Method for reconstructing first-order continuous centerline of complex catheter based on scanned point cloud data
By using a method based on scanned point cloud data, the straight and circular segments of complex catheters are segmented and fitted to construct a first-order continuous centerline, which solves the problems of complex catheter shape description and measurement equipment calibration, and achieves accurate catheter reconstruction and equipment evaluation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING CHANGCHENG INST OF METROLOGY & MEASUREMENT AVIATION IND CORP OF CHINA
- Filing Date
- 2025-12-21
- Publication Date
- 2026-06-05
Smart Images
Figure CN122156599A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for reconstructing the first-order continuous centerline of a complex duct based on scanned point cloud data, belonging to the field of digital detection of engine geometric parameters. Background Technology
[0002] The piping system of an aircraft engine connects engine components and accessories via conduits. Due to limited installation space, hundreds of conduits are typically distributed in a crisscrossing and overlapping manner on the surface of the engine casing. However, to prevent accidents caused by friction in the piping under high-temperature and vibration conditions, the minimum distance between conduits and between conduits and the casing must be sufficiently large. Therefore, the machining errors of the conduits must meet tolerance requirements; otherwise, after installation, the conduits will have a small spacing or large assembly stress at the clamp connections.
[0003] After the actual pipeline is manufactured, it needs to be inspected using specialized pipeline measuring equipment to measure geometric parameters such as the pipe's length L, in-plane angle R, and inter-plane angle A. When L, R, and A all meet the requirements, the pipeline is considered qualified. Similarly, currently, high-precision coordinate measuring machines (CMMs) are mainly used to calibrate standard pipelines, providing values such as the pipe's outer diameter, LRA, and intersection / tangency coordinates. Based on these calibration values, standard pipelines can be used to evaluate the measurement capabilities of specialized pipeline measuring equipment. However, both the pipeline measurement results and the calibration results of standard pipelines use multiple geometric values to characterize the entire pipeline, neglecting the description of contour changes in curved and straight sections, such as the radius of curvature in curved sections and the straightness of straight sections. Summary of the Invention
[0004] Addressing the issue that multiple dimensional parameters cannot accurately describe the spatial shape variations of complex conduits, and aiming to accurately evaluate the processing precision of physical conduits and comprehensively assess the measurement capabilities of pipeline-specific measuring equipment, this invention provides a method for reconstructing the first-order continuous centerline of complex conduits based on scanned point cloud data. Using high-precision scanned point cloud data of the outer surface of complex conduits, the method solves for the center points of different vertical cross-sections of the conduit and performs first-order continuous curve fitting on these points to obtain the reconstructed centerline of a standard conduit. This reconstructed centerline is then used as a reference for calibrating the measurement capabilities of pipeline-specific measuring equipment.
[0005] The objective of this invention is achieved through the following technical solution:
[0006] The present invention discloses a method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data, comprising the following steps:
[0007] Step 1: After obtaining the scanning point cloud data of the outer surface of the conduit, the straight pipe data and curved pipe data of the complex conduit are segmented to achieve the segmentation of straight pipe segment data and circular pipe segment data based on unit sphere projection point clustering.
[0008] Step 2: For the data of the segmented straight pipe and curved pipe sections, perform centerline data fitting to obtain multiple discontinuous centerline segments of the complex conduit.
[0009] Step 3: For discontinuous adjacent straight line segments and circular arc segments, solve for the center points of different pipeline segments based on equally spaced vertical cross-sections, and perform first-order continuous curve fitting on the circular points to obtain multiple discontinuous center line segments of complex ducts.
[0010] Step 4: Using the centerline reconstructed in Step 3 as a reference, calibrate the measurement capabilities of the pipeline-specific measuring equipment.
[0011] Furthermore, the specific implementation method of "segmentation of straight pipe and circular pipe data based on unit sphere projection point clustering" is as follows: the point cloud data of the pipe surface is projected onto the surface of a unit sphere along its main direction, and clustering is performed according to the distribution density of the projection points and the Euclidean distance. After the projection points are back-projected back into the point cloud data, the surface point cloud data of the straight pipe and the circular pipe are obtained respectively. At the same time, noise points that cannot be clustered are deleted.
