Mercator projection method based on axis control engineering projection deformation
By determining the latitude range and the preset axis of the project in engineering measurement, estimating the length deformation of the Mercator projection, and quickly determining the standard latitude for projection, the problem of high computational complexity in the existing technology is solved, and the efficiency and accuracy of engineering measurement are achieved.
Patent Information
- Application Number
- CN202511108204.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-08
- Publication Date
- 2025-10-14
AI Technical Summary
The existing technology has high computational complexity and is time-consuming when improving the length deformation caused by Mercator projection in engineering measurement, and it is difficult to quickly obtain projection parameters that meet engineering requirements.
By determining the latitude range of the engineering survey area and the preset axis of the project, the σ criterion is used to eliminate invalid measurement points, the Mercator projection length deformation of each measurement point is estimated, the standard latitude with the smallest total length deformation is determined, the Mercator projection is performed, and a deformation assessment report is output.
The processing speed is improved, the calculation complexity is reduced, the accuracy of the control point coordinates after projection is ensured, the probability of staggered penetration points is reduced, and engineering requirements are met.
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Figure CN120778075A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of engineering measurement, and in particular relates to a Mercator projection method 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 engineering construction are becoming higher and higher.
[0003] Typically, for engineering purposes, during the engineering survey process, it is necessary to project the edges on the sphere onto a developable surface, which is then unfolded to determine the engineering control points for project layout. However, map projections can cause distortion, and Mercator projections can cause length distortion. To ensure the accuracy of the coordinates of the engineering control points, it is necessary to limit the extent of the length distortion caused by projection. Generally, engineering surveys require that the difference between the side lengths directly calculated from the projected control point coordinates and the side lengths measured in situ meet engineering requirements. If the length distortion does not meet engineering requirements, some processing methods are needed to improve the length distortion of the edges within the engineering survey area.
[0004] However, many current processing methods have high computational complexity and are time-consuming when improving length deformation. Therefore, there is an urgent need for a processing method that can quickly obtain projection parameters that meet the engineering projection deformation tolerance requirements for projection.
[0005] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the Invention
[0006] In order to overcome the problems existing in the related art, the embodiment of the present disclosure provides a Mercator projection method based on axis control of engineering projection deformation, which can quickly obtain projection parameters that meet the engineering projection deformation tolerance requirements for projection.
[0007] A Mercator projection method for controlling engineering projection deformation based on an axis, the method comprising:
[0008] Determine the latitude range of the project survey area and the measurement points of the project preset axis, pre-process the measurement points, and use the σ criterion to eliminate invalid measurement points;
[0009] estimating the Mercator projection length deformation of each measurement point on the preset engineering axis based on the latitude of each measurement point;
[0010] Determine 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;
[0011] projecting the engineering preset axis in the engineering survey area according to a Mercator projection based on the latitude of the standard parallel;
[0012] outputting a deformation evaluation report, including a list of deformation values, a total deformation calculation process, and a deformation distribution curve diagram.
[0013] Further, based on the latitude of each measurement point of the engineering preset axis, the method further comprises:
[0014] based on the estimated Mercator projection length deformation of each measurement point, estimating the Mercator projection total length deformation of the engineering preset axis.
[0015] Further, the estimating the Mercator projection length deformation of each measurement point based on the latitude of each measurement point of the engineering preset axis comprises:
[0016] In the case that the total number of measurement points is greater than or equal to a first threshold value, estimating the Mercator projection length deformation of the measurement point with latitude B i based on a first preset formula, the first preset formula comprising:
[0017]
[0018] wherein B o represents the latitude of the target parallel, and B i represents the latitude of the i-th measurement point of the engineering preset axis.
[0019] Further, the estimating the Mercator projection total length deformation of the engineering preset axis based on the estimated Mercator projection length deformation of each measurement point comprises:
[0020] based on the estimated Mercator projection length deformation of each measurement point and a second preset formula, estimating the Mercator projection total length deformation of the engineering preset axis; the second preset formula comprising:
[0021]
[0022] wherein B N represents the latitude of the north end point of the engineering preset axis, and B S represents the latitude of the south end point of the engineering preset axis.
[0023] Further, the estimating the Mercator projection total length deformation of the engineering preset axis based on the estimated Mercator projection length deformation of each measurement point comprises:
[0024] The total length deformation of the Mercator projection of the preset axis of the project is estimated based on the estimated Mercator projection length deformation of each measuring point and a third preset formula; the third preset formula includes:
[0025]
[0026] Among them, B N Indicates the latitude of the northern end point of the preset axis of the project, B S Indicates the latitude of the southern endpoint of the preset axis of the project.
