Region boundary determination method and device and electronic equipment
By acquiring and integrating mesh position data in the rasterized map and determining the boundaries of complex polygonal regions, the problem of low boundary accuracy in the prior art is solved, and higher accuracy and efficiency are achieved.
Patent Information
- Application Number
- CN202510052114.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-13
- Publication Date
- 2025-05-13
AI Technical Summary
When handling complex and irregular polygonal areas, the prior art directly generates boundaries based on the set of latitude and longitude coordinate points, resulting in low accuracy.
By obtaining the position data of all grids in the target area in the rasterized map, the first boundaries of multiple sub-regions are determined, and these boundaries are integrated to obtain the second boundaries of the target area.
It has achieved improvement in the accuracy and efficiency of regional boundary determination, and solved the problem of low boundary accuracy of complex and irregular polygonal regions.
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Figure CN119992121A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of map processing technology, and in particular to a method, device and electronic device for determining a region boundary. Background Art
[0002] In geographic information systems, boundaries are usually engraved based on rasterized maps. However, for complex and irregular polygonal areas, related technologies directly generate boundaries based on longitude and latitude coordinate point sets, resulting in low boundary accuracy.
[0003] To address the above-mentioned problems, no effective solution has been proposed yet. Summary of the invention
[0004] The embodiments of the present application provide a method, device and electronic device for determining area boundaries, so as to at least solve the technical problem that for complex and irregular polygonal areas, the related technology directly generates boundaries based on a set of longitude and latitude coordinate points, resulting in low accuracy.
[0005] According to one aspect of an embodiment of the present application, a method for determining a region boundary is provided, comprising: obtaining position data of all grids in a target region in a rasterized map, wherein the target region includes multiple sub-regions, a grid is a minimum maintenance unit in the rasterized map, and each sub-region includes at least one grid; determining first boundaries corresponding to the multiple sub-regions respectively based on the position data; and integrating the first boundaries corresponding to the multiple sub-regions respectively to obtain a second boundary of the target region.
[0006] In some embodiments of the present application, first boundaries corresponding to multiple sub-areas are determined based on position data, including: determining a first data set from the position data, wherein the first data set includes position data corresponding to all grids in any sub-area; determining a first first endpoint and a first last endpoint from the first data set, and generating a first initial boundary corresponding to the first first endpoint and the first last endpoint; traversing the first data set, determining first target data from the first data set, wherein the first target data is used to expand the coverage range corresponding to the first initial boundary; updating the first initial boundary based on the first target data, and determining the updated initial boundary as the first boundary.
[0007] In some embodiments of the present application, traversing the first data set and determining the first target data from the first data set includes: obtaining first position data and second position data on a first initial boundary, wherein the first position data and the second position data are adjacent and continuous on the first initial boundary; determining a cross product between any data in the first data set, the first position data, and the second position data, wherein the cross product is used to represent the positional relationship between any data and the first position data and the second position data; and when the cross product is greater than zero, determining that the data corresponding to the cross product is the first target data.
[0008] In some embodiments of the present application, the first position data and the second position data are determined to be adjacent and continuous on the first initial boundary in the following case: when the first position data and the second position data are respectively two endpoints of the first initial boundary, the first position data and the second position data are determined to be adjacent and continuous on the first initial boundary.
[0009] In some embodiments of the present application, after determining the first boundary, the method also includes: traversing all position data on the first boundary, determining second target data from all position data on the first boundary, wherein the second target data is used to reflect the concave features of the first boundary; and updating the first boundary based on the second target data.
[0010] In some embodiments of the present application, all position data on the first boundary are traversed to determine the second target data from all position data on the first boundary, including: obtaining third position data, fourth position data and fifth position data on the first boundary, wherein the third position data, the fourth position data and the fifth position data are sequentially adjacent on the first boundary; generating a first vector corresponding to the fourth position data and the third position data, and a second vector corresponding to the fourth position data and the fifth position data; determining the cosine value of the angle between the first vector and the second vector; and when the cosine value of the angle is less than zero, determining that the fourth position data is the second target data.
[0011] In some embodiments of the present application, the first boundaries corresponding to multiple sub-areas are integrated to obtain the second boundary of the target area, including: obtaining a second data set corresponding to the first boundary, wherein the second data set includes the position data contained in the first boundaries corresponding to all sub-areas; determining the second first endpoint and the second last endpoint from the second data set, and generating a second initial boundary corresponding to the second first endpoint and the second last endpoint; traversing the second data set to determine the third target data, wherein the third target data is used to expand the coverage corresponding to the second initial boundary; updating the second initial boundary according to the third target data, and determining the updated second initial boundary as the second boundary.
[0012] In some embodiments of the present application, after determining the second boundary, the method also includes: traversing all position data on the second boundary, determining fourth target data from all position data on the second boundary, wherein the fourth target data is used to reflect the concave features of the second boundary; and updating the second boundary based on the fourth target data.
[0013] In some embodiments of the present application, a first beginning endpoint and a first end endpoint are determined from a first data set, and a first initial boundary corresponding to the first beginning endpoint and the first end endpoint is generated, including: sorting all position data in the first data set according to a preset rule to obtain a data sequence; determining the beginning data of the data sequence as the first beginning endpoint, and determining the end data of the data sequence as the first end endpoint; determining the line connecting the first beginning endpoint and the first end endpoint as the first initial boundary.
[0014] According to another aspect of an embodiment of the present application, a device for determining a region boundary is also provided, including: an acquisition module for acquiring location data of all grids in a target region in a rasterized map, wherein the target region includes multiple sub-regions, a grid is the smallest maintenance unit in the rasterized map, and each sub-region includes at least one grid; a determination module for determining first boundaries corresponding to the multiple sub-regions respectively based on the location data; and an integration module for integrating the first boundaries corresponding to the multiple sub-regions respectively to obtain a second boundary of the target region.
[0015] According to another aspect of the embodiments of the present application, there is also provided an electronic device, including: a memory and a processor, the memory being used to store program instructions; the processor being connected to the memory and being used to execute the above-mentioned method for determining the area boundary.
