A local geometry-based ITZ thickness correction calculation method and system

Abstract

The application provides a local geometry-based ITZ thickness correction calculation method and system, which is aimed at input point cloud data, first constructs a KD-tree, and establishes a neighborhood point set for each point in a k-neighbor or radius neighborhood manner; adopts local PCA or equivalent surface triangular mesh to calculate the unit normal vector of each point; performs quadratic surface fitting on the neighborhood points in a local tangent plane coordinate system to obtain principal curvatures and calculate the curvature and the curvature radius; and on this basis, performs ITZ thickness geometric correction based on local geometry. The application explicitly uses local curvature information for ITZ thickness correction, can effectively reduce the system error caused by two-dimensional / projection measurement, simultaneously provides interactive software implementation, realizes the visualization and result export of point cloud normal, curvature and ITZ corrected thickness, and has high calculation efficiency and strong robustness.

Description

Technical Field

[0001] This invention relates to the technical field of three-dimensional point cloud processing and quantitative characterization of material microstructure, specifically to an ITZ thickness correction calculation method and system based on local geometry. Background Technology

[0002] In current microscopic methods, measuring the ITZ thickness around aggregates is often based on the concentric expansion method, which delineates several continuous strips along the capture boundary at different distances from the aggregate surface to the cement paste. These strips of continuous, uniform thickness are distributed along the aggregate surface and used to measure the proportions of porosity, anhydrous cement, and hydration products in each strip, indicating how these fractions vary with distance from the aggregate surface. The results for each strip are averaged, and the cross-sectional images for analysis are typically selected along the aggregate surface.

[0003] However, this method of determining ITZ thickness using cross-sections is essentially based on two-dimensional sections, rarely along the normal direction of the aggregate surface, and the initial section position is difficult to determine. The thickness is often calculated from a series of grayscale / porosity-distance curves measured on the planar section, leading to an overestimation of the measured distance compared to the true vertical distance in 3D. The apparent boundary on the two-dimensional section is limited by the way the three-dimensional interface is cut, and the measured distance field may deviate due to local curvature, bending, and section orientation. In actual concrete, the shape of the aggregate is irregular, so the cross-sectional plane during observation is not necessarily perpendicular to the aggregate surface, resulting in a difference between the obtained apparent interface transition zone thickness and the actual interface transition zone thickness. As long as the cross-sectional plane is not perpendicular to the interface between the aggregate and the paste, the apparent interface transition zone thickness obtained by the cross-sectional observation method will be larger than the actual thickness. The magnitude of the deviation depends on the sphericity / shape of the particles and whether the sampling simulates the actual normal direction measurement or uses a systematic linear rule. Therefore, it is necessary to correct the directly measured ITZ thickness t0 of the slice method to obtain the true ITZ thickness t along the normal direction.

[0004] Existing point cloud processing methods typically focus on the calculation and visualization of geometric quantities such as surface normals and curvature, but lack a dedicated step for further applying these "local geometric quantities" to ITZ thickness correction, especially lacking a thickness correction formula that simultaneously considers the normal tilt angle and the radius of curvature, and an interactive implementation. Therefore, there is an urgent need for a calculation scheme that can uniformly obtain the normal and curvature at the point cloud level and further complete the ITZ thickness correction. Summary of the Invention

[0005] This invention is made to solve the above-mentioned problems, and aims to provide an ITZ thickness correction calculation method and system based on local geometry.

[0006] This invention provides an ITZ thickness correction calculation method based on local geometry, characterized by the following steps: S1: Data acquisition and preprocessing step, acquiring point cloud data containing three-dimensional coordinates and constructing a KD-tree to support spatial neighborhood retrieval; S2: Neighborhood construction step, for each point in the point cloud, constructing a neighborhood point set for each point based on the KD-tree; S3: Unit normal vector calculation step, for each point, calculating the unit normal vector based on its neighborhood point set; S4: Curvature calculation step, based on the unit normal vector, performing quadratic surface fitting on the neighborhood point set of each point in the local tangent plane coordinate system to obtain the principal curvature, and calculating the radius of curvature based on the principal curvature; S5: ITZ thickness correction step, for any query point and its initial thickness, acquiring the unit normal vector and radius of curvature of its nearest point in the point cloud, and calculating the corrected thickness based on the tilt angle of the nearest point's unit normal vector relative to the preset observation plane and the radius of curvature; S6: Result output and visualization step, outputting the geometric information and corrected thickness of each point and visualizing it.

[0007] The ITZ thickness correction calculation method based on local geometry provided by this invention may also have the following feature: wherein, in S2, each point p i Methods for constructing the neighborhood set of a point include: k-nearest neighbor method: retrieving the nearest neighbor to the current point p in the KD-tree. i The k nearest points in Euclidean distance are taken as the neighborhood point set S. i Radius neighborhood method: Search for points p in the KD-tree that are adjacent to the current point p. i All points whose Euclidean distance is no more than r are considered as the neighborhood point set S. i r is the neighborhood radius set by the user.

[0008] The ITZ thickness correction calculation method based on local geometry provided by this invention may also have the following features: In S3, the calculation method of the unit normal vector includes: local PCA method: constructing a covariance matrix based on the neighborhood point set and performing eigenvalue decomposition, taking the eigenvector corresponding to the smallest eigenvalue as the unit normal vector, and unifying the orientation of the unit normal vector.

