CN107729292B - Large ground wire interpolation method based on azimuth arch height tolerance constraint of mercator projection - Google Patents

Large ground wire interpolation method based on azimuth arch height tolerance constraint of mercator projection Download PDF

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CN107729292B
CN107729292B CN201711136554.4A CN201711136554A CN107729292B CN 107729292 B CN107729292 B CN 107729292B CN 201711136554 A CN201711136554 A CN 201711136554A CN 107729292 B CN107729292 B CN 107729292B
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彭认灿
董箭
周唯
张志衡
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PLA Dalian Naval Academy
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Abstract

A big ground wire interpolation method based on azimuth arch height tolerance constraint of mercator projection comprises the following steps: reading longitude and latitude coordinates of a starting point and an ending point of the geodesic; setting arch height limit difference of the large ground wire; calculating a geodesic initial azimuth angle and a homodesic initial azimuth angle between a current point and a geodesic terminal point by using a geodesic subject inverse solution and a homodesic line inverse solution method in geodesy; calculating an included angle between the initial azimuth angle of the geodesic line and the initial azimuth angle of the homotaxic line, and dividing the arch height limit difference of the geodesic line by the sine value of the included angle to serve as the interpolation distance of the next interpolation point; calculating the longitude and latitude coordinates of the next interpolation point by using the calculated interpolation distance, the longitude and latitude coordinates of the current point position and the initial azimuth angle of the geodesic line by using a geodetic subject forward solution method in geodetic survey; and repeating the steps until the point location interpolation is finished. The invention realizes the precise plotting of the large ground wire with any length under the condition of a specified precision threshold value by the self-adaptive adjustment and matching of the plotting precision and the interpolation distance of the large ground wire.

Description

Large ground wire interpolation method based on azimuth arch height tolerance constraint of mercator projection
Technical Field
The invention relates to the technical field of ocean mapping.
Background
From geodetic knowledge, two points on any given earth ellipsoid must have only one geodesic. By utilizing the characteristic, accurate expression of various 'straight lines' such as a straight sea leading base line and the like can be realized on a given earth ellipsoid, so that the various 'straight lines' are considered as geodesic lines in the sea demarcation and are accepted by more and more sea countries. As shown in fig. 1-3, since most of the geodesies usually show quite complex curves on various projection planes and it is not easy to realize their representation on the sea-chart plane in a strict mathematical model, it is necessary to try to realize their accurate plotting.
In order to solve the above problems, geodess at home and abroad have intensively and exhaustively studied and have proposed respective solutions. The currently commonly used interpolation method of "replacing curved lines with straight lines" is adopted when drawing any curve, as shown in fig. 4, the key step is to obtain the maximum interpolation distance, and the solution of the parameter can be obtained according to the length of the earth ellipsoid corresponding to the geodesic line replaced by a straight line (broken line segment) determined by the curvature of the earth. However, the change of the earth curvature at each position of the geodesic line is not uniform, the difference of the earth curvature at each position of the long-distance geodesic line is large, the obtaining of the maximum interpolation distance involves more resolving of the differential equation of the geodesic line, and the method is relatively complex and is not easy to implement. In addition, although the method can ensure that any small segment of straight line (broken line segment) approaches the absolute accuracy of the large ground wire, the method does not discuss the overall accumulated error of the large ground wire exhibition, and cannot realize the accurate exhibition of the large ground wire under the condition of any accuracy threshold.
The most important point of the accurate plotting of the large ground wire is to construct a large ground wire interpolation model with strictly controllable accuracy threshold value and realize the adaptive adjustment and matching of the large ground wire plotting accuracy and the interpolation distance. As shown in FIG. 4, P (B)1,L1)、Q(B2,L2) Representing any two points on the ellipsoid of the earth; w represents a geodesic line formed by P, Q on the earth ellipsoid; w' represents a polygonal line formed by connecting P, Q and the interpolation point; h represents the maximum distance from any point on the geodesic line w to the straight line w', which is called the geodesic arch height. The arch height h of the geodesic line is positively correlated with the length S (w) of the geodesic line under the influence of the oblateness f of the earth and the curvature of the earth at P, Q.
