# 3D Design Platform of Virtual National Costume Based on Digital Nonlinear Random Matrix

Authors: Mingyan Zhang; Luolan Shen
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The traditional two-dimensional clothing CAD system is more and more difficult to meet the needs of the three-dimensional design of virtual national clothing products. Based on the digital nonlinear random matrix theory, this paper constructs a three-dimensional design platform for virtual ethnic clothing and proposes a weighted graph tree representation method for the deviation transfer process of nonlinear ethnic clothing. The model first analyzes the business links and information related to the deviation transfer modeling of ethnic clothing and establishes a hierarchical relationship tree, a method of expressing the order of ethnic clothing, and a method of expressing deviation. The weighted graph tree model and construction rules of the deviation transmission process realize the integrated expression of the deviation transmission information of ethnic clothing and solve the nonlinear problem in the transmission of ethnic clothing deviation. During the simulation process, the article uses the three-dimensional geometric modeling tool POSER to establish a standard entry model, edit it in 3DS MAX and export the file, read it, and parameterize it through programming, and realize the drawing of the three-dimensional avatar model based on OpenGL. The experimental results show that the parametric avatar model established by the system is accurate and realistic and can quickly convert the 3D style to the N-dimensional pattern.


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## Body

## 1. Introduction

With the rapid development of science and technology and the advent of the digital age, the study of nonlinear related problems has become the focus of various disciplines [1]. People gradually realize the complex and nonlinear nature of the world, and the social economy and life structure begin to change to diversification and networking [2]. Nowadays, nonlinear science and digital technology have been widely studied and applied in the field of ethnic clothing. Under its influence, ethnic clothing modeling presents an uncertain, complex, and dynamic nonlinear development trend and is more and more elegant. The flexible, flowing, and soft space modeling is presented in front of people’s eyes [3]. The designer’s design thinking has changed, prompting them to observe the world from a macro and micro-perspective at the same time, combining the nonlinear scientific thinking mode with modern digital technology to provide a new design angle for ethnic clothing modeling. The performance is more diverse [4–6].However, the traditional 2D clothing CAD system has been difficult to meet the needs of enterprise product development, and enterprises urgently need a more convenient, efficient, and brand-new 3D clothing design system as a design tool [7]. Digital national costume coordination represents the development direction of national costume coordination technology, which is of great significance for improving the accuracy and success rate of national costumes, shortening the development cycle, and reducing production costs [8]. At present, the region has a relatively extensive understanding of the basic principles and system composition of digital national costume coordination technology, but it is still necessary to understand and master the basic theories such as deviation transfer modeling, analysis, and tolerance allocation in digital national costume coordination [9]. It is not conducive to the in-depth application of digital national clothing coordination technology and the full play of its efficacy [10]. The system builds a parametric 3D mannequin model on the website. After the user selects the 2D clothing, the system will automatically sew the 2D clothing pieces to the established 3D model, allowing the user to predict the wearing effect of the clothing [11–13].Aiming at the identification of key product characteristics (ethnic clothing), this paper establishes an extended derivation matching constraint graph, and based on this, a search method for alternative characteristics of ethnic clothing is proposed; the Taguchi quality loss theory is introduced, and a method for evaluating the influence of alternative characteristics of ethnic clothing is proposed, and the identification of ethnic clothing according to the relative size of the influence degree of the alternative characteristics of ethnic clothing is completed. For distant objects and the entire large scene system, using a single texture instead, the rendering speed is much faster than rendering hundreds or even thousands of polygon models. Based on this, the algorithm flow of digital nonlinear random matrix inference recognition is proposed. The above method overcomes the shortcomings of the existing key feature identification methods that rely on engineering experience and the related process knowledge is not easy to express. Based on the existing research results of nonlinear science and the theoretical methods of digital design, the thesis summarizes and discusses the nonlinear characteristics and digital logic thinking of ethnic clothing modeling and analyzes the ethnic clothing conditions of ethnic clothing modeling using nonlinear digital design, space attributes, and technical support, then summarizes the generation mechanism of ethnic clothing modeling of nonlinear digital design, and analyzes its specific implementation through case studies.


## 2. Related Work

As a new type of functional material that can perceive external stimuli, judge, and appropriately process and can perform itself, smart materials have sensing functions, response functions, and self-control functions. It combines the functions of traditional structural materials and functional materials, there is no longer a clear distinction between them, and the functionalization of the structure and the diversification of functions are realized [14]. The characteristics of artificial intelligence contained in smart materials are consistent with the concept of parametric integration of internal relations of objects and self-adaptation of national clothing [15]. With the in-depth research of scholars, intelligent materials will be used by designers in national costume modeling through digital construction. At present, smart materials can be roughly divided into two categories: embedded smart materials and autonomous smart materials [16].Rallis et al. [17] used the Tolerance Specification Language (TSL) to describe the tolerance and realized the formalization of the drift model. Bhatnagar et al. [18] interpreted tolerance as a parameter of a series of point vectors on a geometric model and proposed a vector tolerance expression model, in which points on the model have deviations and are constrained by tolerances. Li et al. [19] further normalized the above idea, defined the mutually independent geometric variables as the basic vector of the vector space, and gave the tolerance model based on the feasible tolerance region and the feasible vector space tolerance model on the basis of the variable solid modeling [20]. The deviation surface model is proposed to simulate the actual surface of the 3D mapping and display it in the 3D environment, and its essence is the extension of the vector model. The concept of T-MAP is further proposed, which “maps” all variations of the feature surface or its derived features within the tolerance domain with the volume of the assumed point set. Cheng et al. [21] proposed a Small Displacement Torsor (SDT) method that maps the tolerance zone into 6 screws and studied the three-dimensional tolerance analysis and design method on this basis.Many scholars have also conducted research on the tolerance expression model. Scholars have studied the national clothing tolerance modeling method based on feature change, which belongs to the degree of freedom model. It is proposed to introduce the SDT into the tolerance mathematical modeling and systematically study the position degree of the shaft’s hole feature. Different constraints of tolerance under MMR and LMR conditions and the corresponding position tolerance model are given [22]. Starting from the difficulty of solving the parameters in the SDT model, scholars proposed a method for solving the cylindricity tolerance model based on the combination of Monte Carlo and the response surface method [23]. Other researchers proposed a contour expression and analysis method based on integral mapping and extended the traditional dimensional chain model [24].