[0012] Furthermore, the specific implementation method of "solving the center point of different pipeline segments based on equally spaced vertical cross-sections" is as follows: fitting the trend line of the cylindrical pipeline segment through a random sampling strategy, obtaining the trend line of the annular pipeline segment by intersecting the principal plane with the normal vector point, then constructing equally spaced vertical cross-sections of the pipeline segment along the trend line, and projecting the point cloud data of the outer surface of the conduit onto the vertical cross-sections for circle fitting, with the center of the fitted circle as the center point of the vertical cross-section.
[0013] Furthermore, the specific implementation method of step three is as follows: after fitting the center point of the straight section of the pipeline and the center point of the circular section of the pipeline with straight lines and arcs, a step of clamping cubic spline curve fitting is introduced between adjacent straight line segments and circular arc segments to constrain the endpoints of the cubic spline to be tangent to both the straight line segment and the circular arc segment at the same time, and finally obtain the first-order continuous centerline of the complex conduit.
[0014] Beneficial effects:
[0015] 1. The present invention discloses a method for reconstructing the first-order continuous centerline of complex conduits based on scanned point cloud data. After obtaining the scanned point cloud data of the outer surface of the conduit, the straight pipe data and curved pipe data of the complex conduit are segmented to achieve the segmentation of straight pipe segments and circular pipe segments based on unit sphere projection point clustering. The continuous centerline of the conduit reconstructed based on the scanned point cloud data of the outer surface of the conduit can be used, on the one hand, to reconstruct the centerline of the standard conduit used for calibration of pipeline-specific measuring equipment. This reconstructed centerline serves as a standard value to evaluate the centerline contour measurement capability of the pipeline-specific measuring equipment. On the other hand, it can be used for reverse modeling of conduit parts in the virtual assembly of complex engine piping systems and the delivery of digital products, as well as for the digital detection of the minimum spacing of engine conduit assembly.
[0016] 2. This invention discloses a method for reconstructing the first-order continuous centerline of complex conduits based on scanned point cloud data. Using high-precision scanned point cloud data of the outer surface of complex conduits, the method solves for the center points of circles at different vertical cross-sections of the conduit and performs first-order continuous curve fitting on these circles to obtain the reconstructed centerline of a standard conduit. This reconstructed centerline is used as a reference for calibrating the measurement capabilities of pipeline-specific measuring equipment. This invention can be applied in multiple scenarios, including the processing and inspection of complex conduits, assembly guidance, and assembly gap detection. Attached Figure Description
[0017] Figure 1 This is a flowchart of pipeline segmentation based on the main direction projection clustering of point cloud data on the duct surface;
[0018] Figure 2 This is a method for determining the center point of straight and circular pipe sections;
[0019] Figure 3 It is a method for constructing trend lines in straight pipelines based on a random sampling consistency strategy;
[0020] Figure 4 It is the construction of the center trend line of the circular pipe section;
[0021] Figure 5 It is the result of reconstructing the first-order continuous centerline of a complex duct based on multilinear piecewise fitting. Detailed Implementation
[0022] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.
[0023] Example 1:
[0024] The method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data disclosed in this embodiment is implemented in the following steps:
[0025] Step 1: Perform unit sphere vector projection on the point cloud data of the conduit surface, and perform density clustering and Euclidean distance clustering on the projected points to obtain point cloud data of straight sections and circular sections of complex conduits. Segment the straight and curved pipe data of complex conduits, that is, realize the segmentation of straight and circular sections of pipe data based on unit sphere projection point clustering.
[0026] Step 2: For the point cloud data of straight pipeline sections, a trend line is constructed using the random sampling consistency method. For the point cloud data of circular pipeline sections, the trend line is solved by finding the intersection of the normal vector point and the principal plane. Equally spaced vertical cross-sections are constructed along the trend line of the pipeline section. After projecting the point cloud data of the pipeline section surface onto the nearest vertical cross-section, the cross-section data is fitted with a least-squares circle, and the center of the fitted circle is taken as the center point of the vertical cross-section of the pipeline.
