Three-coordinate measurement method based on incomplete curved surface fitting

Abstract

The invention belongs to the technical field of three-coordinate measurement, and particularly discloses a three-coordinate measurement method based on incomplete curved surface fitting, which comprises the following steps: hierarchically extracting geometric features from incomplete point clouds, and dividing a workpiece to be measured into a plurality of ordered curved surfaces; adding a curved surface label to each point cloud data, and generating a plurality of ordered point cloud sets based on the curved surface labels; generating virtual points based on the geometric features to fill the missing region; reconstructing a three-dimensional sub-model of each ordered curved surface based on the ordered point cloud set, the virtual points and the edge point cloud; and fitting the three-dimensional sub-model to generate a continuous curved surface model, and obtaining workpiece measurement parameters based on the continuous curved surface model. By extracting geometric features, classifying point clouds and generating virtual points, the limitation that a traditional method depends on a prior model is broken through, unknown or non-standard geometry can be processed, global continuous modeling of incomplete point clouds is achieved through ordinal curved surface division, three-dimensional sub-model reconstruction and continuous curved surface fitting, and the accuracy of measurement parameters is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of coordinate measuring technology, and particularly relates to a coordinate measuring method based on incomplete surface fitting. Background Art

[0002] A coordinate measuring system (CMM) obtains three-dimensional coordinate points on the surface of an object through a probe contact or non-contact sensor, and is used for dimensional inspection, reverse engineering, and quality control. During the actual measurement process, for a probe-type coordinate measuring system, the internal structure of the part (such as gear teeth, inner wall of a pipe) cannot be completely captured. For a coordinate measuring system with a laser or optical probe, the structured light / laser scan data is lost due to metal or polished surfaces. Therefore, data loss is a common problem in three-dimensional measurement.

[0003] The traditional method is to use the geometric relationships of known measurement points (such as neighboring points, curve continuity) to fill in the missing area through mathematical interpolation, or rely on known CAD models or standard geometric shapes (such as cylinders, planes) to fill in the missing data by comparing with the design model. However, the former has poor adaptability to complex geometries (such as sharp edges, multi-scale features), and the latter relies on an accurate prior model and cannot handle unknown or non-standard geometric workpieces. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects existing in the prior art and provide a coordinate measuring method based on incomplete surface fitting.

[0005] The present invention provides a coordinate measuring method based on incomplete surface fitting, including the following steps: (1) Obtain the incomplete point cloud of the workpiece to be measured, extract geometric features from the incomplete point cloud layer by layer, and divide the workpiece to be measured into several ordered surfaces based on the geometric features; (2) Classify the incomplete point cloud data, add surface labels to each point cloud data, and generate several ordered point cloud sets based on the surface labels; (3) Generate virtual points based on the geometric features to fill in the missing area; (4) Reconstruct the three-dimensional sub-model of each ordered surface based on the ordered point cloud set, virtual points, and edge point cloud; the edge point cloud is the same point cloud data of different ordered point cloud sets; (5) Fit the three-dimensional sub-model to generate a continuous surface model, and obtain the workpiece measurement parameters based on the continuous surface model.

[0006] A further solution is that the step (1) includes: Obtain the incomplete point cloud data of the workpiece to be measured through a multi-modal sensor, and filter the incomplete point cloud data; Calculate the curvature of the point cloud, select the points with curvature lower than the preset threshold K1 as seed points, use the random sample consensus algorithm to randomly select sampling points from the seed points to initialize the plane model, and combine the density clustering algorithm to group the point cloud to identify the candidate plane region; Analyze the change rate of the normal direction of the non-planar region, fit a cylindrical surface or a spherical surface according to the change rate characteristics, and use the least squares method to solve the axis and radius of the cylindrical surface or the center and radius of the spherical surface; the analysis of the change rate of the normal direction includes: calculating the change rate of the included angle of the normal directions of adjacent points in the point cloud region; when the change rate is less than the preset threshold θ1, it is determined as a cylindrical surface feature; when the change rate is greater than the preset threshold θ2, it is determined as a spherical surface feature; where, the value range of θ1 is 5° to 15°, and the value range of θ2 is 30° to 45°.

