A method of oblique cylindrical equal-area projection suitable for strip engineering

Abstract

The application discloses a slant-axis spherical projection method suitable for a strip-shaped project, calculates the geocentric space rectangular coordinates of each control point of the strip-shaped project area; rotates the central meridian of the earth ellipsoid to obtain a slant-axis ellipsoid E1, so that the sum of the distances from each control point of the strip-shaped project area to the central meridian of the slant-axis ellipsoid E1 is the shortest; changes the slant-axis ellipsoid E1 into a slant-axis sphere E2, and the radius of the slant-axis sphere E2 is the distance from the average elevation of the whole strip-shaped project area to the coordinate origin; calculates the geodetic coordinates of each control point on the slant-axis sphere E2; and finally, performs Gauss projection based on the slant-axis sphere E2 to obtain the Gauss plane coordinates of each control point. The application makes the meridian direction of the strip-shaped project consistent with that of the slant-axis sphere by rotating the ellipsoid, and reduces the deformation caused by the Gauss projection process.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of engineering survey coordinate conversion, and particularly relates to a slant axis spheroid projection method suitable for strip-shaped engineering. BACKGROUND

[0002] The real earth is a closed and irregular ellipsoid, and when the ellipsoid is compressed from three-dimensional space to two-dimensional plane, the length, angle, area and other geometric elements will be compressed in some directions and stretched in other directions, and the original size will change, which is called projection deformation. The currently widely used Gauss-Kruger projection is a projection method that can keep the angle unchanged, but still accompanied by length and area deformation.

[0003] In engineering practice, the measurement data is based on the irregular earth surface, and the corresponding reference surface for calculation is the reference ellipsoid, which does not coincide with each other. Therefore, the obtained measurement data needs to be first normalized in height, and converted to the reference ellipsoid, which will affect the height; and then the Gauss projection is carried out, which will affect the plane coordinates. In summary, the length projection deformation mainly includes two factors of height normalization correction and Gauss projection process.

[0004] In view of the above two factors, the length projection deformation can be reduced by changing the height reference surface and moving the central meridian, and within a certain range, especially for the overall north-south trending engineering line, the projection deformation can be well controlled within the required range. However, when the line length is long or the east-west span is large, only through strip and adjacent strip conversion, the size of the projection deformation can be controlled, but it will cause calculation complexity and coordinate expression discontinuity.

[0005] In order to solve the deformation problem of Gauss transverse axis projection in strip-shaped engineering, a slant axis spheroid projection model meeting the engineering projection deformation requirement (25mm / km) is proposed. SUMMARY

[0006] The purpose of the present application is to solve the above problems existing in the prior art, and a slant axis spheroid projection method suitable for strip-shaped engineering is proposed, which changes the previous working mode of strip-shaped engineering, such as strip division, strip conversion and multiple coordinate transfer, which is easy to cause error out-of-limit, can reduce the engineering length projection deformation, and improve the coordinate precision.

[0007] The above purpose of the present application is realized by the following technical means:

[0008] A slant axis spheroid projection method suitable for strip-shaped engineering, comprising the following steps:

[0009] Step 1, after obtaining the geodetic coordinates of each control point of the strip-shaped engineering area based on the earth ellipsoid E0, the control points are converted into the rectangular coordinates in the geocentric coordinate system;

[0010] Step 2, the central meridian of the earth ellipsoid E0 is rotated while keeping the center of the earth ellipsoid E0 unchanged and the major axis in the equatorial plane, to obtain the oblique ellipsoid E1, so that the sum of the distances from each control point of the strip-shaped engineering area to the central meridian of the oblique ellipsoid E1 is the shortest, and the coordinates of each control point in the geocentric coordinate system of the oblique ellipsoid E1 are calculated;

[0011] Step 3, the oblique ellipsoid E1 is changed into the oblique sphere E2, the origins and coordinate axes of the oblique ellipsoid E1 and the oblique sphere E2 are the same, the radius of the oblique sphere E2 is the distance from the average elevation of the whole strip-shaped engineering area to the coordinate origin, the origins and coordinate axes of the oblique ellipsoid E1 and the oblique sphere E2 are unchanged, and the coordinates of each control point in the geocentric coordinate system of the oblique sphere E2 are the same as those in the geocentric coordinate system of the oblique ellipsoid E1;

[0012] Step 4, the coordinates of each control point in the geocentric coordinate system of the oblique sphere E2 are converted into the geodetic coordinates of the oblique sphere E2;

[0013] Step 5, finally, the Gauss projection is performed based on the oblique sphere E2, to obtain the Gauss plane coordinates of each control point.