## 3. Construction of 3D Design Model of Virtual National Costume Based on Digital Nonlinear Random Matrix

### 3.1. Digital Hierarchy Distribution

In the digital nonlinear random matrix, it is determined whether optimization is needed according to the optimization conditions. The optimization conditions are set as follows: the sum of two interior angles opposite to the common side is greater than 1800 (it can be proved that only this condition can satisfy the Delaunay digital nonlinear random matrix characteristics; this detailed proof is not provided), and then we need to exchange the diagonal, that is, replace the diagonal AC with BD, thus forming two new digital nonlinear random matrices; it may record the vertices of the two digital nonlinear random matrices at the same time indexing and adjacency digitized nonlinear random matrix indexing. There are as many control points in a curve as there are B-spline basis functions, each of which is a B-spline function of degreek. The elements of these support intervals together constitute the nodal order of the B-spline function. The B-spline function has some excellent geometric properties, which make it play a very important role in the modeling of Figure 1.Figure 1
Schematic diagram of the distribution of digital layers.The creator modeling tool has powerful polygon modeling capabilities. First, it uses its own geometry toolbox to cover the corresponding surface and volume modeling tools to generate models of different sizes such as triangular surfaces, rectangular surfaces, and round bars. Moreover, it can only obtain positive values when the value of the parameter is on and all other positions are zero. Therefore, the shape of the k-order B-spline curve at a certain point is only related to the relatedk control points and has nothing to do with other control points. The analytical method in the ethnic clothing tolerance optimization algorithm generally needs to obtain the gradient information of the objective function, and the solution efficiency is high, but when the nonlinear degree of the model is high, it is often difficult to solve; the genetic algorithm and other intelligent algorithms do not require gradient information, which is not suitable for it. There are no special requirements for the objective function, and it is suitable for complex ethnic costumes.


### 3.2. Nonlinear Stochastic Matrix Optimization

The nonlinear random matrix optimization condition summarizes the analysis of ethnic clothing deviation into two key problems: The transformation of matching constraints to positioning point constraints and the solution of the three-dimensional mapping positioning model; the theoretical method of positioning point selection is established with geometric stability as the evaluation index, and the surface calculation method of positioning point coupling deviation in surface fit constraint and hole-pin fit constraint establishes an approximate relationship between positioning point coupling deviation and 3D mapping pose deviation, which changes the process of ethnic clothing deviation analysis from “implicit” to “explicit,” and reduces the degree of nonlinearity, replaces random sampling in Monte Carlo method with low variance sequence sampling, and proposes a 3D mapping pose parameter statistical analysis method based on quasi-Monte Carlo (QMC) method:(1)α1α2α3αn=0−βtm−βt−1m−βt−nm,xi−1∪xi−t=αθtpi,t∪αθt−1pi,t−1αθtpi,t∪αθt−npi,t−n.When the nonlinear random matrix optimization modeling technology establishes the virtual three-dimensional space, the geometric modeling technology is used for the solid modeling of the virtual objects that require the user to perform real-time operation.It is necessary to realize the interaction between users and virtual objects in the scene, such as parts implementation of design and assembly. Geometric modeling in virtual reality includes geometric modeling of regular objects, geometric modeling of irregular objects, and geometric modeling of irregular fuzzy objects. It can not only meet the real-time requirements of browsing but also achieve real-time manipulation of physical objects and realize a friendly human-computer interaction environment.(2)mps,t−1,nps,t−1⟶Noneidexp−a−b−Noneidexpa+b,deltax,xt∩deltat,tx=1ℤdeltaa,deltab=1..The brightness, shadow intensity, and direction of solid objects generated under the illumination of the virtual light source should also exactly match the brightness, shadow intensity, and direction of pure virtual objects. In addition, this seamless connection between virtual and real must also satisfy real-time interactivity, that is, as the user’s perspective and position change, it must be able to immediately generate a new viewpoint national costume, and the operation of the entity object must be able to get immediate feedback.(3)dermgerx,tx−dermgert⊆dermgerxdermgert,x⊆t⟶gx,xt⊆gistxtgistx⊆gistt..The LOP function is also used very frequently in the Delaunay network, and each insertion of a point will cause the reconstruction of the surrounding digital nonlinear random matrix, including the update of the vertex index and the update of the topological relationship. The situation is quite complicated. In order to uniformly deal with various situations and improve the speed of local optimization, we design the following algorithm:(4)〈1+xtpx,t∈fx,t−1px,tpx−1,t∈1.In this data structure, the structure of the vertex is very simple, only need to record the seat cup, and its index number is the position of the vertex in the vertex array. Similarly, the index number of the digital nonlinear random matrix is the position of the digital nonlinear random matrix in the digital nonlinear random matrix array, and the topological relationship between Figure2 is clear through the noTriangle array.Figure 2
Data record distribution of nonlinear random matrix.Among them, the member functions ForwardRotate0 and BackRotate0 are used to ensure that various situations can be handled with a unified code (see the description of the LOP function below). We use MFC’s template class CArray to record vertex arrays and digitized nonlinear random matrix arrays. The outstanding features of i-id are easy to insert and delete, fast to search, and flexible to change in length. Obviously, these characteristics are very suitable for recording vertices and digitizing nonlinear random matrices during network construction.It can obtain the DEM data mining points in Figure3 and find the point with the largest distance from the plane where the digital nonlinear random matrix is located. If the distance from the point to the plane is greater than the specified resolution, insert the point into the triangle and carry out local optimization; otherwise, the digitized nonlinear random matrix is recorded as no need to continue inserting points, and the rectangle is divided into BLKNUM blocks (BI = 16 or other values), denoted as a two-dimensional array m, and each item of the array is an array to record the index numbers of all digital nonlinear random matrices intersecting with the block. For the sake of distinction, we call this block “virtual block” because it does not actually exist; it is only needed for algorithm optimization.(5)deltas2−t2,s2+t2=sigmods2+t2,s2+t2,s2−t2,s2−t2,deltas2+t2−1=gertdeltas+t,s+tdeltas2−t2−1=gertdeltas−t,s−t..Figure 3
Nonlinear random matrix optimization topology.When inserting each digital nonlinear random matrix, we obtain the minimum circumscribed rectangle of the digital nonlinear random matrix, obtain the virtual blocks contained in the circumscribed rectangle, and determine the positional relationship between each virtual block and the digital nonlinear random matrix. If one of them intersects, add the digitized nonlinear random matrix to the virtual block (add the index number of the digitized nonlinear random matrix to the one-dimensional array block).(6)∑s,ts<1,t<1gestts,txts,t−i∑txts,t∗j∑txts,t=1.The analytical method in the ethnic clothing tolerance optimization algorithm generally needs to find the gradient information of the objective function, and the solution efficiency is high. The growth and the increase in the number of iterations eventually bring the states of the various sensors into agreement. On the one hand, the proposed algorithm improves the information transfer efficiency between each sensor node, and on the other hand, it enables the cooperative work between sensor nodes to be completed efficiently. In the pretransformation stage, the two input data images are first transformed into two parallel view planes, and the corresponding points are on the same scan line.


