The Branch
both a line through the origin and also the principal branch of
the logarithm of a rotor.
Directions in are represented using points at infinity (homogeneous coordinate 0).
Having a homogeneous coordinate of zero ensures that directions are translation-invariant.
Dual Number
Euler Angles
A horizon represents a line at infinity and corresponds to the multivector: e₀₁ + e₀₂ + e₀₃
A Line
A Motor is a combination of a translation along a line combined
with a rotation about an axis parallel to that line.
In other words, it is the geometric product of a Translator and a Rotor.
Origin
ae₁ + be₂ + ce₃ + de₀
xe₀₃₂ + ye₀₁₃ + ze₀₂₁ + e₁₂₃
The rotor is an entity that represents a rigid rotation about an axis.