[0014] Compared with the prior art, the present application has the following beneficial effects:

[0015] The present application rotates the ellipsoid to make the meridians of the strip-shaped engineering area consistent with those of the oblique sphere, thereby reducing the deformation caused by the Gauss projection process; for the change of the elevation reference surface, compared with the deformation ellipsoid obtained by adjusting the flattening, the present application simplifies the calculation amount and can also meet the accuracy requirement. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is the flow chart of the present application;

[0017] Figure 2 is the distribution diagram of each control point of the strip-shaped engineering area in Example 2;

[0018] Figure 3 is the longitude and latitude distribution diagram of the strip-shaped engineering area on the basic ellipsoid E0, the oblique ellipsoid E1 and the oblique sphere E2; wherein (a) is the longitude and latitude distribution diagram of the strip-shaped engineering area on the basic ellipsoid E0, (b) is the longitude and latitude distribution diagram of the strip-shaped engineering area on the oblique ellipsoid E1, and (c) is the longitude and latitude distribution diagram of the strip-shaped engineering area on the oblique sphere E2;

[0019] Figure 4 is the positive and negative calculation difference schematic diagram. DETAILED DESCRIPTION

[0020] In order to facilitate those skilled in the art to understand and implement the present application, the present application is further described in detail below in combination with examples, and it should be understood that the examples described herein are only used to illustrate and explain the present application, and are not used to limit the present application.

[0021] Example 1

[0022] The oblique-axis spherical projection method suitable for strip engineering provided by the present application is based on two processes of height normalization and Gauss projection, and comprehensively controls length projection deformation, overcomes the difficulty of establishing an independent coordinate system for strip engineering, and the projection result is more continuous and more intuitive in surface information expression.

[0023] As shown in Figure 1 An oblique-axis spherical projection method suitable for strip engineering includes the following steps:

[0024] Step 1, after obtaining the geodetic coordinates (B0, L0, H0) of each control point of the strip engineering area based on the earth ellipsoid E0, the control points are converted into the geocentric and fixed space rectangular coordinates (X0, Y0, Z0) ;

[0025] Step 2, keeping the center of the earth ellipsoid E0 unchanged and the long semi-axis on the equatorial plane, the central meridian of the earth ellipsoid E0 is rotated to obtain the oblique-axis ellipsoid E1, so that the sum of the distances of each control point of the strip engineering area to the central meridian of the oblique-axis ellipsoid E1 is the shortest, thereby making the central meridian of the oblique-axis ellipsoid E1 coincide with the overall trend of the strip engineering as much as possible, and the length deformation of the Gauss projection is well reduced, and the coordinates (X1, Y1, Z1) of each control point in the geocentric and fixed coordinate system of the oblique-axis ellipsoid E1 are calculated;

[0026] Step 3, the oblique-axis ellipsoid E1 is further changed into the oblique-axis sphere E2 that fits the actual strip engineering area, the origins and coordinate axes of the oblique-axis ellipsoid E1 and the oblique-axis sphere E2 are the same, the radius of the oblique-axis sphere E2 is the distance from the average elevation of the overall strip engineering area to the coordinate origin, so that the oblique-axis sphere E2 passes through the average elevation surface of the overall strip engineering, since the origins and coordinate axes of the oblique-axis ellipsoid E1 and the oblique-axis sphere E2 are unchanged, the coordinates (X2, Y2, Z2) of each control point in the geocentric and fixed coordinate system of the oblique-axis sphere E2 are the same as the coordinates (X1, Y1, Z1) in the geocentric and fixed coordinate system of the oblique-axis ellipsoid E1;

[0027] Step 4, the coordinates (X2, Y2, Z2) of each control point in the geocentric and fixed coordinate system of the oblique-axis sphere E2 are converted into the geodetic coordinates (B2, L2, H2) of the oblique-axis sphere E2;

[0028] Step 5: Finally, perform Gaussian projection based on the oblique axis sphere E2 to obtain the Gaussian plane coordinates (x, y) of each control point.

