I'm trying to understand this issue myself, and keep on discovering
new things. Please examine my findings.

First of all, EPSG has totally purged EPSG:3785 from their database,
at least as of version 7.6. The proj.4 epsg file [1] lists identical
parameters for both EPSG:3785 and EPSG:3857, though comments that
EPSG:3785 is deprecated. Basically EPSG:3785 should never have
existed.

I think the confusion relates to datums vs. projections. OpenStreetMap
stores coordinates in the WGS84 datum [2], which uses an ellipsoidal
model of the earth. EPSG:3857 uses the WGS 84 datum, but it also
projects that datum using a spherical model. Thus the inverse
flattening that Martin mentions refers to the WGS 84 datum, not the
EPSG:3857 projection from that datum.

You can also read about this on the proj.4 wiki [3].

-Josh

[1]: http://trac.osgeo.org/proj/browser/trunk/proj/nad/epsg
[2]: 
http://josm.openstreetmap.de/wiki/Help/Concepts/Coordinates#Openstreetmapcoordinates
[3]: 
http://trac.osgeo.org/proj/wiki/FAQ#ChangingEllipsoidWhycantIconvertfromWGS84toGoogleEarthVirtualGlobeMercator

On Tue, Mar 8, 2011 at 7:24 AM, Tobias Wendorff
<tobias.wendo...@tu-dortmund.de> wrote:
> Am 25.02.2011 20:13, schrieb M∡rtin Koppenhoefer:
>>
>> I know that EPSG says "NOT VALID". Who cares?
>
> EPSG are creating and releasing the codes. You have to face *why*
> they do that. They need it for surveys and for geodetic use.
>
> EPSG:3785 uses a sphere, which is "outdated" nowerdays. But it's
> much more easy to use in OSM. A simple formular with good looking
> results.
>
> EPSG:3857 uses an ellipsoid, which is more equal to real Earth,
> since it uses WGS84 as background.
>
> For OSM, it would be much better to use EPSG:3857 instead of
> EPSG:3785. The reason is: our coordinates are in WGS84. Normally,
> you have to transform the WGS84 ellipsoid to some WGS84 sphere
> to get correct results, but noone does this.
>
> When using EPSG:3857 you're in "one system" and you don't have
> to transform anything. But the formulars to draw the map are
> much more complicated, since you have to deal with integrals
> or expansion in series.
>
> HTH
> Tobias
>
>

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