A Method and System for Deformation Analysis of Global Hexagonal Wargaming Maps Based on Dynamic Comprehensive Deformation Index

Abstract

This invention relates to the field of global wargaming technology, and particularly to a method and system for deformation analysis of a global hexagonal wargaming map based on a dynamic comprehensive deformation index. The method analyzes the area deformation of the global hexagonal wargaming map based on the standard deviation of cell area; it analyzes the shape deformation of the global hexagonal wargaming map based on the standard deviation of adjacent distance; it introduces the average cell area and the average cell adjacent distance to propose a grid area deformation index and a grid shape deformation index; and it constructs a dynamic comprehensive deformation index using these indices to perform an overall deformation analysis of the area and shape deformation of the HGWM. This invention proposes a dynamic comprehensive deformation index to measure the overall deformation of the HGWM, overcoming the limitations of deformation analysis based solely on area and perimeter differences; by dynamically adjusting weight variables, it achieves dynamic analysis of the overall deformation degree of the grid, enabling the selection of a more suitable global hexagonal wargaming map for different types of global wargaming.

Description

Technical Field

[0001] This invention relates to the field of global wargaming technology, and in particular to a method and system for analyzing the deformation of a global hexagonal wargaming map based on a dynamic comprehensive deformation index. Background Technology

[0002] With the rapid development of sensor and remote sensing technologies, high-resolution Earth observation data are rapidly increasing in quality, data types are constantly expanding, and the spatial scope is continuously extending globally. Traditional spatial data models, represented by vector and raster data, are no longer sufficient to meet the demands for accessing and analyzing massive amounts of global data across multiple scales and time series. Global discrete grid systems can effectively integrate geospatial information from different data formats, spatial reference systems, and multiple scales and time series, enabling efficient querying and analysis of massive spatial data. Due to the discrete nature of global discrete grid systems, they have demonstrated significant advantages in parallel computing, which plays a crucial role in promoting spatiotemporal big data analysis.

[0003] Hexagonal Discrete Global Grid Systems (HDGGS) are global discrete grid systems that subdivide the Earth's surface using hexagonal grid cells. Due to the characteristics of hexagons, such as equal adjacency distances, consistent adjacency relationships, and maximum angular resolution, they have been widely used in geographic information science, remote sensing, geophysics, environmental science, and especially in global dynamic modeling. The Hexagonal Global Wargame Map (HGWM) is a wargame map built on HDGGS, integrating data from various environmental elements such as terrain, weather, and oceanography. It supports global wargame simulations and can efficiently interact with various combat models, including maneuver, reconnaissance, and damage models.

[0004] Hexagonal grids on a plane possess favorable geometric properties, such as being closer to a circle than triangles and quadrilaterals, having equal distances to all adjacent cells, exhibiting minimal average error when tiling a plane, and having a discrete distance metric closer to Cartesian distance. However, in HDGGS, individual hexagonal cells do not fully retain these geometric properties, exhibiting varying degrees of area and shape deformation. To provide guidance for different types of specialized applications, many scholars have studied the area and shape deformation of HDGGS.

[0005] White, Kimerling, Sahr, and Song calculated various density ratios and concluded that the icosahedral Schnyder Equal Area (ISEA) projection performed best in terms of area distortion, while the Gnomonic projection performed best in terms of compactness. Kimerling, Sahr, White, and Song argued that comparisons of global mesh geometry should at least consider surface area and compactness, and these metrics should be calculated at the same mesh resolution level. They also calculated spherical surface area, compactness, and center point spacing. Ben Jin et al. proposed two indices—the maximum / minimum side length ratio and the root mean square error of the element perimeter—to analyze the deformation of spherical equal-area hexagonal discrete meshes.

[0006] Since the cell area and perimeter of HDGGS are mainly related to the mesh level, some scholars have proposed an area normalization method to compare and analyze the area and shape deformation of HDGGS at different levels. This method compares and analyzes the degree of mesh deformation between different levels by dividing the area by the average area of ​​all cells at the same resolution level. Alexander Kmoch et al. proposed using normalized area and compactness to compare and analyze the area and shape deformation of cells in five types of DGGS: Uber H3, Google S2, RiskAwareOpenEAGGR, rHEALPix, and DGGRID. Lei et al. proposed using region-normalized compactness to compare and analyze the area and shape deformation of DGGS. Kevin Sahr used the minimum, maximum, average, and standard deviation of the grid spacing to compare and analyze the deformation of various DGGS such as ISEA3H, ISEA4H, PLANETRISK, and ISEA43H.

