A method for correcting the machined surface of a CNC milling machining center

Abstract

This invention relates to the field of CNC machining measurement and correction technology, and discloses a method for correcting the machining surface of a CNC milling machining center. The method includes: establishing an original point cloud of the machining surface and extracting its feature structures; analyzing each feature structure to form a structured description list; inputting the list into a geometric growth model, and generating a virtual feature structure set through iterative evolution according to rules; extracting its contour and height field and rasterizing it, registering and fusing it with the reference surface equation, and obtaining a smooth intermediate geometric surface through variational calculation; adaptively resampling the intermediate surface to generate an intermediate point cloud; and finally, adaptively determining the weights based on the spatial frequency distribution of the topological residual field formed by the difference between the original point cloud and the intermediate point cloud, and weighted mixing the two to generate an optimized surface point cloud. This method achieves intelligent evolution of machining surface features and frequency domain adaptive data fusion, improving the accuracy of correction machining and the surface forming quality.

Description

Technical Field

[0001] This invention relates to the field of CNC machining measurement and correction technology, specifically a method for correcting the machining surface of a CNC milling machining center. Background Technology

[0002] In CNC milling, high-precision calibration of machined surfaces is a critical and complex task. Existing calibration techniques typically rely on direct geometric processing of measured point clouds. Common methods include fitting the point cloud data of the entire machined surface to a reference plane, or performing simple region division and fitting separately. Another approach is to compensate for the deviation between the original measured point cloud and the theoretical model by superimposing the compensation amount onto the machining path using fixed empirical formulas or globally uniform weights. These methods treat the features of the machined surface as static geometric deviations.

[0003] The aforementioned conventional technical solutions have shortcomings. Direct global fitting will erase the differences in local features, leading to distortion of the corrected feature contours. Partial fitting will produce discontinuous steps or sharp seams at the junctions of regions, affecting the overall smoothness of the surface. Methods that use fixed rules or global weights for data mixing cannot adapt to the complex spatial distribution characteristics of surface deviations. They either over-smooth the fine features that should be preserved, or fail to effectively suppress high-frequency errors in areas requiring smooth transitions, resulting in coarse correction results that are difficult to meet the process requirements of high-precision surfaces.

[0004] Current technology faces two core challenges: how to intelligently predict and generate deformations of various feature structures on the processed surface to obtain a more natural and reasonable transition geometry; and how to perform refined weight allocation based on the local characteristics of the deviation field when integrating the original data and the newly generated geometry to achieve frequency-domain controllable adaptive correction, thereby eliminating macroscopic errors while preserving or optimizing the microscopic morphology to the maximum extent. Summary of the Invention

[0005] The purpose of this invention is to provide a method for correcting the machining surface of a CNC milling machining center, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides a method for correcting the machining surface of a CNC milling machining center, the method comprising:

[0007] Establish the original spatial point cloud of the processed surface and generate a set of feature structures of the processed surface;

[0008] For each feature structure in the set of feature structures, perform structural parsing to extract the skeleton line, enclosing region and height distribution model of each feature structure to form a structured description list;

[0009] The structured description list is input into the geometric growth model. The geometric growth model iteratively expands, contracts and deforms each feature structure according to preset growth rules and constraints, simulating its evolution process in virtual space and generating a set of virtual feature structures.

[0010] Extract the contour edge and internal height field of each virtual feature structure from the set of virtual feature structures, and rasterize the contour edge and internal height field into a two-dimensional feature mask and a height increment field.

[0011] The two-dimensional feature mask and height increment field are registered and fused with the reference surface equation, and the intermediate geometric surface with smooth transition is calculated by solving the variational problem.

[0012] Based on the density distribution of the original spatial point cloud of the processed surface, the intermediate geometric surface of the smooth transition is adaptively resampled to generate a dense and uniform intermediate point cloud.

[0013] The dense and uniform intermediate point cloud is weighted and mixed with the original spatial point cloud. The weighting coefficients of the weighting are determined according to the spatial frequency distribution of the topological residual field. The optimized surface point cloud is then calculated and generated to drive the CNC milling machining center for correction machining.

[0014] Preferably, the step of establishing the original spatial point cloud of the processed surface and generating a set of feature structures of the processed surface includes:

[0015] The original spatial point cloud is derived from the geometric coordinates and reflection intensity signals collected at different locations on the processing surface;

[0016] A reference surface fitting and residual separation are performed on the original spatial point cloud to generate a reference surface equation for the processed surface and a topological residual field relative to the reference surface equation.

[0017] Based on the topological residual field, a characteristic connected graph of the processed surface is constructed. The nodes of the characteristic connected graph are composed of local curvature extrema of the topological residual field, and the edges of the characteristic connected graph are composed of geodesic paths between nodes that satisfy distance constraints and curvature similarity constraints.

[0018] Path search and subgraph segmentation are performed in the feature connectivity graph to identify all closed loops and radial branches, and each closed loop and radial branch is marked as an independent feature structure to generate a set of feature structures.

[0019] Preferably, the step of performing reference surface fitting and residual separation on the original spatial point cloud includes:

[0020] The random sampling consensus algorithm is used to select an interior point set from the original spatial point cloud;

[0021] A plane equation is obtained by fitting the interior point set using the least squares method, and this plane equation is determined as the reference surface equation.

[0022] Calculate the symbolic distance from each point in the original spatial point cloud to the reference surface equation, and organize all symbolic distances according to their corresponding two-dimensional projected coordinates of the original spatial point cloud to form the topological residual field.

[0023] Preferably, the step of constructing a feature connectivity graph of the processed surface based on the topological residual field includes:

[0024] Calculate the Gaussian curvature and mean curvature of each data point on the topological residual field;

[0025] Detect all points where both the Gaussian curvature and the mean curvature satisfy the local extremum condition, and mark these points as candidate feature points;

[0026] Calculate the Euclidean distance and geodesic distance between each pair of candidate feature points, and compare the angle between the curvature vectors of the pair of candidate feature points;

[0027] When the Euclidean distance between a pair of candidate feature points is less than a distance threshold, the geodesic distance is less than a preset multiple of the Euclidean distance, and the angle between the curvature vectors is less than an angle threshold, an undirected edge is established between the pair of candidate feature points.

[0028] The feature connectivity graph is composed of all candidate feature points and all undirected edges that satisfy the conditions.

[0029] Preferably, the step of performing path search and subgraph segmentation in the feature connected graph to identify all closed loops and radial branches includes:

[0030] In the feature connectivity graph, starting from any node with a degree of 1, a depth-first search is performed until another node with a degree of 1 or a previously visited node is encountered. The search path is recorded and marked as a radial branch.

