A method, apparatus, device, and storage medium for post-processing triangular meshes.

Abstract

This application discloses a method, apparatus, device, and storage medium for post-processing triangular meshes, relating to the field of computer graphics technology. The method includes: classifying an initial triangular mesh to obtain initial inner elements and initial boundary elements; classifying the initial boundary elements to obtain single-boundary-edge elements, two-boundary-edge elements, and three-boundary-edge elements; filling in the gaps between adjacent three-boundary-edge elements and two-boundary-edge elements to obtain a new triangular mesh; extracting the boundary points of all boundary elements in the new triangular mesh and connecting them sequentially to obtain connected boundary information; filling in new elements at locations with concave or deformed areas in the connected boundary information to obtain a new triangular queue, which is then spliced ​​to obtain a first filled triangular mesh; and removing all elements with angular distortions to obtain the target triangular mesh. This application can quickly and automatically obtain triangular meshes suitable for finite element calculations without relying on manual parameter tuning.

Description

Technical Field

[0001] This application relates to the field of computer graphics technology, and in particular to a method, apparatus, device and storage medium for post-processing triangular meshes. Background Technology

[0002] Currently, the DISTMESH method is applicable to both simply connected and multi-connected discrete regions. Simply connected regions contain only the outer boundary, while multi-connected regions contain both the outer and inner boundaries. The DISTMESH method uses computer iteration to bring the mesh to meet quality and resolution requirements within a given timeframe. Each iteration includes three steps: 1) For a given set of points, the Delaunay triangulation algorithm is used to mesh and determine the topology; 2) A distance function is used to determine the points within the region, i.e., the set of points remaining in the region after the previous iteration is retained; 3) After determining the location and topology of the retained point set, a force-displacement relationship is determined using a resolution function, thereby moving the points to new locations, which also provides the initial set of points for the next iteration. The distance function, with positive and negative signs, corresponds to the outside and inside of the region, respectively. The sign determines the set of points to retain, and the absolute value of the distance function is the shortest distance from each point on the plane to the boundary. The Delaunay triangulation algorithm possesses the characteristics of an empty circumcircle and maximizing the minimum angle, thus providing a topology of optimal quality for a given set of points. The resolution function specifies the resolution of each point in the mesh required for model calculation, outlining the requirements for the target mesh resolution, i.e., the size and distribution of the cells. The force-displacement relationship, determined by the resolution function, constructs a pulling force on the sides of the triangle based on the difference between the existing mesh resolution and the target resolution. This force causes the side length to "deform," i.e., the points to "displace." Through continuous iteration, the establishment and solution of the force-displacement relationship ultimately ensures that the mesh resolution meets the requirements.

[0003] However, in practical problems such as finite element calculations of aircraft tires and related components, complex boundaries and specific resolutions exist. The DISTMESH method relies too heavily on the initial mesh size, mesh density function, and number of iterations, as well as the relationship between these three factors. This results in obtaining suitable mesh information for finite element calculations requiring complex autonomous adjustments to the input parameters of the DISTMESH method or multiple manual adjustments to the program parameters. Therefore, it cannot achieve complete program automation, and there are very few post-processing methods for optimizing the mesh generated by the DISTMESH method. Summary of the Invention

[0004] In view of this, the purpose of this application is to provide a method, apparatus, device, and storage medium for post-processing triangular meshes, which can quickly and automatically obtain triangular meshes suitable for finite element calculations without relying on manual parameter tuning. The specific solution is as follows:

[0005] In a first aspect, this application discloses a post-processing method for triangular meshes, including:

[0006] The initial triangular mesh is classified into inner and boundary elements to obtain the initial inner and initial boundary elements.

[0007] All the initial boundary elements are classified according to the number of boundary edges to obtain single-boundary-edge elements, two-boundary-edge elements, and three-boundary-edge elements;

[0008] Based on the initial triangular mesh, the adjacent gaps of the three boundary edge units and the two boundary edge units are filled to obtain a new triangular mesh;

[0009] Extract the boundary points of all boundary cells in the new triangular mesh, and connect the boundary points end to end in order to obtain the boundary information after connection;

[0010] New units are filled at the concave and deformed locations in the connected boundary information to obtain a new triangular queue, and the new triangular queue is spliced ​​to obtain the first filled triangular mesh;

[0011] Remove all angularly distorted cells from the first filled triangular mesh to obtain the target triangular mesh.

[0012] Optionally, the step of classifying the initial triangular mesh into inner and boundary elements to obtain initial inner and initial boundary elements includes:

[0013] The nodes in the initial triangular mesh are adjusted to move nodes located outside the boundary of the initial triangular mesh to a preset contour boundary, resulting in an adjusted triangular mesh.

[0014] The adjusted triangular mesh is classified into inner and boundary elements to obtain initial inner and initial boundary elements.

[0015] Optionally, the step of filling in the adjacent gaps between the three boundary edge units and the two boundary edge units based on the initial triangular mesh to obtain a new triangular mesh includes:

[0016] On the initial triangular mesh, determine the first node in the three boundary edge element that is not shared with other triangles;

[0017] Each of the three boundary edge units, except for the first node, is identified.

[0018] The cells adjacent to the three boundary edge cells are determined by the other nodes and based on the local coordinate system method to obtain the first adjacent cell, and new cells are filled between the first adjacent cell and the three boundary edge cells to obtain the second filled triangular mesh;

[0019] On the second filled triangular mesh, the edge that is uniquely common to the other triangles in the two boundary edge cells is determined, and the node opposite the uniquely common edge is determined from the two boundary edge cells to obtain the second node;

[0020] The second node determines the cells adjacent to the two boundary edge cells, thus obtaining the second adjacent cells. New cells are then filled between the second adjacent cells and the two boundary edge cells to obtain a new triangular mesh.

