# 3D Visualization Analysis of Motion Trajectory of Knee Joint in Sports Training Based on Digital Twin

Authors: Jian Chen
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

With the development of China’s social economy, the pace of people’s life is also accelerating. Therefore, in the face of the increasing pressure of life and work, people have begun to pay more and more attention to improving their physical fitness and they also pay more and more attention to sports in their spare time. The knee joint is a very important body part that will be involved in sports. Therefore, in sports, it is very important for healthy sports to pay attention to the state of the knee joint at all times and avoid injury to the knee joint during sports. The three-dimensional visual analysis of the knee joint movement trajectory in sports training refers to the trajectory capture and three-dimensional visual analysis of the knee joint movement in sports training based on the computer-based description and understanding of model technology. The three-dimensional visual analysis of the motion trajectory of the knee joint in sports training is conducive to the attention and analysis of the motion state of the knee joint in sports training, so as to help find problems and avoid knee joint damage during sports training as much as possible. This paper aims to study the 3D visualization analysis of knee joint motion trajectory in sports training based on digital twin and establish a 3D visualization system of knee joint motion trajectory based on digital twin technology, and based on this system, the three-dimensional visualization experiment of knee joint movement trajectory in sports training is carried out. The experiment concluded that the signal-to-noise ratio of the three-dimensional visualization image of the knee joint movement trajectory in sports training based on the three-dimensional visualization system established by the digital twin is 68% and the clarity is 89%. It shows that the system has a good 3D visualization effect.


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## Body

## 1. Introduction

With the rapid development of the contemporary social economy, people’s social production, work, and life are becoming more and more busy. The ever-accelerating pace of life and work has made people’s body more and more overdrawn. The overdraft of the body will cause certain harm to people’s physical quality so that people sometimes feel powerless in life and work, which is not conducive to people’s physical and mental development. Therefore, people have begun to pay more and more attention to the improvement of their physical fitness. In order to improve physical fitness, it is necessary to carry out appropriate physical exercise. Therefore, people’s attention to physical exercise is also increasing. The national sports fever in recent years fully reflects this. In the process of sports training, the knee joint is a very important part of the body and it needs to be used in almost all sports. For example, in sports such as running, basketball, and badminton, all the movements involved, such as running and bouncing, do not need to be completed through the knee joint. Therefore, the knee joint occupies an important position in sports training, and the importance of protecting the knee joint from injury in sports is self-evident. The three-dimensional visualization analysis of the knee joint movement trajectory in sports training has a certain role in protecting the knee joint. This is because the three-dimensional visual analysis of the motion trajectory of the knee joint in sports training can capture the state of the knee joint in real time. And, through the analysis of the state of the knee joint in sports, we can find out the problems that may induce the knee joint injury, so as to avoid the knee joint injury in the process of sports training as much as possible. However, the three-dimensional visualization analysis of the knee joint movement trajectory in the process of sports training is inseparable from the support of relevant science and technology. In this paper, the three-dimensional visualization analysis of the motion trajectory of the knee joint in sports training is mainly combined with the digital twin technology.The innovations of this paper are as follows: (1) This paper combines the digital twin technology to conduct a three-dimensional visualization analysis of the knee joint movement trajectory in sports training. (2) This paper establishes a three-dimensional visualization system of knee joint motion trajectory based on digital twin technology and draws effective conclusions through experiments, which proves the effectiveness of the system.


## 2. Related Work

In recent years, a lot of research studies related to digital twin technology have emerged in academia. Among them, Zhuang C’s research proposes the concept of digital twin technology on the basis of reviewing the background of the digital twin. Then, he proposed a digital twin product architecture on the basis of a systematic analysis of its connotation and studied the future development trend of the architecture [1]. Li C mainly carried out research on digital twin vision. Based on digital twin technology, he constructed a diagnostic and prognostic probability model for health monitoring of aircraft fuselage, and based on this model, the experimental analysis was carried out [2]. Zhao L’s research mainly focuses on the application of digital twin technology in reducing carbon emissions in manufacturing. He established a digital model of CNC machine tools based on digital twin technology and used the model to optimize carbon emission reduction parameters [3]. Liu J mainly studied the importance of digital twin technology to realize virtual and real cyber-physical systems. Based on digital twin technology, he proposed a workshop DT construction method for systems engineering [4]. He B mainly studies the application of digital twin technology in the intelligent manufacturing industry. He found that digital twin technology can grasp the status of the intelligent manufacturing system in real time and predict system failures [5]. Zhou C studied the application of digital twin technology in sheet metal deformation based on a new incremental bending process and introduced a digital twin stamping system framework [6]. Although the above-mentioned research studies are closely related to digital twin technology, the practicability of these research studies for the three-dimensional visualization analysis of knee joint movement trajectory in sports training is not strong enough and the experiment is more complicated and difficult to operate.


