A method for structured conversion of geometry data of CATIA part files

Abstract

This invention discloses a method for structured conversion of geometric data in CATIA part files, relating to the field of CAD data processing technology. The method includes: establishing a Beltrami partial differential equation in the complex domain based on the directional attribute of directed common edges; substituting the complex coordinates of the two-dimensional parameter domain curve as Dirichlet boundary conditions into the Beltrami partial differential equation; and numerically solving the equation using the finite element method to obtain the three-dimensional boundary curve of the two-dimensional parameter domain curve in three-dimensional space; determining whether the three-dimensional boundary curve and the three-dimensional space curve satisfy the geometric consistency condition based on the curve consistency deviation; and when the geometric consistency condition is met, converting the B-Rep geometric data and directed common edges into structured geometric data using JSON format. This invention improves the data fidelity and geometric robustness of computer-aided design part files during the structured conversion process.

Description

Technical Field

[0001] This invention relates to the field of CAD data processing technology, and in particular to a method for the structured conversion of geometric data in CATIA part files. Background Technology

[0002] With the profound evolution of computer-aided design technology, 3D modeling software such as CATIA, NX, and SolidWorks have become core supports for modern industrial design and manufacturing. In the field of complex geometric modeling, boundary representation, with its ability to accurately describe the topological structure and geometric shape of objects, has become the mainstream standard for describing 3D solid models in industry. Existing related technologies typically use industry standard formats as an intermediary, extracting basic geometric elements such as faces, loops, edges, and vertices by parsing the topological relationship flow within the model. To achieve data interoperability between different platforms, traditional technical approaches often rely on the API interfaces provided by the geometric kernel to linearly thin or discretize the underlying parametric surfaces and their corresponding 2D parametric domain curves, thereby constructing a geometric topology network that can be used for downstream simulation or rendering.

[0003] However, existing technologies still face significant challenges when acquiring and converting data for industrial parts with complex manifold characteristics or high-order continuity requirements. Conventional conversion processes often focus on extracting static data, lacking deep physical constraint verification mechanisms when dealing with the consistency of mapping between the two-dimensional parameter domain coordinates and the three-dimensional spatial analytical curves in the B-Rep model. Due to slight deviations in geometric tolerance settings, parameterization methods, and trimming surface algorithms among different modeling software, nonlinear geometric deviations may occur between the boundary curves mapped from the two-dimensional parameter domain to three-dimensional space and the three-dimensional spatial curves in the original B-Rep definition. In complex topological loop reconstruction processes, this deviation can easily lead to directional ambiguities or topological gaps in shared edges, making it difficult to achieve high-precision structured conversion requirements in terms of accuracy consistency of the converted geometric data, thus affecting the rigor of subsequent lightweight format conversions. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a method for structuring geometric data in CATIA part files to solve the problems of topological geometric deviation and conversion accuracy loss.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: This invention provides a method for structuring geometric data in CATIA part files, comprising: acquiring CATIA part files and reading accessible B-Rep geometric data from the CATIA part files; wherein the B-Rep geometric data includes patches, corresponding underlying parametric surfaces, two-dimensional parametric domain curves, and three-dimensional spatial curves; Based on the actual orientation of the boundary ring in the patch on the patch, construct the directed common edge corresponding to the topological edge in the boundary ring; Beltrami partial differential equations in the complex domain are established based on the directional properties of the directed common edge. The complex coordinates of the two-dimensional parameter domain curves are substituted into the Beltrami partial differential equations as Dirichlet boundary conditions. The three-dimensional boundary curves of the two-dimensional parameter domain curves in three-dimensional space are obtained by numerical solution using the finite element method. Based on three-dimensional boundary curves and three-dimensional spatial curves, curve consistency deviations are calculated using the Laplace operator and the Frobenius norm. The geometric consistency condition is determined based on the curve consistency deviation. When the geometric consistency condition is met, the B-Rep geometric data and the directed common edge are converted into structured geometric data in JSON format.

[0007] As a preferred embodiment of the geometric data structure conversion method for CATIA part files described in this invention, the specific steps of acquiring CATIA part files and reading accessible B-Rep geometric data from CATIA part files are as follows: The underlying geometry interface is called to parse the CATIA part file and obtain the internal logical organization structure of the CATIA part file. Locate the target geometry set within the logical organizational structure, perform a topological association search on the target geometry set, and output the topological description information corresponding to the target geometry set; Extract the underlying data items related to geometry and topological connections from the topology description information to obtain B-Rep geometric data.

[0008] As a preferred embodiment of the geometric data structure conversion method for CATIA part files described in this invention, the specific steps for constructing directed common edges corresponding to the topological edges in the boundary rings based on the actual orientation of the boundary rings on the surface are as follows: Project the boundary loop in the patch onto the two-dimensional parameter domain corresponding to the underlying parametric surface to obtain the closed parameter domain curve loop; Calculate the algebraic area of ​​the closed parametric domain curve loop in the two-dimensional parametric domain, and determine the rotation direction of the closed parametric domain curve loop based on the sign of the algebraic area. Based on the rotation direction of the closed parameter domain curve loop, the corresponding topological edges are encapsulated in a directed manner to generate directed common edges.

[0009] As a preferred embodiment of the geometric data structure conversion method for CATIA part files described in this invention, the specific steps of calculating the algebraic area of ​​the closed parameter domain curve loop in the two-dimensional parameter domain and determining the rotation direction of the closed parameter domain curve loop based on the positive or negative sign of the algebraic area are as follows: The algebraic area is obtained by calculating the line integral of a closed parametric domain curve loop using Green's theorem. When the area of ​​the current number is positive, the rotation direction of the closed parametric domain curve loop is determined to be counterclockwise; When the area of ​​the current number is negative, the rotation direction of the closed parametric domain curve loop is determined to be clockwise.

[0010] As a preferred embodiment of the geometric data structure conversion method for CATIA part files described in this invention, the specific steps for obtaining the three-dimensional boundary curve of the two-dimensional parameter domain curve in three-dimensional space are as follows: The two-dimensional parameter domain curve is represented as a complex variable function, and transformation operators are assigned to the complex variable function based on the directional property of the directed common edge. Calculate the Beltrami coefficients of the underlying parametric surface based on the first fundamental form of the underlying parametric surface; Using Beltrami coefficients as the parameters for measuring mapping distortion, and employing transformation operators to apply linear weighting constraints to the derivative terms of complex variable functions, Beltrami partial differential equations in the complex domain are established. Substituting the complex coordinates of the two-dimensional parametric domain curve as Dirichlet boundary conditions into the Beltrami partial differential equation, a mapping boundary value equation is generated. The finite element method is used to discretize the mapping boundary equations and obtain the quasi-conformal mapping solution function. The quasi-conformal mapping solution function is inversely mapped to three-dimensional real-domain coordinates to generate a three-dimensional boundary curve.