[0007] The aforementioned studies analyzed area and shape deformation separately, using minimum / maximum, average, and normalized area to analyze area deformation, and maximum / minimum side length ratio, mean square error of cell perimeter, compactness, average grid spacing, and standard deviation to analyze shape deformation. However, they lacked a comprehensive analysis of the overall deformation of HDGGS, which impacts the application of HDGGS-based global hexagonal wargaming maps in fields where global wargaming simulations require consideration of both area and shape deformation. Summary of the Invention

[0008] This invention aims to address the aforementioned deficiencies in the existing technology by proposing a deformation analysis method and system for global hexagonal wargame maps based on a dynamic comprehensive deformation index. The dynamic comprehensive deformation index is proposed to comprehensively measure the area and shape deformation of the HGWM, thus overcoming the limitations of deformation analysis based solely on area and perimeter differences.

[0009] To achieve the above objectives, the technical solution adopted is:

[0010] A deformation analysis method for a global hexagonal wargame map based on a dynamic comprehensive deformation index, comprising:

[0011] Analysis of area deformation of global hexagonal wargame map based on grid area standard deviation;

[0012] Analysis of shape deformation of global hexagonal war game map based on adjacent standard deviation;

[0013] The average cell area and the average cell neighbor distance are introduced, and the mesh area deformation index and the mesh shape deformation index are proposed.

[0014] A dynamic comprehensive deformation index is constructed using the grid area deformation index and the grid shape deformation index to conduct an overall deformation analysis of the area deformation and shape deformation of the global hexagonal wargaming map.

[0015] According to the global hexagonal wargame map deformation analysis method based on dynamic comprehensive deformation index of the present invention, the area deformation analysis of the global hexagonal wargame map based on the standard deviation of cell area further includes:

[0016] For a certain level of a global hexagonal wargame map, the formula for calculating the average area of ​​all cells is as follows:

[0017]

[0018] Where L is the current level of HGWM, and CellNum L Let L be the total number of pentagonal and hexagonal lattice elements in the Lth level of HGWM. Let be the area of ​​the i-th cell in the L-th level of HGWM;

[0019] The formula for calculating the standard deviation of the cell area at level L of HGWM is as follows:

[0020]

[0021] The larger the value, the greater the difference in cell area at the Lth level of HGWM, and the greater the area deformation; conversely, the smaller the area deformation. This indicates that all cells in the current level have the same area.

[0022] According to the global hexagonal wargame map deformation analysis method based on dynamic comprehensive deformation index of the present invention, the grid area deformation index is further proposed by introducing the average grid area, which includes:

[0023] The formula for calculating the mesh area deformation index at level L of HGWM is as follows:

[0024]

[0025] in, Let AvgArea be the standard deviation of the cell area at level L of HGWM. L The area of ​​all cells in the Lth level of HGWM is the average area; GADI L The larger the value, the greater the relative deformation of the Lth level cell area in HGWM, and vice versa.

[0026] According to the global hexagonal wargame map deformation analysis method based on dynamic comprehensive deformation index of the present invention, the global hexagonal wargame map shape deformation analysis based on adjacent standard deviation further includes:

[0027] For a certain level of a global hexagonal wargame map, the formula for calculating the average neighbor distance of all cells is as follows:

[0028]

[0029] Where L is the current level of HGWM, and CellNum L Let NborNum be the total number of pentagonal and hexagonal cells in the L-th level of HGWM, and let NborNum be the number of adjacent cells of the i-th cell in the L-th level of HGWM. It is the distance between the i-th cell and its i-th adjacent cell;

[0030] The formula for calculating the standard deviation of a single neighbor distance in the Lth level of HGWM is as follows:

[0031]

[0032] The larger the value, the greater the difference in neighbor distances between cells at level L of the HGWM, and the greater the shape deformation; conversely, the smaller the value, the smaller the shape deformation. This indicates that all cells in the current level have the same neighbor distance.

[0033] According to the global hexagonal wargame map deformation analysis method based on dynamic comprehensive deformation index of the present invention, the grid shape deformation index is further proposed by introducing the average value of cell neighbor distance, which includes:

[0034] The formula for calculating the mesh shape deformation index at level L of HGWM is as follows:

[0035]

[0036] in, Let AvgNborDis be the standard deviation of the individual neighbor distances of cells at level L of HGWM. L The average neighbor distance of all cells in the Lth level of HGWM; GSDI LThe larger the value, the greater the relative deformation of the L-th level lattice shape in HGWM, and vice versa.

