Route horizontal and longitudinal curve three-dimensional integrated linkage design method and system, terminal and medium

Abstract

The invention discloses a route horizontal and longitudinal curve three-dimensional integrated linkage design method and system, a terminal and a medium, and the method comprises the steps: decomposing a route into easement curve combinations of a horizontal curve and a vertical curve, unifying the easement curve combinations into a curvature gradient model, and defining curvature parameters; under a unified three-dimensional coordinate system, synchronously generating coordinates by taking the arc length as a parameter; coordinate back calculation is realized through iterative calculation of a numerical iterative algorithm with adaptive step length adjustment; and realizing the three-dimensional linkage design of the horizontal and longitudinal curves of the route based on a coordinate back calculation result. The method has the advantages that efficient and high-precision calculation of horizontal and vertical curve three-dimensional linkage design and complex curved surface modeling is achieved, and an innovative solution is provided for the fields of road engineering, industrial design and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of road and traffic engineering design, and in particular to a method, system, terminal and medium for three-dimensional integrated linkage design of horizontal, vertical and curve routes, which can be extended to the industrial design field of complex surface modeling. Background Art

[0002] In road and traffic engineering design, horizontal curves (horizontal direction) and vertical curves (longitudinal elevation) are usually considered as independent design objects in traditional modeling and design methods. This leads to the following drawbacks: 1. Separation of horizontal, vertical and curved design In traditional methods, horizontal and vertical curves are designed using different mathematical models and their parameters are calculated independently, making data linkage difficult. Modifying a horizontal curve requires manual recalculation of the vertical curve, which is inefficient and prone to errors. The calculation of horizontal curves relies on piecewise approximate formulas (such as the expansion of the clothoid curve), and the forward and inverse calculations of complex linear coordinates are cumbersome; the calculation of vertical curves is based on approximate models of parabolas or circular curves, which lack accuracy.

[0003] 2. Insufficient computational efficiency and accuracy Traditional horizontal curve coordinate inversion requires multiple trials (such as linear interpolation), which has a slow convergence speed; vertical curve elevation calculation requires segmented processing, which has complex logic and significant error accumulation.

[0004] 3. Poor three-dimensional spatial coordination It is difficult to seamlessly connect horizontal and vertical curve data in a unified three-dimensional coordinate system, resulting in inaccurate description of the three-dimensional shape of the road, affecting driving safety and comfort.

[0005] In summary, the existing technology lacks a universal method for unified modeling of horizontal and vertical curves. It is necessary to realize three-dimensional linkage calculation through numerical integration and iterative algorithms to improve design efficiency, accuracy and coordination. Summary of the Invention

[0006] In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a three-dimensional integrated linkage design method, system, terminal and medium for horizontal and vertical curves of routes. By introducing the fourth dimension, the route mileage is introduced as the fourth dimension of the calculation coordinates. Both horizontal curves and vertical curves are calculated according to the mileage using a unified formula, realizing the integrated linkage calculation of horizontal, vertical and horizontal curves, which can improve the design efficiency, accuracy and coordination.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is as follows: In the first aspect, the present invention proposes a three-dimensional integrated linkage design method for horizontal, vertical and curve routes, the key of which is that it includes the following steps: Step 1: Decompose the route into a combination of horizontal curves and vertical curves, unify them into a curvature gradient model, and define curvature parameters; Step 2: In a unified 3D coordinate system, coordinates are generated synchronously using arc length as a parameter; Step 3: Coordinate inversion is achieved through iterative calculation using a numerical iterative algorithm with adaptive step size adjustment; Step 4: Realize the three-dimensional linkage design of the route horizontal and vertical curves based on the coordinate inverse calculation results.

[0008] Furthermore, the curvature expression of the curvature gradient model is:

[0009] in, is the curvature, is the radius of curvature, is the starting radius of the horizontal curve, is the end point radius of the horizontal curve, is the length between the start and end points of the horizontal curve, is the arc length.

[0010] Furthermore, the curvature parameters defined in step 1 are (M, N): , .

[0011] Furthermore, in step 2, the complex Simpson integral method is used to calculate the coordinates.

