Three-coordinate measurement method based on incomplete surface fitting

Abstract

The present invention belongs to the field of three-coordinate measurement technology, and specifically discloses a three-coordinate measurement method based on incomplete surface fitting, including: extracting geometric features from an incomplete point cloud in layers, dividing the workpiece to be measured into several ordered surfaces; adding surface labels to each point cloud data, and generating several ordered point cloud sets based on the surface labels; generating virtual points based on geometric features to fill in missing areas; reconstructing a three-dimensional sub-model of each ordered surface based on the ordered point cloud set, virtual points, and edge point clouds; fitting the three-dimensional sub-model to generate a continuous surface model, and obtaining workpiece measurement parameters based on the continuous surface model. By extracting geometric features, classifying point clouds, and generating virtual points, the present invention breaks through the limitations of traditional methods that rely on prior models, can handle unknown or non-standard geometry, and achieves global continuous modeling of incomplete point clouds through ordered surface division, three-dimensional sub-model reconstruction, and continuous surface fitting, ensuring the accuracy of measurement parameters.

Description

Technical Field

[0001] The invention belongs to the technical field of three-coordinate measurement, and in particular relates to a three-coordinate measurement method based on incomplete surface fitting. Background Art

[0002] Coordinate measurement systems (CMMs) use contact or non-contact probe sensors to acquire three-dimensional coordinate points on an object's surface for dimensional inspection, reverse engineering, and quality control. However, in actual measurement, probe-based CMMs cannot fully capture the internal structure of a part (such as gear teeth or pipe walls). Laser and optical probe CMMs, on the other hand, can lose data from structured light or laser scanning due to metal or polished surfaces. Therefore, data loss is a common problem in 3D measurement.

[0003] Traditional methods use the geometric relationships of known measurement points (such as neighborhood points and curve continuity) to fill in missing areas through mathematical interpolation, or rely on known CAD models or standard geometric shapes (such as cylinders and planes) to fill in missing data by comparing design models. However, the former has poor adaptability to complex geometries (such as sharp edges and multi-scale features), and the latter relies on precise prior models 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 in the prior art and provide a three-coordinate measurement method based on incomplete surface fitting.

[0005] The present invention provides a three-coordinate measurement method based on non-holonomic surface fitting, comprising the following steps:

[0006] (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;

[0007] (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;

[0008] (3) Generate virtual points based on geometric features to fill the missing areas;

[0009] (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;

[0010] (5) Fitting the three-dimensional sub-model to generate a continuous surface model, and obtaining workpiece measurement parameters based on the continuous surface model.

[0011] A further solution is that step (1) includes:

[0012] Acquiring incomplete point cloud data of the workpiece to be measured through a multimodal sensor, and filtering the incomplete point cloud data;

[0013] Calculate the curvature of the point cloud and 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. Combined with the density clustering algorithm, group the point cloud and identify candidate plane areas.

[0014] The normal direction change rate analysis is performed on non-planar areas, and a cylinder or sphere is fitted based on the change rate characteristics. The least squares method is used to solve the cylinder axis and radius or the spherical center and radius. The normal direction change rate analysis includes: calculating the change rate of the normal direction angle of adjacent points in the point cloud area; when the change rate is less than the preset threshold θ1, it is determined to be a cylindrical feature; when the change rate is greater than the preset threshold θ2, it is determined to be a spherical feature; where the value range of θ1 is 5° to 15°, and the value range of θ2 is 30° to 45°.

[0015] Extract the remaining point cloud area after plane, cylinder, and spherical surface feature extraction as the free surface feature, and calculate the curvature extreme points of the area to identify edge and transition area features;

[0016] Based on the curvature similarity condition, a region growing algorithm is used to segment the point cloud into several surface patches, and the curvature difference of the points in each surface patch is less than a preset threshold K2. The specific steps of the region growing algorithm include:

[0017] Select points with similar curvature as seed points;

[0018] Expand the neighboring points and determine whether the curvature difference between the neighboring points and the current surface patch is less than the preset threshold K2. The value range of the preset threshold K2 is 0.001mm. -1 to 0.01mm -1 ;

[0019] Repeat the expansion process until the curvature similarity condition cannot be met, forming an independent surface patch;

[0020] The free-form surface features are extracted, and the surface patches are segmented using the region growing algorithm based on curvature similarity. The ordered surfaces are obtained by sorting them in the order of complete plane > ordinary plane > cylinder > sphere > free-form surface.

