Characteristics of several Projection Methods

 

I. I will only talk about the most common types of projection: mocato projection, Gaussian-kerlenge projection, UTM projection, and lanbote"

1. Mercator projection

1.1 Introduction to Mercator projection
Gerhardus Mercator 1512-1594 was developed in 1569 as an equi-angular tangent cylindrical projection, in which the Earth was enclosed in a hollow cylinder, the standard weft is in tangent contact with the cylinder, and 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, and then the cylinder is expanded, this is a map drawn from the mocato projection on the selected Standard weft. Mocato projection has no angle deformation. The ratio of each point to the length of each direction is equal. Its linear line is a parallel line, and the intersection is a right angle, and the longitude line interval is equal, the weft interval increases gradually from the standard weft to the pole. The length and area of the mokto projection map have obvious deformation, but the standard weft has no deformation, and the deformation gradually increases from the standard weft to the pole, but it has the characteristics of equal expansion in all directions, maintains the correct relationship between directions and locations. The advantage of mocato projection is to maintain the correct direction and angle on the map. mocato projection maps are often used as aerial charts and aerial charts, the constant direction can always reach the destination, so it has favorable conditions for the ship to locate and determine the course while sailing, which brings great convenience to the navigators.
According to the specification for preparing topographic maps of the seabed (GB/T 17834-1999, drafted by the Ministry of navy and air security), a chart of or a smaller scale is projected using mocato, the basic scale submarine Topographic Map (, 1: 1 million) adopts a unified baseline of 30 °, and the non-basic scale map uses the middle latitude of the drawing area as the reference weft. The baseline is rounded to an integer or an integral point.

1.2 The mokto projection coordinate system uses the zero meridian or custom origin Meridian (L0) as the origin for the projection of the cross point of the equator, and the zero meridian or custom origin meridian projection is the X axis of the Y coordinate, the projection of the equator is the Y axis, which forms the Cartesian coordinate system of the mocato plane.

2. Gaussian-kruger projection and UTM (Universal Transverse Mercator) Projection

2.1 Introduction to Gaussian-kerluge projection
It is a kind of "equisigned cross-sectional cylindrical projection ". German mathematician, physicist, astronomy Gaussian (Carl Friedrich Gauss, 1777-1855) was developed in 1820s, after the German Land Surveyors Kluge (Johannes Kruger, 1857 ~ 1928) the projection formula was added on January 1, 1912. Imagine a central meridian that uses a cylinder to cross the sphere and is projected as a straight line based on the conditions where the length remains unchanged and the equator projection is a straight line, projection the spherical surface in a certain longitude difference range on both sides of the central longitude line to the cylindrical surface. Then the cylindrical surface along the north and south poles of the bus is cut and flattened, that is, a Gaussian grid projection plane. After Gaussian kerlenge projection, except the central meridian line and the equator are straight lines, other meridian lines are symmetric in the central meridian line curve. Gaussian-gram projection has no angle deformation, and the deformation on the length and area is also small. The central meridian line has no deformation, and the deformation increases gradually from the central meridian line to the projection band edge, the maximum deformation is at the two ends of the inner equator in the projection band. The projection accuracy is high, the deformation is small, and the computation is simple (the coordinates of each projection are the same, as long as the data of one belt is calculated, other bands can be applied ), therefore, the application in large-scale topographic maps can meet various military needs and perform precise measurement and calculation on the charts. The earth's elliptical sphere is divided into several projection bands by a certain longitude difference, which is the most effective method for limiting length deformation in Gaussian projection. The length deformation should be controlled to make it not greater than the ing error, but also to reduce the calculation of the number of bands, based on this principle, the elliptical sphere of the earth is divided along the meridian into the melons and petals with equal longitude to facilitate the projection of daughter bands. Generally, it is divided into six-degree or three-degree bands based on the longitude difference of 6 degrees or 3 degrees. The 6th degree band starts from the 0th degree meridian and goes from the west to the east at intervals of 6 degrees.
1, 2... 60. The three-degree belt is divided based on the six-degree belt. Its central meridian and the central meridian of the six-degree belt coincide with that of the sub-band, that is, every third degree of longitude deviation from the meridian of 1.5 degrees from the West to the East, with numbers in sequence for three degrees with 1st, 2... 120. China's longitude ranges from 73 ° to 135 ° to the West, which can be divided into eleven of the six degrees, with the central longitude lines of 75 °, 81 °, 87 ° ,...... , 117 °, 123 °, 129 °, 135 °, or three degrees with 22. Large and Medium Scale Topographic maps with a value greater than or equal to 0.5 million in China use the Six-Degree Gaussian-kerluge projection, and the three-degree Gaussian-kerluge projection are mostly used for large-scale ing, for example, the urban construction coordinates usually use Gaussian-kerluge projection with a three-degree belt.

2.2 UTM projection Overview
UTM projection is called the general horizontal axis mocato projection. It is an equal-angle horizontal axis cut cylindrical projection. The Elliptical Cylinder cut the Earth at 80 degrees south latitude and 84 degrees north latitude, there is no deformation on the online cut of the two phases after projection, and the length of the central meridian is 0.9996. UTM projection was created for the global war. In 1948, the United States completed the computing of this general projection system. Similar to Gaussian-kerluge projection, the projection angle is not deformed. The central meridian line is a straight line and the axis of symmetry of the projection, the ratio factor of the central longitude line is 0.9996 to ensure there are two standard longitude lines about 330km away from the central longitude line. The UTM projection zoning method is similar to the Gaussian-gram projection method. It is a 6 degree deviation from the west to the east at intervals of 180 ° from the west longitude and divides the earth into 60 projection bands. UTM projection is often used for satellite image data in China.

