Mercator Projection Method and Device for Controlling Engineering Projection Deformation Based on Axis Control

Abstract

The present disclosure provides a Mercator projection method and apparatus for controlling engineering projection deformation based on an axis, which relates to the technical field of engineering surveying. The method includes: determining the latitude range of an engineering survey area and the measurement points of an engineering preset axis, where the measurement points include the southern end point and the northern end point of the latitude range; estimating the Mercator projection length deformation of each measurement point of the engineering preset axis based on the latitudes of each measurement point of the engineering preset axis; determining the target latitude line with the minimum total Mercator projection length deformation of the engineering preset axis within the latitude range as the standard latitude line; and performing Mercator projection on the engineering preset axis within the engineering survey area based on the latitude of the standard latitude line. Based on this technical solution, projection parameters that meet the requirements of engineering projection deformation tolerances can be quickly obtained for projection.

Description

Technical Field

[0001] The present disclosure relates to the technical field of engineering surveying, and in particular, to a Mercator projection method and device for controlling engineering projection deformation based on an axis. Background Art

[0002] With the development of engineering surveying technology, more and more large-scale projects are being implemented, and the requirements for project construction are also getting higher and higher.

[0003] Generally, for the convenience of engineering use, during the engineering survey process, it is necessary to project the edges on the sphere onto a developable surface, and then expand it to determine the engineering control network points for engineering layout. However, map projection will cause deformation, and Mercator projection will cause length deformation. In order to ensure the accuracy of the coordinates of the engineering control network points, it is necessary to limit the degree of length deformation caused by the projection. Generally, the engineering survey requires that the difference between the side length directly calculated from the projected control point coordinates and the side length measured on the ground meets the engineering requirements. When the length deformation cannot meet the engineering requirements, some treatment means are needed to improve the length deformation of the edges within the engineering survey area.

[0004] However, at present, many treatment means have high computational complexity and long time consumption when improving the length deformation. Therefore, there is an urgent need for a treatment method that can quickly obtain projection parameters that meet the requirements of the engineering projection deformation tolerance for projection.

[0005] It should be noted that the information disclosed in the above background art section is only used to enhance the understanding of the background of the present disclosure, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0006] To overcome the problems existing in the related art, embodiments of the present disclosure provide a Mercator projection method and device for controlling engineering projection deformation based on an axis, which can quickly obtain projection parameters that meet the requirements of the engineering projection deformation tolerance for projection.

[0007] According to a first aspect of an embodiment of the present disclosure, there is provided a Mercator projection method for controlling engineering projection deformation based on an axis, the method including: determining the latitude range of the engineering survey area and the measurement points of the engineering preset axis, the measurement points including the south end point and the north end point of the latitude range; estimating the Mercator projection length deformation of each measurement point of the engineering preset axis based on the latitude of each measurement point of the engineering preset axis; determining a target latitude line with the smallest total Mercator projection length deformation of the engineering preset axis within the latitude range as the standard latitude line; performing Mercator projection on the engineering preset axis within the engineering survey area based on the latitude of the standard latitude line.

[0008] Optionally, after estimating the Mercator projection length deformation of each measurement point based on the latitude of each measurement point on the project preset axis, the method further includes: estimating the total Mercator projection length deformation of the project preset axis based on the estimated Mercator projection length deformation of each measurement point.

[0009] Optionally, when the total number of measurement points is greater than or equal to the first threshold, based on the first preset formula, estimate the Mercator projection length deformation of the measurement point with a latitude of B i , the first preset formula includes: ; where B 0 represents the latitude of the target parallel, B i represents the latitude at the i th measurement point of the project preset axis.

[0010] Optionally, based on the estimated Mercator projection length deformation of each measurement point and the second preset formula, estimate the total Mercator projection length deformation of the project preset axis; the second preset formula includes: ; where B N represents the latitude at the north end point of the project preset axis, B S represents the latitude at the south end point of the project preset axis.

[0011] Optionally, based on the estimated Mercator projection length deformation of each measurement point and the third preset formula, estimate the total Mercator projection length deformation of the project preset axis; the third preset formula includes: ; where B N represents the latitude at the north end point of the project preset axis, B S represents the latitude at the south end point of the project preset axis.

[0012] Optionally, based on the target formula, determine the target parallel with zero total Mercator projection length deformation of the project preset axis within the latitude range as the standard parallel; where the target formula is the second preset formula or the third preset formula; the latitude of the target parallel with zero total Mercator projection length deformation of the project preset axis is .

[0013] Optionally, when the total number of measurement points is less than the first threshold, based on the fourth preset formula, estimate the Mercator projection length deformation of the i th measurement point; the fourth preset formula includes: ; n is the total number of measurement points of the project preset axis, Indicates the measurement error; based on the estimated Mercator projection length deformation of each measurement point and the fifth preset formula, when the iterative stop condition is met, the target latitude line with the minimum total Mercator projection length deformation of the engineering preset axis within the latitude range is determined as the standard latitude line; the fifth preset formula includes: 。

[0014] According to the second aspect of the embodiments of the present disclosure, a Mercator projection device for controlling engineering projection deformation based on an axis is provided. The Mercator projection device for controlling engineering projection deformation based on an axis includes: a measurement point determination module, a length deformation estimation module, a standard latitude line determination module, and a projection module; the measurement point determination module is configured to determine the latitude range of the engineering measurement area and the measurement points of the engineering preset axis; the length deformation estimation module is configured to estimate the Mercator projection length deformation of each measurement point of the engineering preset axis based on the latitude of each measurement point of the engineering preset axis; the standard latitude line determination module is configured to determine the target latitude line with the minimum total Mercator projection length deformation of the engineering preset axis within the latitude range as the standard latitude line; the projection module is configured to perform a Mercator projection on the engineering preset axis within the engineering measurement area based on the latitude of the standard latitude line.

