Force-oriented and curved surface interpolation-based relationship network 3D visualization method, system, device and medium

Abstract

The method comprises the following steps: fusing node characteristic indexes and force-oriented plane layout, optimizing force-oriented layout algorithm, calculating repulsion and attraction between nodes respectively, and quickly reaching a convergent state; generating a composite curved surface through a 3D curved surface interpolation algorithm; drawing and generating a grid curved surface in a dense grid manner, fitting and calculating the grid curved surface to generate the composite curved surface; and reflecting community relationships and distribution between nodes; the system, device and medium can realize the 3D visualization method of the relationship network based on force orientation and curved surface interpolation; have the advantages of high calculation efficiency, being capable of intuitively analyzing the community and distribution characteristics of data from the image, and simple and controllable image generation parameters.

Description

Technical Field

[0001] This invention belongs to the fields of visualization and visual analysis, community discovery technology, and in particular relates to a 3D visualization method, system, device and medium for relational networks based on force guidance and surface interpolation. Background Technology

[0002] Relational networks fall under the research scope of graphs in data structures, and their study relies on the implementation and development of various graph algorithms. Visualization of relational networks is one branch of graph analysis. Achieving network visualization requires the rational design and allocation of the graph's spatial layout to achieve optimal visual effects, thereby uncovering more useful information.

[0003] Force-directed (also known as force-guided or force-oriented) algorithms are the core algorithms for graph visualization. This algorithm references physical and mechanical models such as the spring model and the charge model. It applies repulsive forces between each pair of vertices in the network and attractive forces between each pair of vertices connected by edges. By relying on force-driven adjustments, it makes the overall network layout in planar space more scientific and orderly. The force-directed layout calculation process includes three stages: initialization, iteration, and convergence / termination. The initialization stage randomly initializes the nodes in planar space; the iteration stage calculates the forces acting on the nodes and adjusts their positions according to the magnitude and direction of the forces; when the positions of all nodes no longer change during the iteration process, the force-directed layout calculation reaches the convergence condition, and the process enters the convergence stage.

[0004] However, force-directed algorithms have two major flaws. First, when the number of nodes in the network is large, nodes are prone to overlapping within a small area, causing the attractive and repulsive forces between nodes to largely cancel each other out, making it impossible to effectively reach convergence. Second, layout algorithms in planar space often face problems such as "edge intersections" and "node overlaps." Especially when the graph data is large, the visualized image is prone to element stacking, resulting in the "pom-pom phenomenon," which is detrimental to visualized data exploration and community discovery.

[0005] With the development of computer graphics, current visualization technology supports the creation of various types of charts, and has spawned a variety of related software or plugins for chart creation, including some programs that support 3D chart rendering. However, research on surface fitting networks is still relatively lacking. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, the present invention aims to propose a 3D visualization method, system, device, and medium for relational networks based on force-guided and surface interpolation. By fusing node feature indicators with force-guided planar layout, a composite surface is calculated using a 3D surface interpolation algorithm to construct a complex network visualization image in three-dimensional space. A grid surface is generated by drawing a dense grid, and the grid surface is fitted to the calculated composite surface. It has the advantages of high computational efficiency, the ability to intuitively analyze the community and distribution characteristics of data from the image, and simple and controllable image generation parameters.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A 3D visualization method based on the relationship network between force guidance and surface interpolation is proposed, with the following specific steps:

[0009] Step 1: Integrate node feature indicators with force-directed plane layout, optimize the force-directed layout algorithm, and calculate the repulsive and attractive forces between nodes to quickly reach convergence. Specifically, for the repulsive force calculation, the repulsive force is weighted based on the node centrality metric; for the attractive force calculation, the attractive force is added in batches during the iteration process based on the edge weight.

[0010] Step 2: Construct a complex network visualization image in three-dimensional space using a 3D surface interpolation algorithm: After calculating the node layout in planar space using the optimized force-directed layout algorithm in Step 1, the layout coordinates of all nodes in the xOy plane can be obtained; the weight values ​​of the nodes are used as the coordinates of the third dimension z-axis to construct a mapping from the xOy plane space to the xOyz three-dimensional space; a surface is generated based on the position coordinates of the nodes, and the surface generated by a single vertex is calculated using the surface generation formula. Then, all surfaces are combined to obtain a composite surface.

