Spliced curved surface reinforcement method fusing graph theory and UV parameterization

Abstract

The invention discloses a splicing curved surface reinforcement method fusing a graph theory and UV parameterization. The splicing curved surface reinforcement method comprises the steps of creating a component BIM three-dimensional model, inputting reinforcement parameters, searching an arrangement path and generating reinforcing steel bars. In order to solve the technical problem of splicing curved surface reinforcement in the BIM three-dimensional design process of complex structure engineering, a graph theory is introduced to construct an edge and surface topological connected graph model, so that the problem of steel bar path planning in disordered splicing surfaces is effectively solved, and the construction efficiency is improved. The rapid routing of the steel bar arrangement path in the curved surface topology network and the rapid positioning of the steel bar arrangement path in a plurality of sampling points on the topology edge are realized. Meanwhile, by combining a UV bidirectional parameterization mapping mechanism, the problem of self-adaptive arrangement of the reinforcing steel bars in the three-dimensional curved surface is solved, so that efficient solving and accurate control of the reinforcing steel bars of the complex spliced curved surface are achieved, a traditional reinforcing steel bar mode dominated by manual experience is broken through, the automation degree and engineering reliability of the reinforcing steel bar design of the complex spliced curved surface are remarkably improved, and the construction cost is reduced. Good application prospects are realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of BIM (Building Information Modeling) and three-dimensional reinforcement design methods, and particularly relates to a splicing surface reinforcement method integrating graph theory and UV parameterization. Background Art

[0002] In recent years, with the popularization and application of the forward design of "3D modeling - reinforcement - drawing", it has been increasingly widely used in the fields of water conservancy projects, underground tunnels, special-shaped buildings, etc. Among them, the three-dimensional irregular surface splicing modeling is inevitably used. Such surfaces are usually composed of multiple surfaces spliced together, such as tunnel lining walls, spillway diversion walls, draft tube surface walls, etc. The irregularity and splicing of their geometric forms pose higher requirements for the arrangement of steel bars. Traditional steel bar design methods mostly rely on manual experience for segmented projection fitting and local adjustment, and it is difficult to efficiently handle the path planning problem of large-scale irregular surface splicing, resulting in a long design cycle, insufficient accuracy, and it is difficult to meet the requirements of digital construction for automated three-dimensional reinforcement.

[0003] When facing the multi-surface topological relationship, the existing three-dimensional reinforcement technology often lacks a systematic modeling of the connectivity between surfaces, resulting in broken or repeated intersections of steel bar paths, and a large amount of manual intervention is required to correct the deviation, which limits the design efficiency and large-scale application. With the popularization of BIM applications, high precision and high automation in the field of three-dimensional reinforcement are the inevitable development directions, and there is an urgent need for a solution for automatic path optimization to support the three-dimensional steel bar arrangement of complex surface structures. Summary of the Invention

[0004] The purpose of the present invention is to provide a splicing surface reinforcement method integrating graph theory and UV parameterization, which solves the problems of insufficient automation and engineering reliability in the existing reinforcement design of complex splicing surfaces.

[0005] The technical solution adopted by the present invention is: a splicing surface reinforcement method integrating graph theory and UV parameterization, including the following steps: Step 1, create a BIM three-dimensional model of the component; Step 2, based on the model obtained in Step 1, input the reinforcement parameters; Step 3, based on the reinforcement parameters in Step 2, search for the layout path and generate steel bars.

[0006] The present invention is also characterized in that Step 2 specifically includes the following steps: Step 2.1, input the continuous splicing surface of the steel bars to be reinforced by picking, and record it as the reinforcement surface; Step 2.2, input several guiding lines by picking, which are used for sampling to obtain the control points of the steel bar line, and mark the reference guiding line; Step 2.3: Input the steel bar specifications; Step 2.4: Input the offset value from the model surface to the outer surface of the steel bar; Step 2.5: Input the steel bar array parameters, including the steel bar spacing, starting distance, and ending distance.

[0007] The steel bar specifications input in Step 2.3 include the steel bar grade and diameter.

[0008] Step 3 specifically includes the following steps: Step 3.1: Combine the array parameters, and sequentially arrange distribution points along the reference guide line input in Step 2.2, and establish the association relationship between the distribution points and the reference guide line; Step 3.2: Uniformly arrange distribution points on other guide lines except the reference guide line input in Step 2.2. The number of distribution points on other guide lines is equal to that on the reference guide line, and establish the association relationship between the distribution points on other guide lines and their respective guide lines; Step 3.3: Serialize and sort the reinforcement surface input in Step 2.1 and the guide line input in Step 2.2; Step 3.4: Based on the distribution points obtained in Step 3.1 and Step 3.2, and the reinforcement surface data obtained in Step 3.3, group according to the requirements for creating a single steel bar, that is, each group of data corresponds to generating one steel bar; Step 3.5: Sequentially traverse the results obtained by grouping in Step 3.4, and define a segment list in the currently obtained group , and one segment in the segment list corresponds to generating a section of a single steel bar, that is, a steel bar segment:

[0009] In the formula, l is the total number of segments; represents the i th segment, 's data includes the points on the guide line a , the points on the adjacent guide line , and b 's points , and a , b a group of reinforcement surfaces connecting between two adjacent guide lines :

[0010] Step 3.6: Traverse the segment list obtained in Step 3.5 , for the i th segment take from it and create an undirected graph :

[0011]

[0012] ,

[0013] In the formula, is the set of vertices in the undirected graph; is the th vertex, is the total number of vertices; is the adjacency matrix representing the relationship between edges and vertices in the undirected graph; represents the edge connecting the th vertex and the th vertex. The connectivity weight of all edges is 1, and ; Step 3.7: In the undirected graph obtained in Step 3.6, find the two vertices corresponding to the guiding line where is located in the segment in Step 3.5, and use the Dijkstra algorithm to search for the shortest path between them ;