[0015] Optionally, the length deformation estimation module is specifically configured to, after estimating the Mercator projection length deformation of each measurement point based on the latitude of each measurement point of the engineering preset axis, estimate the total Mercator projection length deformation of the engineering preset axis based on the estimated Mercator projection length deformation of each measurement point.

[0016] Optionally, the length deformation estimation module is specifically configured to, when the total number of measurement points is greater than or equal to the first threshold, estimate the Mercator projection length deformation of the measurement point with a latitude of B i based on the first preset formula, and the first preset formula includes: ; where B 0 represents the latitude of the target latitude line, B i represents the latitude at the i th measurement point of the engineering preset axis.

[0017] Optionally, the length deformation estimation module is specifically configured to estimate the total Mercator projection length deformation of the engineering preset axis based on the estimated Mercator projection length deformation of each measurement point and the second preset formula; the second preset formula includes: ; where B N represents the latitude at the north end point of the engineering preset axis, B S represents the latitude at the south end point of the engineering preset axis.

[0018] Optionally, the length deformation estimation module is specifically configured to estimate the total Mercator projection length deformation of the engineering preset axis based on the estimated Mercator projection length deformation of each measurement point and a third preset formula; the third preset formula includes: ; where B N represents the latitude at the north end point of the engineering preset axis, B S represents the latitude at the south end point of the engineering preset axis.

[0019] Optionally, the standard latitude determination module is specifically configured to determine, based on a target formula, that the target latitude where the total Mercator projection length deformation of the engineering preset axis within the latitude range is zero is the standard latitude; where the target formula is the second preset formula or the third preset formula; the latitude of the target latitude where the total Mercator projection length deformation of the engineering preset axis is zero is .

[0020] Optionally, the length deformation estimation module is specifically configured to, when the total number of measurement points is less than a first threshold, estimate the Mercator projection length deformation of the i th measurement point based on a fourth preset formula; the fourth preset formula includes: ; n is the total number of measurement points of the engineering preset axis, represents the measurement error; the standard latitude determination module is specifically configured to, based on the estimated Mercator projection length deformation of each measurement point and a fifth preset formula, when the iteration stop condition is met, determine that the target latitude where the total Mercator projection length deformation of the engineering preset axis within the latitude range is the smallest is the standard latitude; the fifth preset formula includes: .

[0021] According to a third aspect of the embodiments of the present disclosure, there is provided a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the Mercator projection method for controlling engineering projection deformation based on an axis as described in the first aspect is implemented.

[0022] According to a fourth aspect of the embodiments of the present disclosure, there is provided a computer device, a memory, a processor, and computer-readable instructions stored on the memory and executable on the processor, where when the computer-readable instructions are executed by the processor, the Mercator projection method for controlling engineering projection deformation based on an axis as described in the first aspect is implemented.

[0023] The technical solutions provided by the embodiments of the present disclosure may include the following beneficial effects:

[0024] In the disclosed embodiment, first, the latitude range of the engineering survey area is determined, and then measurement is performed based on the preset axis of the engineering within the latitude range to obtain the latitude of each measurement point, and based on the latitude of each measurement point, the Mercator projection length deformation of each measurement point of the preset axis of the engineering is estimated in advance, and the latitude with the smallest total length deformation of the Mercator projection within the latitude range is determined as the standard latitude for the final Mercator projection based on the preset axis of the engineering, and then the final Mercator projection is performed based on the standard latitude. On the one hand, since the estimation is based on the length deformation of the selected axis (i.e., the preset axis of the project), compared with the method of estimating the deformation of the projection area in the related art, the processing speed is fast and the complexity is low, which can improve the speed of determining the standard parallel; on the other hand, in the embodiment disclosed in the present invention, only the latitude of each measuring point within the latitude range is concerned, and there is no need to introduce longitude for deformation estimation. The calculation complexity is low, the accuracy is high, and it is closer to the actual deformation. The difference between the side length directly calculated based on the control point coordinates after projection and the side length obtained by field measurement can meet the engineering requirements, and the coordinates of the engineering control points can be guaranteed, which is convenient for layout in various stages of the project, so that the linear engineering penetration with high requirements for projection deformation can be more accurate and the probability of misalignment at the penetration point can be reduced.

[0025] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate embodiments consistent with the present disclosure and, together with the description, serve to explain the principles of the present disclosure.

[0027] Figure 1 A schematic diagram of the system architecture of a Mercator projection method based on axis-controlled engineering projection deformation provided in an embodiment of the present disclosure.

[0028] Figure 2 A flow chart of a Mercator projection method based on axis-controlled engineering projection deformation provided in an embodiment of the present disclosure.

[0029] Figure 3 A schematic diagram of the length deformation of a Mercator projection provided in an embodiment of the present disclosure.

[0030] Figure 4 A schematic diagram of the penetration condition of a linear project provided in an embodiment of the present disclosure.

[0031] Figure 5 A hardware structure diagram of a computer device in which a Mercator projection device for controlling engineering projection deformation based on axis lines is located according to an embodiment of the present disclosure.

