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authorKristian Evers <kristianevers@gmail.com>2018-02-28 22:37:13 +0100
committerKristian Evers <kristianevers@gmail.com>2018-02-28 22:37:13 +0100
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+.. _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>`_
+