Three-dimensional Coordinate System Research Articles

A paradigm for building fire safety

The aim of study is to describe the fire safety paradigm using the concept of T. Kuhn, its components, and its role and significance for the further development of construction science, particularly the fire safety of buildings. The components of the fire safety paradigm form a complex structure (system) that is presented graphically to illustrate the interconnections and interactions between them. This structure is built by analogy with a three-dimensional coordinate system using linguistic quantities. Currently, it is not yet possible to assign a sequence of numbers representing the coordinates of a point in the space of this system. The three axes of this system determine the major groups of paradigm elements: - fire safety; - components; - activities and inputs. For each group, the components were distinguished, which were then briefly described and characterised, emphasising their mutual connections and importance for the fire safety of buildings. Some significant gaps in the systemic approach to fire safety in the EU were discussed and illustrated by the example of Grenfell Tower fire in London. The paradigm described is universal, and its universality is based on the possession of certain common attributes characteristic of the fire safety environment and their interpretation, as well as the manner in which fire safety entities implement them. A paradigm shift will result in the introduction of a fire toxicity criterion for the assessment of construction products, which, for unknown reasons, has so far only been implemented in relation to cables. The second necessary amendment is the addition of a requirement for the spread of fires on building facades.

Structural Design and Kinematic Analysis of Cable-Driven Soft Robot

Continuous robots have attracted more and more attention from the robotics community due to their high degree of flexibility and pliability, and have shown great potential for application in a variety of fields. With the continuous progress of material science, control technology, and artificial intelligence, the performance and application range of soft robotics have been further expanded, in which the cable drive has the advantages of large workspace, high flexibility, etc. The cable-driven soft robotic arm serves as an ultra-redundant robot that can operate in cramped and confined environments. In this paper, a cable-driven soft robot based on soft continuums and a cross gimbal is presented. The kinematics of the cable-driven soft robot is modeled and the mapping relations of the kinematics are solved by the D–H method and piecewise constant curvature, and the relations between the cable length, joint angle, and pose are further derived. Finally, the motion space of the cable-driven soft robot in the three-dimensional coordinate system is obtained by MATLAB2021b, and the single-segment soft body is simulated and analyzed using ADAMS to compare the theoretical data with the actual data and verify the reliability of this structure and method.

Deep Fusion of Skeleton Spatial-Temporal and Dynamic Information for Action Recognition.

Focusing on the issue of the low recognition rates achieved by traditional deep-information-based action recognition algorithms, an action recognition approach was developed based on skeleton spatial-temporal and dynamic features combined with a two-stream convolutional neural network (TS-CNN). Firstly, the skeleton's three-dimensional coordinate system was transformed to obtain coordinate information related to relative joint positions. Subsequently, this relevant joint information was encoded as a color texture map to construct the spatial-temporal feature descriptor of the skeleton. Furthermore, physical structure constraints of the human body were considered to enhance class differences. Additionally, the speed information for each joint was estimated and encoded as a color texture map to achieve the skeleton motion feature descriptor. The resulting spatial-temporal and dynamic features were further enhanced using motion saliency and morphology operators to improve their expression ability. Finally, these enhanced skeleton spatial-temporal and dynamic features were deeply fused via TS-CNN for implementing action recognition. Numerous results from experiments conducted on the publicly available datasets NTU RGB-D, Northwestern-UCLA, and UTD-MHAD demonstrate that the recognition rates achieved via the developed approach are 86.25%, 87.37%, and 93.75%, respectively, indicating that the approach can effectively improve the accuracy of action recognition in complex environments compared to state-of-the-art algorithms.

Automated Posterior Scleral Topography Assessment for Enhanced Staphyloma Visualization and Quantification With Improved Maculopathy Correlation.

To quantitatively characterize the posterior morphology of high myopia eyes with posterior staphyloma. Surface points of the eyeball were automatically extracted from magnetic resonance imaging scans using deep learning. Subsequently, the topography of posterior staphylomas was constructed to facilitate accurate visualization and quantification of their location and severity. In the three-dimensional Cartesian coordinate system established with surface points, measurements of distances (D) from each point to the hypothetical pre-elongation eye center within the eyeball and local curvatures (C) at each point on the posterior sclera were computed. Using this data, specific parameters were formulated. The concordance of these parameters with traditional staphyloma classification methods and their association with myopic traction maculopathy (MTM) grades based on the ATN classifications were investigated. The study included 102 eyes from 52 participants. The measured parameters, particularly the variance of distance (Dvar) and the maximum value of the curvature and distance product (C · Dmax), demonstrated efficacy in differentiating various types of posterior staphyloma and exhibited strong correlations with the grades of MTM. The automated generation of the posterior scleral topography facilitated visualization and quantification of staphyloma location and severity. Simple geometric parameters can quantify staphyloma shape and correlate well with retinal complications. Future works on expanding these measures to more imaging modalities could improve their clinical use and deepen insights into the link between posterior staphyloma and related retinal diseases. This work has the potential to be translated into clinical practice, allowing for the accurate assessment of staphyloma severity and ultimately improving disease management.

