102 results about "Geometric mapping" patented technology

The invention discloses a method for optimizing micro-crack segmentation based on deep learning and super-resolution reconstruction, and the method comprises the steps: cutting an image in real time, obtaining an image block which takes a component as a target main body, and synchronously recording a homography matrix for geometric mapping; selecting an amplification strategy to improve the resolution, and recording a scale mapping relation; inputting the enhanced image block into a double-flow network; adaptive fusion and reconstruction are carried out on the two branch features, and a high-resolution texture image is output; generating a geometrically corrected ortho-image, fusing the geometrically corrected ortho-image with original illumination information, and outputting a corrected image with a known pixel size; identifying cracks, spalling and honeycomb diseases in parallel; generating a unified defect confidence map; calculating real geometric parameters of the BIM in a BIM global coordinate system through coordinate back projection; and generating quantitative defect reports and maintenance suggestions. The method has the advantage that seamless connection between the detection result and the BIM global coordinates is realized.

The invention discloses a cross-view multi-target collaborative perception and global tracking method. The method comprises the following steps: receiving original video streams of different views in parallel; carrying out feature extraction and content perception feature recombination processing; establishing a homography transformation matrix representing the mapping relation between the visual angles; performing forward geometric mapping by using the homography transformation matrix, and performing reverse mapping, secondary confirmation and state updating; a joint cost model based on space-time-appearance fusion is constructed, the potential association degree of unassociated residual targets is quantified, and missing targets are recalled; performing duplicate removal and optimization on the targets in the association set; and training and optimizing the network. According to the embodiment of the invention, the method achieves the capturing of a pixel-level target, and improves the texture and edge expression capability of a tiny target in a deep feature map. Efficient fusion of multi-dimensional spatio-temporal information among visual angles is realized; higher robustness and tracking continuity are achieved, and the integrity and fineness of a final trajectory result are improved; and the recall is ensured, and the generation of redundant tracks is avoided at the same time.

The invention relates to the technical field of airborne wind power measurement, and discloses an airborne wind measurement laser radar method and system. The method comprises the following steps: generating a scanning time sequence identifier and a path correction mark structure through scanning beat synchronization and stray light shielding processing; executing time-frequency demodulation and quality gating based on the back scattering signal to generate an observation wind speed initial value sequence; performing time alignment and motion compensation in combination with inertial navigation data, and generating a wind speed vector grid fragment through spatial interpolation and scanning geometric mapping; and finally, generating a configuration updating instruction structure through coordinate alignment and grid splicing. According to the invention, the precision and the anti-interference capability of wind field measurement in an airborne environment are effectively improved, and the data reliability and the system stability under a complex meteorological condition are remarkably enhanced through multi-source data fusion and a self-adaptive compensation mechanism.

The invention discloses a tunnel cross-sectional image analysis method based on image processing, and aims to solve the problems that a surface image is not clear in correspondence with a transient seismic wave method, a geological radar and a resistivity imaging section space, and anomalies at a certain distance in front are difficult to map to a tunnel face. According to the method, anisotropic reforming is carried out by adopting a Fourier neural operator, cross-modal Transform registration of a micro attention mask based on sector geometry, curve mileage and section polar coordinate position coding is combined, analytic geometry mapping and uncertainty propagation are matched, tunnel face structure traces and water seepage texture evidences are fused, and the tunnel face structure traces and the water seepage texture evidences are combined. The technical effects of accurate positioning of abnormity on the tunnel face, position confidence range estimation, risk grading early warning, stripe artifact suppression, abnormal boundary reservation and output of structured results of mileage stake numbers, azimuth angles, distance intervals and the like are achieved.

The invention discloses a geometric analytic expression three-dimensional reconstruction method, and relates to the technical field of computer vision and three-dimensional environment perception. According to the method, for an application scene with a target area located in a known space attitude plane, an accurate geometric mapping relation among a navigation coordinate system, a camera coordinate system and an imaging plane is constructed by fusing a visible light image, a single-point distance measurement value and attitude information output by an attitude sensor (such as an IMU); and pixel-level depth estimation is realized by adopting an analytic expression calculation strategy, so that high-precision and low-complexity three-dimensional reconstruction of a coplanar region is completed.

