Mathematical model dynamic display device and demonstration method

Abstract

The invention relates to the field of mathematical model display, and particularly discloses a mathematical model dynamic display device and method, and the method comprises the following steps: 1, collecting and sorting basic data, including model parameters, initial conditions and boundary conditions, required by a mathematical model in a data preparation stage, performing quantitative evaluation on the data by using an integrity evaluation function S1 to ensure that the value of the S1 reaches a preset threshold value, and providing a solid foundation for subsequent AR demonstration; according to the method, the advanced AR technology and the three-dimensional graph rendering capability are adopted, the dynamic change process of the model is displayed to the user in a high-interaction mode, the user can observe and understand the model personally on the scene, and the user experience and the participation degree are greatly improved; meanwhile, the immersion and interactivity of the user are further enhanced by configuring demonstration parameters and specific interaction elements of AR and providing rich interaction operations.

Description

Technical Field

[0001] The invention belongs to the field of mathematical model display, in particular to a mathematical model dynamic display device and a demonstration method. Background Art

[0002] In daily mathematics teaching, mathematical models are often needed to enable students to feel and simulate real objects, so as to have a deeper understanding of mathematical knowledge. Mathematical model dynamic display devices and demonstration methods, as an important teaching auxiliary tool, play an important role in improving students' learning interest, enriching perceptual knowledge, helping to form clear concepts, and developing students' observation and thinking abilities.

[0003] The dynamic demonstration method of mathematical models in the prior art often lacks intuitiveness and interactivity, making it difficult for users to deeply understand the dynamic change process of the mathematical model. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a mathematical model dynamic display device to solve the problem that the dynamic demonstration method of mathematical models in the prior art often lacks intuitiveness and interactivity, making it difficult for users to deeply understand the dynamic change process of the mathematical model.

[0005] A mathematical model dynamic demonstration method comprises the following steps:

[0006] Step 1: Data preparation

[0007] Collect and organize the basic data required for the mathematical model, including model parameters, initial conditions and boundary conditions, and use the integrity assessment function S1 to quantitatively evaluate the data to ensure that the value of S1 reaches the preset threshold, providing a solid foundation for subsequent AR demonstrations;

[0008] Step 2: Model building phase

[0009] Based on the prepared basic data, a corresponding mathematical model is constructed in the computer system, and the model construction process is quantitatively evaluated using the complexity evaluation function S2 to ensure that the value of S2 is within a reasonable range to balance the complexity of the model and the computational efficiency;

[0010] Step 3: Dynamic Demonstration Phase

[0011] The dynamic demonstration system receives and analyzes the mathematical model, and displays the dynamic change process of the model to the user in a three-dimensional, stereoscopic and highly interactive way. The dynamic demonstration system has powerful graphics rendering capabilities to present a realistic virtual environment. At the same time, the interactive efficiency evaluation function S3 is used to quantitatively evaluate the interactive efficiency of the dynamic demonstration system to ensure that the value of S3 meets the user's satisfaction standard.

[0012] Step 4: Demonstration parameter configuration phase

[0013] Configure presentation parameters in the dynamic presentation system, including presentation speed, viewing angle selection, and graphics rendering style, while also considering AR-specific interactive elements, including head tracking and gesture recognition;

[0014] Step 5: Dynamic Demonstration Stage

[0015] Run the mathematical model and display the dynamic changes of the model in real time through the AR dynamic demonstration system. Users wear AR glasses to observe and understand the dynamic changes of the model in an immersive way. They can control the play, pause, fast forward and rewind of the demonstration through the interactive interface and interact with the elements in the virtual environment, including rotating the model, zooming the view and adjusting parameters.

[0016] Step 6: Result analysis and feedback stage

[0017] After the demonstration, analysis tools for the demonstration results are provided, allowing users to interpret, compare and verify the model output, and provide users with in-depth feedback based on the interaction data in the AR demonstration.