### 3.3. Assignment of Virtual National Costume Elements

The digital nonlinear random matrix method depends on the process of ethnic clothing. The virtual ethnic clothing elements are generated in the process design links such as the division of ethnic clothing units, the planning of ethnic clothing sequences, the selection of positioning benchmarks, and the allocation of initial tolerances and are directly related.(7)k−lamdax−lamdaylamdai−xs,t−k″−lamdas+t=0,∑gxt,xt,xt,t−1=1−tix−jy∑pi−tix−jy−t..For the virtual scene modeling method based on the ethnic costumes in Figure4, the basic data come from the photos of ethnic costumes taken by cameras rather than the graphics generated by geometric modeling. Therefore, the processing of virtual scenes is completely different from the processing of general geometric scenes, and the focus of processing is changed from geometric drawing, texture, and lighting to the transformation of national costumes. At the same time, ethnic costumes are usually shot according to certain requirements and combined into virtual scenes according to certain rules.(8)hemiti,j=sini,j,i−j=h−1cosi,j,i−j=h+1,yt=1−xt1−xtxα+yβ+zμ=1−xt1−2x−yt..Figure 4
Element allocation of virtual national costumes.The virtual scene established by geometric modeling with the increase of the complexity of the environment will be difficult to meet the real-time performance required by virtual reality, and the phenomenon of surface jitter is easy to appear in the process of browsing the virtual scene. The method of establishing virtual objects in the virtual world through geometric modeling is usually suitable for situations where the complexity of the scene is not large, and it is necessary to realize the interaction between users and virtual objects in the scene, such as the realization of 3D mapping design and national clothing.In the filtering problem of a class of discrete time-varying systems with random uncertainty and channel fading in the finite time domain, the error dynamic system of the filter is guaranteed to be bounded by designing an appropriate filter structure and by solving the linear matrix inequality that results in the filter gain. Therefore, when there are too many elements in the scene constructed by this method, the frame speed will become very slow due to the large amount of calculation, which will affect the real-time response speed. Since the above methods have their own advantages and disadvantages, the system actually adopts comprehensive utilization: the criss-cross method is used for the distant trees, and the billboard method is used for the nearby ones.(9)sina−byx∩yt=RArgcosa−byx∪yt=∅,Sigmarx,x−1,x+1Sigmarx−1,x+1=1−fx2−fxx−fx.Although the ethnic costume elements are vertically aligned with gravity, horizontal and near-horizontal ethnic costume elements can only be formed when the fabric is stiff or stretched along the path of the ethnic costume elements. If user-placed pleats are on loose parts of the garment, there is no guarantee that they will generate horizontal ethnic clothing elements without significant changes to the style of the garment. However, if the garment is locally tight, we can improve the viability of the ethnic costume element by ensuring at least a weak stretch in the direction of the ethnic costume element.


### 3.4. Topological Deformation of 3D Design

In order to obtain the corresponding expansion amount of the 3D design topological clothing piece, we need to convert the expansion amount in the 3D clothing space to the 2D clothing piece through mapping. After the results are transferred to the GarmentStudio software simulation, the expected ethnic clothing elements can be formed on the three-dimensional clothing. First, we unify the 2D and 3D clothing triangular patches on thexy plane by rotation and set a unified coordinate system, so that the two digital nonlinear random matrices are both at the origin and have a given common edge u; the edge is aligned with the x-axis. In the simulation case, the intrinsic transformation matrix of each triangular patch is t. In addition to considering the stretch orthogonal and ethnic costume element orientation during initial drape, we also consider ethnic costume element feasibility.Each subsystem of the fractal geometry system has the same compositional characteristics as the upper-level system in terms of form, function, structure, space, and so on, which makes the systems at all levels in Figure5 have similarities, which is the self-similar feature of fractal geometry. Using self-similarity, modeling units at different levels are similar in shape and form a larger whole in a certain way, which can create complex graphic textures in spatial modeling. For the case of acting in the extended area, we hope that the shape of the place can be changed according to the designer’s design requirements.Figure 5
Superposition of digital nonlinear random matrix elements.The wrinkle design has strong limitations, and it is difficult to achieve a detailed design, such as the design of curved wrinkles. On the contrary, the hand-painted method is free to operate and can meet diverse design needs, but it is relatively cumbersome to draw. Therefore, in the process of use, we need to analyze specific problems and choose a method that is more suitable for the current situation. This requires us to add constraints to the grid in the region: any change in the normal vector must satisfy the direction of the orthogonal and path trajectory of Figure6.Figure 6
3D design normal vertex position topology.According to the characteristics of topological deformation and using corresponding digital technology, designers can perform virtual deformation according to various conditions, realize the form generation of continuous forms, form changes and flows of spatial modeling, and obtain experience at all levels. Under the guidance of topological thinking, even the irregular interior surface modeling can be pieced together into a continuous overall surface modeling by dividing the unit shape. Those distorted surface space shapes through continuous nonlinear deformation can be understood as the result of such operations and their own form deformations. We simulate the expanded 2D garment in an unconstrained simulator with no added synthetic forces, and the resulting structure should be similar to the final draped 3D garment. In order to make the generated results as close as possible to our expected 3D clothing model, we need to evaluate the generated results in a way that follows the evaluation method mentioned in Bartle’s schema update framework. Specifically, we measure the intrinsic difference between the target 3D clothing and the current simulated 3D clothing and update the pattern iteratively in a way that aims to minimize the difference of Figure7; we repeat the simulation and update steps until convergence.Figure 7
Attribute distribution of digital nonlinear random matrix.When constructing multiple objects with the same shape and the same properties, if the normal copy method is used, the number of polygons will be doubled for each additional object, while the instance technology can increase the number of similar objects without increasing the number of polygons. For example, in the virtual national costume element scene, there are many elements with the same structure, shape, and texture, and the difference between the elements is only in their position, size, and direction. The way to obtain the extension is to decompose the extension into two components that are easy to obtain—the extension direction and the extension size. Before the expansion size is calculated, we need to determine the expansion area, and the determination of the expansion area depends on the expansion size.


