Draw some vectors over a sphere, just like latitude and longitudes with the help of 2D texture

I want to create some vectors all around the sphere just like longitudes and latitudes wireframe on earth, then i can edit those vectors to get the maze type thing. Well I'm thinking to design the intersection points in photoshop and import it as the 2d texture, then derive those points to create the spherical coordinates through a script and place the gameobject on those points over a sphere. But i don't know how it should be done ?

Below is the thing i want to achieve, sorry for bad photoshop ! ;-)