Ideally, when h → 0, the geodesic line w coincides with the polyline w'. Therefore, for the accurate plotting of the large ground wire, the precision threshold value (the arch height difference h of the large ground wire w) for the plotting of the large ground wire can be presetΩ) Calculating an arbitrary interpolation point Ti(i∈[0,n+1]) (n represents the number of interpolation points on the large ground line w, n is 0,1, 2.) (T)0＝P，Tn+1Q), Q interval large earth wire initial azimuth angle AiAnd the initial azimuth angle a of the constant direction lineiAngle of (theta)i＝|Ai-aiAnd interpolated distance
Figure BDA0001470563640000011
Initial azimuth angle Ai、TiOf dotsLatitude and longitude coordinates
Figure BDA0001470563640000021
Calculating the tail end T of the next small segment of the earth wire under the known conditioni+1Longitude and latitude coordinates of
Figure BDA0001470563640000022
Until the point location interpolation is finished.
In long-term practice, the accurate plotting of the large ground wire mainly depends on the calculation of the maximum interpolation distance of the large ground wire and the local accuracy evaluation that a small segment of straight line (broken line segment) approaches the large ground wire, and no published literature data can quantitatively evaluate the overall accuracy index of the plotting of the large ground wire and realize the encrypted interpolation of the large ground wire with strictly controllable accuracy threshold.
Disclosure of Invention
In order to overcome the problems of the traditional qualitative analysis method, the invention provides a geodesic interpolation algorithm based on azimuth arch height difference constraint of mercator projection.
The technical scheme adopted by the invention for realizing the purpose is as follows: a big ground wire interpolation method based on azimuth arch height tolerance constraint of mercator projection comprises the following steps:
a. inputting longitude and latitude coordinates (B) of a geodesic starting point P1,L1) And latitude and longitude coordinates (B) of the end point Q2,L2)；
b. Determining the arch height difference h of the large ground wire w of the starting point P and the end point Q of the large ground wireΩ；
c. According to longitude and latitude coordinates (B) of a starting point P and an end point Q of the geodesic line1,L1) And (B)2,L2) Calculating the initial azimuth angle A of the geodesic line between the starting point P and the end point Q of the geodesic line0And the starting azimuth angle a of the constant direction line0；
d. Calculating the initial azimuth angle A of the geodesic line between the starting point P and the end point Q of the geodesic line0And the initial azimuth angle a of the constant direction line0Angle of (theta)0＝|A0-a0I, interpolation distance
Figure BDA0001470563640000023
Initial azimuth angle A0Longitude and latitude coordinates of point P of origin of geodesic line (B)1,L1) Calculating the terminal T of the small segment of the earth wire under the known condition1Longitude and latitude coordinates of
Figure BDA0001470563640000024
e. According to T1Longitude and latitude coordinates of Q
Figure BDA0001470563640000025
And (B)2,L2) Calculating T1Q-interval large earth wire initial azimuth angle A1And the starting azimuth angle a of the constant direction line1；
f. Calculating T1Q-interval large earth wire initial azimuth angle A1And the initial azimuth angle a of the constant direction line1Angle of (theta)1＝|A1-a1I, interpolation distance
Figure BDA0001470563640000026
Initial azimuth angle A1、T1Longitude and latitude coordinates of points
Figure BDA0001470563640000027
Calculating the terminal T of the small segment of the earth wire under the known condition2Longitude and latitude coordinates of
Figure BDA0001470563640000028
g. And so on, each time according to the last obtained small segment earth wire terminal TiLongitude and latitude coordinates of Q
Figure BDA0001470563640000029
(B2,L2) Calculating TiQ-interval large earth wire initial azimuth angle AiAnd the initial azimuth angle a of the constant direction lineiAngle of (theta)i＝|Ai-aiL, |; by interpolation distance
Figure BDA0001470563640000031
Initial azimuth angle Ai、TiLongitude and latitude coordinates of points
Figure BDA0001470563640000032
Calculating the tail end T of the next small segment of the earth wire under the known conditioni+1Longitude and latitude coordinates of
Figure BDA0001470563640000037
Until the point location interpolation is finished.