[0016] According to another aspect of the embodiments of the present application, a non-volatile storage medium is provided, which includes a stored computer program, wherein the device where the non-volatile storage medium is located executes the above-mentioned method for determining the area boundary by running the computer program.
[0017] According to another aspect of the embodiments of the present application, a computer program product is provided, including computer instructions, which implement the above-mentioned method for determining the region boundary when executed by a processor.
[0018] In an embodiment of the present application, by acquiring the position data of all grids in the target area, determining the first boundary of the sub-area, and then integrating the first boundary to obtain the second boundary of the target area, the purpose of depicting the boundary of the upper-level area step by step is achieved, thereby achieving the technical effect of improving the accuracy and efficiency of determining the regional boundaries, and further solving the technical problem of low accuracy in the related technology of directly generating boundaries based on longitude and latitude coordinate point sets for complex and irregular polygonal areas. BRIEF DESCRIPTION OF THE DRAWINGS
[0019] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:
[0020] Figure 1 It is a hardware structure block diagram of a computer terminal according to a method for determining a region boundary according to an embodiment of the present application;
[0021] Figure 2 is a flow chart of a method for determining a region boundary according to an embodiment of the present application;
[0022] Figure 3 is a grid schematic diagram of a method for determining a region boundary according to an embodiment of the present application;
[0023] Figure 4 is a grid position data point bitmap of a method for determining a region boundary according to an embodiment of the present application;
[0024] Figure 5 is a schematic diagram of a convex boundary of a method for determining a region boundary according to an embodiment of the present application;
[0025] Figure 6 is a schematic diagram of boundary indentation of a method for determining a region boundary according to an embodiment of the present application;
[0026] Figure 7 is a schematic diagram of a concave boundary of a method for determining a region boundary according to an embodiment of the present application;
[0027] Figure 8 is a schematic diagram of a target boundary of a method for determining a region boundary according to an embodiment of the present application;
[0028] Fig. 9 It is a schematic diagram of a hierarchical characterization process of a method for determining a region boundary according to an embodiment of the present application;
[0029] Fig.10 is a calculation flow chart of a method for determining a region boundary according to an embodiment of the present application;
[0030] Fig.11 It is a structural schematic diagram of a device for determining a region boundary according to an embodiment of the present application. DETAILED DESCRIPTION
[0031] In order to enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of this application.
[0032] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.
[0033] In order to better understand the embodiments of the present application, the technical terms involved in the embodiments of the present application are explained as follows:
[0034] Convex Hull Algorithm (Convex Hull for short): Convex Hull Algorithm is a geometric algorithm used to generate the smallest convex polygon or convex hull containing all points from a set of points. Its main goal is to find the convex hull of all points in two-dimensional or three-dimensional space, which can contain all points without concavity.
[0035] Concave Hull Algorithm (Concave Hull for short): The concave hull algorithm is a geometric algorithm used to generate the minimum concave polygon containing a set of points. Unlike the convex hull algorithm, it can capture the concave features in the point set, and the generated boundary can contain depressions to more accurately reflect the actual shape of the point set.
[0036] In geographic information systems, raster maps and convex hull boundary characterization methods are usually used. However, these methods often lack accuracy in the characterization of complex, polygonal areas and have a large amount of calculation. Raster maps achieve discretization of space by dividing geographic space into fixed-size pixel units, which is suitable for processing continuous spatial data. However, for complex and irregular polygonal areas, especially at low resolution, the boundaries are difficult to describe accurately and are prone to "jaggies". The convex hull algorithm is a classic geometric algorithm that is often used to generate the smallest convex polygon on a set of points, including all points. The algorithm forms a convex polygon by finding the outermost boundary points surrounding all points, so it is suitable for areas with regular shapes and convex shapes. The main advantage of the convex hull algorithm is that it is simple to implement and is particularly suitable for processing large-scale data sets. However, its limitations are also very obvious, that is, for concave or complex polygonal areas, the convex hull algorithm cannot accurately characterize the boundaries of the area. For example, if the target area has a clear concave shape, the convex hull algorithm will not be able to capture these concave features, resulting in a loss of accuracy. Therefore, although the convex hull algorithm performs well in some simple application scenarios, its accuracy and flexibility need to be improved for more complex geographical areas.
[0037] It can be seen that the related technology is prone to losing details when processing polygonal boundaries, concave areas or complex areas, and the high-precision algorithm involves a large number of point calculations, which is inefficient under large-scale data processing. In order to solve the above technical problems, the embodiments of the present application provide corresponding solutions, which are described in detail below.
[0038] The method for determining the region boundary provided in the embodiment of the present application may be executed in a mobile terminal, a computer terminal or a similar computing device. Figure 1 FIG. 1 shows a hardware structure block diagram of a computer terminal for implementing a method for determining a region boundary. Figure 1 As shown, the computer terminal 10 may include one or more (102a, 102b, ..., 102n are used to illustrate) processors (the processor may include but is not limited to a processing device such as a microprocessor MCU or a programmable logic device FPGA), a memory 104 for storing data, and a transmission module 106 for communication functions connected via a wired and / or wireless network. In addition, it may also include: a display, a keyboard, a cursor control device, an input / output interface (I / O interface), a universal serial bus (USB) port (which may be included as one of the ports of the I / O interface), a network interface, and a BUS bus. Those skilled in the art can understand that Figure 1 The structure shown is only for illustration and does not limit the structure of the above electronic device. Figure 1 More or fewer components as shown, or with Figure 1Different configurations are shown.
[0039] It should be noted that the one or more processors and / or other data processing circuits described above may generally be referred to herein as "data processing circuits". The data processing circuits may be embodied in whole or in part as software, hardware, firmware, or any other combination thereof. In addition, the data processing circuit may be a single independent processing module, or may be incorporated in whole or in part into any of the other components in the computer terminal 10. As described in the embodiments of the present application, the data processing circuit acts as a processor control (e.g., selection of a variable resistor terminal path connected to an interface).
