A refined projection distortion calculation method and program based on 3D traversal grid.

Abstract

This application relates to the field of geodesy technology, and particularly to a refined projection deformation calculation method and program product based on a three-dimensional traversal grid. The method includes: dividing the projected elevation surface of the area to be measured into a grid, and obtaining the first planar coordinate data and first geodetic coordinate data of the grid vertices; generating circular regions with preset radii centered on the grid vertices, and generating rays from the centers at preset intervals, and identifying the second planar coordinate data and second geodetic coordinate data of the intersection points formed by the rays and the circular regions; calculating the length deformation and / or angular deformation between the grid vertices and the intersection points to obtain the projection deformation result. This solves the problem in related technologies where experience-driven sampling inspection and evaluation easily overlooks projection deformation exceeding limits when the terrain is undulating or the area is irregular, thus creating potential risks in engineering decision-making.

Description

Technical Field

[0001] This application relates to the field of geodesy technology, and in particular to a refined projection deformation calculation method and program product based on a three-dimensional traversal grid. Background Technology

[0002] In related technologies, the core function of map projection is to transform measurement elements such as coordinates, side lengths, and azimuths on an ellipsoid into a plane coordinate system using certain mathematical rules. This provides a unified coordinate benchmark for the design, construction, and operation of engineering projects. Gaussian projection is often chosen to achieve this goal. However, in linear projects with long east-west extensions, such as highways, railways, water conservancy projects, and oil pipelines, which cross multiple Gaussian projection zones, using the standard Gaussian projection would result in large projection distortion and coordinate discontinuities. Therefore, oblique projection or methods such as moving the projection's central meridian and changing the projection surface elevation are often used to establish an independent coordinate system for the project. This minimizes projection distortion across the entire route, and the applicability of the chosen projection method to the entire project area is determined based on expert experience.

[0003] However, in related technologies, experience-driven sampling inspection-based evaluation may miss cases of excessive projection deformation in projects with large terrain undulations or irregular regional shapes, which poses potential risks to subsequent engineering decisions and urgently needs improvement. Summary of the Invention

[0004] This application provides a refined projection deformation calculation method and program product based on a three-dimensional traversal grid to solve the problem that the experience-driven sampling inspection evaluation method in related technologies has great limitations in engineering projects with significant terrain undulations or irregular regional shapes. It is very likely to miss cases where the projection deformation exceeds the limit, thus creating potential risks for subsequent engineering decisions.

[0005] The first aspect of this application provides a method for calculating refined projection deformation based on a three-dimensional traversal grid, comprising the following steps: dividing the at least one projection elevation surface into a grid based on elevation surface data of at least one projection elevation surface of the area to be measured, generating at least one grid vertex, and acquiring first planar coordinate data and first geodetic coordinate data of the at least one grid vertex in a planar coordinate system and a geodetic coordinate system, respectively; generating a circular region with the at least one grid vertex as the center and a preset radius value, and generating at least one ray from the center at a preset interval value, and identifying second planar coordinate data and second geodetic coordinate data of at least one intersection point formed by the at least one ray and the circular region; calculating the length deformation and / or angular deformation between the at least one grid vertex and the at least one intersection point, based on the first planar coordinate data, the first geodetic coordinate data, the second planar coordinate data, and the second geodetic coordinate data, to obtain the projection deformation result of the at least one projection elevation surface according to the length deformation and / or the angular deformation.

[0006] Optionally, in one embodiment of this application, calculating the length deformation between the at least one grid vertex and the at least one intersection point based on the first planar coordinate data, the first geodetic coordinate data, the second planar coordinate data, and the second geodetic coordinate data includes: calculating the planar length value of a line segment formed with the at least one grid vertex and the at least one intersection point as endpoints based on the first planar coordinate data and the second planar coordinate data; calculating the starting geodetic data and the ending geodetic data of a geodetic line based on the first geodetic coordinate data and the second geodetic coordinate data; calculating the geodetic arc length value of the line segment based on the starting geodetic data and the ending geodetic data; and calculating the length deformation based on the planar length value and the geodetic arc length value.

[0007] Optionally, in one embodiment of this application, calculating the geodetic arc length of the line segment based on the starting geodetic data and the ending geodetic data includes: obtaining the starting and ending normalized latitude data based on the starting and ending geodetic data; calculating the positive azimuth value of the positive geodetic azimuth based on the starting and ending normalized latitude data, and calculating the negative azimuth value of the negative geodetic azimuth based on the positive azimuth value; and calculating the geodetic arc length based on the positive azimuth value, the negative azimuth value, the starting geodetic data, and the ending geodetic data.

[0008] Optionally, in one embodiment of this application, the step of calculating the reverse azimuth value of the reverse geodetic azimuth based on the positive azimuth value includes: calculating the angular distance value of the spherical angular distance based on the positive azimuth value; calculating the correction number of the spherical longitude difference based on the angular distance value and the positive azimuth value; and obtaining the reverse azimuth value based on the positive azimuth value in response to the correction number being less than a preset correction number.

[0009] Optionally, in one embodiment of this application, calculating the angular deformation between the at least one grid vertex and the at least one intersection point based on the first planar coordinate data, the first geodetic coordinate data, the second planar coordinate data, and the second geodetic coordinate data includes: identifying the planar angle value of the angle formed between the at least one grid vertex and the at least one intersection point based on the first planar coordinate data and the second planar coordinate data; calculating the geodetic angle value of the angle based on the positive azimuth value; and calculating the angular deformation based on the planar angle value and the geodetic angle value.

[0010] Optionally, in one embodiment of this application, obtaining the projection deformation result of the at least one projection elevation surface based on the length deformation and / or the angle deformation includes: obtaining a final length deformation in response to the length deformation being greater than a preset length deformation; and obtaining the projection deformation result based on the final length deformation.

[0011] Optionally, in one embodiment of this application, obtaining the projection deformation result of the at least one projection elevation surface based on the length deformation and / or the angle deformation includes: obtaining a final angle deformation in response to the angle deformation being greater than a preset angle deformation; and obtaining the projection deformation result based on the final angle deformation.

[0012] Optionally, in one embodiment of this application, the formula for calculating the length deformation may be, but is not limited to, the following:

[0013] ,

[0014] in, Indicates the amount of length deformation; Represents length in a planar coordinate system; Indicates the arc length of a geodetic line in a geodetic coordinate system; superscript , … Indicates the central angle; subscript This indicates the row and column number of the grid vertex.