In the step b, for the situation that the big ground wire is stretched to the paper chart, the arch height difference h of the big ground wire wΩAdopting the minimum resolution distance d on the paper chartchartCorresponding field distance DchartThe chart scale denominator is l, and the calculation method comprises the following steps: dchart＝ldchart/100。
In said step c, the latitude and longitude coordinates (B) of P, Q are known1,L1) And (B)2,L2) Calculating the initial azimuth angle A of the geodesic line between the starting point P and the end point Q of the geodesic line0And the starting azimuth angle a of the constant direction line0Initial azimuth angle A0Obtained by a geodetic topic inverse solution method, which comprises the following steps:
solving the following equation set:
Figure BDA0001470563640000033
in the formula: s (w) represents the length of the geodesic line; a'0Representing the big ground line negative azimuth angle;
initial azimuth angle a of constant direction line0The method is obtained by a reverse solution method of the constant direction line, and comprises the following steps:
solving the following equation set:
Figure BDA0001470563640000034
in the formula: s (w) represents a length of a constant direction line; a'0Indicating the homodyne counter-azimuth.
In said step d, by geodeticsThe method for positively solving the geodetic theme calculates the tail end T of the small segment of the geodetic wire1Longitude and latitude coordinates of
Figure BDA0001470563640000035
The method comprises the following steps: knowing the latitude and longitude coordinates of P (B)1,L1) The length of the large ground line S (w) and its initial azimuth angle A0Calculating the geodetic longitude and latitude coordinates (B) of the geodetic terminal point Q2,L2) By geodetic topic forward solution methods in geodetics, i.e. solving a system of equations:
Figure BDA0001470563640000036
in the step e, T is calculated by using an inverse solution and a constant line inverse solution method of the geodetic subject in the geodety1Q-interval large earth wire initial azimuth angle A1And the starting azimuth angle a of the constant direction line1；
In the step f, the earth theme forward solution method in the geodety science is utilized to calculate the tail end T of the small segment of the earth wire2Longitude and latitude coordinates of
Figure BDA0001470563640000041
The big ground wire interpolation method based on the azimuth arch height tolerance constraint of the mercator projection realizes the precise plotting of the big ground wires with any length under the condition of a specified precision threshold value through the self-adaptive adjustment and matching of the plotting precision and the interpolation distance of the big ground wires.
Drawings
Fig. 1 is a representation of the present geodesic on the mercator projection plane.
Fig. 2 is a representation of the present geodesic on the mercator projection plane.
Fig. 3 is a representation of the present geodesic on the mercator projection plane.
Fig. 4 is a schematic diagram showing the concept of "straight instead of curved" of the geodesic in the background art of the present invention.
FIG. 5 is a schematic diagram of a geodesic interpolation algorithm based on the orientation angle vault height difference constraint of mercator projection in the background art of the present invention.
FIG. 6 is a main flow chart of the geodesic interpolation algorithm based on the orientation angle vault height difference constraint of the mercator projection of the present invention.
FIG. 7 is a schematic diagram of an unconstrained equi-spaced geodesic (bisection) interpolation algorithm in an exemplary analysis of the present invention.
Detailed Description
The invention relates to a big ground wire interpolation algorithm based on azimuth arch height tolerance constraint of mercator projection, which adopts a computer to realize the precise plotting of a big ground wire and adopts the method to realize the self-adaptive adjustment and matching of the plotting precision and the interpolation distance of the big ground wire. The starting point and the end point of the geodesic line w are respectively assumed to be a point P and a point Q; p, Q and interpolation point Ti(i∈[1,n]) (n represents the number of interpolation points on the geodesic line w, and n is 0,1, 2.) a broken line formed by connecting is represented by w'; n is initially 0 and represents the geodesic w without interpolation.