[0040] The memory 104 can be used to store software programs and modules of application software, such as program instructions / data storage devices corresponding to the method for determining the regional boundary in the embodiment of the present application. The processor executes various functional applications and data processing by running the software programs and modules stored in the memory 104, that is, the method for determining the regional boundary described above is realized. The memory 104 may include a high-speed random access memory, and may also include a non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some examples, the memory 104 may further include a memory remotely arranged relative to the processor, and these remote memories may be connected to the computer terminal 10 via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.
[0041] The transmission module 106 is used to receive or send data via a network. The specific example of the above network may include a wireless network provided by a communication provider of the computer terminal 10. In one example, the transmission module 106 includes a network adapter (Network Interface Controller, NIC), which can be connected to other network devices through a base station so as to communicate with the Internet. In one example, the transmission module 106 can be a radio frequency (RF) module, which is used to communicate with the Internet wirelessly.
[0042] The display may be, for example, a touch screen liquid crystal display (LCD) that enables a user to interact with a user interface of the computer terminal 10 .
[0043] It should be noted that, in some optional embodiments, the above Figure 1 The computer terminal shown may include hardware elements (including circuits), software elements (including computer code stored on a computer-readable medium), or a combination of hardware elements and software elements. It should be noted that Figure 1This is merely one example of a particular embodiment and is intended to illustrate the types of components that may be present in the computer terminal described above.
[0044] In the above-mentioned operating environment, an embodiment of the present application provides an embodiment of a method for determining a region boundary. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from that shown here.
[0045] Figure 2 is a flow chart of a method for determining a region boundary according to an embodiment of the present application, such as Figure 2 As shown, the method comprises the following steps:
[0046] Step S202, obtaining the position data of all grids in the target area in the rasterized map, wherein the target area includes multiple sub-areas, the grid is the smallest maintenance unit in the rasterized map, and each sub-area includes at least one grid.
[0047] In the above step S202, the rasterized map is a representation of a geographic space divided into grids or cells of a fixed size, each grid or cell having a specific latitude and longitude range to represent a specific part of the earth's surface.
[0048] The target area refers to a specific geographical area selected in network maintenance and management, such as a city, a county, or a specific telecommunications service area. The target area can contain multiple sub-areas, each of which can represent a different management unit or service package area. A sub-area is a subdivided geographical area within the target area, such as a grid set or a specific service area in network maintenance, for more refined management and maintenance operations.
[0049] A grid refers to the smallest maintenance unit in a rasterized map. A grid can have a fixed size and shape, such as a square or rectangle, or an irregular size and shape, such as a grid of irregular shape and size formed based on natural or artificial boundaries (such as rivers, roads, administrative divisions, etc.). Each grid has unique latitude and longitude coordinates to define its boundaries, which are used to accurately locate network equipment, lines or coverage in network maintenance.
[0050] Location data refers to data used in a geographic information system to describe the exact location of a geographic entity or feature on the earth's surface, such as the longitude and latitude coordinate information of each grid in a rasterized map. In some embodiments of the present application, in a GIS database, each grid has its own location data storage, and a database query statement (such as SQL) can be used to extract the longitude and latitude coordinates of all grids in the target area (that is, the location data can be the location point corresponding to the longitude and latitude coordinates).
[0051] Step S204: determining first boundaries corresponding to the plurality of sub-regions respectively according to the position data.
[0052] In the above step S204, the first boundary refers to a preliminary boundary outline of each sub-region calculated by the position data, which can be calculated by a specific algorithm based on the grid position data and is used to depict the shape and range of the sub-region.
[0053] In some embodiments of the present application, the set of longitude and latitude coordinate points of all grids in each sub-region can be regarded as a group of points, and the convex hull algorithm is applied to determine the minimum convex boundary of this group of points to quickly generate a closed boundary as a preliminary sub-region boundary outline. In addition, the Alpha Shape algorithm can also be applied to generate the preliminary boundary of each sub-region, and the degree of convexity of the generated shape can be controlled by adjusting the Alpha parameter in the algorithm.
[0054] In order to ensure the integrity and accuracy of the boundary coverage, the first boundaries corresponding to multiple sub-areas can be determined by the following steps: determine a first data set from the position data, wherein the first data set includes the position data corresponding to all grids in any sub-area; determine a first endpoint and a first tail endpoint from the first data set, and generate a first initial boundary corresponding to the first endpoint and the first tail endpoint; traverse the first data set and determine first target data from the first data set, wherein the first target data is used to expand the coverage corresponding to the first initial boundary; update the first initial boundary according to the first target data, and determine the updated initial boundary as the first boundary.
[0055] The first initial boundary can be a straight line boundary generated by the first first endpoint and the first tail endpoint, which is used as the starting point for subsequent boundary calculations. In some embodiments of the present application, the first data set can be analyzed to find the outermost or extreme latitude and longitude coordinate points, such as the northernmost, southernmost, easternmost, and westernmost points, as the first first endpoint and the first tail endpoint, and a straight line is generated using the first first endpoint and the first tail endpoint as the first initial boundary.
[0056] In order to quickly generate the initial boundary, the first initial boundary can be generated by the following steps: sorting all position data in the first data set according to preset rules to obtain a data sequence; determining the head data of the data sequence as the first head endpoint, and determining the tail data of the data sequence as the first tail endpoint; determining the line connecting the first head endpoint and the first tail endpoint as the first initial boundary.
[0057] Sorting refers to reorganizing the order of elements in a data set according to preset rules. The preset rules for sorting can be based on longitude and latitude coordinates, such as arranging in ascending or descending order of longitude or latitude.
[0058] The first target data refers to the grid position data used to expand the coverage of the first initial boundary in the process of traversing the first data set, such as grid points located near the boundary but not yet covered by the initial boundary. In some embodiments of the present application, the position data of each grid can be checked in turn from the first data set, and its relative position with the current first initial boundary can be evaluated to identify the first target data, such as data points located outside the current boundary but adjacent to the boundary, which may be used to optimize the boundary to more completely cover the sub-area.
