3 ° and 6 ° Gaussian-gram projection

The purpose of projection selection is to make the properties and features of the selected projection suitable for the purpose of the map, while considering that the map has a small deformation within the graphic range and the deformation distribution is even. GEO charts used in sea areas usually adopt angle-preserving projection, because they can maintain correct azimuth angles.

Basic Scale Topographic Map of China. gaussian-kruger projection (Gauss-Kruger) is used for values greater than or equal to 50 thousand of 0.5 million ), this is an equal-angle cross-section elliptical projection, also known as Transverse Mercator. A topographic map smaller than 0.5 million uses an equal-angle positive axis Cut Cone projection, also known as Lambert conformal conic ); topographic Maps smaller than 0.5 million on the sea are usually projected using an equal-angular cylindrical projection, also known as Mercator ). Generally, the map projection system should be consistent with the basic scale topographic map series in China.
The map coordinate system is determined by the and map projection. The is an approximation of the earth surface in a specific region using a specific elliptical body. Therefore, each country or region has its own, we usually refer to the Beijing 54 coordinate system and the Xi'an 80 coordinate system as China's two Earth baselines. China has established China's Beijing 54 coordinate system with reference to the former Soviet Union's use of the clarsovsky elliptical body since 1953, in 1978, the IAG 75 Earth elliptical body recommended by the International Survey Institute was used to establish China's New Earth coordinate system-Xi'an 80 coordinate system. Currently, the GPS positioning results all belong to the WGS84 coordinate system, the WGS84 datum plane uses the WGS84 elliptical body. It is a coordinate system that uses the earth as the center of the elliptical body. Therefore, their longitude and latitude coordinates are different for different Earth datum planes in the same geographic location.
The following three elliptical parameters are used (derived from the GPS measurement specification GB/T 18314-2001 "):

Elliptical body	Long Half Axis	Short Half Axis
*	6378245	6356863.0188
IAG 75	6378140	6356755.2882
WGS 84	6378137	6356752.3142

There is a one-to-many relationship between the elliptical and, that is, the Al is built on the basis of the elliptical, but the elliptical cannot represent the Al, the same elliptical physical fitness defines different baselines. For example, the former Soviet Pulkovo 1942 and Afgooye baselines of Somalia in Africa all adopt the Krasovsky elliptical bodies. However, their geobaselines are obviously different. In the current commercial GIS software, the is defined through the conversion 7 parameter of the local benchmark for WGS84, that is, the three translation parameters, Delta X, Delta Y, and Delta Z, represent the translation values of the two coordinate origins; the three rotation parameters ε x, ε y, and ε z indicate the rotation angles around Xt, Yt, and Zt when the local coordinate system is rotated in parallel with the central coordinate system. Finally, the proportional correction factor is used, used to adjust the elliptical size. The conversion parameters of beijing 54 and Xi'an 80 relative to WGS84 have not yet been made public. In actual work, you can use the known BEIJING 54 or Xi'an 80 coordinate control points in the work area to convert the coordinates of WGS84, when there is only one known Control Point (this is often the case), the difference between the coordinates of Beijing 54 and WGS84 of known points is used as the translation parameter. When the work area is not large, such as Qingdao, precision is enough.

Taking the Gaussian-gram projection result of (32 °, 121 °) as an example, the projection results of beijing 54 and WGS84 are about 63 meters in the North-South direction (see the table below ), this error is insignificant for dozens or millions of maps, but it should be considered in engineering maps.

	Input coordinate (degree)	BEIJING 54 Gaussian projection (meters)	WGS84 Gaussian projection (meters)
Latitude value (X)	32	3543664	3543601
Longitude value (y)	121	21310994	21310997

Gaussian-kerluge projection

(1) Gaussian-kerluge projection Properties

Gaussian-Kruger (Gauss-Kruger) projection is short for "Gaussian projection", also known as "cross-section elliptical projection", a type of projective between the Earth's elliptical sphere and the plane. German mathematician, physicist, astronomy Gauss (Carl FriedrichGauss, 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. According to the projection condition that the central meridian projection is a straight line with the same length and the equator projection is a straight line, the form of the function is determined, and a Gaussian lüge projection formula is obtained. After projection, except that the central meridian and the equator are straight lines, the other meridian curves are symmetric in the central Meridian. Imagine a central meridian that uses an Elliptical Cylinder to cross the elliptical sphere and projection the positive shape of the elliptical sphere within a certain deviation range on both sides of the central meridian to the Elliptical Cylinder according to the projection conditions above. The Elliptical Cylinder is flattened by cutting the bus along the North and South Poles, that is, the Gaussian projection plane. Take the projection of the central meridian and the cross point of the Equator as the origin, the projection of the central meridian is the X-axis of the ordinate axis, and the projection of the equator is the y-axis of the horizontal coordinate, which constitutes the Cartesian coordinate system of the Gaussian Keru plane.

