grid('points',100,'MAXTHETA',75*degree);  % specify maximum theta angle

Plots

plot(equispacedS2Grid('points',100,'antipodal'))  % plot the grid of nodes

Complete Function list

`Syntax`
`S2Grid(theta,rho) % fills a Sphere with N`	odes
`regularS2Grid('resolution',5*degree) % construct regular polar and azimuthal spacing`
`equispacedS2Grid('resolution',5*degree) % construct equispaced nodes`

`Input`
`nodes`	@vector3d

`Options`
`POINTS`	[nrho,ntheta] number of points to be generated
`RESOLUTION`	resolution of a equispaced grid
`HEMISPHERE`	'lower', 'uper', 'complete', 'sphere', 'identified'}
`THETA`	theta angle
`RHO`	rho angle
`MINRHO`	starting rho angle (default 0)
`MAXRHO`	maximum rho angle (default 2*pi)
`MINTHETA`	starting theta angle (default 0)
`MAXTHETA`	maximum theta angle (default pi)

`Flags`
`REGULAR`	generate a regular grid
`EQUISPACED`	generate equidistribution
`ANTIPODAL`	include antipodal symmetry
`PLOT`	generate plotting grid
`NO_CENTER`	ommit point at center
`RESTRICT2MINMAX`	restrict margins to min / max

`Examples`
`regularS2Grid('points',[72 19])`

`regularS2Grid('resolution',[5degree 2.5degree])`

`equispacedS2Grid('resolution',5*degree,'maxrho',pi)`
`plot(ans)`

`See also`
`vector3d/vector3d`