[0021] Optionally, extracting the boundary points of all boundary cells in the new triangular mesh includes:

[0022] The boundary cells in the new triangular mesh are classified according to the number of boundary edges to obtain new single-boundary-edge cells and new two-boundary-edge cells.

[0023] The boundary points of the new single-boundary edge unit and the new double-boundary edge unit are extracted in a counter-clockwise order.

[0024] Optionally, the step of filling new units at the locations of concave or deformed areas in the post-connection boundary information to obtain a new triangular queue includes:

[0025] All nodes located inside the boundary are obtained from the connection boundary information, resulting in nodes inside the boundary. New units are then filled in the recessed or deformed positions of the nodes inside the boundary to obtain a new triangular queue.

[0026] Optionally, removing all angularly distorted cells from the first filled triangular mesh to obtain the target triangular mesh includes:

[0027] Determine whether the minimum angle of each triangle unit in the first filled triangle grid is less than or equal to a first preset angle or whether the maximum angle in the triangle unit is greater than or equal to a second preset angle;

[0028] If so, the triangular units with angles less than or equal to the first preset angle and the triangular units with angles greater than or equal to the second preset angle are determined to be angularly distorted units, thus obtaining the first angularly distorted unit;

[0029] The nodes corresponding to the largest angle greater than or equal to the second preset angle in the first angle-distorted unit are identified to obtain the third node;

[0030] Determine the polygon formed by all triangular units sharing the third node in the first filled triangular mesh, determine the centroid position of the polygon, and then move the third node in the first filled triangular mesh to the centroid position to obtain the moved triangular mesh.

[0031] The triangles in the moved triangle mesh whose minimum angle is less than or equal to the first preset angle or whose maximum angle is greater than or equal to the second preset angle are identified as angle-distorted units, thus obtaining the second angle-distorted units.

[0032] The deformed units in the second angle deformity whose minimum angle is less than or equal to the first preset angle are classified to obtain the target inner unit and the target boundary unit;

[0033] In the moved triangular mesh, the nodes at both ends of the smallest angle opposite the edge in the target boundary cell that are not boundary points are moved to the nodes that are boundary points. Then, all the deformed cells in the target boundary cell where the nodes at both ends of the smallest angle opposite the edge are boundary points and the nodes at both ends of the smallest angle opposite the edge in the target inner cell are moved to the midpoint of this edge to obtain the processed triangular mesh.

[0034] Determine whether there is an angle less than or equal to the first preset angle or greater than or equal to the second preset angle among all triangular units in the processed triangular mesh; otherwise, use the processed triangular mesh as the target triangular mesh.

[0035] Optionally, the triangular mesh post-processing method further includes:

[0036] Each triangle in the target triangular mesh is numbered, and the coordinates of each node in the target triangular mesh are calculated so that the numbering and coordinates can be used to perform the corresponding finite element calculations.

[0037] Secondly, this application discloses a triangular mesh post-processing apparatus, comprising:

[0038] The mesh classification module is used to classify the initial triangular mesh into inner and boundary elements, thus obtaining the initial inner and initial boundary elements.

[0039] The boundary unit classification module is used to classify all the initial boundary units according to the number of boundary edges, resulting in single-boundary-edge units, two-boundary-edge units, and three-boundary-edge units.

[0040] The first filling module is used to fill the gaps between the three boundary edge units and the two boundary edge units based on the initial triangular mesh to obtain a new triangular mesh.

[0041] The boundary point connection module is used to extract the boundary points of all boundary cells in the new triangular mesh and connect the boundary points in a sequential order to obtain the connected boundary information.

[0042] The second filling module is used to fill new units at the locations of depressions and deformities in the post-connection boundary information to obtain a new triangle queue, and to splice the new triangle queue to obtain a first filled triangle mesh.

[0043] The deformed cell removal module is used to remove all angularly deformed cells in the first filled triangular mesh to obtain the target triangular mesh.

[0044] Thirdly, this application discloses an electronic device, including a processor and a memory; wherein, when the processor executes a computer program stored in the memory, it implements the aforementioned triangular mesh post-processing method.

[0045] Fourthly, this application discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned triangular mesh post-processing method.

[0046] As can be seen, this application first classifies the initial triangular mesh into inner and boundary elements to obtain initial inner and initial boundary elements. Then, it classifies all the initial boundary elements according to the number of boundary edges to obtain single-boundary-edge elements, two-boundary-edge elements, and three-boundary-edge elements. Next, based on the initial triangular mesh, it fills the adjacent gaps between the three-boundary-edge elements and the two-boundary-edge elements to obtain a new triangular mesh. Then, it extracts the boundary points of all boundary elements in the new triangular mesh and connects the boundary points sequentially to obtain the connected boundary information. Then, it fills the concave and deformed positions in the connected boundary information with new elements to obtain a new triangular queue. The new triangular queues are then spliced ​​to obtain the first filled triangular mesh. Finally, it removes all elements with angular distortions from the first filled triangular mesh to obtain the target triangular mesh. This application can quickly and automatically obtain a triangular mesh suitable for finite element calculations without relying on manual adjustment of the initial mesh size, mesh density function, and number of iterations and the relationship between these three parameters. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0048] Figure 1 This is a flowchart of a triangular mesh post-processing method disclosed in this application;

[0049] Figure 2 This application discloses a specific flowchart for removing angular deformed units;

[0050] Figure 3 This is a schematic diagram of a specific triangular mesh disclosed in this application;

[0051] Figure 4 This is a schematic diagram of a specific triangular mesh disclosed in this application;

[0052] Figure 5 This is a schematic diagram of a specific triangular mesh disclosed in this application;

[0053] Figure 6 This is a schematic diagram of a specific triangular mesh disclosed in this application;

[0054] Figure 7 This is a flowchart of a specific triangular mesh post-processing method disclosed in this application;

[0055] Figure 8 This is a schematic diagram of a triangular mesh post-processing device disclosed in this application;

[0056] Figure 9 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0057] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0058] This application discloses a post-processing method for triangular meshes. See also... Figure 1 As shown, the method includes:

[0059] Step S11: Classify the initial triangular mesh into inner elements and boundary elements to obtain the initial inner elements and initial boundary elements.

