# Ming-Style Furniture Display Design Based on Immersive 5G Virtual Reality

Authors: Huabai Liu
Journal: Security and Communication Networks
 (2022)

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## Abstract

No matter the traditional Ming-style furniture is made of exquisite materials, elegant, and simple, or the literati philosophy, connotation, and literati spiritual outlook, values, world outlook, etc. reflected behind it, all have left us with excellent cultural heritage. As a fast-developing technology, virtual reality has a bright future. This paper mainly studies the Ming-style furniture display based on immersive 5G virtual reality technology. Ming-style furniture displays design prototype system development based on user experience. The prototype of the guided design drawings is completed, the Ming-style furniture and display space is modeled in Unity3d, interactive elements are added, and finally it is realized that users can roam in the scene from a first-person perspective and the furniture in the scene, color, material, etc., as well as the detailed display of the items in the scene, the control of the lights in the scene, the control of the sound, and so on are changed. After the establishment of the system, a certain user evaluation is performed on the established system. Questionnaire surveys, focus group interviews, and other methods are used to conduct very detailed investigations and usability tests on users. Then, the test results are realized and the system is optimized to a certain extent. Finally, the user experience of the system design is improved. The experimental survey results show that the average user experience score is 43.7 points and the rating is in the “good” range, which basically meets the user experience. This research plays an important role in improving user experience and at the same time enriches the research in the field of domestic furniture virtual display and has certain significance for the future development of furniture companies.


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## Body

## 1. Introduction

Mobile communications are about to enter the 5G era. 5G will have key indicators such as higher user experience rate, million-level connection density, millisecond-level end-to-end latency, and multiple application scenarios. Immersive virtual reality (immersive VR) provides users with an experience of being in a virtual world [1]. At present, as virtual reality receives more and more attention from the industry, hundreds of companies at home and abroad have joined the field of virtual reality within a short period of time. The reason why virtual reality technology has received attention is that the technology can simulate realistic scenes and allow users to meet the needs of each body’s senses in the simulated virtual environment. Its obvious feature is to use a head-mounted display to seal the user’s vision and hearing to produce virtual vision. At the same time, it uses data gloves to control the user. The feel channel is closed, producing a virtual touch. The user can control the perspective and position of the virtual world through head movement, hand movement, and even eye movement and interact with objects in the virtual world. The user can also issue operating commands to the system host through a voice recognizer. Common immersive systems include Head Mount Display (HMD) and projection virtual reality systems.The Ming Dynasty is the most glorious historical period in the history of Chinese furniture. The furniture style of the Ming Dynasty is considered to be the highest standard of Chinese classical furniture and has been sought after for a long time [2]. Ming-style furniture has superb craftsmanship, simple and beautiful appearance, unique decoration, and artistic style and has a complete system. At present, most of the furniture sales process mainly focuses on store display when introducing consumers. When traditional furniture stores develop e-commerce, they mainly use some traditional methods such as flash animation, pictures, and text introduction, and the promotion of products is only staying at the level of introducing product features, and customers can only watch furniture products from the angle of the furniture that the merchant has photographed in advance and cannot choose their favorite angle to observe the furniture products, which makes the online display effect of furniture products greatly reduced [3]. In order to thoroughly realize the three-dimensional display effect of furniture products and make viewers feel like they are on the scene, the Ming-style furniture display based on immersive 5G virtual reality technology has been studied in depth.The visualization of 3D models in virtual reality has been recognized as an efficient, fast, and simple method to represent various objects around the world. These users have strict requirements and high expectations. The Koeva M study showed the integration of high-resolution spherical panoramas, various maps, global navigation satellite systems, sound, video, and text information to showcase many cultural heritage. Then display the content in a web-based portal with an intuitive interface. Users have the opportunity to choose freely from the information provided and decide for themselves what content they want to access. His system is unstable and errors are prone to occur during use [4]. In the past few years, consumer virtual reality (VR) devices have made some significant progress. Devices such as Oculus Rift, HTC Vive, Leap Motion Controller, and Microsoft Kinect bring immersive virtual reality experiences to consumers’ homes, and their cost and space requirements are much lower than previous generations of VR hardware. These new devices also lower the barriers to entry for virtual reality engineering applications. Past research has shown that using virtual reality technology in design tasks can improve results and shorten development time. Coburn J Q studied the latest generation of virtual reality hardware and focused on the past research projects of virtual reality in the design process. In addition, his work also proposes some new use cases, which are too resource intensive when exploring using previously available hardware, not very practical [5]. Aiming at the shortcomings of the existing algorithms that are easy to fall into local optimality, poor robustness, and poor transparency and cannot resist various common attacks due to the fixed step size, Zhang Y proposed a digital image watermark optimization algorithm based on fruit flies. With the support of virtual reality technology, he converted the original color host image from RGB space to YCrCb space and divided the pixel blocks of the Y component into certain sizes. The watermark type is determined according to the watermark type and watermark preprocessing method and the pretreatment method adopts Drosophila optimization algorithm. At the same time, the embedding, extraction rules, and initial steps of the digital watermark are selected and identified. His method can not eliminate visual interference very well [6]. It is undeniable that these studies have greatly contributed to the development of the corresponding fields. We can learn a lot from the methods and data analysis. However, relatively little research has been done in the field of virtual reality technology for the design of Ming furniture displays, and there is a need to fully apply these algorithms to research in this field.This paper focuses on the design of Ming furniture display based on immersive 5G virtual reality, with innovations as follows: (1) In terms of the establishment and optimization of 3D models, this system chooses to use a combination of 2D drawing technology and 3D modeling technology to establish a 3D scene model for furniture product display and uses corresponding technology to process the model surface to reduce computer traffic, to achieve the purpose of accelerating the operation speed of the entire system. (2) This system combines image-based three-dimensional display and model-based three-dimensional display, optimizes and integrates the characteristics of the two display methods, combines the three-dimensional model with the physical image, and combines the furniture products and the scene environment to be displayed in 3D form better present in front of users, and enhances the realism and visual beauty of the product browsing experience through humanized interaction design and artistic interface design. (3) While considering the operating efficiency of the entire system and the operating quality of images, image optimization technology and dynamic loading technology is used, to create a system that can meet users’ realism needs for furniture products, has a three-dimensional scene environment, and can dynamically interact.


## 2. Immersive 5G Virtual Reality Technology

### 2.1. Virtual Reality Technology

Virtual reality technology in the general sense refers to the use of various technologies such as computer technology, three-dimensional modeling technology, physical engine technology, and sensor technology to create a virtual three-dimensional environment that enables participants to feel like they are in the real world. That is to say, in a three-dimensional virtual environment, it is necessary to enable participants to produce and place themselves in the real world with kind of visual, auditory, tactile, smell, and taste experience [7]. The virtual reality is real to the human senses, but it is indeed a fiction. However, acting on the fiction often leads to correct results. Due to various reasons, there are more researches on virtual reality technology in the world, and the research algorithms are relatively mature, mainly in the first three items.The three-dimensional perception of virtual objects, the presence of virtual objects, multisensitivity, the closed-loop interaction with the virtual environment, and the dynamic display of virtual objects constitute the five basic characteristics of what people usually call virtual reality technology. Among them, the three-dimensional sense of virtual objects, the sense of existence of virtual objects, and the real-time interaction with the virtual environment are the three most basic characteristics of virtual reality technology. With the use of virtual reality technology, a person can communicate with a computer without having to be aware that he or she is dealing with a computer, but rather as if he or she were dealing with things in an everyday environment. This frees the person from the complex task of operating a computer. Virtual reality technology needs to study a wide range of content, including three-dimensional terrain modeling technology; multidimensional information representation technology; real-time generation and synthesis of graphic images; real-time processing technology; fusion technology of participants and scenes; concurrent processing technology; objects simulation technology; computer graphics processing technology; application technology of virtual reality interface in intelligent computer systems and virtual reality research based on network environment [8, 9].As an important high-tech in the field of information technology, virtual reality technology has been widely used in various industries, such as art, education, entertainment, medicine, and other fields [10]. For example, medical experts use computers to simulate human tissues and organs in a virtual space where students can perform simulated operations and feel the sensation of a scalpel cutting into human muscle tissue and touching bones, enabling students to grasp the essentials of surgery more quickly. In foreign countries, virtual reality technology is used in various fields of business activities. The VR system will actually be constructed according to the differences in specific applications and tasks. Therefore, the actual hardware and software used are also different. However, the formal operation of a VR system requires five major links, namely, virtual world, software, computers, and supporting input and output devices, etc. [11].The virtual world in it refers to a virtual atmosphere capable of effective interaction, which contains supporting virtual models and databases, which are related to scene models, dynamics, and related physical characteristics, etc. Generally speaking, in this environment designers among them can carry out continuous observation activities from multiple angles; and computers provide supporting computing functions to achieve image transmission and processing. Generally speaking, they are advanced graphics computers or specialized workers [12], providing effective data processing and image rendering functions; and the software belongs to the VR software platform provided for actual application objects. In the overall development process, it is responsible for specific scene-driven construction and redevelopment of related applications and also handles related work of connecting external devices, three-dimensional modeling, and sorting out related data [13]; the more commonly used include Vega, Virtools, etc.; input devices are mainly used to allow the VR system to recognize the control data from the user, and the more common ones include 3D position tracker, data equipment, sound input, three-dimensional probe, etc.; output devices are mostly used for sound output, force feedback, or three-dimensional graphics, so that the operator can get an immersive experience. Hardware facilities include data capture device, binocular omnidirectional display, and part model, on the actual equipment system hardware and its software system display [14].