[0037] According to the global hexagonal wargame map deformation analysis method based on the dynamic comprehensive deformation index of the present invention, the dynamic comprehensive deformation index is further constructed using the grid area deformation index and the grid shape deformation index, including:

[0038] The formula for calculating the dynamic composite deformation index of the Lth level of HGWM is as follows:

[0039] DIDI L =α·GADI L +(1-α)·GSDI L

[0040] Among them, GADI L gSDI is the mesh area deformation index at level L of HGWM. L Let α be the mesh shape deformation index at level L of HGWM, and let α be the weight variable.

[0041] According to the global hexagonal wargame map deformation analysis method based on dynamic comprehensive deformation index of the present invention, the weight variable α is further used to adjust the weight of area deformation and shape deformation in the overall deformation analysis, so as to dynamically meet the different requirements of different types of global wargame simulations for HGWM area deformation and shape deformation.

[0042] Furthermore, this invention also proposes a global hexagonal wargame map deformation analysis system based on a dynamic comprehensive deformation index, used to implement the aforementioned global hexagonal wargame map deformation analysis method based on a dynamic comprehensive deformation index. The system includes:

[0043] The grid area standard deviation calculation module is used to perform area deformation analysis of the global hexagonal wargame map based on the grid area standard deviation.

[0044] The adjacent distance standard deviation calculation module is used to perform shape deformation analysis of the global hexagonal wargame map based on the adjacent distance standard deviation.

[0045] The deformation index calculation module is used to introduce the average cell area and the average cell neighbor distance to propose the mesh area deformation index and the mesh shape deformation index.

[0046] The Dynamic Integrated Deformation Index Calculation Module is used to construct a dynamic integrated deformation index using the grid area deformation index and the grid shape deformation index, and to perform overall deformation analysis on the area deformation and shape deformation of the global hexagonal wargaming map.

[0047] The beneficial effects achieved by adopting the above technical solution are:

[0048] To describe the overall deformation degree of a global hexagonal wargame map, a dynamic comprehensive deformation index is proposed to comprehensively measure the area and shape deformation of the HGWM, overcoming the limitations of deformation analysis based solely on area and perimeter differences. This invention can also dynamically adjust weight variables according to the different needs of global wargame simulations for area and shape deformation, enabling dynamic analysis of the overall deformation degree of the grid and allowing for the selection of a more suitable global hexagonal wargame map for different types of global wargame simulations. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments of the present invention will be briefly described below. The drawings are merely illustrative of some embodiments of the present invention and are not intended to limit the scope of the present invention to all embodiments.

[0050] Figure 1 This is a flowchart illustrating the deformation analysis method for a global hexagonal wargame map based on a dynamic comprehensive deformation index, according to an embodiment of the present invention.

[0051] Figure 2 This is a schematic diagram of two types of adjacency in HGWM according to an embodiment of the present invention. Detailed Implementation

[0052] The exemplary solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art.

[0053] The Global Discrete Grid System (GDS) employs spatial discretization to subdivide the Earth's surface into multiple grid cells, serving as a global spatial reference system and data model. The Hexagonal Global Discrete Grid System utilizes hexagons to subdivide the Earth's surface and has been widely applied in fields such as environmental science. Global hexagonal wargame maps are constructed based on the Hexagonal Global Discrete Grid System and are used to support global wargame simulations. Due to varying degrees of area and shape distortion within the Hexagonal Global Discrete Grid System, the hexagonal cells in a global hexagonal wargame map are not entirely identical.

[0054] To analyze the overall deformation degree of a global hexagonal wargame map, this embodiment discloses a deformation analysis method for a global hexagonal wargame map based on a dynamic comprehensive deformation index, such as... Figure 1 As shown, it includes the following:

[0055] Step S101: Perform area deformation analysis of the global hexagonal wargame map based on the standard deviation of the grid area.

[0056] Cell area variance refers to the arithmetic mean of the squared differences between the area of ​​a cell at a specific level in an HGWM and the average area of ​​all cells at that level. Cell area standard deviation is the arithmetic square root of cell area variance. It measures the dispersion of cell area at a specific level in an HGWM from the average area of ​​all cells at that level, and quantitatively describes the degree of area distortion of cells at a specific level.