Multiple-output network for simultaneous target classification and moving direction estimation in automotive radar systems

To ensure the stable operation of autonomous driving, a rich understanding of road conditions is indispensable. Therefore, in this paper, we propose a method that uses a single deep learning (DL) network structure to classify commonly encountered on-road objects, such as vehicles, cyclists, and pedestrians, and simultaneously estimating their moving direction. First, we obtain information about the target, such as range, velocity, azimuth angle, and elevation angle, using a four-dimensional imaging radar. Next, we convert the detection results into point cloud data and represent them within a three-dimensional spatial coordinate system. Then, the point cloud data is projected onto the XY-plane to classify the target’s class and estimate the moving direction of the target. In the XY-plane, we apply a preprocessing step using density-based spatial clustering to remove noise from the detection results, cluster the targets, and convert this processed data into image data. Subsequently, we conduct training on a multiple-output DL network designed to simultaneously perform object classification and predict the moving direction using the image data. Finally, the performance evaluation of the proposed method results in an object classification accuracy of 96.10%, and the root mean square error for estimated moving directions is 5.54∘, 3.89∘, and 15.35∘ for vehicles, cyclists, and pedestrians, respectively, with a runtime of 0.1 s, demonstrating its efficiency.

Talar and Calcaneal Coordinate Axes Definitions across Foot Pathologies

The understanding of foot and ankle biomechanics is improving as new technology provides more detailed information about the motion of foot and ankle bones with biplane fluoroscopy, as well as the ability to analyze the hindfoot under weightbearing conditions with weightbearing computed tomography. Three-dimensional anatomical coordinate systems are necessary to describe the 3D alignment and kinematics of the foot and ankle. The lack of standard coordinate systems across research study sites can significantly alter experimental data analyses used for pre-surgical evaluation and post-operative outcome assessments. Clinical treatment paradigms are changing based on the expanding knowledge of complex pes planovalgus morphologies or progressive collapsing foot deformity, which is present in both neurologic and non-neurologic populations. Four patient cohorts were created from 10 flexible PCFD, 10 rigid PCFD, 10 adult cerebral palsy, and 10 asymptomatic control patients. Six coordinate systems were tested on both the talus and calcaneus for all groups. The aim of this study was to evaluate axes definitions for the subtalar joint across four different patient populations to determine the influence of morphology on the implementation of previously defined coordinate systems. Different morphologic presentations from various pathologies have a substantial impact on coordinate system definitions, given that numerous axes definitions are defined through geometric fits or manual landmark selection. Automated coordinate systems that align with clinically relevant anatomic planes are preferred. Principal component axes are automatic, but do not align with clinically relevant planes and should not be used for such analysis where anatomic planes are critical.

Comparison analysis of moisture-dependent orthotropic elasticity between earlywood and latewood in Chinese fir using digital image correlation

Given its orthotropic and hygroscopic nature, Chinese fir exhibits varying mechanical behaviors in earlywood and latewood due to its naturally inhomogeneous structure when exposed to changes in loading direction and given moisture content (MC) range from 7.9 % to 16.1 %. In this study, we combined micro-tensile testing and the digital image correlation (DIC) technique to derive the moisture -dependent orthotropic elastic constants, i.e., Young’s modulus (E), Poisson’s ratio (ν) and shear modulus (G) for both earlywood and latewood in Chinese fir. The findings revealed that when loading in the parallel direction, the restraining effect caused by latewood on earlywood resulted in a difference compared with loading in series. Interestingly, the loading direction impacted the restraining effect more significantly than MC. Additionally, both Young’s modulus and shear modulus exhibited decreases with increasing MC within above range for both earlywood and latewood. Notably, the Young’s modulus of earlywood showed a higher sensitivity to MC variations compared to latewood. However, Poisson’s ratio did not consistently correlate with MC within above range in all orthotropic directions. A three-dimensional coordinate system visualization of the compliance parameters highlighted the differing sensitivities of earlywood and latewood to moisture. The independent moisture-dependent elastic components of earlywood and latewood derived in this study extended the moisture-dependent mechanical model of wood, offering theoretical guidance for the practical application of Chinese fir and other wood species.

