A method for calculating the three-dimensional coordinates of an arbitrary point

Abstract

This application provides a method for calculating the three-dimensional coordinates of an arbitrary point. The invention uses a combination of numerical and graphical methods, while also incorporating interdisciplinary research. Following the conventions of heterogeneous coordinate systems, it directly inputs the K coordinates corresponding to any point P from the existing coordinates in the design drawings. P J P H P and L P Four elements are used to calculate the three-dimensional coordinates P(X) of the route in the overall coordinate system of the point. P Y P , Z P This invention uses a heterogeneous coordinate system model and algorithm, a point domain model and algorithm, a perpendicular domain model and algorithm, and a quantum mathematical model and algorithm. It applies the principles of computational geometry and uses trigonometric functions and a mixed arithmetic operation of addition, subtraction, multiplication, and division to perform forward and inverse calculations of the plane coordinates of horizontal curves. This reduces the workload, speeds up the calculation, and improves the accuracy of the calculation results. It also ensures that the accuracy of all measurement and calculation results is 100%. It can be applied to the entire process of construction engineering survey and design, construction surveying, and measurement and testing.

Description

Technical Field

[0001] This application relates to a method and processor for calculating the three-dimensional coordinates of an arbitrary point, belonging to the fields of applied science, interdisciplinary research, engineering technology research, applied mathematics research, and information science research, specifically involving sub-fields of engineering surveying such as line and bridge and tunnel engineering surveying technology research, construction engineering surveying and testing technology research, quantum mathematical model and algorithm research, computational geometry application research, algebraic field theory application research, information digitization research, data processing and transmission, etc. Background Technology

[0002] The mathematical model of the existing line and bridge and tunnel measurement algorithm is to "treat straight segments as a special type of curve element, with the turning angle of the curve element of a straight segment being 0°, and the turning angle of the curve element of a non-straight segment being greater than 0°".

[0003] The monograph with essentially the same scope of professional technology involved in this invention is "CASIOfx-5800P Calculator and Road Construction Layout Program" edited by Professor Wang Zhongwei of Hunan Transportation Vocational College. Within the same scope of professional technology, its viewpoints and methods include:

[0004] 200: Unified calculation formula for line element elements and coordinates (P106~3.3.3); Numerical algorithm for calculating route coordinate integrals (P110~3.3.4).

[0005] 300: Calculation of coordinates of a point outside the centerline of the road (P114~3.4.1);

[0006] 400: Calculation of station number from a point outside the route (P116~3.4.2): A stepwise approximation algorithm;

[0007] 500: Longitudinal section calculation: Calculation mode of center stake coordinates and design elevation (P196~6.3.1);

[0008] 600: Cross-section calculation: Roadbed cut and fill layout mode (P207~6.3.4).

[0009] The invention patents that contain parts of the same content as this invention include: Application Publication No. CN112651068A, Application Publication Date 2021.04.13, a method for calculating the coordinates of arbitrary line elements of various types of lines; Application Publication No. CN113934974A, Application Publication Date 2022.01.14, a method for calculating the coordinates of arbitrary station numbers on a route; and Application Publication No. CN112733223A, Application Publication Date 2021.04.30, a method for back-calculating the corresponding line mileage and offset from known coordinate points.

[0010] The calculation methods derived from existing basic models of route and bridge / tunnel surveying algorithms have limitations. Sometimes, the lack of calculation results leads to dead loops, making it impossible to guarantee 100% accuracy of all surveying calculations. Current surveying calculations rely heavily on the experience and technical skills of individual surveying engineers. To avoid significant deviations in surveying calculations, current regulations and industry standards require a verification system: the project team's surveying engineer submits the report, and a third-party surveying engineer reviews it. Therefore, it is necessary to improve the reliability, accuracy, and speed of surveying calculations, innovate a surveying calculation method with 100% accuracy of all results, and establish a surveying and testing standard to enable effective and reliable surveying and testing during the construction engineering surveying, design, and construction processes. Summary of the Invention

[0011] The purpose of this application is to provide a method and processor for calculating the three-dimensional coordinates of an arbitrary point.

[0012] This invention is groundbreaking, representing a completely new technical solution unprecedented in technological history. Compared with existing technologies, it possesses outstanding substantive features and significant progress. The invention's inventiveness includes: employing an interdisciplinary research method, it summarizes the problems that need to be solved in engineering surveying and design, construction surveying, and measurement and testing into a mathematical problem of calculating the three-dimensional coordinates of any point. Then, using mathematical research methods, it innovates models and algorithms, and combines them with computer programming technology to calculate the three-dimensional coordinate values ​​of any point, ultimately applying them to engineering surveying and design, construction surveying, and measurement and testing processes. This invention establishes a point domain mathematical model and a perpendicular domain. Mathematical models, quantum mathematical models, and heterogeneous coordinate coefficient mathematical models enable the mutual crossing between the actual macroscopic world and the virtual quantum microscopic world. The models and algorithms of this invention are completely opposite to those of existing technologies, assuming that curves are special straight lines, while existing models and algorithms assume that straight lines are special curves. This invention applies the principles of computational geometry, using trigonometric functions and mixed arithmetic operations of addition, subtraction, multiplication, and division to replace the integral calculation methods of existing technologies. It can easily, quickly, and accurately calculate the planar coordinates of any point on a straight line, circular curve, and transition curve, and inversely calculate and determine the perpendicular midpoint and offset corresponding to any point with known coordinate values.

[0013] To achieve the above objectives, the first aspect of this application provides a method for calculating the three-dimensional coordinates of an arbitrary point, comprising the following steps:

[0014] Step 100: Establish a database, invent a heterogeneous coordinate system, and input the auxiliary parameter K corresponding to any point P in the design drawings, according to the specifications of the heterogeneous coordinate system. P J P H P L P K PIt is an arbitrary center stake, which is data describing the center position of a physical engineering project; J P It is the angle, which is data describing the geometric shape of a physical engineering project; H P L P These are detailed dimensional data for the engineering components;

[0015] Step 200: Based on the Kp value of any center stake and the data in the horizontal curve element sub-database, calculate the plane coordinate value K of any center stake. P (X) K Y K ) and tangent azimuth qie-ang1;

[0016] Step 300: Based on data J P H P L P X K Y K Calculate the plane coordinates P(X) of any point. P Y P );

[0017] Step 400: Calculate and determine any point P(X) with known coordinates. P Y P The corresponding perpendicular foot center stake A and offset AP;

[0018] Step 500: Longitudinal section calculation: Calculate the elevation Z1 of the vertical curve element sub-database, based on the data of the vertical curve element sub-database;

[0019] Step 600: Cross-section calculation: Based on the data from the cross-section slope and width sub-database and the elevation Z1 of the perpendicular center stake A, calculate the elevation Z of any point. P ;

[0020] Step 700: The three-dimensional coordinates of any point are P(X) P Y P , Z P ).

[0021] In the embodiments of this application, the calculation method is a targeted calculation method invented based on various specific conditions and scenarios of route and bridge / tunnel surveys, combined with the geometric shape of the data. Its features include: inventing a heterogeneous coordinate system model and algorithm to directly calculate three-dimensional coordinate values ​​based on the overall coordinate system of the route; inventing a quantum mathematical model and algorithm to directly calculate and determine the perpendicular center stake and offset corresponding to any point with known coordinate values; the calculation method is applicable to three linear elements of horizontal curves: straight lines, circular curves, and transition curves; the calculation method is applicable to circular curves with arbitrary turning angles and various types of transition curves; and the calculation method is applicable to any point on roads, bridges, culverts, and tunnels.

[0022] In the embodiments of this application, the database of the calculation method includes a horizontal curve element sub-database, a vertical curve element sub-database, and a cross-sectional slope and width sub-database.

[0023] The second aspect of this application provides a point domain model and algorithm for calculating the planar coordinates of any center stake. The point domain is a set of points, which is a real number domain. All points within the point domain share common characteristics: a common center stake number, the same planar coordinate values, and the same tangent azimuth angle. A horizontal curve is a string of beads composed of a finite number of point domains, and is a special straight line. The turning angle of a straight arrow is 0°, while the turning angle of a bow or crescent is not 0°. The three shapes of the horizontal curve—bow, crescent, and straight arrow—correspond to three linear elements: transition curve, circular curve, and straight line, respectively. The point domain model and algorithm first calculate the chord length of the transition curve and circular curve using a local planar coordinate system, and calculate the turning angle of the transition curve and circular curve using a local polar coordinate system. Then, the planar coordinates of any center stake of the straight line, circular curve, and transition curve are calculated uniformly using the polar coordinate method.

[0024] The third aspect of this application provides a method for calculating the plane coordinates of an arbitrary center stake, wherein step 200 includes the following steps:

[0025] Step 201: Taking a known center stake K0 as the origin, and the tangent direction of the known center stake K0 as... Establish a local plane coordinate system with the normal direction as the y-axis, and calculate the position of any center stake in the local plane coordinate system. y-value;

[0026] Step 202: Using the tangent direction of the known center stake K0 as the starting edge, establish a local polar coordinate system and calculate the rotation angle and tangent angle of any center stake in the local polar coordinate system;

[0027] Step 203: Calculate the plane coordinates and tangent azimuth of any center stake.

