How to find 3 points in a sphere?

I want to find 3 points on a sphere whose radius and centre is known. The points should form a circle on the sphere's surface. I am using peter corke robotics toolbox

[Matt J]

A great circle?

[Kuruvilla Joseph]

Yes

[Adam Danz]

Any 3 points or do you also know the azimuth and elevation of at least 2 of the points?

[Kuruvilla Joseph]

Any three points which form a circle on the sphere ,like a great circle

Answer 1

[Adam Danz]

The question is: how to get any 3 points along a great circle on a sphere with known radius and center

Here's how I think of the problem.

Assume unit sphere with radius 1 centered at (0,0,0) and a great circle laying on the xy plane. The point to the far left, upward, and far right sections of the sphere are

xyzn = [-1 0 0;  % left
     0 1 0;      % upper
     1 0 0];     % right

Now all you have to do is scale it and shift it to the sphere's center.

r = 12;         %radius
cnt = [-10,8,20]; % center points (x,y,z)
xyz = xyzn.*r + cnt

xyz = 3×3

-22 8 20 -10 20 20 2 8 20

xyz are 3 coordinates (row-wise) that lay on a great circle that lies on the xy plane passing through the center of the sphere.

Now let's plot it,

[sx,sy,sz] = sphere(20); 
sx = sx*r+cnt(1); 
sy = sy*r+cnt(2); 
sz = sz*r+cnt(3); 
mesh(sx,sy,sz,'LineWidth',2,'FaceAlpha',.6)
axis equal
hold on
plot3(xyz(:,1),xyz(:,2),xyz(:,3), 'k*', 'MarkerSize', 12, 'LineWidth',2)
xlabel('x'); ylabel('y'); zlabel('z')
view([-187, 23])

[Kuruvilla Joseph]

Thanks, i will try to do this way