Global hexagonal war game map deformation analysis method and system based on dynamic comprehensive deformation index

Abstract

The invention relates to the technical field of global war game deduction, in particular to a global hexagonal war game map deformation analysis method and system based on a dynamic comprehensive deformation index, and the global hexagonal war game map area deformation analysis is carried out based on a lattice area standard deviation. Performing global hexagonal war chess map shape deformation analysis based on the adjacent distance standard deviation; introducing a cell area average value and a cell adjacent distance average value, and proposing a grid area deformation index and a grid shape deformation index; and constructing a dynamic comprehensive deformation index by using the grid area deformation index and the grid shape deformation index, and carrying out overall deformation analysis on the area deformation and the shape deformation of the HGWM. According to the method, the dynamic comprehensive deformation index is put forward to carry out overall measurement on the deformation of the HGWM, and the limitation that deformation analysis is carried out only through area difference and perimeter difference is made up; by dynamically adjusting the weight variable, the dynamic analysis of the overall deformation degree of the grid is realized, and a more suitable global hexagonal war chess map is selected for different types of global war chess deduction.

Description

Technical Field

[0001] The present invention relates to the field of global war game simulation technology, and in particular to a global hexagonal war game map deformation analysis method and system based on a dynamic comprehensive deformation index. Background Art

[0002] With the rapid development of sensor technology and remote sensing technology, various high-resolution earth observation data have been rapidly enhanced, the data types have continued to increase, and the spatial scope has been continuously expanded to the world. Traditional spatial data models represented by vectors and rasters have been unable to meet the needs of multi-scale, cross-time global massive data access and spatial analysis. The global discrete grid system can effectively integrate different data formats, spatial reference systems, multi-scale, cross-time geographic spatial information, and efficiently query and analyze massive spatial data. Due to its discreteness, the global discrete grid system has shown good parallel computing advantages, which has an important role in promoting spatiotemporal big data analysis.

[0003] Hexagonal Discrete Global Grid Systems (HDGGS) is a global discrete grid system that subdivides the earth's surface based on hexagonal cells. Due to the characteristics of hexagons such as equal adjacency distance, consistent adjacency relationship, and maximum angular resolution, they have been widely used in the fields of geographic information science, remote sensing, geophysics, environmental science, and especially in the field of global dynamic modeling. The Hexagonal Global Wargame Map (HGWM) is a wargame map built based on HDGGS. It integrates data on multiple environmental elements such as terrain, meteorology, and oceans. It can support global wargame simulations and can interact efficiently with multiple combat models such as mobility, reconnaissance, and damage.

[0004] The regular hexagonal grid on the plane has good geometric properties, such as hexagons are closer to circles than triangles and quadrilaterals, the distances from hexagons to all adjacent cells are equal, the average error is minimal when tiling the plane, and the discrete distance measurement result is closer to the Cartesian distance. However, in HDGGS, each hexagonal cell cannot maintain all of the above geometric properties, but has different degrees of area deformation and shape deformation. In order to provide guidance for different types of professional applications, many scholars have studied the area deformation and shape deformation of HDGGS.

[0005] White, Kimerling, Sahr, and Song calculated various density ratios and believed that the Icosahedral Snyder Equal Area (ISEA) projection performed best in terms of area distortion, and the Gnomonic projection performed best in terms of compactness. Kimerling, Sahr, White, and Song believed that the comparison of global mesh geometric characteristics should at least consider surface area and compactness, and these metrics should be calculated at the same level of mesh resolution. They also calculated the spherical surface area, compactness, and center point spacing. Ben Jin et al. proposed two indicators, the maximum / minimum side length ratio and the mean square error of the unit perimeter, and analyzed the deformation of the spherical equal-area hexagonal discrete grid.