[0060] In this embodiment, an initial triangular mesh to be processed is first obtained. Then, the initial triangular mesh is classified into inner and boundary elements to obtain the corresponding initial inner and boundary elements. Specifically, the initial triangular mesh can be a triangular mesh obtained after processing by the DISTMESH method. For example, see... Figure 2 As shown, Figure 2A specific multi-connected triangular mesh is shown, which includes both inner and boundary elements.

[0061] Step S12: Classify all the initial boundary elements according to the number of boundary edges to obtain single boundary edge elements, two boundary edge elements, and three boundary edge elements.

[0062] Next, all the initial boundary elements described above can be classified according to the number of boundary edges to obtain corresponding single-boundary-edge elements, two-boundary-edge elements, and three-boundary-edge elements. For example, Figure 2 In the diagram, ①, ②, and ③ represent single-boundary edge element, two-boundary edge element, and three-boundary edge element, respectively.

[0063] Step S13: Based on the initial triangular mesh, fill the gaps between the three boundary edge units and the two boundary edge units to obtain a new triangular mesh.

[0064] Furthermore, based on the initial triangular mesh, new cells are added to fill the adjacent gaps between the three-boundary-edge cells and the two-boundary-edge cells to obtain a new triangular mesh. It should be noted that the new triangular mesh no longer contains malformed cells where all three edges are boundary edges, or cells with two boundary edges where the two boundary edges belong to different boundaries. See also... Figure 3 As shown, Figure 3 It shows the Figure 2 The new triangular mesh is obtained by filling the gaps between three-boundary edge elements and two-boundary edge elements. It should be noted that, in this embodiment, filling the gaps between two-boundary edge elements specifically involves filling new elements into two-boundary edge elements whose two boundary edges do not belong to the same boundary. For example, let the node opposite the unique common edge in the two-boundary edge elements be defined as the cusp of the two-boundary edge elements, and then find two boundary elements belonging to different boundaries that share the cusp node with the two-boundary edge elements and fill them with new elements.

[0065] Step S14: Extract the boundary points of all boundary cells in the new triangular mesh, and connect the boundary points in the order of their beginning and end to obtain the connected boundary information.

[0066] In this embodiment, after filling the gaps between the three boundary edge units and the two boundary edge units to obtain a new triangular mesh based on the initial triangular mesh, the boundary points of all boundary units in the new triangular mesh are extracted. Then, all the boundary points are connected in the order of their beginning and end to obtain the connected boundary information. It should be noted that the connected boundary information is specifically the point list information of the boundary points.

[0067] In one specific implementation, extracting the boundary points of all boundary cells in the new triangular mesh may specifically include: classifying the boundary cells in the new triangular mesh according to the number of boundary edges to obtain new single-boundary-edge cells and new two-boundary-edge cells; and extracting the boundary points of the new single-boundary-edge cells and the new two-boundary-edge cells. It is understood that since there are no three-boundary-edge cells or two-boundary-edge cells where the two boundary edges belong to different boundaries in the new triangular mesh, reclassifying the boundary cells in the new triangular mesh according to the number of boundary edges only yields new single-boundary-edge cells and new two-boundary-edge cells; that is, there are no three-boundary-edge cells. Then, all boundary points of the aforementioned new single-boundary-edge cells and new two-boundary-edge cells are extracted.

[0068] Step S15: Fill new cells at the concave and deformed locations in the connected boundary information to obtain a new triangle queue, and splice the new triangle queue to obtain the first filled triangle mesh.

[0069] In this embodiment, see Figure 4 As shown, after connecting the boundary points end to end to obtain the connected boundary information, new units are filled in the concave and deformed positions in the connected boundary information to obtain a new triangle queue. Then, the new triangle queue is spliced ​​to obtain the filled triangle mesh. By optimizing the concave and deformed units in the boundary, i.e., filling in new units, the boundary can be made smoother.

[0070] Step S16: Remove all angularly distorted cells in the first filled triangular mesh to obtain the target triangular mesh.

[0071] In this embodiment, after splicing the new triangle queue to obtain the first filled triangle mesh, all angle-distorted cells in the first filled triangle mesh are identified, and then the angle-distorted cells are removed through corresponding processing to obtain a new triangle mesh.

[0072] In one specific implementation, see Figure 4 As shown, removing all angularly distorted cells from the first filled triangular mesh to obtain the target triangular mesh can specifically include:

[0073] Step S21: Determine whether the minimum angle of each triangle unit in the first filled triangle grid is less than or equal to a first preset angle or whether the maximum angle in the triangle unit is greater than or equal to a second preset angle;

[0074] Step S22: If so, the triangular units with angles less than or equal to the first preset angle and the triangular units with angles greater than or equal to the second preset angle are determined as angularly distorted units, thus obtaining the first angularly distorted unit;

[0075] Step S23: Determine the nodes in the first angle-distorted unit whose maximum angle is greater than or equal to the second preset angle to obtain the third node;

[0076] Step S24: Determine the polygon formed by all triangular units sharing the third node in the first filled triangular mesh, and determine the centroid position of the polygon. Then move the third node in the first filled triangular mesh to the centroid position to obtain the moved triangular mesh.