[0021] A further solution is that 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.

[0022] A further solution is that the point cloud data classification in step (2) 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. Specifically, the incomplete point cloud data after adaptive filtering is input into the trained convolutional neural network CNN. The model has the ability to automatically extract the geometric features of the point cloud (such as curvature, normal direction, and neighborhood topology) by learning a large amount of known geometric feature data (plane, cylinder, sphere, free surface, etc.). The model infers each data point of the input point cloud and outputs the probability value of it belonging to each type of geometric feature; 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 dataset.

[0023] A further solution is that the process of generating the ordered point cloud set in step (2) is:

[0024] Project each ordered surface to obtain the projection surface / line corresponding to the ordered surface, and perform mirror processing on the point cloud data based on the projection surface / line;

[0025] Choose any two point cloud data points A(x1,y1,z1) and B(x2,y2,z2). If the intersection lines of these two points with the mirror points A′(x1′,y1′,z1′) and B′(x2′,y2′,z2′) intersect on the projection plane / line, then they are considered to belong to the surface and are included in the corresponding point cloud set.

[0026] Traverse all point clouds and ensure that the intersection lines between any two points and their mirror images have no intersection on the projection plane / line;

[0027] Repeat until all ordered point cloud sets are generated.

[0028] A further solution is that the process of generating the virtual point in step (3) is:

[0029] Construct a polynomial model of the workpiece's local thickness and curvature, infer the geometric features of the missing area based on neighboring points, and determine the position and attributes of the virtual point based on the inference results.

[0030] Calculate the distance weights and geometric feature weights of neighboring points and generate virtual points through weighted interpolation. Specifically, the calculation of spatial distance and geometric feature weights includes:

[0031] The spatial distance weight adopts Gaussian decay function: , where d is the Euclidean distance from the neighboring point to the missing area, is the distance attenuation factor;

[0032] The geometric feature similarity weight adopts the inverse function of curvature difference:

[0033]

[0034] in is the curvature of the neighboring point, is the target curvature of the missing area.

[0035] Virtual points are generated by linear weighted interpolation, and the calculation formula is:

[0036] in are the coordinates of the neighboring points, and are spatial distance weight and geometric feature similarity weight respectively.

[0037] Verify the curvature smoothness of the virtual point (the curvature difference with the adjacent points is less than the preset threshold) and the topological continuity (forming a continuous surface with the adjacent points).

[0038] A further solution is that the three-dimensional sub-model generation process in step (4) is:

[0039] A surface fitting algorithm based on the calculus of variations is used to construct an energy function that includes a data fitting term, a smoothness term, and a boundary constraint term. The 3D submodel is reconstructed by minimizing the energy function. The data fitting term is used to measure the degree of fit between the surface and the ordered point cloud set, the smoothness term is used to constrain the surface smoothness, and the boundary constraint term is used to ensure the geometric continuity between the surface boundary and adjacent surfaces.

[0040] Calculate the local curvature and sharpness characteristics of the surface, and dynamically adjust the mesh density based on the curvature:

[0041] In areas where the curvature is greater than the preset threshold K3, a dense grid is used, and the grid unit size is 1 / 2-1 / 4 of the reference size;

[0042] In areas where the curvature is less than the preset threshold K4, sparse grid division is adopted, and the grid unit size is 1-2 times the reference size;

[0043] The overlapping areas of different ordered point cloud sets are extracted as edge point clouds. Noise points are filtered through the curvature threshold, and virtual points are used to supplement the missing edges to ensure that the density of the boundary point cloud is not less than 80% of the main area. The main surface fitting results are fused with the edge processing data to generate an independent 3D sub-model containing surface type, geometric parameters and boundary feature information.