The invention discloses a determination method for an injection orifice of an enhanced vapor injection compressor, the opening angle theta open and the closing angle theta close of the injection orifice in an enhanced vapor injection loop in the compressor are determined, accurate determination of the position of the injection orifice is realized by combining a three-circle positioning geometric mapping method, and the injection orifice can be accurately determined through geometric constraints of a base circle, an auxiliary circle and a rotor inner circle trajectory circle. The settable area of the jet orifice on the partition plate is precisely defined, the maximum allowable outline of the jet orifice is determined through the inscribed circle, it is ensured that the jet orifice can be reliably opened and sealed within the calculated ideal angle range in the rotor movement process, gas backflow and mechanical interference are prevented, the timing precision of enhanced vapor injection and the control accuracy of the gas injection amount are improved, and the service life of the jet orifice is prolonged. The adaptability and the operation stability of the compressor under different working conditions are improved, and the injection efficiency is improved.

The invention relates to the technical field of medical auxiliary diagnosis, and discloses a hypospadias penis curvature measuring method based on physical simulation inversion. The invention aims to solve the technical pain point that the penile erection curvature and the internal fibrosis focus distribution are difficult to quantify noninvasively and accurately before the operation in the existing hypospadias diagnosis and treatment. According to the method, a standard white mold containing fine anatomical partitions is constructed, personalized geometric mapping is realized by using a static look-around image, and constraint physical parameter inversion is performed in combination with a multi-attitude dynamic stress image, so that the digital twin with real biomechanical properties is reconstructed in a virtual environment. According to the method, the erection bending form can be accurately predicted in the non-erection state, the mechanical property abnormal area range is positioned, operation planning is assisted, experience medical treatment is spanned to accurate digital medical treatment, and the wound diagnosis and treatment and operation risks are remarkably reduced.

The invention discloses a virtual reality roaming method and system based on a multi-view panoramic image model, and belongs to the technical field of computer vision and virtual reality. Through a multi-viewpoint panoramic image set, real-time generation of a high-quality panoramic image from a known viewpoint to any unknown viewpoint is realized based on a spherical projection viewpoint transformation algorithm. Modeling generation methods for a road scene and a region scene are respectively designed according to scene feature differences, so that scene representation with complete coverage is constructed. According to the system, adjacent viewpoints are quickly positioned through a spatial index mechanism, geometric mapping and multi-viewpoint weighted fusion are performed by using the spherical projection algorithm, and a smooth and continuous free viewpoint roaming picture is rendered in a virtual reality environment. According to the method, on the premise of ensuring high fidelity of the scene, real-time rendering is realized on common consumption-level hardware, and the coherence and the degree of freedom of immersive interactive experience are improved.

The invention provides a deployable flexible GMR eddy current testing method and system for a complex curved surface component, and relates to the technical field of nondestructive testing. The method comprises the following steps: establishing a curved surface coordinate system and an expansion domain coordinate system, constructing a geometric mapping relation of a flexible sensing array, and performing clearance compensation, attitude correction and temperature drift correction on multi-frequency response data in an expansion domain to form a unified response data set; defect response distribution is generated through robust reconstruction and reprojected to the curved surface coordinate system, and space positioning and size and orientation recognition of defects are achieved; and adaptively updating the attitude, the path and the excitation scheme in combination with the fitting state parameters until the detection coverage and the confidence meet the requirements. According to the method, high-precision detection and process traceability of the defects of the complex curved surface component are realized.

The invention provides a semantic scene reconstruction and interaction method and system based on a visual language model, and relates to the technical field of artificial intelligence and robots. The method comprises the following steps: acquiring image data shot by a camera; estimating a world pose of the camera; inputting the image data to a Visual Language Model (VLM) to generate a structured description containing an object semantic tag and quantitative spatial information thereof relative to the camera; calculating the world pose of the object according to the camera pose and the quantitative space information; a node representative of the object is created or updated in a hierarchical scene graph. The invention further provides a corresponding interaction system. According to the method, a rich and visual three-dimensional semantic map facing natural language interaction is constructed by deeply fusing the semantic understanding ability of the VLM and the geometric mapping ability of the SLAM, and the intelligent level of robot environment perception and man-machine interaction is greatly improved.