[0014]

[0015] In the formula, vertex is the starting point of ; is the ending point of ; , represent any adjacent terms in; is the list of edges between adjacent vertices in , is the first edge of , is the last edge of , represents any term in and satisfies ; Step 3.8: Based on the shortest path obtained in Step 3.7 and the corresponding edge list , combined with the point in Step 3.5, use graph theory and UV parameterization methods in except Search and calculate a point respectively on other vertices except , so that from Pass through , to The connection distance on the UV two-dimensional plane is the shortest. Finally, ensure that a topological surface has two control points; among them, the connection between two adjacent points , is the projection curve of the edge on the corresponding topological surface; calculate the list of points on the topological edges represented by the vertices on the shortest path :

[0016] In the formula, , , , represent Any adjacent terms in; Step 3.9. Offset the list of edges obtained in Step 3.7 Each topological surface in, the offset distance is the offset value input in Step 2.4, and the list of offset topological surfaces is obtained:

[0017] In the formula, is The offset topological surface, is The offset topological surface, represents Any term in; Step 3.10. As the topological surface in Step 3.9 is offset, project the start and end points in the list of shortest path points obtained in Step 3.8 onto the edge lines of the start and end surfaces of , and project the other points in the point list onto the intersection line of two adjacent surfaces in , and the list of projected points is obtained:

[0018] In the formula, is The projected point, is The projected point, , represent Any adjacent terms in; Step 3.11. Traverse the point list obtained in Step 3.10 simultaneously and the list of topological surfaces obtained in step 3.9 , take two adjacent points in 、 , and at the same time take the topological surface in 、 corresponding to , and use the UV parameterization method to obtain the projection curve connecting on the topological surface 、 . Finally, connect all the obtained projection curves, which is a segment of a single reinforcing bar; Step 3.12: Repeat steps 3.6 to 3.11, calculate all segments of a single reinforcing bar, and then connect all segments to generate a complete reinforcing bar; Step 3.13: Repeat steps 3.5 to 3.12, calculate and generate all reinforcing bars to complete the layout.

[0019] Step 3.4 specifically includes the following steps: Step 3.4.1: With the goal of having a group of topological surfaces connected between two adjacent guiding lines, group the spliced surfaces input in step 2.1 to obtain a list composed of a data structure of two guiding lines sandwiching a group of topological surfaces; Step 3.4.2: Assume that there are w distribution points on each guiding line. Based on the order of the data structure list of two guiding lines sandwiching a group of topological surfaces obtained in step 3.4.1, form a point sequence from the distribution points at the same order position on each guiding line, so that the distribution points obtained in steps 3.1 and 3.2 finally form w point sequences; Step 3.4.3: Sequentially take out the point sequences formed by the distribution points at the same order position on each guiding line obtained in step 3.4.2, and associate the point sequences with the list composed of the data structure of two guiding lines sandwiching a group of topological surfaces obtained in step 3.4.1 according to the association relationship between the distribution points and the guiding lines, to form a list composed of two guiding lines and two control points on them sandwiching a group of topological surfaces; Step 3.4.4: Repeat step 3.4.3 to realize the grouping of the reinforcement input data, where each group of data corresponds to generating a reinforcing bar.

[0020] Step 3.8 specifically includes the following steps: Step 3.8.1: Set the number of iterations iter and the number of sampling points s ; Step 3.8.2: Uniformly sample on the topological edges represented by the vertices other than the start and end vertices in the shortest path in step 3.7 ​s sample points, where one topological edge is defined as a sampling layer, and there are layers, sample points. The sampling area is determined by the result of the previous iteration, and the first iteration area is the parameter space at the head and tail ends of the topological edge; Step 3.8.3, Create a directed graph , and use the points in Step 3.5 and all the sampling points obtained in Step 3.8.2 as vertices, and unidirectionally connect the sampling points between adjacent layers as edges. The weight of the edge is the length of the projection curve on the surface;

[0021]

[0022] In the formula, is the vertex set, corresponding to the shortest path in Step 3.7 There are m layers, vertices; is the edge, and only unidirectional connection between vertices of adjacent layers is allowed; is the weight of the edge, corresponding to the length of the projection curve on the surface between two vertices, where the surface is indexed in the corresponding edge list according to the corresponding relationship with the shortest path ; in the corresponding edge list; Step 3.8.4, Use the Dijkstra algorithm to calculate the shortest path between the points in Step 3.5, and mark the points included in the shortest path among the sampling points of each layer as ; Step 3.8.5, Obtain the two sampling points adjacent to the point before and after in Step 3.8.4, and define the area between the two sampling points as the new sampling area of the sampling layer; Step 3.8.6, Repeat Steps 3.8.2 to 3.8.5 for the next iteration until the number of iterations is equal to the iter set in Step 3.8.1, and then terminate the iteration.

[0023] Step 3.10 specifically includes the following steps: Step 3.10.1, For the head and tail points of the point list in Step 3.8, that is, , and then index the head and tail points through the list of topological surfaces after offset in Step 3.9Their respective topological edges, then calculate the shortest distance from the point to the topological edge, and obtain the projection point corresponding to the shortest distance on the topological edge ; Step 3.10.2: For the point list in Step 3.8 except for other points , and then through the list of topological surfaces offset in Step 3.9 index the adjacent faces of the topological edges corresponding to other points , then find the intersection line edge by intersecting the two adjacent faces, and then calculate the shortest distance from the point to the intersection line edge, and obtain the projection point corresponding to the shortest distance on the intersection line edge ; Step 3.10.3: Combine the results of Step 3.10.1 and Step 3.10.2 to obtain the list of projected points .

