Merge remote-tracking branch 'osgeo/master' into bertin1953

4 files changed, 197 insertions, 2 deletions

diff --git a/docs/source/operations/projections/lsat.rst b/docs/source/operations/projections/lsat.rst
index 4df944b5..c2b2d902 100644
--- a/docs/source/operations/projections/lsat.rst
+++ b/docs/source/operations/projections/lsat.rst
@@ -19,11 +19,11 @@ Required
 
 .. option:: +lsat=<value>
 
-    Landsat satelite used for the projection. Value between 1 and 5.
+    Landsat satellite used for the projection. Value between 1 and 5.
 
 .. option:: +path=<value>
 
-    Selected path of satelite. Value between 1 and 253 when :option:`+lsat` is
+    Selected path of satellite. Value between 1 and 253 when :option:`+lsat` is
     set to 1,2 or 3, otherwise valid input is between 1 and 233.
 
 
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
new file mode 100644
index 00000000..f643485e
--- /dev/null
+++ b/docs/source/operations/transformations/geogoffset.rst
@@ -0,0 +1,70 @@
+.. _geogoffset:
+
+================================================================================
+Geographic offsets
+================================================================================
+
+.. versionadded:: 6.0.0
+
+The Geographic offsets transformation adds an offset to the geographic longitude,
+latitude coordinates, and an offset to the ellipsoidal height.
+
++---------------------+----------------------------------------------------------+
+| **Alias**           | geogoffset                                               |
++---------------------+----------------------------------------------------------+
+| **Domain**          | 3D                                                       |
++---------------------+----------------------------------------------------------+
+| **Input type**      | Geodetic coordinates (horizontal), meters (vertical)     |
++---------------------+----------------------------------------------------------+
+| **output type**     | Geodetic coordinates (horizontal), meters (vertical)     |
++---------------------+----------------------------------------------------------+
+
+This method is normally only used when low accuracy is tolerated. It is documented
+as coordinate operation method code 9619 (for geographic 2D) and 9660 (for
+geographic 3D) in the EPSG dataset (:cite:`EPSGGuidanceNumber7Part2`)
+
+It can also be used to implement the method Geographic2D with Height Offsets
+(code 9618) by noting that the input vertical component is a gravity-related
+height and the output vertical component is the ellispoid height (dh being
+the geoid undulation).
+
+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
+###############################################################################
+
+Geographic offset from the old Greek geographic 2D CRS to the newer GGRS87 CRS::
+
+    proj=geogoffset dlon=0.28 dlat=-5.86
+
+Conversion from Tokyo + JSLD69 height to WGS 84::
+
+    proj=geogoffset dlon=-13.97 dlat=7.94 dh=26.9
+
+Conversion from Baltic 1977 height to Black Sea height::
+
+    proj=geogoffset dh=0.4
+
+
+Parameters
+################################################################################
+
+Optional
+-------------------------------------------------------------------------------
+
+.. option:: +dlon=<value>
+
+    Offset in longitude, expressed in arc-second, to add.
+
+.. option:: +dlat=<value>
+
+    Offset in latitude, expressed in arc-second, to add.
+
+.. option:: +dh=<value>
+
+    Offset in height, expressed in meter, to add.
+
diff --git a/docs/source/operations/transformations/index.rst b/docs/source/operations/transformations/index.rst
index 5112ffa2..121215f7 100644
--- a/docs/source/operations/transformations/index.rst
+++ b/docs/source/operations/transformations/index.rst
@@ -10,7 +10,9 @@ systems are based on different datums.
 .. toctree::
    :maxdepth: 1
 
+   affine
    deformation
+   geogoffset
    helmert
    molodensky
    hgridshift