Irregular triangle mesh curved surface sheet cutting B-spline reconstruction method

Abstract

This invention discloses a method for reconstructing B-splines from irregular triangular mesh surface patches, relating to the fields of computer-aided design and geometric modeling. The method includes: mapping irregular triangular mesh surface patches onto a two-dimensional parameter plane and expanding it to obtain a parameter domain for constructing the B-spline surface; constructing a UV mesh on the parameter domain, including node vectors in the U and V directions and step sizes in the U and V directions; estimating the Hermite information of each mesh point in three-dimensional space; constructing the B-spline surface based on the estimated Hermite information; extracting and segmenting the irregular triangular mesh surface patches into boundaries; interpolating the boundary segment points to fit and generate boundary curves; and using the boundary curves to trim the B-spline surface to obtain the final trimmed surface. This invention is applicable to irregular triangular meshes with arbitrary topologies, effectively handling complex boundaries and holes, and reconstructing a smooth surface with good shape preservation.

Description

Technical Field

[0001] This invention relates to the fields of computer-aided geometric design and 3D modeling technology, and in particular to a method for reconstructing B-splines from irregular triangular mesh surface patches. Background Technology

[0002] In computer-aided geometric design and 3D modeling, triangular meshes and parametric surfaces are two important geometric representations. Triangular meshes offer advantages such as flexible representation and ease of rendering, but they have limitations in applications requiring high geometric manipulation and precision. B-spline surfaces, on the other hand, possess favorable mathematical properties, are easy to manipulate geometrically, and allow for precise precision control, thus finding widespread application in CAD and CAM systems.

[0003] Existing methods for reconstructing B-spline surfaces from triangular meshes mainly include: mesh parameterization-based methods, discrete fitting-based methods, and feature extraction-based methods. However, these methods suffer from the following problems in handling complex boundaries and preserving geometric features: 1. Insufficiently precise boundary treatment leads to inconsistencies between the reconstructed surface and the original mesh boundary; 2. For meshes with complex topologies, the reconstruction results are not ideal; 3. Geometric discontinuities are prone to occur at the joints of curved surfaces; 4. For large-scale grids, computational efficiency is low.

[0004] Especially when dealing with irregular triangular mesh surface patches, how to accurately estimate the geometric information at the boundary and perform high-quality B-spline surface reconstruction based on this is a challenge currently facing the technology. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention provides a method for reconstructing B-spline surfaces by cutting irregular triangular mesh surfaces, which can achieve high-precision reconstruction from triangular meshes to B-spline surfaces.

[0006] To achieve the above objectives, the present invention adopts the following technical solution, including: A method for reconstructing B-splines from irregular triangular mesh surfaces includes the following steps: S1. Map the irregular triangular mesh surface patch onto the two-dimensional parametric plane to obtain the parametric mesh. Expand the parametric mesh region to obtain the parametric domain for constructing the B-spline surface. Construct the UV mesh on the parametric domain, including the node vectors in the U and V directions and the step size in the U and V directions. S2, for each grid point, estimate the Hermite information of the grid point in three-dimensional space, including three-dimensional spatial coordinates, gradient in the U direction, gradient in the V direction and mixed gradient; S3, based on the estimated Hermite information of all grid points in three-dimensional space, construct a B-spline surface; S4 performs boundary extraction and segmentation on irregular triangular mesh surface patches, including boundary edge identification, boundary loop construction, and boundary segmentation. S5, extract the boundary segmentation points for boundary segmentation, and interpolate the boundary segmentation points to generate a B-spline curve, i.e., the boundary curve; S6. Use the boundary curve fitted in step S5 to trim the B-spline surface constructed in step S3 to obtain the final trimmed surface.

[0007] Preferably, in step S1, the irregular triangular mesh surface patch is mapped to the two-dimensional parameter plane using the surface parameterization method to obtain the parameterized mesh. The axis-aligned bounding box of the parameterized mesh region is used as the basic rectangle, and the bounding box is expanded outward in the U and V directions by a set ratio to obtain the parameter domain for constructing the B-spline surface.

