CN112732849B - High-precision vector map compression method based on polar coordinate system - Google Patents
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Abstract
The invention discloses a high-precision vector map compression method based on a polar coordinate system, which comprises the following steps of firstly, defining the north as the polar axis direction of the polar coordinate system, and taking a starting point as an origin; then, according to the characteristic that the included angle between the linear road and the polar axis is a fixed value, judging whether the difference of the tangent values of the included angles between the polar axis and the linear road composed of two or more continuous points and the starting point meets a preset threshold value, if so, determining that the road is the linear road, otherwise, determining that the road is the curve road; and finally, compressing data of different road sections in the map according to different types of roads. For a straight line highway, representing the straight line highway by using longitude and latitude of an initial point, an included angle between the straight line highway and a polar axis and the length of the straight line highway; for the curve highway, firstly carrying out nonlinear curve fitting, carrying out equal-angle interval sampling on a fitting curve, and then representing the section of the curve highway by utilizing longitude and latitude of a starting point, angle intervals and the polar diameter of each sampling point; the map data storage memory can be reduced on the premise of not losing the map precision.
Description
Technical Field
The invention relates to the technical field of high-precision vector map-assisted matching navigation positioning, in particular to a high-precision vector map compression method based on a polar coordinate system.
Background
With the rapid development of science and technology, no matter intelligent vehicles, unmanned planes or high-precision accurate striking weapons, the research and development of the intelligent vehicles, the unmanned planes and the high-precision accurate striking weapons cannot be separated from the high-precision vector maps. The high-precision vector map can provide high-precision geographic data information for the navigation and positioning of intelligent and automatic machinery, assists in obtaining high-precision poses, and has irreplaceable important effects in the mechanized era.
For the traditional high-precision vector map preparation process, if the map preparation process is too fine, a huge data storage memory is needed; conversely, if the data sampling interval of the map preparation process is too large, the map accuracy will be affected. At present, the storage of most high-precision vector maps requires a very large storage space, and the data storage of one high-precision vector map usually requires a storage space of at least tens of G or even hundreds of G. Although there are many scholars studying the problem of storing data for high-precision vector maps, most of them reduce the storage space at the expense of map precision. Taking an automatic driving automobile as an example, if unmanned driving of the automobile is to be realized and the intelligence of the automobile is to be improved, the precision requirement of a vehicle-mounted high-precision vector map is required to be in the centimeter magnitude, the requirement is that the sampling point in the preparation process of the high-precision vector map in the vehicle-mounted navigation field is far more than that of a traditional electronic map, namely, the data of the sampling point to be stored is huge, and each sampling point contains a longitude and latitude data pair, which will certainly cause a huge data storage memory. Therefore, the traditional high-precision vector map preparation method cannot simultaneously ensure map precision and light weight of a map data storage memory.
The compression of the high-precision vector map data can not only reduce the data storage memory, but also reduce the map manufacturing cost, and most importantly, the map precision can not be lost. The research on the data compression of the high-precision vector map can not only promote the development of the automatic driving field, but also is very important for the development of the related fields of the navigation and positioning assisted by the high-precision vector map.
Disclosure of Invention
In view of this, the present invention provides a high-precision vector map compression method based on a polar coordinate system, so as to reduce a map data storage memory on the premise of ensuring that the precision of the high-precision vector map is not lost.
The invention provides a high-precision vector map compression method based on a polar coordinate system, which comprises the following steps:
s1: dividing a current road in a high-precision vector map into a plurality of sections of straight-line roads and a plurality of sections of curve roads;
s2: aiming at each section of linear highway, representing the section of linear highway by utilizing the longitude and latitude of the initial point of the section of linear highway, the included angle between the section of linear highway and a polar axis under a polar coordinate system and the length of the section of linear highway;
s3: aiming at each section of curve highway, carrying out nonlinear curve fitting on the section of curve highway according to a sampling point sequence on a central axis of the section of curve highway, carrying out equal-angle interval sampling on a fitting curve of the section of curve highway, and representing the section of curve highway by utilizing longitude and latitude of a starting point of the section of curve highway, angle intervals and polar diameter of each equal-angle interval sampling point under a polar coordinate system; completing compression of data of the current road;
s4: returning to the step S1, repeating the steps S1-S3, compressing the data of the next road until the compression of the data of all roads in the high-precision vector map is completed.