[0027] Step 3: Perform least-squares straight line and circular arc fitting on the center points of the straight and circular pipe sections respectively. Fit a clamped cubic spline curve between all adjacent straight and circular segments, ensuring the clamped cubic spline curve is tangent to both the straight and circular segments. Connect the spline curves to obtain the first-order continuous centerline of the complex conduit.
[0028] Step 4: Using the centerline reconstructed in Step 3 as a reference, calibrate the measurement capability of the pipeline-specific measuring equipment.
[0029] Example 2:
[0030] The method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data disclosed in this embodiment is implemented in the following steps:
[0031] Step 1: For the complete point cloud data of the outer surface of the conduit, the data of the straight section of the conduit and the data of the circular section of the conduit are first divided into N sets of straight section data and N-1 sets of circular section data using the main direction unit sphere projection clustering strategy.
[0032] Step 2: For the 2N-1 sets of data, construct and analyze the vertical cross-sectional data of each pipeline segment, and solve for the center point of the vertical cross-sectional data of different pipeline segments.
[0033] Step 3: Fit the center points of different pipeline sections with straight lines or circles, and use spline curve fitting to connect adjacent straight line segments and arc segments in a first-order continuous manner to obtain the first-order continuous centerline of the complex conduit.
[0034] Step 4: Using the centerline reconstructed in Step 3 as a reference, calibrate the measurement capability of the pipeline-specific measuring equipment.
[0035] Example 3:
[0036] The method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data disclosed in this embodiment is implemented in the following steps:
[0037] Step 1: Starting from the contour features of the outer surface of the conduit, a data segmentation method based on unit sphere projection clustering of the main direction of the outer surface data points is adopted to achieve data segmentation of different pipeline segments by unit sphere projection clustering in the main direction.
[0038] Step 1.1: Move the starting point of the principal direction vector of all points on the outer surface of the conduit to the center of the unit sphere. Simultaneously, the principal direction vector intersects the surface of the unit sphere to obtain the intersection point. (See Appendix) Figure 1 (b) Map the point cloud data of the outer surface of the duct to the surface of a unit sphere. In this case, the closer the principal direction vector is to the data point on the outer surface of the duct, the closer the projection point on the surface of the unit sphere will be.
[0039] Considering the discrete distribution of actual point cloud data and the influence of errors in calculating the principal direction vector, the projection points of the actual cylindrical pipe section surface data are distributed within a small area of the unit sphere surface, while the projection points of the actual annular pipe section surface data appear as an arc with a certain width on the unit sphere surface (see Appendix). Figure 1 (c).
[0040] Step 1.2: Based on the distribution characteristics of the projection points on the surface of the unit sphere, the density-based spatial clustering method DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is used to perform clustering and noise determination based on the number of data points within a fixed neighborhood radius of a single data point.
[0041] Clustering results and neighborhood radius The choice of is related to the value of the minimum neighborhood threshold MinPts. The specific clustering calculation process is as follows:
[0042] 1) Point cloud data of the outer surface of the conduit The middle point is represented as Calculate the location of it according to equation (1) - The number of data points in the neighborhood.
[0043] (1)
[0044] In formula (1) Representing data points of - Neighborhood data set Let be the Euclidean norm, expressed in equation (2). For data points One - Neighborhood data points;
[0045] (2)
[0046] In formula (2) ( ) T Represents vector [ The transpose of ].
[0047] 2) If any point -If the number of points in the neighborhood is not less than the threshold MinPts, then a new cluster is started with that point as the core point, and all density-reachable points in its neighborhood are added to the cluster.
[0048] 3) If the neighborhood of any point is insufficient to form a cluster, then mark it as a noise point;
[0049] 4) Repeat the above process until all points have been processed.
[0050] The DBSCAN method was used to identify the projection points of different cylindrical pipe segments on the surface of a unit sphere. Projection points from the same cluster were then mapped onto point cloud data to obtain surface point cloud data for different cylindrical pipe segments, as shown in the attached figure. Figure 1 (c) The data points corresponding to the three colors of red, yellow, and blue are attached. Figure 1 (d) Data for three cylindrical pipe segments. When there are parallel straight pipes in a complex conduit, the data sets mapped back to the point cloud data are further clustered using Euclidean distance to separate the data for different straight pipe segments.