[0018] Preferably, in step 1, the calculation formula of S1 is:

[0019]

[0020] Where N is the total number of data points, A i Score the accuracy of the i-th data point, C i is the integrity score of the i-th data point, D i is the consistency index of the i-th data point, α, β, γ are weight coefficients, and α+β+γ=1; the value range of S1 is [0,1], and the closer the value is to 1, the higher the integrity of the data preparation stage.

[0021] Preferably, in step 2, the calculation formula of S2 is:

[0022]

[0023] Where M is the number of equations in the model, d j is the dimension of the jth equation, e j is the coefficient of the jth equation, CCF(f j ) is the computational complexity function of the jth equation, δ, ε are weight coefficients, and δ+ε=1; the range of S2 is [log 10 (1), +∞), that is, [0, +∞), the larger the value, the higher the complexity of the model construction stage.

[0024] Preferably, the calculation formula of S3 is:

[0025]

[0026] Wherein, T is the total length of the evaluation period, RT(t) is the system response time at time t, IS(t) is the interaction fluency score at time t, US(t) is the user satisfaction score at time t, η, θ are weight coefficients, and η+θ=1; the value range of S3 is [0,1], and the closer the value is to 1, the higher the interaction efficiency of the dynamic demonstration system.

[0027] Preferably, the dynamic demonstration system supports multiple mathematical model formats, including but not limited to differential equation models, statistical models and machine learning models, thereby enhancing the versatility and flexibility of the system.

[0028] Preferably, the dynamic demonstration system uses three-dimensional graphics rendering technology to simulate real-world physical phenomena, including gravity, collision, and light and shadow effects, to improve the realism and intuitiveness of the demonstration.

[0029] Preferably, the dynamic demonstration system further includes a user-defined interface, allowing the user to adjust the color, transparency, and lighting effect visual parameters in the demonstration as needed to meet the needs of different application scenarios.

[0030] A mathematical model dynamic display device, comprising:

[0031] Data processing module: used to collect and organize the basic data required for the mathematical model, including model parameters, initial conditions and boundary conditions, and use integrity assessment functions to quantitatively evaluate the data to ensure the integrity and accuracy of the data;

[0032] Model building module: constructs the corresponding mathematical model in the computer system based on the processed data, and uses the complexity evaluation function to quantitatively evaluate the model building process to balance the complexity and computational efficiency of the model;

[0033] Dynamic demonstration module: Receives and analyzes mathematical models, and uses 3D graphics rendering technology to present the dynamic changes of the model to users in a three-dimensional and highly interactive way. It also uses the interaction efficiency evaluation function to quantitatively evaluate the interaction efficiency of the system.

[0034] Parameter configuration module: used to configure demonstration parameters in the dynamic demonstration system, including demonstration speed, viewing angle selection, graphics rendering style, and AR-specific interactive elements such as head tracking and gesture recognition.

[0035] Preferably, it also includes:

[0036] User interaction module: allows users to observe and understand the dynamic changes of the model in an immersive way by wearing devices such as AR glasses, control the playback, pause, fast forward, and rewind operations of the demonstration through the interactive interface, and interact with elements in the virtual environment.

[0037] Preferably, it also includes:

[0038] Results Analysis Module: Provides analysis tools for demonstration results after the demonstration, allowing users to interpret, compare and verify model outputs, and provide users with in-depth feedback based on interaction data in the AR demonstration.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] By adopting advanced AR technology and 3D graphics rendering capabilities, the dynamic changes of the model are presented to users in a highly interactive way, allowing users to observe and understand the model in an immersive way, greatly improving user experience and participation. At the same time, by configuring demonstration parameters and AR-specific interactive elements, as well as providing rich interactive operations, the user's immersion and interactivity are further enhanced.

