Method for measuring and calculating elevation of any point location of road surface based on triangulated irregular network

Abstract

The invention discloses a method for measuring and calculating the elevation of any point location of a pavement based on a triangulated irregular network, and belongs to the technical field of pavement point location elevation measurement and calculation in road design and construction, and the method comprises the following steps: obtaining a horizontal curve element table and a vertical curve element table of road design; inputting a horizontal curve element and a vertical curve element in a measurement coordinate calculation program to obtain a three-dimensional coordinate; performing triangulation to form an irregular triangulation network in the three-dimensional coordinates; setting a point corresponding to any point of the pavement to be measured and calculated in the triangulated irregular network as a point P, and determining a triangle closest to the point P; obtaining a triangular plane equation; and calculating the elevation of the P point. According to the method, the pavement topographic conditions are precisely restored by using the triangulated irregular network, the construction of the triangulated irregular network under the complex topography is remarkably optimized by using the triangular plane calculation equation, the elevation measurement and calculation error is reduced, and the efficiency and the precision of measuring and calculating the elevation of any point position of the pavement in the complex topography are remarkably improved.

Description

Technical Field

[0001] The invention belongs to the technical field of road surface point elevation measurement in road design and construction, and specifically relates to a method for measuring the elevation of any road surface point based on an irregular triangulated network. Background Art

[0002] During the road design and construction phase, real-time measurement and control of road surface elevation plays a vital role in the rationality of design (including road slope design, drainage system optimization, etc.), accuracy during construction (improving measurement accuracy) and high efficiency (reducing rework).

[0003] Usually, the design data of roads only give the coordinates of the intersections of three types of lines: straight lines, transition curves, and circular curves. If you want to calculate the three-dimensional coordinates of other points, you first need to classify the points to be found, determine which type of linear segment they are located on (including straight line segments, circular curve segments, and transition curve segments), and then select the corresponding mathematical model for calculation (including straight line segment-straight line equation, circular curve segment-circular curve equation, and transition curve segment-circular curve equation), substitute the X and Y coordinates of the points to be found, and solve the Z coordinate of the points to get the elevation of the points. This calculation method is labor-intensive and cumbersome, and will increase the measurement error in complex terrain. Therefore, how to quickly, efficiently, and accurately measure the elevation of the road surface has become a focus of attention for industry professionals.

[0004] With the advancement of science and technology, intelligent and information technology has gradually become a new trend in the field of road design and construction. In the field of geological science, an irregular triangulated network model, namely the TIN model, has been proposed. It uses the uneven inflection points on the surface to connect triangles to build a digital ground model that accurately represents the changes in surface height. However, at present, irregular triangulated networks are mostly used in surface model generation, contour line drawing, and longitudinal and cross-section drawing. There is no complete and systematic method to use it for the measurement of road elevation.

[0005] Directly based on the existing irregular triangulated network application method, the irregular triangulated network of the road surface can be constructed to find the triangle of the desired point, and the elevation of the desired point can be calculated using the linear interpolation or quadratic interpolation calculation method. However, this conventional interpolation calculation method relies on the elevation change between the triangle vertices being linear or being approximated by some simple functional relationship. Although this method is simple and fast, it has a large error when facing complex terrain conditions. Therefore, when facing complex terrain conditions, traditional common methods cannot solve the technical problem of reducing errors and measuring road elevation with high precision. Summary of the invention

[0006] The purpose of the present invention is to provide a method for calculating the elevation of any point on the road surface based on an irregular triangulated network in order to solve the above-mentioned problem, which can efficiently and accurately calculate the elevation of any point on the road surface in complex terrain.

[0007] The present invention achieves the above-mentioned purpose through the following technical solutions:

[0008] A method for calculating the elevation of any point on a road surface based on an irregular triangulated network comprises the following steps:

[0009] Step 1, obtain the horizontal curve element table and vertical curve element table of road design;

[0010] Step 2, input the horizontal curve element and the vertical curve element into the measurement coordinate calculation program (a macro language program secondary developed by Microsoft Office software, that is, a spreadsheet program, which is the prior art), and obtain the three-dimensional coordinates including the left pile, the middle pile, and the right pile of the road, the three-dimensional coordinates including the X-axis, the Y-axis, and the Z-axis, wherein the Z-axis represents the elevation of a certain point;

[0011] The method for calculating the elevation of any point on the road surface based on the irregular triangulated network also includes the following steps:

