# 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 transformation

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

2D / 3D domain
Translation defined by Description
a vector Coordinate system for definition

Vector components (DX, DY, (DZ))

2 points and a ratio

Points defining the vector (vector tail and vector head)

Ratio
2D domain

Rotation defined by

Description
an angle and pivot point coordinates Coordinate system for definition Coordinates of the pivot point Rotation angle about Z-axis
an angle and existing pivot point Coordinate system for definition Pivot point Rotation angle about Z-axis
3D domain

Rotation defined by

Description
3 angles and pivot point coordinates Coordinate system for definition Coordinates of the pivot point 3 rotation angles about X, Y, Z-axis
3 angles and existing pivot point Coordinate system for definition Pivot point 3 rotation angles about X, Y, Z-axis
3 points and an angle Points for definition (tail point for direction, head point for direction, pivot point) Rotation angle in degree
2D / 3D Domain
Symmetry with respect to Description
a point Center point of the symmetry
a line defined by two points

Points for definition of symmetry (1st and 2nd points of the straight line)

3D Domain
Symmetry with respect to Description
a plane defined by three points

Points for definition of symmetry plane (1st, 2nd and 3rd points of plane)

2D / 3D domain
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
3D domain
Affine transformation with respect to Description
a plane defined by three points

Points for definition of affinity plane (1st, 2nd and 3rd points of plane)

Scaling factor
3D domain
Helical transformation defined by Description
pivot point coordinates Coordinate system for definition Pivot point coordinates Components of directing vector Helix height and helix angle
existing pivot point Coordinate system for definition Pivot point Components of directing vector Helix height and helix angle
2D / 3D domain
Transformation Description
combining two transformations Two transformations defined beforehand