[0007] Extract the remaining point cloud region after the extraction of plane, cylindrical surface, and spherical surface features as the free-form surface feature, and calculate the curvature extreme points of this region to identify the edge and transition region features; Based on the curvature similarity condition, use the region growing algorithm to divide the point cloud into several surface patches, and the curvature difference of the points within each surface patch is less than the preset threshold K2; the specific steps of the region growing algorithm include: Select points with similar curvature as seed points; Expand the neighborhood points, and judge whether the curvature difference between the neighborhood points and the current surface patch is less than the preset threshold K2, and the value range of the preset threshold K2 is 0.001mm -1 to 0.01mm -1 ; Repeat the expansion process until the curvature similarity condition cannot be satisfied, and form independent surface patches; Extract the free-form surface feature, divide the surface patch based on the curvature similarity through the region growing algorithm, and obtain the ordered surface according to the priority order of complete layer plane > ordinary plane > cylindrical surface > spherical surface > free-form surface.

[0008] A further solution is that in step (1), the multi-modal sensor includes a probe-type sensor and a non-contact sensor, and the non-contact sensor is a laser probe or an optical probe.

[0009] A further solution is that in step (2), deep learning models are used for classifying the point cloud data. The deep learning models are used for classifying the geometric features of the point cloud data and adding surface labels. Specifically, the incomplete point cloud data after adaptive filtering is input into a trained convolutional neural network CNN. Through learning a large amount of known geometric feature data (plane, cylinder, sphere, free surface, etc.), the model has the ability to automatically extract the geometric features of the point cloud (such as curvature, normal direction, neighborhood topological structure). The model infers each data point of the input point cloud and outputs the probability value of belonging to various geometric features. A classification threshold is set (such as probability > 0.8), and a corresponding surface label (such as plane, cylinder, free surface) is assigned to each point cloud data to form a labeled point cloud data set.

[0010] A further solution is that the generation process of the ordered point cloud set in step (2) is as follows: Project each ordered surface to obtain the corresponding projection plane / line, and perform mirror processing on the point cloud data based on the projection plane / line; Arbitrarily select two point cloud data A(x1, y1, z1) and B(x2, y2, z2). If the intersection line of the two points and their mirror points A'(x1', y1', z1') and B'(x2', y2', z2') has an intersection point on the projection plane / line, it is determined to belong to this surface and is classified into the corresponding point cloud set; Traverse all point clouds to ensure that the intersection line of any two points and their mirror points has no intersection point on the projection plane / line; Repeat until all ordered point cloud sets are generated.

[0011] A further solution is that the process of generating the virtual points in step (3) is as follows: Construct a polynomial model of the local thickness and curvature of the workpiece, and infer the geometric features of the missing area based on the neighboring points; determine the position and attributes of the virtual points according to the inference results; Calculate the distance weight and geometric feature weight of the neighboring points, and generate virtual points through weighted interpolation. Specifically, the calculation of the spatial distance and geometric feature weights includes: The spatial distance weight adopts a Gaussian decay function: , where d is the Euclidean distance from the neighboring point to the missing area, is the distance decay factor; The geometric feature similarity weight adopts a reciprocal function of curvature difference:

[0012] where is the curvature of the neighboring point, is the target curvature of the missing area.

[0013] The virtual points are generated through linear weighted interpolation, and the calculation formula is: wherein are the coordinates of adjacent points, and are the spatial distance weight and the geometric feature similarity weight, respectively.

[0014] Verify the curvature smoothness (the curvature difference from adjacent points < preset threshold) and topological continuity (forming a continuous surface with adjacent points) of the virtual points.