[0012] Furthermore, the calculation formula for synchronously generating coordinates using the complex Simpson integral method with arc length as a parameter is: , , , in, is the vertical curve elevation, ( ) is the curvature parameter of the vertical curve, j is the longitudinal slope turning coefficient.

[0013] Furthermore, in step 2, when calculating the coordinates: The coordinates of the center stake of the horizontal curve are calculated based on the starting point coordinates and mileage; The vertical curve calculates the center pile elevation based on the starting point elevation and the zenith distance, where the zenith distance is converted from the slope.

[0014] Furthermore, in step 2, when calculating the cross-section coordinates, the cross-section line shape of the cross section is replaced by a straight line or a circular curve and a transition curve; and the coordinates are calculated after the replacement.

[0015] In a second aspect, the present invention provides a three-dimensional integrated linkage design system for horizontal, vertical and curve routes, for implementing the method described in the first aspect, characterized by comprising: Route decomposition module, used to decompose the route into a combination of horizontal curves and vertical curves, unify them into a curvature gradient model, and define curvature parameters; The first calculation module is used to synchronously generate coordinates using arc length as a parameter in a unified three-dimensional coordinate system; The second calculation module is used to iteratively calculate the coordinate inverse through a numerical iterative algorithm with adaptive step size adjustment; The linkage design module is used to realize the three-dimensional linkage design of the horizontal and vertical curves of the route according to the coordinate inverse calculation results of the second calculation module.

[0016] In a third aspect, the present invention provides a computer terminal, comprising: one or more processors; a memory having one or more programs stored therein; When the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method according to the first aspect.

[0017] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the method described in the first aspect when executed.

[0018] The present invention regards horizontal curves and vertical curves as projections of a unified three-dimensional space curve on the horizontal plane and the vertical plane respectively. Therefore, by regarding the route as a continuous curve in three-dimensional space, with the mileage direction (s) as the fourth dimension parameter, the three-dimensional coordinates (x, y, z) are uniformly expressed as a function of s, that is, x=x(s), y=y(s), z=z(s). At this time, the horizontal curve is the plane projection of x(s) and y(s), and the vertical curve is the longitudinal section projection of s and z(s); by introducing a vertical plane transition curve, the curvature change of the vertical curve and the horizontal curve are unified into the same gradient model, thereby realizing the introduction of the fourth dimension and introducing the route mileage as the fourth dimension of the calculation coordinate. Whether it is a horizontal curve or a vertical curve, it is calculated using a unified formula according to the mileage, realizing the integrated linkage calculation of horizontal, vertical and horizontal curves, and effectively solving the problems of low efficiency and data inconsistency caused by the separation of horizontal and vertical curve calculations in the prior art, insufficient accuracy of traditional approximate formulas and cumbersomeness of complex linear calculations, and poor linear coordination in three-dimensional space.

[0019] The remarkable effects of the present invention are: 1. Improved computing efficiency The horizontal and vertical curves share the same integral formula and calculation module, avoiding algorithm switching and increasing the calculation speed by more than 40%. The numerical iterative algorithm with adaptive step size adjustment is adopted, which does not rely on the specific form of the parametric equation of the transition curve. The convergence speed of the coordinate inverse calculation is increased to within 2-3 iterations, and the calculation accuracy is high.

[0020] 2. Enhanced accuracy and consistency The complex Simpson integral method can control the calculation error to the millimeter level, meeting the needs of high-precision engineering; the horizontal and vertical curve data are seamlessly connected in the three-dimensional coordinate system, eliminating the error accumulation of traditional segmented calculations.

[0021] 3. Design optimization and scalability It supports collaborative optimization of horizontal and vertical curves, and automatically generates linear combinations that meet driving comfort, safety, and economy. It can be expanded to fields such as smart city 3D modeling and aerospace surface design. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a flow chart of the method of the present invention; Figure 2 It is a schematic diagram of a horizontal vertical curve; Figure 3 It is a structural diagram of the system of the present invention; Figure 4 It is a structural diagram of the terminal of the present invention. DETAILED DESCRIPTION

[0023] The specific implementation manner and working principle of the present invention will be further described in detail below with reference to the accompanying drawings.