[0027] Furthermore, 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 includes:
[0028] Determine, based on the target formula, the target latitude line where the total length deformation of the Mercator projection of the preset axis of the project within the latitude range is zero as the standard latitude line;
[0029] The target formula is the second preset formula or the third preset formula; the latitude of the target latitude line at which the total length deformation of the Mercator projection of the preset axis of the project is zero is:
[0030]
[0031] Among them, B N Indicates the latitude of the northern end point of the preset axis of the project, B S Indicates the latitude of the southern endpoint of the preset axis of the project
[0032] Furthermore, the estimating the total length deformation of the Mercator projection of the preset engineering axis based on the latitude of each measurement point of the preset engineering axis includes:
[0033] When the total number of measurement points is less than the first threshold, the Mercator projection length deformation of the i-th measurement point is estimated based on a fourth preset formula; the fourth preset formula includes:
[0034]
[0035] n is the total number of measurement points along the preset axis of the project, and ε represents the measurement error;
[0036] The step of determining the target latitude line with the minimum total length deformation of the Mercator projection of the preset axis of the project within the latitude range as the standard latitude line includes:
[0037] Based on the estimated Mercator projection length deformation of each measuring point and a fifth preset formula, when an iteration stop condition is satisfied, a target latitude line with the minimum total Mercator projection length deformation of the preset axis of the project within the latitude range is determined as the standard latitude line; the fifth preset formula includes:
[0038]
[0039] wherein B o represents the latitude of the target parallel.
[0040] Further, the deformation evaluation report comprises a deformation value list, a total deformation calculation process and a deformation distribution curve.
[0041] Compared with the prior art, the present application has the following advantages:
[0042] In the embodiments of the present disclosure, first, the latitude range of the engineering survey area is determined, then the engineering preset axis in the latitude range is measured to obtain the latitude of each measurement point, the length deformation of the Mercator projection of each measurement point on the engineering preset axis is estimated in advance based on the latitude of each measurement point, the latitude in the latitude range with the minimum total length deformation of the Mercator projection is determined as the standard latitude for the final Mercator projection based on the engineering preset axis, 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 engineering preset axis), compared with the related art which estimates the projection area deformation, the processing speed is fast, the complexity is low, and the speed of determining the standard latitude can be improved. On the other hand, in the embodiments of the present disclosure, only the latitude of each measurement point in the latitude range is concerned, without introducing the longitude for deformation estimation, the complexity of calculation is low, the accuracy is high, and the deformation is closer to the true deformation. The difference between the side length directly calculated based on the projected control point coordinates and the side length obtained by field measurement can meet the engineering requirements, which can ensure the engineering control network point coordinates and facilitate the lofting in each stage of the project, so that the linear engineering can be more accurately connected, and the probability of misalignment at the connection point can be reduced. BRIEF DESCRIPTION OF DRAWINGS
[0043] The accompanying drawings are included to provide a further understanding of the various embodiments and are incorporated in and constitute a part of this specification. The drawings are not intended to be restrictive in any way, and are presented for illustrative purposes together with the description. In the drawings, like numerals refer to like or similar elements, where appropriate. Such embodiments are illustrative, and not intended to be exhaustive or exclusive, of possible implementations of the present devices and methods.
[0044] Figure 1 A flowchart of a Mercator projection method for controlling engineering projection deformation based on an axis is provided for the embodiments of the present disclosure.
[0045] Figure 2 A schematic diagram of length deformation of a Mercator projection is provided for the embodiments of the present disclosure.
[0046] Figure 3A schematic diagram of a linear engineering through situation provided by an embodiment of the present disclosure. DETAILED DESCRIPTION
[0047] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the drawings and in combination with embodiments.
[0048] As shown in Figure 1 , Figure 1 A flowchart of a Mercator projection method based on axis control engineering projection deformation provided by an embodiment of the present disclosure, comprising the following steps:
[0049] S101, determine the latitude range of the engineering survey area and the measurement points of the engineering preset axis.
[0050] Exemplarily, the engineering preset axis can be an axis selected by the staff based on the actual engineering, which can be selected according to the engineering requirements. In the embodiment of the present disclosure, the position of the engineering preset axis can be changed, and after the change, the determination of the standard latitude can be re-performed.
[0051] Optionally, the engineering preset axis can be a straight line, or a polyline with at least one inflection point, or a curve, which is not specifically limited in the embodiment of the present disclosure.