[0011] Step 3: Generate a mesh surface by drawing a dense mesh, and fit the mesh surface to the composite surface calculated in Step 2; adjust the style of the edges between the endpoints in the figure to make the direction of the edges fit the surface better.

[0012] The specific method for step one is as follows:

[0013] 1) Weighted repulsion force based on node weights

[0014] Record each node v i The weight is q i Calculate the repulsive force between each pair of nodes:

[0015] The repulsive force is weighted according to the weights of the two nodes, with the weight being the product of the node weights. This results in the central node generating a greater repulsive force against other nodes with higher weights. After weighting the repulsive force, for any two nodes v... iWith v j The formula for calculating its repulsive force is:

[0016]

[0017] For networks without node weights, node centrality metrics are used to calculate node v. i weight q i This weighted repulsion calculation method can accelerate the separation of high-weight nodes belonging to different communities, avoid entanglement between vertices, and prevent the algorithm from having a slow convergence speed.

[0018] 2) Gravity is added in batches during the iteration process based on edge weights.

[0019] Prioritize clustering nodes within the same community. During the initialization phase, sort all edges in descending order of weight. At the start of the iteration, remove all edges between vertices, ignoring the gravitational pull between them. During the iteration, evaluate each sorted edge sequentially according to the following relationship: Let t be the iteration number, w(e i (e) represents the i-th edge after sorting. i The weights; during the iteration process, when w(e) i The relationship between ) and t satisfies the following condition:

[0020]

[0021] Edge e can be i In the calculation process of incorporating force-oriented layout, edge e is calculated. i The attraction between the two nodes, i = i + 1; where t0 is a parameter; in the network, the higher the weight of an edge, the greater the correlation between its two nodes, and the closer they are in the layout; this method of adding the attraction relationship of the edges to the force calculation process in turn during the iteration process can make nodes with high correlation gather first, thus speeding up the convergence speed.

[0022] For networks lacking edge weights, edge centrality is used as a weight in the calculation.

[0023] Step two involves generating surfaces based on the node's position coordinates, calculating the surface generated by a single vertex using the surface generation formula, and then combining all surfaces to obtain a composite surface. The specific method is as follows:

[0024] Let the surface be F(x, y), and let each node v i and its coordinates (x) i y i , z i ) satisfies F(x) i y i )≈z iFurthermore, F(x, y) → 0 as x → ∞ or y → ∞; simultaneously, surface calculations are performed with the goal of generating a continuous and as smooth a surface as possible.

[0025] 1) Construct a point interpolation surface for a single node.

[0026] From the perspective of a single node, in the xOy space, points closer to this node are more affected, while points farther away are relatively less affected; therefore, for node v i Set a surface constructor f i (x, y), this function makes the surface smooth while also producing the "objects appear larger when closer and smaller when farther away" property; let the point (x, y) in the planar space be the same as the node v. i The distance is r. According to the surface constructor, the z-coordinate of this point has the following relationship with the node:

[0027]

[0028] The final surface generation formula is as follows:

[0029]

[0030] In the formula, (x i y i , z i ) is node v i In three-dimensional space, k is the coordinate, and k is a coefficient that controls the magnitude of the influence; f is generated by all nodes. i By performing multi-surface composition on (x, y), a complete surface image can be obtained;

[0031] 2) Multi-surface composition: Surfaces are generated through superposition, summation, interpolation, or maximum interpolation.

[0032] When there are negative values ​​in the node weights of the network, the superposition and summation interpolation method should be used to generate the surface; when all the node weights of the network are non-negative, the maximum interpolation method should be used to generate the surface.

[0033] 2.1) Generating surfaces through superposition, summation, and interpolation.

[0034] The basic calculation formula for surfaces obtained by superposition and summation interpolation is as follows:

[0035]

[0036] For scenarios where nodes are too densely distributed in the xOy space, the overall value of the dense portion will be much larger than the true value. Therefore, a weighted summation interpolation method is used for each f. i (x, y) are weighted by distance and then summed:

[0037]

[0038] 2.2) Generating surfaces through maximum interpolation

[0039] The basic calculation formula for surfaces using maximum interpolation is as follows:

[0040] F(x,y)=max{f1(x,y),f2(x,y)…f n (x, y)}

[0041] The surface generated by the maximum interpolation has indentations. Convolution in image processing is used to eliminate the indentations on the surface.