[0051] Step 1.3: Segmentation of circular pipe data based on Euclidean distance clustering. This involves directly calculating the Euclidean distance between point cloud data on the pipe surface and determining whether data points belong to the same cluster based on the distance. For each point within the same cluster, its neighboring points are searched. If the distance between neighboring points is less than a threshold and they are not clustered, they are merged into the current cluster. Clustering is complete when all points have undergone clustering calculation or no further cluster expansion is possible. The results of segmenting the circular pipe data using this method are shown in the appendix. Figure 1 (e).
[0052] Step 2: For the segmented point cloud data of straight pipe sections and circular pipe sections, a method for constructing vertical cross-sections based on pipe section trend lines and a method for fitting and calculating the center point of the cross-section are proposed. This method first analyzes and constructs the spatial distribution trend line of the pipe section. Then, it establishes equally spaced vertical cross-sections along this trend line and projects the pipe point cloud data onto the nearest vertical cross-section. Next, it performs circle fitting on the projected points on the vertical cross-section, with the center of the fitted circle serving as the center point of the pipe's vertical cross-section. The calculation process of this method is shown in the appendix. Figure 2 The following section details the calculation methods for the center points of straight and circular pipelines.
[0053] Step 2.1: The point cloud data of the pipe's outer surface acquired by the industrial scanner contains noise, interfering with the analysis of the pipe trend line. The Random Sample Consensus (RANSAC) strategy is used to first search for valid data on the straight pipe's outer surface in the point cloud data. This valid data is then fitted with a least-squares cylinder, and the fitted cylinder axis is used as the trend line of the straight pipe section. The calculation process for solving the straight pipe trend line using the RANSAC strategy is shown in the appendix. Figure 3 .
[0054] After obtaining the trend line of the cylindrical pipe section using the RANSAC strategy, the trend line is discretized into a set of equally spaced discrete points. At each discrete point, a vertical cross-section is constructed: the plane passes through the discrete data point and its normal is parallel to the trend line direction.
[0055] Projecting all surface point cloud data of the same straight pipe section onto the nearest vertical cross-section results in a set of discrete data points distributed in a circle on each vertical cross-section. A least-squares circle fit is then performed on the discrete data points on each vertical cross-section, and the center of the fitted circle is taken as the center point of that cross-section. The center points on all vertical cross-sections constitute the center point set of the straight pipe section.
[0056] Step 2.2: The plane passing through the centerline of the circular pipeline is called the main plane of the pipeline segment. Based on the geometric characteristics of the circular pipeline: for pipeline surface data outside the main plane, the intersection of its normal and the main plane is located on the centerline of the circular pipeline. A trend line construction method is proposed to solve for the intersection of the vector points on the outer surface of the pipeline and the main plane. This method can obtain the spatial distribution trend line of the circular pipeline segment. Then, multiple vertical cross-sections are constructed at equal intervals along the constructed spatial distribution trend line, and the center point on each vertical cross-section is solved using the same method as for the straight pipeline segment.
[0057] The method for determining the center point of a circular pipe is as follows:
[0058] 1) Solving the principal plane of the circular pipeline
[0059] The principal plane is solved primarily using principal component analysis. First, a covariance matrix is constructed using all point cloud data from the circular pipeline. Then, singular value decomposition (SVD) is used to solve for the eigenvalues and eigenvectors of the covariance matrix. The eigenvector corresponding to the smallest eigenvalue is used as the normal to the principal plane, and the mean of the coordinates of all data points is used as the points that the principal plane must pass through to constrain its position.
[0060] 2) Trendline construction method based on the intersection of pipeline surface vector points and the principal plane
[0061] Due to factors such as environmental noise, scanning equipment accuracy, and errors in point cloud data normal calculation, the data points with normal information on the pipeline surface, i.e., vector points, intersect with the principal plane within a range near the center line of the annulus, as shown in the attached figure. Figure 4 As shown in (a).