[0031] After removing the edges of all radial branches, find all simple cycles in the remaining part of the characteristic connected graph and mark each simple cycle as a closed loop;

[0032] Each radial branch and each closed loop is encapsulated as a subgraph, and the set of all subgraphs constitutes the set of feature structures.

[0033] Preferably, performing structural parsing on each feature structure in the feature structure set includes:

[0034] For the feature structure marked as radial branches, extract all its nodes and connect them in order to form a center line. Smooth and resample the center line to generate a skeleton line. Calculate the point set within a certain distance on both sides of the skeleton line to form an enclosing region. Perform polynomial fitting on the topological residual field values ​​within the enclosing region to generate a height distribution model.

[0035] For a structure marked as a closed loop, the internal region enclosed by the loop edge is extracted, the centroid of the internal region is calculated, and the line connecting the centroid to the edge point forms a radial skeleton line. The enclosed region is defined with the closed loop edge as the boundary, and the topological residual field value of the internal region is fitted to the surface to generate a height distribution model.

[0036] Preferably, inputting the structured description list into the geometric growth model includes:

[0037] Define growth rules for the geometric growth model, including skeleton line extension, enclosing region expansion, and scaling of the height distribution model according to a preset ratio;

[0038] Define constraints for the geometric growth model, including that spatial interference is not allowed between different virtual feature structures and that the total height variation of the virtual feature structures must be kept within a predetermined range.

[0039] The geometric growth model takes the structured description list as the initial state, adjusts each feature structure according to the growth rules in each iteration step, and checks whether all constraints are met after each adjustment. If not, it backtracks to the previous step until all feature structures reach the preset growth generation or fall into a steady state, and outputs the final set of virtual feature structures.

[0040] Preferably, the step of extracting the contour edge and internal height field of each virtual feature structure from the set of virtual feature structures includes:

[0041] Triangulate the region enclosed by each virtual feature structure;

[0042] Extract the boundary edge sequence of the triangular mesh, project the boundary edge sequence onto the reference plane, and perform corner detection and polygon approximation on the projected boundary edge sequence to obtain the contour edge of the virtual feature structure.

[0043] Within the polygonal region defined by the contour edge, the height value of each grid point is calculated based on the height distribution model of the virtual feature structure, forming a two-dimensional height increment field.

[0044] All contour edges are rasterized into a binary image with the same spatial resolution as the topological residual field, which serves as a two-dimensional feature mask.

[0045] Preferably, the registration and fusion of the two-dimensional feature mask and height increment field with the reference surface equation includes:

[0046] The two-dimensional feature masks are superimposed onto the two-dimensional parameter domain of the reference plane. By maximizing the cross-correlation coefficient, each two-dimensional feature mask is slightly translated and rotated to complete the registration.

[0047] Each registered height increment field is added to the reference surface equation at the corresponding position to obtain a preliminary composite surface;

[0048] An energy functional is established with the goal of minimizing surface smoothness and deviation from the initial composite surface. By solving the Euler-Lagrange equation corresponding to this energy functional, an intermediate geometric surface with smooth transitions that is globally smooth and has continuous detail transitions is obtained.

[0049] Preferably, the weighted mixing of the dense and uniform intermediate point cloud with the original spatial point cloud includes:

[0050] Calculate the two-dimensional Fourier spectrum of the topological residual field;

[0051] Analyze the two-dimensional Fourier spectrum to determine the low-frequency band characterizing the main features of the processed surface and the high-frequency band characterizing noise;

[0052] A spatial frequency component in the low-frequency band is assigned a high weight value, and a spatial frequency component in the high-frequency band is assigned a low weight value, thereby generating a spatial frequency-related weight coefficient field.

[0053] In the spatial domain, the optimized surface point cloud is generated by using a weighting coefficient field to control the linear combination ratio of the dense and uniform intermediate point cloud and the original spatial point cloud at corresponding locations.

[0054] Compared with the prior art, the beneficial effects of the present invention are:

[0055] By introducing a geometric growth model to simulate the evolution of feature structures, this method changes the paradigm of traditional static geometric processing. Based on preset growth rules and constraints, the model iteratively expands, contracts, and deforms the extracted skeleton, enclosing region, and height distribution. This dynamic evolution process can simulate the physical process of material removal or filling, generating a set of virtual feature structures that naturally extend or contract in virtual space. The resulting virtual structural outline and its internal height field are no longer simple scaling or translation of the original features, but possess morphological continuity and rationality. This provides a better geometric prior for the subsequent generation of smoothly transitioning intermediate geometric surfaces, avoiding the subjectivity and rigidity of manually defined deformation rules.

[0056] The weighting coefficients for the final point cloud blending are determined based on the spatial frequency distribution of the topological residual field, achieving frequency-domain adaptive control of the correction process. The topological residual field reflects the geometric differences between the original surface and the generated intermediate surface, and its spatial frequency distribution reveals the characteristics of the difference components. High-frequency residuals typically correspond to fine features or noise that need to be preserved, while low-frequency residuals represent overall shape errors that need to be corrected. By dynamically adjusting the weights through analysis of this frequency distribution, high-frequency components can be assigned weights that favor the original point cloud to preserve details, while low-frequency components can be assigned weights that favor the intermediate point cloud to achieve overall shape correction. This frequency-aware blending mechanism can intelligently distinguish and handle geometric deviations of different natures, thereby synergistically achieving macroscopic shape accuracy improvement and microscopic feature integrity preservation in a single processing flow. Attached Figure Description

[0057] Figure 1 This is a schematic diagram illustrating the working principle of the machining surface correction method for CNC milling machining centers described in this invention.