Research on Optimization Design of Heliostat Field Based on Genetic Algorithm

This article aims to design various variable parameters of the heliostat field while achieving the rated power of the heliostat field is an innovative solar heating system that focuses solar radiation on the absorption tower through a reflector, thereby generating high-temperature heat energy. This article mainly discusses the performance analysis and parameter optimization of the heliostat field to achieve optimal performance while meeting the rated power requirements. A simulated solar model was established using a three-dimensional Cartesian coordinate system, taking into account the effects of solar altitude angle and direct normal irradiance. The model in this paper comprehensively considers the effects of shadow occlusion loss, cosine efficiency, atmospheric transmittance, collector truncation efficiency, and mirror reflectance on the mirror field. To solve the problem, it is necessary to establish a three-dimensional coordinate system model, with the position of the absorption tower as the origin position of the coordinate system. Then, based on the size and installation height of the heliostat, the position of each heliostat is obtained, and optimized design is carried out to ensure that the total output thermal power is within the rated power range. Therefore, this article establishes a three-dimensional coordinate system model, taking the position of the absorption tower as the origin position of the coordinate system. Based on the size and installation height of the heliostat, the position of each heliostat is obtained. The annual average optical efficiency, annual average output thermal power, and annual average output thermal power per unit mirror area of the heliostat field are optimized and solved using genetic algorithm.

Geometric Error Identification of Gantry-Type CNC Machine Tool Based on Multi-Station Synchronization Laser Tracers

Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial measurement. We propose a geometric error identification method based on multi-station synchronization laser tracers to enable the rapid and high-precision measurement of geometric errors for gantry-type computer numerical control (CNC) machine tools. This method also improves on the existing measurement efficiency issues in the single-base station measurement method and multi-base station time-sharing measurement method. We consider a three-axis gantry-type CNC machine tool, and the geometric error mathematical model is derived and established based on the combination of screw theory and a topological analysis of the machine kinematic chain. The four-station laser tracers position and measurement points are realized based on the multi-point positioning principle. A self-calibration algorithm is proposed for the coordinate calibration process of a laser tracer using the Levenberg–Marquardt nonlinear least squares method, and the geometric error is solved using Taylor’s first-order linearization iteration. The experimental results show that the geometric error calculated based on this modeling method is comparable to the results from the Etalon laser tracer. For a volume of 800 mm × 1000 mm × 350 mm, the maximum differences of the linear, angular, and spatial position errors were 2.0 μm, 2.7 μrad, and 12.0 μm, respectively, which verifies the accuracy of the proposed algorithm. This research proposes a modeling method for the precise measurement of errors in machine tools, and the applied nature of this study also makes it relevant both to researchers and those in the industrial sector.

Finite Element Mode-ling of Damping of a Squeeze Gas Film in High-Frequency Microelectromechanical Switches with Capacitive Contact

The damping effects of a squeeze gas film are one of the main components of damping and naturally arise in the designs of dynamic micromechanical devices, in particular, in high-frequency micromechanical switches with an electrostatic activation mechanism, in which the electrostatic drive consists of a fixed electrode in the form of a plate and a movable electrode in the form of a movable plate suspended on elastic suspensions for the case of capacitive contact. In the static mode of the device, a thin film of gas consisting of air molecules or other inert gas surrounding the device is located and held between the electrodes of the electrostatic drive. This article presents a mathematical model based on the obtained linear inhomogeneous Reynolds differential equation and performs finite element modeling of the pressure distribution in the plate of a suspended movable electrode during compression of a gas film during electrostatic activation of micromechanical switches with a capacitive contact and parallel arrangement of the electrodes of an electrostatic drive depending on the magnitude of the coefficient of this component of damping in a three-dimensional coordinate system, the dependences between the damping force and the elastic force of the compressible gas film on the value of the damping coefficient are also presented. The presented results are applicable to assess the effect of isothermal damping of a squeeze gas film on the dynamics of micromechanical devices, in particular, on the dynamic characteristics of high-frequency micromechanical switches with an electrostatic activation mechanism and a capacitive contact.

