[Proj] Proj Digest, Vol 77, Issue 1

[Melita Kennedy]

-----Original Message-----
>   1. Web Mercator vs. Web Mercator Auxiliary Sphere (Aaron Friesen)
>----------------------------------------------------------------------
>
>Message: 1
>Date: Fri, 1 Oct 2010 11:34:01 -0400
>From: Aaron Friesen <aaron at cartopac.com>
>Subject: [Proj] Web Mercator vs. Web Mercator Auxiliary Sphere
>To: "proj at lists.maptools.org" <proj at lists.maptools.org>
>Message-ID:
>	<90200BC582E4FF488816D357540C1D4D2271E4D5E1 at VMBX103.ihostexchange.net>
>Content-Type: text/plain; charset="us-ascii"
>
>Curiosity question ...
>
>>From the Proj4 FAQ, for Web Mercator, the setting should be:
>
>+proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 \
>                   +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +no_defs
>
>I am having to deal with data in "Web Mercator Auxiliary Sphere",
>as apparently defined by ESRI.
>
>The WKT form spatialreference.org is:
>
>PROJCS["WGS_1984_Web_Mercator_Auxiliary_Sphere",
>    GEOGCS["GCS_WGS_1984",
>        DATUM["D_WGS_1984",
>            SPHEROID["WGS_1984",6378137.0,298.257223563]],
>        PRIMEM["Greenwich",0.0],
>        UNIT["Degree",0.0174532925199433]],
>    PROJECTION["Mercator_Auxiliary_Sphere"],
>    PARAMETER["False_Easting",0.0],
>    PARAMETER["False_Northing",0.0],
>    PARAMETER["Central_Meridian",0.0],
>    PARAMETER["Standard_Parallel_1",0.0],
>    PARAMETER["Auxiliary_Sphere_Type",0.0],
>    UNIT["Meter",1.0],
>    AUTHORITY["ESRI","102100"]]
>
>How does the proj4 definition need to change to match?
>
>Is setting b=6356752.314245 sufficient?
>
>Aaron

Hi Aaron, 

No, it doesn't. This definition is just another way of emulating the 
Mercator definition used by the online mapping services. It has to use 
the spherical equations for Mercator. One way is to use a sphere. 
The way Esri has decided to do it to use a special implementation of 
Mercator that has a "auxiliary sphere type" parameter. If zero, and 
the geographic coordinate system is based on an ellipsoid, use the 
semimajor axis for the sphere's radius. 

Going this way means that we can use the 'normal' WGS84, rather than a 
custom sphere and makes datum transformations easier.

Melita

Melita Kennedy
Esri product engineer