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Diffstat (limited to 'docs/source')
| -rw-r--r-- | docs/source/operations/transformations/affine.rst | 123 | ||||
| -rw-r--r-- | docs/source/operations/transformations/geogoffset.rst | 70 | ||||
| -rw-r--r-- | docs/source/operations/transformations/index.rst | 2 | ||||
| -rw-r--r-- | docs/source/references.bib | 8 |
4 files changed, 203 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 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 diff --git a/docs/source/references.bib b/docs/source/references.bib index bd3089ee..0fb077ec 100644 --- a/docs/source/references.bib +++ b/docs/source/references.bib @@ -82,6 +82,14 @@ Url = {http://www.calcofi.org/publications/calcofireports/v20/Vol_20_Eber___Hewitt.pdf} } +@Manual{EPSGGuidanceNumber7Part2, + Title = {Geomatics Guidance Note 7, part 2 - Coordinate Conversions & Transformations including Formulas}, + Institution = {International Association For Oil And Gas Producers}, + Year = {2018}, + + Url = {https://www.iogp.org/bookstore/product/coordinate-conversions-and-transformation-including-formulas/} +} + @Manual{Evenden2005, Title = {libproj4: A Comprehensive Library of Cartographic Projection Functions (Preliminary Draft)}, Author = {G. I. Evenden}, |