# Transformation: definition (structure)

## Definition

A transformation is defined by:

- a name (and a comment)
- a type
- specific characteristics belonging to a type

## Name

The name to identify the transformation is set by the user during the creation of this one.

A comment (optional) can be added to the name.

## Types of transformations

The different types of transformations and the characteristics useful for their description are presented in the table below.

Translation defined by | Description | |
---|---|---|

a vector | Coordinate system for definition |
Vector components (DX, DY, DZ) |

two points and a ratio | Points defining the vector (vector tail and vector head) | Ratio |

Rotation defined by | Description | ||
---|---|---|---|

three angles and pivot point coordinates | Coordinate system for definition | Coordinates of the pivot point | three rotation angles about X, Y, Z axis |

three angles and existing pivot point | Coordinate system for definition | Pivot point | three rotation angles about X, Y, Z axis |

Affine transformation with respect to | Description | |
---|---|---|

a point | Center point of the affinity | Scaling factor |

a line defined by two points | Points for definition of affinity line (1 |
Scaling factor |

a plane defined by three points | Points for definition of affinity plane (1^{st}, 2^{nd}
and 3^{rd} points of plane) |
Scaling factor |

Symmetry with respect to | Description | |
---|---|---|

a point | Coordinate system for definition | Coordinates of the center point of symmetry |

a line defined by two points | Coordinate system for definition | Coordinates of the points defining the line of symmetry (points 1 and 2 of the line) |

a plane defined by three points | Coordinate system for definition | Coordinates of the points defining the plane of symmetry (points 1, 2 and 3 of the plane) |

Transformation | Description |
---|---|

combining two transformations | Two transformations defined beforehand |

## Affinity / Symmetry

A symmetry is a particular case of affine transformation, when scaling factor k = -1, but they differ in their definition:

- an affinity is described by using already existing geometric points;
- symmetry is described by coordinates in a coordinate system. This means that there are no points before to define the symmetry and the points are not created thereafter.