[0015] The formula for calculating the angular deformation may be, but is not limited to, the following:

[0016] ,

[0017] in, Indicates the amount of angular deformation; Represents the angle between planes in a planar coordinate system; Indicates the angle between geodesics in a geodetic coordinate system; the superscript indicates the two central angles corresponding to the two sides forming the angle; the subscript indicates the angle between geodesics. This indicates the row and column number of the grid vertex corresponding to the included angle vertex.

[0018] A second aspect of this application provides a refined projection deformation calculation device based on a three-dimensional traversal grid, comprising: an acquisition module, configured to divide the at least one projection elevation surface into a grid based on elevation surface data of at least one projection elevation surface of the area to be measured, to generate at least one grid vertex, and to acquire first planar coordinate data and first geodetic coordinate data of the at least one grid vertex in a planar coordinate system; an identification module, configured to generate a circular region with the at least one grid vertex as the center and a preset radius value, and to generate at least one ray from the center at a preset interval value, and to identify the second planar coordinate data and second geodetic coordinate data of at least one intersection point formed by the at least one ray and the circular region in a planar coordinate system; and a calculation module, configured to calculate the length deformation and / or angular deformation between the at least one grid vertex and the at least one intersection point based on the first planar coordinate data, the first geodetic coordinate data, the second planar coordinate data, and the second geodetic coordinate data, so as to obtain the projection deformation result of the at least one projection elevation surface according to the length deformation and / or the angular deformation.

[0019] Optionally, in one embodiment of this application, the calculation module includes: a first calculation unit, configured to calculate the planar length value of a line segment formed with the at least one grid vertex and the at least one intersection point as endpoints based on the first planar coordinate data and the second planar coordinate data; a second calculation unit, configured to calculate the starting geodetic data and ending geodetic data of a geodetic line based on the first geodetic coordinate data and the second geodetic coordinate data; a third calculation unit, configured to calculate the geodetic arc length value of the line segment based on the starting geodetic data and the ending geodetic data; and a fourth calculation unit, configured to calculate the length deformation based on the planar length value and the geodetic arc length value.

[0020] Optionally, in one embodiment of this application, the third calculation unit includes: an acquisition subunit, configured to acquire the origin-normalized latitude data and the destination-normalized latitude data based on the origin-normalized latitude data and the destination-normalized latitude data; a first calculation subunit, configured to calculate the positive azimuth value of the positive geodetic azimuth based on the origin-normalized latitude data and the destination-normalized latitude data, and calculate the negative azimuth value of the negative geodetic azimuth based on the positive azimuth value; and a second calculation subunit, configured to calculate the geodetic arc length value based on the positive azimuth value, the negative azimuth value, the origin-normalized geodetic data, and the destination-normalized geodetic data.

[0021] Optionally, in one embodiment of this application, the first calculation subunit includes: a first calculation sub-component, used to calculate the angular distance value of the spherical angular distance based on the positive azimuth value; a second calculation sub-component, used to calculate the correction number of the spherical longitude difference based on the angular distance value and the positive azimuth value; and a generation sub-component, used to obtain the reverse azimuth value based on the positive azimuth value in response to the correction number being less than a preset correction number.

[0022] Optionally, in one embodiment of this application, the calculation module includes: an identification unit, configured to identify the plane angle value of the angle formed between the at least one grid vertex and the at least one intersection point based on the first plane coordinate data and the second plane coordinate data; a fourth calculation unit, configured to calculate the geodetic angle value of the angle based on the positive azimuth angle value; and a fifth calculation unit, configured to calculate the angular deformation amount based on the plane angle value and the geodetic angle value.

[0023] Optionally, in one embodiment of this application, the calculation module includes: a first generation unit, configured to obtain a final length deformation amount in response to the length deformation amount being greater than a preset length deformation amount; and a second generation unit, configured to obtain the projection deformation result based on the final length deformation amount.

[0024] Optionally, in one embodiment of this application, the calculation module includes: a third generation unit, configured to obtain a final angle deformation amount in response to the angle deformation amount being greater than a preset angle deformation amount; and a fourth generation unit, configured to obtain the projection deformation result based on the final angle deformation amount.

[0025] Optionally, in one embodiment of this application, the formula for calculating the length deformation may be, but is not limited to, the following:

[0026] ,

[0027] in, Indicates the amount of length deformation; Represents length in a planar coordinate system; Indicates the arc length of a geodetic line in a geodetic coordinate system; superscript , … Indicates the central angle; subscript This indicates the row and column number of the grid vertex.

[0028] The formula for calculating the angular deformation may be, but is not limited to, the following:

[0029] ,

[0030] in, Indicates the amount of angular deformation; Represents the angle between planes in a planar coordinate system; Indicates the angle between geodesics in a geodetic coordinate system; the superscript indicates the two central angles corresponding to the two sides forming the angle; the subscript indicates the angle between geodesics. This indicates the row and column number of the grid vertex corresponding to the included angle vertex.

[0031] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the program to implement the refined projection deformation calculation method based on a three-dimensional traversal grid as described in the above embodiments.

[0032] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for calculating refined projection deformation based on a three-dimensional traversal grid.

[0033] A fifth aspect of this application provides a computer program product, including a computer program that, when executed, implements the above-described method for calculating refined projection deformation based on a three-dimensional traversal grid.

[0034] This application embodiment can divide the projected elevation surface into a grid based on the elevation surface data of at least one projected elevation surface of the area to be measured, thereby generating grid vertices. The first planar coordinate data of each grid vertex in the planar coordinate system and the first geodetic coordinate data in the geodetic coordinate system are then acquired. A circular region is generated with a certain radius centered on each grid vertex. Corresponding rays are generated from the center of the circle at certain intervals. The second planar coordinate data of the intersection points formed by the rays and the circular regions in the planar coordinate system and the second geodetic coordinate data in the geodetic coordinate system are identified. The length deformation and / or angular deformation between the grid vertices and the intersection points are then calculated to obtain the projection deformation result of the projected elevation surface. Through multi-step precise coordinate data acquisition and deformation calculation, the projection deformation of the projected elevation surface of the area to be measured can be comprehensively and accurately evaluated, providing a reliable basis for engineering decisions. This solves the problem that experience-driven sampling inspection evaluation methods in related technologies have significant limitations in engineering projects with significant terrain variations or irregular regional shapes. They may miss cases where projection deformation exceeds the limit, thus creating potential risks for subsequent engineering decisions.

[0035] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0036] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0037] Figure 1 This is a flowchart illustrating a refined projection deformation calculation method based on a three-dimensional traversal grid, according to an embodiment of this application.

