CN113934974A - Method for calculating coordinates of any pile number on route - Google Patents

Method for calculating coordinates of any pile number on route Download PDF

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CN113934974A
CN113934974A CN202111192511.4A CN202111192511A CN113934974A CN 113934974 A CN113934974 A CN 113934974A CN 202111192511 A CN202111192511 A CN 202111192511A CN 113934974 A CN113934974 A CN 113934974A
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point
coordinate
calculation
route
line
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韩富庆
娄健
马增琦
郭国和
曾雄鹰
吴勇生
孙文晋
蔡敏
万永涛
姬亚磊
文言
杨承昆
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Guangdong Yunmao Expressway Co ltd
Hunan Lianzhi Technology Co Ltd
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Guangdong Yunmao Expressway Co ltd
Hunan Lianzhi Technology Co Ltd
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Abstract

The invention discloses a method for calculating coordinates of any pile number on a route, which comprises the following steps: judging the intersection point interval and the line shape of the P point according to the design route information and the pile number sn of the P point; calculating the line coordinate of the point P by using a numerical integration method according to the linear information of the point P; and calculating the control coordinate of the side pile according to the coordinate of the point P. According to the invention, a general calculation formula of a side pile in the line is deduced according to an integral relation between curvature and mileage, and then a numerical calculation method of integral is utilized, so that calculation models of all line elements are the same, and different calculation methods are not required to be selected according to different line elements; according to the calculation method provided by the invention, the calculation result is the same coordinate in the circuit control coordinate system, and secondary coordinate conversion is not needed; the calculation method provided by the invention is strict in theory, simple in formula and convenient for programming realization.

