Learning Moebius Transformations

Educational Area: Hobby + Games

Möbius transformations should not be confused with the Möbius transform or the Möbius function.
In geometry, a Möbius transformation is a function:
f(z) = frac{a z + b}{c z + d}
where z, a, b, c, d are complex numbers satisfying ad − bc ≠ 0.
Equivalently, a Möbius transformation may beperformed by performing a stereographic projection from a plane to a sphere, rotating and moving that sphere to a new arbitrary location and orientation, and performing a stereographic projection back to the plane.
Möbius transformations are named in honor of August Ferdinand Möbius, although they are also called homographic transformations or fractional linear transformations. (more)(less)

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