Heterogeneous multi-platform cooperative reconnaissance area distribution method

Through a heterogeneous multi-platform allocation method that takes into account aircraft sensor performance and maneuver turning factors in collaborative reconnaissance area division, the problems of aviation route conflict and low efficiency in the prior art are solved, and more efficient reconnaissance area allocation is achieved.

CN119850640AActive Publication Date: 2025-04-18LUOYANG INST OF ELECTRO OPTICAL EQUIP OF AVIC
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Patent Information

Application Number
CN202411712824.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-27
Publication Date
2025-04-18
Estimated Expiration
2044-11-27

AI Technical Summary

Technical Problem

The prior art fails to fully consider the differences in aircraft sensor performance and the factors that the aircraft maneuver turn are the least during reconnaissance process when dividing coordinated reconnaissance areas, resulting in low route conflicts and reconnaissance efficiency.

Method used

The heterogeneous multi-platform collaborative reconnaissance area allocation method is adopted. By obtaining aircraft and sensor parameters, the percentage of the allocated area of ​​each aircraft accounts for the total area is calculated, and based on the segmentation line of the external rectangle with the minimum area, the dichotomy is used to iterate the segmentation line until the segmentation accuracy requirements are met, and the final allocation area is generated.

Benefits of technology

It effectively reduces the number of maneuverable turns of the aircraft, improves reconnaissance efficiency, reduces the possibility of route conflicts, and is fast in computing speed and is easy to be applied in engineering.

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Abstract

The invention provides a heterogeneous multi-platform cooperative reconnaissance area distribution method, and belongs to the technical field of aviation firepower control. According to the method, a heterogeneous platform sensor detection performance function is established, a region area in direct proportion to the sensor performance of each aircraft platform is distributed for each aircraft platform, and based on the principle of minimum aircraft maneuvering turning, the area of a polygon region is segmented in the long side direction parallel to a bounding rectangle of the minimum area of a polygon in a reconnaissance region, so that the area of the polygon region is obtained. The cooperative reconnaissance area is divided into the sub-areas with the same number as the aircraft platforms, so that the cooperative reconnaissance area is distributed, and no-omission cooperative reconnaissance coverage of the target area is ensured.
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Description

Technical Field

[0001] The present invention relates to the technical field of aviation fire control, and in particular provides a method for allocating areas for heterogeneous multi-platform collaborative reconnaissance. Background Art

[0002] The coordinated execution of reconnaissance missions by multiple aircraft will become an important combat method on the battlefield in the future. By dividing the coordinated reconnaissance area into sub-areas equal to the number of aircraft performing the mission, effective coverage of the entire reconnaissance area can be achieved, which can reduce the complexity of coordinated reconnaissance planning. The rationality of regional division directly affects the realization and efficiency of reconnaissance missions.

[0003] At present, the methods of regional division include centroid Voronoi diagram division, fuzzy c-means clustering, area segmentation based on polygon vertices, regional grid allocation, etc., which do not take into account the differences in sensor performance and the minimum maneuvering turns of aircraft during reconnaissance. This may lead to route conflicts during the execution of collaborative reconnaissance missions and is not conducive to improving reconnaissance efficiency. Summary of the invention

[0004] The purpose of this application is to provide a method for allocating areas for collaborative reconnaissance of heterogeneous multi-platforms, which realizes the allocation of collaborative reconnaissance area polygons based on area, taking into account factors such as different performance parameters of sensors mounted on different aircraft and the minimum maneuvering turns of aircraft during reconnaissance.

