A reinforcement method for spliced ​​surfaces integrating graph theory and UV parameterization

Abstract

The present invention discloses a method for reinforcement of spliced ​​surfaces that integrates graph theory and UV parameterization, including creating a BIM three-dimensional model of a component, inputting reinforcement parameters, searching for layout paths, and generating reinforcement. The present invention addresses the technical difficulties in reinforcement of spliced ​​surfaces in the BIM three-dimensional design process of complex structural engineering. By introducing graph theory and constructing an edge and surface topological connectivity graph model, the present invention effectively solves the problem of reinforcement path planning in disordered spliced ​​surfaces, and realizes rapid path finding of reinforcement layout paths in the surface topological network and rapid positioning of numerous sampling points on the topological edge. At the same time, combined with the UV bidirectional parameterized mapping mechanism, the problem of adaptive arrangement of reinforcement in three-dimensional surfaces is solved, thereby realizing efficient solution and precise control of reinforcement of complex spliced ​​surfaces, breaking through the traditional reinforcement mode dominated by manual experience, and significantly improving the degree of automation and engineering reliability of complex spliced ​​surface reinforcement design, and has good application prospects.

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 promotion and application of the "3D modeling-reinforcement-drawing" forward design, its application in water conservancy projects, underground tunnels, special-shaped buildings and other fields has become increasingly widespread. Among them, the use of 3D irregular surface splicing modeling is inevitable. Such surfaces are usually composed of multiple surfaces, such as tunnel lining walls, spillway diversion walls, tailwater pipe curved walls, etc. The irregularity and splicing of their geometric shapes place higher requirements on the arrangement of reinforcement. Traditional reinforcement design methods mostly rely on manual experience for segmented projection fitting and local adjustment. It is difficult to efficiently handle the path planning problem of large-scale irregular surface splicing, resulting in long design cycles, insufficient accuracy, and difficulty in adapting to the needs of digital construction for automated 3D reinforcement.

[0003] Existing 3D reinforcement technology often lacks systematic modeling of inter-surface connectivity when dealing with multi-faceted topological relationships, resulting in broken or repeated reinforcement paths. This requires extensive manual intervention to correct these deviations, limiting design efficiency and scalable application. With the widespread adoption of BIM, high-precision and high-automation 3D reinforcement are inevitable developments, and an automated path optimization solution is urgently needed to support 3D reinforcement placement on complex curved structures. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for reinforcement of spliced ​​curved surfaces that integrates graph theory and UV parameterization, thereby solving the problems of insufficient automation and engineering reliability in the existing reinforcement design of complex spliced ​​curved surfaces.

[0005] The technical solution adopted by the present invention is: a method for reinforcing a spliced ​​surface by integrating graph theory and UV parameterization, comprising the following steps:

[0006] Step 1: Create a component BIM 3D model;

[0007] Step 2: Based on the model obtained in step 1, input reinforcement parameters;

[0008] Step 3: Based on the reinforcement parameters in step 2, search for the layout path and generate reinforcement.

[0009] The present invention is also characterized in that:

[0010] Step 2 specifically includes the following steps:

[0011] Step 2.1: Input the continuous splicing surface to be reinforced by picking, and record it as the reinforcement surface;

[0012] Step 2.2: Input several guide lines by picking them up for sampling to obtain the reinforcement line control points and mark the reference guide lines;

[0013] Step 2.3, enter the steel bar specifications;

[0014] Step 2.4, enter the offset value from the model surface to the outer surface of the steel bar;

[0015] Step 2.5. Enter the reinforcement array parameters, including reinforcement spacing, start distance, and end distance.

[0016] The steel bar specifications entered in step 2.3 include the steel bar grade and diameter.

[0017] Step 3 specifically includes the following steps:

[0018] Step 3.1: Based on the array parameters, distribute the distribution points along the reference guide line input in step 2.2, and establish the association between the distribution points and the reference guide line;

[0019] Step 3.2: Evenly distribute distribution points on all guide lines other than the baseline guide line input in step 2.2. The number of distribution points on all other guide lines is equal to the number of distribution points on the baseline guide line. Establish associations between the distribution points on all other guide lines and the guide lines to which they belong.

[0020] Step 3.3, arranging the reinforcement surface input in step 2.1 and the guide line input in step 2.2 in series;

[0021] Step 3.4: Based on the distribution points obtained in Steps 3.1 and 3.2, and the reinforcement surface data obtained in Step 3.3, group them according to the requirements for creating a single steel bar, that is, each group of data corresponds to generating a steel bar;

[0022] Step 3.5: Traverse the results of the grouping in step 3.4 and define a segment list in the current group. , segment list A segment in the diagram corresponds to a section of a single steel bar, namely a steel bar segment:

[0023]

[0024] Where, l is the total number of segments; Representative i segments, The data contains guide lines a Point on , adjacent guide lines b Point on ,and a 、 b A set of reinforcement surfaces connected between two adjacent guide lines :

[0025]

[0026] Step 3.6: Traverse the segment list obtained in step 3.5 , for the i Segments Take from it , creating an undirected graph :

[0027]

[0028]