[0012] Step 3, using the Delaunay triangulation function written in Matlab software to triangulate all the design points of the road to form an irregular triangulated network in three-dimensional coordinates and satisfy the following conditions: each point in the given point set is the vertex of a triangle in the irregular triangulated network and there is no other point in the irregular triangulated network inside its circumscribed circle; the irregular triangulated network, namely the TIN (Triangulated Irregular Network) model, uses a series of connected triangles to fit the ground surface or other irregular surfaces, and is often used to construct digital ground models, especially digital elevation models, which is a prior art; Matlab software is a commercial mathematical software produced by MathWorks, USA, and is used in data analysis, wireless communication, deep learning, image processing and computer vision, signal processing, quantitative finance and risk management, robotics, control systems and other fields, which is a prior art; Delaunay is transliterated as Delaunay (or Delaunay), and using the Delaunay triangulation function to triangulate can obtain a set of a series of connected but non-overlapping triangles, namely the Delaunay triangulated network, which is a prior art;

[0013] Step 4: Assume that the point corresponding to any point on the road surface to be measured in the irregular triangulated network is point P, calculate the Euclidean distance between all vertices in the irregular triangulated network and point P, which is the distance between each point in the irregular triangulated network after being projected onto the XY plane in the three-dimensional coordinate system, determine the vertex closest to point P and set the vertex as point A, determine which triangle with point A as one of the vertices encloses point P and set the other two vertices of the triangle as point B and point C;

[0014] Step 5. Calculate the relevant parameters using the following triangular plane equation:

[0015] ax A +by A +cz A +d=0

[0016] ax B +by B +cz B +d=0

[0017] ax C +by C +cz C +d=0

[0018] Among them, x A is the X-axis coordinate of point A in the three-dimensional coordinate system, x B is the X-axis coordinate of point B in the three-dimensional coordinate system, x C is the X-axis coordinate of point C in the three-dimensional coordinate system, y A is the Y-axis coordinate of point A in the three-dimensional coordinate system, y B is the Y-axis coordinate of point B in the three-dimensional coordinate system, y C is the Y-axis coordinate of point C in the three-dimensional coordinate system, z A is the Z-axis coordinate of point A in the three-dimensional coordinate system, z B is the Z-axis coordinate of point B in the three-dimensional coordinate system, z C is the Z-axis coordinate of point C in the three-dimensional coordinate system, x A 、x B 、x C ,y A ,y B ,y C 、z A 、z B 、z C All of them are obtained by direct query of irregular triangulated network. a, b, c, and d are four parameters to be determined. a, b, and c are used to define the normal vector of the plane, and d is a parameter related to the distance from the plane to the origin of the coordinate system.

[0019] According to the above formula, the values ​​of the four parameters a, b, c, and d are calculated;

[0020] Step 6: Calculate the elevation z of point P according to the following formula: P :

[0021] z P =-(ax P +by P +d) / c

[0022] Among them, x P ,y P They are the X-axis coordinate and Y-axis coordinate of point P in the three-dimensional coordinates, both of which are obtained based on the Beidou differential system.

[0023] Preferably, in order to achieve a better Delaunay triangulation, the step 3 includes the following steps:

[0024] Step 3.1, Initialization: Construct a super triangle whose vertices contain all the points in the point set;

[0025] Step 3.2, add points: add the points in the point set to the triangular mesh one by one;

[0026] Step 3.3, Reconstruction: According to the Delaunay property, after each new point is added, find all triangles that need to be reconstructed and delete them;

[0027] Step 3.4, connect the new point: connect the new point with the vertices of the surrounding triangles to form a new triangle;

[0028] Step 3.5: Repeat steps 3.2 to 3.4 until all points are added to obtain an irregular triangulated network in three-dimensional coordinates.