In a possible implementation manner, in the method for compressing a high-precision vector map based on a polar coordinate system provided by the present invention, in step S1, dividing a current road in the high-precision vector map into multiple segments of straight roads and multiple segments of curved roads, specifically including:
the geographical coordinate of the starting point A of the current road in the high-precision vector map is set as (x) a ,y a ) The geographical coordinates of any point I except the starting point A on the central axis of the current road in the high-precision vector map are (x) i ,y i ) And taking the starting point A of the current road as the origin of the polar coordinate system, and the due north direction in the high-precision vector map as the polar axis direction of the polar coordinate system, wherein the distance between the point I in the high-precision vector map and the starting point A is as follows:
wherein, Δ x i Representing the component in the longitudinal direction of the distance of point I from the starting point A, Δ y i Representing the component of the distance from the point I to the starting point A in the direction of latitude; r N Representing the radius of the earth's longitude circle, R M Representing the latitude circle radius of the earth;
the tangent value of an included angle between the connecting line of the point I and the starting point A and the polar axis direction of the polar coordinate system is as follows:
order to
Then the above equation (2) is simplified to:
the discriminant of the road type in the high-precision vector map is as follows:
Δf＝f(K i )-f(K j ) (4)
wherein,
(x i ,y i ) Representing the geographical coordinates of any point J on the central axis of the current road except the starting point A and the point I in the high-precision vector map;
establishing a confidence interval for judging the road type, wherein the confidence interval under the condition that the confidence degree is 99% is as follows:
Δf∈[Δf min ,Δf max ] (5)
wherein, Δ f min Is the minimum value of the confidence interval, Δ f max The maximum value of the confidence interval;
all points in each straight road section of the current road satisfy the above formula (5), and all points in each curved road section of the current road do not satisfy the above formula (5).
In a possible implementation manner, in the polar coordinate system-based high-precision vector map compression method provided by the present invention, in step S3, for each section of curved road, according to a sequence of sampling points on a central axis of the section of curved road, performing non-linear curve fitting on the section of curved road, performing equal-angle-interval sampling on a fitted curve of the section of curved road, and representing the section of curved road by using longitude and latitude of a starting point of the section of curved road, an angle interval, and a polar diameter of each equal-angle-interval sampling point in the polar coordinate system, specifically, the method includes:
the sequence of sampling points on the central axis of the section of curve highway is set as follows:
[(X 1 ,Y 1 ) (X 2 ,Y 2 ) ... (X n ,Y n )] (6)
wherein, X 1 ,X 2 ,...,X n Are different from each other;
the polar coordinate sequence on the central axis of the section of curved highway is calculated according to the formula (6) as follows:
[(ρ 1 ,θ 1 ) (ρ 2 ,θ 2 ) ... (ρ n ,θ n )] (7)
in the above-mentioned formula (7),
wherein, m is 1,2, n, (X) 0 ,Y 0 ) Representing the origin coordinates of a straight coordinate system;
by fitting the nonlinear curve to the above equation (7), the nonlinear equation of the fitted curve of the section of curve road is obtained as follows:
P＝f(Θ,c)＝c n Θ n +c n-1 Θ n-1 +...+c 1 Θ 1 +c 0 (8)
wherein c ═ c 0 c 1 c 2 … c n ]For the undetermined parameter, theta represents the polar angle of any point on the fitting curve, and P represents the polar diameter of the point with the polar angle being theta on the fitting curve;
the coordinate of the starting point of the section of curve road in the high-precision vector map is (X) 1 ,Y 1 ) The end point coordinate is (X) n ,Y n ) And (3) making a tangent line of the fitting curve by passing through the initial point, wherein the expression of the obtained tangent line is as follows:
Y＝k 1 X+b 1 (9)
wherein k is 1 ＝tanθ 1 Representing the slope of the tangent, b 1 ＝Y 1 -k 1 X 1 Is a constant;
connecting the end point with the initial point to obtain an expression of the connecting line as follows:
Y＝k 2 X+b 2 (10)
wherein k is 2 ＝tanθ n Representing the slope of the connecting line, b 2 ＝Y n -k 2 X n Is a constant;
the included angle between the tangent line and the polar axis of the polar coordinate system is obtained according to the formula (9):
α＝arctan(k 1 ) (11)
