After a lot of literature reading and practical research, the paper uses the parametric modelling method of curve simulation characteristic line to establish the mathematical model of the furniture product leg shape. This article first uses the surface construction method to analyse the composition of the leg size of the industrialised production and manufacture of furniture products, and makes the solid modelling according to the construction method of non-uniform rational spline mathematical curve and surface simulation. At the same time, the parameter function of furniture leg type is set on SolidWorks, and the research results obtained in the paper are found by simulation, which opens up a new research path for the application of mathematical curve model in furniture design.

#### Keywords

- Non-Uniform Rational B-Splines furniture product leg shape
- mathematical curve simulation
- industrialised manufacturing
- computer-aided geometric design

At present, the focus of research on Ming and Qing furniture at home and abroad still lies in collecting antiques and drawings. In the design and manufacture of antique furniture, the handicraft industry is still the mainstay. After my country joined the WTO, with the further opening of the Chinese market, computer-aided furniture design and manufacturing technology are the general trends [1]. From the perspective of integrating theoretical research and engineering application, the author studied the critical technical issues of the nonuniform rational B-splines mathematical curve simulation method in the leg shape design. Further, it is realised in the developed CAD system of Ming and Qing furniture surface modelling.

Furniture can be categorised into beds, cabinets, tables, chairs, etc., according to varieties. Among them, chair and bed are the more representative types of furniture [2]. Chair is composed of chair brain, front foot, back foot, armrest, backrest, seat frame and other parts. The more typical curved parts are the chair brain, rear legs, armrests and front legs, as shown in Figure 1. The chair brain is the top crossbar on the back of the chair, and its curve forms are mainly curved, corrugated and arched. The back foot has generally three stages, and there are two main types of curves: one is a trapezoid, the other is based on the backrest and the upper and lower sides are arcs with a certain angle to the vertical. The armrests are two crossbars parallel to the seat surface on both sides of the chair. Most of the curves are wavy, and some are similar to ‘S’-shaped curves. The front legs are two vertical planks of wood connected to the chair frame. There are three main types of curves: (1) The upper part of the front foot is rectangular, and the lower part is an ‘S’ curve; (2) the upper part of the front foot is rectangular, and the lower part is sloping outward. Saber shape; (3) Improved saber leg.

Bed furniture is mainly composed of four parts: headboard, footboard, bed support and mattress. The curved parts mainly include the head (tail) top line and the head (bottom) foot. The curve of the full line of the head (bottom) of the bed is symmetrical, mainly including arc, arch, wave etc. The curvilinear shape of the head (tail) foot of the bed is an extension of the sleigh bed’s head (tail) foot style.

The curve shapes of furniture parts mainly include arcs, waves, ‘S’ shapes, saber shapes etc. These curve shapes are similar to some mathematical curves. By analysing the correlation that the curve shapes of furniture parts bear with mathematical curves, it is possible to simulate these parts with mathematical curves. The curvilinear modelling shown in Figure 2 is partly related.

It can be seen that these mathematical curves are similar to the curves of certain parts of furniture. These curve shapes can be simulated through the setting of mathematical curve variables and intervals. For example, a cosine curve can be modified by determining its period and amplitude and using symmetric intervals [3]. We adopt the method of mathematical curve simulation and use its calculation formula to generate the curve characteristics of the required part quickly, thereby further generating the three-dimensional model of the position. Since the mathematical curves are relatively rigid, different angles can only be obtained by changing the variables and value ranges. However, designers often have many random variations when drawing these part curves; moreover, it is not easy to achieve a complete match in the simulation process. We can use the approximation method to fit to find a closer angle continuously.

Free-form curve and surface design is often a difficult point in CAD. Recently, the methods that have been more successful and widely used in the design of free-form curves and surfaces include the Bezier method, the 13-spline method and the non-uniform rational B-splines method [4]. Because of the outstanding advantages of the non-uniform rational B-splines method. In 1991, the International Organisation for Standardisation (ISO) officially promulgated the STEP standard for the geometric definition of industrial products as an international standard for product data exchange. In the STEP standard, free-form curves and surfaces are uniquely represented by non-uniform rational B-splines. This technology has been applied to professional software in many industries such as machinery manufacturing, automobiles, aviation and shipbuilding.

We assume that the control points _{0},_{1},...,_{m}_{0},_{1},...,_{m}_{0},_{1},...,_{m−k}_{+1}; then the

The primary objective is to find a unified mathematical method with other forms through which free-form curves and surfaces can be described and accurately represent elementary analytical curves and surfaces. From Eq. (1), it can be seen that non-uniform rational B-splines has not only more denominators but also more weight factors than non-rational B-spline curves. We can use it to adjust the fullness of the curve, provide sufficient flexibility for geometric calculations and make it an additional modelling parameter.

