Visualization Rendering Method for Generating Projection Fusion of Digital Twin Thermal Images Based on WebGL

Abstract

The present invention relates to the field of digital twin technology, and specifically relates to a visualization rendering method for generating digital twin thermal image projection fusion based on WebGL. The method includes cloning and extracting the regional model that needs to generate the thermal map texture in the virtual scene constructed based on the physical scene, and performing cube UV mapping on the extracted model texture; mapping the scatter set of the heat source distribution in the entity domain in the texture mapping UV coordinate system to generate a square picture with the heat source distribution on the entity domain; constructing a two-dimensional coordinate of the heat source distribution in the twin domain in Canvas, naming and identifying the three-dimensional model in the twin domain, and then storing and exporting it in the GLTF format file; parsing the GLTF format file based on WebGL, obtaining the model information storing the UV mapping information, and constructing the mapping between the thermal image projection fusion twin domain and the entity domain. The present invention effectively solves the technical problems existing in the prior art.

Description

Technical Field

[0001] The present invention relates to the technical field of digital twins, and particularly to a visualization rendering method for generating digital twin thermal image projection fusion based on WebGL. Background Art

[0002] Digital Twin is to use big data technology to store the data information of the physical world in a big data cluster in the form of virtual simulation, so as to improve the efficiency of data storage and calculation in the real world; in recent years, with the development of CPS (Cyber-Physical Svstems) technology, digital twin technology has gradually become a research hotspot. By constructing a twin body of a physical entity in the digital space, the physical space and the digital space coexist in virtual reality, realizing a comprehensive, real and objective mapping of the digital world to the physical world. With the above technical advantages, digital twin technology has continued to develop rapidly. Its application fields have gradually expanded to product design, product manufacturing, medical analysis, engineering construction and other fields, and have played a huge promoting role in related fields. The technical advantages of digital twin technology have brought a qualitative leap to model-based application analysis.

[0003] When the digital twin technology is actually applied, taking applications such as industrial facility equipment wear monitoring, sensor early warning and alarm monitoring (natural gas plants, gas gathering plants, water treatment plants, etc.), passenger flow monitoring, visitor volume monitoring (smart cities, smart parks, etc.) as examples, digital twin can make full use of physical models and sensor data, integrate the simulation processes of multiple disciplines, multiple physical quantities and multiple scales, and complete the mapping in the virtual space, so as to reflect the full life cycle process of the corresponding entity. However, there is a lack of an interface for thermal image projection fusion, and the monitoring data obtained in the entity domain cannot be transmitted and reflected in the twin domain, which affects the result diagnosis and prediction in the subsequent stage and reduces the processing efficiency. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a visualization rendering method for generating digital twin thermal image projection fusion based on WebGL, so as to solve the above technical problems existing in the prior art.

[0005] To achieve the above purpose, the visualization rendering method for generating digital twin thermal image projection fusion based on WebGL provided by the present invention adopts the following technical solutions:

[0006] The visualization rendering method for generating digital twin thermal image projection fusion based on WebGL includes the following steps:

[0007] In a virtual scene constructed based on a physical scene, clone and extract the area model that needs to generate a thermal map texture, and perform cube UV mapping on the extracted model texture;

[0008] Map the scatter set of the thermal source distribution in the entity domain in the texture mapping UV coordinate system to generate a square picture with the thermal source distribution in the entity domain. Construct the two-dimensional coordinates of the thermal source distribution in the twin domain in Canvas, name and identify the three-dimensional model in the twin domain, and then store and export the GLTF format file.

[0009] Based on the principle of the heat map, construct the two-dimensional coordinate interface of the thermal source distribution in the twin domain in Canvas and draw the initialized square heat map texture.

[0010] Based on WebGL, parse the GLTF format file, obtain the model information storing the UV mapping information, and construct the mapping between the twin domain and the entity domain for the heat map image projection fusion.

[0011] Furthermore, in the virtual scene constructed based on the physical scene, clone and extract the model grid vertex information of the area where the heat map texture needs to be generated to generate a three-dimensional grid model HeatMap_Area01 independent of the original virtual scene, and perform cube UV mapping on the texture of the three-dimensional grid model HeatMap_Area01.

