How can I place spheres along a circle/ring ?

Hi everyone! I am working on a project where I have a sphere.Now I want to replicate the sphere and place them in a circular manner(3D plot).I would be glad, If someone could help me with this!

Eg: Imagine showing the position of the earth in its orbit(Circular orbit in this case) every month of the year. Now I imagine, we would have 12 spheres in a orbit.

[Aquatris]

Easy way is to use built-in Matlab functions. Here is the website for it.

You can also use the sphere equation in polar coordinates, where you can find an example here .

Shifting the center of the sphere is as easy as adding a bias to the respective coordinate (x, y and/or z)

[Guillaume]

@Aquatris, why don't you write that as an answer rather than a comment?

[Aquatris]

@Guillaume, cause those are not my answers and in my opinion, it would be unethical to copy paste others work. That is why I just referenced them as a comment.

Answer 1

[Anton Semechko]

See example below. All relevant functions used to generate this example can be found here .

% Unit sphere 
TR=IcosahedronMesh;
TR=SubdivideSphericalMesh(TR,5);
[Tri,X]=GetMeshData(TR);

% Reference meridian
t=linspace(0,pi,5E2)';
M=zeros(numel(t),3);
M(:,2)=sin(t);
M(:,3)=cos(t);

% Circular orbit
t=linspace(0,2*pi,1E3+1)';
R=10;                       % radius of the orbit
O=R*[cos(t) sin(t)];

% 12 equaly spaced points along the orbit
t_o=linspace(0,2*pi,13)'; t_o(end)=[];
C=R*[cos(t_o) sin(t_o)];
C(:,3)=0;

% Visualize orbit
figure('color','w')
axis equal off
hold on
plot(O(:,1),O(:,2),'--b','LineWidth',2)
view([20 20])

% Visualize sphere at 12 equally-spaced positions along the orbit
for i=1:size(C,1)

      % Rotation around z-axis
      c=cos(t_o(i));
      s=sin(t_o(i));
      R=[c -s 0;s c 0;0 0 1];

      % Rotate and translate mesh
      Xi=bsxfun(@plus,(R*X')',C(i,:));
      h=trimesh(triangulation(Tri,Xi));
      set(h,'EdgeColor','none','FaceColor',0.75*[1 1 1],'FaceAlpha',0.9);

      % Rotate and translate reference meridian
      Mi=bsxfun(@plus,(R*M')',C(i,:));
      plot3(Mi(:,1),Mi(:,2),Mi(:,3),'-k','LineWidth',2)

end
zoom(2)

[Shankar Lingesh Dhanuskodi]

Hello Mr.Semechko! Thank you so much for helping with the code. Could you please tell me how can I modify the radius of the sphere ?

[Anton Semechko]

Let's say 'rad' is the variable specifying the radius of the sphere, then replace the following two lines of the code

Xi=bsxfun(@plus,(R*X')',C(i,:));
Mi=bsxfun(@plus,(R*M')',C(i,:));

with

Xi=bsxfun(@plus,(rad*R*X')',C(i,:));
Mi=bsxfun(@plus,(rad*R*M')',C(i,:));

Make sure to adjust the radius of the "orbit" accordingly, so there is no overlap between the spheres.

[Shankar Lingesh Dhanuskodi]

Thank you so much ! This works :) Last question , is there a way by which I can delete(or make invisible) those black curved lines on the spheres?

[Guillaume]

@Shankar, is there a way by which I can delete(or make invisible) those black curved lines on the spheres

Well, yes, don't do the step under

% Rotate and translate reference meridian

@Anton, I can see that your code may useful to others. Why don't you post it on the FileExchange which would make it easier to find and possibly more permanent?

[Shankar Lingesh Dhanuskodi]

Hey Guillaume! That did not help . When I don't use the steps under "% Rotate and translate reference meridian", the sphere goes away and only the black curved lines stay. I want the sphere to stay and the black line to disappear.Is there also a possibility to make the sphere black in color. Could you please help?

[Guillaume]

The code under

% Rotate and translate mesh

draws the spheres. The code under

% Rotate and translate reference meridian

plots the black line. You must have suppressed the wrong section.

As for the properties of the sphere they're all defined by

set(h,'EdgeColor','none','FaceColor',0.75*[1 1 1],'FaceAlpha',0.9);

Change the FaceColor to black if you want black:

 set(h,'EdgeColor','none','FaceColor', 'k');

[Anton Semechko]

@ Guillaume, all functions used in this demo can be found on FEX as part of 'Suite of functions to perform uniform sampling of a sphere'