Interactive design of intelligent wearable products based on network communication technology

At this stage, network communication technology is increasingly mature, and intelligent wearable products are also widely used in human daily life. Wearable products are popular with users because of their numerous types, complete functions and convenient services. Wearable products integrate interaction technology, and users can interact with products. However, how to improve the user’s interaction experience and reduce the user’s cognitive burden on the interaction interface is an urgent problem in the current product interaction design. Therefore, based on the analysis of the types and related technologies of wearable products, this paper made a specific analysis of the interaction design of wearable products, and established an interaction design model. At the same time, the wearable fall detection system was also tested by machine learning algorithm. The experimental results showed that the average test result of the algorithm in this paper was 87.39%, while the average test result of the traditional algorithm was 83.79%. In terms of the missed alarm rate of fall detection, the average test result of this algorithm was 6.4%, while the average test result of the traditional algorithm was 12.33%. In terms of fall detection sensitivity, the average test result of this algorithm was 92.50%, while the average test result of the traditional algorithm was 88.24%. Compared with traditional algorithms, this method performs better, with lower missed detection rate and higher sensitivity. Innovative combination of machine learning algorithm, through three-dimensional coordinate system, differentiation and vector sum formula, improves the accuracy and reliability of fall detection. In conclusion, the algorithm in this paper can effectively optimize the relevant performance of the system, thus improving the accuracy of the system’s fall detection.

Application of Laser-Induced Acoustic Desorption for Molecular Rotational Resonance Spectroscopy.

Molecular Rotational Resonance (MRR) spectroscopy is a uniquely precise tool for the determination of molecular structures of volatile compounds in mixtures, as the characteristic rotational transition frequencies of a molecule are extremely sensitive to its 3D structure through the moments of inertia in a three-dimensional coordinate system. This enables identification of the compounds based on just a few parameters that can be calculated, as opposed to, for example, mass spectrometric data, which often require expert analysis of 10-20 different signals and the use of many standards/model compounds. This paper introduces a new sampling technique for MRR, laser-induced acoustic desorption (LIAD), to allow the vaporization of nonvolatile and thermally labile analytes without the need for excessive heating or derivatization. In this proof-of-concept study, LIAD was successfully coupled to an MRR instrument to conduct measurements on seven compounds with differing polarities, molecular weights, and melting and boiling points. Identification of three isomers in a mixture was also successfully performed using LIAD/MRR. Based on these results, LIAD/MRR is demonstrated to provide a powerful approach for the identification of nonvolatile and/or thermally labile analytes with molecular weights up to 600 Da in simple mixtures, which does not require the use of reference compounds. In the future, applications to more complex mixtures, such as those relevant to pharmaceutical research, and quantitative aspects of LIAD/MRR will be reported.

Novel approach to locate micro-scale mineral regions of interest in real ores

The surface of minerals plays a pivotal role throughout the process of mineral beneficiation and utilization. Studies on surface properties, such as surface chemistries, of mineral phases of interest in real ores enable the selective separation of minerals, thereby enhancing the utilization of mineral resources. Nevertheless, obtaining specific mineral phases, especially for finely disseminated or poorly crystalized minerals, from real ores without altering their surface chemistries remains a challenge. The challenge also persists in investigating the same micro-scale mineral region in real ores using various surface characterization techniques, such as scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS). This paper proposes a novel approach and procedures for locating micro-scale mineral regions of interest in real ores based on a three-dimensional coordinate system etched onto the ore surface using laser etching technology. A copper-nickel ore from Jinchuan, China, served as an illustrative example, with the finely disseminated chalcopyrite and pentlandite regions in the real ore sample being located and investigated using SEM and XPS. The approach presented in this study enables the in-situ detection of surface chemistries of specific mineral phase in real ores, ensuring the homogeneity and in-situ nature of the obtained surface chemistry data. This approach holds considerable promise, especially in the investigation of surface chemistries of minerals with fine dissemination and poor crystallization.

