Local subdivision geometric modeling method for additive manufacturing

Abstract

The invention relates to the technical field of geometric modeling, in particular to an additive manufacturing-oriented local subdivision geometric modeling method, which comprises the following steps of: 1, inputting a three-dimensional point cloud model; 2, assembling a matrix on k layers of T grids of the three-dimensional point cloud model, and constructing a fitting model; 3, calculating an error of the fitting model, searching a target cell set based on the error, and if the target cell set does not exist, directly outputting the fitting model to complete modeling; if the target cell set exists, performing the step 4; 4, subdividing the target cell set, and obtaining (k + 1) layers of T grids; 5, constructing a primary function of the (k + 1)-layer T grid by using isomorphic mapping; and step 6, constructing a next fitting model based on the primary function, and iteratively performing the steps 3-6 until modeling is completed. According to the method, the low-order and simple spline space is used for researching the high-order and complex spline space, the limitation on mesh generation is broken through, and accurate geometric modeling and isogeometric analysis are carried out.

Description

Technical Field

[0001] The present invention relates to the field of geometric modeling technology, and in particular to a local subdivision geometric modeling method for additive manufacturing. Background Art

[0002] With the rapid development of information technology and the continuous prosperity of the computer industry, traditional surface processing technology can no longer meet the high standards of modern industry in terms of accuracy, modeling, performance and cost. Against this background, computer-aided design and manufacturing (CAD / CAM) technology came into being and gradually became an important force in promoting the transformation of modern industrial manufacturing models. CAD / CAM technology integrates multifunctional software such as CAD, CAE, CAPP, CAM and PPC to achieve comprehensive digitization and automation of design, manufacturing, information management, production control and other links, greatly improving production efficiency and market competitiveness. The application scope of CAD / CAM technology is extremely wide, covering electronics, machinery, shipbuilding, automobiles, architecture, textiles, clothing design, model reconstruction, virtual reality, physical simulation and natural resource description. With accurate data calculation, efficient drawing function, intelligent information management and precise production control, it has greatly improved the shortcomings of traditional industries, spawned the advantages of emerging industries, and promoted the modernization process of the entire industrial design and manufacturing industry.

[0003] Computer-aided geometric design (CAGD), as the theoretical basis of CAD / CAM technology, has become an important subject in the intersection of computer science and mathematics since it was proposed at the University of Utah in 1974. CAGD mainly studies the mathematical representation, calculation, design and modification of geometric shapes in a computer environment, and its theoretical results directly support the application of CAD / CAM technology in geometric modeling. In particular, NURBS, as an international standard mathematical method for defining the geometric shape of industrial products, has encountered some challenges in its application, but its basic position cannot be ignored.

[0004] In order to solve the difficulties of NURBS in representing anisotropic surfaces, reduce redundant control vertices, reduce the amount of calculation, and construct splines with local subdivision capabilities, researchers have proposed a series of local subdivision splines on T-grids. Among them, starting from the spline space, the dimension formula is derived, and then a complete local subdivision spline space can be defined based on the dimension formula. For the low-smooth-order spline space on the T-grid, the existing PHT spline basis can be spanned into a complete analysis space with excellent properties such as linear independence, unit subdivision, non-negativity, and local support. It has been widely used in geometric modeling, isogeometric analysis, topology optimization, and implicit surface reconstruction. It can be extended to three dimensions and can be improved to more general T-grids. However, with the widespread application of PHT splines, the disadvantage of rapid dimensional expansion caused by its low smoothness order characteristics has gradually emerged. Although high-smooth-order splines on T-grids can overcome this problem, the existing methods still have many limitations in mesh subdivision, resulting in more redundant subdivisions, increased degrees of freedom and increased computational complexity.

