Space level system construction method and system based on multiplication weighted Voronoi diagram

Abstract

The invention discloses a spatial level system construction method and system based on a multiplication weighted Voronoi diagram, and the method comprises the steps: carrying out the abstract processing of a geographic entity space, and constructing a geographic entity point set; generating a multiplication weighted Voronoi diagram according to the geographic entity point set, constructing a corresponding spatial level, and determining a local center point level; according to the level of the local center point, carrying out space level structure division on the geographic entity point set, and constructing a divided k-level multiplication weighted Voronoi graph; and determining the spatial level of the geographic entity point set according to the divided k-level multiplication weighted Voronoi diagram, and realizing the construction of a spatial level system. The spatial mutual influence can be considered during spatial hierarchy establishment and spatial level system division, and the spatial hierarchy level division precision is improved. The spatial hierarchy level construction method and system based on the multiplication weighted Voronoi diagram can be widely applied to the field of geographic entity spatial planning.

Description

Technical Field

[0001] This invention relates to the field of spatial planning of geographic entities, and in particular to a method and system for constructing a spatial hierarchy system based on multiplicative weighted Voronoi diagrams. Background Technology

[0002] Spatial hierarchy is a comprehensive representation of the spatial and hierarchical structure of geographic entities. Generally, geographic entities with spatial hierarchy have three characteristics: first, geographic entities can be abstracted into points with attribute information; second, spatial hierarchy can be distinguished through the attribute information of abstract points; and third, geographic entities can be configured into a reasonable spatial hierarchy system based on their spatial location and attribute information. Studying spatial hierarchy has significant theoretical and practical implications, effectively revealing the spatial order of a system. For example, studying urban hierarchy systems can provide auxiliary decision-making for urban agglomeration division and urban development strategy formulation; studying the hierarchy systems of educational, elderly care, and commercial facilities can establish regional supply and demand balances, providing decision support for facility site selection and resource allocation.

[0003] Voronoi diagram method, weighted Voronoi Figure 2 Step-by-step clustering and gravity modeling are three commonly used methods for constructing spatial hierarchies of geographic entities. Among them, the Voronoi diagram method, when establishing the spatial hierarchy of a geographic entity set P, determines the hierarchy by the weight relationship between each generator in P and its neighboring Voronoi region generators. It is a bottom-up hierarchy confirmation method, highly objective, requiring no manual grading, and producing unique results. Furthermore, P represents different spatial features, which does not affect its spatial hierarchy classification. However, its current shortcoming is that when determining the inclusion relationship between hierarchical geographic entities using Voronoi regions, it does not consider the spatial interactions between geographic entities. Multiplicative weighted Voronoi diagrams are another method. Figure 2 Step-by-step clustering and gravity modeling are top-down hierarchical identification methods that consider spatial interactions between geographic entities when establishing the hierarchy of a geographic entity set P. However, they require manual hierarchical assignment and are highly subjective. Since the hierarchy principles change depending on the different geographic entities represented by P, the generated results are not unique. Summary of the Invention

[0004] To address the aforementioned technical problems, the present invention aims to provide a method and system for constructing a spatial hierarchy based on a multiplicative weighted Voronoi diagram. This method and system can consider the mutual influence of spaces when establishing spatial levels and dividing spatial hierarchy systems, thereby improving the accuracy of spatial hierarchy division.

[0005] The first technical solution adopted in this invention is: a method for constructing a spatial hierarchy system based on multiplicative weighted Voronoi diagrams, comprising the following steps: Abstracting the spatial representation of geographic entities to construct a set of geographic entity points; A multiplicative weighted Voronoi diagram is generated based on the set of geographic entity points, and the corresponding spatial hierarchy is constructed to determine the local center point hierarchy. Based on the local center point hierarchy, the spatial structure of the geographic entity point set is divided, and a k-level multiplicative weighted Voronoi diagram is constructed after the division. The spatial hierarchy of geographic entity point sets is determined based on the k-level multiplicative weighted Voronoi diagram after partitioning, thereby realizing the construction of a spatial hierarchy system.

[0006] Furthermore, the step of abstracting the geographic entity space and constructing a set of geographic entity points specifically includes: Abstracting geographic entities into a set of points; Assign a weight value to each point in the point set to construct a weight set; By combining point sets and weight sets, a spatial configuration of point sets is constructed to generate geographic entity point sets.

