102100 vs. 102113 is mixed up?

[YasunariTosa]

I found the following in http://help.arcgis.com/en/arcgisserver/10.0/apis/rest/index.html?pcs.html.

The definition DATUM are mixed up between 102100 (3857) and 102113,
since DATUM for 102100 should be using a sphere vs. 102113 should be using pancake.
(the same thing happens for 3857).    3785 is gone from the list.

If you look at the DATUM section, 102100 is using a pancake but 102113 is using sphere.

Can you clarify?

102100  WGS_1984_Web_Mercator_Auxiliary_Sphere
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]]

102113  WGS_1984_Web_Mercator
PROJCS["WGS_1984_Web_Mercator",GEOGCS["GCS_WGS_1984_Major_Auxiliary_Sphere",DATUM["D_WGS_1984_Major_Auxiliary_Sphere",SPHEROID["WGS_1984_Major_Auxiliary_Sphere",6378137.0,0.0]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Mercator"],PARAMETER["False_Easting",0.0],PARAMETER["False_Northing",0.0],PARAMETER["Central_Meridian",0.0],PARAMETER["Standard_Parallel_1",0.0],UNIT["Meter",1.0]]

[MelitaKennedy]

In 102100 and 3857, we can use an ellipsoid/spheroid-based geographic coordinate system because the map projection algorithm is handling the conversion to a sphere internally.

102100: PROJECTION["Mercator_Auxiliary_Sphere"]
102113: PROJECTION["Mercator"]

This parameter: PARAMETER["Auxiliary_Sphere_Type",0.0]

determines how an ellipsoid-based GCS should be handled in a map projection that supports spheres only. The zero value means to use the semimajor axis for the sphere's radius. "1": use semiminor axis, "2": calculate authalic sphere's radius, "3": calculate authalic sphere's radius and convert geodetic latitudes to authalic latitudes.

With 102113 (3785), because the GCS was sphere-based, technically you would have to do a geographic (datum) transformation from WGS 1984 to the sphere-based GCS before the projection could occur. This is more difficult to handle because it means all data has to go through a geographic transformation. In 102100 (3857) only non-WGS84 data has to go through a geographic transformation.

Both definitions give exactly the same results.

Melita

(edited to add sentence about results, 1:22pm PDT)