[0005] In additive manufacturing, local subdivision splines play a key role. By allowing accurate modeling and local control of complex geometries, it is able to add details in required areas and optimize material usage while ensuring model smoothness and continuity. This method not only improves manufacturing efficiency, reduces printing time and material waste, but also adapts to a variety of additive manufacturing technologies, making the design of complex surfaces more efficient and flexible, thereby improving the quality and performance of the final product. Therefore, a local subdivision geometry modeling method for additive manufacturing is proposed. Summary of the invention

[0006] The purpose of this invention is to provide a local subdivision geometry modeling method for additive manufacturing, which uses the isomorphic mapping method to study the dimension formula and spline construction of high-order smooth spline space on T grids, and uses low-order and simple spline space to study high-order and complex spline space, so as to improve the simplicity and effectiveness of the research.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A local subdivision geometry modeling method for additive manufacturing, comprising:

[0009] Step 1: Input 3D point cloud model;

[0010] Step 2, assembling a matrix on the k-layer T grid of the three-dimensional point cloud model to construct a fitting model;

[0011] Step 3, calculating the error of the fitting model, and finding the target cell cavity set based on the error. If the target cell cavity set does not exist, directly output the fitting model to complete the modeling; if the target cell cavity set exists, proceed to step 4;

[0012] Step 4: subdivide the target cell set to obtain a k+1 layer T grid;

[0013] Step 5: Use isomorphic mapping to construct the basis function of the k+1 layer T grid;

[0014] Step 6: construct the next fitting model based on the basis function, and iterate steps 3 to 6 until the modeling is completed.

[0015] Optionally, the fitting model is:

[0016]

[0017] Among them, S k (x,y) is the k-layer fitting model; P k i is the control point of k-layer spline i; b k i (x,y) is the function of k-layer spline i, and n is the number of k-layer splines.

[0018] Optionally, the method for calculating the error of the fitting model is:

[0019] E θ =max θ ‖V l -S k (x l ,y l )‖

[0020] Among them, V l is the sampling point of the 3D point cloud model, l=1,2,…,N; S k (x l ,y l ) is the sampling point V l The k-layer fitting model at , θ is the cavity in the cavity set.

[0021] Optionally, searching for a target cell set based on the error includes:

[0022] Preset threshold value;

[0023] If the error is smaller than a threshold, it is determined that the target cell cavity set does not exist; if the error is larger than a threshold, it is determined that the target cell cavity set exists.

[0024] Optionally, the basis functions for constructing the k+1-layer T-grid using isomorphic mapping include:

[0025] Initialize the weights of the k+1 layer basis function and obtain the support area of ​​the k+1 layer basis function;

[0026] The B ordinates of the k+1 layer basis functions are calculated using the T grid, all cells in the support region are traversed, and the cells whose B ordinates are not all 0 and their B ordinates are retained to complete the construction of the k+1 layer basis functions.

[0027] Optionally, using the T grid to calculate the B ordinate of the k+1 layer basis function includes:

[0028] The T branches covering the support area are obtained, all T structures in the T branches in the support area are sorted, and the T branches are re-sorted, and the B ordinates of the k+1 layer basis functions on each T branch are calculated in sequence according to the sorting, and the B ordinates of each cell cavity in the support area are obtained.

[0029] Optionally, sorting all T structures in the T branches in the support region includes:

[0030] The preset storage set V and the new T branch set {TSB0,TSB1,…,TSB c};

[0031] Select the T structure with the lowest level in the first T branch and put it into the first new T branch TSB0, traverse other T structures in the first T branch to see if they are connected to the T structure in the first new T branch TSB0, if so, put them into the storage set V and delete them in the first T branch;

[0032] After the traversal is completed, the T structure in the storage set V is assigned to the first new T branch TSB0, and the sorting of all T structures in the first T branch is completed;

[0033] Traverse all T branches, complete the T structure sorting of all T branches in the support area, and output the new T branch set {TSB0,TSB1,…,TSB c}.

[0034] Optionally, obtaining the B ordinate of each cell cavity in the support region includes:

[0035] Calculate the B ordinate of the basis function on the first T structure in the T branch TSB0, store the first T structure in the storage set V, and delete the first T structure in the T branch TSB0, repeat until there is no remaining T structure in the T branch TSB0, and obtain the B ordinate on the T branch TSB0;

[0036] Calculate the basis functions in T branches TSB1, TSB2, ..., TSB in turn c The B ordinate on the support region is calculated by using the first-order continuity conditions between different cell cavities in the support region to calculate the B ordinate of each cell cavity in the support region.

