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Animating a Surface

This example shows how to animate a surface. Specifically, this example animates a spherical harmonic. Spherical harmonics are spherical versions of Fourier series and can be used to model the free oscillations of the Earth.

Define the Spherical Grid

Define a set of points on a spherical grid to calculate the harmonic.

theta = 0:pi/40:pi;                   % polar angle
phi = 0:pi/20:2*pi;                   % azimuth angle

[phi,theta] = meshgrid(phi,theta);    % define the grid

Calculate the Spherical Harmonic

Calculate the spherical harmonic with a degree of six, an order of one, and an amplitude of 0.5 on the surface of a sphere with a radius equal to five. Then, convert the values to Cartesian coordinates.

degree = 6;
order = 1;
amplitude = 0.5;
radius = 5;

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 = radius + amplitude*yy/order;

r = rho.*sin(theta);    % convert to Cartesian coordinates
x = r.*cos(phi);
y = r.*sin(phi);
z = rho.*cos(theta);

Plot the Spherical Harmonic on the Surface of a Sphere

Using the surf function, plot the spherical harmonic on the surface of the sphere.

figure
s = surf(x,y,z);

light               % add a light
lighting gouraud    % preferred lighting for a curved surface
axis equal off      % set axis equal and remove axis
view(40,30)         % set viewpoint
camzoom(1.5)        % zoom into scene

Animate the Surface

To animate the surface, use a for loop to change the data in your plot. To replace the surface data, set the XData, YData, and ZData properties of the surface to new values. To control the speed of the animation, use pause after updating the surface data.

scale = [linspace(0,1,20) linspace(1,-1,40)];    % surface scaling (0 to 1 to -1)

for ii = 1:length(scale)
    
    rho = radius + scale(ii)*amplitude*yy/order;   
   
    r = rho.*sin(theta);
    x = r.*cos(phi);       
    y = r.*sin(phi);
    z = rho.*cos(theta);
    
    s.XData = x;    % replace surface x values
    s.YData = y;    % replace surface y values
    s.ZData = z;    % replace surface z values
    
    pause(0.05)     % pause to control animation speed
end

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