[0007] Furthermore, the step of generating a multiplicative weighted Voronoi diagram based on the set of geographic entity points, constructing the corresponding spatial hierarchy, and determining the local center point hierarchy specifically includes: Generate a multiplicative weighted Voronoi diagram of the set of geographic entity points, and obtain a multiplicative weighted Voronoi region set; The points in the multiplicative weighted Voronoi region set that satisfy the neighborhood weight condition are determined as the local center points of the multiplicative weighted Voronoi region set; If the spatial configuration of the point set is defined as the 0th level spatial configuration, then the local center points of the multiplicative weighted Voronoi region set are determined as the 1st level local center point set and the 1st level spatial configuration. Repeat the steps of generating multiplicative weighted Voronoi diagrams and determining local centroids until the number of points in the local centroid set of the m-th layer is less than a set threshold, and then determine the local centroid level. Based on the local center point hierarchy, the set of local center points at level m is defined as the first-level point set, thus determining the local center point level.

[0008] Furthermore, the expression for the neighborhood weight condition is as follows: ; In the above formula, express The point set corresponding to the first-order multiplicative weighted Voronoi neighborhood. express One of the points, This indicates the formula for calculating the weights.

[0009] Furthermore, the step of dividing the spatial hierarchy of geographic entity point sets based on the local center point hierarchy and constructing the divided k-level multiplicative weighted Voronoi diagram specifically includes: Determine the set of k-level geographic entity points based on the local center point level; Based on the first-level spatial configuration, generate a first-level multiplicative weighted Voronoi diagram; Based on the spatial inclusion relationship between the second-level point set and the first-level multiplicative weighted Voronoi graph, and combined with the preset spatial hierarchy association conditions of neighboring points, the subsets that intersect between the second-level point set and the first-level multiplicative weighted Voronoi graph are reorganized to construct the second-level multiplicative weighted Voronoi graph. Repeatedly construct the next level of multiplicative weighted Voronoi diagram until the k-level geographic entity point set is traversed, and construct the partitioned k-level multiplicative weighted Voronoi diagram.

[0010] Furthermore, the expression for the preset spatial hierarchy association condition of neighboring points is as follows: ; In the above formula, This represents the first-level point set. Indicates a first-level point. express Remove Other points, Indicates a second-level point. This represents the multiplicative weighted Voronoi region of a point.

[0011] Furthermore, the step of determining the spatial hierarchy of geographic entity point sets based on the partitioned k-level multiplicative weighted Voronoi diagram, thereby constructing a spatial hierarchy system, specifically includes: The spatial hierarchy of the geographic entity point set is determined based on the k-level multiplicative weighted Voronoi diagram after partitioning; Based on the spatial hierarchy of the geographic entity point set, a spatial hierarchy relationship diagram of the geographic entity point set is drawn to realize the spatial hierarchy construction.

[0012] The second technical solution adopted in this invention is: a spatial hierarchy system construction system based on multiplicative weighted Voronoi diagrams, comprising: The first module is used to abstract the spatial representation of geographic entities and construct a set of geographic entity points. The second module is used to generate a multiplicative weighted Voronoi diagram based on the set of geographic entity points, construct the corresponding spatial hierarchy, and determine the level of local center points. The third module is used to divide the spatial hierarchy of geographic entity point sets according to the local center point level, and to construct the k-level multiplicative weighted Voronoi diagram after the division. The fourth module is used to determine the spatial hierarchy of the geographic entity point set based on the k-level multiplicative weighted Voronoi diagram after partitioning, thereby realizing the construction of the spatial hierarchy system.

[0013] The beneficial effects of the method and system of this invention are as follows: This invention abstracts the spatial structure of geographic entities to construct a set of geographic entity points; then, it generates a multiplicative weighted Voronoi diagram based on the geographic entity point set and constructs a corresponding spatial hierarchy to determine the level of local centroids; based on the spatial location and weight of the point set, and taking into account the spatial interaction of the point set, it generates a multiplicative weighted Voronoi diagram; further, it divides the spatial hierarchy structure of the geographic entity point set according to the level of local centroids, constructing a k-level multiplicative weighted Voronoi diagram; finally, it determines the spatial hierarchy of the geographic entity point set based on the k-level multiplicative weighted Voronoi diagram, realizing the construction of a spatial hierarchy system. This overcomes the problem that the Voronoi diagram method does not consider the spatial interaction between geographic entities, and also overcomes the limitations of the multiplicative weighted Voronoi diagram method. Figure 2 The step clustering method and the gravity model method require human classification, which is highly subjective. The method considers the mutual influence of space when establishing spatial hierarchy and dividing spatial hierarchy system, generates unique results, and improves the accuracy of spatial hierarchy classification. It is a process of first establishing spatial hierarchy from bottom to top and then establishing spatial hierarchy from top to bottom. Attached Figure Description

