[MetaCRS] Re: Google Spherical Mercator (EPSG:3785)

[Melita Kennedy]

Hi Frank,

On a side note, is the list standard to top-post or bottom-post?

On 8/15/08, "Frank Warmerdam" <warmerdam at pobox.com> wrote:
>
> Folks,
>
> I am trying to add support for EPSG:3785 (Google Spherical
> Mercator) to GDAL/OGR and PROJ.4 per bug report:
>
>  http://trac.osgeo.org/proj/ticket/9
>
> The problem i see is that I end up with the WKT definition:
>
> PROJCS["Popular Visualisation CRS / Mercator",
>    GEOGCS["Popular Visualisation CRS",
>        DATUM["Popular_Visualisation_Datum",
>            SPHEROID["Popular Visualisation Sphere",6378137,0,
>                AUTHORITY["EPSG","7059"]],
>            TOWGS84[0,0,0,0,0,0,0],
>            AUTHORITY["EPSG","6055"]],
>        PRIMEM["Greenwich",0,
>            AUTHORITY["EPSG","8901"]],
>        UNIT["degree",0.01745329251994328,
>            AUTHORITY["EPSG","9122"]],
>        AUTHORITY["EPSG","4055"]],
>    UNIT["metre",1,
>        AUTHORITY["EPSG","9001"]],
>    PROJECTION["Mercator_1SP"],
>    PARAMETER["central_meridian",0],
>    PARAMETER["scale_factor",1],
>    PARAMETER["false_easting",0],
>    PARAMETER["false_northing",0],
>    AUTHORITY["EPSG","3785"],
>    AXIS["X",EAST],
>    AXIS["Y",NORTH]]
>
> This definition includes TOWGS84[0,0,0,0,0,0,0].
>
> My understanding is that we really want to treat the lat/long values
> on datum EPSG:6055 as if they were equivelent to lat/long values
> on the WGS84 datum.
>
> However, the way I apply TOWGS84[] translations is to convert
> the lat/long values to geocentric coordinates on the source spheroid,
> apply the offset, and then transform back to lat/long on the destination
> spheroid. The vast difference between the WGS84 and spherical
> spheroids is resulting in a large latitude shift.
>
> So my question is what is in error?
>
> 1) Is the EPSG dictionary wrong in suggesting a TOWGS84[0,0,0]
> transformation?
>
> 2) Am I wrong in applying TOWGS84[] transformations by using
> the different spheroids to go from and to geocentric coordinates?
>
> 3) Am I going wrong in how I look things up in the EPSG database?

Mixing in a sphere-based CRS is always problematic. I think it is
probably more correct to convert between an ellipsoid and a sphere
through the datum transformation than ignore the latitude differences.
In this case it is incorrect because Google Maps and Microsoft Virtual
Earth are projecting the WGS84
lat/lon values directly to Mercator (sphere equations) with no
latitude changes.

[Disclaimer: ESRI employee]
ESRI now has two ways to emulate this definition in WKT. We added a
sphere-based geographic CRS and used it with the standard Mercator
definition (to trigger the sphere equations). Due to some other work,
we then added an implementation of Mercator that supports a new
parameter. It determines how to convert the base geographic CRS
ellipsoid into a sphere. That way we can use the standard WGS84
definition and pick up all the existing datum transformations. The
parameter values are:

0 - use semimajor axis as sphere radius
1 - use semiminor axis
2 - calculate and use authalic radius
3 - authalic radius _and_ convert geodetic latitudes to authalic latitudes

The last option may be the most mathematically correct if the target
projection is equal area.

Melita