[0024] Step 3.11 specifically includes the following steps: Step 3.11.1: Traverse simultaneously the point list calculated in Step 3.10 and the list of topological surfaces obtained in Step 3.9 , take two adjacent points , and in , and the topological surfaces corresponding to , then use the UV parameterization method to unfold , and obtain two UV points corresponding to , after unfolding, and finally construct a two-dimensional line segment from the two UV points; Step 3.11.2: Map the two-dimensional line segment obtained in Step 3.11.1 to the target surface to obtain a three-dimensional curve, and finally connect all the projected curves obtained by traversal, which is a segment of a single reinforcing bar.

[0025] The beneficial effects of the present invention are as follows: The present invention combines the graph theory and the UV parameterization method for reinforcing bars on spliced surfaces, aiming at the technical problem of reinforcing bar arrangement on spliced surfaces in the BIM three-dimensional design process of complex structural engineering. By introducing graph theory, an edge and face topological connectivity graph model is constructed, effectively solving the problem of reinforcing bar path planning in disordered spliced surfaces, and realizing the rapid path finding of the reinforcing bar arrangement path in the surface topological network and the rapid positioning among numerous sampling points on the topological edges. At the same time, combined with the UV bidirectional parameterization mapping mechanism, the problem of self-adaptive arrangement of reinforcing bars in the three-dimensional surface is solved, thus realizing the efficient solution and precise control of reinforcing bars on complex spliced surfaces, breaking through the traditional reinforcement mode dominated by manual experience, significantly improving the automation degree and engineering reliability of the reinforcing bar design on complex spliced surfaces, and having good application prospects. Description of the Drawings

[0026] Figure 1 is a schematic flow chart of the method for reinforcing bars on spliced surfaces by combining graph theory and UV parameterization of the present invention; Figure 2 is the undirected graph of the present invention application representation graph; Figure 3 is the directed graph of the present invention application representation graph; Figure 4 is a schematic diagram of the input parameters of the example of reinforcing bars on spliced surfaces of the present invention; Figure 5 is a schematic diagram of the reinforcing bar control points and reinforcing bar segments of the example of reinforcing bars on spliced surfaces of the present invention; Figure 6 is a single segment of the example of reinforcing bars on spliced surfaces of the present invention and the explanatory diagram of the generated reinforcing bar segments; Figure 7 is the local reinforcing bar arrangement effect diagram of the example of reinforcing bars on spliced surfaces of the present invention. Detailed Embodiment

[0027] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0028] Embodiment 1 The present invention provides a method for reinforcing spliced curved surfaces by integrating graph theory and UV parameterization. Based on the input adjacent guiding lines and a set of connected topological surfaces between them, a topological mapping model is constructed using graph theory, mapping the topological edges of the three-dimensional structure to graph theory vertices and the topological surfaces to graph theory edges to form a topological element relationship graph. Based on this, the Dijkstra algorithm is used to calculate the shortest path for the reinforcement bars to be arranged along the topological surfaces and edges, quickly locating the topological elements between the adjacent guiding lines associated with the reinforcement bar layout. Then, combined with the UV parameterization technology, a bidirectional mapping between the three-dimensional surface and the two-dimensional plane is established. According to the principle that the path of the reinforcement bar along the surface is the shortest, taking the control points determined by the input guiding lines as the start and end points, the control points of the reinforcement bar path on the non-guiding lines between them are calculated to ensure that one topological surface has two control points. Finally, on the final reinforced surface after offsetting the input parameters, the UV parameterization technology is still used to convert the reinforcement bar layout of a single three-dimensional surface into a two-dimensional plane straight line layout problem. The three-dimensional reinforcement bar segments are generated through the reverse mapping of the reinforcement bar layout in the parameter domain, and finally connected to form a complete reinforcement bar. As Figure 1 shown, it includes the following steps: Step 1: Create or import a BIM three-dimensional model.

[0029] Step 2: Based on the model obtained in Step 1, input the reinforcement parameters. Specifically, it includes the following steps: Step 2.1: Input the continuous spliced curved surface to be reinforced by picking, denoted as the reinforced surface.

[0030] Step 2.2: Input several guiding lines by picking, which are used for sampling to obtain the control points of the reinforcement bar lines. Among them, one belongs to the reference guiding line and needs to be marked, and the guiding line is valid only when it is connected to the reinforced surface.

[0031] Step 2.3: Input the reinforcement bar specifications, including the grade and diameter of the reinforcement bar.

[0032] Step 2.4: Input the offset value from the model surface to the outer surface of the reinforcement bar.

[0033] Step 2.5: Input the reinforcement bar array parameters, including the reinforcement bar spacing, starting distance, and ending distance.

[0034] Step 3: Based on the reinforcement parameters in Step 2, search for the layout path and generate the reinforcement bar. Specifically, it includes the following steps: Step 3.1: Combining the array parameters, sequentially arrange distribution points along the reference guiding line input in Step 2.2, and establish the association relationship between the distribution points and the reference guiding line.

[0035] Step 3.2: Following the principle of having the same number of distribution points as obtained in Step 3.1, evenly arrange distribution points on the guiding lines input in Step 2.2, and establish the association relationship with the respective guiding lines.

[0036] Step 3.3: With the goal of having a surface connection between adjacent guiding lines, sort the reinforcement surface input in Step 2.1 and the guiding lines input in Step 2.2 in series. It should be noted that there can be multiple connection surfaces between adjacent guiding lines.

