connect two points on sphere

I want to connect at least 2 points on a sphere. The first point is at north pole (0,0,1). I am struggling with how to connect these successive points using the loop. I appreciate your help. Here is how I start:

wx0=0;
wy0=0;
wz0=1;
w0=[wx0;wy0;wz0];% initial position at north pole
% use the vector in spherical coordinates to update the position
%w=[sin(theta)*cos(phi);sin(theta)*sin(phi);cos(theta)];

where theta is the angle that w makes with the z axis and is between zero and pi. phi is the angle that the projection of w in xy plane makes with x axis and it is between zero and 2 pi. So the initial angles are theta=0 and phi=0 because I am at the north pole. The angles will be updated by solving a system of ODE and then use the solution to locate w position (say w1) then obtain new theta and phi and substitute in w to locate w2 (second point that I need to move to) an so on. Suppose I want to move 100 points from the north pole ( my initial position) so I need to use for loop to obtain the w1 , w2 ,..., w100. From this point, I do not know how to proceed.

[Geoff Hayes]

Mari - you may want to show your code so that we can get a better idea of what you are trying to attempt.

[Geoff Hayes]

Mari - what are phi and theta? Also, where is the loop that you mention in your question? Why is it necessary?