[0044] A further solution is that, in step (5), generating the continuous surface model includes:

[0045] 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;

[0046] For regular surfaces: position continuity constraints and normal continuity constraints are imposed, and the stitching error is optimized through the transformation matrix; for free-form surfaces: least squares optimization with a penalty term is used 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;

[0047] A joint optimization objective function including all surface patches is constructed to minimize the overall fitting error and boundary discontinuity, and generate a globally continuous complete surface model.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] The present invention extracts geometric features in layers, classifies point clouds, and generates virtual points to fill missing areas. It does not rely on known CAD models or standard geometric shapes, breaking through the limitations of traditional methods that rely on prior models. It can handle unknown or non-standard geometries. Through ordered surface division, three-dimensional sub-model reconstruction and continuous surface fitting, it achieves 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 particularly suitable for internal structures that cannot be reached by probes or blind spots in non-contact scanning.

[0050] This method uses convolutional neural networks to automatically extract local features from point clouds, achieving high-precision classification of geometric types such as planes, cylinders, and freeform surfaces, avoiding the inefficiencies and errors associated with traditional manual intervention. Through mirroring of projected surfaces and lines and determining intersection points, point cloud data is accurately assigned to corresponding sets based on surface labels, avoiding cross-surface data confusion and providing a clean dataset for subsequent regional modeling.

[0051] This method uses the complete layer plane as a reference and aligns the submodels using the Iterative Closest Point (ICP) algorithm. Combining position / normal continuity constraints (G0 / G1) for regular surfaces with penalized least-squares optimization for free-form surfaces, it minimizes stitching errors and boundary discontinuities, generating a globally continuous complete surface model. The penalty factor is dynamically adjusted based on the proportion of virtual points, ensuring that stitching accuracy is maintained in areas containing large amounts of infill data. Based on this continuous surface model, parameters such as workpiece dimensions and geometric tolerances can be directly obtained, avoiding the limited adaptability of traditional interpolation methods to complex features (such as sharp edges and multi-scale structures). This makes it suitable for reverse engineering and quality inspection of unknown CAD models. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The following drawings are merely provided for illustrative purposes only and are not intended to limit the scope of the present invention.

[0053] Figure 1 : Flow chart of the measuring method of the present invention;

[0054] Figure 2 : Schematic diagram of determining the intersection of cross lines;

[0055] In the figure: A and B are point cloud data, A′ and B′ are the mirror points of A and B, and L is the projection surface / line. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solution, design method and advantages of the present invention more clear, the present invention is further described in detail below through specific embodiments in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0057] like Figure 1 As shown, the present invention provides a three-coordinate measurement method based on non-holonomic surface fitting, comprising the following steps:

[0058] (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; in this process, the incomplete point cloud of the workpiece to be measured is obtained by a multimodal sensor, wherein the multimodal sensor uses a probe sensor and a laser line scanning sensor to work together. For highly reflective surfaces, it automatically switches to the laser sensor and enables the blue light mode to reduce reflective interference; for structures such as deep holes and narrow grooves, a probe sensor is used for contact supplementary measurement. The data acquisition process includes: performing a global laser scan on the workpiece to be measured to obtain a surface point cloud; using a probe sensor to perform contact measurement on the laser scanning blind area to obtain a supplementary point cloud; through the multi-sensor registration module, the two types of data are unified into the same coordinate system based on the iterative closest point algorithm (ICP). The process of filtering the point cloud data is: with each point as the center, count the number of points within a 2mm radius neighborhood, and automatically determine the density threshold of 20 points / mm through the Otsu algorithm. 3, dividing the high-density area and the low-density area. For the high-density area, adaptive Gaussian filtering is used, the filter kernel standard deviation σ=0.005mm, and it is iterated 3 times to remove outliers; for the low-density area, adaptive bilateral filtering is used, the spatial domain standard deviation σs=0.1mm, the intensity domain standard deviation σr=0.02mm, and the edge features are retained. After the filtering is completed, the curvature of the point cloud is calculated, and the points with curvature lower than the preset threshold K1 are screened as seed points. The random sampling consistency algorithm is used to randomly select sampling points from the seed points to initialize the plane model. The point cloud is grouped in combination with the density clustering algorithm to identify candidate plane areas; the normal direction change rate of the non-planar area is analyzed, and the cylinder or sphere is fitted according to the change rate characteristics. The least squares method is used to solve the cylinder axis, radius or the spherical center, radius; the remaining point cloud area after the plane, cylinder, and spherical features are extracted as the free surface feature, and the curvature of the area is calculated. The method uses the region growing algorithm to segment the point cloud into several surface patches based on the curvature similarity condition, and the curvature difference of the points 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 the curvature similarity. The ordered surfaces are obtained by sorting them in the order of complete layer plane > ordinary plane > cylinder > sphere > free-form surface. The complete layer plane is used as the global reference to reduce the cumulative alignment error. Regular surfaces (plane, cylinder, sphere) are fitted first to improve the modeling efficiency by utilizing geometric constraints.