obtaining the included angle between the connecting line and the polar axis of the polar coordinate system according to the formula (10):
φ＝arctan(k 2 ) (12)
the total angle change of the curved road section is as follows:
γ＝|arctan(k 2 )-arctan(k 1 )| (13)
n points are sampled at equal angle intervals on a fitting curve of the curve road section,
sigma represents angle interval, and the value range is 0.001-0.01 degrees; and representing the section of curve road by using the longitude and latitude of the starting point of the section of curve road, the angle interval sigma and the polar diameter of N equal-angle interval sampling points under a polar coordinate system.
The invention provides a high-precision vector map compression method based on a polar coordinate system, which comprises the following steps of firstly, defining the north direction in the high-precision vector map as the polar axis direction of the polar coordinate system, and taking the starting point of a road as the origin of the polar coordinate system; then, according to the characteristic that the included angle between the linear highway and the polar axis direction in the polar coordinate system is a fixed value, taking the tangent value of the included angle between the linear highway formed by any sampling point and the initial point on the central axis of the highway and the polar axis direction as a judgment condition, if the difference of the tangent values of the included angles formed by two or more continuous points meets a preset threshold value, considering the highway as the linear highway, and if the difference does not meet the threshold value condition, considering the highway as the curved highway; and finally, compressing data of different road sections in the high-precision vector map according to the characteristics of different types of roads. For a linear highway, the longitude and latitude of the starting point of the section of the linear highway, the included angle between the section of the linear highway and a polar axis under a polar coordinate system and the length of the section of the linear highway are used for representing the section of the linear highway, the linear highway can be completely represented by only four parameters, and the precision is guaranteed not to be lost; for the curve highway, nonlinear curve fitting is firstly carried out, equal-angle-interval sampling is carried out on a fitting curve, then the longitude and latitude of the starting point of the section of the curve highway, the angle interval and the polar diameter of each equal-angle-interval sampling point under a polar coordinate system are utilized to represent the section of the curve highway, so that map data can be compressed by at least half, and the precision is guaranteed not to be lost. The method can greatly reduce the map data storage memory on the premise of ensuring that the map precision is not lost.
Drawings
FIG. 1 is a flowchart of a high-precision vector map compression method based on a polar coordinate system according to the present invention;
FIG. 2 is a flowchart of example 1 of the present invention;
fig. 3 is a schematic diagram of compression of straight road data in embodiment 1 of the present invention;
fig. 4 is a schematic diagram of compression of curved road data in embodiment 1 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only illustrative and are not intended to limit the present invention.
The invention provides a high-precision vector map compression method based on a polar coordinate system, which comprises the following steps as shown in figure 1:
s1: dividing a current road in a high-precision vector map into a plurality of sections of straight-line roads and a plurality of sections of curve roads;
s2: aiming at each section of linear highway, representing the section of linear highway by utilizing the longitude and latitude of the initial point of the section of linear highway, the included angle between the section of linear highway and a polar axis under a polar coordinate system and the length of the section of linear highway;
s3: aiming at each section of curve highway, carrying out nonlinear curve fitting on the section of curve highway according to a sampling point sequence on a central axis of the section of curve highway, carrying out equal-angle interval sampling on a fitting curve of the section of curve highway, and representing the section of curve highway by utilizing longitude and latitude of a starting point of the section of curve highway, angle intervals and polar diameters of each equal-angle interval sampling point under a polar coordinate system; completing compression of data of the current road;
s4: and returning to the step S1, repeating the steps S1-S3, compressing the data of the next road until the compression of the data of all roads in the high-precision vector map is completed.