## 3.1. Digital Hierarchy Distribution

In the digital nonlinear random matrix, it is determined whether optimization is needed according to the optimization conditions. The optimization conditions are set as follows: the sum of two interior angles opposite to the common side is greater than 1800 (it can be proved that only this condition can satisfy the Delaunay digital nonlinear random matrix characteristics; this detailed proof is not provided), and then we need to exchange the diagonal, that is, replace the diagonal AC with BD, thus forming two new digital nonlinear random matrices; it may record the vertices of the two digital nonlinear random matrices at the same time indexing and adjacency digitized nonlinear random matrix indexing. There are as many control points in a curve as there are B-spline basis functions, each of which is a B-spline function of degreek. The elements of these support intervals together constitute the nodal order of the B-spline function. The B-spline function has some excellent geometric properties, which make it play a very important role in the modeling of Figure 1.Figure 1
Schematic diagram of the distribution of digital layers.The creator modeling tool has powerful polygon modeling capabilities. First, it uses its own geometry toolbox to cover the corresponding surface and volume modeling tools to generate models of different sizes such as triangular surfaces, rectangular surfaces, and round bars. Moreover, it can only obtain positive values when the value of the parameter is on and all other positions are zero. Therefore, the shape of the k-order B-spline curve at a certain point is only related to the relatedk control points and has nothing to do with other control points. The analytical method in the ethnic clothing tolerance optimization algorithm generally needs to obtain the gradient information of the objective function, and the solution efficiency is high, but when the nonlinear degree of the model is high, it is often difficult to solve; the genetic algorithm and other intelligent algorithms do not require gradient information, which is not suitable for it. There are no special requirements for the objective function, and it is suitable for complex ethnic costumes.


## 3.2. Nonlinear Stochastic Matrix Optimization

The nonlinear random matrix optimization condition summarizes the analysis of ethnic clothing deviation into two key problems: The transformation of matching constraints to positioning point constraints and the solution of the three-dimensional mapping positioning model; the theoretical method of positioning point selection is established with geometric stability as the evaluation index, and the surface calculation method of positioning point coupling deviation in surface fit constraint and hole-pin fit constraint establishes an approximate relationship between positioning point coupling deviation and 3D mapping pose deviation, which changes the process of ethnic clothing deviation analysis from “implicit” to “explicit,” and reduces the degree of nonlinearity, replaces random sampling in Monte Carlo method with low variance sequence sampling, and proposes a 3D mapping pose parameter statistical analysis method based on quasi-Monte Carlo (QMC) method:(1)α1α2α3αn=0−βtm−βt−1m−βt−nm,xi−1∪xi−t=αθtpi,t∪αθt−1pi,t−1αθtpi,t∪αθt−npi,t−n.When the nonlinear random matrix optimization modeling technology establishes the virtual three-dimensional space, the geometric modeling technology is used for the solid modeling of the virtual objects that require the user to perform real-time operation.It is necessary to realize the interaction between users and virtual objects in the scene, such as parts implementation of design and assembly. Geometric modeling in virtual reality includes geometric modeling of regular objects, geometric modeling of irregular objects, and geometric modeling of irregular fuzzy objects. It can not only meet the real-time requirements of browsing but also achieve real-time manipulation of physical objects and realize a friendly human-computer interaction environment.(2)mps,t−1,nps,t−1⟶Noneidexp−a−b−Noneidexpa+b,deltax,xt∩deltat,tx=1ℤdeltaa,deltab=1..The brightness, shadow intensity, and direction of solid objects generated under the illumination of the virtual light source should also exactly match the brightness, shadow intensity, and direction of pure virtual objects. In addition, this seamless connection between virtual and real must also satisfy real-time interactivity, that is, as the user’s perspective and position change, it must be able to immediately generate a new viewpoint national costume, and the operation of the entity object must be able to get immediate feedback.(3)dermgerx,tx−dermgert⊆dermgerxdermgert,x⊆t⟶gx,xt⊆gistxtgistx⊆gistt..The LOP function is also used very frequently in the Delaunay network, and each insertion of a point will cause the reconstruction of the surrounding digital nonlinear random matrix, including the update of the vertex index and the update of the topological relationship. The situation is quite complicated. In order to uniformly deal with various situations and improve the speed of local optimization, we design the following algorithm:(4)〈1+xtpx,t∈fx,t−1px,tpx−1,t∈1.In this data structure, the structure of the vertex is very simple, only need to record the seat cup, and its index number is the position of the vertex in the vertex array. Similarly, the index number of the digital nonlinear random matrix is the position of the digital nonlinear random matrix in the digital nonlinear random matrix array, and the topological relationship between Figure2 is clear through the noTriangle array.Figure 2
Data record distribution of nonlinear random matrix.Among them, the member functions ForwardRotate0 and BackRotate0 are used to ensure that various situations can be handled with a unified code (see the description of the LOP function below). We use MFC’s template class CArray to record vertex arrays and digitized nonlinear random matrix arrays. The outstanding features of i-id are easy to insert and delete, fast to search, and flexible to change in length. Obviously, these characteristics are very suitable for recording vertices and digitizing nonlinear random matrices during network construction.It can obtain the DEM data mining points in Figure3 and find the point with the largest distance from the plane where the digital nonlinear random matrix is located. If the distance from the point to the plane is greater than the specified resolution, insert the point into the triangle and carry out local optimization; otherwise, the digitized nonlinear random matrix is recorded as no need to continue inserting points, and the rectangle is divided into BLKNUM blocks (BI = 16 or other values), denoted as a two-dimensional array m, and each item of the array is an array to record the index numbers of all digital nonlinear random matrices intersecting with the block. For the sake of distinction, we call this block “virtual block” because it does not actually exist; it is only needed for algorithm optimization.(5)deltas2−t2,s2+t2=sigmods2+t2,s2+t2,s2−t2,s2−t2,deltas2+t2−1=gertdeltas+t,s+tdeltas2−t2−1=gertdeltas−t,s−t..Figure 3
Nonlinear random matrix optimization topology.When inserting each digital nonlinear random matrix, we obtain the minimum circumscribed rectangle of the digital nonlinear random matrix, obtain the virtual blocks contained in the circumscribed rectangle, and determine the positional relationship between each virtual block and the digital nonlinear random matrix. If one of them intersects, add the digitized nonlinear random matrix to the virtual block (add the index number of the digitized nonlinear random matrix to the one-dimensional array block).(6)∑s,ts<1,t<1gestts,txts,t−i∑txts,t∗j∑txts,t=1.The analytical method in the ethnic clothing tolerance optimization algorithm generally needs to find the gradient information of the objective function, and the solution efficiency is high. The growth and the increase in the number of iterations eventually bring the states of the various sensors into agreement. On the one hand, the proposed algorithm improves the information transfer efficiency between each sensor node, and on the other hand, it enables the cooperative work between sensor nodes to be completed efficiently. In the pretransformation stage, the two input data images are first transformed into two parallel view planes, and the corresponding points are on the same scan line.


