A general line shape calculation method for railway line
By constructing a line model to manage linked list containers and curvature expressions, and combining numerical integration and nonlinear equation solving, the problem of insufficient calculation accuracy in traditional railway line design is solved, achieving high accuracy and high efficiency in railway line shape calculation, which is applicable to various railway line designs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA RAILWAY DESIGN GRP CO LTD
- Filing Date
- 2022-09-19
- Publication Date
- 2026-05-29
AI Technical Summary
In existing railway line design, traditional calculation methods cannot meet the high-precision requirements, especially for calculations of complex alignments, where it is difficult to derive analytical solutions and they lack universality.
A linked list container for managing route models is constructed. By combining curvature expressions and numerical integration with the solution of nonlinear equations, route parameters can be calculated. Flexible conversion between intersection method and element method models is supported. Route models can be split, merged and edited, and compliance checks can be performed to improve calculation accuracy and efficiency.
It achieves high precision and efficiency in railway line shape calculation, possesses strong versatility and scalability, and is suitable for various railway line designs.
Smart Images
Figure CN115525947B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of railway design technology, and in particular to a general method for calculating the alignment of railway lines. Background Technology
[0002] In railway line design, straight lines, circular curves, and transition curves are used to express the horizontal alignment. Among them, a transition curve is a curve with continuously changing curvature, which is placed between a straight line and a circular curve, between two circular curves in the same direction with a large difference in radius, or between two circular curves in opposite directions.
[0003] In traditional railway design, a cubic parabolic transition curve is used. This transition curve is an approximation of the spiral transition curve. Its calculation formula is an infinite series expansion. Generally, only the first two terms of the expansion are used in the calculation. As the railway grade increases, the requirements for the accuracy of transition curve calculation continue to increase, and this approximation formula can no longer meet the requirements.
[0004] For transition curves connecting two circular curves in the same direction, traditional calculations generally use incomplete transition curves for special processing, which lacks universality. For transition curves connecting two circular curves in opposite directions, only two transition curves of equal length can be used for connection. For complex alignments such as the single-wave sinusoidal transition curve used in maglev railways, it is difficult to derive analytical solutions, and there is an urgent need to study a universal alignment calculation method for railway lines. Summary of the Invention
[0005] The purpose of this invention is to provide a general method for calculating the alignment of railway lines, in order to solve the technical problem that existing calculation methods are not applicable to the complex alignments of upgraded railways and that it is difficult to derive analytical solutions.
[0006] This invention provides a general method for calculating the alignment of railway lines, which includes the following steps:
[0007] S1. Create a model management linked list container.
[0008] Based on the data representation characteristics of railway line units, a railway line management model is constructed. Railway lines consist of three basic units: straight lines, circular curves, and transition curves. Adjacent units are connected end-to-end, and their data structure can be represented by a linked list. The data prototype is as follows:
[0009] class CElement:public CList<CElement*,CElement*> .
[0010] S2 creates a general linear data structure based on curvature representation.
[0011] The curvature of a curve is the rate of rotation of the tangent angle at a calculation point on the curve with respect to the arc length. It indicates the degree to which the curve deviates from a straight line and is defined by differentiation. The radius of curvature is the reciprocal of the curvature and equal to the radius of the arc at that point. Basic straight lines, circular curves, and transition curves in a line model can all be defined as curves. The curvature of straight lines and circular curves is a constant value; the curvature of a straight line is 0, and the curvature of a circular curve is the reciprocal of the curve radius, equal to the radius of the arc at that point. The curvature of a transition curve differs at its starting and ending points, and the curvature changes with its length. The trend of curvature change can be described by a curvature expression. By using the unit starting point curvature, unit ending point curvature, and unit length parameters, a curvature expression is constructed to describe the geometric characteristics of commonly used linear basic units in line design, including straight lines, circular curves, spiral-shaped transition curves, S-shaped transition curves, quintic parabolic transition curves, septtic parabolic transition curves, half-wave sine curve transition curves, and single-wave sine curve transition curves. For other transition curve types, this can be extended by defining a curvature expression.