[0059] By calculating the cross product, the positional relationship between data points on the boundary can be intelligently identified to accurately determine the first target data, specifically: obtaining the first position data and the second position data on the first initial boundary, wherein the first position data and the second position data are adjacent and continuous on the first initial boundary; determining the cross product between any data in the first data set, the first position data, and the second position data, wherein the cross product is used to represent the positional relationship between any data and the first position data and the second position data; when the cross product is greater than zero, determining the data corresponding to the cross product as the first target data.
[0060] The first position data and the second position data refer to data of any two consecutive points on the first initial boundary, which can be represented by longitude and latitude coordinates and are used to calculate the cross product with other data points in the first data set. In some embodiments of the present application, the first position data and the second position data can be selected in the order of the data sequence, that is, two consecutive points are selected from the sorted data sequence as the first position data and the second position data.
[0061] In some embodiments of the present application, the first position data and the second position data can be determined to be adjacent and continuous on the first initial boundary in the following case: when the first position data and the second position data are respectively the two endpoints of the first initial boundary, the first position data and the second position data are determined to be adjacent and continuous on the first initial boundary.
[0062] The first position data and the second position data are adjacent and continuous on the first initial boundary, that is, the two are two directly connected points on the boundary, and no other points are inserted between them.
[0063] The cross product is a type of vector operation used to calculate the perpendicular vector of two vectors in three-dimensional space. In two-dimensional space, the cross product can be used to determine whether three points form a left turn or a right turn, and to identify whether a point is inside or outside a boundary. In some embodiments of the present application, the cross product can be calculated by the following formula:
[0064] cross(P a , P b , Pi )=(x b -x a )·(y i -y a )-(y b -y a )·(x i -x a )
[0065] Among them, P a (x a ,y a ) and P b (x b ,y b ) represents any two consecutive points on the current boundary, P a Indicates the first position data, x a ,y a Respectively represent the longitude and latitude coordinates of the first position data, P b Indicates the second position data, x b ,y b represent the longitude and latitude coordinates of the second position data, respectively, i (x i ,y i ) represents any data in the first data set to be judged, x i ,y i Respectively represent P i (x i ,y i )'s longitude and latitude coordinates, cross(P a ,P b ,P i ) represents the cross product.
[0066] The cross product can be used to determine P i Is it in P a and P b The "inside" or "outside" of the defined edge, that is, by calculating the cross product between the three points, we can determine whether the point P i Location, specifically:
[0067] (1) When cross(P a ,P b ,P i )>0: indicates point P i "Outside" the boundary line (corresponding to the first target data);
[0068] (2) When cross(P a ,P b ,P i )<0: indicates point P i “Inside” the borderline;
[0069] (3) When cross(P a ,P b ,P i )=0: Indicates that the three points are collinear and do not affect the current boundary.
[0070] If you click P i When "outside" the boundary, the first initial boundary can be updated to include the point based on its relationship to the current boundary.
[0071] The first boundary is the boundary of the sub-region finally determined by traversing the first data set and updating the first initial boundary according to the first target data, which accurately describes the scope and shape of the sub-region. In some embodiments of the present application, for each first target data, it is checked whether it can be included in the sub-region by adjusting the boundary. If so, the first initial boundary is updated to make it closer to the point distribution in the first data set.
[0072] In order to further optimize the boundary shape and make the boundary more consistent with the actual terrain, after determining the first boundary, the following steps can also be performed: traverse all position data on the first boundary, determine second target data from all position data on the first boundary, wherein the second target data is used to reflect the concave features of the first boundary; and update the first boundary according to the second target data.
[0073] The second target data refers to specific position data points on the first boundary that are used to reflect the concave features, and helps the algorithm identify the boundary portion that needs to be corrected to generate a more accurate first boundary.
[0074] In order to accurately identify the depression points on the boundary, the second target data can be determined by the following steps, specifically: obtaining the third position data, the fourth position data and the fifth position data on the first boundary, wherein the third position data, the fourth position data and the fifth position data are sequentially adjacent on the first boundary; generating a first vector corresponding to the fourth position data and the third position data, and a second vector corresponding to the fourth position data and the fifth position data; determining the cosine value of the angle between the first vector and the second vector; and determining the fourth position data as the second target data when the cosine value of the angle is less than zero.
[0075] The third position data, the fourth position data, and the fifth position data refer to any three adjacent position data points on the first boundary, which are used to calculate and evaluate the concave features on the boundary. Through the positional relationship between these points, it is possible to determine whether there is a concave on the boundary, and then identify the second target data. In some embodiments of the present application, when processing the data on the first boundary, a loop structure can be used to obtain the current point (fourth position data), the previous point (third position data), and the next point (fifth position data) each time to ensure that three consecutive points are analyzed each time.
[0076] The first vector is a vector pointing from the third position data to the fourth position data, and the second vector is a vector pointing from the fourth position data to the fifth position data. In some embodiments of the present application, the generation of the vector can be based on the coordinate difference between two points. For example, assuming three adjacent points: the third position data point P i-1 (x i-1 ,y i-1 ), the fourth position data point P i′ (x i′ ,y i′ ), the fifth position data point P i+1 (x i+1 ,y i+1 ),
[0077] Define the first vector A from P i-1 To P i′ :A=(x i′ -x i-1 ,y i′ -y i-1 );
[0078] Define the second vector B from P i′ To P i+1 :B=(x i+1 -x i′ ,y i+1 -y i′ ).
[0079] The angle cosine value is the cosine value of the angle between the first vector and the second vector. By comparing the angle cosine value with zero, it can be determined whether the fourth position data causes a depression on the boundary. If the angle cosine value is less than zero, it indicates that the angle between the vectors is greater than 180 degrees, that is, the fourth position data causes a depression. In some embodiments of the present application, the angle cosine value can be calculated by the following formula:
[0080]
[0081] Among them, x i-1 ,y i-1 Respectively represent the longitude and latitude coordinates of the third location data point, xi′ ,y i′ Respectively represent the longitude and latitude coordinates of the fourth position data point, x i+1 ,y i+1 They respectively represent the longitude and latitude coordinates of the fifth position data point, and cos(θ) represents the cosine value of the angle.