## 3.3. Assignment of Virtual National Costume Elements

The digital nonlinear random matrix method depends on the process of ethnic clothing. The virtual ethnic clothing elements are generated in the process design links such as the division of ethnic clothing units, the planning of ethnic clothing sequences, the selection of positioning benchmarks, and the allocation of initial tolerances and are directly related.(7)k−lamdax−lamdaylamdai−xs,t−k″−lamdas+t=0,∑gxt,xt,xt,t−1=1−tix−jy∑pi−tix−jy−t..For the virtual scene modeling method based on the ethnic costumes in Figure4, the basic data come from the photos of ethnic costumes taken by cameras rather than the graphics generated by geometric modeling. Therefore, the processing of virtual scenes is completely different from the processing of general geometric scenes, and the focus of processing is changed from geometric drawing, texture, and lighting to the transformation of national costumes. At the same time, ethnic costumes are usually shot according to certain requirements and combined into virtual scenes according to certain rules.(8)hemiti,j=sini,j,i−j=h−1cosi,j,i−j=h+1,yt=1−xt1−xtxα+yβ+zμ=1−xt1−2x−yt..Figure 4
Element allocation of virtual national costumes.The virtual scene established by geometric modeling with the increase of the complexity of the environment will be difficult to meet the real-time performance required by virtual reality, and the phenomenon of surface jitter is easy to appear in the process of browsing the virtual scene. The method of establishing virtual objects in the virtual world through geometric modeling is usually suitable for situations where the complexity of the scene is not large, and it is necessary to realize the interaction between users and virtual objects in the scene, such as the realization of 3D mapping design and national clothing.In the filtering problem of a class of discrete time-varying systems with random uncertainty and channel fading in the finite time domain, the error dynamic system of the filter is guaranteed to be bounded by designing an appropriate filter structure and by solving the linear matrix inequality that results in the filter gain. Therefore, when there are too many elements in the scene constructed by this method, the frame speed will become very slow due to the large amount of calculation, which will affect the real-time response speed. Since the above methods have their own advantages and disadvantages, the system actually adopts comprehensive utilization: the criss-cross method is used for the distant trees, and the billboard method is used for the nearby ones.(9)sina−byx∩yt=RArgcosa−byx∪yt=∅,Sigmarx,x−1,x+1Sigmarx−1,x+1=1−fx2−fxx−fx.Although the ethnic costume elements are vertically aligned with gravity, horizontal and near-horizontal ethnic costume elements can only be formed when the fabric is stiff or stretched along the path of the ethnic costume elements. If user-placed pleats are on loose parts of the garment, there is no guarantee that they will generate horizontal ethnic clothing elements without significant changes to the style of the garment. However, if the garment is locally tight, we can improve the viability of the ethnic costume element by ensuring at least a weak stretch in the direction of the ethnic costume element.


## 3.4. Topological Deformation of 3D Design

In order to obtain the corresponding expansion amount of the 3D design topological clothing piece, we need to convert the expansion amount in the 3D clothing space to the 2D clothing piece through mapping. After the results are transferred to the GarmentStudio software simulation, the expected ethnic clothing elements can be formed on the three-dimensional clothing. First, we unify the 2D and 3D clothing triangular patches on thexy plane by rotation and set a unified coordinate system, so that the two digital nonlinear random matrices are both at the origin and have a given common edge u; the edge is aligned with the x-axis. In the simulation case, the intrinsic transformation matrix of each triangular patch is t. In addition to considering the stretch orthogonal and ethnic costume element orientation during initial drape, we also consider ethnic costume element feasibility.Each subsystem of the fractal geometry system has the same compositional characteristics as the upper-level system in terms of form, function, structure, space, and so on, which makes the systems at all levels in Figure5 have similarities, which is the self-similar feature of fractal geometry. Using self-similarity, modeling units at different levels are similar in shape and form a larger whole in a certain way, which can create complex graphic textures in spatial modeling. For the case of acting in the extended area, we hope that the shape of the place can be changed according to the designer’s design requirements.Figure 5
Superposition of digital nonlinear random matrix elements.The wrinkle design has strong limitations, and it is difficult to achieve a detailed design, such as the design of curved wrinkles. On the contrary, the hand-painted method is free to operate and can meet diverse design needs, but it is relatively cumbersome to draw. Therefore, in the process of use, we need to analyze specific problems and choose a method that is more suitable for the current situation. This requires us to add constraints to the grid in the region: any change in the normal vector must satisfy the direction of the orthogonal and path trajectory of Figure6.Figure 6
3D design normal vertex position topology.According to the characteristics of topological deformation and using corresponding digital technology, designers can perform virtual deformation according to various conditions, realize the form generation of continuous forms, form changes and flows of spatial modeling, and obtain experience at all levels. Under the guidance of topological thinking, even the irregular interior surface modeling can be pieced together into a continuous overall surface modeling by dividing the unit shape. Those distorted surface space shapes through continuous nonlinear deformation can be understood as the result of such operations and their own form deformations. We simulate the expanded 2D garment in an unconstrained simulator with no added synthetic forces, and the resulting structure should be similar to the final draped 3D garment. In order to make the generated results as close as possible to our expected 3D clothing model, we need to evaluate the generated results in a way that follows the evaluation method mentioned in Bartle’s schema update framework. Specifically, we measure the intrinsic difference between the target 3D clothing and the current simulated 3D clothing and update the pattern iteratively in a way that aims to minimize the difference of Figure7; we repeat the simulation and update steps until convergence.Figure 7
Attribute distribution of digital nonlinear random matrix.When constructing multiple objects with the same shape and the same properties, if the normal copy method is used, the number of polygons will be doubled for each additional object, while the instance technology can increase the number of similar objects without increasing the number of polygons. For example, in the virtual national costume element scene, there are many elements with the same structure, shape, and texture, and the difference between the elements is only in their position, size, and direction. The way to obtain the extension is to decompose the extension into two components that are easy to obtain—the extension direction and the extension size. Before the expansion size is calculated, we need to determine the expansion area, and the determination of the expansion area depends on the expansion size.