[0015] A further solution is that the three-dimensional sub-model generation process described in step (4) is as follows: Adopt a surface fitting algorithm based on the variational method to construct an energy function containing a data fitting term, a smoothness term, and a boundary constraint term, and reconstruct the three-dimensional sub-model by minimizing the energy function; the data fitting term is used to measure the fitting degree of the surface to the ordered point cloud set, the smoothness term is used to constrain the smoothness of the surface, and the boundary constraint term is used to ensure the geometric continuity of the surface boundary and adjacent surfaces; Calculate the local curvature and sharpness characteristics of the surface, and dynamically adjust the grid density according to the curvature magnitude: In the area where the curvature is greater than the preset threshold K3, use a dense grid division, and the grid cell size is 1 / 2 - 1 / 4 of the reference size; In the area where the curvature is less than the preset threshold K4, use a sparse grid division, and the grid cell size is 1 - 2 times the reference size; Extract the overlapping area of different ordered point cloud sets as the edge point cloud, filter out the noise points through the curvature threshold, supplement the missing edges with virtual points, ensure that the density of the boundary point cloud is not less than 80% of the main area, and fuse the main surface fitting result with the edge processing data to generate an independent three-dimensional sub-model containing surface type, geometric parameters, and boundary feature information.

[0016] A further solution is that in step (5), generating the continuous surface model includes: Select the complete layer plane with the highest priority as the reference, fit the complete layer plane through the algorithm and align it to the global coordinate system; use the iterative closest point algorithm to align the point cloud of each sub-model to the reference plane and establish a preliminary positional relationship; For regular surfaces: impose position continuity constraints and normal continuity constraints, and optimize the stitching error through the transformation matrix; for free-form surfaces: adopt least squares optimization with penalty terms to enforce the continuity of the edge point cloud and adjacent surface patches, and the penalty factor is dynamically adjusted according to the proportion of virtual points; Construct a joint optimization objective function containing all surface patches, minimize the overall fitting error and boundary discontinuity degree, and generate a globally continuous complete surface model.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention extracts geometric features layer by layer, classifies point clouds, and generates virtual points to fill in missing areas. Without relying on known CAD models or standard geometric shapes, it breaks through the limitation of traditional methods that rely on prior models, can handle unknown or non-standard geometries, and through ordered surface division, three-dimensional sub-model reconstruction, and continuous surface fitting, realizes global continuous modeling of incomplete point clouds, avoids the insufficient adaptability of traditional interpolation methods to complex structures, ensures the accuracy of measurement parameters, and is especially suitable for internal structures that the probe cannot contact or non-contact scanning blind spots.

[0018] The present invention uses a convolutional neural network to automatically extract local features of point clouds, realizes high-precision classification of geometric types such as planes, cylinders, and free-form surfaces, and avoids the inefficiency and errors of traditional manual intervention. Through projection plane / line mirror processing and cross-line intersection determination, it ensures that point cloud data is accurately divided into corresponding sets according to surface labels, avoids cross-surface data confusion, and provides a pure data set for subsequent regional modeling.

[0019] The present invention takes the complete layer plane as a reference, aligns each sub-model through the Iterative Closest Point algorithm (ICP), combines the position / normal continuity constraints (G0 / G1) of regular surfaces and the least squares optimization with penalty terms of free-form surfaces, minimizes the stitching error and boundary discontinuity, generates a globally continuous complete surface model, and the penalty factor is dynamically adjusted according to the proportion of virtual points to ensure that the stitching accuracy in areas with a large amount of filled data does not decrease. Based on the continuous surface model, parameters such as workpiece dimensions and geometric tolerances can be directly obtained, avoiding the insufficient adaptability of traditional interpolation methods to complex features (such as sharp edges and multi-scale structures), and is applicable to reverse engineering and quality inspection of unknown CAD models. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The following drawings are only for illustrative explanation of the present invention and do not limit the scope of the present invention, where: Figure 1 : Flow chart of the measurement method of the present invention; Figure 2 : Schematic diagram of cross-line intersection determination; In the figure: A and B are point cloud data, A' and B' are mirror points of A and B, and L is the projection plane / line. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] In order to make the purpose, technical solutions, design methods, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings through specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and do not limit the present invention.