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

[0007] In the above studies, area and shape deformations were analyzed separately. Area deformation was analyzed using the minimum / maximum value, average value, normalized area, etc., and shape deformation was analyzed using the maximum / minimum side length ratio, unit perimeter mean square error, compactness, grid spacing average and standard deviation. There was a lack of comprehensive analysis of the overall deformation of HDGGS, which has affected the application of the global hexagonal wargame map based on HDGGS in the field of global wargame simulations that need to take into account both area and shape deformation. Summary of the invention

[0008] The present invention aims to solve the above-mentioned defects in the prior art, and proposes a global hexagonal wargame map deformation analysis method and system based on a dynamic comprehensive deformation index. The dynamic comprehensive deformation index is proposed to measure the area and shape deformation of the HGWM as a whole, which makes up for the limitation of deformation analysis only using area difference and perimeter difference.

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

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

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

[0012] Shape deformation analysis of global hexagonal wargame maps based on standard deviation of neighbor distances;

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

[0014] The 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 wargame map.

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

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

[0017]

[0018] Among them, L is the current level of HGWM, CellNum L is the total number of pentagonal and hexagonal cells at level L of HGWM, is the area of ​​the i-th cell at the L-th level of HGWM;

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

[0020]

[0021] The larger the value of , the greater the difference in the cell area of ​​the Lth level of HGWM, and the greater the area deformation; conversely, the smaller the area deformation; if This means that the areas of all cells in the current level are equal.

[0022] According to the global hexagonal wargame map deformation analysis method based on the dynamic comprehensive deformation index of the present invention, further, the grid area average value is introduced to propose that the grid area deformation index includes:

[0023] The calculation formula of the grid area deformation index of the Lth level of HGWM is as follows:

[0024]

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

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

[0027] For a certain level of the global hexagonal wargame map, the average value of the neighbor distances of all cells is calculated as follows:

[0028]

[0029] Among them, L is the current level of HGWM, CellNum L is the total number of pentagonal and hexagonal cells at the Lth level of HGWM, NborNum is the number of adjacent cells of the i-th cell at the Lth level of HGWM, is the distance from the ith cell to its ith adjacent cell;

[0030] The calculation formula for the standard deviation of the single neighbor distance of the HGWM level L is as follows:

[0031]

[0032] The larger the value of , the greater the difference in the cell neighbor distances at the Lth level of HGWM, and the greater the shape deformation; conversely, the smaller the shape deformation; if This means that the neighbor distances of all cells in the current level are equal.

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

[0034] The calculation formula of the grid shape deformation index of the Lth level of HGWM is as follows:

[0035]

[0036] in, AvgNborDis is the standard deviation of the single neighbor distance of the L-th level of HGWM. L is the average distance between all cells at level L of HGWM; GSDI LThe larger the value of , the greater the relative deformation of the cell shape at the Lth level of 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, further, using the grid area deformation index and the grid shape deformation index to construct the dynamic comprehensive deformation index comprises:

[0038] The calculation formula of the dynamic comprehensive deformation index of HGWM level L is as follows:

[0039] DIDI L =α·GADI L +(1-α)·GSDI L

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

[0041] According to the global hexagonal wargame map deformation analysis method based on the dynamic comprehensive deformation index of the present invention, further, 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 different types of global wargame simulations for HGWM area deformation and shape deformation.

[0042] Furthermore, the present invention also proposes a global hexagonal wargame map deformation analysis system based on a dynamic comprehensive deformation index, which is used to implement the global hexagonal wargame map deformation analysis method based on a dynamic comprehensive deformation index as described above, and the system comprises:

[0043] The cell area standard deviation calculation module is used to analyze the area deformation of the global hexagonal war game map based on the cell area standard deviation;

[0044] Neighborhood standard deviation calculation module, used to analyze the shape deformation of the global hexagonal war game map based on the neighborhood standard deviation;

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

[0046] The dynamic comprehensive deformation index calculation module is used to construct a dynamic comprehensive deformation index using the grid area deformation index and the grid shape deformation index, and to perform an overall deformation analysis on the area deformation and shape deformation of the global hexagonal war game map.