[0009] The ITZ thickness correction calculation method based on local geometry provided by this invention may also have the following features: In S3, the calculation method of the unit normal vector further includes: the isosurface triangular mesh method: the point cloud is rasterized and the three-dimensional distance field is calculated. A triangular mesh is obtained through the isosurface extraction algorithm. The vertex normal vector is calculated from the triangular patch normal vector and mapped back to each point in the original point cloud as the unit normal vector of that point.

[0010] The ITZ thickness correction calculation method based on local geometry provided by this invention may also have the following feature: wherein, in S4, the method for obtaining the principal curvature is as follows:

[0011] S4-1: For each point p i With its unit normal vector As normal, construct a local orthogonal basis, and choose the direction with... Non-parallel auxiliary vectors , thus obtaining the tangential basis vector , :

[0012]

[0013]

[0014] Where ε is a very small positive number to prevent division by zero.

[0015] S4-2: Perform coordinate transformation of neighboring points. ,make Then its local coordinates are:

[0016]

[0017] in, for neighborhood point set S i The first in Neighboring points, For distance,

[0018] S4-3: In the local tangent plane coordinate system, the following quadratic surface model is used for fitting:

[0019]

[0020] Where x and y are the two orthogonal coordinate components of the neighborhood point in the local tangent plane; z is the height offset of the neighborhood point along the local normal direction; a and c are the surface along the local tangent plane. x direction and y Second-order bending strength in the direction; b is xy Coupling term coefficients; d and e are coefficients of the first-order term.

[0021] Write it in linear least squares form:

[0022]

[0023] Where A is the design matrix, Coeff is the parameter vector to be determined, and represents the five fitting coefficients of the local quadratic surface. ,

[0024] The least squares solution is expressed as:

[0025]

[0026] This means that among all possible quadratic surface parameters, we find a set of a, b, c, d, e that minimizes the sum of squared deviations of the normal heights between the fitted surface and the neighboring points, thereby obtaining the surface in the neighborhood of that point that best represents the true local morphology.

[0027] S4-4: Construct the second derivative matrix Hessian as follows:

[0028]

[0029] Where H is the Hessian matrix of the local surface, representing the second-order curvature property of the surface in the neighborhood of that point; a is the second-order curvature component in the x-direction; c is the second-order curvature component in the y-direction; and b is the mixed second-order curvature component, reflecting the coupled curvature in the two directions.

[0030] The eigenvalues ​​of H, namely the principal curvatures k1 and k2, are calculated using the trace and determinant:

[0031]

[0032] .

[0033] Where tr is the trace of matrix H, which is equal to the sum of two eigenvalues; det is the determinant of matrix H, which is equal to the product of two eigenvalues; k1 and k2 are the two principal curvatures at that point, representing the maximum and minimum curvature of the surface in the two principal directions, respectively; sqrt is the square root.

[0034] The ITZ thickness correction calculation method based on local geometry provided by this invention may also have the following feature: wherein, in S4, at least one of the following curvature scalars, curv, is calculated based on the principal curvature according to the user's selection:

[0035] Gaussian curvature: K = k1·k2;

[0036] Mean curvature: ;

[0037] Maximum curvature: ;

[0038] Second-order curvature: ,

[0039] Define the radius of curvature as: R = 1 / (k + ε), where k is the chosen curvature scalar, and ε is a very small positive number to prevent division by zero.

[0040] When the number of neighborhood points m is insufficient or the normal vector is invalid, set curv=0 and R=∞ to avoid anomalies.

[0041] The ITZ thickness correction calculation method based on local geometry provided by this invention may also have the following feature: wherein, in S5, the method for calculating the corrected thickness is as follows:

[0042] S5-1: Calculate point coordinates Given an initial thickness t0, use a KD-tree to retrieve the nearest point cloud point for q: Its index is denoted as i*, and it obtains the unit normal vector at the nearest point. With radius of curvature r,

[0043] S5-2: Define α as the angle between the unit normal vector n and the XY plane, then:

[0044]

[0045] in, Let α represent the projection of n onto the XY plane. Since n is a unit vector, cosα takes values ​​in the range [0,1].

[0046] S5-3: When the radius of curvature is infinite or numerically non-finite, the corrected thickness is obtained by projecting the initial thickness t0 onto the normal tilt angle. ,

[0047] S5-4: When the interface has curvature, the local interface is considered as an arc of radius r within the normal section. The center of curvature of this arc is taken as the origin, and the distance from the interface point p* to the origin is r. After moving t0 along the normal projection direction in the observation plane to reach the outer boundary point, the angle between this moving direction and the unit normal vector n at the interface point p* is α. Then the distance from the outer boundary point to the center of curvature is... for:

[0048]

[0049] The actual corrected thickness t along the normal direction is equal to the radius increment: ,Right now:

[0050] .

[0051] The ITZ thickness correction calculation method based on local geometry provided by the present invention may also have the following features: S5 further includes: S5-5: validity check, if the unit normal vector length of the nearest point is less than the preset threshold, or the radius of curvature of the nearest point is invalid, then the correction is stopped or the preset default value is output.

[0052] The ITZ thickness correction calculation method based on local geometry provided by this invention may also have the following features: In S6, the geometric information includes: three-dimensional coordinates, normal vector components, curvature scalar and curvature radius, and the visualization includes: normal vector map, curvature cloud map and curvature radius cloud map and the corrected thickness display of the query point.

