Information visualization method and system applied to parallel turbulent transport

Abstract

The embodiment of the invention discloses an information visualization method and system applied to parallel turbulent transport, and belongs to the technical field of data visualization. According to the embodiment of the invention, trajectory integral operation is performed on flow field sampling points through a Lagrange tracking method, and an original streamline set containing time evolution information is generated; performing topological structure analysis processing on the original streamline set to generate a streamline topological characteristic spectrum containing branch points, sink points and saddle points; constructing a multi-scale parallel rendering task queue based on the map, and distributing an original streamline set to a plurality of computing nodes for collaborative rendering through a spatial region division algorithm to obtain a collaborative rendering intermediate result; and according to the result, streamline density self-adaptive adjustment processing is executed, a turbulent transport visualization image sequence with a dynamic detail level is generated, the turbulent transport visualization image sequence is used for presenting the spatial distribution characteristics and the time evolution trend of the turbulent transport phenomenon in the flow field, and the efficiency and the accuracy of flow field visualization are improved.

Description

Technical Field

[0001] This invention relates to the field of data visualization technology, specifically to an information visualization method and system applied to parallel turbulent transport. Background Technology

[0002] In research fields such as magnetic confinement fusion and tokamak scenarios, the visualization of turbulent transport phenomena in flow fields is an important research topic. Currently, some existing flow field visualization techniques describe the flow field using the simple Eulerian method. While this method can obtain some basic information about the flow field, it cannot accurately capture the temporal evolution information of fluid particles and is not comprehensive enough for complex flow fields. Furthermore, some existing visualization techniques lack in-depth analysis of the topological structure when processing flow field data, making it difficult to clearly show the spatial correlation between streamlines and the distribution patterns of critical points, thus hindering researchers from accurately grasping the intrinsic structure of the flow field. In addition, when generating visualization images, existing techniques cannot adaptively adjust streamline density according to the actual flow field conditions, resulting in images that cannot accurately represent the spatial distribution characteristics and temporal evolution trends of turbulent transport phenomena in the flow field. Therefore, how to effectively improve the efficiency and accuracy of flow field visualization is a technical problem that needs to be solved. Summary of the Invention

[0003] The present invention provides an information visualization method and system for parallel turbulent transport, which can solve or partially solve the technical problems involved in the background art.

[0004] This invention provides an information visualization method for parallel turbulent transport, applied to an information visualization system. The method includes: performing trajectory integration on sampling points of the flow field using the Lagrange pursuit method to generate an original streamline set containing time evolution information, wherein the original streamline set is composed of a sequence of spatial position coordinates of fluid particles at continuous time intervals; performing topological structure analysis processing on the original streamline set to generate a streamline topological feature map containing branch points, sink points, and saddle points, wherein the streamline topological feature map is used to describe the spatial correlation and critical point distribution patterns between streamlines; constructing a multi-scale parallel rendering task queue based on the streamline topological feature map, and distributing the original streamline set to multiple computing nodes for collaborative rendering processing using a spatial region partitioning algorithm to obtain intermediate collaborative rendering results; and performing adaptive streamline density adjustment processing based on the intermediate collaborative rendering results to generate a turbulent transport visualization image sequence with dynamic detail levels, wherein the turbulent transport visualization image sequence is used to present the spatial distribution characteristics and temporal evolution trends of turbulent transport phenomena in the flow field.

[0005] This invention provides an information visualization system, including at least one processor and a memory; the memory stores computer execution instructions; the at least one processor executes the computer execution instructions stored in the memory, causing the at least one processor to perform the above-described method.

[0006] This invention provides a readable storage medium on which a program or instruction is stored, and when the program or instruction is executed by a processor, it implements the steps of the above method.

[0007] This invention generates a raw streamline set containing temporal evolution information using the Lagrange trace method, resulting in a more comprehensive and accurate description of fluid motion. Based on this, topological analysis is performed on the raw streamline set, generating a streamline topological feature map that clearly describes the spatial relationships between streamlines and the distribution patterns of critical points, enabling in-depth analysis of the flow field's intrinsic structure. A multi-scale parallel rendering task queue is constructed based on the streamline topological feature map, and a spatial region partitioning algorithm distributes the raw streamline set to multiple computing nodes for collaborative rendering, significantly improving rendering efficiency. Simultaneously, the computational power of multiple nodes enables the processing of large-scale flow field data. Finally, adaptive streamline density adjustment is performed based on the intermediate results of the collaborative rendering, generating a sequence of turbulent transport visualization images with dynamic detail levels, accurately presenting the spatial distribution characteristics and temporal evolution trends of turbulent transport phenomena in the flow field.

[0008] With this design, the embodiments of the present invention not only improve the efficiency and quality of flow field visualization, but also provide more in-depth and accurate information for flow field research. Attached Figure Description

[0009] Figure 1 This is a flowchart of an information visualization method for parallel turbulent transport provided in an embodiment of the present invention.

[0010] Figure 2 This is a schematic diagram of the structure of an information visualization system provided in an embodiment of the present invention. Detailed Implementation

[0011] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the embodiments of the present invention.

[0012] In the embodiments of this invention, the terms "first," "second," etc., are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of this invention can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class, without limiting the number of objects; for example, a first object can be one or more. Furthermore, in the embodiments of this invention, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects have an "or" relationship.

[0013] Figure 1 An information visualization method for parallel turbulent transport is shown, which is applied to an information visualization system. The method includes the following steps 110-140.

[0014] Step 110: Perform trajectory integration on the flow field sampling points using the Lagrange pursuit method to generate an original streamline set containing time evolution information. The original streamline set consists of a sequence of spatial position coordinates of fluid particles at continuous time intervals.

[0015] In magnetic confinement fusion and tokamak scenarios, the study of the flow field is crucial for understanding plasma turbulent transport phenomena. The Lagrange tracking method is an effective means of capturing the trajectories of fluid particles. First, a series of representative sampling points are selected within the flow field inside the tokamak device. These sampling points act as "monitoring stations" distributed throughout the flow field, used to record the motion information of the fluid particles.

[0016] At the start of the tracking, each sampling point serves as the starting point. As time progresses, the fluid particles move within the flow field. Within each consecutive time interval, the spatial coordinates of the fluid particles are precisely recorded. For example, at the end of the first time interval, the new coordinates of each fluid particle relative to the initial sampling point are recorded; at the end of the second time interval, the new coordinates are recorded again, and so on.

[0017] As time progresses, these continuously recorded spatial coordinates form the trajectories of fluid particles. For each fluid particle, its trajectory consists of a series of spatial coordinates arranged in chronological order. The trajectories of numerous fluid particles combine to form a set of primordial streamlines. This set of primordial streamlines not only contains information about the spatial distribution of the flow field at a given moment but also information about the evolution of the flow field over time. By analyzing this set of primordial streamlines, we can understand the motion of fluid particles at different times and the overall dynamic trend of the flow field.

[0018] Step 120: Perform topological structure analysis on the original streamline set to generate a streamline topological feature map containing branch points, sink points and saddle points. The streamline topological feature map is used to describe the spatial correlation between streamlines and the distribution law of critical points.

[0019] Understandably, after obtaining the original streamline set, topological analysis is needed to gain a deeper understanding of the flow field's structure and characteristics. The purpose of topological analysis is to identify key feature points in the flow field, namely branch points, sink points, and saddle points, and to generate a map that describes the distribution patterns of these feature points and the spatial relationships between streamlines.

[0020] A branch point indicates that streamlines branch at this point, implying a tendency for the flow field to disperse in the vicinity of the point, which may be related to some kind of diffusion phenomenon in the flow field; a sink point indicates that streamlines converge at this point, reflecting a tendency for the flow field to concentrate in the vicinity of the point, which may be related to some kind of convergence effect in the flow field; a saddle point is a special critical point in the flow field, where the streamlines in the vicinity exhibit a unique topological structure.

[0021] By performing topological analysis on the original streamline ensemble, the location and number of key feature points can be determined, and their information can be integrated into a map, known as the streamline topological feature map. This map intuitively displays the spatial relationships between streamlines and the distribution patterns of key feature points. In magnetic confinement fusion and tokamak scenarios, the streamline topological feature map can help researchers better understand the structure and dynamic changes of plasma flow fields.

[0022] As an optional embodiment, step 120 includes: Step 121: Extract the spatial position coordinate sequence of each streamline in the original streamline set, calculate the displacement vector of the fluid particle under adjacent time intervals, and determine the local curvature extremum of the streamline based on the direction change rate of the displacement vector.

[0023] When performing topological analysis on the original streamline set, the first step is to extract the spatial coordinate sequence of each streamline, because the spatial coordinate sequence of each streamline records the specific position of the fluid particles at different times.

[0024] After extracting the spatial coordinate sequence of each streamline, the displacement vector of the fluid particle is calculated for adjacent time intervals. The displacement vector represents the positional change of the fluid particle within adjacent time intervals, containing two important pieces of information: direction and magnitude. By comparing the displacement vectors of adjacent time intervals, we can understand the changes in the direction of motion of the fluid particle.

[0025] The local curvature extrema of streamlines are determined based on the rate of change of the direction of the displacement vector. These local curvature extrema reflect the locations where the curvature of the streamline reaches its maximum or minimum in a local region. Specifically, a large rate of change of the direction of the displacement vector indicates a significant change in the direction of fluid particle motion within a short period, resulting in a greater degree of curvature in the streamline and potentially the existence of local curvature extrema. By analyzing and judging the rate of change of the direction of the displacement vector, local curvature extrema of streamlines can be accurately identified. These local curvature extrema play an important role in the topological analysis of the flow field and may be related to key feature points in the flow field (such as branch points, sink points, and saddle points).

[0026] Step 122: Perform neighborhood search processing on the local curvature extrema points, identify the set of intersection points where the spatial distance between the local curvature extrema points of different streamlines is less than a preset threshold, and mark the intersection points in the set of intersection points where the number of connected streamlines exceeds a preset number as branch points.

[0027] After identifying the local curvature extrema of streamlines, a neighborhood search is needed to determine the branching points in the flow field. The purpose of the neighborhood search is to find points that are close to each other among the local curvature extrema of different streamlines; these points may be intersections between streamlines.

