Add a affine transformation method, and make geogoffset as a particular case of it (fixes #535)

3 files changed, 126 insertions, 0 deletions

diff --git a/docs/source/operations/transformations/affine.rst b/docs/source/operations/transformations/affine.rst
new file mode 100644
index 00000000..8b1681b3
--- /dev/null
+++ b/docs/source/operations/transformations/affine.rst
@@ -0,0 +1,123 @@
+.. _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 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
+-------------------------------------------------------------------------------
+
+.. 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}
+
+
diff --git a/docs/source/operations/transformations/geogoffset.rst b/docs/source/operations/transformations/geogoffset.rst
index 91c91c83..f643485e 100644
--- a/docs/source/operations/transformations/geogoffset.rst
+++ b/docs/source/operations/transformations/geogoffset.rst
@@ -32,6 +32,8 @@ It can also be used to implement the method Vertical offset (code 9616)
 
 The reverse transformation simply consists in subtracting the offsets.
 
+This method is a conveniency wrapper for the more general :ref:`affine`.
+
 Examples
 ###############################################################################
 
diff --git a/docs/source/operations/transformations/index.rst b/docs/source/operations/transformations/index.rst
index c2fe6baa..121215f7 100644
--- a/docs/source/operations/transformations/index.rst
+++ b/docs/source/operations/transformations/index.rst
@@ -10,6 +10,7 @@ systems are based on different datums.
 .. toctree::
    :maxdepth: 1
 
+   affine
    deformation
    geogoffset
    helmert