S2FunHarmonicSym edit page

S2FunHarmonicSym is an extension of the S2FunHarmonic class which stores the symmetry with the function.

Defining a S2FunHarmonic

Definition via symmetrisation

The simplest way to define a S2FunHarmonicSym is through the symmetrisation of an ordinary S2FunHarmonic.

sF = S2Fun.smiley
cs = crystalSymmetry('432');

sFs1 = symmetrise(sF, cs);
sF = S2FunHarmonic
 bandwidth: 128
  • this symmetrises the function and gives back the result with the symmetry attached
plot(sFs1)
  • Note that only the important part with respect to the symmetry is plotted
  • you can plot the full sphere using the argument 'complete'

Definition via function handle

If you have a function handle for the function you could create a S2FunHarmonicSym via quadrature. At first lets define a symmetry and a function handle which takes vector3d as an argument and returns double:

f = @(v) 0.1*(v.theta+sin(8*v.x).*sin(8*v.y));
cs = crystalSymmetry('6/m');

Now you can call the quadrature command to get sFs2 of type S2FunHarmonicSym

sFs2 = S2FunHarmonicSym.quadrature(f, cs)
sFs2 = S2FunHarmonicSym (6/m)
 bandwidth: 128
 antipodal: true

Visualization

The plot commands for a S2FunHarmonicSym by default plot the function only on the fundamenta Sector of the symmetry. E.g. the default plot-command look as follows

plot(sFs1);

Another Example is the contour plot

contour(sFs2);