A three-dimensional geometric modeling method and system for precast concrete components

Abstract

This invention relates to the field of three-dimensional geometric modeling technology, specifically to a three-dimensional geometric modeling method and system for precast concrete components. The method includes the following steps: acquiring the three-dimensional contour data of the precast component substrate and a specified bonding surface region; calling the input shear key geometric feature parameters; establishing a local coordinate system for the bonding surface; and calculating the peak height, wavelength, and arrangement period values ​​within the local coordinate system based on the shear key geometric feature parameters. In this invention, a geometric offset vector is used to drive the mesh vertices to move along the normal direction to generate a replaced geometric surface, realistically restoring the physical convex-concave morphology of the rough concrete surface. By identifying the geometric gap between the edge of the replaced surface and the original side surface, calculating the stitching path, and generating transition patches for geometric closure, the topological cracks caused by vertex displacement are eliminated, ensuring that the generated solid boundary representation model possesses strict watertightness.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional geometric modeling technology, and in particular to a three-dimensional geometric modeling method and system for precast concrete components. Background Technology

[0002] Three-dimensional geometric modeling technology mainly utilizes computer graphics, computational geometry principles, and mathematical algorithms to mathematically describe, construct, process, and analyze the geometric shape, topological structure, and surface properties of physical objects in a virtual digital space.

[0003] Current 3D geometric modeling techniques, when dealing with complex surfaces with a massive number of tiny, repetitive features, typically employ solid geometry construction methods with Boolean operations or rely on general surface reconstruction algorithms. However, when modeling precast concrete components with thousands of shear keys or rough textures, performing Boolean summation or difference operations on each feature leads to an exponential increase in computational load. This is prone to topological errors or computational crashes due to floating-point precision issues, reducing modeling efficiency. Furthermore, using a uniform mesh density to capture minute surface details results in a large amount of redundant vertex and face data in flat areas, leading to massive model file sizes and slowing down rendering and subsequent calculations. Therefore, improvements are needed. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and to propose a three-dimensional geometric modeling method and system for precast concrete components.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a three-dimensional geometric modeling method for precast concrete components, comprising the following steps: Obtain the three-dimensional contour data of the precast component substrate and the specified joint surface area, call the input shear key geometric feature parameters, establish a local coordinate system of the joint surface, calculate the peak height value, wavelength value and arrangement period value in the local coordinate system of the joint surface according to the shear key geometric feature parameters, and generate a roughness parameter control matrix. According to the roughness parameter control matrix, UV mapping coordinates are constructed on the bonding surface region. Gray scalar values ​​of corresponding pixels are generated according to the waveform definition in the shear key geometric feature parameters. Elevation displacement gray data is generated. The elevation displacement gray data is mapped to each grid node of the UV mapping coordinates. A virtual geometric texture mapping set is calculated and generated. The virtual geometric texture mapping set is called to perform initial meshing on the bonding surface region, obtain quadrilateral mesh cells, and calculate the mesh warpage index. The mesh warpage index is compared with a preset threshold constant to generate a high-density subdivided mesh topology. Based on the geometric offset vector in the virtual geometric texture mapping set, the mesh vertices in the high-density subdivided mesh topology are driven to move along the normal direction to generate a permuted geometric surface. The geometric gap between the edge contour of the permuted geometric surface and the original side surface of the precast component matrix is ​​identified, the boundary stitching path is calculated, and geometric closure is performed along the path to generate a solid boundary representation model of the precast concrete component.

[0006] Preferably, the step of obtaining the roughness parameter control matrix is ​​as follows: Obtain the three-dimensional contour data of the precast component substrate and the specified bonding surface area, parse the vertex coordinate sequence and patch topology in the three-dimensional contour data, extract the boundary and internal annotations of the bonding surface area, verify the boundary closure and normal consistency, and obtain the three-dimensional contour data and the annotations of the bonding surface area. Based on the three-dimensional contour data and the annotation of the interface region, the edge positioning parameters and normal limit parameters in the input shear key geometric feature parameters are called. The minimum and maximum coordinates are extracted along the boundary of the interface region. The normal direction is statistically analyzed according to the orientation of the facet to form the coordinate range of the interface boundary and the direction of the normal vector. Based on the boundary coordinate range and normal vector direction of the bonding surface, the center point is set as the geometric center of the boundary coordinate range, and the local axis direction is set as determined by the normal vector direction and the principal direction of the boundary. A local coordinate system for the bonding surface is established. Based on the waveform type parameter, peak spacing parameter, and peak amplitude parameter in the shear key geometric characteristic parameters, the peak height value, wavelength value, and arrangement period value are calculated along the local principal axis and written into the matrix according to the row and column index to generate the roughness parameter control matrix.

[0007] Preferably, the steps for obtaining the elevation displacement grayscale data are as follows: Based on the roughness parameter control matrix, a regular sampling grid is established in the joint surface region. The three-dimensional coordinates of the sampling points are projected and normalized according to the principal axis direction of the local coordinate system of the joint surface to form a UV mapping coordinate matrix. The gray scalar value is calculated for each sampling point according to the waveform definition of the shear key geometric feature parameters to generate elevation displacement gray data.

[0008] Preferably, the step of obtaining the virtual geometric texture mapping set is as follows: Calculate the geometric offset vector based on the elevation displacement grayscale data; Based on the geometric offset vector, displacement is applied along the normal direction of the mesh node corresponding to each UV mapping coordinate. The spatial position coordinates of each node are added element by element to the corresponding geometric offset vector to update the three-dimensional coordinate data of all nodes and generate a virtual geometric texture mapping set.

[0009] Preferably, the step of obtaining the grid warpage index is as follows: Based on the virtual geometric texture mapping set, an initial mesh is generated in the bonding area to generate a quadrilateral mesh unit composed of four vertices. The three-dimensional coordinate information of the four vertices of each quadrilateral mesh unit is extracted and a vertex sequence is established. The plane that minimizes the sum of the squared distances from the four vertices to the plane is determined as the best fitting plane. The vertical distance from each vertex to the best fitting plane is calculated to obtain the vertical distance sequence of the quadrilateral mesh unit vertices. The grid warpage index is calculated based on the vertical distance sequence of the vertices of the quadrilateral grid cells.

