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:

$\begin{align} & dx = a_\text{map} \left(\frac{a}{\sqrt{1-e^2 \sin^2 \varphi }}\right)^{-1} \sec \varphi \, dE ,\\ & dy = a_\text{map} \left(\frac{a(1- e^2)}{\left(1-e^2 \sin^2 \varphi\right)^{3/2}}\right)^{-1} \sec \varphi \, dN, \end{align}$

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.

Famous quotes containing the words map and/or projection:

“Unless, governor, teacher inspector, visitor,
This map becomes their window and these windows
That open on their lives like crouching tombs
Break, O break open,”
—Stephen Spender (1909–1995)

“My image is a statement of the symbols of the harsh, impersonal products and brash materialistic objects on which America is built today. It is a projection of everything that can be bought and sold, the practical but impermanent symbols that sustain us.”
—Andy Warhol (1928–1987)