[0052] It should be noted that the specific selection of the engineering preset axis is not specifically limited in the embodiment of the present disclosure, and the estimation of the Mercator projection deformation of the selected engineering preset axis is mainly based on the estimation of the Mercator projection deformation of the selected engineering preset axis to obtain the standard latitude with the minimum total length deformation of the Mercator projection of the engineering preset axis (which can also be referred to as the total projection length deformation).
[0053] Generally, for the through of some linear engineering, such as the through of long-distance water diversion power tunnel, railway, submarine tunnel, cross-sea bridge, etc., the requirement for the projection deformation value of the engineering preset axis side length is higher, the smaller the Mercator projection total length deformation value of the selected axis side length, the smaller the deviation after subsequent projection, and the higher the accuracy of the through.
[0054] It should be noted that in actual measurement applications, the actual measurement points can be selected on the engineering preset axis or near the engineering preset axis. For example, some positions that cannot be reached can select positions east or west of the engineering preset axis as actual measurement points for measurement, that is, the actual measurement points can not all be on the engineering preset axis.
[0055] Among them, the measurement points include the south end point and the north end point of the latitude range, and the measurement points on the engineering preset axis and the measurement points near the engineering preset axis.
[0056] It should be noted that the deformation of the Mercator projection (here referring to the normal Mercator projection) is generally related to the latitude and is independent of the longitude.
[0057] The measurement points are pre-processed, and the invalid measurement points are proposed by using the sigma criterion.
[0058] S102, based on the latitude of each measurement point of the engineering preset axis, estimating the length deformation of the Mercator projection of each measurement point of the engineering preset axis.
[0059] It should be noted that in the embodiments of the present disclosure, the length deformation of the Mercator projection of each measurement point can be estimated first. The length deformation of the Mercator projection is a variable related to the selection of the standard latitude, and therefore the determined length deformation of the Mercator projection is a deformation relationship related to the standard latitude and the latitude of the measurement point.
[0060] It should be noted that in the embodiments of the present disclosure, the normal Mercator projection is used in the engineering projection. Before the projection is performed, the standard latitude with the minimum total length deformation of the Mercator projection is determined, that is, the projection deformation is related to the standard latitude, and therefore before the map projection (i.e. the Mercator projection) is performed, the estimated length deformation of the Mercator projection of each measurement point of the engineering preset axis is a variable related to the latitude of the standard latitude to be determined. Based on the length deformation of the Mercator projection of each measurement point, the dimension of the latitude with the minimum total length deformation of the Mercator projection of the engineering preset axis can be determined. In the engineering, the standard latitude selected based on the engineering preset axis is the latitude corresponding to the latitude with the minimum total length deformation of the Mercator projection of the engineering preset axis.
[0061] S103, determining the target latitude with the minimum total length deformation of the Mercator projection of the engineering preset axis in the latitude range as the standard latitude.
[0062] Wherein, the length deformation of the Mercator projection of each measurement point of the selected axis is the length deformation of the line segment between the measurement point and the adjacent measurement point of the measurement point projected to the projection plane by the Mercator projection, and the total length deformation of the Mercator projection of the selected axis is the length deformation of the selected axis projected to the projection plane by the Mercator projection.
[0063] It should be noted that according to the calculation, two latitudes can be obtained, one in the southern hemisphere and one in the northern hemisphere, and the latitude corresponding to the latitude within the latitude range of the engineering preset axis is determined as the target latitude.
[0064] 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. When the cylindrical surface selected by the Mercator projection is tangent to the earth, there are two standard parallels, one in the southern and northern hemispheres. The projection length deformation is negative between the standard parallels (the standard parallels indicate the area corresponding to the parallel circle) and positive outside the standard parallels. Generally, 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.
[0065] 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 parallel 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.
[0066] S104. Based on the latitude of the standard parallel, perform Mercator projection on the preset axis of the project within the project survey area.
[0067] It should be noted that in the embodiment of the present disclosure, after the standard parallel is estimated, 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 latitude of each measuring point within the latitude range of the preset axis of the project, after obtaining the standard parallel, Mercator projection based on the standard parallel can make the accuracy of the penetration at this latitude higher during the actual construction of the linear project based on the preset axis of the project.