### 2.2. Three-Dimensional Display of Furniture Products

In traditional product display systems, images have long been an indispensable means of display: merchants use images to show users products that are temporarily unable to provide physical goods [15]. On the early network platforms, images were the most effective display medium. However, due to the small amount of information in a single image, it is impossible to provide comprehensive product information [16]. In recent years, with the rapid advancement of computer graphics and image processing technologies, advanced technology can be used to directly generate simulated real scenes from a number of single images. Panoramic technology is one of them [17, 18].Panorama is a three-dimensional display mode that simulates three-dimensional display. It mainly realizes the free look around and three-dimensional drag display of objects through the stitching of pictures or videos. The panoramic technology is to take a group of photos from different positions by looking around from the center point and then seamlessly merge them to form a three-dimensional panoramic image [19]. Simulate the two-dimensional plan into a real three-dimensional space and present it to the user. Users can use the mouse or keyboard to move up and down, left and right in multiple dimensions, zoom, observe the scene from any angle of view, realize looking around, looking down, looking up, etc., and experience the real scene or image perspective effect [20]. Its design and implementation are relatively simple and have low hardware requirements, saving a lot of modeling and rendering work. It has a high quality picture with high definition full-screen scenes, which makes the details perform perfectly. The panoramic technology uses photos of the actual scene as the material, and the image information of the entire scene can be captured by a professional camera, and very clear picture quality can be obtained. However, the amount of data is large, and it is not suitable for Internet-based file transfer [21, 22].With its strong immersion and advanced interactivity, panoramic roaming technology provides a new form of expression for all walks of life, and applying panoramic roaming technology to display design will certainly bring new development opportunities to display design. The furniture panoramic electronic magazine can give a comprehensive and detailed introduction to furniture products and furniture companies. The content can include company profile, company factory display, product display, furniture exhibition hall panoramic display, product animation photo, company store overview, company national marketing network introduction, Franchise support, and corporate contact information of the store. Panorama e-magazines can be browsed online by users on the company’s website or can be made into exquisite CDs for users to browse or sent to potential users’ mailboxes by e-mail, which is a new way of marketing.Model-based 3D display technology uses various modeling software (such as 3DS MAX, Maya) to build a virtual environment with geometric entities and performs motion, texture, and rendering processing that meets technical conditions and then implements interactive operations by adding event response and finally integrates multimedia information and output applications. In the display process, it mainly involves modeling, drawing, and interactive realization, which are generally used in the design of nonimmersive virtual reality display of personal computers. This display design method can more realistically represent the scenes and objects in the real world and can also generate animation [23]. However, due to the limitations of the software and the network, it cannot provide the photo-quality realistic effects like the image-based method.With the rapid development of the Internet, many virtual home furnishing websites such as Xinju, Juwuyou, and IKEA have appeared. Users can download design software for free on these websites and use the massive furniture product information in the database to design homes. After the user downloads the relevant software, he can carry out the virtual design of the home. According to the effect of DIY furniture placed in the virtual scene, he can change the color and type of the furniture at will to form a satisfactory creative home layout [24].When household products are displayed in 3D, they often rely on 3D modeling related technologies. Next, 3D modeling related technologies will be introduced.


### 2.3. Commonly Used Model Simplification Algorithms

The first is the vertex extraction algorithm. The idea of the vertex clustering algorithm is similar to our voxel downsampling in point clouds, where we divide the grid into many small grids, which we call voxels, each of which has several vertices or none, and merge the vertices inside the voxels containing vertices into a single vertex. The vertices of the voxels that are connected are reconnected into triangular face pieces to form a new mesh. Compared with other simplified algorithms, the implementation process of the vertex extraction algorithm is relatively simple and the simplification speed is fast. The basic idea is shown in Figure1 [25].Figure 1
Basic idea of vertex extraction algorithm.The second is the vertex clustering algorithm. This algorithm is also one of the more commonly used 3D model simplification algorithms [26]. This algorithm is simple, efficient, and easy to implement and can quickly simplify any 3D mesh model. The basic idea is shown in Figure 2.Figure 2
Basic idea of vertex clustering algorithm.This algorithm uses the bounding box to divide the 3D mesh model into small pieces. In the simplification process, all vertices in each bounding box are aggregated into a new vertex. Usually the position of this new vertex is determined by all the vertices in the bounding box. The average position of is obtained, and finally all the vertices of the aggregation are connected according to the original topological relationship to obtain a simplified model [27]. Only triangles that span three different bounding boxes can be retained in the simplified model, and other different types of triangles will be simplified into vertices or edges, as shown in Figure 3, 4, and 5 for the step-by-step diagrams of the simplified process.Figure 3
The triangle simplified to vertices.Figure 4
The triangle is retained.Figure 5
The triangle simplified to edges.The third is the side-folding algorithm. The side-folding algorithm is currently the most commonly used simplification method [28]. This algorithm has high simplification quality, but also has a faster simplification speed, and the implementation process is relatively simple. The basic idea is shown in Figure 6.Figure 6
The basic idea of the edge folding algorithm.


### 2.4. Edge Folding Simplified Algorithm Based on Quadratic Error

Based on the simplified edge folding algorithm, Garland proposed a quantitative evaluation of the edge folding cost by calculating the error measurement criterion of the quadratic error matrix, and based on this, the priority queue of the folded edge was established, and then the new vertex was determined through further calculations, the best location.


#### 2.4.1. Quadratic Error Matrix

The quadratic error matrix expresses the position coordinates of the vertex in a 4-dimensional homogeneous coordinate, that is, the coordinate of any vertex v on the three-dimensional model. In the three-dimensional space, any planep can be expressed as ax + by + cz + d = 0. The basic idea of the quadratic error matrix is to take the sum of the squares of the distance from the vertex to all the planes containing the vertex as the error measure. Suppose the set of all planes containing a vertex is planes (v); then, the quadratic error is(1)Δv=Δvxvyvz1T=∑peplanesvPTV2.The secondary error can be rewritten as(2)Δv=∑peplanesvVTPPTV=∑peplanesvVTPPTV=VT∑peplanesvKPV.We have(3)KP=PPT=a2abacadabb2bcbdacbcc2cdadbdcdd2.LetQ=∑peplanesKP be the quadratic error matrix of vertex v; then, the quadratic error can be expressed as(4)Δv=vTQv,(5)Q=q11q12q13q14q21q22q23q24q31q32q33q34q41q42q43q44.The process of solving the quadratic error matrix is equivalent to solving the system of equations:(6)a1x+b1y+c1z+d1=0a2x+b2y+c2z+d2=0......anx+bny+cnz+dn=0.


#### 2.4.2. Determination of the Position of the New Vertex

In the process of edge folding operation, it is necessary to delete the two vertices (vi, vj) of an edge, replace the folded edge with a new vertex v, and reconnect with the relevant vertices around the folded edge to generate a new topology mesh. The choice of the new vertex position will affect the similarity between the simplified model and the original model. The easiest way to think of is to insert the new vertex at the position that minimizesΔv¯ between the two ends or the midpoint of the folded edge. The method has a small amount of calculation, which can shorten the time required for the simplification process to a certain extent, but it cannot guarantee that the simplified model produces the smallest error. According to the principle of least squares, the vertex position with the smallest error should have the smallest sum of squared distances from all planes related to the folded edge. In order to find this position, the partial derivatives of Δv¯ with respect to x, y, and z can all be 0, namely,(7)∂Δ∂x=∂Δ∂y=∂Δ∂z=0.We have(8)Δv¯=v¯Tqi+qjv¯.According to the previous formula, we can obtain the solution system of formula (7):(9)q11q12q13q14q12q22q23q24q13q23q33q340001v¯=0001.Assuming that the left-hand matrix in (9) is invertible, then(10)v¯q11q12q13q14q12q22q23q24q13q23q33q340001−10001.


### 2.5. Based on Trackball Rotation

#### 2.5.1. Establishment of the Trackball Coordinate System

In order to establish the trackball coordinate system, the screen coordinate system needs to be converted to a normalized screen coordinate system. The screen coordinate system is a two-dimensional coordinate system, the origin is located at the upper left corner of the screen, theX-axis is the positive direction to the left, and the Y-axis is the positive direction down. The normalized screen coordinate system normalizes the screen coordinates into a range from (-1,1) to (1,1), with the origin at the center of the screen, the X-axis to the left is the positive direction, and the Y-axis is up to the positive direction. Assuming that the screen coordinates are (screen X, screen Y), the normalized screen coordinates are (x, y), and the width and height of the screen are W and H, respectively, then a simple linear calculation can be obtained:(11)x=screenXW∗2−1y=1−screenYH∗2.In order to complete the conversion from the normalized screen coordinate system to the trackball coordinate system, suppose that the normalized screen coordinates are (x, y) and the trackball coordinates are (u, v, w), because not all of them are in the normalized screen coordinate system. The points are all located in the trackball coordinate system, so the points on the normalized screen coordinate system can be divided into two parts, one part is inside the sphere and the other part is outside the sphere. Since the conversion of the trackball coordinate system is a conversion from a two-dimensional coordinate system to a three-dimensional coordinate system, the depth of the point needs to be considered. Suppose P trackball coordinates are (u0, v0, w0), and P normalized screen coordinates are (x, y); you can get(12)u1=cosθ=xx2+y2v1=sinθ=yx2+y2w1=0.In summary, the conversion formula from the normalized screen coordinate system to the trackball coordinate system can be obtained as(13)u,v,w=x,y,1−x2−y2,x2+y2≤1xx2+y2,yx2+y2,0,x2+y2>1.