[0028] The specific operation involves, for each local curvature extremum point, searching within a certain spatial range using that point as the center to find the local curvature extremum points of other streamlines. The spatial distance between these local curvature extremum points of different streamlines is calculated and compared with a preset threshold. If the spatial distance is less than the preset threshold, these local curvature extremum points are considered to form an intersection set.

[0029] After obtaining the set of intersection points, the number of streamlines connected to each intersection point is further analyzed. Intersection points with more than a preset number of connected streamlines are marked as branch points. This is because a key characteristic of branch points is the presence of numerous streamlines connecting and branching at that location. By determining the number of connected streamlines, branch points in the flow field can be accurately identified. In magnetic confinement fusion and tokamak scenarios, the existence of branch points may be related to diffusion and transport processes in the plasma flow field. Accurate identification of branch points allows for a deeper understanding of the complex behavior of the plasma flow field.

[0030] Step 123: Calculate the velocity divergence value of each streamline in the original streamline set, mark the spatial location with negative velocity divergence value and surrounding streamlines showing a converging trend as the sink point, and mark the spatial location with positive velocity divergence value and surrounding streamlines showing a diverging trend as the saddle point.

[0031] To determine the sink and saddle points in the flow field, it is necessary to calculate the velocity divergence value of each streamline in the original streamline set. The velocity divergence value reflects whether the fluid in the flow field tends to converge or diverge near a certain point.

[0032] When calculating the velocity divergence value of each streamline, it is necessary to consider the velocity variation of fluid particles near that point. A negative velocity divergence value indicates that the flow field tends to converge near that point, meaning the fluid concentrates towards that point; a positive velocity divergence value indicates that the flow field tends to diverge near that point, meaning the fluid diffuses outward from that point.

[0033] After calculating the velocity divergence value, the sink and saddle points are determined by considering the distribution of surrounding streamlines. When the velocity divergence value is negative and the surrounding streamlines exhibit a clear converging trend, this spatial location is marked as the sink. A sink typically represents an "attraction center" in the flow field, where fluid gradually converges. For example, in a tokamak device, the sink may be related to some confinement mechanism of the plasma; fluid convergence near the sink may help improve the plasma confinement efficiency.

[0034] When the velocity divergence is positive and the surrounding streamlines exhibit a diverging trend, this spatial location is marked as a saddle point. A saddle point is a special critical point in a flow field, and the streamline distribution around it has a unique topological structure. Near a saddle point, the fluid exhibits both an outward diffusion tendency and a certain directionality. Through this complex flow behavior, we can gain a deeper understanding of the overall structure and dynamic changes of the flow field.

[0035] Step 124: Construct a topological correlation matrix based on the spatial coordinates of the branch points, sink points, and saddle points. The row vectors of the topological correlation matrix represent the critical point types, and the column vectors represent the spatial connection relationships between the critical points.

[0036] After determining the spatial coordinates of the branch points, sink points, and saddle points, a topological incidence matrix needs to be constructed to more clearly describe the relationships between these critical points. The topological incidence matrix is ​​a mathematical tool used to represent the spatial connectivity between critical points.

[0037] The row vectors of the topological incidence matrix represent the types of critical points, namely branch points, sink points, and saddle points. Each row corresponds to a type of critical point, thus distinguishing the positions of different types of critical points within the matrix.

[0038] The column vectors represent the spatial connections between critical points. For each critical point, we check whether it has a spatial connection with other critical points. If a connection exists, a set value is marked at the corresponding position in the matrix, indicating that a connection exists; if no connection exists, another set value is used. In this way, the spatial connections between all critical points can be integrated into a single matrix.

[0039] Topological incidence matrices can visually represent the spatial connectivity between branch points, sink points, and saddle points. In magnetic confinement fusion and tokamak scenarios, topological incidence matrices can help researchers better understand the interactions and influences between key feature points in the plasma flow field.

[0040] Step 125: Generate a directed graph structure with critical points as nodes and streamline connections as edges based on the topological association matrix, and combine the directed graph structure and the set of spatial coordinates of the critical points into a streamline topological feature map.

[0041] After constructing the topological association matrix, a directed graph structure is generated based on this matrix. A directed graph structure is a graphical tool used to represent the relationships between objects. In this scenario, critical points such as branch points, sink points, and saddle points are used as nodes, and streamline connections are used as edges.

[0042] For critical point pairs marked as connected in the topological incidence matrix, a directed edge connects the corresponding nodes in the directed graph structure. The direction of the directed edge indicates the flow direction of the streamlines, thus visually demonstrating the streamline connection relationship between critical points.

[0043] Combining the generated directed graph structure with the set of spatial coordinates of critical points forms a streamline topology feature map. This map not only contains the connectivity between critical points but also their specific spatial locations. Through this map, researchers can gain a comprehensive understanding of the distribution of key feature points in the flow field and their interrelationships. In magnetic confinement fusion and tokamak scenarios, streamline topology feature maps can help researchers analyze the topological structure of plasma flow fields in greater depth.

[0044] Step 130: Construct a multi-scale parallel rendering task queue based on the streamline topology feature map, and distribute the original streamline set to multiple computing nodes to perform collaborative rendering processing through a spatial region partitioning algorithm to obtain intermediate collaborative rendering results.

[0045] After obtaining the streamline topology feature map, a multi-scale parallel rendering task queue needs to be constructed to achieve efficient rendering of the original streamline set. The construction of the multi-scale parallel rendering task queue is based on the information in the streamline topology feature map, taking into account the different scales and complexities of the flow field, and the rendering tasks are reasonably divided and organized.

[0046] The original streamline set is allocated to multiple computing nodes using a spatial region partitioning algorithm. The purpose of this algorithm is to divide the entire flow field space into multiple sub-regions, each corresponding to a computing node. Based on the spatial location information of the streamlines in the original streamline set, the streamlines are assigned to the corresponding sub-regions, and each computing node is responsible for rendering the streamlines within its assigned sub-region.

[0047] Multiple compute nodes perform collaborative rendering simultaneously. Each compute node independently renders the streamlines within its assigned sub-region, generating a local rendering result. During the rendering process, compute nodes can leverage their own computing resources and parallel computing capabilities to improve rendering efficiency.

[0048] After local rendering is completed on multiple computing nodes, these local rendering results are integrated to obtain the intermediate collaborative rendering result. The intermediate collaborative rendering result is the result of rendering the entire original streamline set, containing rendering information for each sub-region, providing a foundation for generating the final visualization image. In magnetic confinement fusion and tokamak scenarios, through multi-scale parallel rendering task queues and collaborative rendering processing, complex plasma flow fields can be visualized quickly and efficiently, providing researchers with intuitive flow field information.

[0049] In another embodiment, step 130 includes: Step 131: Analyze the directed graph structure in the streamline topology feature map, extract the spatial coordinate set of branch points, sink points and saddle points, and generate a spatial bounding box with the spatial coordinate set as the center. The side length of the spatial bounding box is determined according to the maximum distance between critical points.

[0050] When constructing a multi-scale parallel rendering task queue, the first step is to parse the directed graph structure in the streamline topology feature map. The directed graph structure contains the connection relationships and positional information of critical points such as branch points, sink points, and saddle points. By parsing the directed graph structure, the spatial coordinate set of these critical points can be extracted.

[0051] A bounding box is generated centered on the extracted set of spatial coordinates. The bounding box is the smallest cube or cuboid that can contain all critical points, effectively defining the region where the critical points are located. The side length of the bounding box is determined based on the maximum distance between the critical points. Specifically, the distances between all critical points are calculated, the maximum distance is found, and then the side length of the bounding box is determined based on this maximum distance. This ensures that the bounding box completely contains all critical points, providing accurate range information for subsequent spatial region division and rendering task allocation.

[0052] Step 132: Perform uniform meshing on the spatial bounding box to generate a spatial mesh containing multiple sub-region units. The boundary coordinates of each sub-region unit are calculated based on the number of meshes and the bounding box size.

[0053] After generating the spatial bounding box, a uniform mesh generation process is performed on it. The purpose of uniform mesh generation is to divide the spatial bounding box into multiple sub-regions of equal size so that the original streamline set can be distributed to different computing nodes for parallel rendering.

[0054] Based on a pre-defined number of grid divisions, the bounding box is uniformly divided along each dimension. For example, in three-dimensional space, the bounding box can be divided into equal intervals along the x, y, and z dimensions. Each small region obtained after division is a sub-region unit.

[0055] The boundary coordinates of each sub-region cell are calculated based on the number of mesh divisions and the bounding box size. Specifically, the boundary position of each sub-region cell can be accurately determined based on the mesh interval and the boundary coordinates of the bounding box. This boundary coordinate information is crucial for subsequent streamline allocation and rendering task scheduling, ensuring that the scope of each sub-region cell is clear and facilitating independent rendering processing by the compute nodes.

[0056] Step 133: Count the sub-region unit identifiers traversed by each streamline in the original streamline set, and construct a mapping relationship table between streamlines and sub-region units. The mapping relationship table is used to record all sub-region unit numbers associated with a single streamline.

[0057] After completing the uniform mesh generation of the spatial bounding box, it is necessary to count the sub-region cell identifiers traversed by each streamline in the original streamline set. For each streamline, based on its spatial coordinate sequence, check which sub-region cells it traversed during its flow. Record the numbers of the sub-region cells traversed by each streamline; these numbers are the sub-region cell identifiers.

[0058] Each streamline is associated with the identifier of the sub-region cell it traverses, constructing a mapping table between streamlines and sub-region cells. This mapping table records all sub-region cell numbers associated with a single streamline and is an important data structure used for subsequent streamline allocation and rendering task scheduling. Through the mapping table, it is clear which sub-region cells each streamline is distributed in, thus allowing streamlines to be rationally allocated to the corresponding computing nodes for rendering.

[0059] Step 134: Based on the mapping table, split the original streamline set into multiple sub-streamline sets. Each sub-streamline set contains streamline segments that are completely located within the same sub-region unit and streamline segments that cross sub-region units.