[0024] In the traditional modeling and design process of road and traffic engineering, horizontal curves (horizontal direction) and vertical curves (vertical elevation) are usually treated as independent design objects. Different mathematical models are used in the design of the two, and the parameters are calculated independently. As a result, the traditional design method has the following defects: the separation of horizontal and vertical curve design, insufficient calculation efficiency and accuracy, and poor three-dimensional spatial coordination. Based on the above-mentioned defects of the existing technology, it can be seen that the present invention aims to solve the following technical problems: 1. Inefficiency and data inconsistency caused by the separation of horizontal and vertical curve calculations.

[0025] 2. The lack of accuracy of traditional approximate formulas and the tediousness of complex linear calculations.

[0026] 3. The problem of poor linear coordination in three-dimensional space.

[0027] 4. How to realize the integrated calculation of horizontal, vertical and horizontal curves.

[0028] Example 1: like Figure 1 As shown, this embodiment provides a three-dimensional integrated linkage design method for route horizontal, vertical and curves, and the specific steps are as follows: Step 1: Decompose the route into a combination of horizontal curves and vertical curves, unify them into a curvature gradient model, and define curvature parameters; Specific: such as Figure 2 As shown, the horizontal curve is actually the projection of the spatial curve on the plane, and the vertical line shape is actually the real shape of the spatial curve. It is just stretched into a line shape on the vertical plane because of the need to draw the longitudinal section. Since the horizontal curve shape can be unified into a line shape and a formula (non-complete transition curve), the vertical curve calculation should also be unified into the same line shape as the horizontal curve. In order to facilitate the calculation expression, the present invention introduces the mileage direction of the horizontal curve as the fourth dimension (as shown in the schematic diagram), and its origin is the starting point of the road (K+000), and proposes the concept of the vertical transition curve (the spiral curve on the vertical plane). Through the introduction of the above new concepts, after changing the perspective and thinking, the calculation methods, calculation formulas, and calculation modules of the horizontal and vertical curves are very cleverly unified, bringing a breakthrough to the three-dimensional linkage integrated design calculation.

[0029] Step 2: In a unified 3D coordinate system, coordinates are generated synchronously using arc length as a parameter; Step 3: Inversely calculate coordinates (such as mileage and width) through an iterative numerical algorithm with adaptive step size adjustment. Step 4: Based on the coordinate inverse calculation results such as mileage and width, realize the three-dimensional linkage design of the route horizontal and vertical curves.

[0030] In some specific implementations, the curvature expression of the curvature gradient model in step 1 is:

[0031] in, is the curvature, is the radius of curvature, is the starting radius of the horizontal curve, is the end point radius of the horizontal curve, is the length between the start and end points of the horizontal curve, is the arc length.

[0032] From the curvature expression of the curvature gradient model, we can see that the curvature is the arc length The linear function of , indicating that the curvature of the clothoid curve changes uniformly.

[0033] Let the curvature parameters be defined as (M, N), and , , then the curvature expression of the curvature gradient model can be rewritten as: .

[0034] When the vertical curve uses a longitudinal slope transition curve instead of a traditional parabola or circular curve, the curvature formula is the same as that of the horizontal curve. Then: 1) Circular curve ( ) Curvature characteristics: , (constant curvature), The tangent azimuth and coordinates are simplified to: , , .

[0035] Physical meaning: The circular curve is a special case of the clothoid curve, and the integral can be solved analytically as a trigonometric function.

[0036] 2) Straight line segment ( ) Curvature characteristics: , (curvature is zero), Coordinate simplification: , .

[0037] Physical meaning: A straight line is a special case of a circular curve, and the coordinates degenerate into uniform linear motion.

[0038] In some embodiments, the complex Simpson integral method is used to calculate the coordinates in step 2. Specifically, the calculation formula for synchronously generating the coordinates using arc length as a parameter is: , , , in, is the vertical curve elevation, ( ) is the curvature parameter of the vertical curve, j is the longitudinal slope turning coefficient.

[0039] According to the above formula, both horizontal and vertical curves are calculated using the same formula. Therefore, in step 3, the coordinate inversion is performed through the iterative calculation of the numerical iterative algorithm with adaptive step size adjustment, specifically including: coordinate inversion to obtain mileage and width.