[0077] Step S25: Determine the triangular units in the moved triangular mesh whose minimum angle is less than or equal to the first preset angle or whose maximum angle is greater than or equal to the second preset angle as angularly distorted units, and obtain the second angularly distorted units;

[0078] Step S26: Classify the deformed units in the second angle deformed units whose minimum angle is less than or equal to the first preset angle to obtain target inner units and target boundary units;

[0079] Step S27: Move the nodes that are not boundary points at both ends of the smallest angle opposite side in the target boundary cell of the moved triangular mesh to the nodes that are boundary points. Then move all the deformed cells in the target boundary cell where the nodes at both ends of the smallest angle opposite side are boundary points and the nodes at both ends of the smallest angle opposite side in the target inner cell to the midpoint of this side to obtain the processed triangular mesh.

[0080] Step S28: Determine whether there is an angle less than or equal to the first preset angle or greater than or equal to the second preset angle among all triangular units in the processed triangular mesh; otherwise, take the processed triangular mesh as the target triangular mesh.

[0081] For example, after obtaining the first filled triangular mesh, see Figure 5As shown, it is determined whether any triangular elements in all boundary elements and all internal elements of the first filled triangular mesh have an angle less than or equal to 20° or greater than or equal to 125°. If so, the corresponding triangular element is identified as an angle-distorted element. Next, the nodes corresponding to angles greater than or equal to 125° in the aforementioned angle-distorted elements are designated as distorted nodes. Then, all triangular elements in the first filled triangular mesh sharing the aforementioned distorted nodes are identified and grouped into a polygon. The aforementioned distorted nodes in the first filled triangular mesh are moved to the centroid of the polygon, resulting in a moved triangular mesh. Further, it is re-determined whether any triangular elements in the moved triangular mesh have an angle less than or equal to 20° or greater than or equal to 125°. If so, they are identified as angle-distorted elements, resulting in a second angle-distorted element. Then, the distorted elements less than or equal to 20° or greater than or equal to 125° in the second angle-distorted element are further analyzed. The elements are classified to obtain target inner elements and target boundary elements. Then, for the target boundary elements where, besides the node corresponding to the smallest angle, one of the other two nodes is a boundary point and the other is not, the nodes at both ends of the side opposite the smallest angle in the target boundary element within the moved triangular mesh that are not boundary points can be moved to the boundary point. Additionally, for distorted elements where both ends of the side opposite the smallest angle in the target boundary element are boundary points, and for the target inner elements, their smallest angle can be used as the distorted angle, and the node corresponding to the distorted angle can be used as the distorted node. The nodes at both ends of the side opposite the distorted node can then be moved to the midpoint of the edge connecting these two nodes, thus obtaining the processed triangular mesh. It should be noted that after obtaining the processed triangular mesh, further judgment is needed to determine whether any triangular elements in the processed triangular mesh have an angle less than or equal to 20° or greater than or equal to 125°. If not, it can be used as the target triangular mesh; if it does, the node adjustment operation to remove distorted elements can be further performed. For details, see [link to documentation]. Figure 6 As shown, Figure 6 Yes Figure 5 The triangular mesh obtained after removing the angularly distorted elements present in the mesh.

[0082] Furthermore, after removing all angularly distorted elements from the first filled triangular mesh to obtain the target triangular mesh, the process may further include: numbering each triangle in the target triangular mesh and calculating the coordinates of each node in the target triangular mesh, so as to perform corresponding finite element calculations using the numbering and the coordinates. For example, for Figure 6 Each triangular element in the triangular mesh is numbered, starting from 1. Then, the coordinates of the three nodes of each numbered triangular element are calculated for subsequent finite element calculations.

[0083] As can be seen, this embodiment first classifies the initial triangular mesh into inner and boundary elements to obtain initial inner and initial boundary elements. Then, it classifies all the initial boundary elements according to the number of boundary edges to obtain single-boundary-edge elements, two-boundary-edge elements, and three-boundary-edge elements. Next, based on the initial triangular mesh, it fills the adjacent gaps between the three-boundary-edge elements and the two-boundary-edge elements to obtain a new triangular mesh. Then, it extracts the boundary points of all boundary elements in the new triangular mesh and connects the boundary points sequentially to obtain the connected boundary information. Then, it fills the concave and deformed positions in the connected boundary information with new elements to obtain a new triangular queue. The new triangular queues are then spliced ​​to obtain the first filled triangular mesh. Finally, it removes all elements with angular distortions from the first filled triangular mesh to obtain the target triangular mesh. This embodiment can quickly and automatically obtain a triangular mesh suitable for finite element calculations without relying on manual adjustment of the initial mesh size, mesh density function, and number of iterations and the relationship between these three parameters.

[0084] This application discloses a specific post-processing method for triangular meshes. See [link to relevant documentation]. Figure 7 As shown, the method includes:

[0085] Step S31: Adjust the nodes in the initial triangular mesh to move the nodes located outside the boundary of the initial triangular mesh to the preset contour boundary to obtain the adjusted triangular mesh.

[0086] In this embodiment, the nodes located outside the preset contour boundary in the initial triangular mesh are first identified, and then the identified nodes located outside the contour boundary are moved to the contour boundary to obtain the triangular mesh information t1.

[0087] Step S32: Classify the adjusted triangular mesh into inner and boundary elements to obtain initial inner and initial boundary elements.

[0088] In this embodiment, after moving the nodes located outside the boundary of the initial triangular mesh to the preset contour boundary to obtain the adjusted triangular mesh, the adjusted triangular mesh is then classified into inner and boundary elements to obtain the corresponding initial inner and initial boundary elements.

[0089] Step S33: Classify all the initial boundary elements according to the number of boundary edges to obtain single boundary edge elements, two boundary edge elements, and three boundary edge elements.

[0090] For example, after classifying the above triangular mesh information t1, we obtain inner cells and boundary cells. Furthermore, the boundary cells are divided into three categories: cells with all three sides as boundaries, denoted as bround_3; cells with two sides as boundaries, denoted as bround_2; and cells with only one side as boundaries, denoted as bround_1.

[0091] Step S34: Determine the first node in the three boundary edge cells that is not shared with other triangles on the initial triangular mesh.

