An automatic method for normalizing composite boundary lines

Abstract

The present application relates to the technical field of land surveying and delimiting, and particularly discloses an automatic normalization method for a composite boundary line, which mainly comprises the following steps: converting a composite multi-segment line with a circular arc into a common multi-segment line to obtain the common multi-segment line; removing self-intersection of a boundary line with an island to obtain the boundary line; converting a starting point of the boundary line to a left upper corner to obtain a new boundary line; and finally, realizing algorithm and instance analysis on the new boundary line to complete automatic normalization of the boundary line. Through the method, a formula for inversely calculating the number of circular arc nodes according to the accuracy requirement is proposed, a method for automatically adding nodes on the island connecting line to avoid self-intersection of the boundary line is proposed, and an algorithm for automatically converting the starting point of the boundary line to the left upper corner is proposed. The automatic normalization of the composite boundary line is realized by VBA programming in AutoCAD, which can greatly improve the work efficiency and improve the data quality of the boundary line processing.

Description

Technical Field

[0001] This invention belongs to the field of land surveying and demarcation technology, and specifically relates to an automatic standardization method for composite boundary lines. Background Technology

[0002] Land surveying and demarcation is a technical service provided to natural resources administrative departments to offer scientific and accurate basic data for land use approval and cadastral management. The boundary lines are typically represented using polylines generated by AutoCAD software, while approval and management departments often use areal features from Geographic Information System (GIS) software. This inevitably involves data format conversion issues. Composite boundary lines with arcs or holes (islands) inevitably suffer from deviations, misalignments, and self-intersections after conversion.

[0003] The accurate extraction and conversion of boundary line results is a crucial task, and the current manual operation mode urgently needs optimization; otherwise, it will directly affect the scientific nature of land use approval and cadastral management. During data production and conversion, composite boundary lines often suffer from the following problems: ① Composite boundary lines combining arcs and polylines frequently exhibit deviations, misalignments, or are incorrectly converted into oddly positioned arcs; ② Some boundary lines with isolated islands fail to convert to GIS areas due to self-intersections between the inner and outer polyline connectors, and manually adding nodes makes it difficult to control accuracy; ③ Boundary point numbering should, in principle, be based on the land use area, uniformly numbered from left to right and top to bottom. Therefore, the starting point of the boundary line should ideally be converted to the upper left corner; otherwise, due to software defects, it may be impossible to generate boundary point results that meet the specifications. Manually modifying boundary points greatly increases the workload of operators and is prone to errors.

[0004] Currently, several automatic processing algorithms exist for the above problems. For example, Li Chao-kui et al. proposed an optimized algorithm for extracting boundary points and boundary lines; He Chun-lin used ArcGIS software's model builder to automate the conversion of red-line arcs to polylines; Yang Guang, Liu Hu, Liu Jing et al. proposed an algorithm for converting polylines with arcs to ordinary polylines; Wang De-qiang et al. used a C# program to find a numbering method for boundary point numbering with different requirements. However, there are few research results on the automatic standardization of problem ②; research results on the unified processing of the above three problems are also rare. In practical work, problems ① and ③ are often processed using CASS and ArcGIS software, while problem ② is usually solved by manual editing, which is not only time-consuming and laborious but also prone to errors. Therefore, we propose an automatic standardization method for composite boundary lines to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide an automatic normalization method for composite boundary lines, which can significantly improve work efficiency and enhance the data quality of boundary line processing, thereby solving the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] An automatic normalization method for composite boundary lines includes the following steps:

[0008] S1. Convert the composite polyline with arcs into a regular polyline to obtain a regular polyline;

[0009] S2. Remove the self-intersections from the boundary lines containing isolated islands to obtain the boundary lines;

[0010] S3. Move the starting point of the boundary line to the upper left corner to obtain the new boundary line;

[0011] S4. Implement the new boundary lines using algorithms and analyze examples to complete the automatic normalization of the boundary lines.

[0012] Preferably, the composite polyline in step 1 includes a lightweight polyline and a polyline. The node coordinate array of the lightweight polyline consists of X and Y coordinates, and the node coordinates of the polyline consist of X, Y, and Z coordinates. The arc stores parameters such as radius, center, starting point coordinates, ending point coordinates, and starting and ending azimuth angles.