[0041] The data preparation stage is quantitatively evaluated through the integrity assessment function to ensure the accuracy and integrity of the basic data, providing reliable data support for subsequent mathematical model construction and dynamic demonstration, thereby improving the accuracy and credibility of the entire demonstration method;

[0042] The application of complexity evaluation functions makes it possible to balance the complexity and computational efficiency of the model during the model building phase, which not only ensures the accuracy of the model, but also avoids the problem of low computational efficiency caused by overly complex models, and improves the fluency and practicality of the overall demonstration. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the demonstration method of the present invention. DETAILED DESCRIPTION

[0044] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0045] like Figure 1 As shown:

[0046] Embodiment 1: The present invention provides a mathematical model dynamic demonstration method, comprising the following steps:

[0047] Step 1: Data preparation

[0048] Collect and organize the basic data required for the mathematical model, including model parameters, initial conditions and boundary conditions, and use the integrity assessment function S1 to quantitatively evaluate the data to ensure that the value of S1 reaches the preset threshold, providing a solid foundation for subsequent AR demonstrations;

[0049] Step 2: Model building phase

[0050] Based on the prepared basic data, a corresponding mathematical model is constructed in the computer system, and the model construction process is quantitatively evaluated using the complexity evaluation function S2 to ensure that the value of S2 is within a reasonable range to balance the complexity of the model and the computational efficiency;

[0051] Step 3: Dynamic Demonstration Phase

[0052] The dynamic demonstration system receives and analyzes the mathematical model, and displays the dynamic change process of the model to the user in a three-dimensional, stereoscopic and highly interactive way. The dynamic demonstration system has powerful graphics rendering capabilities to present a realistic virtual environment. At the same time, the interactive efficiency evaluation function S3 is used to quantitatively evaluate the interactive efficiency of the dynamic demonstration system to ensure that the value of S3 meets the user's satisfaction standard.

[0053] Step 4: Demonstration parameter configuration phase

[0054] Configure presentation parameters in the dynamic presentation system, including presentation speed, viewing angle selection, and graphics rendering style, while also considering AR-specific interactive elements, including head tracking and gesture recognition;

[0055] Step 5: Dynamic Demonstration Stage

[0056] Run the mathematical model and display the dynamic changes of the model in real time through the AR dynamic demonstration system. Users wear AR glasses to observe and understand the dynamic changes of the model in an immersive way. They can control the play, pause, fast forward and rewind of the demonstration through the interactive interface and interact with the elements in the virtual environment, including rotating the model, zooming the view and adjusting parameters.

[0057] Step 6: Result analysis and feedback stage

[0058] After the demonstration, analysis tools for the demonstration results are provided, allowing users to interpret, compare and verify the model output, and provide users with in-depth feedback based on the interaction data in the AR demonstration.

[0059] As can be seen from the above, this method covers the complete process from data preparation to result analysis and feedback. In the data preparation stage, by collecting and organizing basic data and using integrity assessment functions to ensure data quality, a solid foundation is laid for subsequent steps; the model construction stage builds a mathematical model in the computer system based on these data, and balances the complexity and computational efficiency of the model through complexity assessment functions; the dynamic demonstration stage is the highlight of this method. Through advanced AR technology and three-dimensional graphics rendering capabilities, the dynamic change process of the model is presented to the user in a highly interactive way, allowing the user to observe and understand the model in an immersive way; in addition, this method also focuses on the user interaction experience, by configuring demonstration parameters and AR-specific interactive elements, and providing rich interactive operations, it enhances the user's sense of participation and understanding. Finally, in the result analysis and feedback stage, this method provides analysis tools for the demonstration results and provides users with in-depth feedback based on the interactive data, which helps users better understand and apply mathematical models.

[0060] Embodiment 2: This embodiment is basically the same as the previous embodiment, except that, in step 1, the calculation formula of S1 is:

[0061]

[0062] Where N is the total number of data points, A i Score the accuracy of the i-th data point, C i is the integrity score of the i-th data point, D i is the consistency index of the i-th data point, α, β, γ are weight coefficients, and α+β+γ=1; the value range of S1 is [0,1], and the closer the value is to 1, the higher the integrity of the data preparation stage.