[0014] Figure 1 This is a flowchart illustrating the steps of the spatial hierarchy construction method based on multiplicative weighted Voronoi diagrams in this invention. Figure 2 This is a structural block diagram of the spatial hierarchy system based on multiplicative weighted Voronoi diagrams of this invention; Figure 3 This is a schematic diagram of the multiplicative weighted Voronoi diagram of the point set P provided in a specific embodiment of the present invention; Figure 4 This is a schematic diagram of the first-order multiplicative weighted Voronoi region of the local center point p14 provided in a specific embodiment of the present invention; Figure 5 This is a schematic diagram of the multiplicative weighted Voronoi region generated by the first layer local center and the first-order multiplicative weighted Voronoi region of the local center point p14 provided in a specific embodiment of the present invention; Figure 6 This is a schematic diagram of the spatial hierarchy of point set P provided in a specific embodiment of the present invention; Figure 7 This is a schematic diagram of the spatial hierarchy of point set P provided in a specific embodiment of the present invention. Detailed Implementation

[0015] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.

[0016] Reference Figure 1 This invention provides a method for constructing a spatial hierarchy based on a multiplicative weighted Voronoi diagram, the method comprising the following steps: S100. Abstract the spatial representation of geographic entities and construct a set of geographic entity points; Specifically, the geographic entity space is abstracted into a point set; each point in the point set is assigned a weight value to construct a weight set; the point set and the weight set are combined to construct the spatial configuration of the point set and generate the geographic entity point set.

[0017] In this embodiment, the set of geographic entities is abstracted as a set of points. Each point corresponds to a weight value, and the set of weights can be represented as... Then the point set The spatial configuration can be represented as .

[0018] S200. Generate a multiplicative weighted Voronoi diagram based on the set of geographic entity points, construct the corresponding spatial hierarchy, and determine the local center point level; Specifically, a multiplicative weighted Voronoi diagram of the geographic entity point set is generated, resulting in a multiplicative weighted Voronoi region set. Points in the multiplicative weighted Voronoi region set that satisfy the neighborhood weight condition are identified as local centroids of the multiplicative weighted Voronoi region set. The spatial configuration of the point set is defined as the 0th layer spatial configuration, and the local centroids of the multiplicative weighted Voronoi region set are identified as the 1st layer local centroid set and the 1st layer spatial configuration. The steps of generating the multiplicative weighted Voronoi diagram and determining the local centroids are repeated until the number of points in the m-th layer local centroid set is less than a set threshold, thus determining the local centroid level. Based on the local centroid level, the m-th layer local centroid set is defined as the 1st level point set, thus determining the local centroid grade.

[0019] In this embodiment, establish Spatial hierarchy, first generated The multiplicative weighted Voronoi diagram yields the multiplicative weighted Voronoi region set. The outer boundary of a multiplicative weighted Voronoi diagram is a set of points. The smallest outer rectangle is obtained by expanding it outward by a certain distance.

[0020] like Figure 3 The diagram shows a multiplicative weighted Voronoi plot containing 27 points, where each point corresponds to a unique multiplicative weighted Voronoi region. Each point in the plot can be represented as... ,in, Indicates the point number. This represents the weight of a point.

[0021] Further determine the local center point. If... a certain point in the middle A point that satisfies the following neighborhood weight formula can be established as a local center point, and its expression is: ; In the above formula, express The point set corresponding to the first-order multiplicative weighted Voronoi neighborhood. express One of the points, This indicates the formula for calculating the weights. The formula above shows that if... a certain point in the middle If the weight of a point is greater than the weight of the points in its first-order multiplicative weighted Voronoi neighborhood, then... It can be established as a local center point.