[0005] In order to achieve the above object, the present invention adopts the following technical solution: a method for allocating heterogeneous multi-platform collaborative reconnaissance areas, the method comprising:

[0006] S1: Obtain the polygon parameters of the cooperative reconnaissance area, the parameters of the aircraft performing the cooperative reconnaissance mission, the performance parameters of the optoelectronic sensor and the reconnaissance altitude;

[0007] S2: Obtain the vertex coordinates and area of ​​the projection area of ​​the photoelectric sensor detection range of each aircraft in the ground plane;

[0008] S3: Based on the area obtained in S2, calculate the percentage of the area assigned to each aircraft to the area of ​​the collaborative reconnaissance area;

[0009] S4: Obtain the polygonal area of ​​the collaborative reconnaissance area, and calculate the area of ​​the area to be allocated to each aircraft according to the percentage obtained in S3;

[0010] S5: Obtain the two long sides and two short sides of the minimum area circumscribed rectangle of the collaborative reconnaissance area polygon, use the two long sides as the starting left and right segmentation boundary lines, and calculate the initial segmentation line of the area parallel to the starting left and right segmentation boundary lines according to the two short side vertices and the area percentage obtained in S3;

[0011] S6: Use the initial segmentation line calculated in S5 to segment the polygon of the collaborative reconnaissance area, calculate the area of ​​the segmented polygon, and iteratively calculate the segmentation line using the binary method until the difference between the area of ​​the segmented polygon and the area of ​​the area to be allocated meets the area segmentation accuracy requirement, generate the allocated area and the remaining unallocated area, and record the segmentation line;

[0012] S7: Calculate the area percentage of the next aircraft to be allocated to the remaining unallocated area, calculate the initial segmentation line of the next aircraft based on the segmentation line obtained in S6 and the initial right segmentation boundary line, repeat S6 to calculate the allocation area of ​​the next aircraft;

[0013] S8: Repeat S6-S7 until the allocation areas of all aircraft platforms are calculated, and obtain the final collaborative search area allocation result.

[0014] The heterogeneous multi-platform collaborative reconnaissance area allocation method provided by the present invention also has the following technical features: the photoelectric sensor performance parameters in S1 include the sensor initial azimuth angle θ, the sensor initial pitch angle β, the sensor azimuth field of view angle α AZ and the sensor pitch field of view α EL .

[0015] The heterogeneous multi-platform collaborative reconnaissance area allocation method provided by the present invention also has the following technical features: in S2, the projection area of ​​the detection range of each aircraft's photoelectric sensor on the ground plane includes four vertices A, B, C, and D, and the coordinates of the four vertices are respectively:

[0016]

[0017] Among them, H is the reconnaissance altitude of the aircraft, β is the initial pitch angle of the sensor, α EL is the sensor's pitch angle, θ is the sensor's initial azimuth angle, α AZ is the sensor azimuth field of view.

[0018] The heterogeneous multi-platform collaborative reconnaissance area allocation method provided by the present invention also has the following technical features: in S2, the projection area S of the detection range of each aircraft photoelectric sensor on the ground plane is i for:

[0019]

[0020] The heterogeneous multi-platform collaborative reconnaissance area allocation method provided by the present invention also has the following technical features: S4 includes:

[0021] S4.1: Calculate the coordinates of the center point of the collaborative reconnaissance area polygon;

[0022] S4.2: Calculate the azimuth angles of the vertices of the collaborative reconnaissance area polygon relative to the center;

[0023] S4.3: Sort the azimuth angles of the polygon vertices relative to the center in ascending order, and find the counterclockwise order of the polygon vertices;

[0024] S4.4: Calculate the polygonal area of ​​the collaborative reconnaissance region;

[0025] S4.5: Calculate the area assigned to each aircraft based on the percentage of the area assigned to each aircraft in the collaborative reconnaissance area.

[0026] The heterogeneous multi-platform collaborative reconnaissance area allocation method provided by the present invention also has the following technical features: S5 includes:

[0027] S5.1: Calculate the minimum area circumscribed rectangle of the collaborative reconnaissance area polygon;

[0028] S5.2: Use the two long sides of the minimum area circumscribed rectangle as the starting left dividing boundary line LINE min and the starting right dividing line LINE max ;

[0029] S5.3: Calculate the length of the two short sides based on the two short side vertices and area percentages. The line segment formed by the two points is used as the initial dividing line LINE0 for the first aircraft area allocation. The initial dividing line LINE0 is parallel to the long side of the rectangle and perpendicular to the short side of the rectangle.