[0063] Specifically, in step 2, the calculation formula of S2 is:

[0064]

[0065] Where M is the number of equations in the model, d j is the dimension of the jth equation, e j is the coefficient of the jth equation, CCF(f j ) is the computational complexity function of the jth equation, δ, ε are weight coefficients, and δ+ε=1; the range of S2 is [log 10 (1), +∞), that is, [0, +∞), the larger the value, the higher the complexity of the model construction stage.

[0066] Specifically, the calculation formula of S3 is:

[0067]

[0068] Wherein, T is the total length of the evaluation period, RT(t) is the system response time at time t, IS(t) is the interaction fluency score at time t, US(t) is the user satisfaction score at time t, η, θ are weight coefficients, and η+θ=1; the value range of S3 is [0,1], and the closer the value is to 1, the higher the interaction efficiency of the dynamic demonstration system.

[0069] Specifically, the dynamic demonstration system supports multiple mathematical model formats, including but not limited to differential equation models, statistical models and machine learning models, thereby enhancing the versatility and flexibility of the system.

[0070] Specifically, the dynamic demonstration system uses three-dimensional graphics rendering technology to simulate real-world physical phenomena, including gravity, collision, and light and shadow effects, to improve the realism and intuitiveness of the demonstration.

[0071] Specifically, the dynamic demonstration system also includes a user-defined interface, allowing the user to adjust the color, transparency, and lighting effect visual parameters in the demonstration as needed to meet the needs of different application scenarios.

[0072] As can be seen from the above, this embodiment further refines and enhances the specific techniques and features of the dynamic demonstration method of the mathematical model. In the data preparation stage, the second embodiment introduces a specific integrity assessment function calculation formula, which ensures the high integrity of the data preparation stage by comprehensively considering the total number of data points, accuracy score, integrity score and consistency index, as well as the corresponding weight coefficients, and provides reliable protection for subsequent steps; in the model construction stage, the calculation formula of the complexity assessment function is given, and the balance between model complexity and computational efficiency is achieved by evaluating the number, dimension, quantity coefficient and computational complexity function of the equations in the model, as well as the corresponding weight coefficients;

[0073] In addition, this embodiment also emphasizes the interaction efficiency evaluation of the dynamic demonstration system and provides a specific calculation formula. By evaluating indicators such as system response time, interaction fluency and user satisfaction, the high interaction efficiency of the dynamic demonstration system is ensured. At the same time, the dynamic demonstration system supports multiple mathematical model formats and uses three-dimensional graphics rendering technology to simulate real-world physical phenomena, thereby improving the realism and intuitiveness of the demonstration. The introduction of a user-defined interface allows users to adjust the visual parameters in the demonstration as needed, further enhancing the system's versatility, flexibility and user experience.

[0074] Embodiment 3: A mathematical model dynamic display device, comprising:

[0075] Data processing module: used to collect and organize the basic data required for the mathematical model, including model parameters, initial conditions and boundary conditions, and use integrity assessment functions to quantitatively evaluate the data to ensure the integrity and accuracy of the data;

[0076] Model building module: constructs the corresponding mathematical model in the computer system based on the processed data, and uses the complexity evaluation function to quantitatively evaluate the model building process to balance the complexity and computational efficiency of the model;

[0077] Dynamic demonstration module: Receives and analyzes mathematical models, and uses 3D graphics rendering technology to present the dynamic changes of the model to users in a three-dimensional and highly interactive way. It also uses the interaction efficiency evaluation function to quantitatively evaluate the interaction efficiency of the system.

[0078] Parameter configuration module: used to configure demonstration parameters in the dynamic demonstration system, including demonstration speed, viewing angle selection, graphics rendering style, and AR-specific interactive elements such as head tracking and gesture recognition.

[0079] Specifically, it also includes:

[0080] User interaction module: allows users to observe and understand the dynamic changes of the model in an immersive way by wearing devices such as AR glasses, control the playback, pause, fast forward, and rewind operations of the demonstration through the interactive interface, and interact with elements in the virtual environment.