[0022] like Figure 4 As shown, point The first-order multiplicative weighted Voronoi neighborhood is marked in gray, corresponding to the set of generators. .because, Weight greater than The weights of all generators within a neighborhood satisfy the neighborhood weight formula; therefore, we establish... It is the local center. Similarly, it can be determined that... and It is the local center.

[0023] Further determine the local center point hierarchy. Defined as the 0th level spatial configuration, i.e. After determining the local center points and the hierarchy of local center points, the set of local center points at the first level can be determined. and the configuration of the first layer of space By repeatedly determining the local center point and the hierarchy of local center points, the spatial configuration can be obtained. , When the first When the number of points in the local centroid set of a layer is less than a set threshold (the threshold is usually set to 1), the layering process ends, and the final local centroid set configuration is determined. .

[0024] Depend on Figure 4The local center of the first layer can be determined. .generate The multiplicative weighted Voronoi diagram, as shown in Figure 5, can determine the local centers of the second layer. .

[0025] Finally, the local center point level was determined. The local center point set of a layer is defined as the first-level point set, denoted as... Then the first The local center point set of a layer is defined as the first Level Center .

[0026] For the first and second layer local centers formed in the previous steps , The local center can be represented by a hierarchy of local centers: the first-level local center is... The second-level local center is .

[0027] S300. Divide the spatial hierarchy of geographic entity point sets according to the local center point level, and construct the k-level multiplicative weighted Voronoi diagram after the division. Specifically, based on the local center point level, a k-level geographic entity point set is determined; based on the first-level spatial configuration, a first-level multiplicative weighted Voronoi diagram is generated; based on the spatial inclusion relationship between the second-level point set and the first-level multiplicative weighted Voronoi diagram, and combined with the preset spatial level association conditions of adjacent points, the subsets intersecting the second-level point set and the first-level multiplicative weighted Voronoi diagram are reorganized to construct a second-level multiplicative weighted Voronoi diagram; the next level multiplicative weighted Voronoi diagram is constructed repeatedly until the k-level geographic entity point set is traversed, and the partitioned k-level multiplicative weighted Voronoi diagram is constructed.

[0028] In this embodiment, the spatial hierarchy of P is established by first assuming that a k-level point set is established based on the point set P. Based on the first-level spatial configuration... Generate a first-order multiplicative weighted Voronoi diagram. . Indicates the first level point The multiplicative weighted Voronoi region.

[0029] like Figure 6 As shown, The first-level local center is represented by a square, and the gray area is its multiplicative weighted Voronoi region.

[0030] Then, based on the spatial configuration Determine the level 2 point set Voronoi diagram with first-order multiplicative weighted graph The spatial inclusion relationships of each multiplicative weighted Voronoi region are recombined. , represented as . Indicates the relationship with the first-level point The set of points intersecting the multiplicative weighted Voronoi regions, for any The spatial hierarchy association formula for adjacent points must be satisfied: ; In the above formula, This represents the first-level point set. Indicates a first-level point. express Remove Other points, Indicates a second-level point. This represents the multiplicative weighted Voronoi region of a point.

[0031] The above formula shows that: for a set of points at the next level that has a spatial hierarchical relationship with a point at the next level, each point in the set is contained in the multiplicative weighted Voronoi region of the point at the next level.

[0032] Utilize point set Corresponding division The resulting multiplicative weighted Voronoi region set This is called a second-order multiplicative weighted Voronoi diagram. For any It must satisfy the adjacent-level multiplicative weighted Voronoi spatial hierarchy correlation formula: ; In the above formula, This represents the first-level point set. Indicates a first-level point. express Remove Other points, Indicates a second-level point. This represents the multiplicative weighted Voronoi region of a point. This indicates the area function. The spatial hierarchy relation formula of the neighboring multiplicative weighted Voronoi region shows that for a set of points in the next level that has a spatial hierarchy relationship with a point in the previous level, the multiplicative weighted Voronoi region of each point in the set is contained in the multiplicative weighted Voronoi region of the point in the previous level.

[0033] Repeat the above steps until the k-th level multiplicative weighted Voronoi diagram partitioning is completed.