The invention discloses an integrated circuit electrical characteristic simulation method and device, a terminal and a storage medium, and the method comprises the steps: obtaining a to-be-simulated integrated circuit model, carrying out the mesh generation of the to-be-simulated integrated circuit model, so as to obtain an integrated circuit mesh data set composed of a plurality of mesh units, constructing a corresponding charge basis function and a current basis function based on the grid units; step-by-step fusion updating of the charge primary function is realized by taking the charge primary function as a fusion object, and meanwhile, corresponding fusion updating is performed on the current primary function in a geometric mapping mode; and after all fusion updating is completed, obtaining an integrated circuit primary function data set, and performing electrical characteristic simulation on the to-be-simulated integrated circuit based on the integrated circuit primary function data set. According to the method, fast updating and low-order representation of a complex coupling capacitance matrix are achieved, compared with a traditional post-order reduction method, the theoretical complexity is reduced from O (n3) to O (n), and meanwhile the model order reduction efficiency is greatly improved while the model precision and the order reduction effect are guaranteed.

The invention relates to the technical field of mode recognition, in particular to a switch cabinet drawer early warning system based on multi-mode perception, and the system comprises the steps: obtaining a visible light video, an infrared thermal image, a mechanical waveform, an electrical time sequence signal and asynchronous event stream data in the operation process of a switch cabinet through a data collection module; a tensor construction module is used for executing geometric mapping correction and timestamp synchronization by taking the visible light video as a space reference, and constructing a multi-modal spatial-temporal feature tensor containing texture, temperature and electromechanical response; the state variable calculation module projects the electrical time sequence signal to an orthogonal feature space, decouples and extracts an active component feature vector, and calculates a dynamic resistance state variable; and the abnormity identification module further constructs a physical information neural network which introduces a physical equation residual error as a constraint term, the tribological parameters are solved through online iteration, and through virtual trajectory comparison and parameter time-varying trend analysis, classified judgment of lubrication failure, mechanical jamming and contact faults is realized.

The present application relates to the technical field of fusion design, in particular to a three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method, in the present application, by setting the implicit function equation of the three-period minimal surface and screening the control points according to the spatial distribution and geometric constraints, the accurate selection and positioning of the structure unit in the design target area are realized, the accuracy of geometric mapping is improved, the inverse distance weighting calculation is carried out through the convolutional neural network, the difference of the geometric region in the space can be effectively identified, the response ability of structure fusion is improved, the weight is calculated combined with the spatial distribution of the control points, and the weight distribution mechanism is formed by using the actual geometric distance between the control points, the continuity and smoothness of the geometric response in the interpolation region are guaranteed, the graph neural network is introduced to process the surface continuity problem, the local geometric mutation area is identified and corrected through the edge weight and topological structure between nodes, and the geometric smoothness and boundary consistency of the whole structure are improved.

The invention provides a data closed-loop method and system, and the method comprises the following steps: importing a model format file, and obtaining the unstructured data of the model format file; packaging the unstructured data to form standard data, wherein the standard data comprises a geometric mapping relationship; a configuration file is imported, the configuration file comprises configuration parameter information, and a parameter mapping relation between the configuration parameter information and the standard data is obtained; and constructing a closed-loop data set according to the geometric mapping relationship and the parameter mapping relationship, wherein the closed-loop data set is suitable for feeding back the hierarchical relationship of the model format file. According to the data closed-loop method and system provided by the invention, the transparency of a data closed-loop process can be improved.

The application relates to the technical field of indoor positioning, in particular to an indoor personnel positioning method and system based on multi-modal perception. The application proposes the following scheme: by acquiring the ultra-wideband channel impulse response, millimeter wave radar data and thermal imaging data of each layer, combining building information for double-base geometric mapping, reconstructing an indoor ray path and generating an occupancy grid map. Further, the water mist distribution intensity generated by a spraying device is collected, phase correction and beam domain purification are performed on the millimeter wave data, and flow direction filtering and flicker suppression are performed on the thermal imaging data to obtain pretreatment data. On this basis, motion prior information and boundary constraint information are extracted, and fusion is realized through mass conservation update and normalization synthesis in the occupancy grid map, and finally the position information and motion direction of the object to be positioned are output. The application can maintain positioning stability and accuracy under the interference of fire smoke, water mist and multipath effect, and is suitable for high-risk scenes such as fire rescue.