Gaussian-gram projection has little deformation in length and area, and the central meridian line does not have deformation. The center meridian line is directed to the edge of the projection band, and the deformation increases gradually. The maximum deformation is at the two ends of the 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, it can be used in large-scale topographic maps to meet various military needs and perform precise measurement and calculation on the charts.

(2) Gaussian-kerluge projection band

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 six-degree belt starts from the zero-degree meridian and goes from the west to the east at intervals of 6 degrees. The belt numbers are sequential 1st, 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. The six-degree belt can be used for small and medium scale (such as) ing, and the three-degree belt can be used for large-scale (such as) ing. The urban construction coordinates usually use the Gaussian projection of the Three-degree belt.

(3) Gaussian-gram projection Coordinate

Gaussian-gram projection is based on the split-band method, so the coordinates of each belt are independent systems. The central longitude line projection is used as the vertical axis (x), the equator projection is the horizontal axis (Y), and the intersection of the two axes is the coordinate origin of each belt. The ordinate coordinates start from zero in the equator. The north of the equator is positive, and the south is negative. China is located in the northern hemisphere, and the ordinate values are positive. If the X axis starts from zero in the central longitude line, the East of the central longitude line is positive, the West is negative, and the X axis is negative. Therefore, it is inconvenient to use it. Therefore, it is required that the X axis be shifted to the West by 500 kilometers as the start axis, the X-axis value of the inband is 500 kilometers. Since the coordinates of each projection belt in Gaussian-gram projection are relative values of the local coordinate origin, the coordinates of each belt are identical. In order to distinguish which region a coordinate system belongs, add a belt sign before the x-axis coordinate, for example, (4231898 M, 21655933 M). Among them, 21 is the belt number.

(4) Gaussian-gram projection and UTM projection

Some foreign software, such as ARC/INFO or supporting software of foreign instruments, such as multi-beam data processing software, often does not support Gaussian-gram projection, but supports UTM projection, therefore, the UTM projection coordinates are often submitted as Gaussian-gram projection coordinates.

UTM projection is called the general horizontal axis mocato projection. It is an equi-angular horizontal axis cut cylindrical projection (Gaussian-gram is an equi-angular horizontal axis cut cylindrical projection ), the cylindrical cut Earth is located in two high circles at 80 degrees south latitude and 84 degrees north latitude. The projection divides the earth into 60 projection bands with a longitude difference of 6 degrees, it has been used by many countries as the mathematical basis of topographic maps. The main difference between UTM projection and Gaussian projection is the proportional coefficient of the north-south GRID network cable. The length remains unchanged after the central meridian projection of Gaussian-kerluge projection, that is, the proportional coefficient is 1, UTM projection has a proportional coefficient of 0.9996. UTM projection shows a constant proportional coefficient of each North-South GRID network cable. It is a variable in the east-west direction. The proportional coefficient of the center GRID network cable is 0.9996, on the edge of the widest part of the north-south vertical line, the distance from the center is about 363 kilometers, and the proportional coefficient is 1.00158.

Gaussian-gram projection and UTM projection are similar to Xutm = 0.9996 * X Gaussian, and Yutm = 0.9996 * Y Gaussian for coordinate transformation. The following is an example (the datum is WGS84 ):

	Input coordinate (degree)	Gaussian projection (meters)	UTM projection (meter)	Xutm = 0.9996 * x Gaussian, Yutm = 0.9996 * Y Gaussian
Latitude value (X)	32	3543600.9	3542183.5	3543600.9*0.9996 ≈ 3542183.5
Longitude value (y)	121	21310996.8	311072.4	(310996.8-500000) * 0.9996 + 500000 ≈ 311072.4

Note: The coordinate point (32,121) is located in the 21 band of Gaussian projection, and the first two "21" in the Y value of Gaussian projection is the coordinate point (21310996.8) is located in the 51 band of UTM projection, in the preceding table, the Y value of the UTM projection does not contain a comma. Because the vertical axis of the coordinates is 500000 meters west, the Y value must be subtracted from the 500000 multiplied proportional factor and then added to 500000.