[0062] The distribution of all intersection points exhibits an approximate circular arc shape. A small number of noise points are due to the failure to remove noise during data segmentation. This noise can be removed by setting appropriate DBSCAN clustering parameters during the data segmentation stage. After setting appropriate DBSCAN clustering parameters, the distribution area of all intersection points near the center line of the circular guide tube becomes more concentrated, as shown in the appendix. Figure 4 (b) Perform least-squares circle fitting on all intersection points to obtain the distribution trend line of the circular pipeline.
[0063] 3) Analyze the center point of the vertical cross-sectional data of the distribution trend line of the circular pipeline.
[0064] The distribution trend line of the circular pipeline is discretized at equal angular intervals to obtain a set of uniformly distributed discrete data points. A vertical cross-section is constructed at each data point, and the normal of the vertical cross-section is parallel to the tangent of the trend line at that location. The surface point cloud data of the circular pipeline is projected onto the nearest vertical cross-section. On each vertical cross-section, the projection points are fitted with a least-squares circle, and the center of the fitted circle is used as the center point of each vertical cross-section.
[0065] Step 3: When calibrating the pipeline-specific measuring equipment, the equipment only needs to measure a set of discretely distributed center points. When evaluating the deviation of the measured center points, a continuous centerline is required as a reference value. Therefore, from the perspective of evaluating pipeline measurement results, a piecewise fitting method for constructing a first-order continuous centerline is adopted. Considering that the straight line segment and the arc segment intersect on the first-order continuous centerline, and the tangent direction at the intersection point is parallel to the straight line segment and tangent to the arc segment, this continuity can be achieved by fitting spline curves to the data points at the intersection. Therefore, this embodiment adopts a piecewise fitting strategy of fitting a small number of data points at the intersection of the straight line segment centerline and the arc segment centerline with cubic spline curves. By applying constraints to the fitting process that ensure the continuity of the data points and tangent vectors, a cubic spline curve that can smoothly connect adjacent straight line segments and arc segments is obtained, reconstructing the first-order continuous centerline of the complex conduit.
[0066] The specific calculation process for solving the first-order continuous centerline using piecewise fitting is as follows:
[0067] Step 3.1: Center fitting of straight pipe sections
[0068] Least squares plane fitting is performed on the discrete center points of each cylindrical pipe segment, and a local coordinate system is constructed based on this plane: the normal of this plane is taken as the Z-axis direction, and a point in the plane is taken as the origin; then the center point of the cylindrical pipe segment is projected onto this plane, and the center point of the cylindrical pipe segment is a two-dimensional data point in the local coordinate system. Least squares line fitting is performed on this two-dimensional data point, and according to the transformation relationship between the local coordinate system and the global coordinate system, the fitted line is transformed to the global coordinate system to obtain the center line of the cylindrical pipe segment in the global coordinate system.
[0069] Step 3.2: Fitting the center of the circular arc segment of the annular pipe
[0070] The same processing method as for the cylindrical pipe section is adopted: a local coordinate system is created for circle fitting, and the two endpoints of the arc centerline are determined based on the projection of the discrete center point of the circular pipe section onto the fitted circle. Similarly, the centerline solution is transformed to the global coordinate system to obtain the centerline of the circular pipe section in the global coordinate system.
[0071] Step 3.3: Cubic spline curve fitting at the intersection of adjacent straight line segments and circular arc segments
[0072] To achieve first-order continuous intersection of adjacent straight line segments and circular arc segments, a method of clamping cubic spline continuous fitting is proposed. This method adds constraints on the endpoint derivative values during spline curve fitting to ensure that the fitted spline curve is tangent to both adjacent straight line segments and circular arc segments.
[0073] Given a set of three-dimensional points and its parameter sequence and with and Using the starting and ending derivatives as the starting and ending points, the goal is to construct a continuous three-dimensional curve of C1. ,in An independent structure is a one-dimensional clamped cubic spline, which must simultaneously satisfy the following conditions:
[0074] 1) Interpolation condition: The curve strictly passes through all data points, i.e. ;
[0075] 2) Continuity constraint: At internal nodes, the first and second derivatives are continuous;
[0076] 3) Boundary conditions: , , , , , ;
[0077] In any interval of the parameter sequence Above, where i = 0, 1, ..., n-1, cubic spline segments Through the second derivative of the node Represented as:
[0078] (3)
[0079] In formula (3) = .