[0038] Figure 2 This is a schematic diagram of a projected length deformation field diagram provided according to an embodiment of this application;

[0039] Figure 3 This is a schematic diagram of a projection angle deformation field diagram provided according to an embodiment of this application;

[0040] Figure 4 A flowchart illustrating the working principle of a refined projection deformation calculation method based on a three-dimensional traversal grid according to an embodiment of this application;

[0041] Figure 5 This is a block diagram of a refined projection deformation calculation device based on a three-dimensional traversal grid provided in an embodiment of this application;

[0042] Figure 6 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0043] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0044] The following describes, with reference to the accompanying drawings, a refined projection deformation calculation method and program product based on a three-dimensional traversal grid, according to embodiments of this application. Addressing the issue that the experience-driven sampling inspection method mentioned in the background art has significant limitations in engineering projects with significant terrain undulations or irregular regional shapes, it is highly likely to miss cases where projection deformation exceeds limits, thus creating potential risks for subsequent engineering decisions. This application provides a refined projection deformation calculation method based on a three-dimensional traversal grid. In this method, the projection elevation surface can be divided into a grid based on elevation surface data of at least one projection elevation surface of the area to be measured, thereby generating grid vertices. The first plane coordinate data of each grid vertex in the plane coordinate system and the coordinates on the ground are then obtained. The system uses the first geodetic coordinate data in a coordinate system, and generates circular regions with a certain radius centered on grid vertices. Rays are then generated from these vertices at regular intervals. The intersection points of these rays with the circular regions are identified using the second plane coordinate data in the plane coordinate system and the second geodetic coordinate data in the geodetic coordinate system. The length and / or angular deformation between the grid vertices and the intersection points are then calculated to obtain the projection deformation result of the projected elevation surface. Through multi-step precise coordinate data acquisition and deformation calculation, the projection deformation of the projected elevation surface of the area under test can be comprehensively and accurately assessed, providing a reliable basis for engineering decisions. This solves the problem that experience-driven sampling inspection methods in related technologies have significant limitations in engineering projects with significant terrain variations or irregular shapes, and may potentially miss cases where projection deformation exceeds limits, thus creating potential risks for subsequent engineering decisions.

[0045] Specifically, Figure 1 This is a flowchart of a refined projection deformation calculation method based on a three-dimensional traversal grid, according to an embodiment of this application.

[0046] like Figure 1 As shown, the refined projection deformation calculation method based on a three-dimensional traversal grid includes the following steps:

[0047] In step S101, based on the elevation surface data of at least one projected elevation surface of the area to be measured, at least one projected elevation surface is divided into grids to generate at least one grid vertex, and the first planar coordinate data of at least one grid vertex in the plane coordinate system and the first geodetic coordinate data in the geodetic coordinate system are obtained respectively.

[0048] As one possible implementation method, embodiments of this application can divide the projected elevation surface into a grid based on the elevation surface data corresponding to different projected elevation surfaces in the area to be measured, thereby generating at least one grid vertex, and obtaining the first planar coordinate data of each grid vertex in the planar coordinate system and the first geodetic coordinate data in the geodetic coordinate system.

[0049] For example, in this application embodiment, the terrain undulation data of the area to be measured can be obtained first, and then the area to be measured can be divided into... A projected elevation surface can be expressed, but is not limited to, as follows:

[0050] (1)

[0051] in, This is considered normal high.

[0052] Furthermore, the embodiments of this application use the first... Taking a projected elevation surface as an example, in the plane coordinate system obtained by projection, according to length intervals... Divide the area into square grids, thereby obtaining the grid vertices of all grids on the corresponding projected elevation surface, and acquire the first planar coordinate data of each grid vertex in the planar coordinate system. The expression for this can be, but is not limited to, as follows:

[0053] (2)

[0054] in, These are the engineering-independent coordinates of the grid vertices, i.e., the first-plane coordinate data in the planar coordinate system; superscript. , , ..., This indicates the row and column number of the grid vertex.

[0055] Furthermore, in this embodiment of the application, the first geodetic coordinate data of each grid vertex in the geodetic coordinate system can be obtained through coordinate projection inverse calculation. The expression for coordinate projection inverse calculation can be, but is not limited to, expressed as:

[0056] (3)

[0057] in, The latitude and longitude are the geodetic coordinates of the grid vertices. This indicates the inverse calculation of coordinate projection.

[0058] The expression for the first geodetic coordinate data can be, but is not limited to, as follows:

[0059] (4)

[0060] In step S102, a circular region is generated with at least one grid vertex as the center and a preset radius value. Starting from the center, at least one ray is generated at a preset interval value. The second planar coordinate data of the intersection point formed by the at least one ray and the circular region is identified in the plane coordinate system and the second geodetic coordinate data in the geodetic coordinate system.

[0061] In actual implementation, this application embodiment can take at least one grid vertex as the center, construct a corresponding circular region according to a preset radius value, extend the corresponding ray from the center according to a preset interval value, determine the intersection point formed by the ray and the corresponding circular region, and obtain the second planar coordinate data of the intersection point in the planar coordinate system and the second geodetic coordinate data in the geodetic coordinate system.

[0062] The preset radius value and preset interval value can be set by those skilled in the art according to the actual situation, and this application does not impose specific restrictions.

[0063] For example, the embodiments of this application use the first... Okay, number Column grid vertices For example, in a planar coordinate system, with the grid vertices as centers, and according to a preset radius value... Draw a circular area according to a preset interval value, such as a central angle interval of 1. This application does not impose specific limitations, but draws rays originating from the center of the circle, and then obtains... The intersection points of each ray and the circle are used to obtain the second plane coordinate data of each intersection point in the plane coordinate system. The expression of this second plane coordinate data can be, but is not limited to, the following:

[0064] (5)

[0065] Among them, the superscript of the coordinates , … Indicates the central angle as , … The point of intersection on the circle corresponding to the time.

[0066] Furthermore, in this embodiment of the application, the second geodetic coordinate data of each intersection point in the geodetic coordinate system is obtained by inverse calculation of coordinate projection using formula (3). The expression of this data may be, but is not limited to, as follows:

[0067] (6)

[0068] In step S103, based on the first plane coordinate data, the first geodetic coordinate data, the second plane coordinate data, and the second geodetic coordinate data, the length deformation and / or angular deformation between at least one grid vertex and at least one intersection point are calculated, so as to obtain the projection deformation result of at least one projection elevation surface according to the length deformation and / or angular deformation.

[0069] In some embodiments, this application uses first plane coordinate data, first geodetic coordinate data, second plane coordinate data, and second geodetic coordinate data to calculate the length deformation between grid vertices and intersections, thereby obtaining the projection deformation result of the projected elevation surface.

