[Proj] Google maps <3857> datum

[Noel Zinn (cc)]

There is no ellipsoid-to-sphere transformation involved in the EPSG 3857 
(Web Mercator) map projection.  EPSG 3857 is a conversion from WGS84 
ellipsoidal (lat/lon) to grid Easting/Northing using spherical Mercator 
equations, but there is no intervening sphere.  It's just another map 
projection (though it has its own distortions that are not the same as 
either the ellipsoidal Mercator or the Spherical Mercator).  It is 
completely reversible LL <=> EN.

More about the distortions at:
http://www.hydrometronics.com/downloads/Web%20Mercator%20-%20Non-Conformal,%20Non-Mercator%20(notes).pdf

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)

-----Original Message----- 
From: Alain Orsoni
Sent: Monday, January 27, 2014 3:47 AM
To: proj at lists.maptools.org
Subject: [Proj] Google maps  datum

Hi,

I have to implement the 3857 projection in a software.
My problem is the following : it seems that when a point on earth having 
long1 and lat1 coordinates in WGS84 datum is projection in this direct 
mercator projection based on a spheric ellipsoid (I could say directly a 
sphere), this point is considered by proj4 to have the same lon1 and lat1 
coordinates on the sphere. After the transform to Mercator occurs.
I noticed this because when I transform from WGS84 datum to Google sphere 
(the +a=6378137 +b=6378137 sphere given in 3857 description) I get lon2 and 
lat2 coordinates for our point where lon2=lon1 and lat2 not equal lat1 
(except for lat=0 or 90). This is normal but doesn't seem to be the process 
applied by proj4.

When I consider lon1 and lat1 being the coordinates of the point on the 
sphere (saying that I don"t transform from WGS84 to the sphere), I get the 
same Marcator coordinates than the ones I get through proj4 transform from 
WGS84 to 3857.

Could someone confirm or document this particular application of the 
transform done for 3857 datum.

Hopping my problem is clearly expressed, and waiting to ear from you.

Alain ORSONI
Institut Géographique National, FRANCE

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