[0080] make To solve Construct the following system of linear equations (4):
[0081] (4)
[0082] Rearrange the above system of equations as follows Matrix form, where , Given a sparse diagonal matrix, solve for... Then, by substituting the spline expression, we obtain the following results: The piecewise functions are ultimately combined to form a three-dimensional curve that satisfies the constraints. At all adjacent straight and circular arc segments, the aforementioned cubic spline curve fitting algorithm was used to achieve first-order derivative continuity, obtaining the first-order continuous centerline of the complex duct. The fitting results are shown in the appendix. Figure 5 .
[0083] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data, characterized in that: Includes the following steps: Step 1: After obtaining the scanning point cloud data of the outer surface of the conduit, the straight pipe data and curved pipe data of the complex conduit are segmented to achieve the segmentation of straight pipe segment data and circular pipe segment data based on unit sphere projection point clustering. Step 2: For the data of the segmented straight pipe and curved pipe sections, perform centerline data fitting to obtain multiple discontinuous centerline segments of the complex conduit. Step 3: For discontinuous adjacent straight line segments and circular arc segments, solve for the center points of different pipeline segments based on equally spaced vertical cross-sections, and perform first-order continuous curve fitting on the circular points to obtain multiple discontinuous center line segments of complex ducts.
2. The method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data as described in claim 1, characterized in that: It also includes step four: using the centerline reconstructed in step three as a reference for calibrating the measurement capabilities of pipeline-specific measuring equipment.
3. The method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data as described in claim 1 or 2, characterized in that: The specific implementation method of "segmentation of straight and circular pipeline data based on unit sphere projection point clustering" is as follows: the point cloud data of the pipeline surface is projected onto the surface of a unit sphere along its main direction, and clustering is performed according to the distribution density of the projection points and the Euclidean distance. After the projection points are back-projected back to the point cloud data, the surface point cloud data of the straight pipeline and the circular pipeline are obtained respectively. At the same time, noise points that cannot be clustered are deleted.
4. The method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data as described in claim 1 or 2, characterized in that: The specific implementation method for "solving the center point of different pipeline segments based on equally spaced vertical cross-sections" is as follows: a trend line of cylindrical pipeline segments is fitted by a random sampling strategy, and the trend line of circular pipeline segments is obtained by intersecting the principal plane with the normal vector point. Then, equally spaced vertical cross-sections of pipeline segments are constructed along the trend line, and the point cloud data of the outer surface of the conduit is projected onto the vertical cross-sections for circle fitting. The center of the fitted circle is taken as the center point of the vertical cross-section.
5. The method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data as described in claim 1 or 2, characterized in that: The specific implementation method of step three is as follows: After fitting the center point of the straight section pipe and the center point of the circular section pipe with straight lines and arcs, a step of clamping cubic spline curve fitting is introduced between adjacent straight line segments and circular arc segments to constrain the endpoints of the cubic spline to be tangent to both the straight line segment and the circular arc segment at the same time, and finally obtain the first-order continuous centerline of the complex conduit.
