Langbo projection

xiaoxiao2021-03-06  78

The purpose of choosing projections is to make the nature of the selected projection, and is suitable for the map of the map, while considering that the map is small in the layout range and is uniformly distributed. The map used in the sea is multi-use manifold, because it can maintain the correct position of the azimuth.

China's basic scale topographic map (1: 5,000, 1: 10,000, 1: 25,000, 1: 50,000, 1: 10,000, 1: 250,000, 1: 500,000, 1: 1 million), greater than Equal to 500,000, Gauss-Kruger, is a striped cross-cut elliptical projection, also called transverse mercator; less than 500,000 topographic maps are used, etc. The angle positive axial macating garden cone projection, is a lambert conformal conic; a topographic map of less than 500,000 is multi-use and other angular positive axis cylindrical projection, and the Mercator is called. A map projection system consistent with my country's basic proportional topographic map series should generally be used. Selection of the geodetic side

The map coordinate system is determined by the geodetic side and map projection, and the geodetic side is approximated using a particular ellipsoid on a particular region of Earth surface, so each country or region has its own geodetic side, and we usually call the Beijing 54 coordinate system. The Xi'an 80 coordinate system actually refers to the two geodes of my country. In the first Soviet Union, my country has established my country's Beijing 54 coordinate system from 1953. In 1978, I use the IAG 75 Ellipsoid recommended by the International Earth Measurement Association. - Xi'an 80 coordinate system, the result of the current GPS positioning belongs to the WGS84 coordinate system, the WGS84 reference surface adopts WGS84 ellipsoid, which is a coordinate system in the center of the ellipsoid. Therefore, there is a difference in the coordinates of their latitude and longitude relative to the same geographic location.

The three ellipsoid parameters used in this program are as follows (derived from "Global Positioning System Measurement Specification GB / T 18314-2001"):

Ellipsoid

Half-axis

Short half shaft

Krassovsky

6378245

6356863.0188

IAG 75

6378140

6356755.2882

WGS 84

6378137

6356752.3142

The relationship between the ellipsoid and the geodetic side is a pair of relationships, that is, the reference surface is based on the ellipsoid, but the ellipsoid cannot represent the reference surface, the same ellipsoid can define different reference faces, such as Former Pulkovo 1942 of the Soviet Union, the Afgoye reference papers in Africa Somalia have adopted Krassovsky ellipsoid, but their land reference faces are obviously different. In the current GIS commercial software, the geodial reference faces are defined by the conversion of the local reference face to the WGS84, that is, three translation parameters Δx, ΔY, Δz represent the translation value of the two situats; three rotation parameters εx, εy, εz indicates that the local coordinate system is rotated in parallel to the central coordinate system, respectively, respectively, respectively, respectively, respectively, respectively, respectively, the proportional correction factor, for adjusting the ellipsoid size. Beijing 54, Xi'an 80 relative to the conversion parameters of WGS84 have not been open, and the actual work can be used in Beijing 54 or Xi'an 80 coordinate control points to carry out the conversion of WGS84 coordinate values ​​in the work area. Only one known control point is Under (ever), the difference between Beijing 54 and WGS84 coordinates is used as a translation parameter, when the work area is not large, such as Qingdao, the accuracy is also enough. Take (32 °, 121 °) 25 °, 40 ° double standard latitude, origin length of 110 °, the origin of the Lanbuto projection results of 10 °, the original point of 10 °, Beijing 54 and WGS84 reference face, the projection results in the east and west direction The gap is about 18 meters, and the north-south direction is about 45 meters (see table below), for dozens or millions of maps, this error is not enough, but in the engineering map, it should be considered. Enter coordinate (degree)

Beijing 54 Lanbuto Projection (Mi)

WGS84 Loble Projection (Mi)

Latitude value (x)

32

2531235

2531190

Sleek value (Y)

121

1028805

1028787

Return to the Lanbuto projection (1) Lambo projection nature, Lamberto projected, namely "Israeli is cutting the cone projection", is prepared in 1772 by German mathematician Lanbud (J.LAMBERT). It is envisaged with a positive conical cut or cut in the spherical surface, and the equipped condition is applied to the conical surface, and then the bus is unfolded, that is, the Lanbuto projection plane. The projection rear weft is a concentric circular arc, and the wire is a circular radius.  Lanbuto projection is divided into two standard weft, which is related to the use of single standard weft, and the projection deformation is small, and the deformation distribution of the Lanbuto projection is:

a) The angle is not deformed, that is, the differential area of ​​the corresponding differential area before and after the projection is similar, so it can be referred to as a dominant projection; b), the same latitude, that is, the same weft is equal;

c) There are no deformation on both standard weft;