The following describes a specific implementation of the above-mentioned high-precision vector map compression method based on a polar coordinate system according to a specific embodiment.
Example 1: the specific flow chart is shown in fig. 2.
The first step is as follows: and dividing the current road in the high-precision vector map into a plurality of sections of straight-line roads and a plurality of sections of curve roads, namely identifying different types of road sections (straight-line roads or curve roads).
Setting the geographic coordinates (namely the coordinates under a straight coordinate system) of the starting point A of the current road in the high-precision vector map as (x) a ,y a ) The geographical coordinates of any point I except the starting point A on the central axis of the current road in the high-precision vector map are (x) i ,y i ) Taking the starting point a of the current road as the origin of the polar coordinate system, and the due north direction in the high-precision vector map as the polar axis direction (i.e. the positive direction) of the polar coordinate system, the distance between the point I in the high-precision vector map and the starting point a is:
wherein, Δ x i Representing the component in the longitudinal direction of the distance of the point I from the starting point A, Delay i Representing the component of the distance from the point I to the starting point A in the direction of latitude; r is N Representing the radius of the earth's longitude circle, R M Representing the latitude circle radius of the earth;
the tangent value of an included angle between the connecting line of the point I and the starting point A and the polar axis direction of the polar coordinate system is as follows:
due to high precision vectorThe coordinates of different geographical location points in the map are related to the location of the different points, and therefore, equation (2) above can be abstracted as a function of the different geographical location points, such that
Then equation (2) above can be simplified to:
through the above analysis, the discriminant of the road type in the high-precision vector map can be written as:
Δf＝f(K i )-f(K j ) (4)
wherein,
(x i ,y i ) The geographical coordinates of any point J on the central axis of the current road except the starting point A and the point I in the high-precision vector map are represented; if Δ f is equal to 0, it indicates that the slopes of the point I and the point J are the same, and it may be determined that the link where the point I and the point J are located is a straight road; similarly, if Δ f is not equal to 0, which indicates that the slopes of the point I and the point J are different, it may be determined that the road segment where the point I and the point J are located is a curved road;
considering the reasons such as high-precision vector map preparation errors, system errors are indirectly introduced in the calculation process, so that in order to ensure the reliability of data, a confidence interval for judging the road type can be established, and the confidence interval under the condition that the confidence degree is 99% is as follows:
Δf∈[Δf min ,Δf max ] (5)
wherein, Δ f min Is the minimum value of the confidence interval, Δ f max The maximum value of the confidence interval;
in summary, when a certain road section of the current road meets the above formula (5), the road section can be determined to be a straight road; when a certain road section of the current road does not satisfy the above equation (5), the road section can be determined as a curved road until the above equation (5) is satisfied. That is, all points in each straight road of the current road satisfy the above equation (5), and all points in each curved road of the current road do not satisfy the above equation (5).
The second step is that: and aiming at each section of linear highway, representing the section of linear highway by utilizing the longitude and latitude of the starting point of the section of linear highway, the included angle between the section of linear highway and a polar axis under a polar coordinate system and the length of the section of linear highway.