[0012] S3, the numerical integration and equation solving calculation
[0013] Using curvature expressions, combined with numerical integration and nonlinear equation solving, the line parameters are calculated, including: calculating the coordinates of the line position at the marked mileage, calculating the coordinates of the perpendicular point of the specified point projected onto the line model, and calculating the coordinates of the intersection points of straight line units, circular curve units, transition curve units and the line model.
[0014] The steps for calculating the coordinates of the marked mileage are: (1) Calculate the continuous mileage based on the marked mileage and locate the unit where the continuous mileage is located; (2) Construct integral expressions for the x and y coordinates in the local coordinate system based on the curvature of the unit's starting point, the curvature of the unit's ending point, and the geometric length of the unit; (3) Calculate the x and y coordinates using Romberg numerical integration; (4) Calculate the coordinates in the global coordinate system by transforming the coordinates in the local coordinate system.
[0015] The steps to calculate the coordinates of the perpendicular point of a specified point P1 projected onto the line model are: (1) Traverse the linked list of the line model; (2) For each unit, first construct the normals L1 and L2 of the unit's start and end points, and then calculate the directed distances D1 and D2 from P1 to L1 and L2 respectively. If the signs of D1 and D2 are opposite, it means that P1 has a perpendicular point in the unit; otherwise, there is no perpendicular point; (3) Construct the directed distance equation from P1 to the normal at mileage l on the unit, and solve the continuous mileage L when the equation is 0 using a nonlinear equation, which is taken as the perpendicular mileage; (4) Calculate the coordinates of the perpendicular point P2 based on the continuous mileage L, and calculate the distance D from P1 to P2; (5) If there are multiple perpendicular points, select the perpendicular point with the smallest D value as the final perpendicular point P, and the corresponding continuous mileage is the perpendicular point mileage.
[0016] S4, flexible conversion between intersection method model and element method model
[0017] Based on different design requirements, the two data organization models, intersection method and unit method, are converted to each other.
[0018] In a conventional line model, the unit arrangement is "straight line - transition curve - circular curve - transition curve - straight line - transition curve - circular curve - transition curve - straight line". For special line designs, adjacent circular curves are directly connected by transition curves, and the unit arrangement is "straight line - transition curve - circular curve - transition curve - circular curve - transition curve - straight line". Both of these structures can be managed directly using the unit method. Alternatively, for the first structure, adjacent "transition curve - circular curve - transition curve" lines can be viewed as a curve set, and the intersection point of the starting tangent of the previous transition curve and the ending tangent of the next transition curve in the curve set can be calculated. This intersection point method is used for management, and its data structure is "straight line - curve set - straight line - curve set - straight line".
[0019] The steps to convert the intersection method into the unit method are as follows: find each curve set in the model management linked list, take out the "transition curve-circular curve-transition curve" from the curve set, insert it into the position of the curve set in the linked list, and finally delete the curve set.
[0020] The steps to convert the unit method to the intersection method are as follows: First, traverse the model management linked list and determine whether the unit arrangement order is in the form of "straight line-transition curve-circular curve-transition curve-straight line-transition curve-circular curve-transition curve-straight line". If so, for each group of "transition curve-circular curve-transition curve", construct a curve set and replace the corresponding "transition curve-circular curve-transition curve" in the linked list to complete the conversion.
[0021] S5. Conversion between line model mileage and chain breakage
[0022] Based on the model's field chain breakage, element geometric length, element start point label mileage, and element end point label mileage, calculate the continuous mileage of the element start and end points, the element start and end point label mileage, the element label length, and the element internal chain breakage, and perform the conversion between continuous mileage and label mileage.
[0023] Calculate continuous mileage based on marked mileage: First, use field link break to convert marked mileage to converted mileage. Then, find the corresponding unit based on the converted mileage. Finally, interpolate to calculate continuous mileage based on the continuous mileage of the unit's start and end points and the converted mileage of the unit's start and end points.