[0034] like Figure 6 As shown, The second-level local center is represented by a triangle. Located in the first-order multiplicative weighted Voronoi region ,Right now In the middle, utilizing space configuration Division This yields the second-order multiplicative weighted Voronoi region. Each area is represented by a solid black line. The third-level local center is represented by a circular symbol. lie in In the middle, the spatial configuration ; lie in In the middle, the spatial configuration ; lie in In the middle, the spatial configuration Utilizing space configuration Division Utilizing space configuration Division Utilizing space configuration Division This yields the third-order multiplicative weighted Voronoi region. ,in, Depend on It consists of a multiplicative weighted Voronoi region of 15 points. Depend on It consists of a multiplicative weighted Voronoi region of 9 points. Depend on The weighted Voronoi region with four points is represented by a blue solid line.

[0035] S400. Determine the spatial hierarchy of the geographic entity point set based on the k-level multiplicative weighted Voronoi diagram after partitioning, and realize the construction of the spatial hierarchy system.

[0036] Specifically, the spatial hierarchy of the geographic entity point set is determined based on the k-level multiplicative weighted Voronoi diagram after partitioning; a spatial hierarchy relationship diagram of the geographic entity point set is drawn based on the spatial hierarchy of the geographic entity point set, thereby realizing the construction of the spatial hierarchy system.

[0037] In this embodiment, based on the determined spatial hierarchy of point set P, a spatial hierarchy relationship diagram of point P is established using GIS software. Points of different levels can be represented by different point symbols, and points of different levels can be represented by different line symbols.

[0038] like Figure 7As shown, the first to third level local centers are represented by square, triangle and circle symbols respectively. The line connecting the first level local center and the second level local center is represented by a thick blue solid line. The second level local center and the third level local center are represented by a thin gray solid line, forming a spatial hierarchy connection diagram of point set P.

[0039] In summary, this invention provides a spatial hierarchy classification method based on multiplicative weighted Voronoi diagrams. First, geographic entities are abstracted into sets of spatial points with weights and location information. Based on the spatial location and weights of these points, and considering their spatial interactions, a multiplicative weighted Voronoi diagram is generated. Then, based on the spatial location relationships within the multiplicative weighted Voronoi diagram and the point weights, the spatial hierarchy of the point sets is determined from bottom to top. Next, the spatial levels of the point sets are determined in reverse order based on their spatial levels, generating multiplicative weighted Voronoi diagrams level by level to define the spatial hierarchy structure between point sets. Finally, using GIS software, a spatial hierarchy structure relationship diagram of the point sets is constructed. This method overcomes the problem of Voronoi diagrams not considering spatial interactions between geographic entities and also overcomes the limitations of multiplicative weighted Voronoi diagrams. Figure 2 While methods like step-by-step clustering and gravity models require manual grading and are highly subjective, this approach considers spatial interactions when establishing spatial hierarchies and classifying spatial hierarchical systems, thus better representing geographical patterns. The implementation process is unaffected by subjective factors, generating unique results, making it a relatively objective method for modeling spatial hierarchical systems. In a GIS environment, through map refinement, it displays the spatial hierarchy of geographic entities, making it a highly applicable method for visualizing geoscientific hierarchical data.

[0040] Reference Figure 2 A spatial hierarchy system based on multiplicative weighted Voronoi diagrams includes: The first module 201 is used to abstract the spatial data of geographic entities and construct a set of geographic entity points. The second module 202 is used to generate a multiplicative weighted Voronoi diagram based on the set of geographic entity points, construct the corresponding spatial hierarchy, and determine the level of local center points; The third module 203 is used to divide the spatial hierarchy of geographic entity point sets according to the local center point level, and to construct the k-level multiplicative weighted Voronoi diagram after the division. Module 404 is used to determine the spatial hierarchy of the geographic entity point set based on the k-level multiplicative weighted Voronoi diagram after partitioning, thereby realizing the construction of a spatial hierarchy system.

[0041] The content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0042] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A method for constructing a spatial hierarchy based on multiplicative weighted Voronoi diagrams, characterized in that, Includes the following steps: Abstracting the spatial representation of geographic entities to construct a set of geographic entity points; A multiplicative weighted Voronoi diagram is generated from the set of geographic entity points, and the corresponding spatial hierarchy is constructed to determine the level of local center points. Based on the local center point level, the spatial hierarchy of the geographic entity point set is divided, and a k-level multiplicative weighted Voronoi diagram is constructed. The spatial hierarchy of geographic entity point sets is determined based on the k-level multiplicative weighted Voronoi diagram after partitioning, thereby realizing the construction of a spatial hierarchical system.