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

[0048] In order to describe the overall deformation degree of the global hexagonal wargame map, a dynamic comprehensive deformation index is proposed to measure the area and shape deformation of the HGWM as a whole, which makes up for the limitation of deformation analysis based only on area difference and perimeter difference. The present invention can also dynamically adjust the weight variables according to the different requirements of global wargame simulation for area deformation and shape deformation, realize 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings of the embodiments of the present invention, wherein the drawings are only used to illustrate some embodiments of the present invention, but not to limit all embodiments of the present invention thereto.

[0050] Figure 1 It is a schematic flow chart of a method for analyzing deformation of a global hexagonal wargame map based on a dynamic comprehensive deformation index according to an embodiment of the present invention;

[0051] Figure 2 Schematic diagram of two types of proximity in the HGWM according to an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings of specific embodiments of the present invention to clearly and completely describe the exemplary scheme of the embodiment of the present invention. Unless otherwise defined, the technical terms or scientific terms used in the present invention should be the common meanings understood by people with ordinary skills in the field.

[0053] The global discrete grid system adopts the idea of ​​spatial discretization to subdivide the earth's surface into multiple grid units. It is a spatial reference system and data model applicable to the world. The hexagonal global discrete grid system uses hexagons to subdivide the earth's surface and is widely used in fields such as environmental science. The global hexagonal wargame map is built based on the hexagonal global discrete grid system and is used to support global wargame simulations. Due to the different degrees of area deformation and shape deformation of the hexagonal global discrete grid system, the hexagonal cells in the global hexagonal wargame map are not exactly the same.

[0054] In order to analyze the overall deformation degree of the global hexagonal wargame map, this embodiment discloses a deformation analysis method of the global hexagonal wargame map based on a dynamic comprehensive deformation index, such as Figure 1 As shown, it contains the following contents:

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

[0056] The cell area variance refers to the arithmetic mean of the square difference between the area of ​​a cell at a specific level in the HGWM and the average area of ​​all cells at that level. The cell area standard deviation is the arithmetic square root of the cell area variance. It can measure the degree of dispersion from the cell area at a specific level in the HGWM to the average area of ​​all cells at that level, and quantitatively describe the degree of area deformation of cells at a specific level.

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

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

[0059]

[0060] Among them, L is the current level of HGWM, CellNum L is the total number of pentagonal and hexagonal cells at level L of HGWM, is the area of ​​the i-th cell at the L-th level of HGWM.

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

[0062]

[0063] The larger the value of , the greater the difference in the cell area of ​​the Lth level of HGWM, and the greater the area deformation. On the contrary, it means that the area deformation is smaller. If This means that the areas of all cells in the current level are equal.

[0064] Step S102: introducing the average cell area value to propose a grid area deformation index.

[0065] The standard deviation of the cell area is a measure of the absolute deformation degree of the cell area at a specific level in the HGWM, which 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 standard deviation of the cell area corresponding to the HGWM at that level On the contrary, if the subdivision level is higher, the area of ​​each cell is smaller, and the standard deviation of the cell area corresponding to the HGWM of this level is The smaller.

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

[0067] The calculation formula of the grid area deformation index of the Lth level of HGWM is as follows:

[0068]

[0069] in, is the standard deviation of the cell area at the Lth level of HGWM, AvgArea L It is the average area of ​​all cells at level L of HGWM.

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

[0071] Step S103: performing shape deformation analysis of the global hexagonal war chess map based on the standard deviation of neighbor distances.

[0072] Shape deformation analysis methods such as maximum / minimum side length ratio, unit perimeter mean square error, and compactness focus on the shape deformation analysis of a cell in HGWM, but there is little research on the shape deformation between cells. One of the important characteristics of the hexagonal grid is that the distance from the current cell to the six adjacent cells is equal, which is of great significance for the application of global war game simulation. Therefore, this embodiment focuses on measuring the shape deformation of HGWM by using the change of the cell adjacent distance.