[0057] Since there are 12 pentagons and several hexagons at each level in HGWM (the number of hexagons increases with the increase of the subdivision level), and the standard deviation of the cell area is calculated for the area deformation of all cells, the standard deviation of the area is no longer calculated separately for pentagons and hexagons.

[0058] For a certain level of a global hexagonal wargame map, the formula for calculating the average area of ​​all cells is as follows:

[0059]

[0060] Where L is the current level of HGWM, and CellNum L Let L be the total number of pentagonal and hexagonal lattice elements in the Lth level of HGWM. Let be the area of ​​the i-th cell in the L-th level of HGWM.

[0061] Therefore, the formula for calculating the standard deviation of the cell area at level L of HGWM is as follows:

[0062]

[0063] A larger value indicates a greater difference in cell area among the Lth level of the HGWM, and thus a greater area deformation. Conversely, a smaller value indicates a smaller area deformation. If This indicates that all cells in the current level have the same area.

[0064] Step S102: Introduce the average grid area to propose the grid area deformation index.

[0065] The standard deviation of cell area is a measure of the absolute degree of deformation of cell area at a specific level in an HGWM, and it is related to the subdivision level of the HGWM. For the same HGWM, the lower the subdivision level, the larger the area of ​​each cell, and the higher the standard deviation of cell area corresponding to that level of HGWM. The larger the area of ​​each cell, the lower the standard deviation of the HGWM at that level. Conversely, the higher the partitioning level, the smaller the area of ​​each cell, and the lower the standard deviation of the cell area at that level. The smaller.

[0066] To eliminate the influence of HGWM subdivision level on area standard deviation and to achieve comparative analysis of area deformation of HGWM at different levels, this embodiment combines the average cell area with the standard deviation of cell area to obtain the grid area distortion index (GADI) for a specific level of HGWM.

[0067] The formula for calculating the mesh area deformation index at level L of HGWM is as follows:

[0068]

[0069] in, Let AvgArea be the standard deviation of the cell area at level L of HGWM. L This represents the average area of ​​all cells in the Lth level of the HGWM.

[0070] GADI L The larger the value, the greater the relative deformation of the Lth level cell area in HGWM, and vice versa.

[0071] Step S103: Perform shape deformation analysis of the global hexagonal wargame map based on the adjacent standard deviation.

[0072] Shape deformation analysis methods such as maximum / minimum side length ratio, element perimeter root mean square error, and compactness focus on the shape deformation analysis of a single cell within an HGWM, but studies on the shape deformation between cells are relatively limited. One of the important characteristics of hexagonal meshes is that the distance from the current cell to its six adjacent cells is equal, a characteristic of great significance in the field of global wargaming. Therefore, this embodiment focuses on using the change in cell adjacency distance to measure the shape deformation of the HGWM.

[0073] Each level of the HGWM contains 12 pentagons and several hexagons. Each pentagon has 5 adjacent hexagons, and each hexagon has 6 adjacent hexagons (or 5 adjacent hexagons and 1 adjacent pentagon). Therefore, the HGWM contains two types of adjacency distances: distance from a pentagon to its adjacent hexagon and distance from a hexagon to its adjacent hexagon. Figure 2 As shown, Figure 2 In the diagram, the red lines represent the lines connecting the center of a hexagonal grid cell to the center of an adjacent hexagonal grid cell, and the blue lines represent the lines connecting the center of a hexagonal grid cell to the center of an adjacent pentagonal grid cell.

[0074] Since the adjacency distances from each cell to its 5 or 6 neighboring cells may vary, and the average adjacency distances from different cells to their surrounding neighboring cells may also vary, but for global wargaming, each cell may interact with all its neighboring cells. To more comprehensively evaluate the variation patterns of cell adjacency distances in HGWM, it is necessary to analyze the adjacency distance variations from each cell to each neighboring cell. Therefore, this embodiment proposes a standard deviation for individual cell adjacency distances.

[0075] The variance of a cell's individual neighbor distance is the arithmetic mean of the squared differences between the individual neighbor distance of a cell at a specific level in an HGWM and the average neighbor distance of all cells at that level. The standard deviation of a cell's individual neighbor distance is the arithmetic square root of the variance of the cell's individual neighbor distance. It measures the dispersion of the cell's neighbor distance at a specific level in an HGWM from the average neighbor distance of all cells at that level, and quantitatively describes the degree of variation in the neighbor distance of cells at a specific level.

