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| author | Kristian Evers <kristianevers@gmail.com> | 2017-11-29 21:58:15 +0100 |
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| committer | Kristian Evers <kristianevers@gmail.com> | 2017-11-29 21:58:15 +0100 |
| commit | 7b0e97df22d32608355d1f235ee22ffedcc9f06e (patch) | |
| tree | 17456194fb938b7044e47e959b53ef71cb5616b8 /docs/source/usage | |
| parent | 28ead8822488f0cd382f8966a18000f17ef1e958 (diff) | |
| download | PROJ-7b0e97df22d32608355d1f235ee22ffedcc9f06e.tar.gz PROJ-7b0e97df22d32608355d1f235ee22ffedcc9f06e.zip | |
Fill out Molodensky docs [skip ci]
Diffstat (limited to 'docs/source/usage')
| -rw-r--r-- | docs/source/usage/operations/transformations/molodensky.rst | 69 |
1 files changed, 68 insertions, 1 deletions
diff --git a/docs/source/usage/operations/transformations/molodensky.rst b/docs/source/usage/operations/transformations/molodensky.rst index 3fa8f9a8..d4ff3e79 100644 --- a/docs/source/usage/operations/transformations/molodensky.rst +++ b/docs/source/usage/operations/transformations/molodensky.rst @@ -4,4 +4,71 @@ Molodensky transform ================================================================================ -Perform a datum shift in geodetic coordinate space. +The Molodensky transformation resembles a :ref:`Helmert` with zero +rotations and a scale of unity, but converts directly from geodetic coordinates to +geodetic coordinates, without the intermediate shifts to and from cartesian +geocentric coordinates, associated with the Helmert transformation. +The Molodensky transformation is simple to implement and to parameterize, requiring +only the 3 shifts between the input and output frame, and the corresponding +differences between the semimajor axes and flattening parameters of the reference +ellipsoids. Due to its algorithmic simplicity, it was popular prior to the +ubiquity of digital computers. Today, it is mostly interesting for historical +reasons, but nevertheless indispensable due to the large amount of data that has +already been transformed that way [EversKnudsen2017]_. + ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates. | ++---------------------+----------------------------------------------------------+ +| **Output type** | Geodetic coordinates. | ++---------------------+----------------------------------------------------------+ +| **Options** | ++---------------------+----------------------------------------------------------+ +| `+da` | Difference in semimajor axis of the defining ellipsoids. | ++---------------------+----------------------------------------------------------+ +| `+df` | Difference in flattening of the defining ellipsoids. | ++---------------------+----------------------------------------------------------+ +| `+dx` | Offset of the X-axes of the defining ellipsoids. | ++---------------------+----------------------------------------------------------+ +| `+dy` | Offset of the Y-axes of the defining ellipsoids. | ++---------------------+----------------------------------------------------------+ +| `+dz` | Offset of the Z-axes of the defining ellipsoids. | ++---------------------+----------------------------------------------------------+ +| `+ellps` | Ellipsoid definition of source coordinates. | +| | Any specification can be used (e.g. `+a`, `+rf`, etc). | +| | If not specified, default ellipsoid is used. | ++---------------------+----------------------------------------------------------+ +| `+abridged` | Use the abridged version of the Molodensky transform. | +| | Optional. | ++---------------------+----------------------------------------------------------+ + +The Molodensky transform can be used to perform a datum shift from coordinate +:math:`(\phi_1, \lambda_1, h_1)` to :math:`(\phi_2, \lambda_2, h_2)` where the two +coordinates are referenced to different ellipsoids. This is based on three +assumptions: + + 1. The cartesian axes, :math:`X, Y, Z`, of the two ellipsoids are parallel. + 2. The offset, :math:`\delta X, \delta Y, \delta Z`, between the two ellipsoid + are known. + 3. The characteristics of the two ellipsoids, expressed as the difference in + semimajor axis (:math:`\delta a`) and flattening (:math:`\delta f`), are known. + +The Molodensky transform is mostly used for transforming between old systems +dating back to the time before computers. The advantage of the Molodensky transform +is that it is fairly simple to compute by hand. The ease of computation come at the +cost of limited accuracy. + +A derivation of the mathematical formulas for the Molodensky transform can be found +in [Deakin2004]_. + + +Examples +############################################################################### + +The abridged Molodensky:: + + proj=molodensky a=6378160 rf=298.25 da=-23 df=-8.120449e-8 dx=-134 dy=-48 dz=149 abridged + +The same transformation using the standard Molodensky:: + + proj=molodensky a=6378160 rf=298.25 da=-23 df=-8.120449e-8 dx=-134 dy=-48 dz=149 + |
