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.