A tracking system for tracking an expansion state of an object is provided. The tracking system includes at least one processor and a memory having stored therein instructions that, when executed by the at least one processor, cause the tracking system to perform a probabilistic filter that iteratively tracks a confidence of the expansion state of the object, wherein the confidence is predicted using a motion model of the object and further updated using a composite measurement model of the object. The composite measurement model includes a plurality of probability distributions constrained to lie on a contour of the object and has a predetermined relative geometric mapping to a center of the object. Further, the tracking system tracks the expansion state of the object based on the updated confidence of the expansion state.

The invention provides an indoor 3D scene semantic segmentation method and system based on multi-view solid geometry guidance, and relates to the technical field of indoor 3D scene understanding, and the method comprises the following steps: constructing a multi-view geometric mapping relation model; establishing a 2D-3D feature combined 3D scene semantic segmentation network based on a multi-view geometric mapping relation; constructing a cross-view 2D feature fusion device, and performing conversion and adaptive fusion on the multi-view 2D features to obtain multi-view complementary information enhanced 2D features; further constructing a cross-modal 2D-3D feature fusion device, and performing adaptive fusion on the 2D features and the 3D features after multi-view information enhancement to obtain 3D features with rich information representation; and finally, inputting the fused 3D features into a simple classifier to obtain a semantic segmentation result of the 3D point cloud model. According to the method, the semantic segmentation precision of the 3D point cloud model in the indoor complex scene is improved.

The application provides an unmanned aerial vehicle optimal track planning method and system fusing image recognition and M-RRT and APF algorithms. Wind power generator point cloud and visual data are acquired in real time through a multi-modal sensor, key components of blades are recognized based on deep learning, a geometric mapping model is constructed, tip point is corrected in combination with DBSCAN clustering, and a shutdown posture is predicted. A global path adopts an M-RRT algorithm improved by a direction heuristic factor, and a key area of the blade is guided to search; a local track is optimized through a dynamic weight APF algorithm, and a repulsive force field is adjusted in real time to cope with posture changes. An online replanning mechanism is introduced, NSGA-III multi-objective optimization is triggered when an environment mutates or a tracking error exceeds a threshold, and optimal tracks are generated by comprehensively considering energy consumption, time and safety. The system integrates high-precision perception, adaptive planning and dynamic optimization, and significantly improves inspection coverage and track safety under a complex shutdown posture.

The invention relates to the technical field of data processing, in particular to a code disc concentricity adjusting method for a DD motor, and the method comprises the steps: obtaining a rotor absolute angle, a pulse error and a rotor angular velocity of each sampling point, and calculating the credibility weight of each sampling point according to the rotor angular velocity; a weighted vector integral model is introduced, the mode length of an eccentric main vector and an eccentric phase angle are obtained through the combined operation of orthogonal decomposition and full-period accumulation, and the physical adjustment distance of the code disc is calculated based on the mode length of the eccentric main vector in combination with a geometric mapping coefficient and a friction compensation amount. According to the eccentric phase angle and the physical adjustment distance, visual guide information is generated, an operator is instructed to conduct concentricity adjustment on the coded disc, noise and deformation interference are effectively filtered out, pulse errors are converted into specific physical displacement instructions, and standardization and high efficiency of debugging operation are achieved.

This application relates to the field of cloud storage technology and discloses a file management system and method based on cloud storage, including: a data encryption module for homomorphically encrypting user-uploaded files and storing the encrypted files in the cloud; an algebraic geometry mapping module for mapping the encrypted files to an algebraic variety and optimizing the storage path according to the algebraic geometry structure; a query processing module for receiving user query requests, performing geometric measurement calculations on the encrypted files, and returning matching results while in an encrypted state; and an adaptive storage management module for dynamically adjusting the file storage location according to the file access frequency, enabling fast retrieval of frequently accessed files. This invention uses homomorphic encryption technology to encrypt user-uploaded files, achieving the technical effect of effectively protecting data privacy during cloud storage and computation.

The invention belongs to the field of X-ray imaging, and provides a double-energy-point double-magnification imaging device and method based on a time broadening type framing camera, and the device comprises a pinhole sheet and the time broadening type framing camera; the method comprises the steps of pinhole piece and time broadening type framing camera imaging, geometric mapping model construction, distortion correction function fitting and image calibration. According to the invention, photoelectron imaging and transmission light imaging are realized at the same time by using the time-broadening framing camera, so that two spatially corresponding images are formed; the difference between electron acceleration and focusing characteristics in the time-broadening framing camera can be reflected by comparing the size and distortion difference of the straight-through light image and the photoelectron image, and dual-channel response mutual calibration is achieved.