[0022] As Figure 1 shown, the present invention provides a coordinate measurement method based on non-complete surface fitting, including the following steps: (1)Obtain the incomplete point cloud of the workpiece to be measured, extract geometric features layer by layer from the incomplete point cloud, and divide the workpiece to be measured into several ordered surfaces based on the geometric features; in this process, the incomplete point cloud of the workpiece to be measured is obtained by a multi-modal sensor, where the multi-modal sensor uses a probe sensor and a laser line scanning sensor to work together. For high-reflection surfaces, it automatically switches to the laser sensor and enables the blue light mode to reduce the reflection interference; for structures such as deep holes and narrow grooves, the probe sensor is used for contact supplementary measurement. The data acquisition process includes: globally laser scanning the workpiece to be measured to obtain the surface point cloud; using the probe sensor for contact measurement in the laser scanning blind area to obtain the supplementary point cloud; through the multi-sensor registration module, unify the two types of data into the same coordinate system based on the iterative closest point algorithm (ICP). The process of filtering the point cloud data is as follows: taking each point as the center, counting the number of points in the neighborhood with a radius of 2 mm, and automatically determining the density threshold of 20 points / mm 3 , and dividing the high-density area and the low-density area. For the high-density area, adaptive Gaussian filtering is used, with the standard deviation of the filtering kernel σ = 0.005 mm, and outliers are removed by iterating 3 times; for the low-density area, adaptive bilateral filtering is used, with the standard deviation in the spatial domain σs = 0.1 mm and the standard deviation in the intensity domain σr = 0.02 mm, and the edge features are retained. After filtering, calculate the curvature of the point cloud, select the points with curvature lower than the preset threshold K1 as seed points, use the random sample consensus algorithm, randomly select sampling points from the seed points to initialize the plane model, and group the point cloud by combining the density clustering algorithm to identify the candidate plane area; analyze the change rate of the normal direction of the non-planar area, fit the cylindrical surface or spherical surface according to the change rate characteristics, and use the least squares method to solve the axis and radius of the cylindrical surface or the center and radius of the spherical surface; extract the remaining point cloud area after the extraction of plane, cylindrical surface, and spherical surface features as the free surface feature, calculate the curvature extreme points of this area to identify the edge and transition area features; based on the curvature similarity condition, use the region growing algorithm to divide the point cloud into several surface patches, and the curvature difference within each surface patch is less than the preset threshold K2; extract the free surface feature, divide the surface patch by the region growing algorithm based on the curvature similarity, and sort the ordered surfaces according to the priority of complete layer plane > ordinary plane > cylindrical surface > spherical surface > free surface, where the complete layer plane is used as the global reference to reduce the cumulative alignment error, and the regular surfaces (plane, cylindrical surface, spherical surface) are preferentially fitted to improve the modeling efficiency using geometric constraints.

[0023] Among them, the random sample consensus (RANSAC) algorithm includes: preferentially selecting the points in the locally flat area with curvature lower than the preset threshold K1 as seed points, and the value range of the preset threshold K1 is 0.005 mm -1 to 0.02 mm -1Randomly select sampling points from the seed point set to initialize the plane model, avoiding blind sampling in the entire point cloud by the traditional RANSAC algorithm; group the point cloud through the density clustering algorithm, limiting the clustering search range within the neighborhood of the seed points to improve the plane recognition efficiency.

[0024] The analysis of the normal direction change rate includes: calculating the change rate of the included angle of the normal directions of adjacent points within the point cloud region; when the change rate is less than the preset threshold , it is determined as a cylindrical feature; when the change rate is greater than the preset threshold , it is determined as a spherical feature; where ranges from 5° to 15°, ranges from 30° to 45°.

[0025] The specific steps of the region growing algorithm include: selecting points with similar curvatures as seed points; expanding the neighborhood points, and judging whether the curvature difference between the neighborhood points and the current surface patch is less than the preset threshold K2, and the value range of the preset threshold K2 is 0.001mm -1 to 0.01mm -1 ; repeat the expansion process until the curvature similarity condition cannot be satisfied to form an independent surface patch.

[0026] The specific rules for feature priority sorting are: Complete layer plane feature: a plane without missing areas and with uniform curvature, which is preferentially used as the global reference; Ordinary plane feature: a region with local missing but can be globally fitted to a plane; Cylindrical feature: a region with obvious cylindrical geometric features; Spherical feature: a region with obvious spherical geometric features; Free-form surface feature: a complex surface region that cannot be accurately represented by a plane, cylinder, or sphere.

