## Rotation Transforms for Computer GraphicsRotation transforms are used everywhere in computer graphics from rotating pictures in editing software, to providing an arbitrary view of a 3D virtual environment. Although the former is a trivial operation, the latter can be a challenging task.
The book includes introductory chapters on complex numbers, matrices, quaternions and geometric algebra, and further chapters on how these techniques are employed in 2D and 3D computer graphics. In particular, matrix and bivector transforms are developed and evaluated to rotate points in a fixed frame of reference, and vice versa. |

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### Contents

2 | |

5 | |

Vectors | 17 |

Matrices | 33 |

Quaternions | 59 |

Multivectors | 66 |

Rotation Transforms in the Plane | 85 |

Frames of Reference in the Plane | 103 |

Quaternion Transforms in Space | 155 |

Bivector Rotors | 181 |

Conclusion | 197 |

Appendix A Composite Point Rotation Sequences | 198 |

Appendix B Composite Frame Rotation Sequences | 213 |

Appendix C The Four nSquare Algebras | 227 |

229 | |

230 | |