## 4. Application and Analysis of 3D Design Model of Virtual National Costume Based on Digital Nonlinear Random Matrix

### 4.1. 3D Design Simulation of Virtual National Costumes

The graphics in the virtual environment that we use MultiGen Creator for 3D design modeling only have the structure of the body and surface, which cannot produce the real feeling of the simulation environment. It is also necessary to process the surface, that is, add reflection and texture on the surface of national clothing. In the past, the main way to improve the realism of an object was to increase the polygon size of the object.A kinematic body class can include multiple objects and intersection vectors at the same time. However, a kinematic body can only select an instance of a kinematic model class or a bounding body class. In the past, the main way to improve the realism of an object was to increase the polygon of the object. However, the real-time simulation of adding polygons will slow down the graphics speed. The fitting degree of the linear relationship between the local basic parameters of the garment and the local area factor of the garment is low, especially for the shoulders, buttocks, and thighs, the fitting degree R2 is very small. The reason for the low degree of fit is related to the calculation model of the basic thermal resistance of the clothing and the clothing area factor. Usually, the models of basic parameters of clothing and parameters of the surface air layer are established based on more fit. In this simplified model, the torso and limbs of the national costume are simplified as standard cylinders of different diameters.In the parametric modeling of 3D design, it is difficult to manually calculate the convexity value of each arc of the polyline. Therefore, in order to effectively carry out the parametric description of Figure8, we analyze the calculation process of the convexity value of the arc. Combined with the above definitions, arcs are divided into two categories. User-defined means that the user directly specifies the convexity value: the default definition is automatically calculated by the computer, and the classification is discussed as follows. The input parameter is (n, n), which means that the number of lobes in the vertical and horizontal directions is n. There are n to 1 intermediate separation points that need to be defined and calculated. First of all, because the final 3D clothes are interactively modified based on the initial 3D clothes, there is a strong correlation between the two, and the shapes are generally similar. Second, although we do not directly control the shape of the output 3D clothes, we indirectly control the shape of the clothes through a series of calculations, so that the final result generated meets the designer’s requirements. Then, the system automatically generates the corresponding transformation matrix and defines the following data structure to represent the corresponding transformation matrix.Figure 8
3D design convexity value of virtual ethnic clothing.The size chain model in Figure9 represents the size transfer relationship in ethnic clothing with vectors connected end to end, in which the size to be analyzed is called a closed loop, and the size other than the closed loop is called a constituent loop, and all size vectors are projected in a certain direction, and the linear relationship between the closed ring and the constituent ring can be obtained by simple processing. The virtual scene established by geometric modeling, with the increase of the complexity of the environment, will be difficult to meet the real-time performance required by virtual reality, and the phenomenon of surface jitter is easy to appear in the process of browsing the virtual scene. The method of establishing virtual objects in the virtual world through geometric modeling is usually suitable for situations where the complexity of the scene is not large, and it is necessary to realize the interaction between users and virtual objects in the scene, such as the realization of 3D mapping design and national clothing.Figure 9
Parametric transformation matrix modeling of 3D design.In order to generate clothes that meet the designer’s expectations, referring to the traditional design methods of the clothing manufacturing industry, the calculation method of the final 3D clothes is based on the following two observations. Referring to the traditional hand-made clothing design method, using the design structure from two-dimensional to three-dimensional, designers only need to draw the two-dimensional clothing pieces and set the initial position of the clothing pieces, and then send it to the clothing simulation software to simulate it. The final 3D clothes are generated by stitching. Some of these softwares also include the design function of ethnic clothing elements. The method in Table1 is to manually edit the 2D clothing pieces. The whole process may also need to be iteratively modified many times.Table 1
Digital modeling parameters of ethnic clothing.
Digital symbolNode typeDigital gradientEthnic clothingvalueX11Boolean48.960.56X22Boolean18.590.30X33Boolean32.190.41Y11Long int34.570.67Y22Long int63.770.43Y33Long int55.880.22Z11Short int29.500.55Z22Short int41.200.94Z33Short int52.490.81According to CSG modeling theory, the 3D solid modeling commands provided by AutoCAD can already complete most of the 3D solid modeling. In our research on the digital modeling of ethnic clothing, the realization platform of software development is fully considered, and the parametric modeling research is carried out in combination with AutoCAD 3D modeling commands, which increases the feasibility of realization.In addition to avoiding undesired wrinkling in 3D clothing, we also need to minimize the displacement of the clothing boundary relative to the body tangent. This constraint is implicitly enforced at all seams of the garment. For boundaries that are not stitched but still within the scope of action (such as the lower boundary of a skirt), we use an alternative amount similar to the tangent displacement as the enforced constraint. However, the dimensional chain model also has some limitations, which are mainly manifested in: because it only considers the size and fit constraints inside the product, it is suitable for the preliminary analysis of deviation transfer in simple products or designs, but it cannot be well applied to the need for a large number of tooling and fixtures. When combined with three-dimensional tolerance expression models such as DOF, SDT, and T-Map, the dimensional chain model can consider the geometric tolerance to a certain extent, but it is only applicable to the dimensional chain which can be composed of a serial geometric feature or motion pair to express the situation.


### 4.2. Example Application and Analysis

The experiment combines the left-order traversal method of a binary tree and defines some rules to realize the parametric description of the modeling process. First, relying on the nonlinear relationship view of the weighted graph tree model, a structural framework of ethnic clothing tolerance collaborative assignment is established, and the ethnic clothing tolerance assignment problem is transformed into a series of subproblems. Based on the data flow, the national costume tolerance collaborative allocation model is established; finally, the augmented Lagrangian equation is used to establish the coordination strategy of the national costume tolerance collaborative allocation model, and the subproblem solution based on the genetic algorithm is established. In order to calculate the expansion size within the scope of the path trajectory, first, for each path trajectory, we need to achieve a smooth transition of the expansion size. We set the expansion ratio at the position closest to the shape track (the start point of the path track) as the length of the shape track at that point divided by the length of the corresponding clothing piece boundary and set the extension ratio at the position farthest from the shape track (the end point of the path track) to 1 (i.e., no expansion has occurred). Then, we will constrain the expansion of all digital nonlinear random matrices traversed by the path trajectory, and the expansion size in the area of Figure10 is set to the average expansion size.Figure 10
Cooperative allocation of ethnic clothing tolerances.The designer selects the drawing method of ethnic clothing elements and the type of ethnic clothing elements through the drop-down button and adds shape traces on the corresponding borders. Similar to path trajectories, shape trajectories also provide us with some data we need to compute the expansion. The shape track mainly provides the property of expanded size. In order to facilitate the calculation, we usually are default to the uniform elements of national clothing. Using path trajectories, shape trajectories, and 2D clothing pieces and 3D clothing, our algorithm can use these input information to generate a new piece of clothing with ethnic clothing elements added. This set of interactions enables the addition of garments with different textures using schematic input.The cloth in the area should bend to form the expected wrinkle, so the normal vectors and normal vertex positions of the triangular patches in the area will change. However, it is worth noting that we need to avoid the cloth bending in unreasonable ways. This requires us to add constraints to the mesh in the region: any change in the normal vector must satisfy the direction of the orthogonal and path trajectory. The method based on the construction process automatically captures the designer’s intention with the help of modeling commands in the process of graphic input. This method records every operation of the user in the modeling process. The basic idea is that there is a corresponding relationship between modeling operations and geometric constraints. The modeling process can be used to manage and maintain the content data structure that reflects the constraint relationship between geometric elements, and the modification of the design can be obtained through the parameters in Table2 of the modeling process.Table 2
Digital nonlinear random matrix algorithm.
Nonlinear random stepNonlinear random matrix algorithmStep 1:a2+b2 to be addedImport numpy as npStep 2: which the designer expectsi−1Import matplotlib.pyplot as pltStep 3: when developingαi−1Dx = 0.01; dy = 0.01Step 4: location, length, and direction inX = np.arange(−2.0, 2.0, dx)Step 5: a virtual simulation system1−xtY = np.arange(−2.0, 2.0, dy)Step 6: ethnic clothing elementsX, y = np.meshgrid(x, y)Step 7:a−b must be consideredDeff(x, y):Step 8: path trajectory describes the1−xtReturn(1 −y∗∗5 + x∗∗5)∗np.exp(−x∗∗2 − y∗∗2)Step 9: the non-model informationC = plt.contour(x, y, f(x, y), 8, colors = “black”)Step 10: in the model isxα+yβPlt.contourf(x, y, f(x, y), 8)Step 11: the entity extension dataPlt.clable(c, inline = 1, fontsize = 10)Therefore, when developing a virtual simulation system, the nonmodel information in the model, that is, the entity extension data, must be considered. Combined with the STL file, we can output the STL file in AutoCAD and at the same time write the entity extended data stored in the 3D model into the STL file, which we call the ESTL file (Extended STL). Our interactive system is built on the GarmentStudio simulation platform. Since the design of the system ethnic clothing elements is drawn directly after the 3D clothing, all our interactions and computations start after the 3D clothing is draped on the ethnic clothing model. First, the designer adds one or more path trajectories to the draped 3D garment. The path trajectory describes the location, length, and direction in which the designer expects ethnic clothing elements to be added. As described above, in order to add ethnic clothing element designs to existing clothes, the designer needs to expand one or more clothing pieces and change the boundary attributes (length, shape, and so on.) of the clothing pieces to form ethnic clothing elements. It is worth noting that although we can judge the choice of the boundary formed by the wrinkle by the endpoints of the path trajectory (i.e., one end is next to the boundary and the other end does not touch any boundary), in other cases, such as the endpoints of the path trajectory are, respectively, acting on two different boundaries, there is a risk of ambiguity, and in order to generate the expected ethnic clothing elements, the position, length, and direction of ethnic clothing elements are not enough; the designer also needs to define the ethnic clothing elements and the desired amount of border extension.