[0012] Furthermore, the implementation steps of the cube UV mapping include: using the cube intermediate space, mapping the two-dimensional texture space T(u, v) to the cube surface T’(x’, y’, z’) through the S mapping.

[0013] Map the texture on the cube surface to the surface of the three-dimensional grid model O(x, y, z) through the O mapping to generate a grid model HeatMap_Arae01_UV with square UV texture information. At this time, the UV coordinate points corresponding to all the grid vertices of HeatMap_Arae01_UV are mapped within a square with a side length of 1.

[0014] Furthermore, process the three-dimensional grid model: generate a scatter set square picture Texture_Square with the thermal source distribution information through the spatial point information {P1, P2,..., P19, P20} of the entity thermal sources distributed on the three-dimensional grid model and the scatter set {Q1, Q2,..., Q19, Q20} in the HeatMap_Arae01_UV texture space coordinate system.

[0015] Further, process the square picture: Based on the Canvas tag in Html5, map the point position information of the scatter point set with heat source distribution in the picture Texture_Square onto a square canvas with a length and width of 1000 pixels respectively, so as to obtain the two-dimensional coordinate array of the Position scatter point set of the heat source points in the 2D canvas Canvas.

[0016] Further, in the virtual scene constructed based on the physical scene, perform texture mapping on other areas in the scene where heat sources need to be generated, and name the new mesh models after mapping as HeatMap_Arae02_UV, HeatMap_Area03_UV,.. HeatMap_AreaN_UV in sequence. Store and export the information of the three-dimensional mesh model and the scene mesh model that have completed texture mapping using the GLTF model format.

[0017] Further, the steps for drawing the initialized square heat map texture include: taking the two-dimensional coordinate values of the Position scatter point set as the center of the circle, using [(0, 255, 255), (0, 255, 0), (255, 255, 0), (255, 0, 0)] cyan, green, yellow, and red as the color band gradient, and respectively drawing radially gradient circles in a square 2D canvas Canvas with a length and width of 1000 pixels with a radius Radius equal to 10 pixels and a radius Radius equal to a random value pixel in the interval [1, 30], then generating a square initialized heat texture map Texture_HeatMap_Init with a side length of 1000.

[0018] Further, process the square initialized heat texture map: Pass the square initialized heat texture map Texture_HeatMap_Init to the material of the HeatMap_Arae01_UV, so that the spatial position information of the heat source distribution points in the entity domain is transferred to the two-dimensional Canvas canvas through the UV coordinate system and the initialized heat map texture is rendered and fused in the twin domain.

[0019] Further, the specific steps of mapping and rendering the magnitude of the physical domain heat source in the heat map texture of the 3D grid model in the digital twin domain are as follows: Multiply the radius R of the radially gradient circle by the weight value K of the magnitude, where K is the ratio of the magnitude at a certain moment in the physical domain to the maximum value Kmax of the magnitude interval: Radius = R(K / Kmax), to generate a square heat texture map Texture_HeatMap_R(K / Kmax) in the digital twin domain where the magnitude in the physical domain is mapped. Transfer the heat texture map Texture_HeatMap_R(K / Kmax) to the material of the HeatMap_Arae01_UV grid model. At this time, the magnitude of the physical domain heat source is also mapped and rendered in the heat map texture of the 3D grid model in the digital twin domain.

[0020] The beneficial effects of the visualization rendering method for generating digital twin heat image projection fusion based on WebGL provided by the present invention are as follows:

[0021] 1) The spatial information interface of the physical domain heat source is mapped in the texture space of the digital twin 3D model;

[0022] 2) The magnitude information interface of the physical domain heat source is mapped in the heat map texture of the digital twin domain;

[0023] 3) An interface for heat image projection fusion is provided for the digital twin field in related fields such as passenger flow monitoring, industrial facility and equipment wear monitoring, and sensor early warning and alarm monitoring;

[0024] 4) Monitoring data such as sensors in the physical domain can be transmitted and reflected in the digital twin domain;

[0025] 5) An efficient and feasible solution is provided for result diagnosis and prediction in subsequent stages in related fields such as passenger flow monitoring, industrial facility and equipment wear monitoring, and sensor early warning and alarm monitoring in the digital twin field. Description of the Drawings

