diff options
| author | Kristian Evers <kristianevers@gmail.com> | 2018-02-28 22:37:13 +0100 |
|---|---|---|
| committer | Kristian Evers <kristianevers@gmail.com> | 2018-02-28 22:37:13 +0100 |
| commit | be3791ffd5e802d5a3d38fa08f5ed24715b73c7c (patch) | |
| tree | 25eff60d91fed8ffce3302e37818f5bc452b16ca /docs/source/operations/projections/mill.rst | |
| parent | db2bfdce6df26801584be562f0ac74648ef8cefd (diff) | |
| download | PROJ-be3791ffd5e802d5a3d38fa08f5ed24715b73c7c.tar.gz PROJ-be3791ffd5e802d5a3d38fa08f5ed24715b73c7c.zip | |
Move 'Coordinate operations' to top level of docs [skip ci]
Diffstat (limited to 'docs/source/operations/projections/mill.rst')
| -rw-r--r-- | docs/source/operations/projections/mill.rst | 72 |
1 files changed, 72 insertions, 0 deletions
diff --git a/docs/source/operations/projections/mill.rst b/docs/source/operations/projections/mill.rst new file mode 100644 index 00000000..eb9c2092 --- /dev/null +++ b/docs/source/operations/projections/mill.rst @@ -0,0 +1,72 @@ +.. _mill: + +******************************************************************************** +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>`_ + |