[0028] The fourth aspect of this application provides a heterogeneous coordinate system mathematical model and algorithm for calculating the planar or three-dimensional coordinates of any point. The model includes: a heterogeneous coordinate system with the center stake K as the origin, the H-axis as the tangent direction of the route or the short axis direction of the structure, and the L-axis as the long axis direction; the angle between the H-axis and the L-axis is J; the heterogeneous coordinate system is a planar oblique coordinate system; the heterogeneous coordinate system is a custom engineering coordinate system based on the method of combining numerical and graphical representations and utilizing local resources; the heterogeneous coordinate system mathematical model is a comprehensive model, summarizing and generalizing commonly used mathematical models in roads, bridges, culverts, and tunnels, encompassing both local planar coordinate systems and local polar coordinate systems; when J is 90°, the heterogeneous coordinate system is equivalent to the local planar coordinate system; when H or L is 0, the heterogeneous coordinate system is equivalent to the local polar coordinate system; the heterogeneous coordinate system mathematical model and algorithm belong to the field of computational geometry, meaning the model is always convergent and does not require training or learning, but directly uses planar geometric formulas to calculate the results of the mathematical model.

[0029] The fifth aspect of this application provides a method for calculating the planar coordinates of any point, which transforms from a heterogeneous coordinate system to the overall coordinate system of the route, and directly calculates the planar coordinate values ​​of any point.

[0030] The sixth aspect of this application provides a quantum mathematical model and algorithm, which are pioneering, including: the perpendicular domain is a set of points and is a real number field; the perpendicular foot, in plane analytic geometry, is a point where two lines intersect, with an angle ≡ 90°, and is a point without size, a special point in the perpendicular domain; all points in the perpendicular domain are the same as the perpendicular foot, satisfying the requirement of approximate perpendicularity; the quantum perpendicular domain collision model is a quantum mathematical model and also a plane geometric model; K0 is an arbitrary midpoint of the road segment under study with known coordinates, a known point; connecting the arbitrary midpoint K0 with the arbitrary point P with known coordinates, a known line segment PK0 is obtained; then, the perpendicular foot B0 of the arbitrary point P with known coordinates is drawn in the tangent direction of the arbitrary midpoint K0, resulting in a right triangle PK0B0 with different strengths; in the right triangle with different strengths, PK0 is the hypotenuse with different strengths, PB0 is the sine side with different strengths, and K0B0 is the cosine side with different strengths. It is the angle between the hypotenuse PK0 and the tangent direction of any center stake K0; then, taking the quantum dot domain K0 as the standard, with The direction indicated by the cosine value: when The cosine value is positive, and the quantum dot domain K1 that collides with the quantum dot domain K0 is found in the direction of the larger station. If the cosine value is negative, then find the quantum dot domain K1 that collides with the quantum dot domain K0 in the direction of the smaller station, and establish a right triangle PK1B1 with different strengths; It is the angle between the tangent direction of the hypotenuse PK1 and the center stake K1; following the above method, for point K on the horizontal curve of the route... n Each of them sequentially establishes a right triangle PK with different strengths.n B n The included angle is obtained. ,until Until the perpendicularity requirement is met; the quantum geometric model is always convergent. It is a qualitative indicator for determining verticality, when When the value differs from the perpendicular condition by less than 1°, its corresponding quantum dot domain K n Located in the core area; within the core area, Gradually approaching the vertical condition, the quantum dot domain K n When a collision or intersection occurs with the quantum perpendicular domain A, When the value satisfies the perpendicular condition, the quantum dot domain K n Training ends when the perpendicular foot domain A intersects or coincides with the quantum perpendicular foot domain; the absolute value of the heterosine edge Yq is a quantitative indicator for determining the perpendicular foot. The absolute value of Yq is larger outside the core region and smaller inside the core region; as... As the perpendicularity condition gradually approaches, the value of the opposite strong cosine edge Yq reaches the quantum level and gradually approaches 0, with the central pile K... n It gradually approaches the value of the perpendicular midpoint A, and training ends; Learning rate: using the point domain as a learning rate results in slow model convergence; Strong cosine edge, a dynamic value, is a very suitable learning rate value. Outside the core region, the absolute value of the strong cosine edge is larger, and the model converges quickly; inside the core region, the absolute value of the strong cosine edge is smaller, and the model converges more slowly; in the central part of the core region, the model converges even slower, as... As the model approaches the perpendicular condition, the value of the heterosine edge reaches the quantum level and gradually approaches 0. Overall, choosing the heterosine edge value as the learning rate slows down the model's convergence speed, resulting in particularly ideal results. Algorithm: First, determine the computational precision; the engineering measurement precision is 10. -4 m, when the condition is met, the number of sides of the heterodyne cosine is less than 10. -4 When m, the value of the perpendicular foot of the middle stake A is equal to the value of the middle stake K. n The value of the offset AP is equal to the value of the opposite sine side.

[0031] The seventh aspect of this application provides a method for calculating and determining the perpendicular foot center stake and offset corresponding to the known coordinates of any point, characterized in that step 400 includes the following steps:

[0032] Step 401: Determine the accuracy of engineering survey calculations (10). -4 m;

[0033] Step 402: K0 is an arbitrary center stake with known coordinates of the road segment under study. It is a known point. Connect the arbitrary center stake K0 with known coordinates and the arbitrary point P with known coordinates to obtain the known line segment PK0. Then, draw the foot of the perpendicular B0 of the arbitrary point P with known coordinates in the tangent direction of the arbitrary center stake K0 with known coordinates to obtain the right triangle PK0B0 with different strengths.

[0034] Step 403: Calculate the length of the hypotenuse PK0;

[0035] Step 404: Calculate the azimuth of the hypotenuse PK0;

[0036] Step 405: Calculate the angle between the hypotenuse and the tangent direction of any center stake K0 with known coordinates. ;

[0037] Step 406: Calculate the length value Yq0 of the cosine side with different strengths;

[0038] Step 407: If Yq0 ≥ 10 -4 If m, then: K1 = K0 + Yq0;

[0039] or Yq n ≥10 -4 m, then: K n+1 =K n +Yq n ;

[0040] Calculate the center pile K n+1 Planar coordinates and tangent azimuth X n+1 Y n+1 、qie-ang n+1 And replace the data of any known coordinate value of center stake K0 with the data of center stake K1, or use the data of center stake K n+1 Data replacement for center pile K n Data;

[0041] Step 408: Repeat steps 402 to 407 until Yq is satisfied. n <10 -4 Given the condition m, we obtain the perpendicular foot center stake A and the offset AP;

[0042] Step 409: For complex curves with multiple perpendicular center stakes, the start or end point of the study section can be taken as K0, and a differential strength correction coefficient can be set to make... The process gradually approaches the perpendicular condition from a single direction until the first perpendicular center stake A and offset AP are obtained. Then, the sum of A and an empirical value is used as the starting point of the second study section. The study continues in a single direction until the end or beginning of the study section, and all perpendicular center stakes and offsets are obtained.

[0043] The eighth aspect of this application provides a processor configured to perform the above-described method for calculating the three-dimensional coordinates of any point.

[0044] The beneficial effects of the above technical solution include:

[0045] This invention is an applied technology, belonging to the category of third-party testing. It is a new technology for construction engineering testing, a method for calculating the three-dimensional coordinates of any point, also known as the heterogeneous coordinate system line and bridge tunnel measurement and testing method, or simply the heterogeneous coordinate system measurement and testing method. It can be applied to the entire process of line and bridge tunnel engineering survey and design, construction surveying and measurement and testing. It can identify, analyze and solve major problems affecting quality and safety in the design and construction stages of specific engineering projects, based on the specific actual conditions of the project.

[0046] During the engineering survey and design process, this invention can be used to determine the relationship between the proposed design line and known landmark features or structures. During the engineering survey and design acceptance stage, the spatial positional relationship between known landmark features or structures and the proposed project can be calculated.

[0047] During the review of design drawings, the algorithm of this invention is used to verify the calculations using geometric formulas. This can provide scientific, reasonable, and feasible suggestions for optimizing the design drawings that are in line with the actual site conditions. The design drawings are drawn using general drawing software and geometric drawing methods. Under normal circumstances, there may be some omissions or even errors.

[0048] During construction, directly facing the project design drawings, we can conduct pre-construction and in-construction control. By using scientific, accurate, and authoritative measurement and calculation results to guide the surveying engineers of the construction and supervision parties, we can avoid blind measurement and layout, avoid rework, improve work efficiency, and improve the accuracy of measurement and layout work.

[0049] During the construction and acceptance phase, standardized, procedural, and 100% accurate measurement and calculation results are used to inspect the measurement and layout results of the completed engineering entity. This includes checking the main control indicators of the project, such as the route's horizontal alignment, longitudinal profile, cross profile, sight distance, superelevation, and widening; verifying that the longitudinal and transverse slopes and side slopes of the road surface conform to the approved design documents; checking that the location, elevation, dimensions, and geometry of bridges, culverts, and tunnel structures are consistent with the approved design documents; and ensuring that the project meets the requirements of the specifications. This ensures that the completed project entity is consistent with the design drawings, guaranteeing continuous alignment, balanced indicators, good visual appeal, and harmonious landscape, ultimately ensuring safe, comfortable, and fast driving.

[0050] Other features and advantages of the embodiments of this application will be described in detail in the following detailed description section. Attached Figure Description

[0051] The accompanying drawings are provided to further illustrate the embodiments of this application and constitute a part of the specification. They are used together with the following detailed description to explain the embodiments of this application, but do not constitute a limitation on the embodiments of this application. All drawings are plan views, in which:

[0052] Figure 1 The illustration shows a flowchart of a method for calculating the three-dimensional coordinates of an arbitrary point according to an embodiment of this application;

[0053] Figure 2 The illustration shows a flowchart of determining the perpendicular midstake and offset corresponding to any point with known coordinate values ​​according to an embodiment of this application.