[0024] Calculating labeled mileage based on continuous mileage: First, find the corresponding unit based on the continuous mileage. Then, interpolate the converted mileage based on the continuous mileage of the unit's start and end points and the converted mileage of the unit's start and end points. Finally, use field link break to convert the converted mileage into labeled mileage.
[0025] S6. Circuit Model Splitting, Merging, and Editing
[0026] For a route model, a split point is determined on a straight line element, splitting the model into two parts. The continuous mileage is calculated separately for each part, and then each part is edited independently. The two route models are then merged into one. During merging, it is necessary to ensure that the merging point of the two models is on a straight line, and that the coordinates and tangent vector of the endpoint of the first model are equal to the coordinates and tangent vector of the starting point of the second model. After merging, the continuous mileage is recalculated. Editing the intersection point model includes adding intersection points, inserting intersection points, freely moving intersection points, moving intersection points along the forward tangent, moving intersection points along the backward tangent, modifying the curve data of intersection points, and deleting intersection points. Editing the element model includes adding, deleting, and modifying elements. Adding elements includes creating connecting transition curves based on straight line elements and circular curve elements, creating connecting transition curves based on two circular curve elements, and creating circular curve elements based on two straight line elements. Modifying elements includes moving elements, modifying lengths, and modifying radii.
[0027] S7, Line Model Compliance Check
[0028] Based on the design specifications and design speed adopted by the line model, conduct compliance checks on the line model, including checks on the minimum circular curve length, minimum straight section length, minimum transition curve length, minimum radius of circular curve, and maximum radius of circular curve.
[0029] S8. Calculation and output of line model coordinates and line spacing.
[0030] Based on the marked mileage array of the route model, calculate the corresponding route coordinate array and output a station-by-station coordinate table that meets the design requirements; based on the marked mileage array of the baseline route model and the reference route model, calculate the line spacing between the baseline route model and the reference route model at each marked mileage and output a line spacing table that meets the design requirements.
[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0032] This invention first constructs a linked list container for managing railway line models, and creates a general linear data structure by constructing curvature expressions for straight lines, circular curves, and transition curves. Then, it constructs integral expressions and uses numerical integration and nonlinear equations to solve them, achieving general calculations of coordinates, vectors, perpendiculars, and distances. It enables flexible conversion between intersection method and element method models. By constructing a mileage conversion system, it facilitates the handling of broken links in field and office operations, and the mutual conversion between labeled mileage, converted mileage, and continuous mileage. Through model splitting, merging, and editing, it enables interactive modification of the railway line model. It also uses design specifications to check the compliance of the railway line model. This method can greatly improve the accuracy and efficiency of railway line shape calculations, and has strong versatility and scalability. Attached Figure Description
[0033] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0034] Figure 1 A flowchart illustrating a general railway alignment calculation method provided in an embodiment of the present invention. Detailed Implementation
[0035] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.
[0036] The components of the embodiments of the invention described and shown in the accompanying drawings can typically be arranged and designed in a variety of different configurations. Therefore, the following detailed description of the embodiments of the invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention.
[0037] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0038] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.
[0039] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.
[0040] Depend on Figure 1 As shown in the flowchart, the steps of a general railway line alignment calculation method involved in this invention include: creating a model management linked list container, creating a general alignment data structure based on curvature expression, numerical integration and equation solving calculation, flexible conversion between intersection method model and element method model, conversion of line model mileage and chain breakage, splitting, merging and editing of line model, compliance check of line model, calculation of line model coordinates and line spacing and output of results.
[0041] Specifically:
[0042] S1. Create a model management linked list container.
[0043] Based on the data representation characteristics of railway line units, a railway line management model is constructed. Railway lines consist of three basic units: straight lines, circular curves, and transition curves. Adjacent units are connected end-to-end, and their data structure can be represented by a linked list. The data prototype is as follows:
[0044] class CElement:public CList<CElement*,CElement*> .