[0010] Preferably, the step of obtaining the high-density subdivided mesh topology is as follows: The grid warpage index is compared with the threshold constant one by one. For quadrilateral grid cells whose grid warpage index exceeds the threshold constant, diagonal subdivision and edge interpolation are performed. The local topological relationships and node connection relationships after subdivision are recalculated to form a high-density subdivided grid topology.

[0011] Preferably, the step of obtaining the permuted geometric surface is as follows: Based on the geometric offset vector in the virtual geometric texture mapping set, the spatial position coordinates and normal directions of the mesh vertices are read one by one at the mesh vertex level of the high-density subdivided mesh topology. The geometric offset vectors are then superimposed along the normal direction according to the mesh vertex index, and the spatial position coordinates of the mesh vertices are updated to generate the permuted geometric surface.

[0012] Preferably, the steps for obtaining the solid boundary representation model of the precast concrete component are as follows: Based on the replaced geometric surface, extract the edge vertex sequence on the edge contour of the replaced geometric surface according to the boundary direction and construct a continuous polyline. Extract the contour line corresponding to the original side of the precast component substrate and calculate the nearest point-to-point distance from the edge vertex to the original side of the precast component substrate. Identify the continuous segment of the geometric gap according to the distance threshold and generate the boundary stitching path. According to the boundary stitching path, transition patches are generated segment by segment between the edge contour of the replaced geometric surface and the original side surface of the precast component matrix along the boundary stitching path, and closed bands are inserted. The normal direction of the newly generated patches is corrected and the topological index of the high-density subdivision mesh is updated to generate a solid boundary representation model of the precast concrete component.

[0013] The present invention also provides a system comprising: The data acquisition module is used to acquire the three-dimensional contour data of the precast component substrate and the specified joint surface area, call the input shear key geometric feature parameters, establish a local coordinate system of the joint surface, calculate the peak height value, wavelength value and arrangement period value in the local coordinate system of the joint surface according to the shear key geometric feature parameters, and generate a roughness parameter control matrix. The texture generation module is used to construct UV mapping coordinates on the bonding surface region according to the roughness parameter control matrix, generate grayscale scalar values ​​of corresponding pixels according to the waveform definition in the shear key geometric feature parameters, generate elevation displacement grayscale data, map the elevation displacement grayscale data to each grid node of the UV mapping coordinates, and calculate and generate a virtual geometric texture mapping set. The mesh generation module is used to call the virtual geometric texture mapping set to perform initial mesh generation on the bonding surface area, obtain quadrilateral mesh cells, calculate the mesh warpage index, compare the mesh warpage index with a preset threshold constant, and generate a high-density subdivided mesh topology. The geometry generation module is used to drive the mesh vertices in the high-density subdivided mesh topology to move along the normal direction according to the geometric offset vector in the virtual geometric texture mapping set, generate a permuted geometric surface, identify the geometric gap between the edge contour of the permuted geometric surface and the original side of the precast component matrix, calculate the boundary stitching path, perform geometric closure along the path, and generate a solid boundary representation model of the precast concrete component.

[0014] Compared with the prior art, the advantages and positive effects of the present invention are as follows: In this invention, based on the three-dimensional contour data of the precast component substrate and the specified joint surface area, a local coordinate system is established by calling the shear key geometric feature parameters, and key values ​​such as peak height, wavelength, and arrangement period are calculated to generate a roughness parameter control matrix. This achieves digital parameter definition for complex micro-geometric features, avoiding the random errors of manual modeling. UV mapping coordinates are constructed in the joint surface area, and pixel grayscale scalar values ​​and elevation displacement grayscale data are generated based on waveform definition, transforming discrete geometric features into continuous image grayscale information. A virtual geometric texture mapping set is used to calculate the geometric offset vector, providing a data-driven foundation for the batch generation of massive micro-features. By calculating the mesh warpage index of quadrilateral mesh units and comparing it with a threshold constant, recursive subdivision is performed on high-curvature or severely deformed areas to generate a high-density subdivided mesh topology. This adaptive mesh generation strategy significantly reduces the model data volume while ensuring the degree of geometric detail restoration, resolving the contradiction between accuracy and performance. The geometric offset vector is used to drive the mesh vertices to move along the normal direction to generate a permuted geometric surface, realistically restoring the physical convex and concave morphology of the rough concrete surface. By identifying the geometric gap between the edge of the permuted surface and the original side surface, calculating the stitching path, and generating transition patches for geometric closure, the topological cracks caused by vertex displacement are eliminated, ensuring that the generated solid boundary representation model has strict watertightness. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the steps of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0017] Please see Figure 1 This invention provides a technical solution: a three-dimensional geometric modeling method for precast concrete components, comprising the following steps: Obtain the three-dimensional contour data of the precast component substrate and the specified joint surface area, call the input shear key geometric feature parameters, establish a local coordinate system of the joint surface, calculate the peak height value, wavelength value and arrangement period value in the local coordinate system of the joint surface according to the shear key geometric feature parameters, and generate a roughness parameter control matrix. Based on the roughness parameter control matrix, UV mapping coordinates are constructed on the bonding surface region. Gray scalar values ​​of corresponding pixels are generated according to the waveform definition in the shear key geometric feature parameters. Elevation displacement gray data is generated and mapped to each grid node of the UV mapping coordinates. A virtual geometric texture mapping set is calculated and generated. The virtual geometric texture mapping set is called to perform initial meshing of the bonding surface region, obtain quadrilateral mesh cells, calculate the mesh warpage index, compare the mesh warpage index with the preset threshold constant, and generate a high-density subdivided mesh topology. Based on the geometric offset vector in the virtual geometric texture mapping set, the mesh vertices in the high-density subdivided mesh topology are driven to move along the normal direction to generate a permuted geometric surface. The geometric gap between the edge contour of the permuted geometric surface and the original side surface of the precast component matrix is ​​identified, the boundary stitching path is calculated, and geometric closure is performed along the path to generate a solid boundary representation model of the precast concrete component.