[0030] The heterogeneous multi-platform collaborative reconnaissance area allocation method provided by the present invention also has the following technical features: the binary iterative calculation of the dividing line in S6 includes:

[0031] Calculate the area S(P1) of the segmented polygon P1 and compare it with the area S1 of the area to be allocated;

[0032] If the difference between S(P1) and S1 meets the area segmentation accuracy requirement, then polygon P1 is output as the area allocated to aircraft 1;

[0033] If S(P1) is less than S1 and the difference does not meet the area segmentation accuracy requirement, the initial segmentation line LINE0 is used as the left segmentation boundary LINE min , right split boundary LINE max No change, calculate the left segmentation boundary LINE min , right split boundary LINE max The line at the 50% center position between the two polygons is used as the new dividing line LINE1 to re-divide the polygon P.

[0034] If S(P1) is greater than S1 and the difference does not meet the area segmentation accuracy requirement, the initial segmentation line LINE0 is used as the right segmentation boundary LINE max , left split boundary LINE min No change, calculate the left segmentation boundary LINE min , right split boundary LINE max The line at the 50% center position between the two polygons is used as the new dividing line LINE1 to re-divide the polygon P.

[0035] Calculate the vertices of the polygon P1 and the remaining polygon P2, as well as the area S(P1) of the polygon P1, and compare them with the area S1 of the area to be allocated.

[0036] Beneficial Effects

[0037] The heterogeneous multi-platform collaborative reconnaissance area allocation method provided by the present invention fully considers the differences in sensor performance of different aircraft platforms in the process of realizing area-based collaborative reconnaissance area segmentation, selects the long side direction parallel to the minimum area circumscribed rectangle of the reconnaissance area polygon, and segments the area of ​​the polygonal area, so that the reconnaissance aircraft has the least maneuvering turns, improves the reconnaissance efficiency, reduces the possibility of conflict when multiple aircraft perform collaborative reconnaissance tasks, and has fast calculation speed and is easy to apply in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0039] Figure 1 A schematic diagram of the detection field of view of the photoelectric sensor mentioned in an embodiment of the present invention;

[0040] Figure 2 Select a schematic diagram for the initial segmentation line;

[0041] Figure 3 This is a schematic diagram of the area divided by dichotomy according to area;

[0042] Figure 4 This is a schematic diagram of the remaining ratio division. DETAILED DESCRIPTION

[0043] The present application is further described in detail below in conjunction with the accompanying drawings and examples, but it should be noted that these implementation methods are not limitations of the present application, and equivalent changes or substitutions in functions, methods, or structures made by ordinary technicians in the field based on these implementation methods are all within the scope of protection of the present application.

[0044] In the description of the embodiments of the present application, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the creation of the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the creation of the present application.

[0045] In addition, the terms "first", "second", "third", etc. are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the invention of this application, unless otherwise specified, the meaning of "plurality" is two or more.

[0046] The terms "installed", "connected" and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention of this application can be understood by specific circumstances.

[0047] like Figure 1-4 As shown, an embodiment of the present application provides a method for allocating heterogeneous multi-platform collaborative reconnaissance areas, the method comprising:

[0048] S1: The number of vertices of the polygon P in the collaborative reconnaissance area is n, and the vertex coordinates in the rectangular coordinate system of the geodetic plane are respectively (P 1x ,P 1y ),(P 2x ,P 2y ),…,(P nx ,P ny ), the number of aircraft performing coordinated reconnaissance missions m, the reconnaissance altitude H of each aircraft, and the performance of optoelectronic sensors;

[0049] S2: Obtain the vertex coordinates and area of ​​the projection area of ​​the photoelectric sensor detection range of each aircraft in the ground plane;

[0050] S3: Based on the area obtained in S2, calculate the percentage of the area assigned to each aircraft to the area of ​​the collaborative reconnaissance area;

[0051] S4: Obtain the polygonal area of ​​the collaborative reconnaissance area, and calculate the area of ​​the area to be allocated to each aircraft according to the percentage obtained in S3;