[0070] In some embodiments, this application uses first plane coordinate data, first geodetic coordinate data, second plane coordinate data, and second geodetic coordinate data to calculate the angular deformation between grid vertices and intersections, thereby obtaining the projection deformation result of the projected elevation surface.

[0071] In some embodiments, this application uses first plane coordinate data, first geodetic coordinate data, second plane coordinate data, and second geodetic coordinate data to calculate the length deformation and angle deformation between grid vertices and intersections, thereby obtaining the projection deformation result of the projection elevation surface.

[0072] Optionally, in one embodiment of this application, calculating the length deformation between at least one grid vertex and at least one intersection point based on first planar coordinate data, first geodetic coordinate data, second planar coordinate data, and second geodetic coordinate data includes: calculating the planar length value of a line segment formed with at least one grid vertex and at least one intersection point as endpoints based on the first planar coordinate data and the second planar coordinate data; calculating the starting geodetic data and ending geodetic data of a geodetic line based on the first geodetic coordinate data and the second geodetic coordinate data; calculating the geodetic arc length value of the line segment based on the starting geodetic data and the ending geodetic data; and calculating the length deformation based on the planar length value and the geodetic arc length value. The formula for calculating the length deformation may be, but is not limited to, the following:

[0073] ,

[0074] in, Indicates the amount of length deformation; Represents length in a planar coordinate system; Indicates the arc length of a geodetic line in a geodetic coordinate system; superscript , … Indicates the central angle; subscript This indicates the row and column number of the grid vertex.

[0075] In some embodiments, the present application can use first planar coordinate data and second planar coordinate data to calculate the planar length of the line segment formed by the grid vertices and intersections as endpoints.

[0076] For example, embodiments of this application can calculate the planar length of a line segment formed with grid vertices and intersections as endpoints in a planar coordinate system. Its expression can be, but is not limited to, as:

[0077] (7)

[0078] Among them, length The superscript and subscript indicate the endpoints of the line segment. The superscript indicates the central angle corresponding to the intersection point of the circles, and the subscript indicates the row and column numbers of the grid vertices. There are a total of The length of a line segment.

[0079] In some embodiments of this application, the starting geodetic data and ending geodetic data of the geodetic line can be calculated based on the first geodetic coordinate data and the second geodetic coordinate data. Then, based on the starting geodetic data and the ending geodetic data, the arc length value of the line segment in the geodetic coordinate system can be calculated. The expression can be, but is not limited to, as follows:

[0080] (8)

[0081] Therefore, embodiments of this application can use the plane length value and the geodetic arc length value to calculate The length deformation of the strip can be expressed, but is not limited to, as:

[0082] (9)

[0083] in, Indicates the amount of length deformation; Represents length in a planar coordinate system; Indicates the arc length of a geodetic line in a geodetic coordinate system; superscript , … Indicates the central angle; subscript This indicates the row and column number of the grid vertex.

[0084] Optionally, in one embodiment of this application, calculating the geodetic arc length of a line segment based on the starting geodetic data and the ending geodetic data includes: obtaining the starting and ending normalized latitude data based on the starting and ending geodetic data; calculating the positive azimuth value of the positive geodetic azimuth based on the starting and ending normalized latitude data, and calculating the negative azimuth value of the negative geodetic azimuth based on the positive azimuth value; and calculating the geodetic arc length based on the positive azimuth value, the negative azimuth value, the starting geodetic data, and the ending geodetic data.

[0085] In some embodiments, this application can obtain the normalized latitude data corresponding to the origin and destination latitude based on the origin geodetic data and the destination geodetic data. Then, based on the origin and destination normalized latitude data, the positive azimuth value corresponding to the positive geodetic azimuth is calculated, and the negative azimuth value of the negative geodetic azimuth is derived based on the positive azimuth value. Thus, the geodetic arc length value is calculated based on the positive azimuth value, the negative azimuth value, the origin geodetic data, and the destination geodetic data.

[0086] For example, in this embodiment of the application, to calculate the geodetic arc length corresponding to the plane length value, the arc length of the geodetic line formed by the two endpoints can be used as a reference. Since the calculation of the geodetic arc length is related to the projected elevation surface where the endpoints are located, this embodiment of the application can first perform ellipsoidal expansion: First, define the semi-major axis of the original ellipsoid as... Flatness The variation of the semi-major axis of the ellipsoid is determined using the ramusoidal radius of curvature method. This leads to the semi-major axis of the expanded ellipsoid. :

[0087] (10)

[0088] in, This represents the change in the semi-major axis of the ellipsoid; Indicates the flattening of the ellipsoid; Represents the geodetic latitude of the grid vertices; Indicates the ground height of a grid vertex; This represents the normal height of a grid vertex; Indicates elevation anomaly; This represents the semi-major axis of the expanded ellipsoid; This represents the semi-major axis of the ellipsoid before expansion.

[0089] Furthermore, in this embodiment, based on an expanded ellipsoid, the geodetic arc length between the two endpoints is obtained through inverse calculation using the Bessel geodetic theme. , the true azimuth , reverse local azimuth Its calculation formula can be expressed as, but is not limited to, as:

[0090] (11)

[0091] in, This represents the inverse calculation function for the Bessel geodetic theme based on the dilated ellipsoid; The geodetic coordinates representing the starting point of the geodetic line, i.e., the first geodetic coordinate data of the grid vertex; This represents the geodetic coordinates of the endpoint of the geodetic line, i.e., the second geodetic coordinate data of the intersection point.

[0092] It should be noted that, in the embodiments of this application, the inverse calculation function of the Bessel geodetic theme based on the dilated ellipsoid is used. The core idea is to project the ellipsoidal problem onto an auxiliary sphere for solution, and then transform it back to the ellipsoid. This may include, but is not limited to, calculation of auxiliary quantities, calculation of spherical elements, iterative successive approximation method, and calculation of geodesic length. This application does not impose specific limitations.

[0093] Among them, the auxiliary quantity calculation includes calculating the normalized dimension. The corresponding trigonometric function values, including the originating and ending point normalized latitude data, transform the ellipsoidal coordinates to the sphere. The expression for this transformation can be, but is not limited to, as follows:

[0094] (12)

[0095] in, , Indicates the naturalized latitude of the starting point of the geodesic. The corresponding sine and cosine values; , Indicates the naturalized latitude of the terminus of the geodesic. The corresponding sine and cosine values.

[0096] Spherical element calculation includes calculating the difference in spherical length. and spherical elements Its expression can be, but is not limited to, as:

[0097] (13)

[0098] The successive approximation method iteratively includes calculating the tangent value of the positive azimuth angle. Its expression can be, but is not limited to, as:

[0099] (14)

[0100] Furthermore, in this embodiment, the corresponding positive azimuth angle value is obtained by inverse calculation using trigonometric functions. Its expression can be, but is not limited to, represented as: .