[0011] As a preferred embodiment of the geometric data structure conversion method for CATIA part files described in this invention, the specific steps for calculating curve consistency deviation based on three-dimensional boundary curves and three-dimensional spatial curves using the Laplacian operator and Frobenius norm are as follows: The Laplacian operator is used to perform multi-scale smoothing iterations on the three-dimensional boundary curves and the three-dimensional space curves to obtain scale space curves at different iteration scales. Calculate the curvature and torsion of the scale space curve, and construct the three-dimensional boundary curve feature matrix and the three-dimensional space curve feature matrix based on the curvature and torsion through serialization and recombination; The Frobenius norm is used to calculate the second-order norm distance between the feature matrix of the three-dimensional boundary curve and the feature matrix of the three-dimensional space curve, and the second-order norm distance is defined as the matrix residual. Weighted summation of matrix residuals at different iteration scales generates curve consistency deviation.

[0012] As a preferred embodiment of the geometric data structure conversion method for CATIA part files described in this invention, the step of determining whether the three-dimensional boundary curve and the three-dimensional space curve meet the geometric consistency condition based on the curve consistency deviation, and when the geometric consistency condition is met, converting the B-Rep geometric data and directed common edge data into structured geometric data using JSON format, is as follows: Map the 3D boundary curve and the 3D spatial curve to a higher-dimensional Riemannian manifold space, and calculate the discrete Fraser distance between the 3D boundary curve and the 3D spatial curve in the higher-dimensional Riemannian manifold space; The structural correlation coefficient between the three-dimensional boundary curve and the three-dimensional spatial curve is calculated using the local linear embedding algorithm. When both the curve consistency deviation and the discrete Fraser distance are less than the preset upper limit of geometric tolerance, and the structural correlation coefficient is greater than the preset geometric similarity threshold, the geometric consistency condition is determined to be met, and the B-Rep geometric data and the directed common edge are written into the corresponding JSON fields to generate structured geometric data.

[0013] As a preferred embodiment of the geometric data structuring conversion method for CATIA part files described in this invention, the specific steps of mapping the three-dimensional boundary curves and three-dimensional spatial curves to a high-dimensional Riemannian manifold space and calculating the discrete Fréchet distance between the three-dimensional boundary curves and three-dimensional spatial curves in the high-dimensional Riemannian manifold space are as follows: The three-dimensional boundary curve and the three-dimensional space curve are resampled with equal arc lengths to obtain a discrete set of sampling points. Calculate differential geometric properties at discrete sampling points in a discrete sampling point set, and construct multidimensional feature vectors based on differential geometric properties; We define a high-dimensional Riemannian manifold space with differential geometric properties as coordinate axes, and use the weighted Euclidean inner product of the attribute components in the multidimensional eigenvector as the Riemannian metric of the high-dimensional Riemannian manifold space. Multidimensional feature vectors are mapped to manifold point sets on a high-dimensional Riemannian manifold space, and geodesic distances between manifold point sets are calculated based on Riemannian metrics to generate a geodesic distance cost matrix. A dynamic programming algorithm is used to search for point-to-point coupling paths that satisfy monotonicity constraints in the geodesic distance cost matrix; Calculate the maximum geodesic distance in the coupled path of each point pair, and generate a set of maximum geodesic distances; The global minimum value in the set of maximum distances to the ground line is taken as the discrete Fraser distance between the three-dimensional boundary curve and the three-dimensional spatial curve in the high-dimensional Riemannian manifold space.

[0014] As a preferred embodiment of the geometric data structure conversion method for CATIA part files described in this invention, the step of calculating the structural correlation coefficient between the three-dimensional boundary curve and the three-dimensional spatial curve using a local linear embedding algorithm is as follows: The local neighborhood point set is extracted from the discrete sampling point set based on the criterion of minimizing Euclidean distance, and a local reconstruction error function is constructed based on the local neighborhood point set with the goal of minimizing the linear combination residual. The local reconstruction error function is solved using the Lagrange multiplier method to generate the local reconstruction weight matrix. Using the local reconstruction weight matrix as a structural invariance constraint, the multidimensional eigenvectors are mapped to a low-dimensional linear space through eigenvalue decomposition to obtain the low-dimensional embedding coordinates. Covariance analysis is performed on the low-dimensional embedded coordinates corresponding to the three-dimensional boundary curve and the three-dimensional spatial curve to obtain structural feature vectors, and the cosine similarity between the structural feature vectors is calculated to generate structural correlation coefficients.

[0015] As a preferred embodiment of the geometric data structure conversion method for CATIA part files described in this invention, the upper limit of the geometric tolerance is set based on the modeling accuracy of the CATIA part file; The geometric similarity threshold is set based on the curvature fluctuation rate of the high-dimensional Riemannian manifold space.

[0016] The beneficial effects of this invention are as follows: by establishing a quasi-conformal mapping reconstruction logic driven by Beltrami equations, geometric distortion in parameter space transformation is accurately compensated to eliminate boundary cracking. Combined with geodesic distance and structural correlation verification under high-dimensional Riemannian manifolds, a deep consistency verification from numerical accuracy to topological structure is achieved, which effectively improves the data fidelity and geometric robustness of computer-aided design part files in the process of structural transformation. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the method for structuring geometric data in CATIA part files.

[0019] Figure 2 A flowchart for determining the rotation direction of a closed parameter domain curve loop.

[0020] Figure 3 A flowchart for reading accessible B-Rep geometry data.

[0021] Figure 4 This is a flowchart for calculating the structural correlation coefficient. Detailed Implementation

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0023] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0024] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0025] Reference Figures 1-4 This is one embodiment of the present invention, which provides a method for structuring geometric data for CATIA part files, including the following steps: S1. Acquire CATIA part files and read accessible B-Rep geometric data from the CATIA part files.

[0026] It should be noted that CATIA (Computer-Aided Tri-Dimensional Interactive Application) is a 3D design software.

[0027] B-rep (Boundary Representation) is a method for representing three-dimensional solids by accurately describing all the geometric elements that constitute the boundary of an object and their topological connections.

[0028] S1.1 Call the underlying geometry interface to parse the CATIA part file and obtain the internal logical organization structure of the CATIA part file.

[0029] Furthermore, the root container of the CATIA part file is read through the underlying geometry interface. The child objects of each node under the root container are recursively enumerated. If a child object is a set of geometric shapes, it is treated as a branch node for further enumeration; if a child object is a geometric element, it is treated as a leaf node. All enumerated nodes are connected according to parent-child relationships, forming a multi-branch tree structure from the root node to the leaf nodes of each geometric element. This multi-branch tree is the logical organizational structure.

[0030] S1.2 Locate the target geometric set in the logical organization structure, perform a topological association search on the target geometric set, and output the topological description information corresponding to the target geometric set.