#### 2.5.2. Determination of the Model Rotation Matrix

After the trackball coordinate system is established, in order to realize the rotation of the 3D model based on the trackball, the rotation axis and the rotation angle need to be determined first. When P1 slides to P2, the rotation axis is OA and the rotation angle isθ. It is easy to know that the vector OA is the normal vector of the plane composed of the vector OP1 and the vector OP2, so(14)OA⟶=OP1⟶∗OP2⟶.According to simple three-dimensional geometric calculations, it is easy to get(15)θ=arccosOP1⟶∗OP2⟶OP1⟶OP2⟶.Through the above calculation, the rotation axis and the rotation angle can be obtained, as shown in Figure7.Figure 7
Rotation axis and rotation angle.After obtaining the rotation axis and the rotation angle, the computer realizes the posture change of the three-dimensional model by multiplying a 4-dimensional transformation matrix and the model matrix. Therefore, in order to realize the rotation of the model, it is also necessary to calculate the rotation matrix of the model. Assuming that the rotation axis vector is (a,b, c) and the rotation angle is θ, the following formula can be used to obtain the rotation matrix of the three-dimensional model:(16)MR=a2+1−a2cosθab1−cosθ+csinθac1−cosθ−bsinθ0ab1−cosθ−csinθb2+1−b2cosθbc1−cosθ+asinθ0ab1−cosθ+bsinθbc1−cosθ−asinθc2+1−c2cosθ00001.Suppose the initial model matrix isM, and multiply the model matrix by formulas (4)-(6); the rotated model matrix M1 can be obtained, namely,(17)M1=M∗MR.Figure8 shows that the continuous sliding operation of the three-dimensional model does not cause the phenomenon that the sliding direction is inconsistent with the rotation direction of the model, and the rotation effect is good.Figure 8
Implementation based on trackball rotation.


### 2.6. Picking Up the Three-Dimensional Model

#### 2.6.1. Introduction to 3D Model Picking

In order to realize the measurement function of the 3D model, such as the distance between any two points on the model surface, it is necessary to obtain the vertex coordinates selected on the model surface through interaction. This process is called the picking of the 3D model. Since the three-dimensional model displayed on the computer screen is obtained by the computer through a series of model transformations and has no direct relationship with the screen coordinate system, in order to realize the picking of the three-dimensional model, a series of coordinate system transformations are required. In order to realize the corresponding coordinate conversion, you first need to understand the process of computer model conversion. The general process is shown in Figure9.Figure 9
Model transformation process.Projection transformation is divided into orthogonal projection transformation and perspective projection transformation: orthogonal projection transformation uses a rectangular parallelepiped to project and cut the model, so regardless of the distance between the model and the projection surface, the size of the model projection will always remain the same, with perspective projection. The transformation uses a frustum to project the model. The closer the model is to the projection surface, the larger the model projection is. This projection method is more in line with our habit of observing objects. The process of viewport transformation mainly moves the image of the projection surface to a suitable position of the screen window for display. Generally, the image and the origin of the window are located. After the above several model transformation processes, the 3D model is transformed from the world coordinate system to the screen coordinate system. Figure10 shows the projection transformation diagram.Figure 10
Projection transformation.


#### 2.6.2. The Principle of 3D Model Pickup

In order to select the vertices of the 3D model surface from the screen, you first need to introduce a ray from the screen. The ray direction is the direction from the viewpoint to the selected point on the screen. The intersection of the ray and the model surface closest to the viewpoint is the picked model surface vertex; the general principle is shown in Figure11.Figure 11
Three-dimensional model picking principle.Through the understanding of the picking principle, we can know that the ray P1P2 and the model intersect at the point P0. In order to obtain the three-dimensional space coordinates of the vertex P0, the coordinates of the ray P1 and P2 in the three-dimensional space need to be determined first, where P1 and P2 are the rays, respectively, with the intersection point with the near plane (z = 0) and far plane (z = 1) of the projection frustum. It can be seen from the previous section that the conversion of 3D model world coordinates to screen coordinates requires model view transformation, projection transformation, and viewport transformation. Obviously, the conversion from screen coordinates to world coordinates only needs to be reversed in the reverse process. Assuming that the model view transformation matrix is V, the projection transformation matrix is P, and the viewport transformation matrix is W, the transformation matrix M from the screen coordinate system to the world coordinate system is(18)M=W−1∗P−1∗V−1.From (18), the coordinates of P1 and P2 in the three-dimensional world coordinate system can be determined, thereby determining the ray in the world coordinate system. Next, it is necessary to determine the intersection of the ray and the three-dimensional model. The three-dimensional mesh model is generally composed of triangles, so to determine whether the ray intersects the model, only the intersection of the ray and the triangle on the surface of the model is judged. Assuming that the three vertices of the triangle are v1, v2, and v3, the coordinates of any point in the triangle can be obtained as(19)v0=v1+u∗v2−v1+v∗v3−v1.In formulas (4)-(9), the point v0 is determined by variables u and v, where 0<u < 1, 0<v < 1, and 0<u + v < 1. Assuming that the coordinates of P1 and P2 are, respectively, Vp1 and Vp2, the coordinates of any point on the ray P1P2 can be obtained as(20)v0=vp1+vp2−vp1∗L.Figure12 is an effect diagram of the realization of three-dimensional model picking.Figure 12
Realization of 3D model picking.


### 2.7. User Association

The goal of the user association problem is to associate users with RRH that can provide better channel quality. First, the wideband SINR associated with the userki and RRHl is defined as follows:(21)ψk,lt=plmaxhki,lt2∑s∈τ\lpsmaxhki,st2.Among them,ψk,lt is the wideband signal-to-interference and noise ratio associated with RRH l of time slot user ki and hki,lt is the channel gain between ki and RRH l of time slot t user. In this paper, the user association problem is modeled as the problem of maximizing the sum of the broadband signal-to-interference and noise ratio of all users:(22)maxakijt∑l∈τ∑ki∈Ukakj,jtψki,jt,(23)s.t.∑b∈β∑ki∈Uaki,jtRkimin≤Cl,max,∀l∈τ,(24)∑l∈τakllt=1,∀ki∈U,(25)aki,lt=1,∀ki∈U.Formula (23) indicates that the fronthaul link capacity on the RRH can carry at least the minimum data rate required by the user associated with it. Formula (24) indicates that a user can only be associated with one RRH, and formula (25) indicates that the correlation factor is a binary variable.This problem is a 0–1 multiple knapsack problem. The core idea of this method is that the user is associated with the RRH whose remaining fronthaul capacity can accommodate the user and can provide the maximum bandwidth SINR. First, calculate the bandwidth SINR associated with all RRHs for each user in all slices. Then, if the condition of formula (23) is satisfied, the user will select the RRH association that can provide the maximum bandwidth SINR. The RRH association that provides the next largest bandwidth SINR is selected.


## 2.1. Virtual Reality Technology

Virtual reality technology in the general sense refers to the use of various technologies such as computer technology, three-dimensional modeling technology, physical engine technology, and sensor technology to create a virtual three-dimensional environment that enables participants to feel like they are in the real world. That is to say, in a three-dimensional virtual environment, it is necessary to enable participants to produce and place themselves in the real world with kind of visual, auditory, tactile, smell, and taste experience [7]. The virtual reality is real to the human senses, but it is indeed a fiction. However, acting on the fiction often leads to correct results. Due to various reasons, there are more researches on virtual reality technology in the world, and the research algorithms are relatively mature, mainly in the first three items.The three-dimensional perception of virtual objects, the presence of virtual objects, multisensitivity, the closed-loop interaction with the virtual environment, and the dynamic display of virtual objects constitute the five basic characteristics of what people usually call virtual reality technology. Among them, the three-dimensional sense of virtual objects, the sense of existence of virtual objects, and the real-time interaction with the virtual environment are the three most basic characteristics of virtual reality technology. With the use of virtual reality technology, a person can communicate with a computer without having to be aware that he or she is dealing with a computer, but rather as if he or she were dealing with things in an everyday environment. This frees the person from the complex task of operating a computer. Virtual reality technology needs to study a wide range of content, including three-dimensional terrain modeling technology; multidimensional information representation technology; real-time generation and synthesis of graphic images; real-time processing technology; fusion technology of participants and scenes; concurrent processing technology; objects simulation technology; computer graphics processing technology; application technology of virtual reality interface in intelligent computer systems and virtual reality research based on network environment [8, 9].As an important high-tech in the field of information technology, virtual reality technology has been widely used in various industries, such as art, education, entertainment, medicine, and other fields [10]. For example, medical experts use computers to simulate human tissues and organs in a virtual space where students can perform simulated operations and feel the sensation of a scalpel cutting into human muscle tissue and touching bones, enabling students to grasp the essentials of surgery more quickly. In foreign countries, virtual reality technology is used in various fields of business activities. The VR system will actually be constructed according to the differences in specific applications and tasks. Therefore, the actual hardware and software used are also different. However, the formal operation of a VR system requires five major links, namely, virtual world, software, computers, and supporting input and output devices, etc. [11].The virtual world in it refers to a virtual atmosphere capable of effective interaction, which contains supporting virtual models and databases, which are related to scene models, dynamics, and related physical characteristics, etc. Generally speaking, in this environment designers among them can carry out continuous observation activities from multiple angles; and computers provide supporting computing functions to achieve image transmission and processing. Generally speaking, they are advanced graphics computers or specialized workers [12], providing effective data processing and image rendering functions; and the software belongs to the VR software platform provided for actual application objects. In the overall development process, it is responsible for specific scene-driven construction and redevelopment of related applications and also handles related work of connecting external devices, three-dimensional modeling, and sorting out related data [13]; the more commonly used include Vega, Virtools, etc.; input devices are mainly used to allow the VR system to recognize the control data from the user, and the more common ones include 3D position tracker, data equipment, sound input, three-dimensional probe, etc.; output devices are mostly used for sound output, force feedback, or three-dimensional graphics, so that the operator can get an immersive experience. Hardware facilities include data capture device, binocular omnidirectional display, and part model, on the actual equipment system hardware and its software system display [14].