[0082] If cos(θ)<0, the angle is obtuse, indicating that P i′ is a concave point, which means that the current boundary is concave inward at this point and the boundary needs to be adjusted to remove the concave.
[0083] The second target data is a specific position data point on the first boundary that causes a boundary concave feature, that is, a point that needs to be corrected to generate a smoother and more accurate first boundary. In some embodiments of the present application, after calculating the cosine value of the angle, it can be determined by numerical comparison (such as less than zero) whether the fourth position data causes a boundary concave, and if the condition is met, it is marked as the second target data.
[0084] Step S206: integrating the first boundaries corresponding to the plurality of sub-regions to obtain a second boundary of the target region.
[0085] In the above step S206, the integration process refers to the process of merging the first boundaries of multiple sub-regions into a continuous boundary outline (i.e., the second boundary). The second boundary is the final boundary description of the target area, which is obtained by integrating the first boundaries of multiple sub-regions. In some embodiments of the present application, a topological algorithm can be used to identify the connection relationship between the sub-region boundaries to ensure that the boundaries of adjacent sub-regions can be correctly connected together to form a continuous boundary outline, or a boundary merging technology can be used to merge the overlapping boundary parts to avoid duplication of boundary descriptions and ensure the uniqueness and integrity of the target area boundary.
[0086] In order to effectively integrate the sub-region boundaries and form a complete target region boundary, the second boundary of the target region can be determined by the following steps: obtaining a second data set corresponding to the first boundary, wherein the second data set includes the position data contained in the first boundary corresponding to all sub-regions; determining the second first endpoint and the second last endpoint from the second data set, and generating a second initial boundary corresponding to the second first endpoint and the second last endpoint; traversing the second data set to determine the third target data, wherein the third target data is used to expand the coverage corresponding to the second initial boundary; updating the second initial boundary according to the third target data, and determining the updated second initial boundary as the second boundary.
[0087] The second data set contains the position data of the first boundaries of all sub-regions, that is, the set of all final boundary points after the sub-region boundary optimization process. In some embodiments of the present application, all coordinate points on the first boundaries of each sub-region can be merged to form a unified data set. In an optional embodiment, data deduplication and sorting technology can also be used to ensure the uniqueness and order of the position data points in the second data set, providing orderly data input for subsequent boundary generation and optimization.
[0088] The method for generating the second initial boundary can refer to the first initial boundary, which will not be described in detail here.
[0089] The third target data refers to the position data used to expand the coverage of the second initial boundary when traversing the second data set. In some embodiments of the present application, by checking the relationship between each point in the second data set and the second initial boundary, points (i.e., third target data) that may need to adjust the boundary shape to more completely cover the target area can be identified in turn. It should be noted that the determination of the third target data can refer to the determination process of the first target data, which will not be repeated here.
[0090] After the third target data is determined, the second initial boundary can be adjusted by adding the third target data points to cover a wider area. For example, for each point determined as the third target data, its relationship with the points on the second initial boundary is checked. If it is outside the boundary and significantly deviates from the boundary, the point can be added to the second initial boundary to generate an updated boundary. A dynamic boundary adjustment algorithm can also be used, such as adding points to the nearest boundary segment, or connecting the third target data points by generating new boundary segments to cover a wider area and form an updated second boundary.
[0091] By optimizing the boundary again, the authenticity and integrity of the target area boundary can be ensured. That is, after determining the second boundary, the following steps can also be performed: traverse all position data on the second boundary, determine fourth target data from all position data on the second boundary, wherein the fourth target data is used to reflect the concave features of the second boundary; and update the second boundary based on the fourth target data.
[0092] The fourth target data refers to the position data on the second boundary that causes the boundary to have concave features. By identifying and correcting these concave points, the second boundary can be made smoother and more accurate, avoiding distortion of the boundary description and more accurately reflecting the actual shape of the target area. It should be noted that the determination of the fourth target data can refer to the determination process of the second target data, which will not be repeated here.
[0093] After determining the fourth target data, the depression on the boundary can be eliminated by adjusting or removing the fourth target data point to generate an updated boundary. In some embodiments of the present application, for each point marked as the fourth target data, it can be checked whether it can be deleted or adjusted without affecting the complete coverage of the target area. If the second boundary can still completely cover the target area after deleting or adjusting a depression point, and the boundary shape is smoother, then the operation can be performed to update the second boundary. Alternatively, a concave hull algorithm, such as a quick concave hull algorithm (QuickHull) or an incremental concave hull algorithm (Incremental Hull), is used to process all position data on the second boundary to automatically identify and eliminate depressions.
[0094] Through the above steps S202 to S206, by obtaining the position data of all grids in the target area, determining the first boundary of the sub-area, and then integrating the first boundary to obtain the second boundary of the target area, the purpose of depicting the boundary of the upper-level area step by step is achieved, thereby achieving the technical effect of improving the accuracy and efficiency of determining the regional boundary, and further solving the technical problem of low accuracy in the related technology of directly generating boundaries based on longitude and latitude coordinate point sets for complex and irregular polygonal areas.
[0095] In order to facilitate understanding of the above process, an explanation is provided below in conjunction with a specific embodiment.
[0096] Figure 3 is a grid diagram of a method for determining a region boundary according to an embodiment of the present application, such as Figure 3 As shown in the figure, it shows the original grid division of a region. Each grid represents the smallest maintenance unit of the rasterized map, which is used to collect location information. Grid division is the basis of the entire boundary determination method. The data acquisition module collects data from these grids to provide original information for determining the boundaries of sub-regions and target regions.
[0097] In order to ensure data consistency and accuracy during the boundary delineation process, the location data of the smallest unit grid (such as longitude and latitude data) from different sources can be standardized by the following steps:
[0098] (1) Data reading: Read the latitude and longitude data of the smallest unit grid (i.e., grid) through CSV, Excel, GeoJSON, database, etc.