[0040] In a horizontal curve, the coordinates of the center stake are calculated based on the starting point coordinates and mileage; In a vertical curve, the center pile elevation is calculated based on the starting point elevation and the zenith distance, where the zenith distance is converted from the slope.

[0041] In addition, the cross-section is the cross-section line shape that moves along the spatial curve and moves up and down. The cross-section line shape can also use a straight line or circular curve and a transition curve to replace the existing various line shapes. Because the line shape is the same, the cross-section calculation is also unified into one calculation formula and calculation module.

[0042] In some embodiments, the adaptive step-size adjustment numerical iterative algorithm described in step 3 can be found in (New Method for Highway Edge Staking, by Cao Zhixiang, Journal of Chongqing Jiaotong University, Vol. 20, No. 2, June 2001). Because this method is prior art, it is not described in detail in this embodiment. Of course, in other embodiments, other variable step-size adaptive numerical iterative algorithms can also be used for coordinate inversion.

[0043] Example 2: See attached Figure 3 This embodiment provides a three-dimensional integrated linkage design system for horizontal, vertical and curve routes for implementing the method described in Example 1, including: Route decomposition module, used to decompose the route into a combination of horizontal curves and vertical curves, unify them into a curvature gradient model, and define curvature parameters; The first calculation module is used to synchronously generate coordinates using arc length as a parameter in a unified three-dimensional coordinate system; The second calculation module is used to iteratively calculate the coordinate inverse through a numerical iterative algorithm with adaptive step size adjustment; The linkage design module is used to realize the three-dimensional linkage design of the horizontal and vertical curves of the route according to the coordinate inverse calculation results of the second calculation module.

[0044] Example 3: like Figure 4 As shown, this embodiment provides a computer terminal, including: one or more processors; a memory having one or more programs stored therein; When the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method as described in Example 1.

[0045] It should be understood that in the embodiment of the present invention, the processor may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc. The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the type of device. The power supply can meet the power requirements of the computer device for normal operation or overclocking. The operating system, for example TM, MacOSXTM, UnixTM, LinuxTM, etc. When choosing an operating system, pay attention to the correspondence between the version of the running code and the operating system.

[0046] Example 4: This embodiment provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the method described in Embodiment 1 when executed.

[0047] The computer-readable storage medium may be an internal storage unit of the controller, such as a hard disk or memory of the controller. The computer-readable storage medium may also be an external storage device of the controller, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, etc. equipped on the controller. The computer-readable storage medium may also include both the internal storage unit of the controller and an external storage device.

[0048] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, apparatus, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0049] The present invention is described with reference to the flowcharts and / or block diagrams of the method, terminal device (system), and computer program product according to the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal device generate instructions for implementing the process in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0050] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing terminal device to operate in a specific manner, so that the instructions stored in the computer readable memory produce a manufactured product including an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0051] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device so that a series of operating steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, thereby providing instructions for executing on the computer or other programmable terminal device to implement the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0052] The present invention can also be expanded as follows: 1) The calculation logic is encapsulated as an independent module, supporting the coordinated adjustment of horizontal and vertical curve parameters.

[0053] 2) On this basis, time, speed, and acceleration are introduced as new dimensions to achieve lightweight true 3D real-world navigation; 3) It can be extended to industrial surface modeling (such as automobile appearance and mold manufacturing) to generate complex continuous smooth surfaces by combining curvature parameters.

[0054] Next, the effects of the present invention are verified by combining two specific application examples: Application Example 1: 3D Linkage Design in Road Design S1. Input parameters: radius of the starting point of the horizontal curve , end point radius ; Vertical curve longitudinal slope , ; S2. Calculation of curvature parameters: Flat curve: , ; Vertical curve: , .

[0055] S3, numerical integration and iteration: The coordinates (X, Y, Z) are calculated using the complex Simpson integral method, with a step size of 0.1 m. The Newton iteration method is used for coordinate inverse calculation. The initial guess value is the design pile number ±10m. After three iterations, the error is less than 1mm.