[0092] In this embodiment, after obtaining the above-mentioned bore_3, bore_2 and bore_1, the nodes in the bore_3 unit that are not shared with other triangles are further determined to obtain the first node.

[0093] Step S35: Determine the other nodes from the three boundary edge units, excluding the first node.

[0094] In this embodiment, after determining the first node in the bore_3 cell that is not shared with other triangles on the initial triangular mesh, other nodes besides the first node are determined from the bore_3 cell.

[0095] Step S36: Determine the cells adjacent to the three boundary edge cells using the other nodes and the local coordinate system method to obtain the first adjacent cell, and fill the gap between the first adjacent cell and the three boundary edge cells to obtain the second filled triangular mesh.

[0096] For example, after determining the nodes other than the first node from the bround_3 unit, the first adjacent unit can be obtained by determining the units adjacent to the three boundary edge units based on the local coordinate system method through the other nodes. Then, new units are filled between the first adjacent units and the three boundary edge units to obtain the corresponding second filled triangular mesh.

[0097] Step S37: On the second filled triangle mesh, determine the edge that is uniquely common to the other triangles in the two boundary edge cells, and determine the node opposite the uniquely common edge from the two boundary edge cells to obtain the second node.

[0098] In this embodiment, for the two boundary edge cells in the second filled triangular mesh, the unique edge shared by the two boundary edge cells with other triangles can be determined first. Then, the node opposite the unique shared edge can be determined from the two boundary edge cells to obtain the second node. For example, the node opposite the unique shared edge in the bore_2 cell can be found and defined as the cusp of the bore_2 cell.

[0099] Step S38: Determine the unit adjacent to the two boundary edge units through the second node to obtain the second adjacent unit, and fill the gap between the second adjacent unit and the two boundary edge units to obtain a new triangular mesh.

[0100] Furthermore, it is determined whether the two boundary edges in the bore_2 element belong to the same boundary. If the two boundary edges of the bore_2 element do not belong to the same boundary, that is, the cusp of the bore_2 element is shared, then two adjacent boundary elements belonging to different boundaries that share a node with the cusp of the bore_2 element are found respectively. Then, the cusp of the bore_2 element, another boundary node of the bore_2 element on the same boundary, and the boundary nodes of the adjacent elements on the same boundary other than the cusp are taken to obtain an angle with the cusp as the vertex. Then, the size of the angle formed by the two boundaries is compared, the boundary with the smaller angle is found, and then the new element is filled. Finally, it is added to the above triangular mesh information t1.

[0101] Step S39: Extract the boundary points of all boundary cells in the new triangular mesh, and connect the boundary points in the order of their beginning and end to obtain the connected boundary information.

[0102] It is understandable that after the above processing, there is no case in the triangular mesh information t1 where the boundary edges of the bore_3 unit and the bore_2 unit belong to different boundaries. Furthermore, the triangular mesh information t1 after adding units is reclassified and organized. The classified boundary units are divided into two categories: units with two edges as boundaries, denoted as bore_2_new, and units with only one edge as boundaries, bore_1_new. Then, all boundary units are found, and the boundary nodes of all the above boundary units are extracted and connected end to end in sequence to obtain the connected boundary information.

[0103] Specifically, the process of finding all boundary elements can include: arranging the nodes in the triangular mesh information t1 counterclockwise and labeling them as i, j, m. When extracting the boundary information of the bore_2_new element, the corresponding cusp position can be found first from the unique shared edge. Then, the position of the node is shifted according to the counterclockwise node order of the mesh, placing the cusp at position j, thus obtaining new mesh information. Next, the order of all bore_2_new elements is updated, and then the i, j and j, m columns of the new bore_2_new mesh information are extracted and concatenated to form the information set of the boundary edges of the bore_2_new element. For the boundary extraction of the bore_1_new element, the information set of the corresponding single boundary edge element can be obtained first from the unique boundary position without shared edges. Finally, the information of the boundary edge nodes of the bore_2_new and bore_1_new elements is concatenated to obtain all boundary edge information.

[0104] Step S310: Obtain all nodes located inside the boundary from the connected boundary information to obtain the nodes inside the boundary, and fill new units at the concave and deformed positions of the nodes inside the boundary to obtain a new triangle queue, and then splice the new triangle queue to obtain the first filled triangle mesh.

[0105] Furthermore, the distance from the boundary node to the boundary can be used to find all the concave points of the triangle queue after connection, i.e., the boundary node positions that are not on the boundary. Then, the concavity and convexity of the two nodes before and after each concave point are determined. Only the V-shaped boundary position that is both an internal point of the boundary and forms a concave point with the adjacent nodes before and after it is retained as the boundary concave deformity position. Then, the three nodes obtained from the concave deformity position are sorted counterclockwise to obtain the set of newly added boundary concave deformity units. This set is then spliced ​​into the original unit information to fill in the new units and make the boundary smoother.

[0106] Step S311: Remove all angularly distorted cells in the first filled triangular mesh to obtain the target triangular mesh.

[0107] For a more detailed description of the process of step S311, please refer to the relevant content disclosed in the foregoing embodiments, which will not be repeated here.

[0108] As can be seen, this embodiment first classifies the initial triangular mesh into internal and boundary elements. Boundary elements are further divided into three categories: single-boundary-edge elements, two-boundary-edge elements, and three-boundary-edge elements. Then, the three-boundary-edge elements are processed and optimized. Next, elements with two boundary edges that do not belong to the same boundary are processed and optimized. Further, all nodes and triangular mesh information are reclassified and reorganized. At this point, boundary elements are only of two types: elements with two edges as boundaries and elements with only one edge as a boundary. Then, all boundary edge node information of the boundary elements is extracted, and the boundary nodes are connected sequentially. Next, boundary concave deformities are optimized and filled with new elements to make the boundaries smooth. Finally, angularly deformed elements are processed and optimized. This embodiment can achieve fully automated parameter adjustment without relying on manual parameter tuning. It is not only applicable to finite element calculations in aircraft tires but also to the post-processing of any mesh completed using the DISTMESH method.