[0059] The RANSAC algorithm includes: preferentially selecting local flat area points with curvature lower than a preset threshold K1 as seed points, and the value range of the preset threshold K1 is 0.005mm. -1 to 0.02mm -1 ; Randomly select sampling points from the seed point set to initialize the plane model to avoid blind sampling of the traditional RANSAC algorithm in the entire point cloud; group the point cloud through the density clustering algorithm, limit the clustering search range to the neighborhood of the seed point, and improve the efficiency of plane recognition.

[0060] Normal direction change rate analysis includes: calculating the change rate of the normal direction angle of adjacent points in the point cloud area; when the change rate is less than the preset threshold When the change rate is greater than the preset threshold, it is determined to be a cylindrical feature; when the change rate is greater than the preset threshold When , it is determined to be a spherical feature; among them, The value range is 5° to 15°. The value range is 30° to 45°.

[0061] The specific steps of the region growing algorithm include: selecting points with similar curvature as seed points; expanding neighboring points, and judging whether the curvature difference between the neighboring points and the current surface patch is less than a preset threshold K2, and the value range of the preset threshold K2 is 0.001mm. -1to 0.01mm -1 ; Repeat the expansion process until the curvature similarity condition cannot be met, forming an independent surface patch.

[0062] The specific rules for feature priority sorting are:

[0063] Complete layer plane features: planes with no missing areas and uniform curvature are preferred as global datums;

[0064] Ordinary plane features: areas with local missing parts but can be fitted into a plane as a whole;

[0065] Cylindrical features: areas with obvious cylindrical geometric features;

[0066] Spherical features: areas with obvious spherical geometric features;

[0067] Free-form surface features: complex surface areas that cannot be accurately represented by planes, cylinders, or spheres.

[0068] (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, a deep learning model is used to classify the geometric features of the point cloud data and add surface labels. Specifically, the incomplete point cloud data after adaptive filtering is input into a trained convolutional neural network (CNN). The model has the ability to automatically extract the geometric features of the point cloud (such as curvature, normal direction, and neighborhood topology) by learning a large amount of known geometric feature data (planes, cylinders, spheres, free-form surfaces, etc.). The model infers each data point of the input point cloud and outputs the probability value of its belonging to each type of geometric feature; set the classification threshold (such as probability > 0.8), assign the corresponding surface label (such as plane, cylinder, free-form surface) to each point cloud data, and form a labeled point cloud dataset. In this embodiment, the convolutional neural network CNN includes an input layer: receiving 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 multi-scale features into a global descriptor of fixed length through adaptive maximum pooling; and an output layer: mapping to the probability distribution of four types of surfaces through a fully connected layer, and outputting normalized probabilities using the Softmax function.

[0069] The construction process of the convolutional neural network (CNN) includes: using multimodal sensors to obtain point cloud data on the workpiece surface, constructing a mixed data set containing planes, cylinders, spheres, and free-form surfaces, artificially introducing missing areas such as occlusion and insufficient sampling to simulate real measurement scenarios; human experts use three-dimensional visualization tools to label each point cloud data with a surface type label (plane / cylinder / spherical / free-form surface); obtaining several sets of point cloud data-surface type arrays, inputting the point cloud data-surface type arrays into the input layer of the convolutional neural network (CNN) for iterative training, outputting the surface type, and obtaining a convolutional neural network (CNN) that outputs the surface type of the point cloud based on the point cloud data.