[0037] The beneficial effects of the present invention are:

[0038] The present invention adopts an isomorphic mapping method to study the dimension formula and spline construction of a high-order smooth spline space on a T-grid, and uses a low-order, simple spline space to study a high-order, complex spline space, thereby improving the simplicity and effectiveness of the research; it breaks through the limitation of grid division, and can construct a basis function with excellent properties such as linear independence, unit division, local support and completeness on a grid without level difference restrictions through the isomorphic mapping method; the basis function constructed by the isomorphic mapping method can perform accurate geometric modeling and isogeometric analysis without the need to subdivide more grids to meet the level difference requirements, thereby reducing the amount of calculation and improving the calculation efficiency; it can ensure that the number of equations is the same as the number of unknowns in the fitting process, and the assembly matrix is ​​relatively small, so that the fitting process is more accurate and the calculation efficiency is higher, and a powerful tool is provided for the accurate modeling and analysis of complex grid models. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1 A flow chart of a local subdivision geometric modeling method for additive manufacturing according to an embodiment of the present invention;

[0041] Figure 2 A three-dimensional point cloud model according to an embodiment of the present invention;

[0042] Figure 3 This is the T grid model and output model of an embodiment of the present invention. DETAILED DESCRIPTION

[0043] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] This embodiment provides a local subdivision geometry modeling method for additive manufacturing, such as Figure 1 As shown, including:

[0046] Step 1: Input 3D point cloud model;

[0047] Step 2, assembling a matrix on the k-layer T grid of the three-dimensional point cloud model to construct a fitting model;

[0048] Step 3, calculating the error of the fitting model, and finding the target cell cavity set based on the error. If the target cell cavity set does not exist, directly output the fitting model to complete the modeling; if the target cell cavity set exists, proceed to step 4;

[0049] Step 4: subdivide the target cell set to obtain a k+1 layer T grid;

[0050] Step 5: Use isomorphic mapping to construct the basis function of the k+1 layer T grid;

[0051] Step 6: construct the next fitting model based on the basis function, and iterate steps 3 to 6 until the modeling is completed.

[0052] Combine the following Figure 1-3 A local subdivision geometric modeling method for additive manufacturing proposed in this embodiment is described in detail, which specifically includes the following steps:

[0053] Step 1. Model import: Import a sampling point as V l ,l=1,2,…,N 3D point cloud model, the points inside this model are connected by triangles, such as Figure 2 shown.

[0054] Step 2: Assemble k-layer matrices on the k-layer grid, solve the layer control vertices, and generate the fitting model:

[0055]

[0056] Among them, S k (x,y) is the k-layer fitting model; P k i is the control point of k-layer spline i; b k i (x,y) is the function of k-layer spline i, and n is the number of k-layer splines.

[0057] Solve AP = V′ k Obtain the corresponding control fixed-point sequence P, where A is the assembly matrix, P is the control fixed-point sequence, V′ k are the model points obtained by linear interpolation;

[0058] Different from the traditional assembly method, this embodiment uses the basis center of the basis function as the parameter point to assemble the n×n coefficient matrix: for the basis functions b0(x,y),b1(x,y),…,b n(x,y), at the parameter points (x1,y1),(x2,y2),…,(x n ,y n ) where the basis functions are assembled;

[0059]

[0060] in, is the domain on the k-layer T grid g , and g is the entire hierarchical T grid of all cell cavities.

[0061] The right-hand term uses piecewise linear interpolation corresponding to the parameter point, with the weight being the barycentric coordinates, and the expression is:

[0062] V′ k =ω k1 V k1 +ω k2 V k3 +ω k3 V k3

[0063] Step 3: Calculate the model error and find the k-layer cell set θ that needs to be subdivided based on the error. If the cell set is not empty, go to step 4; if the cell set is empty, output the model and complete the modeling, such as Figure 3 .