[0031] Furthermore, in the logical organization structure, node matching is performed based on the name or identifier of the target geometry set to locate the node of the geometry set. Starting from the node, all leaf nodes of the geometry elements under it are traversed. For each point, line, face, and volume geometry element represented by the leaf node, the adjacency and dependency relationships between the geometry element and other geometry elements in the same geometry set are queried. The adjacency relationship includes the common edge between faces, the common vertex between edges, and the boundary dependency between the volume and the face. The dependency relationship includes which face an edge belongs to and which edge a vertex belongs to.

[0032] All adjacency and dependency relationships are grouped and organized according to the identifiers of geometric elements to form a complete set of descriptive data that records the connection methods and hierarchical dependencies between geometric elements within the target geometry set. This descriptive data is the topology description information.

[0033] S1.3 Extract the underlying data items related to geometry and topological connections from the topology description information to obtain B-Rep geometric data.

[0034] Furthermore, from the topology description information, patch indexes, coefficients of the underlying parameter surface equation, control points of the two-dimensional parameter domain curve, and geometric parameters of the three-dimensional space curve are filtered and extracted. The patch indexes, coefficients of the underlying parameter surface equation, control points of the two-dimensional parameter domain curve, and geometric parameters of the three-dimensional space curve are then encapsulated in a structured manner to obtain B-Rep geometric data.

[0035] It should be noted that B-Rep geometric data includes patches, the underlying parametric surfaces corresponding to the patches, two-dimensional parametric domain curves, and three-dimensional spatial curves.

[0036] S2. Based on the actual orientation of the boundary ring in the patch on the patch, construct directed common edges corresponding to the topological edges in the boundary ring.

[0037] S2.1 Project the boundary loop in the patch onto the two-dimensional parameter domain corresponding to the underlying parametric surface to obtain the closed parameter domain curve loop.

[0038] Furthermore, by uniformly sampling along each topological edge of the boundary ring at a preset arc length step, the boundary ring in the patch is discretized into a series of three-dimensional points. For each three-dimensional point, its coordinates are substituted into the nonlinear equation system corresponding to the parameterized equation of the underlying parametric surface. Using the known parameter points near the point on the surface as initial values, the inverse function of the nonlinear equation system is solved using the Newton-Raphson iteration method. When the iteration converges to the preset convergence accuracy, the parameter coordinates corresponding to the three-dimensional point in the two-dimensional parameter domain are obtained. All parameter coordinates are connected sequentially according to the connection order of the original boundary ring to form a closed parameter domain curve loop.

[0039] It should be noted that the arc length step size is set based on the maximum permissible chord height difference between adjacent 3D points on the boundary loop; the convergence accuracy is set based on the upper limit of the coordinate reconstruction error when 3D points are mapped to the 2D parameter domain.

[0040] Newton's method is a method for approximating the solution of equations in the real and complex number fields. The principle is to use the intersection of the tangent line of the function at the current point and the horizontal axis as the approximation for the next iteration and to repeat the process to approximate the true solution.

[0041] S2.2 Calculate the algebraic area of ​​the closed parametric domain curve loop in the two-dimensional parametric domain, and determine the rotation direction of the closed parametric domain curve loop based on the positive or negative sign of the algebraic area.

[0042] S2.2.1. Use Green's theorem to calculate the algebraic area by performing line integrals on the closed parametric domain curve loop.

[0043] Furthermore, the closed parametric domain curve loop is divided into a series of interconnected parametric curve segments based on adjacent parametric coordinate points. For each parametric curve segment, its starting and ending coordinates are taken, and the product of the starting x-coordinate and the ending y-coordinate, and the product of the ending x-coordinate and the starting y-coordinate are calculated. The difference between these two products is taken as the contribution value of that segment to the algebraic area. The contributions of all parametric curve segments are summed, and half of the summation result is taken as the algebraic area of ​​the closed parametric domain curve loop.

[0044] S2.2.2 When the area of ​​the current number is positive, the rotation direction of the closed parametric domain curve loop is determined to be counterclockwise.

[0045] S2.2.3 When the area of ​​the current number is negative, the rotation direction of the closed parameter domain curve loop is determined to be clockwise.

[0046] S2.3. Based on the rotation direction of the closed parameter domain curve loop, the corresponding topological edges are encapsulated in a directed manner to generate directed common edges.

[0047] Furthermore, based on the rotation direction (counterclockwise or clockwise) of the closed parameter domain curve loop, a direction attribute is assigned to each topological edge in the boundary loop: if the rotation direction is counterclockwise, the outer side of the boundary loop is positive; otherwise, the inner side is positive. The geometric data of the topological edges and the assigned direction attribute are encapsulated into a directed common edge data structure, outputting a directed common edge object containing topological edge references and direction identifiers.

[0048] S3. Based on the directional property of the directed common edge, establish the Beltrami partial differential equation in the complex domain, and substitute the complex coordinates of the two-dimensional parameter domain curve as the Dirichlet boundary condition into the Beltrami partial differential equation. Then, use the finite element method to numerically solve the equation and obtain the three-dimensional boundary curve of the two-dimensional parameter domain curve in three-dimensional space.

[0049] S3.1 Represent the two-dimensional parameter domain curve as a complex variable function, and assign transformation operators to the complex variable function based on the directional property of the directed common edge.

[0050] Furthermore, the parameter coordinates in the two-dimensional parameter domain curve are combined to form the real and imaginary parts of the complex variable function, constructing a complex variable function defined on the two-dimensional parameter domain. The direction identifiers recorded in the directed shared edge objects are checked. If the direction identifier indicates that the directed shared edge is positive, an identity mapping is assigned as a complex transformation operator to the complex variable function corresponding to the directed shared edge. The identity mapping means keeping the real and imaginary parts of the complex variable function unchanged. If the direction identifier indicates that the directed shared edge is negative, a complex conjugate mapping is assigned as a complex transformation operator to the complex variable function corresponding to the directed shared edge. The complex conjugate mapping means inverting the imaginary part of the complex variable function.

[0051] S3.2 Calculate the Beltrami coefficients of the underlying parametric surface based on the first fundamental form of the underlying parametric surface.

[0052] Furthermore, the underlying parametric surface is determined by the surface equation defined by two independent parameterized coordinates u and v. The first fundamental form of the underlying parametric surface is the second differential form formed by the dot product of the partial derivative vectors after taking the partial derivatives of the surface equation with respect to the two parametric coordinates. Three fundamental coefficients are extracted from the first fundamental form of the underlying parametric surface, among which... The first fundamental coefficient is formed by taking the dot product of the vector obtained by taking the partial derivative of the surface equation with respect to the parameter u and itself, and is used to describe the length of the surface along the direction of the parameter u. The second fundamental coefficient is formed by taking the dot product of the vector obtained by taking the partial derivative of the surface equation with respect to the parameter u and the vector obtained by taking the partial derivative with respect to the parameter v. It is used to describe the angle between the surface in the direction of parameter u and the direction of parameter v. The third fundamental coefficient is formed by taking the dot product of the vector obtained by taking the partial derivative of the surface equation with respect to the parameter v and itself, and is used to describe the length of the surface along the direction of the parameter v.