[0026] Figure 1 It is a schematic diagram of performing cube UV mapping on the texture of the extracted regional model in step S1 of the present invention;

[0027] Figure 2 It is to map the scatter point set of the physical domain heat source distribution in the texture mapping UV coordinate system of the present invention to generate a square picture with the physical domain heat source distribution;

[0028] Figure 3 It is to map the picture with the physical domain heat source distribution point information in the canvas to a two-dimensional array in the interval [0, 1000] in the present invention;

[0029] Figure 4The present invention draws an initialized thermal texture map in the canvas with the coordinates of the thermal source distribution points in the physical domain as the center and different colors as color bands;

[0030] Figure 5 The present invention parses the GLTF file based on WebGL, obtains the model information storing UV mapping information, and performs the rendering of the initialized thermal texture map and the thermal texture map with the physical domain quantity value weight;

[0031] Figure 6 It is the thermal image projection fusion mapping result diagram of the multi-region physical domain and the twin domain in the present invention;

[0032] Figure 7 It is the flow block diagram of the visualization rendering method for generating digital twin thermal image projection fusion provided by the present invention. Detailed implementation manners

[0033] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the described embodiments of the present invention fall within the scope of protection of the present invention.

[0034] The problem to be solved by the present invention is to provide an interface for thermal image projection fusion for digital twin technology in related fields such as passenger flow monitoring, industrial field facility and equipment wear monitoring, and sensor early warning and alarm monitoring, so that monitoring data such as sensors in the physical domain can be transmitted and reflected in the twin domain, and provide an efficient and feasible solution for the result diagnosis and prediction in related fields such as passenger flow monitoring, industrial field facility and equipment wear monitoring, and sensor early warning and alarm monitoring.

[0035] Based on the above objectives, the visualization rendering method for generating digital twin thermal image projection fusion provided by the present invention includes the following steps:

[0036] In the virtual scene constructed based on the physical scene, clone and extract the regional model that needs to generate the thermal map texture, and perform cube UV mapping on the extracted model texture;

[0037] Map the scatter set of the thermal source distribution in the physical domain in the texture mapping UV coordinate system, generate a square picture with the thermal source distribution in the physical domain, construct the two-dimensional coordinates of the thermal source distribution in the twin domain in Canvas, and store and export the GLTF format file after naming and identifying the three-dimensional model in the twin domain;

[0038] Construct a two-dimensional coordinate interface for the distribution of twin-domain heat sources in Canvas based on the heat map principle, and draw an initialized square heat map texture;

[0039] Parse the GLTF format file based on WebGL, obtain the model information storing UV mapping information, and construct the mapping between the heat map image projection fusion twin domain and the entity domain.

[0040] For digital three-dimensional mesh models, there are two of the most important coordinate systems. One is the three-dimensional space coordinate system (x, y, z) of the vertex information that constructs the three-dimensional model mesh structure; the other is the UV coordinate system (u, v) that resides on the vertices of the polygon mesh and is used to define the two-dimensional texture space of the three-dimensional model. The UV points are the points associated with the vertices of the polygon mesh, which can correspond the pixel points on the texture map to the vertices on the model mesh, so as to provide the position information required when applying textures to objects. Therefore, in this application, the UV coordinate system is adopted to provide the position information required when applying textures to objects.

[0041] As Figure 1 shown, in the virtual scene constructed based on the physical scene, clone and extract the vertex information of the model mesh for the area where the heat map texture needs to be generated, generate a three-dimensional mesh model HeatMap_Area01 independent of the original virtual scene, and perform cube UV mapping on the texture of this three-dimensional mesh model HeatMap_Area01.

[0042] The implementation steps of the cube UV mapping include: based on the two-step texture mapping technology, first use the cube intermediate space, and map the two-dimensional texture space T(u, v) to the cube surface T'(x', y', z') through the S mapping; map the texture on the cube surface to the surface O(x, y, z) of the three-dimensional mesh model HeatMap_Area01 through the O mapping, and generate a mesh model HeatMap_Arae01_UV with square UV texture information. At this time, the UV coordinate points corresponding to all the mesh vertices of HeatMap_Area01_UV are mapped within a square with a side length of 1, that is, the scatter point set P(u, v) of the HeatMap_Area01_UV texture space is within the interval [0, 1].