[0058] Figure 2 A flowchart for generating a set of feature structures;

[0059] Figure 3 A flowchart for constructing a feature connectivity graph;

[0060] Figure 4 A heatmap of the normalized cross-correlation coefficient distribution during the registration process;

[0061] Figure 5 A thermal diagram showing the spatial distribution of the topological residual field on a CNC milled surface. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] Please see Figure 1This invention provides a method for machining surface correction in CNC milling machining centers. The method includes: acquiring the original spatial point cloud of the machining surface by measurement, separating the reference surface and the topological residual field characterizing the surface's unevenness details from it, constructing a feature connectivity graph based on the topological residual field and performing subgraph segmentation to generate a feature structure set composed of multiple independent feature structures. Subsequently, structural analysis is performed on each feature structure in the feature structure set to extract its skeleton line, enclosing region, and height distribution model, forming a structured description list. This list is input into a geometric growth model with preset growth rules and constraints. This model simulates the evolution of the feature structure through iterative expansion, contraction, and deformation operations, generating a set of virtual feature structures. Next, the contour edge and internal height field of each structure are extracted from the virtual feature structure set and rasterized into a two-dimensional feature mask and a height increment field, respectively. These two-dimensional data are registered and fused with the reference surface equation. By solving a variational problem aimed at achieving surface smoothness and geometric approximation, a smoothly transitioning intermediate geometric surface is calculated. Based on the density distribution of the original spatial point cloud, the intermediate geometric surface is adaptively resampled to generate a dense and uniform intermediate point cloud. Finally, this intermediate point cloud is weighted and mixed with the original spatial point cloud, where the mixing weight coefficients are determined by the spatial frequency distribution of the topological residual field, thereby calculating and generating the optimized surface point cloud that is ultimately used to drive the CNC milling machining center for correction machining.

[0064] Example 1: See Figure 2 The original spatial point cloud originates from the geometric coordinates and reflection intensity signals collected by a scanning probe at different locations on the processed surface. A reference plane fitting and residual separation are performed on the original spatial point cloud to generate a reference plane equation for the processed surface and a topological residual field relative to the reference plane equation. Specifically, this process includes selecting an interior point set from the original spatial point cloud using a random sampling consensus algorithm, fitting a plane equation using the least squares method based on the interior point set, and defining this plane equation as the reference plane equation. Then, the signed distance from each point in the original spatial point cloud to the reference plane equation is calculated, and all signed distances are organized according to their corresponding two-dimensional projected coordinates in the original spatial point cloud to form the topological residual field. Based on the topological residual field, a feature connectivity graph of the processed surface is constructed. The nodes of the feature connectivity graph are composed of local curvature extrema of the topological residual field, and the edges of the feature connectivity graph are composed of geodesic paths between nodes that satisfy distance constraints and curvature similarity constraints. Path search and subgraph segmentation are performed on the feature connectivity graph to identify all closed loops and radial branches, and each closed loop and radial branch is marked as an independent feature structure, generating a set of feature structures.

[0065] In practice, the original spatial point cloud is derived from the geometric coordinates and reflection intensity signals collected at different locations on the processing surface. For example, a three-dimensional optical scan is performed on the sealing surface of a car engine cylinder head with multiple heat dissipation bosses and flow channel grooves to obtain an original spatial point cloud dataset containing hundreds of thousands of points with uneven density. The purpose of performing datum plane fitting and residual separation on the original spatial point cloud is to separate the ideal datum plane of the sealing surface from the microscopic morphology representing the boss and groove, and to generate the datum plane equation for the machined surface and the topological residual field relative to the datum plane equation. The specific process includes: selecting an interior point set from the original spatial point cloud using a random sampling consensus algorithm; fitting and evaluating the consistency of the random sampling consensus algorithm with randomly sampled point sets; iteratively eliminating "exterior points" belonging to features such as bosses and grooves; finally obtaining an interior point set representing the main datum plane; obtaining a plane equation by fitting the interior point set using the least squares method; determining the plane equation as the datum plane equation; minimizing the sum of squares of the distances from all points in the interior point set to the plane using the least squares method to solve for the plane parameters; calculating the signed distance from each point in the original spatial point cloud to the datum plane equation; and organizing all signed distances according to their corresponding two-dimensional projected coordinates of the original spatial point cloud to form a topological residual field image indexed by two-dimensional grid coordinates and with the signed distance value as the height. In the image, the boss area is displayed as a positive distance value, and the groove area is displayed as a negative distance value. In some embodiments, two-dimensional projected coordinates are represented by projecting the XYZ coordinates of the original spatial point cloud onto a plane defined by the datum plane equation, and using a UV coordinate system constructed by two orthogonal vectors on that plane.

[0066] The feature connectivity graph of the processed surface is constructed based on the topological residual field. The nodes of the feature connectivity graph are composed of local curvature extrema of the topological residual field. Specifically, after calculating the Gaussian curvature and mean curvature of each point in the topological residual field, the points whose curvature values ​​are local maxima or minima are located. These points usually correspond to the vertices of the boss or the turning points of the valley lines of the groove. The edges of the feature connectivity graph are composed of geodesic paths between nodes that satisfy distance constraints and curvature similarity constraints. The distance constraint requires that the three-dimensional Euclidean distance between nodes is less than a threshold, such as 5 mm. The curvature similarity constraint requires that the angle between the principal curvature directions between nodes is less than 15 degrees. The geodesic path is obtained by calculating the shortest surface path between two points on the surface characterized by the topological residual field. In the feature connected graph, path search and subgraph segmentation are performed to identify all closed loops and radial branches. Taking the engine cylinder head sealing surface as an example, the feature points corresponding to an isolated circular boss will form a closed loop in the graph, while the feature points corresponding to a slender reinforcing rib will form a radial branch. Each closed loop and radial branch is marked as an independent feature structure, generating a feature structure set. The feature structure set is stored in the form of a data structure list, where each element contains all the node and edge information of a feature structure. In specific implementation, radial branches are identified from the feature connected graph as follows: starting from any node with one connected edge, a depth-first search is performed to traverse the nodes along the edges until another node with one connected edge is encountered or a previously visited node is revisited. This traversal path is recorded, and this path corresponds to a radial branch structure. In specific implementation, closed loops are identified by removing the edges corresponding to all identified radial branches and then searching for all simple cyclic paths in the remaining part of the feature connected graph. Each simple cycle corresponds to a closed loop structure. It is understandable that segmenting a connected feature graph using graph theory methods can decompose continuous, complex surface morphology into discrete feature units with clear geometric meanings. For example, a closed loop might correspond to a bolt boss, and a radial branch might correspond to a cooling channel. In some embodiments, the sign distance from a point to the reference surface equation is calculated using the formula...

[0067]

[0068] in: It is the symbolic distance. It is the unit normal vector of the datum plane equation. It is the coordinate vector of a point in the original spatial point cloud. It is the coordinate vector of any point on the reference plane. It can be understood that this formula directly gives the signed vertical distance. Optionally, when constructing the feature connectivity graph, in addition to curvature extrema, points in the topological residual field whose gradient magnitude exceeds a certain threshold can also be included as candidate nodes to enhance the representation ability of smooth but broad features.

