Complementation method for three-dimensional point cloud reverse material distribution simulation of complex roadway

Abstract

The invention discloses a complex roadway three-dimensional point cloud reverse distribution simulation completion method, which comprises the following steps: S1, acquiring a three-dimensional point cloud of an underground roadway scene by utilizing a three-dimensional laser scanning technology, calculating the gravity center of the three-dimensional point cloud through a principal component analysis method, and establishing a polar coordinate system by taking the gravity center of the three-dimensional point cloud as an original point, translating the three-dimensional point cloud into a polar coordinate system; s2, constructing a material distribution grid model on the outer side of the roadway, shrinking material distribution particles in the material distribution grid model through the centrifugal gravitational action of the gravity center of the three-dimensional point cloud, and stopping movement of the material distribution particles until the distance between the material distribution particles and the three-dimensional point cloud is smaller than a set threshold value or reaches the maximum number of iterations; and S3, uniformly distributed random point cloud sampling is carried out on the triangular mesh in the generated material distribution particles, so that a complemented three-dimensional point cloud roadway model can be obtained.

Description

Technical Field

[0001] This invention relates to the field of coal mining, and in particular to a method for reverse placement simulation and completion of three-dimensional point clouds in complex roadways. Background Technology

[0002] In the wave of global energy transition and green, low-carbon development, the intelligent upgrading of the mining industry is imperative. As the "arteries" of mine production, the safety, stability, and efficient operation and maintenance of roadways are the core foundation for achieving intelligent mining. However, traditional roadway management models relying on single-point measurements or manual inspections are no longer sufficient to meet the urgent needs of modern mines for refined, comprehensive, and long-term monitoring of surrounding rock stability, support structure deformation, and geological hazards. Therefore, introducing a revolutionary technology capable of rapid and accurate three-dimensional digital modeling of complex roadway environments is not only key to improving mine safety management but also the data foundation for building digital twins of mines and realizing intelligent decision-making.

[0003] Against this backdrop, 3D laser scanning technology, with its unique advantages of high precision, high efficiency, and non-contact measurement, has become the preferred solution for acquiring 3D information of roadways. Through a mobile scanning platform, this technology can acquire high-density 3D point clouds of the entire roadway in a short time. In the process of intelligent coal mine construction, the accurate acquisition of 3D spatial information plays a fundamental supporting role, providing reliable data for key aspects such as real-time positioning of mining equipment, optimization of work routes, and allocation of equipment resources. However, due to the complex underground working environment, such as equipment obstruction, dust interference, and scanning path limitations, the raw point cloud data acquired by laser scanning often suffers from problems such as holes, missing data, and sparseness. This incompleteness severely restricts the reliability of subsequent high-precision modeling, deformation analysis, and even intelligent inspection algorithms, becoming a key technical bottleneck hindering the full value of 3D laser technology in roadway scenarios. To obtain more complete and accurate roadway spatial data, 3D point cloud completion technology for missing areas is particularly crucial. This type of technology can effectively fill in the missing parts of spatial data, improving the overall quality and practicality of digital modeling of underground roadways. A topologically complete and geometrically continuous high-fidelity model is a necessary prerequisite for the subsequent realization of advanced applications such as intelligent deformation monitoring of roadways and disaster simulation and early warning. Therefore, point cloud completion has become one of the key technologies that urgently need to be broken through in the field of intelligent mining.

[0004] Traditional point cloud completion techniques primarily employ three core methods to address data missingness issues. Geometric symmetry methods identify and utilize the object's inherent symmetry features to establish a symmetry plane and use mirror mapping to achieve data repair, employing appropriate completion strategies for different degrees of missingness. Surface reconstruction methods rely on various mathematical interpolation and surface fitting algorithms to generate the geometric surface of the missing region, including techniques such as nearest neighbor interpolation, linear fitting, and Gaussian processes; however, they are prone to accuracy loss when dealing with complex geometries. Template matching methods construct a shape template library and search for the most similar known geometric template to the missing region to estimate the shape features of the missing part. The effectiveness of this method largely depends on the richness of the template library and the accuracy of the matching algorithm, while also facing a high computational burden.

[0005] In 2016, the introduction of PointNet marked the initial exploration of deep learning in the field of point cloud processing. Subsequently, methods such as VConv-DAE and 3D-EPN were proposed, achieving preliminary completion of missing point clouds through voxelization and 3D convolutional networks, respectively. After 2017, with the maturity of deep learning technology, voxel-based and convolutional methods gradually became mainstream. 3D-EPN completes point clouds through 3D convolutional networks and combines implicit surface representations to predict missing regions. Subsequently, in order to reduce the dependence on voxelization representations, researchers began to explore point-based methods. For example, PCN and TopNet directly complete the original point cloud, avoiding the information loss caused by voxelization. However, these multilayer perceptron (MLP)-based architectures have limited ability to capture local geometric context. When dealing with large-scale or non-uniform point clouds, the reconstructed details are prone to over-smoothing or artifacts. Subsequently, point cloud completion methods based on generative adversarial networks (GANs) and Transformers were also proposed to improve the diversity and detail representation of the completion results. While the former can generate diverse results, it faces the challenge of unstable training; the latter, while possessing strong global perception capabilities, is limited by computational complexity on the order of quadratic points, making it difficult to scale to large-scale scenarios. More importantly, these supervised learning methods generally suffer from the common problems of strong dependence on training data and weak generalization ability. Since 2020, multimodal and autoregressive methods have made significant breakthroughs in the field of point cloud completion. Methods such as AutoSDF and Diffusion-SDF have achieved efficient completion of multimodal 3D tasks by combining autoregressive priors and diffusion models. However, this comes at the cost of requiring massive amounts of data to learn the priors, and the iterative inference process is difficult to meet real-time requirements. In recent years, implicit field learning based on point denoising for adaptive querying has been proposed, combining 3D Gaussian point shading, diffusion models, and IPoD (implicit field learning with point diffusion). This approach utilizes two backbone networks, PVCNN and Transform models, to further improve the accuracy and effectiveness of point cloud completion. Nevertheless, the model complexity and training cost of these cutting-edge methods have increased dramatically, and their performance is highly dependent on high-quality, large-scale training datasets that are difficult to obtain in specific industrial fields (such as mine tunnels).

[0006] Currently, specialized completion research for point clouds in coal mine roadways is still in the exploratory stage. Existing technical approaches mainly fall into two categories: one is methods relying on geometric priors, represented by the roadway centerline symmetry method. However, this method is based on the idealized assumption of strict symmetry in the roadway structure. In practice, asymmetric deformation of roadways caused by complex geological stresses such as rockbursts is common, which renders the geometric constraints of this method ineffective, making it difficult to guarantee the structural accuracy of the completion results. The other category is data-driven deep learning methods, such as local completion models for roadway coal wall slices. Although such methods can learn and reproduce complex textures in local areas, their generalization ability has bottlenecks. For large-scale irregular voids caused by large equipment occlusion that span multiple structural surfaces (such as from the floor to the sidewalls), the completion effect often fails to maintain structural continuity. Summary of the Invention

[0007] The purpose of this invention is to address the above-mentioned problems by providing a method for reverse fabric simulation and completion of complex three-dimensional point clouds in tunnels. By simulating the physical expansion and wrapping process of flexible mesh under constraints, it can adaptively fit the macroscopic structure of tunnel point clouds and effectively reconstruct the base surface missing due to large-area occlusion.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] A method for reverse cloth simulation and completion of 3D point clouds in complex tunnels includes the following steps:

[0010] S1. Use 3D laser scanning technology to obtain 3D point cloud of underground roadway scene, calculate the centroid of 3D point cloud by principal component analysis, establish polar coordinate system with the centroid of 3D point cloud as origin, and translate 3D point cloud into polar coordinate system.