[0042] Step 2.2) of the above describes the use of convolution in image processing to eliminate dents on curved surfaces. Specifically, this involves detecting dents in the image using an equalization operator, averaging the dent portions using the equalization operator, and performing convolution calculations on the current region. The calculation process at the horizontal coordinates (x, y) is as follows:

[0043]

[0044] If, after calculation, F′(x, y) > F(x, y), it indicates that there is a concave area in the image. In this case, the value of F′(x, y) is used to replace the original F(x, y). The complete process is denoted as:

[0045]

[0046] Multiple iterations were performed to improve the dents in the image.

[0047] The specific method for step three is as follows:

[0048] 1) The surface is drawn by generating a dense mesh, so that the surface image presents a smooth and coherent visual effect: First, a drawing precision α is specified; then, grid points are drawn in space with α as the distance interval; grid lines are drawn between adjacent grid points to divide the surface into multiple tightly joined and non-intersecting triangles or quadrilaterals; finally, the polygons formed by all the grids are filled to obtain a grid surface, which is used to fit the surface image.

[0049] 2) Adjust the style of all edges, set the drawing precision, use the same precision to segment each edge, and adjust the z-axis coordinates of the two endpoints of each segment so that the endpoints of each small segment on each edge are located on the surface calculated in step 2, so as to fit the dense mesh.

[0050] A 3D visualization system based on force-guided relational networks with surface interpolation, comprising:

[0051] The improved force-directed planar layout module optimizes the force-directed layout algorithm by weighting the repulsive force and adding the attractive force in batches, calculates the layout of nodes in the xOy plane space, and obtains the coordinates of all nodes in the planar space.

[0052] The surface calculation and generation module calculates the surface generation formula in the point interpolation surface of a single node to generate the surface corresponding to the node in the network after mapping from planar space to three-dimensional space; through the multi-surface composition method, the surfaces corresponding to multiple nodes are combined to generate a smooth and flat surface, which can also reflect the community division of nodes in the relational network.

[0053] The surface mesh drawing module fits the surface generated in step two by generating a dense mesh with a certain precision, so that the mesh presents an approximately smooth surface; the edge style is fitted with the same precision so that the edge style fits the dense mesh.

[0054] A 3D visualization device based on the relationship network of force guidance and surface interpolation, including

[0055] Memory, used to store computer programs;

[0056] A processor is used to implement the 3D visualization method based on the relationship network of force guidance and surface interpolation described in steps one and two when executing the computer program.

[0057] A computer-readable storage medium storing a computer program that, when executed by a processor, enables 3D visualization of a relational network based on force-guided and surface interpolation.

[0058] Compared with the prior art, the present invention has the following advantages:

[0059] 1. Step one of this invention adopts a method of weighting the repulsive force based on node weights and adding the attractive force in batches during the iteration process based on edge weights to improve the performance of the force-oriented algorithm. This enables vertices belonging to the same community to gather quickly and preferentially, and vertices in different communities to separate. It has the advantages of reducing the number of iterations, improving computational efficiency, and quickly reaching the convergence state.

[0060] 2. This invention establishes a mapping scheme for relationship networks from a two-dimensional planar layout to a three-dimensional layout. Step two proposes a surface calculation generation method of "point interpolation + composite image" to generate a three-dimensional surface of the relationship network. The "convex hull" in the surface can reveal the obvious communities and important nodes in the relationship network. Based on the node weights in the network, two composite image schemes are proposed to generate the surface by superposition summation interpolation or maximum interpolation. Compared with the traditional planar layout, the three-dimensional surface has the advantage of being able to more significantly reflect the changes in vertex weights, which is convenient for analyzing the structure and key nodes of the relationship network. It also has the advantages of being able to visually map the communities and distribution characteristics in the network intuitively, with obvious and easy-to-observe visual elements, and simple and controllable image generation parameters.

[0061] 3. Step three uses a dense mesh method to draw the surface. Drawing the surface by filling with a dense mesh can complete the drawing and presentation of the surface with low time and memory overhead, and has the advantages of fast drawing speed and smooth visual effect.

[0062] In summary, in terms of image quality, the generated images are clearer and have smoother surfaces than two-dimensional force-guided maps, and the clustered parts of nodes will have obvious bulges and depressions. In terms of visual analysis, the generated images can clearly reflect the hierarchy and community relationships in the relationship network, which is helpful for community discovery and group analysis-related research, and can also uncover more potential valuable information through images. Attached Figure Description

[0063] Figure 1 This is a simplified flowchart of the relationship network 3D visualization method of the present invention.