[0076] For a certain level of a global hexagonal wargame map, the formula for calculating the average neighbor distance of all cells is as follows:

[0077]

[0078] Where L is the current level of HGWM, and CellNum L NborNum represents the total number of pentagonal and hexagonal cells in the L-th level of HGWM, and NborNum represents the number of adjacent cells (5 or 6) of the i-th cell in the L-th level of HGWM. Let be the distance between the i-th cell and its j-th neighboring cell. Since each pentagonal cell has only 5 neighboring cells, which is 1 fewer than a hexagonal cell, when calculating the average distance, we need to subtract 12 from the total number of cells (6 times the average distance).

[0079] The formula for calculating the standard deviation of a single neighbor distance in the Lth level of HGWM is as follows:

[0080]

[0081] The larger the value, the greater the difference in neighbor distances between cells at level L of the HGWM, and the greater the shape deformation; conversely, the smaller the value, the smaller the shape deformation. This indicates that all cells in the current level have the same neighbor distance.

[0082] Step S104: Introduce the average value of cell neighbor distance to propose the grid shape deformation index.

[0083] The standard deviation of individual cell neighbor distances is a measure of the absolute degree of deformation of cell neighbor distances at a specific level in an HGWM, and it is related to the partitioning level of the HGWM. For the same HGWM, the lower the partitioning level, the larger the neighbor distances from each cell to its adjacent cells, and the higher the standard deviation of individual cell neighbor distances for that level of HGWM. The larger the value, the lower the standard deviation. Conversely, the higher the partitioning level, the smaller the distance from each cell to its neighboring cells, and the lower the standard deviation of the distance between individual cells. The smaller.

[0084] To eliminate the influence of the partitioning level on the standard deviation of individual cell neighbor distances and to enable comparative analysis of the shape deformation of HGWM at different levels, this embodiment combines the average value of cell neighbor distances with the standard deviation of individual cell neighbor distances to obtain the grid shape deformation index (GSDI) for a specific level of HGWM.

[0085] The formula for calculating the mesh shape deformation index at level L of HGWM is as follows:

[0086]

[0087] in, Let AvgNborDis be the standard deviation of the individual neighbor distances of cells at level L of HGWM. L It is the average neighbor distance of all cells in the Lth level of HGWM.

[0088] GSDI L The larger the value, the greater the relative deformation of the L-th level lattice shape in HGWM, and vice versa.

[0089] Step S105: Construct a dynamic comprehensive deformation index using the grid area deformation index and the grid shape deformation index to perform an overall deformation analysis on the area deformation and shape deformation of the global hexagonal wargaming map.

[0090] Area deformation measures the degree of deformation in a global wargaming (HGWM) from the perspective of changes in cell area, while shape deformation measures the degree of deformation from the perspective of changes in the cell's own shape and distances to adjacent cells. Currently, researchers often focus only on area or shape deformation, attempting to minimize either, but this leads to a sharp increase in the other type of deformation, negatively impacting the scientific validity and accuracy of global wargaming. To comprehensively assess the overall deformation of the HGWM, this embodiment proposes a dynamic comprehensive deformation index to measure both area and shape deformation holistically.

[0091] The formula for calculating the dynamic composite deformation index of the Lth level of HGWM is as follows:

[0092] DIDI L=α·GADI L +(1-α)·GSDI L (7)

[0093] Among them, GADI L GSDI is the mesh area deformation index at level L of HGWM. L α is the mesh shape deformation index at level L of HGWM, and α is a weight variable used to adjust the weights of area deformation and shape deformation in the overall deformation analysis, so as to dynamically meet the different requirements of HGWM area deformation and shape deformation for different types of global wargaming simulations.

[0094] It can be seen that the value range of α is [0.0, 1.0]. When α = 0.0, the dynamic comprehensive deformation index is equal to the grid shape deformation index, i.e., DIDIL = GSDIL, indicating that this type of global wargame focuses more on the shape deformation of the grid, such as a global wargame of material delivery. When α = 1.0, the dynamic comprehensive deformation index is equal to the grid area deformation index, i.e., DIDIL = GADIL, indicating that this type of global wargame focuses more on the area deformation of the grid, such as a global wargame of epidemic prevention and control. When α = 0.5, the dynamic comprehensive deformation index is equal to half of the sum of the grid area deformation index and the grid shape deformation index, i.e. This indicates that a certain type of global wargaming simulation focuses on both the area deformation and shape deformation of the grid, such as a joint operations global wargaming simulation.