[0054] Figure 3 This schematic diagram illustrates the relationship between the heterogeneous coordinate system and the overall route coordinate system according to an embodiment of this application;

[0055] Figure 4 The diagram illustrates the transformation between the heteropolar coordinate system and the global polar coordinate system according to an embodiment of this application.

[0056] Figure 5 This illustration schematically shows a point domain model of a horizontal curve according to an embodiment of the present application;

[0057] Figure 6 A schematic diagram of a quantum model of the perpendicular foot domain of a straight segment according to an embodiment of this application is shown.

[0058] Figure 7 The schematic diagram illustrates the principle of the quantum perpendicular domain collision model of the curve segment according to an embodiment of this application;

[0059] Figure 8 This illustration schematically shows a diagram of the "bow" calculation for the center stake in a transition curve section according to an embodiment of this application;

[0060] Figure 9 This schematic diagram illustrates the calculation of the center stake of a straight segment according to an embodiment of this application.

[0061] Figure 10 This illustration schematically shows a diagram of the calculation of the "crescent moon" at the center stake of a circular curve road section according to an embodiment of this application;

[0062] Figure 11 This schematic diagram illustrates a planar view of the overall coordinate system of a route according to an embodiment of this application;

[0063] Figure 12 A schematic diagram of a partial coordinate system according to an embodiment of this application is shown;

[0064] Figure 13A schematic diagram of a local polar coordinate system according to an embodiment of this application is shown;

[0065] Figure 14 A schematic diagram of the overall polar coordinate system according to an embodiment of this application is shown;

[0066] Figure 15 A simplified quantum perpendicular domain collision model is schematically illustrated according to an embodiment of this application;

[0067] Figure 16 This schematic diagram illustrates a plane diagram showing the inverse calculation of the corresponding perpendicular station number and offset from any known coordinate point according to an embodiment of this application.

[0068] Figure 17 The illustration shows a flowchart of a method for calculating the three-dimensional coordinates of an arbitrary point according to another embodiment of this application. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only for illustration and explanation of the embodiments of this application and are not intended to limit the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0070] To address the aforementioned problems, this invention provides a method for calculating the three-dimensional coordinates of any point.

[0071] The overall inventive concept of a method for calculating the three-dimensional coordinates of an arbitrary point includes the following five inventions, of which method invention 1 is a combination invention and method invention 4 is a pioneering invention.

[0072] Invention 1: A method for calculating the three-dimensional coordinates of an arbitrary point;

[0073] Method Invention 2: A mathematical model and algorithm for arbitrary center stake plane coordinates;

[0074] Method Invention 3: A mathematical model and algorithm for the planar coordinates of an arbitrary point;

[0075] Method Invention 4: A method for inversely calculating and determining the known coordinates P(X) of any point P Y P The mathematical model and algorithm for the corresponding perpendicular foot center stake A and offset AP;

[0076] Product Invention 1: A data processor for a method of measuring and detecting railway lines, bridges, and tunnels;

[0077] In the first general embodiment, a general technical solution for calculating the three-dimensional coordinates of an arbitrary point is provided, and the flowchart of the calculation program is as follows. Figure 1 As shown, it includes the following steps 100 to 700:

[0078] Step 100: Establish a database and, according to the specifications of the heterogeneous coordinate system, input the auxiliary parameter K that is already present in the design drawings and corresponds to any point P. P J P H P L P K P It is the center pile, which is data describing the center position of the physical structure; J P It is the angle, which is data describing the geometric shape of a physical engineering project; H P L P These are detailed dimensional data for the engineering project;

[0079] Step 200: Calculate the plane coordinate value K of the center stake based on the data in the arbitrary center stake Kp and the horizontal curve element sub-database. P (X) K Y K ) and tangent azimuth qie-ang1;

[0080] Step 300: Based on data J P H P L P X K Y K Calculate the plane coordinates P(X) of any point. P Y P );

[0081] Step 400: Calculate and determine any point P(X) with known coordinates. P Y P The corresponding perpendicular foot center stake A and offset AP are calculated using the following flowchart: Figure 2 As shown;

[0082] Step 500: Longitudinal section calculation: Calculate the elevation Z1 of the vertical curve element sub-database, based on the data of the vertical curve element sub-database;

[0083] Step 600: Cross-section calculation: Based on the data from the cross-section slope and width sub-database and the elevation Z1 of the perpendicular center stake A, calculate the elevation Z of any point. P ;

[0084] Step 700: The three-dimensional coordinates of any point are P(X) P Y P , Z P ).

[0085] The overall technical solution shares similarities with existing technologies such as the CASIOfx-5800P calculator and road construction layout program, including:

[0086] 1) Same research field: railway and bridge / tunnel surveying engineering;

[0087] 2) Same research objects: three linear elements, straight lines, circular curves, and transition curves;

[0088] 3) The same five calculation steps: Steps 200 to 600, first calculate the plane coordinate values ​​of the center stake and the side stake, then calculate the corresponding station number and offset, and calculate the elevation in the longitudinal section and cross section;

[0089] 4) The same computing tool products: computer programming technology.

[0090] The overall technical solution differs from existing technologies such as the CASIOfx-5800P calculator and road construction layout program, including:

[0091] 1) The mathematical models are completely opposite: existing technology considers a straight line to be a special type of curve, while this invention considers a curve to be a special type of straight line;

[0092] 2. The research focuses are completely different. Existing technologies focus on the calculation method of transition curves and extend the calculation method to circular curves and straight lines; this invention focuses on the algorithm of straight lines and extends the algorithm to circular curves and transition curves.

[0093] In Example 1, a database for the measurement and detection method using a heterogeneous coordinate system was established, and the auxiliary parameter K corresponding to any point P was determined. P J p H p L p Step 100 includes the following steps:

[0094] Step 101: First, analyze, summarize, and classify all the plan, vertical, and horizontal data corresponding to the three-view solid model of the design drawings, and divide them into the following three categories according to the shape and function of the data:

[0095] 1) Control parameters. Control parameters are essential and indispensable basic parameters for controlling the route alignment and describing route characteristics. Control parameters are used to calculate the centerline coordinates within the intersection area using the intersection method; for example: station number, plane coordinates, curve radius, and transition curve length of the route intersection in horizontal curve elements; station number, elevation, and curve radius of the slope change point in vertical curve elements; standard cross slope value and superelevation value;

[0096] 2) Auxiliary parameters refer to the parameters calculated from the horizontal curve elements in the control parameters. These parameters are essential for calculating the centerline coordinates of other road sections using the line element method. For example, parameters for straight and gentle curve points include station number, plane coordinates, and tangent azimuth.

[0097] 3) Descriptive parameters, used to describe the characteristics of things, are divided into the following two categories:

[0098] 3.1) Original data from design drawings, such as center stake number and detailed dimensions of the project; the center stake number is the only special descriptive parameter, serving as the connecting bridge between horizontal, vertical, and transverse axes, and is indispensable in all three axes; it is also the most frequently used parameter. For a given center stake number, it means that this information is provided, including the specific location, distance from the starting point, three-dimensional coordinate values, tangent azimuth, and normal azimuth.

[0099] 3.2) Non-auxiliary parameters calculated from control parameters, such as horizontal curve turning angle, transition curve angle, curve length, tangent length; vertical curve slope and slope length;

[0100] Step 102: Establish a database model. This database is a dedicated database, built based on the three-view model of the design drawings and the characteristics of the project. A database is created for each project. This database is called the Heterogeneous Coordinate System Measurement and Inspection Method Database. See [link / reference]. Figure 1 It includes the following three sub-databases:

[0101] 1) The horizontal curve element sub-database includes two types: intersection point database and line element database. The intersection point database is a sub-database that stores control parameters, including the station number, plane coordinates, curve radius, and transition curve length of the intersection point. It is used to calculate the center line coordinates and tangent azimuth of the preceding straight line, first transition curve, circular curve, second transition curve, and subsequent straight line within the intersection point. The line element database is also a sub-database that stores auxiliary parameters, including the station number of the main point, plane coordinate value X, tangent azimuth, curve radius, and transition curve length. It is used to calculate the center line coordinates and tangent azimuth of the line element.

[0102] 2) Vertical curve element sub-database, which stores control parameters such as the station number of the slope change point, the elevation of the slope change point, and the curve radius, and is used to calculate the design elevation of the center pile on the longitudinal section;

[0103] 3) Cross-section slope and width sub-database. Stores standard cross slope, superelevation values, widened sections, and widening formula control parameters for calculating the design elevation of any point on the cross section.

[0104] Step 103: Input the auxiliary parameter K that is already in the design drawing and corresponds to any point P. P J p H p Lp ,like Figure 1 , Figure 3 , Figure 4 As shown.

[0105] In Example 2, a point domain model and algorithm are provided for calculating the planar coordinates of any center stake. The point domain is a set of points, which is a real number domain. All points in the point domain have common characteristics: a common center stake number, the same planar coordinate value, and the same tangent azimuth angle. The horizontal curve of the route is a string of beads composed of a finite number of point domains. It is a special straight line. The turning angle of the straight line is 0°, while the turning angle of the curved line and the crescent line is not 0°. The three shapes of the horizontal curve of the route, the curved line, the crescent line, and the straight line, correspond to the three linear elements of the transition curve, the circular curve, and the straight line, respectively. The point domain model and algorithm first calculate the chord length of the transition curve and the circular curve using a local planar coordinate system, and calculate the turning angle of the transition curve and the circular curve using a local polar coordinate system. Then, the planar coordinates of any center stake of the straight line, the circular curve, and the transition curve are calculated uniformly using the polar coordinate method.