[0070] In this embodiment, step (2) uses intersection determination to identify the belonging of the point cloud, and further generates an ordered point cloud set: each ordered surface is projected (the plane surface is projected to the XY plane of its own coordinate system, the cylinder is projected to a one-dimensional straight line along the axis direction, the sphere is projected to the XOY plane passing through the center of the sphere, and the free surface is projected to a plane perpendicular to the eigenvector corresponding to the maximum eigenvalue after the main direction is determined by principal component analysis), and the projection surface / line corresponding to the ordered surface is obtained, and the point cloud data is mirrored based on the projection surface / line; any two point cloud data A(x1, y1, z1) and B(x2, y2, z2), and their mirror points A′(x1′, y1′, z1′) and B′(x2′, y2′, z2′) are selected to construct intersection lines AB′ and A′B; if the intersection lines AB′ and A′B have an intersection on the projection surface / line, it is determined that A and B belong to the surface and are included in the corresponding point cloud set; Figure 2 As shown, the intersection lines AB′ and A′B intersect on the projection plane / line L, indicating that points A and B are on the same side of the plane and belong to the plane point cloud. All labeled point cloud data is traversed and assigned point by point to the corresponding ordered surface point cloud set based on the above-mentioned discrimination rules. This ensures that the intersection lines between any two points and their mirror image points do not intersect on the projection plane / line, ultimately generating a non-overlapping ordered point cloud set corresponding to the ordered surface. For each ordered surface (ordered by priority: complete plane > ordinary plane > cylinder > sphere > freeform surface), the projection method is determined based on its geometric type: for plane-type surfaces, projection onto its own plane generates a two-dimensional projection surface; for cylinder / sphere-type surfaces, projection along the axis or radial direction generates a one-dimensional projection line. Based on the projection plane / line, the labeled point cloud data is mirrored to generate a mirrored point cloud symmetrical to the projection plane / line.

[0071] (3) Generate virtual points based on geometric features to fill the missing area; wherein the process of generating the virtual points 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 points based on 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 between thickness and curvature is established. 2 +bk+c, where t is the local thickness and k is the curvature. The model parameters a, b, and c are determined by fitting the known data points using the least squares method. When fitting using the least squares method, the root mean square error (RMSE) is used as the optimization target. The calculation of spatial distance and geometric feature weights includes:

[0072] The spatial distance weight adopts Gaussian decay function: , where d is the Euclidean distance from the neighboring point to the missing area, is the distance attenuation factor;

[0073] The geometric feature similarity weight adopts the inverse function of curvature difference:

[0074]

[0075] in is the curvature of the neighboring point, is the target curvature of the missing area.

[0076] Virtual points are generated by linear weighted interpolation, and the calculation formula is:

[0077] in are the coordinates of the neighboring points, and are spatial distance weight and geometric feature similarity weight respectively.

[0078] Taking the spherical oil drain hole as an example, we can further explain the virtual point generation: 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;

[0079] Missing area neighboring point P1(0,0,5) (curvature k=0.1mm -1 , distance d = 1mm), P2(0,1,5) (k = 0.08mm -1 , d=1.414mm);

[0080] Spatial distance weight: ω1≈0.134, ω2≈0.017;

[0081] Geometric feature weights: target curvature =0.1mm -1 =1, =0.833;

[0082] Virtual point coordinates = .

[0083] In the above, the virtual point needs to be located on the surface (plane, cylinder or sphere) fitted by the adjacent point cloud. The surface is fitted by the RANSAC algorithm and the virtual point is projected onto the surface. When verifying the virtual point, the curvature difference between the virtual point and the adjacent points is calculated. If the difference exceeds the preset threshold ΔK th If the virtual point position is smaller than 0.01 mm-1, the position of the virtual point is adjusted until the requirement is met. Delaunay triangulation is used to construct the point cloud topology structure, ensuring that the virtual point and adjacent points form continuous triangles and no isolated points exist. For virtual points that fail verification, iterative optimization is performed, adjusting weight parameters or reselecting adjacent points until the geometric and topological constraints are met.

