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Spherical Surface Harmonic

This example shows how spherical harmonics, which are spherical versions of Fourier series, can be used to model the free oscillations of the Earth.

The image pictured is the spherical harmonic of degree 6, order 1, and amplitude 2 plotted on the surface of a sphere of radius 5.

% Define constants.
degree = 6;
order = 1;

% Create the grid
delta = pi/40;
theta = 0 : delta : pi; % altitude
phi = 0 : 2*delta : 2*pi; % azimuth
[phi,theta] = meshgrid(phi,theta);

% Calculate the harmonic
Ymn = legendre(degree,cos(theta(:,1)));
Ymn = Ymn(order+1,:)';
yy = Ymn;
for kk = 2: size(theta,1)
    yy = [yy Ymn];
end;
yy = yy.*cos(order*phi);

order = max(max(abs(yy)));
rho = 5 + 2*yy/order;

% Apply spherical coordinate equations
r = rho.*sin(theta);
x = r.*cos(phi);    % spherical coordinate equations
y = r.*sin(phi);
z = rho.*cos(theta);

% Plot the surface
clf
surf(x,y,z)
light
lighting phong
axis tight equal off
view(40,30)
camzoom(1.5)

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