[0106] A model and algorithm for arbitrary centerline plane coordinates are presented, creating a new term: point-domain mathematical model. The point-domain mathematical model is an application of algebraic field theory and the method of combining numbers and shapes in the field of measurement and calculation. The point-domain mathematical model includes:

[0107] 1) A point field is a set of points, which is the field of real numbers. Field theory is a branch of abstract algebra and the most basic concept in algebra. It is the foundation of many disciplines. The point field originates from and serves the engineering design and construction process. In the engineering design and construction process, the horizontal curve of the route is segmented, and the chord connecting the two endpoints of the curve represents the corresponding curve segment. Then, through technical solutions and management measures, the road surface alignment corresponding to the curve segment is ensured to meet the design and specification requirements.

[0108] 1-1) Design and construction methods for curved bridges and straight bridges;

[0109] 1-2) Arrangement of straight blast holes during curved tunnel mining construction, and setting and adjustment of shield machine attitude during shield tunneling construction;

[0110] 1-3) When constructing the subgrade of curved road sections, a control cross section shall be set every 20 meters; when constructing the pavement, a control cross section shall be set every 5 meters.

[0111] 2) A schematic diagram of the point-domain model of the horizontal curve of the route is shown below. Figure 5 K is the horizontal axis, and X is the vertical axis; the value of the horizontal curve on the X-axis changes regularly as the center stake number K increases; for any center stake A on the horizontal curve, with a length EF of 10 mm, the set of infinitely many center stake points within EF is A-5 mm ≤ K < A+5 mm, which is a real number field, denoted as set A / 10 mm. Figure 5 As shown in the large circle in the middle;

[0112] 3) Global Domain. In this example, we take A / 10mm as the object of study and name it the global domain;

[0113] 4) Subdomains. Divide EF into 10 equal segments, each 1 mm, to obtain 10 non-overlapping subdomains a, b, c, d, e, f, g, h, i, j; the sum of the ten subdomains is the global domain A / 10 mm;

[0114] 5) Subdomains. Dividing subdomain 'a' into 10 equal segments of 0.1 mm each, we obtain 10 non-overlapping subdomains: a1, b1, c1, d1, e1, f1, g1, h1, i1, j1. Therefore, the sum of these 10 adjacent subdomains constitutes one subdomain.

[0115] 6) Beading. Figure 5 In this context, the relationship between 10 mutually neighboring and non-overlapping subdomains a, b, c, d, e, f, g, h, i, j is defined as a beaded string. For example, the beaded string of a, b, c, d, e, f, g, h, i, j is the global domain A / 10.

[0116] 7) Collision. This relationship between adjacent subdomains is defined as a collision, such as... Figure 5 Collision a collides with b, b collides with c, and c collides with d. Figure 6 In the middle, A1 collides with A2;

[0117] 8) Intersection. Two point domains are defined as intersecting if they have some common elements, such as... Figure 7 The point domain K5 intersects with the point domain A.

[0118] 9) Coincidence. Two point domains are defined as coinciding if all elements are exactly the same.

[0119] 10) Characteristics of a point domain. A point domain is a set with a definite diameter. The common characteristics of point domains include: each point domain is a straight line segment; all points within a point domain have a common centerline number; they all have the same planar coordinate values; and they all have the same tangent azimuth angle. As the centerline number increases, the planar position of the point domain changes according to mathematical geometric formulas, and the tangent azimuth angle also changes according to regular patterns.

[0120] 11) The purpose of a point domain is to simplify complex horizontal curves and routes, transforming them into a finite set of shapes, thus achieving a combination of numerical and graphical representations. Figure 5 In Chinese, a horizontal curve is a complex curve composed of countless geometric points; however, according to point domain theory, a horizontal curve is a string of beads composed of a finite number of point domains, and is a special straight line. The turning angle of a straight line is 0°, while the turning angle of a transition curve or a circular curve is not 0°.

[0121] A model and algorithm for arbitrary centerline plane coordinates are categorized into three types based on the geometric properties and shape of the horizontal curve of the route:

[0122] 1) Bow, indicating a gentle curve section, see Figure 8 The thick solid line portion, the straight-to-straight point of the transition curve, or the straight-to-straight point, is connected to any midpoint on the transition curve to form a chord. The chord does not conform to the actual route; the actual route is gentler. The shape formed by the chord and the actual route resembles a bow.

[0123] 3) Straight arrows indicate straight road sections, see Figure 9 The thick solid line portion, where the chord coincides with the actual route, is a straight line shaped like an arrow.

[0124] 2) Crescent moon, representing a circular curve section, see Figure 10 The thick solid line portion is formed by connecting the gentle curve point with any midpoint on the curve to form a chord. The chord does not match the actual route, which is an arc. The shape formed by the chord and the actual arc route resembles a crescent moon.

[0125] In Example 3, a method for calculating the plane coordinates of an arbitrary center pile is provided. Step 200 includes the following steps:

[0126] Step 201: Taking a known center stake K0 as the origin, and the direction of the tangent to the known center stake route as... Establish a local plane coordinate system with the normal direction as the y-axis, and calculate the position of any center stake in the local plane coordinate system. y-value. In this invention, the local planar coordinate system is used only for calculating the chord length;

[0127] Calculate the center stake K of any straight segment P The coordinate values ​​in the local coordinate system are determined using the following formula:

[0128] =K P -K0 (Formula 1)

[0129] y = 0 (Formula 2)

[0130] In the formula above: K0 is the intersection station number, which is data from the horizontal curve element sub-database. y—Middle pile K P Coordinate values ​​in the local coordinate system;

[0131] Calculate the center stake K of any transition curve segment P The coordinate values ​​in the local coordinate system are determined using the following formula:

[0132] =(K P -ZH) (Formula 3)

[0133] (Formula 4)

[0134] (Formula 5)

[0135] In the formula above: R is the curve radius, Ls is the transition curve length, and R and Ls are data from the horizontal curve feature sub-database; ,! Factorial, *—multiplication, / —division, n is the term number, where n is a natural number from 3 to 19. y—Middle pile K P Coordinate values ​​in the local coordinate system;

[0136] Calculate the center stake K of any circular curve segment P The coordinate values ​​in the local coordinate system are determined using the following formula:

[0137] =Rsinβ (Formula 6)

[0138] y=R(1-cosβ) (Formula 7)

[0139] In the formula above: R is the curve radius, which is data from the horizontal curve feature sub-database; y—Middle pile K P Coordinate values ​​in the local coordinate system;

[0140] Step 202: Using the tangent direction of the known center stake K0 as the starting edge, establish a local polar coordinate system and calculate the coordinates of any center stake K. P The rotation angle and tangent angle in the local polar coordinate system. In this invention, the local polar coordinate system is used only for calculating the rotation angle and tangent angle;

[0141] Calculate the center stake K of any straight segment P The angles of rotation and tangents are determined using the following formulas:

[0142] β=0 (Formula 8)

[0143] α=0 (Formula 9)

[0144] In the formula above: β—rotation angle, α—tangential angle;

[0145] Calculate the center stake K of any transition curve segment P The angles of rotation and tangents are calculated using the following formulas:

[0146] β=90 (K) P -ZH) 2 ÷ (π*R*Ls) (Formula 10)

[0147] α=tan -1 (y / )≈β / 3 (Formula 11)

[0148] In the formula above: ZH is the station number of the straight-curve point, which is data from the horizontal curve element sub-database; β—angle of rotation, α—angle between chord and tangent y—Middle pile K P Coordinate values ​​in the local coordinate system;

[0149] Calculate the center stake K of any circular curve segment P The angles of rotation and tangents are calculated using the following formulas:

[0150] β=180 (K) P -HY)÷πR (Formula 12)

[0151] α = 90 (K) P -HY)÷πR (Formula 13)

[0152] In the formula above: HY is the station number of the transition point, which is data from the horizontal curve element sub-database; β—turning angle, α—chord-tangent angle;

[0153] Step 203: Calculate the plane coordinates and tangent azimuth of any center stake. Specifically, calculate the coordinates of any center stake K for three linear elements: transition curve, circular curve, and straight line. P The method for using coordinates and tangent azimuth angles uses the same straight line calculation formula as follows:

[0154] C-ang1=qie-ang0+α (Formula 14)

[0155] C= (Formula 15)

[0156] X K =X0+C*cos(C-ang1)(Formula 16)

[0157] Y K =Y0+C*sin(C-ang1)(Formula 17)

[0158] qie-ang1=qie-ang0+β (Formula 18)

[0159] In the formula above: X0, Y0, qie-ang0—coordinates and tangent azimuth of the intersection point, straight-to-curved point, or curvature point, which are data from the horizontal curve element sub-database; C-ang1—chord length azimuth, C—chord length, X K Y K qie-ang1—Middle pile K P Coordinates and tangent azimuth.

[0160] A method for calculating the plane coordinates of an arbitrary center stake uses the following coordinate systems:

[0161] 1) The overall coordinate system of the route is denoted as X-0-Y, with due north as the X-axis and due east as the Y-axis. See [reference needed]. Figure 11 P(1000, 1000) indicates that the horizontal length of point P along the X-axis is 1000 meters and the horizontal length along the Y-axis is 1000 meters; M(600, 500) indicates that the horizontal length of point M along the X-axis is 600 meters and the horizontal length along the Y-axis is 500 meters; the overall coordinate system of the route is the commonly used surveying coordinate system in China, which is the coordinate system specified by the design drawings. It can be directly converted to geodetic latitude and longitude. Similar to the characteristics of geodetic latitude and longitude, the X-axis corresponds to latitude and the Y-axis corresponds to longitude; generally, the 1980 Xi'an coordinate system and the 1985 National Yellow Sea Elevation Datum are adopted.

