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.. _affine:
================================================================================
Affine transformation
================================================================================
.. versionadded:: 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 coordinate.
+---------------------+----------------------------------------------------------+
| **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
-------------------------------------------------------------------------------
.. option:: +xoff=<value>
Offset in X. Default value: 0
.. option:: +yoff=<value>
Offset in Y. Default value: 0
.. option:: +zoff=<value>
Offset in Z. Default value: 0
.. option:: +toff=<value>
Offset in T. Default value: 0
.. option:: +s11=<value>
Rotation/scaling term. Default value: 1
.. option:: +s12=<value>
Rotation/scaling term. Default value: 0
.. option:: +s13=<value>
Rotation/scaling term. Default value: 0
.. option:: +s21=<value>
Rotation/scaling term. Default value: 0
.. option:: +s22=<value>
Rotation/scaling term. Default value: 1
.. option:: +s23=<value>
Rotation/scaling term. Default value: 0
.. option:: +s31=<value>
Rotation/scaling term. Default value: 0
.. option:: +s32=<value>
Rotation/scaling term. Default value: 0
.. option:: +s33=<value>
Rotation/scaling term. Default value: 1
.. option:: +tscale=<value>
Time scaling term. Default value: 1
Mathematical description
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
.. math::
:label: formula
\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}
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