[0032] Figure 6Schematic diagram of a Mercator projection device based on axis control for engineering projection deformation provided by an embodiment of the present disclosure. Detailed implementation manners

[0033] Here, exemplary embodiments will be described in detail, and examples thereof are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementation manners described in the following exemplary embodiments do not represent all implementation manners consistent with the present disclosure. On the contrary, they are merely examples of devices and methods consistent with some aspects of the present disclosure as detailed in the appended claims.

[0034] The terms used in the present disclosure are only for the purpose of describing specific embodiments and are not intended to limit the present disclosure. The singular forms "a", "the", and "said" used in the present disclosure and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0035] It should be understood that although the terms first, second, third, etc. may be used in the present disclosure to describe various information, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present disclosure, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "when" or "while" or "in response to determining".

[0036] Next, the embodiments of the present disclosure will be described in detail.

[0037] Figure 1 The schematic diagram of the system architecture of a Mercator projection method based on axis control for engineering projection deformation to which the embodiments of the present disclosure can be applied is shown.

[0038] As Figure 1 shown, the system architecture 100 may include one or more of terminal devices such as a smart phone 101, a portable computer 102, a desktop computer 103, etc., a network 104, and a server 105. The network 104 is used to provide a medium for a communication link between the terminal device and the server 105. The network 104 may include various connection types, such as wired, wireless communication links, or fiber optic cables, etc.

[0039] The terminal device can be various electronic devices with data processing functions. There is a display screen on the electronic device, and the display screen is used to show the latitude of the measurement point, the measured area, the projection result of the engineering preset axis based on the obtained standard latitude, etc. The electronic device includes, but is not limited to, the above-mentioned desktop computers, portable computers, smart phones, tablet computers, and so on.

[0040] It should be understood that Figure 1 the numbers of the terminal devices, networks, and servers in

[0041] The Mercator projection method for controlling engineering projection deformation based on the axis provided by the embodiments of the present disclosure can be executed by the terminal device. Correspondingly, the Mercator projection device for controlling engineering projection deformation based on the axis can be set in the terminal device. However, those skilled in the art can easily understand that the Mercator projection method for controlling engineering projection deformation based on the axis provided by the embodiments of the present disclosure can also be executed by the server 105. Correspondingly, the Mercator projection device for controlling engineering projection deformation based on the axis can also be set in the server 105. No special limitation is made in this exemplary embodiment.

[0042] The embodiments of the present disclosure limit the side length deformation through the minimum condition of side length projection deformation, providing a more scientific and accurate calculation method for engineering survey. This method is applicable to projects with high requirements for side length projection deformation, such as the penetration of linear projects, such as the penetration of long-distance water diversion and power generation tunnels, railways, undersea tunnels, cross-sea bridges, etc., and can effectively meet the project requirements.

[0043] As Figure 2 shown, Figure 2 is a schematic flowchart of a Mercator projection method for controlling engineering projection deformation based on the axis provided by the embodiments of the present disclosure, including the following steps:

[0044] S201. Determine the latitude range of the engineering survey area and the measurement points of the engineering preset axis.

[0045] Exemplarily, the engineering preset axis can be an axis selected by the staff based on the actual project, and can be selected according to the project requirements. In the embodiments of the present disclosure, the position of the engineering preset axis can be changed, and after the change, the standard latitude can be determined again.

[0046] Optionally, the engineering preset axis can be a straight line, a broken line with at least one inflection point, or a curve. No specific limitation is made in the embodiments of the present disclosure.

[0047] It should be noted that the embodiment of the present disclosure does not specifically limit the specific selection of the preset engineering axis. It mainly estimates the Mercator projection deformation based on the selected preset engineering axis to obtain the standard latitude where the total length deformation of the Mercator projection of the preset engineering axis (also called the total projection length deformation) is the smallest.

[0048] Usually, for the penetration of some linear projects, such as long-distance water diversion and power generation tunnels, railways, undersea tunnels, cross-sea bridges, etc., the requirements for the projection deformation value of the preset axis side length of the project are relatively high. The smaller the total length deformation value of the Mercator projection of the selected axis side length, the smaller the deviation after subsequent projection, and the higher the accuracy of the penetration.

[0049] It should be noted that in actual measurement applications, the actual measurement points can be selected on the preset axis of the project or near the preset axis of the project. For example, for some inaccessible locations, the locations to the east or west of the preset axis of the project can be selected as the actual measurement points for measurement, that is, the actual measurement points may not all be on the preset axis of the project.

[0050] Among them, the measuring points include the southern end point and the northern end point of the latitude range, as well as the measuring points located on the preset axis of the project and the measuring points located near the preset axis of the project.

[0051] It should be noted that the deformation of the Mercator projection (here refers to the Orthotropic Mercator projection) is generally related to latitude but not longitude.

[0052] S202, estimating the Mercator projection length deformation of each measuring point on the preset axis of the project based on the latitude of each measuring point on the preset axis of the project.

[0053] It should be noted that in the embodiment of the present disclosure, the length deformation of the Mercator projection of each measuring point can be estimated first. The length deformation of the Mercator projection is a variable related to the selection of the standard latitude. Therefore, the determined length deformation of the Mercator projection is a deformation relationship related to the standard latitude and the latitude of the measuring point.