[0073] There are 12 pentagons and several hexagons at each level of HGWM. Each pentagon has 5 adjacent hexagons, and each hexagon has 6 adjacent hexagons (or 5 adjacent hexagons and 1 adjacent pentagon). Therefore, there are two types of neighbor distances in HGWM: the distance from pentagon to adjacent hexagon and the distance from hexagon to adjacent hexagon. For example, Figure 2 As shown, Figure 2 In the figure, the red straight line represents the line connecting the center of a hexagonal cell with the center of an adjacent hexagonal cell, and the blue straight line represents the line connecting the center of a hexagonal cell with the center of an adjacent pentagonal cell.

[0074] Since the distances between each cell and the adjacent 5 or 6 cells may vary, and the average distances between different cells and the surrounding adjacent cells may also vary, each cell may interact with all adjacent cells for global war games. In order to more comprehensively evaluate the variation of the cell neighbor distances in HGWM, it is necessary to analyze the variation of the neighbor distances between each cell and each adjacent cell. Therefore, this embodiment proposes the standard deviation of the cell single neighbor distance.

[0075] The variance of a cell's single neighbor distance refers to the arithmetic mean of the square difference between a cell's single neighbor distance and the average neighbor distance of all cells at that level in the HGWM. The standard deviation of a cell's single neighbor distance is the arithmetic square root of the variance of a cell's single neighbor distance. It can measure the degree of dispersion from the cell's neighbor distance at a specific level in the HGWM to the average neighbor distance of all cells at that level, and quantitatively describe the degree of change in the neighbor distance of cells at a specific level.

[0076] For a certain level of the global hexagonal wargame map, the average value of the neighbor distances of all cells is calculated as follows:

[0077]

[0078] Among them, L is the current level of HGWM, CellNum L is the total number of pentagonal and hexagonal cells at the Lth level of HGWM, NborNum is the number of adjacent cells of the i-th cell at the Lth level of HGWM (5 or 6), is the distance from the ith cell to its jth adjacent cell; since each pentagonal cell has only 5 adjacent cells, which is 1 less than the hexagonal cell, when calculating the average value of the adjacent distance, it is necessary to subtract 12 from 6 times the total number of cells.

[0079] The calculation formula for the standard deviation of the single neighbor distance of the HGWM level L is as follows:

[0080]

[0081] The larger the value of , the greater the difference in the cell neighbor distances at the Lth level of HGWM, and the greater the shape deformation; conversely, the smaller the shape deformation; if This means that the neighbor distances of all cells in the current level are equal.

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

[0083] The standard deviation of the distance between cells is a measure of the absolute deformation of the distance between cells at a specific level in the HGWM, which is related to the subdivision level of the HGWM. For the same HGWM, the lower the subdivision level, the larger the distance between each cell and the adjacent cell. The standard deviation of the distance between cells corresponding to the HGWM at this level is On the contrary, if the subdivision level is higher, the distance between each cell and the adjacent cell is smaller, and the standard deviation of the single cell distance is The smaller.

[0084] In order to eliminate the influence of the subdivision level on the standard deviation of the single neighbor distance of the cell and realize the comparative analysis of the shape deformation of HGWM at different levels, this embodiment combines the average value of the cell neighbor distance with the standard deviation of the single neighbor distance of the cell to obtain the grid shape deformation index (GSDI) of a specific level of HGWM.

[0085] The calculation formula of the grid shape deformation index of the Lth level of HGWM is as follows:

[0086]

[0087] in, AvgNborDis is the standard deviation of the single neighbor distance of the L-th level of HGWM. L is the average of the neighbor distances of all cells at the Lth level of HGWM.

[0088] GSDI L The larger the value of , the greater the relative deformation of the cell shape at the Lth level of 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, and perform overall deformation analysis on the area deformation and shape deformation of the global hexagonal war chess map.

[0090] Area deformation measures the deformation degree of HGWM from the perspective of the change in the cell area, and shape deformation measures the deformation degree of HGWM from the perspective of the change in the cell shape itself and the distance between adjacent cells. At present, people tend to only focus on area deformation or shape deformation, trying to minimize area deformation or shape deformation, but the other deformation increases sharply, which has an adverse impact on the scientificity and accuracy of global war game simulation. In order to comprehensively evaluate the overall deformation degree of HGWM, this embodiment proposes a dynamic comprehensive deformation index to measure the area deformation and shape deformation as a whole.