[0069] Example 2: See Figure 3 The Gaussian curvature and mean curvature of each data point are calculated on the topological residual field. Points whose Gaussian curvature and mean curvature simultaneously satisfy the local extremum condition are detected and marked as candidate feature points. The Euclidean distance and geodesic distance between each pair of candidate feature points are calculated, and the angle between the curvature vectors of the pair of candidate feature points is compared. When the Euclidean distance between a pair of candidate feature points is less than a preset distance threshold, their geodesic distance is less than a preset multiple of the Euclidean distance, and the angle between their curvature vectors is less than a preset angle threshold, an undirected edge is established between the pair of candidate feature points. The feature connected graph is formed by all candidate feature points and all undirected edges that satisfy the conditions. In the feature connected graph, a depth-first search is performed starting from any node with a degree of 1 until another node with a degree of 1 or a previously visited node is encountered. The search path is recorded and marked as a radial branch. After removing the edges of all radial branches, all simple cycles are searched in the remaining part of the feature connected graph and each simple cycle is marked as a closed loop. Each radial branch and each closed loop is encapsulated as a subgraph. The set of all subgraphs constitutes the feature structure set.

[0070] In practice, the Gaussian curvature and mean curvature of each data point are calculated on the topological residual field. Based on discrete triangular meshes or local surface fitting methods, differential geometric property analysis is performed on the surface represented by the topological residual field. The Gaussian curvature reflects the local bending degree of the surface at that point, such as convexity or concavity, while the mean curvature reflects the average bending trend of the surface at that point. Points whose Gaussian curvature and mean curvature simultaneously satisfy local extremum conditions are detected and marked as candidate feature points. The local extremum condition means that within a certain neighborhood of a point, the absolute values ​​of both the Gaussian curvature and mean curvature of that point are greater than or less than the corresponding values ​​of all its neighboring points. These points typically correspond to inflection points of surface features such as ridges, valleys, or local convex or concave points. The Euclidean distance and geodesic distance between each pair of candidate feature points are calculated. The Euclidean distance is the straight-line distance in three-dimensional space, and the geodesic distance is the shortest path distance calculated along the surface represented by the topological residual field. The angle between the curvature vectors of the pair of candidate feature points is compared. The curvature vector is defined by the principal curvature direction and the normal vector of the point. In specific implementation, when the Euclidean distance between a pair of candidate feature points is less than a preset distance threshold, their geodesic distance is less than a preset multiple of the Euclidean distance, and the angle between their curvature vectors is less than a preset angle threshold, an undirected edge is established between these candidate feature points. The distance threshold is used to constrain the spatial proximity of feature points, the ratio of the geodesic distance to the Euclidean distance is used to ensure that there is a direct surface path between the two points that does not cross other significant features, and the angle threshold is used to ensure that the two points have similar local geometric orientations. A feature connectivity graph is formed by all candidate feature points and all undirected edges that meet the conditions. In some embodiments, the formula for calculating the angle θ between the curvature vectors is:

[0071]

[0072] Where θ represents the angle between the two curvature vectors. and These represent the curvature direction vectors of candidate feature points i and j, respectively, and are used to compare them with a preset angle threshold.

[0073] In practical implementation, path search and subgraph segmentation are performed in the feature connected graph. Starting from any node with one connected edge, a depth-first search is performed until another node with one connected edge or a previously visited node is encountered. The depth-first search traverses the nodes along the edges of the feature connected graph and records the path, marking it as a radial branch. Radial branches correspond to surface features such as stiffeners or linearly extended flow channels. After removing the edges of all radial branches, all simple cycles are searched in the remaining part of the feature connected graph, and each simple cycle is marked as a closed loop. A simple cycle is a closed path with the same starting and ending points and does not repeatedly pass through any nodes except the starting point. Closed loops correspond to surface features such as protrusions or closed contours of depressions. Each radial branch and each closed loop is encapsulated into a subgraph, containing a set of all its nodes and edges, as well as their type identifiers. The set of all subgraphs constitutes the feature structure set. It can be understood that through graph traversal and cycle detection algorithms, the feature connected graph is decomposed into several sub-components with clear topological structures. In some embodiments, the preset distance threshold can be set according to the overall size of the processed surface and the expected size of the feature. For example, for a workpiece with a side length of 200 mm, the distance threshold can be set to 5 mm. Optionally, the geodesic distance can be calculated by running Dijkstra's algorithm on a triangular mesh surface constructed from a topological residual field. Dijkstra's algorithm is applied to the graph to calculate the shortest path between two candidate feature points. The algorithm is initialized starting from the initial candidate feature point, setting its distance to 0, and the distances of other vertices to infinity. A priority queue is used to manage the vertices to be processed. The algorithm iteratively selects the vertex with the smallest current distance and performs a relaxation operation on all its neighboring vertices, i.e., checks whether the path to the neighbor through the current vertex is shorter. If it is shorter, the distance value of the neighbor is updated. This process is repeated until the target candidate feature point is reached. At this point, the distance value of the target point is the geodesic distance. It can be understood that the construction of the feature connectivity graph connects discrete candidate feature points according to geometric and topological relationships, forming an abstract expression of the surface feature skeleton structure. In practice, all simple cycles can be found using a backtracking algorithm based on depth-first search, which systematically identifies all basic cycles in the remaining graph after removing radial branches.

[0074] Example 3: For a feature structure marked as radial branches, all its nodes are extracted and connected sequentially to form a centerline. This centerline is smoothed and resampled to generate a skeleton line. The point set within a certain distance on both sides of the skeleton line is calculated to form an enclosing region. The topological residual field value within the enclosing region is then fitted with a polynomial to generate a height distribution model. For a structure marked as a closed loop, the internal region enclosed by the loop edge is extracted. The centroid of this internal region is calculated, and the line connecting the centroid to the edge point forms a radial skeleton line. The enclosing region is defined with the closed loop edge as the boundary, and the topological residual field value of the internal region is fitted with a surface to generate a height distribution model. The structured description list containing the analysis results of all feature structures is input into the geometric growth model. Growth rules are defined for the geometric growth model, including skeleton line extension, enclosing region expansion, and scaling of the height distribution model according to a preset ratio. Constraints are also defined, including that spatial interference between different virtual feature structures is not allowed and the total height change of virtual feature structures must be kept within a predetermined range. The geometric growth model starts with the structured description list as the initial state and adjusts each feature structure according to the growth rules in each iteration. After each adjustment, it checks whether all constraints are met. If not, it backtracks to the previous step until all feature structures reach the preset growth generation or fall into a steady state, and outputs the final set of virtual feature structures.