[0018] The steps for obtaining the roughness parameter control matrix are as follows: Obtain the three-dimensional contour data of the precast component substrate and the specified bonding surface area, parse the vertex coordinate sequence and patch topology in the three-dimensional contour data, extract the boundary and internal annotations of the bonding surface area, verify the boundary closure and normal consistency, and obtain the three-dimensional contour data and the annotations of the bonding surface area. Based on the 3D contour data and the annotation of the interface region, the edge positioning parameters and normal limit parameters in the input shear key geometric feature parameters are called. The minimum and maximum coordinates are extracted along the boundary of the interface region. The normal direction is statistically analyzed according to the orientation of the facet to form the coordinate range of the interface boundary and the direction of the normal vector. Based on the boundary coordinate range and normal vector direction of the bonding surface, the center point is set as the geometric center of the boundary coordinate range. The local axis direction is determined by the normal vector direction and the principal direction of the boundary. A local coordinate system for the bonding surface is established. Based on the waveform type parameter, peak spacing parameter, and peak amplitude parameter in the shear key geometric characteristic parameters, the peak height value, wavelength value, and arrangement period value are calculated along the local principal axis. The values ​​are written into the matrix according to the row and column index to generate the roughness parameter control matrix.

[0019] Specifically, the process involves acquiring the 3D contour data of the precast component substrate and the specified bonding surface area, reading the 3D model file of the precast component stored in the engineering database (this file is stored in a common 3D data exchange format such as OBJ or IFC), reconstructing the 3D geometric information by reading the file content line by line through a file parsing interface, traversing the vertex data blocks defined in the file, and extracting the spatial coordinate data of each vertex. The process reads data into memory and constructs a vertex index list, while parsing the face definition data block. Based on the vertex indices, three or four vertices are combined to form a face topology. During this process, based on material attribute labels or layer names pre-defined in the model design phase, such as a layer identifier named "Bonding_Zone_01," all face sets belonging to the specified bonding area are selected. Then, the boundary extraction program is started, constructing a half-edge data structure for the selected face sets. Each edge is traversed, and the number of times each edge is referenced is counted. Edges referenced only once are identified as boundary edges of the bonding area, and these boundary edges are connected end-to-end in the connection order. Boundary closure is checked, i.e., whether the starting vertex index of the first boundary edge matches the ending vertex index of the last boundary edge. If they do not match, vertex welding is performed, with a welding distance tolerance set to [value missing]. That is, when the distance between two endpoints is less than the tolerance, they are merged into one vertex to force closure. Then, normal consistency check is performed, the geometric center coordinates of all vertices of the precast component base are calculated, and for each facet in the joint surface area, its face normal vector is calculated. A reference vector is constructed from the geometric center to the centroid of the facet. The dot product of the face normal vector and the reference vector is calculated. If the dot product result is less than zero, it is determined that the normal direction of the facet points to the inside of the component. The arrangement order of the facet vertices needs to be reversed to flip the normal direction, ensuring that the normals of all facets point to the outside of the component. The three-dimensional contour data and the joint surface area annotation are obtained.

[0020] Based on the 3D contour data and the annotation of the interface region, the edge positioning parameters and normal constraint parameters from the input shear key geometric feature parameters are called, where the edge positioning parameters are set to the retention distance. This parameter is set according to the concrete cover thickness specification. To prevent shear keys from being placed too close to the edge, causing concrete spalling, the normal limit parameter is set to an angle threshold. For example, set to To eliminate regions with excessive curvature changes, the process first iterates through all the normals of the mating surface region, then calculates the average normal vector of the mating surface region using an area-weighted average method. This average normal vector is used as the principal normal direction. Subsequently, using this principal normal direction as the projection axis, the boundary vertices of the mating surface region are projected onto a two-dimensional plane perpendicular to the principal normal direction. The extreme values ​​of the boundary vertex coordinates are searched within the two-dimensional plane, and the minimum x-coordinate in the projected coordinate system is determined accordingly. Maximum x-coordinate Minimum y-coordinate and the maximum ordinate Based on edge positioning parameters By shrinking the coordinate range, the coordinate range of the effective layout area can be calculated. as well as Simultaneously, iterate through the independent normal vectors of all patches within the combined surface region again, calculate the angle between each independent normal vector and the principal normal direction, and then compare this angle with the angle threshold in the normal constraint parameters. If the angle is greater than the threshold, the area is marked as an undesirable region and removed in the subsequent coordinate range statistics. Through the above screening and calculation process, the effective geometric boundary and reference direction for shear key generation are established, forming the boundary coordinate range and normal vector direction of the bonding surface.

[0021] Based on the boundary coordinate range and normal vector direction of the interface, the center point is set as the geometric center of the boundary coordinate range. This geometric center is calculated from the extreme coordinates of the effective arrangement area, i.e. Let the local axis direction be determined by the direction of the normal vector and the principal direction of the boundary. The principal normal direction of the interface region is selected as the Z-axis of the local coordinate system, and the long side direction of the boundary coordinate range is selected as the X-axis. The Y-axis of the local coordinate system is determined by the cross product of the Z-axis and X-axis, thus constructing an orthogonal interface local coordinate system. In this coordinate system, based on the waveform type parameter, peak spacing parameter, and peak amplitude parameter in the shear key geometric characteristic parameters, the waveform type parameter is set to "trapezoidal sinusoidal hybrid wave," and the peak spacing parameter is set to... For example, the value is Set the peak amplitude parameter as For example, the value is A parameter control mesh is established based on the dimensions of the interface region, and the mesh resolution is set to [value missing]. Iterate through each node in the parameter control mesh, calculate the position coordinates of that node in the local coordinate system, and calculate the peak height value based on the position coordinates. Wavelength values and the periodic value During the calculation process, an edge decay function is introduced to determine the distance from the current node to the boundary. ,like Smaller than the preset transition area width (e.g.) Then, the peak height value will be calculated using linear interpolation. from Gradually increase to Otherwise, assign a value directly. Similarly, the wavelength value Assigned value Arrange periodic values Assigned value The three calculated values ​​are used as a parameter vector. The number of rows and columns of the parameter control matrix is ​​determined by dividing the boundary coordinate range of the mating surface by the grid resolution. Through point-by-point calculation and assignment, the roughness distribution characteristics of the entire mating surface region are digitally defined, and the roughness parameter control matrix is ​​generated.