[0053] This invention also provides an ITZ thickness correction calculation system based on local geometry, characterized by the following features: a data acquisition and preprocessing module, which acquires point cloud data containing three-dimensional coordinates and constructs a KD-tree to support spatial neighborhood retrieval; a neighborhood construction module, which constructs a neighborhood point set for each point in the point cloud based on the KD-tree; a unit normal vector calculation module, which calculates a unit normal vector for each point based on its neighborhood point set; a curvature calculation module, which performs quadratic surface fitting on the neighborhood point set of each point in the local tangent plane coordinate system based on the unit normal vector to obtain the principal curvature, and calculates the radius of curvature based on the principal curvature; an ITZ thickness correction module, which, for any query point and its initial thickness, acquires the unit normal vector and radius of curvature of its nearest point in the point cloud, and calculates the corrected thickness based on the tilt angle of the unit normal vector of the nearest point relative to the preset observation plane and the radius of curvature; and a result output and visualization module, which outputs the geometric information and corrected thickness of each point and displays it visually.

[0054] Compared with the prior art, the present invention has the following advantages:

[0055] This invention, after obtaining the unit normal vector and radius of curvature of the interface point cloud, establishes a thickness correction formula to achieve the conversion from the initial 2D / projective thickness t0 to the 3D geometrically consistent corrected thickness t, thereby improving the accuracy and repeatability of ITZ thickness assessment. Specifically:

[0056] (1) This invention provides a local PCA method for calculating unit normal vectors. The PCA method has high computational efficiency, supports distance weighting, assigns greater weight to nearest neighbors, suppresses the influence of distant neighbor noise on normal vectors, and improves robustness.

[0057] (2) The present invention also provides a method for calculating unit normal vectors using the isosurface triangular mesh method. The distance transformation in the isosurface triangular mesh method uses an efficient three-dimensional distance transformation algorithm (such as bwdist) to quickly calculate the distance field, which can improve the path efficiency of the isosurface mesh and meet the needs of practical engineering applications.

[0058] (3) This invention proposes and implements a geometric correction step for ITZ thickness, which explicitly introduces the local normal tilt angle and radius of curvature into the thickness calculation, reducing the deviation of two-dimensional / projection measurement.

[0059] (4) The modified formula of the present invention is applicable to both near planar interfaces (r→∞) and curved interfaces (finite r), and provides a numerically stable calculation form that can convert the initial slice thickness t0 into the true thickness t along the interface normal, so that the measurement results are consistent with the three-dimensional geometry.

[0060] (5) The present invention provides an interactive software implementation that supports free switching of normal vector calculation methods, flexible configuration of neighborhood parameters, and one-click correction of thickness calculation and result visualization of query points, which facilitates parameter debugging and result analysis in engineering applications and improves the ease of use and adaptability of the method. Attached Figure Description

[0061] Figure 1 This is a flowchart of the ITZ thickness correction calculation method based on local geometry in an embodiment of the present invention.

[0062] Figure 2 This is a flowchart illustrating the calculation of the unit normal vector using the local PCA method in an embodiment of the present invention.

[0063] Figure 3 This is a flowchart illustrating the calculation of the unit normal vector using the isosurface triangular mesh method in an embodiment of the present invention.

[0064] Figure 4 This is a flowchart of the curvature calculation steps in an embodiment of the present invention.

[0065] Figure 5 This is a schematic diagram of the geometric relationship of ITZ thickness correction in an embodiment of the present invention.

[0066] Figure 6 These are example diagrams of the spherical aggregate normal vector diagram, curvature cloud diagram, and curvature radius cloud diagram (based on triangular mesh) in embodiments of the present invention.

[0067] Figure 7 These are example diagrams of the spherical aggregate normal vector diagram, curvature cloud diagram, and curvature radius cloud diagram in embodiments of the present invention (based on local PCA).

[0068] Figure 8 These are example diagrams of the actual aggregate normal vector diagram, curvature cloud diagram, and curvature radius cloud diagram (based on triangular mesh) in embodiments of the present invention.

[0069] Figure 9 These are example diagrams of the actual aggregate normal vector diagram, curvature cloud diagram, and curvature radius cloud diagram in embodiments of the present invention (based on local PCA).

[0070] Figure 10 This is a diagram showing the ITZ correction calculation results for spherical aggregate in an embodiment of the present invention (based on a triangular mesh).

[0071] Figure 11This is a diagram showing the ITZ correction calculation results for spherical aggregates in an embodiment of the present invention (based on local PCA).

[0072] Figure 12 This is a diagram showing the actual aggregate ITZ correction calculation results (based on triangular mesh) in an embodiment of the present invention.

[0073] Figure 13 This is a diagram showing the actual aggregate ITZ correction calculation results (based on local PCA) in an embodiment of the present invention. Detailed Implementation

[0074] To make the technical means, creative features, objectives and effects of the present invention easy to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate the ITZ thickness correction calculation method and system based on local geometry of the present invention.

[0075] This embodiment provides an ITZ thickness correction calculation method based on local geometry, including the following steps:

[0076] Figure 1 This is a flowchart of the ITZ thickness correction calculation method based on local geometry in an embodiment of the present invention.

[0077] like Figure 1 As shown, step S1 is the data acquisition and preprocessing step, which involves acquiring point cloud data containing 3D coordinates and constructing a KD-tree to support spatial neighborhood retrieval. Specifically:

[0078] A point cloud dataset is obtained using the coordinate information input by the user. The point cloud is denoted as... The center represents the centroid of the point cloud. .