[0081] Specifically, it also includes:

[0082] Results Analysis Module: Provides analysis tools for demonstration results after the demonstration, allowing users to interpret, compare and verify model outputs, and provide users with in-depth feedback based on interaction data in the AR demonstration.

[0083] As can be seen from the above, this device integrates multiple functional modules such as data processing, model building, dynamic demonstration, parameter configuration, user interaction and result analysis. The data processing module ensures the integrity and accuracy of the basic data; the model building module builds a mathematical model based on these data and balances its complexity and computational efficiency; the dynamic demonstration module uses three-dimensional graphics rendering technology to display the dynamic changes of the model in a three-dimensional and highly interactive way, while evaluating the interaction efficiency of the system; the parameter configuration module allows users to customize demonstration parameters and AR interaction elements to enhance user experience; the user interaction module enables users wearing AR devices to observe model changes in an immersive way and interact with the virtual environment; finally, the result analysis module provides analysis tools for demonstration results to help users interpret, compare and verify model outputs and give feedback.

[0084] The standard parts used in the present invention can all be purchased from the market, and the special-shaped parts can be customized according to the description and the drawings. The specific connection methods of each part adopt conventional means such as mature bolts, rivets, welding, etc. in the prior art. The machinery, parts and equipment all adopt conventional models in the prior art, and the circuit connection adopts the conventional connection method in the prior art, which will not be described in detail here. The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field.

[0085] In the description of the present invention, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. "Multiple" means two or more, unless otherwise clearly and specifically defined.

[0086] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0087] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may mean that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. Moreover, a first feature being "above", "above" or "above" a second feature may mean that the first feature is directly above or obliquely above the second feature, or simply means that the first feature is higher in level than the second feature. A first feature being "below", "below" or "below" a second feature may mean that the first feature is directly below or obliquely below the second feature, or simply means that the first feature is lower in level than the second feature.

[0088] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

[0089] In the drawings of the embodiments disclosed in the present invention, only the structures related to the embodiments disclosed in the present invention are involved, and other structures can refer to the general design. In the absence of conflict, the same embodiment and different embodiments of the present invention can be combined with each other.

[0090] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A mathematical model dynamic demonstration method, characterized in that: The following steps are involved: Step 1: Data preparation Collect and organize the basic data required for the mathematical model, including model parameters, initial conditions and boundary conditions, and use the integrity assessment function S1 to quantitatively evaluate the data to ensure that the value of S1 reaches the preset threshold, providing a solid foundation for subsequent AR demonstrations; Step 2: Model building phase Based on the prepared basic data, a corresponding mathematical model is constructed in the computer system, and the model construction process is quantitatively evaluated using the complexity evaluation function S2 to ensure that the value of S2 is within a reasonable range to balance the complexity of the model and the computational efficiency; Step 3: Dynamic Demonstration Phase The dynamic demonstration system receives and analyzes the mathematical model, and displays the dynamic change process of the model to the user in a three-dimensional, stereoscopic and highly interactive way. The dynamic demonstration system has powerful graphics rendering capabilities to present a realistic virtual environment. At the same time, the interactive efficiency evaluation function S3 is used to quantitatively evaluate the interactive efficiency of the dynamic demonstration system to ensure that the value of S3 meets the user's satisfaction standard. Step 4: Demonstration parameter configuration phase Configure presentation parameters in the dynamic presentation system, including presentation speed, viewing angle selection, and graphics rendering style, while also considering AR-specific interactive elements, including head tracking and gesture recognition; Step 5: Dynamic Demonstration Stage Run the mathematical model and display the dynamic changes of the model in real time through the AR dynamic demonstration system. Users wear AR glasses to observe and understand the dynamic changes of the model in an immersive way. They can control the play, pause, fast forward and rewind of the demonstration through the interactive interface and interact with the elements in the virtual environment, including rotating the model, zooming the view and adjusting parameters. Step 6: Result analysis and feedback stage After the demonstration, analysis tools for the demonstration results are provided, allowing users to interpret, compare and verify the model output, and provide users with in-depth feedback based on the interaction data in the AR demonstration.