Treatment Efficacy of CT-Guided Percutaneous Kyphoplasty Combined with Three-Dimensional Coordinate Guidance System on Osteoporotic Vertebral Compression Fracture

Purpose: To investigate the clinical effect of percutaneous kyphoplasty (PKP) guided by computed tomography (CT) combined with the three-dimensional coordinate guidance system on the treatment of osteoporotic vertebral compression fracture (OVCF). Methods: 32 cases of OVCF in the elderly admitted to our hospital from October 2019 to March 2021 underwent CT-guided PKP combined with the three-dimensional coordinate guidance system, and 36 vertebrae were treated. The patients’ VAS pain scores (visual analog scale) and ODI (Oswestry disability index) were observed after surgery, and the paired t-test was used to compare these indexes. Results: The 36 vertebrae that were treated with CT-guided PKP combined with the three-dimensional coordinate guidance system underwent unilateral pedicle puncture according to the path planned by CT images. With the ideal position of the puncture needle and a high success rate of puncture, the puncture time was 1.2–2.6 minutes, with an average of about 1.5 minutes; the injected bone cement ranged from 3 to 5.5 mL, with an average of 4.2 mL, and there were no spinal nerve injuries or leakage of the cement in the canal. VAS score decreased from 7.65 ± 0.60 before the operation to 2.59 ± 0.28 one day after the operation (P < 0.01); ODI decreased from 62.3 ± 2.18 before the operation to 27.91 ± 1.32 after the operation (P < 0.01). Conclusion: The application of CT-guided PKP combined with the three-dimensional coordinate guidance system has the advantages of accurate puncture, short operation time, less intraoperative bleeding, and low complications. This treatment is safe, reliable, and satisfactory for patients, and is worthy of clinical promotion.

Different methods of determining centric relation – comparison with a digital mandibular motion analyser

BackgroundFinding and registering the maxillary–mandibular jaw relation is crucial in dental practice. Several comparative studies have been conducted to investigate the reproducibility and accuracy of techniques for determining the centric relation (CR) position of the mandible. The aim of our study was to determine which of seven different CR determination methods had the smallest deviation from the theoretical zero with the help of a digital mandibular motion analyser. The chosen theoretical zero position, the maximal intercuspal position (MIP), is the most reproducible and widely used position.MethodsThirty-four volunteers (24 females and 10 males) with a mean (SD) age of 29.1 (± 7.3) years with a negative history of temporomandibular disorder (TMD) participated in the study. A digital mandibular motion analyser was used to register the condylar position after the use of each technique for the determination of CR. The calibration was performed to the maximal intercuspal position (MIP) for each volunteer. The investigated techniques were (A) the gothic arch tracer, (B) the adduction field method, (C) Dawson’s bimanual manipulation, (D) the patient placing the tongue tip on the palatal rugae, (E) the patient placing the tongue tip to the border of the hard and soft palate, (F) the patient actively pulling the chin backwards, and (G) the examiner pushing the patient’s chin back.ResultsThe position of the mandibular condyle was illustrated in a three-dimensional coordinate system, where the origin represented the MIP. Among the seven methods examined, five showed significant deviations compared to the MIP. Among these, two methods resulted in posterior deviation of the condyles. Methods C and E coincided with the MIP in all directions.ConclusionsWithin the limitations of our study, we found that the smallest deviations from our theoretical zero (MIP) among the investigated centric relation determining methods were obtained with the bimanual mandibular manipulation technique derived from Dawson and the placement of the tongue tip on the border of the hard and soft palate (linguomandibular homotrophy theory).

Research on multi-beam problems based on geometric modeling and underwater detection

This paper aims to establish and solve the mathematical model of coverage width under multi-beam bathymetry, rising from a one-dimensional sea area measurement problem to a two-dimensional sea area measurement problem. First, this paper takes the center of the sea area as the coordinate origin, establishes a one-dimensional coordinate system, and derives the functional relationship between the coordinate position of the measured ship axis and the angle of the seabed slope through the triangle edge relationship. At the same time, the mathematical relationship between the depth of the water body and the position of the measuring ship is constructed, and the relationship between the single coverage width of the detection system and the depth of the water body is found using the sine theorem. Subsequently, this paper established a two-dimensional sea area measurement model. Taking the center point of the sea area to be measured as the coordinate origin, a three-dimensional coordinate system was constructed. The normal vector projection direction was taken into account to obtain the new slope angle, and the two-dimensional sea area measurement was converted into a one-dimensional sea area. Measurement. Finally, this article uses MATLAB to conduct simulation experiments and gives the relationship between the coverage width and the position of the survey ship at different angles between survey line directions, providing an effective reference for the multi-beam sounding strategy.