[0064] Figure 2 This is a layout image of the force-guided layout method of the present invention in the xOy plane space.

[0065] Figure 3 It is an image directly drawn in 3D space by the relational network of this invention.

[0066] Figure 4 This is a diagram showing the roughness of the surface when k is 1.0, 2.0, 3.0, and 5.0 respectively.

[0067] Figure 5 This invention generates surface plots by summing, superimposing, and interpolating.

[0068] Figure 6 This invention generates surface plots using weighted summation interpolation.

[0069] Figure 7 This invention generates surface plots using maximum interpolation.

[0070] Figure 8This is a "dent" image in the surface generated by the maximum interpolation of this invention.

[0071] Figure 9 (a) is a detailed view of the dent before optimization according to the present invention. Figure 9 (b) is a detailed view of the indentation after 20 iterations of the present invention.

[0072] Figure 10 From top to bottom, these are images of the visualization of the Karate Karate Club, the relationships between characters in Les Misérables, and the network data of the American College Football League, based on this invention.

[0073] Figure 11 This invention generates 3D visualization layout images on images of three random network models. Detailed Implementation

[0074] The present invention will now be described in further detail with reference to the accompanying drawings.

[0075] See Figure 1 A 3D visualization method based on the relationship network between force guidance and surface interpolation is presented, with the following specific steps:

[0076] Step 1: Integrate node feature indicators with force-directed plane layout, optimize the force-directed layout algorithm, and calculate the repulsive and attractive forces between nodes to quickly reach convergence. Specifically, for the repulsive force calculation, the repulsive force is weighted based on the node centrality metric; for the attractive force calculation, the attractive force is added in batches during the iteration process based on the edge weight.

[0077] Step 2: Construct a complex network visualization image in three-dimensional space using a 3D surface interpolation algorithm: After calculating the node layout in planar space using the optimized force-directed layout algorithm in Step 1, the layout coordinates of all nodes in the xOy plane can be obtained; the weight values ​​of the nodes are used as the coordinates of the third dimension z-axis to construct a mapping from the xOy plane space to the xOyz three-dimensional space; a surface is generated based on the position coordinates of the nodes, and the surface generated by a single vertex is calculated using the surface generation formula. Then, all surfaces are combined to obtain a composite surface.

[0078] Step 3: Generate a mesh surface by drawing a dense mesh, and fit the mesh surface to the composite surface calculated in Step 2; adjust the style of the edges between the vertices in the figure to make the direction of the edges fit the surface better.

[0079] The specific method for step one is as follows:

[0080] 1) Weighted repulsion force based on node weights

[0081] Record each node v i The weight is q iCalculate the repulsive force between each pair of nodes:

[0082] The repulsive force is weighted according to the weights of the two nodes, with the weight being the product of the node weights. This results in the central node generating a greater repulsive force against other nodes with higher weights. After weighting the repulsive force, for any two nodes v... i With v j The formula for calculating its repulsive force is:

[0083]

[0084] For networks without node weights, node centrality metrics are used to calculate node v. i weight q i Examples include node degree centrality, node PageRank centrality, and node eigenvalue centrality.

[0085] 2) Gravity is added in batches during the iteration process based on edge weights.

[0086] Prioritize clustering nodes within the same community. During the initialization phase, sort all edges in descending order of weight. At the start of the iteration, remove all edges between vertices, ignoring the gravitational pull between them. During the iteration, evaluate each sorted edge sequentially according to the following relationship: Let t be the iteration number, w(e i (e) represents the i-th edge after sorting. i The weights; during the iteration process, when w(e) i The relationship between ) and t satisfies the following condition:

[0087]

[0088] Edge e can be i In the calculation process of incorporating force-oriented layout, edge e is calculated. i The attraction between the two nodes, i = i + 1; where t0 is a parameter; since in the network, the higher the weight of the edge, the greater the correlation between its two nodes, and the closer they are in the layout; this method of adding the attraction relationship of the edge to the force calculation process in turn during the iteration process can make nodes with high correlation gather first, thus speeding up the convergence speed.

[0089] For networks lacking edge weights, edge centrality measures are used as weights in the calculation, including betweenness centrality, Jaccard coefficient centrality, etc.