## 3. Three-Dimensional Visualization Analysis Method of Knee Joint Motion Trajectory

### 3.1. Digital Twin Technology

Digital twin, also known as digital mapping, is a digital model for physical objects, which can analyze, predict, diagnose, and simulate physical objects by receiving real-time data of physical objects [7]. The digital twin can be consistent with the physical object throughout the life cycle and return the results obtained by the digital model to the physical object, thereby helping the physical object to optimize and make decisions. As a mirror of the physical entity in the virtual space, it reflects the whole life cycle process of the corresponding physical entity product. The digital twin also refers to the process of using information technology to digitally define and model the composition, features, functions, and performance of physical entities, that is, simulation analysis and optimization of physical entities based on digital twins [8, 9]. As a universally adapted theoretical technology system, the digital twin has been applied in many fields [10]. For example, digital twin technology is currently most used in product design, product manufacturing, medical analysis, and engineering construction. The digital twin technology architecture is shown in Figure 1.Figure 1
Digital twin technology architecture.The general definition of the digital twin includes the virtualization of the physical system of the environment and the state and properties of the physical object itself and the update of the information exchange between the physical objects [11]. The definitions related to the digital twin are shown in Tables 1 and 2.Table 1
Definitions related to digital twin 1.
Definition wordDefining word substituteVirtual representationDigital, networked, computational, living, system model, replication, and mirroringSystemObject, element, structure, instance, twin, peer, and process stateInformationData, sensor updates, physics knowledge, data space, and performance maintenanceRenewIntegrate, merge, synchronize, adapt, reflect, and mirrorTable 2
Definitions related to digital twin 2.
Definition wordDefining word substitutePositionObject location informationRotationRotation angle information of the objectScaleThe scale of the objectDigital twin technology needs the support of the following key technologies.


#### 3.1.1. Digital Twin Software Platform

The construction of a digital twin software platform is a necessary condition for the application of digital twin technology. Using this software platform, system simulation, data management, big data processing and analysis, simulation real-time calculation, and data visualization can be integrated. The virtual world can quickly and accurately reflect the state of the actual physical system and guide the operation of the system in time, making the system control and optimization more efficient [12].


#### 3.1.2. Data Collection and Transmission

The real-time collection and transmission of high-precision sensor data can ensure that the digital twin system can perceive the state performance and external boundary information of the physical entity in real time, which is the key to the real-time monitoring of the current state of the system and the prediction of the future state of the digital twin system. For old complex equipment or industrial systems, their perception capabilities are weak and there is still a big gap between building an intelligent system. How to build a low-cost system integrating sensing, data acquisition, and data transmission is a key part of supporting the application of digital twin technology [13].


#### 3.1.3. Big Data Processing Technology

Twin data processing is a key link in the digital twin modeling process. For the different data processing modes of stream processing and batch processing, how to use parallelization and distributed computing to realize data decomposition and parameter grouping and reduce the dimensionality of data and optimization algorithms is a hot issue that needs to be studied. How to combine big data analysis technology with modern artificial intelligence algorithms is the key to realize big data processing and modeling [14].


#### 3.1.4. Visualization Technology

The visualization technology of the digital twin system is the most effective means to help people understand useful information and make decisions and is an important part of building a digital twin system. The three-dimensional and virtual reality visualization technology can give the manufacturing, operation, and maintenance status of the system in a hyper-realistic form and can perform multiscale status monitoring and evaluation of the key subsystems of the complex system. The results of intelligent monitoring and analysis are attached to the various subsystems and components of the system, and the digital analysis results are superimposed on the created mathematical model system in the form of virtual mapping, while the physical system is perfectly reproduced. It can provide an immersive virtual reality experience from various aspects such as vision, hearing, and touch and realize real-time continuous human-computer interaction [15].


### 3.2. 3D Visualization

A 3D visualization is a tool used to display, describe, and understand the characteristics of many subsurface and surface geological phenomena; it is a means of describing and understanding models that is widely used in the fields of geology and geophysics, a representation of data volumes, and not a simulation technique [16]. The 3D visualization technology integrates various technologies such as multimedia, Internet of Things, and 3D image characterization to complete the virtualization of data processing. The real scene is made into a virtual simulation scene through modeling and other methods, which corresponds to the real world one by one. According to the monitoring data generated by various sensors and their spatial positions, the objects are monitored in multiple directions and the actual effect of 3D virtual reality technology based on reality is built to make the data presentation more intuitive. 3D visualization technology has been widely used in the fields of film and television, animation, architecture, industrial manufacturing, and medical treatment [17, 18]. The 3D visualization technology is shown in Figure 2.Figure 2
3D visualization technology.Several common 3D visualization methods are as follows.