[0011] S2. Construct a cloth mesh model on the outside of the alleyway. The cloth particles in the cloth mesh model are shrunk by the centrifugal force of the centroid of the three-dimensional point cloud until the distance between the cloth particles and the three-dimensional point cloud is less than the set threshold or the maximum number of iterations is reached. The cloth particles then stop moving.

[0012] S3. Randomly sample the triangular mesh in the generated cloth particles to obtain the completed 3D point cloud tunnel model.

[0013] Furthermore, step S1 specifically includes the following steps:

[0014] S11. A 3D point cloud of the underground tunnel scene is obtained using 3D laser scanning technology. The centroid of the 3D point cloud is the average value of all points. The formula for calculating the centroid of the 3D point cloud is:

[0015]

[0016] in, is the centroid of the 3D point cloud, and n is the number of points in the 3D point cloud. It is the position vector of the i-th point in the 3D point cloud;

[0017] S12. Obtain the centroid vector and position vectors of each point in the 3D point cloud, and calculate the covariance of the 3D point cloud. The calculation formula is as follows:

[0018]

[0019] Expand it into a 3×3 matrix form:

[0020]

[0021] S13. The eigenvalues ​​and eigenvectors of the covariance matrix satisfy the equation:

[0022]

[0023] in, λ is the eigenvector, and λ is the eigenvalue corresponding to the 3D point cloud;

[0024] S14. Establish a polar coordinate system with the centroid of the 3D point cloud as the origin. Rotate the 3D point cloud so that its principal direction is aligned with the x-axis in the polar coordinate system. The rotation transformation formula is:

[0025]

[0026] S15. Transform the coordinates of the 3D point cloud to the polar coordinate system. The transformation formula is as follows:

[0027]

[0028] Furthermore, step S2 specifically includes the following steps:

[0029] S21. Invert the three-dimensional point cloud in polar coordinates onto the ground;

[0030] S22. Place the preset cloth mesh model on the 3D point cloud. The cloth particles in the cloth mesh model gradually sink under the action of gravity.

[0031] S23. During the descent of the fabric particles, collision detection is performed until the height of the fabric particle is lower than the minimum elevation of the nearest laser point. At that point, the fabric particle is marked as a fixed point and anchored at the current lowest position.

[0032] S24. Based on the interaction forces of the cloth particles, pull up and adjust the cloth particles with large positional differences until the change in the displacement of the cloth particles is small enough or the maximum number of iterations is reached, at which point the cloth particles stop moving and the cloth mesh model completely conforms to the ground.

[0033] Furthermore, in step S22, the equation of motion for the fabric particles during their sinking process in polar coordinates is:

[0034]

[0035] in, Indicates radial acceleration. Indicates radial velocity, Represents angular acceleration. F represents angular velocity. r F is the radial contraction force along the radial direction. θ It is a lateral force perpendicular to the radial direction;

[0036] After simplification, we get:

[0037]

[0038] Furthermore, in step S22, the gravitational force acting on the fabric particles is:

[0039]

[0040] Where G is the gravitational constant, M is the mass of the central pole, and m is the mass of the cloth particle.

[0041] Furthermore, in step S23, when the fabric particles undergo collision detection during the sinking process, if both particles can move, the fabric particles... The force formula is:

[0042]

[0043] in, For fabric particles With fabric particles The radial difference vector; α(t) is the correction coefficient based on the number of iterations;

[0044] When there are only single fabric particles When movable, fabric particles The force formula is:

[0045]

[0046] Where β(t) is a correction coefficient based on the number of iterations.

[0047] Furthermore, step S3 specifically includes the following steps:

[0048] S31. Obtain the coordinates of the three vertices of the triangular mesh in the generated cloth particles, and denote them as points. point point The area of ​​a triangular mesh is calculated using the cross product of vectors, and the formula is as follows:

[0049]

[0050] S32. For each triangular grid, the number of basic sampling points is determined by multiplying the area of ​​the triangular grid by the preset sampling density.

[0051] S33. For each point to be generated within the triangular mesh, generate two random numbers x and y in the interval [0,1]. If x + y > 1, adjust the values ​​so that x = 1 - x and y = 1 - y. Then calculate the centroid coordinates of the triangular mesh. Where a = 1 - xy, b = x, c = y, so that the centroid coordinates generate point Q = aA + bB + cC within the triangular grid;

[0052] S34. Based on the preset sampling density, perform point cloud sampling on all triangular meshes in the cloth mesh model to generate a completed three-dimensional point cloud tunnel model.

[0053] Compared with the prior art, the advantages and positive effects of the present invention are:

[0054] This invention proposes a method for inverse fabric simulation and completion of 3D point clouds in complex tunnels. This method achieves robust completion of tunnel models through a series of steps, including point cloud preprocessing, centerline extraction based on principal component analysis, core axial-guided fabric shrinkage fitting, and final point cloud resampling. When dealing with severe data loss caused by large equipment occlusion, scanning blind spots, or denoising, this method can generate geometrically continuous and topologically complete completed surfaces, filling the gap in the field for methods to handle large-scale irregular voids. It provides a reliable technical path for 3D modeling of complex underground spaces, and the generated complete digital model lays a solid foundation for subsequent cutting-edge applications such as intelligent deformation monitoring and disaster early warning. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a logic flowchart of the present invention;

[0057] Figure 2 This is a schematic diagram of a fabric simulation filtering algorithm;

[0058] Figure 3 A schematic diagram for initializing the cloth mesh;

[0059] Figure 4 This is a schematic diagram of the final shrinkage of the fabric mesh;

[0060] Figure 5 This is a graph showing the vertex coordinates of a triangular mesh.

[0061] Figure 6 Generate a graph for the centroid coordinates of the triangular mesh;

[0062] Figure 7 A schematic diagram of particle point cloudification for a fabric mesh;

[0063] Figure 8 Point cloud data map of an experimental roadway with a single angle and single side;

[0064] Figure 9 A diagram showing the wrapping effect of the maximum number of iterations parameter for a single-angle, single-sided, heterogeneous tunnel;

[0065] Figure 10 A diagram showing the effect of wrapping the attraction intensity parameters of a single-angle, single-sided, heterogeneous tunnel;

[0066] Figure 11 Point cloud data map of the experimental tunnel for the double-angled, double-sided irregular tunnel;

[0067] Figure 12 Wrapping effect diagram of the maximum number of iterations parameter for double-angled double-sided irregular tunnels

[0068] Figure 13 A diagram showing the effect of wrapping the attraction intensity parameters of a double-angled, double-sided irregular tunnel;

[0069] Figure 14 Display data graph of point cloud density;

[0070] Figure 15 This is a schematic diagram of the point cloudification result;

[0071] Figure 16 A typical tunnel point cloud data map;

[0072] Figure 17 Point cloud data of the tunnel after noise reduction;

[0073] Figure 18 To complete the point cloud data map of the rear tunnel;

[0074] Figure 19 To complete the comparison map of the tunnel point cloud data;

[0075] Figure 20 A rendering showing the wrapping effect of the tunnel's detailed dimensions (Td).