[0162] 2) Local planar coordinate system, see Figure 12 Taking the station number K in the route as the origin, and the tangent direction of the route as... The axis, with the normal direction as the y-axis, is a local planar coordinate system. The y-axis is not due north, and the y-axis is not due east. In this invention, its function is only to calculate the chord length C.

[0163] 3) Local polar coordinate system, see Figure 13 ; denoted as (θ′, ρ), with the tangent direction N′ of the center pile K as the starting side, θ′ represents the angle between the line connecting the point and the center pile K and this side, and ρ represents the distance from the point to the center pile K; In this invention, the angle values ​​θ′ of the tangent angle and the turning angle of the crescent and the bow curve element are calculated using a local polar coordinate system. Therefore, the calculation method of this invention is applicable to circular curves with arbitrary turning angles and various types of transition curves.

[0164] 4) Global polar coordinate system, see Figure 14 Let , be denoted as (θ, ρ), where θ represents the angle between the line connecting the point to the origin and the north X direction, and ρ represents the distance from the point to the origin.

[0165] 5) The correspondence between the coordinate values ​​(X, Y) of the overall route coordinate system is as follows:

[0166] X=ρcosθ (Formula 19)

[0167] Y=ρsinθ (Formula 20)

[0168] 6) Formula for calculating the global polar coordinate system (θ, ρ):

[0169] θ=tan -1 (Y / X) (Formula 21)

[0170] = (Formula 22)

[0171] A method for calculating the plane coordinates of an arbitrary center stake, with related custom features including:

[0172] 1) Define relevant data variables so that they can directly participate in calculations regardless of whether their values ​​are positive or negative;

[0173] 2) The default unit for length is meters, and the default unit for angle is degrees, unless otherwise specified.

[0174] 3) The overall coordinate system of the route is the default coordinate system. For any point P(X... P Y P , Z P The three-dimensional coordinates of the ) are all positive numbers;

[0175] 4) Both the overall coordinate system and the local plane coordinate system of the route adopt the right-hand measurement coordinate system; the X-axis in the overall coordinate system of the route is due north, which is labeled as Y in the mathematical plane rectangular coordinate system; the Y-axis in the overall coordinate system of the route is due east, which is labeled as X in the mathematical plane rectangular coordinate system, and the two are exactly interchanged.

[0176] 5) In the global polar coordinate system (θ, ρ) and the local polar coordinate system (θ′, ρ), the values ​​of θ and θ′ range from -∞ to +∞, generally between -720° and 720°; the value of ρ ranges from -∞ to +∞.

[0177] 5.1) When θ′ < 0, it means rotating counterclockwise by this angle value starting from the N′ direction; for example... Figure 13 Medium: KA "-30, 100";

[0178] 5.2) When θ′ > 0, it means rotating this angle value clockwise from the N′ direction as the starting point; for example... Figure 13 Chinese: KB "45,100";

[0179] 5.3) When ρ < 0, it indicates that the point is in the direction of angle value +180°, such as... Figure 13 In Chinese: KC“45,-100”=KC“225,100”.

[0180] 6) A horizontal curve radius R less than 0 indicates a left-turn horizontal curve, and a horizontal curve greater than 0 indicates a right-turn horizontal curve; when R=0, it indicates that the road segment is a straight line.

[0181] 7) The left and right turn attributes of horizontal curves are simplified, as are the concepts of concave and convex vertical curves. The attributes are automatically determined by the measurement software after calculation.

[0182] 8) For bridges that are "curved but straight", the direction of the short axis of the structure is uniformly the tangent direction of the bridge center station. When the program calculates the input value of K, add a negative sign in front of the K value. At this time, the program will prompt you to input an angle value θ as the H-axis azimuth angle value.

[0183] In Example 4, a heterogeneous coordinate system mathematical model and algorithm are provided for calculating the planar or three-dimensional coordinates of any point. Its features include: the heterogeneous coordinate system is a custom engineering coordinate system based on a combination of numerical and graphical methods, utilizing readily available resources. For example... Figure 3 As shown, the heterogeneous coordinate system has the center stake station K as the origin, the H-axis as the tangent direction of the route or the short axis direction of the structure, and the L-axis as the long axis direction. The angle between the H-axis and the L-axis is J. Here, J is not necessarily 90°. For example, if J is not 90°, the heterogeneous coordinate system can be a planar oblique coordinate system.

[0184] The heterogeneous coordinate system mathematical model is a comprehensive model that summarizes and generalizes commonly used mathematical models in roads, bridges, culverts, and tunnels. It encompasses both local planar coordinate systems and local polar coordinate systems. When J is 90°, the heterogeneous coordinate system is equivalent to the local planar coordinate system. When H or L is 0, the heterogeneous coordinate system is equivalent to the local polar coordinate system. Therefore, the heterogeneous coordinate system mathematical model and algorithm are applicable to any point on roads, bridges, culverts, and tunnels.

[0185] The transformation between heterogeneous coordinate systems and the overall coordinate system of the route, such as... Figure 3 As shown, any point P on the route, denoted as P(K, J, H, L) in a heterogeneous coordinate system, corresponds to the coordinate value P(X, Y) of the overall coordinate system of the route as follows:

[0186] X=X K +HCos(qie-ang1)+LCos(qie-ang1+J) (Formula 23)

[0187] Y=Y K +HSin(qie-ang1)+LSin(qie-ang1+J) (Formula 24)

[0188] In the formula above: X K Y K is the known coordinate value of center stake K, and qie-ang1 is the known tangent azimuth angle of center stake K;

[0189] like Figure 4 As shown, the heterogeneous coordinate system and the global polar coordinate system P( , The correspondence between ) is as follows:

[0190] X = L P +H P *cosJP (Formula 25)

[0191] Y=H P *SinJ P (Formula 26)

[0192] =Tan -1 (Y÷X) (Formula 27)

[0193] =qie-ang1+J P - (Formula 28)

[0194] (Formula 29)

[0195] In the formula above: qie-ang1 is the known center stake K. P The tangent azimuth angle, where X and Y are the coordinates of the local plane coordinate system, and θ′ is the angle between any point P and the known center stake K. P The angle between the line and the L-axis.

[0196] In Example 5, a method for calculating the planar coordinates of an arbitrary point P includes step 300, which involves transforming from a heterogeneous coordinate system to the overall route coordinate system. When directly calculating the planar coordinate values ​​of an arbitrary point, the following formula is used:

[0197] X P =X K +H P Cos(qie-ang1)+L P Cos(qie-ang1+J) P ) (Formula 30)

[0198] Y P =Y K +H P Sin(qie-ang1)+L P Sin(qie-ang1+J) P ) (Formula 31)

[0199] In the formula above: X K Y K qie-ang1 is the center pile K P The coordinates and tangent azimuth.

[0200] In Example 6, a method for calculating and determining the perpendicular foot center stake and offset corresponding to any point with known coordinate values ​​is presented. This method creates a new term, the perpendicular foot domain, which is a comprehensive application of algebraic field theory and fuzzy mathematics in the field of measurement and calculation. Its characteristics include:

[0201] 1) The perpendicular field is a set of points, a real number field, and a concept in engineering mathematics. The angle of intersection is approximately 90°. The foot of the perpendicular is a point without size. In plane analytic geometry, two lines are orthogonal at this point, and the angle of intersection is not exactly 90°. The theory of the perpendicular field states that the foot of the perpendicular is a special point in the perpendicular field. All points in the perpendicular field are the same as the foot of the perpendicular, satisfying the requirement of approximate perpendicularity.

[0202] 2) Figure 6 This is a schematic diagram of a quantum model of the perpendicular foot domain of a straight line segment. The length of the line segment A1 to A9 is 9 nm, divided into 9 point domains: point domain A1, point domain A2... point domain A9. P is a point on the bisector of the line segment, and point A5 is the geometric foot of the perpendicular. Point P is connected to A1, forming an angle α1 with the line segment; point P is connected to A2, forming an angle α2 with the line segment; and so on, connecting to A9 to obtain α9.

[0203] 3) When the calculation accuracy is 9nm, the points on the A1~A9 domains are all approximate feet of point P, α1≈90°, and are denoted as the foot domain P / A1A9;

[0204] 4) When the calculation accuracy is 7nm, the points in the A2~A8 domain are all approximate perpendicular feet of point P; α2>α1, α2≈90°, denoted as the perpendicular foot domain P / A2A8;

[0205] 5) When the calculation accuracy is 5nm, the points in the A3~A7 domain are all approximate perpendicular feet of point P; α3>α2, α3≈90°, denoted as the perpendicular foot domain P / A3A7;

[0206] 6) When the calculation accuracy is 3nm, the points in the A4~A6 domain are all approximate feet of point P; α4>α3, α4≈90°, denoted as the foot domain P / A4A6;

[0207] 7) When the calculation accuracy is 1nm, all points in the A5 domain are approximate perpendicular feet of point P, α5 > α4, and α5 ≡ 90°, denoted as P / A5.

[0208] A simplified quantum perpendicular domain collision model, a first-generation model, such as... Figure 15 As shown, in the overall coordinate system of the route, the starting point coordinates of the straight line OC are O(0, 0), the tangent azimuth angle is 0°, and the ending point is C(240, 0). Given point P(200, 300), find the foot of the perpendicular A(X) of the line corresponding to point P. A The coordinates X of (0) A .