[0027] (2)Classify the incomplete point cloud data, add surface labels to each point cloud data, and generate several ordered point cloud sets based on the surface labels; when classifying the point cloud data, use a deep learning model, which is used to classify the geometric features of the point cloud data and add surface labels. Specifically, input the incomplete point cloud data after adaptive filtering into the trained convolutional neural network CNN. Through learning a large number of known geometric feature data (plane, cylinder, sphere, free surface, etc.), this model has the ability to automatically extract the geometric features of the point cloud (such as curvature, normal direction, neighborhood topological structure). The model infers each data point of the input point cloud and outputs the probability value of its belonging to various geometric features; set a classification threshold (such as probability > 0.8), and assign corresponding surface labels (such as plane, cylinder, free surface) to each point cloud data to form a labeled point cloud data set. In this embodiment, the convolutional neural network CNN includes an input layer: receiving the preprocessed point cloud features and converting them into a three-dimensional voxel grid; a feature extraction layer: stacking multiple 3D convolutional layers and pooling layers to extract local geometric features layer by layer; global feature aggregation: compressing the multi-scale features into a global descriptor with a fixed length through adaptive max pooling; an output layer: mapping to the probability distribution of 4 types of surfaces through a fully connected layer and using the Softmax function to output the normalized probability.

[0028] The construction process of the convolutional neural network CNN includes: using a multi-modal sensor to obtain the point cloud data on the workpiece surface, constructing a mixed data set including planes, cylinders, spheres, and free surfaces, artificially introducing missing areas such as occlusion and insufficient sampling to simulate the real measurement scenario; an artificial expert uses a three-dimensional visualization tool to label the surface type labels (plane / cylinder / sphere / free surface) for each point cloud data; obtain several groups of point cloud data - surface type arrays, input the point cloud data - surface type arrays into the input layer of the convolutional neural network CNN for iterative training, output the surface type, and obtain the convolutional neural network CNN that outputs the surface type to which the point cloud belongs based on the point cloud data.

[0029] In this embodiment, in step (2), the cross-line intersection determination is used to determine the point cloud attribution, and an ordered point cloud set is further generated: each ordered surface is projected (a planar surface is projected onto the XY plane of its own coordinate system, a cylindrical surface is projected onto a one-dimensional line along the axis direction, a spherical surface is projected onto the XOY plane passing through the center of the sphere, and a free-form surface is projected onto a plane perpendicular to the eigenvector corresponding to the maximum eigenvalue after determining the main direction through principal component analysis), and a projection plane / line corresponding to the ordered surface is obtained. The point cloud data is mirrored based on the projection plane / line; any two point cloud data A(x1, y1, z1), B(x2, y2, z2), and their mirror points A'(x1', y1', z1', B'(x2', y2', z2') are selected to construct the cross-line AB' and A'B; if the cross-line AB' and A'B have an intersection on the projection plane / line, it is determined that A and B belong to this surface and are classified into the corresponding point cloud set; as Figure 2 shown, the cross-line AB' and A'B have an intersection on the projection plane / line L, indicating that points A and B are on the same side of the plane and belong to the point cloud of this plane. All the labeled point cloud data is traversed, and each point is assigned to the point cloud set corresponding to the ordered surface based on the above discrimination rule; ensure that the cross-lines of any two points and their mirror points have no intersection on the projection plane / line, and finally an ordered point cloud set that does not overlap with each other and corresponds to the ordered surface is generated. In the above, for each ordered surface (sorted by the priority of "complete layer plane > ordinary plane > cylindrical surface > spherical surface > free-form surface"), the projection method is determined according to its geometric type: planar surface type: projected onto its own plane to generate a two-dimensional projection plane; cylindrical / spherical surface type: projected along the axis direction or radially to generate a one-dimensional projection line; based on the projection plane / line, the labeled point cloud data is mirror-transformed to generate a mirror point cloud symmetric to the projection plane / line.