For interpolation distance in the present invention
Figure BDA0001470563640000042
Interpolation processing is carried out on the large ground wire w to ensure adjacent interpolation points Ti、Ti+1Arch height h of inter-large ground wireiNot greater than w arch height limit difference h of large ground wireΩAs shown in fig. 5, the following was demonstrated:
insert point T1For example, calculate T0Initial azimuth angle A of large earth wire between (P) and Q0And the initial azimuth angle a of the constant direction line0Angle of (theta)0＝|A0-a0|；
② at right angle delta PT'1H'1Of medium, T'1H'1The length of the arc is equal to the w arch height limit difference h of the large ground wireΩFrom PT'1Length of (2)
Figure BDA0001470563640000043
As an interpolation point T1Is interpolated by an interpolation distance Δ S0
Figure BDA0001470563640000051
And by an interpolation distance deltaS0Initial azimuth angle A0Longitude and latitude coordinates of point P (B)1,L1) Calculating the terminal T of the small segment of the earth wire under the known condition1Longitude and latitude coordinates of
Figure BDA0001470563640000052
For T0(P)、T1The arch height h of the large ground wire of the connected small sections of large ground wires0Is a broken line PT1The maximum distance to the small section of the great earth wire, and the maximum arch height of the great earth wire does not exceed a right angle delta PT1H1Middle T1H1Length (h) of0(max)) I.e. h0(max)≥h0；
Fourthly, right angle delta PT1H1Middle, PT1Length of (2) and PT'1Are equal in length (are all interpolation distances Δ S0) And T is1H1Length (h) of0(max)) And PT1Length (Δ S) of0) There is a sine function relationship between them, i.e.
Figure BDA0001470563640000053
Is prepared from
Figure BDA0001470563640000054
And is
Figure BDA0001470563640000055
Then
Figure BDA0001470563640000056
Theta in the drawing0≥∠T1PH1Then sin (theta)0)≥sin(∠T1PH1) Is combined with
Figure BDA0001470563640000057
Then h isΩ≥h0(max)≥h0I.e. T0(P)、T1Arch height h of inter-large ground wire0Not greater than w arch height limit difference h of large ground wireΩ；
Seventhly, by analogy, interpolation distance is adopted
Figure BDA0001470563640000058
Interpolating the large ground wire w, adjacent interpolation points Ti、Ti+1Arch height h of inter-large ground wireiNot greater than w arch height limit difference h of large ground wireΩAfter the syndrome is confirmed.
At a given large ground wire w arch height limit difference hΩOn the premise of (1), calculating an arbitrary interpolation point Ti(i∈[0,n+1]) (n represents the number of interpolation points on the large ground line w, n is 0,1, 2.) (T)0＝P，Tn+1Q), Q interval large earth wire initial azimuth angle AiAnd the initial azimuth angle a of the constant direction lineiAngle of (theta)i＝|Ai-aiAnd interpolated distance
Figure BDA0001470563640000059
Initial azimuth angle Ai、TiLongitude and latitude coordinates of points
Figure BDA00014705636400000510
Calculating the tail end T of the next small segment of the earth wire under the known conditioni+1Longitude and latitude coordinates of
Figure BDA00014705636400000511
Comprising the following steps, as shown in fig. 6:
step a, reading in longitude and latitude coordinates (B) of a starting point P of a geodesic wire w1,L1) And latitude and longitude coordinates (B) of the end point Q2,L2)；
Step b, setting a w arch height limit difference h of the large ground wireΩ(unit: m). Big ground wire w arch height tolerance hΩIn theory any given height threshold (unit: m) can be used. For the situation that the big ground wire is drawn to the paper chart, the arch height limit difference h of the big ground wire wΩThe minimum resolution distance d on a paper chart (the chart scale denominator is l) can be adoptedchartSolid distance D corresponding to (unit: cm)chart(unit: m), the calculation method is as follows:
Dchart＝ldchart/100；
step c, using the longitude and latitude coordinates of P, Q (B)1,L1) And (B)2,L2) Calculating P, Q the initial azimuth A of geodesic line under known conditions by using the inverse solution of geodesic subject and the inverse solution of constant direction line in geodesic survey0And the starting azimuth angle a of the constant direction line0(ii) a The longitude and latitude coordinates (B) of P, Q are known1,L1) And (B)2,L2) Calculating P, Q interval geodesic initial azimuth angle A0And the starting azimuth angle a of the constant direction line0The problems of (1) relate to the geodetic topic inverse problem and the constant-line inverse problem in geodesy,
the geodetic topic inverse solution problem can be summarized as a solution to the following equation set:
Figure BDA0001470563640000061
in the formula: s (w) represents the length of the geodesic line; a'0Representing the geodesic negative azimuth angle.
