Maps tile-related computing

Most online maps useMercator projection (mocato projection),Mocato projection"Equality"This feature ensures that the shape of an object remains unchanged. After a square object is projected, it will not become a rectangle."Equality"It also ensures the correctness of the direction and position of each other. Therefore, it is often used in navigation and air, and online maps also use this feature to calculate the direction of a person's query of a ground object without errors.However,"Equality"The inevitable huge deformation of the area, especially the two poles, is enough for our conventional use.

However, most online maps do not use standardMercator projection (equal tangent ),It is also called Web mocato projection.

X axis: Because the equator radius is 6378137 meters, the Equator perimeter is 2 * pI * r = 2*20037508.3427892. Therefore, the value range of the X axis is [-20037508.3427892, 20037508.3427892].

YAxis: When latitudePhiClose to two poles, that is90°,YThe value tends to be infinite. This is"Lazy Engineer"Just putYThe value range of the axis is also limited[-20037508.3427892, 20037508.3427892]And create a square.

Therefore, the range in the projection coordinate system (meters) is: Minimum(-20037508.3427892,-20037508.3427892)To maximum(20037508.3427892, 20037508.3427892).

After Inverse Calculation, latitude can be obtained85.05112877980659. Therefore, the latitude value range is[-85.05112877980659,85.05112877980659].

The geographic coordinate system (longitude and latitude) corresponds to the following range: Minimum(-180,-85.05112877980659), Maximum(180, 85.05112877980659).

Ground Resolution, ground resolution, similar to spatial resolution (spatial resolution). Here we mainly focus on the format represented by pixel size: a pixel) represents the ground size (meters ). Taking Virtual Earth as an example, when level is 1, the image size is 512*512 (4 tile), so the resolution of the equator space is: the equator perimeter/512. The spatial resolution of other latitudes is the latitude circle length/512, and the extreme Arctic is 0. When the level is 2, the spatial resolution of the equator is the circumference of the equator/1024, And the other latitude is the latitude circle length of 1024. Obviously, the ground resolution depends on two parameters: the zoom level and latitude. The level determines the number of pixels and the latitude determines the distance between the ground. The formula for ground resolution is, in meters/pixels:

Ground Resolution = (COS (latitude * PI/180) * 2 * pI * 6378137 meters)/(256*2 level pixels)

Map scale, that is, the map scale. The distance between the map and the field is usually in meters. In the calculation of ground resolution, the pixel size of the image can be obtained by level. Therefore, you need to convert the pixel size to the distance in meters, involving DPI (DOT per inch ), it can be understood as a similar PPI (pixelper inch), that is, how many pixels each inch represents. 256*2 level/DPI to get the corresponding inch, and then divide the inch by 0.0254 to the meter. The field distance is still cos (latitude * PI/180) * 2 * pI * 6378137 meters. Therefore, the scale formula is generally set to 1: XXX, with no unit:

Map scale = 1: ground resolution * screen DPI/0.0254 meters/inch

= 256*2 level/screen DPI/0.0254/(COS (latitude * PI/180) * 2 * pI * 6378137)

= 1: (COS (latitude * PI/180) * 2 * pI * 6378137 * screen DPI)/(256*2 level * 0.0254)

Quadkeys computing

For example, level 3 (3, 5)

Tilex = 3 = 011 2

Tiley = 5 = 101 2

Quadkey = 100111 2 = 2134 = 213"

The rule in does not explain.