[0052] S5: Obtain the two long sides and two short sides of the minimum area circumscribed rectangle of the collaborative reconnaissance area polygon, use the two long sides as the starting left and right dividing boundary lines, and calculate the initial dividing line of the area parallel to the starting left and right dividing boundary lines according to the two short side vertices and the area percentage obtained in S3. The initial dividing line is parallel to the long side of the rectangle and perpendicular to the short side of the rectangle, ensuring the minimum number of turns during the aircraft platform reconnaissance process;

[0053] S6: Use the initial segmentation line calculated in S5 to segment the polygon of the collaborative reconnaissance area, calculate the area of ​​the segmented polygon, and iteratively calculate the segmentation line using the binary method until the difference between the area of ​​the segmented polygon and the area of ​​the area to be allocated meets the area segmentation accuracy requirement, generate the allocated area and the remaining unallocated area, and record the segmentation line;

[0054] S7: Calculate the area percentage of the next aircraft to be allocated to the remaining unallocated area, calculate the initial segmentation line of the next aircraft based on the segmentation line obtained in S6 and the initial right segmentation boundary line, repeat S6 to calculate the allocation area of ​​the next aircraft;

[0055] S8: Repeat S6-S7 until the allocation areas of all aircraft platforms are calculated, and obtain the final collaborative search area allocation result.

[0056] In some embodiments, the photoelectric sensor performance parameters in S1 include the sensor initial azimuth angle θ, the sensor initial pitch angle β, the sensor azimuth field angle α in the body coordinate system OXYZf AZ and the sensor pitch field of view α EL .

[0057] In some embodiments, in S2, it is assumed that the aircraft is flying levelly facing north, and the projection area of ​​the detection range of the photoelectric sensor of each aircraft on the ground plane includes four vertices A, B, C, and D, and the coordinates of the four vertices are respectively:

[0058]

[0059] Among them, H is the reconnaissance altitude of the aircraft, β is the initial pitch angle of the sensor, α EL is the sensor's pitch angle, θ is the sensor's initial azimuth angle, α AZ is the sensor azimuth field of view.

[0060] In some embodiments, in S2, the projection area S of the detection range of each aircraft photoelectric sensor on the ground plane is i for:

[0061]

[0062] In some embodiments, based on the detection area of ​​each aircraft's photoelectric sensor, the percentage of the area allocated to each aircraft to the area of ​​the collaborative reconnaissance area is calculated as:

[0063]

[0064] In some embodiments, the S4 includes:

[0065] S4.1: Calculate the coordinates of the center point of the collaborative reconnaissance area polygon as follows:

[0066]

[0067] S4.2: Calculate the azimuth angles of the vertices of the collaborative reconnaissance area polygon relative to the center:

[0068]

[0069] S4.3: Sort the azimuth angles of the polygon vertices relative to the center in ascending order, and find the counterclockwise order of the polygon vertices;

[0070] S4.4: Calculate the area of ​​the collaborative reconnaissance polygon as:

[0071]

[0072] Among them, P n+1x =P 1x ,P n+1y =P 1y ;

[0073] S4.5: Calculate the area assigned to each aircraft based on the percentage of the area of ​​the coordinated reconnaissance area assigned to each aircraft:

[0074]

[0075] In some embodiments, the S5 includes:

[0076] S5.1: Calculate the minimum area circumscribed rectangle of the collaborative reconnaissance area polygon;

[0077] S5.2: Use the two long sides of the minimum area circumscribed rectangle as the starting left dividing boundary line LINE min and the starting right dividing line LINE max ;

[0078] S5.3: Calculate the length of the two short sides based on the two short side vertices and area percentages. The line segment formed by the two points is used as the initial dividing line LINE0 for the first aircraft area allocation. The initial dividing line LINE0 is parallel to the long side of the rectangle and perpendicular to the short side of the rectangle.

[0079] In some embodiments, the S5.1 includes:

[0080] 1) Rotate the polygon around its center point, with an angle interval of 1°, within the angle range of [0°, 90°], and calculate the position of each vertex of the polygon after each rotation.