## 2.2. Three-Dimensional Display of Furniture Products

In traditional product display systems, images have long been an indispensable means of display: merchants use images to show users products that are temporarily unable to provide physical goods [15]. On the early network platforms, images were the most effective display medium. However, due to the small amount of information in a single image, it is impossible to provide comprehensive product information [16]. In recent years, with the rapid advancement of computer graphics and image processing technologies, advanced technology can be used to directly generate simulated real scenes from a number of single images. Panoramic technology is one of them [17, 18].Panorama is a three-dimensional display mode that simulates three-dimensional display. It mainly realizes the free look around and three-dimensional drag display of objects through the stitching of pictures or videos. The panoramic technology is to take a group of photos from different positions by looking around from the center point and then seamlessly merge them to form a three-dimensional panoramic image [19]. Simulate the two-dimensional plan into a real three-dimensional space and present it to the user. Users can use the mouse or keyboard to move up and down, left and right in multiple dimensions, zoom, observe the scene from any angle of view, realize looking around, looking down, looking up, etc., and experience the real scene or image perspective effect [20]. Its design and implementation are relatively simple and have low hardware requirements, saving a lot of modeling and rendering work. It has a high quality picture with high definition full-screen scenes, which makes the details perform perfectly. The panoramic technology uses photos of the actual scene as the material, and the image information of the entire scene can be captured by a professional camera, and very clear picture quality can be obtained. However, the amount of data is large, and it is not suitable for Internet-based file transfer [21, 22].With its strong immersion and advanced interactivity, panoramic roaming technology provides a new form of expression for all walks of life, and applying panoramic roaming technology to display design will certainly bring new development opportunities to display design. The furniture panoramic electronic magazine can give a comprehensive and detailed introduction to furniture products and furniture companies. The content can include company profile, company factory display, product display, furniture exhibition hall panoramic display, product animation photo, company store overview, company national marketing network introduction, Franchise support, and corporate contact information of the store. Panorama e-magazines can be browsed online by users on the company’s website or can be made into exquisite CDs for users to browse or sent to potential users’ mailboxes by e-mail, which is a new way of marketing.Model-based 3D display technology uses various modeling software (such as 3DS MAX, Maya) to build a virtual environment with geometric entities and performs motion, texture, and rendering processing that meets technical conditions and then implements interactive operations by adding event response and finally integrates multimedia information and output applications. In the display process, it mainly involves modeling, drawing, and interactive realization, which are generally used in the design of nonimmersive virtual reality display of personal computers. This display design method can more realistically represent the scenes and objects in the real world and can also generate animation [23]. However, due to the limitations of the software and the network, it cannot provide the photo-quality realistic effects like the image-based method.With the rapid development of the Internet, many virtual home furnishing websites such as Xinju, Juwuyou, and IKEA have appeared. Users can download design software for free on these websites and use the massive furniture product information in the database to design homes. After the user downloads the relevant software, he can carry out the virtual design of the home. According to the effect of DIY furniture placed in the virtual scene, he can change the color and type of the furniture at will to form a satisfactory creative home layout [24].When household products are displayed in 3D, they often rely on 3D modeling related technologies. Next, 3D modeling related technologies will be introduced.


## 2.3. Commonly Used Model Simplification Algorithms

The first is the vertex extraction algorithm. The idea of the vertex clustering algorithm is similar to our voxel downsampling in point clouds, where we divide the grid into many small grids, which we call voxels, each of which has several vertices or none, and merge the vertices inside the voxels containing vertices into a single vertex. The vertices of the voxels that are connected are reconnected into triangular face pieces to form a new mesh. Compared with other simplified algorithms, the implementation process of the vertex extraction algorithm is relatively simple and the simplification speed is fast. The basic idea is shown in Figure1 [25].Figure 1
Basic idea of vertex extraction algorithm.The second is the vertex clustering algorithm. This algorithm is also one of the more commonly used 3D model simplification algorithms [26]. This algorithm is simple, efficient, and easy to implement and can quickly simplify any 3D mesh model. The basic idea is shown in Figure 2.Figure 2
Basic idea of vertex clustering algorithm.This algorithm uses the bounding box to divide the 3D mesh model into small pieces. In the simplification process, all vertices in each bounding box are aggregated into a new vertex. Usually the position of this new vertex is determined by all the vertices in the bounding box. The average position of is obtained, and finally all the vertices of the aggregation are connected according to the original topological relationship to obtain a simplified model [27]. Only triangles that span three different bounding boxes can be retained in the simplified model, and other different types of triangles will be simplified into vertices or edges, as shown in Figure 3, 4, and 5 for the step-by-step diagrams of the simplified process.Figure 3
The triangle simplified to vertices.Figure 4
The triangle is retained.Figure 5
The triangle simplified to edges.The third is the side-folding algorithm. The side-folding algorithm is currently the most commonly used simplification method [28]. This algorithm has high simplification quality, but also has a faster simplification speed, and the implementation process is relatively simple. The basic idea is shown in Figure 6.Figure 6
The basic idea of the edge folding algorithm.


## 2.4. Edge Folding Simplified Algorithm Based on Quadratic Error

Based on the simplified edge folding algorithm, Garland proposed a quantitative evaluation of the edge folding cost by calculating the error measurement criterion of the quadratic error matrix, and based on this, the priority queue of the folded edge was established, and then the new vertex was determined through further calculations, the best location.


### 2.4.1. Quadratic Error Matrix

The quadratic error matrix expresses the position coordinates of the vertex in a 4-dimensional homogeneous coordinate, that is, the coordinate of any vertex v on the three-dimensional model. In the three-dimensional space, any planep can be expressed as ax + by + cz + d = 0. The basic idea of the quadratic error matrix is to take the sum of the squares of the distance from the vertex to all the planes containing the vertex as the error measure. Suppose the set of all planes containing a vertex is planes (v); then, the quadratic error is(1)Δv=Δvxvyvz1T=∑peplanesvPTV2.The secondary error can be rewritten as(2)Δv=∑peplanesvVTPPTV=∑peplanesvVTPPTV=VT∑peplanesvKPV.We have(3)KP=PPT=a2abacadabb2bcbdacbcc2cdadbdcdd2.LetQ=∑peplanesKP be the quadratic error matrix of vertex v; then, the quadratic error can be expressed as(4)Δv=vTQv,(5)Q=q11q12q13q14q21q22q23q24q31q32q33q34q41q42q43q44.The process of solving the quadratic error matrix is equivalent to solving the system of equations:(6)a1x+b1y+c1z+d1=0a2x+b2y+c2z+d2=0......anx+bny+cnz+dn=0.


### 2.4.2. Determination of the Position of the New Vertex

In the process of edge folding operation, it is necessary to delete the two vertices (vi, vj) of an edge, replace the folded edge with a new vertex v, and reconnect with the relevant vertices around the folded edge to generate a new topology mesh. The choice of the new vertex position will affect the similarity between the simplified model and the original model. The easiest way to think of is to insert the new vertex at the position that minimizesΔv¯ between the two ends or the midpoint of the folded edge. The method has a small amount of calculation, which can shorten the time required for the simplification process to a certain extent, but it cannot guarantee that the simplified model produces the smallest error. According to the principle of least squares, the vertex position with the smallest error should have the smallest sum of squared distances from all planes related to the folded edge. In order to find this position, the partial derivatives of Δv¯ with respect to x, y, and z can all be 0, namely,(7)∂Δ∂x=∂Δ∂y=∂Δ∂z=0.We have(8)Δv¯=v¯Tqi+qjv¯.According to the previous formula, we can obtain the solution system of formula (7):(9)q11q12q13q14q12q22q23q24q13q23q33q340001v¯=0001.Assuming that the left-hand matrix in (9) is invertible, then(10)v¯q11q12q13q14q12q22q23q24q13q23q33q340001−10001.