[0099] (2) Data cleaning: First, identify and filter out invalid coordinate points in the data source (for example, longitude and latitude that exceed the geographic range, low accuracy, null values, or missing values) to ensure the integrity of the input data.
[0100] (3) Coordinate conversion: Different data sources may use different formats or different coordinate systems, such as (WGS84, CGCS2000, BD09), etc. These data are uniformly converted and all coordinate points are converted to the WGS84 coordinate system format.
[0101] (4) Unified coordinate accuracy: Since the coordinate accuracy of different data sources may be different, all coordinate points are standardized to the same decimal precision (such as retaining 6 decimal places) to ensure the accuracy of subsequent calculation results.
[0102] (5) Deduplication and sorting: For duplicate coordinate points, deduplication operations will be performed and the coordinate points will be sorted according to the order of longitude and latitude to provide ordered input for subsequent boundary calculations.
[0103] (6) Standardized output: The processed latitude and longitude data are output in a unified format.
[0104] Figure 4 is a grid position data point bitmap of a method for determining a region boundary according to an embodiment of the present application, Figure 4 Yes Figure 3 The results of standardization of the grid location data collected in the process are shown. Standardization usually involves converting the location data into a unified format, such as longitude and latitude coordinates, to ensure the consistency and comparability of the data as input for subsequent boundary determination.
[0105] The standardized longitude and latitude data are passed to the boundary algorithm for concave hull boundary calculation. Specifically, the standardized longitude and latitude points are sorted according to their x-coordinates (longitude) or y-coordinates (latitude) to reduce the complexity of subsequent calculations; the first point p1 (x1, y1) and the last point p n (x n ,y n ) as the two endpoints of the initial boundary; check each point in turn to determine whether it is "inside" or "outside" of the current boundary, and "inside" and "outside" are based on the geometric position relationship and are realized through the vector cross product formula (refer to the determination of the first target data mentioned above). Figure 5 is a schematic diagram of a convex boundary of a method for determining a region boundary according to an embodiment of the present application, such as Figure 5 As shown, a convex boundary map generated by processing grid location data is shown. The convex boundary map reflects the boundary of a sub-area, but may not completely conform to the actual geographical features, especially when there are complex depressions on the boundary. The convex boundary map is the basis for determining the first boundary, but further processing is required to reflect a more accurate boundary shape.
[0106] After the first boundary is constructed (ref. Figure 5), the concave points can be further checked, such as detecting the concave by determining the angle θ between adjacent points. Figure 6 is a schematic diagram of a boundary indentation of a method for determining a region boundary according to an embodiment of the present application, which is based on Figure 5 The convex boundary map is the result of updating the boundary to reflect the concave features. This process involves traversing all position data on the first boundary, identifying the concave points by calculating the cosine value of the angle, and making adjustments. The boundary indentation map provides a more accurate representation of the sub-region boundary and provides a more precise basis for subsequent boundary integration.
[0107] After the concave hull detection is completed, the key boundary points can also be optimized, redundant points can be automatically removed, and the curvature of the boundary can be adjusted as needed to achieve the best accuracy. For example, the threshold for retaining boundary points can be set by the scaling factor, and points that contribute little to the boundary shape or are repeated can be automatically removed. Figure 6 For each pair of adjacent boundary points on the network, the spatial distance between them (such as Euclidean distance) can be calculated; a distance threshold is defined according to the scaling factor. If the distance between two points is less than this threshold, one of the points can be considered redundant and can be deleted; the boundary points are traversed, and when it is detected that the distance between two points is less than the threshold, one of the points is deleted until the distance between all points is greater than the threshold.
[0108] In addition, a curvature threshold can be set based on the size of the scaling factor to determine whether curve fitting is required when connecting boundary points to improve the smoothness of the boundary description. For the retained boundary points, check whether the line between each pair of points needs to be adjusted to a curve. If the straight line connection between the points exceeds the set curvature threshold (i.e., it looks too stiff or unnatural), a curve fitting algorithm (such as Bezier curve, spline curve) is used to connect these points to form a smoother boundary.
[0109] Figure 7 is a schematic diagram of a concave boundary of a method for determining a region boundary according to an embodiment of the present application, such as Figure 7 As shown, it is optimized based on the boundary indentation map using the scaling factor to ensure that the boundary is visually smooth enough without losing key geographic precision, maintaining the accuracy and reliability of the boundary description.
[0110] On the basis of generating the first boundary of the sub-region, the second boundary of the final target region may be generated in the same manner (such as boundary algorithm, detecting depressions, etc.), which will not be described in detail herein.
[0111] After completing the boundary calculation of the target area, a set of optimized boundary longitude and latitude coordinate points can be generated and the results can be output to the next step for processing. The longitude and latitude data processed by the boundary algorithm needs to be further restored to ensure that the data remains compatible in the final application. The specific steps are as follows:
[0112] (1) Format restoration: The longitude and latitude data output by the boundary algorithm is restored to a standard format that meets the application requirements. For example, the corresponding format is output according to different application requirements.
[0113] (2) Precision adjustment: For the precision adjusted during the boundary calculation process, the coordinate precision can be reset according to the output requirements to ensure that the boundary reaches the required level of detail in the display or analysis.
[0114] (3) Data verification: Perform quality control on the converted data to ensure that no errors are introduced. This includes checking data integrity and verifying the validity of polygons (such as the absence of self-intersections).
[0115] (4) Coordinate serialization: In order to be compatible with different data formats or application platforms, the processed coordinate points are serialized and converted into JSON, XML or other formats to ensure that the boundary data can be used across platforms or systems.
[0116] (5) Data output: Finally, the processed data is output to the specified target, which can be a file in the file system, a database table, or other application.
[0117] Figure 8 is a schematic diagram of a target boundary of a method for determining a region boundary according to an embodiment of the present application, such as Figure 8 As shown in the figure, the precise boundary of the target area is generated by integrating and adjusting the boundaries of multiple sub-areas. This boundary map not only includes the boundaries of all sub-areas, but also more accurately depicts the shape of the target area by updating the concave features, providing accurate basic data for geographic information processing.