[0060] Based on the established mapping table between streamlines and sub-regional units, the original streamline set is divided into multiple sub-streamline sets. Each sub-streamline set corresponds to a sub-regional unit, which contains all streamline segments related to that sub-regional unit.

[0061] Streamline segments in a sub-streamline set can be divided into two categories: streamline segments that are entirely within the same sub-regional cell and streamline segments that span multiple sub-regional cells. Streamline segments that are entirely within the same sub-regional cell indicate that the streamline does not leave the sub-regional cell during the entire flow process; streamline segments that span multiple sub-regional cells indicate that the streamline passes through multiple sub-regional cells during the flow process.

[0062] By splitting the original streamline set into multiple sub-stream sets, rendering tasks can be more finely distributed across different compute nodes. Each compute node is responsible for rendering one or more sub-stream sets, thereby fully utilizing the parallel computing capabilities of the compute nodes and improving rendering efficiency.

[0063] In one embodiment, step 134 includes: Step 1341: Traverse the sub-region unit numbers associated with each streamline in the mapping table and determine whether the number of sub-region unit numbers is 1.

[0064] When splitting the original streamline set into multiple sub-stream sets, the sub-region cell numbers associated with each streamline are first traversed in the mapping table. For each streamline, the number of its associated sub-region cell numbers is checked. Determining whether the number of sub-region cell numbers is 1 is to distinguish whether the streamline is entirely within the same sub-region cell or spans multiple sub-region cells. If the number of sub-region cell numbers is 1, it means the streamline is entirely within a single sub-region cell; if the number of sub-region cell numbers is greater than 1, it means the streamline spans multiple sub-region cells.

[0065] Step 1342: When the number of sub-region unit numbers is 1, the streamline is directly assigned to the sub-streamline set of the corresponding sub-region unit as a streamline segment located entirely within the same sub-region unit; when the number of sub-region unit numbers is greater than 1, the spatial position coordinate sequence of the streamline is segmented according to the spatial position order of the sub-region units, and the streamline is truncated into multiple streamline segments at the boundary coordinates of adjacent sub-region units.

[0066] If it is determined that the number of sub-regional unit numbers associated with a certain streamline is 1, it means that the streamline is completely located within a sub-regional unit. The streamline is then directly assigned to the sub-streamline set of the corresponding sub-regional unit. This ensures that the sub-streamline set of each sub-regional unit contains complete streamline information within the region.

[0067] If a streamline is associated with more than one sub-regional unit, it means that the streamline spans multiple sub-regional units. In this case, the spatial coordinate sequence of the streamline is segmented according to the spatial order of the sub-regional units. Specifically, the boundary coordinates of adjacent sub-regional units are found, and the streamline is truncated into multiple streamline segments at these boundary coordinates. This allows streamlines spanning multiple sub-regional units to be rationally allocated to different sub-regional units.

[0068] Step 1343: Extract the starting spatial coordinates and ending spatial coordinates of each streamline segment, determine whether the starting spatial coordinates and ending spatial coordinates are located within the same sub-region unit, and classify the streamline segments located within the same sub-region unit into the sub-streamline set of the corresponding sub-region unit.

[0069] After truncating the streamline into multiple streamline segments, the starting and ending spatial coordinates of each streamline segment are extracted. By determining whether the starting and ending spatial coordinates are located within the same sub-region cell, it can be further determined which sub-region cell's sub-streamline set each streamline segment should be assigned to. If both the starting and ending spatial coordinates are within the same sub-region cell, it means that the streamline segment is entirely within that sub-region cell, and it is assigned to the corresponding sub-streamline set of that sub-region cell; if the starting and ending spatial coordinates are located within different sub-region cells, it means that the streamline segment spans multiple sub-region cells, and further processing is required.

[0070] Step 1344: Add region identifier tags to the streamline segments across sub-region units. The region identifier tags contain the original streamline number, the starting region number, and the ending region number of the rendering results exchanged between computing nodes.

[0071] For streamline segments spanning sub-region units, region identifier tags need to be added to facilitate the exchange of rendering results between computation nodes. The region identifier tag contains three important pieces of information: the original streamline number, the starting region number, and the ending region number. The original streamline number identifies the original streamline to which the streamline segment belongs; the starting region number indicates the starting sub-region unit number of the streamline segment; and the ending region number indicates the ending sub-region unit number of the streamline segment. By adding region identifier tags, it is ensured that streamline segments spanning sub-region units can be accurately identified and processed when exchanging rendering results between computation nodes.

[0072] Step 1345: Simultaneously store the cross-region streamline segment containing the region identifier label into the sub-streamline set corresponding to all sub-region units traversed by the cross-region streamline segment, so that the sub-streamline set of each sub-region unit contains complete intra-region streamline information and cross-region streamline segment information.

[0073] Cross-region streamline segments with added region identifier tags are simultaneously stored in the sub-streamline sets corresponding to all sub-region units traversed by the cross-region streamline segment. This ensures that each sub-region unit's sub-streamline set contains complete intra-region streamline information and cross-region streamline segment information. During rendering, the computation node of each sub-region unit can accurately process cross-region streamline segments based on the region identifier tags, avoiding information loss or duplicate rendering. This approach guarantees the accuracy and completeness of the final collaborative rendering result.

[0074] Step 135: Construct a multi-scale parallel rendering task queue based on the spatial location of the sub-region unit and the data size of the sub-streamline set. Allocate the sub-streamline set to multiple computing nodes according to the priority sorting rules of the multi-scale parallel rendering task queue. Each computing node receives a sub-streamline set that matches the computing power of that computing node.

[0075] After splitting the sub-streamline set, a multi-scale parallel rendering task queue is constructed based on the spatial location of the sub-region units and the data size of the sub-streamline set. The spatial location information of the sub-region units reflects their relative position in the entire flow field, which is of great significance for the rational allocation of rendering tasks. The data size of the sub-streamline set directly affects the complexity of the rendering task and the required computing resources.

[0076] Based on the spatial location of the sub-region units and the data volume of the sub-stream sets, the rendering task is divided into different scales and priorities. For example, sub-stream sets with large data volumes and located in critical regions can be assigned higher priorities, while sub-stream sets with small data volumes and located in non-critical regions can be assigned lower priorities.

[0077] Following the priority sorting rules of the multi-scale parallel rendering task queue, the sub-stream sets are allocated to multiple computing nodes. Each computing node receives a sub-stream set that matches its computing power, thereby fully utilizing the computing resources of each node and improving rendering efficiency. For example, computing nodes with stronger computing power can be allocated to sub-stream sets with larger data volumes and higher priority; computing nodes with weaker computing power can be allocated to sub-stream sets with smaller data volumes and lower priority.

[0078] Step 136: Perform initial rendering processing on the received sub-stream set through each computing node to generate a local rendering result containing streamline color encoding information and line width parameters. The color encoding information is determined according to the speed of the streamline, and the line width parameters are dynamically adjusted according to the curvature value of the streamline.

[0079] It is understandable that after each computing node receives the assigned set of sub-streams, it performs initial rendering processing on them. The purpose of the initial rendering processing is to add color-coded information and linewidth parameters to each stream to better display the characteristics of the flow field.

[0080] The color coding information is determined based on the velocity of the streamlines. Different streamlines with different velocities correspond to different colors, and the distribution of velocity in the flow field can be visually displayed through color changes. For example, faster streamlines can be represented by brighter colors, and slower streamlines can be represented by darker colors.

[0081] The linewidth parameter is dynamically adjusted based on the curvature value of the streamline. The curvature value of a streamline reflects its degree of curvature; the larger the curvature value, the more curved the streamline. By dynamically adjusting the linewidth parameter based on the curvature value, the larger the curvature value, the larger the linewidth parameter becomes. This makes streamlines with greater curvature more prominent, facilitating the observation of complex structures in the flow field.

[0082] During the initial rendering process, the compute nodes also perform other necessary processing on each streamline, such as culling invisible streamline segments and performing anti-aliasing. Finally, the color encoding information, linewidth parameters, and the processed streamline pixel coordinate set are combined into a local rendering result, which includes the color value and depth value of each pixel.

[0083] As an alternative embodiment, step 136 includes: Step 1361: Analyze the spatial position coordinate sequence and corresponding timestamp information of each streamline in the set of sub-streamlines, and calculate the velocity magnitude of each streamline under the timestamp sequence. The velocity magnitude is determined by the ratio of the Euclidean distance between the spatial position coordinates of adjacent timestamps to the time interval.

[0084] During the initial rendering of the received set of sub-streams, the spatial coordinate sequence and corresponding timestamp information of each stream are first parsed. The spatial coordinate sequence records the specific position of the fluid particles at different times, while the timestamp information records the time corresponding to each position.

[0085] The velocity of each streamline in the time-stamp sequence is calculated by dividing the Euclidean distance between the spatial coordinates of adjacent time stamps by the time interval. Specifically, for two adjacent time stamps, the Euclidean distance between the spatial coordinates of the fluid particles at those two time stamps is calculated, and then this Euclidean distance is divided by the time interval to obtain the average velocity of the fluid particles within that time interval. By performing this calculation for all adjacent time stamps, the velocity of each streamline in the entire time-stamp sequence can be obtained.

[0086] Step 1362: Based on the speed magnitude, query a preset color mapping table. The speed magnitude and color channel values ​​in the color mapping table have a monotonic mapping relationship. Generate color coding information for each streamline based on the query results. The color coding information includes the values ​​of the red, green, and blue channels.

[0087] After obtaining the velocity of each streamline, a pre-defined color map is consulted based on that velocity. The color map is a pre-defined table that records the monotonic mapping between velocity magnitudes and color channel values. By consulting the color map, the corresponding color channel value can be found for each streamline based on its velocity magnitude.

[0088] The color coding information includes values ​​for three channels: red, green, and blue. Based on the query results, the corresponding values ​​for the three channels are combined to generate the color coding information for each streamline. Thus, each streamline has a color corresponding to its velocity magnitude, and the velocity distribution in the flow field can be intuitively displayed through color changes.

[0089] Step 1363: Calculate the curvature value of the spatial position coordinate sequence of each streamline. The curvature value is determined by the ratio of the second derivative magnitude of the streamline to the cube of the first derivative magnitude. Adjust the streamline width parameter according to the curvature value. The larger the curvature value, the larger the streamline width parameter.

