Mercator and web Mercator projection __ Sailing

Google Maps, Virtual earth and other network geographic use of map projection, often known as the web Mercator or spherical Mercator, its main difference with the conventional Mercator projection is to simulate the world as a sphere rather than ellipsoid. It is recommended to do a basic understanding of map projection knowledge, "map projection why".

What is Mercator projection.

Mercator (Mercator) projection, also known as "isometric positive-axis cylindrical projection", the Dutch map biologist Mercator (Mercator) in 1569, the assumption that the earth is surrounded by a hollow cylinder, its equator and cylinder contact, and then imagine the Earth Center has a lamp, Projecting the graph on the sphere onto the cylinder, and then expanding the cylinder, is a map of the world drawn by the "Mercator projection" of a standard parallel to zero (i.e., the equator). From the ball to the plane, there is a conversion formula, which is no longer listed here.

Why did Google choose Mercator projection?

The "isometric" feature of the Mercator projection ensures that the object's shape is invariant, and that the square object does not become rectangular after projection. "Isometric" also guarantees the correctness of direction and location, so it is often used in navigation and aviation, and Google does not make mistakes in calculating the direction of people querying objects.

The "cylindrical" character of the Mercator projection ensures that the North and south (latitude) and the east (longitude) are parallel and perpendicular to each other. And the warp spacing is the same, the latitude interval from the standard latitude (here is the equator, may also be other parallels) to the two level gradually increased.

However, the "isometric" inevitably brings large deformations in the area, especially in the polar regions, notably as Greenland than the actual area of the enlarged N-fold. But if you go to the polar regions to explore or science test comrades, generally have more detailed information, will not come to see the network map, this does not matter.

(Photo source, Nelson Jhon)

Why is it a round sphere, not an ellipsoid.

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

Web Mercator projection coordinate system:

To the whole world, the equator as the standard latitude, meridian as the central Warp, the intersection points as the coordinate origin, east to north for positive, west to south for negative.

X axis: Because the equator radius is 6378137 meters, then the equator circumference is 2*pi*r = 2*20037508.3427892, therefore the X axis takes the range of values: [ -20037508.3427892,20037508.3427892].

Y-axis: The formula from the Mercator projection shows that at the same time the diagram above also has a schematic, when the latitude φ is close to the poles, i.e. 90°, the Y value tends to infinity. These are the "lazy engineers" that limit the values of the y-axis to [ -20037508.3427892,20037508.3427892], making a square.

The advantage of lazy people, as we all know, in advance to cut the static picture, improve access efficiency and so on. I'm just telling you why it's like this. Therefore the range under the projection coordinate system (m) is: min (-20037508.3427892,-20037508.3427892) to Maximum (20037508.3427892, 20037508.3427892).

Corresponding geographical coordinate system:

According to the truth, first of all, the geographical coordinate system, such as the sphere or ellipsoid is a geographical coordinate system, and Mercator projection is not related. In simple terms, the projection coordinate system (PROJCS) is a planar coordinate system, in meters, while the geographical coordinate system (GEOGCS) is the ellipsoid coordinate system, which is in the latitude and longitude of the unit. Specific reference to the "coordinate system, coordinate reference, coordinate transformation, projection transformation."

Longitude: This way is OK, the global scope: [-180,180].

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

Therefore, the geographical coordinate system (latitude and longitude) corresponds to the range is: the smallest ( -180,-85.05112877980659), the largest (180, 85.05112877980659). As for the datum, coordinate conversion and so on, no more words.

If you want to know the coordinates of how to calculate, please see the 2nd quarter of the full resolution of related coordinates calculation, more in-depth and GIS-related 3rd quarter "wkt form".

Note: In addition to Google Maps, there are Bing Maps, MAPABC map online map services are using the Web Mercator projection, ESRI's onlilne map also use this map projection, in addition to cutting the number of images in the cut, or everyone in order to marshup convenience, Have adopted the Web Mercator projection method, but in the map display above for everyone to understand, or converted into a latitude and longitude of the way to display.

Transferred from http://blog.csdn.net/liyan_gis/article/details/8021514