[0045] S2. Create a general linear data structure based on curvature representation.
[0046] The curvature of a curve is the rate of rotation of the tangent angle at a calculation point on the curve with respect to the arc length. It indicates the degree to which the curve deviates from a straight line and is defined by differentiation. The radius of curvature is the reciprocal of the curvature and equal to the radius of the arc at that point. Basic straight lines, circular curves, and transition curves in a line model can all be defined as curves. The curvature of straight lines and circular curves is a constant value; the curvature of a straight line is 0, and the curvature of a circular curve is the reciprocal of the curve radius, equal to the radius of the arc at that point. The curvature of a transition curve differs at its starting and ending points, and the curvature changes with its length. The trend of curvature change can be described by a curvature expression. By using the unit starting point curvature, unit ending point curvature, and unit length parameters, a curvature expression is constructed to describe the geometric characteristics of commonly used linear basic units in line design, including straight lines, circular curves, spiral-shaped transition curves, S-shaped transition curves, quintic parabolic transition curves, septtic parabolic transition curves, half-wave sine curve transition curves, and single-wave sine curve transition curves. For other types of transition curves, this can be extended by defining curvature expressions.
[0047] Curvature is a directional curvature, which can be used to represent the transition curve between two arbitrary curvatures, including the transition curve between a straight line and a circular curve, the transition curve between two circular curves in the same direction, and the transition curve between two circular curves in opposite directions.
[0048] S3. Numerical Integration and Equation Solving
[0049] Using curvature expressions, combined with numerical integration and nonlinear equation solving, the line parameters are calculated, including: calculating the coordinates of the line position at the marked mileage, calculating the coordinates of the perpendicular point of the specified point projected onto the line model, and calculating the coordinates of the intersection points of straight line units, circular curve units, transition curve units and the line model.
[0050] The steps for calculating the coordinates of the marked mileage are: (1) Calculate the continuous mileage based on the marked mileage and locate the unit where the continuous mileage is located; (2) Construct integral expressions for the x and y coordinates in the local coordinate system based on the curvature of the unit's starting point, the curvature of the unit's ending point, and the geometric length of the unit; (3) Calculate the x and y coordinates using Romberg numerical integration; (4) Calculate the coordinates in the global coordinate system by transforming the coordinates in the local coordinate system.
[0051] The steps for calculating the perpendicular point coordinates of a specified point P1 projected onto the line model are as follows: (1) Traverse the linked list of the line model; (2) For each unit, first construct the normals L1 and L2 of the unit's start and end points, and then calculate the directed distances D1 and D2 from P1 to L1 and L2 respectively. If the signs of D1 and D2 are opposite, it means that P1 has a perpendicular point in the unit; otherwise, there is no perpendicular point; (3) Construct the directed distance equation from P1 to the normal at mileage l on the unit, and solve the continuous mileage L when the equation is 0 using a nonlinear equation, which is taken as the perpendicular mileage; (4) Calculate the perpendicular point coordinates P2 based on the continuous mileage L, and calculate the distance D from P1 to P2; (5) If there are multiple perpendicular points, select the perpendicular point with the smallest D value as the final perpendicular point P, and the corresponding continuous mileage is the perpendicular point mileage. If P1 is a point on the line model, this method can also be extended to calculate the line mileage corresponding to the coordinates of a specified point on the line model.
[0052] S4, flexible conversion between intersection method model and element method model
[0053] The intersection method model uses intersections as the basic design unit, and the linkage modification of units is achieved by manipulating the intersections. It is relatively simple to operate and is the most commonly used design method in railway design. The element method model uses units as the basic design unit, which is more flexible, but its operation is more cumbersome and it cannot achieve linkage modification of units. Depending on different design requirements, the intersection method and the element method data organization models can be converted to each other.
