Map Projection: mocato projection (2)

In fact, this article should be called (1). After all, this article mainly focuses on theoretical knowledge and the previous article focuses on implementation formulas.

Map projection used by network maps such as Google Maps and Bing (it seems that Baidu map is also a mocato projection), which is often called Web Mercator, the main difference between it and conventional mocato projection is to simulate the Earth as a sphere rather than an elliptical body.

 

What is mocato projection?

 

Mercator projection, also known as "equisigned positive axis cylindrical projection", was developed by Dutch cartographer Mercator In 1569:

1. assume that the Earth is enclosed in a hollow cylinder, and its equator is in contact with the cylinder. Then it is assumed that there is a lamp in the center of the earth, and the graphics on the sphere are projected onto the cylinder, expand the cylinder, which is a map of the world drawn from the mocato projection with the standard weft at zero (that is, the Equator.

2. assume that the Earth is enclosed in a hollow cylinder, and its equator is in contact with the cylinder. Then, assuming that the Earth is constantly expanding, the expanded Earth's surface is "pasted" on the cylinder, expand the cylinder in sequence.

There is a conversion formula from the ball to the plane. For details, refer to the previous article [map projection] mocato projection (1 ).

 

Why do Google choose mocato projection?

 

The "equal angle" feature of mocato projection ensures that the shape of an object remains unchanged. After a square object is projected, it will not become a rectangle. "Angular" also ensures the correctness of the direction and position of each other. Therefore, it is often used in navigation and air, while Google does not make errors when calculating the direction of people to query the ground features.

The "cylindrical" feature of mocato projection ensures that both the North and South (weft) and the East and West (meridian) are parallel straight lines and perpendicular to each other. In addition, the longitude line interval is the same, and the weft line interval increases gradually from the standard weft line (here it is the equator, or other weft lines) to two levels.

However, "Angular" inevitably results in huge deformation of the area, especially in the bipolar area. Obviously, Greenland is n times larger than the actual area. However, it doesn't matter if more detailed information is provided to the comrades who are exploring the polar region or taking the scientific examination.

 

Why is it a Circular Sphere instead of an elliptical sphere?

 

This is simple because it is easy to implement and easy to calculate. The accuracy is less than 0.33% in theory, especially when the scale is larger and the terrain is more detailed.

 

Web mocato projection coordinate system:

 

Take the whole world, the Equator as the standard weft, the primary meridian as the central meridian, the intersection of the two is the coordinate origin, east to north is positive, and west to south is negative.

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].

Y axis: It can be seen from the mocato projection formula, but also has a signal, when the latitude Phi is close to the pole, that is, 90 °, the Y value tends to be infinite. These "lazy engineers" set the value range of the Y axis to [-20037508.3427892, 20037508.3427892] to a square.

As we all know, we cut static images in advance to improve access efficiency. I just tell you why it is like this. Therefore, the range in the projection coordinate system (meters) is: Minimum (-20037508.3427892,-20037508.3427892) to maximum (20037508.3427892, 20037508.3427892 ).

Corresponding geographic coordinate system:

According to the principle, the geographical coordinate system is the first thing. For example, whether a sphere or an elliptical body is a geographical coordinate system is not associated with the mocato projection. In short, the projection coordinate system (projcs) is a plane coordinate system, in meters, while the geographic coordinate system (geogcs) is an elliptical coordinate system, measured in longitude and latitude. For details, see coordinate system, coordinate reference system, coordinate transformation, and projection transformation.

Longitude: No problem. The global range is recommended: [-180,180].

Latitude: It is known above that the latitude cannot reach 90 °. The Lazy gets-20037508.3427892 for the square. After Inverse calculation, the latitude is 85.05112877980659. Therefore, the latitude value range is [-85.05112877980659, 85.05112877980659]. What about other regions? No, penguins and polar bears don't care.

Therefore, the range of the geographic coordinate system (longitude and latitude) is: Minimum (-180,-85.05112877980659), maximum (180, 85.05112877980659 ).

Well, let's talk about it.

References: http://wenku.baidu.com/view/2b152429e2bd960590c677f8.html