[0090] While generating color-coded information, the curvature value of the spatial coordinate sequence of each streamline is calculated. The curvature value reflects the degree of curvature of the streamline and is determined by the ratio of the second derivative magnitude to the cube of the first derivative magnitude. Specifically, the spatial coordinate sequence of each streamline is differentiated to obtain the first and second derivatives. Then, the magnitude of the second derivative and the cube of the first derivative magnitude are calculated. Finally, the curvature value of the streamline is obtained by dividing the second derivative magnitude by the cube of the first derivative magnitude.

[0091] Adjust the streamline width parameter based on the curvature value. A larger curvature value indicates a greater degree of curvature in the streamline, and the linewidth parameter should be set larger accordingly. This makes the more curved streamlines more prominent, facilitating the observation of complex structures in the flow field.

[0092] Step 1364: Perform visibility judgment processing on the streamline segments in the sub-streamline set, and remove streamline segments located outside the view frustum based on the viewer's view frustum parameters, while retaining streamline segments located inside the view frustum.

[0093] During rendering, to improve rendering efficiency, visibility determination processing needs to be performed on the streamline segments in the sub-streamlet set. Based on the view frustum parameters from the observer's perspective, it is determined whether each streamline segment is located within the view frustum. The view frustum is a three-dimensional spatial region that defines the range that the observer can see.

[0094] If a streamline fragment is located outside the view frustum, it means that the streamline fragment is invisible to the observer and is discarded without rendering. If a streamline fragment is located within the view frustum, it means that the streamline fragment is visible to the observer and is retained for subsequent rendering. In this way, unnecessary rendering calculations can be reduced, improving rendering efficiency.

[0095] Step 1365: Add transition color values ​​at pixel-level positions of the streamlines using a line segment sampling algorithm to perform anti-aliasing on the preserved streamline segments.

[0096] After preserving the streamline segments located within the view frustum, anti-aliasing needs to be performed on these streamline segments to make the rendering result smoother and clearer. Transition color values ​​are added to the pixel-level locations of the streamlines using a segment sampling algorithm.

[0097] The basic principle of the line segment sampling algorithm is to sample at the pixel level of the streamline, and calculate transition color values ​​based on the location of the sampling point and the color values ​​of surrounding pixels. These transition color values ​​are then added to the pixel level of the streamline, making the edges smoother and reducing jagged edges. Anti-aliasing improves the quality of the rendering results, making the visualized image more aesthetically pleasing and accurate.

[0098] Step 1366: Combine the color encoding information, line width parameters, and the set of pixel coordinates after anti-aliasing processing into a local rendering result, wherein the local rendering result includes the color value and depth value of each pixel.

[0099] After generating color-coded information, adjusting linewidth parameters, handling visibility checks, and performing anti-aliasing, the color-coded information, linewidth parameters, and the anti-aliased pixel coordinates are combined into a local rendering result. This local rendering result includes the color and depth values ​​for each pixel.

[0100] Color values ​​represent the color of each pixel, and changes in color can reveal the velocity distribution and other characteristics of the flow field. Depth values ​​represent the distance between each pixel and the observer, enabling accurate occlusion relationships and making the rendering results more realistic and three-dimensional. Combining this information forms the local rendering result of each computation node.

[0101] Step 137: Use multiple computing nodes and a distributed communication protocol to exchange the local rendering results of streamline segments across sub-region units, and perform weighted fusion processing on the local rendering results of overlapping areas to obtain intermediate collaborative rendering results.

[0102] After each computing node completes its local rendering process, it is necessary to exchange the local rendering results of the streamline segments across sub-region units using multiple computing nodes and a distributed communication protocol. Since the streamline segments across sub-region units may be processed by multiple computing nodes, it is necessary to exchange these local rendering results among the computing nodes to ensure that each computing node obtains complete rendering information.

[0103] Distributed communication protocols are used for data transmission and communication between multiple computing nodes. Through these protocols, computing nodes can send the local rendering results of streamline segments across sub-region units they are processing to other relevant computing nodes, while simultaneously receiving local rendering results from other computing nodes.

[0104] After exchanging the local rendering results, some overlapping areas will be found. Overlapping areas refer to the spatial overlap of streamline segments processed by multiple computing nodes. For the local rendering results in these overlapping areas, a weighted fusion process needs to be performed. The purpose of the weighted fusion process is to reasonably merge the local rendering results from multiple computing nodes, avoiding inconsistencies or duplication. Specifically, based on the reliability or weight of each computing node's rendering result, a weighted average or other weighted calculation is performed on the local rendering results of the overlapping areas to obtain the final fused result.

[0105] The local rendering results of all computing nodes are integrated, including the weighted fusion results of overlapping areas, to obtain the intermediate collaborative rendering result. The intermediate collaborative rendering result is the result of the intermediate stage of rendering the entire original streamline set, and it contains the rendering information of each computing node.

[0106] Step 140: Perform streamline density adaptive adjustment processing based on the intermediate results of the collaborative rendering to generate a turbulent transport visualization image sequence with dynamic detail levels. The turbulent transport visualization image sequence is used to present the spatial distribution characteristics and temporal evolution trend of turbulent transport phenomena in the flow field.

[0107] It is understandable that after obtaining the intermediate results of the collaborative rendering, in order to better present the spatial distribution characteristics and temporal evolution trend of turbulent transport phenomena in the flow field, it is necessary to perform adaptive streamline density adjustment processing based on the intermediate results of the collaborative rendering. The purpose of adaptive streamline density adjustment processing is to reasonably simplify or refine the streamlines according to the streamline density conditions of different regions in the flow field, so as to generate a sequence of turbulent transport visualization images with dynamic detail levels.

[0108] In a flow field, the streamline density can vary significantly across different regions. Some regions may have high streamline density, resulting in overly dense images that obscure the details of the flow field; conversely, some regions may have low streamline density, leading to overly sparse images that fail to fully represent the characteristics of the flow field. Adaptive streamline density adjustment can address these issues.

[0109] For regions with high streamline density, streamline simplification is performed to reduce the number of streamlines while retaining their main geometric features, making the image clearer and easier to observe. For regions with low streamline density, streamline refinement is performed to increase the number of streamlines and fill in blank areas, making the image more complete and comprehensive.

[0110] By sequentially processing the intermediate results of collaborative rendering at continuous time intervals, a sequence of turbulent transport visualization images containing multiple frames is generated. This image sequence has a dynamic level of detail and can demonstrate the spatial distribution characteristics and temporal evolution trends of turbulent transport phenomena in the flow field over time. In magnetic confinement fusion and tokamak scenarios, the turbulent transport visualization image sequence can help researchers better understand the dynamic changes in plasma flow fields.

[0111] In a preferred embodiment, step 140 includes: Step 141: Analyze the intermediate results of the collaborative rendering, extract the set of pixel coordinates of all streamlines and their corresponding depth values, and construct a streamline density statistics matrix indexed by pixel coordinates. Each element of the streamline density statistics matrix represents the number of streamline overlaps at the corresponding pixel position.

[0112] When performing adaptive streamline density adjustment, the intermediate results of the collaborative rendering are first parsed to extract the pixel coordinate set and corresponding depth value of all streamlines. The pixel coordinate set records the pixel position of each streamline in the image, and the depth value represents the distance of each pixel from the observer.

[0113] A streamline density statistics matrix is ​​constructed using pixel coordinates as indices. This matrix is ​​a two-dimensional matrix where each element represents the number of overlapping streamlines at the corresponding pixel location. By iterating through the set of pixel coordinates for all streamlines, the number of overlapping streamlines at each pixel location is counted and recorded in the corresponding position within the streamline density statistics matrix.

[0114] The streamline density statistical matrix can intuitively display the streamline density at different pixel locations in a flow field. In magnetic confinement fusion and tokamak scenarios, analyzing the streamline density statistical matrix can reveal the streamline distribution characteristics in different regions of the plasma flow field.

[0115] Step 142: Perform Gaussian filtering on the streamline density statistics matrix to generate a smoothed streamline density distribution heatmap. The standard deviation of the kernel function of the Gaussian filtering is dynamically adjusted according to the viewport resolution.

[0116] After constructing the streamline density statistical matrix, Gaussian filtering is applied to it to make the streamline density distribution smoother and easier to analyze. Gaussian filtering is a commonly used smoothing filtering method that can reduce noise and abrupt changes in the data, making the data more continuous and smooth.

[0117] When performing Gaussian filtering, the standard deviation of the kernel function is dynamically adjusted according to the viewport resolution. Viewport resolution represents the sharpness and detail of the image; different viewport resolutions require different filtering intensities. When the viewport resolution is high, a finer filtering is needed, and the standard deviation of the kernel function can be set smaller; when the viewport resolution is low, a coarser filtering is needed, and the standard deviation of the kernel function can be set larger.

[0118] Gaussian filtering is used to transform the streamline density statistical matrix into a smoothed streamline density distribution heatmap. A heatmap is a visualization method that uses color to represent data magnitude; different colors correspond to different streamline density values. The streamline density distribution heatmap provides a more intuitive observation of the streamline density distribution in the flow field.

[0119] Step 143: Based on the streamline density distribution heatmap, determine the boundary threshold between high-density regions and low-density regions using the maximum inter-class variance method. Regions with density values ​​greater than the boundary threshold are marked as high-density regions, and regions with density values ​​less than the boundary threshold are marked as low-density regions.

[0120] After obtaining the smoothed streamline density distribution heatmap, the boundary threshold between high-density and low-density regions is determined based on this heatmap using the Otsu's method. Otsu's method is a commonly used image segmentation method. Its basic principle is to find a suitable threshold to divide pixels in the image into two classes, maximizing the variance between these two classes.

[0121] In the streamline density distribution thermogram, regions with density values ​​greater than a boundary threshold are marked as high-density regions, and regions with density values ​​less than the boundary threshold are marked as low-density regions. This method divides the flow field into high-density and low-density regions, providing a clear target for subsequent streamline simplification and refinement. In magnetic confinement fusion and tokamak scenarios, the division into high-density and low-density regions can help researchers better understand the characteristics of different regions within the plasma flow field.