[0109] Accordingly, this application also discloses a triangular mesh post-processing device, see [link to relevant documentation]. Figure 8 As shown, the device includes:

[0110] Mesh classification module 11 is used to classify the initial triangular mesh into inner and boundary elements to obtain the initial inner and initial boundary elements.

[0111] Boundary unit classification module 12 is used to classify all the initial boundary units according to the number of boundary edges to obtain single boundary edge units, two boundary edge units and three boundary edge units;

[0112] The first filling module 13 is used to fill the gaps between the three boundary edge units and the two boundary edge units based on the initial triangular mesh to obtain a new triangular mesh.

[0113] Boundary point connection module 14 is used to extract the boundary points of all boundary units in the new triangular mesh and connect the boundary points in a sequential order to obtain the connected boundary information;

[0114] The second filling module 15 is used to fill new units at the locations of depressions and deformities in the connected boundary information to obtain a new triangle queue, and to splice the new triangle queue to obtain a first filled triangle mesh.

[0115] The deformed cell removal module 16 is used to remove all angularly deformed cells in the first filled triangular mesh to obtain the target triangular mesh.

[0116] The specific workflow of each of the above modules can be found in the relevant content disclosed in the foregoing embodiments, and will not be repeated here.

[0117] As can be seen, in this embodiment, the initial triangular mesh is first classified into inner and boundary elements to obtain initial inner and boundary elements. Then, all the initial boundary elements are classified according to the number of boundary edges to obtain single-boundary-edge elements, two-boundary-edge elements, and three-boundary-edge elements. Next, based on the initial triangular mesh, the adjacent gaps of the three-boundary-edge elements and the two-boundary-edge elements are filled to obtain a new triangular mesh. Then, the boundary points of all boundary elements in the new triangular mesh are extracted, and the boundary points are connected end-to-end to obtain the connected boundary information. Next, new elements are filled at the concave and deformed positions in the connected boundary information to obtain a new triangular queue. The new triangular queues are then spliced ​​to obtain the first filled triangular mesh. Finally, all elements with angular distortions in the first filled triangular mesh are removed to obtain the target triangular mesh. This embodiment can quickly and automatically obtain a triangular mesh suitable for finite element calculations without relying on manual adjustment of the initial mesh size, mesh density function, and iteration number, and the relationship between these three parameters.

[0118] In some specific embodiments, the grid classification module 11 may specifically include:

[0119] A node adjustment unit is used to adjust the nodes in the initial triangular mesh to move nodes located outside the boundary of the initial triangular mesh to a preset contour boundary, thereby obtaining an adjusted triangular mesh.

[0120] The first mesh classification unit is used to classify the adjusted triangular mesh into inner and boundary units to obtain initial inner and initial boundary units.

[0121] In some specific embodiments, the first filling module 13 may specifically include:

[0122] The first node determination unit is used to determine the first node in the three boundary edge units that is not shared with other triangles on the initial triangular mesh;

[0123] Other node determination units are used to determine other nodes besides the first node from the three boundary edge units respectively;

[0124] The first adjacent unit determination unit is used to determine the unit adjacent to the three boundary edge unit through the other nodes and based on the local coordinate system method, so as to obtain the first adjacent unit;

[0125] The first filling unit is used to fill new units between the first adjacent unit and the three boundary edge units to obtain the second filled triangular mesh;

[0126] A common edge determination unit is used to determine the edge that is uniquely shared with other triangles in the two boundary edge units on the second filled triangle mesh;

[0127] The second node determination unit is used to determine the node located opposite the unique common edge from the two boundary edge units to obtain the second node;

[0128] The second adjacent unit determination unit is used to determine the unit adjacent to the two boundary edge units through the second node, and thus obtain the second adjacent unit;

[0129] The second filling unit is used to fill new units between the second adjacent unit and the two boundary edge units to obtain a new triangular mesh.

[0130] In some specific embodiments, the boundary point connection module 14 may specifically include:

[0131] The second grid classification unit is used to classify the boundary units in the new triangular grid according to the number of boundary edges, so as to obtain new single boundary edge units and new two boundary edge units.

[0132] The first boundary point extraction unit is used to extract the boundary points of the new single boundary edge unit and the new double boundary edge unit in a counterclockwise sorting manner.

[0133] In some specific embodiments, the second filling module 15 may specifically include:

[0134] An internal node acquisition unit is used to acquire all nodes located inside the boundary from the connected boundary information to obtain the internal nodes of the boundary.

[0135] The third filling unit is used to fill new units at the concave and deformed positions in the internal nodes of the boundary to obtain a new triangular queue.

[0136] In some specific embodiments, the deformed unit removal module 16 may specifically include:

[0137] The first judgment unit is used to determine whether the minimum angle of each triangle unit in the first filled triangle grid is less than or equal to a first preset angle or whether the maximum angle in the triangle unit is greater than or equal to a second preset angle.

[0138] The first angle distortion unit is used to determine the triangle units with angle distortion less than or equal to the first preset angle and the triangle units with angle distortion greater than or equal to the second preset angle as units with angle distortion, and to obtain the first angle distortion unit.

[0139] The third node determination unit is used to determine the nodes in the first angle distortion unit whose maximum angle is greater than or equal to the second preset angle, and obtain the third node;

[0140] A polygon construction unit is used to determine a polygon composed of all triangle units sharing the third node in the first filled triangle mesh;

[0141] A centroid position determination unit is used to determine the centroid position of the polygon.

[0142] A center-of-gravity shifting unit is used to move the third node in the first filled triangular mesh to the center-of-gravity position to obtain a shifted triangular mesh.