[0030] (3) Generate virtual points based on geometric features to fill in the missing areas; among them, the process of generating the virtual points is as follows: construct a polynomial model of the local thickness and curvature of the workpiece, and infer the geometric features of the missing area based on the neighboring points; determine the position and attributes of the virtual points according to the inference results; calculate the distance weight and geometric feature weight of the neighboring points, and generate virtual points through weighted interpolation; verify the curvature smoothness and topological continuity of the virtual points. In this embodiment, since the thickness of the workpiece to be measured is related to the curvature, a polynomial relationship model t(k) = ak 2 + bk + c is established, where t is the local thickness, k is the curvature, and the model parameters a, b, and c are determined by least squares fitting of the known data points. When performing least squares fitting, the root mean square error (RMSE) is used as the optimization target. The calculation of the spatial distance and geometric feature weights includes: The spatial distance weight uses a Gaussian decay function: , where d is the Euclidean distance from the neighboring point to the missing area, is the distance decay factor; The geometric feature similarity weight adopts the reciprocal function of curvature difference:

[0031] where is the curvature of the neighboring point, is the curvature of the target in the missing area.

[0032] The virtual point is generated by linear weighted interpolation, and the calculation formula is: where is the coordinate of the neighboring point, and are the spatial distance weight and the geometric feature similarity weight respectively.

[0033] Taking the oil drain hole on the spherical surface as an example, the generation of virtual points is further illustrated: Measure the point cloud of the hole edge, and establish a quadratic polynomial model of thickness t and curvature k: t(k)=-0.5k 2 +0.2k+5; The neighboring points in the missing area are P1(0,0,5) (curvature k = 0.1mm -1 , distance d = 1mm), P2(0,1,5) (k = 0.08mm -1 , d = 1.414mm); Spatial distance weight: ω1≈0.134, ω2≈0.017; Geometric feature weight: target curvature =0.1mm -1 =1, =0.833; Virtual point coordinate = .

[0034] In the above, the virtual point needs to be located on the surface (plane, cylindrical surface or spherical surface) fitted by the neighboring point cloud. The surface is fitted by the RANSAC algorithm and the virtual point is projected onto the surface. When verifying the virtual point, calculate the curvature difference between the virtual point and the adjacent point. If the difference exceeds the preset threshold ΔK th (such as 0.01mm-1), then adjust the position of the virtual point until the requirements are met; Use Delaunay triangulation to construct the point cloud topological structure to ensure that the virtual point and the adjacent points form continuous triangles and there are no isolated points. Iteratively optimize the virtual points that do not pass the verification, adjust the weight parameters or reselect the neighboring points until the geometric and topological constraint conditions are met.

[0035] Reconstruct the three-dimensional sub-model of each ordered surface based on the ordered point cloud set, virtual points, and edge point clouds; the edge point clouds are the same point cloud data of different ordered point cloud sets; among them, the generation process of the three-dimensional sub-model is as follows: adopt a surface fitting algorithm based on the variational method to construct an energy function including a data fitting term, a smoothness term, and a boundary constraint term Reconstruct the three-dimensional sub-model by minimizing the energy function, where , , are all weight coefficients, and + = 1, , , are the data fitting term, the smoothness term, and the boundary constraint term respectively; the data fitting term is used to measure the fitting degree of the surface and the ordered point cloud set, the smoothness term is used to constrain the smoothness of the surface, and the boundary constraint term is used to ensure the geometric continuity of the surface boundary and the adjacent surface; calculate the local curvature and sharpness characteristics of the surface, and dynamically adjust the mesh density according to the curvature magnitude: in the area where the curvature is greater than the preset threshold K3, use a dense mesh division, and the mesh cell size is 1 / 2 - 1 / 4 of the reference size. In this embodiment, the preset threshold K3 ≥ 0.02 mm -1 , and the mesh size is 0.25 mm; in the area where the curvature is less than the preset threshold K4, use a sparse mesh division, and the mesh cell size is 1 - 2 times the reference size. In this embodiment, the preset threshold K4 ≤ 0.005 mm -1 , and the mesh size is 1 mm; extract the overlapping area of different ordered point cloud sets as the edge point cloud, filter out the noise points through the curvature threshold, ensure that the density of the boundary point cloud is not less than 80% of the main area, supplement the missing edge with virtual points, and fuse the main surface fitting result with the edge processing data to generate an independent three-dimensional sub-model including surface type, geometric parameters, and boundary feature information.