[0101] Then, based on the positive azimuth value, the negative azimuth value can be calculated, and its expression can be, but is not limited to, as follows:

[0102] (15)

[0103] in, This indicates the meridian convergence angle correction, which is determined by the latitude and longitude of the starting and ending points of the geodetic line. It can be calculated using existing geodetic formulas, which will not be elaborated here.

[0104] The formula for calculating the length of the geodesic line can be, but is not limited to, the following:

[0105] (16)

[0106] in, Indicates the length of the geodesic. This represents the function for calculating the length of the geodesic line.

[0107] Optionally, in one embodiment of this application, calculating the reverse azimuth value of the reverse azimuth based on the positive azimuth value includes: calculating the angular distance value of the spherical angular distance based on the positive azimuth value; calculating the correction number of the spherical longitude difference based on the angular distance value and the positive azimuth value; and obtaining the reverse azimuth value based on the positive azimuth value in response to the correction number being less than a preset correction number.

[0108] In some embodiments of this application, the angular distance value of the spherical angular distance can be calculated based on the positive azimuth angle value, and its expression can be, but is not limited to, as follows:

[0109] (17)

[0110] Furthermore, in this embodiment, the correction for the spherical longitude difference is calculated based on the angular distance and positive azimuth angle values. and the new spherical difference The calculation formula can be, but is not limited to, the following:

[0111] (18)

[0112] in, This represents the function for calculating the correction after difference. Repeat formulas (12)-(14), as well as formulas (17) and (18), until the correction is less than the preset correction. Its expression can be, but is not limited to, as:

[0113] (19)

[0114] Among them, the number of corrections subscript , This represents two iterations. After each iteration, the corresponding positive azimuth angle value is calculated using trigonometric functions, and the negative azimuth angle value is obtained based on the positive azimuth angle value. The preset correction value can be set by those skilled in the art according to actual conditions; this application does not impose specific limitations.

[0115] Optionally, in one embodiment of this application, calculating the angular deformation between at least one grid vertex and at least one intersection point based on first planar coordinate data, first geodetic coordinate data, second planar coordinate data, and second geodetic coordinate data includes: identifying the planar angle value of the angle formed between at least one grid vertex and at least one intersection point based on the first planar coordinate data and the second planar coordinate data; calculating the geodetic angle value of the angle based on the positive azimuth angle value; and calculating the angular deformation based on the planar angle value and the geodetic angle value. The formula for calculating the angular deformation may be, but is not limited to, the following:

[0116] ,

[0117] in, Indicates the amount of angular deformation; Represents the angle between planes in a planar coordinate system; Indicates the angle between geodesics in a geodetic coordinate system; the superscript indicates the two central angles corresponding to the two sides forming the angle; the subscript indicates the angle between geodesics. This indicates the row and column number of the grid vertex corresponding to the included angle vertex.

[0118] In some embodiments, the present application embodiments can identify the plane angle value of the angle formed between grid vertices and intersections based on the first plane coordinate data and the second plane coordinate data.

[0119] For example, in this embodiment of the application, the included angle value of the plane with grid vertices as vertices is calculated based on the intersection point of the circles in a planar coordinate system. Its expression can be, but is not limited to, as:

[0120] (20)

[0121] Among them, the included angle of the plane The superscript indicates the start and end points of the included angle, represented by the central angle of the intersection of the circles; the subscript indicates the corner point, represented by the row and column number of the grid vertex, for a total of Angle between two planes.

[0122] In some embodiments of this application, the geodetic angle value of the included angle can be calculated based on the positive azimuth angle value obtained above.

[0123] For example, in order to calculate the deformation of the plane angle in the plane coordinate system, the geodetic angle with the grid vertex as the reference can be used in this embodiment of the application. First, the ellipsoid is expanded to the elevation of the grid vertex using formula (10), and then the Bessel geodetic theme of formula (8) is used for inverse calculation to obtain the azimuth of the geodetic line formed by the grid vertex and the intersection point, thus obtaining the geodetic angle values ​​of different angles. Its expression can be, but is not limited to, represented as:

[0124] ,(twenty one)

[0125] It should be noted that the embodiments of this application can obtain The angle between the geodesics can be simplified using, but is not limited to, the following formula:

[0126] ,(twenty two)

[0127] Furthermore, in this embodiment of the application, the corresponding angular deformation is calculated based on the plane angle value and the earth line angle value.

[0128] For example, embodiments of this application can be obtained The angular deformation can be expressed, but is not limited to, as follows:

[0129] ,(twenty three)

[0130] Optionally, in one embodiment of this application, obtaining the projection deformation result of at least one projection elevation surface based on the length deformation and / or angle deformation includes: obtaining the final length deformation in response to the length deformation being greater than a preset length deformation; and obtaining the projection deformation result based on the final length deformation.

[0131] In some embodiments, this application can determine the final length deformation amount when the length deformation amount is greater than a preset length deformation amount, thereby obtaining the projection deformation result. The preset length deformation amount can be set by those skilled in the art according to actual conditions, and this application does not impose specific limitations.

[0132] For example, embodiments of this application may select The maximum deformation in a strip, which is the final length deformation at a grid vertex, can be expressed, but is not limited to, as:

[0133] ,(twenty four)

[0134] Therefore, the embodiments of this application can be applied to all projected elevation surfaces, i.e. For each projected elevation surface, the grid vertices are used. The above calculations are repeated to obtain the final length deformation at all grid vertices in the 3D grid. Based on the final length deformation, color bands are set in stages, and a deformation heat map is drawn through color rendering. The hue depth is proportional to the deformation magnitude, thus clearly presenting the spatial distribution and gradation characteristics of the projected deformation on the plane, thereby rendering... Zhang projected length deformation field map, one of which is illustrated in the diagram below. Figure 2 As shown.

[0135] Optionally, in one embodiment of this application, obtaining the projection deformation result of at least one projection elevation surface based on the length deformation and / or angle deformation includes: obtaining the final angle deformation in response to the angle deformation being greater than a preset angle deformation; and obtaining the projection deformation result based on the final angle deformation.

[0136] In some embodiments, this application can determine the final angle deformation amount when the angle deformation amount is greater than a preset angle deformation amount, and then obtain the projection deformation result based on the final angle deformation amount. The preset angle deformation amount can be set by those skilled in the art according to actual conditions, and this application does not impose specific limitations.