[0079] For each point p i Its neighborhood point set is denoted as The number of neighboring points is The unit normal vector is denoted as... ,and The curvature scalar is denoted as The radius of curvature is denoted as .

[0080] Step S2 is the neighborhood construction step. For each point in the point cloud, based on the KD-tree, a neighborhood set is constructed using either the k-nearest neighbor method or the radius neighborhood method. The neighborhood set is used for subsequent normal vector estimation and curvature fitting. Specifically:

[0081] k-nearest neighbor method: Search for the nearest neighbor to the current point p in the KD-tree. i The k nearest points in Euclidean distance are taken as the neighborhood point set S. i (It is recommended that k ≥ 10 to ensure the stability of the fit).

[0082] Radius neighborhood method: Search for points p in the KD-tree that are adjacent to the current point p. i All points whose Euclidean distance is no more than r are considered as the neighborhood point set S. i r is the neighborhood radius set by the user.

[0083] Step S3 is the unit normal vector calculation step. For each point, the unit normal vector is calculated based on its neighborhood point set. In this embodiment, two calculation methods are provided, including the local PCA method and the isosurface triangular mesh method.

[0084] Step S4 is the curvature calculation step. Based on the unit normal vector, a quadratic surface is fitted to the neighborhood point set of each point in the local tangent plane coordinate system to obtain the principal curvature, and the radius of curvature is calculated based on the principal curvature.

[0085] Step S5 is the ITZ thickness correction step. For any query point q and its initial thickness t0 (t0≥0), obtain the unit normal vector n and radius of curvature r of its nearest point p* in the point cloud, and calculate the corrected thickness t based on the tilt angle of the unit normal vector of the nearest point relative to the preset observation plane and the radius of curvature.

[0086] Step S6 is the result output and visualization step, which outputs the geometric information and corrected thickness of each point and displays them visually.

[0087] Geometric information includes: three-dimensional coordinates, normal vector components, curvature scalar, and radius of curvature.

[0088] The visualization includes: normal vector map, curvature cloud map and curvature radius cloud map, and the corrected thickness display of the query point.

[0089] Figure 2 This is a flowchart illustrating the calculation of the unit normal vector using the local PCA method in an embodiment of the present invention.

[0090] Local PCA method: Constructs a covariance matrix based on a neighborhood point set and performs eigenvalue decomposition. The eigenvector corresponding to the smallest eigenvalue is taken as the unit normal vector, and the orientation of this unit normal vector is unified, such as... Figure 2 As shown, perform the calculation according to the following steps:

[0091] a. For point p i and its neighborhood point set S i Construct neighborhood relative vectors :

[0092]

[0093] in, for neighborhood point set S i The first in Neighboring points, For the neighborhood point set S i The total number of midpoints.

[0094] b. When distance weighting is enabled, calculate the distance. And define weights :

[0095]

[0096] Where σ is the weighting scale parameter, and ε is a very small positive number to prevent division by zero. When distance weighting is not enabled, then... .

[0097] c. Construct the covariance matrix based on the above definition:

[0098]

[0099] d. For the covariance matrix Perform eigenvalue decomposition and extract the eigenvector corresponding to the smallest eigenvalue. As the unit normal vector :

[0100]

[0101] e. The orientation of the unit normal vector is unified using the centroid consistency rule, expressed as:

[0102] like Then let .

[0103] Here, dot is the dot product symbol for vectors.

[0104] Figure 3 This is a flowchart illustrating the calculation of the unit normal vector using the isosurface triangular mesh method in an embodiment of the present invention.

[0105] Isosurface triangular mesh method: The point cloud is rasterized and a 3D distance field is calculated. A triangular mesh is obtained through an isosurface extraction algorithm (marching cubes). Vertex normals are calculated from the normals of the triangular facets, and these vertex normals are mapped back to each point in the original point cloud as the unit normal vector for that point. Figure 3 As shown, perform the calculation according to the following steps:

[0106] a. Construct a cubic voxel mesh: Calculate the bounding box of the point cloud and scale it up by bboxScale to obtain the cube boundary [minB, maxB]. Assuming the mesh resolution is N, the voxel size is:

[0107]

[0108] Where L is the side length of the cube.

[0109] b. Rasterization Occupation: Occupy each point p i Mapping to voxel index In occupying the grid .

[0110] c. Calculate the 3D Euclidean distance field: Perform a 3D distance transformation (such as bwdist) on the mask to obtain distVolVoxel (in voxels), and convert it to the true distance:

[0111]

[0112] Where h is the voxel size.

[0113] If distance transformation is not available, a nearest neighbor distance query to the point cloud can be performed for each grid sampling point to obtain D.

[0114] d. Select isosurface (iso): User inputs r iso As the radius of the isosurface, when r iso Not in [D min D max When within the specified range, it will automatically adjust to the valid range.

[0115] e. Isosurface extraction: Extract isosurfaces with D=iso on D to obtain triangular meshes (vertices V, triangular facets f), using the marching cubes algorithm.

