Web Mercator / Pseudo Mercator¶
New in version 5.1.0.
The Web Mercator / Pseudo Mercator projection is a cylindrical map projection. This is a variant of the regular Mercator projection, except that the computation is done on a sphere, using the semi-major axis of the ellipsoid.
From Wikipedia:
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) |
| Available forms | Forward and inverse |
| Defined area | Global |
| Alias | webmerc |
| Domain | 2D |
| Input type | Geodetic coordinates |
| Output type | Projected coordinates |
Parameters¶
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.
-
+lon_0=<value>¶ Longitude of projection center.
Defaults to 0.0.
-
+x_0=<value>¶ False easting.
Defaults to 0.0.
-
+y_0=<value>¶ False northing.
Defaults to 0.0.
Mathematical definition¶
The formulas describing the Mercator projection are all taken from G. Evenden’s libproj manuals [Evenden2005].
Forward projection¶
\[x = \lambda\]
\[y = \ln \left[ \tan \left(\frac{\pi}{4} + \frac{\phi}{2} \right) \right]\]