[0137] For example, embodiments of this application may select The maximum deformation among the included angles, which is the final angular deformation at the grid vertex, can be expressed, but is not limited to, as:

[0138] (25)

[0139] Therefore, the embodiments of this application can be applied to all projected elevation surfaces, i.e. For each projected elevation surface, the grid vertices are used. The above calculations are repeated to obtain the projection angle deformation at all grid vertices in the 3D grid. Based on the final angle deformation, color bands are set in stages, and a deformation heat map is drawn through color rendering. The hue depth is proportional to the deformation magnitude, thus clearly presenting the spatial distribution pattern and gradation characteristics of the projection deformation on the plane, thereby rendering... Zhang's projection angle deformation field map, one of which is illustrated in the diagram below. Figure 3 As shown.

[0140] The working principle of the refined projection deformation calculation method based on a three-dimensional traversal grid proposed in this application will be introduced below with reference to a specific embodiment.

[0141] in, Figure 4 This is a flowchart illustrating the working principle of a refined projection deformation calculation method based on a three-dimensional traversal grid provided in an embodiment of this application.

[0142] Step 1: Three-dimensional traversal grid division.

[0143] In this embodiment, the terrain undulation data of the area to be measured is first obtained, and then the area to be measured is divided into... The projection elevation surface is given by formula (1), and is expressed as follows: Taking a projected elevation surface as an example, in the plane coordinate system obtained by projection, according to length intervals... Divide the grid into square grids, and then obtain the grid vertices of all grids on the corresponding projected elevation surface.

[0144] Step 2: Obtain the projected length deformation field.

[0145] In this embodiment, the first planar coordinate data of each grid vertex in the planar coordinate system can be obtained, and its expression is shown in formula (2), and the first geodetic coordinate data of each grid vertex in the geodetic coordinate system can be obtained, and its expression is shown in formula (4).

[0146] Furthermore, the embodiments of this application use the first... Okay, number Column grid vertices For example, in a planar coordinate system, with the grid vertices as centers, and according to a preset radius value... Draw a circular area according to a preset interval value, such as a central angle interval of 1. This application does not impose specific limitations, but draws rays originating from the center of the circle, and then obtains... The intersection points of each ray and the circle are obtained, thus obtaining the second plane coordinate data of each intersection point in the plane coordinate system, the expression of which is shown in formula (5), and the second geodetic coordinate data of each intersection point in the geodetic coordinate system, the expression of which is shown in formula (6).

[0147] Furthermore, in order to calculate the length deformation between grid vertices and intersections, this embodiment of the application can first calculate the plane length of the line segment formed with grid vertices and intersections as endpoints, and its expression is shown in formula (7).

[0148] In order to calculate the geodetic arc length value corresponding to the plane length value, the embodiment of this application can use the arc length of the geodetic line formed by the two endpoints as a reference, and combine formula (10)-formula (19) to calculate the geodetic arc length value of the line segment in the geodetic coordinate system, the expression of which is shown in formula (8).

[0149] Then calculate The length deformation of the strip is expressed as shown in formula (9).

[0150] Furthermore, the embodiments of this application select The maximum deformation in the edge is taken as the final length deformation at the grid vertex, and its expression is shown in formula (24). Based on the final length deformation, color bands are set in stages, and a deformation heat map is drawn by color rendering, thereby rendering the result. Zhang's projected length deformation field diagram, the schematic diagram of which is shown below. Figure 2 As shown.

[0151] Step 3: Obtain the deformation field of the projection angle.

[0152] In this embodiment, the first planar coordinate data of each grid vertex in the planar coordinate system can be obtained, and its expression is shown in formula (2), and the first geodetic coordinate data of each grid vertex in the geodetic coordinate system can be obtained, and its expression is shown in formula (4).

[0153] Furthermore, the embodiments of this application use the first... Okay, number Column grid vertices For example, in a planar coordinate system, with the grid vertices as centers, and according to a preset radius value... Draw a circular area according to a preset interval value, such as a central angle interval of 1. This application does not impose specific limitations, but draws rays originating from the center of the circle, and then obtains... The intersection points of each ray and the circle are obtained, thus obtaining the second plane coordinate data of each intersection point in the plane coordinate system, the expression of which is shown in formula (5), and the second geodetic coordinate data of each intersection point in the geodetic coordinate system, the expression of which is shown in formula (6).

[0154] Furthermore, in order to calculate the angular deformation between grid vertices and intersections in this embodiment, the planar angle value with grid vertices as vertices can be calculated based on the intersections on the circle in a planar coordinate system. The expression is shown in formula (20). The ellipsoid is expanded to the grid vertex elevation using formula (10), and then the Bessel geodetic theme of formula (8) is used for inverse calculation to obtain the azimuth of the geodetic line formed by the grid vertices and intersections. Thus, the geodetic line angle values ​​for different angles are expressed as shown in formula (21), and then... The angular deformation is expressed as shown in formula (23).

[0155] Furthermore, the embodiments of this application select The maximum deformation among the included angles is taken as the final angular deformation at the grid vertex, and its expression is shown in formula (25). Based on the final angular deformation, color bands are set in stages, and a deformation heat map is drawn by color rendering, thereby rendering the desired result. Zhang's projection angle deformation field diagram, the schematic diagram of which is shown below. Figure 3 As shown.

[0156] The refined projection deformation calculation method based on a three-dimensional traversal grid proposed in this application can divide the projection elevation surface into a grid based on the elevation surface data of at least one projection elevation surface of the area to be measured, thereby generating grid vertices. The method then acquires the first planar coordinate data of each grid vertex in the planar coordinate system and the first geodetic coordinate data in the geodetic coordinate system. A circular region is generated with a certain radius centered on each grid vertex, and corresponding rays are generated at certain intervals from the center. The second planar coordinate data of the intersection point formed by the ray and the circular region in the planar coordinate system and the second geodetic coordinate data in the geodetic coordinate system are identified. The method then calculates the length deformation and / or angular deformation between the grid vertex and the intersection point, thus obtaining the projection deformation result of the projection elevation surface. Through multi-step precise coordinate data acquisition and deformation calculation, the projection deformation of the projection elevation surface of the area to be measured can be comprehensively and accurately evaluated, providing a reliable basis for engineering decisions. This solves the problem that experience-driven sampling inspection evaluation methods in related technologies have significant limitations in engineering projects with significant terrain variations or irregular regional shapes. They may miss cases where projection deformation exceeds the limit, thus creating potential risks for subsequent engineering decisions.

[0157] Next, referring to the accompanying drawings, a refined projection deformation calculation device based on a three-dimensional traversal grid is described according to an embodiment of this application.

