diff options
| author | julien2512 <moquet.julien@gmail.com> | 2017-02-03 11:06:26 +0100 |
|---|---|---|
| committer | Kristian Evers <kristianevers@gmail.com> | 2017-02-03 11:06:26 +0100 |
| commit | 8abeb3224ef6e6a3ed1be9558899fa89807b65b4 (patch) | |
| tree | 63e82e6435832df650a80032952b570ef491ae70 /docs | |
| parent | 090a259958cc5316ecdba37f2f99ab87a8affe4b (diff) | |
| download | PROJ-8abeb3224ef6e6a3ed1be9558899fa89807b65b4.tar.gz PROJ-8abeb3224ef6e6a3ed1be9558899fa89807b65b4.zip | |
Added doc page for Miller projection
Diffstat (limited to 'docs')
| -rw-r--r-- | docs/source/projections/mill.rst | 62 |
1 files changed, 62 insertions, 0 deletions
diff --git a/docs/source/projections/mill.rst b/docs/source/projections/mill.rst index 0e5aa08b..eb9c2092 100644 --- a/docs/source/projections/mill.rst +++ b/docs/source/projections/mill.rst @@ -4,7 +4,69 @@ Miller Cylindrical ******************************************************************************** +The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. +The latitude is scaled by a factor of :math:`\frac{4}{5}`, projected according to Mercator, and then the result is multiplied by :math:`\frac{5}{4}` to retain scale along the equator. + ++---------------------+--------------------------------------------------------------------------------+ +| **Classification** | Neither conformal nor equal area cylindrical | ++---------------------+--------------------------------------------------------------------------------+ +| **Available forms** | Forward and inverse spherical | ++---------------------+--------------------------------------------------------------------------------+ +| **Defined area** | Global, but best used near the equator | ++---------------------+--------------------------------------------------------------------------------+ +| **Implemented by** | Gerald I. Evenden | ++---------------------+--------------------------------------------------------------------------------+ +| **Options** | ++---------------------+--------------------------------------------------------------------------------+ +| `+lat_0` | Latitude of origin (Default to 0) | ++---------------------+--------------------------------------------------------------------------------+ + .. image:: ./images/mill.png :scale: 50% :alt: Miller Cylindrical +Usage +######## + +The Miller Cylindrical projection is used for world maps and in several atlases, +including the National Atlas of the United States (USGS, 1970, p. 330-331) [Snyder1987]_. + +Example using Central meridian 90°W:: + + $ echo -100 35 | proj +proj=mill +lon_0=90w + -1113194.91 4061217.24 + +Mathematical definition +####################### + +The formulas describing the Miller projection are all taken from Snyder's manuals [Snyder1987]_. + + +Forward projection +================== + +.. math:: + + x = \lambda + +.. math:: + + y = 1.25 * \ln \left[ \tan \left(\frac{\pi}{4} + 0.4 * \phi \right) \right] + + +Inverse projection +================== + +.. math:: + + \lambda = x + +.. math:: + + \phi = 2.5 * ( \arctan \left[ e^{0.8 * y} \right] - \frac{\pi}{4} ) + +Further reading +############### + +#. `Wikipedia <https://en.wikipedia.org/wiki/Miller_cylindrical_projection>`_ + |