The problem of inverse solution to the galvanostatic line can be summarized as the solution of the following equation set:
Figure BDA0001470563640000062
in the formula: s (w) represents a length of a constant direction line; a'0Indicating the homodyne counter-azimuth. In addition, the latitude and longitude coordinates of P are known (B)1,L1) The length of the large ground line S (w) and its initial azimuth angle A0Calculating the geodetic longitude and latitude coordinates (B) of the geodetic terminal point Q2,L2) The problem of (a) is ascribed to the geodetic topic forward solution problem in geodetics, i.e. the system of equations is solved:
Figure BDA0001470563640000063
step d, calculating P, Q interval geodesic initial azimuth angle A0And the initial azimuth angle a of the constant direction line0Angle of (theta)0＝|A0-a0I, interpolation distance
Figure BDA0001470563640000064
Initial azimuth angle A0Longitude and latitude coordinates of point P (B)1,L1) Calculating the tail end T of the small segment of the geodesic line by utilizing a geodesic subject forward solution method in geodesic survey under known conditions1Longitude and latitude coordinates of
Figure BDA0001470563640000065
Step e, with T1Longitude and latitude coordinates of Q
Figure BDA0001470563640000066
And (B)2,L2) Calculating T for known conditions by using an inverse solution method of geodetic subject and an inverse solution method of a constant line in geodety1Q-interval large earth wire initial azimuth angle A1And the starting azimuth angle a of the constant direction line1；
Step f, calculating T1Q-interval large earth wire initial azimuth angle A1And the initial azimuth angle a of the constant direction line1Angle of (theta)1＝|A1-a1I, interpolation distance
Figure BDA0001470563640000071
Initial azimuth angle A1、T1Longitude and latitude coordinates of points
Figure BDA0001470563640000072
Calculating the tail end T of the small segment of the geodesic line by utilizing a geodesic subject forward solution method in geodesic survey under known conditions2Longitude and latitude coordinates of
Figure BDA0001470563640000073
Step g, analogizing, and obtaining the tail end T of the small section of the large ground wire according to the previous time each timeiLongitude and latitude coordinates of Q
Figure BDA0001470563640000074
(B2,L2) Calculating TiQ-interval large earth wire initial azimuth angle AiAnd the initial azimuth angle a of the constant direction lineiAngle of (theta)i＝|Ai-aiL, |; by interpolation distance
Figure BDA0001470563640000075
Initial azimuth angle Ai、TiLongitude and latitude coordinates of points
Figure BDA0001470563640000076
Calculating the tail end T of the next small segment of the earth wire under the known conditioni+1Longitude and latitude coordinates of
Figure BDA0001470563640000077
Until the point location interpolation is finished.
Analysis by calculation example:
description of the drawings: the "arch height error" parameter in the following calculation example is the maximum value statistics of arch heights of small sections of large ground wires between adjacent interpolation points (including starting points and end points of large ground wires).