#### 3.2.1. Visualization Method Based on Geometry

This method refers to the method of visual rendering of the geometric shape of things, mainly including point icon method, vector line method, vector surface method, and particle system [19].


#### 3.2.2. Texture-Based Visualization Method

Texture-based visualization is a method of visually representing things based on the color and shape of their textures. The main methods are point noise method, line integral convolution algorithm, and image-based flow field visualization [20].


#### 3.2.3. Feature-Based Visualization Methods

The features in this method generally refer to two aspects: one is the meaningful shapes, phenomena, and changes (such as eddy currents and shock waves) contained in the vector field. The second is the part of the vector field that the user needs and is interested in. The advantages of this method are high abstraction, less redundant information, and low complexity. The disadvantage of this method is that it is directly related to the information contained in the data field and has a great dependence on the field in which it is applied [21].


### 3.3. Geometric Surface Feature Representation Based on Digital Twin

Geometric surface feature representation based on digital twin is an important method for 3D visualization by describing the geometric surface features of physical objects. In the process of 3D visualization based on digital twin, sometimes the surface roughness of the visualized object is high; that is, when there are many small features such as protrusions and depressions, the polynomial fitting visualization method often has large errors. Therefore, digital twin-based geometric surface feature representation is needed to improve this problem [22].First, the discrete value formula for calculating the line feature visualization containing N elements is as follows:(1)Fk=ck∑i=1N−1ficoskπ2N.That is,(2)Fk=∑i=1N−1ficos2Nck.Here,k is the order, f(i) is the z-direction deviation displacement of the i-th discrete point, and the value of c(k) is as follows:(3)ck=1N，K=0.That is,(4)ck=2N,k=1,2,N−1.According to the properties of discrete cosine transform, its inverse transform and forward transform have the same form, which can be expressed by the following formula to obtain the fitted contour of the line feature:(5)fi=∑i=0N−1ckFkcoskπ2N.That is,(6)fi=1NF0+2N∑k=1N−1Fk.The geometric surface feature method based on the digital twin can be extended from line features to general three-dimensional plane features. If the number of point clouds scanned by discrete points in thex and y directions is M and N, respectively, the discrete cosine transform formula of the surface feature is extended to the following formula:(7)Fu,v=cucv∑i=0M−1∑i=0N−1fM,N.That is,(8)Fu,v=cu,v∑i=0M−1,N−1.Here,u and v are the frequency orders in the x-axis and y-axis directions, respectively, and i and j together determine the coordinate position of the discrete point. F (i, j) corresponds to the z-direction deviation displacement of discrete points, and c(u) and c(v) are similar, as shown in the following formula:(9)cu=1M+2M,u=0,1,2,M−1.And also,(10)cv=1N+2N,v=1,2,N−1.Similar to formula (10), the geometric surface feature of the three-dimensional plane feature is expressed as follows:(11)fM,N=∑U=0M−1∑v=0N−1Fu,vcosuπ2M.That is,(12)fM,N=1NFu,v+2N∑u=1M−1Fu,0.The deviation displacement is subjected to discrete cosine transformation to obtain the corresponding value of thez-direction deviation of each discrete point in the frequency domain. The larger the value, the greater the amount of information contained in the discrete point. When the number of scanning points n is large, the calculation amount of discrete cosine transform is very large and the influence of high-order basis shape on the actual geometric shape of the surface is getting smaller and smaller. Therefore, the sum of truncated order base shapes is often used to describe the actual surface, so that the linear superposition of lower order trigonometric functions is used to fit the characteristic contour close to the real shape [23]. Taking the first p∗q order base shape to represent the three-dimensional plane feature is shown in the following formula:(13)Fu,v=∑u=op−1∑v=0q−1cu,cvFu,vcosuπ2M.That is,(14)Fu,v=∑u=0,v=0pq−1cosuπ2M.When the number of discrete points obtained by scanning in theu and v directions is the same, that is, M = N, the matrix f composed of the deviation and displacement f(u; v) of each discrete point is a square matrix and it is converted into a matrix form, which is expressed as F = AfA, where A is a real matrix of N∗N and the elements A(i, j) in the i-th row and the j-th column of A and the A matrix are, respectively, as follows:(15)Ai,j=cicosπ2i.And,(16)A=2Ncos2N−1π2NN−1.For any positive integerN, the matrix A is an orthogonal matrix, that is, there is A = AT, so f = AFA can be obtained, and the discrete cosine forward and reverse transformation of the discrete point deviation displacement field can be more easily performed. The entire digital twin-based geometric surface feature representation process is shown in Figure 3.Figure 3
Geometric surface feature representation process based on digital twin.