[0116] f. Patch normal vector: For each triangular patch Calculate the edge vectors , The area vector of the facets is:

[0117]

[0118] g. Accumulation of vertex normal vectors:

[0119] Area weighting: The area of ​​f adjacent to the vertex is weighted. n Accumulate and normalize;

[0120] Angle weighting: First, normalize the normal vector of the surface to... And calculate the interior angle θ of the face at each vertex, according to Accumulate and normalize. The angle θ can be calculated using the cosine theorem:

[0121]

[0122] h. Unit normal vector direction is unified: Let ,like Then flip .

[0123] in, Here, is the unit normal vector of the vertex, and dirs is the direction vector from the centroid of the point cloud to that vertex.

[0124] i. Optional smoothing: Build an adjacency matrix A based on grid edge relationships, and then... Perform several iterations and normalize. Among them, is the unit normal vector of the smoothed vertex, and deg is the vertex degree.

[0125] j. Map back to the point cloud: For each point p i Find the nearest vertex index in V ,make And normalize.

[0126] Figure 4 This is a flowchart of the curvature calculation steps in an embodiment of the present invention.

[0127] S4-1: As Figure 4 As shown, for each point p i With its unit normal vector As normal, construct a local orthogonal basis, and choose the direction with... Non-parallel auxiliary vectors , thus obtaining the tangential basis vector , :

[0128]

[0129]

[0130] Where ε is a very small positive number to prevent division by zero.

[0131] S4-2: Perform coordinate transformation of neighboring points. ,make Then its local coordinates are:

[0132]

[0133] S4-3: In the local tangent plane coordinate system, the following quadratic surface model is used for fitting:

[0134]

[0135] Where x and y are the two orthogonal coordinate components of the neighborhood point in the local tangent plane; z is the height offset of the neighborhood point along the local normal direction; a and c are the surface along the local tangent plane. x direction and y Second-order bending strength in the direction; b is xyCoupling term coefficients; d and e are coefficients of the first-order term.

[0136] Write it in linear least squares form:

[0137]

[0138] Where A is the design matrix, Coeff is the parameter vector to be determined, and represents the five fitting coefficients of the local quadratic surface. .

[0139] The least squares solution is expressed as:

[0140]

[0141] This means that among all possible quadratic surface parameters, we find a set of a, b, c, d, e that minimizes the sum of squared deviations of the normal heights between the fitted surface and the neighboring points, thereby obtaining the surface in the neighborhood of that point that best represents the true local morphology.

[0142] In practice, this can be achieved by solving the normal equations or by directly using a linear equation solver.

[0143] S4-4: Construct the second derivative matrix Hessian as follows:

[0144]

[0145] Where H is the Hessian matrix of the local surface, representing the second-order curvature property of the surface in the neighborhood of that point; a is the second-order curvature component in the x-direction; c is the second-order curvature component in the y-direction; and b is the mixed second-order curvature component, reflecting the coupled curvature in the two directions.

[0146] The eigenvalues ​​of H, namely the principal curvatures k1 and k2, are calculated using the trace and determinant:

[0147]

[0148]

[0149] Where tr is the trace of matrix H, which is equal to the sum of two eigenvalues; det is the determinant of matrix H, which is equal to the product of two eigenvalues; k1 and k2 are the two principal curvatures at that point, representing the maximum and minimum curvature of the surface in the two principal directions, respectively; sqrt is the square root.

[0150] Based on the user's selection, calculate at least one of the following curvature scalars, curv, based on the principal curvature:

[0151] Gaussian curvature: K = k1·k2;

[0152] Mean curvature: ;

[0153] Maximum curvature: ;

[0154] Second-order curvature: ,

[0155] Define the radius of curvature as: R = 1 / (k + ε), where k is the chosen curvature scalar and ε is a very small positive number to prevent division by zero.

[0156] When the number of neighborhood points m is insufficient or the normal vector is invalid, set curv=0 and R=∞ to avoid anomalies.

[0157] After obtaining the local unit normal vector n and radius of curvature r of the point cloud, the initial ITZ thickness t0 is geometrically corrected. Here, t0 can be understood as the "in-plane thickness" measured using the strip method within the observation plane (e.g., the XY plane). When the normal vector of the calculated point is not perpendicular to the XY plane, t0 deviates from the actual thickness along the interface normal, requiring geometric correction.

[0158] The unit normal vector and local curvature (radius of curvature) obtained by the aforementioned steps are used to perform local ITZ thickness correction.

[0159] S5-1: Point Association and Parameter Acquisition: Calculating Point Coordinates Given an initial thickness t0, use a KD-tree to retrieve the nearest point cloud point for q: Its index is denoted as i*, and it obtains the unit normal vector at the nearest point. With the radius of curvature r.

[0160] S5-2: Calculation of Normal Inclination Angle: Define α as the angle between the unit normal vector n and the XY plane, then:

[0161]

[0162] in, Let α represent the projection of n onto the XY plane. Since n is a unit vector, the range of cosα is [0,1].

[0163] S5-3: Correction formula for planar interfaces (r→∞): When the interface is approximately planar (radius of curvature r→∞ or numerically non-finite), the corrected thickness is obtained by projecting the initial thickness t0 onto the normal tilt angle: .

[0164] Figure 5This is a schematic diagram of the geometric relationship of ITZ thickness correction in an embodiment of the present invention (symbols in the figure: radius of curvature r, ITZ thickness t0 in two-dimensional slicing method, angle α between the normal and the XY plane, and corrected ITZ thickness t).