Description

Method for calculating coordinates of any pile number on route
Technical Field
The invention relates to the technical field of road surveying and construction lofting, in particular to a method for calculating coordinates of any pile number on a route.
Background
According to '2016 transport industry development statistics bulletin', published by the department of transportation, the total mileage of roads in China reaches 469.63 km and the density of roads reaches 48.92km/km at the end of 2016 years2The highway 422.65 km above the grade and the highway 13.10 km above the grade. Lofting is needed to be carried out according to design line types in the process of determining and measuring roads such as highways, railways and the like so as to determine longitudinal and transverse sections and design a construction drawing; in the construction process, more lofting work needs to be carried out on bridges, tunnels, roadbeds and the like.
The lofting method is converted into a more flexible and convenient polar coordinate method and a GPS RTK lofting method from the traditional deflection angle method and the traditional offset distance method. No matter which method is used for lofting, the line control coordinates of the point to be lofted need to be known; due to the characteristics of road engineering, almost all lofting points can be regarded as middle piles or side piles of the road. Therefore, the calculation of the line coordinates occupies a very important position in lofting.
The traditional line coordinate calculation method can select different methods according to different line elements (mainly straight lines, circular curves and gentle curves), and has the disadvantages of large calculation amount, complex calculation and easy error. For the straight line segment, the calculation is simple, and the control coordinate can be directly calculated only by knowing the coordinates and the azimuth angle of the starting point; for circular curves and easement curves, the calculation is very complicated, and an independent coordinate system based on a tangent line and a normal line at a certain point on the curve needs to be established first, and then the independent coordinate system is converted into a circuit control coordinate game.
Disclosure of Invention
The invention aims to provide a method for calculating coordinates of any pile number on a route. According to the calculation method provided by the invention, the calculation models of all the line elements are the same, and different calculation methods are not required to be selected according to the difference of the line elements; according to the calculation method provided by the invention, the calculation result is the same coordinate in the circuit control coordinate system, and secondary coordinate conversion is not needed; the calculation method provided by the invention is strict in theory, simple in formula and convenient for programming realization. The specific technical scheme is as follows:
a method for calculating coordinates of any stake mark on a route comprises the following steps:
step 1: judging the intersection point interval and the line shape of the P point according to the design route information and the pile number sn of the P point;
step 2: calculating the line coordinate of the point P by using a numerical integration method according to the linear information of the point P;
and step 3: and calculating the control coordinate of the side pile according to the coordinate of the point P.
Optionally, the method for judging the intersection point S of the intersection point interval to which the mileage sn belongs by the point P specifically comprises the following steps:
finding the nearest intersection JD to snm，JDm＝min(|JDiSn-sn), i 1,2,3, …, k, where k is the number of intersections in the design line, JDiSn is JDiMin is a function for taking the minimum value;
if sn < JDm_sn-Tm1-Dm1In the formula, Tm1Is JDmFirst tangent length of (D)m1Is JDmThe first straight line is long, S is JDm-1；
If JDm_sn-Tm1-Dm1≤sn≤JDm_sn-Tm1+Lm+Dm2In the formula LmIs JDmLength of curve of (D)m2Is JDmThe second line is long, S is JDm；
If sn > JDn_sn-Tm1+Lm+Dm2S is JDm+1。
Optional, JD, of the present inventionm-1M in (1) or JDm+1M in (1) is k, which indicates that the point P is beyond the range of the design route, i.e. the point P is not on the current design route.
The length of the line element where the point P is located is l, and the starting point A (X) is optionalA，YA) Has a curvature of κAAzimuth angle of coordinate is alphaAThe curvature of the end point B is κBAnd the route length of the point P from the point A is s, the route coordinate calculation method of the point P is as follows:
Figure BDA0003301760420000021
in the formula: viIs a Gaussian node, RiIs a node coefficient, kAB＝κB-κAF is a sign function, and is-1 when the curve is biased to the left and 1 when the curve is biased to the right.
Optionally, the azimuth of the coordinate at the point P is as follows:
Figure BDA0003301760420000022
optionally, the calculation formula of the control coordinate of the side pile of the point P is as follows:
Figure BDA0003301760420000031
in the formula: d is the offset distance between the side pile and the corresponding middle pile. Optionally, the method for calculating the length s of the route is s-snAIn the formula, sn is the pile number at the P point, snAIs the pile number at the starting point A; the control coordinate calculation formula of the C point of the middle pile can be calculated from A to B and from B to A, and only corresponding parameters are exchanged.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic diagram illustrating a judgment of an intersection point to which a point P belongs according to an embodiment of the present invention;
fig. 2 is a schematic diagram of derivation of a line coordinate general integral formula in the embodiment of the present invention.
Detailed Description
Embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways, which are defined and covered by the claims.
Example (b):
a method for calculating coordinates of any stake on a route, as shown in detail in fig. 1-2, comprises the following steps:
step 1: judging the intersection point interval and the line shape of the P point according to the design route information and the pile number sn of the P point;
step 2: calculating the line coordinate of the point P by using a numerical integration method according to the linear information of the point P;
and step 3: and calculating the control coordinate of the side pile according to the coordinate of the point P.
Optionally, the method for judging the intersection point S of the intersection point interval to which the mileage sn belongs by the point P specifically comprises the following steps:
finding the nearest intersection JD to snm，JDm＝min(|JDiSn-sn), i 1,2,3, …, k, where k is the number of intersections in the design line, JDiSn is JDiMin is a function for taking the minimum value;
if sn < JDm-sn-Tm1-Dm1In the formula, Tm1Is JDmFirst tangent length of (D)m1Is JDmThe first straight line is long, S is JDm-1；
If JDm_sn-Tm1-Dm1≤sn≤JDm_sn-Tm1+Lm+Dm2In the formula LmIs JDmLength of curve of (D)m2Is JDmThe second line is long, S is JDm；
If sn > JDn_sn-Tm1+Lm+Dm2S is JDm+1。
Optional, JD, of the present inventionm-1M in (1) or JDm+1M in (1) is k, which indicates that the point P is beyond the range of the design route, i.e. the point P is not on the current design route.
The length of the line element where the point P is located is l, and the starting point A (X) is optionalA，YA) Has a curvature of κAAzimuth angle of coordinate is alphaAThe curvature of the end point B is κBAnd the route length of the point P from the point A is s, the route coordinate calculation method of the point P is as follows:
Figure BDA0003301760420000041
in the formula: viIs a Gaussian node, RiIs a node coefficient, kAB＝κB-κAF is a sign function, taken when the curve is left-biased-1, right offset is 1.
Optionally, the azimuth of the coordinate at the point P is as follows:
Figure BDA0003301760420000042
optionally, the calculation formula of the control coordinate of the side pile of the point P is as follows:
Figure BDA0003301760420000043
in the formula: d is the offset distance between the side pile and the corresponding middle pile. Optionally, the method for calculating the length s of the route is s-snAIn the formula, sn is the pile number at the P point, snAIs the pile number at the starting point A; the control coordinate calculation formula of the C point of the middle pile can be calculated from A to B and from B to A, and only corresponding parameters are exchanged.
With the technical solution of this embodiment, the designed flat curve elements of a certain highway are shown in table 1, and the line coordinates are calculated according to the flat curve design information of the highway.
TABLE 1A flat curve element table (part) for a certain highway
Figure BDA0003301760420000051
Three representative peg numbers, namely K5+800, K6+000 and K6+500, were selected for the calculation.
Aiming at the following steps: k5+800 (on the circle curve)
And (3) calculating the middle pile coordinates:
s＝800-61.081＝738.919mκA＝1/1500，κAB＝0；
Figure BDA0003301760420000052
Figure BDA0003301760420000053
left peg coordinate calculation (D ═ 12.5 m):
Figure BDA0003301760420000054
aiming at the following steps: k6+000 (on the easement curve)
And (3) calculating the middle pile coordinates:
s＝1000-900.089＝99.911mκA＝1/1500，κAB＝-1/1500；
Figure BDA0003301760420000068
Figure BDA0003301760420000061
left peg coordinate calculation (D ═ 12.5 m):
Figure BDA0003301760420000062
right stake coordinate calculation (D ═ 12.5 m):
Figure BDA0003301760420000063
aiming at the following steps: k6+600 (on the straight line)
And (3) calculating the middle pile coordinates:
Figure BDA0003301760420000064
Figure BDA0003301760420000065
left peg coordinate calculation (D ═ 12.5 m):
Figure BDA0003301760420000066
right stake coordinate calculation (D ═ 12.5 m):
Figure BDA0003301760420000067
the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. A method for calculating coordinates of any stake on a route is characterized by comprising the following steps:
step 1: judging the intersection point interval and the line shape of the P point according to the design route information and the pile number sn of the P point;
step 2: calculating the line coordinate of the point P by using a numerical integration method according to the linear information of the point P;
and step 3: and calculating the control coordinate of the side pile according to the coordinate of the point P.
2. The calculation method according to claim 1, wherein the method of determining the intersection point S of the intersection point section to which the P-point mileage sn belongs is specifically:
finding the nearest intersection JD to snm，JDm＝min(|JDiSn-sn), i 1,2,3, …, k, where k is the number of intersections in the design line, JDiSn is JDiMin is a function for taking the minimum value;
if sn < JDm_sn-Tm1-Dm1In the formula, Tm1Is JDmFirst tangent length of (D)m1Is JDmThe first straight line is long, S is JDm-1；
If JDm_sn-Tm1-Dm1≤sn≤JDm_sn-Tm1+Lm+Dm2In the formula LmIs JDmLength of curve of (D)m2Is JDmThe second line is long, S is JDm；
If sn > JDn_sn-Tm1+Lm+Dm2S is JDm+1。
3. The computing method of claim 2, wherein JDm-1M in (1) or JDm+1M in (1) is k, which indicates that the point P is beyond the range of the design route, i.e. the point P is not on the current design route.
4. The calculation method according to claim 2, wherein the length of the line element where the point P is located is l, and the starting point A (X) isA,YA) Has a curvature of κAAzimuth angle of coordinate is alphaAThe curvature of the end point B is κBAnd the route length of the point P from the point A is s, the route coordinate calculation method of the point P is as follows:
Figure FDA0003301760410000011
in the formula: viIs a Gaussian node, RiIs a node coefficient, kAB＝κB-κAF is a sign function, and is-1 when the curve is biased to the left and 1 when the curve is biased to the right.
5. The method of claim 4, wherein the azimuth of the coordinate at point P is given by:
Figure FDA0003301760410000021
6. the calculation method according to claim 5, wherein the control coordinate calculation formula of the side pile of the point P is as follows:
Figure FDA0003301760410000022
in the formula: d is the offset distance between the side pile and the corresponding middle pile.
7. The calculation method according to claim 5, wherein the azimuth α is a coordinate azimuth in the control coordinate system.
8. The method according to claim 2, wherein the route length s is calculated by s-snAIn the formula, sn is the pile number at the P point, snAIs the stake number at the starting point a.
9. The calculation method according to claim 1, wherein the calculation formula of the control coordinate of the point C of the middle pile can be calculated from A to B and from B to A, and only corresponding parameters are exchanged.
CN202111192511.4A 2021-10-13 2021-10-13 Method for calculating coordinates of any pile number on route Pending CN113934974A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115200525A (en) * 2022-07-26 2022-10-18 软通动力信息技术(集团)股份有限公司 Line mileage detection method, device, electronic equipment and storage medium

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115200525A (en) * 2022-07-26 2022-10-18 软通动力信息技术(集团)股份有限公司 Line mileage detection method, device, electronic equipment and storage medium

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