## 3.1. Digital Twin Technology

Digital twin, also known as digital mapping, is a digital model for physical objects, which can analyze, predict, diagnose, and simulate physical objects by receiving real-time data of physical objects [7]. The digital twin can be consistent with the physical object throughout the life cycle and return the results obtained by the digital model to the physical object, thereby helping the physical object to optimize and make decisions. As a mirror of the physical entity in the virtual space, it reflects the whole life cycle process of the corresponding physical entity product. The digital twin also refers to the process of using information technology to digitally define and model the composition, features, functions, and performance of physical entities, that is, simulation analysis and optimization of physical entities based on digital twins [8, 9]. As a universally adapted theoretical technology system, the digital twin has been applied in many fields [10]. For example, digital twin technology is currently most used in product design, product manufacturing, medical analysis, and engineering construction. The digital twin technology architecture is shown in Figure 1.Figure 1
Digital twin technology architecture.The general definition of the digital twin includes the virtualization of the physical system of the environment and the state and properties of the physical object itself and the update of the information exchange between the physical objects [11]. The definitions related to the digital twin are shown in Tables 1 and 2.Table 1
Definitions related to digital twin 1.
Definition wordDefining word substituteVirtual representationDigital, networked, computational, living, system model, replication, and mirroringSystemObject, element, structure, instance, twin, peer, and process stateInformationData, sensor updates, physics knowledge, data space, and performance maintenanceRenewIntegrate, merge, synchronize, adapt, reflect, and mirrorTable 2
Definitions related to digital twin 2.
Definition wordDefining word substitutePositionObject location informationRotationRotation angle information of the objectScaleThe scale of the objectDigital twin technology needs the support of the following key technologies.


### 3.1.1. Digital Twin Software Platform

The construction of a digital twin software platform is a necessary condition for the application of digital twin technology. Using this software platform, system simulation, data management, big data processing and analysis, simulation real-time calculation, and data visualization can be integrated. The virtual world can quickly and accurately reflect the state of the actual physical system and guide the operation of the system in time, making the system control and optimization more efficient [12].


### 3.1.2. Data Collection and Transmission

The real-time collection and transmission of high-precision sensor data can ensure that the digital twin system can perceive the state performance and external boundary information of the physical entity in real time, which is the key to the real-time monitoring of the current state of the system and the prediction of the future state of the digital twin system. For old complex equipment or industrial systems, their perception capabilities are weak and there is still a big gap between building an intelligent system. How to build a low-cost system integrating sensing, data acquisition, and data transmission is a key part of supporting the application of digital twin technology [13].


### 3.1.3. Big Data Processing Technology

Twin data processing is a key link in the digital twin modeling process. For the different data processing modes of stream processing and batch processing, how to use parallelization and distributed computing to realize data decomposition and parameter grouping and reduce the dimensionality of data and optimization algorithms is a hot issue that needs to be studied. How to combine big data analysis technology with modern artificial intelligence algorithms is the key to realize big data processing and modeling [14].


### 3.1.4. Visualization Technology

The visualization technology of the digital twin system is the most effective means to help people understand useful information and make decisions and is an important part of building a digital twin system. The three-dimensional and virtual reality visualization technology can give the manufacturing, operation, and maintenance status of the system in a hyper-realistic form and can perform multiscale status monitoring and evaluation of the key subsystems of the complex system. The results of intelligent monitoring and analysis are attached to the various subsystems and components of the system, and the digital analysis results are superimposed on the created mathematical model system in the form of virtual mapping, while the physical system is perfectly reproduced. It can provide an immersive virtual reality experience from various aspects such as vision, hearing, and touch and realize real-time continuous human-computer interaction [15].


## 3.1.1. Digital Twin Software Platform

The construction of a digital twin software platform is a necessary condition for the application of digital twin technology. Using this software platform, system simulation, data management, big data processing and analysis, simulation real-time calculation, and data visualization can be integrated. The virtual world can quickly and accurately reflect the state of the actual physical system and guide the operation of the system in time, making the system control and optimization more efficient [12].