[0143] The second angle distortion unit is used to determine the triangle units in the moved triangle grid whose minimum angle is less than or equal to the first preset angle or whose maximum angle is greater than or equal to the second preset angle as angle distortion units, and thus obtain the second angle distortion unit.

[0144] The deformed unit classification unit is used to classify deformed units in the second angle deformed units whose minimum angle is less than or equal to the first preset angle, to obtain target inner units and target boundary units;

[0145] A node moving unit is used to move nodes that are not boundary points at both ends of the smallest angle opposite side in the target boundary cell of the moved triangular mesh to nodes that are boundary points. Then, all deformed cells in the target boundary cell where both ends of the smallest angle opposite side are boundary points and nodes in the target inner cell where both ends of the smallest angle opposite side are boundary points are moved to the midpoint of this side to obtain the processed triangular mesh.

[0146] The second judgment unit is used to determine whether there is an angle less than or equal to the first preset angle or greater than or equal to the second preset angle among all the triangle elements in the processed triangle grid;

[0147] The target triangle mesh determination unit is used to determine the processed triangle mesh as the target triangle mesh if there is no angle less than or equal to the first preset angle or greater than or equal to the second preset angle among all triangle elements in the processed triangle mesh.

[0148] In some specific embodiments, the triangular mesh post-processing device may further include:

[0149] A numbering unit is used to number each triangle in the target triangular grid;

[0150] The coordinate calculation unit is used to calculate the coordinates of each node in the target triangular mesh, so as to perform corresponding finite element calculations using the number and the coordinates.

[0151] Furthermore, embodiments of this application also disclose an electronic device, Figure 9 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application.

[0152] Figure 9 This is a schematic diagram of the structure of an electronic device 20 provided in an embodiment of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the triangular mesh post-processing method disclosed in any of the foregoing embodiments. Alternatively, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0153] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0154] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0155] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the triangular mesh post-processing method executed by the electronic device 20 as disclosed in any of the foregoing embodiments, the computer program 222 may further include a computer program capable of performing other specific tasks.

[0156] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned disclosed triangular mesh post-processing method. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0157] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0158] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0159] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0160] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0161] The above provides a detailed description of a triangular mesh post-processing method, apparatus, device, and storage medium provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for generating a mesh for adhesive in aircraft tire parts, characterized in that, include: The initial triangular mesh is classified into inner elements and boundary elements to obtain initial inner elements and initial boundary elements; the initial triangular mesh is a triangular mesh obtained after the DISTMESH method is used to treat the glue on the aircraft tire part. All initial boundary units are classified according to the number of boundary edges to obtain single-boundary-edge units, two-boundary-edge units, and three-boundary-edge units; a single-boundary-edge unit is a unit with only one edge as a boundary, a two-boundary-edge unit is a unit with two edges as boundaries, and a three-boundary-edge unit is a unit with all three edges as boundaries. Based on the initial triangular mesh, the adjacent gaps of the three boundary edge units and the two boundary edge units are filled to obtain a new triangular mesh; Extract the boundary points of all boundary cells in the new triangular mesh, and connect the boundary points end to end in order to obtain the boundary information after connection; New cells are filled at the concave and deformed locations in the connected boundary information to obtain a new triangular queue, and the new triangular queue is spliced ​​to obtain the first filled triangular mesh; the concave and deformed location is both an internal point of the boundary and a V-shaped boundary location formed by the concave and adjacent nodes; Remove all angularly distorted cells from the first filled triangular mesh to obtain the target triangular mesh corresponding to the adhesive in the aircraft tire part; The process of removing all angularly distorted cells from the first filled triangular mesh to obtain the target triangular mesh corresponding to the adhesive in the aircraft tire area includes: Determine whether the minimum angle of each triangle unit in the first filled triangle grid is less than or equal to a first preset angle or whether the maximum angle in the triangle unit is greater than or equal to a second preset angle; If so, the triangular units with angles less than or equal to the first preset angle and the triangular units with angles greater than or equal to the second preset angle are determined to be angularly distorted units, thus obtaining the first angularly distorted unit; The nodes corresponding to the largest angle greater than or equal to the second preset angle in the first angle-distorted unit are identified to obtain the third node; Determine the polygon formed by all triangular units sharing the third node in the first filled triangular mesh, determine the centroid position of the polygon, and then move the third node in the first filled triangular mesh to the centroid position to obtain the moved triangular mesh. The triangles in the moved triangle mesh whose minimum angle is less than or equal to the first preset angle or whose maximum angle is greater than or equal to the second preset angle are identified as angle-distorted units, thus obtaining the second angle-distorted units. The deformed units in the second angle deformity whose minimum angle is less than or equal to the first preset angle are classified to obtain the target inner unit and the target boundary unit; In the moved triangular mesh, the nodes at both ends of the smallest angle opposite the edge in the target boundary cell that are not boundary points are moved to the nodes that are boundary points. Then, all the deformed cells in the target boundary cell where the nodes at both ends of the smallest angle opposite the edge are boundary points and the nodes at both ends of the smallest angle opposite the edge in the target inner cell are moved to the midpoint of this edge to obtain the processed triangular mesh. Determine whether there is an angle less than or equal to the first preset angle or greater than or equal to the second preset angle among all triangular units in the processed triangular mesh. If not, use the processed triangular mesh as the target triangular mesh corresponding to the glue in the aircraft tire part. If so, perform the node adjustment operation to remove all angularly distorted units in the first filled triangular mesh.

2. The mesh generation method for adhesive in aircraft tire parts according to claim 1, characterized in that, The process of classifying the initial triangular mesh into inner and boundary elements to obtain initial inner and initial boundary elements includes: The nodes in the initial triangular mesh are adjusted to move nodes located outside the boundary of the initial triangular mesh to a preset contour boundary, resulting in an adjusted triangular mesh. The adjusted triangular mesh is classified into inner and boundary elements to obtain initial inner and initial boundary elements.