[0022] The steps for obtaining grayscale data of elevation displacement are as follows: Based on the roughness parameter control matrix, a regular sampling grid is established in the interface region. The three-dimensional coordinates of the sampling points are projected and normalized according to the principal axis direction of the local coordinate system of the interface to form a UV mapping coordinate matrix. The gray scalar value is calculated for each sampling point according to the waveform definition of the shear key geometric characteristic parameters to generate elevation displacement gray data.

[0023] Specifically, based on the roughness parameter control matrix, a regular sampling grid is established in the interface region, and the sampling step size is set to [value missing]. The step size is set according to the surface treatment precision specifications of precast components, which can ensure texture details while avoiding excessive data volume. A double loop is performed along the X and Y axes of the local coordinate system of the joint surface to generate a discrete sampling point set covering the entire joint surface area. For each sampling point, its three-dimensional coordinates in the local coordinate system are extracted. The three-dimensional coordinates of the sampling points are projected and normalized according to the principal axis direction of the local coordinate system of the interface, and the normalization reference range is set. The value range of the U direction is determined by the minimum abscissa of the interface boundary. To the maximum x-coordinate It is determined that the range of values ​​in the V direction is determined by the minimum ordinate. To the maximum ordinate Determine, using the formula Calculate the U-coordinate using the formula Calculate the V-coordinates to map the physical coordinates to The dimensionless texture space is used to form a UV mapping coordinate matrix. Based on the waveform definition of the shear key geometric feature parameters, the grayscale scalar value is calculated for each sampling point. The peak height values ​​of the corresponding rows and columns in the roughness parameter control matrix are read. Wavelength values and the periodic value The calculation is performed using a trapezoidal sinusoidal mixed wave function, which is defined as follows: ,in Let U be the total physical length of the mating surface in the U direction. If the calculated... If the value is less than 0, it is corrected to 0 to simulate the unidirectional convex shear key shape, while introducing a random perturbation term. This disturbance term is generated by calling the standard normal distribution function, with a mean of 0 and a standard deviation set to 0. This is used to simulate random micropores on the surface of concrete during pouring and to calculate the final height value. Divide the height value by the preset maximum possible height (e.g., The standardization process is performed to obtain floating-point numbers between 0 and 1 as grayscale scalar values. All sampling points are traversed and the calculation results are stored in a double-precision floating-point array to generate grayscale data of elevation displacement.

[0024] The steps for obtaining the virtual geometry texture mapping set are as follows: Based on the elevation displacement grayscale data, the geometric offset vector is calculated using the following formula: ; in, Mesh nodes corresponding to UV mapping coordinates The geometric offset vector, The wave crest height is determined by the waveform amplitude term in the shear key geometric characteristic parameters. Mesh nodes corresponding to UV mapping coordinates The grayscale scalar value is obtained from the elevation displacement grayscale data. Here, represents the upper bound of the grayscale scalar values, and represents the maximum value of the entire set of grayscale scalar values. is the waveform sharpness factor, an exponential term that controls the sharpness of the grayscale surface. This is the direction modulation coefficient, used to adjust the modulation amplitude in the normal direction. Mesh nodes corresponding to UV mapping coordinates The normal vector, is the reference direction vector, and is the global average normal direction of the interface region; Based on the geometric offset vector, displacement is applied along the normal direction of the mesh node corresponding to each UV mapping coordinate. The spatial position coordinates of each node are added element by element to the corresponding geometric offset vector to update the three-dimensional coordinate data of all nodes and generate a virtual geometric texture mapping set.

[0025] Specifically, in the geometric offset vector calculation formula, the two-dimensional grayscale scalar data is transformed into a three-dimensional physical displacement vector through nonlinear mapping and direction modulation mechanism. It not only considers the geometric height of the shear key, but also simulates the flow characteristics of concrete material during the molding process and the influence of demolding on the surface normal through sharpness factor and direction coefficient, thereby generating virtual texture geometry that conforms to the real manufacturing characteristics. This is the peak height value, representing the maximum protrusion height in shear key design. It is obtained by consulting the technical requirements for the rough surface of precast components and is typically set to [value missing]. to In this process, the average keyway depth of precast component samples from the same batch is measured, for example, by taking the average value of 10 measuring points. This value directly determines the upper limit of the physical dimensions of the generated geometry. If it is set too small, the shear resistance requirement cannot be met; if it is set too large, it may cause demolding difficulties. It needs to be determined according to the specific mold design parameters. Mesh nodes corresponding to UV mapping coordinates The grayscale scalar value, derived from the elevation displacement grayscale data generated in the previous step, represents the relative position of the current grid node in the normalized height field, and its value range is [value range missing]. By reading the grayscale data array stored in memory, based on the grid nodes The row and column indices are retrieved directly using the index; for example, the value read from the node in row 10 and column 20 is... This value reflects the proportion of the instantaneous amplitude of the waveform function at that position; This parameter represents the upper bound of the grayscale scalar value set. It is the maximum value of the entire set of grayscale scalar values ​​and is used to normalize the grayscale data, ensuring that the ratio is no greater than 1. It is obtained by iterating through the entire elevation displacement grayscale data array, comparing and recording the maximum value. For example, in this generation process, after scanning the entire field of data, the maximum grayscale value was found to be... Then Set as This parameter eliminates the risk of local numerical overflow caused by random perturbations; The waveform sharpness factor is an exponential term controlling the sharpness of the grayscale surface. This parameter adjusts the transition slope from trough to crest, simulating the natural angle of repose characteristic formed by concrete aggregate accumulation. It is determined by comparing the fit between the surface profile under different exponents and the actual scanned point cloud. In a laboratory environment, a standard rough surface is laser-scanned and adjusted. The value minimizes the root mean square error between the generated curve and the scanning curve, and is typically taken in the range of [value missing]. to Set here as This indicates that the waveform is attenuated according to a quadratic law, resulting in a smoother top and a wider root. This is the directional modulation coefficient, used to adjust the modulation amplitude in the normal direction. This parameter reflects the anisotropic influence of gravity or pouring direction on surface texture. It is set by analyzing the rheological properties of concrete slurry under gravity. The setting process is as follows: a set of inclined pouring test blocks are prepared, and the difference ratio of texture depth along the flow direction and perpendicular to the flow direction is measured. The difference coefficient is calculated. For example, if the average texture depth along the flow direction is deeper than that perpendicular to the flow direction... Then set for This introduces directional geometric deviations during the generation process; Mesh nodes corresponding to UV mapping coordinates The normal vector, which indicates the orientation of the current base surface, is obtained by calculating the unit normal vector of the facet containing the mesh node. For example, if the mating surface is a plane, then this vector is a unit vector perpendicular to the mating surface. For instance, in the local coordinate system, it is represented as... If the interface is a curved surface, then take the average value of the normals of all adjacent surfaces sharing the node and normalize it. The reference direction vector is the global average normal direction of the interface region. This parameter serves as the modulation reference axis. It is obtained by statistically summing the normal vectors of all patches within the interface region, averaging the sums, and then normalizing the average. This average is used to determine the main orientation. For example, it can be calculated as follows: (Normalized), indicating that the overall surface is roughly oriented towards the positive Z-axis but with a slight tilt; Calculations based on parameters: Select a typical grid node in the central region of the interface. Perform verification calculations. Set the peak height value , Read the grayscale scalar value of this node. , Obtain the upper bound of grayscale scalar values , Set waveform sharpness factor , Setting the directional modulation coefficient , The normal vector of this node , Reference direction vector ; Step 1: Calculate the height ratio: ; The second step is to calculate the nonlinear decay term: ; The third step is to calculate the direction modulation term: First, calculate the dot product. ; Then calculate the modulation factor. ; Step 4: Calculate the scalar modulus: ; Step 5: Calculate the final geometric offset vector: ; Under the set parameter conditions, this mesh node will generate approximately [value missing] along the normal direction. The geometric displacement, which is less than the maximum design height. Furthermore, after nonlinear sharpening and directional enhancement processing, it can realistically reflect the actual physical protrusion height at this gray level, taking into account the material stacking characteristics and the influence of the casting direction. These vector sets will collectively constitute realistic rough surface geometric features.