## 3.1.2. Data Collection and Transmission

The real-time collection and transmission of high-precision sensor data can ensure that the digital twin system can perceive the state performance and external boundary information of the physical entity in real time, which is the key to the real-time monitoring of the current state of the system and the prediction of the future state of the digital twin system. For old complex equipment or industrial systems, their perception capabilities are weak and there is still a big gap between building an intelligent system. How to build a low-cost system integrating sensing, data acquisition, and data transmission is a key part of supporting the application of digital twin technology [13].


## 3.1.3. Big Data Processing Technology

Twin data processing is a key link in the digital twin modeling process. For the different data processing modes of stream processing and batch processing, how to use parallelization and distributed computing to realize data decomposition and parameter grouping and reduce the dimensionality of data and optimization algorithms is a hot issue that needs to be studied. How to combine big data analysis technology with modern artificial intelligence algorithms is the key to realize big data processing and modeling [14].


## 3.1.4. Visualization Technology

The visualization technology of the digital twin system is the most effective means to help people understand useful information and make decisions and is an important part of building a digital twin system. The three-dimensional and virtual reality visualization technology can give the manufacturing, operation, and maintenance status of the system in a hyper-realistic form and can perform multiscale status monitoring and evaluation of the key subsystems of the complex system. The results of intelligent monitoring and analysis are attached to the various subsystems and components of the system, and the digital analysis results are superimposed on the created mathematical model system in the form of virtual mapping, while the physical system is perfectly reproduced. It can provide an immersive virtual reality experience from various aspects such as vision, hearing, and touch and realize real-time continuous human-computer interaction [15].


## 3.2. 3D Visualization

A 3D visualization is a tool used to display, describe, and understand the characteristics of many subsurface and surface geological phenomena; it is a means of describing and understanding models that is widely used in the fields of geology and geophysics, a representation of data volumes, and not a simulation technique [16]. The 3D visualization technology integrates various technologies such as multimedia, Internet of Things, and 3D image characterization to complete the virtualization of data processing. The real scene is made into a virtual simulation scene through modeling and other methods, which corresponds to the real world one by one. According to the monitoring data generated by various sensors and their spatial positions, the objects are monitored in multiple directions and the actual effect of 3D virtual reality technology based on reality is built to make the data presentation more intuitive. 3D visualization technology has been widely used in the fields of film and television, animation, architecture, industrial manufacturing, and medical treatment [17, 18]. The 3D visualization technology is shown in Figure 2.Figure 2
3D visualization technology.Several common 3D visualization methods are as follows.


### 3.2.1. Visualization Method Based on Geometry

This method refers to the method of visual rendering of the geometric shape of things, mainly including point icon method, vector line method, vector surface method, and particle system [19].


### 3.2.2. Texture-Based Visualization Method

Texture-based visualization is a method of visually representing things based on the color and shape of their textures. The main methods are point noise method, line integral convolution algorithm, and image-based flow field visualization [20].


### 3.2.3. Feature-Based Visualization Methods

The features in this method generally refer to two aspects: one is the meaningful shapes, phenomena, and changes (such as eddy currents and shock waves) contained in the vector field. The second is the part of the vector field that the user needs and is interested in. The advantages of this method are high abstraction, less redundant information, and low complexity. The disadvantage of this method is that it is directly related to the information contained in the data field and has a great dependence on the field in which it is applied [21].


## 3.2.1. Visualization Method Based on Geometry

This method refers to the method of visual rendering of the geometric shape of things, mainly including point icon method, vector line method, vector surface method, and particle system [19].


## 3.2.2. Texture-Based Visualization Method

Texture-based visualization is a method of visually representing things based on the color and shape of their textures. The main methods are point noise method, line integral convolution algorithm, and image-based flow field visualization [20].


## 3.2.3. Feature-Based Visualization Methods

The features in this method generally refer to two aspects: one is the meaningful shapes, phenomena, and changes (such as eddy currents and shock waves) contained in the vector field. The second is the part of the vector field that the user needs and is interested in. The advantages of this method are high abstraction, less redundant information, and low complexity. The disadvantage of this method is that it is directly related to the information contained in the data field and has a great dependence on the field in which it is applied [21].