[0013] Preferably, the process of converting a polyline with an arc to a regular polyline includes the following steps:

[0014] A1. Determine the direction of the compound polyline to obtain a new array of node coordinates;

[0015] A2. Convert the arc to a regular polyline and obtain the coordinates of any point on the arc;

[0016] A3. Calculation and control of conversion error to obtain a common polyline.

[0017] Preferably, when determining the direction of the composite polyline in step A1, it is necessary to first determine whether its direction is clockwise or counterclockwise, and then, according to the direction of the polyline, interpolate nodes sequentially to generate a new node coordinate array; the method for determining the clockwise or counterclockwise direction is to calculate the algebraic sum s using Green's formula. If S is positive, it is counterclockwise. Green's formula is as follows:

[0018]

[0019] In the formula, S is the area of ​​the polyline, (x i y i ) represents the coordinates of node i.

[0020] Preferably, in step A2, the coordinates of any point are obtained by using the polar coordinate method with an isoangular bisector algorithm to calculate the coordinates of any position on the arc. Using the built-in attributes of AutoCAD arcs, such as center coordinates, radius, arc length, angle, starting point coordinates, and starting azimuth, the polar coordinate method according to the following formula can conveniently obtain the coordinates of any point on the arc.

[0021] x i =X0 + R × cos(a0 + a)

[0022] Y i =Y0 + R × sin(a0 + a)

[0023] In the formula, (X0, Y0) are the coordinates of the center point of the arc, R is the radius of the arc, a0 is the azimuth of the starting point of the arc, and a is the angle between point i on the arc and the starting point. All of these can be obtained from the parameters provided by VBA.

[0024] Preferably, in step A3, when calculating and controlling the conversion error, the number of manually modulated nodes is improved based on the derived conversion error calculation formula, and then the number of nodes is automatically set in the program. After conversion, the arc becomes an isosceles triangle, and the area introduces an error. The derived conversion error calculation formula is as follows:

[0025]

[0026]

[0027]

[0028] In the formula, S1 is the area of ​​the original arc, R and a are the radius and central angle of the arc, S2 is the area of ​​the converted isosceles triangle, n is the number of converted isosceles triangles, and ΔS is the conversion error.

[0029] Preferably, in step S2, when removing self-intersecting boundary lines with islands, the program uses a user-interactive method to prompt the user to select the self-intersecting line segment AB. If self-intersecting occurs, the user clicks to select at points A and B respectively; otherwise, it skips the process. Then, based on the coordinates of nodes A and B, the program automatically moves a vertical distance D at the midpoint of line segment AB to add a new node, which can save a lot of time.

[0030] Preferably, when the starting point of the boundary line in step 3 is switched to the upper left corner, the following process is included:

[0031] B1. The GetBoundingBox method can be used to directly obtain the bounding rectangle of the entire polyline. Its return value is the coordinates of the lower left and upper right corners of the bounding rectangle. The average value is the center of the bounding rectangle, which is taken as the origin. Then, the azimuth angle from the origin to each node is calculated. The point with the azimuth angle between 270° and 360° and the farthest from the origin is found. The point obtained at this time is the upper left corner as specified by the standard, and it is a convex point relative to other nodes, which is suitable as the starting point.

[0032] B2. Record the position of the new starting point in the node array, and generate a new array using the forward / reverse order method according to whether the boundary line is clockwise or counterclockwise. Finally, use the new array to generate a new boundary line and delete the original boundary line to generate a boundary line with the starting point in the upper left corner clockwise. This is conducive to the smooth progress of subsequent processes and can ensure that the final result is successfully imported into the GIS system.

[0033] Preferably, when implementing the algorithm and analyzing examples of the new boundary lines described in step 4, since land survey and demarcation maps not only involve boundary points and boundary lines, but also require the content of map names, map frames, and boundary point result tables, the above algorithm is implemented using VBA programming in AutoCAD. It is directly embedded in AutoCAD as a toolbar to be used in conjunction with the existing Southern CASS software. The content of map names, map frames, and boundary point result tables still uses the original functions of CASS. The program is simple and easy to use, with a fast response speed, achieving better debugging and usage effects. In the process of algorithm implementation, the built-in functions of AutoCAD are fully utilized, which can improve the stability and running efficiency of the program.