[0165] S5-4: Correction formula and geometric interpretation for curved surfaces (finite r): as follows Figure 5 As shown, when the interface has curvature, the local interface can be regarded as an arc of radius r within the normal section, with the center of curvature of this arc as the origin, and the distance from the interface point p* to the origin as r. After moving t0 along the normal projection direction in the observation plane to reach the outer boundary point, the angle between this moving direction and the unit normal vector n at the interface point p* is α. Then the distance from the outer boundary point to the center of curvature is... for:

[0166]

[0167] The actual corrected thickness t along the normal direction is equal to the radius increment: ,Right now:

[0168] .

[0169] To avoid numerical cancellation errors when r is large and t is small, the following equivalent rationalization form is preferred in this embodiment:

[0170]

[0171] Where ε is a very small positive number, used to avoid the denominator being zero.

[0172] S5-5: Validity check. If the unit normal vector length of the nearest point is less than the preset threshold, the geometric information at that point is considered invalid; or if the radius of curvature of the nearest point is invalid, the correction is stopped or the preset default value is output.

[0173] Figure 6 These are example diagrams of the spherical aggregate normal vector diagram, curvature cloud diagram, and curvature radius cloud diagram (based on triangular mesh) in embodiments of the present invention. Figure 7 These are example diagrams of the spherical aggregate normal vector diagram, curvature cloud diagram, and curvature radius cloud diagram in embodiments of the present invention (based on local PCA). Figure 8 These are example diagrams of the actual aggregate normal vector diagram, curvature cloud diagram, and curvature radius cloud diagram (based on triangular mesh) in embodiments of the present invention. Figure 9 These are example diagrams of the actual aggregate normal vector diagram, curvature cloud diagram, and curvature radius cloud diagram in embodiments of the present invention (based on local PCA). Figure 10 This is a diagram showing the ITZ correction calculation results for spherical aggregate in an embodiment of the present invention (based on a triangular mesh). Figure 11This is a diagram showing the ITZ correction calculation results for spherical aggregates in an embodiment of the present invention (based on local PCA). Figure 12 This is a diagram showing the actual aggregate ITZ correction calculation results (based on triangular mesh) in an embodiment of the present invention. Figure 13 This is a diagram showing the actual aggregate ITZ correction calculation results (based on local PCA) in an embodiment of the present invention.

[0174] In this embodiment, two calculation examples are used to verify and demonstrate the effectiveness of the ITZ thickness correction calculation method based on local geometry proposed in this invention. The two examples are: a spherical aggregate with a radius of 2 mm (theoretically, the radius of curvature is constant) and real aggregate obtained from a CT scan (only a portion of the aggregate is included to reduce operating costs). The normal vector and curvature are calculated using the local PCA method and the isosurface triangular mesh method, respectively, resulting in a normal vector map, curvature contour map, and radius of curvature contour map, as shown below. Figures 6-9 As shown; simultaneously, randomly select query points and calculate their corrected thickness, the results are as follows. Figures 10 to 13 As shown.

[0175] like Figures 6-7 As shown, for spherical aggregates, the normal vectors calculated by both methods are uniformly distributed radially, consistent with the theoretical spherical normal; the curvature cloud map shows that the curvature value of the entire surface is approximately constant, consistent with the geometric characteristics of the sphere; the curvature radius cloud map also shows a uniform distribution, with a value close to the spherical radius of 2 mm, verifying the accuracy of the curvature calculation of the present invention.

[0176] like Figures 8-9 As shown, for real aggregates, the normal vector map clearly reflects the surface irregularities and angular features, while the curvature / radius of curvature cloud map highlights the angular, flat, and curved areas of the aggregate surface. These results demonstrate that both methods can effectively calculate the local geometric information of complex surfaces.

[0177] Based on the above results, it is demonstrated that the method of the present invention can stably and accurately extract the normal vector and curvature information necessary for subsequent thickness correction from point clouds.

[0178] like Figures 10-11 As shown, the corrected thickness calculation results of both methods exhibit a globally approximately uniform numerical distribution with no obvious local deviations. This indicates that the calculation results of the corrected formula on regular curved surfaces are stable and consistent with theoretical expectations, and can effectively convert the two-dimensional initial thickness t0 into the true thickness t of the three-dimensional normal.

[0179] like Figure 12-13As shown, the corrected thickness calculation results of the actual aggregate are displayed. The corrected thickness at different query points varies due to differences in local curvature and normal inclination. The corrected thickness is smaller than the initial thickness, indicating that the method of the present invention can adaptively adjust the corrected thickness according to the local radius of curvature and normal inclination. The results have a good correspondence with the geometric features of the aggregate surface, proving the effectiveness of the thickness correction method of the present invention.

[0180] The above examples demonstrate the robustness and effectiveness of the method of the present invention under different aggregate morphologies.

[0181] This embodiment also provides an ITZ thickness correction calculation system based on local geometry, including:

[0182] The data acquisition and preprocessing module is used to implement step S1, namely: acquiring point cloud data containing three-dimensional coordinates and constructing a KD-tree to support spatial neighborhood retrieval.

[0183] The neighborhood construction module is used to implement step S2, which is to construct a set of neighboring points for each point in the point cloud based on a KD-tree.

[0184] The unit normal vector calculation module is used to implement step S3, that is, for each point, calculate the unit normal vector based on its neighborhood point set.

[0185] The curvature calculation module is used to implement step S4, namely: based on the unit normal vector, perform quadratic surface fitting on the neighborhood point set of each point in the local tangent plane coordinate system to obtain the principal curvature, and calculate the radius of curvature based on the principal curvature.