[0029] The beneficial effects of the present invention are:

[0030] The present invention utilizes irregular triangulated networks to triangulate the designed road surface and accurately restore the road surface terrain conditions. It can efficiently and quickly calculate the elevation of any point on the road surface, and utilizes triangular plane calculation equations to significantly optimize the construction of irregular triangulated networks under complex terrain, effectively solving the problem of uneven distribution of triangulated networks due to complex terrain and difficulty in fully reflecting the real terrain characteristics, reducing elevation measurement errors, and significantly improving the efficiency and accuracy of measuring the elevation of any point on the road surface in complex terrain, so that the road surface elevation measurement results are closer to actual road design and construction conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a planar schematic diagram of the Delaunay triangulation of the present invention;

[0032] Figure 2 is a schematic diagram of the irregular triangulated network of the present invention;

[0033] Figure 3 It is a schematic diagram of projecting multiple triangles related to point A in the irregular triangulated network in the three-dimensional coordinates of the present invention and point P to be measured onto the XY plane. DETAILED DESCRIPTION

[0034] The present invention will be further described below in conjunction with the accompanying drawings:

[0035] A method for calculating the elevation of any point on a road surface based on an irregular triangulated network comprises the following steps:

[0036] Step 1: Obtain the horizontal curve element table and vertical curve element table of the road design; the common horizontal curve element table and vertical curve element table are shown in the following table:

[0037] Table 5-10 Road design horizontal curve elements

[0038]

[0039] Table 5-11 Vertical curve elements of road design

[0040]

[0041] Step 2: Input the horizontal curve elements and the vertical curve elements into the measurement coordinate calculation program to obtain the three-dimensional coordinates of the left pile, the middle pile and the right pile of the road. The three-dimensional coordinates include the X axis, the Y axis and the Z axis, wherein the Z axis represents the elevation of a certain point.

[0042] Common three-dimensional coordinate related data are shown in the following table:

[0043] Table 5-12 Three-dimensional coordinates of some road design points

[0044] Pile No. x y z DK249+150.657 3613067.496 479160.3729 39.78275 DK249200 3613087.745 479205.3698 39.78275 DK249300 3613128.781 479296.562 40.112575 DK249400 3613169.818 479387.7541 40.612575 DK249500 3613210.854 479478.9463 41.112575 DK249588.9312 3613247.348 479560.0445 41.55723102 DK249600 3613251.891 479570.1384 41.612575 DK249700 3613292.877 479661.3532 42.112575 ... ... ... ... ;

[0045] Step 3: Use the Delaunay triangulation function written in Matlab software to triangulate all the design points of the road to form an irregular triangulated network in three-dimensional coordinates and meet the following conditions: each point in the given point set is a vertex of a triangle in the irregular triangulated network and no other point in the irregular triangulated network is inside its circumscribed circle; the plane effect of Delaunay triangulation is as follows: Figure 1 As shown, the irregular triangulated network is Figure 2 As shown;

[0046] The step 3 specifically comprises the following steps:

[0047] Step 3.1, Initialization: Construct a super triangle whose vertices contain all the points in the point set;

[0048] Step 3.2, add points: add the points in the point set to the triangular mesh one by one;

[0049] Step 3.3, Reconstruction: According to the Delaunay property, after each new point is added, find all triangles that need to be reconstructed and delete them;

[0050] Step 3.4, connect the new point: connect the new point with the vertices of the surrounding triangles to form a new triangle;

[0051] Step 3.5, repeat steps 3.2 to 3.4 until all points are added to obtain an irregular triangulated network in three-dimensional coordinates;

[0052] Step 4: Assume that the point corresponding to any point on the road surface to be measured in the irregular triangulated network is point P, calculate the Euclidean distance between all vertices in the irregular triangulated network and point P, which is the distance between each point in the irregular triangulated network after being projected on the XY plane in the three-dimensional coordinate system, determine the vertex closest to point P and set the vertex as point A, determine which triangle with point A as one of the vertices of point P is enclosed by point P and set the other two vertices of the triangle as points B and C, such as Figure 3 As shown;

[0053] Step 5. Calculate the relevant parameters using the following triangular plane equation:

[0054] ax A +by A +cz A +d=0

[0055] ax B +by B +cz B +d=0

[0056] ax C +by C +cz C +d=0

[0057] Among them, x A is the X-axis coordinate of point A in the three-dimensional coordinate system, x B is the X-axis coordinate of point B in the three-dimensional coordinate system, x C is the X-axis coordinate of point C in the three-dimensional coordinate system, y A is the Y-axis coordinate of point A in the three-dimensional coordinate system, y B is the Y-axis coordinate of point B in the three-dimensional coordinate system, y C is the Y-axis coordinate of point C in the three-dimensional coordinate system, z A is the Z-axis coordinate of point A in the three-dimensional coordinate system, z B is the Z-axis coordinate of point B in the three-dimensional coordinate system, z Cis the Z-axis coordinate of point C in the three-dimensional coordinate system, x A 、x B 、x C ,y A ,y B ,y C 、z A 、z B 、z C They are all obtained by direct query of irregular triangulated networks. a, b, c, and d are four parameters to be determined. a, b, and c are used to define the normal vector of the plane, and d is a parameter related to the distance from the plane to the origin of the coordinate system.