[0034] Preferably, the specific process of the algorithm implementation and instance analysis is as follows: first, set the parameters, then determine the direction of the polyline. If an arc is found, convert the arc to a polyline and remove the arc to generate a new polyline. If no arc is found, directly remove the arc to generate a new polyline. After removing the arc polyline, determine whether there is an island. If an island exists, add nodes to the island and then proceed to convert the polyline starting point. If no island exists, convert the polyline starting point.

[0035] The automatic normalization method for composite boundary lines proposed in this invention has the following advantages compared with the prior art:

[0036] This invention primarily involves first converting composite polylines with arcs into ordinary polylines, then removing self-intersections from boundary lines with islands to obtain new boundary lines. Next, the starting point of the new boundary lines is moved to the upper left corner. Finally, the new boundary lines are used for algorithm implementation and example analysis to achieve automatic standardization. This method proposes a formula to deduce the number of arc nodes based on accuracy requirements, a method to automatically add nodes on island connecting lines to avoid self-intersections, and an algorithm to automatically convert the starting point of the boundary lines to the upper left corner. The automatic standardization of composite boundary lines is implemented using VBA programming in AutoCAD, which can significantly improve work efficiency and enhance the data quality of boundary line processing. Attached Figure Description

[0037] Figure 1 This is a flowchart of the present invention;

[0038] Figure 2 This is a flowchart illustrating the implementation and example analysis of the present invention.

[0039] like Figure 3 This is a schematic diagram of a polyline with an arc.

[0040] Figure 4 This is a schematic diagram of a regular polyline after converting to an arc;

[0041] Figure 5 A schematic diagram for calculating the coordinates of any position on a circular arc using the polar coordinate method;

[0042] Figure 6 A schematic diagram illustrating the error when converting an arc into a regular polyline:

[0043] Figure 7 A schematic diagram of the boundary line with an isolated island;

[0044] Figure 8 This is a schematic diagram of the boundary lines with isolated islands after adding nodes;

[0045] Figure 9 A schematic diagram illustrating the automatic addition of nodes to isolated boundary lines;

[0046] Figure 10 To obtain a schematic diagram of the circumscribed rectangle of the address lines;

[0047] Figure 11 A schematic diagram for finding the new starting point of the boundary line;

[0048] Figure 12 A schematic diagram for generating new sets of numbers in clockwise or counterclockwise order based on the boundary lines;

[0049] Figure 13 This is a schematic diagram of the automatic normalization results for complex boundary lines. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The specific embodiments described herein are merely used to explain the present invention and are not intended to limit the present invention. 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.

[0051] This invention provides an automatic normalization method for composite boundary lines, comprising the following steps:

[0052] S1. Convert the composite polyline with arcs into a regular polyline to obtain a regular polyline;

[0053] Among them, composite polylines include lightweight polylines and polylines. The node coordinate array of a lightweight polyline consists of X and Y coordinates, while the node coordinate array of a polyline consists of X, Y, and Z coordinates. The arc stores parameters such as radius, center, starting point coordinates, ending point coordinates, and starting and ending azimuth angles. Figure 3 The image shows a polyline with an arc. Figure 4 This is a regular polyline after converting an arc.

[0054] The process of converting a polyline with an arc to a regular polyline includes the following steps:

[0055] A1. Determine the direction of the compound polyline to obtain a new array of node coordinates;

[0056] When determining the direction of a compound polyline, it is necessary to first determine whether it is clockwise or counterclockwise. Then, based on the direction of the polyline, nodes are interpolated sequentially to generate a new array of node coordinates. The method for determining clockwise or counterclockwise direction is to calculate the algebraic sum S using Green's formula. If S is positive, it is counterclockwise, and S is the area of ​​the polygon. This method not only determines the direction of the compound polyline but also obtains the area of ​​the polygon, which helps control conversion errors. Green's formula is as follows:

[0057]

[0058] In the formula, S is the area of ​​the polyline, (x i y i ) represents the coordinates of node i.