[0186] The ITZ thickness correction module is used to implement step S5, namely: for any query point and its initial thickness, obtain the unit normal vector and radius of curvature of the nearest point in the point cloud, and calculate the corrected thickness based on the tilt angle and radius of curvature of the unit normal vector of the nearest point relative to the preset observation plane.

[0187] The results output and visualization module is used to implement step S6, namely: outputting the geometric information and corrected thickness of each point and displaying it visually.

[0188] The role and effect of the embodiments

[0189] The ITZ thickness correction calculation method and system based on local geometry according to the present invention have the following beneficial effects:

[0190] Step S3 of this invention provides two methods for calculating normal vectors: local PCA and isosurface triangular mesh. PCA offers high computational efficiency, supports distance weighting, assigns greater weight to nearest neighbors, suppresses the influence of distant neighbor noise on the normal vector, and improves robustness. The isosurface mesh method obtains smooth normal vectors through a three-dimensional distance field and isosurface extraction, exhibiting stronger robustness to point clouds with high noise and uneven sampling. Users can flexibly choose the method based on the characteristics of their actual data, ensuring computational stability under various conditions. Furthermore, the isosurface triangular mesh method of this invention employs an efficient three-dimensional distance transformation algorithm (such as bwdist) to quickly calculate the distance field, improving the isosurface mesh path efficiency and meeting the needs of practical engineering applications.

[0191] In step S5 of this invention, the local geometric information of the point cloud (normal tilt angle and radius of curvature) is explicitly introduced into the thickness calculation, effectively overcoming the problem of overestimation of thickness caused by the traditional two-dimensional cross-section observation method due to the cross-section not being perpendicular to the aggregate surface. The modified formula of this invention is applicable to both approximate planar interfaces (r→∞) and curved interfaces (finite r), providing a numerically stable calculation form that can convert the initial slice thickness t0 into the true thickness t along the interface normal, making the measurement results consistent with the three-dimensional geometry.

[0192] This invention provides an interactive software implementation that supports free switching between normal vector calculation methods (local PCA method or isosurface triangular mesh method in step S3), flexible configuration of neighborhood parameters (k value of k nearest neighbor or radius r of radius neighborhood in step S2), and one-click correction of thickness calculation and result visualization of query points. This facilitates parameter debugging and result analysis in engineering applications and improves the ease of use and adaptability of the method.

[0193] This invention verifies the effectiveness of its method using two examples: spherical aggregate and real aggregate, employing two different normal vector calculation methods. Experimental results show that the normal vector, curvature, and radius of curvature on the spherical aggregate closely match the theoretical values, and the corrected thickness is uniform across the entire surface. Calculation results on the real aggregate demonstrate that the method can adaptively adjust the corrected thickness based on the local radius of curvature and normal inclination angle, and the results correspond well to the geometric characteristics of the aggregate surface, proving the effectiveness and robustness of the invention.

[0194] Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to this invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating ITZ thickness correction based on local geometry, characterized in that, Includes the following steps: S1: Data acquisition and preprocessing steps, acquiring point cloud data containing three-dimensional coordinates, and constructing a KD-tree to support spatial neighborhood retrieval; S2: Neighborhood construction step: For each point in the point cloud, construct a neighborhood point set for each point based on the KD-tree; S3: Unit normal vector calculation step: For each point, calculate the unit normal vector based on its neighborhood point set; S4: Curvature calculation step: Based on the unit normal vector, perform quadratic surface fitting on the neighborhood point set of each point in the local tangent plane coordinate system to obtain the principal curvature, and calculate the radius of curvature based on the principal curvature; S5: ITZ thickness correction step: For any query point and its initial thickness, obtain the unit normal vector and the radius of curvature of the nearest point in the point cloud, and calculate the corrected thickness based on the tilt angle of the unit normal vector of the nearest point relative to the preset observation plane and the radius of curvature. S6: Result Output and Visualization Steps. Output the geometric information and corrected thickness of each point, and visualize the results. In step S5, the method for calculating the corrected thickness is as follows: S5-1: Calculate point coordinates Given an initial thickness t0, use a KD-tree to retrieve the nearest point cloud point for q: Its index is denoted as i*, and it obtains the unit normal vector at the nearest point. With radius of curvature r, S5-2: Define α as the angle between the unit normal vector n and the XY plane, then: ， in, Let α represent the projection of n onto the XY plane. Since n is a unit vector, the range of cosα is [0,1]. S5-3: When the radius of curvature is infinite or numerically non-finite, the corrected thickness is obtained by projecting the initial thickness t0 onto the normal tilt angle. , S5-4: When the interface has curvature, the local interface is considered as an arc of radius r within the normal section. The center of curvature of this arc is taken as the origin, and the distance from the interface point p* to the origin is r. After moving t0 along the normal projection direction in the observation plane to reach the outer boundary point, the angle between this moving direction and the unit normal vector n at the interface point p* is α. Then the distance from the outer boundary point to the center of curvature is... for: ， The actual corrected thickness t along the normal direction is equal to the radius increment: ,Right now: 。 2. The ITZ thickness correction calculation method based on local geometry according to claim 1, characterized in that: in, In S2, each point p i Methods for constructing a neighborhood point set include: k-nearest neighbor method: Search for the nearest neighbor to the current point p in the KD-tree. i The k nearest points in Euclidean distance are taken as the neighborhood point set S. i ; Radius neighborhood method: Search for points p in the KD-tree that are adjacent to the current point p. i All points whose Euclidean distance is no more than r are considered as the neighborhood point set S. i r is the neighborhood radius set by the user.