[0158] Figure 5 This is a block diagram of a refined projection deformation calculation device based on a three-dimensional traversal grid provided in an embodiment of this application.

[0159] like Figure 5 As shown, the refined projection deformation calculation device 10 based on a three-dimensional traversal grid includes: an acquisition module 100, an identification module 200, and a calculation module 300.

[0160] The acquisition module 100 is used to divide at least one projected elevation surface into a grid based on the elevation surface data of at least one projected elevation surface of the area to be measured, so as to generate at least one grid vertex, and to acquire the first planar coordinate data of at least one grid vertex in the planar coordinate system and the first geodetic coordinate data in the geodetic coordinate system.

[0161] The identification module 200 is used to generate a circular region with at least one grid vertex as the center and a preset radius value, and generate at least one ray from the center according to a preset interval value, and identify the second planar coordinate data of at least one intersection point formed by the at least one ray and the circular region in the plane coordinate system and the second geodetic coordinate data in the geodetic coordinate system.

[0162] The calculation module 300 is used to calculate the length deformation and / or angular deformation between at least one grid vertex and at least one intersection point based on the first plane coordinate data, the first geodetic coordinate data, the second plane coordinate data, and the second geodetic coordinate data, so as to obtain the projection deformation result of at least one projection elevation surface according to the length deformation and / or angular deformation.

[0163] Optionally, in one embodiment of this application, the calculation module 300 includes: a first calculation unit, a second calculation unit, a third calculation unit, and a fourth calculation unit.

[0164] The first calculation unit is used to calculate the planar length value of a line segment formed with at least one grid vertex and at least one intersection point as endpoints, based on the first planar coordinate data and the second planar coordinate data.

[0165] The second calculation unit is used to calculate the starting geodetic data and ending geodetic data of the geodetic line based on the first geodetic coordinate data and the second geodetic coordinate data.

[0166] The third calculation unit is used to calculate the geodetic arc length of a line segment based on the geodetic data of the starting point and the geodetic data of the ending point.

[0167] The fourth calculation unit is used to calculate the length deformation based on the plane length value and the geodetic arc length value.

[0168] Optionally, in one embodiment of this application, the third calculation unit includes: an acquisition subunit, a first calculation subunit, and a second calculation subunit.

[0169] The acquisition sub-unit is used to acquire the origin-normalized latitude data and the destination-normalized latitude data based on the origin-geometry data and the destination-geometry data.

[0170] The first calculation subunit is used to calculate the positive azimuth value of the positive geodetic azimuth based on the origin-normalized latitude data and the destination-normalized latitude data, and to calculate the negative azimuth value of the negative geodetic azimuth based on the positive azimuth value.

[0171] The second calculation subunit is used to calculate the geodetic arc length based on the positive azimuth angle value, the negative azimuth angle value, the starting geodetic data, and the ending geodetic data.

[0172] Optionally, in one embodiment of this application, the first computing subunit includes: a first computing component, a second computing component, and a generation component.

[0173] The first calculation sub-component is used to calculate the angular distance value of the spherical angular distance based on the positive azimuth angle value.

[0174] The second calculation sub-component is used to calculate the correction for spherical longitude difference based on the angular distance value and the positive azimuth value.

[0175] Generate a sub-component to obtain the reverse azimuth value based on the positive azimuth value in response to a correction value being less than a preset correction value.

[0176] Optionally, in one embodiment of this application, the calculation module 300 includes: an identification unit, a fourth calculation unit, and a fifth calculation unit.

[0177] The identification unit is used to identify the plane angle value of the angle formed between at least one grid vertex and at least one intersection point based on the first plane coordinate data and the second plane coordinate data.

[0178] The fourth calculation unit is used to calculate the geodetic angle value based on the positive azimuth value.

[0179] The fifth calculation unit is used to calculate the angular deformation based on the plane angle value and the geodetic angle value.

[0180] Optionally, in one embodiment of this application, the calculation module 300 includes: a first generation unit and a second generation unit.

[0181] The first generating unit is used to obtain the final length deformation amount in response to the length deformation amount being greater than the preset length deformation amount.

[0182] The second generation unit is used to obtain the projection deformation result based on the final length deformation.

[0183] Optionally, in one embodiment of this application, the calculation module includes a third generation unit and a fourth generation unit.

[0184] The third generation unit is used to obtain the final angle deformation amount in response to the angle deformation amount being greater than the preset angle deformation amount.

[0185] The fourth generation unit is used to obtain the projection deformation result based on the final angular deformation amount.

[0186] Optionally, in one embodiment of this application, the formula for calculating the length deformation may be, but is not limited to, the following:

[0187] ,

[0188] in, Indicates the amount of length deformation; Represents length in a planar coordinate system; Indicates the arc length of a geodetic line in a geodetic coordinate system; superscript , … Indicates the central angle; subscript This indicates the row and column number of the grid vertex.

[0189] The formula for calculating angular deformation can be, but is not limited to, the following:

[0190] ,

[0191] in, Indicates the amount of angular deformation; Represents the angle between planes in a planar coordinate system; Indicates the angle between geodesics in a geodetic coordinate system; the superscript indicates the two central angles corresponding to the two sides forming the angle; the subscript indicates the angle between geodesics. This indicates the row and column number of the grid vertex corresponding to the included angle vertex.

[0192] It should be noted that the foregoing explanation of the embodiment of the refined projection deformation calculation method based on three-dimensional traversal grid also applies to the refined projection deformation calculation device based on three-dimensional traversal grid in this embodiment, and will not be repeated here.

[0193] The refined projection deformation calculation device based on a three-dimensional traversal grid proposed in this application can divide the projection elevation surface into a grid based on the elevation surface data of at least one projection elevation surface of the area to be measured, thereby generating grid vertices. It then acquires the first planar coordinate data of the grid vertices in the planar coordinate system and the first geodetic coordinate data in the geodetic coordinate system. A circular region is generated with the grid vertices as centers and a certain radius. Corresponding rays are generated from the centers at certain intervals. The second planar coordinate data of the intersection points formed by the rays and the circular regions in the planar coordinate system and the second geodetic coordinate data in the geodetic coordinate system are identified. The device then calculates the length deformation and / or angular deformation between the grid vertices and the intersection points, thereby obtaining the projection deformation result of the projection elevation surface. Through multi-step precise coordinate data acquisition and deformation calculation, the projection deformation of the projection elevation surface of the area to be measured can be comprehensively and accurately evaluated, providing a reliable basis for engineering decisions. This solves the problem that experience-driven sampling inspection evaluation methods in related technologies have significant limitations in engineering projects with significant terrain variations or irregular regional shapes. They may miss cases where projection deformation exceeds the limit, thus creating potential risks for subsequent engineering decisions.