[0026] Based on the geometric offset vector, a displacement is applied along the normal direction of the mesh node corresponding to each UV mapping coordinate. A geometric transformation loop is established to traverse each node index in the virtual geometric texture mapping set and read the original spatial position coordinates of that node from memory. Simultaneously read the corresponding calculated geometric offset vector. Perform vector addition, the calculation formula is: This involves adding the X components of the original coordinates to the X components of the offset vector, adding the Y components to the Y components, and adding the Z components to the Z components to obtain the permuted spatial coordinates. Before performing the addition, a boundary safety check mechanism is set to determine whether the new coordinate position will cause mesh self-intersection or patch flipping. The rate of change of distance between adjacent nodes after displacement is calculated. If the rate of change exceeds a preset safety threshold (e.g., the length of adjacent sides), the mechanism will be checked. Then, for the geometric offset vector Perform damping attenuation processing, multiply by the attenuation coefficient. The positions are then recalculated to prevent geometric topology breakage. After the coordinate update is completed, all new node coordinate data is written back to the data buffer of the 3D model. At the same time, the normal properties of the vertices are updated. The weighted average method is used to recalculate the normal of each vertex based on the new face geometry to ensure the accuracy of lighting rendering and physical collision detection. The updated vertex list is combined with the original index list to construct a surface mesh structure with micro-geometric details and generate a virtual geometric texture mapping set.

[0027] The steps to obtain the grid warpage index are as follows: Based on the virtual geometric texture mapping set, the initial mesh is divided in the bonding area to generate quadrilateral mesh cells composed of four vertices. The three-dimensional coordinate information of the four vertices of each quadrilateral mesh cell is extracted and a vertex sequence is established. The plane that minimizes the sum of the squared distances from the four vertices to the plane is determined as the best fitting plane. The vertical distance from each vertex to the best fitting plane is calculated to obtain the vertical distance sequence of the vertices of the quadrilateral mesh cell. The mesh warpage index is calculated based on the vertical distance sequence of the vertices of the quadrilateral mesh cells. The calculation formula is as follows: ; Where S is the grid warpage index. denoted as the standard deviation of the vertical distance from the vertices, representing the overall dispersion of the four vertices to the best-fit plane. , The element feature size is the maximum value among the two diagonal lengths of the current quadrilateral mesh element. These are the vertical distances from the four vertices arranged in order to the best-fit plane. The distortion penalty weight is used to adjust the dimensionless constant of the quadrilateral saddle distortion effect. The difference between the vertical distances to the diagonal vertices is used to reflect the degree of distortion of the quadrilateral, where u is the number of vertices. Let be the perpendicular distance from the t-th vertex to the best-fit plane. This is the average vertical distance of all vertices.

[0028] Specifically, based on the virtual geometric texture mapping set, initial meshing is performed in the bonding area, and an initial mesh step size parameter is set. This parameter is determined based on the ratio of the overall size of the prefabricated component to the minimum wavelength of the texture feature, for example, set to the minimum wavelength of the texture. Using this step size, a regular two-dimensional index mesh is constructed in the UV domain. Each cell generated by the index mesh is traversed, and the corresponding four corner indexes are extracted. The three-dimensional spatial coordinates of these four vertices are then read from the vertex buffer of the virtual geometry texture mapping set. To construct a local vertex sequence and quantify the flatness of the quadrilateral unit, a reference plane needs to be found. The plane that minimizes the sum of the squared distances from the four vertices to the plane is determined as the best-fit plane. Principal component analysis is used to solve this problem. First, the coordinates of the geometric center points of the four vertices are calculated, and a system of coordinates of the four vertices relative to the center points is constructed. The covariance matrix is ​​used for eigenvalue decomposition. The eigenvector with the smallest eigenvalue among the three eigenvectors obtained is the normal direction of the best-fit plane. Combined with the coordinates of the center point, the spatial equation of the plane can be uniquely determined. Then, projection calculation is performed. Using the distance formula from a point to a plane, the coordinates of the four vertices are substituted into the plane equation one by one to calculate the directed perpendicular distance from each vertex to the best-fit plane. Considering the characteristics of the fitted plane, the algebraic sum of these distance values ​​theoretically approaches zero. The absolute values ​​and signs of these four distance values ​​are recorded to form a dataset that reflects the deviation of the cell from the ideal plane, resulting in the vertical distance sequence of the vertices of the quadrilateral mesh cell.