[0090] Using PageRank centrality as vertex weights and Jaccard coefficient centrality as edge weights, the layout effect of the method described in step one is as follows: Figure 2 As shown.

[0091] In step two, a surface is generated based on the position coordinates of the node. The surface generated by a single vertex is calculated using the surface generation formula. Then, all surfaces are combined to obtain a composite surface. The specific method is as follows:

[0092] Let the surface be F(x, y), and let each node v i and its coordinates (x) i y i , z i ) satisfies F(x) i y i )≈z i Furthermore, F(x, y) → 0 as x → ∞ or y → ∞; simultaneously, surface calculations are performed with the goal of generating a continuous and as smooth a surface as possible.

[0093] 1) Construct a point interpolation surface for a single node.

[0094] From the perspective of a single node, consider the surface effect generated by the layout of nodes in 3D space. For a single node, in xOy space, points closer to this node are more affected, while points farther away are relatively less affected. Therefore, for node v... i Set a surface constructor f i (x,y), this function makes the surface smooth while also producing the "objects appear larger when closer and smaller when farther away" property; let the point (x,y) in the planar space be the same as the node v. i The distance is r. According to the surface constructor, the z-coordinate of this point has the following relationship with the node:

[0095]

[0096] The final surface generation formula is as follows:

[0097]

[0098] In the formula, (x i ,y i ,z i ) is node v i In three-dimensional space, k is the coordinate, and k is a coefficient that controls the magnitude of the influence; f is generated by all nodes. i By performing multi-surface composition on (x, y), a complete surface image can be obtained. In this embodiment, k is set to 2. The value of k affects the ruggedness of the surface. Assuming there is a single node located at the center of the coordinate axis with a node weight of 1, the ruggedness of the generated surface varies with different values ​​of k, as shown below. Figure 4 As shown.

[0099] 2) Multi-surface composition: Surfaces are generated through superposition, summation, interpolation, or maximum interpolation.

[0100] When there are negative values ​​in the node weights of the network, the superposition and summation interpolation method is used to generate the surface; when all the node weights of the network are non-negative, the maximum value interpolation is used to generate the surface, and the value of the node at the plane projection coordinate is closer to the true weight of the node.

[0101] 2.1) Generating surfaces through superposition, summation, and interpolation.

[0102] The basic calculation formula for surfaces obtained by superposition and summation interpolation is as follows:

[0103]

[0104] For scenarios where nodes are too densely distributed in the xOy space, the overall value of the dense portion will be much larger than the true value. Therefore, a weighted summation interpolation method is used for each f. i (x, y) are weighted by distance and then summed:

[0105]

[0106] The obtained surface image is as follows Figure 6 As shown.

[0107] 2.2) Generating surfaces through maximum interpolation

[0108] The basic calculation formula for surfaces using maximum interpolation is as follows:

[0109] F(x,y)=max{f1(x,y),f2(x,y)…f n (x, y)}

[0110] The interpolated surface image calculated using this formula is as follows: Figure 7 As shown, F(x, y) at most nodes is the true value. The extremum function is usually accompanied by non-differentiable breakpoints, which appear as obvious concave creases in the image, such as... Figure 8 As shown.

[0111] Using the concept of convolution in image processing, we detect concave parts in the image through operators and use an equalization operator to calculate the average value of these parts.

[0112] The operator uses a 3×3 8-neighborhood convolution template to perform convolution calculations on the current region. The calculation process at the horizontal coordinate (x, y) is as follows:

[0113]

[0114] If, after calculation, F′(x, y) > F(x, y), it indicates that there is a concave area in the image. In this case, the value of F′(x, y) is used to replace the original F(x, y). The complete process is denoted as:

[0115]

[0116] After 20 iterations, the indentation effect in the image was improved, such as... Figure 9 As shown.

[0117] The specific method for step three is as follows:

[0118] 1) Surfaces are drawn by generating dense meshes to achieve a smooth and coherent visual appearance: First, a drawing precision of α = 0.05 and a layout space of 10×10×1 are used. For each node v... i Then, grid lines are drawn between adjacent grid points to divide the surface into multiple tightly joined and non-intersecting triangles or quadrilaterals; finally, the polygons formed by all the grids are filled to obtain a grid surface, which is used to fit the expected surface image.