[0122] Step 144: Perform streamline simplification on the high-density region. Use the Douglas-Peucker algorithm to simplify the spatial coordinate sequence of streamlines in the high-density region, retain the main geometric features of the streamlines and reduce the number of vertices.

[0123] It is understandable that after identifying high-density and low-density regions, streamline simplification is performed on the high-density regions. Because there are a large number of streamlines in high-density regions, the image may become overly complex, making it difficult to observe the details of the flow field; therefore, streamlining is necessary.

[0124] The Douglas-Peucker algorithm is used to simplify the spatial coordinate sequence of streamlines in high-density regions. The Douglas-Peucker algorithm is a commonly used curve simplification algorithm. Its basic principle is to recursively remove some vertices on the curve while preserving the main geometric features of the curve.

[0125] Specifically, for each streamline within a high-density region, its spatial coordinate sequence is represented as an ordered set of vertices. The starting and ending vertices are selected from this set as simplified retained vertices. Then, the perpendicular distance from each intermediate vertex to the line segment formed by the starting and ending vertices is calculated. This perpendicular distance is compared to a preset simplification threshold. If the perpendicular distance is greater than the threshold, it indicates that the intermediate vertex has a significant impact on the curve's shape, and it is marked as a retained vertex. If the perpendicular distance is less than the threshold, it indicates that the intermediate vertex has a relatively small impact on the curve's shape, and it is deleted.

[0126] The comparison and segmentation steps described above are repeated for each sub-vertex set until the vertical distance between all intermediate vertices is less than the simplification threshold. Finally, all marked retained vertices are collected and rearranged according to the original vertex set order to generate a simplified vertex sequence. This simplified vertex sequence constitutes the simplified streamline geometry data, which retains the main geometric features of the streamlines while reducing the number of vertices, making the image clearer and easier to observe.

[0127] In one embodiment, step 144 includes: Step 1440: Extract the spatial coordinate sequence of each streamline within the high-density region, and represent the spatial coordinate sequence as an ordered set of vertices, the set of vertices including the starting vertex, intermediate vertex, and ending vertex of the streamline; designate the starting vertex and ending vertex in the set of vertices as simplified retained vertices, and calculate the perpendicular distance from the intermediate vertex to the line segment formed by the starting vertex and the ending vertex; compare the perpendicular distance with a preset simplification threshold, and when the perpendicular distance is greater than the simplification threshold, mark the intermediate vertex as a retained vertex, and divide the vertex set into two sub-vertex sets using the intermediate vertex as the boundary; repeat the above comparison and division steps for each sub-vertex set until all intermediate vertices are retained. The vertical distance between all points is less than the simplification threshold; all marked retained vertices are collected and rearranged according to the order of the original vertex set to generate a simplified vertex sequence, which constitutes the simplified streamline geometry data; the length error of the streamlines before and after simplification is calculated, and the length error is determined by the difference between the length of the broken line formed by the simplified vertex sequence and the length of the broken line formed by the original vertex sequence. When the length error is greater than the preset error threshold, the simplification threshold is adjusted backtracking, and vertex simplification processing is re-executed until the length error is less than the preset error threshold; the simplified vertex sequence and the corresponding color coding information and line width parameters are combined into simplified streamline data, replacing the original streamline data in the high-density area.

[0128] When simplifying streamlines in high-density regions, the spatial coordinate sequence of each streamline is first extracted and represented as an ordered set of vertices. This set of vertices includes the starting vertex, intermediate vertex, and ending vertex of the streamline, arranged according to the flow order of the streamline.

[0129] The starting and ending vertices in the vertex set are designated as the simplified retained vertices because they are crucial for determining the overall position and orientation of the streamline and must be preserved. Then, the perpendicular distance from the intermediate vertex to the line segment formed by the starting and ending vertices is calculated. This perpendicular distance reflects the degree of deviation of the intermediate vertex from the line segment; the greater the deviation, the greater the influence of the intermediate vertex on the shape of the curve.

[0130] The vertical distance is compared with a preset simplification threshold. If the vertical distance is greater than the simplification threshold, it means that the intermediate vertex has a significant impact on the shape of the curve. It is marked as a retained vertex, and the vertex set is divided into two sub-vertex sets with the intermediate vertex as the boundary. In this way, a complex curve can be simplified into two relatively simple sub-curves, which is convenient for further processing.

[0131] Repeat the comparison and segmentation steps for each sub-vertex set until the vertical distance of all intermediate vertices is less than the simplification threshold. At this point, all intermediate vertices that have little impact on the curve shape are deleted, and the remaining vertices constitute the simplified vertex sequence.

[0132] The length error of the streamlines before and after simplification is calculated. This length error is determined by the difference between the length of the broken line formed by the simplified vertex sequence and the length of the broken line formed by the original vertex sequence. If the length error is greater than a preset error threshold, it indicates a significant difference in length between the simplified and original streamlines, which may affect the accurate description of the flow field. In this case, the simplification threshold is adjusted back, and vertex simplification is re-executed until the length error is less than the preset error threshold.

[0133] The simplified vertex sequence, along with the corresponding color coding information and linewidth parameters, is combined into simplified streamline data, which replaces the original streamline data in the high-density region. As a result, the streamlines in the high-density region are effectively simplified, making the image clearer and easier to observe.

[0134] Step 145: Perform streamline refinement on the low-density region by inserting new streamline segments between the streamlines in the low-density region. The spatial coordinates of the new streamline segments are generated based on the coordinate sequence of adjacent streamlines using an interpolation algorithm.

[0135] While simplifying the streamlines in high-density regions, streamline refinement is performed in low-density regions. Since there are fewer streamlines in low-density regions, the image may be too sparse and unable to fully display the characteristics of the flow field. Therefore, it is necessary to insert new streamline segments between these streamlines.

[0136] The spatial coordinates of new streamline segments are generated based on the coordinate sequences of adjacent streamlines using an interpolation algorithm. Interpolation is a commonly used mathematical method that estimates the values ​​of unknown data points based on known data points. In this scenario, the coordinate sequences of adjacent streamlines are known data points, and the interpolation algorithm can estimate the spatial coordinates of new streamline segments between these adjacent streamlines.

[0137] Specifically, firstly, all streamlines within the low-density region are extracted, and an adjacency graph of the streamlines is constructed. Nodes in the adjacency graph represent streamlines, and edges represent the spatial distance between streamlines being less than a preset proximity threshold. By traversing each edge in the adjacency graph, the spatial coordinate sequence of two adjacent streamlines is obtained.

[0138] Synchronous sampling is performed on the spatial coordinate sequences of two adjacent streamlines. The spatial coordinates of the two streamlines are extracted at the same timestamp, resulting in a set of sampling points containing multiple coordinate pairs. Linear interpolation is then performed on each coordinate pair in the sampling point set to calculate the spatial coordinates of the interpolated point. The weighting coefficients of the interpolated points are dynamically adjusted based on the distance between the two streamlines; the smaller the distance, the closer the weighting coefficients are to the preset coefficients.

[0139] Connect all interpolation points in timed order to generate a new sequence of spatial coordinates for streamline segments. The start and end timestamps of the new streamline segments are kept consistent with those of adjacent streamlines to ensure temporal continuity between the new streamline segments and their neighbors.

[0140] The velocity magnitude and curvature value of the new streamline segment are calculated. Based on the velocity magnitude, a color map is consulted to generate color-coded information, and the linewidth parameter is determined based on the curvature value. The spatial coordinate sequence, color-coded information, and linewidth parameter of the new streamline segment are added to the streamline set in the low-density region, completing the streamline refinement process. In this way, the number of streamlines in the low-density region is increased, resulting in a more complete and comprehensive image.

[0141] In one embodiment, step 145 includes: Step 1450: Extract all streamlines within the low-density region and construct an adjacency graph of the streamlines. Nodes in the adjacency graph represent streamlines, and edges represent spatial distances between streamlines less than a preset proximity threshold. Traverse each edge in the adjacency graph to obtain the spatial coordinate sequences of two adjacent streamlines. Perform synchronous sampling on the spatial coordinate sequences of two adjacent streamlines, extracting the spatial coordinates of the two streamlines at the same timestamp, resulting in a set of sampling points containing multiple coordinate pairs. Perform linear interpolation on each coordinate pair in the sampling point set to calculate the spatial coordinates of the interpolated points. The weighting coefficient is dynamically adjusted based on the distance between two streamlines; the smaller the distance, the closer the weighting coefficient is to the preset coefficient. All interpolation points are connected in time stamp order to generate a new sequence of spatial coordinates for streamline segments. The start and end timestamps of the new streamline segments are consistent with those of adjacent streamlines. The velocity magnitude and curvature value of the new streamline segments are calculated. Based on the velocity magnitude, a color mapping table is queried to generate color coding information, and based on the curvature value, the linewidth parameter is determined. The spatial coordinate sequence, color coding information, and linewidth parameter of the new streamline segments are added to the streamline set in the low-density region to complete the streamline refinement process.

[0142] When refining streamlines in low-density regions, the first step is to extract all streamlines within the region and construct an adjacency graph. An adjacency graph is a graphical tool used to represent the adjacency relationships between objects. In this scenario, nodes represent streamlines, and edges represent the spatial distance between streamlines that is less than a preset proximity threshold. By constructing the adjacency graph, the adjacency relationships between streamlines within the low-density region can be clearly understood, providing a foundation for subsequent interpolation processing.

[0143] Traverse each edge in the adjacency graph to obtain the spatial coordinate sequence of two adjacent streamlines. The spatial coordinate sequence of two adjacent streamlines records their specific positions at different times and is the basic data for interpolation.

[0144] Synchronous sampling is performed on the spatial coordinate sequences of two adjacent streamlines, extracting their spatial coordinates at the same timestamp, resulting in a set of sampling points containing multiple coordinate pairs. This synchronous sampling ensures that adjacent streamlines are sampled at the same time point, making the generation of interpolation points more accurate.