2. The spatial hierarchy construction method based on multiplicative weighted Voronoi diagrams according to claim 1, characterized in that, The step of abstracting geographic entity space and constructing a set of geographic entity points specifically includes: Abstracting geographic entities into a set of points; Assign a weight value to each point in the point set to construct a weight set; By combining point sets and weight sets, a spatial configuration of point sets is constructed to generate geographic entity point sets.

3. The method for constructing a spatial hierarchy based on a multiplicative weighted Voronoi diagram according to claim 2, characterized in that, The step of generating a multiplicative weighted Voronoi diagram based on a set of geographic entity points, constructing a corresponding spatial hierarchy, and determining the level of local centroids specifically includes: Generate a multiplicative weighted Voronoi diagram of the set of geographic entity points, and obtain a multiplicative weighted Voronoi region set; The points in the multiplicative weighted Voronoi region set that satisfy the neighborhood weight condition are determined as the local center points of the multiplicative weighted Voronoi region set; If the spatial configuration of the point set is defined as the 0th level spatial configuration, then the local center points of the multiplicative weighted Voronoi region set are determined as the 1st level local center point set and the 1st level spatial configuration. Repeat the steps of generating multiplicative weighted Voronoi diagrams and determining local centroids until the number of points in the local centroid set of the m-th layer is less than a set threshold, and then determine the local centroid level. Based on the local center point hierarchy, the set of local center points at level m is defined as the first-level point set, thus determining the local center point level.

4. The spatial hierarchy construction method based on multiplicative weighted Voronoi diagrams according to claim 3, characterized in that, The specific expression for the neighborhood weight condition is as follows: ； In the above formula, express The point set corresponding to the first-order multiplicative weighted Voronoi neighborhood. express One of the points, This indicates the formula for calculating the weights.

5. The method for constructing a spatial hierarchy based on a multiplicative weighted Voronoi diagram according to claim 4, characterized in that, The step of dividing the spatial hierarchy of geographic entity point sets according to the local centroid level and constructing the k-level multiplicative weighted Voronoi diagram after division specifically includes: Determine the set of k-level geographic entity points based on the local center point level; Based on the first-level spatial configuration, generate a first-level multiplicative weighted Voronoi diagram; Based on the spatial inclusion relationship between the second-level point set and the first-level multiplicative weighted Voronoi graph, and combined with the preset spatial hierarchy association conditions of neighboring points, the subsets that intersect between the second-level point set and the first-level multiplicative weighted Voronoi graph are reorganized to construct the second-level multiplicative weighted Voronoi graph. Repeatedly construct the next level of multiplicative weighted Voronoi diagram until the k-level geographic entity point set is traversed, and construct the partitioned k-level multiplicative weighted Voronoi diagram.

6. The spatial hierarchy construction method based on multiplicative weighted Voronoi diagrams according to claim 5, characterized in that, The expression for the preset spatial hierarchy association condition of adjacent points is as follows: ； In the above formula, This represents the first-level point set. Indicates a first-level point. express Remove Other points, Indicates a second-level point. This represents the multiplicative weighted Voronoi region of a point.

7. The method for constructing a spatial hierarchy based on a multiplicative weighted Voronoi diagram according to claim 6, characterized in that, The step of determining the spatial hierarchy of geographic entity point sets based on the partitioned k-level multiplicative weighted Voronoi diagram, thereby constructing the spatial hierarchy system, specifically includes: The spatial hierarchy of the geographic entity point set is determined based on the k-level multiplicative weighted Voronoi diagram after partitioning; Based on the spatial hierarchy of geographic entity point sets, a spatial hierarchy relationship diagram of geographic entity point sets is drawn to realize the construction of a spatial hierarchy system.

8. A spatial hierarchy system based on multiplicative weighted Voronoi diagrams, characterized in that, Includes the following modules: The first module is used to abstract the spatial representation of geographic entities and construct a set of geographic entity points. The second module is used to generate a multiplicative weighted Voronoi diagram based on the set of geographic entity points, construct the corresponding spatial hierarchy, and determine the level of local center points. The third module is used to divide the spatial hierarchy of geographic entity point sets according to the local center point level, and to construct the k-level multiplicative weighted Voronoi diagram after the division. The fourth module is used to determine the spatial hierarchy of geographic entity point sets based on the k-level multiplicative weighted Voronoi diagram after partitioning, thereby realizing the construction of a spatial hierarchy system.

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