[0075] In specific implementation, for feature structures marked as radial branches, all nodes of the radial branch feature structure are extracted and connected in sequence to form a center line. The node order is determined according to the connection relationship and spatial orientation in the feature connectivity graph. The center line is smoothed and resampled to generate a skeleton line. Smoothing uses moving average or spline interpolation methods to eliminate noise. Resampling ensures that the points on the skeleton line have uniform arc length spacing. The set of points within a certain distance on both sides of the skeleton line is calculated to form an enclosing region. The distance threshold is set according to the average width of the feature structure. The set of points within the enclosing region contains all the topological residual field data points corresponding to the radial branch feature structure. The topological residual field values ​​within the enclosing region are then subjected to polynomial fitting to generate a height distribution model. The polynomial fitting uses the least squares method to fit the discrete height data into a continuous polynomial function about the two-dimensional position coordinates. For structures labeled as closed loops, the internal region enclosed by the loop edge is extracted. This internal region consists of nodes on the closed loop and all their internal topological residual field data points. The centroid of the internal region is calculated, and lines connecting the centroid to the edge points form radial skeleton lines. These radial skeleton lines extend from the centroid in multiple directions to the loop edge to characterize the radial geometric support within the structure. The enclosing region is defined with the closed loop edge as the boundary; this enclosing region is the two-dimensional plane covered by the closed loop polygon. A surface fitting is performed on the topological residual field values ​​of the internal region to generate a height distribution model. The surface fitting uses bivariate polynomials or radial basis functions to establish the mapping relationship between two-dimensional coordinates and height values. In essence, the structural analysis process transforms discrete graph structural features into geometric entities with continuous mathematical descriptions, including skeleton lines describing the central direction, enclosing regions describing the spatial extent, and a height distribution model describing height variations.

[0076] The structured description list containing all feature structure analysis results is input into the geometric growth model. This list is a dataset where each entry corresponds to the skeleton line, enclosing region, and height distribution model parameters of a feature structure. Growth rules are defined for the geometric growth model, including skeleton line extension, enclosing region expansion, and scaling of the height distribution model according to a preset ratio. Skeleton line extension refers to increasing the length along the tangent direction of the skeleton line endpoints; enclosing region expansion refers to expanding outward along the normal direction of the region boundary; and scaling of the height distribution model according to a preset ratio refers to multiplying the function describing the height values ​​by a scaling factor. Constraints are defined for the geometric growth model, including prohibition of spatial interference between different virtual feature structures and the requirement that the total height change of virtual feature structures remain within a predetermined range. Spatial interference refers to the overlap of the enclosing regions of two virtual feature structures in a two-dimensional plane or the intersection of their three-dimensional solid models in space. The total height change is measured by statistically analyzing the difference between the total volume or average height of all virtual feature structures before and after scaling their height distribution models.

[0077] In some embodiments, the geometric growth model starts with a structured description list as its initial state and adjusts each feature structure according to growth rules at each iteration step. The adjustment operation includes randomly selecting a feature structure and applying skeleton line extensions, enclosing region expansions, or height distribution model scaling by random magnitudes. After each adjustment, it checks whether all constraints are met. This check involves calculating the updated enclosing region of the virtual feature structure and determining overlap, while simultaneously calculating the total height change and comparing it with a predetermined range. If the constraints are not met, the adjustment step is rolled back. Rollback means reversing all modifications made to the feature structures in this iteration and restoring them to their pre-iteration state. This continues until all feature structures reach a preset growth generation or enter a steady state. The growth generation is a preset maximum number of iterations. Entering a steady state means rolling back for several consecutive iterations due to non-compliance with constraints. The final set of virtual feature structures is output, containing the latest skeleton line, enclosing region, and height distribution model for each feature structure after evolution. Optionally, the length increment of the skeleton line extension, the width increment of the enclosing region expansion, and the scaling factor of the height distribution model can be generated according to a random distribution or deterministic rule in each iteration step. It is understandable that the geometric growth model, through constrained stochastic evolution, simulates the merging, expansion, or morphological changes that may occur in the processed surface features during physical processes. In specific implementations, the preset number of growth generations can be set to 1000, and the criterion for falling into a steady state can be set to rollback after 50 consecutive iterations. Optionally, spatial interference can be checked by calculating whether the overlapping area of ​​the two-dimensional enclosing polygon is greater than zero; if it is greater than zero, interference is determined to have occurred. In some embodiments, the scaling of the height distribution model can be expressed as...

[0078]

[0079] in: It is the scaled height distribution function. It is the height distribution function before scaling. It is the preset scaling factor. It is a two-dimensional position coordinate.

[0080] Example 4: Triangulate the region enclosing each virtual feature structure, extract the boundary edge sequence of the triangular mesh, project the boundary edge sequence onto the reference plane, and perform corner detection and polygon approximation on the projected boundary edge sequence to obtain the contour edge of the virtual feature structure. Within the polygonal region defined by the contour edge, calculate the height value of each grid point according to the height distribution model of the virtual feature structure to form a two-dimensional height increment field. Rasterize all contour edges into a binary image with the same spatial resolution as the topological residual field as a two-dimensional feature mask. Superimpose the two-dimensional feature mask onto the two-dimensional parameter domain of the reference plane, and perform small translation and rotation adjustments on each two-dimensional feature mask by maximizing the cross-correlation coefficient to complete the registration. Add each registered height increment field to the reference plane equation at the corresponding position to obtain a preliminary composite surface. Establish an energy functional with the goal of minimizing surface smoothness and deviation from the preliminary composite surface. Solve the Euler-Lagrange equation corresponding to the energy functional to obtain a globally smooth intermediate geometric surface with continuous detail transitions.

