Where2 - Map Projection

Map Projection

Google Maps is based on a close variant of the Mercator projection. If the Earth were perfectly spherical, the projection would be the same as the Mercator. Google Maps uses the formulæ for the spherical Mercator, but the coordinates of features on Google Maps are the GPS coordinates based on the WGS 84 datum. The difference between a sphere and the WGS 84 ellipsoid causes the resultant projection not to be precisely conformal. The discrepancy is imperceptible at the global scale but causes maps of local areas to deviate slightly from true ellipsoidal Mercator maps at the same scale.

Assuming that and are the components of infinitesmal local ENU coordinates, their breadth and length projected on the map are described as follows:

 begin{align} & dx = a_text{<a href=map} left(frac{a}{sqrt{1-e^2 sin^2 varphi }}right)^{-1} sec varphi , dE ,\ & dy = a_text{map} left(frac{a(1- e^2)}{left(1-e^2 sin^2 varphiright)^{3/2}}right)^{-1} sec varphi , dN, end{align} " src="http://upload.wikimedia.org/math/9/4/d/94db75468e8277ad30f8befffd32eb1c.png" />

where is geodetic latitude, is the first eccentricity of the ellipsoid of the Earth, is the semi-major axis of the Earth, and is that at the scale of the map as drawn (see "Geodetic system" and "Mercator projection"). Google Maps uses

 a_text{map} = frac{256 times 2^{zoomLevel}}{2 pi}  text{pixels} .

Because the Mercator projects the poles at infinity, Google Maps cannot show the poles. Instead it cuts off coverage at 85.051125° north and south which is atan(sinh(π))×180/π, a requirement that the map is a square. This is not considered a limitation, given the purpose of the service.

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