[0029] Example 2:

[0030] In this embodiment, the control points of the strip engineering area are distributed within a range of 82.60 km east-west and 56.48 km north-south, with a maximum elevation of 89.52 m and a minimum elevation of 73.33 m. Figure 2 As shown, Gaussian projection is performed using a spherical projection method suitable for strip engineering described in Example 1.

[0031] The minor axis b1 of the oblique ellipsoid E1 is calculated to be 6366546.8m. When traveling from the oblique ellipsoid E1 to the oblique sphere E2, the latitude B of the reference point S is... S =40.3°, geodetic height variation ΔH = 85.9m. The leftmost longitude difference of the strip engineering area on the oblique axis sphere E2 is 1′49.1″, and the distance to the central meridian is 2.6km; the rightmost longitude difference is 1′48.9″, and the distance to the central meridian is also 2.6km; the maximum geodetic height is 84.5m, and the minimum is -84.4m. The latitude and longitude distribution of the strip engineering area on the basic ellipsoid E0, oblique axis ellipsoid E1, and oblique axis sphere E2 is as follows: Figure 3 As shown.

[0032] Gaussian projection is performed based on the oblique sphere E2, and the difference between forward and inverse calculations are as follows: Figure 4 As shown.

[0033] The Gaussian plane coordinates of the oblique sphere E2 were calculated, and the forward and inverse calculations of the Gaussian coordinate projection were performed based on the oblique sphere E2. The results were then organized and analyzed into the projection side lengths and coordinates, as shown in Table 1 below.

[0034] Table 1 Length Deformation Analysis Table

[0035]

[0036] According to the table above, the overall length deformation meets the requirement that the projected deformation is less than 25 mm / km.

[0037] The maximum absolute value of the difference between the forward and inverse calculations of Gaussian coordinate projection is shown in Table 2 below:

[0038] Table 2. Maximum absolute value of the difference between forward and inverse calculations of Gaussian coordinate projection.

[0039] Analysis item Oblique axis sphere model Latitude / sec 4.58e-11 Longitude / sec 2.24e-14

[0040] According to the table above, the mutual difference between coordinate projections satisfies 10. -5″ The required precision.

[0041] The specific embodiments described herein are merely illustrative of the spirit of the application. Various modifications or changes in the specific embodiments described herein can occur to those skilled in the art to which the application pertains without departing from the spirit of the application, and it is understood that such modifications or changes are to be considered as within the scope of the application as defined by the appended claims.

Claims

1. A method for oblique spherical projection suitable for strip-shaped engineering projects, characterized in that, Includes the following steps: Step 1: After measuring the geodetic coordinates of each control point in the strip engineering area based on the Earth ellipsoid, convert each control point into geocentric rectangular coordinates. Step 2: Keeping the center of the Earth ellipsoid unchanged and the semi-major axis on the equatorial plane, rotate the central meridian of the Earth ellipsoid to obtain the oblique axis ellipsoid, so that the sum of the distances from each control point in the strip engineering area to the central meridian of the oblique axis ellipsoid is the shortest, and calculate the coordinates of each control point in the geocentric geofixed coordinate system of the oblique axis ellipsoid. Step 3: Transform the oblique axis ellipsoid into an oblique axis sphere. The origin and coordinate axes of the oblique axis ellipsoid and the oblique axis sphere have the same direction. The radius of the oblique axis sphere is the distance from the average elevation of the entire strip engineering area to the origin of the coordinate system. The origin and coordinate axes of the oblique axis ellipsoid and the oblique axis sphere remain unchanged. The coordinates of each control point in the geocentric geofixed coordinate system of the oblique axis sphere are the same as the coordinates in the geocentric geofixed coordinate system of the oblique axis ellipsoid. Step 4: Convert the coordinates of each control point in the geocentric coordinate system of the oblique axis sphere to geodetic coordinates of the oblique axis sphere; Step 5: Perform Gaussian projection based on the oblique axis sphere to obtain the Gaussian plane coordinates of each control point.

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