[0145] Linear interpolation is performed on each coordinate pair in the sampling point set to calculate the spatial coordinates of the interpolation point. The weighting coefficient of the interpolation point is dynamically adjusted according to the distance between the two streamlines. The smaller the distance, the closer the weighting coefficient is to the preset coefficient. Thus, the position of the interpolation point can be reasonably determined according to the distance between adjacent streamlines, making the newly generated streamline segments more natural and reasonable.

[0146] Connect all interpolation points in timed order to generate a new sequence of spatial coordinates for streamline segments. The start and end timestamps of the new streamline segments are consistent with those of adjacent streamlines, ensuring temporal continuity between the new streamline segments and their neighbors.

[0147] The velocity magnitude and curvature value of the new streamline segment are calculated. Based on the velocity magnitude, a color mapping table is queried to generate color coding information. Based on the curvature value, the line width parameter is determined. Thus, the new streamline segment has the same visual characteristics as other streamlines, which is convenient for unified display.

[0148] The spatial coordinate sequence, color-coded information, and linewidth parameters of the new streamline segments are added to the streamline set in the low-density region to complete the streamline refinement process. In this way, the number of streamlines in the low-density region is increased, the image is more complete and comprehensive, and it can better display the characteristics of the flow field.

[0149] Step 146: Reconstruct the global streamline set based on the simplified high-density region streamlines and the refined low-density region streamlines. The global streamline set includes the spatial position coordinate sequence, color coding information and line width parameters of all streamlines after adjustment.

[0150] After simplifying the streamlines in high-density regions and refining the streamlines in low-density regions, it is necessary to reconstruct the global streamline set based on the processed results. The global streamline set contains the spatial coordinate sequence of all adjusted streamlines, color-coded information, and linewidth parameters.

[0151] First, the spatial coordinate sequence, color coding information, and linewidth parameters of streamlines in the simplified high-density region are collected and labeled as the first streamline subset; the spatial coordinate sequence, color coding information, and linewidth parameters of streamlines in the refined low-density region are collected and labeled as the second streamline subset.

[0152] Extract the boundary region streamlines of the first and second streamline subsets. Boundary region streamlines are those located at the boundary between high-density and low-density regions. Due to the different processing methods for high-density and low-density regions, abrupt changes in streamline width may occur in the boundary region streamlines, which need to be addressed.

[0153] The spatial coordinate sequence of streamlines in the boundary region is processed to achieve a smooth transition. The curvature difference between adjacent streamlines is calculated, and the linewidth parameter of the boundary streamlines is adjusted by a weighted average algorithm to eliminate abrupt changes in linewidth between high-density and low-density regions. This makes the streamlines in the boundary region more natural and smooth, avoiding visual discontinuities.

[0154] Check whether there are duplicate streamline segments between the first streamline subset and the second streamline subset. Remove duplicate segments by comparing the similarity of spatial position coordinate sequences and retain unique streamline segments. This can avoid repeated rendering and improve rendering efficiency.

[0155] The processed first and second streamline subsets are merged and sorted according to their timestamp information to generate a global streamline set containing all adjusted streamlines. Each streamline in the global streamline set is assigned a unique identifier containing the streamline's generation timestamp and the original fluid particle number for easy management and querying later.

[0156] Step 147: Perform frame buffer synthesis processing on the global streamline set, write the pixel coordinates, color values ​​and depth values ​​of the streamlines into the frame buffer object, and generate a single-frame turbulent transport visualization image.

[0157] After constructing the global streamline set, frame buffer synthesis is performed on it to generate a single-frame visualization image of turbulent transport. Frame buffer synthesis is a key step in converting streamline information from the global streamline set into a visualization image.

[0158] Initialize the frame buffer object. The resolution of the frame buffer object is consistent with the resolution of the target display device to ensure that the generated visualization image can be displayed correctly on the target display device. The frame buffer object contains two channels: a color buffer and a depth buffer. The color buffer is used to store the color value of each pixel, and the depth buffer is used to store the depth value of each pixel.

[0159] Configure rendering state parameters, set the blending mode to additive blending, enable the depth test function, and set the depth test comparison function to less than or equal to. These rendering state parameter settings ensure that color blending and occlusion relationships can be correctly handled during the rendering process, making the visualized image more realistic and three-dimensional.

[0160] Iterate through each streamline in the global streamline set, reading its spatial coordinate sequence, color encoding information, and linewidth parameters. Convert the streamline's spatial coordinate sequence from the world coordinate system to the screen coordinate system, and calculate the pixel coordinate sequence of each streamline using a perspective projection matrix.

[0161] The line segment drawing interface is called based on the pixel coordinate sequence and line width parameters to draw streamlines into the color buffer of the frame buffer object, while simultaneously updating the depth values ​​in the depth buffer. During the drawing process, gamma correction is performed on the pixel color values ​​in the color buffer to make the colors more vibrant and accurate.

[0162] After rendering is complete, the color cache data of the frame buffer object is read, converted into a standard image format, and a single-frame turbulent transport visualization image is generated. The temporary memory resources occupied by the frame buffer object are released, and the generated single-frame turbulent transport visualization image data is retained for subsequent image sequence synthesis.

[0163] Step 148: Repeat steps 141-147 above to process the intermediate results of collaborative rendering at continuous time intervals in sequence, and generate a turbulent transport visualization image sequence containing multiple frames of images. The frame rate of the turbulent transport visualization image sequence matches the time interval of the original streamline set.

[0164] To visualize the temporal evolution of turbulent transport phenomena in the flow field, a sequence of turbulent transport visualization images containing multiple frames needs to be generated. Steps 141-147 are repeated to process the intermediate results of the collaborative rendering at consecutive time intervals.

[0165] For each consecutive time interval, the corresponding intermediate result of collaborative rendering is obtained and processed according to steps 141-147 to generate a single-frame turbulent transport visualization image. These single-frame images are arranged sequentially in chronological order to form a sequence of turbulent transport visualization images.

[0166] The frame rate of the turbulent transport visualization image sequence matches the time interval of the original streamline set, ensuring that the image sequence accurately reflects the temporal evolution of the flow field. In magnetic confinement fusion and tokamak scenarios, observing the turbulent transport visualization image sequence provides an intuitive understanding of the dynamic changes of turbulent transport phenomena in the plasma flow field.

[0167] As an extended embodiment, after generating a turbulent transport visualization image sequence with dynamic detail levels, the method further includes: receiving the turbulent transport visualization image sequence and streamline topology feature map; extracting the spatial coordinate change sequences of branch points, sink points, and saddle points corresponding to adjacent frames in the image sequence; constructing a set of critical point motion trajectories, wherein the set of critical point motion trajectories consists of the spatial coordinate sequences of the same critical point in consecutive time frames; calculating the displacement vectors of corresponding critical points between adjacent frames based on the set of critical point motion trajectories; generating a spatiotemporal motion feature matrix, wherein the row vectors of the spatiotemporal motion feature matrix represent the critical point type, and the column vectors represent the displacement magnitude and direction under the time frame index; performing motion compensation filtering on streamline pixels in the turbulent transport visualization image sequence according to the spatiotemporal motion feature matrix; adjusting the pixel transition weights in the overlapping areas of adjacent frames, wherein the transition weights are positively correlated with the magnitude of the displacement vectors; and recombining the pixel set after motion compensation filtering into frame images to generate an optimized turbulent transport visualization image sequence with enhanced temporal coherence, wherein the optimized turbulent transport visualization image sequence is used to improve the dynamic visual smoothness during the flow field evolution process.

[0168] It is understandable that after generating a sequence of turbulent transport visualization images with dynamic detail levels, the image sequence needs to be optimized to further improve the dynamic visual smoothness during the flow field evolution process. The process involves receiving the turbulent transport visualization image sequence and streamline topology feature maps, and extracting the spatial coordinate change sequences of branch points, sink points, and saddle points corresponding to adjacent frames in the image sequence. These spatial coordinate change sequences record the positional changes of key critical points at different time frames.

[0169] A set of critical point motion trajectories is constructed, consisting of a sequence of spatial coordinates of the same critical point across consecutive time frames. This set of trajectory images visually displays the motion trajectory of key critical points. Based on this set, the displacement vectors of corresponding critical points between adjacent frames are calculated. These vectors represent the positional changes of the critical points between adjacent time frames, including displacement magnitude and direction information. A spatiotemporal motion feature matrix is ​​generated based on these displacement vectors. The row vectors of the matrix represent the critical point type, and the column vectors represent the displacement magnitude and direction under the time frame index.

[0170] Based on the spatiotemporal motion feature matrix, motion-compensated filtering is performed on streamline pixels in the turbulent transport visualization image sequence. The purpose of motion-compensated filtering is to adjust the pixel transition weights in the overlapping areas of adjacent frames, making the transition between adjacent frames smoother and more natural. The transition weights are positively correlated with the magnitude of the displacement vector; the larger the magnitude of the displacement vector, the larger the transition weight.

[0171] The pixel set after motion compensation filtering is resynthesized into a frame image to generate an optimized turbulent transport visualization image sequence with enhanced temporal coherence. This optimized image sequence has better dynamic visual smoothness during the flow field evolution, allowing researchers to observe the changes in the flow field more clearly.

[0172] As an extended embodiment, after generating a turbulent transport visualization image sequence with dynamic detail levels, the method further includes: receiving the turbulent transport visualization image sequence and a streamline topology feature map; parsing the spatial coordinates of branch points, sink points, and saddle points in the streamline topology feature map; marking corresponding pixel regions in each frame of the image sequence; generating a key topology region mask set, wherein the elements of the key topology region mask set are binary matrices, and a matrix element value of 1 indicates that the corresponding pixel belongs to a key topology region; for each mask region in the key topology region mask set, extracting the pixel gradient magnitude of the corresponding image frame; and generating... A regional gradient feature vector is generated, the dimension of which is consistent with the number of pixels in the masked region. Based on the regional gradient feature vector, adaptive contrast enhancement processing is performed on the pixels in the masked region, adjusting the brightness channel value of the pixels while keeping the original color coding information and linewidth parameters of the pixels in the non-masked region unchanged. The contrast-enhanced pixels in the masked region and the pixels in the non-masked region are then subjected to boundary smoothing fusion processing to generate an optimized turbulent transport visualization image sequence with salient key topological regions. The optimized turbulent transport visualization image sequence is used to highlight the core turbulent transport region associated with critical points in the flow field.

