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Implementation of webmerc projection #1080

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Implementation of webmerc projection #1080

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c33d2ca
Implementation of Web Mercator projection
Jul 20, 2018
d1cfa5b
Better explanation of Web Mercator projection
Jul 20, 2018
500b346
Update webmerc.rst
Jul 20, 2018
70f6724
Review of parameters of Web Mercator projection
Jul 20, 2018
a531dc3
Update webmerc.rst
Jul 20, 2018
ab1e5f9
Update webmerc.rst
Jul 20, 2018
22ac611
Update webmerc.rst
Jul 20, 2018
c148d09
Update PJ_merc.c
Jul 20, 2018
38bb740
Override of ellipsoid and always using WGS84
Jul 20, 2018
45f9e0a
Update PJ_merc.c
Jul 20, 2018
f17ca0d
Renamed Web Mercator
Jul 20, 2018
c334fb2
Update pj_list.h
Jul 20, 2018
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44 changes: 19 additions & 25 deletions docs/source/operations/projections/webmerc.rst
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@@ -1,14 +1,13 @@
.. _webmerc:

********************************************************************************
Web Mercator / Pseudo Mercator
WGS 84 Web Mercator / WGS 84 Pseudo Mercator
********************************************************************************

.. versionadded:: 5.1.0

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.
The WGS 84 Web Mercator / WGS 84 Pseudo Mercator projection is a cylindrical map projection.
It is defined only for ellipsoid WGS 84, motivated by the regular :ref:`merc` projection, but the equations for the ellispoid are chosen to be the same as equations for Mercator projection of a sphere, with radius same as semi-major axis of the WGS 84 ellipsoid. As a consequence it is not a conformal projection.

From `Wikipedia <https://en.wikipedia.org/wiki/Web_Mercator>`_:

Expand All @@ -21,21 +20,21 @@ From `Wikipedia <https://en.wikipedia.org/wiki/Web_Mercator>`_:
historically.


+---------------------+----------------------------------------------------------+
| **Classification** | Cylindrical (non conformant if used with ellipsoid) |
+---------------------+----------------------------------------------------------+
| **Available forms** | Forward and inverse, spherical projection |
+---------------------+----------------------------------------------------------+
| **Defined area** | Global, but best used near the equator |
+---------------------+----------------------------------------------------------+
| **Alias** | webmerc |
+---------------------+----------------------------------------------------------+
| **Domain** | 2D |
+---------------------+----------------------------------------------------------+
| **Input type** | Geodetic coordinates |
+---------------------+----------------------------------------------------------+
| **Output type** | Projected coordinates |
+---------------------+----------------------------------------------------------+
+---------------------+-----------------------------------------------------------------+
| **Classification** | Non-conformal cylindrical projection of an WGS 84 ellipsoid |
+---------------------+-----------------------------------------------------------------+
| **Available forms** | Forward and inverse, ellipsoidal projection |
+---------------------+-----------------------------------------------------------------+
| **Defined area** | Global, low linear distortions near the equator |
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I think it is better to just say that it is globally defined and not go into where distortions are at a minimum. The original text is just a copy of what's written for Mercator which is kind of not valid here anyway.

+---------------------+-----------------------------------------------------------------+
| **Alias** | webmerc |
+---------------------+-----------------------------------------------------------------+
| **Domain** | 2D |
+---------------------+-----------------------------------------------------------------+
| **Input type** | Geodetic coordinates |
+---------------------+-----------------------------------------------------------------+
| **Output type** | Projected coordinates |
+---------------------+-----------------------------------------------------------------+


Usage
Expand All @@ -49,13 +48,8 @@ Example::
Parameters
################################################################################

.. note:: All parameters for the projection are optional.
.. note:: Projection does not have any additional parameters. See `EPSG.io <http://epsg.io/3857>`_
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I think it is better to refer to Wikipedia here? The epsg.io site doesn't go into much detail. Also, it is easily mistaken as official outlet of the EPSG (which it is not). It is already mentioned under "Further reading".


.. include:: ../options/R.rst

.. include:: ../options/x_0.rst

.. include:: ../options/y_0.rst

Mathematical definition
#######################
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16 changes: 10 additions & 6 deletions src/PJ_merc.c
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Expand Up @@ -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, "WGS 84 Web Mercator / WGS 84 Pseudo Mercator") "\n\tCyl, Ell\n\t";

#define EPS10 1.e-10
static double logtanpfpim1(double x) { /* log(tan(x/2 + M_FORTPI)) */
Expand Down Expand Up @@ -92,15 +92,19 @@ PJ *PROJECTION(merc) {

PJ *PROJECTION(webmerc) {

/* Overriding k_0, lat_0 and lon_0 with fixed parameters */
/* Overriding k_0, lat_0, lon_0, x_0 and y_0 with fixed parameters */
P->k0 = 1.0;
P->phi0 = 0.0;
P->lam0 = 0.0;
P->x0 = 0;
P->y0 = 0;

/* Overriding ellipsoid and using WGS 84 */
P->f = 1.0/298.257223563;
P->a = 6378137.0;
P->es = P->f*(2-P->f);
pj_calc_ellipsoid_params (P, P->a, P->es);

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;
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2 changes: 1 addition & 1 deletion src/pj_list.h
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Expand Up @@ -156,7 +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(webmerc, "WGS 84 Web Mercator / WGS 84 Pseudo Mercator")
PROJ_HEAD(weren, "Werenskiold I")
PROJ_HEAD(wink1, "Winkel I")
PROJ_HEAD(wink2, "Winkel II")
Expand Down