Mobius Transformation is defined as z → (a*z+b)/(c*z+d)
Pre-image and post-image of the function: z → (z-1)/(z+1)
above: the post-image stereographically projected onto a sphere of radius 1/2.
above: preimage and postimage on the polar grid.
above: the post-image stereographically projected onto a sphere of radius 1/2.
above: preimage and postimage on most of the upper half of the polar grid.
above: the post-image stereographically projected onto a sphere of radius 1/2.
Mathematica notebook for this page: mobius.nb.zip