[0118] This application adopts a step-by-step convergence method to clarify and optimize the boundary division between grids, package areas (corresponding to the sub-areas of the target area) and branches (corresponding to the target area). Specifically, this process starts with the lower-level grid, whose boundary data is converged and integrated, and the boundary outline of the package area is constructed on this basis. Subsequently, the boundary information of these package areas is merged again to form the boundary definition of the branch. This process is progressive layer by layer until the boundaries of higher-level areas are accurately depicted, ensuring the clarity of the data level and the seamless transmission of boundary information. Through this grid-based hierarchical bearing and step-by-step convergence mechanism, not only can the integrity and accuracy of the boundaries of different levels be maintained, but also excellent computing efficiency is demonstrated in the face of large-scale data processing, making full use of the bearing relationship between levels to achieve effective integration and transmission of boundary information, laying the foundation for the accuracy and efficiency of the entire regional boundary characterization.
[0119] Fig. 9 is a schematic diagram of a hierarchical characterization process of a method for determining a region boundary according to an embodiment of the present application, such as Fig. 9 As shown, first, the package area is composed of multiple grids, each of which has its own boundary description. These boundary descriptions are based on the latitude and longitude coordinates of the smallest cell and are used to define the specific range of the grid. From grid 1 to grid n, each grid points to the package area to which it belongs through an arrow. For example, grid 1 and grid 2 both point to package area 1, indicating that they are components of package area 1. Secondly, a branch office is composed of one or more package areas, representing a larger maintenance and management area. From package area 1, package area 2 to package area n, arrows point to the branch office. For example, package area 1 and package area 2 both point to branch office 1, and package area n points to branch office n, indicating that multiple package areas can belong to the same branch office.
[0120] The boundary characterization process starts from the grid, and finally forms the boundary description of the branch through standardization, concave hull boundary calculation, boundary convergence, boundary optimization, etc. This process ensures the consistency, accuracy and compatibility of boundary data, while improving the efficiency and accuracy of boundary description in complex areas.
[0121] Fig.10 This is a flow chart of a method for determining a region boundary according to an embodiment of the present application, which describes in detail the process from acquiring data to outputting a standardized boundary, specifically including the following steps:
[0122] (1) Obtaining the minimum unit boundary data: that is, obtaining the grid data from the original grid map, collecting the position data of all grids, and preparing for subsequent processing.
[0123] (2) Data standardization: Based on the location data obtained in step 1, standardization is performed. This process may include format unification, data cleaning and preprocessing to ensure data consistency and accuracy.
[0124] (3) Concave hull algorithm processing: After data standardization, the concave hull algorithm is applied to the standardized data to identify and correct possible boundary concavity problems. For example, it can include traversing all position data on the first boundary, determining the concavity points that need to be adjusted by calculating the cross product and the cosine value of the angle, and generating a more accurate boundary representation.
[0125] This application makes special adjustments and improvements to the boundary algorithm to adapt to the special needs and data characteristics of more complex enterprise management areas, maintenance areas, etc.: First, the standard boundary algorithm usually directly processes a given set of coordinate points, while this application aggregates and pre-processes the longitude and latitude data of multiple minimum cells before starting the calculation. This step not only reads the data, but also includes deduplication, sorting, and conversion of coordinate formats to ensure that all input data is unified and non-redundant. Secondly, the minimum cell convex hull algorithm is used to perform preliminary boundary calculations on the input longitude and latitude data. By constructing the minimum outer boundary, the area range of the minimum cell can be more accurately depicted, and a clear starting point is provided for subsequent boundary algorithm processing. Finally, special attention is paid to boundary optimization, especially in concave hull detection and precision control of boundary points. For example, through sophisticated vector angle calculation and concave detection, irregular or concave parts in the boundary can be identified and corrected, and the precise outline of the regional boundary can be depicted.
[0126] (4) Data standardization output: After the concave hull algorithm is used, the boundary data is standardized again to generate the final boundary map. The standardized output ensures the consistency of the data format, which is convenient for storage, transmission and further processing. The format restoration process ensures the compatibility of the boundary data with various geographic information systems, which facilitates the cross-platform application and display of data. The restored data can adapt to different coordinate format requirements while maintaining high details and accuracy, so that the boundary delineation results can be more widely used in geographic information systems and large-scale geographic data processing tasks.
[0127] Fig.11 is a structural diagram of a device for determining a region boundary according to an embodiment of the present application, such as Fig.11 As shown, the device comprises:
[0128] An acquisition module 1102 is used to acquire the position data of all grids in a target area in a rasterized map, wherein the target area includes multiple sub-areas, a grid is a minimum maintenance unit in the rasterized map, and each sub-area includes at least one grid;
[0129] A determination module 1104, configured to determine first boundaries corresponding to the plurality of sub-areas respectively according to the position data;
[0130] The integration module 1106 is used to integrate the first boundaries corresponding to the multiple sub-regions to obtain the second boundary of the target region.
[0131] It should be noted that Fig.11 The region boundary determination device shown is used to perform Figure 2 The method for determining the region boundaries shown is therefore Figure 2 The relevant explanations in the method of determining the regional boundaries in Fig.11 The device for determining the area boundary shown will not be described in detail here.
[0132] An embodiment of the present application also provides an electronic device, which includes a memory and a processor, wherein the memory is used to store program instructions; the processor is connected to the memory and is used to execute the steps of the method for determining the area boundary in each embodiment of the present application.
[0133] For example, the processor performs the following functions by executing program instructions stored in the memory:
[0134] The position data of all grids in the target area in the rasterized map are obtained, wherein the target area includes multiple sub-areas, the grid is the smallest maintenance unit in the rasterized map, and each sub-area includes at least one grid; first boundaries corresponding to the multiple sub-areas are determined according to the position data; and the first boundaries corresponding to the multiple sub-areas are integrated to obtain a second boundary of the target area.