[0076] Figure 21 A rendering showing the wrapping effect of the RI parameters for the detailed dimensions of the alleyway;

[0077] Figure 22 A parameter analysis diagram for a single-angle, single-sided, heterogeneous roadway;

[0078] Figure 23 This is a parameter analysis diagram for a double-angled, double-sided, heterogeneous roadway. Detailed Implementation

[0079] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art to all other embodiments obtained without creative effort should be included within the protection scope of the present invention.

[0080] This invention proposes a method for inverse fabric simulation and completion of 3D point clouds in complex tunnels. First, it utilizes 3D laser scanning technology to acquire 3D point cloud information of the underground tunnel scene. Principal component analysis is used to calculate the centroid of the point cloud, and then the point cloud is translated to establish a polar coordinate system with the centroid as the origin. Next, fabric particles are initialized on the outside of the tunnel. Through the centrifugal force of the centroid, the fabric particles are contracted until the distance between the fabric particles and the actual point cloud is less than a set threshold or the maximum number of iterations is reached, at which point the fabric particles stop moving. Finally, the triangular meshes in the generated fabric particles are uniformly distributed with random point cloud sampling to obtain the completed 3D point cloud. This method is implemented based on a secondary development of Cloud Compare.

[0081] I. Methodology and Principles

[0082] The reverse cloth simulation completion method in this invention performs three-dimensional tunnel completion through a dynamic physical simulation process, as follows: Figure 1 As shown;

[0083] First, the point cloud data is cleaned and geometrically normalized, and its central axis and orientation are calibrated using principal component analysis. Then, a virtual cloth mesh enveloping the tunnel begins to iteratively shrink towards the central axis under constant inward gravity. The key to this method is that the intrinsic tension mechanism between cloth particles effectively resists deformation. This strong geometrical smoothness constraint ensures that the mesh closely approximates the complex point cloud structure without breaking or wrinkling. Once the cloth shape stabilizes and meets the convergence condition, the simulation stops, and the final locked particle positions accurately delineate the complete tunnel surface. The finally generated cloth particles are then sampled from a uniformly distributed random point cloud to obtain the completed 3D point cloud.

[0084] 1. Determination and transformation of the centerline

[0085] The principal orientation of the point cloud data is calculated using Principal Component Analysis (PCA), such as... Figure 1 As shown above, after confirming the main direction, adjust the original point cloud to the central axis so that it coincides with the x-axis of the spatial coordinate system.

[0086] In point cloud processing, PCA is commonly used to find the dominant orientation and features of a point cloud. The centroid of a point cloud is the average value of all points, and the formula for calculating the centroid of a point cloud is:

[0087]

[0088] in, is the centroid of the 3D point cloud, and n is the number of points in the 3D point cloud. Let be the position vector of the i-th point in the 3D point cloud. The covariance of the point cloud is calculated using the obtained centroid vector and the position vectors of each particle. The covariance matrix formula is as follows:

[0089]

[0090] Expand into a 3×3 matrix:

[0091]

[0092] The eigenvalues ​​and eigenvectors of the covariance matrix satisfy the following equation:

[0093]

[0094] in, Here, λ is the eigenvector, and λ is the eigenvalue corresponding to the 3D point cloud. In a 3D point cloud, the covariance matrix has three eigenvalues ​​and corresponding eigenvectors. The magnitude of the eigenvalues ​​represents the variance of the point cloud along the direction of the corresponding eigenvector. The eigenvector corresponding to the largest eigenvalue is usually the principal axis direction of the channel. Transforming the point cloud to this new coordinate system, aligning the principal direction with the x-axis, is done using the following formula:

[0095]

[0096] Here, v1, v2, and v3 are three eigenvectors. The three variables in these three rows are the three components of the three eigenvectors v1, v2, and v3. The matrix they form is a rotation matrix. This rotation matrix rotates the point cloud so that the principal direction (the eigenvector corresponding to the largest eigenvalue) is aligned with the X-axis, the secondary direction with the Y-axis, and the third direction with the Z-axis.

[0097] After axial normalization, the direction of the tunnel point cloud is completely consistent with the positive x-axis. Based on formula (6), a corresponding polar coordinate system is constructed on the YOZ plane of each section in the Cartesian coordinate system, and the results are as follows: Figure 2 As shown in the figure on the right.

[0098]

[0099] The coordinates of the point cloud after rotation and translation are (x, y, z), which are represented as (L, r, θ) in the polar coordinate system. At this time, each section along the tunnel excavation direction corresponds to an independent polar coordinate system.

[0100] 2. Reverse Fabric Simulation Completion Method

[0101] 2.1 Fabric Simulation Filtering Algorithm

[0102] Cloth Simulation Filtering (CSF) is a ground point extraction method from LiDAR point clouds based on the cloth simulation principle in a physical model. For example... Figure 2 As shown, the acquired ground point cloud data is first inverted. Then, a cloth mesh model with certain stiffness and relaxation characteristics is placed above the ground, and the cloth mesh model is gradually lowered by gravity. Collision detection is performed during the descent. When a particle's height is lower than the minimum elevation of the nearest laser point, the particle is marked as a fixed point and anchored at the current lowest position. Then, based on the interaction forces of the particles, particles with excessively large positional differences are pulled upwards for adjustment. This process is repeated until the change in particle displacement is small enough or the maximum number of iterations is reached, at which point the cloth mesh model will completely conform to the ground.

[0103] Meanwhile, the steep terrain causes internal forces to pull particles upwards, preventing the cloth mesh model from perfectly conforming to the ground when it's higher at the top and lower at the bottom. CSF provides a post-processing procedure to detect immovable particles in the four neighborhoods of each movable particle and calculate the height difference between the corresponding locations. If the height difference is less than a preset threshold, the location is marked as a ground point.

[0104] 2.2 Stress Analysis of Polar Coordinate Cloth Mesh Model

[0105] The equations of motion for particle m in polar coordinates are shown in the following formulas.

[0106]

[0107] in, Indicates radial acceleration. Indicates radial velocity, Represents angular acceleration. F represents angular velocity. rF is the radial contraction force along the radial direction. θ A lateral force perpendicular to the radius changes the object's velocity about its center. Since the particle is restricted to radial motion rather than angular motion, this means the object's angular velocity... Therefore, the object will not rotate around the pole, but will only undergo radial displacement. In this case, the angular motion equations no longer apply, and the radial motion equations can be simplified to the following form:

[0108]

[0109] Based on the improved CSF algorithm, this cloth mesh polar coordinate shrinkage algorithm, in the YOZ plane, is also calculated in two independent steps. First, only the gravitational force of the centerline particles is considered; after fixing the particles, the internal forces between them are then considered. As shown in the formula below:

[0110] F r =F G +F int (9)

[0111] Among them, F G F is the gravitational force acting on the particle. int This refers to the internal forces between particles.

