Since version 2026, Flux 3D and Flux PEEC are no longer available.

Please use SimLab to create a new 3D project or to import an existing Flux 3D project.

Please use SimLab to create a new PEEC project (not possible to import an existing Flux PEEC project).

/!\ Documentation updates are in progress – some mentions of 3D may still appear.

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 domain
Translation vector Translation defined by 2 points and a ratio
  • the direction and the distance are defined by:
    • a working coordinate system
    • a vector (its components DX and DY define the direction and the amplitude of the vector)
  • the direction is defined by two points (vector tail and vector head)
  • the distance is equal to the distance between the two points (vector tail and vector head) multiplied by the ratio (proportionality coefficient)

Rotation

A rotation is defined by a rotation axis and an angle.

2D
Rotation defined by angles and a pivot point (its coordinates or reference number)
  • rotation axis is defined by:
    • a working coordinate system
    • and a pivot point
  • rotation angle is defined about Z-axis
Note: The positive value of the angle corresponds to the anti-clockwise rotation.

Affinity

Affinity is defined with respect to a point or to a straight line .

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 domain
Affine transformation with respect to a point Affine transformation with respect to a line
CAUTION: The affinity ratio = 0 causes an error in the application of affinity transformation with respect to a point because the line is degenerated and reduced to a point.

Composed transformation

It is possible to create composed geometric functions.

Domain 2D
Transformation combining two transformations
  • a translation following OY axis (defined by DX=0, and DY)
  • a rotation about Z-axis (defined by the pivot point and an angle α)
CAUTION: You do not obtain the same result by using different order of 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.