[0054] In a conventional line model, the unit arrangement is "straight line - transition curve - circular curve - transition curve - straight line - transition curve - circular curve - transition curve - straight line". For special line designs, adjacent circular curves are directly connected by transition curves, and the unit arrangement is "straight line - transition curve - circular curve - transition curve - circular curve - transition curve - straight line". Both of these structures can be managed directly using the unit method. Alternatively, for the first structure, adjacent "transition curve - circular curve - transition curve" lines can be viewed as a curve set, and the intersection point of the starting tangent of the previous transition curve and the ending tangent of the next transition curve in the curve set can be calculated. This intersection point method is used for management, and its data structure is "straight line - curve set - straight line - curve set - straight line".
[0055] The steps to convert the intersection method into the unit method are as follows: find each curve set in the model management linked list, take out the "transition curve-circular curve-transition curve" from the curve set, insert it into the position of the curve set in the linked list, and finally delete the curve set.
[0056] The steps to convert the unit method to the intersection method are as follows: First, traverse the model management linked list and determine whether the unit arrangement order is in the form of "straight line-transition curve-circular curve-transition curve-straight line-transition curve-circular curve-transition curve-straight line". If so, for each group of "transition curve-circular curve-transition curve", construct a curve set and replace the corresponding "transition curve-circular curve-transition curve" in the linked list to complete the conversion.
[0057] When converting from the element method model to the intersection method model, it is necessary to ensure that the starting tangent of the previous transition curve and the ending tangent of the next transition curve in each curve set have an intersection point; otherwise, the conversion will not be successful.
[0058] S5. Conversion between line model mileage and chain breakage
[0059] Based on the model's field chain breakage, element geometric length, element start point label mileage, and element end point label mileage, calculate the continuous mileage of the element start and end points, the element start and end point label mileage, the element label length, and the element internal chain breakage, and perform the conversion between continuous mileage and label mileage.
[0060] Calculate the continuous mileage of the start and end points of the unit: The continuous mileage of the start point of the first unit in the model is 0, the continuous mileage of the start point of other units is equal to the continuous mileage of the end point of the previous unit, and the continuous mileage of the end point of the unit is equal to the continuous mileage of the start point of the unit plus the geometric length of the unit.
[0061] The calculation includes the conversion mileage of the unit's starting point, the conversion mileage of the unit's ending point, the conversion length of the unit, and the internal chain break of the unit: The conversion mileage of the model is calculated through the external chain break. The conversion mileage of the starting point of the first unit is 0, and the conversion mileage of the starting point of other units is equal to the conversion mileage of the ending point of the previous unit. The conversion mileage of the unit's ending point is calculated through the external chain break using the unit's ending point marked mileage and the unit's ending chain break sequence number. The conversion length of the unit is equal to the conversion mileage of the unit's ending point minus the conversion mileage of the unit's starting point, and the internal chain break of the unit is equal to the conversion length of the unit minus the geometric length of the unit.
[0062] The relationship between the unit conversion length and the unit geometric length can also be expressed as the length error rate, that is: length error rate = 1 - unit conversion length / unit geometric length.
[0063] Calculate continuous mileage based on marked mileage: First, use field link break to convert marked mileage to converted mileage. Then, find the corresponding unit based on the converted mileage. Finally, interpolate to calculate continuous mileage based on the continuous mileage of the unit's start and end points and the converted mileage of the unit's start and end points.
[0064] Calculate labeled mileage based on continuous mileage: First, find the corresponding unit based on continuous mileage. Then, interpolate the converted mileage based on the continuous mileage of the unit's start and end points and the converted mileage of the unit's start and end points. Finally, use field link break to convert the converted mileage into labeled mileage.