[0112] A cylindrical cloth mesh particle model with mass is established on the outer side of the tunnel interface, such as... Figure 3 As shown, its radius is larger than the tunnel radius. It is assumed that the central pole of the tunnel cross-section has a certain mass. For each cloth particle... Analyzing only the projection along the YOZ direction, an attractive force pointing towards the center line is applied. Let the distance between the cloth particle and the central pole be r. Then the formula for the gravitational force on the cloth particle is:

[0113]

[0114] Wherein, the gravitational constant G = 6.674 x 10⁻¹¹ Nm² / kg², M is the mass of the central pole, and m is the mass of the virtual cloth particle.

[0115] Particles, under the influence of gravity, continuously contract inwards. Collision detection is performed on moving particles, and particles that penetrate the tunnel surface are repositioned to the tunnel surface and set to an immovable state. For example... Figure 4 As shown.

[0116] Because the particle distribution on the tunnel surface is uneven and contains cavities, a very small number of movable particles are uncontrollably pulled inward by gravity. Therefore, internal forces are considered after gravitational displacement.

[0117] Two particles in this invention The internal forces are applied using Position-Based Dynamics (PBD), which directly modifies position rather than calculating forces and accelerations. Physical constraints are satisfied through multiple iterations, and position correction is typically proportional to the constraint violation velocity. This process can be understood as a special virtual spring system where a radial spring exists between each adjacent particle, and the natural states of these springs have the same radial distance (projected onto the YOZ plane).

[0118] for Particles, with a radial distance of r1, for Particles, with a radial distance of r2, Let r1 be the direction vector, at... The mathematical expression for the particle radial difference vector is:

[0119]

[0120] When both particles can move The force formula is:

[0121]

[0122] This is a vector force, with its direction along it. It only acts radially. α(t) is a correction coefficient based on the number of iterations, which eventually converges to 0.5.

[0123] When a single particle When the object is movable, the formula for correcting the force is:

[0124]

[0125] Where β(t) is a correction coefficient based on the number of iterations, which eventually converges to 1.

[0126] The correction coefficient changes with the number of iterations, exhibiting a relaxation process. Smaller coefficients are used in the initial iterations to avoid system oscillations. As iterations progress, the coefficients gradually increase to ensure constraint satisfaction. The final convergence value (0.5 or 1) represents the displacement distribution under ideal constraints. Each particle only processes its own constraints, relying on the iteration process to propagate constraint effects without moving other particles. because It has its own constraints to handle this, and achieves global consistency through multiple iterations.

[0127] 3. Point cloud sampling of mesh model

[0128] For the fabric mesh model constructed close to the outer surface of the tunnel, point cloud sampling is required for subsequent processing. This point cloud sampling consists of three steps: First, the mesh model is typically composed of a large number of triangular meshes. The area of ​​each triangle is calculated using the cross product of vectors. Then, based on a preset sampling density, the corresponding number of sampling points is determined according to the area of ​​the triangles. Finally, a uniformly distributed random point cloud is generated within each triangular mesh. After generating point clouds in each triangle, the tunnel point cloud is finally completed.

[0129] To obtain the coordinates of the three vertices of a triangle, such as... Figure 5 As shown, denoted as point point point The area of ​​a triangle can be calculated using the cross product of vectors, as follows:

[0130]

[0131] For each triangle, the number of basic sampling points is determined by multiplying the triangle's area by a preset sampling density. For the decimal part, a probabilistic method is used to determine whether to add a point.

[0132] For each point to be generated within the triangle, perform the following steps: Generate two random numbers x and y in the interval [0,1]. If x + y > 1, adjust them so that x = 1 - x and y = 1 - y. Then calculate the centroid coordinates. Given a = 1 - xy, b = x, and c = y, make the coordinates of the centroid lie within the triangle. The internally generated point Q = aA + bB + cC, such as Figure 6 As shown:

[0133] The mesh model is sampled according to a preset sampling density. The resulting 3D point cloud tunnel model is compared before and after sampling. Figure 7 As shown.

[0134] II. Experiments and Results

[0135] 1. Point cloud tunnel data acquisition and processing

[0136] Based on the need for point cloud completion technology verification, this study conducted an engineering application test in a certain coalfield. The test area was selected as the point cloud data acquisition sites for the 21406 main haulage roadway working face and the 21407 return airway in the fourth panel of the 2-1 coal seam. The 21406 main haulage roadway working face adopts a rectangular cross-section design, with a net width of 4.8m and a net height of 2.95m, forming a passage space with a net cross-sectional area of ​​14.4m2. The 21407 return airway also has a rectangular cross-section configuration, with a net width of 5.4m, a net height of 3.75m, and a net cross-sectional area of ​​20.25m2, and adopts a single support mode of anchor mesh spraying.

[0137] The geological conditions of the test area are as follows: the average burial depth of the coal seam is approximately 650m, the coal thickness varies from 2.95m to 5.27m, the average coal seam thickness is 4.0m, the strata dip angle is within the range of 1° to 3°, and a sandy mudstone interbedded with gangue layer of 0.2m to 0.4m thickness is developed in the middle of the coal seam. A 6m wide safety coal pillar is left in the return airway and goaf area of ​​the working face. Technicians used a portable 3D laser scanning device to carry out point cloud acquisition operations in the 21406 main haulage roadway working face section and the 21407 return airway, respectively, to provide basic data support for the point cloud completion method.

[0138] The collected raw tunnel point cloud data is massive in volume and contains a large amount of non-target information due to the complex and diverse underground environment. Noise points generated by advanced support, equipment pipelines, and personnel activities often obscure the true tunnel outline, while some randomly distributed outliers may interfere with subsequent geometric analysis. To ensure the purity of the experimental data, the raw data was first preprocessed manually to remove noise and outliers one by one. After processing, the point cloud was checked from different perspectives to confirm that all irrelevant points had been completely removed.

[0139] 2. Performance Evaluation and Comparison

[0140] This invention uses custom parameters based on the CSF algorithm. The rigidity coefficient (RI) controls the tightness of terrain fitting by adjusting the fabric stiffness; the maximum number of iterations (Mi) is used as the basis for particle collision detection and internal force magnitude; the attraction strength (As) is responsible for regulating the strength of the gravitational field between fabric particles; and the tunnel detail (Td) is used to refine the tunnel details, and the smaller the Td, the better the tunnel detail is contained.

[0141] Lower stiffness values ​​enhance the fabric's flexibility, resulting in better tunnel contour fit; reducing the tunnel detail dimension parameter helps improve the algorithm's ability to capture detailed features of the tunnel surface. Given that the influence of these two parameters is relatively clear, this invention will focus on exploring the impact of the two core parameters, maximum number of iterations and attraction strength, on algorithm performance.