## 2.4.1. Quadratic Error Matrix

The quadratic error matrix expresses the position coordinates of the vertex in a 4-dimensional homogeneous coordinate, that is, the coordinate of any vertex v on the three-dimensional model. In the three-dimensional space, any planep can be expressed as ax + by + cz + d = 0. The basic idea of the quadratic error matrix is to take the sum of the squares of the distance from the vertex to all the planes containing the vertex as the error measure. Suppose the set of all planes containing a vertex is planes (v); then, the quadratic error is(1)Δv=Δvxvyvz1T=∑peplanesvPTV2.The secondary error can be rewritten as(2)Δv=∑peplanesvVTPPTV=∑peplanesvVTPPTV=VT∑peplanesvKPV.We have(3)KP=PPT=a2abacadabb2bcbdacbcc2cdadbdcdd2.LetQ=∑peplanesKP be the quadratic error matrix of vertex v; then, the quadratic error can be expressed as(4)Δv=vTQv,(5)Q=q11q12q13q14q21q22q23q24q31q32q33q34q41q42q43q44.The process of solving the quadratic error matrix is equivalent to solving the system of equations:(6)a1x+b1y+c1z+d1=0a2x+b2y+c2z+d2=0......anx+bny+cnz+dn=0.


## 2.4.2. Determination of the Position of the New Vertex

In the process of edge folding operation, it is necessary to delete the two vertices (vi, vj) of an edge, replace the folded edge with a new vertex v, and reconnect with the relevant vertices around the folded edge to generate a new topology mesh. The choice of the new vertex position will affect the similarity between the simplified model and the original model. The easiest way to think of is to insert the new vertex at the position that minimizesΔv¯ between the two ends or the midpoint of the folded edge. The method has a small amount of calculation, which can shorten the time required for the simplification process to a certain extent, but it cannot guarantee that the simplified model produces the smallest error. According to the principle of least squares, the vertex position with the smallest error should have the smallest sum of squared distances from all planes related to the folded edge. In order to find this position, the partial derivatives of Δv¯ with respect to x, y, and z can all be 0, namely,(7)∂Δ∂x=∂Δ∂y=∂Δ∂z=0.We have(8)Δv¯=v¯Tqi+qjv¯.According to the previous formula, we can obtain the solution system of formula (7):(9)q11q12q13q14q12q22q23q24q13q23q33q340001v¯=0001.Assuming that the left-hand matrix in (9) is invertible, then(10)v¯q11q12q13q14q12q22q23q24q13q23q33q340001−10001.


## 2.5. Based on Trackball Rotation

### 2.5.1. Establishment of the Trackball Coordinate System

In order to establish the trackball coordinate system, the screen coordinate system needs to be converted to a normalized screen coordinate system. The screen coordinate system is a two-dimensional coordinate system, the origin is located at the upper left corner of the screen, theX-axis is the positive direction to the left, and the Y-axis is the positive direction down. The normalized screen coordinate system normalizes the screen coordinates into a range from (-1,1) to (1,1), with the origin at the center of the screen, the X-axis to the left is the positive direction, and the Y-axis is up to the positive direction. Assuming that the screen coordinates are (screen X, screen Y), the normalized screen coordinates are (x, y), and the width and height of the screen are W and H, respectively, then a simple linear calculation can be obtained:(11)x=screenXW∗2−1y=1−screenYH∗2.In order to complete the conversion from the normalized screen coordinate system to the trackball coordinate system, suppose that the normalized screen coordinates are (x, y) and the trackball coordinates are (u, v, w), because not all of them are in the normalized screen coordinate system. The points are all located in the trackball coordinate system, so the points on the normalized screen coordinate system can be divided into two parts, one part is inside the sphere and the other part is outside the sphere. Since the conversion of the trackball coordinate system is a conversion from a two-dimensional coordinate system to a three-dimensional coordinate system, the depth of the point needs to be considered. Suppose P trackball coordinates are (u0, v0, w0), and P normalized screen coordinates are (x, y); you can get(12)u1=cosθ=xx2+y2v1=sinθ=yx2+y2w1=0.In summary, the conversion formula from the normalized screen coordinate system to the trackball coordinate system can be obtained as(13)u,v,w=x,y,1−x2−y2,x2+y2≤1xx2+y2,yx2+y2,0,x2+y2>1.


### 2.5.2. Determination of the Model Rotation Matrix

After the trackball coordinate system is established, in order to realize the rotation of the 3D model based on the trackball, the rotation axis and the rotation angle need to be determined first. When P1 slides to P2, the rotation axis is OA and the rotation angle isθ. It is easy to know that the vector OA is the normal vector of the plane composed of the vector OP1 and the vector OP2, so(14)OA⟶=OP1⟶∗OP2⟶.According to simple three-dimensional geometric calculations, it is easy to get(15)θ=arccosOP1⟶∗OP2⟶OP1⟶OP2⟶.Through the above calculation, the rotation axis and the rotation angle can be obtained, as shown in Figure7.Figure 7
Rotation axis and rotation angle.After obtaining the rotation axis and the rotation angle, the computer realizes the posture change of the three-dimensional model by multiplying a 4-dimensional transformation matrix and the model matrix. Therefore, in order to realize the rotation of the model, it is also necessary to calculate the rotation matrix of the model. Assuming that the rotation axis vector is (a,b, c) and the rotation angle is θ, the following formula can be used to obtain the rotation matrix of the three-dimensional model:(16)MR=a2+1−a2cosθab1−cosθ+csinθac1−cosθ−bsinθ0ab1−cosθ−csinθb2+1−b2cosθbc1−cosθ+asinθ0ab1−cosθ+bsinθbc1−cosθ−asinθc2+1−c2cosθ00001.Suppose the initial model matrix isM, and multiply the model matrix by formulas (4)-(6); the rotated model matrix M1 can be obtained, namely,(17)M1=M∗MR.Figure8 shows that the continuous sliding operation of the three-dimensional model does not cause the phenomenon that the sliding direction is inconsistent with the rotation direction of the model, and the rotation effect is good.Figure 8
Implementation based on trackball rotation.


## 2.5.1. Establishment of the Trackball Coordinate System

In order to establish the trackball coordinate system, the screen coordinate system needs to be converted to a normalized screen coordinate system. The screen coordinate system is a two-dimensional coordinate system, the origin is located at the upper left corner of the screen, theX-axis is the positive direction to the left, and the Y-axis is the positive direction down. The normalized screen coordinate system normalizes the screen coordinates into a range from (-1,1) to (1,1), with the origin at the center of the screen, the X-axis to the left is the positive direction, and the Y-axis is up to the positive direction. Assuming that the screen coordinates are (screen X, screen Y), the normalized screen coordinates are (x, y), and the width and height of the screen are W and H, respectively, then a simple linear calculation can be obtained:(11)x=screenXW∗2−1y=1−screenYH∗2.In order to complete the conversion from the normalized screen coordinate system to the trackball coordinate system, suppose that the normalized screen coordinates are (x, y) and the trackball coordinates are (u, v, w), because not all of them are in the normalized screen coordinate system. The points are all located in the trackball coordinate system, so the points on the normalized screen coordinate system can be divided into two parts, one part is inside the sphere and the other part is outside the sphere. Since the conversion of the trackball coordinate system is a conversion from a two-dimensional coordinate system to a three-dimensional coordinate system, the depth of the point needs to be considered. Suppose P trackball coordinates are (u0, v0, w0), and P normalized screen coordinates are (x, y); you can get(12)u1=cosθ=xx2+y2v1=sinθ=yx2+y2w1=0.In summary, the conversion formula from the normalized screen coordinate system to the trackball coordinate system can be obtained as(13)u,v,w=x,y,1−x2−y2,x2+y2≤1xx2+y2,yx2+y2,0,x2+y2>1.


## 2.5.2. Determination of the Model Rotation Matrix

After the trackball coordinate system is established, in order to realize the rotation of the 3D model based on the trackball, the rotation axis and the rotation angle need to be determined first. When P1 slides to P2, the rotation axis is OA and the rotation angle isθ. It is easy to know that the vector OA is the normal vector of the plane composed of the vector OP1 and the vector OP2, so(14)OA⟶=OP1⟶∗OP2⟶.According to simple three-dimensional geometric calculations, it is easy to get(15)θ=arccosOP1⟶∗OP2⟶OP1⟶OP2⟶.Through the above calculation, the rotation axis and the rotation angle can be obtained, as shown in Figure7.Figure 7
Rotation axis and rotation angle.After obtaining the rotation axis and the rotation angle, the computer realizes the posture change of the three-dimensional model by multiplying a 4-dimensional transformation matrix and the model matrix. Therefore, in order to realize the rotation of the model, it is also necessary to calculate the rotation matrix of the model. Assuming that the rotation axis vector is (a,b, c) and the rotation angle is θ, the following formula can be used to obtain the rotation matrix of the three-dimensional model:(16)MR=a2+1−a2cosθab1−cosθ+csinθac1−cosθ−bsinθ0ab1−cosθ−csinθb2+1−b2cosθbc1−cosθ+asinθ0ab1−cosθ+bsinθbc1−cosθ−asinθc2+1−c2cosθ00001.Suppose the initial model matrix isM, and multiply the model matrix by formulas (4)-(6); the rotated model matrix M1 can be obtained, namely,(17)M1=M∗MR.Figure8 shows that the continuous sliding operation of the three-dimensional model does not cause the phenomenon that the sliding direction is inconsistent with the rotation direction of the model, and the rotation effect is good.Figure 8
Implementation based on trackball rotation.