[0037] Step 3.4: Based on the distribution points obtained in Step 3.1 and Step 3.2, and the reinforcement surface data obtained in Step 3.3, group them according to the requirements for creating a single reinforcing bar, that is, each group of data corresponds to generating one reinforcing bar.

[0038] Step 3.5: Traverse the results obtained by grouping in Step 3.4 in sequence. Define a segment list in the currently obtained group. One segment in the list corresponds to generating one section of a single reinforcing bar, denoted as a reinforcing bar segment.

[0039]

[0040] In the formula, is the segment list; represents the i th segment; l is the total number of segments; Among them, the data of one segment includes the points a on the guiding line , the points b on the adjacent guiding line , and a group of reinforcement surfaces connected between these two adjacent guiding lines:

[0041] In the formula, is a group of reinforcement surfaces between the adjacent guiding lines where

[0042] Step 3.6: Traverse the segment list in Step 3.5 , for the current i th segment , obtain from it, and create an undirected graph based on this, as shown in Figure 2 :

[0043]

[0044] ,

[0045] In the formula, is the undirected graph; is the set of vertices in the undirected graph; is the th vertex, is the total number of vertices; is the adjacency matrix representing the relationship between edges and vertices in an undirected graph, which has symmetry; represents the edge connecting the -th vertex and the -th vertex. The connectivity weight of all edges is 1, and ; It should be noted that one topological face in corresponds to an undirected edge of the graph, and one topological edge on the topological face corresponds to a vertex of the graph. It can be seen that all topological edges of the same topological face are connected pairwise.

[0046] If , it means there is no edge connection between the two vertices, that is, there is no topological face connection between the two topological edges; when , .

[0047] Step 3.7, find the two vertices corresponding to the guiding line (topological edge) where the segment in Step 3.5 is located in the undirected graph in Step 3.6, and use the Dijkstra algorithm to search for the shortest path between them ; ;

[0048]

[0049] In the formula, vertex is the starting point of ; is the ending point of ; , represent any adjacent terms in ; is the list of edges between adjacent vertices in , is the first edge of , is the last edge of , represents any term in and satisfies .

[0050] Step 3.8, based on the shortest path obtained in Step 3.7 and the corresponding , and combined with the in Step 3.5, use graph theory and UV parameterization technology in except Search and calculate a point on each of the other vertices (i.e., topological edges) outside such that from in sequence through , to the connection distance on the UV two-dimensional plane is the shortest, and finally ensure that a topological surface has two control points. Among them, the connection between two adjacent points , is the projection curve of the edge on the corresponding topological surface;

[0051] In the formula, is the list of points on the topological edges represented by the vertices on the shortest path calculated according to the above objective; where , , , represent any adjacent terms in.

[0052] Step 3.9. Based on obtained in Step 3.7, offset each topological surface by the offset value input in Step 2.4; obtain:

[0053] In the formula, is the list of offset topological surfaces, is the offset topological surface, is the offset topological surface, represents any term in.

[0054] Step 3.10. As the topological surfaces are offset in Step 3.9, in accordance with the principle of the shortest projection distance, project the start and end points of the shortest path list to the edge lines of the start and end surfaces of , and project the other points in the list to the intersection line of two adjacent surfaces in to obtain the projected point list:

[0055] In the formula, is the projected point list, is the projected point, is the projected point, , representation any adjacent items in

[0056] Step 3.11. Traverse simultaneously the obtained in Step 3.10 and the offset in Step 3.9, take two adjacent points in , , and simultaneously take the topological surface in , corresponding to . Based on this, use the UV parameterization method to obtain the projection curve connecting on the topological surface , . Finally, connect all the obtained projection curves, which is one segment of a single reinforcing bar.

[0057] Step 3.12. Repeat Steps 3.6 - 3.11 to calculate all segments of a single reinforcing bar, and then connect them to generate a complete reinforcing bar.

[0058] Step 3.13. Repeat Steps 3.5 - 3.12 to calculate and generate all reinforcing bars to complete the layout.

[0059] Embodiment 2 The present invention provides a method for arranging steel bars on a spliced surface by integrating graph theory and UV parameterization. On the basis of Embodiment 1, Step 3.4 preferably includes the following steps: Step 3.4.1. With the goal that there is a group of topological surfaces connected between two adjacent guiding lines, group the spliced surfaces input in Step 2.1 to obtain a list composed of a data structure in which two guiding lines sandwich a group of topological surfaces.

[0060] Step 3.4.2. Assume that there are w distribution points on each guiding line. Based on the order of the data structure list obtained in Step 3.4.1 in which two guiding lines sandwich a group of topological surfaces, form a point sequence with the distribution points at the same order position on each guiding line. Finally, make the distribution points obtained in Steps 3.1 and 3.2 form w such point sequences.

[0061] Step 3.4.3. Sequentially take out the point sequences composed of the distribution points at the same order position on each guiding line obtained in Step 3.4.2, and associate the point sequences with the list composed of the data structure in which two guiding lines sandwich a group of topological surfaces obtained in Step 3.4.1 according to the association relationship between the distribution points and the guiding lines. Finally, form a list composed of two guiding lines and two control points on them sandwiching a group of topological surfaces.

[0062] Step 3.4.4. Repeat Step 3.4.3 to finally realize the grouping of the reinforcement input data, where each group of data corresponds to generating one steel bar.

[0063] Example 3 The present invention provides a method for reinforcing a spliced surface by integrating graph theory and UV parameterization. On the basis of Example 1, Step 3.8 preferably includes the following steps: Step 3.8.1. Set the number of iterations iter and the number of sampling points s . The larger the value, the more accurate the calculated value.