[0053] The difference between the first and third fundamental coefficients is taken as the real part, and twice the second fundamental coefficient is taken as the imaginary part, and the two are combined to form the complex numerator. The sum of the first and third fundamental coefficients is superimposed with twice the surface area element (i.e., the square root of the determinant of the first fundamental form), and the resulting real value is used as the denominator. Calculate the ratio of the numerator to the denominator above, and the resulting quotient is the Beltrami coefficient, expressed as: ; in, It is the Beltrami coefficient; It is the first fundamental coefficient; It is the second fundamental coefficient; It is the third fundamental coefficient; It is the imaginary unit.

[0054] It should be noted that since the first fundamental coefficient and the determinant both originate from the vector dot product in the real number field, and the area elements of the regular surface are always positive real numbers, the denominator, as the sum of the square roots of each term and the coefficients, must be a real number. Geometrically, this formula describes the metric distortion of the basis vectors in the tangent space. By introducing an area term, the denominator is always greater than the complex modulus of the numerator, thus mathematically strictly limiting the norm of the ratio to less than one. This ensures that the mapping process possesses good uniform ellipticity and avoids patch folding or topological degradation during coordinate reconstruction.

[0055] S3.3 Using Beltrami coefficients as the mapping distortion metric, a transformation operator is used to apply linear weighting constraints to the derivative terms of the complex variable function to establish Beltrami partial differential equations in the complex domain.

[0056] Furthermore, based on the directional properties of the directed shared edges, the corresponding transformation operator is selected and applied to the derivative terms of the equation, where, When the direction is marked as positive, the unit transformation operator is applied to maintain the original complex partial derivative structure. When the direction is marked as reversed, the conjugate transformation operator is applied to replace the complex variable function in the equation with its conjugate form in order to counteract the mapping distortion direction deviation caused by the opposite rotation direction.

[0057] By combining the partial derivative terms processed by the transformation operator in a linear proportion according to the Beltrami coefficients and setting the difference to zero, a Beltrami partial differential equation defined on the complex field is constructed.

[0058] When the direction is marked as positive (unit transformation), Beltrami partial differential equations retain their standard form: ; When the direction is indicated as reverse (conjugate transformation), the Beltrami partial differential equation is corrected to: ; in, It is a complex variable function; It is a complex coordinate in a two-dimensional parameter domain, composed of two-dimensional parameter coordinates; yes The conjugate of complex numbers; yes The conjugate complex function, that is, the function value at any point in the domain is . The conjugate complex number of the corresponding function value (keeping the real part unchanged and inverting the imaginary part).

[0059] It should be noted that when dealing with B-Rep topology, the rotation direction (counterclockwise / clockwise) of the parameter domain determines the orientation of the local coordinate system of the facet. Directly using the standard Beltrami equations to handle "reverse edges" will lead to an error in the sign of the Jacobian determinant after mapping, resulting in a folded mapping. By introducing the conjugate transformation operator, a mirror reflection of space is actually achieved in the complex domain through conjugate operations, thereby compensating for the reversal of the tangent space direction caused by the switching of the directed common edge direction attribute, ensuring the geometric consistency of the quasi-conformal mapping in numerical solutions.

[0060] S3.4 Substitute the complex coordinates of the two-dimensional parametric domain curve as Dirichlet boundary conditions into the Beltrami partial differential equation to generate the mapping boundary equation.

[0061] Furthermore, the complex coordinates corresponding to each discrete point on the two-dimensional parameter domain curve are decomposed into real and imaginary values, which are used as Dirichlet boundary conditions. On the boundary of the solution domain defined by the Beltrami partial differential equation, the values ​​of the complex variable functions at each boundary node are forcibly fixed, so that the real part of the complex variable function is equal to the real part of the complex coordinate at the corresponding position, and the imaginary part of the complex variable function is equal to the imaginary part of the complex coordinate at the corresponding position. In this way, the value of the complex variable function at each node on the boundary of the solution domain is completely determined and no longer participates in the subsequent solution as an unknown. Thus, the original partial differential equation is combined with the known fixed value conditions at the boundary to form a mapping boundary equation with complete and closed boundary conditions.

[0062] It should be noted that Dirichlet boundary conditions refer to specifying the exact values ​​of a function at the boundary of the domain when solving differential equations. Dirichlet boundary conditions determine the precise values ​​of the physical field at the edge of space and are commonly used in constant surface temperature in heat conduction or fixed endpoint displacement in wave problems, ensuring that the solution of the equation is unique and deterministic throughout the entire space.

[0063] Beltrami partial differential equations are the core equations in the field of complex analysis that describe quasi-conformal mappings. They characterize the deformation law of a plane mapping that transforms a circle into an ellipse at an infinitesimal scale. They play a key role in surface parameterization, geometric image processing, and differential geometry research, defining the geometric properties of the mapping by constraining the proportional relationship between complex derivatives.

[0064] S3.5. The finite element method is used to discretize the mapping boundary equations and obtain the quasi-conformal mapping solution function.

[0065] Furthermore, the domain of the mapping boundary value equation is divided into a finite number of triangular or quadrilateral elements. On each element, a Lagrange-type basis function with local support properties is selected. The unknown complex variable function to be solved in the mapping boundary value equation is approximated as a linear combination of the Lagrange-type basis function and the undetermined coefficients. Using the Galerkin weighted residual method, with the Lagrange-type basis function as the weight function, a weighted residual condition is applied to the mapping boundary value equation, transforming it into a system of complex-domain algebraic equations about the undetermined coefficients.

[0066] Gaussian numerical integration is applied to the integral terms on each element to calculate the element stiffness matrix and element load vector. By assembling the element stiffness matrix and element load vector with global indices, a global stiffness matrix and global load vector are generated. At this point, the global stiffness matrix and global load vector constitute the matrix form of a system of complex-domain algebraic equations. The given nodal complex function values ​​from the Dirichlet boundary conditions are forcibly substituted into the global stiffness matrix and global load vector of the complex-domain algebraic equations, correcting the equations in the corresponding rows to eliminate the degrees of freedom of unknown quantities, resulting in a solvable system of constraint algebraic equations. The system of constraint algebraic equations is solved using a sparse direct solver (e.g., UMFPACK) to obtain the complex function values ​​at each node. The complex function values ​​at each node are then reconstructed by interpolation with Lagrange basis functions, constructing a continuous quasi-conformal mapping solution function over the entire domain.

[0067] It should be noted that the Galerkin weighted residual method is a numerical analysis method that integrates the residual and weight function obtained by substituting the approximate solution of the governing equation into the equation and sets the integral to zero in the domain. It is used to solve numerical approximations of partial differential equations. The principle is to select a function with the same form as the basis function in the approximate solution as the weight function. By making the residual orthogonal to the basis function in the entire domain, the differential equation is transformed into a system of linear equations and the approximate solution is optimized in a certain sense.