[0008] Preferably, in step S1, rules are established on the parameter domain. The UV mesh has the following node vectors and step sizes configured in the U and V directions: U-direction node vector for: ; V-direction node vector for: ; in, For the U direction One parameter point; For the V direction One parameter point; , ; , , , ; Let U be the maximum and minimum values ​​of the expanded parameter domain in the U direction. , These are the maximum and minimum values ​​of the expanded parameter domain in the V direction; Length in the U direction Length in the V direction ; U-direction step size and step size in the V direction for: , ; Then we have: , .

[0009] Preferably, in step S2, the grid points The corresponding three-dimensional spatial coordinates are calculated using the barycentric coordinate method. : Search distance grid points Parametric triangles in the latest parametric mesh The distance refers to the distance between grid points. The average distance to the three vertices of the triangle; where, , , for The three vertices The coordinates in the two-dimensional parametric plane correspond to the three-dimensional spatial coordinates as follows: , , ; For grid points Coordinates in a two-dimensional parametric plane; Then grid points Corresponding surface points Three-dimensional spatial coordinates for: ; in, For grid points Compared to The coordinates of the centroid: ; in, For grid points Parameter values ​​in the U and V directions; , , In the parameterized mesh The three vertices Parameter values ​​in the U and V directions; For grid points Corresponding surface points Coordinate values ​​in the X, Y, and Z directions; , , In the parameterized mesh The three vertices The coordinates of the corresponding points on the surface in the X, Y, and Z directions.

[0010] Preferably, in step S2, the grid points are divided into internal points and boundary points: if a grid point is located on the boundary of the expanded parameter domain, it is recorded as a boundary point; otherwise, it is recorded as an internal point. For boundary points, the gradients in the U and V directions are calculated using first-order one-sided difference and second-order central difference. For interior points, the second-order central difference is used to calculate the gradients in the U and V directions.

[0011] Preferably, in step S2, the mixed gradient at each grid point is defined as 0.

[0012] Preferably, in step S3, control points are calculated by estimating the Hermite information of all grid points in three-dimensional space, and the control points and node vectors are substituted into the B-spline surface formula to generate a B-spline surface.

[0013] Preferably, step S4 is as follows: Boundary edge identification: Traverse all edges of the triangular mesh and determine whether an edge is a boundary edge by the number of triangles it shares with. Define an edge that is shared by only one triangle as a boundary edge. Boundary ring construction: Organize the boundary edges into boundary rings in a sequence where the first and last edges are connected. Boundary segmentation: For boundary nodes Calculate its predecessor node and current boundary node. The cosine value of the angle formed by successor nodes When the cosine of the included angle satisfies At that time, at the boundary node Boundary segmentation is performed at this point, and the boundary node... These are the boundary segmentation points.

[0014] Preferably, in step S5, boundary segmentation points for boundary segmentation are extracted to form a boundary segmentation point set. Construct B-spline curves , making , ,in, For node parameters; The node parameters are determined by the cumulative chord length parameters: First, calculate the cumulative chord length and define the cumulative chord length parameter sequence. ,in: ; in, Represents Euclidean distance; Then the cumulative chord length parameter sequence Normalize to the interval [0,1] to obtain the node parameter sequence. .

[0015] The present invention also provides a computer program product comprising a computer program / instruction that, when executed by a processor, implements the aforementioned method for reconstructing B-splines from irregular triangular mesh surfaces.

[0016] The advantages of this invention are: (1) The present invention can handle irregular triangular meshes with arbitrary topological structures.

[0017] (2) The present invention guarantees the geometric properties of the reconstructed surface by estimating accurate Hermite information (including three-dimensional spatial coordinates, gradient in the U direction, gradient in the V direction and mixed gradient).

[0018] (3) The boundary segmentation method based on the angle criterion of the present invention can effectively capture geometric features.