[0095] Therefore, the weight variable α can be dynamically adjusted according to the application requirements of HGWM area deformation and shape deformation in different types of global wargaming (such as global wargaming for epidemic prevention and control, global wargaming for material delivery, and global wargaming for joint operations), so as to achieve dynamic analysis of the overall deformation degree of HGWM.

[0096] Corresponding to the above method, this embodiment also proposes a global hexagonal wargaming map deformation analysis system based on a dynamic comprehensive deformation index, comprising:

[0097] The grid area standard deviation calculation module is used to perform area deformation analysis on a global hexagonal wargame map based on the grid area standard deviation.

[0098] The adjacent distance standard deviation calculation module is used to perform shape deformation analysis of the global hexagonal wargame map based on the adjacent distance standard deviation.

[0099] The deformation index calculation module is used to introduce the average cell area and the average cell neighbor distance to propose the mesh area deformation index and the mesh shape deformation index.

[0100] The Dynamic Integrated Deformation Index Calculation Module is used to construct a dynamic integrated deformation index using the grid area deformation index and the grid shape deformation index, and to perform overall deformation analysis on the area deformation and shape deformation of the global hexagonal wargaming map.

[0101] The effectiveness of the present invention will be verified through experiments below.

[0102] This experiment focuses on the comprehensive deformation analysis of HGWM for three projections: Fuller, ISEA, and Gnomonic. The DGGRID and H3 open-source libraries were used to generate HGWM for the three projection types: Fuller3H, ISEA3H, and Uber H3, respectively, to verify the effectiveness of the above deformation analysis method and to provide a reference for selecting the appropriate HGWM for different global wargames.

[0103] Because these three types of HGWMs have different mesh apertures, the number and size of cells corresponding to each mesh level are different. In order to compare and analyze the deformation degree of various HGWMs at similar scales, it is necessary to select mesh levels with similar cell counts and cell sizes for comparison. The total number of cells in the fourth level of Fuller3H and ISEA3H is 812, and the total number of cells in the first level of Uber H3 is 842. Therefore, the deformation analysis is performed on the HGWMs of Fuller3H and ISEA3H at levels 4-10, and Uber H3 at levels 1-4.

[0104] (1) Mesh area deformation analysis

[0105] The average cell area, standard deviation of cell area, and mesh area deformation index of multiple levels of three HGWMs, namely Fuller3H, ISEA3H, and Uber H3, were calculated using formulas (1), (2), and (3), respectively. The analysis results are shown in Table 1.

[0106] Table 1. Mesh area deformation analysis at multiple levels of three HGWM types.

[0107]

[0108]

[0109] It can be seen that for HGWM of the same projection type, the mesh area distortion index gradually decreases as the subdivision level increases. This is because there are always 12 pentagons in HGWM, and the area of ​​a pentagon is five-sixths of the area of ​​a hexagon. The lower the subdivision level, the larger the mesh size, and the larger the proportion of pentagons in all cells, resulting in a larger mesh area distortion index. As the subdivision level increases, the proportion of pentagons decreases, thus reducing the mesh area distortion index.

[0110] Furthermore, for the three projection types of HGWM, the grid area distortion index of Uber H3 is approximately 4.6 times that of Fuller3H and approximately 44.3 times that of ISEA3H. Therefore, the area distortion of HGWM based on Gnomonic projection is the largest, followed by HGWM based on Fuller projection, and HGWM based on ISEA projection has the smallest area distortion.

[0111] (2) Mesh shape deformation analysis

[0112] Using formulas (4), (5), and (6), the average neighbor distance, standard deviation of individual neighbor distance, and mesh shape deformation index of multiple levels of Fuller3H, ISEA3H, and Uber H3 HGWM were calculated respectively. The analysis results are shown in Table 2.

[0113] Table 2. Analysis of lattice shape deformation at multiple levels of three HGWMs

[0114]

[0115]

[0116] It can be seen that for the three projection types of HGWM, the mesh shape distortion index of ISEA3H is approximately 1.3 times that of Fuller3H and approximately 2.3 times that of Uber H3. Therefore, the shape distortion of HGWM based on Gnomonic projection is the smallest, followed by the surface shape distortion of HGWM based on Fuller projection, and the shape distortion of HGWM based on ISEA projection is the largest.