[0068] Lagrange basis functions are fundamental functions for constructing interpolation polynomials, used to generate continuous functions between discrete points. Lagrange basis functions take the value of one at specific nodes and zero at all other nodes. Through linear superposition, they achieve accurate fitting of target data and play a core supporting role in numerical analysis, finite element analysis, and computational geometry.

[0069] S3.6. Reverse map the quasi-conformal mapping solution function to three-dimensional real domain coordinates to generate a three-dimensional boundary curve.

[0070] Furthermore, the real and imaginary parts of the complex values ​​output by the quasi-conformal mapping solution function at each sampling point within the domain are extracted as two-dimensional parametric coordinates. These two-dimensional parametric coordinates are then substituted into the parameterized equations of the underlying parametric surface to calculate the corresponding three-dimensional spatial coordinates. The three-dimensional spatial coordinates corresponding to all sampling points are calculated sequentially along the parametric curve within the domain, and the three-dimensional spatial points are connected sequentially according to the original connection order in the parametric curve to generate a three-dimensional boundary curve.

[0071] S4. Based on the three-dimensional boundary curve and the three-dimensional space curve, calculate the curve consistency deviation using the Laplace operator and the Frobenius norm.

[0072] S4.1. Use the Laplacian operator to perform multi-scale smoothing iterations on the three-dimensional boundary curve and the three-dimensional space curve to obtain scale space curves at different iteration scales.

[0073] Furthermore, the 3D boundary curve is discretized into an ordered set of points. For each point in the ordered set, the average of the position coordinates of the two adjacent points is calculated. The difference between the current point's position coordinates and the average is calculated, and this difference is defined as a Laplacian vector. The current point's position coordinates are summed with the product of the Laplacian vector and the smoothing step size to obtain the updated point position coordinates. After updating all points sequentially, a smoothing iteration is completed. After each iteration, the ordered set of points at the current scale is recorded as the scale space curve for that scale. The above smoothing iteration process is repeated multiple times for the same initial 3D boundary curve, using the curve generated in the previous iteration as input each time, thereby obtaining a set of scale space curves at different iteration scales. The same multi-scale smoothing iteration process is performed independently on the 3D space curve to obtain a set of scale space curves corresponding to the 3D space curve.

[0074] It should be noted that the scale space curve is an intermediate curve shape obtained at each level of smoothing after successively applying Laplace smoothing to the original three-dimensional curve. It is used to uniformly analyze and compare the macroscopic contour features and microscopic local changes of the curve at multiple observation granularities.

[0075] S4.2 Calculate the curvature and torsion of the scale space curve, and construct the three-dimensional boundary curve feature matrix and the three-dimensional space curve feature matrix based on the curvature and torsion through serialization and recombination.

[0076] Furthermore, for each scale space curve, the discrete points on the curve are arranged in order of arc length. For each discrete point, its tangent vector, normal vector, and binormal vector are calculated. The curvature of the point is calculated using the rate of change of the tangent vector with respect to the arc length. The magnitude of the derivative vector obtained by differentiating the binormal vector with respect to the arc length is the torsion of the point. Thus, the curvature sequence and torsion sequence corresponding to all discrete points on the curve are obtained.

[0077] The curvature and torsion sequences are arranged side-by-side according to their point positions, forming a two-column numerical matrix. The first column contains curvature values, and the second column contains torsion values. Each row corresponds to a discrete point on the curve. This matrix is ​​defined as the feature matrix of the scale-space curve. The above process is performed independently on all scale-space curves corresponding to the 3D boundary curve, resulting in a set of feature matrices. These feature matrices are then concatenated into a 3D boundary curve feature matrix in ascending order of iteration scale. The same operation is performed independently on all 3D space curves to obtain the 3D space curve feature matrix.

[0078] S4.3. Using the Frobenius norm, calculate the second-order norm distance between the characteristic matrix of the three-dimensional boundary curve and the characteristic matrix of the three-dimensional space curve, and define the second-order norm distance as the matrix residual.

[0079] Furthermore, according to the definition of the Frobenius norm, the feature matrix of the three-dimensional boundary curve and the feature matrix of the three-dimensional space curve are used as two input matrices. The difference matrix is ​​obtained by taking the difference of the corresponding elements of the two matrices. The sum of the squares of all elements in the difference matrix and the square root are then taken. The resulting value is the second-order norm distance between the two matrices. This second-order norm distance is defined as the matrix residual.

[0080] S4.4. Weighted summation of matrix residuals under different iteration scales generates curve consistency deviation.

[0081] Furthermore, a preset weight coefficient is assigned to each iteration scale. The matrix residual calculated at that iteration scale is multiplied by the weight coefficient to obtain the weighted residual for that scale. The weighted residuals corresponding to all iteration scales are summed, and the summation result is defined as the curve consistency deviation.

[0082] It should be noted that the weighting coefficients are set based on prior knowledge of the contribution of different smoothing scales to the macroscopic contour and microscopic details of the curve. For example, the fewer the smoothing iterations, the smaller the scale, and the scale space curve retains more microscopic details, so a smaller weighting coefficient can be assigned. The more the smoothing iterations, the larger the scale, and the scale space curve better reflects the macroscopic contour features of the curve, so a larger weighting coefficient can be assigned. The weighting coefficients can be set as a sequence that increases with the number of iterations. For example, from the first iteration to the kth iteration, the weighting coefficients take values ​​of one, two, up to k, and then the weighting coefficients are normalized so that their sum is one.

[0083] S5. Determine whether the three-dimensional boundary curve and the three-dimensional space curve meet the geometric consistency condition based on the curve consistency deviation. When the geometric consistency condition is met, convert the B-Rep geometric data and the directed common edge into structured geometric data in JSON format.

[0084] S5.1 Map the three-dimensional boundary curve and the three-dimensional spatial curve to a higher-dimensional Riemannian manifold space, and calculate the discrete Fraser distance between the three-dimensional boundary curve and the three-dimensional spatial curve in the higher-dimensional Riemannian manifold space.

[0085] S5.1.1 Perform equal arc length resampling on the three-dimensional boundary curve and the three-dimensional space curve respectively to obtain a discrete sampling point set.

[0086] Furthermore, the total arc length of the three-dimensional boundary curve is calculated, and the ratio of the total arc length to the preset number of sampling points is used as the sampling arc length interval. Starting from the beginning of the curve, the process proceeds along the curve, recording the three-dimensional coordinates of the current point at each sampling arc length interval until the end of the curve is reached. All the recorded three-dimensional coordinates are arranged in sequence to form a discrete sampling point set of the three-dimensional boundary curve. The same equal arc length resampling process is performed independently on the three-dimensional spatial curve to obtain a discrete sampling point set of the three-dimensional spatial curve.

[0087] It should be noted that the number of sampling points is set based on the geometric complexity of the curve and the performance requirements of numerical computation for discrete accuracy.

[0088] S5.1.2 Calculate the differential geometric properties at the discrete sampling points in the discrete sampling point set, and construct a multidimensional feature vector based on the differential geometric properties.