[0194] Figure 6 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. The electronic device may include:

[0195] The memory 601, the processor 602, and the computer program stored on the memory 601 and capable of running on the processor 602.

[0196] When the processor 602 executes the program, it implements the refined projection deformation calculation method based on a three-dimensional traversal grid provided in the above embodiments.

[0197] Furthermore, electronic devices also include:

[0198] Communication interface 603 is used for communication between memory 601 and processor 602.

[0199] The memory 601 is used to store computer programs that can run on the processor 602.

[0200] The memory 601 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0201] If the memory 601, processor 602, and communication interface 603 are implemented independently, then the communication interface 603, memory 601, and processor 602 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 6 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0202] Optionally, in a specific implementation, if the memory 601, processor 602, and communication interface 603 are integrated on a single chip, then the memory 601, processor 602, and communication interface 603 can communicate with each other through an internal interface.

[0203] The processor 602 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0204] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for calculating refined projection deformation based on a three-dimensional traversal grid.

[0205] This application also provides a computer program product, including a computer program that, when executed, implements the above-described method for calculating refined projection deformation based on a three-dimensional traversal grid.

[0206] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0207] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0208] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0209] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0210] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or more of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0211] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0212] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0213] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A method for calculating a refined projection deformation based on a three-dimensional traversed grid, characterized in that, Includes the following steps: Based on the elevation surface data of at least one projected elevation surface of the area to be measured, the at least one projected elevation surface is divided into grids to generate at least one grid vertex, and the first planar coordinate data of the at least one grid vertex in the plane coordinate system and the first geodetic coordinate data in the geodetic coordinate system are obtained respectively, wherein the projected elevation surface is obtained by dividing the terrain undulation data of the area to be measured. A circular region is generated with the at least one grid vertex as the center and a preset radius value. Starting from the center, at least one ray is generated at a preset interval value. The second plane coordinate data and the second geodetic coordinate data of the at least one intersection point formed by the at least one ray and the circular region are identified in the plane coordinate system and the geodetic coordinate system. The azimuth angle of the ray is distributed in the range of 0° to 360° according to the preset interval value. Based on the first planar coordinate data, the first geodetic coordinate data, the second planar coordinate data, and the second geodetic coordinate data, calculate the length deformation and / or angular deformation between the at least one grid vertex and the at least one intersection point, so as to obtain the projection deformation result of the at least one projection elevation surface according to the length deformation and / or the angular deformation. The step of obtaining the projection deformation result of the at least one projection elevation surface based on the length deformation and / or the angle deformation includes: In response to the length deformation being greater than a preset length deformation, the final length deformation is obtained; The projection deformation result is obtained based on the final length deformation amount; The expression for the final length deformation is as follows: ， wherein denotes the length deformation; superscript , , denotes the central angle; subscript denotes the row number, column number of the grid vertex; The step of obtaining the projection deformation result of the at least one projection elevation surface based on the length deformation and / or the angle deformation includes: In response to the angle deformation being greater than a preset angle deformation, the final angle deformation is obtained; The projection deformation result is obtained based on the final angular deformation amount; The expression for the final angular deformation is as follows: ， in, Indicates the amount of angular deformation; superscript indicates the two central angles corresponding to the two sides forming the included angle; subscript indicates the amount of angular deformation. This indicates the row and column number of the grid vertex corresponding to the included angle vertex.

2. The method according to claim 1, characterized in that, The step of calculating the length deformation between at least one grid vertex and at least one intersection point based on the first planar coordinate data, the first geodetic coordinate data, the second planar coordinate data, and the second geodetic coordinate data includes: Based on the first planar coordinate data and the second planar coordinate data, calculate the planar length value of the line segment formed with the at least one grid vertex and the at least one intersection point as endpoints; Based on the first geodetic coordinate data and the second geodetic coordinate data, calculate the geodetic data of the starting point and the geodetic data of the ending point of the geodetic line; Based on the geodetic data of the starting point and the geodetic data of the ending point, calculate the geodetic arc length of the line segment; The length deformation is calculated based on the plane length value and the earth line arc length value.

3. The method according to claim 2, characterized in that, The calculation of the geodetic arc length of the line segment based on the starting point geodetic data and the ending point geodetic data includes: Based on the starting point geodetic data and the ending point geodetic data, obtain the starting point normalized latitude data and the ending point normalized latitude data; Based on the origin-normalized latitude data and the destination-normalized latitude data, calculate the positive azimuth value of the positive geodetic azimuth, and calculate the negative azimuth value of the negative geodetic azimuth based on the positive azimuth value. The geodetic arc length is calculated based on the positive azimuth value, the negative azimuth value, the starting geodetic data, and the ending geodetic data.

4. The method according to claim 3, characterized in that, The step of calculating the reverse azimuth value of the reverse geodetic azimuth based on the positive azimuth value includes: Based on the positive azimuth angle value, calculate the angular distance value of the spherical angular distance; Based on the angular distance value and the positive azimuth value, calculate the correction for the spherical longitude difference; In response to the correction value being less than a preset correction value, the negative azimuth value is obtained based on the positive azimuth value.

5. The method according to claim 3, characterized in that, The step of calculating the angular deformation between at least one grid vertex and at least one intersection point based on the first planar coordinate data, the first geodetic coordinate data, the second planar coordinate data, and the second geodetic coordinate data includes: Based on the first planar coordinate data and the second planar coordinate data, identify the planar angle value of the angle formed between the at least one grid vertex and the at least one intersection point; Based on the positive azimuth angle value, calculate the geodetic angle value of the included angle; The angular deformation is calculated based on the plane angle value and the earth line angle value.

6. The method according to claim 1, characterized in that, in, The formula for calculating the length deformation is: ， in, Indicates the amount of length deformation; Represents length in a planar coordinate system; Indicates the arc length of a geodetic line in a geodetic coordinate system; superscript , … Indicates the central angle; subscript Indicates the row and column number of the grid vertex; The formula for calculating the angular deformation is: ， in, Indicates the amount of angular deformation; Represents the angle between planes in a planar coordinate system; Indicates the angle between geodesics in a geodetic coordinate system; the superscript indicates the two central angles corresponding to the two sides forming the angle; the subscript indicates the angle between geodesics. This indicates the row and column number of the grid vertex corresponding to the included angle vertex.

7. A computer program product, characterized in that, Includes a computer program, which, when executed, is used to implement the refined projection deformation calculation method based on a three-dimensional traversal grid as described in any one of claims 1-6.

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