[0036] (5) Fit the three-dimensional sub-models to generate a continuous surface model, and obtain workpiece measurement parameters based on the continuous surface model. Among them, generating the continuous surface model includes: Selecting the complete layer plane with the highest priority as the reference, fitting the complete layer plane through the least squares algorithm and aligning it to the global coordinate system; Using the Iterative Closest Point (ICP) algorithm to align the point clouds of each sub-model with the reference plane to establish a preliminary positional relationship. Among them, the global coordinate system is a reference coordinate system used to unify all data in three-dimensional measurement and modeling. The process of aligning the global coordinate system through the fitted plane is as follows: Extract the complete layer plane (such as the bottom surface or side surface of the workpiece) from the point cloud, fit its plane equation Ax + By + Cz + D = 0 through the least squares method, where A, B, and C are the coefficients of the plane equation, and D is the constant term, representing the normal direction of the plane (defined by the vector [A, B, C]). Align the normal direction of this plane (determined by the coefficients A, B, and C) with the Z-axis of the global coordinate system, and set the origin of the plane as the origin of the global coordinate system. Use the Iterative Closest Point (ICP) algorithm to register the point clouds of other sub-models with the aligned plane to ensure that the spatial positions of all data are consistent under the global coordinate system. Apply position continuity constraints and normal continuity constraints to the regular surface, and optimize the stitching error through the transformation matrix; For free surfaces: Adopt least squares optimization with a penalty term to enforce the continuity between the edge point cloud and adjacent surface patches, and the penalty factor is dynamically adjusted according to the virtual point ratio; Construct a joint optimization objective function that includes all surface patches to minimize the overall fitting error and boundary discontinuity, and generate a globally continuous complete surface model. In this embodiment, applying position continuity constraints and normal continuity constraints ensures that there is no gap at the stitching position and the normal direction has a smooth transition; Optimizing the stitching error through the transformation matrix is to use transformations such as translation and rotation to adjust the position and direction of the surface to minimize the stitching error. For example, align two planes to the same coordinate system so that their edges completely coincide. Adopting least squares optimization with a penalty term is to add a penalty term to the optimization objective function to enforce the continuity at the stitching position. If there is a discontinuity (such as a position or normal deviation) between the edge point cloud and adjacent surface patches, then suppress such deviations by increasing the penalty value. The process of dynamically adjusting the penalty factor according to the virtual point ratio is as follows: Define the virtual point ratio ρ as the ratio of the number of virtual points generated in the missing area to the total number of point clouds of this surface; The initial value of the penalty factor λ is set to 1 and is dynamically adjusted according to ρ: λ = Ensure that when the virtual point ratio exceeds 25%, the penalty intensity increases at a slower rate to balance the calculation efficiency and fitting accuracy.

[0037] The embodiments of the present invention have been described above. The above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The choice of terms used herein is intended to best explain the principles of the embodiments, the practical application, or the improvement of technologies in the market, or to enable other ordinary technical personnel in the art to understand the embodiments disclosed herein.

Claims

1. A three - coordinate measuring method based on non - complete surface fitting, characterized in that, The following steps are involved: (1) Obtain an incomplete point cloud of the workpiece to be measured, extract geometric features from the incomplete point cloud in layers, and divide the workpiece to be measured into several ordered surfaces based on the geometric features; (2) Classify the incomplete point cloud data, add surface labels to each point cloud data, and generate several ordered point cloud sets based on the surface labels; (3) Generate virtual points based on geometric features to fill in the missing areas; (4) reconstructing a three-dimensional sub-model of each ordered surface based on the ordered point cloud set, the virtual points, and the edge point cloud; the edge point cloud is the same point cloud data of different ordered point cloud sets; (5) Fitting the three-dimensional sub-model to generate a continuous surface model, and obtaining workpiece measurement parameters based on the continuous surface model.

2. The three - coordinate measurement method based on non - complete surface fitting according to claim 1, wherein The step (1) comprises: Acquire incomplete point cloud data of the workpiece to be measured through a multimodal sensor, and filter the incomplete point cloud data; Calculate the curvature of the point cloud, select points with curvature lower than the preset threshold K1 as seed points, use the random sampling consistency algorithm to randomly select sampling points from the seed points to initialize the plane model, combine the density clustering algorithm to group the point cloud, and identify the candidate plane area; Analyze the rate of change of the normal direction of the non-planar area, fit the cylinder or sphere according to the rate of change characteristics, and use the least squares method to solve the cylinder axis and radius or the spherical center and radius; Extract the remaining point cloud area after plane, cylinder and spherical surface feature extraction as free surface feature, calculate the curvature extreme point of the area to identify edge and transition area features; Based on the curvature similarity condition, the region growing algorithm is used to segment the point cloud into several surface patches, and the point curvature difference in each surface patch is less than the preset threshold K2; The free-form surface features are extracted, and the surface patches are segmented by the region growing algorithm based on curvature similarity. The ordered surfaces are obtained by sorting them in the priority order of complete layer plane > ordinary plane > cylinder > sphere > free-form surface.