[0054] It should be noted that in the disclosed embodiment, the orthographic Mercator projection is used in the engineering projection. Before the projection is performed, the standard latitude with the smallest deformation of the total length of the Mercator projection is determined, that is, the projection deformation is associated with the standard latitude. Therefore, before the map projection (i.e., Mercator projection) is performed, the estimated Mercator projection length deformation of each measuring point of the preset axis of the project is a variable, which is related to the latitude of the standard latitude that needs to be determined. Based on the Mercator projection length deformation of each measuring point, the dimension of the latitude with the smallest deformation of the total length of the Mercator projection of the preset axis of the project can be determined. In the project, the standard latitude selected based on the preset axis of the project is the latitude corresponding to the latitude with the smallest deformation of the total length of the Mercator projection of the preset axis of the project.

[0055] S203, determining the target latitude line with the smallest total length deformation of the Mercator projection of the preset axis of the project within the latitude range as the standard latitude line.

[0056] Among them, the Mercator projection length deformation of each measuring point of the selected axis is the length deformation of the line segment between the measuring point and the measuring point adjacent to the measuring point projected onto the projection surface through the Mercator projection method, and the total Mercator projection length deformation of the selected axis is the length deformation of the selected axis projected onto the projection surface through the Mercator projection method.

[0057] It should be noted that two latitudes can be obtained according to calculation, one in the southern hemisphere and one in the northern hemisphere, and the latitude corresponding to the latitude within the latitude range of the preset axis of the project is determined as the target latitude.

[0058] It should be noted that when the cylindrical surface selected by the Mercator projection is tangent to the earth, there is one standard parallel with a latitude of 0°, and the projection length deformation in the rest of the latitude range is positive deformation; when the cylindrical surface selected by the Mercator projection is intersecting with the earth, there are two standard parallels, one in the southern and northern hemispheres, and the projection length deformation is negative between the standard parallels (the standard parallels indicate the area corresponding to the latitude circle) and positive outside the standard parallels. In general, the measurement area includes only one standard parallel. Taking the northern hemisphere as an example, the projection length deformation in the measurement area south of the standard parallel is negative, and the projection length deformation in the measurement area north of the standard parallel is positive.

[0059] The smaller the deformation of the estimated total length of the Mercator projection of the preset axis of the project, the more accurate the subsequent engineering calculations based on the determined standard latitude projection will be, so that the linear project can be accurately connected and the probability of staggered connection at the joint when the two ends start construction at the same time will be reduced.

[0060] S204. Based on the latitude of the standard parallel, perform Mercator projection on the preset axis of the project within the project survey area.

[0061] It should be noted that in the embodiment of the present disclosure, after estimating the standard parallel, Mercator projection within the engineering measurement area can be performed based on the standard parallel. Since the standard parallel is the parallel with the smallest deformation of the total length of the Mercator projection estimated based on the latitudes of each measuring point within the latitude range of the preset axis of the project, after obtaining the standard parallel, performing Mercator projection based on the standard parallel can make the accuracy of the linear project based on the preset axis of the project at this latitude higher during actual construction.

[0062] Figure 3 A schematic diagram of the length deformation of a Mercator projection provided by an embodiment of the present disclosure, such as Figure 3As shown in , taking the earth as a sphere as an example, the center O of the earth coincides with the center of the cylinder, where the latitude range of the preset axis of the project is [ B S , B N ]. Among them, the latitude value is B S Edge L S Projected onto the cylinder as the edge , the side length is negatively deformed; the latitude value is B i1 Edge L i1 Projected onto the cylinder as the edge , the side length is negatively deformed; the latitude value is B 0 (standard latitude) L 0 is projected onto the cylinder as an edge , the side length is not deformed; the latitude value is B i2 Edge L i2 Projected onto the cylinder as the edge , the side length undergoes positive deformation; the latitude value is B N Edge L N Projected onto the cylinder as the edge , the side length undergoes positive deformation.

[0063] Figure 4 A schematic diagram of the penetration of a linear project provided by an embodiment of the present disclosure is shown. The smaller the total length deformation of the Mercator projection of the preset axis of the project is, the higher the accuracy of the penetration is. Figure 4 As shown in (a), construction is being carried out from both the south and north boundaries, and the project can be accurately penetrated at the expected penetration point. The greater the total length deformation of the Mercator projection of the preset axis of the project, the lower the accuracy of the penetration. For example, Figure 4 As shown in (b), construction was carried out simultaneously from the south boundary and the north boundary, resulting in a misalignment problem at the expected penetration point.

[0064] The disclosed embodiment provides a Mercator projection method for controlling the deformation of engineering projection based on an axis line. First, the latitude range of the engineering survey area is determined. Then, measurement is performed based on a preset engineering axis line within the latitude range to obtain the latitude of each measurement point. Based on the latitude of each measurement point, the total length deformation of the Mercator projection of the preset engineering axis line is estimated. The latitude with the smallest total length deformation is determined as the latitude of the standard latitude for the final Mercator projection based on the preset engineering axis line. Then, the final Mercator projection is performed based on the standard latitude line. On the one hand, since the estimation is based on the length deformation of the selected axis (i.e., the preset axis of the project), compared with the method of calculating the projection area deformation in the related art, the processing speed is fast and the complexity is low, which can improve the speed and efficiency of determining the standard parallel; on the other hand, in the embodiment disclosed in the present invention, only the latitude of each measuring point within the latitude range of the preset axis of the project is concerned, and there is no need to introduce longitude for deformation estimation. The complexity is low, the accuracy is high, and it is closer to the actual deformation. The difference between the side length directly calculated based on the coordinates of the control points after projection and the side length obtained by field measurement can meet the engineering requirements, and the coordinates of the engineering control points can be guaranteed, which is convenient for layout in various stages of the project, thereby making the accuracy of linear engineering with high requirements on side length projection deformation higher and reducing the probability of misalignment at the penetration point.

