Crate g3

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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.

Constants

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

Traits

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