[0068] Figure 2 A schematic diagram of length deformation of a Mercator projection provided in an embodiment of the present disclosure, such as Figure 2 As 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 The side L S Projected onto the cylinder is edge L′ S , the side length is negatively deformed; the side Li1 with latitude value Bi1 is projected onto the cylinder as side L' i1 , the side length is negatively deformed; the side L0 with latitude value B0 (i.e. standard latitude) is projected onto the cylinder as side L′0, and the side length is not deformed; the latitude value is B i2 The side L i2 Projected onto the cylinder is edge L′ i2 , the side length is positively deformed; the side LN with latitude value BN is projected onto the cylinder as side L′N , the side length undergoes positive deformation.
[0069] Figure 3 This is a schematic diagram of the penetration of a linear project provided by an embodiment of the present disclosure. The smaller the total length deformation of the Mercator projection of the preset axis of the project, the higher the accuracy of the penetration. Figure 3 As shown in (a), construction is underway 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 3 As shown in (b), construction was carried out simultaneously from the south and north boundaries, resulting in a misalignment problem at the expected penetration point.
[0070] An embodiment of the present disclosure provides a Mercator projection method for controlling engineering projection deformation based on an axis. First, the latitude range of the engineering survey area is determined. Then, measurement is performed based on the preset engineering axis 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 is estimated. The latitude with the smallest total length deformation is determined as the latitude of the standard parallel for the final Mercator projection based on the preset engineering axis. Then, the final Mercator projection is performed based on the standard parallel. 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 of the present disclosure, 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 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 network 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 for side length projection deformation higher and reducing the probability of misalignment at the penetration point.
[0071] It should be noted that the embodiments of the present disclosure provide 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. Among them, when a sufficient number of actual measurement points can be obtained, the Mercator projection length deformation of each measurement point is first estimated, and then the total length deformation of the Mercator projection of the preset axis of the project is estimated based on the Mercator projection length deformation of each measurement point through 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 first estimated in combination with the measurement error, and then the matrix composed of the Mercator projection length deformations of each measurement point can be 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, which is the processing method of method two.
[0072] Method 1:
[0073] Optionally, in the Mercator projection method based on axis control engineering projection deformation provided by the embodiment of the present disclosure, after the above S102, the following S105 may be further performed:
[0074] S105 , estimating the total length deformation of the Mercator projection of the preset axis of the project based on the estimated Mercator projection length deformation of each measuring point.
[0075] 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 will be, and the closer it will be to the actual projection deformation.
[0076] Based on this scheme, we can first estimate the Mercator projection length deformation of each measuring point (i.e., each latitude value) within the latitude range of the project axis, and then estimate the total Mercator projection length deformation of the project preset axis based on the estimated Mercator projection length deformation of each measuring point. This can accurately obtain a deformation that is closer to the actual projection, making the determined standard latitude more in line with project needs.
[0077] Specifically, in method 1, after determining the Mercator projection length deformation of each measuring point, the total length deformation of the Mercator projection of the preset axis of the project can be estimated by two processing methods, including the following first processing method (direct summation) and the second processing method (single integration).
[0078] Optionally, in the Mercator projection method based on axis-controlled engineering projection deformation provided in the embodiment of the present disclosure, the above-mentioned S202 can be specifically performed by the following S202a:
[0079] S102a: When the total number of measurement points is greater than or equal to the first threshold, the latitude is estimated to be B based on the first preset formula. i The Mercator projection length of the measurement point is distorted.
[0080]
[0081] Among them, B i It represents the latitude of the i-th measurement point of the preset axis of the project, and B0 represents the latitude of the target latitude.
[0082] It should be noted that, in the embodiment of the present disclosure, in order to simplify the calculation, the earth ellipsoid is regarded as a sphere, wherein, The cos B0 represents the distance between the measurement point on the standard parallel and the Mercator projection axis. i Indicates the distance of the measurement point at latitude Bi from the Mercator projection axis, which indicates the central axis of the cylinder used in the Mercator projection, which coincides with the earth's axis.
[0083] Furthermore, in the first processing mode, the above-mentioned S105 can be executed by the following S105a:
[0084] S105a. Based on the estimated Mercator projection length deformation of each measurement point and formula (2), the total Mercator projection length deformation of the preset axis of the project is estimated.
[0085]
[0086] Among them, BN represents the latitude of the northern end point of the project's preset axis, and BS represents the latitude of the southern end point of the project's preset axis.
[0087] Based on this scheme, the total length deformation of the Mercator projection of the preset axis of the project can be determined based on the sum of the Mercator projection length deformations of each measuring point. When the latitudes of a large number of actual measuring points can be obtained, the more measuring points there are, the more accurate the total length deformation of the Mercator projection of the preset axis of the project estimated by summation, thereby making the subsequent estimation of the standard latitude more accurate, and the accurate standard latitude can be quickly obtained when the number of measuring points is large.