[0209] like Figure 15 As shown, a quantum perpendicular domain is established at the starting point O of the straight line. The quantum perpendicular domain O is a set of points in the range of -5nm to 5nm. Moving the quantum perpendicular domain O 10nm in the X-axis direction, a quantum perpendicular domain O1 that collides with it is obtained. This process is repeated to obtain quantum perpendicular domains O1 and O2 that collide with each other. n-1It is the quantum perpendicular domain O of the collision relationship. n When n=2*10 10 At that time, the quantum perpendicular domain O n It coincides with the quantum perpendicular domain A. Through the... Figure 15 Analysis of the right triangle PA0 revealed three solutions, each starting from points O(0, 0), B(50, 0), and C(240, 0). The relevant calculation data are shown in Tables 1-3 below. All three results are 200m, indicating they are correct. When n=8, the calculation accuracy reaches 10. -4 When n=16, the calculation precision reaches 10. -9 m.

[0210] Table 1. Statistical table of relevant calculation data starting from O(0, 0)

[0211]

[0212] Table 2. Statistical table of relevant calculation data starting from B(50, 0)

[0213]

[0214] Table 3. Statistical table of relevant calculation data starting from C(240, 0)

[0215]

[0216] Analysis of the calculated data can be understood as follows: In a known point domain equipped with detection equipment, the angle is first measured. Based on the measured angle and distance, select a correction coefficient, calculate an empirical distance value, and then move this value along the straight line towards the foot of the perpendicular to obtain the first point. Continue this process until the 8th point, at which point the distance to point A is less than 10. -3 m, when moved to the 16th point, the distance from point A is less than 10. -8 m.

[0217] The research results on straight line segments can be extended to the entire horizontal curve, including straight lines, circular curves, and transition curves, and a second-generation quantum perpendicular domain collision model can be established.

[0218] A method for inversely calculating and determining the perpendicular midpoint and offset corresponding to any point with known coordinates provides a quantum mathematical model and algorithm, such as... Figure 16 As shown, a kind of creation was created. Figure 7As shown, the model and algorithm are pioneering. The perpendicular domain is a set of points, which is the real number domain. The perpendicular foot, in plane analytic geometry, is a point where two lines intersect, with an angle ≡ 90°. It is a point without magnitude and a special point in the perpendicular domain. All points in the perpendicular domain are like the perpendicular foot, satisfying the requirement of approximate perpendicularity. The quantum mathematical model: the quantum perpendicular domain collision model, is a plane geometric model that is a comprehensive application of fuzzy mathematics, quantum mathematics, mathematical model theory, computational geometry, and the method of combining numbers and shapes. Its purpose is to determine the perpendicular foot midpoint A and offset AP corresponding to any point with known coordinate values. Stake A is the theoretical foot of the perpendicular. Based on stake A, a theoretical perpendicular domain A is established, where all points satisfy the approximately perpendicular condition. K0 is an arbitrary stake with known coordinates in the road segment under study, and is a known point. Connecting the arbitrary stake K0 with known coordinates to the arbitrary point P with known coordinates yields the known line segment PK0. Then, along the tangent direction of the arbitrary stake K0, the foot of the perpendicular B0 to the arbitrary point P with known coordinates is drawn, resulting in a right triangle PK0B0 with different strengths. In this right triangle, PK0 is the hypotenuse with different strengths, PB0 is the sine side with different strengths, and K0B0 is the cosine side with different strengths. It is the angle between the hypotenuse PK0 and the tangent direction of any center stake K0;

[0219] Then, using the quantum dot domain K0 as the standard, The direction indicated by the cosine value: when The cosine value is positive, and the quantum dot domain K1 that collides with the quantum dot domain K0 is found in the direction of the larger station. If the cosine value is negative, find the quantum dot domain K1 that collides with quantum dot domain K0 in the direction of the smaller station; establish a right triangle PK1B1 with different strengths; It is the angle between the hypotenuse PK1 and the tangent direction of the center stake K1; similarly, for a point Kn on the horizontal curve of the route, a similar right triangle PKnBn can be constructed to obtain a similar angle.

[0220] The length value PB of the sinusoidal side of the opposite strength n =PK n ×sin (Formula 32)

[0221] The length of the cosine side Yq n = K n B n =PK n ×cos (Formula 33)

[0222] The quantum geometric model is always convergent: using fuzzy mathematics, an approximate perpendicular concept is defined between perpendicularity and non-perpendicularity. It is a qualitative indicator for determining verticality. When When the value differs from the perpendicular condition by less than 1°, its corresponding quantum dot domain K n Located in the core area; within the core area, Gradually approaching the vertical condition, the quantum dot domain K n When a collision or intersection occurs with the quantum perpendicular domain A, When the value satisfies the perpendicular condition, the quantum dot domain K n Training ends when the perpendicular foot domain A intersects or coincides with the quantum perpendicular foot domain. Following quantum mathematics methods, the distinct cosine edge Yq is studied in detail: the distinct cosine edge Yq is a quantitative indicator for determining the perpendicular foot; the absolute value of the distinct cosine edge Yq is larger outside the core region, and smaller inside the core region. With... As the perpendicularity condition gradually approaches, the value of the opposite strong cosine edge Yq reaches the quantum level and gradually approaches 0, with the central pile K... n It gradually approaches the value of the vertical foot midpoint A, and the training ends;

[0223] Learning rate: Using the point domain as a learning rate results in slow model convergence. The heterosine edge, a dynamic value, is a very suitable learning rate. Outside the core region, the absolute value of the heterosine edge is larger, leading to fast model convergence. Inside the core region, the absolute value of the heterosine edge is smaller, slowing down model convergence. In the central part of the core region, model convergence becomes increasingly slower. As the condition of verticality approaches, the value of the strong cosine edge reaches the quantum level and gradually approaches 0. Overall, choosing the value of the strong cosine edge as the learning rate makes the model convergence speed slow down, and the results are particularly ideal.

[0224] Determine any point P(X) with known coordinates. P ,Y P The specific algorithms for the corresponding perpendicular foot center stake A and offset AP are as follows: First, determine the calculation accuracy. Under ordinary PC computer conditions, the maximum allowable accuracy is 10. -15 m, based on the accuracy of existing measuring instruments 10 -3 m, the measurement and calculation accuracy is generally taken as 10. -4 m, when the condition is satisfied, the heterogeneous cosine edge Yq n <10 -4 When m, the value of the perpendicular foot of the middle stake A is equal to the value of the middle stake K. n The value of the offset AP is equal to the value of the opposite sinusoidal side;

[0225] In the heart of the core area lies the quantum microscopic world: straight lines, circular curves, and transition curves—all three linear elements—can be determined using the same method to pinpoint any point P(X) with known coordinates. P Y PThe corresponding perpendicular center stake A and offset AP are used for the calculation method, which is applicable to three types of linear elements of horizontal curves: straight lines, circular curves, and transition curves.

[0226] In Example 7, a method is provided for back-calculating and determining the perpendicular foot center stake and offset corresponding to the known coordinates of any point, such as... Figure 7 and Figure 16 As shown, step 400 includes the following steps:

[0227] Step 401: Determine the accuracy of engineering survey calculations (10). -4 m;

[0228] Step 402: K0 is an arbitrary center stake with known coordinates of the road segment under study. It is a known point. Connect the arbitrary center stake K0 with known coordinates and the arbitrary point P with known coordinates to obtain the known line segment PK0. Then, draw the foot of the perpendicular B0 of the arbitrary point P with known coordinates in the tangent direction of the arbitrary center stake K0 with known coordinates to obtain the right triangle PK0B0 with different strengths.

[0229] Step 403: Calculate the length PK0 of the line connecting any point P and the center stake K0 using the following formula:

[0230] PK0= (Formula 34)

[0231] Step 404: Calculate the azimuth angle PK of the hypotenuse PK0. 0- ang, use the following formula:

[0232]

[0233] Step 405: Calculate the angle α0 between the hypotenuse and the tangent direction of any center stake K0 with known coordinates, using the following formula:

[0234] 0= PK0-ang-qie-ang0 (Formula 36)

[0235] Step 406: Calculate the length value Yq0 of the cosine side with different strengths using the following formula:

[0236] Yq0 = PK0 × cos 0 (Formula 37)

[0237] Step 407: If Yq0 ≥ 10 -4 If m, then: K1 = K0 + Yq0;

[0238] or Yq n ≥10 -4 m, then: K n+1 =K n +Yq n ;(Formula 38)

[0239] Calculate the center pile K n+1 Planar coordinates and tangent azimuth X n+1 Y n+1 、qie-ang n+1 And replace the data of any known coordinate value of center stake K0 with the data of center stake K1, or use the data of center stake K n+1 Data replacement for center pile K n Data;

[0240] Step 408: Repeat steps 402 to 407 until Yq is satisfied. n <10 -4 Given the condition m, we obtain the perpendicular foot midpoint A and offset AP. The flowchart of the inverse calculation is as follows: Figure 2 As shown;

[0241] A = Kn (Equation 39)

[0242] AP=PKn× sinαn (Formula 40)

[0243] When AP < 0, it means that any point P is to the left of the perpendicular foot stake A;

[0244] When AP=0, it means that any point P is the center stake;

[0245] When AP > 0, it means that any point P is to the right of the perpendicular foot stake A;

[0246] The above formula and Figure 2 In the diagram: X0, Y0, and qie-ang0 are the known plane coordinates and tangent azimuth of the starting point K0; X P Y P Let P be the plane coordinates of any known point; Kn is the station number, and PKn is the line connecting points P and Kn; It is the angle between the line connecting PKn and the tangent direction of Kn; PKn×sin The calculated value is the value of the opposite sine wave; Yq n It is the value of the opposite strong cosine edge or the corrected value of the opposite strong cosine edge;

[0247] Step 409: Normally, when the turning angle of a horizontal curve is less than 180°, there is only one perpendicular foot A. For complex curves with multiple perpendicular foot stakes, first calculate the total turning angle of the horizontal curve to determine the number of perpendicular feet; then, take the start or end point of the studied section as K0, and simultaneously set the differential correction coefficient. If necessary, absolute values ​​can also be used to... The process gradually approaches the perpendicular condition from a single direction until the first perpendicular center stake A and offset AP are obtained. Then, the sum of A and an empirical value is used as the starting point of the second study section. The study continues in a single direction until the end or beginning of the study section, and all perpendicular center stakes and offsets are obtained.

