clifford.tools.rotor_decomp

clifford.tools.rotor_decomp(V: clifford._multivector.MultiVector, x: clifford._multivector.MultiVector) → Tuple[clifford._multivector.MultiVector, clifford._multivector.MultiVector]

Rotor decomposition of rotor V

Given a rotor V, and a vector x, this will decompose V into a series of two rotations, U and H, where U leaves x invariant and H contains x.

Limited to 4D for now.

See [Hes15], Appendix B, Theorem 4.

Parameters

• V (clifford.MultiVector) – rotor

• x (clifford.MultiVector) – vector

Returns

• H (clifford.Multivector) – rotor which contains x

• U (clifford.Multivector) – rotor which leaves x invariant