Because the included angle between the linear highway and the polar axis is fixed and unchanged in the polar coordinate system, the compression of the linear highway in the high-precision vector map can uniquely represent a section of the linear highway only by the longitude and latitude (lon, lat) of the starting point of the linear highway, the included angle theta between the linear highway and the polar axis in the polar coordinate system and the length R of the linear highway. In a traditional high-precision vector map, assuming that the number of sampling points on a central axis of a straight road is n, each sampling point has two geographic parameters of longitude and latitude, and if the road is to be completely stored, 2n data need to be stored; after the high-precision vector map compression method based on the polar coordinate system is adopted, a complete linear highway can be represented only by four data parameters of lon, lat, theta and R.
For example, as shown in FIG. 3, a straight road AB may pass through a starting point A (x) a ,y a ) The longitude and latitude of the straight road AB, the included angle theta between the straight road AB and the polar axis AX under a polar coordinate system, and the length R of the straight road AB.
The third step: and aiming at each section of curve highway, carrying out nonlinear curve fitting on the section of curve highway according to the sequence of sampling points on the central axis of the section of curve highway, carrying out equal-angle-interval sampling on a fitting curve of the section of curve highway, and representing the section of curve highway by utilizing the longitude and latitude of the starting point of the section of curve highway, the angle interval and the polar diameter of each equal-angle-interval sampling point under a polar coordinate system.
Because the line shape of the curve road in the high-precision vector map is complex, the curve road cannot be directly represented by a mathematical model. The angle change of the connecting line of each sampling point and the original point on the curve road in the high-precision vector map relative to the polar axis is not equal interval, in order to realize the compression of the curve road, the non-linear curve fitting is needed to be carried out on the curve road, then the equal angle interval sampling is carried out on the curve road according to the fitting curve, and thus, the curve road can only represent a section of curve road only by the longitude and latitude of the original point, the angle interval and the polar diameter of each equal angle interval sampling point under the polar coordinate system. The compression method for the curved road can compress the map data by at least half and ensure that the precision is not lost.
The sequence of sampling points on the central axis of the section of curve highway is set as follows:
[(X 1 ,Y 1 ) (X 2 ,Y 2 ) ... (X n ,Y n )] (6)
wherein, X 1 ,X 2 ,...,X n Are different from each other;
according to the above formula (6), the polar coordinate sequence on the central axis of the curved road is calculated as follows:
[(ρ 1 ,θ 1 ) (ρ 2 ,θ 2 ) ... (ρ n ,θ n )] (7)
in the above-mentioned formula (7),
wherein, m is 1, 2.., n, (X) 0 ,Y 0 ) Representing the origin coordinates of a straight coordinate system;
by fitting the nonlinear curve to the above equation (7), the nonlinear equation of the fitted curve of the curved road segment can be obtained as follows:
P＝f(Θ,c)＝c n Θ n +c n-1 Θ n-1 +...+c 1 Θ 1 +c 0 (8)
wherein c ═ c 0 c 1 c 2 … c n ]The theta represents the polar angle of any point on the fitting curve, and the P represents the polar diameter of the point with the polar angle theta on the fitting curve;
as shown in fig. 4, the coordinate of the starting point O of the curved road in the high-precision vector map is (X) 1 ,Y 1 ) The coordinate of the end point D is (X) n ,Y n ) The over-starting point O is taken as a tangent OC of the fitting curve,the expression for the tangent OC is found as:
Y＝k 1 X+b 1 (9)
wherein k is 1 ＝tanθ 1 Represents the slope of the tangent OC, b 1 ＝Y 1 -k 1 X 1 Is a constant;
connecting the end point D with the starting point O to obtain an expression of a connecting line OD as follows:
Y＝k 2 X+b 2 (10)
wherein k is 2 ＝tanθ n Represents the slope of the connecting line OD, b 2 ＝Y n -k 2 X n Is a constant;
the included angle between the tangent line OC and the polar axis OX of the polar coordinate system is obtained according to the formula (9):
α＝arctan(k 1 ) (11)
obtaining the included angle between the connecting line OD and the polar axis OX of the polar coordinate system according to the formula (10):
φ＝arctan(k 2 ) (12)
the total angle change of the curved road section is as follows:
γ＝|arctan(k 2 )-arctan(k 1 )| (13)
n points are sampled at equal angle intervals on a fitting curve of the curve road,
sigma represents angle interval, and the value range is 0.001-0.01 degrees; and representing the section of curve road by using the longitude and latitude of the starting point of the section of curve road, the angle interval sigma and the polar diameter of N equal-angle interval sampling points under a polar coordinate system, thereby completing the compression of the data of the current road.