[0043] As Figure 2 shown, the spatial point information (P1, P2,..., P19, P20) of the entity heat sources distributed on the three-dimensional mesh model HeatMap_Arae01 mesh model, and the scatter point set (Q1, Q2,..., Q19, Q20) in the HeatMap_Area01_UV texture space coordinate system, generate a scatter point set square picture Texture_Square with heat source distribution information; As Figure 3As shown in the figure, based on the Canvas tag in Html5, the scatter point set with the heat source distribution in the entity domain in the picture Texture_Square is mapped onto a square canvas with a length and width of 1000 pixels respectively, so as to obtain the two-dimensional coordinate array of the Position scatter point set of the heat source point position in the 2D canvas Canvas. This two-dimensional coordinate group is the mapping position information of the entity domain heat source in the twin domain, and is also the parameter value used in constructing the two-dimensional coordinate interface of the twin domain heat source distribution.

[0044] Similarly, texture mapping can be performed on other areas that need to generate heat sources in the virtual scene constructed based on the physical scene, and the newly mapped mesh models are named HeatMap_Arae02_UV, HeatMap_Area03_UV,.. HeatMap_AreaN_UV in sequence. The three-dimensional mesh models and scene mesh models after texture mapping are stored and exported using the GLTF model format for information.

[0045] Based on the heat map principle, a diagram showing the geographical area where the visitor is located is displayed in a special highlighted form. In reality, to obtain the heat map presentation of a certain geographical area, at least two-dimensional parameters are required. One is the location of the area, that is, the coordinate value; the other is the number of people gathered in the area or the temperature of the area, that is, the quantity value.

[0046] Based on the Canvas tag in Html5, graphics can be dynamically drawn in the 2D canvas Canvas two-dimensional canvas. For the heat map presentation of the quantity value at a certain coordinate point in the entity domain, only a transparency Alpha radial gradient circle corresponding to the quantity value needs to be drawn at each coordinate point, and at the same time, customized color band values are rendered for the pixel points with different Alpha gradient levels in the Canvas canvas. Then a diagram in a special highlighted form that conforms to the heat map principle can be drawn.

[0047] As Figure 4 shown, the steps for drawing the initialized square heat map texture include: using the two-dimensional coordinate values of the Position scatter point set as the center of the circle, with [(0, 255, 255), (0, 255, 0), (255, 255, 0), (255, 0, 0)] cyan, green, yellow, and red as the color band gradients, and respectively using a radius Radius equal to 10 pixels and a radius Radius equal to a random value pixel in the range of [1, 30] to draw a radial gradient circle in a square 2D canvas Canvas with a length and width of 1000 pixels, then generating a square initialized heat texture map Texture_HeatMap_Init with a side length of 1000.

[0048] As Figure 5As shown in the left half of the figure, the initialized thermal texture map of the square is processed: The initialized thermal texture map of the square, Texture_HeatMap_Init, is passed into the material of HeatMap_Area01_UV, so that the spatial position of the thermal source distribution point information in the physical domain in the 3D mesh model of the digital twin domain is transferred to the 2D Canvas through the UV coordinate system and the initialized thermal map texture is rendered and fused in the digital twin domain, that is, the coordinate interface for the projection fusion of the digital twin thermal image.

[0049] In addition to the thermal source coordinate information in the physical domain, there are also thermal source magnitudes (i.e., temperature values, passenger flow values, visitor quantity values, etc. in actual business requirements).

[0050] The specific steps for mapping, rendering, and fusing the magnitude of the thermal source in the physical domain in the thermal map texture of the 3D mesh model in the digital twin domain include: multiplying the radius R of the radially gradient circle by the weight value K of the magnitude, where K is the ratio of the magnitude at a certain moment in the physical domain to the maximum value Kmax of the magnitude interval: Radius = R(K / Kmax), generating the square thermal texture map Texture_HeatMap_R(K / Kmax) in the digital twin domain where the magnitude in the physical domain is mapped, and passing the thermal texture map Texture_HeatMap_R(K / Kmax) into the material of the HeatMap_Arae01_UV mesh model. At this time, the magnitude of the thermal source in the physical domain is also mapped, rendered, and fused in the thermal map texture of the 3D mesh model in the digital twin domain, that is, the magnitude interface for the projection fusion of the digital twin thermal image. Thus, the method for generating the visual rendering of the projection fusion of the digital twin thermal image based on WebGL has been realized.