[0059] A2. Convert the arc to a regular polyline and obtain the coordinates of any point on the arc;

[0060] like Figure 5The diagram illustrates the calculation of coordinates at any point on an arc using polar coordinates. The coordinates of any point are obtained using the isoangular bisector algorithm of polar coordinates. By utilizing AutoCAD's built-in properties for arcs, such as center coordinates, radius, arc length, angle, starting point coordinates, and starting azimuth, the polar coordinate method, according to the following formula, can conveniently obtain the coordinates of any point on the arc.

[0061] X i =X0 + R × cos(a0 + a)

[0062] Y i =Y0 + R × sin(a0 + a)

[0063] In the formula, (X0, Y0) are the coordinates of the center point of the arc, R is the radius of the arc, a0 is the azimuth of the starting point of the arc, and a is the angle between point i on the arc and the starting point. All of these can be obtained from the parameters provided by VBA.

[0064] A3. Calculation and control of conversion error to obtain a common polyline;

[0065] When calculating and controlling conversion errors, such as Figure 6 The diagram illustrates the error when converting an arc to a regular polyline. Based on the derived formula for calculating the conversion error, the manual adjustment of the number of nodes was improved, and then the number of nodes was automatically set in the program. After conversion, the arc became an isosceles triangle, resulting in an error in the area. The derived formula for calculating the conversion error is as follows:

[0066]

[0067]

[0068]

[0069] In the formula, S1 is the area of ​​the original arc, R and a are the radius and central angle of the arc, S2 is the area of ​​the converted isosceles triangle, n is the number of converted isosceles triangles, and ΔS is the conversion error.

[0070] According to the "Regulations for Land Surveying and Demarcation", the difference between two area measurements calculated using the graphical method should satisfy the following formula:

[0071]

[0072] In the formula, M is the denominator of the scale on the survey and demarcation map. If M is taken as 1:500, it will result in a large error margin, which does not meet the conversion requirements. In practice, the error in the converted area of ​​non-municipal land parcels is generally controlled within ±1m. 2Within this range, the error in the red-line conversion area for municipal engineering projects (linear projects) is within ±0.03% of the red-line area. To calculate a reasonable number of nodes n, this paper defaults to a value of 10 for M, which is provided as a parameter for users to adjust to suit the accuracy requirements of different projects.

[0073]

[0074] The sine function in equation (1) can be expanded using a Taylor series as follows:

[0075]

[0076] Substituting these into equations (1) and (2), we get:

[0077]

[0078] After rearranging equation (3), we get:

[0079]

[0080] The above formula is the formula for the number of arc nodes that meets the corresponding accuracy requirements. Before conversion, the number of nodes n can be calculated based on the arc radius R and the central angle a to ensure conversion accuracy. For a composite polyline containing multiple arcs, the number of conversion nodes n for each arc can be calculated separately according to its central angle and area using formula (10).

[0081] S2. Remove the self-intersections from the boundary lines containing isolated islands to obtain the boundary lines;

[0082] When removing self-intersections from boundary lines containing isolated islands, such as... Figure 9 The example shown demonstrates the automatic addition of nodes to isolated boundary lines. Using a user-interactive approach, the program prompts the user to select a self-intersecting line segment AB. If a self-intersection exists, the user clicks on points A and B respectively; otherwise, the process is skipped. Then, based on the coordinates of nodes A and B, the program automatically adds a new node by moving vertically a distance D from the midpoint of line segment AB. This saves a significant amount of time. Figure 7 The image shows a boundary line with an isolated island, as shown below. Figure 8 This refers to the boundary line with isolated islands after adding nodes.

[0083] S3. Move the starting point of the boundary line to the upper left corner to obtain the new boundary line;

[0084] When the starting point of the boundary line is switched to the upper left corner, the following process is involved:

[0085] B1, such as Figure 10The image shows how to obtain the bounding rectangle of a polyline. The `GetBoundingBox` method can directly retrieve the bounding rectangle of the entire polyline. Its return value is the coordinates of the bottom-left and top-right corners of the bounding rectangle. Taking the average of these coordinates gives the center of the bounding rectangle as the origin. Then, the azimuth angle from the origin to each node is calculated. The point with the azimuth angle between 270° and 360° and farthest from the origin is found. This point is the top-left corner as defined by the standard, and it is a convex point relative to other nodes, suitable as a starting point. Figure 11 The diagram shown illustrates the search for a new starting point for the boundary line.