[0064] Step 3.8.2. Uniformly sample points on the topological edges represented by the vertices other than the start and end vertices in the shortest path in Step 3.7. One topological edge is defined as one sampling layer, and there are s layers and layers, sampling points. The sampling area is determined by the result of the previous iteration and will gradually shrink. The first iteration area is the parameter space at the start and end of the topological edge.

[0065] Step 3.8.3. Create a directed graph , as shown in Figure 3 , where all the sampling points obtained in in Step 3.5 and Step 3.8.2 are used as vertices, and the unidirectional connection between the sampling points in adjacent layers is used as an edge. The weight of the edge is the length of the projection curve on the surface;

[0066]

[0067] In the formula, is the directed graph; is the vertex set, corresponding to the shortest path in Step 3.7 There are m layers, vertices; is the edge, and only the unidirectional connection between the vertices in adjacent layers is allowed; is the weight of the edge, corresponding to the length of the projection curve on the surface between two vertices, where the surface is indexed in according to the corresponding relationship between and .

[0068] Step 3.8.4. Use the Dijkstra algorithm to calculate the shortest path between in Step 3.5, and mark the points included in the shortest path among the sampling points in each layer as .

[0069] Step 3.8.5: Obtain the two adjacent sampling points before and after in Step 3.8.4, and define the area between them as the new sampling area of this sampling layer.

[0070] Step 3.8.6: Repeat Steps 3.8.2 to 3.8.5 for the next iteration. Until the number of iterations is equal to that set in iter Step 3.8.1, terminate the iteration.

[0071] Example 4 The present invention provides a method for reinforcing the spliced curved surface by integrating graph theory and UV parameterization. On the basis of Example 1, Step 3.10 preferably includes the following steps: Step 3.10.1: For the start and end points in Step 3.8, that is , and then index their respective corresponding topological edges in after being offset by Step 3.9. Then calculate the shortest distance from the point to the topological edge, and finally obtain the projection point corresponding to this distance on the topological edge . .

[0072] Step 3.10.2: For the other points in Step 3.8 except , and then index the adjacent faces of their corresponding topological edges in after being offset by Step 3.9. Then find the intersection line edge by taking the intersection of the two adjacent faces, and then calculate the shortest distance from the point to this intersection line. Finally, obtain the projection point corresponding to this distance on the intersection line edge . .

[0073] Step 3.10.3: Combine the results of Step 3.10.1 and Step 3.10.2 to obtain .

[0074] Example 5 The present invention provides a method for reinforcing the spliced curved surface by integrating graph theory and UV parameterization. On the basis of Example 1, Step 3.11 preferably includes the following steps: Step 3.11.1: Traverse simultaneously the calculated in Step 3.10 and the offset in Step 3.9. Take two adjacent points in , and , and the topological faces , corresponding to in . Then use the UV parameterization method to unfold , For the corresponding two UV points, finally construct a two-dimensional line segment from these two points.

[0075] Step 3.11.2: Map the two-dimensional line segment obtained in Step 3.11.1 to the target surface , obtain a three-dimensional curve, and finally connect all the projected curves obtained by traversal, which is a steel bar segment.

[0076] Example 6 The present invention provides a method for arranging steel bars on a spliced surface by integrating graph theory and UV parameterization, which can be specifically implemented according to the following steps: S1: Select a BIM platform built based on the open-source modeling engine OpenCASCADE (hereinafter referred to as "Occ") as the modeling engine, and select to create a new one or import a draft tube model as shown Figure 4 as an example. Since the model contains too many topological elements, under the premise of ensuring that the application situation can be explained, select a local area to arrange steel bars.

[0077] S2: Select surfaces 1 to 6 as shown Figure 4 as the steel bar arrangement surfaces. At the same time, select the reference guide line and the other three guide lines shown in the figure and set the steel bar array parameters (see Table 1), and finally uniformly use them as input parameters.

[0078] Table 1 Steel bar distribution parameters (unit: cm)

[0079] S3: According to the array parameters of steel bar spacing, start distance, and end distance, arrange distribution points along the reference guide line input in Step S2 in sequence, and then arrange the distribution points on the other guide lines in sequence on the premise of ensuring that the number of distribution points on each guide line is equal. The schematic diagram of the distribution points on each guide line is shown in Figure 5 .

[0080] S4: Based on the underlying topological relationship network, sort the input parameters in series. Regarding the identification of the guide line and the steel bar arrangement surface in Figure 4 , the corresponding sorted result is: reference guide line → surfaces 1 and 2 → guide line 1 → surfaces 3 and 4 → guide line 2 → surfaces 5 and 6 → guide line 3.

[0081] S5: Group the sorting result obtained in S4, and generate one steel bar for each group of data.

[0082] S6: Traverse the grouping results in Step S5 in sequence. The current group obtained contains a segment list, and each segment corresponds to generating one segment of a single steel bar, as shown in the steel bar segment represented in Figure 5 .

[0083]

[0084] In the formula, is a list of segments; represents the i th segment; l is the total number of segments; Each segment contains two adjacent guiding lines and a set of steel bar surfaces connected therebetween. If the points on the guiding lines are defined as and , respectively, then:

[0085] In the formula, is a set of steel bar surfaces between the adjacent guiding lines where

[0086] Taking the group represented by the steel bar line (example steel bar) in Figure 5 as an example, it contains 3 segments, that is, l = 3; among them, combining Figure 4 gives: , , .