The invention discloses a continuous fiber 3D printing trajectory optimization method based on curvature constraint, and the method comprises the steps: determining a minimum stable turning radius according to fiber deposition failure experiments at different corners, and obtaining a maximum forming curvature constraint value; establishing a geometric mapping relation between a fiber deposition path and a nozzle movement path by quantifying the hysteresis offset characteristic of the fiber center in a nozzle pipe cavity; performing continuous curvature detection on the path by using a quintic polynomial, constructing a Hermite bridging curve for a curvature overrun section, and solving a tangent vector parameter by taking the maximum curvature as a constraint and the cavity area minimization as an optimization target to obtain an optimal compensation curve; and according to the fiber-nozzle relative motion track model and the optimal compensation curve, the actual printing track of the nozzle is reversely solved. The defects of fiber edge warping, stripping and wire breaking in the printing process are avoided from the physical level, and it is guaranteed that printing is conducted successfully; deposition defects at corners are reduced to the maximum extent while physical forming constraints are met.

This invention discloses a GIM data processing method and system for digital handover, relating to the field of data processing technology. The method includes: acquiring heterogeneous GIM handover data from different departments, including spatial location data, equipment attribute data, status monitoring data, and semantic data; performing standardization processing and setting hierarchical relationships according to the processing objectives of power grid equipment; converting the handover data into a unified geometric algebra multivector based on a high-dimensional geometric mapping relationship and configuring geometric dimension identifiers; and projecting the unified geometric algebra multivector onto a constructed high-dimensional geometric algebra space. This invention solves the technical problems of inefficiently integrating multi-source heterogeneous GIM handover data and the lack of a unified mathematical framework for integrated computational expression of complex relationships between equipment in existing technologies. It achieves the standardization, structuring, and deep integration of cross-departmental GIM data, improving the quality, consistency, and analyzability of digital handover data.

The invention provides a track intrusion early warning method and system based on a three-dimensional space digital positioning technology, and relates to the technical field of track safety early warning, and the method comprises the steps: obtaining a track region video image stream and a preset track three-dimensional digital twinborn model; generating a pixel-model background registration field for eliminating perspective distortion according to the video image stream and the track three-dimensional digital twin model; obtaining a separation result according to the pixel-model background registration field; generating a spatial pose transformation parameter set according to a separation result; according to the space pose transformation parameter set and the orbit three-dimensional digital twinborn model, calculating to obtain a distance change rate vector; and performing space-time joint threat decision according to the distance change rate vector, and outputting an early warning result. According to the method, the millimeter-level positioning precision early warning of the intrusion behavior in the complex track scene is realized by establishing the differential geometric mapping reference of the pixel space and the track three-dimensional digital twinborn model and fusing the manifold optimization processing of the dynamic target identification and the track surface constraint space.

The present application belongs to the technical field of engineering structure optimization design, and discloses a kind of topological optimization method and equipment of three-dimensional curved surface composite material thin shell structure, steps are as follows: S1, using conformal geometric mapping algorithm three-dimensional curved surface grid is mapped to the parameterization coordinate of two-dimensional plane parameter domain angle-preserving, obtain the mapping relationship of three-dimensional curved surface composite material thin shell structure from three-dimensional curved surface to two-dimensional plane;S2, construct shell element stiffness matrix of finite element grid;S3, in two-dimensional plane parameter domain, with the relative density of shell element and the direction of element as design variable, establish the topological optimization model of finite element grid based on conformal mapping;S4, based on moving asymptote method and topological optimization model to update design variable;S5, based on the design variable and mapping relationship of updated inversion mapping back original three-dimensional curved surface, thus obtain the three-dimensional configuration of optimal material distribution of three-dimensional curved surface composite material thin shell structure.The present application improves optimization efficiency.