[0142] 2.1 Single-angle, single-sided, irregularly shaped roadway (partially trapezoidal roadway)

[0143] Rectangular cross-section roadways are often used in main haulage roadways with good surrounding rock stability. Their square geometry maximizes the cross-sectional utilization coefficient and facilitates the arrangement of multiple conveyor belts and various pipeline facilities. During construction, the stress concentration at the four right angles of this type of roadway needs to be addressed, typically using anchor-mesh-shotcrete combined support or cast-in-place concrete lining to ensure long-term stability. Single-angle, single-sided irregular roadways are non-standard cross-sectional structures formed under specific geological conditions and mining disturbances. Their geometric characteristics are characterized by local abrupt changes at a certain sidewall or bottom corner, breaking the symmetry of traditional rectangular roadways. This invention discusses the wrapping of the roadway by the distributed mesh particles under this irregular shape.

[0144] This study uses experimental tunnel data in point cloud format. A computable geometric model was obtained through meshing, yielding a measured surface area of ​​238.64 m², corresponding to 1,003,965 point clouds. Based on this, the average surface sampling density of the preprocessed data was calculated to be 4057 points / m². 2 This density parameter serves as a benchmark for point cloud completion in the cloth mesh particle system, guiding the subsequent point cloud data generation process. For example... Figure 8 As shown.

[0145] (1) Analysis of the impact of the maximum number of iterations on the roadway encapsulation

[0146] This invention discusses and tests the effect of the maximum number of iterations (Mi) on the particle wrapping properties of the fabric under the conditions of Td = 0.1 m and AS = 8. Figure 10 The algorithm generates cloth mesh particles, and the generation results are compared under different preset values.

[0147] Based on the analysis of experimental phenomena, Mi has a significant impact on the deformation adaptability of the fabric mesh particle system. When Mi is too small, the fabric particles do not conform well to the roadway, resulting in large gaps (such as...). Figure 9 (a) shows); as the iteration parameter values ​​increase, a high-precision fit with the target contour can be achieved (e.g., Figure 9 (b) shows. However, when Mi reaches 170, it was observed that some mesh nodes experienced a magnification effect of the correction factor due to excessive iteration, resulting in a decrease in inter-particle constraint force and thus producing an abnormal phenomenon of local nodes shifting inward (e.g. Figure 9 (d) As shown; when the iteration parameter is increased to 185, the internal constraint correction mechanism becomes unbalanced, resulting in excessive coverage of the target tunnel geometry by the cloth particles, exhibiting excessive shrinkage characteristics, which is not conducive to the construction of a complete peripheral structure model (such as...). Figure 9 (f) is shown.

[0148] As shown in Table 1, the wrapping rate index defined in the table represents the quantitative relationship between the reconstructed surface area of ​​the cloth mesh particles and the original tunnel surface area. This parameter can accurately reflect the particle system's ability to fit the deformation of the target geometry. The point cloud generation rate describes the proportional relationship between the number of reconstructed particles and the size of the original point cloud. Due to the geometric defects in the original tunnel caused by pipeline facilities, the surface area of ​​the reconstructed particle system and the number of point clouds are increased compared to the original data.

[0149] The data shows that an excessively large Mi results in an excessively high wrapping rate and point cloud generation rate, reflecting excessive contraction; an excessively small Mi results in insufficient attraction, weak wrapping, and a loose and uncompacted appearance, leading to a high wrapping rate and point cloud generation rate. Comparative analysis reveals that when Mi is 160, the wrapping rate is the lowest, and the point cloud generation rate is also relatively low, indicating greater accuracy.

[0150] Table 1. Analysis of the wrapping effect of the maximum iteration count parameter.

[0151] Maximum number of iterations (Mi) Reconstructed surface area Number of point clouds generated Package rate Point cloud generation rate 60 268.41 1089071 112.47％ 108.48％ 160 264.75 1074228 110.94％ 107.00％ 165 266.65 1081898 111.74％ 107.76％ 170 266.84 1083107 111.82％ 107.88％ 180 337.12 1367842 141.27％ 136.24％ 185 420.88 1707675 176.37％ 170.10％

[0152] (2) Analysis of the influence of attraction intensity on tunnel envelopment

[0153] This invention discusses and tests the effect of attraction intensity (As) on the encapsulation of fabric particles under the condition that the tunnel detail dimension Td = 0.10 meters and Mi = 160. Figure 11 The algorithm generates cloth mesh particles, and the generation results are compared under different preset values.

[0154] Based on experimental observations, As also affects the deformation adaptability of fabric mesh particles. The magnitude of the attraction is directly proportional to As and inversely proportional to the square of the distance. When As is small, the centripetal force on the particles is weak, and the particles remain relatively dispersed, resulting in a slower contraction rate. This makes it difficult to construct a tightly packed outer structure model, and gaps exist between the top and bottom of the channels and the original channels (e.g., ...). Figure 10 (as shown in (a)). As As increases, the distance between the generated cloth mesh particles and the original alleyway becomes smaller and smaller until it closely fits the target contour (as shown in (a)). Figure 10 (d) As is shown. When As is large, particles experience a stronger centripetal force and tend to cluster towards the central axis. Particles contract inward more quickly, forming a denser structure, which may lead to excessive aggregation of particles near the axis (e.g., Figure 10 (c) is shown.

[0155] As shown in Table 2, an excessively large As value leads to excessively high wrapping rate and point cloud generation rate, while an excessively small As value results in insufficient wrapping of the aisle, also leading to relatively high wrapping rate and point cloud generation rate. Comparative analysis shows that when As is 7.50, the wrapping rate is the lowest, and the point cloud generation rate is also relatively low, resulting in more perfect data.

[0156] Table 2. Analysis of the Enveloping Effect of Attraction Strength Parameters

[0157]

[0158]

[0159] 2.2 Double-angled, double-sided irregular tunnel (trapezoidal tunnel)

[0160] Due to the limited width of the coal pillar, small coal pillar roadways experience significant plastic deformation at their base corners under concentrated stress due to long-term mining disturbance. As mining time increases, the floor continues to bulge upwards, while the sidewalls contract inwards. The anchor bolts originally installed at the base corners are gradually encased and buried by the deformed floor and sidewall rock. Through this deformation process, the roadway cross-section gradually evolves from a rectangular shape to a trapezoidal shape that is wide at the top and narrow at the bottom. This irregular geometric feature also presents new technical requirements for the envelope simulation of the fabric mesh particles. This invention focuses on the geometric characteristics of such trapezoidal deformed roadways and deeply analyzes the adhesion effect of fabric particles under irregular cross-sectional conditions and its influencing mechanism.

[0161] This study uses point cloud format experimental tunnel data and obtains a computable geometric model through gridding, measuring a surface area of ​​271.00.

[0162] m2 corresponds to 1,275,186 point clouds. Based on this, the average sampling density of the preprocessed data surface is calculated to be 5,280 points / m. 2 This density parameter serves as a benchmark for point cloud reconstruction of the cloth mesh particle system, guiding subsequent point cloud data generation processes. For example... Figure 11 As shown.

[0163] (1) Analysis of the impact of the maximum number of iterations on the roadway encapsulation

[0164] Under the conditions of a fixed tunnel detail size Td of 0.10 meters and As set to 7.50, this invention focuses on analyzing the effect of the maximum number of iterations (Mi) parameter on the tunnel bonding effect of cloth particles. The cloth mesh particle results obtained after algorithm execution are as follows: Figure 12 As shown in the figure, the differences in particle generation effects under different preset iteration numbers are clearly demonstrated.