[0064] The error of the fitted model is calculated as:

[0065] E θ =max θ ‖V l -S k (x l ,y l )‖

[0066] Among them, V l is the sampling point of the 3D point cloud model, l=1,2,…,N; S k (x l ,y l ) is the sampling point V l The k-layer fitting model at , θ is the cavity in the cavity set.

[0067] Finding the k-layer cell set Θ that needs to be subdivided based on the error includes:

[0068] Preset threshold value;

[0069] If the error is less than the threshold, it is determined that the cell set does not need to be subdivided; if the error is greater than the threshold, it is determined that the cell set needs to be subdivided.

[0070] Step 4: Subdivide the cell θ in the cell set Θ to obtain g k+1 ;

[0071] In this embodiment, each cell cavity θ in the cell cavity set Θ is subdivided into four sub-cell cavities of the same size to obtain g k+1 .

[0072] Step 5: Use isomorphic mapping to construct S(2,2,1,1,g k+1 ) basis functions, where S(2,2,1,1,g k+1 ) is g k+1 The biquadratic first-order continuous spline space on g k+1 is the level T grid after being subdivided k+1 times.

[0073] Initialize the weights of the k+1 layer basis function and obtain the support area of ​​the k+1 layer basis function;

[0074] The B ordinates of the k+1 layer basis functions are calculated using the T grid, all cells in the support region are traversed, the cells whose B ordinates are not all 0 and their B ordinates are retained, and the construction of the k+1 layer basis functions is completed.

[0075] The specific process is as follows:

[0076] Step 5.1: Initialize any newly added basis function b k+1 Weight of (x,y):

[0077]

[0078] Step 5.2, get b k +1 The support region E of (x,y): Due to the hierarchical structure of the level T grid, the k+1 level basis function b k+1 The support area E of (x,y) must be a sub-area supported by a certain k-layer basis function, so the area supported by this k-layer basis function can be defined as E.

[0079] Step 5.3: Calculate b using the T structure k+1 The B ordinate of (x,t):

[0080] Get the T branches covering the support area, sort all T structures in the T branches in the support area, re-sort the T branches, calculate the B ordinates of the k+1 layer basis functions on each T branch in sequence according to the sorting, and get the B ordinate of each cell in the support area.

[0081] Sorting all T structures within a T branch within the support region includes:

[0082] The preset storage set V and the new T branch set {TSB0,TSB1,…,TSB c};

[0083] Select the lowest-level T structure in the first T branch and put it into the first new T branch TSB0, traverse other T structures in the first T branch to see if they are connected to the T structure in the first new T branch TSB0, if so, put them into the storage set V and delete them in the first T branch;

[0084] After the traversal is completed, the T structure in the storage set V is assigned to the first new T branch TSB0, completing the sorting of all T structures in the first T branch;

[0085] Traverse all T branches, complete the T structure sorting of all T branches in the support area, and output the new T branch set {TSB0,TSB1,…,TSB c}.

[0086] Obtaining the B ordinate of each cell in the support region includes:

[0087] Calculate the B ordinate of the basis function on the first T structure in the T branch TSB0, and store the first T structure in the storage set V. At the same time, delete the first T structure in the T branch TSB0. Repeat until there are no remaining T structures in the T branch TSB0, and obtain the B ordinate on the T branch TSB0.

[0088] Calculate the basis functions in T branches TSB1, TSB2, ..., TSB in turn c The B ordinate on the support region is calculated by using the first-order continuity conditions between different cell cavities in the support region to calculate the B ordinate of each cell cavity in the support region.

[0089] The specific process is as follows:

[0090] (a) Obtain all T branches covering E: According to the initialization, the weight or B ordinate of each T union and P-type cell in E has been obtained. We only need to find the corresponding T branch, that is, all T branches covering E to calculate all B ordinates in E.