[0248] In Example 8, step 500 includes: longitudinal profile calculation: based on the data in the vertical curve element sub-database, calculate the elevation Z1 of the vertical foot center stake A; the elevation Z1 calculation method is existing technology, and the calculation process is relatively simple. On the longitudinal profile of the route, based on the station number, elevation, and vertical curve radius of the three adjacent slope change points, calculate the longitudinal slope, tangent length, and correction value, and then obtain the Z1 value.

[0249] In Example 9, step 600 includes: cross-section calculation: based on the data in the cross-section slope and width sub-database and the elevation Z1 of the vertical center stake A, calculate the elevation Z of any point. P The method is also existing technology.

[0250] In Example 10, step 700 includes: the three-dimensional coordinate value of any point is P(X). P Y P , Z P This is an input statement, without any calculation process.

[0251] In a second general embodiment, a processor is provided for running a program, wherein the program executes the above-described method for calculating the three-dimensional coordinates of any point.

[0252] In Example 11, as Figure 17 As shown, a flowchart illustrating another method for calculating the three-dimensional coordinates of an arbitrary point is provided.

[0253] For any point P, the processor can determine the anisotropic coordinates corresponding to point P. These anisotropic coordinates can include any center stake K corresponding to point P. p The corresponding structural intersection angle J p Corresponding detailed dimensions of the structure and Here, any point P can refer to any detection point outside the line or bridge / tunnel. Any point P can also refer to a point in a heterogeneous coordinate system. The heterogeneous coordinate system can include the H-axis and the L-axis. and This can refer to the detailed dimensions of a structure. Specifically, for any point P, It can refer to the length of any point P along the H-axis in a different coordinate system. It can refer to the length of any point P along the L-axis in a heterogeneous coordinate system. The angle between the H-axis and the L-axis in the heterogeneous coordinate system can refer to the intersection angle J of the structure.p Angle J p It doesn't have to be 90°.

[0254] Given the coordinate values ​​of the different strengths corresponding to any point P, the processor can determine the arbitrary center stake K corresponding to any point P. p Data from the flat curve element sub-database determines the arbitrary center stake K. p plane coordinates X K and Y K The horizontal curve element sub-database can include an intersection-type database and a line element-type database. The intersection-type database can include control parameters. These control parameters can include the centerline coordinates and tangent azimuth angles of the preceding straight line, first transition curve, circular curve, second transition curve, and subsequent straight line within the intersection point. The line element-type database can include auxiliary parameters. These auxiliary parameters can include the main point station number, plane coordinate values, tangent azimuth angle, curve radius, and transition curve length.

[0255] Determine any center stake K p plane coordinates X K and Y K In this case, the processor can determine the length. ,length Angle J p and any middle pile K p plane coordinates X K and Y K Determine the coordinates X of any point P. p and Y p Then, the processor can further determine the route perpendicular midpoint stake A and the offset AP corresponding to any point P. The processor can determine the elevation Z1 of the route perpendicular midpoint stake A based on data from the vertical curve element sub-database, and can further determine the coordinate value Z of any point P based on data from the cross-sectional slope and width sub-databases and the elevation Z1 of the route perpendicular midpoint stake A. p Given the coordinates X of any point P. p Y p and Z p In this case, the three-dimensional coordinates of any point P can be determined. The data in the vertical curve element sub-database can include the station number, elevation, and curve radius of the slope change point. The data in the cross-section slope and width sub-database can include cross slope and slope length, etc.

[0256] In Example 12, the route type corresponding to any point P can include a straight road segment. When the route type corresponding to any point P is a straight road segment, the processor can determine any center stake K. p plane coordinates X K and Y KFurthermore, the processor determines any center stake K. p plane coordinates X K and Y K The formulas used may include: ; C-ang1=qie-ang0+ ; ; ; ;X K =X0+C*cos(C-ang1); Y K =Y0+C*sin(C-ang1); qie-ang1=qie-ang0+ .in, For the tangent angle, Let C-ang1 be the azimuth angle of the chord, and C be the chord length. y represents the center pile K P The coordinate value of K in the local coordinate system. p Let X be any center stake corresponding to any point P. K and Y K For any center pile K P The planar coordinate values. Specifically, X K This could refer to the center pile K. P In a plane coordinate system, the coordinate values ​​of the X-axis and Y-axis are... K This could refer to the center pile K. P The coordinate value on the Y-axis of the plane coordinate system. qie-ang1 can refer to the azimuth angle of the tangent.

[0257] In Example 13, the route type corresponding to any point P can include a circular curve segment. When the route type corresponding to any point P is a circular curve segment, the processor can determine any center stake K. p plane coordinates X K and Y K Furthermore, the processor determines any center stake K. p plane coordinates X K and Y K The formulas used may include: ; C-ang1=qie-ang0+ y=R(1-cos ), C= X K =X0+C*cos(C-ang1); Y K =Y0+C*sin(C-ang1), qie-ang1=qie-ang0+ .in, For the tangent angle, Let HY be the turning angle, R be the curve radius, C-ang1 be the chord azimuth, and C be the chord length. y is any center stake K P The coordinate value of K in the local coordinate system. p Let X be any center stake corresponding to any point P. K and Y K For any center pile K P The planar coordinate values. Specifically, X K This could refer to the center pile K. P In a plane coordinate system, the coordinate values ​​of the X-axis and Y-axis are... K This could refer to the center pile K. P The coordinate value on the Y-axis of the plane coordinate system. qie-ang1 can refer to the azimuth angle of the tangent.

[0258] In Example 14, the route type corresponding to any point P may include a transition curve segment. When the route type corresponding to any point P is a transition curve segment, the processor can determine any center stake K. p plane coordinates X K and Y K Furthermore, the processor determines any center stake K. p plane coordinates X K and Y K The formulas used may include:

[0259] ;

[0260] ;

[0261] ; C-ang1=qie-ang0+ C= X K =X0+C*cos(C-ang1); Y K =Y0+C*sin(C-ang1), qie-ang1=qie-ang0+ .in, For the tangent angle, ZH is the turning point, and ZH is the straight-to-gradient point. To completely reduce the curve length, The calculated length of the transition curve is given by R, where R is the curve radius, C-ang1 is the chord azimuth angle, and C is the chord length. y is any center stake K P The coordinate value of K in the local coordinate system. p Let X be any center stake corresponding to any point P.K and Y K For any center pile K P The planar coordinate values. Specifically, X K This could refer to the center pile K. P In a plane coordinate system, the coordinate values ​​of the X-axis and Y-axis are... K This could refer to the center pile K. P The coordinate value on the Y-axis of the plane coordinate system. qie-ang1 can refer to the azimuth angle of the tangent.

[0262] In Example 15, the coordinates X of any point P are... p and Y p It can be determined using the following formula:

[0263] X P =X K +H P Cos(qie-ang1)+L P Cos(qie-ang1+J) P )

[0264] Y P =Y K +H P Sin(qie-ang1)+L P Sin(qie-ang1+J) P ).

[0265] In Example 16, the station number A of the perpendicular foot of any point P and the offset AP can be determined by the following formulas: AP= Where A is the station number of the perpendicular midpoint of the route from any point P, and AP is the offset between any point P and the station number A of the perpendicular midpoint of the route. For the quantum perpendicular field, Let P be any point and Connecting and The angle between the tangent directions.

[0266] In Example 17, the processor can obtain the station numbers of three adjacent slope change points and the curve radius from the vertical curve element sub-database, and determine the elevation Z1 of the route perpendicular mid-stake station A based on the station numbers, elevations, and curve radii of the three slope change points.

[0267] In Example 18, the processor can first obtain the cross slope and slope length from the cross-sectional slope and width sub-database, and then determine the elevation difference based on the cross slope and slope length. Once the elevation difference is determined, the processor can use the sum of the elevation difference and the elevation Z1 of the route's vertical midpoint stake A as the coordinate value Z of any point P. p .

[0268] In Example 19 of the highway construction project, calculations were performed on any center stake, and the results are shown in Table 4. For any point, the three-dimensional coordinate values ​​of the overall coordinate system were directly calculated from the heterogeneous coordinate system, and the results are shown in Table 5. For any point with known coordinates, coordinate inverse calculation and verification were performed, and the calculation error values ​​were all 0, as shown in Table 6. Summary of known coordinate inverse calculation and verification results of a highway construction project.

[0269] Table 4. Summary of Calculation Results for Arbitrary Centerline of a Highway Project Under Construction

[0270]

[0271] Table 5. Summary of Calculation Results of Three-Dimensional Coordinates of Any Point in a Highway Project Under Construction

[0272]

[0273] Table 6. Summary of Results of Inverse Calculation of Perpendicular Foot, Center Stake, and Offset from Known Coordinates, and Verification

[0274]

[0275] The three-dimensional model of this invention adopts the planar, longitudinal, and transverse three-view model provided by the design unit, and uses algorithms for other three-dimensional models, including spherical coordinate systems, which should be included within the scope of the claims of this application.

[0276] The quantum mathematical model of this invention, after being upgraded to a three-dimensional model, can be applied to other fields, including precise positioning of CNC equipment and precision machining of mechanical parts.