[0019] (4) The B-spline surface after being cut according to the method of the present invention has the same height as the original mesh boundary.

[0020] (5) The method of the present invention has good numerical stability and computational efficiency.

[0021] (6) The present invention can achieve high-precision reconstruction from triangular mesh to B-spline surface, is applicable to irregular triangular mesh with arbitrary topology, can effectively handle complex boundaries and holes, and the reconstructed surface is smooth and has good shape preservation. Attached Figure Description

[0022] Figure 1 This is an overall flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the original curved surface in this embodiment; Figure 3 This is a schematic diagram of the parametric surface in this embodiment; Figure 4 This is a schematic diagram of the untrimmed fitted surface in this embodiment; Figure 5 This is a schematic diagram of the boundary segmentation points extracted in this embodiment; Figure 6 This is a schematic diagram of the successfully fitted B-spline boundary curve in this embodiment; Figure 7 This is the final result of the surface reconstruction in this embodiment. Detailed Implementation

[0023] 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, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] like Figure 1As shown, a method for reconstructing B-splines from irregular triangular mesh surfaces, using external Hermite information for estimation, includes the following steps: S1 maps the irregular triangular mesh surface patch onto the two-dimensional parametric plane to obtain a parametric mesh, and expands the parametric mesh region to obtain the parametric domain for constructing the spline surface. Then, a UV mesh is constructed on the parametric domain, including the node vectors in the U and V directions and the step size in the U and V directions.

[0025] In step S1, an irregular triangular mesh surface patch is first mapped onto a two-dimensional parameter plane using an existing surface parameterization method to obtain a parameterized mesh. Since the standard domain of a bicubic B-spline surface is a rectangular domain, the parameterized mesh region is embedded within a rectangular domain (the domain of the B-spline). This invention uses the axis-aligned bounding box of this parameterized mesh region as the base rectangle and expands it proportionally in two parameter directions (U and V directions) to obtain the parameter domain for constructing the B-spline surface.

[0026] The construction of the parameter domain consists of the following four steps: (1) Calculate the original UV boundary range of the parameterized mesh region.

[0027] Find the maximum value in the U direction and minimum value and the maximum value in the V direction and minimum value .

[0028] (2) Calculate the original UV direction length.

[0029] Length in the U direction Length in the V direction .

[0030] (3) Expand the original UV boundary range (each expands outward by 10%).

[0031] Maximum value in the U direction after expansion and minimum value and the maximum value in the V direction after expansion. and minimum value They are respectively: , ; , .

[0032] (4) Construct the parameter domain.

[0033] U-direction interval: ; V-direction interval: .

[0034] At this point, the parameter domain completely covers the parameterized mesh area.

[0035] In step S1, in order to perform subsequent Hermite information estimation and B-spline fitting, a rule is established in the parameter domain. The UV mesh has the node vectors and step sizes in the U and V directions configured as follows: For those with U-direction parameter mesh for each parameter interval, U-direction node vector for: .

[0036] For those with A parameter grid in the V direction for each parameter interval, and node vectors in the V direction. for: .

[0037] in, , , , .

[0038] Length in the U direction Length in the V direction .

[0039] Uniform step size in the U direction and uniform step size in the V direction for: , .

[0040] Then we have: , .

[0041] in, For the U direction One parameter point; For the V direction One parameter point; , .

[0042] UV mesh density scale for: .

[0043] S2, for each UV mesh node (mesh point), estimate the Hermite information of the mesh point in three-dimensional space, including three-dimensional spatial coordinates, gradient in the U direction, gradient in the V direction, and mixed gradient.

[0044] Grid points are divided into internal points and boundary points: if a grid point is located on the boundary of the parameter domain, i.e. or or or Points that are not boundary points are denoted as boundary points; otherwise, they are denoted as interior points. For interior and boundary points, Hermite information (gradient in the U direction and gradient in the V direction) needs to be estimated for classification.

[0045] (1) Estimate the three-dimensional spatial coordinates.