[0081] In practice, the enclosing region of each virtual feature structure is triangulated. The enclosing region of the virtual feature structure is a polygon defined by a set of ordered two-dimensional vertices. The constrained Delaunay triangulation algorithm is used to divide these polygonal regions into a continuous set of triangular facets. The triangulation process ensures that the interior of the region is completely covered by non-overlapping and seamless triangles. For example, a virtual feature structure representing a boss has an enclosing region that is approximately circular. After triangulation, a mesh composed of hundreds of triangles is generated. The boundary edge sequence of the triangular mesh is extracted, projected onto the reference plane, and corner detection and polygon approximation are performed on the projected boundary edge sequence. The boundary edge sequence refers to the closed loop formed by connecting all the edges that belong to only one triangle according to the adjacency relationship. Projecting onto the reference plane involves projecting the coordinates of the three-dimensional vertices on these boundary edges along the reference plane normal to obtain a two-dimensional polyline. Corner detection identifies vertices with a turning angle greater than a threshold by calculating the dot product of the direction vectors of adjacent line segments. Polygon approximation uses the Douglas-Puk algorithm to simplify the two-dimensional polyline with a specified distance tolerance, obtaining the contour edge of the virtual feature structure. The contour edge is finally represented by a set of simplified two-dimensional vertex coordinates, which accurately describes the two-dimensional projection shape of the feature on the reference plane. Within the polygonal region defined by the contour edge, the height value of each grid point is calculated based on the height distribution model of the virtual feature structure to form a two-dimensional height increment field. The height distribution model is a mathematical function defined on a two-dimensional parameter domain, such as a cubic polynomial surface. Grid points generate a regular rectangular grid on the parameter plane at fixed physical intervals. The height value of each grid point (u,v) is directly calculated by substituting the coordinates into the height distribution model function. The height values ​​of all grid points constitute a two-dimensional matrix aligned with the spatial position, i.e., the height increment field. All contour edges are rasterized into a binary image with the same spatial resolution as the topological residual field as a two-dimensional feature mask. The rasterization process uses a scanline filling algorithm to set the internal pixels of each contour edge polygon to 1 and the external pixels to 0, filling a blank image with the same number of rows, columns, and physical dimensions as the topological residual field. The generated binary image is the two-dimensional feature mask, where the pixel regions with a value of 1 correspond to the positions occupied by the virtual feature structure.

[0082] Registration is achieved by superimposing two-dimensional feature masks onto the two-dimensional parameter domain of a reference plane and performing minute translations and rotations on each two-dimensional feature mask by maximizing the cross-correlation coefficient. The two-dimensional parameter domain of the reference plane is a UV coordinate system plane corresponding to the physical processing surface. Superposition involves placing each two-dimensional feature mask image on this plane with its initial position and orientation recorded in the virtual feature structure set. Maximizing the cross-correlation coefficient is achieved by iteratively optimizing the translation (ΔX, ΔY) and rotation Δθ of the two-dimensional feature mask, calculating the normalized cross-correlation coefficient between it and the binary feature image extracted from the original topological residual field, and seeking the maximum value. This completes the fine alignment of each virtual feature structure with the original feature in terms of position and orientation. Each registered height increment field is added to the reference surface equation at the corresponding position to obtain a preliminary composite surface. The reference surface equation gives the base height Z_base(u,v). The addition operation means that at each pixel position (u,v) of the 2D feature mask (1), the reference surface height Z_base(u,v) is summed with the corresponding registered height increment field value ΔH(u,v) to generate a preliminary composite surface S_initial(u,v). This surface has convex or concave geometric details in the feature region. An energy functional is established with the goal of minimizing surface smoothness and deviation from the preliminary composite surface. By solving the Euler-Lagrange equation corresponding to this energy functional, a smooth intermediate geometric surface with global smoothness and continuous detail transition is obtained. The energy functional is defined as the weighted integral of the smoothness penalty term of the target surface function and its difference term with the preliminary composite surface. The corresponding partial differential equation is derived through the variational principle and solved numerically to obtain a continuous surface that is both smooth and retains the main shape of the original features.

[0083] In some embodiments, the specific parameters involved in the rasterization and registration process are shown in Table 1:

[0084] Table 1: Rasterization and Registration Parameters

[0085] Parameter categories Parameter name Example values Remark Rasterization parameters Pixel corresponding physical size 0.05mm / pixel Determines spatial resolution Image width (pixels) 2400 pixels Coverage parameter domain U direction Image height (pixels) 1800 pixels Coverage parameter domain V direction Registration parameters Maximum translation adjustment ±5 pixels (±0.25 mm) Fine-tuning range limitations Maximum rotation adjustment ±3 degrees Fine-tuning range limitations Optimize iteration step size 0.5 pixel, 0.2 degree Search step increment

[0086] It is understandable that the registration process that maximizes the cross-correlation coefficient is a matching method based on image grayscale, which can effectively compensate for minor positional deviations that may exist during the virtual feature generation process. In some embodiments, the established dimensionlessly consistent energy functional can be expressed in the following form:

[0087]

[0088] in: It is the height function of the intermediate geometric surface with the smooth transition to be determined; It is a preliminary function of the height of the composite surface; , and yes The second-order partial derivative; It is a regularization parameter. It is a two-dimensional parameter domain. It can be understood that by solving the Euler-Lagrange equation corresponding to the minimization of this energy functional, a mathematically reasonable and smoothly transitioning intermediate geometric surface can be obtained. Optional, regularization parameters The specific value can be determined through trial and error or based on prior estimation using characteristic dimensions. Optionally, the solution process typically discretizes the partial differential equation into a large system of linear equations and uses the conjugate gradient method for iterative solution to obtain the value. The values ​​at each discrete grid point.

[0089] See Figure 4 In the registration stage of CNC milling surface correction, the distribution characteristics of the normalized cross-correlation coefficient between the two-dimensional feature mask and the original topological residual field binary feature image under the translation adjustment in the X and Y directions are presented. Specifically, the figure uses the translation adjustment in the X and Y directions (unit: pixels) as the coordinate axis and the normalized cross-correlation coefficient as the color map (value range 0~1). The heatmap visually shows the matching degree under different translation adjustments: the central region (cross-correlation coefficient close to 1) corresponds to the region with a high matching degree, while the edge region (cross-correlation coefficient close to 0) has a low matching degree. The red star in the figure marks the position of the maximum cross-correlation coefficient, which corresponds to the translation adjustment ΔX=0.3px and ΔY=-0.3px. This position is the optimal solution for registration optimization, realizing the fine alignment of the virtual feature structure and the original feature in the two-dimensional parameter domain. Based on the parameters of the embodiment, this translation adjustment is within the constraint range of "maximum translation adjustment ± 5 pixels", which verifies the effectiveness of the registration process. This result can be directly used for the subsequent fusion calculation of the height increment field and the reference surface equation.