[0135] An embodiment of the present application further provides a non-volatile storage medium, which includes a stored computer program, wherein the device where the non-volatile storage medium is located executes the steps of the method for determining the area boundary in each embodiment of the present application by running the computer program.
[0136] An embodiment of the present application further provides a computer program product, including computer instructions, which, when executed by a processor, implement the steps of the method for determining the region boundary in each embodiment of the present application.
[0137] The embodiments of the present application also provide a computer program, which, when executed by a processor, implements the steps of the method for determining the region boundary in each embodiment of the present application.
[0138] The serial numbers of the above-mentioned embodiments of the present application are for description only and do not represent the advantages or disadvantages of the embodiments.
[0139] In the above embodiments of the present application, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, please refer to the relevant description of other embodiments.
[0140] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only schematic. For example, the division of the units can be a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of units or modules, which can be electrical or other forms.
[0141] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple units. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.
[0142] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.
[0143] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, a server or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, disk or optical disk and other media that can store program codes.
[0144] 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 modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.
Claims
1. A method for determining a region boundary, characterized in that: include: Acquire location data of all grids in a target area in a rasterized map, wherein the target area includes a plurality of sub-areas, the grid is a minimum maintenance unit in the rasterized map, and each sub-area includes at least one grid; Determining first boundaries corresponding to the plurality of sub-areas respectively according to the position data; The first boundaries respectively corresponding to the multiple sub-regions are integrated to obtain a second boundary of the target region.
2. The method according to claim 1, characterized in that Determining first boundaries corresponding to the plurality of sub-areas respectively according to the position data includes: Determine a first data set from the position data, wherein the first data set includes position data corresponding to all grids in any sub-area; Determine a first first endpoint and a first last endpoint from the first data set, and generate a first initial boundary corresponding to the first first endpoint and the first last endpoint; Traversing the first data set, determining first target data from the first data set, wherein the first target data is used to expand the coverage corresponding to the first initial boundary; The first initial boundary is updated according to the first target data, and the updated first initial boundary is determined as the first boundary.
3. The method according to claim 2, characterized in that Traversing the first data set and determining first target data from the first data set includes: Acquire first position data and second position data on the first initial boundary, wherein the first position data and the second position data are adjacent and continuous on the first initial boundary; Determine a cross product between any one data in the first data set, the first position data, and the second position data, wherein the cross product is used to represent a positional relationship between the any one data and the first position data and the second position data; When the cross product is greater than zero, the data corresponding to the cross product is determined to be the first target data.
4. The method according to claim 3, characterized in that It is determined that the first position data and the second position data are adjacent and continuous on the first initial boundary in the following case: In a case where the first position data and the second position data are two end points of the first initial boundary respectively, it is determined that the first position data and the second position data are adjacent and continuous on the first initial boundary.
5. The method according to claim 1, characterized in that After determining the first boundary, the method further includes: Traversing all position data on the first boundary, and determining second target data from all position data on the first boundary, wherein the second target data is used to reflect the concave feature of the first boundary; The first boundary is updated according to the second target data.
6. The method according to claim 5, characterized in that Traversing all the position data on the first boundary and determining the second target data from all the position data on the first boundary includes: Acquire third position data, fourth position data, and fifth position data on the first boundary, wherein the third position data, the fourth position data, and the fifth position data are sequentially adjacent on the first boundary; Generate a first vector corresponding to the fourth position data and the third position data, and a second vector corresponding to the fourth position data and the fifth position data; determining a cosine value of an angle between the first vector and the second vector; When the cosine value of the angle is less than zero, the fourth position data is determined to be the second target data.
7. The method according to claim 1, characterized in that Integrating the first boundaries respectively corresponding to the plurality of sub-regions to obtain a second boundary of the target region includes: Acquire a second data set corresponding to the first boundary, wherein the second data set includes position data contained in the first boundary corresponding to all sub-areas; Determine a second first endpoint and a second last endpoint from the second data set, and generate a second initial boundary corresponding to the second first endpoint and the second last endpoint; Traversing the second data set to determine third target data, wherein the third target data is used to expand the coverage corresponding to the second initial boundary; The second initial boundary is updated according to the third target data, and the updated second initial boundary is determined as the second boundary.
8. The method according to claim 1, characterized in that After determining the second boundary, the method further includes: Traversing all position data on the second boundary, and determining fourth target data from all position data on the second boundary, wherein the fourth target data is used to reflect the concave feature of the second boundary; The second boundary is updated according to the fourth target data.
9. The method according to claim 2, characterized in that: Determining a first first endpoint and a first last endpoint from the first data set, and generating a first initial boundary corresponding to the first first endpoint and the first last endpoint, includes: Sorting all the position data in the first data set according to a preset rule to obtain a data sequence; Determine the head end data of the data sequence as the first head end point, and determine the tail end data of the data sequence as the first tail end point; A line connecting the first first endpoint and the first tail endpoint is determined as the first initial boundary.
10. A device for determining a region boundary, characterized in that: include: An acquisition module, used for acquiring the position data of all grids in a target area in a rasterized map, wherein the target area includes a plurality of sub-areas, the grid is the smallest maintenance unit in the rasterized map, and each sub-area includes at least one grid; A determination module, configured to determine first boundaries corresponding to each of the plurality of sub-areas according to the position data; The integration module is used to integrate the first boundaries respectively corresponding to the multiple sub-areas to obtain the second boundary of the target area.
11. An electronic device, characterized in that: include: A memory and a processor, wherein the memory is used to store program instructions; the processor is connected to the memory and is used to execute the method for determining the area boundary as described in any one of claims 1 to 9.
12. A non-volatile storage medium, characterized in that: The non-volatile storage medium includes a stored computer program, wherein the device where the non-volatile storage medium is located executes the method for determining the area boundary according to any one of claims 1 to 9 by running the computer program.
13. A computer program product comprising computer instructions, characterized in that: When the computer instructions are executed by a processor, the method for determining the region boundary described in any one of claims 1 to 9 is implemented.