[0089] Furthermore, for each sampling point in the discrete sampling point set, the point and its neighboring points are taken, and the tangent vector, principal normal vector, and binormal vector at that point are calculated using the local difference method. Then, the curvature and torsion at that point are calculated. The three components of the tangent vector, the three components of the principal normal vector, the three components of the binormal vector, the value of curvature, and the value of torsion are combined into a multidimensional feature vector, where each component corresponds to a specific geometric attribute value. Thus, each sampling point corresponds to a multidimensional feature vector, and the multidimensional feature vectors of all sampling points together constitute the multidimensional feature vector set of the curve.

[0090] S5.1.3 Define a high-dimensional Riemannian manifold space with differential geometric properties as coordinate axes, and use the weighted Euclidean inner product of the attribute components in the multidimensional eigenvector as the Riemannian metric of the high-dimensional Riemannian manifold space.

[0091] Furthermore, each component in the multidimensional eigenvector is used as the coordinate axis of the high-dimensional Riemannian manifold space. Each coordinate axis uniquely corresponds to a differential geometric property, and each point on the manifold is identified by a set of determined multidimensional eigenvector component values. In the tangent space of each point of the manifold, the Riemann inner product of any two tangent vectors is defined as: the Euclidean inner product of the sum of the terms of each coordinate component of the two tangent vectors multiplied by the pre-defined positive real weights of their corresponding differential geometric properties. Among them, the positive real number weight coefficients are set according to their relative importance in the description of the local shape of the curve. The tangent vector component, the principal normal vector component, and the binormal vector component can be assigned the same set of weights. The curvature component and the torsion component can be assigned weights separately according to their respective magnitudes. This weighted Euclidean inner product is the same everywhere in the entire coordinate space, thereby configuring the high-dimensional real space (i.e., the high-dimensional space spanned by multi-dimensional eigenvectors) into a Riemannian manifold with a flat Riemannian metric with constant coefficients.

[0092] It should be noted that the Riemann inner product is used to define the geodesic distance between any two points on the point set of a high-dimensional Riemannian manifold. The Riemannian metric is the Riemann inner product in the tangent space of every point on the manifold.

[0093] S5.1.4 Map the multidimensional feature vectors to a set of manifold points in a high-dimensional Riemannian manifold space, and calculate the geodesic distance between the manifold points based on the Riemannian metric to generate the geodesic distance cost matrix.

[0094] Furthermore, for each discrete sampling point, the components of its multidimensional feature vector are directly used as the coordinate values ​​of that point in the manifold space according to the order of the corresponding coordinate axes in the high-dimensional Riemannian manifold space. In this way, each multidimensional feature vector is transformed into a point in the manifold space, and the points corresponding to all discrete sampling points together constitute the manifold point set. For every two manifold points in the manifold point set, based on the constant coefficient flat Riemann metric configured on the manifold, the vector difference between the coordinates of the two points is substituted into the Riemann inner product defined by the metric for calculation. The square root of the result is the geodesic distance between the two points.

[0095] Repeat this calculation for all manifold point pairs, and arrange the calculated geodesic distances according to the index of the first point in the row and the index of the second point in the column to generate the geodesic distance cost matrix.

[0096] S5.1.5. Using a dynamic programming algorithm, search for point-to-point coupling paths that satisfy monotonicity constraints in the geodesic distance cost matrix.

[0097] Furthermore, a two-dimensional grid is constructed by using the discrete sampling point set indices of the 3D boundary curve and the 3D spatial curve as the two dimensions of the path. Each grid node corresponds to a pair of indexes, and the cost of this grid node is the element of the corresponding row and column in the geodesic distance cost matrix. The starting grid node is initialized as the index pair corresponding to the first sampling point of the two curves. The index pairs are traversed sequentially along the grid in a monotonically increasing direction. The monotonicity constraint requires that the path can only move to the right, up, or upper right on the grid, meaning that the indices of the two curves do not decrease. For each grid node, the cumulative cost from the starting point to the current node is calculated. The cumulative cost is equal to the sum of the minimum cost of the current node and the cumulative cost of all possible predecessor nodes. Predecessor nodes include the grid nodes corresponding to each index pair minus one, only the first index minus one, and only the second index minus one. Repeat this traversal process until the index pair corresponding to the last sampling point of the two curves is reached. Then, backtrack from the end grid node to the starting grid node, and record the index pairs corresponding to the grid nodes passed through in sequence. Arrange these index pairs in order to form a point-to-point coupling path that satisfies the monotonicity constraint.

[0098] S5.1.6 Calculate the maximum value of the geodesic distance in the coupled path of each point pair, and generate a set of maximum geodesic distances.

[0099] Furthermore, for each point-pair coupling path, all point pairs on the path are traversed. Each point pair corresponds to an element value in the geodesic distance cost matrix. The largest value is selected from these element values ​​and recorded as the maximum geodesic distance value of the path. The above selection operation is performed independently on all point-pair coupling paths, and all the obtained maximum geodesic distance values ​​are combined into a set, which is defined as the set of maximum geodesic distance values.

[0100] S5.1.7. Take the global minimum value in the set of maximum distances from the ground line as the discrete Fraser distance between the three-dimensional boundary curve and the three-dimensional spatial curve in the high-dimensional Riemannian manifold space.

[0101] Furthermore, iterate through all the values ​​in the set of maximum geodesic distances, and select the smallest value by comparing them one by one. Record this minimum value as the discrete Fraser distance between the three-dimensional boundary curve and the three-dimensional spatial curve in the high-dimensional Riemannian manifold space.

[0102] It should be noted that the discrete Fraser distance is a measure of the spatial similarity between two curves between discrete sampling points, used to quantitatively assess the overall proximity of a three-dimensional boundary curve and a three-dimensional spatial curve on a high-dimensional Riemannian manifold.

[0103] S5.2 Calculate the structural correlation coefficient between the three-dimensional boundary curve and the three-dimensional spatial curve using the local linear embedding algorithm.

[0104] S5.2.1 Extract local neighborhood point sets from the discrete sampling point set based on the criterion of minimizing Euclidean distance, and construct a local reconstruction error function based on the local neighborhood point sets with the goal of minimizing the linear combination residual.

[0105] Furthermore, for each sampling point in the discrete sampling point set, the Euclidean distance between that sampling point and all other sampling points is calculated. A predetermined number of neighboring points (set based on the local density of the discrete sampling point set) are selected in ascending order of Euclidean distance, forming a local neighborhood point set for that sampling point. The position vector of the sampling point is represented as a linear combination of the position vectors of all points in the local neighborhood point set. The coefficients of this linear combination are used as variables to be solved. The square norm of the difference vector between this linear combination and the true position vector is established, and this square norm is defined as the local reconstruction error function for that sampling point.

[0106] S5.2.2 Solve the local reconstruction error function using the Lagrange multiplier method to generate the local reconstruction weight matrix.