[0065] It should be noted that the disclosed embodiment provides three different methods for estimating the standard parallel that minimizes the total length deformation of the Mercator projection of the preset axis of the project, wherein, when enough actual measurement points can be obtained, the Mercator projection length deformation of each measurement point is first estimated, and then based on the Mercator projection length deformation of each measurement point, the total length deformation of the Mercator projection of the preset axis of the project is estimated by the method of method one. When the number of actual measurement points that can be obtained is limited, the Mercator projection length deformation of each measurement point can be estimated first in combination with the measurement error, and then the matrix composed of the Mercator projection length deformation of each measurement point is processed based on the least squares method to directly determine the total length deformation of the Mercator projection of the preset axis of the project, that is, the processing method of method two.

[0066] Method 1:

[0067] Optionally, in the Mercator projection method based on axis control engineering projection deformation provided by the embodiment of the present disclosure, after the above S202, the following S205 may be further performed:

[0068] S205. Based on the estimated Mercator projection length deformation of each measuring point, estimate the total Mercator projection length deformation of the preset axis of the project.

[0069] It can be understood that the more measurement points there are, the more accurate the estimation of the total length deformation of the Mercator projection is, and the closer it is to the actual projection deformation.

[0070] Based on this solution, the Mercator projection length deformation of each measurement point (i.e., each latitude value) within the latitude range of the engineering axis can be estimated first, and then the total Mercator projection length deformation of the engineering preset axis can be estimated based on the estimated Mercator projection length deformation of each measurement point, so that the deformation closer to the actual projection can be accurately obtained, making the determined standard latitude more in line with the engineering requirements.

[0071] Specifically, in the first method, after determining the Mercator projection length deformation of each measurement point, the total Mercator projection length deformation of the engineering preset axis can be estimated through two processing methods, including the following first processing method (direct summation) and the second processing method (single integral).

[0072] Optionally, in the Mercator projection method for controlling engineering projection deformation based on the axis provided in the embodiments of the present disclosure, the above-mentioned S202 can be specifically executed through the following S202a:

[0073] S202a. When the total number of measurement points is greater than or equal to the first threshold, based on the first preset formula, estimate the Mercator projection length deformation of the measurement point with latitude B i .

[0074] ; Formula (1)

[0075] Where B i represents the latitude at the i th measurement point of the engineering preset axis, B 0 represents the latitude of the target latitude line.

[0076] It should be noted that in the embodiments of the present disclosure, in order to simplify the calculation, the earth ellipsoid is regarded as a sphere, where can represent the projection length ratio at each measurement point on the earth, represents the distance from the measurement point located on the standard latitude line to the Mercator projection axis, represents the distance from the measurement point with latitude B i to the Mercator projection axis. The Mercator projection axis indicates the central axis of the cylinder used in the Mercator projection, and this central axis coincides with the earth's axis.

[0077] Furthermore, in the first processing method, the above-mentioned S205 can be executed through the following S205a:

[0078] S205a. Based on the estimated Mercator projection length deformation of each measurement point and Formula (2), estimate the total Mercator projection length deformation of the engineering preset axis.

[0079] ; Formula (2)

[0080] Wherein, B N represents the latitude at the north end point of the project - preset axis, B S represents the latitude at the south end point of the project - preset axis.

[0081] Based on this scheme, the total Mercator projection length deformation of the project - preset axis can be determined based on the sum of the Mercator projection length deformations of each measurement point. When the latitudes of a large number of actual measurement points can be obtained, the more the number of measurement points, the more accurate the total Mercator projection length deformation of the project - preset axis estimated by summation. Thus, the subsequent estimated standard latitude is more accurate, and an accurate standard latitude can be quickly obtained when the number of measurement points is large.

[0082] Optionally, in the second processing method, in the Mercator projection method for controlling engineering projection deformation based on the axis provided in the embodiments of the present disclosure, the above - mentioned S205 can be specifically executed through the following S205b:

[0083] S205b. Estimate the total Mercator projection length deformation of the project - preset axis based on the sum of the Mercator projection length deformations of each estimated measurement point and Formula (3).

[0084] ; Formula (3)

[0085] Based on this scheme, when the number of measurement points within the latitude range that can be obtained for the project - preset axis is large enough, the total Mercator projection length deformation on the project - preset axis can be quickly and accurately determined in the above - mentioned integral form according to the Mercator projection length deformation of each estimated measurement point.

[0086] After estimating the total Mercator projection length deformation on the above - mentioned project - preset axis through the above two processing methods, since the error of the projection length deformation estimated based on a sufficient number of measurement points is small and the accuracy is high, therefore, based on the above - mentioned and estimate the latitude when the total Mercator projection length deformation is 0.

[0087] Optionally, in the Mercator projection method for controlling engineering projection deformation based on the axis provided in the embodiments of the present disclosure, the above - mentioned S203 can be executed through the following S203a:

[0088] S203a. Determine the target latitude at which the total Mercator projection length deformation of the project - preset axis within the latitude range is zero based on the target formula as the standard latitude.

[0089] Wherein, the target formula is the above - mentioned Formula (2) or Formula (3).