[0091] The calculation formula of the dynamic comprehensive deformation index of HGWM level L is as follows:

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

[0093] Among them, GADI L is the grid area deformation index of the Lth level of HGWM, GSDI L is the grid shape deformation index of the Lth level of HGWM, and α is the weight variable, which is used to adjust the weights of area deformation and shape deformation in the overall deformation analysis to dynamically meet the different requirements of different types of global war games for HGWM area deformation and shape deformation.

[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, that is, DIDIL = GSDIL, indicating that this type of global war game simulation pays more attention to the shape deformation of the grid, such as the global war game simulation of material delivery. When α = 1.0, the dynamic comprehensive deformation index is equal to the grid area deformation index, that is, DIDIL = GADIL, indicating that this type of global war game simulation pays more attention to the area deformation of the grid, such as the global war game simulation 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, that is It indicates that a certain type of global war game focuses on both the area deformation and shape deformation of the grid, such as the joint operations global war game.

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

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

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

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

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

[0100] The dynamic comprehensive deformation index calculation module is used to construct a dynamic comprehensive deformation index using the grid area deformation index and the grid shape deformation index, and to perform an overall deformation analysis on the area deformation and shape deformation of the global hexagonal war game map.

[0101] The effectiveness of the present invention is verified by experiments below.

[0102] This experiment focuses on the comprehensive deformation analysis of HGWMs of three projections, namely Fuller, ISEA, and Gnomonic, and uses two open source libraries, DGGRID and H3, to generate HGWMs of three projection types, namely Fuller3H, ISEA3H, and Uber H3, respectively, to verify the effectiveness of the above deformation analysis method and provide a reference for selecting appropriate HGWMs for different global war games.

[0103] Since the three types of HGWMs have different mesh apertures, the number and size of cells corresponding to each level of mesh 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 number and size of cells for comparison. The total number of cells at the 4th level of Fuller3H and ISEA3H is 812, and the total number of cells at the 1st level of Uber H3 is 842. Therefore, HGWMs of Fuller3H and ISEA3H with 4-10 levels and Uber H3 with 1-4 levels are selected for deformation analysis.

[0104] (1) Mesh area deformation analysis

[0105] Formula (1), (2) and (3) are used to calculate the average cell area, standard deviation of cell area and grid area deformation index of multiple levels of three HGWMs: Fuller3H, ISEA3H and Uber H3. The analysis results are shown in Table 1.

[0106] Table 1 Analysis of mesh area deformation at multiple levels of three HGWMs

[0107]

[0108]

[0109] It can be seen that for the same projection type of HGWM, the mesh area deformation index gradually decreases with the increase of the subdivision level. This is because there are always 12 pentagons in HGWM, and the area of ​​pentagons is five-sixths of the area of ​​hexagons. The lower the subdivision level, the larger the grid size, and the greater the proportion of pentagons in all cells, resulting in a larger mesh area deformation index; as the subdivision level increases, the proportion of pentagons decreases, making the mesh area deformation index smaller.

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

[0111] (2) Mesh shape deformation analysis

[0112] Formula (4), (5) and (6) are used to calculate the average neighbor distances, standard deviation of single neighbor distances and grid shape deformation index of three HGWMs of Fuller3H, ISEA3H and Uber H3 at multiple levels respectively. The analysis results are shown in Table 2.

[0113] Table 2 Analysis of cell 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 deformation index of ISEA3H is about 1.3 times that of Fuller3H, and about 2.3 times that of Uber H3. Therefore, the shape deformation of HGWM based on Gnomonic projection is the smallest, followed by that of HGWM based on Fuller projection, and the shape deformation of HGWM based on ISEA projection is the largest.

[0117] (3) Analysis of overall mesh deformation

[0118] Formula (7) is used to calculate the overall deformation index of the grids at multiple levels of three types of HGWM: Fuller3H, ISEA3H, and Uber H3. 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 deformation of the grid, the weight variable α is set to 0, 0.25, 0.5, 0.75, and 1, respectively, and the dynamic comprehensive deformation index of different types of HGWM is calculated.

