I'm trying to accurately draw the mappings depicted.
Finitely many geodesics (the curved lines) of the 2-sphere are being mapped to the unit square. I'm not sure if that is captured in the notation but I was not sure how to incorporate the geodesics into the notation. The poles of the sphere are mapped to (0,0) and (1,1) (as pictured below), and for the rotated one, (1,0) and (0,1). The intersections of the two graphs can be seen in the uppermost graph.
Are the drawings accurate representations of the mappings or could they be improved?
$ S^2 \mapsto [0,1]\times[0,1] $