2. A mathematical model dynamic demonstration method as claimed in claim 1, characterized in that: In step 1, the calculation formula of S1 is: Where N is the total number of data points, A i Score the accuracy of the i-th data point, C i is the integrity score of the i-th data point, D i is the consistency index of the i-th data point, α, β, γ are weight coefficients, and α+β+γ=1; the value range of S1 is [0,1], and the closer the value is to 1, the higher the integrity of the data preparation stage.

3. A mathematical model dynamic demonstration method as claimed in claim 2, characterized in that: In step 2, the calculation formula of S2 is: Where M is the number of equations in the model, d j is the dimension of the jth equation, e j is the coefficient of the jth equation, CCF(f j ) is the computational complexity function of the jth equation, δ, ε are weight coefficients, and δ+ε=1; the range of S2 is [log 10 (1), +∞), that is, [0, +∞), the larger the value, the higher the complexity of the model construction stage.

4. A mathematical model dynamic demonstration method as claimed in claim 3, characterized in that: The calculation formula of S3 is: Wherein, T is the total length of the evaluation period, RT(t) is the system response time at time t, IS(t) is the interaction fluency score at time t, US(t) is the user satisfaction score at time t, η, θ are weight coefficients, and η+θ=1; the value range of S3 is [0,1], and the closer the value is to 1, the higher the interaction efficiency of the dynamic demonstration system.

5. A mathematical model dynamic demonstration method as claimed in claim 4, characterized in that: The dynamic demonstration system supports multiple mathematical model formats, including but not limited to differential equation models, statistical models and machine learning models, thereby enhancing the versatility and flexibility of the system.

6. A mathematical model dynamic demonstration method as claimed in claim 5, characterized in that: The dynamic demonstration system uses three-dimensional graphics rendering technology to simulate real-world physical phenomena, including gravity, collision, and light and shadow effects, to improve the realism and intuitiveness of the demonstration.

7. A mathematical model dynamic demonstration method as claimed in claim 6, characterized in that: The dynamic demonstration system also includes a user-defined interface, allowing the user to adjust the color, transparency, and lighting effect visual parameters in the demonstration as needed to meet the needs of different application scenarios.

8. A mathematical model dynamic display device, characterized in that: include, Data processing module: used to collect and organize the basic data required for the mathematical model, including model parameters, initial conditions and boundary conditions, and use integrity assessment functions to quantitatively evaluate the data to ensure the integrity and accuracy of the data; Model building module: constructs the corresponding mathematical model in the computer system based on the processed data, and uses the complexity evaluation function to quantitatively evaluate the model building process to balance the complexity and computational efficiency of the model; Dynamic demonstration module: Receives and analyzes mathematical models, and uses 3D graphics rendering technology to present the dynamic changes of the model to users in a three-dimensional and highly interactive way. It also uses the interaction efficiency evaluation function to quantitatively evaluate the interaction efficiency of the system. Parameter configuration module: used to configure demonstration parameters in the dynamic demonstration system, including demonstration speed, viewing angle selection, graphics rendering style, and AR-specific interactive elements such as head tracking and gesture recognition.

9. A mathematical model dynamic display device as claimed in claim 8, characterized in that: Also includes: User interaction module: allows users to observe and understand the dynamic changes of the model in an immersive way by wearing devices such as AR glasses, control the playback, pause, fast forward, and rewind operations of the demonstration through the interactive interface, and interact with elements in the virtual environment.

10. A mathematical model dynamic display device as claimed in claim 8, characterized in that: Also includes: Results Analysis Module: Provides analysis tools for demonstration results after the demonstration, allowing users to interpret, compare and verify model outputs, and provide users with in-depth feedback based on interaction data in the AR demonstration.

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