[0029] In the formula for calculating the mesh warpage index, the non-planarity of the quadrilateral mesh is decoupled into disordered discrete fluctuation components and ordered saddle-shaped twist components through the idea of ​​orthogonal decomposition. The first term measures the overall dispersion of the vertices relative to the fitted plane, and the second term specifically captures the warpage pattern in the diagonal direction. This allows us to distinguish between roughness and severe structural distortion. Based on this, we can perform targeted mesh subdivision, which can avoid geometric topological errors in subsequent Boolean operations or CNC machining path generation. Let be the standard deviation of the vertical distance between the vertices, representing the overall dispersion of the four vertices to the best-fit plane. The steps to obtain it are as follows: First, read the four values ​​from the sequence of vertical distances between the vertices of the quadrilateral mesh cells. Calculate its average value Since it is based on the best-fit plane of the least squares method, Theoretically, it is very close to 0. Then, the square of the difference between each distance value and the average value is calculated, summed, and divided by the number of vertices. Finally, the square root is taken to obtain the result. For example, in a test unit, the distances to the four vertices are measured as follows: Then the mean is 0 and the variance is Standard deviation That is ; The element feature size is the maximum of the two diagonal lengths of the current quadrilateral mesh element. It is obtained by calculating the length of the first diagonal connecting vertex 1 and vertex 3 based on the three-dimensional coordinates of the four vertices. And the length of the second diagonal connecting vertex 2 and vertex 4 ,Compare and The larger of the two values ​​is taken as the value. This parameter is used to normalize the distance deviation, eliminating the influence of mesh size on the warpage evaluation. For example, it is calculated as follows: ,but Values ; The distortion penalty weight, a dimensionless constant used to adjust the quadrilateral saddle-shaped distortion effect, is obtained through the following steps: A standardized set of test meshes is established, encompassing various distortion types from perfectly planar to extreme saddle-shaped distortion. Finite element stress analysis simulations are performed on each test mesh, and the calculation error rate caused by mesh distortion is recorded. A curve relating the degree of distortion to the error rate is established through regression analysis. The inflection point where the error rate rises sharply is identified. The geometric parameters corresponding to this inflection point are substituted into the calculation to determine the weight value that balances the discrete error and the distortion error. This weight is typically set at [value missing]. to Between, set here as This indicates a higher sensitivity penalty for saddle-shaped distortion of the rules; These are the vertical distances from the four sequentially arranged vertices to the best-fit plane. This parameter is directly read from the vertex vertical distance sequence generated in the previous step, in counter-clockwise or clockwise vertex index order. For example, the sequence read is... (Unit: mm); Calculations based on parameters: We selected typical quadrilateral mesh elements exhibiting saddle-shaped warping for computation. Set the vertex vertical distance sequence as , Calculate the average value , Calculate the standard deviation , Set the feature size of the unit , Set the distortion penalty weight , The first step is to calculate the discrete component terms: ; ; The second step is to calculate the tortuosity component: Calculate the difference in diagonal distances ; Calculate the weighted ratio ; ; The third step is to calculate the overall index: ; The warpage index of this grid cell is The contribution of the distortion component ( The contribution of the discrete components is much greater than that of the discrete components. This indicates that the unit mainly exhibits regular saddle-shaped distortion. This value quantifies the complexity of its spatial morphology. If the subsequent threshold is set to... If the condition is not met, the unit will be deemed unqualified and requires further subdivision to smooth the geometric transition.

[0030] The steps for obtaining the high-density subdivision mesh topology are as follows: Each grid warpage index is compared with the threshold constant. For quadrilateral grid cells whose grid warpage index exceeds the threshold constant, diagonal subdivision and edge interpolation are performed. The local topological relationships and node connection relationships after subdivision are recalculated to form a high-density subdivided grid topology.

[0031] Specifically, the grid warpage index is compared with the threshold constant one by one, and the threshold constant is set accordingly. The basis for obtaining this information is based on statistical analysis of the mesh warpage distribution data of a large number of historical qualified component models. The 95th percentile value is calculated, and combined with the tolerance requirements of the subsequent CNC machining module for surface approximation accuracy (e.g., the machining path generation algorithm requires adjacent normal deflection angles to not exceed a certain limit), the corresponding geometric warpage threshold is derived, and finally set. Start the traversal program and check the calculated values ​​of each quadrilateral grid cell. Value, if If a cell is marked as a cell to be subdivided, diagonal subdivision and edge interpolation are performed on quadrilateral cells whose mesh warpage index exceeds the threshold constant. First, the coordinates of the geometric center point of the quadrilateral cell are calculated as the newly added internal vertex. Then, the coordinates of the midpoints of the four sides are calculated, and these five new vertices are added to the mesh vertex list. The original vertex, edge midpoint, and center point are connected to decompose the original quadrilateral into four smaller quadrilateral sub-cells, or the diagonal is connected to divide it into four triangular sub-cells, depending on the specific topology data structure requirements. At the same time, bilinear interpolation or curvature interpolation based on surface normals is used to correct the normal vector and texture coordinates of the newly generated vertices to ensure a smooth transition of the subdivided surface. The local topology relationships and node connection relationships after subdivision are recalculated, the global half-edge data structure or adjacency matrix is ​​updated, the newly generated patch index is inserted into the main mesh list, and the original coarse cell index is removed. A new vertex-patch reference chain is established to form a high-density subdivided mesh topology.

[0032] The steps for obtaining the geometric surface after permutation are as follows: Based on the geometric offset vectors in the virtual geometric texture mapping set, the spatial position coordinates and normal directions of the mesh vertices are read one by one at the mesh vertex level of the high-density subdivided mesh topology. The geometric offset vectors are then superimposed along the normal direction according to the mesh vertex index, and the spatial position coordinates of the mesh vertices are updated to generate the permuted geometric surface.

