Details

Affine transformations are a class of transformations that include translation, rotation, scaling, and their combinations. They preserve points, straight lines, and planes. Parallel lines remain parallel after an affine transformation.

The `atrafo` data type encapsulates these transformations and allows for their application to geometric entities within trCAD. Transformations can be combined sequentially using the `>>` operator, which corresponds to matrix multiplication of their respective transformation matrices.

Several different constructors are available for creating `atrafo` objects. The identity constructor (1) creates a neutral transformation. The translation constructor (2) performs a translation along a given offset vector. The rotation constructors define rotations with an angle around a given axis vector that starts in the coordinate system origin (3) or in a given onset space point (4). The scaling constructors (5) and (7) perform a uniform scaling while constructors (6) and (8) scale into each coordinate axis individually. (7) and (8) take an onset space point defining the neutral point of the scaling. The general affine transformation constructor (9) creates a general affine transformation from a given matrix.

Each transformation can be represented by a 3x4 transformation matrix, which can be accessed through the `tmatrix` member of the `atrafo` object.

 make rotation( <[0.0, 0.0, 1.0]>, rad( 45 ) ) >> box()
 

Applies a 45-degree rotation around the Z-axis to a box.

 atrafo t = rotation(<[0.0, 0.0, 1.0]>, rad(45)) >> scaling(0.5)
 echo(t)
 

 atrafo(<[<[0.353553,-0.353553,0,0]>,<[0.353553,0.353553,0,0]>,<[0,0,0.5,0]>]>)
 

Outputs the transformation matrix of a combined rotation and scaling transformation.