6. The method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data as described in claim 1, characterized in that: The specific implementation steps are as follows: Step 1: Starting from the contour features of the outer surface of the conduit, a data segmentation method based on unit sphere projection clustering of the main direction of the outer surface data points is adopted to achieve data segmentation of different pipeline segments by unit sphere projection clustering in the main direction; Step 1.1: Move the starting point of the principal direction vector of all points on the outer surface of the conduit to the center of the unit sphere. At the same time, the principal direction vector intersects the surface of the unit sphere to obtain the intersection point. Map the point cloud data of the outer surface of the duct to the surface of a unit sphere; the closer the principal direction vectors are to the data points on the outer surface of the duct, the closer their projection points are to the surface of the unit sphere. Step 1.2: Based on the distribution characteristics of the projection points on the surface of the unit sphere, the density-based spatial clustering method DBSCAN is used to perform clustering and noise determination based on the number of data points within a fixed neighborhood radius of a single data point; Clustering results and neighborhood radius The choice of is related to the value of the minimum neighborhood threshold MinPts. The specific clustering calculation process is as follows: 1) Point cloud data of the outer surface of the conduit The middle point is represented as Calculate the location of it according to equation (1) - The number of data points in the neighborhood; （1） In formula (1) Representing data points of - Neighborhood data set Let be the Euclidean norm, expressed in equation (2). For data points One - Neighborhood data points; （2） In formula (2) ( ) T Represents vector [ ] transpose 2) If any point -If the number of points in the neighborhood is not less than the threshold MinPts, then a new cluster is started with that point as the core point, and all density-reachable points in its neighborhood are added to the cluster. 3) If the neighborhood of any point is insufficient to form a cluster, then mark it as a noise point; 4) Repeat the above process until all points have been processed, thus achieving data point clustering; The DBSCAN method is used to identify the projection points of different cylindrical pipe segments on the surface of a unit sphere. The projection points of the same cluster are mapped to the point cloud data to obtain the surface point cloud data of different cylindrical pipe segments. When there are parallel straight pipes in complex ducts, the data groups mapped back to the point cloud data are further clustered by Euclidean distance to separate the data of different straight pipe segments. Step 1.3: Directly calculate the Euclidean distance between the point cloud data on the duct surface, and determine whether the data points belong to the same cluster based on the distance; for each point in the same cluster, continue to find its neighboring points. If the distance between neighboring points is less than the threshold and they have not been clustered, they are merged into the current cluster. When all points have been clustered or the cluster cannot be expanded further, the clustering is complete; segment the circular pipe data according to this method. Step 2: For the segmented point cloud data of straight pipe sections and circular pipe sections, analyze and construct the spatial distribution trend line of the pipe sections. Establish equally spaced vertical cross-sections along the trend line and project the pipe point cloud data onto the nearest vertical cross-section. Perform circle fitting on the projected points on the vertical cross-section, and use the center of the fitted circle as the center point of the vertical cross-section of the pipe. Step 2.1: The point cloud data of the outer surface of the pipeline collected by the industrial scanner contains noise, which interferes with the analysis of the pipeline trend line; the Random Sampling Consensus (RANSAC) strategy is adopted to first search for valid data of the outer surface of the straight section of the pipeline in the point cloud data, and perform least squares cylindrical fitting on the valid data, and use the fitted cylinder axis as the trend line of the straight section of the pipeline. After obtaining the trend line of the cylindrical pipe section using the RANSAC strategy, the trend line is discretized into a set of equally spaced discrete points. At each discrete point, a vertical cross-section is constructed: the plane passes through the discrete data point and its normal is parallel to the trend line direction. Projecting all surface point cloud data of the same straight pipe section onto the nearest vertical cross-section, a set of discrete data points distributed in a circle is obtained on each vertical cross-section. Least square circle fitting is performed on the discrete data points on each vertical cross-section, and the center of the fitted circle is taken as the center point of the cross-section. The center points on all vertical cross-sections constitute the center point set of the straight pipe section. Step 2.2: The plane passing through the centerline of the circular pipeline is called the main plane of the pipeline segment; according to the geometric characteristics of the circular pipeline: for pipeline surface data outside the main plane, the intersection of its normal and the main plane is located on the centerline of the circular pipeline; construct a trend line construction method to solve the intersection of the vector points on the outer surface of the pipeline and the main plane, obtain the spatial distribution trend line of the circular pipeline segment, and then construct multiple vertical cross-sections at equal intervals along the constructed spatial distribution trend line, and use the same method as for the straight pipeline segment to solve for the center point on each vertical cross-section; The method for determining the center point of a circular pipe is as follows: 1) The principal plane is solved mainly by principal component analysis. First, the covariance matrix is constructed using all point cloud data of the circular pipe. Then, the eigenvalues and eigenvectors of the covariance matrix are solved by singular value decomposition. The eigenvector corresponding to the smallest eigenvalue is used as the normal of the principal plane, and the mean of the coordinates of all data points is used as the point that the principal plane must pass through to constrain the position of the principal plane. 