[0058] According to the above formula, the values ​​of the four parameters a, b, c, and d are calculated;

[0059] Step 6: Calculate the elevation z of point P according to the following formula: P :

[0060] z P =-(ax P +by P +d) / c

[0061] Among them, x P ,y P They are the X-axis coordinate and Y-axis coordinate of point P in the three-dimensional coordinates, both of which are obtained based on the Beidou differential system.

[0062] Get high-precision elevation z of point P P After that, it can be used in the design and construction of roads to achieve more precise design and construction control and improve road construction efficiency.

Claims

1. A method for calculating the elevation of any point on a road surface based on an irregular triangulated network, comprising the following steps: Step 1, obtain the horizontal curve element table and vertical curve element table of road design; Step 2: Input the horizontal curve elements and the vertical curve elements into the measurement coordinate calculation program to obtain the three-dimensional coordinates of the left pile, the middle pile and the right pile of the road. The three-dimensional coordinates include the X axis, the Y axis and the Z axis, wherein the Z axis represents the elevation of a certain point. It is characterized in that: the method for calculating the elevation of any point on the road surface based on the irregular triangulated network also includes the following steps: Step 3: Use the Delaunay triangulation function written in Matlab software to triangulate all the design points of the road to form an irregular triangulated network in three-dimensional coordinates and meet the following conditions: each point in the given point set is a vertex of a triangle in the irregular triangulated network and there is no other point in the irregular triangulated network inside its circumscribed circle; Step 4: Assume that the point corresponding to any point on the road surface to be measured in the irregular triangulated network is point P, calculate the Euclidean distance between all vertices in the irregular triangulated network and point P, which is the distance between each point in the irregular triangulated network after being projected onto the XY plane in the three-dimensional coordinate system, determine the vertex closest to point P and set the vertex as point A, determine which triangle with point A as one of the vertices encloses point P and set the other two vertices of the triangle as point B and point C; Step 5. Calculate the relevant parameters using the following triangular plane equation: ax+by+Cz+d=0 axB+byB+CzB+d=0 axC+byc+Czc+d=0 Among them, x A is the X-axis coordinate of point A in the three-dimensional coordinate system, x B is the X-axis coordinate of point B in the three-dimensional coordinate system, x C is the X-axis coordinate of point C in the three-dimensional coordinate system, y A is the Y-axis coordinate of point A in the three-dimensional coordinate system, y B is the Y-axis coordinate of point B in the three-dimensional coordinate system, y C is the Y-axis coordinate of point C in the three-dimensional coordinate system, z A is the Z-axis coordinate of point A in the three-dimensional coordinate system, z B is the Z-axis coordinate of point B in the three-dimensional coordinate system, z C is the Z-axis coordinate of point C in the three-dimensional coordinate system, x A 、x B 、x C ,y A ,y B ,y C 、z A 、z B 、z C All of them are obtained by direct query of irregular triangulated network. a, b, c, and d are four parameters to be determined. a, b, and c are used to define the normal vector of the plane, and d is a parameter related to the distance from the plane to the origin of the coordinate system. According to the above formula, the values ​​of the four parameters a, b, c, and d are calculated; Step 6: Calculate the elevation z of point P according to the following formula: P : ZP=-(axp+byP+d) / c Among them, x P ,y P They are the X-axis coordinate and Y-axis coordinate of point P in the three-dimensional coordinates, both of which are obtained based on the Beidou differential system.

2. The method for calculating the elevation of any point on a road surface based on an irregular triangulated network according to claim 1 is characterized in that: The step 3 comprises the following steps: Step 3.1, Initialization: Construct a super triangle whose vertices contain all the points in the point set; Step 3.2, add points: add the points in the point set to the triangular mesh one by one; Step 3.3, Reconstruction: According to the Delaunay property, after each new point is added, find all the triangles that need to be reconstructed and delete them; Step 3.4, connect the new point: connect the new point with the vertices of the surrounding triangles to form a new triangle; Step 3.5: Repeat steps 3.2 to 3.4 until all points are added to obtain an irregular triangulated network in three-dimensional coordinates.

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