It has been well known that every Mobius transformation can be constructed by stereographi projection of the complex plane onto a sphere, followed by a rigid motion of the sphere and projection back onto the plane. Related to the article: Constructing Mobius Transformations with Spheres

But I'm wondering what will **specifically** happened between the mapping of the two spheres on which I want to explore more; a rotation, translation etc etc. From what I understood, I think I want to explore more on 3-D version of conformal mappings.

Any suggestions to work on this task is much appreciated.