+
+ +
+

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 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

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