## 3.3. Geometric Surface Feature Representation Based on Digital Twin

Geometric surface feature representation based on digital twin is an important method for 3D visualization by describing the geometric surface features of physical objects. In the process of 3D visualization based on digital twin, sometimes the surface roughness of the visualized object is high; that is, when there are many small features such as protrusions and depressions, the polynomial fitting visualization method often has large errors. Therefore, digital twin-based geometric surface feature representation is needed to improve this problem [22].First, the discrete value formula for calculating the line feature visualization containing N elements is as follows:(1)Fk=ck∑i=1N−1ficoskπ2N.That is,(2)Fk=∑i=1N−1ficos2Nck.Here,k is the order, f(i) is the z-direction deviation displacement of the i-th discrete point, and the value of c(k) is as follows:(3)ck=1N，K=0.That is,(4)ck=2N,k=1,2,N−1.According to the properties of discrete cosine transform, its inverse transform and forward transform have the same form, which can be expressed by the following formula to obtain the fitted contour of the line feature:(5)fi=∑i=0N−1ckFkcoskπ2N.That is,(6)fi=1NF0+2N∑k=1N−1Fk.The geometric surface feature method based on the digital twin can be extended from line features to general three-dimensional plane features. If the number of point clouds scanned by discrete points in thex and y directions is M and N, respectively, the discrete cosine transform formula of the surface feature is extended to the following formula:(7)Fu,v=cucv∑i=0M−1∑i=0N−1fM,N.That is,(8)Fu,v=cu,v∑i=0M−1,N−1.Here,u and v are the frequency orders in the x-axis and y-axis directions, respectively, and i and j together determine the coordinate position of the discrete point. F (i, j) corresponds to the z-direction deviation displacement of discrete points, and c(u) and c(v) are similar, as shown in the following formula:(9)cu=1M+2M,u=0,1,2,M−1.And also,(10)cv=1N+2N,v=1,2,N−1.Similar to formula (10), the geometric surface feature of the three-dimensional plane feature is expressed as follows:(11)fM,N=∑U=0M−1∑v=0N−1Fu,vcosuπ2M.That is,(12)fM,N=1NFu,v+2N∑u=1M−1Fu,0.The deviation displacement is subjected to discrete cosine transformation to obtain the corresponding value of thez-direction deviation of each discrete point in the frequency domain. The larger the value, the greater the amount of information contained in the discrete point. When the number of scanning points n is large, the calculation amount of discrete cosine transform is very large and the influence of high-order basis shape on the actual geometric shape of the surface is getting smaller and smaller. Therefore, the sum of truncated order base shapes is often used to describe the actual surface, so that the linear superposition of lower order trigonometric functions is used to fit the characteristic contour close to the real shape [23]. Taking the first p∗q order base shape to represent the three-dimensional plane feature is shown in the following formula:(13)Fu,v=∑u=op−1∑v=0q−1cu,cvFu,vcosuπ2M.That is,(14)Fu,v=∑u=0,v=0pq−1cosuπ2M.When the number of discrete points obtained by scanning in theu and v directions is the same, that is, M = N, the matrix f composed of the deviation and displacement f(u; v) of each discrete point is a square matrix and it is converted into a matrix form, which is expressed as F = AfA, where A is a real matrix of N∗N and the elements A(i, j) in the i-th row and the j-th column of A and the A matrix are, respectively, as follows:(15)Ai,j=cicosπ2i.And,(16)A=2Ncos2N−1π2NN−1.For any positive integerN, the matrix A is an orthogonal matrix, that is, there is A = AT, so f = AFA can be obtained, and the discrete cosine forward and reverse transformation of the discrete point deviation displacement field can be more easily performed. The entire digital twin-based geometric surface feature representation process is shown in Figure 3.Figure 3
Geometric surface feature representation process based on digital twin.


## 4. Three-Dimensional Visualization Analysis Experiment of Knee Joint Movement Trajectory

### 4.1. Experimental Design

In this experiment, two images of the knee joint movement trajectory during the sports training process were randomly intercepted as the experimental object of the three-dimensional visualization of the knee joint movement trajectory, as shown in Figure4.Figure 4
Knee motion trajectory in sports. (a) Knee joint movement trajectory 1. (b) Knee joint movement trajectory 2.
(a)(b)After selecting the experimental object, it is necessary to determine the experimental method of this experiment. In view of the purpose of this experiment to analyze the 3D visualization of knee joint motion trajectory in digital twin-based sports training, the method adopted in this experiment is as follows: The first step is to establish a 3D visualization system for knee joint movement trajectory in sports training based on digital twin technology. In the second step, the three-dimensional visualization system is used to perform three-dimensional visualization analysis on the motion trajectory diagram of the knee joint during the selected sports training process and calculate the image signal-to-noise ratio and clarity of the knee joint motion trajectory map based on the three-dimensional visualization analysis of the system. Finally, according to the calculated image signal-to-noise ratio and clarity analysis, the three-dimensional visualization analysis effect of the knee joint movement trajectory in sports training based on digital twin technology is judged.


