Klein vs Poincare

stereographic projection
transparent sphere
plane at south pole
light at north pole

              [demo: torus.math.uiuc.edu/jms/java/stereop/]

transformation from Klein to Poincare
vertically project disc to hemisphere
stereographically project hemisphere to Poincare disc

           [video: www.geom.umn.edu/~crobles/hyperbolic/hypr/ibm/mkb/K2P.mpg]

graphics 
Klein: 4x4 real matrix
Poincare: 2x2 complex matrix


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