[0046] For grid points on a two-dimensional parametric plane The barycentric coordinate method is used to calculate the grid points. Corresponding surface points Three-dimensional spatial coordinates Define grid points The distance to a triangle is the grid point. The average distance to the three vertices of the triangle. Based on this distance, search for distance grid points. Parametric triangles in the latest parametric mesh .in, , , for The three vertices The coordinates in the two-dimensional parametric plane correspond to the three-dimensional spatial coordinates as follows: , , ; For grid points Coordinates in a two-dimensional parametric plane.

[0047] Grid points Compared to barycentric coordinates The geometric meaning of is grid point Compared to Area ratio: , , ; Calculate grid points Compared to barycentric coordinates It satisfies the following system of linear equations: ; The solution obtained using Cramer's rule is: ; Then grid points Corresponding surface points Three-dimensional spatial coordinates for: ; This method, based on local linear interpolation on the parametric triangle and local linear extension in the extended region, can provide a stable three-dimensional point approximation for subsequent Hermite information estimation.

[0048] (2) First-order partial derivative estimation based on difference (U and V direction gradient estimation).

[0049] First-order difference is used for boundary points, and second-order central difference is used for interior points.

[0050] This invention estimates the first-order partial derivative on a UV grid using finite difference, namely the first-order one-sided difference and the center difference at the boundary points, and the center difference at the interior points.

[0051] For interior points (surface points) gradient in the U direction and gradient in the V direction They are respectively: ; This format has second-order precision, and its truncation error is of order 1. That is, when the sampling is more dense When, the partial derivative error is calculated according to The magnitude is reduced, and it can be used This form unifies the control of the upper bound, in which... It is a constant.

[0052] For boundary points (surface points) in the U direction , ,in gradient in the U direction , Calculated using first-order one-sided difference: ; gradient in the V direction , Calculated using the central difference: ; For boundary points (surface points) in the V direction , ,in gradient in the U direction , Calculated using the central difference: ; gradient in the V direction , Calculated using first-order one-sided difference: ; For the four corner points (surface points) , , , The gradients in both the U and V directions are calculated using the first-order one-sided difference method described above.

[0053] Its truncation error order is .

[0054] This method is based on Taylor expansion theory, which ensures the numerical stability of the first-order partial derivative estimation.

[0055] (3) The mixed partial derivative (mixed gradient) is set to zero.

[0056] The theoretical basis for treating the mixed partial derivative as zero is as follows: From a computational complexity perspective, accurately estimating the mixed partial derivative requires higher-order numerical methods, significantly increasing computational complexity. Furthermore, in most engineering applications, its impact on the surface approximation order is relatively small; therefore, treating it as zero simplifies calculations. That is, the mixed partial derivative (mixed gradient) at each grid point is approximately: .

[0057] Meanwhile, experiments show that this setting method has an acceptable impact on the final surface quality. This assumption is equivalent to believing that the changes in the U and V directions in the parameter domain are locally approximately independent.

[0058] S3. Based on the estimated Hermite information of all grid points in 3D space, a bicubic B-spline surface is constructed. This process requires calculating control points using the estimated Hermite information, and then substituting the control points and node vectors into the standard bicubic B-spline surface formula to generate the bicubic B-spline surface.

[0059] For a bicubic B-spline surface, its expression is: ; in, As control points, and These are the B-spline basis functions in the U and V directions, respectively.

[0060] S4 performs boundary extraction and segmentation on irregular triangular mesh surface patches, including boundary edge identification, boundary loop construction, and boundary segmentation.

[0061] (1) Boundary edge identification.

[0062] Traverse all edges of the triangular mesh and determine whether an edge is a boundary edge by the number of triangles it shares with. Define an edge that is shared by only one triangle as a boundary edge.

[0063] (2) Boundary ring construction.

[0064] Organize the boundary edges into a boundary loop by connecting the first and last edges. Specifically, starting from any boundary edge, find adjacent boundary edges in sequence until a closed loop is formed.