[0086] B2. Record the position of the new starting point in the node array, and generate a new array using ascending / descending order methods depending on whether the boundary lines are clockwise or counterclockwise. Figure 12 The diagram shows how new groups of numbers are generated in clockwise or counterclockwise order based on the boundary lines. Finally, a new boundary line is generated using the new array, and the original boundary line is deleted, thus generating a boundary line starting from the upper left corner and moving clockwise. This facilitates the smooth progress of subsequent processes and ensures that the final result is successfully imported into the GIS system.

[0087] S4. Implement the new boundary lines using algorithms and analyze examples to achieve automatic standardization of the boundary lines;

[0088] When implementing the algorithm and conducting case analysis for the new boundary lines, since land survey and demarcation maps not only involve boundary points and boundary lines, but also require the content of map titles, map frames, and boundary point result tables, the above algorithm is implemented using VBA programming in AutoCAD. It is directly embedded in AutoCAD as a toolbar to be used in conjunction with the existing Southern CASS software. The content of map titles, map frames, and boundary point result tables still uses the original functions of CASS. The program is simple and easy to use, with a fast response speed, achieving better debugging and usage effects. In the process of algorithm implementation, the built-in functions of AutoCAD are fully utilized, which can improve the stability and running efficiency of the program.

[0089] The specific process of algorithm implementation and instance analysis is as follows: Figure 2 As shown, the parameters are set first, then the polyline direction is determined. If an arc is found, the arc is converted into a polyline and then the arc is removed to generate a new polyline. If no arc is found, the arc is removed directly to generate a new polyline. After removing the arc polyline, it is determined whether there is an island. If an island exists, nodes are added to the island, and then the polyline start point is converted. If no island exists, the polyline start point is converted.

[0090] like Figure 7 Taking a composite boundary line containing two arcs and an island as an example, after running the program, the arcs are automatically replaced with ordinary polylines, and a node is added at the connection of the islands, resulting in the following: Figure 13The results show that the starting point of the normalized boundary line is at the starting point of the arc in the upper left corner. Taking the arc in the upper left corner of the figure as an example, the radius of the arc is 228.72m and the central angle is 60°. According to formula (4), the number of nodes should be 98.11. The program automatically performs equiangular division based on the number of nodes. Analysis of the error after automatic normalization shows that the area before and after is 0.84m2, which achieves the normalization target.

[0091] In summary, this invention addresses the problems arising during the conversion of composite boundary lines in surveying and demarcation, explores relevant algorithms for the automatic standardization of composite boundary lines, proposes a formula for calculating the number of arc nodes based on accuracy requirements, a method for automatically adding nodes on isolated connecting lines to avoid self-intersection of boundary lines, and an algorithm for automatically converting the boundary line starting point to the upper left corner. The automatic standardization of composite boundary lines is implemented using VBA programming in AutoCAD, which can significantly improve work efficiency and enhance the data quality of boundary line processing.

[0092] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An automatic normalization method for composite boundary lines, characterized in that: Includes the following steps: S1. Convert the composite polyline with arcs into a regular polyline to obtain a regular polyline; S2. Remove the self-intersections from the boundary lines containing isolated islands to obtain the boundary lines; S3. Move the starting point of the boundary line to the upper left corner to obtain the new boundary line; When the starting point of the boundary line is switched to the upper left corner, the following process is included: B1. The GetBoundingBox method can be used to directly obtain the bounding rectangle of the entire polyline. Its return value is the coordinates of the lower left and upper right corners of the bounding rectangle. The average value is the center of the bounding rectangle as the origin. Then, the azimuth angle from the origin to each node is calculated. The point with the azimuth angle between 270° and 360° and the farthest from the origin is found. The point obtained at this time is the upper left corner as specified in the standard. B2. Record the position of the new starting point in the node array, and generate a new array using the forward / reverse order method according to whether the boundary line is clockwise or counterclockwise. Finally, use the new array to generate a new boundary line, and delete the original boundary line to generate a boundary line with the starting point in the upper left corner clockwise. S4. Implement the new boundary lines using algorithms and analyze examples to complete the automatic normalization of the boundary lines.

