# 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

(1st and 2nd points of the straight line)

Scaling factor
a plane defined by three points Points for definition of affinity plane (1st, 2nd and 3rd 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.