Research on Optimization Design Based on Heliostat Field

This study aims to deeply explore the mathematical modeling and performance optimization of solar heliostat fields, in order to improve their energy output efficiency. The solar heliostat field is an innovative solar heating system that focuses solar radiation on the absorption tower through a reflector, thereby generating high-temperature heat energy. This article mainly discusses the performance analysis and parameter optimization of the heliostat field to achieve optimal performance while meeting the rated power requirements. A simulated solar model was established using a three-dimensional Cartesian coordinate system, taking into account the effects of solar altitude angle and direct normal irradiance (DNI). The model in this paper comprehensively considers the effects of shadow occlusion loss, cosine efficiency, atmospheric transmittance, collector truncation efficiency, and mirror reflectance on the mirror field. The specific values of each parameter were calculated using model algorithms such as the HFLCAL model, To provide a basis for accurate performance analysis and solve the problem of parameter optimization, this article defines an objective function aimed at improving the energy utilization efficiency of the heliostat field by adjusting the parameters of the reflector, in order to achieve optimal performance. The above parameters are determined by establishing a genetic algorithm to define constants and initial parameters, and initializing the overall layout of the heliostat field to calculate the optical efficiency of the heliostat. In each iteration, the optimal heliostat field layout can be recorded. The final optimal solution includes parameters such as the position coordinates of the absorption tower, heliostat size, installation height, number of heliostats, and heliostat position.

Design of Convergent and Accurate Guidance Law with Finite Time in Complex Adversarial Scenarios

The target can deceive the flight vehicle by releasing an infrared decoy to make the line-of-sight (LOS) angle rate deflect greatly, thus causing the flight vehicle to miss the target. Therefore, in order to accurately strike the target in complex adversarial scenarios, this paper proposes a finite-time convergence guidance law (FTCG) combined with a finite-time disturbance observer (FTDO). The complex adversarial scenario is established by combining the relative motion model between the flight vehicle and the target and the motion model of the infrared decoy. Based on this, considering the dynamic characteristic of the flight vehicle’s autopilot, a guidance model is obtained. Utilizing sliding mode control theory and finite-time control theory, an FTCG of the LOS angle rate is designed. Then, the finite-time convergence of the guidance law is proved and the total convergence time is derived. Finally, for the target maneuvering that is difficult to measure in the guidance law, an FTDO is used to estimate and compensate for the target maneuvering in the guidance law. Simulation results show that the FTCG can make the LOS angle rate quickly converge and accurately strike the target in different scenarios, with a good guidance accuracy and robustness. Compared with the sliding mode guidance law (SMGL) and the adaptive sliding mode guidance law (ASMGL) based on an extended state observer (ESO), the advantages of the designed guidance law are illustrated. Finally, FTCG is extended to be three dimensional and compared with the proportional navigation guidance law (PNG) to further illustrate its effectiveness in a three-dimensional coordinate system.

Research on the Logical Direction of Traditional Culture Inheritance and Promotion in the Internet Era

Abstract China’s traditional cultural heritage is facing serious challenges under the impact of modern culture. The somatosensory interaction gestures for cultural relics are designed using the Kinect somatosensory interaction model in this paper. The appearance of virtual cultural relics can be designed and realized using a three-dimensional coordinate system. Combined with the method of digital projection, the interaction projection generated by the Kinect somatic interaction model is corrected by the geometric correction method, and the edge fusion algorithm is applied to correct and fuse the edges of the corrected virtual artifact appearance. Testing the effects of cultural inheritance and promotion in the 38 regions of the application is carried out through the application of the cultural relics interaction. According to the findings, the highest score for traditional culture inheritance among the 38 regions is 28.36, and four regions have inheritance scores above 20 points. In traditional culture promotion, the highest score region is close to 12 points, and the heritage interaction experience can make users feel the inherent culture of the heritage, which has a positive effect on traditional culture inheritance and promotion.

The uniformly continuous theorem of fractal interpolation surface function and its proof

<abstract> <p>In order to research uniform continuity of fractal interpolation surface function on a closed rectangular area, the accumulation principle was applied to prove uniform continuity of fractal interpolation surface function on a closed rectangular area. First, fractal interpolation surface function was constructed by affine mapping. Second, the continuous concept of fractal interpolation surface function at a planar point in a three-dimensional cartesian coordinate space system and uniform continuity of fractal interpolation surface function on a closed rectangular area were defined in the paper. Finally, the uniformly continuous theorem of fractal interpolation surface function was proven through accumulation principle in the paper. The conclusion showed that fractal interpolation surface was uniformly continuous function on a closed rectangular area.</p> </abstract>