[0065] (3) Boundary segmentation.

[0066] For boundary nodes Calculate its predecessor node Current node Successor nodes The cosine value of the formed angle : ; When the cosine value of the included angle satisfies At that time, at the boundary node Boundary segmentation is performed at this point, and the boundary node... These are the boundary segmentation points.

[0067] S5: Extract the boundary segmentation points used for boundary segmentation, interpolate the boundary segmentation points to generate cubic B-spline curves, i.e. boundary curves, and obtain the clipping curves needed to construct the contour.

[0068] For the boundary segmentation point set Construct cubic B-spline curves , so that: , ,in, These are node parameters.

[0069] The node parameters are determined by the cumulative chord length parameters: First, calculate the cumulative chord length and define the cumulative chord length parameter sequence. ,in: ; in, It represents Euclidean distance.

[0070] Then the cumulative chord length parameter sequence Normalize to the interval [0,1]: ; Thus, the node parameter sequence is obtained. .

[0071] S6: Surface trimming: The B-spline surface constructed in step S3 is trimmed using the boundary curve fitted in step S5 to obtain the final trimmed surface.

[0072] (1) Initial surface creation.

[0073] The bicubic B-spline surface generated in step S3 is used as the base surface for the trimming operation.

[0074] (2) Curved surface cutting.

[0075] The bicubic B-spline surface is trimmed using the trimming curve obtained in step S5, hiding the surface region outside the curve and retaining the surface region inside the curve.

[0076] (3) Continuity optimization.

[0077] Perform a local smoothness check on the surface shape near the clipping boundary, and make local adjustments to a small number of control points in the boundary neighborhood if necessary to improve the visual smoothness near the clipping boundary.

[0078] Example 1 This embodiment provides a method for reconstructing irregular triangular mesh surface patches by trimming B-splines. It is used to obtain Hermite information from a known surface and construct a bicubic B-spline surface, and obtain the boundary for trimming to obtain a fitted surface, thereby verifying the effectiveness of the method of the present invention.

[0079] S1, construct the parameter field and node vector configuration.

[0080] Suppose there is an initial surface. (like Figure 2 As shown), after parameterization, a parametric surface is obtained. (like Figure 3 As shown), construct the expanded version The UV mesh completely covers the parametric surface. In the parametric domain... Establish a uniform The UV mesh is generated, and the corresponding information on the expanded UV mesh is mapped to the parameter domain. ,in and Based on the grid complexity and accuracy requirements, this embodiment takes... , .

[0081] Configure node vectors according to the requirements of bicubic B-spline surfaces. and The construction of node vectors follows the node configuration principles in B-spline theory to ensure the continuity and approximation accuracy of curves and surfaces.

[0082] U direction requires There are 10 nodes. Specifically, the node vector in the U direction. for: ; Among them, the first and last four repeated nodes ensure endpoint interpolation, and the internal nodes are evenly distributed.

[0083] The V direction uses the same configuration; specifically, the node vectors in the V direction... for: ; This configuration of node vectors ensures a uniform distribution of B-spline basis functions in the parameter domain, providing a stable mathematical foundation for subsequent Hermite information estimation.

[0084] S2, for each grid point It is necessary to calculate the Hermite information of this point in three-dimensional space.

[0085] (1) Estimate the three-dimensional spatial coordinates.

[0086] For each grid point on the two-dimensional parametric plane The corresponding three-dimensional spatial coordinates are calculated using an accurate interpolation method based on the centroid coordinates.

[0087] (2) Estimate the first-order partial derivatives (gradients in the U and V directions).

[0088] For boundary points, first-order one-sided difference and second-order central difference are used.

[0089] For interior points, use the second-order central difference.

[0090] (3) Set mixed partial derivatives (mixed partial derivatives).

[0091] To simplify the calculation, the mixed partial derivative is set to 0.

[0092] S3, Construction of a bicubic B-spline surface.