## 2.6. Picking Up the Three-Dimensional Model

### 2.6.1. Introduction to 3D Model Picking

In order to realize the measurement function of the 3D model, such as the distance between any two points on the model surface, it is necessary to obtain the vertex coordinates selected on the model surface through interaction. This process is called the picking of the 3D model. Since the three-dimensional model displayed on the computer screen is obtained by the computer through a series of model transformations and has no direct relationship with the screen coordinate system, in order to realize the picking of the three-dimensional model, a series of coordinate system transformations are required. In order to realize the corresponding coordinate conversion, you first need to understand the process of computer model conversion. The general process is shown in Figure9.Figure 9
Model transformation process.Projection transformation is divided into orthogonal projection transformation and perspective projection transformation: orthogonal projection transformation uses a rectangular parallelepiped to project and cut the model, so regardless of the distance between the model and the projection surface, the size of the model projection will always remain the same, with perspective projection. The transformation uses a frustum to project the model. The closer the model is to the projection surface, the larger the model projection is. This projection method is more in line with our habit of observing objects. The process of viewport transformation mainly moves the image of the projection surface to a suitable position of the screen window for display. Generally, the image and the origin of the window are located. After the above several model transformation processes, the 3D model is transformed from the world coordinate system to the screen coordinate system. Figure10 shows the projection transformation diagram.Figure 10
Projection transformation.


### 2.6.2. The Principle of 3D Model Pickup

In order to select the vertices of the 3D model surface from the screen, you first need to introduce a ray from the screen. The ray direction is the direction from the viewpoint to the selected point on the screen. The intersection of the ray and the model surface closest to the viewpoint is the picked model surface vertex; the general principle is shown in Figure11.Figure 11
Three-dimensional model picking principle.Through the understanding of the picking principle, we can know that the ray P1P2 and the model intersect at the point P0. In order to obtain the three-dimensional space coordinates of the vertex P0, the coordinates of the ray P1 and P2 in the three-dimensional space need to be determined first, where P1 and P2 are the rays, respectively, with the intersection point with the near plane (z = 0) and far plane (z = 1) of the projection frustum. It can be seen from the previous section that the conversion of 3D model world coordinates to screen coordinates requires model view transformation, projection transformation, and viewport transformation. Obviously, the conversion from screen coordinates to world coordinates only needs to be reversed in the reverse process. Assuming that the model view transformation matrix is V, the projection transformation matrix is P, and the viewport transformation matrix is W, the transformation matrix M from the screen coordinate system to the world coordinate system is(18)M=W−1∗P−1∗V−1.From (18), the coordinates of P1 and P2 in the three-dimensional world coordinate system can be determined, thereby determining the ray in the world coordinate system. Next, it is necessary to determine the intersection of the ray and the three-dimensional model. The three-dimensional mesh model is generally composed of triangles, so to determine whether the ray intersects the model, only the intersection of the ray and the triangle on the surface of the model is judged. Assuming that the three vertices of the triangle are v1, v2, and v3, the coordinates of any point in the triangle can be obtained as(19)v0=v1+u∗v2−v1+v∗v3−v1.In formulas (4)-(9), the point v0 is determined by variables u and v, where 0<u < 1, 0<v < 1, and 0<u + v < 1. Assuming that the coordinates of P1 and P2 are, respectively, Vp1 and Vp2, the coordinates of any point on the ray P1P2 can be obtained as(20)v0=vp1+vp2−vp1∗L.Figure12 is an effect diagram of the realization of three-dimensional model picking.Figure 12
Realization of 3D model picking.


## 2.6.1. Introduction to 3D Model Picking

In order to realize the measurement function of the 3D model, such as the distance between any two points on the model surface, it is necessary to obtain the vertex coordinates selected on the model surface through interaction. This process is called the picking of the 3D model. Since the three-dimensional model displayed on the computer screen is obtained by the computer through a series of model transformations and has no direct relationship with the screen coordinate system, in order to realize the picking of the three-dimensional model, a series of coordinate system transformations are required. In order to realize the corresponding coordinate conversion, you first need to understand the process of computer model conversion. The general process is shown in Figure9.Figure 9
Model transformation process.Projection transformation is divided into orthogonal projection transformation and perspective projection transformation: orthogonal projection transformation uses a rectangular parallelepiped to project and cut the model, so regardless of the distance between the model and the projection surface, the size of the model projection will always remain the same, with perspective projection. The transformation uses a frustum to project the model. The closer the model is to the projection surface, the larger the model projection is. This projection method is more in line with our habit of observing objects. The process of viewport transformation mainly moves the image of the projection surface to a suitable position of the screen window for display. Generally, the image and the origin of the window are located. After the above several model transformation processes, the 3D model is transformed from the world coordinate system to the screen coordinate system. Figure10 shows the projection transformation diagram.Figure 10
Projection transformation.


## 2.6.2. The Principle of 3D Model Pickup

In order to select the vertices of the 3D model surface from the screen, you first need to introduce a ray from the screen. The ray direction is the direction from the viewpoint to the selected point on the screen. The intersection of the ray and the model surface closest to the viewpoint is the picked model surface vertex; the general principle is shown in Figure11.Figure 11
Three-dimensional model picking principle.Through the understanding of the picking principle, we can know that the ray P1P2 and the model intersect at the point P0. In order to obtain the three-dimensional space coordinates of the vertex P0, the coordinates of the ray P1 and P2 in the three-dimensional space need to be determined first, where P1 and P2 are the rays, respectively, with the intersection point with the near plane (z = 0) and far plane (z = 1) of the projection frustum. It can be seen from the previous section that the conversion of 3D model world coordinates to screen coordinates requires model view transformation, projection transformation, and viewport transformation. Obviously, the conversion from screen coordinates to world coordinates only needs to be reversed in the reverse process. Assuming that the model view transformation matrix is V, the projection transformation matrix is P, and the viewport transformation matrix is W, the transformation matrix M from the screen coordinate system to the world coordinate system is(18)M=W−1∗P−1∗V−1.From (18), the coordinates of P1 and P2 in the three-dimensional world coordinate system can be determined, thereby determining the ray in the world coordinate system. Next, it is necessary to determine the intersection of the ray and the three-dimensional model. The three-dimensional mesh model is generally composed of triangles, so to determine whether the ray intersects the model, only the intersection of the ray and the triangle on the surface of the model is judged. Assuming that the three vertices of the triangle are v1, v2, and v3, the coordinates of any point in the triangle can be obtained as(19)v0=v1+u∗v2−v1+v∗v3−v1.In formulas (4)-(9), the point v0 is determined by variables u and v, where 0<u < 1, 0<v < 1, and 0<u + v < 1. Assuming that the coordinates of P1 and P2 are, respectively, Vp1 and Vp2, the coordinates of any point on the ray P1P2 can be obtained as(20)v0=vp1+vp2−vp1∗L.Figure12 is an effect diagram of the realization of three-dimensional model picking.Figure 12
Realization of 3D model picking.


## 2.7. User Association

The goal of the user association problem is to associate users with RRH that can provide better channel quality. First, the wideband SINR associated with the userki and RRHl is defined as follows:(21)ψk,lt=plmaxhki,lt2∑s∈τ\lpsmaxhki,st2.Among them,ψk,lt is the wideband signal-to-interference and noise ratio associated with RRH l of time slot user ki and hki,lt is the channel gain between ki and RRH l of time slot t user. In this paper, the user association problem is modeled as the problem of maximizing the sum of the broadband signal-to-interference and noise ratio of all users:(22)maxakijt∑l∈τ∑ki∈Ukakj,jtψki,jt,(23)s.t.∑b∈β∑ki∈Uaki,jtRkimin≤Cl,max,∀l∈τ,(24)∑l∈τakllt=1,∀ki∈U,(25)aki,lt=1,∀ki∈U.Formula (23) indicates that the fronthaul link capacity on the RRH can carry at least the minimum data rate required by the user associated with it. Formula (24) indicates that a user can only be associated with one RRH, and formula (25) indicates that the correlation factor is a binary variable.This problem is a 0–1 multiple knapsack problem. The core idea of this method is that the user is associated with the RRH whose remaining fronthaul capacity can accommodate the user and can provide the maximum bandwidth SINR. First, calculate the bandwidth SINR associated with all RRHs for each user in all slices. Then, if the condition of formula (23) is satisfied, the user will select the RRH association that can provide the maximum bandwidth SINR. The RRH association that provides the next largest bandwidth SINR is selected.