2. The automatic normalization method for composite boundary lines according to claim 1, characterized in that: The composite polyline mentioned in step 1 includes a lightweight polyline and a polyline. The node coordinate array of the lightweight polyline consists of X and Y coordinates, while the node coordinate array of the polyline consists of X, Y, and Z coordinates. The arc stores parameters such as radius, center, starting point coordinates, ending point coordinates, and starting and ending azimuth angles.

3. The automatic normalization method for composite boundary lines according to claim 2, characterized in that: The process of converting a polyline with an arc to a regular polyline includes the following steps: A1. Determine the direction of the compound polyline to obtain a new array of node coordinates; A2. Convert the arc to a regular polyline and obtain the coordinates of any point on the arc; A3. Calculation and control of conversion error to obtain a common polyline.

4. The automatic normalization method for composite boundary lines according to claim 3, characterized in that: When determining the direction of the composite polyline in step A1, it is necessary to first determine whether the direction is clockwise or counterclockwise, and then, according to the direction of the polyline, insert nodes sequentially to generate a new node coordinate array. The method for determining clockwise or counterclockwise direction is to calculate the algebraic sum s using Green's theorem. If s is positive, it indicates counterclockwise direction. Green's theorem is as follows: In the formula, s is the area of ​​the polyline, (x i ,y i ) represents the coordinates of node i.

5. The automatic normalization method for composite boundary lines according to claim 3, characterized in that: In step A2, the coordinates of any point are obtained using the polar coordinate method with an equal-angle bisector algorithm to calculate the coordinates of any position on the arc. Using AutoCAD's built-in properties for arcs, such as center coordinates, radius, arc length, angle, starting point coordinates, and starting azimuth, the polar coordinate method can conveniently obtain the coordinates of any point on the arc according to the following formula. X i =X0+R×cos(a0+a) AND i =Y0+R×sin(a0+a) In the formula, (X0, Y0) are the coordinates of the center point of the arc, R is the radius of the arc, a0 is the azimuth of the starting point of the arc, and a is the angle between point i on the arc and the starting point. All of these can be obtained from the parameters provided by VBA.

6. The automatic normalization method for composite boundary lines according to claim 5, characterized in that: In step A3, during the calculation and control of the conversion error, the number of manually modulated nodes was improved based on the derived conversion error calculation formula. Then, the number of nodes was automatically set in the program. After conversion, the arc became an isosceles triangle, resulting in an area error. The derived conversion error calculation formula is as follows: In the formula, S1 is the area of ​​the original arc, R and a are the radius and central angle of the arc, S2 is the area of ​​the converted isosceles triangle, n is the number of converted isosceles triangles, and ΔS is the conversion error.

7. The automatic normalization method for composite boundary lines according to claim 1, characterized in that: In step S2, when removing self-intersecting boundary lines with isolated islands, the program prompts the user to select the self-intersecting line segment AB using a user interaction method. If self-intersecting occurs, the user clicks to select points A and B respectively. If no self-intersecting occurs, the program skips the step. Then, based on the coordinates of nodes A and B, the program automatically moves a vertical distance D at the midpoint of line segment AB to add a new node.

8. The automatic normalization method for composite boundary lines according to claim 1, characterized in that: When implementing the algorithm and analyzing examples of the new boundary lines described in step 4, the algorithm is implemented in AutoCAD using VBA programming. It is directly embedded in AutoCAD as a toolbar to be used in conjunction with the existing Southern CASS software. The drawing title, drawing frame, and boundary point result table content still use the original functions of CASS.

9. The automatic normalization method for composite boundary lines according to claim 8, characterized in that: The specific process of the algorithm implementation and instance analysis is as follows: First, set the parameters, then determine the direction of the polyline. If an arc is found, convert the arc to a polyline and remove the arc to generate a new polyline. If no arc is found, remove the arc directly to generate a new polyline. Then, determine whether there is an island in the new polyline generated by removing the arc. If an island exists, add a node at the connection of the island and then enter the starting point of the polyline conversion. If no island exists, enter the starting point of the polyline conversion.

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