Merge pull request #925 from rouault/aux_sphere_type

Add a dedicated proj=webmerc operation

2 files changed, 79 insertions, 0 deletions

diff --git a/docs/source/operations/projections/index.rst b/docs/source/operations/projections/index.rst
index 9255d9fd..77decd6c 100644
--- a/docs/source/operations/projections/index.rst
+++ b/docs/source/operations/projections/index.rst
@@ -141,6 +141,7 @@ Projections map the spherical 3D space to a flat 2D space.
    wag5
    wag6
    wag7
+   webmerc
    weren
    wink1
    wink2
diff --git a/docs/source/operations/projections/webmerc.rst b/docs/source/operations/projections/webmerc.rst
new file mode 100644
index 00000000..0c465afc
--- /dev/null
+++ b/docs/source/operations/projections/webmerc.rst
@@ -0,0 +1,78 @@
+.. _webmerc:
+
+********************************************************************************
+Web Mercator / Pseudo Mercator
+********************************************************************************
+
+The Web Mercator / Pseudo Mercator projection is a cylindrical map projection.
+This is a variant of the regular :ref:`merc` projection, except that the computation
+is done on a sphere, using the semi-major axis of the ellipsoid.
+
+From `Wikipedia <https://en.wikipedia.org/wiki/Web_Mercator>`_:
+
+    This projection is widely used by the Web Mercator, Google Web Mercator,
+    Spherical Mercator, WGS 84 Web Mercator[1] or WGS 84/Pseudo-Mercator is a
+    variant of the Mercator projection and is the de facto standard for Web
+    mapping applications. [...]
+    It is used by virtually all major online map providers [...]
+    Its official EPSG identifier is EPSG:3857, although others have been used
+    historically.
+
+
++---------------------+----------------------------------------------------------+
+| **Classification**  | Cylindrical (non conformant if used with ellipsoid)      |
++---------------------+----------------------------------------------------------+
+| **Version**         | Added in proj 5.1.0                                      |
++---------------------+----------------------------------------------------------+
+| **Available forms** | Forward and inverse, spherical projection                |
++---------------------+----------------------------------------------------------+
+| **Defined area**    | Global, but best used near the equator                   |
++---------------------+----------------------------------------------------------+
+| **Options**         | Neither lat_0, lon_0, lat_ts or k_0 should be used.      |
++---------------------+----------------------------------------------------------+
+
+Usage
+########
+
+Example::
+
+    $ echo 2 49 | proj +proj=webmerc +datum=WGS84
+    222638.98       6274861.39
+
+Mathematical definition
+#######################
+
+The formulas describing the Mercator projection are all taken from G. Evenden's libproj manuals [Evenden2005]_.
+
+Forward projection
+==================
+
+.. math::
+
+    x = \lambda
+
+.. math::
+
+    y = \ln \left[ \tan \left(\frac{\pi}{4} + \frac{\phi}{2} \right) \right]
+
+
+Inverse projection
+==================
+
+.. math::
+
+    \lambda = {x}
+
+.. math::
+
+    \phi = \frac{\pi}{2} - 2 \arctan \left[ e^{-y} \right]
+
+
+
+Further reading
+###############
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Web_Mercator>`_
+
+
+