Similar to the non-uniform rational B-splines curve, a non-uniform rational B-splines surface of degree

The control vertex _{i}_{i}_{1,m},_{2,m},_{3,m},_{i,m} > 0 at the vertices of the four corners and the remaining _{i} ≥_{i,k}_{(u)}(_{i,k}_{0},_{1},...,_{m}_{+k−1}],_{0},_{1},...,_{m}_{+l−1}] of the

The aggravated leg shape mentioned in the thesis is a kind of leg shape widely used in Ming and Qing furniture, and its lower end is like a horse hoof. The middle future hangs upright, and the upper end turns inward to connect with the teeth. Traditionally, this kind of leg is called a horseshoe leg. The structure and shape of horseshoe legs are relatively finalised, so we use a parametric design method based on shape feature lines to construct a mathematical model of the leg shape [6]. The typical size relationship of the two legs (flat legs and drum legs) is shown in Figure 3 and Table 1. Based on this, we can use a set of parameters to agree on the size relationship of the horseshoe legs.

Furniture leg size relationship.

Tip width | 1/15–1/20 | ||

Outer leg width | 0.5–1.0 | ||

The angle of inclination of the foot | 0.15–0.65 | ||

Inner crotch width | 0.1–0.8 | ||

Foot height | 0.9–1.5 | 0.9–1.1 | |

Inner crotch height | 1.1–1.5 | 1.1a | |

Tip height | 2.0–5.0 | ||

Foot length | 0.7–1.5 | 0.23 |

Most of the parameters for constructing the leg shape are related to the plane curve. Although the curve segment is on the one-dimensional form of the leg shape rather than on the two-dimensional outline, the relevant parts of the three-dimensional body are projected from front to back. Still, the curve change directly affects the construction of the model. Further, from the user’s point of view, when designers in the furniture industry design leg shapes, after determining the main dimensions of the furniture (length, width, height, leg height etc.), the primary consideration is also the change of this line. Therefore, based on the above reviews, we use the mathematical curve as the characteristic line for constructing the leg shape.

The curve non-uniform rational B-splines is expressed as:

Among the 10 model value points on the distinctive line, the points I, II, V and X correspond to the characteristic points A, D, B and C. The two points III and IV are the uniform interpolation points of the DB segment, and the four points VI, VII, VIII and IX are the consistent interpolation points of the BC segment. After defining the characteristic line, the cross-sectional shape of the height of a particular point of the leg shape can be determined, thereby forming the three-dimensional shape of the leg shape [7].

Since the CAD platform system involves geometric configuration and is inseparable from the database and the graphical interface, the database and the graphical interface are substantial software packages. To develop these low-level frameworks at the same time or on the original basis requires a lot of time and energy from developers, which is often difficult to adapt to the rapid development of the software industry. At present, the development of software component technology and object-oriented technology provides an excellent way to solve the problem, making full use of advanced software platforms, and researching and developing their superior products at a higher starting point should be a more feasible technical approach.

The system is operated under the Windows environment using powerful, object-oriented Visual Basic visual-programming software. The system uses SolidWorks as the primary platform for its secondary development and realises the parametric design of the curve of American furniture parts. We use mathematical curves to simulate part curves to achieve a part curve parametric design system that integrates part curve selection, geometric curve design, parametric modelling and engineering drawings.

SolidWorks is a feature-based solid modelling software. The system can give different design schemes to avoid or reduce errors in the design process. It uses intuitive design technology, Windows OLE technology, Para-solid kernel and excellent technology integration with third-party software. SolidWorks is currently a commonly used 3D CAD software.

SolidWorks has an open interface, and provides convenient user-development tools and rich data-exchange methods [8]. The secondary development of SolidWorks is mainly to use its embedded Application Programming Interface (API) objects. Solid Works API provides users with free, open and fully functional development tools. Reliable Works API provides users with many functions that Visual Basic can call, such as Delphi, VBA and Visual C++ through OLE technology. These functions are related to the methods and properties of the object, which improve the programmer’s ability to develop SolidWorks directly. By calling these methods and setting object properties, users can control various operations on SolidWorks in their applications.

According to the characteristics and goals of the system, the system we designed is mainly composed of five parts: curve-type selection module, geometric curve design module, part 3D modelling module, database query module and menu plug-in. Simultaneously, we have established a SolidWorks menu plug-in, from which it is more convenient for users to query and call the required part curves. The overall plan of the system is shown in Figure 4.