[0090] Specifically, for the solution formula (4) or formula (5), B 0 can estimate the target latitude where the total length deformation of the Mercator projection of the engineering preset axis is zero. The latitude of the specifically determined standard latitude is the following formula (6).

[0091] ; formula (4)

[0092] ; formula (5)

[0093] ; formula (6)

[0094] It can be understood that in this case, the latitude of the final target latitude is only related to the latitude range of the engineering preset axis. That is, in the case of estimation based on this scheme, the standard latitude can be quickly obtained based on the latitude range.

[0095] Based on this scheme, if the total length deformation of the Mercator projection of the engineering preset axis is estimated based on the above two processing methods, when the number of measurement points exceeds the preset number, a target latitude with zero overall deformation (the length deformation being zero is the minimum length deformation, that is, there are positive and negative deformations at the measurement points on both sides of the standard latitude, and the sum of the overall deformations is zero) can be obtained. Then, the latitude of the target latitude where the total length deformation of the Mercator projection of the engineering preset axis is zero can be quickly obtained based on the target formula.

[0096] Method 2:

[0097] Optionally, in the Mercator projection method for controlling engineering projection deformation based on an axis provided in the embodiments of the present disclosure, when the actual measurement points within the latitude range (i.e., within the interval) of the engineering preset axis (i.e., the selected axis) that can be obtained are limited, the standard latitude can be determined based on the least squares method. That is, S202 in the above method can further include S202b below. Furthermore, S203 above can further include S203b below:

[0098] S202b. When the total number of measurement points is less than the first threshold, based on formula (7), estimate the Mercator projection length deformation of the i th measurement point.

[0099] ; formula (7)

[0100] Wherein, n is the total number of measurement points of the engineering preset axis, represents the measurement error.

[0101] In the embodiments of the present disclosure, due to the limited number of measurement points and the inevitable errors during the measurement process, introducing measurement errors when estimating the deformation of each measurement point can reduce the total error caused by the limited number of total measurement points and improve the accuracy of the estimation.

[0102] It can be understood that the above is the length deformation at the i th measurement point, which is a variable value. Based on the above formula, the above formula (7) can be expanded to obtain the following formula (8) in matrix form:

[0103] ; Formula (8)

[0104] Among them, represents the unit projection length deformation at the i th measurement point, and represents the distance from the standard parallel to the projection axis.

[0105] S203b. Based on the estimated Mercator projection length deformation of each measurement point and Formula (7), when the iteration stop condition is satisfied, the target parallel with the minimum total Mercator projection length deformation of the engineering preset axis within the latitude range is determined as the standard parallel.

[0106] ; Formula (9)

[0107] It should be noted that the above Formula (9) can be estimated based on the above-expanded Formula (8) and the least squares method, and then based on the given iteration stop condition (such as the iteration times being greater than the preset times, or the difference between two consecutive calculations being less than the set threshold), the standard latitude value B 0 that minimizes the total Mercator projection length deformation value within the latitude range of the engineering preset axis can be obtained. Thus, the standard parallel can be determined to facilitate the Mercator projection of the engineering preset axis, minimize the total Mercator projection length deformation within the latitude range, and minimize the projection deformation of the selected axis side length.

[0108] Based on this solution, in linear engineering such as long-distance water diversion and power generation tunnels, railways, undersea tunnels, and cross-sea bridges that require accurate penetration, when the number of actual measurement points obtained within the latitude range of the engineering preset axis is limited, according to the latitude measured based on the limited number of measurement points, the least squares iterative calculation is performed in the form of the above matrix. Even when the number of actual measurement points is limited, the target latitude value with the minimum overall projection length deformation value within the latitude range of the engineering preset axis can be quickly found.

[0109] Corresponding to the embodiments of the foregoing method, the present disclosure also provides embodiments of a Mercator projection device for controlling engineering projection deformation based on an axis and a computer device to which the same is applied.

[0110] The embodiments of the Mercator projection device for controlling engineering projection deformation based on an axis according to the present disclosure can be applied to a computer device, such as a server or a terminal device. The embodiments of the Mercator projection device for controlling engineering projection deformation based on an axis can be implemented by software, or by hardware, or by a combination of software and hardware. Taking software implementation as an example, as a logically meaningful Mercator projection device for controlling engineering projection deformation based on an axis, it is formed by the processor of the engineering projection where it is located reading the corresponding computer program instructions in the non-volatile memory into the memory for operation. In terms of the hardware level, as Figure 5 shown, it is a hardware structure diagram of the computer device where the Mercator projection device for controlling engineering projection deformation based on an axis according to the embodiment of the present disclosure is located. In addition to Figure 5 the shown processor 510, memory 530, network interface 520, and non-volatile memory 540, the server or electronic device where the Mercator projection method for controlling engineering projection deformation based on an axis according to the embodiment is located usually further includes other hardware according to the actual functions of the computer device, which will not be elaborated herein.

[0111] As Figure 6 shown, Figure 6 it is a schematic structural diagram of a Mercator projection device for controlling engineering projection deformation based on an axis provided by an embodiment of the present disclosure. The Mercator projection device 600 for controlling engineering projection deformation based on an axis includes: a measurement point determination module 601, a length deformation estimation module 602, a standard latitude determination module 603, and a projection module 604; the measurement point determination module 601 is configured to determine the latitude range of the engineering measurement area and the measurement points of the engineering preset axis; the length deformation estimation module 602 is configured to estimate the Mercator projection length deformation of each measurement point of the engineering preset axis based on the latitudes of each measurement point of the engineering preset axis; the standard latitude determination module 603 is configured to determine the target latitude with the smallest total Mercator projection length deformation of the engineering preset axis within the latitude range as the standard latitude; the projection module 604 is configured to perform Mercator projection on the engineering preset axis within the engineering measurement area based on the latitude of the standard latitude.