2.3 similarities and differences between Gaussian-gram projection and UTM projection
Gaussian-kruger projection and UTM projection are both variants of the horizontal mocator projection, at present, some foreign software or the supporting software of imported foreign instruments often do not support Gaussian-gram projection, but support UTM projection. Therefore, UTM projection is often used as Gaussian-gram projection. From the perspective of projection ry, Gaussian-gram projection is an equivalent cross-section cylindrical projection. After projection, the central longitude line remains unchanged, that is, the proportional coefficient is 1; UTM projection is an equal-angular horizontal axis cut cylindrical projection. The cylindrical cut Earth is located at 80 degrees south latitude and 84 degrees north latitude. After the projection, the two cut lines are not deformed, and the central longitude line length ratio is
0.9996. According to the calculation results, the main difference between the two lies in the proportional factor. The proportional coefficient of the center longitude line of Gaussian-gram projection is 1, and the UTM projection is 0.9996, X [UTM] = 0.9996 * X [Gaussian] and y [UTM] = 0.9996 * Y [Gaussian] can be used for coordinate transformation between Gaussian-gram projection and UTM projection (note: for example, if the vertical axis of the coordinate is 500000 meters west, the Y value must be subtracted from the 500000 multiplied proportional factor plus 500000) during conversion ). From the perspective of the split-band method, the start point of the split-band is different from that of the two. Gaussian-gram projects start from the 0-degree meridian and start from the west to the east at intervals of 6 degrees, the central longitude of the 1st band is 3 °; the UTM projection is from the west longitude 180 °, and the longitude of the 1st band is-177 °, therefore, the 1st band of Gaussian-gram projection is the 31st band of UTM. In addition, the East pseudo offset of the two projections is 500 kilometers, the North pseudo offset of Gaussian-gram projection is zero, the northern pseudo offset of UTM projection is zero, and that of the southern hemisphere is 10000 kilometers.

2.4 Gaussian-gram projection and UTM projection Coordinate System
Gaussian-gram projection and UTM projection are independently projected by the binning method. Take the central longitude line (L0) Projection as the vertical axis X, the equator projection as the horizontal axis Y, and the intersection of the two axes is the coordinate origin of each belt. In order to avoid negative horizontal coordinates, the Gaussian-gram projection and UTM Northern Hemisphere projection require that the vertical axis be shifted 500 kilometers west as the starting axis, while the UTM Southern Hemisphere projection not only shifts the vertical axis 500 kilometers west, the horizontal axis is 10000 kilometers south. Since the coordinates of each projection belt of Gaussian-gram projection and UTM projection are relative values of the local coordinate point, the coordinates of each belt are exactly the same. In order to distinguish which region a coordinate system belongs, generally, a belt number is added before the x-axis coordinates, such as (4231898 M, 21655933 M). Among them, 21 is the belt number.

Ii. binning Method
1. China adopts 6-degree and 3-degree bands:
The topographic maps of and adopt a 6-degree band projection, that is, the longitude difference is 6 degrees, starting from the zero-degree meridian, and each longitude difference of 6 degrees from west to east is a projection band, the world is divided into 60 bands, with 1, 2, 3, 4, 5 ,...... Represents. That is, the eastern longitude 0 ~ The longitude of the center longitude is 3 degrees east longitude, And the longitude is 6 degrees east longitude ~ 12 degrees is the second band, and the longitude of the central longitude is 9 degrees.
The-10 thousand Topographic Map adopts a 3-degree band. It starts from the longitude line of the east longitude 1.5 degrees and ranges from 1 to 2, 3 ,...... It indicates that a total of 120 projection bands are divided around the world, that is, the longitude 1.5 ~ The longitude of the central longitude is 3 degrees, and the longitude of the longitude is 4.5 ~ The longitude of the central longitude is 6 degrees east longitude. our province is located in the east longitude 113 degrees-East Longitude 120 degrees, across 38th, 39, 40 a total of 3 belts, of which the east longitude 115.5 degrees to the west is 38th, its central longitude line is east longitude 114 degrees; eastern longitude 115.5 ~ 118.5 degrees for 39 belts, the central longitude line for the east longitude is 117 degrees; 118.5 degrees for the east longitude to the west of the mountain Customs is 40, and the central longitude line for the east longitude is 120 degrees. The first two digits of the Cross-kilometer network coordinate on a topographic map are belt numbers. For example, the cross-coordinate on a-50 thousand topographic map is 20345486, where 20 is the belt number, and 345486 is the X-coordinate value.
2. Calculation of the longitude of the local central longitude line

Calculate the longitude of the six-degree central longitude line: the longitude of the local central longitude line is 6 ° × the longitude of the local longitude line is-3 °. For example, the abscissa of the topographic map is 20345, the longitude of the central longitude of the six-degree belt is 6 ° × 20-3 ° = 117 ° (applicable to and topographic maps ); 6 ° * 49-180-3 ° = 111 ° (applicable to topographic maps below ).

Calculation of longitude of the Three-degree central longitude line: longitude of the central longitude line = 3 ° × Local longitude line number (applicable to topographic map ).

From: http://www.mapenjoy.com/blog/entry/id/ff8080811ea1452b011ef1dafac02a65.html