3. The three - coordinate measurement method based on non - complete surface fitting according to claim 2, wherein The multimodal sensor in step (1) includes a probe sensor and a non-contact sensor, and the non-contact sensor is a laser probe or an optical probe.

4. The three - coordinate measurement method based on non - complete surface fitting according to claim 1, wherein, In step (2), the point cloud data classification adopts a deep learning model, and the deep learning model is used to classify the geometric features of the point cloud data and add surface labels.

5. The three - coordinate measurement method based on non - complete surface fitting according to claim 4, characterized in that, The generation process of the ordered point cloud set in step (2) is as follows: Project each ordered surface to obtain a projection surface / line corresponding to the ordered surface, and perform mirror processing on the point cloud data based on the projection surface / line; Select any two point cloud data A and B. If the intersection line with the mirror point has an intersection on the projection plane / line, it is determined to belong to the surface and is included in the corresponding point cloud set. Traverse all point clouds to ensure that the intersection lines between any two points and their mirror image points have no intersection on the projection plane / line; Repeat until all ordered point cloud sets are generated.

6. The three - coordinate measurement method based on non - complete surface fitting according to claim 1, wherein, The process of generating the virtual point in step (3) is as follows: Construct a polynomial model of the local thickness and curvature of the workpiece, infer the geometric features of the missing area based on the neighboring points; determine the position and attributes of the virtual point based on the inference results; Calculate the distance weights and geometric feature weights of neighboring points, and generate virtual points through weighted interpolation; Verify the curvature smoothness and topological continuity of virtual points.

7. The three - coordinate measurement method based on non - complete surface fitting according to claim 6, characterized in that, The three-dimensional sub-model generation process in step (4) is as follows: Adopt a surface fitting algorithm based on the variational method to construct an energy function including a data fitting term, a smoothness term, and a boundary constraint term, and reconstruct a three-dimensional sub-model by minimizing the energy function; the data fitting term is used to measure the fitting degree between the surface and the ordered point cloud set, the smoothness term is used to constrain the smoothness of the surface, and the boundary constraint term is used to ensure the geometric continuity between the surface boundary and the adjacent surface; Calculate the local curvature and sharpness features of the surface, and dynamically adjust the mesh density according to the curvature magnitude: In the region where the curvature is greater than the preset threshold K3, use a dense mesh division, and the mesh cell size is 1 / 2 - 1 / 4 of the reference size; In the region where the curvature is less than the preset threshold K4, use a sparse mesh division, and the mesh cell size is 1 - 2 times the reference size; Extract the overlapping regions of different ordered point cloud sets as edge point clouds, filter out noise points through the curvature threshold, supplement the missing edges with virtual points, and fuse the main surface fitting results with the edge processing data to generate an independent three-dimensional sub-model containing surface type, geometric parameters, and boundary feature information.

8. The three - coordinate measurement method based on non - complete surface fitting according to claim 7, wherein, In step (5), generating the continuous surface model includes: Select the complete layer plane with the highest priority as the reference, fit the complete layer plane through the algorithm and align it to the global coordinate system; use the iterative closest point algorithm to align the point cloud of each sub-model with the reference plane to establish a preliminary positional relationship; During the splicing process, apply position continuity constraints and normal direction continuity constraints to optimize the splicing error; or adopt least squares optimization with a penalty term to enforce the continuity between the edge point cloud and the adjacent surface patches, and the penalty factor is dynamically adjusted according to the proportion of virtual points; Construct a joint optimization objective function including all surface patches, minimize the overall fitting error and the boundary discontinuity degree, and generate a globally continuous complete surface model.

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