The fourth step: and after the compression of the data of the current road is finished, returning to the first step, repeatedly executing the first step to the third step, and compressing the data of the next road until the compression of the data of all the roads in the high-precision vector map is finished.
The invention provides a high-precision vector map compression method based on a polar coordinate system, which comprises the following steps of firstly, defining the due north direction in the high-precision vector map as the polar axis direction of the polar coordinate system, and taking the starting point of a road as the origin of the polar coordinate system; then, according to the characteristic that the included angle between the linear highway and the polar axis direction in the polar coordinate system is a fixed value, taking the tangent value of the included angle between the linear highway formed by any sampling point and the initial point on the central axis of the highway and the polar axis direction as a judgment condition, if the difference of the tangent values of the included angles formed by two or more continuous points meets a preset threshold value, considering the highway as the linear highway, and if the difference does not meet the threshold value condition, considering the highway as the curved highway; and finally, compressing data of different road sections in the high-precision vector map according to the characteristics of different types of roads. For a straight road, the longitude and latitude of the initial point of the section of the straight road, the included angle between the section of the straight road and a polar axis under a polar coordinate system and the length of the section of the straight road are used for representing the section of the straight road, the straight road can be completely represented by only four parameters, and the precision is ensured not to be lost; for the curve highway, nonlinear curve fitting is firstly carried out, equal-angle-interval sampling is carried out on a fitting curve, then the longitude and latitude of the starting point of the section of the curve highway, the angle interval and the polar diameter of each equal-angle-interval sampling point under a polar coordinate system are utilized to represent the section of the curve highway, so that map data can be compressed by at least half, and the precision is guaranteed not to be lost. The method can greatly reduce the map data storage memory on the premise of ensuring that the map precision is not lost.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (2)
1. A high-precision vector map compression method based on a polar coordinate system is characterized by comprising the following steps:
s1: dividing a current road in a high-precision vector map into a plurality of sections of linear roads and a plurality of sections of curve roads;
s2: aiming at each section of linear highway, representing the section of linear highway by utilizing the longitude and latitude of the initial point of the section of linear highway, the included angle between the section of linear highway and a polar axis under a polar coordinate system and the length of the section of linear highway;
s3: aiming at each section of curve highway, carrying out nonlinear curve fitting on the section of curve highway according to a sampling point sequence on a central axis of the section of curve highway, carrying out equal-angle interval sampling on a fitting curve of the section of curve highway, and representing the section of curve highway by utilizing longitude and latitude of a starting point of the section of curve highway, angle intervals and polar diameters of each equal-angle interval sampling point under a polar coordinate system; completing compression of data of the current road;
s4: returning to the step S1, repeatedly executing the steps S1-S3, and compressing the data of the next road until the compression of the data of all roads in the high-precision vector map is completed;
step S1, dividing the current road in the high-precision vector map into a multi-segment straight-line road and a multi-segment curved road, specifically including:
the geographical coordinate of the starting point A of the current road in the high-precision vector map is set as (x) a ,y a ) The geographic coordinates of any point I except the starting point A on the central axis of the current road in the high-precision vector map are (x) i ,y i ) And taking the starting point A of the current road as the origin of the polar coordinate system, and the due north direction in the high-precision vector map as the polar axis direction of the polar coordinate system, wherein the distance between the point I in the high-precision vector map and the starting point A is as follows:
wherein, Δ x i Representing the component in the longitudinal direction of the distance of point I from the starting point A, Δ y i Representing the component of the distance from the point I to the starting point A in the direction of latitude; r N Representing the radius of the earth's longitude circle, R M Representing the latitude circle radius of the earth;
the tangent value of an included angle between the connecting line of the point I and the starting point A and the polar axis direction of the polar coordinate system is as follows:
order to
Then the above equation (2) is simplified as:
the discriminant of the road type in the high-precision vector map is as follows:
Δf＝f(K i )-f(K j )(4)
wherein,
(x i ,y i ) Representing the geographical coordinates of any point J on the central axis of the current road except the starting point A and the point I in the high-precision vector map;
establishing a confidence interval for judging the road type, wherein the confidence interval under the condition that the confidence degree is 99% is as follows:
Δf∈[Δf min ,Δf max ](5)
wherein, Δ f min Is the minimum value of the confidence interval, Δ f max The maximum value of the confidence interval;
all points in each straight road section of the current road satisfy the above formula (5), and all points in each curved road section of the current road do not satisfy the above formula (5).
