# Crate g3

## Structs

• 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.

• Origin
• e₀₃₂ + e₁₂₃
• e₀₁₃ + e₁₂₃
• e₀₂₃ + e₁₂₃
• e₀
• e₁
• e₂
• e₃
• π
• τ = 2π

## Functions

• ae₂₃ + be₃₁ + ce₁₂
• scalar + pseudoscalar
• ae₀₁ + be₀₂ + ce₀₃
• ae₂₃ + be₃₁ + ce₁₂ + de₀₁ + ee₀₂ + fe₀₃
• a + be₂₃ + ce₃₁ + de₁₂ + ee₀₁ + fe₀₂ + ge₀₃ + he₀₁₂₃
• ae₁ + be₂ + ce₃ + de₀
• xe₀₃₂ + ye₀₁₃ + ze₀₂₁ + e₁₂₃
• angle x y z
• ae₀₁ + be₀₂ + ce₀₃