## 4.1. 3D Design Simulation of Virtual National Costumes

The graphics in the virtual environment that we use MultiGen Creator for 3D design modeling only have the structure of the body and surface, which cannot produce the real feeling of the simulation environment. It is also necessary to process the surface, that is, add reflection and texture on the surface of national clothing. In the past, the main way to improve the realism of an object was to increase the polygon size of the object.A kinematic body class can include multiple objects and intersection vectors at the same time. However, a kinematic body can only select an instance of a kinematic model class or a bounding body class. In the past, the main way to improve the realism of an object was to increase the polygon of the object. However, the real-time simulation of adding polygons will slow down the graphics speed. The fitting degree of the linear relationship between the local basic parameters of the garment and the local area factor of the garment is low, especially for the shoulders, buttocks, and thighs, the fitting degree R2 is very small. The reason for the low degree of fit is related to the calculation model of the basic thermal resistance of the clothing and the clothing area factor. Usually, the models of basic parameters of clothing and parameters of the surface air layer are established based on more fit. In this simplified model, the torso and limbs of the national costume are simplified as standard cylinders of different diameters.In the parametric modeling of 3D design, it is difficult to manually calculate the convexity value of each arc of the polyline. Therefore, in order to effectively carry out the parametric description of Figure8, we analyze the calculation process of the convexity value of the arc. Combined with the above definitions, arcs are divided into two categories. User-defined means that the user directly specifies the convexity value: the default definition is automatically calculated by the computer, and the classification is discussed as follows. The input parameter is (n, n), which means that the number of lobes in the vertical and horizontal directions is n. There are n to 1 intermediate separation points that need to be defined and calculated. First of all, because the final 3D clothes are interactively modified based on the initial 3D clothes, there is a strong correlation between the two, and the shapes are generally similar. Second, although we do not directly control the shape of the output 3D clothes, we indirectly control the shape of the clothes through a series of calculations, so that the final result generated meets the designer’s requirements. Then, the system automatically generates the corresponding transformation matrix and defines the following data structure to represent the corresponding transformation matrix.Figure 8
3D design convexity value of virtual ethnic clothing.The size chain model in Figure9 represents the size transfer relationship in ethnic clothing with vectors connected end to end, in which the size to be analyzed is called a closed loop, and the size other than the closed loop is called a constituent loop, and all size vectors are projected in a certain direction, and the linear relationship between the closed ring and the constituent ring can be obtained by simple processing. The virtual scene established by geometric modeling, with the increase of the complexity of the environment, will be difficult to meet the real-time performance required by virtual reality, and the phenomenon of surface jitter is easy to appear in the process of browsing the virtual scene. The method of establishing virtual objects in the virtual world through geometric modeling is usually suitable for situations where the complexity of the scene is not large, and it is necessary to realize the interaction between users and virtual objects in the scene, such as the realization of 3D mapping design and national clothing.Figure 9
Parametric transformation matrix modeling of 3D design.In order to generate clothes that meet the designer’s expectations, referring to the traditional design methods of the clothing manufacturing industry, the calculation method of the final 3D clothes is based on the following two observations. Referring to the traditional hand-made clothing design method, using the design structure from two-dimensional to three-dimensional, designers only need to draw the two-dimensional clothing pieces and set the initial position of the clothing pieces, and then send it to the clothing simulation software to simulate it. The final 3D clothes are generated by stitching. Some of these softwares also include the design function of ethnic clothing elements. The method in Table1 is to manually edit the 2D clothing pieces. The whole process may also need to be iteratively modified many times.Table 1
Digital modeling parameters of ethnic clothing.
Digital symbolNode typeDigital gradientEthnic clothingvalueX11Boolean48.960.56X22Boolean18.590.30X33Boolean32.190.41Y11Long int34.570.67Y22Long int63.770.43Y33Long int55.880.22Z11Short int29.500.55Z22Short int41.200.94Z33Short int52.490.81According to CSG modeling theory, the 3D solid modeling commands provided by AutoCAD can already complete most of the 3D solid modeling. In our research on the digital modeling of ethnic clothing, the realization platform of software development is fully considered, and the parametric modeling research is carried out in combination with AutoCAD 3D modeling commands, which increases the feasibility of realization.In addition to avoiding undesired wrinkling in 3D clothing, we also need to minimize the displacement of the clothing boundary relative to the body tangent. This constraint is implicitly enforced at all seams of the garment. For boundaries that are not stitched but still within the scope of action (such as the lower boundary of a skirt), we use an alternative amount similar to the tangent displacement as the enforced constraint. However, the dimensional chain model also has some limitations, which are mainly manifested in: because it only considers the size and fit constraints inside the product, it is suitable for the preliminary analysis of deviation transfer in simple products or designs, but it cannot be well applied to the need for a large number of tooling and fixtures. When combined with three-dimensional tolerance expression models such as DOF, SDT, and T-Map, the dimensional chain model can consider the geometric tolerance to a certain extent, but it is only applicable to the dimensional chain which can be composed of a serial geometric feature or motion pair to express the situation.