d) On the same endless line, the outer side of the two standard weft is positive deformation (length ratio greater than 1), and the two standard weft is negatively deformed (length ratio is less than 1). Therefore, the deformation is relatively uniform, and the absolute value of the deformation is also small;

e) The length of the line segment of the same latitude is equal, and the length of the latitude between the two weft is equal. my country 1: 1 million maps use the Lanbundi projection, which is consistent with the main map of the international geographic society. The latitude is divided into 15 projection bands from the south to north. Each projection belt calculates coordinates alone. Each of the two standard weft, the first standard weft is the three-end latitude plus 30 'weft, The second standard weft is the weft latitude minus 30 'from the northern end latitude, which is exactly the same as the coordinate results of each figure in the same projection belt, and the differential variation values ​​of different belts are close to equal, so each projection belt only calculates one of them. The projection results of the graph (4 °, 6 °). Since the latitude is 4 ° strip projection, when the map is spliced ​​in the direction of the weft, no fracture is generated, but when the line is spliced, the splicing line is not in the same. Different curvatures after projection, causing fissure when stitching

.

(2) The Lanbuto projection coordinates use the original line of the figure (generally the central warpline) as a coordinate X-axis, the intersection of the original line and the origin weft (generally the southernmost weft) as the origin, the tangent of this point The coordinate Y axis constitutes a linear coordinate system of the Lanbuto Plane, which has no deformation in two standard weft. In my country 1: 1 million Bambo projection topographic map, since the latitude and weft network graphics are symmetrical with the central warp the axis (the original line selection of the chassis of the chassis, the original surface latitude is selected). Therefore, as long as the right side is calculated from 1 °, 2 °, 3 °, the coordinates of the latitude and latitude intersection of the left side, only the Y value is negative. The right angle coordinate result of a picture can be common in the same latitude belt. Single point conversion single point conversion steps are as follows: (1) Select whether it is Rambo positive conversion or reverse transformation, default is the latitude and longitude to the Lanbuto projection coordinates, the projection coordinate unit is rice. (2) Select the geodetic side, default Beijing 54, if it is GPS positioning data, don't forget to switch to WGS84. (3) Enter the first standard latitude and second standard latitude, unit degree. (4) Enter the latitude latitude and origin of origin, unit degree, default to zero. (5) If a forward projection, select the latitude and longitude input data format, there are three options, default to decurity format. The specific input method is as follows:

Format

Original latitude value

Original longitude value

Input latitude value

Enter longitude value

Decimal system

35.445901 °

122.997344 °

35.445901

122.997344

Degree

35 ° 26.7541 '

122 ° 59.8406 '

3526.7541

12259.8406

Degree

35 ° 26'45.245 "

122 ° 59'50.438 "

352645.245

1225950.438

(6) Positive projection According to the selected format, enter the latitude and longitude value in the "input" field, and the anti-projection input is based on the x, y coordinate value of the meter unit. (7) Click the Single Conversion button. (8) View the calculation result in the "Output" column. The batch conversion batch conversion steps are as follows: (1) Prepare the input data files that need to be converted, require the text file, divided into two columns, the first column latitude value or longitudinal coordinate value, the second column metric value or the lateral coordinate value, two columns Between separation between spaces. When projected, the latitude value and the longitude value format may have three options (see table), the default is treated as a decimal system; when reverse projection, the longitudinal and lateral coordinate values ​​must be in meters. Below is an example of, hour (the WGS84) orthogonal projection of the input data file Lambert testdata.txt 350000.000 1220000.000 351600.519 1225959.506 345800.101 1225959.8 343600.336 1230000.26 341400.018 1225959.897 335159.17 1225959.46 333000.08 1230000.28 332300.674 1232000.103 (2) selecting a conversion or positive anti-Lambert Conversion, default is the latitude and longitude to the Lanbuto projection coordinates, and the projection coordinate unit is rice. (3) Select the geodetic side, default Beijing 54, if it is GPS positioning data, don't forget to switch to WGS84. (4) Enter the first standard latitude and second standard latitude, unit degree. (5) Enter the latitude of origin and origin of origin, unit degree, default to zero. (6) If positive projection, select the latitude and longitude input data format in the input data file, there are three options to default to the decimal format. (7) Click the "Batch Conversion" button. The Open File dialog box will enter your data file name. (8) Enter the conversion result file name, click "Save", the program starts to calculate. (9) Open the output file to view the calculation result, the result is divided into five columns, the first sequence number, the second column input latitude value or the longitudinal coordinate value, the third column input longitude value or the lateral coordinate value, the fourth column conversion latitude value or portrait Coordinate values, fifth columns are converted to the manid value or the lateral coordinate value.

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