[0119] Table 3 Analysis of dynamic comprehensive deformation index of three HGWM at multiple levels

[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.

[0123] When global war game simulation only focuses 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. Then let α = 0. At this time, HGWM based on Gnomonic projection is more applicable.

[0124] When global war game simulations focus more on the interaction between cells and the interaction within each cell, the distance between adjacent cells is required to be kept as equal as possible, and the area of ​​the cells is required to be kept as consistent as possible. Then let α = 0.25, and the HGWM based on Fuller projection is more applicable.

[0125] When global war games focus on the interactions between cells and the interactions within cells at the same time, it is required that the neighbor distance and area of ​​the cells remain consistent as much as possible. In this case, let α = 0.5. At this time, the HGWM of both ISEA and Fuller projections can meet the requirements.

[0126] When global war game simulations focus more on the interactions within cells and between cells, the first requirement is to keep the cell area as consistent as possible, and the second requirement is to keep the distance between adjacent cells as equal as possible. Then let α = 0.75, and the HGWM based on ISEA projection is more applicable.

[0127] When global war game simulation only focuses on the interaction within the grid, HGWM is required to have a good equal area property, that is, the areas of all grids are kept as equal as possible, then α=1. At this time, HGWM based on ISEA projection is more applicable.

[0128] Aiming at the application demand of HGWM in the field of global wargaming, the present invention focuses on the area deformation and shape deformation characteristics of HGWM, and proposes an area deformation analysis method based on the standard deviation of the cell area and a shape deformation analysis method based on the standard deviation of the neighbor distance. In order to eliminate the influence of the cell size on the area deformation and shape deformation degree, two factors, the average cell area value and the average cell neighbor distance value, are introduced respectively, and the grid area deformation index and the grid shape deformation index are proposed. Most importantly, in order to describe the overall deformation degree of HGWM and meet the application requirements of different types of global wargaming, a dynamic comprehensive deformation index is proposed to measure the deformation of HGWM as a whole, which makes up for the limitation of deformation analysis using only area difference and perimeter difference. HGWM with three types of projections, Fuller, ISEA and Gnomonic, are selected, and the area deformation, shape deformation and overall deformation of the cell are compared and analyzed using the above method.

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

[0130] There are many types of global discrete grid systems that have been widely used, and these global discrete grid systems use various types of projection methods. Common projection methods for hexagonal global discrete grid systems include Fuller, ISEA, Gnomonic, etc. The area deformation and shape deformation characteristics of global hexagonal war chess maps constructed by different projection methods are different. The present invention analyzes the shape deformation, area deformation and overall deformation of Fuller and ISEA projection HGWM with a subdivision aperture of 3, and Gnomonic projection HGWM with a subdivision aperture of 7, and verifies the effectiveness of the HGWM overall deformation evaluation method based on the dynamic comprehensive deformation index.

[0131] Those skilled in the art will appreciate that all or part of the steps in the above method can be completed by instructing related hardware through a program, 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 embodiment can also be implemented using one or more integrated circuits, and accordingly, each module / unit in the above embodiment can be implemented in the form of hardware or in the form of software function modules. The present invention is not limited to any specific form of combination of hardware and software.

[0132] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A global hexagonal wargame map deformation analysis method based on a dynamic comprehensive deformation index, characterized in that: Include: Analysis of global hexagonal wargame map area deformation based on cell area standard deviation; Shape deformation analysis of global hexagonal wargame maps based on standard deviation of neighbor distances; The average cell area and the average cell neighbor distance are introduced, and the grid area deformation index and grid shape deformation index are proposed. The 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 wargame map.