[0087] S7: Traverse the segment list in step S6 , get the i th segment , and then get from the segment, and create an undirected graph accordingly:

[0088]

[0089] ,

[0090] In the formula, is an undirected graph; is the set of vertices in the undirected graph, is the th vertex, is the total number of vertices; is a symmetric adjacency matrix representing the relationship between edges and vertices in the undirected graph, where represents the edge connecting the th vertex and the th vertex, the connectivity weight of all edges is 1, and ; Taking as an example, for the sake of convenience of explanation, it is abstracted into the explanatory diagram shown in Figure 6 . It can be seen that the number of vertices can be obtained , namely:

[0091] Then we can get E the upper triangular matrix expression of:

[0092] S8: In the undirected graph obtained in step S7, find the i th segment in and the two vertices corresponding to the guiding line (topological edge) where it is located , and use the Dijkstra algorithm to search for the shortest path between ;

[0093]

[0094] In the formula, vertex is the starting point of ; is the ending point of ; , represent any adjacent terms in ; is the list of edges between adjacent vertices in, is the first edge of, is the last edge of, represents any term in and satisfies .

[0095] Combined with Figure 6 , taking as an example to illustrate, at this time is in the graph, and corresponds to Edge1 and Edge7 in the graph; the shortest path obtained by using the Dijkstra algorithm is:

[0096]

[0097] S9: Set the number of iterations iter = to 10; the number of sampling points s = 6, and then start the iteration; S10: In the shortest path of step S8 Uniform sampling is carried out on other vertices except the first and last vertices. s A number of sampling points are taken, and one topological edge is defined as a sampling layer. There are layers and sampling points in total. The sampling area is determined by the result of the previous iteration and will gradually shrink. The first iteration area is the parameter space at the two ends of the topological edge.

[0098] Continuing with as an example for illustration, combined with Figure 6 . The shortest path has other vertices except the first and last vertices, that is, there is only one topological edge, Edge4. Edge4 is defined as a sampling layer, and 6 sampling points are evenly taken on it. The sampling area is defined by the result of the previous iteration, and the first iteration area is the parameter space at the two ends of Edge4. Specifically for platform implementation, according to the parametric topological curve function provided by Occ, Edge4 is used as the input to initialize the BRepAdaptor_Curve object. Then the sampling area for the first iteration can be set between the FirstParameter and LastParameter of the BRepAdaptor_Curve object.

[0099] S11: Using all the sampling points obtained in step S8 and step S10 as vertices, and the sampling points between adjacent layers are connected unidirectionally as edges to create a directed graph , as shown in Figure 3 ; among them, the weight of the edge is the length of the projected curve on the surface;

[0100]

[0101] In the formula, is the directed graph; is the vertex set, corresponding to the shortest path in step S8 There are m layers and vertices in total; is the edge, and only unidirectional connection between vertices of adjacent layers is allowed; is the weight of the edge, corresponding to the length of the projected curve on the surface between two vertices, where the surface is indexed in and according to the corresponding relationship between .

[0102] According to Figure 6 in as an example, the vertices of the obtained directed graph are:

[0103] The edges of the directed graph are:

[0104] Wherein, Cv g-f represents the projection curve between the first and last vertices (indexed according to the subscript in , here it is and ), and the weight is its length; 0 indicates that the vertices are not connected.

[0105] Calculation process of the projection curve: Relying on the interface provided by Occ, first index the relevant topological surface according to the vertices of the directed graph in , and pass it into the BRepAdaptor_Surface that initializes the adaptation object from topology to geometry, and then obtain the parameterized surface object Geom_Surface. Then extract the coordinate data of the two vertices for generating the projection curve from the directed graph structure. Subsequently, based on each vertex coordinate and the parameterized surface, instantiate the GeomAPI_ProjectPointOnSurf projection tool class respectively to complete the initialization configuration of the geometric projection algorithm. Furthermore, call the LowerDistanceParameters method of the tool class to obtain the two-dimensional points of the two input vertices on the corresponding UV space of the surface respectively. The final inverse mapping process includes: 1) Use the BRepBuilderAPI_MakeEdge construction edge tool class and the two UV points to construct a topological line; 2) Use the CurveOnSurface method of the BRepTool tool class to geometrically parameterize the topological line, and at the same time use the Surface method to geometrically parameterize the surface; 3) After obtaining the geometric parameterization objects of the two, pass them into the BRepBuilderAPI_MakeEdge tool class to construct a topological edge, which is the inverse mapping curve.

[0106] S12: For obtained in step S11, use the Dijkstra algorithm to calculate the shortest path between , and mark the points included in the shortest path among the sampling points of each layer as .

[0107] Wherein, is the list of points on the topological edge represented by the vertices on the shortest path calculated according to the above target; among them , , , represent any adjacent terms in

[0108] corresponding to example, obtain .

[0109] S13: Obtain two adjacent sampling points in step S12, and define the area between them as the new sampling area of this sampling layer. For example, the sampling area for the second iteration is

[0110] Corresponding For example, the sampling area for the second iteration is .

[0111] S14: Repeat steps S10 to S13 for the next iteration. Terminate the iteration after 10 times to obtain the final steel bar control points , from which it can be obtained that , as Figure 5 and Figure 6 shown.

[0112] S15: Based on obtained in step S8, offset each topological surface by the offset value from the model surface to the outer surface of the steel bar input in step S2; obtain:

[0113] In the formula, is the list of offset topological surfaces, is the offset topological surface, is the offset topological surface, represents any item in

[0114] Corresponding For example, .

[0115] S16: As the topological surfaces are offset in step S15, in accordance with the principle of the shortest projection distance, project the start and end points of the shortest path list in step S12 onto the edges of the start and end surfaces, and project the other points in the list onto the intersection line of two adjacent surfaces in

[0116] In the formula, is the list of projected points, is the projected point, is the projected point, , represents any adjacent item in

[0117] corresponding example the start and end points are projected onto the topological edges after the offsets of Edge1 and Edge7; while is projected onto and on the intersection line of, obtaining .