This module is mainly used for curve selection. After entering the system interface, we select the corresponding mathematical curve type according to user needs and ensure that these are equipped with complementary graphics and text descriptions [9]. When you click the ‘OK’ button, you will enter the following design interface. When you click the ‘Cancel’ button, it will return to the program’s main interface.

This module mainly performs geometric curve drawing. Query the parameters of the required part curve in the database. After we input the geometric parameters and complete the design calculation, click the ‘Geometric Curve’ button to draw the geometric curve of the part and save it to the corresponding folder.

This module is mainly used for drawing the three-dimensional model of parts and engineering drawings. Query and enter the corresponding part design parameters in the database. Click the ‘Part Model’ and ‘Export Engineering Drawing’ buttons to enter the SolidWorks interface of the part 3D model and engineering drawing. We save the drawn engineering drawings to the corresponding folder.

This module mainly provides users with a convenient platform for querying part curve geometric parameters and part design parameters [10]. Multiple data tables are used to record different types of part curve data, which can be continuously expanded, modified and updated. The Access database management system completes this module.

The system developed the EXE program of the part curve and developed the SolidWorks menu plug-in (DLL program) for the user’s convenience. The DLL program hangs different part curves on the main menu of the SolidWorks software, making the two systems integrated and more flexible and convenient. The procedure flow of the whole system is shown in Figure 5.

We can use the parametric design method to build the model for the furniture curve and surface modelling with relatively finalised structural shapes. Through parametric drawing design, we can quickly realise the design of serialised products or make partial changes to the design works, avoiding designers’ tedious and repetitive work [11]. The flow chart of furniture leg parameter modelling is shown in Figure 6. The paper adopts the parametric design method based on the characteristic shape line to construct the leg type mathematical model. Since the development of the system adopts a modular programming method, it has an excellent interface to facilitate subsequent development.

After constructing the initial model, we can quickly and efficiently modify the model according to our requirements. The system uses two commonly used non-uniform rational B-splines curve and surface modification methods: changing the control vertices and modifying the weight factors of the control vertices. Since we modify the control vertex coordinates to make the range of the non-uniform rational B-splines curve and surface repair more significant, we are able to use it for rough repair of the non-uniform rational B-splines curve and surface. Modifying the weight factor of the control vertex makes the modification range of the non-uniform rational B-splines curve and surface limited to the convex hull of the control vertex, so it is used to realise the refinement of the non-uniform rational B-splines curve and surface. The actual matching of control vertices and weight factors makes the user’s control of curves and surfaces more flexible and the modelling function is enhanced.

We use the example of a cosine curve to simulate the angle of furniture parts to illustrate the operation method of the whole system, the operation process and the programming code to realise the process.

In the Windows environment, we open the executable program of this system and start the login interface of the furniture part curve parametric design system. We enter the corresponding account and password to enter the following window interface, as shown in Figure 7.

After we enter the login interface, an interface window–shown in Figure 8–will pop up, and we can use it to select the desired curve type. Select the cosine curve here, and then click the button to the right to pop up a legend and text description of the cosine curve. If you are sure of the choice made, click the ‘OK’ button to enter the design interface of the geometric cosine curve.

After viewing the cosine curve data table, enter the name of the required curve part, and we obtain the geometric parameters and enter them in the corresponding positions. The relevant parameters cover four parameters: amplitude, period, left interval and suitable interval. We can calculate the value of through four parameters [12]. In this way, a geometric curve model can be built in SolidWorks and saved to the corresponding folder. After completion, click the ‘Enter Part 3D Modelling Interface’ button to enter the following interface, as shown in Figure 9 [13].

The primary purpose of the three-dimensional modelling design is to generate the three-dimensional model of the part and the creation of the engineering drawing interface, as shown in Figure 10.

After ascertaining the corresponding part design parameters from the data table, we input them into the corresponding position. There are three parameters of straight-line length, part width and stretched thickness [14]. After inputting the parameters, click ‘Part Model’ to build the necessary curve part in SolidWorks, as shown in Figure 11.

According to the actual needs, we can click the ‘engineering drawing’ button to generate the corresponding engineering drawing, as shown in Figure 12.

The paper analyses the modelling characteristics of the furniture leg curve and the method of mathematical curve simulating the leg curve. We use SolidWorks API technology and VB development tools to realise the parametric design of the furniture leg curve. The paper expounds on the principles of system development, parametric modelling methods and overall system planning and uses cosine curve to simulate furniture leg curve as an example to analyse the operation process of the system and the use of the SolidWorks menu plug-in. The design method is simple to operate. The designer can perform curve design and automatic modelling through simple human–computer interaction, which significantly improves the design efficiency, shortens the product development cycle and enables the designer to spend more time and energy in product innovation design.

