#mobius transformation

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procession ----------->

(source code)

(source code)

(via GIPHY)

(via GIPHY)

Again, reference. Mobius transformations and circlines.

Geometrically, a Möbius transformation can be obtained by first performing stereographic projection from the plane to the unit two-sphere, rotating and moving the sphere to a new location and orientation in space, and then performing stereographic projection (from the new position of the sphere) to the plane. These transformations preserve angles, map every straight line to a line or circle, and map every circle to a line or circle. The set of all Möbius transformations forms a group called the Möbius group which, together with its subgroups, finds numerous applications in mathematics and physics.