[0112] Optionally, the length deformation estimation module 602 is specifically configured to, after estimating the Mercator projection length deformation of each measurement point based on the latitudes of each measurement point of the engineering preset axis, estimate the Mercator projection length deformation of the engineering preset axis based on the estimated Mercator projection length deformation of each measurement point.

[0113] Optionally, the length deformation estimation module 602 is specifically configured to estimate the Mercator projection length deformation of the measurement points with a latitude of B i based on a first preset formula when the total number of measurement points is greater than or equal to a first threshold. The first preset formula includes: ; where B 0 represents the latitude of the target parallel, B i represents the latitude at the i th measurement point of the project preset axis.

[0114] Optionally, the length deformation estimation module 602 is specifically configured to estimate the total Mercator projection length deformation of the project preset axis based on the estimated Mercator projection length deformation of each measurement point and a second preset formula. The second preset formula includes: ; where B N represents the latitude at the north end point of the project preset axis, B S represents the latitude at the south end point of the project preset axis.

[0115] Optionally, the length deformation estimation module 602 is specifically configured to estimate the total Mercator projection length deformation of the project preset axis based on the estimated Mercator projection length deformation of each measurement point and a third preset formula. The third preset formula includes: ; where B N represents the latitude at the north end point of the project preset axis, B S represents the latitude at the south end point of the project preset axis.

[0116] Optionally, the standard parallel determination module 603 is specifically configured to determine the target parallel with zero total Mercator projection length deformation of the project preset axis within the latitude range as the standard parallel based on a target formula. The target formula is the second preset formula or the third preset formula. The latitude of the target parallel with zero total Mercator projection length deformation of the project preset axis is .

[0117] Optionally, the length deformation estimation module 602 is specifically configured to estimate the Mercator projection length deformation of the i th measurement point based on a fourth preset formula when the total number of measurement points is less than the first threshold. The fourth preset formula includes: ; n is the total number of measurement points of the project preset axis, Indicates measurement error; standard latitude determination module 603, specifically used to determine the target latitude with the smallest total length deformation of the Mercator projection of the preset axis of the project within the latitude range as the standard latitude based on the estimated Mercator projection length deformation of each measurement point and the fifth preset formula when the iteration stop condition is met; the fifth preset formula includes: .

[0118] The Mercator projection device based on axis line control of engineering projection deformation provided by the embodiment of the present disclosure first determines the latitude range of the engineering measurement area, and then performs measurement based on the preset axis line of the engineering within the latitude range to obtain the latitude of each measurement point; then, the Mercator projection device based on axis line control of engineering projection deformation estimates in advance the total length deformation of the Mercator projection of the preset axis line of the engineering based on the latitude of each measurement point, and determines the latitude with the smallest total length deformation of the Mercator projection within the latitude range as the standard latitude for the final Mercator projection based on the preset axis line of the engineering; finally, the Mercator projection device based on axis line control of engineering projection deformation performs the final Mercator projection based on the standard latitude. On the one hand, since the estimation is based on the length deformation of the selected axis (i.e., the preset axis of the project), compared with the method of estimating the deformation of the projection area in the related art, the processing speed is fast and the complexity is low, which can improve the speed of determining the standard parallel; on the other hand, in the embodiment disclosed in the present invention, only the latitude of each measuring point within the latitude range is concerned, and there is no need to introduce longitude for deformation estimation. The calculation complexity is low, the accuracy is high, and it is closer to the actual deformation. The difference between the side length directly calculated based on the control point coordinates after projection and the side length obtained by field measurement can meet the engineering requirements, and the coordinates of the engineering control points can be guaranteed, which is convenient for layout in various stages of the project, so that the linear engineering penetration with high requirements for projection deformation can be more accurate and the probability of misalignment at the penetration point can be reduced.

[0119] Correspondingly, the present disclosure also provides a Mercator projection device for controlling the deformation of engineering projection based on an axis line, and the Mercator projection device for controlling the deformation of engineering projection based on an axis line includes a processor; a memory for storing instructions executable by the processor; wherein the processor is configured to: determine the latitude range of the engineering survey area and the measurement points of the engineering preset axis line; based on the latitude of each measurement point of the engineering preset axis line, estimate the Mercator projection length deformation of each measurement point of the engineering preset axis line; determine the target latitude line with the smallest total length deformation of the Mercator projection of the engineering preset axis line within the latitude range as the standard latitude line; based on the latitude of the standard latitude line, perform Mercator projection on the engineering preset axis line within the engineering survey area.

[0120] The present disclosure also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, each step in the above-mentioned embodiment of the Mercator projection method based on axis control engineering projection deformation is implemented.

[0121] The present disclosure also provides a computer device, which includes a memory, a processor, and computer-readable instructions stored on the memory and executable on the processor. When the computer-readable instructions are executed by the processor, each step in the above-mentioned embodiment of the Mercator projection method based on axis control engineering projection deformation is implemented.

[0122] For the implementation processes of the functions and actions of each module in the above-mentioned device, please refer to the implementation processes of the corresponding steps in the above-mentioned method for details, which will not be elaborated here.