[0277] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0278] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for calculating the three-dimensional coordinates of an arbitrary point, characterized in that, Includes the following steps: Step 100: Establish a database and, according to the specifications of the heterogeneous coordinate system, input the auxiliary parameter K that is already present in the design drawings and corresponds to any point P. P J P H P L P K P It is an arbitrary center stake, which is data describing the center position of a physical engineering project; J P It is the angle, which is data describing the geometric shape of a physical engineering project; H P L P These are detailed dimensional data for the engineering project; Step 200: Calculate the plane coordinate value K of the arbitrary center stake Kp and the horizontal curve element sub-database. P (X) K Y K ) and tangent azimuth qie-ang1; Step 300: Based on data J P H P L P X K Y K Calculate the planar coordinates P(X) of any point. P Y P ); Step 400: Calculate and determine any point P(X) with known coordinates. P Y P The corresponding perpendicular foot center stake A and offset AP; Step 500: Longitudinal section calculation: Calculate the elevation Z1 of the vertical curve element sub-database; Step 600: Cross-section calculation: Based on the data from the cross-section slope and width sub-database and the elevation Z1 of the vertical center stake A, calculate the elevation Z of any point. P ; Step 700: The three-dimensional coordinates of the arbitrary point are P(X) P Y P , Z P ); The heterogeneous coordinate system has the center pile K as the origin, the H-axis as the tangent direction of the route or the short axis direction of the structure, the L-axis as the long axis direction, and the angle between the H-axis and the L-axis as J. The heterogeneous coordinate system is a custom engineering coordinate system based on the method of combining numbers and shapes, using locally available materials; The heterogeneous coordinate system is a comprehensive model that summarizes and generalizes commonly used mathematical models in roads, bridges, culverts, and tunnels. The heterogeneous coordinate system is a planar oblique coordinate system that also encompasses local planar coordinate systems and local polar coordinate systems. When J is 90°, the heterogeneous coordinate system is equivalent to the local planar coordinate system. When H or L is 0, the heterogeneous coordinate system is equivalent to the local polar coordinate system. The geometric model and algorithm of heterogeneous coordinate coefficients belong to the field of computational geometry. That is, the model is always convergent and does not require training or learning. Instead, the result of the mathematical model is calculated directly using plane geometry formulas.

2. The method for calculating the three-dimensional coordinates of any point according to claim 1, characterized in that: Transform from the heterogeneous coordinate system to the overall coordinate system of the route, and directly calculate the planar coordinate value of any point.

3. The method for calculating the three-dimensional coordinates of any point according to claim 1, wherein the calculation method is a targeted calculation method adopted based on various specific conditions and scenarios of line and bridge / tunnel surveying, combined with the geometric shape of the data, characterized in that: The heterogeneous coordinate coefficient mathematical model and algorithm are used to directly calculate the three-dimensional coordinate values ​​based on the overall coordinate system of the route; A quantum mathematical model and algorithm are used to directly calculate and determine the perpendicular midpoint and offset corresponding to any point with the known coordinate values. The calculation method is applicable to three linear elements of horizontal curves: straight lines, circular curves, and transition curves. The calculation method is applicable to circular curves with arbitrary turning angles and various types of transition curves; The calculation method is applicable to any point on roads, bridges, culverts, and tunnels.

4. The method for calculating the three-dimensional coordinates of any point according to claim 1, characterized in that, The database of the calculation method includes a horizontal curve element sub-database, a vertical curve element sub-database, and a cross-sectional slope and width sub-database.

5. The method for calculating the three-dimensional coordinates of any point according to claim 1, characterized in that, Step 200 includes the following steps: Step 201: Taking a known center stake K0 as the origin, and the tangent direction of the known center stake K0 as... Establish a local plane coordinate system with the normal direction as the y-axis, and calculate the coordinates of any center stake in this local plane coordinate system. y-value; Step 202: Using the tangent direction of the known center pile K0 as the starting edge, establish a local polar coordinate system, and calculate the rotation angle and tangent angle of the arbitrary center pile in the local polar coordinate system; Step 203: Calculate the plane coordinates and tangent azimuth of the arbitrary center stake.

6. The method for calculating the three-dimensional coordinates of any point according to claim 1, characterized in that, The perpendicular domain is a set of points and is the real number domain; the foot of the perpendicular, in plane analytic geometry, is the point where two lines intersect each other with an angle ≡ 90°. It is a point without size and is a special point in the perpendicular domain. All points in the perpendicular domain are the same as the foot of the perpendicular, satisfying the requirement of approximate perpendicularity. The quantum perpendicular-foot collision model is a quantum mathematical model and also a planar geometric model. K0 is an arbitrary center stake with known coordinates of the road segment under study, and is a known point. Connecting the arbitrary center stake K0 with the arbitrary point P with known coordinates, we obtain a known line segment PK0. Then, on the tangent direction of the arbitrary center stake K0, we construct the foot B0 of the perpendicular from the arbitrary point P with known coordinates, resulting in a right triangle PK0B0 with different strengths. In this right triangle, PK0 is the hypotenuse with different strengths, PB0 is the sine side with different strengths, and K0B0 is the cosine side with different strengths. It is the angle between the tangent direction of the hypotenuse PK0 and the arbitrary center stake K0; then, using the quantum dot domain K0 as the standard, with the... The direction indicated by the cosine value: when the... The cosine value is positive, and a quantum dot domain K1 that collides with the quantum dot domain K0 is found in the direction of the larger station number. If the cosine value is negative, then find the quantum dot domain K1 that collides with the quantum dot domain K0 in the direction of the smaller station number; establish a right triangle PK1B1 with different strengths; It is the angle between the hypotenuse PK1 and the tangent direction of the center stake K1; according to the above method for establishing right triangles with different strengths, for point K on the horizontal curve of the route... n Each of them sequentially establishes a right triangle PK with different strengths. n B n The included angle is obtained. until the stated Continue until the vertical requirement is met; The quantum geometric model is always convergent: It is a qualitative indicator for determining verticality, when the aforementioned When the value differs from the perpendicular condition by less than 1°, its corresponding quantum dot domain K n Located in the core area; within the core area, the Gradually approaching the vertical condition, the quantum dot domain K n When a collision or intersection occurs with the quantum perpendicular domain A, When the value of satisfies the perpendicular condition, the quantum dot domain K n Training ends when the perpendicular foot domain A intersects or coincides with the quantum perpendicular foot domain A; the length value Yq of the heterosine side is a quantitative indicator for determining the perpendicular foot, with a larger absolute value of Yq outside the core region and a smaller absolute value of Yq inside the core region; as the... As the condition gradually approaches verticality, the value of the length Yq of the heterosine side reaches the quantum level and gradually approaches 0, with the central pile K... n It also gradually approaches the value of the perpendicular midpoint A, and the training ends; Learning rate: Using the point domain as a learning rate results in slow model convergence. The heterosine edge, a dynamic value, is a very suitable learning rate. Outside the core region, the absolute value of the heterosine edge is larger, leading to faster model convergence; within the core region, the absolute value is smaller, slowing down model convergence; and in the central part of the core region, model convergence becomes increasingly slower. As the condition of verticality approaches, the value of the heterocosine edge reaches the quantum level and gradually approaches 0; in general, choosing the heterocosine edge value as the learning rate value makes the model convergence speed slower. Algorithm: First, determine the calculation precision; the engineering measurement calculation precision is 10. -4 m, when the condition is met, the number of sides of the heterodyne cosine is less than 10. -4 When m, the value of the perpendicular foot center stake A is equal to the value of the center stake K. n The value of the offset AP is equal to the value of the opposite sinusoidal side.

7. The method for calculating the three-dimensional coordinates of any point according to claim 6, characterized in that, Step 400 includes the following steps: Step 401: Determine the accuracy of engineering survey calculations (10). -4 m; Step 402: K0 is an arbitrary center stake with known coordinate values ​​of the road segment under study. It is a known point. Connect the arbitrary center stake K0 with known coordinate values ​​and the arbitrary point P with known coordinate values ​​to obtain the known line segment PK0. Then, draw the foot of the perpendicular B0 of the arbitrary point P with known coordinate values ​​in the tangent direction of the arbitrary center stake K0 with known coordinate values ​​to obtain the right triangle PK0B0 with different strengths. Step 403: Calculate the length of the hypotenuse PK0; Step 404: Calculate the azimuth angle of the hypotenuse PK0; Step 405: Calculate the angle between the hypotenuse and the tangent direction of any known coordinate point K0. ; Step 406: Calculate the length value Yq0 of the cosine side with different strengths; Step 407: If Yq0 ≥ 10 -4 If m, then: K1 = K0 + Yq0; or Yq n ≥10 -4 m, then: K n+1 =K n +Yq n ; Calculate the center pile K n+1 Planar coordinates and tangent azimuth X n+1 Y n+1 、qie-ang n+1 And replace the data of any center pile K0 with the data of center pile K1, or replace the data of the center pile K with the data of center pile K1. n+1 Data replacement for center pile K n Data; Step 408: Repeat steps 402 to 407 until Yq is satisfied. n <10 -4 Given the condition m, the perpendicular foot center pile A and the offset AP are obtained; Step 409: For complex curves with multiple perpendicular center stakes, the starting or ending point of the study section can be taken as K0, and a differential strength correction coefficient can be set to make the... The process gradually approaches the perpendicular condition from a single direction until the first perpendicular center stake A and offset AP are obtained. Then, the sum of the value of A and an empirical value is used as the starting point of the second study segment. The study continues in a single direction until the end or starting point of the study segment is reached, and all the perpendicular center stakes and offsets are obtained.

8. A processor, characterized in that, It is configured to perform the method for calculating the three-dimensional coordinates of any point as described in any one of claims 1 to 7.

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