The geodesic spread-drawing example (I) is introduced from the literature (Huang-Shen. ellipsoidal geodesy [ M ]. Zheng Jun surveying and mapping institute, 1991.), the calculation conclusion of the example in the literature is shown in Table 1, and the calculation conclusion and the calculation deviation from the literature of the example in the invention are shown in Table 2.
TABLE 1 calculation conclusion of the great ground line expansion example (I)
Figure BDA0001470563640000078
TABLE 2 calculation of deviation statistics for big ground line spread-plot example (I)
Figure BDA0001470563640000081
The second geodesic line spreading calculation example (II) is introduced from documents (Malus chinensis, Hai map mathematic basis [ M ] navigation guarantee department of military and military commander department of China civil liberation army, 1985.), the calculation conclusion of the calculation example in the documents is shown in Table 3, and the calculation conclusion of the calculation example and the calculation deviation from the documents are shown in Table 4.
TABLE 3 calculation conclusion of great ground line expansion example (II)
Figure BDA0001470563640000082
TABLE 4 calculation of deviation statistics for big ground line expansion and drawing example (II)
Figure BDA0001470563640000083
The geodesic spread-drawing example (III) is introduced from the literature (Huang-Shen. ellipsoidal geodesy [ M ]. Zheng Jun surveying and mapping institute, 1991.), the calculation conclusion of the example in the literature is shown in Table 5, and the calculation conclusion and the calculation deviation from the literature of the example in the invention are shown in Table 6.
TABLE 5 calculation conclusion of great ground line expansion example (III)
Figure BDA0001470563640000091
TABLE 6 calculation of deviation statistics for big ground line expansion example (III)
Figure BDA0001470563640000092
The lengths of the ground wires in the ground wire stretching calculation examples (one), (two) and (three) are 28230.936m, 225310.09m and 15000000.1m respectively. Comparative analysis it is readily apparent that: the large ground wire spreading error without interpolation treatment is increased sharply along with the increase of the length of the large ground wire; the traditional fixed distance interpolation method (the equal-spacing (bisection) interpolation method without constraint conditions as shown in fig. 5) of "replacing curved with straight" cannot effectively control the overall accumulated error of the large ground line development; the big ground wire interpolation algorithm based on the azimuth arch height tolerance constraint of the mercator projection realizes the precise plotting of the big ground wires with any length under the condition of a specified precision threshold value through the self-adaptive adjustment and matching of the plotting precision and the interpolation distance of the big ground wires.
While the invention has been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (6)

1. A big ground wire interpolation method based on azimuth arch height tolerance constraint of mercator projection is characterized in that: the method comprises the following steps:
a. inputting longitude and latitude coordinates (B) of a geodesic starting point P1,L1) And latitude and longitude coordinates (B) of the end point Q2,L2)；
b. Determining the arch height difference h of the large ground wire w of the starting point P and the end point Q of the large ground wireΩ；
c. According to longitude and latitude coordinates (B) of a starting point P and an end point Q of the geodesic line1,L1) And (B)2,L2) Calculating the initial azimuth angle A of the geodesic line between the starting point P and the end point Q of the geodesic line0And the starting azimuth angle a of the constant direction line0；
d. Calculating the initial azimuth angle A of the geodesic line between the starting point P and the end point Q of the geodesic line0And the initial azimuth angle a of the constant direction line0Angle of (theta)0＝|A0-a0I, interpolation distance
Figure FDA0002642730570000011
Initial azimuth angle A0Longitude and latitude coordinates of point P of origin of geodesic line (B)1,L1) Calculating the tail end T of the small segment of earth wire between the starting point P and the end point Q under the known condition1Longitude and latitude coordinates of
Figure FDA0002642730570000012
e. According to T1Longitude and latitude coordinates of Q
Figure FDA0002642730570000013
And (B)2,L2) Calculating T1Q-interval large earth wire initial azimuth angle A1And the starting azimuth angle a of the constant direction line1；
f. Calculating T1Q-interval large earth wire initial azimuth angle A1And the initial azimuth angle a of the constant direction line1Angle of (theta)1＝|A1-a1I, interpolation distance
Figure FDA0002642730570000014
Initial azimuth angle A1、T1Longitude and latitude coordinates of points
Figure FDA0002642730570000015
For known conditions, T is calculated1Q-interval small section earth wire terminal T2Longitude and latitude coordinates of
Figure FDA0002642730570000016
g. And so on, each time according to the last obtained small segment earth wire terminal TiLongitude and latitude coordinates of Q
Figure FDA0002642730570000017
(B2,L2) Calculating TiQ-interval large earth wire initial azimuth angle AiAnd the initial azimuth angle a of the constant direction lineiAngle of (theta)i＝|Ai-aiL, |; by interpolation distance
Figure FDA0002642730570000018
Initial azimuth angle Ai、TiLongitude and latitude coordinates of points
Figure FDA0002642730570000019
Calculating the tail end T of the next small segment of the earth wire under the known conditioni+1Longitude and latitude coordinates of
Figure FDA00026427305700000110
Until the point location interpolation is finished.