[0091] (b) Sort all T structures in each T branch in E: The set storing all T structures in any T branch of E is recorded as TSB. First, an empty T structure set TSB0 is defined to store the sorted results. Then, the T structure with the lowest level is selected from the input T structure set TSB and stored in TSB0, and then the selected T structure is deleted from TSB. Next, the algorithm enters a loop. When there are still T structures remaining in TSB, for each T structure in TSB0, a new empty set V is defined to store other T structures connected to the current T structure. When traversing each T structure in TSB, the algorithm determines whether it is connected to a T structure in TSB0. If so, the T structure is added to the memory V. After that, the T structures added to V are deleted from TSB, and the elements in V are sorted in descending order. Finally, the elements in V are assigned to TSB0. When all T structures in TSB have been processed, the algorithm finally outputs the sorted TSB0, that is, the T structure branch with internal sorting completed. According to the above sorting, all T structures in the T branch of E are sorted. The sorting result will make the T structures descending and progressive layer by layer, and connected in pairs.

[0092] (c) Calculate b k+1 All B ordinates of (x,y): Determine the g on the given level T grid k+1 The weight of each domain center is obtained, and the pre-support set E is obtained, which contains two sets: c T joint sets {TC0,TC1,…,TC c} and d P cell sets {PC0,PC1,…,PC d}. Then for each TC f Corresponding to find a T branch TSB f ,f=0,1,…,c. Then for each T branch TSB f The T structure in the internal sorting f=0,1,…,c, and these branches are re-sorted in descending order into {TSB0,TSB1,…,TSB c}. After sorting is completed, calculate b k+1 The (x,y) vertical scales on each T branch are:

[0093] First, calculate b k+1(x, y) is found on the B ordinate of the first T structure in TSB0 of the T branch, and the T structure is stored in the set V, and the T structure is deleted from TSB0. Then, the algorithm enters a loop until there are no more T structures left in TSB0. In each loop, the algorithm checks each T structure in TSB0 in turn to determine whether it is connected to a T structure in the set V at the endpoint. If it is found to be connected, the algorithm first calculates the surrounding B ordinate at the other endpoint of the T structure, and then calculates b according to the first-order continuity condition. k+1 (x, y) is the B ordinate on the T structure. After the calculation is completed, the algorithm deletes the T structure from TSB0 and updates the set V to add the T structure to it. This process continues until all T structures have been processed and b is finally completed. k+1 (x,y) is calculated on the B ordinate of all T structures in TSB0. The remaining b k+1 The B ordinate of (x,y) can be obtained by first-order continuity conditions on each small edge.

[0094] Then, calculate b in the same way as above. k+1 (x,y) in T branches TSB1,TSB2,…,TSB c The B vertical mark on the top.

[0095] Finally, the B ordinate of each cavity in the set E is calculated using the first-order continuity conditions between different cavities in the pre-support set E.

[0096] Step 5.4, save b k+1 The B ordinate of (x,y): traverse all the cells in E and retain the cells whose B ordinates are not all 0 and their B ordinates.

[0097] Step 6: Obtain the next fitting model based on the basis function, calculate the error of the next fitting model, and iterate steps 3 to 6 until the modeling is completed.

[0098] The present invention adopts an isomorphic mapping method to study the dimension formula and spline construction of a high-order smooth spline space on a T-grid, and uses a low-order, simple spline space to study a high-order, complex spline space, thereby improving the simplicity and effectiveness of the research; it breaks through the limitation of grid division, and can construct a basis function with excellent properties such as linear independence, unit division, local support and completeness on a grid without level difference restrictions through the isomorphic mapping method; the basis function constructed by the isomorphic mapping method can perform accurate geometric modeling and isogeometric analysis without the need to subdivide more grids to meet the level difference requirements, thereby reducing the amount of calculation and improving the calculation efficiency; it can ensure that the number of equations is the same as the number of unknowns in the fitting process, and the assembly matrix is ​​relatively small, so that the fitting process is more accurate and the calculation efficiency is higher, and a powerful tool is provided for the accurate modeling and analysis of complex grid models.