[0173] It is understandable that after generating a sequence of turbulent transport visualization images with dynamic detail levels, further optimization is needed to highlight the core turbulent transport regions associated with critical points in the flow field. The system receives the turbulent transport visualization image sequence and streamline topology feature maps, and analyzes the spatial coordinates of branch points, sink points, and saddle points in the streamline topology feature maps. These spatial coordinates record the location information of key topological regions.

[0174] In each frame of the image sequence, corresponding pixel regions are marked to generate a key topological region mask set. The elements of the key topological region mask set are binary matrices; a matrix element value of 1 indicates that the corresponding pixel belongs to a key topological region, and a matrix element value of 0 indicates that the corresponding pixel does not belong to a key topological region. Using the key topological region mask set, the location of key topological regions in the image can be accurately identified.

[0175] For each masked region in the key topological region mask set, the pixel gradient magnitude of the corresponding image frame is extracted to generate a region gradient feature vector. The dimension of the region gradient feature vector is the same as the number of pixels in the masked region, and it records the gradient information of the pixels within the masked region.

[0176] Based on the regional gradient feature vector, adaptive contrast enhancement processing is performed on pixels within the masked region. This process adjusts the pixel's luminance channel value according to the pixel's gradient magnitude, making the image within key topological regions clearer and more prominent. Meanwhile, the original color coding information and linewidth parameters of pixels in non-masked regions remain unchanged, ensuring that the image in non-critical regions is unaffected.

[0177] The contrast-enhanced masked region pixels are then blended with the unmasked region pixels using boundary smoothing processing, resulting in a more natural and smooth transition between critical and non-critical regions. This ultimately generates an optimized turbulent transport visualization image sequence that salientizes the critical topological regions. This optimized image sequence highlights the core turbulent transport regions associated with critical points in the flow field, helping researchers to more clearly observe and analyze the characteristics and changes of key regions in the flow field.

[0178] This invention generates a raw streamline set containing temporal evolution information using the Lagrange trace method, resulting in a more comprehensive and accurate description of fluid motion. Based on this, topological analysis is performed on the raw streamline set, generating a streamline topological feature map that clearly describes the spatial relationships between streamlines and the distribution patterns of critical points, enabling in-depth analysis of the flow field's intrinsic structure. A multi-scale parallel rendering task queue is constructed based on the streamline topological feature map, and a spatial region partitioning algorithm distributes the raw streamline set to multiple computing nodes for collaborative rendering, significantly improving rendering efficiency. Simultaneously, the computational power of multiple nodes enables the processing of large-scale flow field data. Finally, adaptive streamline density adjustment is performed based on the intermediate results of the collaborative rendering, generating a sequence of turbulent transport visualization images with dynamic detail levels, accurately presenting the spatial distribution characteristics and temporal evolution trends of turbulent transport phenomena in the flow field.

[0179] With this design, the embodiments of the present invention not only improve the efficiency and quality of flow field visualization, but also provide more in-depth and accurate information for flow field research.

[0180] Furthermore, Figure 2 This is a schematic diagram of the structure of an information visualization system 200 provided in an embodiment of the present invention. Figure 2 The information visualization system 200 shown includes a processor 210, which can call and run computer programs from memory to implement the methods in the embodiments of the present invention.

[0181] Optionally, such as Figure 2 As shown, the information visualization system 200 may further include a memory 230. The processor 210 can retrieve and run computer programs from the memory 230 to implement the methods described in this embodiment of the invention.

[0182] The memory 230 can be a separate device independent of the processor 210, or it can be integrated into the processor 210.

[0183] Optionally, such as Figure 2 As shown, the information visualization system 200 may also include a transceiver 220, which the processor 210 can control to interact with other devices. Specifically, it can send information or data to other devices or receive information or data sent by other devices.

[0184] Optionally, the information visualization system 200 can implement the corresponding processes of the storage engine or components (such as processing modules) in the storage engine or the device on which the storage engine is deployed in the various methods of the embodiments of the present invention. For the sake of brevity, these will not be described in detail here.

[0185] It should be understood that the processor in this embodiment of the invention may be an integrated circuit chip with signal processing capabilities.

[0186] It is understood that the memory in the embodiments of the present invention may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. It should be noted that the memory of the systems and methods described herein is intended to include, but is not limited to, suitable types of memory.

[0187] Based on the above, a readable storage medium is provided, on which a program or instructions are stored, and when the program or instructions are executed by a processor, the steps of the above method are implemented.

[0188] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. Furthermore, it should be noted that the scope of the methods and apparatuses in the embodiments of the present invention is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.

[0189] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solutions of the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of computer software products. These computer software products are stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and include several instructions to cause a terminal (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0190] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the embodiments of the present invention without departing from the spirit and scope of protection of the embodiments of the present invention, and all of these forms are within the protection scope of the embodiments of the present invention.

Claims

1. An information visualization method applied to parallel turbulent transport, characterized in that, The method includes: The Lagrange pursuit method is used to perform trajectory integration on the flow field sampling points to generate an original streamline set containing time evolution information. The original streamline set is composed of the spatial position coordinate sequence of fluid particles in continuous time intervals. The original streamline set is subjected to topological structure analysis processing to generate a streamline topological feature map containing branch points, sink points and saddle points. The streamline topological feature map is used to describe the spatial correlation between streamlines and the distribution law of critical points. Based on the streamline topology feature map, a multi-scale parallel rendering task queue is constructed. The original streamline set is allocated to multiple computing nodes to perform collaborative rendering processing through a spatial region partitioning algorithm to obtain intermediate collaborative rendering results. Based on the intermediate results of the collaborative rendering, streamline density adaptive adjustment processing is performed to generate a turbulent transport visualization image sequence with dynamic detail levels. The turbulent transport visualization image sequence is used to present the spatial distribution characteristics and temporal evolution trend of turbulent transport phenomena in the flow field.

2. The information visualization method applied to parallel turbulent transport as described in claim 1, characterized in that, The step of performing topological structure analysis on the original streamline set to generate a streamline topological feature map containing branch points, sink points, and saddle points includes: Extract the spatial position coordinate sequence of each streamline in the original streamline set, calculate the displacement vector of the fluid particle under adjacent time intervals, and determine the local curvature extremum of the streamline based on the direction change rate of the displacement vector; Neighborhood search processing is performed on the local curvature extrema points to identify the set of intersection points where the spatial distance between the local curvature extrema points of different streamlines is less than a preset threshold. Intersection points in the set of intersection points where the number of connected streamlines exceeds a preset number are marked as branch points. Calculate the velocity divergence value of each streamline in the original streamline set, mark the spatial location with negative velocity divergence value and surrounding streamlines showing a converging trend as the sink point, and mark the spatial location with positive velocity divergence value and surrounding streamlines showing a diverging trend as the saddle point. A topological correlation matrix is ​​constructed based on the spatial coordinates of the branch points, sink points, and saddle points. The row vectors of the topological correlation matrix represent the critical point types, and the column vectors represent the spatial connection relationships between the critical points. Based on the topological association matrix, a directed graph structure is generated with critical points as nodes and streamline connections as edges. The directed graph structure and the set of spatial coordinates of the critical points are combined to form a streamline topological feature map.

3. The information visualization method applied to parallel turbulent transport as described in claim 1, characterized in that, The process involves constructing a multi-scale parallel rendering task queue based on the streamline topology feature map, and using a spatial region partitioning algorithm to distribute the original streamline set to multiple computing nodes for collaborative rendering processing, yielding intermediate collaborative rendering results, including: The directed graph structure in the streamline topology feature map is analyzed, and the spatial coordinate sets of branch points, sink points and saddle points are extracted. A spatial bounding box is generated with the spatial coordinate sets as the center. The side length of the spatial bounding box is determined according to the maximum distance between critical points. The bounding box is subjected to uniform meshing to generate a spatial mesh containing multiple sub-region units. The boundary coordinates of each sub-region unit are calculated based on the number of meshes and the size of the bounding box. The identifiers of the sub-region units traversed by each streamline in the original streamline set are counted, and a mapping table between streamlines and sub-region units is constructed. The mapping table is used to record all sub-region unit numbers associated with a single streamline. Based on the mapping table, the original streamline set is split into multiple sub-stream sets, each of which contains streamline segments that are completely located within the same sub-region unit and streamline segments that cross sub-region units; A multi-scale parallel rendering task queue is constructed based on the spatial location of the sub-region unit and the data size of the sub-streamline set. The sub-streamline set is allocated to multiple computing nodes according to the priority sorting rules of the multi-scale parallel rendering task queue. Each computing node receives a sub-streamline set that matches the computing power of that computing node. Each computing node performs initial rendering processing on the received set of sub-streams to generate a local rendering result containing streamer color coding information and linewidth parameters. The color coding information is determined according to the speed of the streamer, and the linewidth parameters are dynamically adjusted according to the curvature value of the streamer. The local rendering results of streamline segments across sub-region units are exchanged using multiple computing nodes and a distributed communication protocol, and weighted fusion processing is performed on the local rendering results of overlapping regions to obtain intermediate collaborative rendering results.