[0107] Furthermore, an equality constraint is applied to the local reconstruction error function of each sampling point, where the sum of the linear combination coefficients is 1. The local reconstruction error function is then multiplied by the equality constraint by a Lagrange multiplier and added to construct the Lagrange function. Taking the partial derivatives of the linear combination coefficients and Lagrange multipliers in the Lagrange function and setting them to zero yields a system of linear equations. Solving this system yields the optimal weight coefficients for each point in the local neighborhood set corresponding to the sampled point. The optimal weight coefficients of all sampled points are arranged in the order of the sampled points, with each sampled point's weight coefficient occupying one row of a matrix. Each column corresponds to the index position of a point in the local neighborhood set. The weight coefficients for points not appearing in the local neighborhood set are set to zero, thus generating the local reconstruction weight matrix.

[0108] S5.2.3 Using the local reconstruction weight matrix as a structural invariance constraint, the multidimensional eigenvectors are mapped to a low-dimensional linear space through eigenvalue decomposition to obtain the low-dimensional embedding coordinates.

[0109] Furthermore, the difference between the identity matrix and the local reconstruction weight matrix is ​​calculated, and the product of the transpose of the difference matrix and the difference matrix is ​​calculated to obtain a sparse matrix. Eigenvalue decomposition is performed on the sparse matrix to obtain all eigenvalues ​​and the eigenvectors corresponding to each eigenvalue. The eigenvalues ​​are sorted in ascending order of value, and the eigenvectors corresponding to the smallest eigenvalues ​​are discarded. The eigenvectors corresponding to the first few non-smallest eigenvalues ​​after sorting are selected. For the multidimensional eigenvectors of each sampling point, the multidimensional eigenvectors are inner products with each selected eigenvector to obtain the corresponding projection coefficients. The obtained projection coefficients are arranged into a coordinate vector according to the order of the selected eigenvectors. This coordinate vector is defined as the low-dimensional embedding coordinates of the sampling point.

[0110] S5.2.4 Perform covariance analysis on the low-dimensional embedded coordinates corresponding to the three-dimensional boundary curve and the three-dimensional space curve to obtain the structural feature vector, calculate the cosine similarity between the structural feature vectors, and generate the structural correlation coefficient.

[0111] Furthermore, the mean vector of all low-dimensional embedded coordinates is calculated. Subtracting the mean vector from each low-dimensional embedded coordinate yields the centered coordinates. A data matrix is ​​constructed from all centered coordinates. The product of this data matrix and its transpose is calculated to obtain the covariance matrix. Eigenvalue decomposition is performed on this covariance matrix to obtain all eigenvalues ​​and their corresponding eigenvectors. The eigenvector corresponding to the largest eigenvalue is selected as the structural feature vector of the 3D boundary curve. The exact same covariance analysis process is performed independently on the 3D spatial curve to obtain its structural feature vector. The dot product of the structural feature vector of the 3D boundary curve and the structural feature vector of the 3D spatial curve is calculated. The magnitudes of the two structural feature vectors are calculated separately. The dot product is divided by the product of the two magnitudes, and the resulting value is defined as the structural correlation coefficient.

[0112] S5.3 When the curve consistency deviation and discrete Fraser distance are both less than the preset geometric tolerance upper limit, and the structural correlation coefficient is greater than the preset geometric similarity threshold, the geometric consistency condition is determined to be met, and the B-Rep geometric data and directed common edges are written into the corresponding JSON fields to generate structured geometric data.

[0113] Furthermore, the curve consistency deviation is compared with the upper limit of geometric tolerance, the discrete Friesian distance is compared with the upper limit of geometric tolerance, and the structural correlation coefficient is compared with the geometric similarity threshold. When the curve consistency deviation is less than the upper limit of geometric tolerance, the discrete Friesian distance is less than the upper limit of geometric tolerance, and the structural correlation coefficient is greater than the geometric similarity threshold, the geometric consistency condition is determined to be met. After the determination is met, the B-Rep geometric data is written into the corresponding fields according to the predefined geometric data field names in the JSON format, and the directed common edges are written into the corresponding fields according to the predefined topological edge field names in the JSON format, thereby generating structured geometric data containing B-Rep geometric data and directed common edges.

[0114] It should be noted that the upper limit of geometric tolerance is set based on the modeling accuracy of the CATIA part file; The geometric similarity threshold is set based on the curvature fluctuation rate of the high-dimensional Riemannian manifold space, and the example value range is... The range of example values ​​is based on the statistical distribution of local curvature fluctuations on high-dimensional Riemannian manifolds and the tolerance to small geometric deformations; the geometric data field names are set based on the type hierarchy of patches, underlying parametric surfaces, two-dimensional parametric domain curves, and three-dimensional spatial curves in B-Rep geometric data. The topology edge field names are set based on the attribute structure of topology edge references and direction identifiers in directed shared edge objects.

[0115] In summary, this invention achieves in-depth consistency verification from numerical accuracy to topological structure by establishing a quasi-conformal mapping reconstruction logic driven by Beltrami equations, accurately compensating for geometric distortions in parameter space transformation to eliminate boundary cracking, and combining geodesic distance and structural correlation verification under high-dimensional Riemannian manifolds. This effectively improves the data fidelity and geometric robustness of computer-aided design part files during the structural transformation process.

[0116] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for structuring geometric data in CATIA part files, characterized in that, include: Acquire CATIA part files and read accessible B-Rep geometry data from CATIA part files; The B-Rep geometric data includes patches, the underlying parametric surfaces corresponding to the patches, two-dimensional parametric domain curves, and three-dimensional spatial curves. Based on the actual orientation of the boundary ring in the patch on the patch, construct the directed common edge corresponding to the topological edge in the boundary ring; Beltrami partial differential equations in the complex domain are established based on the directional properties of the directed common edge. The complex coordinates of the two-dimensional parameter domain curves are substituted into the Beltrami partial differential equations as Dirichlet boundary conditions. The three-dimensional boundary curves of the two-dimensional parameter domain curves in three-dimensional space are obtained by numerical solution using the finite element method. Based on three-dimensional boundary curves and three-dimensional spatial curves, curve consistency deviations are calculated using the Laplace operator and the Frobenius norm. The geometric consistency condition is determined based on the curve consistency deviation. When the geometric consistency condition is met, the B-Rep geometric data and the directed common edge are converted into structured geometric data in JSON format.

2. The method for geometric data structure conversion of CATIA part files as described in claim 1, characterized in that, The specific steps for acquiring CATIA part files and reading accessible B-Rep geometric data from them are as follows: The underlying geometry interface is called to parse the CATIA part file and obtain the internal logical organization structure of the CATIA part file. Locate the target geometry set within the logical organizational structure, perform a topological association search on the target geometry set, and output the topological description information corresponding to the target geometry set; Extract the underlying data items related to geometry and topological connections from the topology description information to obtain B-Rep geometric data.

