The Microsoft Live Maps and Google Maps projection

by Morten 27. July 2007 05:06

I have lately seen several blogposts confused about which datum and projection Microsoft’s Live Maps (Virtual Earth) and Google Maps use. As most people already know by now, they render the round earth onto a flat screen using a Mercator projection.

I think the confusion comes from that they actually use two spatial reference systems at the same time:

  1. Geographic  Longitude/Latitude coordinatesystem based on the standard WGS84 datum.
  2. Mercator projection using a datum based on WGS84, BUT modified to be spheric.

So when is what used?

The Javascript API’s use (1) as input when you want to add points, lines and polygons. That is, they expect you to input any geometry in geographical coordinates, and click events etc. will also return geometry in this spatial reference. This is the coordinate system most javascript developers will use. The API will automatically project it to the spheric mercator projection.

If you want to create image overlays, or roll your own tile server on top of the map, you will need to project your images into a spheric mercator projection. The JavaScript APIs are not able to do this for you.

Here’s a bit of facts about the two projections:

The valid range of (1) is: [-180,-85.05112877980659] to [180, 85.05112877980659].

The valid range of (2) is: [-20037508.3427892, -20037508.3427892] to [20037508.3427892, 20037508.3427892]

Well-known Text for (1):
GEOGCS["GCS_WGS_1984",DATUM["D_WGS_1984",SPHEROID["WGS_1984",6378137,298.257223563]],PRIMEM["Greenwich",0],UNIT["Degree",0.0174532925199433]]

Well-known Text for (2):
PROJCS["Mercator Spheric", GEOGCS["WGS84basedSpheric_GCS", DATUM["WGS84basedSpheric_Datum", SPHEROID["WGS84based_Sphere", 6378137, 0], TOWGS84[0, 0, 0, 0, 0, 0, 0]], PRIMEM["Greenwich", 0, AUTHORITY["EPSG", "8901"]], UNIT["degree", 0.0174532925199433, AUTHORITY["EPSG", "9102"]], AXIS["E", EAST], AXIS["N", NORTH]], PROJECTION["Mercator"], PARAMETER["False_Easting", 0], PARAMETER["False_Northing", 0], PARAMETER["Central_Meridian", 0], PARAMETER["Latitude_of_origin", 0], UNIT["metre", 1, AUTHORITY["EPSG", "9001"]], AXIS["East", EAST], AXIS["North", NORTH]]

Proj.4 definition for (1):
+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs

Proj.4 definition for (2) (see here for an explanation of the weird ’nadgrids’ parameter):
+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

So why this weird extent for the latitude? First of all, the poles in the Mercator projection extends towards infinity, so at some point they have to cut them off (and who cares about ice anyway - apart from that its melting). If you look at (2) these latitude/longitude values projected into the spheric mercator results in a perfect square, fitting perfectly with squared image tiles, that are simple to sub-divide over and over again, as you zoom in. I expect the reason for the spheric datum is for simplicity and perfomance when reprojecting points from longitude/latitude to screen coordinates. Charlie Savage also has a more mathematical approach to deriving these values.

For a quick introduction to projections, coordinate systems and datums see here.

If you want to know more about how these mapping api's work, keep an eye on Jayant's blog.

Update: We now have an offical EPSG code for the projection. See details here.

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GIS | Google Maps | Spatial References | Virtual Earth

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Morten Nielsen

Silverlight MVP

Morten Nielsen
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