[0093] Based on the estimated Hermite information of all grid points in 3D space, a control mesh is constructed using a bicubic B-spline surface interpolation method. The mathematical expression for the bicubic B-spline surface is: ; in, As control points, and They are respectively direction and B-spline basis functions in the direction.

[0094] Control points are calculated using estimated Hermite information to ensure that the reconstructed surface has the same position and first derivative information at the original grid points as at the original grid points. Figure 4 This is the result of surface reconstruction.

[0095] S4 performs boundary extraction and segmentation processing on irregular triangular mesh surface patches.

[0096] A boundary detection algorithm based on edge adjacency is adopted. All edges of the triangular mesh are traversed, and edges shared by only one triangle are marked as boundary edges. These boundary edges are then organized into closed boundary loops according to topological connections.

[0097] Intelligent segmentation of boundary loops based on geometric features: Local curvature features at each boundary node are calculated, and segmentation occurs at that node when the cosine of the angle between adjacent sides exceeds a preset threshold. This segmentation method based on geometric features effectively captures feature points on the boundary, improving the accuracy of subsequent curve fitting.

[0098] S5, for each boundary segment, extract the boundary segmentation points used for boundary segmentation to obtain the set of boundary segmentation points required for trimming curve fitting (e.g., Figure 5 As shown), the boundary segment points are fitted, the node parameters are determined by the cumulative chord length parameterization method, and the control points are solved using a global interpolation algorithm to ensure that the fitted curve accurately passes through the boundary segment points, thereby obtaining the clipping curve required for clipping (as shown). Figure 6 (As shown).

[0099] S6, use the trimming curve obtained in step S5 to reconstruct the surface (e.g. Figure 4 As shown, trim the surface by hiding the surface region outside the curve and keeping the surface region inside the curve to obtain the final trimmed surface (as shown). Figure 7 (As shown). The trimmed surface is then processed... Perform continuity checks and, if necessary, local optimizations.

[0100] To verify the technical effects of the present invention, Figure 2 A reconstruction experiment was conducted. The experimental results are presented from the following three perspectives: 1. Accuracy indicators: The maximum deviation between the reconstructed surface and the original mesh is 0.00098mm, and the average deviation is 0.00053mm, which meets the accuracy requirement of less than 1e-3 expected by the project.

[0101] 2. Smoothness evaluation: The reconstructed surface maintains C¹ continuity in the feature region, the curvature changes smoothly and naturally, and there are no obvious distortions or wrinkles.

[0102] 3. Computational efficiency: For a mesh model containing 24,365 triangles, the complete reconstruction process takes about 3 seconds on a standard workstation, making it practical for engineering applications.

[0103] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for reconstructing B-splines from irregular triangular mesh surface patches, characterized in that, Includes the following steps: S1. Map the irregular triangular mesh surface patch onto the two-dimensional parametric plane to obtain the parametric mesh. Expand the parametric mesh region to obtain the parametric domain for constructing the B-spline surface. Construct the UV mesh on the parametric domain, including the node vectors in the U and V directions and the step size in the U and V directions. S2, for each grid point, estimate the Hermite information of the grid point in three-dimensional space, including three-dimensional spatial coordinates, gradient in the U direction, gradient in the V direction and mixed gradient; S3, based on the estimated Hermite information of all grid points in three-dimensional space, construct a B-spline surface; S4 performs boundary extraction and segmentation on irregular triangular mesh surface patches, including boundary edge identification, boundary loop construction, and boundary segmentation. S5, extract the boundary segmentation points for boundary segmentation, and interpolate the boundary segmentation points to generate a B-spline curve, i.e., the boundary curve; S6. Use the boundary curve fitted in step S5 to trim the B-spline surface constructed in step S3 to obtain the final trimmed surface. In step S2, grid points The corresponding three-dimensional spatial coordinates are calculated using the barycentric coordinate method. : Search distance grid points Parametric triangles in the latest parametric mesh The distance refers to the distance between grid points. The average distance to the three vertices of the triangle; where, , , for The three vertices The coordinates in the two-dimensional parametric plane correspond to the three-dimensional spatial coordinates as follows: , , ; For grid points Coordinates in a two-dimensional parametric plane; Then grid points Corresponding surface points Three-dimensional spatial coordinates for: ； in, For grid points Compared to The coordinates of the centroid: ； in, For grid points Parameter values ​​in the U and V directions; , , In the parameterized mesh The three vertices Parameter values ​​in the U and V directions; For grid points Corresponding surface points Coordinate values ​​in the X, Y, and Z directions; , , In the parameterized mesh The three vertices The coordinates of the corresponding points on the surface in the X, Y, and Z directions; In step S2, grid points are divided into internal points and boundary points: if a grid point is located on the boundary of the expanded parameter domain, it is recorded as a boundary point; otherwise, it is recorded as an internal point. For boundary points, the gradients in the U and V directions are calculated using first-order one-sided difference and second-order central difference. For interior points, the second-order central difference is used to calculate the gradient in the U-direction and the gradient in the V-direction; In step S2, the mixed gradient at each grid point is defined as 0.