[0056] S4, 3D linkage design: Generate a 3D point cloud based on the results of coordinate inversion and import it into the target software to realize 3D linkage design and modeling.

[0057] Application Example 2: Car Exterior Surface Modeling and Design S1. Decompose the surface: decompose the body surface into 200 transition curve combinations; S2. Parameter setting: define the direction angle of each curve α , curvature , arc length l ; S3. Generate model: Generate 3D point cloud through unified integral formula and import it into CAD software to complete surface modeling design.

[0058] In summary, this invention, by introducing the fourth dimension (mileage direction), uniquely unifies existing calculations for horizontal and vertical curves (straight and circular curves) into a single formula and calculation module. By employing a unified numerical integration and iterative algorithm for the introduction of vertical transition curves, it achieves efficient, high-precision calculations for the three-dimensional coordinated design of horizontal and vertical curves and complex surface modeling, providing innovative solutions for fields such as road engineering and industrial design.

[0059] The technical solution provided by the present invention is introduced in detail above. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, the present invention can also be improved and modified in a number of ways, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A three-dimensional integrated linkage design method for horizontal, vertical and curve routes, characterized by: The steps include: Step 1: Decompose the route into a combination of horizontal curves and vertical curves, unify them into a curvature gradient model, and define curvature parameters; Step 2: In a unified 3D coordinate system, coordinates are generated synchronously using arc length as a parameter; Step 3: Coordinate inversion is achieved through iterative calculation using a numerical iterative algorithm with adaptive step size adjustment; Step 4: Realize the three-dimensional linkage design of the route horizontal and vertical curves based on the coordinate inverse calculation results.

2. The three-dimensional integrated linkage design method for route horizontal and vertical curves according to claim 1 is characterized in that: The curvature expression of the curvature gradient model is: in, is the curvature, is the radius of curvature, is the starting radius of the horizontal curve, is the end point radius of the horizontal curve, is the length between the start and end points of the horizontal curve, is the arc length.

3. The three-dimensional integrated linkage design method for route horizontal and vertical curves according to claim 2 is characterized in that: The curvature parameters defined in step 1 are (M, N): , 。 4. The three-dimensional integrated linkage design method for route horizontal, vertical and curves according to claim 1 is characterized in that: In step 2, the complex Simpson integral method is used to calculate the coordinates.

5. The three-dimensional integrated linkage design method for horizontal, vertical and curve routes according to claim 4 is characterized in that: The calculation formula for the complex Simpson integral method to synchronously generate coordinates using arc length as a parameter is: ， ， ， in, is the vertical curve elevation, ( ) is the curvature parameter of the vertical curve, j is the longitudinal slope turning coefficient.

6. The three-dimensional integrated linkage design method for route horizontal, vertical and curves according to any one of claims 1 to 5, characterized in that: Step 2: When calculating the coordinates: The coordinates of the center stake of the horizontal curve are calculated based on the starting point coordinates and mileage; The vertical curve calculates the center pile elevation based on the starting point elevation and the zenith distance, where the zenith distance is converted from the slope.

7. The three-dimensional integrated linkage design method for horizontal, vertical and curve routes according to claim 6 is characterized in that: In step 2, when calculating the cross-section coordinates, the cross-section line shape of the cross section is replaced by a straight line or a circular curve and a transition curve; after the replacement, the coordinates are calculated.

8. A three-dimensional integrated linkage design system for horizontal, vertical and curve routes, used to implement the method according to any one of claims 1 to 7, characterized in that: include: Route decomposition module, used to decompose the route into a combination of horizontal curves and vertical curves, unify them into a curvature gradient model, and define curvature parameters; The first calculation module is used to synchronously generate coordinates using arc length as a parameter in a unified three-dimensional coordinate system; The second calculation module is used to iteratively calculate the coordinate inverse through a numerical iterative algorithm with adaptive step size adjustment; The linkage design module is used to realize the three-dimensional linkage design of the horizontal and vertical curves of the route according to the coordinate inverse calculation results of the second calculation module.

9. A computer terminal comprising: one or more processors; a memory having one or more programs stored therein; When the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, wherein: When the computer program is executed, the method according to any one of claims 1 to 7 is implemented.

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