How to plot streamlines on a sphere?

I would like to plot streamlines wrapped around the surface of a sphere. Here is what I mean:

A few thoughts:

--Matlab makes it easy to plot scalar functions on spheres using surf (as shown here: http://www.mathworks.com/help/matlab/ref/surf.html), but I do not see how to extend this example to vector fields.

--I know how to plot streamlines on a surface provided the domain of the surface is rectangular (following this example: http://www.mathworks.com/help/matlab/ref/streamslice.html). Unfortunately, I don't see how to extend this to a spherical surface.

Thanks!

Answer 1

[Bob P]

Nevermind, I've figured out what I need. Something like this seems to work:

npts=100;
x = linspace(-1,1,npts);
y = linspace(-1,1,npts);
[X,Y]=meshgrid(x,y);
Z=X;
for r = 1:npts
   for c = 1:npts
      if (X(r,c)^2+Y(r,c)^2)>1
         Z(r,c) = NaN;
   else
      Z(r,c)=sqrt(1-X(r,c)^2-Y(r,c)^2);
      end  
   end
end

surf(X,Y,Z);shading interp
alpha(1)
[u v] = gradient(Z); 
h = streamslice(X,Y,-u,-v); 
set(h,'color','k')
for i=1:length(h); 
  zi = interp2(X,Y,Z,get(h(i),'xdata'),get(h(i),'ydata'));
  set(h(i),'zdata',zi);
end
axis tight 

%hold on;
%surf(X,Y,-Z);shading interp
%hold off;
daspect([1,1,1])
axis tight;

Answer 2

[David Taylor]

Hero! Thanks for sharing.