[0033] Specifically, based on the geometric offset vectors in the virtual geometric texture mapping set, the spatial position coordinates and normal directions of each mesh vertex in the high-density subdivided mesh topology are read one by one to obtain the original coordinate data in the vertex buffer. and the corresponding normal vector Read the magnitude of the geometric offset vector corresponding to the vertex. Execute the vertex replacement algorithm according to the formula Perform calculations, where Original coordinates Given a unit normal vector, this process is not a simple linear superposition, but introduces a Laplacian smoothing constraint. When calculating new coordinates, it considers not only the offset of the current vertex, but also the average offset of all its first-order neighboring vertices. The smoothing coefficient is set to... The newly calculated position is compared with the average position of the neighborhood. The ratio is weighted and blended to prevent the generation of local spikes. At the same time, it checks whether the offset vertex causes the facet to self-intersect. Collision detection is performed by constructing a local bounding box. If an intersection is detected, the displacement of the vertex is backed up to the amount before the intersection. After updating the positions of all vertices, the normal distribution of the entire surface is recalculated. The normals of the facets are reconstructed using the updated vertex coordinates, and the vertex normals are updated using the angle-weighted method to generate the permuted geometric surface.

[0034] The steps for obtaining the solid boundary representation model of precast concrete components are as follows: Based on the replaced geometric surface, extract the edge vertex sequence on the edge contour of the replaced geometric surface according to the boundary direction and construct a continuous polyline. Extract the contour line corresponding to the original side of the precast component substrate and calculate the nearest point-to-point distance from the edge vertex to the original side of the precast component substrate. Identify the continuous segment of the geometric gap according to the distance threshold and generate the boundary stitching path. Based on the boundary stitching path, transition patches are generated segment by segment between the edge contour of the replaced geometric surface and the original side surface of the precast component matrix along the boundary stitching path, and closed bands are inserted. The normal direction of the newly generated patches is corrected and the topological index of the high-density subdivision mesh is updated to generate the solid boundary representation model of the precast concrete component.

[0035] Specifically, based on the replaced geometric surface, the sequence of edge vertices is extracted along the boundary direction on the edge contour of the replaced geometric surface, and continuous polylines are constructed. All edges referenced by only one patch are identified as open boundary edges. These edges are linked together in a head-to-tail order to form closed or open edge loops. The contour line corresponding to the original side surface of the precast component substrate is extracted; this contour line represents the substrate edge before the replacement operation. The distance between the edge vertex and the nearest point pair to the original side surface of the precast component substrate is calculated. For each vertex of the replaced surface edge, the nearest corresponding point is found on the original substrate contour line, and the Euclidean distance is calculated. Identify continuous segments of geometric gaps based on a distance threshold, and set the distance threshold. The threshold is set based on the joint tolerance of the concrete pouring mold, and the joint gap of the mold is usually controlled within a certain range. to Between, to prevent grout leakage, if multiple consecutive vertices All greater than Then, mark this edge segment as the gap segment that needs to be stitched, record the start index and end index of the segment, and generate the boundary stitching path.

[0036] Based on the boundary stitching path, transition patches are generated segment by segment between the edge contour of the replaced geometric surface and the original side surface of the precast component substrate, and closed bands are inserted. For each identified gap, a triangulation algorithm is used to generate sidewall patches connecting the upper and lower boundaries. First, the tangential vectors between corresponding nodes of the two boundaries are calculated. Based on the angle between the tangential vectors, it is determined whether additional intermediate nodes need to be inserted to ensure mesh quality. If the angle is greater than 1, the insertion of additional intermediate nodes is performed. Then, bisection interpolation is performed on the long side to construct regular triangular strips to fill the gaps, correct the normal direction of the newly generated facets, calculate the normal of the newly generated facets to ensure that it points to the outside of the component, specifically by calculating the vector from the center point of the facet to the centroid of the component. If the dot product of the normal and the vector is negative, the vertex order is flipped. Then, a topology stitching operation is performed to merge the vertex indices of the newly generated sidewall facets into the vertex list of the main mesh, eliminate duplicate vertices, update the topology index of the high-density subdivision mesh topology, rebuild the "opposite edge" pointer and "next edge" pointer of the half-side data structure to ensure the closure of the entire mesh manifold, and finally perform a watertightness check, count the Euler characteristic number, verify whether the mesh is closed, and generate the solid boundary representation model of the precast concrete component.

[0037] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A three-dimensional geometric modeling method for precast concrete components, characterized in that, Includes the following steps: Obtain the three-dimensional contour data of the precast component substrate and the specified joint surface area, call the input shear key geometric feature parameters, establish a local coordinate system of the joint surface, calculate the peak height value, wavelength value and arrangement period value in the local coordinate system of the joint surface according to the shear key geometric feature parameters, and generate a roughness parameter control matrix. According to the roughness parameter control matrix, UV mapping coordinates are constructed on the bonding surface region. Gray scalar values ​​of corresponding pixels are generated according to the waveform definition in the shear key geometric feature parameters. Elevation displacement gray data is generated. The elevation displacement gray data is mapped to each grid node of the UV mapping coordinates. A virtual geometric texture mapping set is calculated and generated. The virtual geometric texture mapping set is called to perform initial meshing on the bonding surface region, obtain quadrilateral mesh cells, and calculate the mesh warpage index. The mesh warpage index is compared with a preset threshold constant to generate a high-density subdivided mesh topology. Based on the geometric offset vector in the virtual geometric texture mapping set, the mesh vertices in the high-density subdivided mesh topology are driven to move along the normal direction to generate a permuted geometric surface. The geometric gap between the edge contour of the permuted geometric surface and the original side surface of the precast component matrix is ​​identified, the boundary stitching path is calculated, and geometric closure is performed along the path to generate a solid boundary representation model of the precast concrete component.