### 4.2. System Establishment and Visualization

The three-dimensional visualization system of the knee joint movement trajectory in sports training based on the digital twin technology established in this experiment is shown in Figure5.Figure 5
Knee joint 3D visualization system based on digital twin. (a) System initialization. (b) The system is officially running.Using the 3D visualization system shown in Figure5 to perform 3D visualization of the two selected knee joint motion trajectory diagrams in sports training, the new images obtained are as shown in Figure 6.Figure 6
Three-dimensional trajectory map of knee joint movements in sports. (a) Three-dimensional trajectory of knee joint 1. (b) Three-dimensional trajectory of knee joint 2.
(a)(b)From Figure6, it can be preliminarily judged that the 3D visualization effect of the two selected knee joint motion trajectory diagrams in sports training based on the digital twin 3D visualization system is still good. The obtained new trajectory map is not much different from the original image, and the contours and joint point positions are clearly visible. However, the specific effect judgment also needs to be carried out by calculating the signal-to-noise ratio and clarity of the new image.


### 4.3. Signal-to-Noise Ratio and Definition Calculation

Next, this experiment will calculate the signal-to-noise ratio and clarity of the knee joint motion trajectory images obtained after the 3D visualization analysis by the digital twin 3D visualization system. In order to ensure the reliability of the calculation results, the image signal-to-noise ratio and sharpness were calculated twice in this experiment. The first is the calculation of the signal-to-noise ratio of the obtained 3D visualization image, and the calculation result is shown in Figure7.Figure 7
3D visualization image signal-to-noise ratio results of the knee joint. (a) The first calculation result. (b) The second calculation result.
(a)(b)It can be calculated from Figure7 that the final signal-to-noise ratio result of the three-dimensional visualization image of the knee joint motion trajectory in the selected sports training is 68%.Figure8 shows the result of calculating the clarity of the obtained three-dimensional visual image of the knee joint motion trajectory.Figure 8
3D visualization image clarity results of the knee joint. (a) Calculation result 1. (b) Calculation result 2.
(a)(b)It can be seen from Figure8 that the sharpness of the images is higher than 80%. It can be calculated that the final clarity result of the three-dimensional visualization image of the knee joint motion trajectory in the selected sports training is 89%. It can be seen that the three-dimensional visualization image of the knee joint motion trajectory obtained by the knee joint three-dimensional visualization system based on the digital twin is relatively high-definition.In conclusion, the signal-to-noise ratio of the three-dimensional visualization image of the knee joint movement trajectory in sports training obtained by the three-dimensional visualization system established based on the digital twin in this experiment is 68% and the clarity is 89%. It shows that the system has a good three-dimensional visualization effect on the motion trajectory of the knee joint in sports training.


## 4.1. Experimental Design

In this experiment, two images of the knee joint movement trajectory during the sports training process were randomly intercepted as the experimental object of the three-dimensional visualization of the knee joint movement trajectory, as shown in Figure4.Figure 4
Knee motion trajectory in sports. (a) Knee joint movement trajectory 1. (b) Knee joint movement trajectory 2.
(a)(b)After selecting the experimental object, it is necessary to determine the experimental method of this experiment. In view of the purpose of this experiment to analyze the 3D visualization of knee joint motion trajectory in digital twin-based sports training, the method adopted in this experiment is as follows: The first step is to establish a 3D visualization system for knee joint movement trajectory in sports training based on digital twin technology. In the second step, the three-dimensional visualization system is used to perform three-dimensional visualization analysis on the motion trajectory diagram of the knee joint during the selected sports training process and calculate the image signal-to-noise ratio and clarity of the knee joint motion trajectory map based on the three-dimensional visualization analysis of the system. Finally, according to the calculated image signal-to-noise ratio and clarity analysis, the three-dimensional visualization analysis effect of the knee joint movement trajectory in sports training based on digital twin technology is judged.


## 4.2. System Establishment and Visualization

The three-dimensional visualization system of the knee joint movement trajectory in sports training based on the digital twin technology established in this experiment is shown in Figure5.Figure 5
Knee joint 3D visualization system based on digital twin. (a) System initialization. (b) The system is officially running.Using the 3D visualization system shown in Figure5 to perform 3D visualization of the two selected knee joint motion trajectory diagrams in sports training, the new images obtained are as shown in Figure 6.Figure 6
Three-dimensional trajectory map of knee joint movements in sports. (a) Three-dimensional trajectory of knee joint 1. (b) Three-dimensional trajectory of knee joint 2.
(a)(b)From Figure6, it can be preliminarily judged that the 3D visualization effect of the two selected knee joint motion trajectory diagrams in sports training based on the digital twin 3D visualization system is still good. The obtained new trajectory map is not much different from the original image, and the contours and joint point positions are clearly visible. However, the specific effect judgment also needs to be carried out by calculating the signal-to-noise ratio and clarity of the new image.


