Add webmerc projection

5 files changed, 110 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>`_
+
+
+
diff --git a/src/PJ_merc.c b/src/PJ_merc.c
index 18303c45..a3e5e846 100644
--- a/src/PJ_merc.c
+++ b/src/PJ_merc.c
@@ -1,8 +1,10 @@
 #define PJ_LIB__
+#include "proj_internal.h"
 #include "proj.h"
 #include "projects.h"
 
 PROJ_HEAD(merc, "Mercator") "\n\tCyl, Sph&Ell\n\tlat_ts=";
+PROJ_HEAD(webmerc, "Web Mercator / Pseudo Mercator") "\n\tCyl, Sph\n\t";
 
 #define EPS10 1.e-10
 
@@ -76,3 +78,18 @@ PJ *PROJECTION(merc) {
     return P;
 }
 
+PJ *PROJECTION(webmerc) {
+
+    /* Overriding k_0, lat_0 and lon_0 with fixed parameters */
+    P->k0 = 1.0;
+    P->phi0 = 0.0;
+    P->lam0 = 0.0;
+
+    P->b = P->a;
+    /* Clean up the ellipsoidal parameters to reflect the sphere */
+    P->es = P->e = P->f = 0;
+    pj_calc_ellipsoid_params (P, P->a, 0);
+    P->inv = s_inverse;
+    P->fwd = s_forward;
+    return P;
+}
diff --git a/src/pj_list.h b/src/pj_list.h
index 09a66034..440f7972 100644
--- a/src/pj_list.h
+++ b/src/pj_list.h
@@ -156,6 +156,7 @@ PROJ_HEAD(wag4, "Wagner IV")
 PROJ_HEAD(wag5, "Wagner V")
 PROJ_HEAD(wag6, "Wagner VI")
 PROJ_HEAD(wag7, "Wagner VII")
+PROJ_HEAD(webmerc, "Web Mercator / Pseudo Mercator")
 PROJ_HEAD(weren, "Werenskiold I")
 PROJ_HEAD(wink1, "Winkel I")
 PROJ_HEAD(wink2, "Winkel II")
diff --git a/test/gie/4D-API_cs2cs-style.gie b/test/gie/4D-API_cs2cs-style.gie
index bbd9ee39..6eed4faa 100644
--- a/test/gie/4D-API_cs2cs-style.gie
+++ b/test/gie/4D-API_cs2cs-style.gie
@@ -216,6 +216,19 @@ expect      -10370728.80        5552839.74          0
 -------------------------------------------------------------------------------
 
 -------------------------------------------------------------------------------
+Test that Google's Web Mercator with +proj=webmerc
+-------------------------------------------------------------------------------
+operation   proj=pipeline step init=epsg:26915 inv step proj=webmerc datum=WGS84
+-------------------------------------------------------------------------------
+tolerance   20 cm
+accept      487147.594520173    4934316.46263998
+expect      -10370728.80        5552839.74
+
+accept      487147.594520173    4934316.46263998    0
+expect      -10370728.80        5552839.74          0
+-------------------------------------------------------------------------------
+
+-------------------------------------------------------------------------------
 Test that +datum parameters are handled correctly in pipelines.
 See #872 for details.
 -------------------------------------------------------------------------------