[0088] Optionally, in the second processing manner, in the Mercator projection method based on axis control engineering projection deformation provided in the embodiment of the present disclosure, the above S105 can be specifically performed by the following S105b:
[0089] S105b. Based on the estimated Mercator projection length deformation of each measurement point and formula (3), the total Mercator projection length deformation of the preset axis of the project is estimated.
[0090]
[0091] Based on this scheme, when the number of measurement points within the latitude range of the preset axis of the project can be obtained sufficiently, the above-mentioned integral form can be used to quickly and accurately determine the total length deformation of the Mercator projection on the preset axis of the project based on the estimated Mercator projection length deformation of each measurement point.
[0092] After estimating the total length deformation of the Mercator projection on the preset axis of the above-mentioned project 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, the latitude when the total length deformation of the Mercator projection is 0 can be estimated based on the above-mentioned Δ1 and Δ2.
[0093] Optionally, in the Mercator projection method based on axis-controlled engineering projection deformation provided by the embodiment of the present disclosure, the above-mentioned S103 may be performed by the following S103a:
[0094] S103a. Determine, based on the target formula, the target latitude line where the total length deformation of the Mercator projection of the preset axis of the project within the latitude range is zero as the standard latitude line.
[0095] The target formula is the above formula (2) or formula (3).
[0096] Specifically, by solving B0 in formula (4) or formula (5), we can estimate the target latitude where the total length deformation of the Mercator projection of the preset axis of the project is zero. The latitude of the standard parallel is determined by the following formula (6):
[0097]
[0098] It can be understood that in this case, the latitude of the final target latitude is only related to the latitude range of the preset axis of the project, that is, when estimating based on this scheme, the standard latitude can be quickly obtained based on the latitude range.
[0099] Based on this scheme, if the total length deformation of the Mercator projection of the preset axis of the project is estimated based on the above two processing methods, when the number of measuring points exceeds the preset number, the target latitude line with an overall deformation of zero can be obtained (the length deformation of zero is the minimum length deformation, that is, there are positive deformation and negative deformation at the measuring points on both sides of the standard latitude line, and the sum of the overall deformation is zero). Then, the latitude of the target latitude line with a total length deformation of the Mercator projection of the preset axis of the project can be quickly obtained based on the target formula.
[0100] Method 2:
[0101] Optionally, in the Mercator projection method for controlling engineering projection deformation based on an axis provided in the embodiments of the present disclosure, if the actual measurement points in the latitude range (i.e. interval) of the engineering preset axis (i.e. selected axis) that can be obtained are limited, the determination of the standard latitude can be based on the least square method, i.e. S102 in the above method can further include S102b, and further, S103 in the above method can further include S103b.
[0102] S102b, in the case that the total number of measurement points is less than the first threshold value, estimating the Mercator projection length deformation of the i th measurement point based on formula (7).
[0103]
[0104] wherein n is the total number of measurement points of the engineering preset axis, and ε represents the measurement error.
[0105] In the embodiments of the present disclosure, since the number of measurement points is limited, and since there are inevitable errors in the measurement process, the measurement error is introduced when estimating the deformation of each measurement point, which can reduce the total error caused by the limited number of total measurement points, and can improve the accuracy of the estimation.
[0106] It can be understood that ΔD i 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 matrix form formula (8):
[0107]
[0108] wherein, represents the unit projection length deformation at the i th measurement point, and cos B0represents the distance between the standard latitude and the projection axis.
[0109] S103b, based on the estimated Mercator projection length deformation of each measurement point and formula (7), when the iteration stopping condition is met, the target latitude with the minimum Mercator projection total length deformation of the engineering preset axis in the latitude range is determined as the standard latitude.
[0110]
[0111] It should be noted that the formula (9) can be estimated based on the above expansion formula (8) and the least square method, and then based on a given iteration stopping condition (such as the number of iterations is greater than a preset number, or the difference between the previous and the next calculation is less than a set threshold), the standard latitude value B 0 that minimizes the Mercator projection total length deformation value in the latitude range of the engineering preset axis (in this scheme, due to the limited number of measurement points, there is an error, so the Mercator projection total length deformation value may not be 0, it may be negative or positive) can be obtained, so that the standard latitude line can be determined, so that the engineering preset axis Mercator projection based on the standard latitude line can be facilitated, and the Mercator projection total length deformation in the latitude range can be minimized, and the selected axis length projection deformation can be minimized.
