# Affine transformation¶

New in version 6.0.0.

The affine transformation applies translation and scaling/rotation terms on the x,y,z coordinates, and translation and scaling on the temporal cordinate.

 Alias affine Domain 4D Input type XYZT output type XYZT

By default, the parameters are set for an identity transforms. The transformation is reversible unless the determinant of the sji matrix is 0, or tscale is 0

## Parameters¶

### Optional¶

+xoff=<value>

Offset in X. Default value: 0

+yoff=<value>

Offset in Y. Default value: 0

+zoff=<value>

Offset in Z. Default value: 0

+toff=<value>

Offset in T. Default value: 0

+s11=<value>

Rotation/scaling term. Default value: 1

+s12=<value>

Rotation/scaling term. Default value: 0

+s13=<value>

Rotation/scaling term. Default value: 0

+s21=<value>

Rotation/scaling term. Default value: 0

+s22=<value>

Rotation/scaling term. Default value: 1

+s23=<value>

Rotation/scaling term. Default value: 0

+s31=<value>

Rotation/scaling term. Default value: 0

+s32=<value>

Rotation/scaling term. Default value: 0

+s33=<value>

Rotation/scaling term. Default value: 1

+tscale=<value>

Time scaling term. Default value: 1

#### Mathematical description¶

(1)\begin{split}\begin{align} \begin{bmatrix} X \\ Y \\ Z \\ T \\ \end{bmatrix}^{dest} = \begin{bmatrix} xoff \\ yoff \\ zoff \\ toff \\ \end{bmatrix} + \begin{bmatrix} s11 & s12 & s13 & 0 \\ s21 & s22 & s23 & 0 \\ s31 & s32 & s33 & 0 \\ 0 & 0 & 0 & tscale \\ \end{bmatrix} \begin{bmatrix} X \\ Y \\ Z \\ T \\ \end{bmatrix}^{source} \end{align}\end{split}