## Point and Vector

Operation | Explanation |
---|---|

+/- | point - point = vector, point + vector = point, vector +/- vector = vector |

|| | Return length of vector or point's distance to origin |

normalize | Change length to 1 |

scalar multiplication | Uniform scaling |

component-wise product | Nonuniform scaling |

dot product | a∙b = |a| |b| cos(𝜃) |

cross product | a×b = |a| |b| sin(𝜃) n, direction of n is given by the x-hand rule |

LERP | Linear interpolation |

## Matrix

Operation | Explanation |
---|---|

* | Concatenate transforms; Transform point or vector |

inverse | Undoes transform, only affine matrices (combinations of pure rotations, translations, scales and shears) have inverses. |

transpose | Convert between row- and column-major matrices; Inverse of an orthonormal (pure rotation) matrix is equal to its transpose |

## Quaternion

A faster, less space and interpolate-able alternative to rotation matrix.

Operation | Explanation |
---|---|

* (There are quite a few multiplication methods) | Concatenate quaternions; Part of rotate operation |

conjugate | Inverse of a normalized quaternion is equal to its conjugate |

inverse | Inverse quaternion; Part of rotate operation |

rotate | Rotate |

LERP | Linear interpolation |

SLERP | Another linear interpolation, SLERP is better in quality than LERP, but can be slower |