2. The method for reconstructing B-splines from irregular triangular mesh surfaces according to claim 1, characterized in that, In step S1, the irregular triangular mesh surface patch is mapped to the two-dimensional parameter plane using the surface parameterization method to obtain the parameterized mesh. The axis-aligned bounding box of the parameterized mesh region is used as the basic rectangle, and the bounding box is expanded outward in the U and V directions by a set ratio to obtain the parameter domain for constructing the B-spline surface.

3. The method for reconstructing B-splines from irregular triangular mesh surfaces according to claim 1, characterized in that, In step S1, rules are established on the parameter domain. The UV mesh has the following node vectors and step sizes configured in the U and V directions: U-direction node vector for: ； V-direction node vector for: ； in, For the U direction One parameter point; For the V direction One parameter point; , ; ， ， ， ； Let U be the maximum and minimum values ​​of the expanded parameter domain in the U direction. , These are the maximum and minimum values ​​of the expanded parameter domain in the V direction; Length in the U direction Length in the V direction ; U-direction step size and step size in the V direction for: , ; Then we have: , .

4. The method for reconstructing B-splines from irregular triangular mesh surfaces according to claim 1, characterized in that, In step S3, control points are calculated using the Hermite information of all estimated grid points in three-dimensional space. The control points and node vectors are then substituted into the B-spline surface formula to generate a B-spline surface.

5. The method for reconstructing B-splines from irregular triangular mesh surfaces according to claim 1, characterized in that, Step S4 is as follows: Boundary edge identification: Traverse all edges of the triangular mesh and determine whether an edge is a boundary edge by the number of triangles it shares with. Define an edge that is shared by only one triangle as a boundary edge. Boundary ring construction: Organize the boundary edges into boundary rings in a sequence where the first and last edges are connected. Boundary segmentation: For boundary nodes Calculate its predecessor node and current boundary node. The cosine value of the angle formed by successor nodes When the cosine of the included angle satisfies At that time, at the boundary node Boundary segmentation is performed at this point, and the boundary node... These are the boundary segmentation points.

6. The method for reconstructing B-splines from irregular triangular mesh surfaces according to claim 1, characterized in that, In step S5, boundary segmentation points for boundary segmentation are extracted to form a boundary segmentation point set. Construct B-spline curves , making , ,in, For node parameters; The node parameters are determined by the cumulative chord length parameters: First, calculate the cumulative chord length and define the cumulative chord length parameter sequence. ,in: ； in, Represents Euclidean distance; Then the cumulative chord length parameter sequence Normalize to the interval [0,1] to obtain the node parameter sequence. .

7. A computer program product, characterized in that, It includes a computer program / instruction that, when executed by a processor, implements the method for reconstructing B-splines from irregular triangular mesh surfaces as described in any one of claims 1 to 6.

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