3. The mesh generation method for adhesive in aircraft tire parts according to claim 1, characterized in that, The process involves filling in the gaps between the three boundary edge elements and the two boundary edge elements based on the initial triangular mesh to obtain a new triangular mesh, including: On the initial triangular mesh, determine the first node in the three boundary edge element that is not shared with other triangles; Each of the three boundary edge units, except for the first node, is identified. The cells adjacent to the three boundary edge cells are determined by the other nodes and based on the local coordinate system method to obtain the first adjacent cell. New cells are then filled between the first adjacent cell and the three boundary edge cells to obtain the second filled triangular mesh. The local coordinate system method is a method of constructing a local coordinate system with the nodes of the three boundary edge cells as the origin and retrieving the topological position of adjacent triangular cells based on the coordinate relationship of the local coordinate system. On the second filled triangular mesh, the edge that is uniquely common to the other triangles in the two boundary edge cells is determined, and the node opposite the uniquely common edge is determined from the two boundary edge cells to obtain the second node; The second node determines the cells adjacent to the two boundary edge cells, thus obtaining the second adjacent cells. New cells are then filled between the second adjacent cells and the two boundary edge cells to obtain a new triangular mesh.

4. The mesh generation method for adhesive in aircraft tire parts according to claim 1, characterized in that, The step of extracting the boundary points of all boundary cells in the new triangular mesh includes: The boundary cells in the new triangular mesh are classified according to the number of boundary edges to obtain new single-boundary-edge cells and new two-boundary-edge cells. The boundary points of the new single-boundary edge unit and the new double-boundary edge unit are extracted in a counter-clockwise order.

5. The mesh generation method for adhesive in aircraft tire parts according to claim 1, characterized in that, The step of filling new units at the locations of concave and deformed areas in the post-connection boundary information to obtain a new triangular queue includes: All nodes located inside the boundary are obtained from the connection boundary information, resulting in nodes inside the boundary. New units are then filled in the recessed or deformed positions of the nodes inside the boundary to obtain a new triangular queue.

6. The mesh generation method for adhesive in aircraft tire parts according to any one of claims 1 to 5, characterized in that, Also includes: Each triangle in the target triangular mesh is numbered, and the coordinates of each node in the target triangular mesh are calculated so that the numbering and coordinates can be used to perform the corresponding finite element calculations.

7. A mesh generation device suitable for rubber in aircraft tire parts, characterized in that, include: The mesh classification module is used to classify the initial triangular mesh into inner and boundary elements to obtain the initial inner and boundary elements; the initial triangular mesh is a triangular mesh obtained after applying adhesive to the aircraft tire part using the DISTMESH method. The boundary unit classification module is used to classify all the initial boundary units according to the number of boundary edges to obtain single boundary edge units, two boundary edge units, and three boundary edge units; the single boundary edge unit is a unit with only one edge as a boundary, the two boundary edge unit is a unit with two edges as boundaries, and the three boundary edge unit is a unit with all three edges as boundaries. The first filling module is used to fill the gaps between the three boundary edge units and the two boundary edge units based on the initial triangular mesh to obtain a new triangular mesh. The boundary point connection module is used to extract the boundary points of all boundary cells in the new triangular mesh and connect the boundary points in a sequential order to obtain the connected boundary information. The second filling module is used to fill new units at the concave and deformed positions in the connected boundary information to obtain a new triangle queue, and to splice the new triangle queue to obtain the first filled triangle mesh; the concave and deformed position is both an internal point of the boundary and a V-shaped boundary position formed by the concave and adjacent nodes; The deformed unit removal module is used to remove all angularly deformed units in the first filled triangular mesh to obtain the target triangular mesh corresponding to the adhesive in the aircraft tire part; The deformed unit removal module is specifically used to determine whether the minimum angle of each triangle unit in the first filled triangle mesh is less than or equal to a first preset angle or whether the maximum angle of the triangle unit is greater than or equal to a second preset angle; if so, the triangle units with angles less than or equal to the first preset angle and the triangle units with angles greater than or equal to the second preset angle are determined as angle deformed units, resulting in a first angle deformed unit; the nodes corresponding to the maximum angle of the first angle deformed unit being greater than or equal to the second preset angle are determined, resulting in a third node; the polygon formed by all triangle units sharing the third node in the first filled triangle mesh is determined, and the centroid position of the polygon is determined, and then the third node in the first filled triangle mesh is moved to the centroid position, resulting in a moved triangle mesh; the triangle units with angles less than or equal to the first preset angle or maximum angles greater than or equal to the second preset angle in the moved triangle mesh are determined as angle deformed units, resulting in a second angle deformed unit; Classify the deformed units in the second angle deformity where the minimum angle is less than or equal to the first preset angle to obtain target inner units and target boundary units; move the nodes at both ends of the side opposite the minimum angle in the target boundary unit of the moved triangular mesh that are not boundary points to nodes that are boundary points, and then move all deformed units in the target boundary unit where both ends of the side opposite the minimum angle are boundary points and the nodes at both ends of the side opposite the minimum angle in the target inner unit to the midpoint of this side to obtain the processed triangular mesh; determine whether there is an angle less than or equal to the first preset angle or greater than or equal to the second preset angle in all triangular units in the processed triangular mesh. If not, use the processed triangular mesh as the target triangular mesh corresponding to the glue in the aircraft tire part. If so, perform the node adjustment operation to remove all angle deformed units in the first filled triangular mesh.

8. An electronic device, characterized in that, It includes a processor and a memory; wherein, when the processor executes a computer program stored in the memory, it implements the mesh generation method for adhesives in aircraft tire parts as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, Used to store a computer program; wherein, when the computer program is executed by a processor, it implements the mesh generation method for adhesive in aircraft tire parts as described in any one of claims 1 to 6.

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