[0118] Regarding the mentioned shortest distance principle, it mainly relies on the tool class BRepExtrema_DistShapeShape provided by Occ to calculate the shortest distance between two shapes. After being initialized, calling the PointOnShape1 method can obtain the projection points based on the shortest distance principle. The intersection calculation utilizes the Boolean intersection operation tool class BRepAlgoAPI_Section provided by Occ.

[0119] S17: Traverse simultaneously the calculated in step S16 and the offset in step S15, take two adjacent points in , , and at the same time take the topological surface in , corresponding to . Based on this, using the UV parameterization method, obtain the projection curve on the topological surface connecting , . Finally, connect all the traversed projection curves, which is one of the segments of a single steel bar.

[0120] corresponding example, as Figure 6 shown, the adjacent points , correspond to the topological surface , and the adjacent points , correspond to the topological surface . Using the method of calculating the projection curve according to the UV parameterization described in step S11, obtain the steel bar curve, and finally connect to obtain the steel bar segment shown in the figure.

[0121] S18: Repeat steps S7 - S17, calculate all the segments of a single steel bar, and then connect them to generate a complete steel bar.

[0122] S19: Repeat steps S6 - S18, calculate and generate all the steel bars to complete the layout, as Figure 7 shown.

Claims

1. A splicing surface reinforcement method integrating graph theory and UV parameterization, characterized in that It includes the following steps: Step 1: Create a BIM 3D model of the component; Step 2: Based on the model obtained in Step 1, input the reinforcement parameters; Step 3: Based on the reinforcement parameters in Step 2, search for the layout path and generate reinforcement bars.

2. The method for reinforcing bars on a spliced surface by integrating graph theory and UV parameterization according to claim 1, wherein The specific steps of Step 2 include the following steps: Step 2.1: Input the continuously spliced surface of the reinforcement bars to be configured by picking, denoted as the reinforcement surface; Step 2.2: Input several guiding lines by picking, which are used for sampling to obtain the control points of the reinforcement bar lines, and mark the reference guiding line; Step 2.3: Input the reinforcement bar specifications; Step 2.4: Input the offset value from the model surface to the outer surface of the reinforcement bar; Step 2.5: Input the reinforcement bar array parameters, including the reinforcement bar spacing, starting distance, and ending distance.

3. The method for reinforcing bars of a spliced surface by integrating graph theory and UV parameterization according to claim 2, characterized in that The reinforcement bar specifications input in Step 2.3 include the reinforcement bar grade and diameter.

4. The method for reinforcing the spliced surface with the fusion of graph theory and UV parameterization according to claim 2, characterized in that, The specific steps of Step 3 include the following steps: Step 3.1: Combine the array parameters, and sequentially arrange distribution points along the reference guiding line input in Step 2.2, and establish the association relationship between the distribution points and the reference guiding line; Step 3.2: Uniformly arrange distribution points on other guiding lines except the reference guiding line input in Step 2.

2. The number of distribution points on other guiding lines is equal to that on the reference guiding line, and establish the association relationship between the distribution points on other guiding lines and their respective guiding lines; Step 3.3: Sort the reinforcement surface input in Step 2.1 and the guiding lines input in Step 2.2 in series; Step 3.4: Based on the distribution points obtained in Step 3.1 and Step 3.2, and the reinforcement surface data obtained in Step 3.3, group according to the requirements for creating a single reinforcement bar, that is, each group of data corresponds to generating a single reinforcement bar; Step 3.5: Traverse the results obtained in Step 3.4 in sequence, and define a segment list in the currently obtained group , and in the segment list , one segment corresponds to generating a section of a single steel bar, that is, a steel bar section: In the formula, l is the total number of segments; represents the i th segment, The data of a includes the points on the guiding line , the points on the adjacent guiding line b , , and a , b a set of reinforcement surfaces connected between two adjacent guiding lines : Step 3.6: Traverse the segment list obtained in Step 3.5 , for the i th segment take from it to create an undirected graph : ， In the formula, is the set of vertices in the undirected graph; is the -th vertex, is the total number of vertices; is the adjacency matrix representing the relationship between edges and vertices in the undirected graph; represents the edge connecting the -th vertex and the -th vertex. The connectivity weight of all edges is 1, and ; Step 3.

7. In the undirected graph obtained in Step 3.6 find the two vertices corresponding to the guiding line where the segment in Step 3.5 is located, and use the Dijkstra algorithm to search for the shortest path between them ; wherein, the vertex is the starting point of ; is the ending point of ; , represent any adjacent terms in ; is the list of edges between adjacent vertices in , is the first edge of , is the last edge of ; represents any term in and satisfies ; Step 3.

8. Based on the shortest path obtained in Step 3.7 and the corresponding edge list , combined with the points in Step 3.5 , use graph theory and UV parameterization methods to search and calculate a point respectively on other vertices in except such that the connection distance from through , to is the shortest on the UV two-dimensional plane, and finally ensure that a topological surface has two control points; where the connection between two adjacent points , is the projection curve of the corresponding topological surface of the edge ; calculate the point list on the topological edges represented by the vertices on the shortest path: Wherein, , , 、 represent any adjacent terms in; Step 3.

9. Offset the edge list obtained in Step 3.7 for each topological face in it, with an offset distance of the offset value input in Step 2.4, to obtain a list of offset topological faces :[[]]END]] In the formula, is the offset topological surface, is the offset topological surface, represents any term in; Step 3.