[0090] Example 5: Calculate the two-dimensional Fourier spectrum of the topological residual field, analyze the two-dimensional Fourier spectrum to determine the low-frequency band characterizing the main features of the machined surface and the high-frequency band characterizing noise, assign high weight values ​​to the spatial frequency components in the low-frequency band and low weight values ​​to the spatial frequency components in the high-frequency band to generate a spatial frequency-related weighting coefficient field. In the spatial domain, the weighting coefficient field is used to control the linear combination ratio of the dense and uniform intermediate point cloud and the original spatial point cloud at corresponding positions to calculate and generate an optimized surface point cloud. In specific implementation, calculating the two-dimensional Fourier spectrum of the topological residual field is the first step. The topological residual field is a two-dimensional discrete data matrix that records the height deviation of each position relative to the reference surface. I need to perform a two-dimensional discrete Fourier transform on this matrix to convert it from the spatial domain to the frequency domain, obtaining a complex spectrum. This spectrum can clearly show the distribution of various frequency components in the surface morphology. Some low-frequency components may correspond to major features such as large bosses and pits, while high-frequency components may correspond to details such as machining marks and measurement noise.

[0091] Analyzing the two-dimensional Fourier spectrum helps determine the low-frequency band characterizing the main features of the processed surface and the high-frequency band characterizing noise. This process requires observing the amplitude distribution of the spectrum. Typically, the low-frequency components near the center of the spectrum have higher amplitudes, representing the overall undulation of the surface; while the high-frequency components at the periphery of the spectrum have lower amplitudes, possibly representing noise. I need to set a frequency threshold to separate the low and high frequency bands, which can be determined based on the inflection point of the spectral amplitude decrease or prior knowledge.

[0092] High weight values ​​are assigned to spatial frequency components in the low-frequency band, and low weight values ​​are assigned to spatial frequency components in the high-frequency band, generating a spatial frequency-dependent weighted coefficient field. This means that in the frequency domain, a weight value is assigned to each frequency point based on its frequency band, forming a frequency domain weight template. Then, a two-dimensional inverse Fourier transform is performed on this frequency domain weight template to obtain a spatial domain weighted coefficient field. This weighted coefficient field has a weight value at each spatial location, reflecting whether the surface components corresponding to that location should be preserved more or smoothed more.

[0093] In the spatial domain, a weighted coefficient field is used to control the linear combination ratio of the dense and uniform intermediate point cloud and the original spatial point cloud at corresponding points, thereby generating an optimized surface point cloud. Because the dense and uniform intermediate point cloud and the original spatial point cloud are spatially registered, for the same two-dimensional projected coordinate position, the height value can be interpolated from both point clouds. The final height value of the optimized surface at that point is determined by the weighting ratio of the two height values ​​based on the weighting coefficient field at that point. For example, at a certain position, if the weighting coefficient is high, the final height is closer to the height of the original point cloud; if the weighting coefficient is low, the final height is closer to the height of the intermediate point cloud.

[0094] This weighting process is essentially a spatial domain implementation of a frequency-domain filtering concept, allowing for the suppression of high-frequency noise while preserving the main low-frequency characteristics. In some embodiments, a smoothly transitioning weighting function can be designed instead of a simple binary partition, enabling a smooth transition of frequency components near the cutoff frequency and avoiding the introduction of ringing effects on the final surface. For example, the weighting function can be designed as a Gaussian attenuation form:

[0095]

[0096] in: The frequency coordinates in the frequency domain are The weight of the points, It is a bandwidth parameter that controls the decay rate. This function gives a weight close to 1 in the center of the frequency domain and a weight close to 0 in the outer part of the frequency domain, resulting in a smooth transition.

[0097] Optionally, in actual calculations, the original spatial point cloud may be non-uniform, while the dense and uniform intermediate point cloud is a regular grid. Before blending, it may be necessary to resample or interpolate the original spatial point cloud onto the same regular grid as the intermediate point cloud to ensure that each grid point has two corresponding height values ​​for weighted calculation. It can be understood that through this frequency analysis-based weighted blending, the final optimized surface point cloud retains the main geometric features of the original surface while incorporating the smoothness and regularity of the intermediate geometric surface, making it more suitable for generating high-quality CNC machining paths. In some embodiments, after the weighting coefficient field is generated, a slight Gaussian smoothing filter can be applied in the spatial domain to eliminate spatial discontinuities that may be caused by sharp cutoffs in the frequency domain.

[0098] See Figure 5 In the implementation of the CNC milling surface correction method, this figure presents the spatial distribution characteristics of the topological residual field on a two-dimensional plane (XY coordinates, unit: mm) after the original spatial point cloud of the machined surface is fitted to the reference plane and separated by residuals. The color codes (from purple to yellow) in the figure correspond to residual values ​​(unit: mm), ranging from -0.75 to 1.00. The yellow area represents positive residuals (surface protrusions) relative to the reference plane, the purple area represents negative residuals (surface depressions), and the blue-green area corresponds to areas with residuals close to 0. From the distribution pattern, the topological residual field exhibits an alternating distribution of protrusions (yellow clusters) and depressions (purple clusters) in multiple regions, consistent with the local topological features formed by uneven tool path and material removal on the machined surface. This residual field is the basic data carrier for subsequent construction of feature connectivity graphs and extraction of feature structure sets. Its high and low frequency components in spatial distribution will directly affect the iterative evolution of the geometric growth model and the final weighted mixing coefficients for optimizing the surface point cloud.

[0099] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A machining surface correction method for a numerical control milling machining center, characterized by, include: Establish the original spatial point cloud of the processed surface and generate a set of feature structures of the processed surface; For each feature structure in the set of feature structures, perform structural parsing to extract the skeleton line, enclosing region and height distribution model of each feature structure to form a structured description list; The structured description list is input into the geometric growth model. The geometric growth model iteratively expands, contracts and deforms each feature structure according to preset growth rules and constraints, simulating its evolution process in virtual space and generating a set of virtual feature structures. Extract the contour edge and internal height field of each virtual feature structure from the set of virtual feature structures, and rasterize the contour edge and internal height field into a two-dimensional feature mask and a height increment field. The two-dimensional feature mask and height increment field are registered and fused with the reference surface equation, and the intermediate geometric surface with smooth transition is calculated by solving the variational problem. Based on the density distribution of the original spatial point cloud of the processed surface, the intermediate geometric surface of the smooth transition is adaptively resampled to generate a dense and uniform intermediate point cloud. The dense and uniform intermediate point cloud is weighted and mixed with the original spatial point cloud. The weighting coefficients of the weighting are determined according to the spatial frequency distribution of the topological residual field. The optimized surface point cloud is then calculated and generated to drive the CNC milling machining center for correction machining.

