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A Javascript visualizer for Mobius Transforms.
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A Javascript visualizer for Mobius Transforms.

Mobius transforms are transformations of the function f(z) = (az + b)/(cz + d), where a,b,c,d,z are complex variables.

Mobius transformations are defined on the extended complex plane that is augmented by infinity.

Stereographic Projection - Mappying that projects a sphere onto a plane, where the projection is defined at every point but the projection point (Used to picture the sphere as a plane)

-Stereographic Projections will preserve angles at which curves cross each other, but not area

Mobius transformations can be obtained by obtaining a stereographic projection, then rotating/moving to a different orientation in space, and project the sphere back to a plane (drawing a line from the pole of infinity to the plane)

Riemann Sphere - Model of an extended complex plane in the form of a sphere, consisting of complex numbers and infinity

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