## 3. Display Design and Test of Ming-Style Furniture

### 3.1. Furniture Model Making

In order to show more Ming furniture models, this project also allows users to interact smoothly when using software. There needs to be certain restrictions on the surface of Ming furniture.For furniture models, because the Unreal Engine can only support models with less than and equal to four sides, faces with more than four sides must not be used. Therefore, polygons larger than four sides must be connected to the line segments to change the model into a quadrilateral or triangle. This step requires patience. Although the number of edges and faces of low-mode is much less than that of high-mode, in most cases, the number of edges and faces of low-mode is also a lot. During the connection process, the possibility of omissions is very high. It is large, so it must be carefully and regularly inspected.The requirement of high-modulus wiring is to keep the number of faces of the model as four side faces as much as possible and avoid the appearance of three corners as much as possible. In the low-modulus production of virtual reality scenes, three corners can be used in large quantities. The point is to reduce the number of faces, so three corner faces are a very good choice. Second, the number of faces of the low model needs to be optimized. The method is to minimize the number of parts that are not related to the outer contour of the model and use the number of faces to the part that has the greatest influence on the outer contour. In order to save the number of faces of the model, it is necessary to remove the lines in the middle that do not have a great influence on the contour of the model, so as to produce triangular faces, so that the number of faces of the model can be reduced.The number of low-film surfaces of a complex furniture should be limited to the range of 12000–15000. The model produced is more detailed. If more surfaces are needed, it is best to try not to exceed 20,000.Through the research of the furniture plan, modeling is carried out according to the standard furniture model size. The modeling of the mortise and tenon joint needs to be decomposed and assembled according to the model of the tenon and tenon joint. After modeling, use the motion curve to set the key frame to make the animation effect of the tenon and tenon motion. There are two key points in the production of animation. The first is the total time from the beginning to the end of the tenon and tenon animation. In order to allow users to see the structure of the tenon and tenon joints and not to make the user feel bored, the animation time of the tenon and tenon joints is set to 3 seconds. The second is the visual experience of mortise and tenon disassembly animation. When the tenon-and-mortise structure is opened and closed, the movement speed of the wooden block is an animation with a buffer effect from slow to fast and then to slow. This animation effect makes the joint of the tenon and tenon joint look more natural and comfortable. The combined buffer time also allows users time to see the structure of the tenon and tenon joint.


### 3.2. Test Procedure

In the process of 3D furniture modeling, a set of vrml format model files exported by 3DMax is not optimized, and viewpoint information is not added. In the browsing interface, you can see that the user is too close to the objects in the virtual scene. 3DMax: After the viewpoint information is exported to a vrml format file, when browsing the vrml format file, the scene is completely dark in the initial state. Figure13 is the 3D system modeling structure design.Figure 13
System structure design.In the process of 3D furniture modeling, a group of 3DMax exported vrml format model files are optimized, but only a single viewpoint information is added. When browsing, you can find that because there is only one viewpoint, all viewpoints cannot be switched. Looking at the model from a different angle, it needs to be continuously dragged to judge the light effect.In the process of 3D furniture modeling, optimize a set of vrml format model files exported by 3DMax, and establish multiple viewpoint information from different angles. When browsing, the viewpoints that can be switched are very large. You can click and select quickly. It is very convenient to switch viewpoints to quickly view model information from multiple directions and angles.


### 3.3. Establishment of an Evaluation Index System

After determining the evaluation object, collect the evaluation indicators, and use reasonable methods to screen and classify the evaluation indicators to construct an evaluation indicator model. The selection of evaluation indicators largely affects the scientific rationality of the evaluation results. Therefore, in the early collection process, as many related words as possible that reflect the product’s perceptual characteristics and experience feelings should be collected as much as possible [29].


### 3.4. Collection of Evaluation Indicators

The collection of evaluation indicators is carried out with the help of perceptual vocabulary classification, which is to use the hierarchical inference method to build a tree-like analysis chart and gradually refine the details. The collection process can be based on the immersive experience of the product use environment, using the method of questioning, ask questions to the evaluators, through the evaluators to experience the product use environment, conduct full discussions, and obtain analysis diagrams. First of all, use adjectives to express product strategy and market positioning, which is called zero-time perceptual. Then the 0-time sensibility is discussed in layers, and the first, second, and even N-time sensitivities are obtained, and each design element of the product can be clarified.


## 3.1. Furniture Model Making

In order to show more Ming furniture models, this project also allows users to interact smoothly when using software. There needs to be certain restrictions on the surface of Ming furniture.For furniture models, because the Unreal Engine can only support models with less than and equal to four sides, faces with more than four sides must not be used. Therefore, polygons larger than four sides must be connected to the line segments to change the model into a quadrilateral or triangle. This step requires patience. Although the number of edges and faces of low-mode is much less than that of high-mode, in most cases, the number of edges and faces of low-mode is also a lot. During the connection process, the possibility of omissions is very high. It is large, so it must be carefully and regularly inspected.The requirement of high-modulus wiring is to keep the number of faces of the model as four side faces as much as possible and avoid the appearance of three corners as much as possible. In the low-modulus production of virtual reality scenes, three corners can be used in large quantities. The point is to reduce the number of faces, so three corner faces are a very good choice. Second, the number of faces of the low model needs to be optimized. The method is to minimize the number of parts that are not related to the outer contour of the model and use the number of faces to the part that has the greatest influence on the outer contour. In order to save the number of faces of the model, it is necessary to remove the lines in the middle that do not have a great influence on the contour of the model, so as to produce triangular faces, so that the number of faces of the model can be reduced.The number of low-film surfaces of a complex furniture should be limited to the range of 12000–15000. The model produced is more detailed. If more surfaces are needed, it is best to try not to exceed 20,000.Through the research of the furniture plan, modeling is carried out according to the standard furniture model size. The modeling of the mortise and tenon joint needs to be decomposed and assembled according to the model of the tenon and tenon joint. After modeling, use the motion curve to set the key frame to make the animation effect of the tenon and tenon motion. There are two key points in the production of animation. The first is the total time from the beginning to the end of the tenon and tenon animation. In order to allow users to see the structure of the tenon and tenon joints and not to make the user feel bored, the animation time of the tenon and tenon joints is set to 3 seconds. The second is the visual experience of mortise and tenon disassembly animation. When the tenon-and-mortise structure is opened and closed, the movement speed of the wooden block is an animation with a buffer effect from slow to fast and then to slow. This animation effect makes the joint of the tenon and tenon joint look more natural and comfortable. The combined buffer time also allows users time to see the structure of the tenon and tenon joint.


## 3.2. Test Procedure

In the process of 3D furniture modeling, a set of vrml format model files exported by 3DMax is not optimized, and viewpoint information is not added. In the browsing interface, you can see that the user is too close to the objects in the virtual scene. 3DMax: After the viewpoint information is exported to a vrml format file, when browsing the vrml format file, the scene is completely dark in the initial state. Figure13 is the 3D system modeling structure design.Figure 13
System structure design.In the process of 3D furniture modeling, a group of 3DMax exported vrml format model files are optimized, but only a single viewpoint information is added. When browsing, you can find that because there is only one viewpoint, all viewpoints cannot be switched. Looking at the model from a different angle, it needs to be continuously dragged to judge the light effect.In the process of 3D furniture modeling, optimize a set of vrml format model files exported by 3DMax, and establish multiple viewpoint information from different angles. When browsing, the viewpoints that can be switched are very large. You can click and select quickly. It is very convenient to switch viewpoints to quickly view model information from multiple directions and angles.


## 3.3. Establishment of an Evaluation Index System

After determining the evaluation object, collect the evaluation indicators, and use reasonable methods to screen and classify the evaluation indicators to construct an evaluation indicator model. The selection of evaluation indicators largely affects the scientific rationality of the evaluation results. Therefore, in the early collection process, as many related words as possible that reflect the product’s perceptual characteristics and experience feelings should be collected as much as possible [29].


## 3.4. Collection of Evaluation Indicators

The collection of evaluation indicators is carried out with the help of perceptual vocabulary classification, which is to use the hierarchical inference method to build a tree-like analysis chart and gradually refine the details. The collection process can be based on the immersive experience of the product use environment, using the method of questioning, ask questions to the evaluators, through the evaluators to experience the product use environment, conduct full discussions, and obtain analysis diagrams. First of all, use adjectives to express product strategy and market positioning, which is called zero-time perceptual. Then the 0-time sensibility is discussed in layers, and the first, second, and even N-time sensitivities are obtained, and each design element of the product can be clarified.


## 4. Analysis of Ming-Style Furniture Display Design

According to the research on the market, a statistical table of the scale of the VR virtual reality market in a certain province in China is obtained, as shown in Table1.Table 1
Data of VR market scale in a certain province.
20142015201620172018Number of companies156175186198256Total market1.51.92.53.54.6Shown in Figure14 and 15 are the statistics of China’s virtual reality market scale as well as the 2016–2021 China VR offline experience hall market scale and growth rate statistics table. Since 2015, China’s VR market has made initial development. Although the value is only 1.532 billion yuan, the development momentum is rapid. By 2016, it showed a rapid development trend, and the market value jumped to 6.74 billion yuan. The fast-growing value shows the degree of domestic emphasis on the VR industry. The domestic market size in 2017 will reach 15.07 billion yuan, and by 2020 this figure will reach 91.874 billion yuan. This forecast data indicates that VR in our country will be in a state of comprehensive development, and it will be deeply applied to various industries [30, 31]. Similarly, the market scale and value of China’s VR offline experience pavilions have also maintained a trend of increasing year by year. By 2021, the market size of the VR offline experience pavilions will reach 5.25 billion yuan. It can be seen that, in the future, virtual reality technology has a very bright prospect in our country, from both the scale of development and the offline experience market.Figure 14
The scale of China’s VR virtual reality market.Figure 15
VR offline experience hall market scale and growth rate.


