Web Mercator projection (GO)

Google maps Map Projection full resolution (1): Web Mercator projection

Map projections used by web geography such as Google maps and Virtual Earth are often referred to as Web Mercator or spherical Mercator, and the main difference from regular Mercator projections is that the earth is modeled as a sphere rather than an ellipsoid. It is recommended to do a basic understanding of the map projection knowledge, "map projection why."

What is the Mercator projection?

Mercator (Mercator) projection, also known as "conformal cylindrical projection", the Dutch map Mercator (Mercator) was drawn up in 1569, assuming that the earth is surrounded by a hollow cylinder, its equator in contact with the cylinder, and then imaginary Earth Center has a lamp, Projecting a shape on a spherical surface onto a cylinder, and then expanding the cylinder, this is a world map drawn by the standard parallel "Mercator projection" of zero (that is, the equator). From the ball to the plane, there is a conversion formula, here is no longer listed.

Google Why do we choose Mercator projection?

The "isometric" nature of the Mercator projection ensures that the shape of the object will not be changed, and that the square object does not become rectangular after projection. "Conformal" also guarantees the correctness of direction and mutual position, so it is often used in navigation and aviation, and Google does not make mistakes when calculating the direction of people querying for objects.

The "cylindrical" nature of the Mercator projection ensures that North and south (parallels) and Things (meridians) are parallel lines and are perpendicular to each other. And the warp interval is the same, and the latitude interval increases gradually from the standard parallels (here the equator, or possibly other parallels) to level two.

However, the "conformal" inevitably brings large deformations of the area, especially in the polar regions, where the apparent Greenland is enlarged n times than the actual area. But if you go to the polar regions of the expedition or the subjects of the comrades, generally have more detailed information, will not be able to view the network map, this does not matter.

Why a circular sphere, not an ellipsoid?

This is simple, simply because of the convenience of the implementation, and the calculation of the simple, the accuracy of theoretical differences in 0.33%, especially the larger the scale, more detailed features, the difference can be ignored.

Web Mercator Projection coordinate system :

To the whole world, the equator as the standard parallels, the Prime Meridian as the Central Meridian, the intersection of the two points of the coordinates of the origin, east to north is positive, west to south negative.

X-axis: Due to the equator radius of 6378137 meters, the equatorial perimeter is 2*pi*r = 2*20037508.3427892, so the x-axis values range: [ -20037508.3427892,20037508.3427892].

Y-axis: The formula of Mercator projection shows that the Y value tends to infinity when the latitude φ approaches the poles, that is, 90°. These are the "lazy engineers" that limit the range of the y-axis to [ -20037508.3427892,20037508.3427892] and make a square.

The benefits of lazy people, well-known, pre-cut the static picture, improve access efficiency and so on. I'm just telling you why this is the way it is. So the range under the projected coordinate system (meters) is: Minimum (-20037508.3427892,-20037508.3427892) to Maximum (20037508.3427892, 20037508.3427892).

the corresponding geographic coordinate system :

According to the truth, first of all, the geographical coordinate system is, such as the sphere or ellipsoid is a geographical coordinate system, and Mercator projection this is not very relevant. In simple terms, the projected coordinate system (PROJCS) is a planar coordinate system, in meters, while the geographic coordinate system (GEOGCS) is the ellipsoid coordinate system, in terms of latitude and longitude. Refer to the coordinate system, coordinate reference, coordinate transformation, projection transform, and so on.

Longitude: There's no problem here. Global reach: [-180,180].

Latitude: It is known above, latitude can not reach 90°, lazy people for the square of 20037508.3427892, after the inverse calculation, to obtain latitude 85.05112877980659. The latitude range is therefore [ -85.05112877980659,85.05112877980659]. What about the rest of the area? Yes, the Penguins don't care.

Therefore, the geographic coordinate system (latitude and longitude) corresponds to a range of: min ( -180,-85.05112877980659), Max (180, 85.05112877980659). As for the datum, coordinate conversion and so on will no longer speak.

If you want to know how the coordinates are calculated, please see the full analytic 2nd quarter, "Related coordinate calculation", more in-depth and GIS-related 3rd season "wkt form".

Three, network map projection parameters

Global Spherical Mercator--main Parameters:

	Datum:	WGS84
	Map projection:	Spherical Mercator
	Ellipsoid:	WGS84
	EPSG Code:	epsg:4326	(for coordinates in Latitude/longitude)
	EPSG Code:	epsg:900913	(for coordinates in metres)

Because the same map projection is used to make the tile map of different map service providers overlay Well, although the slicing rules and algorithms are different, the result of stitching is always consistent.