2) Data points with normal information on the pipe surface, i.e. vector points, intersect with the principal plane within an interval of the neighborhood of the ring centerline; after setting the DBSCAN clustering parameters, the distribution area of all intersection points near the centerline of the ring conduit becomes more concentrated; least squares circle fitting is performed on all intersection points to obtain the distribution trend line of the ring conduit; 3) Discretize the distribution trend line of the circular pipeline at equal angular intervals to obtain a set of uniformly distributed discrete data points. Construct a vertical cross-section at each data point, with the normal of the vertical cross-section parallel to the tangent of the trend line at that location. Project the surface point cloud data of the circular pipeline onto the nearest vertical cross-section. On each vertical cross-section, perform least-squares circle fitting on the projected points, and use the center of the fitted circle as the center point on each vertical cross-section. Step 3: When calibrating the pipeline-specific measuring equipment, the equipment only needs to measure a set of discretely distributed center points. When evaluating the deviation of the measured center points, a continuous center line needs to be used as a reference value. Considering that the straight line segment and the arc segment on the first-order continuous center line intersect, and the tangent direction at the intersection point is parallel to the straight line segment and tangent to the arc segment, this continuity is achieved by fitting spline curves to the data points at the intersection. A piecewise fitting strategy is adopted, which involves fitting a small number of data points at the intersection of the center lines of the straight line segment and the arc segment to cubic spline curves. By applying the constraint of continuity through the data points and tangent vectors to the fitting process, a cubic spline curve that smoothly connects adjacent straight line segments and arc segments is obtained, and the first-order continuous center line of the complex conduit is reconstructed.
7. The method for reconstructing the first-order continuous centerline of complex ducts based on scanned point cloud data as described in claim 6, characterized in that: The specific implementation method for step 3 is as follows: Step 3.1: Perform least-squares plane fitting on the discrete center points of each cylindrical pipe segment, and construct a local coordinate system based on this plane: take the normal of this plane as the Z-axis direction, and take a point in the plane as the origin; project the center point of the cylindrical pipe segment onto this plane, then in the local coordinate system, the center point of the cylindrical pipe segment is a two-dimensional data point. Perform least-squares line fitting on this two-dimensional data point, and according to the transformation relationship between the local coordinate system and the global coordinate system, transform the fitted line to the global coordinate system to obtain the center line of the cylindrical pipe segment in the global coordinate system; the specific calculation method is as follows: Step 3.2: Create a local coordinate system for circle fitting. Determine the two endpoints of the arc centerline based on the projection of the discrete center point of the circular pipe segment onto the fitted circle. Transform the centerline solution to the global coordinate system to obtain the centerline of the circular pipe segment in the global coordinate system. Step 3.3: To achieve first-order continuous intersection of adjacent straight line segments and circular arc segments, a clamping cubic spline continuous fitting method is adopted. During the spline curve fitting process, the constraint of the endpoint derivative value is added to ensure that the fitted spline curve is tangent to the adjacent straight line segment and circular arc segment at the same time. Given a set of three-dimensional points and its parameter sequence and with and Using the starting and ending derivatives, the goal is to construct a continuous three-dimensional curve of C1. ,in An independent structure is a one-dimensional clamped cubic spline, which must simultaneously satisfy the following conditions: 1) Interpolation condition: The curve strictly passes through all data points, i.e. ; 2) Continuity constraint: At internal nodes, the first and second derivatives are continuous; 3) Boundary conditions: , , , , , ; In any interval of the parameter sequence Where i = 0, 1, ..., n-1, cubic spline segments Second derivative of the node Represented as: （3） In formula (3) = make To solve Construct the following system of linear equations (4): （4） Rearrange the above system of equations as follows Matrix form, where , Given a sparse diagonal matrix, solve for... Then, by substituting the spline expression, we obtain the following results: The piecewise functions are combined to form a three-dimensional curve that satisfies the constraints. At all adjacent straight line segments and arc segments, the above-mentioned cubic spline curve fitting algorithm is used to continuously connect the first derivatives to obtain the first continuous centerline of the complex duct.