[0051] In actual business requirements, there may be a situation where multiple thermal source distribution points in the physical domain are aggregated into one area, and a thermal map with multiple regions and multiple gradients within the region is presented in the digital twin domain. As Figure 6 shown, by using this method multiple times in the same way, the projection fusion of thermal images between the physical domain with multiple regions and the digital twin domain can also be realized.

[0052] It should be emphasized that the most critical point of the digital twin thermal image projection fusion is: First, construct the mapping relationship between the spatial information of the thermal source distribution in the entity domain and the texture space coordinate system of the three-dimensional grid model in the twin domain. Second, based on the principle of thermal map, construct the two-dimensional coordinate interface of the thermal source distribution in the twin domain in Canvas and draw the thermal map texture. Third, respectively construct the mapping interface of the point information and the value information in the entity domain in the thermal map texture of the twin domain based on the principle of thermal map; for the above three key points, the projection mapping and fusion of the spatial information of the thermal source in the entity domain and the value information in the texture space of the three-dimensional grid model in the twin domain are opened up and connected, so that the transmission and presentation of data between the virtual and real domains are feasible.

[0053] For the specific flow chart, please refer to Figure 7 The beneficial effects of the visualization rendering method for generating digital twin thermal image projection fusion based on WebGL provided by the present invention are:

[0054] 1) The spatial information interface of the thermal source in the entity domain is mapped in the texture space of the twin domain 3D model;

[0055] 2) The entity domain thermal source value information interface is mapped in the twin domain thermal map texture;

[0056] 3) It provides an interface for thermal image projection fusion in the field of digital twins in passenger flow monitoring, industrial facility and equipment wear monitoring, and sensor early warning and alarm monitoring;

[0057] 4) Enable monitoring data such as sensors in the entity domain to be transmitted and reflected in the twin domain;

[0058] 5) It provides efficient and feasible solutions for the diagnosis and prediction of results in the subsequent stages in the fields of passenger flow monitoring in the digital twin field, equipment wear monitoring in the industrial field, and sensor early warning and alarm monitoring.

[0059] In the present invention, unless otherwise clearly stipulated and limited, for example, it can be a fixed connection, a detachable connection, or an integrated one; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. Unless otherwise clearly defined, for ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances.

