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diff --git a/docs/source/usage/operations/projections/merc.rst b/docs/source/usage/operations/projections/merc.rst deleted file mode 100644 index 8895abc8..00000000 --- a/docs/source/usage/operations/projections/merc.rst +++ /dev/null @@ -1,140 +0,0 @@ -.. _merc: - -******************************************************************************** -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 0.0 | -+---------------------+----------------------------------------------------------+ -| `+k_0` | Scaling factor. Defaults to 1.0 | -+---------------------+----------------------------------------------------------+ - - - -.. image:: ./images/merc.png - :scale: 50% - :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 [Evenden1995]_. - - -Example using latitude of true scale:: - - $ echo 56.35 12.32 | proj +proj=merc +lat_ts=56.5 - 3470306.37 759599.90 - -Example using scaling factor:: - - echo 56.35 12.32 | proj +proj=merc +k_0=2 - 12545706.61 2746073.80 - - -Note that ``+lat_ts`` and ``+k_0`` are mutually exclusive. -If used together, ``+lat_ts`` takes precedence over ``+k_0``. - -Mathematical definition -####################### - -The formulas describing the Mercator projection are all taken from G. Evenden's libproj manuals [Evenden2005]_. - -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 \left[ \tan \left(\frac{\pi}{4} + \frac{\phi}{2} \right) \right] - - -Inverse projection -================== - -.. math:: - - \lambda = \frac{x}{k_0} - -.. math:: - - \phi = \frac{\pi}{2} - 2 \arctan \left[ e^{-y/k_0} \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 latitude :math:`\phi`. - -We also use the Isometric Latitude kernel function :math:`t()`. - -.. note:: - m() and t() should be described properly on a separate 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 = \frac{x}{k_0} - -.. math:: - - \phi = t^{-1}\left[ e^{ -y/k_0 } \right] - -Further reading -############### - -#. `Wikipedia <https://en.wikipedia.org/wiki/Mercator_projection>`_ -#. `Wolfram Mathworld <http://mathworld.wolfram.com/MercatorProjection.html>`_ - - |