[0123] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can be referred to the partial description of the method embodiment. The device embodiments described above are only illustrative. The modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed to multiple network modules. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the present disclosure. Those of ordinary skill in the art can understand and implement it without creative work.

[0124] The above describes specific embodiments of the present disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims can be executed in a different order than in the embodiments and still achieve the desired results. Additionally, the processes depicted in the figures do not necessarily require the particular order or sequential order shown to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0125] Those skilled in the art will readily conceive of other embodiments of the present disclosure after considering the specification and practicing the invention herein. The present disclosure is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common general knowledge or conventional technical means in the technical field not claimed in the present disclosure. The specification and embodiments are only to be considered as exemplary, and the true scope and spirit of the present disclosure are pointed out by the following claims.

[0126] It should be understood that the present disclosure is not limited to the exact structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present disclosure is only limited by the appended claims.

[0127] The above are only the preferred embodiments of the present disclosure and are not intended to limit the present disclosure. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present disclosure shall be included within the scope of protection of the present disclosure.

Claims

1. A Mercator projection method based on axis control for engineering projection deformation, characterized in that, The method includes: Determining the latitude range of the engineering survey area of the linear project and the measurement points of the engineering preset axis; When the total number of measurement points is greater than or equal to the first threshold, based on the first preset formula, estimate the Mercator projection length deformation of the measurement points with a latitude of B i . The first preset formula includes: ; represents the Mercator projection length deformation of the i -th measurement point, B 0 represents the latitude of the target parallel, B i represents the latitude at the i -th measurement point of the project preset axis; determine the latitude of the target parallel with the smallest total Mercator projection length deformation of the project preset axis within the latitude range as ; B N represents the latitude at the north end point of the project preset axis, B S represents the latitude at the south end point of the project preset axis; When the total number of measurement points is less than the first threshold, based on the fourth preset formula, estimate the Mercator projection length deformation of the i th measurement point; based on the estimated Mercator projection length deformation of each measurement point and the fifth preset formula, when the iteration stop condition is met, determine the target latitude with the smallest total Mercator projection length deformation of the engineering preset axis within the latitude range; the fourth preset formula includes: ; n is the total number of measurement points of the engineering preset axis, represents the measurement error; the fifth preset formula includes: ; Determining a target parallel with the smallest total length deformation of the Mercator projection of the engineering preset axis within the latitude range as the standard parallel; Performing a Mercator projection on the engineering preset axis within the engineering survey area based on the latitude of the standard parallel.

2. The method according to claim 1, characterized in that, Based on the first preset formula, after estimating the Mercator projection length deformation of the measurement point with a latitude of B i the method further includes: Estimate the total Mercator projection length deformation of the engineering preset axis based on the Mercator projection length deformation of each measurement point estimated and a second preset formula; the second preset formula includes: ; Among them, represents the total length distortion of the Mercator projection, B N represents the latitude at the north end point of the preset axis of the project, B S represents the latitude at the south end point of the preset axis of the project.

3. The method according to claim 1, wherein Based on the first preset formula, after estimating the Mercator projection length deformation of the measurement point with a latitude of B i , the method further includes: Estimate the total Mercator projection length deformation of the engineering preset axis based on the Mercator projection length deformation of each measurement point estimated and a third preset formula; the third preset formula includes: ; Among them, represents the total length distortion of the Mercator projection, B N represents the latitude at the north end point of the preset axis of the project, B S represents the latitude at the south end point of the preset axis of the project.

4. A Mercator projection device based on axis control for engineering projection deformation, characterized in that, The Mercator projection device for controlling engineering projection deformation based on an axis includes: a measurement point determination module, a length deformation estimation module, a standard parallel determination module, and a projection module; The measurement point determination module is configured to determine the latitude range of the engineering survey area of the linear project and the measurement points of the engineering preset axis; The length deformation estimation module is used to estimate the Mercator projection length deformation of the measurement points at a latitude of B i when the total number of measurement points is greater than or equal to the first threshold, and the first preset formula includes: ; represents the Mercator projection length deformation of the i th measurement point, B 0 represents the latitude of the target parallel, B i represents the latitude at the i th measurement point of the project preset axis; determine that the latitude of the target parallel with the minimum total Mercator projection length deformation of the project preset axis within the latitude range is ; B N represents the latitude at the north end point of the project preset axis, B S represents the latitude at the south end point of the project preset axis; When the total number of measurement points is less than the first threshold, based on the fourth preset formula, estimate the Mercator projection length deformation of the i th measurement point; based on the estimated Mercator projection length deformation of each measurement point and the fifth preset formula, when the iteration stop condition is met, determine the target latitude at which the total Mercator projection length deformation of the engineering preset axis within the latitude range is the smallest; the fourth preset formula includes: ; n is the total number of measurement points of the engineering preset axis, represents the measurement error; the fifth preset formula includes: ; The standard parallel determination module is configured to determine a target parallel with the smallest total length deformation of the Mercator projection of the engineering preset axis within the latitude range as the standard parallel; The projection module is configured to perform a Mercator projection on the engineering preset axis within the engineering survey area based on the latitude of the standard parallel.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the Mercator projection method for controlling engineering projection deformation based on an axis according to any one of claims 1-3.

6. A computer device, characterized in that, The computer device includes a memory, a processor, and computer-readable instructions stored on the memory and executable on the processor. When the computer-readable instructions are executed by the processor, they implement the Mercator projection method for controlling engineering projection deformation based on an axis according to any one of claims 1-3.

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