3. The method for geometric data structure conversion of CATIA part files as described in claim 2, characterized in that, The specific steps for constructing directed common edges corresponding to the topological edges in the boundary rings are as follows: Project the boundary loop in the patch onto the two-dimensional parameter domain corresponding to the underlying parametric surface to obtain the closed parameter domain curve loop; Calculate the algebraic area of ​​the closed parametric domain curve loop in the two-dimensional parametric domain, and determine the rotation direction of the closed parametric domain curve loop based on the sign of the algebraic area. Based on the rotation direction of the closed parameter domain curve loop, the corresponding topological edges are encapsulated in a directed manner to generate directed common edges.

4. The method for geometric data structure conversion of CATIA part files as described in claim 3, characterized in that, The specific steps for calculating the algebraic area of ​​the closed parameter domain curve loop in the two-dimensional parameter domain, and determining the rotation direction of the closed parameter domain curve loop based on the sign of the algebraic area, are as follows: The algebraic area is obtained by calculating the line integral of a closed parametric domain curve loop using Green's theorem. When the area of ​​the current number is positive, the rotation direction of the closed parametric domain curve loop is determined to be counterclockwise; When the area of ​​the current number is negative, the rotation direction of the closed parametric domain curve loop is determined to be clockwise.

5. The method for geometric data structure conversion of CATIA part files as described in claim 1, characterized in that, The specific steps for obtaining the three-dimensional boundary curve of the two-dimensional parameter domain curve in three-dimensional space are as follows: The two-dimensional parameter domain curve is represented as a complex variable function, and transformation operators are assigned to the complex variable function based on the directional property of the directed common edge. Calculate the Beltrami coefficients of the underlying parametric surface based on the first fundamental form of the underlying parametric surface; Using Beltrami coefficients as the parameters for measuring mapping distortion, and employing transformation operators to apply linear weighting constraints to the derivative terms of complex variable functions, Beltrami partial differential equations in the complex domain are established. Substituting the complex coordinates of the two-dimensional parametric domain curve as Dirichlet boundary conditions into the Beltrami partial differential equation, a mapping boundary value equation is generated. The finite element method is used to discretize the mapping boundary equations and obtain the quasi-conformal mapping solution function. The quasi-conformal mapping solution function is inversely mapped to three-dimensional real-domain coordinates to generate a three-dimensional boundary curve.

6. The method for geometric data structure conversion of CATIA part files as described in claim 5, characterized in that, The method for calculating curve consistency deviation based on 3D boundary curves and 3D spatial curves using the Laplace operator and Frobenius norm is as follows: The Laplacian operator is used to perform multi-scale smoothing iterations on the three-dimensional boundary curves and the three-dimensional space curves to obtain scale space curves at different iteration scales. Calculate the curvature and torsion of the scale space curve, and construct the three-dimensional boundary curve feature matrix and the three-dimensional space curve feature matrix based on the curvature and torsion through serialization and recombination; The Frobenius norm is used to calculate the second-order norm distance between the feature matrix of the three-dimensional boundary curve and the feature matrix of the three-dimensional space curve, and the second-order norm distance is defined as the matrix residual. Weighted summation of matrix residuals at different iteration scales generates curve consistency deviation.

7. The method for geometric data structure conversion of CATIA part files as described in claim 6, characterized in that, The process involves determining whether the 3D boundary curve and the 3D spatial curve meet the geometric consistency condition based on the curve consistency deviation. When the geometric consistency condition is met, the B-Rep geometric data and directed shared edges are converted into structured geometric data using JSON format. The specific steps are as follows: Map the 3D boundary curve and the 3D spatial curve to a higher-dimensional Riemannian manifold space, and calculate the discrete Fraser distance between the 3D boundary curve and the 3D spatial curve in the higher-dimensional Riemannian manifold space; The structural correlation coefficient between the three-dimensional boundary curve and the three-dimensional spatial curve is calculated using the local linear embedding algorithm. When both the curve consistency deviation and the discrete Fraser distance are less than the preset upper limit of geometric tolerance, and the structural correlation coefficient is greater than the preset geometric similarity threshold, the geometric consistency condition is determined to be met, and the B-Rep geometric data and the directed common edge are written into the corresponding JSON field to generate structured geometric data.

8. The method for geometric data structure conversion of CATIA part files as described in claim 7, characterized in that, The specific steps for mapping the three-dimensional boundary curve and the three-dimensional spatial curve to a higher-dimensional Riemannian manifold space, and calculating the discrete Fréchet distance between the three-dimensional boundary curve and the three-dimensional spatial curve in the higher-dimensional Riemannian manifold space, are as follows: The three-dimensional boundary curve and the three-dimensional space curve are resampled with equal arc lengths to obtain a discrete set of sampling points. Calculate differential geometric properties at discrete sampling points in a discrete sampling point set, and construct multidimensional feature vectors based on differential geometric properties; We define a high-dimensional Riemannian manifold space with differential geometric properties as coordinate axes, and use the weighted Euclidean inner product of the attribute components in the multidimensional eigenvector as the Riemannian metric of the high-dimensional Riemannian manifold space. Multidimensional feature vectors are mapped to manifold point sets on a high-dimensional Riemannian manifold space, and geodesic distances between manifold point sets are calculated based on Riemannian metrics to generate a geodesic distance cost matrix. A dynamic programming algorithm is used to search for point-to-point coupling paths that satisfy monotonicity constraints in the geodesic distance cost matrix; Calculate the maximum geodesic distance in the coupled path of each point pair, and generate a set of maximum geodesic distances; The global minimum value in the set of maximum distances to the ground line is taken as the discrete Fraser distance between the three-dimensional boundary curve and the three-dimensional spatial curve in the high-dimensional Riemannian manifold space.

9. The method for geometric data structure conversion of CATIA part files as described in claim 8, characterized in that, The structural correlation coefficient between the three-dimensional boundary curve and the three-dimensional spatial curve is calculated using a local linear embedding algorithm. The specific steps are as follows: The local neighborhood point set is extracted from the discrete sampling point set based on the criterion of minimizing Euclidean distance, and a local reconstruction error function is constructed based on the local neighborhood point set with the goal of minimizing the linear combination residual. The local reconstruction error function is solved using the Lagrange multiplier method to generate the local reconstruction weight matrix. Using the local reconstruction weight matrix as a structural invariance constraint, the multidimensional eigenvectors are mapped to a low-dimensional linear space through eigenvalue decomposition to obtain the low-dimensional embedding coordinates. Covariance analysis is performed on the low-dimensional embedded coordinates corresponding to the three-dimensional boundary curve and the three-dimensional spatial curve to obtain structural feature vectors, and the cosine similarity between the structural feature vectors is calculated to generate structural correlation coefficients.

10. The method for geometric data structure conversion of CATIA part files as described in claim 7, characterized in that, The upper limit of geometric tolerance is set based on the modeling accuracy of the CATIA part file; The geometric similarity threshold is set based on the curvature fluctuation rate of the high-dimensional Riemannian manifold space.

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