ShearRotations

Autor:Will Le

Both circular rotation R and hyperbolic rotation (squeeze) H can be decomposed into triples of parabolic rotations (shears) S_x, S_y. x-y-x triples:

y-x-y triples:

These are so beautiful with symmetries!

H = tanh ⋅ sinh ⋅ tanh for both triples
R = (-/+)tan ⋅ (+/-)sin ⋅ (-/+)tan for x-t-x / y-x-y

Here

are X & Y shears with shear factors k_x, k_y (parabolic angles), and R(θ), H(ψ) are circular and hyperbolic rotations with angles θ, ψ.

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