10. Along with the offset of the topological surface in Step 3.9, project the start and end points in the list of shortest path points obtained in Step 3.8 onto the edge lines of the start and end surfaces, and project the other points in the point list onto the intersection line of two adjacent surfaces in to obtain the projected point list as follows: : In the formula, is the projected point, is the projected point, , represent any adjacent terms in; Step 3.

11. Traverse the point list obtained in Step 3.10 and the topological surface list obtained in Step 3.9 simultaneously. Take two adjacent points from , and simultaneously take the topological surface 、 corresponding to . Use the UV parameterization method to obtain the projection curve connecting on the topological surface 、 . Finally, connect all the traversed projection curves, which is a segment of a single steel bar; Step 3.12: Repeat Steps 3.6 - 3.11 to calculate all segments of a single reinforcement bar, and then connect all segments to generate a complete single reinforcement bar; Step 3.13: Repeat Steps 3.5 - 3.12 to calculate and generate all reinforcement bars to complete the layout.

5. The method for reinforcing the spliced surface with the fusion of graph theory and UV parameterization according to claim 4, characterized in that, The specific steps of Step 3.4 include the following steps: Step 3.4.1: Take the connection of a group of topological surfaces between two adjacent guiding lines as the goal, group the spliced surface input in Step 2.1, and obtain a list composed of a data structure of two guiding lines sandwiching a group of topological surfaces; Step 3.4.

2. Assume that there are w distribution points on each guiding line. Based on the order of the data structure list of a group of topological surfaces clamped by two guiding lines obtained in Step 3.4.1, the distribution points at the same order positions on each guiding line are combined into a point sequence, so that the distribution points obtained in Step 3.1 and Step 3.2 finally form w point sequences; Step 3.4.3: Sequentially take out the point sequence composed of the distribution points at the same order position on each guiding line obtained in Step 3.4.2, and associate the point sequence with the list composed of the data structure of two guiding lines sandwiching a group of topological surfaces obtained in Step 3.4.1 according to the association relationship between the distribution points and the guiding lines, forming a list composed of two guiding lines and two control points on them sandwiching a group of topological surfaces; Step 3.4.4: Repeat Step 3.4.3 to achieve the grouping of the reinforcement input data, where each group of data corresponds to generating a single reinforcement bar.

6. The method for reinforcing a spliced surface with the integration of graph theory and UV parameterization as described in claim 4, wherein The specific steps of Step 3.8 include the following steps: Step 3.8.1, Set the number of iterations iter and the number of sampling points s ; Step 3.8.

2. On the topological edges represented by the vertices other than the start and end vertices in the shortest path obtained in Step 3.7, sample points are evenly collected. One topological edge is defined as one sampling layer, and there are a total of layers and s sampling points. The sampling area is determined by the result of the previous iteration, and the first iteration area is the parameter space at the start and end of the topological edge; layers, sampling points, the sampling area is determined by the result of the previous iteration, and the first iteration area is the parameter space at the start and end of the topological edge; Step 3.8.3, Create a directed graph , take the points in Step 3.5 and all the sampling points obtained in Step 3.8.2 as vertices, and unidirectionally connect the sampling points between adjacent layers as edges, and the weight of the edge is the length of the projection curve on the surface; Wherein, is the vertex set, corresponding to the shortest path in step 3.7 There are m layers, and each layer has edges, and only one-way connection between vertices of adjacent layers is allowed; is the weight of the edge, corresponding to the length of the projection curve between two vertices on the surface, where the surface is indexed in the corresponding edge list according to the correspondence between and the shortest path; Step 3.8.

4. Calculate the shortest path between the points in Step 3.5 using the Dijkstra algorithm and mark the points included in the shortest path among the sampling points of each layer as ; ​ Step 3.8.

5. Obtain two adjacent sampling points before and after the point in Step 3.8.4, and define the area between the two sampling points as the new sampling area of the sampling layer; ​ Step 3.8.6: Repeat steps 3.8.2 to 3.8.5 for the next iteration until the iteration count is equal to that set in step 3.8.1 iter and then terminate the iteration.

7. The method for arranging steel bars on the spliced surface by integrating graph theory and UV parameterization according to claim 4, characterized in that, The specific steps of Step 3.10 include the following steps: Step 3.10.1: For the start and end points of the point list in Step 3.8 i.e., and then index the corresponding topological edges of the start and end points through the topological surface list offset by Step 3.9 Calculate the shortest distance from the point to the topological edge to obtain the projection point corresponding to the shortest distance on the topological edge ; ; ​ Step 3.10.2: For the points in the list of Step 3.8 except for the other points , index the adjacent faces of the topological edges corresponding to the other points through the list of topological faces offset by Step 3.9 , then find the intersection line between two adjacent faces, and then calculate the shortest distance from the point to the intersection line to obtain the projection point corresponding to the shortest distance on the intersection line ; ; Step 3.10.3, Combine the results of Step 3.10.1 and Step 3.10.2 to obtain the list of projected points .

8. The method for arranging steel bars on the spliced surface by integrating graph theory and UV parameterization according to claim 4, characterized in that, The specific steps of Step 3.11 include the following steps: Step 3.11.

1. Traverse the point list calculated in Step 3.10 and the topological surface list obtained in Step 3.9 simultaneously. Take two adjacent points from and and the topological surface corresponding to from . Then use the UV parameterization method to unfold and obtain two UV points corresponding to and . Finally, construct a two-dimensional line segment from the two UV points; Step 3.11.2: Map the two-dimensional line segment obtained in Step 3.11.1 to the target surface to obtain a three-dimensional curve. Finally, connect all the projected curves obtained by traversal, which is a segment of a single steel bar.

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