2. The machining surface correction method for a numerical control milling machining center according to claim 1, characterized in that, The process of establishing the original spatial point cloud of the processed surface and generating a set of feature structures for the processed surface includes: The original spatial point cloud is derived from the geometric coordinates and reflection intensity signals collected at different locations on the processing surface; A reference surface fitting and residual separation are performed on the original spatial point cloud to generate a reference surface equation for the processed surface and a topological residual field relative to the reference surface equation. Based on the topological residual field, a characteristic connected graph of the processed surface is constructed. The nodes of the characteristic connected graph are composed of local curvature extrema of the topological residual field, and the edges of the characteristic connected graph are composed of geodesic paths between nodes that satisfy distance constraints and curvature similarity constraints. Path search and subgraph segmentation are performed in the feature connectivity graph to identify all closed loops and radial branches, and each closed loop and radial branch is marked as an independent feature structure to generate a set of feature structures.

3. The method of claim 2, wherein the method is used for a machining center. The process of performing reference surface fitting and residual separation on the original spatial point cloud includes: The random sampling consensus algorithm is used to select an interior point set from the original spatial point cloud; A plane equation is obtained by fitting the interior point set using the least squares method, and this plane equation is determined as the reference surface equation. Calculate the symbolic distance from each point in the original spatial point cloud to the reference surface equation, and organize all symbolic distances according to their corresponding two-dimensional projected coordinates of the original spatial point cloud to form the topological residual field.

4. The machining surface correction method for a numerical control milling machining center according to claim 2, characterized in that, The construction of the feature connectivity graph of the processed surface based on the topological residual field includes: Calculate the Gaussian curvature and mean curvature of each data point on the topological residual field; Detect all points where both the Gaussian curvature and the mean curvature satisfy the local extremum condition, and mark these points as candidate feature points; Calculate the Euclidean distance and geodesic distance between each pair of candidate feature points, and compare the angle between the curvature vectors of the pair of candidate feature points; When the Euclidean distance between a pair of candidate feature points is less than a distance threshold, the geodesic distance is less than a preset multiple of the Euclidean distance, and the angle between the curvature vectors is less than an angle threshold, an undirected edge is established between the pair of candidate feature points. The feature connectivity graph is composed of all candidate feature points and all undirected edges that satisfy the conditions.

5. A method for correcting the machining surface of a CNC milling machining center according to claim 4, characterized in that, The process involves performing path search and subgraph segmentation on the featured connected graph to identify all closed loops and radial branches, including: In the feature connectivity graph, starting from any node with a degree of 1, a depth-first search is performed until another node with a degree of 1 or a previously visited node is encountered. The search path is recorded and marked as a radial branch. After removing the edges of all radial branches, find all simple cycles in the remaining part of the characteristic connected graph and mark each simple cycle as a closed loop; Each radial branch and each closed loop is encapsulated as a subgraph, and the set of all subgraphs constitutes the set of feature structures.

6. A method for correcting the machining surface of a CNC milling machining center according to claim 5, characterized in that, The step of performing structural parsing on each feature structure in the feature structure set includes: For the feature structure marked as radial branches, extract all its nodes and connect them in order to form a center line. Smooth and resample the center line to generate a skeleton line. Calculate the point set within a certain distance on both sides of the skeleton line to form an enclosing region. Perform polynomial fitting on the topological residual field values ​​within the enclosing region to generate a height distribution model. For a structure marked as a closed loop, the internal region enclosed by the loop edge is extracted, the centroid of the internal region is calculated, and the line connecting the centroid to the edge point forms a radial skeleton line. The enclosed region is defined with the closed loop edge as the boundary, and the topological residual field value of the internal region is fitted to the surface to generate a height distribution model.

7. A method for correcting the machining surface of a CNC milling machining center according to claim 5, characterized in that, The step of inputting the structured description list into the geometric growth model includes: Define growth rules for the geometric growth model, including skeleton line extension, enclosing region expansion, and scaling of the height distribution model according to a preset ratio; Define constraints for the geometric growth model, including that spatial interference is not allowed between different virtual feature structures and that the total height variation of the virtual feature structures must be kept within a predetermined range. The geometric growth model takes the structured description list as the initial state, adjusts each feature structure according to the growth rules in each iteration step, and checks whether all constraints are met after each adjustment. If not, it backtracks to the previous step until all feature structures reach the preset growth generation or fall into a steady state, and outputs the final set of virtual feature structures.

8. A method for correcting the machining surface of a CNC milling machining center according to claim 6, characterized in that, The step of extracting the contour edge and internal height field of each virtual feature structure from the set of virtual feature structures includes: Triangulate the region enclosed by each virtual feature structure; Extract the boundary edge sequence of the triangular mesh, project the boundary edge sequence onto the reference plane, and perform corner detection and polygon approximation on the projected boundary edge sequence to obtain the contour edge of the virtual feature structure. Within the polygonal region defined by the contour edge, the height value of each grid point is calculated based on the height distribution model of the virtual feature structure, forming a two-dimensional height increment field. All contour edges are rasterized into a binary image with the same spatial resolution as the topological residual field, which serves as a two-dimensional feature mask.

9. A method for correcting the machining surface of a CNC milling machining center according to claim 8, characterized in that, The process of registering and fusing the two-dimensional feature mask and height increment field with the reference surface equation includes: The two-dimensional feature masks are superimposed onto the two-dimensional parameter domain of the reference plane. By maximizing the cross-correlation coefficient, each two-dimensional feature mask is slightly translated and rotated to complete the registration. Each registered height increment field is added to the reference surface equation at the corresponding position to obtain a preliminary composite surface; An energy functional is established with the goal of minimizing surface smoothness and deviation from the initial composite surface. By solving the Euler-Lagrange equation corresponding to this energy functional, an intermediate geometric surface with smooth transitions that is globally smooth and has continuous detail transitions is obtained.

10. A method for correcting the machining surface of a CNC milling machining center according to claim 1, characterized in that, The weighted mixing of the dense and uniform intermediate point cloud with the original spatial point cloud includes: Calculate the two-dimensional Fourier spectrum of the topological residual field; Analyze the two-dimensional Fourier spectrum to determine the low-frequency band characterizing the main features of the processed surface and the high-frequency band characterizing noise; A spatial frequency component in the low-frequency band is assigned a high weight value, and a spatial frequency component in the high-frequency band is assigned a low weight value, thereby generating a spatial frequency-related weight coefficient field. In the spatial domain, the optimized surface point cloud is generated by using a weighting coefficient field to control the linear combination ratio of the dense and uniform intermediate point cloud and the original spatial point cloud at corresponding locations.

Images