[0119] 2) Adjust the style of all edges, set the drawing precision, use the same precision to segment each edge, and adjust the z-axis coordinates of the two endpoints of each segment so that the endpoints of each small segment on each edge are located on the calculated curved surface, thereby fitting the dense mesh.

[0120] For other data, the following examples are provided;

[0121] I. Real Relationship Network Data

[0122] The planar force-directed graphs generated from three models—Karate Karate Club, Les Misérables character relationships, and NCAA football—and the 3D network images generated using two different composite methods are shown below. Figure 10 As shown.

[0123] II. Random Relationship Network Data

[0124] Visualizations of three network models—ER random graph (ER), WS small-world model (WS), and BA scale-free network (BA)—were generated; four network planar force-directed graphs and 3D network images generated using two different composite methods were also presented. Figure 11 As shown.

[0125] As can be seen from the embodiments and figures, compared with the prior art, the planar force-guided algorithm optimization technology proposed in this invention can accelerate the aggregation of vertices within the same community and the separation of vertices in different communities, and has a faster convergence speed in the iterative calculation process.

[0126] The surface generation technology proposed in this invention can present obvious communities and important nodes in a relational network through the "convex hull" of the surface. Compared with the traditional planar layout, the surface in three-dimensional space can more significantly reflect the changes in vertex weights, making it easier for researchers in related fields to analyze the structure and key nodes of the relational network.

[0127] The dense mesh surface drawing scheme proposed in this invention draws curved surfaces by filling them with high-density meshes, which has the characteristics of fast drawing speed and smooth visual effect.

Claims

1. A 3D visualization method based on the relationship network of force guidance and surface interpolation, characterized in that, The specific steps are as follows: Step 1: Integrate node feature indicators with force-directed plane layout, optimize the force-directed layout algorithm, and calculate the repulsive and attractive forces between nodes to quickly reach convergence. Specifically, for the repulsive force calculation, the repulsive force is weighted based on the node centrality metric; for the attractive force calculation, the attractive force is added in batches during the iteration process based on the edge weight. 1) Weighted repulsion force based on node weights Record each node The weight is Calculate the repulsive force between each pair of nodes: The repulsive force is weighted according to the weights of the two nodes, with the weight being the product of the node weights. This results in the central node generating a greater repulsive force against other nodes with higher weights. After weighting the repulsive force, for any two nodes... and The formula for calculating its repulsive force is: For networks without node weights, node centrality metrics can be used to calculate node weights. weight ; 2) Gravity is added in batches during the iteration process based on edge weights. Prioritize clustering nodes from the same community. During the initialization phase, sort all edges in descending order of weight. At the start of the iteration, remove all edges between vertices, ignoring the gravitational pull between them. During the iteration, evaluate each sorted edge sequentially according to the following relationship: [The rest of the text is missing]. For the number of iteration rounds, For the sorted number Strip edge The weights; during the iteration process, when and The relationship satisfies the following conditions: Can the edge In the calculation process of force-oriented layout, the edges are calculated. The gravitational force between the two ends of the node, at the same time In the formula The parameters are: In the network, the higher the weight of an edge, the greater the correlation between the nodes at its two ends, and the closer they are in the layout; This method of adding the gravitational relationship of the edges to the force calculation process in turn during the iteration can make nodes with high correlation cluster first, thus speeding up the convergence speed. For networks lacking edge weights, edge centrality metrics are used as weights in the calculation. Step 2: Construct a complex network visualization image in 3D space using a 3D surface interpolation algorithm: After calculating the node layout in planar space using the optimized force-directed layout algorithm from Step 1, the visualization image of all nodes can be obtained. The layout coordinates of the plane; the weight values ​​of the nodes are used as a third dimension. The coordinates of the axes, constructing from planar space to Mapping in three-dimensional space; generating surfaces based on the position coordinates of nodes, calculating the surface generated by a single vertex using the surface generation formula, and then combining all surfaces to obtain a composite surface; Step 3: Generate a mesh surface by drawing a dense mesh, and fit the mesh surface to the composite surface calculated in Step 2; adjust the style of the edges between the endpoints in the figure to make the direction of the edges fit the surface better.