#### Furniture leg size relationship.

Tip width | 1/15–1/20 | ||

Outer leg width | 0.5–1.0 | ||

The angle of inclination of the foot | 0.15–0.65 | ||

Inner crotch width | 0.1–0.8 | ||

Foot height | 0.9–1.5 | 0.9–1.1 | |

Inner crotch height | 1.1–1.5 | 1.1a | |

Tip height | 2.0–5.0 | ||

Foot length | 0.7–1.5 | 0.23 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Response model for the psychological education of college students based on non-linear finite element equations Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Spatial–temporal graph neural network based on node attention Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory College students’ innovation and entrepreneurship ability based on nonlinear model Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Mathematical simulation analysis of optimal testing of shot puter's throwing path Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings The term structure of economic management rate under the parameter analysis of the estimation model based on common differential equation Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model The improvement of museum information flow based on paste functional mapping method Constraint effect of enterprise productivity based on constrained form variational computing The art design of industrialised manufacturing furniture products based on the simulation of mathematical curves The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 TOPSIS missile target selection method supported by the posterior probability of target recognition Research on Evaluation of Intercultural Competence of Civil Aviation College Students Based on Language Operator Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model The incentive contract of subject librarians in university library under the non-linear task importance Modelling and Simulation of Collaborative Innovation System in Colleges and Universities Based on Interpreted Structural Equation Model Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts The Optimal Solution of Feature Decomposition Based on the Mathematical Model of Nonlinear Landscape Garden Features Composite mechanical performance of prefabricated concrete based on hysteresis curve equation Higher education innovation and reform model based on hierarchical probit Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot The teaching of sports science of track and field-based on nonlinear mathematical equations Visual error correction of continuous aerobics action images based on graph difference function Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Precision algorithms in second-order fractional differential equations Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Fractional differential equations in National Sports Training in Colleges and Universities Radioactive source search problem and optimisation model based on meta-heuristic algorithm Visualized calculation of regional power grid power data based on multiple linear regression equation Application of mathematical probabilistic statistical model of base – FFCA financial data processing Least-squares method and deep learning in the identification and analysis of name-plates of power equipment Research on a method of completeness index based on complex model Distribution network monitoring and management system based on intelligent recognition and judgement Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Topological optimisation technology of gravity dam section structure based on ANSYS partial differential equation operation Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Analysing the action techniques of basketball players’ shooting training using calculus method Engineering project management based on multiple regression equation and building information modelling technology Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Badminton players’ trajectory under numerical calculation method Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Visual positioning system for marine industrial robot assembly based on complex variable function Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Automatic parameter selection ZVD shaping algorithm for crane vibration suppression based on particle swarm optimisation Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Nonlinear Differential Equations in the Teaching Model of Educational Informatisation Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Mathematical model of transforming image elements to structured data based on BP neural network Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}Educational reform informatisation based on fractional differential equation Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption 3D Mathematical Modelling Technology in Visual Rehearsal System of Sports Dance MCM of Student’s Physical Health Based on Mathematical Cone Attitude control for the rigid spacecraft with the improved extended state observer Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Research on tourism income index based on ordinary differential mathematical equation Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Sports Science Teaching of Athletics Based on Nonlinear Mathematical Equation Informatisation of educational reform based on fractional differential equations Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Communication architecture of power monitoring system based on incidence matrix model Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Design of Morlet wavelet neural network to solve the non-linear influenza disease system Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Translog function in government development of low-carbon economy Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode The Model of Sugar Metabolism and Exercise Energy Expenditure Based on Fractional Linear Regression Equation Constructing Artistic Surface Modeling Design Based on Nonlinear Over-limit Interpolation Equation Numerical Simulation Analysis Mathematics of Fluid Mechanics for Semiconductor Circuit Breaker Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Human Body Movement Coupling Model in Physical Education Class in the Educational Mathematical Equation of Reasonable Exercise Course The contribution of structural equation model analysis to higher education agglomeration and innovation and entrepreneurship Study on the evolutionary game theory of the psychological choice for online purchase of fresh produce under replicator dynamics formula The influence of X fuzzy mathematics method in basketball tactics scoring Mathematical statistics algorithm in the bending performance test of corroded reinforced concrete beams under fatigue load Nonlinear strategic human resource management based on organisational mathematical model Back propagation mathematical model for stock price prediction Evolutionary game research on the psychological choice of online shopping of fresh agricultural products based on dynamic simulation model Differential equation model of financial market stability based on big data Multi-attribute decision-making methods based on normal random variables in supply chain risk management Linear fractional differential equations in bank resource allocation and financial risk management model Construction and reform of art design teaching mode under the background of the integration of non-linear equations and the internet