[0165] Experimental results revealed that Mi plays a crucial role in regulating the deformation response of the fabric mesh particles. When the number of iterations is set too low, the adhesion between the particles and the tunnel surface is poor, leaving obvious gaps at the contact interface (e.g., Figure 12 (as shown in (a)); with a reasonable increase in the value of this parameter, the system can achieve a precise matching state with the target geometric contour (as shown in (a)); Figure 12 (b) shows). However, when the number of iterations increased to 170, it was found that some mesh elements, due to the cumulative amplification effect of the correction coefficients during the iteration process, caused the constraint relationship between particles to loosen, thus causing individual nodes to shift unexpectedly inward (e.g. Figure 12 (d) As shown; when the iteration number is further adjusted to 185, the self-correction function of the internal constraint system becomes disordered, causing the cloth particles to have an overly tight envelope on the geometry of the alleyway, exhibiting obvious over-contraction behavior. This phenomenon is not conducive to the effective establishment of the complete external model (such as...). Figure 12 (f) is shown). The corresponding data is shown in Table 3.

[0166] Table 3. Analysis of the wrapping effect of the maximum iteration count parameter.

[0167]

[0168]

[0169] (2) Analysis of the influence of attraction intensity on tunnel envelopment

[0170] Under the conditions of a fixed tunnel detail size Tc of 0.10 meters and Mi set to 160, this invention focuses on analyzing the effect of the attraction intensity (As) parameter on the tunnel bonding effect of fabric particles. The fabric mesh particle results obtained after algorithm execution are as follows: Figure 13 As shown in the figure, the differences in particle generation effects under different preset iteration numbers are clearly demonstrated.

[0171] When As is set too low, the radial convergence force on the fabric particles is insufficient, resulting in a loose distribution between particles and a slow inward convergence process. This makes it difficult to effectively conform to the upper-wide, lower-narrow geometric contour of the trapezoidal channel, leading to noticeable gaps in both the wide upper region and the narrow lower region of the channel (e.g., Figure 13 (a) and Figure 13 (b) As the As parameter gradually increases, the fitting degree between the cloth mesh particles and the trapezoidal cross-section continues to improve, and the particles gradually move closer to the actual boundary of the tunnel, ultimately achieving precise fitting with the irregular contour (as shown in [example]). Figure 13(d) shows. However, when As increases excessively, the radial tension on the particles becomes too strong, causing them to converge rapidly towards the geometric center, resulting in excessive contraction. This is especially true in the narrowing bottom region of the trapezoidal channel, where particles may experience excessive contraction (e.g., Figure 13 (c) is shown). The corresponding data is shown in Table 4.

[0172] Table 4. Analysis of the Enveloping Effect of Attraction Strength Parameters

[0173] Intensity of attraction (As) Reconstructed surface area Number of point clouds generated Package rate Point cloud generation rate 2.50 284.69 1503139 105.05％ 117.88％ 4.00 283.79 1498460 104.72％ 117.51％ 5.00 283.10 1494825 104.47％ 117.23％ 7.50 282.88 1493616 104.39％ 117.14％ 8.50 284.07 1500003 104.82％ 117.63％ 10.00 511.43 2700561 188.72％ 221.78％

[0174] 3. Lane point cloud completion effect

[0175] 3.1 Determination of preset sampling density

[0176] Obtain data for a tunnel with a length of 14.70 meters, a width of 9.91 meters, and a height of 4.84 meters, containing 1,063,961 point clouds. The preset sampling density is determined based on the original tunnel. The point cloud density of the original tunnel can be calculated using CloudCompare, generating a color gradient as shown below. Figure 14 As shown, the point cloud density can also be viewed by saving the point cloud in TXT format. The generated point cloud density data shows that the maximum point cloud density is 14310 points / m². 2 The minimum point cloud density is 340 points / m². 2 The median point cloud density is 3020 points / m². 2 The average point cloud density of all its data is 3637 points / m². 2 .

[0177] To determine the optimal sampling density for converting the final cloth mesh model into a point cloud, this invention is based on the density distribution characteristics of the original point cloud (such as...). Figure 12 As shown in the figure, four key statistical indicators—maximum, minimum, median, and average—were selected as preset parameters for the resampling (i.e., point cloudification) process. The resampling results under different parameters are shown below. Figure 15 As shown.

[0178] Experimental results clearly demonstrate that the choice of sampling density has a decisive impact on the quality of the final point cloud. Using the maximum density ( Figure 15 (a) Resampling resulted in severe oversampling, generating as many as 4,664,792 points, whose shape was almost identical to the original cloth mesh topology, thus losing the geometric meaning of point cloudification. Conversely, using the minimum density ( Figure 15 (b) results in significant undersampling, generating only 111,064 points, which is far less than the original data, leading to a severe loss of geometric details and the model being unable to effectively represent them.

[0179] In comparison, based on median density ( Figure 15(c) and the average density ( Figure 15 The resampling results in (d) all presented a more reasonable point cloud distribution visually, similar in shape to the original data. In quantitative analysis, the number of point clouds generated using the density average (1,185,617) was closer to the magnitude of the point cloud in the original data, while the median results (984,537) were relatively fewer. Considering that the completed model should increase the number of points to fill gaps while maintaining the characteristics of the original data, the average parameter is clearly better at maintaining the statistical consistency of the data.

[0180] In summary, to ensure that the statistical characteristics of the completion results are highly consistent with the original data and to avoid biases introduced by improper density parameter selection, all experiments in this invention use the average density of the original point cloud as the baseline parameter for fabric mesh point cloudification. This ensures that the generated point cloud matches the source data in terms of order of magnitude and achieves optimal visual fidelity and density uniformity.

[0181] 3.2 Lane point cloud completion effect

[0182] like Figure 16 As shown, for the coal mine return airway environment, this experiment identified four typical locations as key monitoring areas for in-depth data collection. The interference sources in each monitoring area are as follows: [Monitoring Points] Figure 16 (a) Interference signals generated by advanced support equipment exist in the area; measuring point Figure 16 (b) The main source of interference at the location is underground transport equipment; measuring point Figure 16 The interfering factor at point (c) is the cable transport system; measuring point Figure 16 (d) Area is affected by the materials piled up on site, resulting in corresponding interference. The noise interference levels at these four measuring points differ significantly, and the specific roadway geometric parameters are detailed in Table 5.

[0183] Table 5 Basic Data of Lanes

[0184] Serial Number Length (m) Width (m) Height (m) Point cloud quantity a 37.206 12.650 6.575 3486516 b 35.716 10.822 8.464 2920383 c 32.493 12.130 5.883 2587595 d 40.612 12.586 4.620 3623644

[0185] This invention performs systematic preprocessing operations on the acquired raw point cloud data of the tunnel, such as... Figure 17 As shown, after noise filtering, although the interference information in the tunnel point cloud data is removed, some valid data is inevitably lost, resulting in irregular blank areas on the tunnel surface. Figure 17 (a) indicates a structural deficiency in the top and bottom slabs. Figure 17 (b) indicates missing point clouds in the base area. Figure 17 (c) Missing point cloud data in the top plate area. Figure 17(d) Irregular data gaps appear inside the roadway. As shown in Table 6, the key parameters of the algorithm are strictly controlled within the range specified in Table 6 for fine-tuning. The optimal parameter combination is determined through multiple sets of comparative experiments to ensure that the completion results not only maintain the true geometric characteristics of the roadway, but also meet the ideal data integrity requirements.