2. The mercator projection-based azimuth vault elevation difference constrained geoline interpolation method of claim 1, wherein: in the step b, for the situation that the big ground wire is stretched to the paper chart, the arch height difference h of the big ground wire wΩAdopting the minimum resolution distance d on the paper chartchartCorresponding field distance DchartThe chart scale denominator is l, and the calculation method comprises the following steps: dchart＝l*dchart/100。
3. The mercator projection-based azimuth vault elevation difference constrained geoline interpolation method of claim 1, wherein: in said step c, the latitude and longitude coordinates (B) of P, Q are known1,L1) And (B)2,L2) Calculating the initial azimuth angle A of the geodesic line between the starting point P and the end point Q of the geodesic line0And the starting azimuth angle a of the constant direction line0Initial azimuth angle A0Obtained by a geodetic topic inverse solution method, which comprises the following steps:
solving the following equation set:
Figure FDA0002642730570000021
in the formula: s (w) represents the length of the geodesic line; a'0Representing the geodesic negative azimuth angle, S represents the length of the geodesic between P, Q; initial azimuth angle a of constant direction line0The method is obtained by a reverse solution method of the constant direction line, and comprises the following steps:
solving the following equation set:
Figure FDA0002642730570000022
in the formula: s (w) represents a length of a constant direction line; a'0Indicating the zenith angle and s the zenith length between P, Q.
4. The mercator projection-based azimuth vault elevation difference constrained geoline interpolation method of claim 1, wherein: in the step d, the tail end T of the small segment earth wire between the starting point P and the end point Q is calculated through a geodetic theme forward solution method in geodetic survey1Longitude and latitude coordinates of
Figure FDA0002642730570000023
The method comprises the following steps: knowing the latitude and longitude coordinates of P (B)1,L1) The length of the large ground line S (w) and its initial azimuth angle A0Calculating the geodetic longitude and latitude coordinates (B) of the geodetic terminal point Q2,L2) By geodetic topic forward solution methods in geodetics, i.e. solving a system of equations:
Figure FDA0002642730570000024
B2abscissa, L, representing the geodetic longitude and latitude of the geodetic terminal Q2Ordinate, A 'representing geodetic longitude and latitude of geodetic terminal point Q'0Representing the geodesic negative azimuth angle.
5. The mercator projection-based azimuth vault elevation difference constrained geoline interpolation method of claim 1, wherein: in the step e, T is calculated by using an inverse solution and a constant line inverse solution method of the geodetic subject in the geodety1Q-interval large earth wire initial azimuth angle A1And the starting azimuth angle a of the constant direction line1。
6. The mercator projection-based azimuth vault elevation difference constrained geoline interpolation method of claim 1, wherein: in the step f, T is calculated by using a geodetic subject forward solution method in geodety1Q-interval small section earth wire terminal T2Longitude and latitude coordinates of
Figure FDA0002642730570000031
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