2. The method for analyzing deformation of a global hexagonal wargame map based on a dynamic comprehensive deformation index according to claim 1, characterized in that: The global hexagonal wargame map area deformation analysis based on the standard deviation of the cell area includes: For a certain level of the global hexagonal wargame map, the average area of ​​all cells is calculated as follows: Among them, L is the current level of HGWM, CellNum L is the total number of pentagonal and hexagonal cells at level L of HGWM, is the area of ​​the i-th cell at the L-th level of HGWM; The calculation formula for the standard deviation of the cell area at the Lth level of HGWM is as follows: The larger the value of , the greater the difference in the cell area of ​​the Lth level of HGWM, and the greater the area deformation; conversely, the smaller the area deformation; if This means that the areas of all cells in the current level are equal.

3. The method for analyzing deformation of a global hexagonal wargame map based on a dynamic comprehensive deformation index according to claim 2, characterized in that: The grid area deformation index is proposed by introducing the average value of the cell area: The calculation formula of the grid area deformation index of the Lth level of HGWM is as follows: in, is the standard deviation of the cell area at the Lth level of HGWM, AvgArea L The average area of ​​all cells at level L of HGWM; GADI L The larger the value of , the greater the relative deformation of the cell area at the Lth level of HGWM, and vice versa.

4. The method for analyzing deformation of a global hexagonal wargame map based on a dynamic comprehensive deformation index according to claim 3 is characterized in that: The shape deformation analysis of the global hexagonal war game map based on the standard deviation of neighbor distances includes: For a certain level of the global hexagonal wargame map, the average value of the neighbor distances of all cells is calculated as follows: Among them, L is the current level of HGWM, CellNum L is the total number of pentagonal and hexagonal cells at the Lth level of HGWM, NborNum is the number of adjacent cells of the i-th cell at the Lth level of HGWM, is the distance from the i-th cell to its j-th adjacent cell; The calculation formula for the standard deviation of the single neighbor distance of the HGWM level L is as follows: The larger the value of , the greater the difference in the cell neighbor distances at the Lth level of HGWM, and the greater the shape deformation; conversely, the smaller the shape deformation; if This means that the neighbor distances of all cells in the current level are equal.

5. The method for analyzing deformation of a global hexagonal wargame map based on a dynamic comprehensive deformation index according to claim 4, characterized in that: The grid shape deformation index is proposed by introducing the average value of the cell neighbor distance, including: The calculation formula of the grid shape deformation index of the Lth level of HGWM is as follows: in, AvgNborDis is the standard deviation of the single neighbor distance of the L-th level of HGWM. L is the average distance between all cells at level L of HGWM; GSDI L The larger the value of , the greater the relative deformation of the cell shape at the Lth level of HGWM, and vice versa.

6. The method for analyzing deformation of a global hexagonal wargame map based on a dynamic comprehensive deformation index according to claim 5, characterized in that: The dynamic comprehensive deformation index constructed by using the mesh area deformation index and the mesh shape deformation index includes: The calculation formula of the dynamic comprehensive deformation index of HGWM level L is as follows: DIDI L =α·GADI L +(1-α)·GSDI L Among them, GADI L is the grid area deformation index of the Lth level of HGWM, GSDI L is the mesh shape deformation index of the Lth level of HGWM, and α is the weight variable.

7. The method for analyzing deformation of a global hexagonal wargame map based on a dynamic comprehensive deformation index according to claim 6, 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 different types of global war games for HGWM area deformation and shape deformation.

8. A global hexagonal wargame map deformation analysis system based on dynamic comprehensive deformation index, characterized in that: The system is used to implement the global hexagonal war game map deformation analysis method based on the dynamic comprehensive deformation index as described in any one of claims 1 to 7, comprising: The cell area standard deviation calculation module is used to analyze the area deformation of the global hexagonal war game map based on the cell area standard deviation; Neighborhood standard deviation calculation module, used to analyze the shape deformation of the global hexagonal war game map based on the neighborhood standard deviation; The deformation index calculation module is used to introduce the average cell area and the average cell neighbor distance, and propose the grid area deformation index and grid shape deformation index; The dynamic comprehensive deformation index calculation module is used to construct a dynamic comprehensive deformation index using the grid area deformation index and the grid shape deformation index, and to perform an overall deformation analysis on the area deformation and shape deformation of the global hexagonal war game map.

9. 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 according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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