Documented mercator projection. Needs more work, but can be used as a template when documenting other projections.

1 files changed, 120 insertions, 1 deletions

diff --git a/docs/source/projections/merc.rst b/docs/source/projections/merc.rst
index 4c7ffb72..26425bdc 100644
--- a/docs/source/projections/merc.rst
+++ b/docs/source/projections/merc.rst
@@ -4,7 +4,126 @@
 Mercator
 ********************************************************************************
 
+The Mercator projection is a cylindrical map projection that origins from the 15th
+century. It is widely recognized as the first regularly used map projection.
+The projection is conformal which makes it suitable for navigational purposes.
+
+
++---------------------+----------------------------------------------------------+
+| **Classification**  | Conformal cylindrical                                    |
++---------------------+----------------------------------------------------------+
+| **Available forms** | Forward and inverse, spherical and elliptical projection |
++---------------------+----------------------------------------------------------+
+| **Defined area**    | Global, but best used near the equator                   |
++---------------------+----------------------------------------------------------+
+| **Implemented by**  | Gerald I. Evenden                                        |
++---------------------+----------------------------------------------------------+
+| **Options**                                                                    |
++---------------------+----------------------------------------------------------+
+| `+lat_ts`           | Latitude of true scale. Defaults to 0.                   |
++---------------------+----------------------------------------------------------+
+
+
+
 .. image:: ./images/merc.png
    :scale: 50%
-   :alt:   Mercator  
+   :alt:   Mercator
+
+
+Usage
+########
+
+Applications should be limited to equatorial regions, but is frequently
+used for navigational charts with latitude of true scale (``+lat_ts``) specified within
+or near chart's boundaries.
+Often inappropriately used for world maps since the regions near the poles
+cannot be shown [0].
+
+
+Example::
+
+    $ echo 56.35 12.32 | proj +proj=merc +lat_ts=56.5
+    3470306.37	759599.90
+
+
+Mathematical definition
+#######################
+
+The formulas describing the Mercator projection are all taken from G. Evenden's libproj manuals [1].
+
+Spherical form
+**************
+For the spherical form of the projection we introduce the scaling factor:
+
+.. math::
+
+    k_0 = \cos \phi_{ts}
+
+Forward projection
+==================
+
+.. math::
+
+    x = k_0 \lambda
+
+.. math::
+
+    y = k_0 \ln \tan \left(\frac{\pi}{4} + \frac{\phi}{2} \right)
+
+
+Inverse projection
+==================
+
+.. math::
+
+    \lambda = x / k_0
+
+.. math::
+
+    \phi = \pi/2 - 2 \arctan \left[ \exp \left( -y/k_0 \right) \right]
+
+
+Elliptical form
+***************
+
+For the elliptical form of the projection we introduce the scaling factor:
+
+.. math::
+
+    k_0 = m\left( \phi_ts \right)
+
+where :math:`m\left(\phi\right)` is the parallel radius at lattitude :math:`\phi`.
+
+We also use the Isometric Latitude kernel function :math:`t()`.
+
+.. note::
+    m() and t() should be described properly on a seperate page about the theory of projections on the ellipsoid.
+
+Forward projection
+==================
+.. math::
+
+    x = k_0 \lambda
+
+.. math::
+
+    y = k_0 \ln t \left( \phi \right)
+
+
+Inverse projection
+==================
+
+.. math::
+
+    \lambda = x / k_0
+
+.. math::
+
+    \phi = t^{-1}\left[ \exp \left( -y/k_0 \right) \right]
+
+
+References
+##########
+[0] Evenden, G. I., 1995, Cartograpic Projection Procedures for the UNIX Environment - A User's Manual.
 
+[1] Evenden, G. I., 2005, libproj4: A Comprehensive Library of Cartographic Projection Functions (Preliminary Draft).