2. The method as claimed in claim 1, wherein the step S3, for each curved road, performing non-linear curve fitting on the curved road according to the sequence of sampling points on the central axis of the curved road, performing sampling at equal angular intervals on the fitted curve of the curved road, and representing the curved road by using the longitude and latitude of the starting point of the curved road, the angular intervals and the polar radius of each sampling point at equal angular intervals in the polar coordinate system, specifically comprises:
the sequence of sampling points on the central axis of the section of curve highway is set as follows:
[(X 1 ,Y 1 ) (X 2 ,Y 2 ) K (X n ,Y n )](6)
wherein X 1 ,X 2 ,...,X n Are different from each other;
the polar coordinate sequence on the central axis of the curve road is calculated according to the formula (6) as follows:
[(ρ 1 ,θ 1 ) (ρ 2 ,θ 2 ) K (ρ n ,θ n )](7)
in the above-mentioned formula (7),
wherein m is 1,2, …, n, (X) 0 ,Y 0 ) Representing the origin coordinates of a straight coordinate system;
by fitting the nonlinear curve to the above equation (7), the nonlinear equation of the fitted curve of the section of curve road is obtained as follows:
P＝f(Θ,c)＝c n Θ n +c n-1 Θ n-1 +K+c 1 Θ 1 +c 0 (8)
wherein c ═ c 0 c 1 c 2 L c n ]For the undetermined parameter, theta represents the polar angle of any point on the fitting curve, and P represents the polar diameter of the point with the polar angle being theta on the fitting curve;
the coordinate of the starting point of the curve road in the high-precision vector map is (X) 1 ,Y 1 ) The end point coordinate is (X) n ,Y n ) And (3) making a tangent line of the fitting curve by passing through the initial point, wherein the expression of the obtained tangent line is as follows:
Y＝k 1 X+b 1 (9)
wherein k is 1 ＝tanθ 1 Representing the slope of the tangent, b 1 ＝Y 1 -k 1 X 1 Is a constant;
connecting the end point with the initial point to obtain an expression of the connecting line as follows:
Y＝k 2 X+b 2 (10)
wherein k is 2 ＝tanθ n Representing the slope of the connecting line, b 2 ＝Y n -k 2 X n Is a constant;
the included angle between the tangent line and the polar axis of the polar coordinate system is obtained according to the formula (9):
α＝arctan(k 1 )(11)
obtaining the included angle between the connecting line and the polar axis of the polar coordinate system according to the formula (10):
φ＝arctan(k 2 )(12)
the total angle change of the curved road section is as follows:
γ＝|arctan(k 2 )-arctan(k 1 )|(13)
n points are sampled at equal angle intervals on a fitting curve of the curve road,
sigma represents angle interval, and the value range is 0.001-0.01 degrees; and representing the section of curve road by using the longitude and latitude of the starting point of the section of curve road, the angle interval sigma and the polar diameter of N equal-angle interval sampling points under a polar coordinate system.
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