[0099] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A local subdivision geometry modeling method for additive manufacturing, characterized in that: include: Step 1: Input 3D point cloud model; Step 2, assembling a matrix on the k-layer T grid of the three-dimensional point cloud model to construct a fitting model; Step 3, calculating the error of the fitting model, and finding the target cell cavity set based on the error. If the target cell cavity set does not exist, directly outputting the fitting model to complete the modeling; If the target cell cavity set exists, proceed to step 4; Step 4: subdivide the target cell set to obtain a k+1 layer T grid; Step 5: Use isomorphic mapping to construct the basis function of the k+1 layer T grid; Step 6: construct the next fitting model based on the basis function, and iterate steps 3 to 6 until the modeling is completed.

2. The local subdivision geometric modeling method for additive manufacturing according to claim 1, characterized in that: The fitting model is: Among them, S k (x,y) is the k-layer fitting model; P k i is the control point of k-layer spline i; b k i (x,y) is the function of k-layer spline i, and n is the number of k-layer splines.

3. The local subdivision geometric modeling method for additive manufacturing according to claim 1, characterized in that: The method for calculating the error of the fitting model is: E θ =max θ ‖V l -S k (x l ,y l )‖ Among them, V l is the sampling point of the 3D point cloud model, l=1,2,…,N; S k (x l ,y l ) is the sampling point V l The k-layer fitting model at , θ is the cavity in the cavity set.

4. The local subdivision geometric modeling method for additive manufacturing according to claim 1, characterized in that: Finding a target cell set based on the error includes: Preset threshold value; If the error is smaller than a threshold, it is determined that the target cell cavity set does not exist; if the error is larger than a threshold, it is determined that the target cell cavity set exists.

5. The local subdivision geometric modeling method for additive manufacturing according to claim 1, characterized in that: The basis functions for constructing k+1 layers of T-grid using isomorphic mapping include: Initialize the weights of the k+1 layer basis function and obtain the support area of ​​the k+1 layer basis function; The B ordinates of the k+1 layer basis functions are calculated using the T grid, all cells in the support region are traversed, and the cells whose B ordinates are not all 0 and their B ordinates are retained to complete the construction of the k+1 layer basis functions.

6. The local subdivision geometric modeling method for additive manufacturing according to claim 5, characterized in that: The B ordinates for calculating the k+1 layer basis functions using the T grid include: The T branches covering the support area are obtained, all T structures in the T branches in the support area are sorted, and the T branches are re-sorted, and the B ordinates of the k+1 layer basis functions on each T branch are calculated in sequence according to the sorting, and the B ordinates of each cell cavity in the support area are obtained.

7. The local subdivision geometric modeling method for additive manufacturing according to claim 6, characterized in that: Sorting all T structures in the T branches within the support region includes: The preset storage set V and the new T branch set {TSB0,TSB1,…,TSB c }; Select the T structure with the lowest level in the first T branch and put it into the first new T branch TSB0, traverse other T structures in the first T branch to see if they are connected to the T structure in the first new T branch TSB0, if so, put them into the storage set V and delete them in the first T branch; After the traversal is completed, the T structure in the storage set V is assigned to the first new T branch TSB0, and the sorting of all T structures in the first T branch is completed; Traverse all T branches, complete the T structure sorting of all T branches in the support area, and output the new T branch set {TSB0,TSB1,…,TSB c }.

8. The local subdivision geometric modeling method for additive manufacturing according to claim 7, characterized in that: Obtaining the B vertical mark of each cell cavity in the support area includes: Calculate the B ordinate of the basis function on the first T structure in the T branch TSB0, store the first T structure in the storage set V, and delete the first T structure in the T branch TSB0, repeat until there is no remaining T structure in the T branch TSB0, and obtain the B ordinate on the T branch TSB0; Calculate the basis functions in T branches TSB1, TSB2, ..., TSB in turn c The B ordinate on the support region is calculated by using the first-order continuity conditions between different cell cavities in the support region to calculate the B ordinate of each cell cavity in the support region.

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