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5. Single Point conversion

The Single Point conversion procedure is as follows:

(1) Select whether it is Gaussian positive conversion or inverse conversion. The default value is latitude and longitude conversion to Gaussian projection coordinate, and the projection coordinate unit is meter.

(2) Select the. The default value is Beijing 54. If the GPS positioning data is used, do not forget to switch to WGS84.

(3) Select the split band, which is 3 degrees or 6 degrees. The default value is 6 degrees.

(4) enter the central longitude, with 20 (114 ° E ~ 120 ° E) The central longitude is 117 degrees, and the 21 band (120 ° E ~ 126 ° E) The central longitude is 123 degrees.

(5) For forward projection, select the input data format of longitude and latitude. The default format is decimal. The input method is as follows:

Lattice	Original latitude value	Original longitude value	Input latitude value	Input longitude value
Decimal	35.445901 °	122.997344 °	35.445901	122.997344
Level score	35 ° 26. 7541 ′	122 ° 59. 8406 ′	3526.7541	12259.8406
Minute/second	35 ° 26' 45.245 ″	122 ° 59' 50.438 ″	352645.245	1225950.438

(6) Input latitude and longitude values in the "input" column in the selected format for positive projection, and X and Y coordinate values in meters for Inverse Projection.

(7) Click "Single Point conversion.

(8) view the calculation result in the "output" column.

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6. batch conversion

The batch conversion procedure is as follows:

(1) Prepare the input data file to be converted, which must be a text file, which is divided into two columns: the latitude value or vertical coordinate value in the first column, and the longitude value or horizontal coordinate value in the second column, separate Two columns with spaces. For forward projection, there are three options for the latitude value and longitude value format (see table). The default value is decimal. For reverse projection, the vertical and horizontal coordinate values must be in meters.

The following example shows the 6 ° input data file testdata.txt with positive projection in the second-level format (WGS84 ).

352645.245 1225950.438
353800.402 1230000.378
351600.519 1225959.506
345800.101 1225959.8
343600.336 1230000.26
341400.018 1225959.897
335159.17 1225959.46
333000.08 1230000.28

(2) Select whether it is Gaussian positive conversion or inverse conversion. The default value is latitude and longitude conversion to Gaussian projection coordinate, and the projection coordinate unit is meter.

(3) Select the. The default value is Beijing 54. If the GPS positioning data is used, do not forget to switch to WGS84.

(4) Select the split band, which is 3 degrees or 6 degrees. The default value is 6 degrees.

(5) enter the central longitude, with 20 (114 ° E ~ 120 ° E) The central longitude is 117 degrees, and the 21 band (120 ° E ~ 126 ° E) The central longitude is 123 degrees.

(6) For forward projection, select the format of latitude and longitude input data in the input data file. There are three options. The default format is decimal.

(7) Click "batch conversion. The open file dialog box is displayed. Enter your data file name.

(8) enter the name of the Conversion Result file and click "save". The program starts computing.

(9) Open the output file and view the calculation result. The result is divided into five columns: the first sequence number, the second column, the latitude value or vertical coordinate value, and the third column, the longitude value or horizontal coordinate value, the latitude value or vertical coordinate value after the fourth column conversion, and the longitude value or horizontal coordinate value after the Fifth Column conversion.

In the following example, the data file result.txt is a 6 ° data file with positive projection Conversion Result (WGS84 ).

1 352645.245 1225950.438 3924063.3 21499758.9
2 353800.402 1230000.378 3944871.4 21500009.5
3 351600.519 1225959.506 3904193.8 21499987.5
4 345800.101 1225959.8 3870898.1 21499994.9
5 343600.336 1230000.26 3830228.5 21500006.6
6 341400.018 1225959.897 3789544.4 21499997.4
7 335159.17 1225959.46 3748846.4 21499986.1
8 333000.08 1230000.28 3708205 21500007.2