Merge pull request #1095 from rouault/webmerc_fixes

Fixes for webmerc projection (fixes #1078)

docs/source/operations/projections/webmerc.rst

@@ -24,9 +24,9 @@ From `Wikipedia <https://en.wikipedia.org/wiki/Web_Mercator>`_:
 +---------------------+----------------------------------------------------------+
 | **Classification**  | Cylindrical (non conformant if used with ellipsoid)      |
 +---------------------+----------------------------------------------------------+
-| **Available forms** | Forward and inverse, spherical projection                |
+| **Available forms** | Forward and inverse                                      |
 +---------------------+----------------------------------------------------------+
-| **Defined area**    | Global, but best used near the equator                   |
+| **Defined area**    | Global                                                   |
 +---------------------+----------------------------------------------------------+
 | **Alias**           | webmerc                                                  |
 +---------------------+----------------------------------------------------------+
@@ -49,9 +49,13 @@ Example::
 Parameters
 ################################################################################
 
-.. note:: All parameters for the projection are optional.
+.. note:: All parameters for the projection are optional, except the ellipsoid
+          definition, which is WGS84 for the typical use case of EPSG:3857.
+          In which case, the other parameters are set to their default 0 value.
 
-.. include:: ../options/R.rst
+.. include:: ../options/ellps.rst
+
+.. include:: ../options/lon_0.rst
 
 .. include:: ../options/x_0.rst
 

src/PJ_merc.c

@@ -9,7 +9,7 @@
 #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";
+PROJ_HEAD(webmerc, "Web Mercator / Pseudo Mercator") "\n\tCyl, Ell\n\t";
 
 #define EPS10 1.e-10
 static double logtanpfpim1(double x) {       /* log(tan(x/2 + M_FORTPI)) */
@@ -92,15 +92,9 @@ PJ *PROJECTION(merc) {
 
 PJ *PROJECTION(webmerc) {
 
-    /* Overriding k_0, lat_0 and lon_0 with fixed parameters */
+    /* Overriding k_0 with fixed parameter */
     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;