[0081] 2) According to the positions of each vertex of the polygon after rotation, find the maximum and minimum values ​​of the two-dimensional plane coordinates, and calculate the coordinates and area of ​​the four vertices of the circumscribed rectangle.

[0082] 3) Store the vertex coordinates, area and rotation angle of the polygon's circumscribed rectangle at each rotation angle.

[0083] 4) Compare each minimum enclosing rectangle and find the one with the smallest area.

[0084] 5) Rotate the smallest circumscribed rectangle in the opposite direction by the same amount to obtain the smallest circumscribed rectangle of the polygon.

[0085] In some embodiments, the iterative calculation of the dividing line by binary division in S6 includes:

[0086] Calculate the area S(P1) of the segmented polygon P1 and compare it with the area S1 of the area to be allocated;

[0087] If the difference between S(P1) and S1 meets the area segmentation accuracy requirement, then polygon P1 is output as the area allocated to aircraft 1;

[0088] If S(P1) is less than S1 and the difference does not meet the area segmentation accuracy requirement, the initial segmentation line LINE0 is used as the left segmentation boundary LINE min , right split boundary LINE max No change, calculate the left segmentation boundary LINE min , right split boundary LINE max The line at the 50% center position between the two polygons is used as the new dividing line LINE1 to re-divide the polygon P.

[0089] If S(P1) is greater than S1 and the difference does not meet the area segmentation accuracy requirement, the initial segmentation line LINE0 is used as the right segmentation boundary LINE max , left split boundary LINE min No change, calculate the left segmentation boundary LINE min , right split boundary LINE maxThe line at the 50% center position between the two polygons is used as the new dividing line LINE1 to re-divide the polygon P.

[0090] Calculate the vertices of the polygon P1 and the remaining polygon P2, as well as the area S(P1) of the polygon P1, and compare them with the area S1 of the area to be allocated.

[0091] In some embodiments, S7 includes: calculating the area percentage of the next aircraft to be allocated area to the remaining unallocated area P2 Use the last final segmentation line LINE as the starting left segmentation boundary LINE min , the right long side of the minimum area circumscribed rectangle of the collaborative reconnaissance area is used as the starting right segmentation boundary LINE max , allocate the unallocated area P2. Use the same method as S6 to obtain the allocation area for the next aircraft.

[0092] The above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the protection scope of the present application. The above is only a preferred implementation of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and variations can be made without departing from the technical principles of the present application, and these improvements and variations should also be regarded as the protection scope of the present application.

Claims

1. A method for allocating areas for collaborative reconnaissance of heterogeneous multi-platforms, characterized in that: The method comprises: S1: Obtain the polygon parameters of the cooperative reconnaissance area, the parameters of the aircraft performing the cooperative reconnaissance mission, the performance parameters of the optoelectronic sensor and the reconnaissance altitude; S2: Obtain the vertex coordinates and area of ​​the projection area of ​​the photoelectric sensor detection range of each aircraft in the ground plane; S3: Based on the area obtained in S2, calculate the percentage of the area assigned to each aircraft to the area of ​​the collaborative reconnaissance area; S4: Obtain the polygonal area of ​​the collaborative reconnaissance area, and calculate the area of ​​the area to be allocated to each aircraft according to the percentage obtained in S3; S5: Obtain the two long sides and two short sides of the minimum area circumscribed rectangle of the collaborative reconnaissance area polygon, use the two long sides as the starting left and right segmentation boundary lines, and calculate the initial segmentation line of the area parallel to the starting left and right segmentation boundary lines according to the two short side vertices and the area percentage obtained in S3; S6: Use the initial segmentation line calculated in S5 to segment the polygon of the collaborative reconnaissance area, calculate the area of ​​the segmented polygon, and iteratively calculate the segmentation line using the binary method until the difference between the area of ​​the segmented polygon and the area of ​​the area to be allocated meets the area segmentation accuracy requirement, generate the allocated area and the remaining unallocated area, and record the segmentation line; S7: Calculate the area percentage of the next aircraft to be allocated to the remaining unallocated area, calculate the initial segmentation line of the next aircraft based on the segmentation line obtained in S6 and the initial right segmentation boundary line, repeat S6 to calculate the allocation area of ​​the next aircraft; S8: Repeat S6-S7 until the allocation areas of all aircraft platforms are calculated, and obtain the final collaborative search area allocation result.

