Any Transformation preserving Collinearity (i.e., all points lying on a Line initially
still lie on a Line after Transformation). An affine transformation is also called an
Affinity. An affine transformation of is a Map
of the
form

(1) |

Dilation (Contraction, Homothecy), Expansion, Reflection,
Rotation, and Translation are all affine transformations, as are their combinations. A particular example
combining Rotation and Expansion is the rotation-enlargement transformation

(2) |

Separating the equations,

(3) | |||

(4) |

This can be also written as

(5) | |||

(6) |

where

(7) | |||

(8) |

The scale factor is then defined by

(9) |

(10) |

**References**

Gray, A. *Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, p. 105, 1993.

© 1996-9

1999-05-25