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| author | Even Rouault <even.rouault@spatialys.com> | 2018-10-01 12:32:52 +0200 |
|---|---|---|
| committer | Even Rouault <even.rouault@spatialys.com> | 2018-10-01 21:31:51 +0200 |
| commit | fe29f8acdce81607c11a597f4bffc7ff61fa9c19 (patch) | |
| tree | 5eb8696603b3b814e4aea7f686266fd72847f035 /docs/source/operations/transformations/affine.rst | |
| parent | 1583a566a208d2451fb1acc8bcf16fbd8151983e (diff) | |
| download | PROJ-fe29f8acdce81607c11a597f4bffc7ff61fa9c19.tar.gz PROJ-fe29f8acdce81607c11a597f4bffc7ff61fa9c19.zip | |
Add a affine transformation method, and make geogoffset as a particular case of it (fixes #535)
Diffstat (limited to 'docs/source/operations/transformations/affine.rst')
| -rw-r--r-- | docs/source/operations/transformations/affine.rst | 123 |
1 files changed, 123 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} + + |