4. The information visualization method applied to parallel turbulent transport as described in claim 3, characterized in that, The step of splitting the original streamline set into multiple sub-stream sets based on the mapping table includes: Traverse the sub-region unit numbers associated with each streamline in the mapping table and determine whether the number of sub-region unit numbers is 1; When the number of sub-region unit numbers is 1, the streamline is directly assigned to the sub-streamline set of the corresponding sub-region unit as a streamline segment that is completely located within the same sub-region unit; When the number of sub-region unit numbers is greater than 1, the spatial position coordinate sequence of the streamline is divided according to the spatial position order of the sub-region units, and the streamline is truncated into multiple streamline segments at the boundary coordinates of adjacent sub-region units. Extract the starting and ending spatial coordinates of each streamline segment, determine whether the starting and ending spatial coordinates are located within the same sub-region unit, and classify the streamline segments located within the same sub-region unit into the sub-streamline set of the corresponding sub-region unit. Add region identifier tags to streamline segments that span sub-region units. The region identifier tags include the original streamline number, the starting region number, and the ending region number of the rendering results exchanged between computing nodes. The cross-region streamline segments containing the region identifier label are simultaneously stored in the sub-stream sets corresponding to all sub-region units that the cross-region streamline segments pass through, so that the sub-stream set of each sub-region unit contains complete intra-region streamline information and cross-region streamline segment information. The initial rendering process is performed on the received sub-stream set by each computing node to generate a local rendering result containing streamer color encoding information and linewidth parameters, including: The spatial position coordinate sequence and corresponding timestamp information of each streamline in the sub-streamlet set are analyzed, and the velocity magnitude of each streamline under the timestamp sequence is calculated. The velocity magnitude is determined by the ratio of the Euclidean distance between the spatial position coordinates of adjacent timestamps to the time interval. Based on the speed magnitude, a preset color mapping table is queried. In the color mapping table, the speed magnitude and the color channel value have a monotonic mapping relationship. Based on the query result, color coding information for each streamline is generated. The color coding information includes the values ​​of the red, green, and blue channels. Calculate the curvature value of the spatial position coordinate sequence of each streamline. The curvature value is determined by the ratio of the second derivative magnitude of the streamline to the cube of the first derivative magnitude. Adjust the streamline width parameter according to the curvature value. The larger the curvature value, the larger the streamline width parameter. Visibility determination processing is performed on the streamline segments in the sub-streamline set. Based on the view frustum parameters from the observer's perspective, streamline segments located outside the view frustum are removed, while streamline segments located inside the view frustum are retained. A transition color value is added to the pixel-level position of the streamline by using a line segment sampling algorithm to perform anti-aliasing on the preserved streamline segments; The color coding information, line width parameters, and anti-aliased pixel coordinates are combined into a local rendering result, which includes the color value and depth value of each pixel.

5. The information visualization method applied to parallel turbulent transport as described in claim 1, characterized in that, The step of performing streamline density adaptive adjustment processing based on the intermediate results of the collaborative rendering to generate a sequence of turbulent transport visualization images with dynamic detail levels includes: The intermediate results of the collaborative rendering are analyzed, and the set of pixel coordinates and corresponding depth values ​​of all streamlines are extracted. A streamline density statistics matrix indexed by pixel coordinates is constructed. Each element of the streamline density statistics matrix represents the number of overlaps of streamlines at the corresponding pixel position. Gaussian filtering is applied to the streamline density statistics matrix to generate a smoothed streamline density distribution heatmap. The standard deviation of the kernel function of the Gaussian filtering is dynamically adjusted according to the viewport resolution. Based on the streamline density distribution heatmap, the boundary threshold between high-density and low-density regions is determined by the maximum inter-class variance method. Regions with density values ​​greater than the boundary threshold are marked as high-density regions, and regions with density values ​​less than the boundary threshold are marked as low-density regions. For high-density regions, streamline simplification is performed by using the Douglas-Peucker algorithm to simplify the spatial coordinate sequence of streamlines within the high-density region, preserving the main geometric features of the streamlines and reducing the number of vertices. Streamline refinement is performed on low-density regions by inserting new streamline segments between the streamlines in the low-density regions. The spatial coordinates of the new streamline segments are generated based on the coordinate sequence of adjacent streamlines using an interpolation algorithm. The global streamline set is reconstructed based on the simplified high-density region streamlines and the refined low-density region streamlines. The global streamline set includes the spatial position coordinate sequence, color coding information and line width parameters of all streamlines after adjustment. Frame buffer synthesis processing is performed on the global streamline set, and the pixel coordinates, color values ​​and depth values ​​of the streamlines are written into the frame buffer object to generate a single-frame turbulent transport visualization image. Repeat the above steps to process the intermediate results of collaborative rendering at consecutive time intervals in sequence, generating a turbulent transport visualization image sequence containing multiple frames of images. The frame rate of the turbulent transport visualization image sequence matches the time interval of the original streamline set.

6. The information visualization method applied to parallel turbulent transport as described in claim 5, characterized in that, The streamline simplification process for high-density regions involves using the Douglas-Peucker algorithm to simplify the spatial coordinate sequence of streamlines within the high-density region, preserving the main geometric features of the streamlines while reducing the number of vertices. This includes: Extract the spatial coordinate sequence of each streamline within a high-density region, and represent the spatial coordinate sequence as an ordered set of vertices, which includes the starting vertex, intermediate vertex, and ending vertex of the streamline. Specify the starting vertex and the ending vertex in the vertex set as simplified retained vertices, and calculate the perpendicular distance from the intermediate vertex to the line segment formed by the starting vertex and the ending vertex. The vertical distance is compared with a preset simplification threshold. When the vertical distance is greater than the simplification threshold, the intermediate vertex is marked as a retained vertex, and the vertex set is divided into two sub-vertex sets with the intermediate vertex as the boundary. Repeat the above comparison and segmentation steps for each set of subvertices until the vertical distance of all intermediate vertices is less than the simplification threshold; Collect all marked vertices and rearrange them according to the order of the original vertex set to generate a simplified vertex sequence, which constitutes the simplified streamline geometry data; The length error of the streamline before and after simplification is calculated. The length error is determined by the difference between the length of the broken line formed by the simplified vertex sequence and the length of the broken line formed by the original vertex sequence. When the length error is greater than the preset error threshold, the simplification threshold is adjusted back and the vertex simplification process is re-executed until the length error is less than the preset error threshold. The simplified vertex sequence, along with the corresponding color coding information and linewidth parameters, is combined into simplified streamline data, which replaces the original streamline data in the high-density region.

7. The information visualization method for parallel turbulent transport as described in claim 5, characterized in that, The streamline refinement process performed on the low-density region, inserting new streamline segments between streamlines within the low-density region, includes: Extract all streamlines within the low-density region and construct an adjacency graph of the streamlines. The nodes of the adjacency graph represent streamlines, and the edges represent that the spatial distance between streamlines is less than a preset proximity distance threshold. Traverse each edge in the adjacency graph to obtain the spatial position coordinate sequence of two adjacent streamlines; Synchronous sampling processing is performed on the spatial position coordinate sequences of two adjacent streamlines. The spatial position coordinates of the two streamlines are extracted at the same timestamp, resulting in a set of sampling points containing multiple coordinate pairs. Linear interpolation is performed on each coordinate pair in the sampling point set to calculate the spatial coordinates of the interpolation point. The weight coefficient of the interpolation point is dynamically adjusted according to the distance between the two streamlines. The smaller the distance, the closer the weight coefficient is to the preset coefficient. Connect all interpolation points in time stamp order to generate a new sequence of spatial coordinates for streamline segments. The start and end timestamps of the new streamline segments are consistent with those of the adjacent streamlines. Calculate the velocity magnitude and curvature value of the new streamline segment, query the color map table based on the velocity magnitude to generate color coding information, and determine the line width parameter based on the curvature value; The spatial coordinate sequence, color coding information, and linewidth parameters of the new streamline segments are added to the streamline set in the low-density region to complete the streamline refinement process.

8. The information visualization method applied to parallel turbulent transport as described in claim 5, characterized in that, The global streamline set is reconstructed based on the simplified high-density region streamlines and the refined low-density region streamlines. This global streamline set includes the spatial coordinate sequence of all streamlines after adjustment, color coding information, and linewidth parameters, including: Collect the spatial coordinate sequence, color-coded information and linewidth parameters of streamlines in the simplified high-density region, and label them as the first streamline subset; Collect the spatial coordinate sequence, color coding information and line width parameters of streamlines in the refined low-density region, and label them as the second streamline subset; Extract the boundary region streamlines of the first streamline subset and the second streamline subset, wherein the boundary region streamlines are streamlines located at the junction of high-density region and low-density region; The spatial position coordinate sequence of the streamlines in the boundary region is subjected to smooth transition processing. The curvature value difference between adjacent streamlines is calculated, and the line width parameter of the boundary streamlines is adjusted by a weighted average algorithm to eliminate the abrupt line width change between high-density and low-density regions. Check whether there are duplicate streamline segments between the first streamline subset and the second streamline subset. Remove duplicate segments by comparing the similarity of spatial location coordinate sequences and retain unique streamline segments. The processed first streamline subset and the second streamline subset are merged and sorted according to the streamline timestamp information to generate a global streamline set containing all adjusted streamlines. Assign a unique identifier to each streamline in the global streamline set. The unique identifier includes the streamline's generation timestamp and the original fluid particle number.

9. The information visualization method applied to parallel turbulent transport as described in claim 5, characterized in that, The step of performing frame buffer synthesis processing on the global streamline set, writing the pixel coordinates, color values, and depth values ​​of the streamlines into a frame buffer object, and generating a single-frame turbulent transport visualization image includes: Initialize a frame buffer object, the resolution of which is consistent with the resolution of the target display device, and the frame buffer object contains two channels: a color buffer and a depth buffer. Configure rendering state parameters, set the blending mode to additive blending, enable the depth test function, and set the depth test comparison function to less than or equal to. Traverse each streamline in the global streamline set and read the spatial position coordinate sequence, color encoding information and line width parameters of the streamline; The spatial coordinate sequence of streamlines is converted from the world coordinate system to the screen coordinate system, and the pixel coordinate sequence of each streamline is calculated through the perspective projection matrix; The line segment drawing interface is called according to the pixel coordinate sequence and line width parameters to draw the streamline into the color cache of the frame buffer object, and the depth value in the depth cache is updated at the same time. During the rendering process, gamma correction is performed on the pixel color values ​​in the color cache; After the drawing is completed, the color cache data of the frame buffer object is read, the color cache data is converted into a standard image format, and a single-frame turbulent transport visualization image is generated. Release the temporary memory resources occupied by the frame buffer object, and retain the generated single-frame turbulent transport visualization image data for subsequent image sequence synthesis.

10. An information visualization system, characterized in that, The method includes at least one processor and a memory; the memory stores computer-executable instructions; the at least one processor executes the computer-executable instructions stored in the memory, causing the at least one processor to perform the method according to any one of claims 1-9.

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