## 4.2. Example Application and Analysis

The experiment combines the left-order traversal method of a binary tree and defines some rules to realize the parametric description of the modeling process. First, relying on the nonlinear relationship view of the weighted graph tree model, a structural framework of ethnic clothing tolerance collaborative assignment is established, and the ethnic clothing tolerance assignment problem is transformed into a series of subproblems. Based on the data flow, the national costume tolerance collaborative allocation model is established; finally, the augmented Lagrangian equation is used to establish the coordination strategy of the national costume tolerance collaborative allocation model, and the subproblem solution based on the genetic algorithm is established. In order to calculate the expansion size within the scope of the path trajectory, first, for each path trajectory, we need to achieve a smooth transition of the expansion size. We set the expansion ratio at the position closest to the shape track (the start point of the path track) as the length of the shape track at that point divided by the length of the corresponding clothing piece boundary and set the extension ratio at the position farthest from the shape track (the end point of the path track) to 1 (i.e., no expansion has occurred). Then, we will constrain the expansion of all digital nonlinear random matrices traversed by the path trajectory, and the expansion size in the area of Figure10 is set to the average expansion size.Figure 10
Cooperative allocation of ethnic clothing tolerances.The designer selects the drawing method of ethnic clothing elements and the type of ethnic clothing elements through the drop-down button and adds shape traces on the corresponding borders. Similar to path trajectories, shape trajectories also provide us with some data we need to compute the expansion. The shape track mainly provides the property of expanded size. In order to facilitate the calculation, we usually are default to the uniform elements of national clothing. Using path trajectories, shape trajectories, and 2D clothing pieces and 3D clothing, our algorithm can use these input information to generate a new piece of clothing with ethnic clothing elements added. This set of interactions enables the addition of garments with different textures using schematic input.The cloth in the area should bend to form the expected wrinkle, so the normal vectors and normal vertex positions of the triangular patches in the area will change. However, it is worth noting that we need to avoid the cloth bending in unreasonable ways. This requires us to add constraints to the mesh in the region: any change in the normal vector must satisfy the direction of the orthogonal and path trajectory. The method based on the construction process automatically captures the designer’s intention with the help of modeling commands in the process of graphic input. This method records every operation of the user in the modeling process. The basic idea is that there is a corresponding relationship between modeling operations and geometric constraints. The modeling process can be used to manage and maintain the content data structure that reflects the constraint relationship between geometric elements, and the modification of the design can be obtained through the parameters in Table2 of the modeling process.Table 2
Digital nonlinear random matrix algorithm.
Nonlinear random stepNonlinear random matrix algorithmStep 1:a2+b2 to be addedImport numpy as npStep 2: which the designer expectsi−1Import matplotlib.pyplot as pltStep 3: when developingαi−1Dx = 0.01; dy = 0.01Step 4: location, length, and direction inX = np.arange(−2.0, 2.0, dx)Step 5: a virtual simulation system1−xtY = np.arange(−2.0, 2.0, dy)Step 6: ethnic clothing elementsX, y = np.meshgrid(x, y)Step 7:a−b must be consideredDeff(x, y):Step 8: path trajectory describes the1−xtReturn(1 −y∗∗5 + x∗∗5)∗np.exp(−x∗∗2 − y∗∗2)Step 9: the non-model informationC = plt.contour(x, y, f(x, y), 8, colors = “black”)Step 10: in the model isxα+yβPlt.contourf(x, y, f(x, y), 8)Step 11: the entity extension dataPlt.clable(c, inline = 1, fontsize = 10)Therefore, when developing a virtual simulation system, the nonmodel information in the model, that is, the entity extension data, must be considered. Combined with the STL file, we can output the STL file in AutoCAD and at the same time write the entity extended data stored in the 3D model into the STL file, which we call the ESTL file (Extended STL). Our interactive system is built on the GarmentStudio simulation platform. Since the design of the system ethnic clothing elements is drawn directly after the 3D clothing, all our interactions and computations start after the 3D clothing is draped on the ethnic clothing model. First, the designer adds one or more path trajectories to the draped 3D garment. The path trajectory describes the location, length, and direction in which the designer expects ethnic clothing elements to be added. As described above, in order to add ethnic clothing element designs to existing clothes, the designer needs to expand one or more clothing pieces and change the boundary attributes (length, shape, and so on.) of the clothing pieces to form ethnic clothing elements. It is worth noting that although we can judge the choice of the boundary formed by the wrinkle by the endpoints of the path trajectory (i.e., one end is next to the boundary and the other end does not touch any boundary), in other cases, such as the endpoints of the path trajectory are, respectively, acting on two different boundaries, there is a risk of ambiguity, and in order to generate the expected ethnic clothing elements, the position, length, and direction of ethnic clothing elements are not enough; the designer also needs to define the ethnic clothing elements and the desired amount of border extension.


## 5. Conclusion

This paper specifically analyzes the 3D design technology of virtual national costume scenes and uses the Multigen Creator modeling tool to establish the geometric model of the cultural heritage scene. On the basis of the established basic model, the related technology of scene model simplification, the use of texture map to accelerate scene rendering, and the algorithm of real-time construction of LOD model based on viewpoint are deeply studied. Collision detection is set for some objects and surfaces in the virtual scene, and an appropriate roaming mode is set. Finally, a real-time virtual roaming system is developed with the help of Vega development platform and toolset. The experiments show that the system has received satisfactory results in terms of display effect and running speed; the 2D clothing piece, 3D model, and user’s drawing results provided by the simulation software are used as input to calculate the grid expansion caused by the elements of ethnic clothing. In order to improve the running efficiency of the algorithm, the GPU is used for parallel operation in the algorithm to reduce the time cost. The algorithm in this paper mainly involves the grid geometric model, the establishment of the energy state equation, the linear approximation of the nonlinear equation, the optimal solution of the linear equation, and GPU parallel computing. Especially long gowns and long skirts are no longer in line with the traditional cylindrical model for the calculation of local basic parameters of clothing and the distribution of surface air layer parameters, and the calculation of local area factors for clothing is not accurate enough. Therefore, it is necessary to carry out more research in the future to improve the accuracy of calculating the local area factor of clothing.



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*Source: 4957672-2022-07-30.xml*