[0065] S6. Circuit Model Splitting, Merging, and Editing
[0066] For a route model, a split point is determined on a straight line unit, splitting the model into two, and the continuous mileage is calculated separately for each, followed by independent editing. The two route models are then merged into one, ensuring the merging point lies on a straight line, and that the coordinates and tangent vector of the endpoint of the first model are equal to the coordinates and tangent vector of the starting point of the second model. After merging, the continuous mileage is recalculated. Editing the intersection method model includes adding, inserting, freely moving, moving along the preceding tangent, moving along the following tangent, modifying the curve data of intersections, and deleting intersections. During design, the intersection point of the starting tangent of the preceding transition curve and the ending tangent of the following transition curve is first calculated in each curve set. Then, all intersection points are connected sequentially to form a polyline, and the linked modification of units is achieved by manipulating the intersection points. Editing the element method model includes adding, deleting, and modifying elements. Adding elements includes creating connecting transition curves based on straight line units and circular curve units, creating connecting transition curves based on two circular curve units, and creating circular curve units based on two straight line units. Modifying elements includes moving, modifying length, and modifying radius.
[0067] S7, Line Model Compliance Check
[0068] Based on the design specifications and design speed adopted by the line model, conduct compliance checks on the line model, including checks on the minimum circular curve length, minimum straight section length, minimum transition curve length, minimum radius of circular curve, and maximum radius of circular curve.
[0069] S8. Calculation and results of line model coordinates and line spacing.
[0070] Based on the marked mileage array of the route model, calculate the corresponding route coordinate array and output a station-by-station coordinate table that meets the design requirements; based on the marked mileage array of the baseline route model and the reference route model, calculate the line spacing between the baseline route model and the reference route model at each marked mileage and output a line spacing table that meets the design requirements.
[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A general method for calculating the alignment of railway lines, characterized in that... It includes the following steps: S1. Based on the data representation characteristics of railway line units, construct a linked list container for line model management; S2. By constructing curvature expressions for straight lines, circular curves, and transition curves, a general linear data structure is created; S3. Using the curvature expression, combined with numerical integration and nonlinear equation solving, calculate the line parameters; S4. Based on different design requirements, the two data organization models, intersection method and unit method, can be converted to each other; S5. Construct a mileage conversion system to convert the mileage of the route model to the mileage of broken links; S6. By using model splitting, merging, and editing techniques, interactive modification of the circuit model can be achieved; S7. Conduct a compliance check on the line model based on the design specifications and design speed adopted by the line model; S8. Calculate the coordinates and spacing of the line model and output the results; In S3, the calculation of line parameters specifically includes: Calculate the coordinates of the line position at the marked mileage, calculate the coordinates of the perpendicular point of the specified point projected onto the line model, and calculate the coordinates of the intersection points of the straight line unit, circular curve unit, transition curve unit and the line model; The steps for calculating the coordinates of the marked mileage are as follows: calculate the continuous mileage based on the marked mileage and locate the unit where the continuous mileage is located; construct integral expressions for the x and y coordinates in the local coordinate system based on the curvature of the unit's starting point, the curvature of the unit's ending point, and the geometric length of the unit; calculate the x and y coordinates using Romberg numerical integration; and calculate the coordinates in the global coordinate system by transforming the coordinates in the local coordinate system. The steps for calculating the coordinates of the perpendicular point P1 projected onto the line model are as follows: traverse the linked list of the line model; for each cell, first construct the normals L1 and L2 of the cell's start and end points, then calculate the directed distances D1 and D2 from P1 to L1 and L2 respectively. If D1 and D2 have opposite signs, it means that P1 has a perpendicular point in that cell; otherwise, there is no perpendicular point. Construct the directed distance equation from P1 to the normal at mileage l on the cell, and solve the equation using a nonlinear equation to obtain the continuous mileage L when the equation equals 0, which is taken as the perpendicular mileage. Calculate the coordinates of the perpendicular point P2 based on the continuous mileage L, and calculate the distance D from P1 to P2. If there are multiple perpendicular points, select the perpendicular point with the smallest D value as the final perpendicular point P, and the corresponding continuous mileage is the perpendicular point mileage. In S4, the steps to convert the intersection method into the unit method are as follows: search for each curve set in the model management linked list, take out the "transition curve-circular curve-transition curve" from the curve set, insert it into the position of the curve set in the linked list, and finally delete the curve set. The steps to convert the unit method to the intersection method are as follows: First, traverse the model management linked list and determine whether the unit arrangement order is in the form of "straight line-transition curve-circular curve-transition curve-straight line-transition curve-circular curve-transition curve-straight line". If so, for each group of "transition curve-circular curve-transition curve", construct a curve set and replace the corresponding "transition curve-circular curve-transition curve" in the linked list to complete the conversion. When converting the unit method to the intersection method, it should be ensured that the starting tangent of the previous transition curve and the ending tangent of the next transition curve in each curve set have an intersection point.