[0112] Based on the scheme, in the need for accurate penetration of linear engineering such as long-distance water diversion power tunnel, railway, submarine tunnel, and cross-sea bridge, if the number of actual measurement points in the latitude range of the engineering preset axis is limited, the least square iteration calculation is performed through the above matrix form based on the latitude measured by the limited number of measurement points. In the case of limited number of actual measurement points, the target latitude value with the minimum overall projection length deformation value in the latitude range of the engineering preset axis can also be quickly found.
[0113] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can make equivalent replacement or change within the technical range disclosed by the present application according to the technical solution and the inventive concept of the present application, which should be covered within the protection scope of the present application.
Claims
1. A Mercator projection method based on axis control engineering projection deformation, characterized in that: The method comprises: Determine the latitude range of the project survey area and the measurement points of the project preset axis, pre-process the measurement points, and use the σ criterion to eliminate invalid measurement points; estimating the Mercator projection length deformation of each measurement point on the preset engineering axis based on the latitude of each measurement point; Determine 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; Based on the latitude of the standard parallel, perform Mercator projection on the preset axis of the project within the project survey area; Output deformation assessment report.
2. The method according to claim 1, characterized in that After estimating the Mercator projection length deformation of each measurement point based on the latitude of each measurement point of the preset engineering axis, the method further includes: Based on the estimated Mercator projection length deformation of each measuring point, the total Mercator projection length deformation of the engineering preset axis is estimated.
3. The method according to claim 2, characterized in that The method of estimating the Mercator projection length deformation of each measurement point based on the latitude of each measurement point of the preset axis of the project includes: estimating the latitude as B based on a first preset formula when the total number of measurement points is greater than or equal to a first threshold. i The Mercator projection length deformation of the measurement point, the first preset formula includes: Among them, B o represents the latitude of the target latitude, B i Indicates the latitude of the i-th measurement point of the preset axis of the project.
4. The method according to claim 3, characterized in that The estimating the total length deformation of the Mercator projection of the preset axis of the project based on the estimated Mercator projection length deformation of each measuring point includes: The total length deformation of the Mercator projection of the preset axis of the project is estimated based on the estimated Mercator projection length deformation of each measuring point and a second preset formula; the second preset formula includes: Among them, B N Indicates the latitude of the northern end point of the preset axis of the project, B S Indicates the latitude of the southern endpoint of the preset axis of the project.
5. The method according to claim 3, characterized in that The estimating the total length deformation of the Mercator projection of the preset axis of the project based on the estimated Mercator projection length deformation of each measuring point includes: The total length deformation of the Mercator projection of the preset axis of the project is estimated based on the estimated Mercator projection length deformation of each measuring point and a third preset formula; the third preset formula includes: Among them, B N Indicates the latitude of the northern end point of the preset axis of the project, B S Indicates the latitude of the southern endpoint of the preset axis of the project.
6. The method according to claim 4 or 5, characterized in that The step of determining the target latitude line with the minimum total length deformation of the Mercator projection of the preset axis of the project within the latitude range as the standard latitude line includes: Determine, based on the target formula, the target latitude line where the total length deformation of the Mercator projection of the preset axis of the project within the latitude range is zero as the standard latitude line; The target formula is the second preset formula or the third preset formula; the latitude of the target latitude line at which the total length deformation of the Mercator projection of the preset axis of the project is zero is: Among them, B N Indicates the latitude of the northern end point of the preset axis of the project, B S Indicates the latitude of the southern endpoint of the preset axis of the project.
7. The method according to claim 1, characterized in that The estimating the total length deformation of the Mercator projection of the preset project axis based on the latitude of each measurement point of the preset project axis includes: When the total number of measurement points is less than the first threshold, the Mercator projection length deformation of the i-th measurement point is estimated based on a fourth preset formula; the fourth preset formula includes: n is the total number of measurement points along the preset axis of the project, and ε represents the measurement error; The step of determining the target latitude line with the minimum total length deformation of the Mercator projection of the preset axis of the project within the latitude range as the standard latitude line includes: Based on the estimated Mercator projection length deformation of each measuring point and a fifth preset formula, when an iteration stop condition is satisfied, a target latitude line with the minimum total Mercator projection length deformation of the preset axis of the project within the latitude range is determined as the standard latitude line; the fifth preset formula includes: Among them, B o Indicates the latitude of the target latitude.
8. The method according to claim 1, characterized in that The deformation assessment report includes a deformation value list, a total deformation calculation process, and a deformation distribution curve diagram.