Transformation: about
Principle of use
The transformations are geometric functions that permit the creation of new objects, starting from objects already created.
Various functions
The various available functions are:
 translation
 rotation
 affinity
 helix
 composed
Translation
A translation is defined by a direction and a distance.
2D / 3D domain  

Translation vector  Translation defined by 2 points and a ratio 


Rotation
A rotation is defined by a rotation axis and an angle.
2D / 3D domain  3D domain 

Rotation defined by angles and a pivot point (its coordinates or reference number) 
Rotation defined by 3 points and 1 angle 


Affinity
Affinity is defined with respect to a point, to a straight line or to a plane (for 3D domain).
The result of this transformation application depends on the affinity ratio (see the table below).
Ratio  Result 

k = 1  symmetry 
k = 1  identity 
k = 0  projection 
k > 1  increasing (increasing homothety) 
0 < k < 1  reducing (reducing homothety) 
k < 1  increasing (increasing negative homothety) 
1 < k < 0  reducing (reducing negative homothety) 
2D / 3D domain  

Affine transformation with respect to a point  Affine transformation with respect to a line 
3D domain 

Affine transformation with respect to a plane 
Helix
The helix transformation is used only for 3D study domain.
A helix is defined by a coordinate system, an axis, a height and an angle.
Domain 3D 

Helix 

Composed transformation
It is possible to create composed geometric functions.
Domain 2D / 3D 

Transformation combining two transformations 

Parameter setting
The characteristics of transformation are parametrized expressions. The vector components, the coordinates of pivot point, the rotation angles and the ratios of affinity can be defined using algebraic expression.
The algebraic expression can contain:
 constants
 geometric parameters (created beforehand)
 basic mathematical functions using operators: +, , *, /, ( )
 usual mathematical functions admitted by FORTRAN.
The mathematical functions are described in section Functions.