3. The ITZ thickness correction calculation method based on local geometry according to claim 1, characterized in that: in, In S3, the method for calculating the unit normal vector includes: Local PCA method: constructing a covariance matrix based on the neighborhood point set and performing eigenvalue decomposition, taking the eigenvector corresponding to the smallest eigenvalue as the unit normal vector, and unifying the orientation of the unit normal vector.

4. The ITZ thickness correction calculation method based on local geometry according to claim 1, characterized in that: in, In S3, the method for calculating the unit normal vector further includes: Isosurface triangular mesh method: The point cloud is rasterized and the three-dimensional distance field is calculated. Triangular meshes are obtained through isosurface extraction algorithm. Vertex normal vectors are calculated from the normals of the triangular patches and mapped back to each point in the original point cloud as the unit normal vector of that point.

5. The ITZ thickness correction calculation method based on local geometry according to claim 1, characterized in that: in, In S4, the method for obtaining the principal curvature is as follows: S4-1: For each point p i With its unit normal vector As normal, construct a local orthogonal basis, and choose the direction with... Non-parallel auxiliary vectors , thus obtaining the tangential basis vector , : ， ， Where ε is a very small positive number to prevent division by zero. S4-2: Perform coordinate transformation of neighboring points. ,make Then its local coordinates are: ， in, for neighborhood point set S i The first in Neighboring points, For distance, S4-3: In the local tangent plane coordinate system, the following quadratic surface model is used for fitting: ， Where x and y are the two orthogonal coordinate components of the neighborhood point in the local tangent plane; z is the height offset of the neighborhood point along the local normal direction; a and c are the surface along the local tangent plane. x direction and y Second-order bending strength in the direction; b is xy Coupling term coefficients; d and e are coefficients of the first-order term. Write it in linear least squares form: ， Where A is the design matrix, Coeff is the parameter vector to be determined, and represents the five fitting coefficients of the local quadratic surface. , The least squares solution is expressed as: ， S4-4: Construct the second derivative matrix Hessian as follows: ， Where H is the Hessian matrix of the local surface, representing the second-order curvature property of the surface in the neighborhood of that point; a is... x The second-order curvature component of the direction, i.e., the surface along the local curvature. x Second-order bending strength in the direction; c is y The second-order curvature component of the direction, i.e., the surface along the local curvature. y The second-order bending strength in the direction; b is the mixed second-order curvature component, reflecting the coupled bending in two directions, i.e. xy Coupling term coefficients, The eigenvalues ​​of H, namely the principal curvatures k1 and k2, are calculated using the trace and determinant: ， ， Where tr is the trace of matrix H, which is equal to the sum of two eigenvalues; det is the determinant of matrix H, which is equal to the product of two eigenvalues; k1 and k2 are the two principal curvatures at that point, representing the maximum and minimum curvature of the surface in the two principal directions, respectively; sqrt is the square root.

6. The ITZ thickness correction calculation method based on local geometry according to claim 5, characterized in that: in, In step S4, at least one of the following curvature scalars, curv, is calculated based on the principal curvature, according to the user's selection: Gaussian curvature: K = k1·k2; Mean curvature: ; Maximum curvature: ; Second-order curvature: , Define the radius of curvature as: R = 1 / (k + ε), where k is the chosen curvature scalar, and ε is a very small positive number to prevent division by zero. When the number of neighborhood points m is insufficient or the normal vector is invalid, set curv=0 and R=∞ to avoid anomalies.

7. The ITZ thickness correction calculation method based on local geometry according to claim 1, characterized in that: in, S5 also includes: S5-5: Validity check. If the unit normal vector length of the nearest point is less than the preset threshold, or the radius of curvature of the nearest point is invalid, then stop the correction or output the preset default value.

8. The ITZ thickness correction calculation method based on local geometry according to claim 7, characterized in that: in, In S6, the geometric information includes: three-dimensional coordinates, normal vector components, curvature scalar, and radius of curvature. The visualization includes: normal vector map, curvature cloud map and curvature radius cloud map, and the corrected thickness display of the query point.

9. A local geometry-based ITZ thickness correction calculation system, used to execute the local geometry-based ITZ thickness correction calculation method according to any one of claims 1-8, characterized in that, include: The data acquisition and preprocessing module acquires point cloud data containing three-dimensional coordinates and constructs a KD-tree to support spatial neighborhood retrieval. The neighborhood construction module constructs a neighborhood point set for each point in the point cloud based on the KD-tree. The unit normal vector calculation module calculates the unit normal vector for each point based on its neighborhood point set; The curvature calculation module, based on the unit normal vector, performs quadratic surface fitting on the neighborhood point set of each point in the local tangent plane coordinate system to obtain the principal curvature, and calculates the radius of curvature based on the principal curvature; The ITZ thickness correction module, for any query point and its initial thickness, obtains the unit normal vector and the radius of curvature of the nearest point in the point cloud, and calculates the corrected thickness based on the tilt angle of the unit normal vector of the nearest point relative to the preset observation plane and the radius of curvature. The results output and visualization module outputs the geometric information and the corrected thickness of each point and displays them visually.

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