[0060] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A visualization rendering method for generating projection fusion of digital twin thermal images based on WebGL, characterized in that, It includes the following steps: In the virtual scene constructed based on the physical scene, clone and extract the area model that needs to generate the heat map texture, and perform cube UV mapping on the extracted model texture to obtain the texture mapping UV coordinate system; Map the scatter point set of the heat source distribution in the entity domain in the texture mapping UV coordinate system to generate a square picture with the heat source distribution in the entity domain. Based on the point position information of the scatter point set of the heat source distribution in the square picture, construct the two-dimensional coordinates of the heat source distribution in the twin domain in Canvas, name and identify the three-dimensional model in the twin domain, and then store and export the GLTF format file; Based on the heat map principle, construct the two-dimensional coordinate interface of the heat source distribution in the twin domain in Canvas, pass in the two-dimensional coordinates of the heat source distribution in the twin domain constructed through the constructed two-dimensional coordinate interface of the heat source distribution in the twin domain, and draw the initialized square heat map texture; Based on WebGL, parse the GLTF format file, obtain the model information storing the UV mapping information, construct the mapping between the twin domain and the entity domain for the heat image projection fusion, and render the initialized square heat map texture to obtain the heat texture map with the entity domain quantity value weight value; 2. The visualization rendering method for generating digital twin thermal image projection fusion based on WebGL according to claim 1, characterized in that: In the virtual scene constructed based on the physical scene, clone and extract the model grid vertex information of the area that needs to generate the heat map texture to generate a three-dimensional grid model HeatMap_Area01 independent of the original virtual scene, and perform cube UV mapping on the texture of the three-dimensional grid model HeatMap_Area01; 3. The visualization rendering method for generating digital twin thermal image projection fusion based on WebGL according to claim 2, characterized in that, The implementation steps of the cube UV mapping include: using the cube intermediate space, and mapping the two-dimensional texture space T(u, v) to the cube surface T’(x’, y’, z’) through the S mapping; Map the texture on the cube surface to the three-dimensional grid model surface O(x, y, z) through the O mapping to generate a grid model HeatMap_Arae01_UV with square UV texture information. At this time, the UV coordinate points corresponding to all grid vertices of HeatMap_Arae01_UV are mapped within a square with a side length of 1; 4. The visualization rendering method for generating digital twin thermal image projection fusion based on WebGL according to claim 3, wherein Process the three-dimensional grid model: Generate a scatter point set square picture Texture_Square with heat source distribution information through the spatial point information {P1, P2,..., P19, P20} of the entity heat source distributed on the three-dimensional grid model and the scatter point set {Q1, Q2,..., Q19, Q20} in the texture space coordinate system corresponding to the HeatMap_Arae01_UV; 5. The visualization rendering method for generating digital twin thermal image projection fusion based on WebGL according to claim 4, characterized in that, Process the square picture: Based on the Canvas tag in Html5, map the point position information of the scatter point set with heat source distribution in the picture Texture_Square to a square canvas with a length and width of 1000 pixels respectively, so as to obtain the two-dimensional coordinate array of the Position scatter point set of the heat source points in the 2D canvas Canvas; 6. The visualization rendering method for generating digital twin thermal image projection fusion based on WebGL according to any one of claims 3 to 5, characterized in that: In the virtual scene constructed based on the physical scene, texture mapping is performed on other areas in the scene that need to generate heat sources, and the newly mapped mesh models are named HeatMap_Arae02_UV, HeatMap_Area03_UV,..HeatMap_AreaN_UV in sequence. The information of the three-dimensional mesh model and the scene mesh model after texture mapping is stored and exported in the GLTF model format.

7. The visualization rendering method for generating digital twin thermal image projection fusion based on WebGL according to claim 5, characterized in that, The steps for drawing the initialized square heat map texture include: taking the two-dimensional coordinate values of the Position scatter set as the center, using [(0, 255, 255), (0, 255, 0), (255, 255, 0), (255, 0, 0)] cyan, green, yellow, and red as the color band gradient, and respectively drawing radially gradient circles in a square 2D canvas Canvas with a length and width of 1000 pixels with a radius Radius equal to 10 pixels and a radius Radius equal to a random value pixel in the interval [1, 30], thus generating an initialized square heat texture map Texture_HeatMap_Init with a side length of 1000.

8. The visualization rendering method for generating digital twin thermal image projection fusion based on WebGL according to claim 7, characterized in that, Process the initialized square heat texture map: Pass the initialized square heat texture map Texture_HeatMap_Init to the material of HeatMap_Arae01_UV, so that the distribution point information of the heat source in the physical domain is transferred to the two-dimensional Canvas canvas through the UV coordinate system in the spatial position of the three-dimensional mesh model in the twin domain and the initialized heat map texture is rendered and fused in the twin domain.

9. The visualization rendering method for generating digital twin thermal image projection fusion based on WebGL according to claim 8, wherein The specific steps for mapping and rendering the magnitude of the heat source in the physical domain in the heat map texture of the three-dimensional mesh model in the twin domain include: multiplying the radius R of the radially gradient circle by the weight value of the magnitude, where the weight value is the ratio of the magnitude K at a certain moment in the physical domain to the maximum value Kmax of the magnitude interval: Radius = R(K / Kmax), generating a square heat texture map Texture_HeatMap_R(K / Kmax) in the twin domain where the magnitude in the physical domain is mapped, and passing the heat texture map Texture_HeatMap_R(K / Kmax) to the material of the HeatMap_Arae01_UV mesh model. At this time, the magnitude of the heat source in the physical domain is also mapped and rendered in the heat map texture of the three-dimensional mesh model in the twin domain.

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