[0186] Table 6 Parameter Setting Table

[0187] Parameter settings scope Parameter settings scope Fabric rigidity 1 Maximum number of iterations 160 Tunnel Detail Dimensions 0.10m Intensity of attraction 7.50

[0188] The visualization results of the completion effect are as follows Figure 18 As shown, this invention effectively overcomes the technical limitations of traditional point cloud processing methods when dealing with large areas of blank data. Then, the invention calculates the CD values ​​for four scenes. Figure 18 (a) The CD value is 0.07. Figure 18 (b) The CD value is 0.08. Figure 18 (c) The CD value is 0.09. Figure 18 (d) The CD value is 0.09.

[0189] Before the completion method was implemented, the 3D point cloud data of the coal mine roadway exhibited obvious data incompleteness, such as... Figure 19 As shown in Figure (a), the specific manifestations are: numerous irregularly distributed data gaps exist on the surface of the surrounding rock in the tunnel, along with varying degrees of porosity and relatively low point cloud density. For example... Figure 19 (b) As shown in the figure, the completed point cloud effectively fills in most of the missing point cloud data, effectively fills in the holes, and also increases the density of the point cloud.

[0190] III. Effect Analysis

[0191] 1. Algorithm Validity Analysis

[0192] The superiority of this method lies in its unique paradigm, successfully circumventing the inherent limitations of existing mainstream technologies. Unlike geometric methods that rely on strictly symmetric priors, this method does not make such assumptions, thus enabling high-fidelity reconstruction of asymmetric deformation roadways caused by ground pressure. Compared to data-driven deep learning models, this method does not require massive amounts of training data, avoiding the risk of insufficient model generalization ability; more importantly, its global physical convergence mechanism exhibits a macroscopic structural perception capability far exceeding local feature learning when dealing with large-scale cross-structure occlusion. Therefore, this method demonstrates significant advantages in model realism, void filling fidelity, and generalization ability to different roadway morphologies. This research not only provides an effective tool for accurately acquiring complete three-dimensional roadway information but also lays a solid data foundation for subsequent mine safety monitoring and digital twin applications.

[0193] 2. Sensitivity analysis and impact of key parameters

[0194] The parameter system of this method references the classic CSF framework and is customized for tunnel scenarios. Among them, the tunnel detail dimension (Td) and stiffness coefficient (RI) are key parameters for setting the basic physical properties of the simulated cloth, primarily affecting the model's static fit to the terrain. Correspondingly, the maximum number of iterations (Mi) and attraction intensity (As) jointly dominate the dynamic convergence process of the cloth simulation.

[0195] In the parameter influence analysis, we found that the interaction between Td and RI is relatively clear. Td defines the resolution of the mesh along the tunnel axis. For example... Figure 20 As shown in (a), a smaller Td value (e.g., 0.10) produces a denser particle distribution, giving the simulated fabric high flexibility, thus accurately capturing and preserving key details such as seams and microcracks on the lining surface. Conversely, a larger Td value (e.g., 5.00) reduces the fabric's resolution, causing it to tend to span fine structures, resulting in smoothing of detailed features, such as... Figure 20 As shown in (b).

[0196] The stiffness coefficient (RI) determines the inherent "stiffness" of the fabric from a physical perspective. For geometrically complex objects such as underground tunnels, a lower RI value is a prerequisite for ensuring good wrapping. It allows the fabric to bend sufficiently to adapt to the rapid changes in the lining surface, achieving precise geometric fit. Figure 21 (a)). However, excessively high RI values ​​can make the fabric too rigid, failing to effectively conform to curved surfaces and resulting in significant "underfitting" at structural changes, leading to poor filtering performance. Figure 21 (b)).

[0197] In summary, while the settings of Td and RI are important, their selection focuses more on the trade-off between "detail fidelity" and "macro-level smoothness," and their influencing mechanisms are relatively independent. In contrast, the maximum number of iterations (Mi) and the attraction strength (As) have a more profound impact on the algorithm's final performance and exhibit significant coupling effects. They are key variables determining whether the algorithm can converge to the optimal state. Therefore, the following section will focus on discussing the mechanisms of action and interrelationships of these two core parameters. Figure 22 (a) and Figure 23 As shown in (a), analysis of Mi reveals a high degree of consistency in the CD value variation curves of the two roadways. Experimental data shows that when Mi increases from 60 to 160, the CD value maintains a stable performance plateau in both roadway models, reaching its minimum at Mi = 160, as indicated by the red reference line in the figure. This indicates that the method has achieved sufficient convergence at this stage. However, exceeding this threshold leads to a significant deterioration in the CD value. After the system reaches mechanical equilibrium, continuous iteration will disrupt the established stable structure, resulting in a degradation of model accuracy.

[0198] according to Figure 22 (b) and Figure 23 As shown in (b), As determines the key trade-off between underfitting and overfitting, and its influence exhibits a typical "U"-shaped characteristic on the CD curve. When the As value is too low, the particle contraction force is insufficient, resulting in inadequate wrapping of the roadway surface (underfitting); conversely, when the As value is too high, excessive tension can cause particles to penetrate sparse areas or produce distortion at sharp geometric points (overfitting). Both types of roadways with different morphologies achieve optimal CD values ​​within the As range of approximately 7.00-7.50, as shown in... Figure 22 (b) and Figure 23 As shown by the red reference line in (b), the universality of this equilibrium point is demonstrated.

[0199] In summary, the effectiveness and robustness of this method highly depend on the precise calibration of the physical simulation parameters. Experiments confirm that the combination of As in the range of 7.00-7.50 and Mi of approximately 160 constitutes the optimal solution space for the method. In practical applications, calibrating and adopting this parameter combination is a necessary prerequisite for achieving high-fidelity completion of point clouds of different roadway morphologies.

[0200] 3. Method limitations

[0201] Although the reverse cloth simulation completion method proposed in this invention has demonstrated its superiority in many aspects, its current implementation still has some limitations, which points the way for future research.

[0202] First, the core limitation lies in the scalability of the method. Current methods demonstrate high computational performance and excellent wrapping effects when processing segmented, short-distance tunnel point clouds. However, when directly applied to ultra-large-scale raw scan data covering the entire mining area, the iterative physical simulation process leads to a significant increase in computation time. Furthermore, in long-distance, large-scale scenarios, the global convergence of a single model may sacrifice local accuracy, resulting in a decrease in wrapping quality. Therefore, future research should focus on performance optimization and adaptability to large-scale scenarios.

[0203] Secondly, this method exhibits high sensitivity to key physical parameters. As demonstrated in this invention, the optimal performance of the method is constrained within a relatively narrow parameter window, which increases the debugging cost for its application in different scenarios. An important future direction is to study adaptive parameter adjustment mechanisms, for example, by analyzing the geometric features of the input point cloud (such as average curvature and point cloud density) to automatically recommend or set optimal parameters, thereby improving the automation level and robustness of the algorithm.