### 4.1. User Evaluation Analysis

After the Ming-style furniture display project was completed, user evaluation was conducted. After experiencing the virtual display of Ming-style furniture, users will score it and take the average to get an evaluation opinion on the entire display design. Usually “excellent,” “good,” “poor,” and “very poor” are used as the standard. As shown in Table2, the schemes with the level of “excellent” meet the needs and experience of users in general, while the level is “good,” it means that the user’s experience is basically satisfied, and then some dissatisfaction points are modified. The schemes that are classified as “medium,” “poor,” or “very bad” must be revised and scored again. Through this intuitive scoring method, you can discover the specific problems in the virtual display design and communicate with users to better improve and modify the design.Table 2
Evaluation criteria.
Points1–1920–2930–3738–4445–50Evaluation resultsVery badPoorMiddleGoodExcellentAccording to the user’s score, the evaluation opinions of the user using the virtual reality environment to operate the Ming-style furniture display system can be calculated. The total score of the survey is 850 points, of which the immersion score is 341 points, the realism score is 285 points, the visual beauty and comfort score is 253 points, and the final average score is 43.7 points, and the grade is in the “good” range. Basically to satisfy the user experience, you only need to modify the partial dissatisfaction. According to the user’s rating results, several local dissatisfaction places such as the lighting position of the scene and the materials of the space furnishings were modified to improve user satisfaction. Figure16 is a survey of domestic users’ satisfaction with VR virtual reality equipment.Figure 16
User’s evaluation of VR virtual reality equipment.


### 4.2. Tolerance Analysis of the Head-Mounted Display Optical System

According to the current level of optical processing technology and visual optical system assembly and adjustment, the tolerance of the center curvature radius should be less than 0.01 mm, the center thickness tolerance should be less than 0.05 mm, the component tilt tolerance should be less than 0.02°, the component eccentricity tolerance should be less than 0.02 mm, and the component spacing tolerance should be less than 0.05 mm.As shown in Table3, the three-chip HMD optical system processed by tolerance analysis has a 90% probability that the average geometric MTF value of the full field of view is higher than 0.36342571 at 8.13 lp/mm, and 80% is higher than 0.36487221. The probability of higher than 0.37792419 is 50%, the probability of higher than 0.39847215 is 20%, and the probability of higher than 0.42187924 is 10%, which meets the requirement of MTF drop not exceeding 30% after tolerance analysis.Table 3
Probability of reaching different geometric mean MTF values of full field of view at 8.15 lp/mm after tolerance analysis.
Probability (%)MTF value900.36342571800.36487221500.37792419200.39847215100.42187924


### 4.3. Comparative Analysis of Robustness

In the process of walking along the positive direction ofX-axis, when walking to a fixed position, it suddenly accelerates back and forth. After many repeated experiments, for the same period of walking, the visual positioning method based on logo and the method in this paper were used to conduct experiments. As shown in Figure 17, the solid line represents the X-axis coordinate change, the dashed line represents the Y-axis coordinate change, and the dotted line represents the z-axis coordinate change [32, 33]. It can be seen from the data in the figure that when the number of samples is less than 200, the visual positioning method based on the mark and the positioning result of this method are basically the same [34, 35], reflecting that the user’s movement trajectory is walking along the positive X-axis. After more than 200 sampling times, the visual positioning method based on the logo began to show that the three-axis coordinates of the sampling points were all 0 for a long period of time, and the algorithm in this paper was between 200 and 300 sampling points, and the user’s X-axis coordinate moved back. The reflected user behavior may be the user’s sudden shaking, which is exactly the user’s behavior during the experiment.Figure 17
Comparison of robustness experiment results.As shown in Figure18, the single frame time-consuming positioning method in this paper is not much different from the logo-based visual positioning method, because the part of the visual positioning failure only accounts for a small part of the entire user movement process, while the accelerometer’s refresh speed is very fast (up to 800 HZ), and the increase in time consumption is mainly due to the calculation process of the acceleration integration algorithm, so the time consumption of a single frame does not increase much, which can fully satisfy the user’s immersive experience.Figure 18
Time-consuming comparison of single frame positioning methods in this paper for different walking distances.


## 4.1. User Evaluation Analysis

After the Ming-style furniture display project was completed, user evaluation was conducted. After experiencing the virtual display of Ming-style furniture, users will score it and take the average to get an evaluation opinion on the entire display design. Usually “excellent,” “good,” “poor,” and “very poor” are used as the standard. As shown in Table2, the schemes with the level of “excellent” meet the needs and experience of users in general, while the level is “good,” it means that the user’s experience is basically satisfied, and then some dissatisfaction points are modified. The schemes that are classified as “medium,” “poor,” or “very bad” must be revised and scored again. Through this intuitive scoring method, you can discover the specific problems in the virtual display design and communicate with users to better improve and modify the design.Table 2
Evaluation criteria.
Points1–1920–2930–3738–4445–50Evaluation resultsVery badPoorMiddleGoodExcellentAccording to the user’s score, the evaluation opinions of the user using the virtual reality environment to operate the Ming-style furniture display system can be calculated. The total score of the survey is 850 points, of which the immersion score is 341 points, the realism score is 285 points, the visual beauty and comfort score is 253 points, and the final average score is 43.7 points, and the grade is in the “good” range. Basically to satisfy the user experience, you only need to modify the partial dissatisfaction. According to the user’s rating results, several local dissatisfaction places such as the lighting position of the scene and the materials of the space furnishings were modified to improve user satisfaction. Figure16 is a survey of domestic users’ satisfaction with VR virtual reality equipment.Figure 16
User’s evaluation of VR virtual reality equipment.


## 4.2. Tolerance Analysis of the Head-Mounted Display Optical System

According to the current level of optical processing technology and visual optical system assembly and adjustment, the tolerance of the center curvature radius should be less than 0.01 mm, the center thickness tolerance should be less than 0.05 mm, the component tilt tolerance should be less than 0.02°, the component eccentricity tolerance should be less than 0.02 mm, and the component spacing tolerance should be less than 0.05 mm.As shown in Table3, the three-chip HMD optical system processed by tolerance analysis has a 90% probability that the average geometric MTF value of the full field of view is higher than 0.36342571 at 8.13 lp/mm, and 80% is higher than 0.36487221. The probability of higher than 0.37792419 is 50%, the probability of higher than 0.39847215 is 20%, and the probability of higher than 0.42187924 is 10%, which meets the requirement of MTF drop not exceeding 30% after tolerance analysis.Table 3
Probability of reaching different geometric mean MTF values of full field of view at 8.15 lp/mm after tolerance analysis.
Probability (%)MTF value900.36342571800.36487221500.37792419200.39847215100.42187924


## 4.3. Comparative Analysis of Robustness

In the process of walking along the positive direction ofX-axis, when walking to a fixed position, it suddenly accelerates back and forth. After many repeated experiments, for the same period of walking, the visual positioning method based on logo and the method in this paper were used to conduct experiments. As shown in Figure 17, the solid line represents the X-axis coordinate change, the dashed line represents the Y-axis coordinate change, and the dotted line represents the z-axis coordinate change [32, 33]. It can be seen from the data in the figure that when the number of samples is less than 200, the visual positioning method based on the mark and the positioning result of this method are basically the same [34, 35], reflecting that the user’s movement trajectory is walking along the positive X-axis. After more than 200 sampling times, the visual positioning method based on the logo began to show that the three-axis coordinates of the sampling points were all 0 for a long period of time, and the algorithm in this paper was between 200 and 300 sampling points, and the user’s X-axis coordinate moved back. The reflected user behavior may be the user’s sudden shaking, which is exactly the user’s behavior during the experiment.Figure 17
Comparison of robustness experiment results.As shown in Figure18, the single frame time-consuming positioning method in this paper is not much different from the logo-based visual positioning method, because the part of the visual positioning failure only accounts for a small part of the entire user movement process, while the accelerometer’s refresh speed is very fast (up to 800 HZ), and the increase in time consumption is mainly due to the calculation process of the acceleration integration algorithm, so the time consumption of a single frame does not increase much, which can fully satisfy the user’s immersive experience.Figure 18
Time-consuming comparison of single frame positioning methods in this paper for different walking distances.


## 5. Conclusions

According to the characteristics of the furniture product three-dimensional display system, this paper puts forward a set of design and development plan of the furniture product three-dimensional display system by integrating the advantages of related technologies. This paper analyzes the relationship between the various links of the three-dimensional display system, establishes the structure, function, and specific development methods of the three-dimensional display system, and makes a more comprehensive overall design for the three-dimensional display system of furniture products. The production of a furniture product three-dimensional display system was realized through the arrangement of the scene 3D modeling method, interface interaction realization technology, and image processing technology, and the original idea of the design was verified through testing.New virtual and real interaction mode: This paper mainly studies the interaction of virtual and real displacement, and the movement of the virtual space is synchronously controlled through the movement of the user in the real space, so that the user has a stronger sense of presence. Of course, in addition to displacement interaction, there are many other interaction methods in virtual reality that are worth continuing to study in the future, such as gesture interaction, eyeball interaction, etc. We hope that more virtual and real interaction methods can be tried to achieve a more efficient and free immersive virtual reality system.According to the specific needs of the system model, this paper chooses the 3D transformation modeling method of 2D graphics. In order to make the model material map better reflect the reality of the real object furniture, a method of using on-site photos taken and processed bitmap as the texture is proposed. At the same time, in order to optimize the model and improve the system operation speed, a two-dimensional image texture mapping method is proposed to achieve purpose of model simplification.



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*Source: 1553296-2022-03-23.xml*