2. The 3D visualization method based on the relationship network of force guidance and surface interpolation according to claim 1, characterized in that, Step two involves generating surfaces based on the node's position coordinates, calculating the surface generated by a single vertex using the surface generation formula, and then combining all surfaces to obtain a composite surface. The specific method is as follows: Let the surface be , with each node and its coordinates satisfy , and when or hour, Simultaneously, with the goal of generating a continuous and as smooth a surface as possible, surface calculations are performed: 1) Construct a point interpolation surface for a single node. From the perspective of a single node, In space, points closer to this node are more affected, while points farther away are relatively less affected; therefore, for nodes... Set up a surface constructor This function makes the surface smooth while also producing the "objects appear larger when closer and smaller when farther away" property; denotes the position of a point in planar space. With nodes The distance is According to the surface constructor, the z-coordinate at this point has the following relationship with the node: The final surface generation formula is as follows: In the formula For nodes Coordinates in three-dimensional space To control the coefficients of influence; generate coefficients from all nodes. By performing multi-surface composite operations, a complete surface image can be obtained; 2) Multi-surface composition: Surfaces are generated through superposition, summation, interpolation, or maximum interpolation. When there are negative values ​​in the node weights of the network, the superposition and summation interpolation method should be used to generate the surface; when all the node weights of the network are non-negative, the maximum interpolation method should be used to generate the surface. 2.1) Generating surfaces through superposition, summation, and interpolation. The basic calculation formula for surfaces obtained by superposition and summation interpolation is as follows: For the node in In scenes where the spatial distribution is too dense, the overall value of the dense portion will be much larger than the true value. Therefore, a weighted summation interpolation method is used for each... Weight the results by distance and then sum them: 2.2) Generating surfaces through maximum interpolation The basic calculation formula for surfaces using maximum interpolation is as follows: The surface generated by the maximum interpolation has indentations. Convolution in image processing is used to eliminate the indentations on the surface.

3. The 3D visualization method based on the relationship network of force guidance and surface interpolation according to claim 2, characterized in that, Step 2.2) of the above describes the use of convolution in image processing to eliminate dents on curved surfaces. Specifically, this involves detecting dents in the image using an equalization operator, averaging the dent portions using the equalization operator, performing convolution calculations on the current region, and then... (The sentence is incomplete and requires further context to translate accurately.) The calculation process at this point is as follows: If after calculation there is This indicates that there is a dent in the image at that location, in which case... Replace the original value with the value The complete process is recorded as follows: Multiple iterations were performed to improve the dents in the image.

4. The 3D visualization method based on the relationship network of force guidance and surface interpolation according to claim 3, characterized in that, The specific method for step three is as follows: 1) Draw surfaces by generating dense meshes to achieve a smooth and coherent visual effect: First, specify a drawing precision. ; then with To create a distance interval, grid points are plotted in space; grid lines are drawn between adjacent grid points to divide the surface into multiple tightly joined and non-intersecting triangles or quadrilaterals; finally, the polygons formed by all the grids are filled to obtain a grid surface, which is used to fit the expected surface image. 2) Adjust the style of all edges, set the drawing precision, divide each edge into segments using the same precision, and adjust the endpoints of each segment. The axis coordinates are used to ensure that the endpoints of each small segment on each edge are located on the surface generated in step two, thereby fitting the dense mesh.

5. The visualization system of the 3D visualization method for relational networks according to any one of claims 1 to 4, characterized in that, include: The improved force-directed planar layout module optimizes the force-directed layout algorithm by weighting repulsive forces and adding attractive forces in batches, calculating the position of nodes in the network. The layout in planar space yields the coordinates of all nodes within that planar space. The surface calculation and generation module calculates the surface generation formula in the point interpolation surface of a single node to generate the surface corresponding to the node in the network after mapping from planar space to three-dimensional space; through the multi-surface composition method, the surfaces corresponding to multiple nodes are combined to generate a smooth and flat surface, which can also reflect the community division of nodes in the relational network. The surface mesh drawing module fits the surface generated in step two by generating a dense mesh with a certain precision, so that the mesh presents an approximately smooth surface; the edge style is fitted with the same precision so that the edge style fits the dense mesh.

6. A 3D visualization device based on a force-guided relational network with surface interpolation, characterized in that, include: Memory, used to store computer programs; A processor, configured to implement the force-guided relational network 3D visualization method based on surface interpolation as described in any one of claims 1 to 4 when executing the computer program.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, enables 3D visualization of a force-guided relational network with surface interpolation based on the method of any one of claims 1 to 4.

Images