The invention relates to the technical field of thickness measurement, in particular to an X-ray thickness gauge material compensation method, which comprises the following steps of: setting a plurality of acquisition angles of an X-ray source and a detector in a range of-15 degrees to + 15 degrees, performing X-ray transmission on a measured object at each angle, and recording a transmission intensity value received by the detector. The X-ray source and the detector are set to carry out multi-angle acquisition in the angle range of-15 degrees to + 15 degrees, the coverage density of information of a detected object in different directions is improved, the analysis capability of a complex structure cross section is enhanced, and on the basis of multi-angle attenuation projection data, the detection accuracy is improved. According to the method, the cross section area of the measured object is discretized into the two-dimensional pixel grid, so that consistent modeling of the heterogeneous object is realized, initial modeling deviation caused by prior insufficiency of materials is avoided, and subsequent iterative correction operation is more accurate through geometric mapping of a pixel path and a projection path.

The present application relates to a kind of virtual livestock modeling method based on digital twinning, the method comprises: collecting the real data of livestock, including the body shape data and behavior characteristics of the livestock, including the environmental conditions, breeding information, physiological performance and production performance of the livestock;Based on the real data, the virtual livestock model of the livestock is constructed, including geometric mapping entity and heat production and heat dissipation model, the geometric mapping entity is used to simulate the appearance and behavior of the livestock based on the body shape data and the behavior characteristics;The heat production and heat dissipation model is obtained based on the training of the environmental conditions, the breeding information, the physiological performance and the production performance;Based on the virtual livestock model, simulation is carried out under the set scene, and simulation result is obtained.The technical scheme of the present application, by modeling and simulation to real livestock, realize the management, monitoring and optimization to livestock, so as to provide fine management for livestock production.

The invention discloses a holographic wall display method based on AI target perception and head-mounted equipment positioning, belongs to the technical field of immersive visualization, and solves the problems that an existing public display system is fixed in view angle, low in view finding intelligence, jittering in picture and inconsistent with a view angle space of head-mounted equipment. The method comprises the following steps: acquiring pose information of head-mounted equipment relative to a world coordinate system in real time, modeling and constructing a virtual camera in combination with human eye position parameters, and rendering a main view angle image; target discovery and saliency detection are synchronously completed, a dynamic framing optimization process is constructed based on detection information to solve an optimal picture, the optimal picture is output to a holographic wall for real-time display after geometric mapping of a holographic wall coordinate system, and the steps are continuously and circularly executed. According to the invention, visual angle space matching of the head-mounted device and the holographic wall is realized, intelligence and stability of public display are improved, and the method is suitable for virtual-real and augmented reality man-machine interaction scenes.

This invention pertains to the fields of unmanned agricultural machinery and computer vision, and discloses a CUDA-accelerated panoramic surround-view system for unmanned agricultural machinery under a WSL environment and its implementation method. The method includes: acquiring calibration images from four fisheye cameras; after standardizing and calibrating the calibration images from the four fisheye cameras, storing the generated camera intrinsic parameter matrix and distortion coefficients in YAML format files respectively; acquiring the YAML format file, calculating the projection matrix by interactively selecting four marker points, and appending the projection matrix to the same YAML format file to form a complete camera parameter file; based on the complete camera parameter file, performing pixel geometric mapping calculations between the bird's-eye view and the original image, and generating a binary lookup table (LUT); synchronously receiving real-time operational images from the four fisheye cameras and the binary LUT file, performing distortion correction and panoramic stitching, and generating a panoramic bird's-eye view for panoramic visualization output.

The invention relates to the technical field of optical element precision manufacturing, in particular to an optical element three-dimensional modeling method based on normal projection inverse transformation. Comprising the steps of establishing an ideal curved surface parameterization vector expression according to optical design parameters, and determining a curved surface body coordinate system and a vector height function; solving the gradient of the rise function to obtain gradient information of each point of the curved surface and calculating a unit normal vector; projecting the three-dimensional curved surface points to a preset reference plane along the normal direction of the curved surface, establishing a forward geometric mapping relation from the three-dimensional coordinates of the curved surface body coordinate system to the measurement coordinates of the interferometer, and obtaining an explicit expression of the measurement coordinates; two-dimensional normal error distribution data of the optical element are collected, errors are overlaid in the normal direction to construct an actual curved surface expression containing manufacturing errors, and the corresponding relation between three-dimensional normal errors and measurement data is established; and on the basis of forward mapping relation numerical value inverse transformation, the measurement coordinates are inversely calculated into curved surface body coordinates, and the curved surface body coordinates are substituted into an actual curved surface expression to obtain a complete three-dimensional curved surface model containing manufacturing errors.