## 4.3. Signal-to-Noise Ratio and Definition Calculation

Next, this experiment will calculate the signal-to-noise ratio and clarity of the knee joint motion trajectory images obtained after the 3D visualization analysis by the digital twin 3D visualization system. In order to ensure the reliability of the calculation results, the image signal-to-noise ratio and sharpness were calculated twice in this experiment. The first is the calculation of the signal-to-noise ratio of the obtained 3D visualization image, and the calculation result is shown in Figure7.Figure 7
3D visualization image signal-to-noise ratio results of the knee joint. (a) The first calculation result. (b) The second calculation result.
(a)(b)It can be calculated from Figure7 that the final signal-to-noise ratio result of the three-dimensional visualization image of the knee joint motion trajectory in the selected sports training is 68%.Figure8 shows the result of calculating the clarity of the obtained three-dimensional visual image of the knee joint motion trajectory.Figure 8
3D visualization image clarity results of the knee joint. (a) Calculation result 1. (b) Calculation result 2.
(a)(b)It can be seen from Figure8 that the sharpness of the images is higher than 80%. It can be calculated that the final clarity result of the three-dimensional visualization image of the knee joint motion trajectory in the selected sports training is 89%. It can be seen that the three-dimensional visualization image of the knee joint motion trajectory obtained by the knee joint three-dimensional visualization system based on the digital twin is relatively high-definition.In conclusion, the signal-to-noise ratio of the three-dimensional visualization image of the knee joint movement trajectory in sports training obtained by the three-dimensional visualization system established based on the digital twin in this experiment is 68% and the clarity is 89%. It shows that the system has a good three-dimensional visualization effect on the motion trajectory of the knee joint in sports training.


## 5. Discussion

Nowadays, sports are much valued by people and have become one of the activities that people are keen on in their leisure time. This is because proper physical exercise can help people keep fit, relieve people’s pressure in life and work, and encourage people to devote themselves to work in a better physical and mental state. There are many types of sports, including running, long jump, and various ball games such as basketball and badminton. The knee joint is one of the most important body parts in any sport. However, in sports activities, the knee joint is also more vulnerable to different degrees of injury. Therefore, protecting the knee joint from injury during sports activities is of great significance to the smooth progress of sports.Three-dimensional visual analysis of the knee joint movement trajectory in sports training is one of the important measures to protect the knee joint. It is conducive to promoting the close attention and analysis of the motion state of the knee joint in sports training, so as to timely detect and improve the problems that may lead to knee joint injury and avoid knee joint injury in sports training as much as possible. The three-dimensional visualization analysis of the knee joint movement trajectory in sports training is inseparable from the corresponding technical support. This paper mainly based on the digital twin technology to carry out the three-dimensional visualization analysis of the knee joint movement trajectory in sports training.In this paper, the three-dimensional visualization analysis of the knee joint motion trajectory in sports training based on digital twin is mainly carried out through experimental analysis. The 3D visualization analysis experiment firstly establishes a 3D visualization system for knee joint movement trajectory in sports training based on digital twin technology. Then, based on the system, a three-dimensional visual analysis of the knee joint movement trajectory in the selected sports training was carried out. The final calculation shows that the signal-to-noise ratio of the three-dimensional visualization image of the knee joint movement trajectory in sports training obtained by the three-dimensional visualization system established based on the digital twin is 68% and the clarity is 89%. Such experimental conclusions show that the 3D visualization system established based on digital twin technology has a good 3D visualization effect on the motion trajectory of the knee joint in sports training.


## 6. Conclusions

In this paper, the 3D visualization analysis of the knee joint movement trajectory in sports training based on the digital twin draws the conclusion: the signal-to-noise ratio of the three-dimensional visualization image of the knee joint movement trajectory in sports training obtained by the three-dimensional visualization system established based on the digital twin is 68% and the clarity is 89%. This conclusion shows that the 3D visualization system established based on digital twin technology has a certain application value for the 3D visualization of knee joint movement trajectory in sports training. The conclusions drawn in this paper have implications for protecting the knee from injury during sports training, and it also has certain reference value to promote the research of digital twin technology for 3D visualization analysis. However, due to the limited experimental level and conditions, the conclusions drawn in this paper also have some limitations; for example, the research angle and methods are not innovative enough and the application of digital twin technology is also insufficient. It is hoped that some improvements will be made in the future to better contribute to the research on 3D visualization analysis of knee joint movement trajectory in sports training.



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*Source: 3988166-2022-06-06.xml*