2. The three-dimensional geometric modeling method for precast concrete components according to claim 1, characterized in that, The steps for obtaining the roughness parameter control matrix are as follows: Obtain the three-dimensional contour data of the precast component substrate and the specified bonding surface area, parse the vertex coordinate sequence and patch topology in the three-dimensional contour data, extract the boundary and internal annotations of the bonding surface area, verify the boundary closure and normal consistency, and obtain the three-dimensional contour data and the annotations of the bonding surface area. Based on the three-dimensional contour data and the annotation of the interface region, the edge positioning parameters and normal limit parameters in the input shear key geometric feature parameters are called. The minimum and maximum coordinates are extracted along the boundary of the interface region. The normal direction is statistically analyzed according to the orientation of the facet to form the coordinate range of the interface boundary and the direction of the normal vector. Based on the boundary coordinate range and normal vector direction of the bonding surface, the center point is set as the geometric center of the boundary coordinate range, and the local axis direction is set as determined by the normal vector direction and the principal direction of the boundary. A local coordinate system for the bonding surface is established. Based on the waveform type parameter, peak spacing parameter, and peak amplitude parameter in the shear key geometric characteristic parameters, the peak height value, wavelength value, and arrangement period value are calculated along the local principal axis and written into the matrix according to the row and column index to generate the roughness parameter control matrix.

3. The three-dimensional geometric modeling method for precast concrete components according to claim 1, characterized in that, The steps for obtaining the elevation displacement grayscale data are as follows: Based on the roughness parameter control matrix, a regular sampling grid is established in the joint surface region. The three-dimensional coordinates of the sampling points are projected and normalized according to the principal axis direction of the local coordinate system of the joint surface to form a UV mapping coordinate matrix. The gray scalar value is calculated for each sampling point according to the waveform definition of the shear key geometric feature parameters to generate elevation displacement gray data.

4. The three-dimensional geometric modeling method for precast concrete components according to claim 1, characterized in that, The steps for obtaining the virtual geometric texture mapping set are as follows: Calculate the geometric offset vector based on the elevation displacement grayscale data; Based on the geometric offset vector, displacement is applied along the normal direction of the mesh node corresponding to each UV mapping coordinate. The spatial position coordinates of each node are added element by element to the corresponding geometric offset vector to update the three-dimensional coordinate data of all nodes and generate a virtual geometric texture mapping set.

5. The three-dimensional geometric modeling method for precast concrete components according to claim 1, characterized in that, The steps for obtaining the grid warpage index are as follows: Based on the virtual geometric texture mapping set, an initial mesh is generated in the bonding area to generate a quadrilateral mesh unit composed of four vertices. The three-dimensional coordinate information of the four vertices of each quadrilateral mesh unit is extracted and a vertex sequence is established. The plane that minimizes the sum of the squared distances from the four vertices to the plane is determined as the best fitting plane. The vertical distance from each vertex to the best fitting plane is calculated to obtain the vertical distance sequence of the quadrilateral mesh unit vertices. The grid warpage index is calculated based on the vertical distance sequence of the vertices of the quadrilateral grid cells.

6. The three-dimensional geometric modeling method for precast concrete components according to claim 1, characterized in that, The steps for obtaining the high-density subdivided mesh topology are as follows: The grid warpage index is compared with the threshold constant one by one. For quadrilateral grid cells whose grid warpage index exceeds the threshold constant, diagonal subdivision and edge interpolation are performed. The local topological relationships and node connection relationships after subdivision are recalculated to form a high-density subdivided grid topology.

7. The three-dimensional geometric modeling method for precast concrete components according to claim 1, characterized in that, The steps for obtaining the permuted geometric surface are as follows: Based on the geometric offset vector in the virtual geometric texture mapping set, the spatial position coordinates and normal directions of the mesh vertices are read one by one at the mesh vertex level of the high-density subdivided mesh topology. The geometric offset vectors are then superimposed along the normal direction according to the mesh vertex index, and the spatial position coordinates of the mesh vertices are updated to generate the permuted geometric surface.

8. The three-dimensional geometric modeling method for precast concrete components according to claim 1, characterized in that, The steps for obtaining the entity boundary representation model of the precast concrete component are as follows: Based on the replaced geometric surface, extract the edge vertex sequence on the edge contour of the replaced geometric surface according to the boundary direction and construct a continuous polyline. Extract the contour line corresponding to the original side of the precast component substrate and calculate the nearest point-to-point distance from the edge vertex to the original side of the precast component substrate. Identify the continuous segment of the geometric gap according to the distance threshold and generate the boundary stitching path. According to the boundary stitching path, transition patches are generated segment by segment between the edge contour of the replaced geometric surface and the original side surface of the precast component matrix along the boundary stitching path, and closed bands are inserted. The normal direction of the newly generated patches is corrected and the topological index of the high-density subdivision mesh is updated to generate a solid boundary representation model of the precast concrete component.

9. A system for three-dimensional geometric modeling of precast concrete components according to any one of claims 1-8, characterized in that, include: The data acquisition module is used to acquire the three-dimensional contour data of the precast component substrate and the specified joint surface area, call the input shear key geometric feature parameters, establish a local coordinate system of the joint surface, calculate the peak height value, wavelength value and arrangement period value in the local coordinate system of the joint surface according to the shear key geometric feature parameters, and generate a roughness parameter control matrix. The texture generation module is used to construct UV mapping coordinates on the bonding surface region according to the roughness parameter control matrix, generate grayscale scalar values ​​of corresponding pixels according to the waveform definition in the shear key geometric feature parameters, generate elevation displacement grayscale data, map the elevation displacement grayscale data to each grid node of the UV mapping coordinates, and calculate and generate a virtual geometric texture mapping set. The mesh generation module is used to call the virtual geometric texture mapping set to perform initial mesh generation on the bonding surface area, obtain quadrilateral mesh cells, calculate the mesh warpage index, compare the mesh warpage index with a preset threshold constant, and generate a high-density subdivided mesh topology. The geometry generation module is used to drive the mesh vertices in the high-density subdivided mesh topology to move along the normal direction according to the geometric offset vector in the virtual geometric texture mapping set, generate a permuted geometric surface, identify the geometric gap between the edge contour of the permuted geometric surface and the original side of the precast component matrix, calculate the boundary stitching path, perform geometric closure along the path, and generate a solid boundary representation model of the precast concrete component.

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