[0117] (3) Overall mesh deformation analysis

[0118] The overall deformation index of the mesh at multiple levels of the three types of HGWM, Fuller3H, ISEA3H, and Uber H3, was calculated using formula (7), and the analysis results are shown in Table 3. In order to compare the influence of different weights of area deformation and shape deformation on the overall mesh deformation, the weight variable α was set to 0, 0.25, 0.5, 0.75, and 1, respectively, and the dynamic comprehensive deformation index of different types of HGWM was calculated.

[0119] Table 3. Dynamic Comprehensive Deformation Index Analysis of Multiple Levels in Three Types of HGWM

[0120]

[0121]

[0122] It can be seen that as the value of the weight variable α changes, the dynamic comprehensive deformation index of the same type of HGWM at the same level also changes accordingly.

[0123] When global wargaming focuses only on the interaction between cells, HGWM is required to have good equidistance, that is, the distance between adjacent cells should be kept as equal as possible. In this case, let α = 0, and HGWM based on Gnomonic projection is more suitable.

[0124] When global wargaming focuses on the interactions between cells and the interactions within cells, it is required that the distance between adjacent cells be kept as equal as possible, and that the cell areas be kept as consistent as possible. In this case, let α = 0.25. HGWM based on Fuller projection is more suitable.

[0125] When global wargaming focuses on both the interactions between grid cells and the interactions within grid cells, it requires that the neighbor distances and areas of grid cells be kept as consistent as possible. Therefore, if we set α = 0.5, both ISEA and Fuller projections' HGWM can meet the requirements.

[0126] When global wargaming focuses on the interaction within a cell as well as the interaction between cells, it is required that the cell area be kept as consistent as possible, and the distance between adjacent cells be kept as equal as possible. Let α = 0.75, then HGWM based on ISEA projection is more suitable.

[0127] When global wargaming focuses only on the interactions within the cells, and requires HGWM to have good equal area properties, that is, the area of ​​all cells should be kept as equal as possible, then let α = 1. In this case, HGWM based on ISEA projection is more suitable.

[0128] This invention addresses the application requirements of HGWM in the field of global wargaming, focusing on the area and shape deformation characteristics of HGWM. It proposes an area deformation analysis method based on the standard deviation of cell area and a shape deformation analysis method based on the standard deviation of neighbor distance. To eliminate the influence of cell size on the degree of area and shape deformation, two factors are introduced: the average cell area and the average cell neighbor distance, resulting in a grid area deformation index and a grid shape deformation index. Most importantly, to describe the overall deformation degree of HGWM and meet the needs of different types of global wargaming applications, a dynamic comprehensive deformation index is proposed to comprehensively measure the deformation of HGWM, overcoming the limitations of deformation analysis based solely on area and perimeter differences. HGWMs with three projection types—Fuller, ISEA, and Gnomonic—were selected, and the above methods were used to compare and analyze the area deformation, shape deformation, and overall deformation of cells.

[0129] Experimental results show that the deformation analysis method of global hexagonal wargame map based on dynamic comprehensive deformation index can dynamically adjust the weight variables according to different requirements for area deformation and shape deformation, realize the dynamic analysis of the overall deformation degree of the grid, and select a more suitable global hexagonal wargame map for different types of global wargame simulations.

[0130] Various types of global discrete grid systems have been widely used, employing diverse projection methods. Common projection methods for hexagonal global discrete grid systems include Fuller, ISEA, and Gnomonic. The area and shape deformation characteristics of global hexagonal wargame maps constructed using different projection methods vary. This invention analyzes the shape, area, and overall deformation of HGWM projected with Fuller and ISEA apertures of 3, as well as HGWM projected with Gnomonic aperture of 7, verifying the effectiveness of the HGWM overall deformation evaluation method based on a dynamic comprehensive deformation index.

[0131] Those skilled in the art will understand that all or part of the steps in the above methods can be implemented by a program instructing related hardware, and the program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk. Optionally, all or part of the steps in the above embodiments can also be implemented using one or more integrated circuits. Accordingly, each module / unit in the above embodiments can be implemented in hardware or as a software functional module. This invention is not limited to any particular combination of hardware and software.