2. The general railway line alignment calculation method according to claim 1, characterized in that, In S1, railway line units are composed of three basic units: straight lines, circular curves, and transition curves, with adjacent units connected end to end.
3. The general railway line alignment calculation method according to claim 1, characterized in that, In S2, the general linear data structure is created as follows: In S2, curvature is a directed curvature, used to represent the transition curve between two arbitrary curvatures, including the transition curve between a straight line and a circular curve, the transition curve between two circular curves in the same direction, and the transition curve between two circular curves in opposite directions.
4. The general railway line alignment calculation method according to claim 1, characterized in that, S5 specifically includes: calculating the continuous mileage of the unit's start and end points, the unit's start and end point labeled mileage, the unit's labeled length, and the unit's internal chain breakage based on the model's field chain breakage, unit geometric length, unit's starting point labeled mileage, and unit's ending point labeled mileage, and converting between continuous mileage and labeled mileage; The steps for calculating continuous mileage based on marked mileage are as follows: First, use field chain break to convert marked mileage into converted mileage; then, find the corresponding unit based on the converted mileage; finally, interpolate to calculate continuous mileage based on the continuous mileage at the start and end of the unit and the converted mileage at the start and end of the unit. The steps for calculating the labeled mileage based on continuous mileage are as follows: First, find the corresponding unit based on the continuous mileage. Then, interpolate the converted mileage based on the continuous mileage of the unit's start and end points and the converted mileage of the unit's start and end points. Finally, use the field link break to convert the converted mileage into the labeled mileage.
5. The general railway line alignment calculation method according to claim 1, characterized in that, In S6, interactive modification of the circuit model specifically includes: For a route model, the split point is determined on the straight line unit, the model is split into two models, the continuous mileage is calculated for each model, and then they are edited independently. Two route models are merged into one route model. During the merging process, it is necessary to ensure that the merging point of the two models is on a straight line, and that the coordinates and tangent vector of the end point of the first model are equal to the coordinates and tangent vector of the starting point of the second model. After merging, the continuous mileage is recalculated. Editing the intersection point model includes adding intersection points, inserting intersection points, freely moving intersection points, moving intersection points along the front tangent, moving intersection points along the back tangent, modifying the curve data of intersection points, and deleting intersection points. Editing the element method model includes adding, deleting, and modifying elements. Adding elements includes creating a connection transition curve based on a straight element and a circular curve element, creating a connection transition curve based on two circular curve elements, and creating a circular curve element based on two straight elements. Modifying elements includes moving elements, modifying their length, and modifying their radius.
6. The general railway line alignment calculation method according to claim 1, characterized in that, In S7, compliance checks include: minimum circular curve length check, minimum clamping straight line length check, minimum transition curve length check, minimum circular curve radius check, and maximum circular curve radius check.
7. The general railway line alignment calculation method according to claim 1, characterized in that, S8 specifically includes: calculating the corresponding line coordinate array based on the marked mileage array of the line model, and outputting a station-by-station coordinate table that meets the design requirements; calculating the line spacing between the benchmark line model and the reference line model at each marked mileage based on the marked mileage array of the benchmark line model and the reference line model, and outputting a line spacing table that meets the design requirements.