Mapping a graph on a sphere.

Hi all, I have this graph :- http://static.inky.ws/image/2485/image.jpg I want to map these points on a unit sphere now (All the 4 points should lie on surface of the sphere, the lines connecting them shouldnt lie on the sphere but should be euclidean distances and thus cutting through the sphere) . Do you know how to do it.

% Generate a unit sphere
theta=linspace(0,2*pi,20);
phi=linspace(0,pi,20);
[theta,phi]=meshgrid(theta,phi);
rho=1;
x=rho*sin(phi).*cos(theta);
y=rho*sin(phi).*sin(theta);
z=rho*cos(phi);
mesh(x,y,z)

Answer 1

[Conrad]

See the code below. It shows how to do it for two points but this is really all you need, just do the same for the other points. Note that you have so set the alpha of the mesh to 0 so that you can see the line that intersects the sphere.

% Generate a unit sphere
theta=linspace(0,2*pi,20);
phi=linspace(0,pi,20);
[theta,phi]=meshgrid(theta,phi);
rho=1;
x=rho*sin(phi).*cos(theta);
y=rho*sin(phi).*sin(theta);
z=rho*cos(phi);
p1 = mesh(x,y,z);

px = [0.1 -0.1]; % x coordinates.
py = [0.5 -0.4]; % y coordinates.
pPhi = asin(sqrt(px.^2+py.^2)/rho);

hold on;
set(p1,'FaceAlpha',0);
p2 = plot3(px,py,rho*cos(pPhi),'ro');
set(p2,'MarkerFaceColor','red','LineStyle','-','LineWidth',2);

Conrad

[Vinita]

Conrad thanks a ton. But my problem is rather complex. Suppose I have a 3 such points (A,B,C) on the surface of this sphere. Each of them connected by a line. What I want to do now is that I want to move the point A slightly on the surface of this sphere (to a coordinate within a certain area nearby its present coordinate). Due to this its connection with B and C will have to be rewired. Now do you have any idea how to do this.

[Albert Yam]

Conrad added the line handle for the line. Use that to remove the line.

delete(p2)
px = [0.1 -0.2]; %new x coordinates
pPhi = asin(sqrt(px.^2+py.^2)/rho);
p3 = plot3(px,py,rho*cos(pPhi),'ro');
set(p3,'MarkerFaceColor','red','LineStyle','-','LineWidth',2);

[Vinita]

Albert that was really helpful.

But the problem is this :- There are three points (p1,p2,p3) on the sphere surface. Connect all these three by an arc on the sphere. Now I'd like to randomly select any of the two points and perform either of these operations based on a certain parameter :-

1.) Move both of them towards each other on the unit sphere itself by 5% of the present distance between them (along the smallest arc connecting them).

2.) Move only single point towards the other point by 5% of the present distance between them (along the smallest arc connecting them). .

The movement has got to be on the spherical surface itself.