[0084] (4) Reconstructing a 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; wherein, the three-dimensional sub-model generation process is: using a surface fitting algorithm based on the variational method, constructing an energy function including data fitting terms, smoothness terms, and boundary constraint terms The 3D sub-model is reconstructed by minimizing the energy function, where 、 、 are weight coefficients, and + =1, 、 、 They are data fitting item, smoothness item, and boundary constraint item; the data fitting item is used to measure the degree of fit between the surface and the ordered point cloud set, the smoothness item is used to constrain the smoothness of the surface, and the boundary constraint item is used to ensure the geometric continuity between the surface boundary and the adjacent surfaces; the local curvature and sharpness characteristics of the surface are calculated, and the grid density is dynamically adjusted according to the curvature size: in the area where the curvature is greater than the preset threshold K3, a dense grid is used, and the grid unit size is 1 / 2-1 / 4 of the reference size. In this embodiment, the preset threshold K3 is ≥ 0.02mm -1 , the grid size is 0.25mm; in the area where the curvature is less than the preset threshold K4, sparse grid division is adopted, and the grid unit size is 1-2 times the reference size. In this embodiment, the preset threshold K4 ≤ 0.005mm -1, the grid size is 1mm; the overlapping areas of different ordered point cloud sets are extracted as edge point clouds, and the noise points are filtered through the curvature threshold to ensure that the density of the boundary point cloud is not less than 80% of the main area. The missing edges are supplemented with virtual points, and the main surface fitting results are fused with the edge processing data to generate an independent 3D sub-model containing surface type, geometric parameters and boundary feature information.

[0085] (5) Fitting the three-dimensional sub-model to generate a continuous surface model, and obtaining the workpiece measurement parameters based on the continuous surface model, wherein generating the continuous surface model includes: selecting the complete layer plane with the highest priority as the reference, fitting the complete layer plane by the least squares algorithm and aligning it to the global coordinate system; using the iterative closest point algorithm to align the point cloud of each sub-model with the reference plane to establish a preliminary positional relationship; wherein, the global coordinate system is a reference reference system used to unify all data in three-dimensional measurement and modeling, and the process of aligning the global coordinate system by fitting the plane is: extracting the complete layer plane (such as the bottom or side of the workpiece) from the point cloud, fitting its plane equation Ax+By+Cz+D=0 by the least squares method, A, B, C are the coefficients of the plane equation, D is a constant term, representing the normal direction of the plane (defined by the vector [A, B, C]), aligning the normal direction of the plane (determined by the coefficients A, B, C) with the Z axis of the global coordinate system, and setting the plane origin as the origin of the global coordinate system. Using the Iterative Closest Point (ICP) algorithm, the point clouds of the other submodels are registered with the aligned plane to ensure that all data are spatially consistent in the global coordinate system. Position continuity constraints and normal continuity constraints are imposed on regular surfaces, and the stitching error is optimized using a transformation matrix. For free-form surfaces, a least-squares optimization with a penalty term is used to enforce continuity between the edge point cloud and adjacent surface patches. The penalty factor is dynamically adjusted based on the proportion of virtual points. A joint optimization objective function encompassing all surface patches is constructed to minimize the overall fitting error and boundary discontinuity, generating a globally continuous complete surface model. In this embodiment, position continuity constraints and normal continuity constraints are imposed to ensure that the joints are gap-free and that the normal direction transitions smoothly. Optimizing the stitching error using a transformation matrix involves adjusting the surface position and orientation using transformations such as translation and rotation to minimize the stitching error. For example, aligning two planes to the same coordinate system so that their edges completely overlap. Least-squares optimization with a penalty term involves adding a penalty term to the optimization objective function to enforce continuity at the joints. If there are discontinuities between the edge point cloud and the adjacent surface patches (such as position or normal deviations), such deviations are suppressed by increasing the penalty value. The penalty factor is dynamically adjusted according to the proportion of virtual points. If there are more virtual points generated in the missing area, the penalty factor is increased to more strictly constrain the continuity; otherwise, the penalty factor is reduced to balance the fitting accuracy and computational efficiency. In the above, the process of dynamically adjusting the penalty factor according to the proportion of virtual points is as follows:

[0086] The virtual point ratio ρ is defined as the ratio of the number of virtual points generated in the missing area to the total number of point clouds on the surface; the penalty factor λ is initially set to 1 and is dynamically adjusted according to ρ: λ = Ensure that when the proportion of virtual points exceeds 25%, the penalty intensity increases slowly, balancing computational efficiency and fitting accuracy.