[0132] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for deformation analysis of a global hexagonal wargame map based on a dynamic comprehensive deformation index, characterized in that, Include: Step 1: Perform area deformation analysis on the global hexagonal wargame map based on the standard deviation of the grid area, including: For a certain level of a global hexagonal wargame map, the formula for calculating the average area of ​​all cells is as follows: Where L is the current level of HGWM, and CellNum L Let L be the total number of pentagonal and hexagonal lattice elements in the Lth level of HGWM. Let be the area of ​​the i-th cell at level L of HGWM; HGWM is a global hexagonal wargame map. The formula for calculating the standard deviation of the cell area at level L of HGWM is as follows: The larger the value, the greater the difference in cell area at the Lth level of HGWM, and the greater the area deformation; conversely, the smaller the area deformation. This indicates that all cells in the current level have the same area; Step 2: Perform shape deformation analysis of the global hexagonal wargame map based on the adjacent distance standard deviation, including: For a certain level of a global hexagonal wargame map, the formula for calculating the average neighbor distance of all cells is as follows: Where L is the current level of HGWM, and CellNum L Let NborNum be the total number of pentagonal and hexagonal cells in the L-th level of HGWM, and let NborNum be the number of adjacent cells of the i-th cell in the L-th level of HGWM. It is the distance between the i-th cell and its j-th adjacent cell; The formula for calculating the standard deviation of a single neighbor distance in the Lth level of HGWM is as follows: The larger the value, the greater the difference in neighbor distances between cells at level L of the HGWM, and the greater the shape deformation; conversely, the smaller the value, the smaller the shape deformation. This indicates that all cells in the current level have the same neighbor distance; Step 3: Introduce the average cell area and average cell neighbor distance, and propose the mesh area deformation index and mesh shape deformation index, including: Introducing the average cell area to propose a mesh area deformation index that includes: The formula for calculating the mesh area deformation index at level L of HGWM is as follows: in, Let AvgArea be the standard deviation of the cell area at level L of HGWM. L The area of ​​all cells in the Lth level of HGWM is the average area; GADI L The larger the value, the greater the relative deformation of the Lth level cell area in HGWM; conversely, the smaller the value, the smaller the relative deformation of the cell area. The grid shape deformation index is proposed by introducing the average neighbor distance of the cells, which includes: The formula for calculating the mesh shape deformation index at level L of HGWM is as follows: in, Let AvgNborDis be the standard deviation of a single neighbor distance for a cell at level L of HGWM. L The average neighbor distance of all cells in the Lth level of HGWM; GSDI L The larger the value, the greater the relative deformation of the Lth level lattice shape in HGWM; conversely, the smaller the value, the smaller the relative deformation of the lattice shape. Step 4: Construct a dynamic comprehensive deformation index using the grid area deformation index and the grid shape deformation index, and conduct an overall deformation analysis of the area and shape deformation of the global hexagonal wargaming map, including: The formula for calculating the dynamic composite deformation index of the Lth level of HGWM is as follows: DIDI L =α·GADI L +(1-α)·GSDI L Among them, GADI L GSDI is the mesh area deformation index at level L of HGWM. L Let α be the mesh shape deformation index at level L of HGWM, and let α be the weight variable.

2. The global hexagonal wargaming map deformation analysis method based on dynamic comprehensive deformation index according to claim 1, characterized in that, The weight variable α is used to adjust the weights of area deformation and shape deformation in the overall deformation analysis, dynamically meeting the different requirements of HGWM area deformation and shape deformation for different types of global wargaming simulations.

3. A deformation analysis system for a global hexagonal wargame map based on a dynamic comprehensive deformation index, characterized in that, For implementing the global hexagonal wargame map deformation analysis method based on dynamic comprehensive deformation index as described in claim 1 or 2, the system comprises: The grid area standard deviation calculation module is used to perform area deformation analysis of the global hexagonal wargame map based on the grid area standard deviation. The adjacent distance standard deviation calculation module is used to perform shape deformation analysis of the global hexagonal wargame map based on the adjacent distance standard deviation. The deformation index calculation module is used to introduce the average cell area and the average cell neighbor distance to propose the mesh area deformation index and the mesh shape deformation index. The Dynamic Integrated Deformation Index Calculation Module is used to construct a dynamic integrated deformation index using the grid area deformation index and the grid shape deformation index, and to perform overall deformation analysis on the area deformation and shape deformation of the global hexagonal wargaming map.

4. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method as described in claim 1 or 2.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in claim 1 or 2.

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