[0204] IV. Conclusion

[0205] 1. This invention proposes a reverse fabric simulation completion method for coal mine roadways, filling a gap in the field for methods to handle large-scale irregular voids. This method achieves robust completion of the roadway model through a series of steps, including point cloud preprocessing, centerline extraction based on principal component analysis, core axial-guided fabric shrinkage fitting, and final point cloud resampling. Experimental results show that this method can generate geometrically continuous and topologically complete completed surfaces even when dealing with severe data loss caused by large equipment occlusion, scanning blind spots, or denoising.

[0206] 2. This study conducted a systematic sensitivity analysis of the key physical parameters of the method—the maximum number of iterations and the attraction strength. The study found that the number of iterations is directly related to the model's convergence; the algorithm reaches its optimal convergence state when Mi is approximately 160. Excessive iterations can lead to the degradation of the established stable structure. As dominates the balance between underfitting and overfitting, and its influence exhibits a typical "U"-shaped characteristic on the accuracy curve. Experiments confirmed that within a narrow range of As of 7.00-7.50, the method achieves optimal performance in various tunnel morphologies. This finding not only reveals the intrinsic mechanism of the model parameters but also provides solid theoretical and data support for calibrating the optimal operating range (Mi≈160, As≈7.50) for this method in engineering applications.

[0207] 3. To verify the effectiveness and robustness of the proposed method under real-world conditions, experiments were conducted using point cloud data from four typical roadways affected by different interference sources (such as support equipment and transport vehicles). After systematically denoising the original data, the proposed completion method was applied to four typical missing scenarios caused by interference removal (structural missing roof and floor slabs, localized missing areas, and irregular internal voids). Experimental results show that the method can effectively repair large-scale data gaps. Quantitative evaluation shows that the completion accuracy for all scenarios reached a CD value below 0.10 (CD value range of 0.07-0.09). Visual comparison also confirms that the completed point cloud significantly improves geometric integrity, void filling, and density. This experiment fully demonstrates the superior performance and engineering practical value of the proposed method in processing real and complex roadway point cloud data.

Claims

1. A method for reverse fabric simulation and completion of 3D point clouds in complex tunnels, characterized in that: Includes the following steps: S1. Use 3D laser scanning technology to obtain 3D point cloud of underground roadway scene, calculate the centroid of 3D point cloud by principal component analysis, establish polar coordinate system with the centroid of 3D point cloud as origin, and translate 3D point cloud into polar coordinate system. S2. Construct a cloth mesh model on the outside of the alleyway. The cloth particles in the cloth mesh model are shrunk by the centrifugal force of the centroid of the three-dimensional point cloud until the distance between the cloth particles and the three-dimensional point cloud is less than the set threshold or the maximum number of iterations is reached. The cloth particles then stop moving. S3. Randomly sample the triangular mesh in the generated cloth particles to obtain the completed 3D point cloud tunnel model.

2. The method for reverse fabric simulation and completion of complex tunnel 3D point cloud as described in claim 1, characterized in that: Step S1 specifically includes the following steps: S11. A 3D point cloud of the underground tunnel scene is obtained using 3D laser scanning technology. The centroid of the 3D point cloud is the average value of all points. The formula for calculating the centroid of the 3D point cloud is: in, is the centroid of the 3D point cloud, and n is the number of points in the 3D point cloud. It is the position vector of the i-th point in the 3D point cloud; S12. Obtain the centroid vector and position vectors of each point in the 3D point cloud, and calculate the covariance of the 3D point cloud. The calculation formula is as follows: Expand it into a 3×3 matrix form: S13. The eigenvalues ​​and eigenvectors of the covariance matrix satisfy the equation: in, λ is the eigenvector, and λ is the eigenvalue corresponding to the 3D point cloud; S14. Establish a polar coordinate system with the centroid of the 3D point cloud as the origin. Rotate the 3D point cloud so that its principal direction is aligned with the x-axis in the polar coordinate system. The rotation transformation formula is: S15. Transform the coordinates of the 3D point cloud to the polar coordinate system. The transformation formula is as follows:

3. The method for reverse fabric simulation and completion of complex tunnel 3D point cloud as described in claim 2, characterized in that: Step S2 specifically includes the following steps: S21. Invert the three-dimensional point cloud in polar coordinates onto the ground; S22. Place the preset cloth mesh model on the 3D point cloud. The cloth particles in the cloth mesh model gradually sink under the action of gravity. S23. During the descent of the fabric particles, collision detection is performed until the height of the fabric particle is lower than the minimum elevation of the nearest laser point. At that point, the fabric particle is marked as a fixed point and anchored at the current lowest position. S24. Based on the interaction forces of the cloth particles, pull up and adjust the cloth particles with large positional differences until the change in the displacement of the cloth particles is small enough or the maximum number of iterations is reached, at which point the cloth particles stop moving and the cloth mesh model completely conforms to the ground.

4. The method for reverse fabric simulation and completion of complex tunnel 3D point cloud as described in claim 3, characterized in that: In step S22, the equation of motion for the fabric particles during their sinking process in polar coordinates is: in, Indicates radial acceleration. surface Indicates radial velocity, Represents angular acceleration. F represents angular velocity. r F is the radial contraction force along the radial direction. θ It is a lateral force perpendicular to the radial direction; After simplification, we get:

5. The method for reverse fabric simulation and completion of complex tunnel 3D point cloud as described in claim 4, characterized in that: In step S22, the gravitational force acting on the fabric particles is: Where G is the gravitational constant, M is the mass of the central pole, and m is the mass of the cloth particle.

6. The method for reverse fabric simulation and completion of complex tunnel 3D point cloud as described in claim 5, characterized in that: In step S23, when the fabric particles undergo collision detection during their descent, if both particles can move, the fabric particles... The force formula is: in, For fabric particles With fabric particles The radial difference vector; α(t) is the correction coefficient based on the number of iterations; When there are only single fabric particles When movable, fabric particles The force formula is: Where β(t) is a correction coefficient based on the number of iterations.

7. The method for reverse fabric simulation and completion of complex tunnel 3D point cloud as described in claim 6, characterized in that: Step S3 specifically includes the following steps: S31. Obtain the coordinates of the three vertices of the triangular mesh in the generated cloth particles, and denote them as points. point point The area of ​​a triangular mesh is calculated using the cross product of vectors, and the formula is as follows: S32. For each triangular grid, the number of basic sampling points is determined by multiplying the area of ​​the triangular grid by the preset sampling density. S33. For each point to be generated within the triangular mesh, generate two random numbers x and y in the interval [0,1]. If x + y > 1, adjust the values ​​so that x = 1 - x and y = 1 - y. Then calculate the centroid coordinates of the triangular mesh. Where a = 1 - xy, b = x, c = y, so that the centroid coordinates generate point Q = aA + bB + cC within the triangular grid; S34. Based on the preset sampling density, perform point cloud sampling on all triangular meshes in the cloth mesh model to generate a completed three-dimensional point cloud tunnel model.

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