Mocato projection of Vernacular map projection

In the introduction to world projection, we mentioned mocato projection, which isBy HollandCartographyG. Mercator was created in 1569. Currently, most popular map websites such as Google map and Baidu map all use this projection (Web mocato projection). Today we will briefly introduce this projection.

What is mocato projection?

Mocato projection, also known as tangent cylindrical projection, is based on a cylindrical surface that is tangent to the Earth at the equator. First, the spherical surface is mapped to the cylindrical surface, expand the cylindrical surface into a plane.

 

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..Assume that there are two points A and B on the earth's surface. On the earth's sphere, the angle of B relative to a is east-north, so after mocato projection, on the planimetric map, B is still east-north compared with. This is very important in sailing, because in the vast sea, there is no reference, you can only judge the Location Based on the compass or the stars, if the end point on the map is different from the azimuth angle of the starting point and the actual azimuth angle, such a map has no practical significance in sailing. Because of this, charts are generally made using mocato Projection Rules.

• For example, if the earth's radius is set to R, it is known that the coordinate of a point P on the Earth is, in which longitude is represented, the range is-<, negative number indicates the west longitude, positive number indicates the east longitude, B indicates the dimension, the value range is-<. A negative value indicates the latitude and a positive value indicates the latitude. Map the earth sphere to the Cartesian coordinate system of the plane through the mocato projection. The ing point of the zero-degree longitude line and the cross point of the equator is the origin, the X axis is parallel to the weft line, and the East is the positive direction; the Y axis is parallel to the longitude line, and the North is taken as the positive direction. Calculates the coordinates (XP, yp') of the point P mapped to the point P in the Cartesian coordinate system of the plane ').

Solution: according to the principle of mocato projection, mocato projection is composed of a cylindrical surface tangent to the earth's equator. Therefore, the width of the expanded image is the length of the earth's equator, the X coordinate of the P 'point is the distance between the longitude line of the P 'point and the cross point of the equator to the zero-degree longitude line and the cross point of the Equator, that is, part of the equator line. Its value is:

Finding the Y coordinate of point P is a little troublesome. Let's see:

 

Because one principle to be followed by mocato projection is that the direction angle remains unchanged, the zooming ratio of the X direction and the Y direction must be the same during the ing process. We can know that the latitude isAfter projection, the weft coil becomes a straight line as long as the equator, so the latitude isA very small area near the point. After projection, the horizontal magnification ratio is:

 

According to the mocato Projection Rules, the magnification ratio in the vertical direction of the small area should also beOn the earth surface before the projection, the vertical side length of the small area is part of the meridian line. We can use the Earth's radius multiplied by a small angle to represent:

 

The vertical side length of the projected small area should be:

In the above formula, we can calculate the point where the latitude is, and the Y coordinate after the projection is:

Therefore, the final result is:

According to the mocato projection, the North and South Poles are projected to an infinite distance, but the world map of Google map is indeed square, therefore, the Geographic Information on Google map is definitely lost.

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 = 20037508.3427892. Therefore, the value range of the X axis is as follows:

[-20037508.3427892, 20037508.3427892]

Y axis: It can be seen from the mocato projection formula, and it also indicates that when the latitudePhiClose to two poles, that is90°,YThe value tends to be infinite. GenerallyYThe value range of the axis is also limited:

[-20037508.3427892, 20037508.3427892]

References:

Http://www.cnblogs.com/GIS_zhou/articles/1525772.html

Http://baike.baidu.com/view/301981.htm