2. The method for allocating heterogeneous multi-platform collaborative reconnaissance areas according to claim 1 is characterized in that: The performance parameters of the photoelectric sensor in S1 include the initial azimuth angle θ of the sensor, the initial pitch angle β of the sensor, the azimuth field angle α of the sensor AZ and the sensor pitch field of view α EL .

3. The heterogeneous multi-platform collaborative reconnaissance area allocation method according to claim 1 is characterized in that: In S2, the projection area of ​​the detection range of each aircraft's photoelectric sensor on the ground plane includes four vertices A, B, C, and D, and the coordinates of the four vertices are: Among them, H is the reconnaissance altitude of the aircraft, β is the initial pitch angle of the sensor, α EL is the sensor's pitch angle, θ is the sensor's initial azimuth angle, α AZ is the sensor azimuth field of view.

4. The method for allocating heterogeneous multi-platform collaborative reconnaissance areas according to claim 3 is characterized in that: In S2, the projection area S of the detection range of each aircraft photoelectric sensor on the ground plane i for:

5. The heterogeneous multi-platform collaborative reconnaissance area allocation method according to claim 1 is characterized in that: The S4 includes: S4.1: Calculate the coordinates of the center point of the collaborative reconnaissance area polygon; S4.2: Calculate the azimuth angles of the vertices of the collaborative reconnaissance area polygon relative to the center; S4.3: Sort the azimuth angles of the polygon vertices relative to the center in ascending order, and find the counterclockwise order of the polygon vertices; S4.4: Calculate the polygonal area of ​​the collaborative reconnaissance region; S4.5: Calculate the area assigned to each aircraft based on the percentage of the area assigned to each aircraft in the collaborative reconnaissance area.

6. The method for allocating heterogeneous multi-platform collaborative reconnaissance areas according to claim 1, characterized in that: The S5 includes: S5.1: Calculate the minimum area circumscribed rectangle of the collaborative reconnaissance area polygon; S5.2: Use the two long sides of the minimum area circumscribed rectangle as the starting left dividing boundary line LINE min and the starting right dividing line LINE max ; S5.3: Calculate the length of the two short sides based on the two short side vertices and area percentages. The line segment formed by the two points is used as the initial dividing line LINE0 for the first aircraft area allocation. The initial dividing line LINE0 is parallel to the long side of the rectangle and perpendicular to the short side of the rectangle.

7. The method for allocating heterogeneous multi-platform collaborative reconnaissance areas according to claim 1, characterized in that: The binary division iterative calculation of the segmentation line in S6 includes: Calculate the area S(P1) of the segmented polygon P1 and compare it with the area S1 of the area to be allocated; If the difference between S(P1) and S1 meets the area segmentation accuracy requirement, then polygon P1 is output as the area allocated to aircraft 1; If S(P1) is less than S1 and the difference does not meet the area segmentation accuracy requirement, the initial segmentation line LINE0 is used as the left segmentation boundary LINE min , right split boundary LINE max No change, calculate the left segmentation boundary LINE min , right split boundary LINE max The line at the 50% center position between the two polygons is used as the new dividing line LINE1 to re-divide the polygon P. If S(P1) is greater than S1 and the difference does not meet the area segmentation accuracy requirement, the initial segmentation line LINE0 is used as the right segmentation boundary LINE max , left split boundary LINE min No change, calculate the left segmentation boundary LINE min , right split boundary LINE max The line at the 50% center position between the two polygons is used as the new dividing line LINE1 to re-divide the polygon P. Calculate the vertices of the polygon P1 and the remaining polygon P2, as well as the area S(P1) of the polygon P1, and compare them with the area S1 of the area to be allocated.

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