S2AxisFieldHarmonic
Defining a S2AxisFieldHarmonic
Definition via function values
At first you need some vertices
nodes = equispacedS2Grid('points', 1e5);
nodes = nodes(:);
Next you define function values for the vertices
y = vector3d(sin(5*nodes.x), 1, nodes.y, 'antipodal');
Now the actual command to get sAF1 of type S2AxisFieldHarmonic
sAF1 = S2AxisFieldHarmonic.approximation(nodes, y)
sAF1 = S2AxisFieldHarmonic bandwidth: 224
Definition via function handle
If you have a function handle for the function you could create a S2AxisFieldHarmonic via quadrature. At first lets define a function handle which takes vector3d as an argument and returns antipodal vector3d:
f = @(v) vector3d(v.x, v.y, 0*v.x, 'antipodal');
Now you can call the quadrature command to get sAF2 of type S2AxisFieldHarmonic
sAF2 = S2AxisFieldHarmonic.quadrature(@(v) f(v))
sAF2 = S2AxisFieldHarmonic bandwidth: 128
Visualization
the default plot-command
plot(sAF1);

- same as quiver(sAF1)
3D plot of a sphere with the axis on itself
clf; quiver3(sAF2);

Complete Function list
S2AxisFieldHarmonic | a class represeneting a axis field on the sphere |
approximation | Syntax |
cross | syntax |
display | standard output |
dot | syntax |
eval | syntax |
quadrature | Syntax |
MTEX 5.0.3 |