[0087] While various embodiments of the present invention have been described above, the above descriptions are intended to be illustrative, non-exhaustive, and not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, their practical applications, or technological improvements in the marketplace, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A three-coordinate measurement method based on incomplete 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 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; The generation process of the ordered point cloud set in step (2) is as follows: Project each ordered surface to obtain the projection surface / line corresponding to the ordered surface, and perform mirror processing on the point cloud data based on the projection surface / line; Choose any two point cloud data A and B. If the intersection line with the mirror point intersects 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 and ensure that the intersection lines between any two points and their mirror images have no intersection on the projection plane / line; Repeat until all ordered point cloud sets are generated.

2. The three-coordinate measurement method based on non-holonomic surface fitting according to claim 1, characterized in that: The step (1) comprises: Acquiring incomplete point cloud data of the workpiece to be measured through a multimodal sensor, and filtering the incomplete point cloud data; Calculate the curvature of the point cloud and 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. Combined with the density clustering algorithm, group the point cloud and identify candidate plane areas. 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 the free surface feature, and calculate the curvature extreme points 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 curvature difference of the points in each surface patch is less than the preset threshold K2; The free-form surface features are extracted, and the surface patches are segmented using the region growing algorithm based on curvature similarity. The ordered surfaces are obtained by sorting them in the order of complete plane > ordinary plane > cylinder > sphere > free-form surface.

3. The three-coordinate measurement method based on non-holonomic surface fitting according to claim 2, characterized in that: 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-holonomic surface fitting according to claim 1, characterized in that: In step (2), the point cloud data classification adopts a deep learning model, which 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-holonomic surface fitting according to claim 1, characterized in that: The process of generating the virtual point in step (3) is as follows: Construct a polynomial model of the workpiece's local thickness and curvature, infer the geometric features of the missing area based on neighboring points, and 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 curvature smoothness and topological continuity of virtual points.

6. The three-coordinate measurement method based on non-holonomic surface fitting according to claim 5, characterized in that: The three-dimensional sub-model generation process in step (4) is as follows: A surface fitting algorithm based on the calculus of variations is used to construct an energy function that includes a data fitting term, a smoothness term, and a boundary constraint term. The 3D submodel is reconstructed by minimizing the energy function. The data fitting term is used to measure the degree of fit between the surface and the ordered point cloud set, the smoothness term is used to constrain the surface smoothness, and the boundary constraint term is used to ensure the geometric continuity between the surface boundary and adjacent surfaces. Calculate the local curvature and sharpness characteristics of the surface, and dynamically adjust the mesh density based on the curvature: In areas where the curvature is greater than the preset threshold K3, a dense grid is used, and the grid unit size is 1 / 2-1 / 4 of the reference size; In areas where the curvature is less than the preset threshold K4, sparse grid division is adopted, and the grid unit size is 1-2 times the reference size; The overlapping areas of different ordered point cloud sets are extracted as edge point clouds. Noise points are filtered through the curvature threshold, and missing edges are supplemented with virtual points. The main surface fitting results are fused with the edge processing data to generate an independent 3D sub-model containing surface type, geometric parameters and boundary feature information.

7. The three-coordinate measurement method based on non-holonomic surface fitting according to claim 6, characterized in 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 with the reference plane to establish a preliminary positional relationship; During the stitching process, position continuity constraints and normal direction continuity constraints are imposed to optimize the stitching error; or least squares optimization with a penalty term is used to enforce the continuity of the edge point cloud and the adjacent surface patches. The penalty factor is dynamically adjusted according to the proportion of virtual points. A joint optimization objective function including all surface patches is constructed to minimize the overall fitting error and boundary discontinuity, and generate a globally continuous complete surface model.

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