[0029] ,

[0030] Where, is the set of vertices in an undirected graph; For the vertices, is the total number of vertices; It is the adjacency matrix that represents the relationship between edges and vertices in an undirected graph; Indicates the connection Vertex and The connectivity weight of all edges between vertices is 1, and ;

[0031] Step 3.7: The undirected graph obtained in step 3.6 Find step 3.5 middle The two vertices corresponding to the guide line , using Dijkstra algorithm to search and get The shortest path between ;

[0032]

[0033]

[0034] In the formula, the vertex ,for The starting point; ,for The end point of 、 express Any adjacent item in ; for A list of edges between adjacent vertices in , for The first edge of for The last edge of express Any item in , and satisfies ;

[0035] 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 , using graph theory and UV parameterization method in Medium Search and calculate the other vertices to get a point , so that from Pass in sequence 、 arrive 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, two adjacent points 、 The lines between The projection curve on the corresponding topological surface; calculate the list of points on the topological edge represented by the vertex on the shortest path :

[0036]

[0037] Where, , , 、 express Any adjacent item in ;

[0038] Step 3.9: Offset the edge list obtained in step 3.7 For each topological surface in , the offset distance is the offset value entered in step 2.4, and the offset topological surface list is obtained. :

[0039]

[0040] Where, for The topological surface after offset, for The topological surface after offset, express Any item in ;

[0041] Step 3.10: With the offset of the topological surface in step 3.9, the shortest path point list obtained in step 3.8 is The first and last points are projected onto On the edge lines of the first and last faces, list the points Other points are projected onto On the intersection line of two adjacent faces, we get the projected point list :

[0042]

[0043] Where, for The projected point, for The projected point, 、 express Any adjacent item in ;

[0044] Step 3.11: Traverse the point list obtained in step 3.10 at the same time and the topological surface list obtained in step 3.9 ,Pick Two adjacent points in 、 , while taking Zhongyu 、 Corresponding topological surface , using UV parameterization method to obtain topological surface Connection on 、 The projection curve of the steel bar is finally connected to form a segment of a single steel bar.

[0045] Step 3.12: Repeat steps 3.6 to 3.11 to calculate all segments of a single steel bar, and then connect all segments to form a complete steel bar.

[0046] Step 3.13: Repeat steps 3.5 to 3.12 to calculate and generate all the reinforcement bars and complete the layout.

[0047] Step 3.4 specifically includes the following steps:

[0048] Step 3.4.1: With a set of topological surfaces connected between two adjacent guide lines as the goal, group the splicing surfaces input in step 2.1 to obtain a list consisting of a data structure consisting of two guide lines and a set of topological surfaces;

[0049] Step 3.4.2: Assume that there are wBased on the order of the data structure list of two guide lines sandwiching a set of topological surfaces obtained in step 3.4.1, the distribution points of the same order on each guide line are combined into a point sequence, and finally the distribution points obtained in steps 3.1 and 3.2 are formed. w A sequence of points;

[0050] Step 3.4.3. Sequentially extract the point sequence consisting of the distributed points of the same order on each guide line obtained in step 3.4.2. Based on the association between the distributed points and the guide lines, associate the point sequence with the list consisting of the data structure of two guide lines and a group of topological surfaces obtained in step 3.4.1, thereby forming a list consisting of two guide lines and two control points on them, each of which is a group of topological surfaces.

[0051] Step 3.4.4: Repeat step 3.4.3 to group the reinforcement input data, where each group of data generates a corresponding steel bar.

[0052] Step 3.8 specifically includes the following steps:

[0053] Step 3.8.1. Set the number of iterations iter and number of sampling points s ;

[0054] Step 3.8.2, the shortest path in step 3.7 The topological edges represented by the vertices other than the first and last vertices are uniformly sampled. s sample points, where a topological edge is defined as a sampling layer, with a total of layer, Sampling points, the sampling area is determined by the result of the previous iteration, and the first iteration area is the parameter space of the topological edge head and tail;

[0055] Step 3.8.3. Create a directed graph , change the point in step 3.5 to All sampling points obtained in step 3.8.2 are used as vertices, and the sampling points between adjacent layers are connected unidirectionally as edges. The weight of the edge is the length of the projected curve on the surface.

[0056]

[0057]

[0058] Where, is the vertex set, corresponding to the shortest path in step 3.7 Total m layer, vertices; is an edge, and only one-way connection is allowed between vertices of adjacent layers; is the weight of the edge, corresponding to the length of the projected curve between two vertices on the surface, where the surface is based on With the shortest path The corresponding relationship is in the corresponding edge list Middle Index;

[0059] Step 3.8.4: Use Dijkstra's algorithm to calculate the midpoint of step 3.5 The shortest path between , and the points included in the shortest path of each layer of sampling points are recorded as ;

[0060] Step 3.8.5: Get the midpoint of step 3.8.4 The two adjacent sampling points are defined as the new sampling area of ​​the sampling layer.

[0061] Step 3.8.6: Repeat steps 3.8.2 to 3.8.5 for the next iteration until the number of iterations reaches the value set in step 3.8.1. iter When they are equal, the iteration terminates.

[0062] Step 3.10 specifically includes the following steps:

[0063] Step 3.10.1: Point list in step 3.8 The beginning and end points ,Right now , and then use the topological surface list after the migration in step 3.9 Index start and end points The corresponding topological edges are then calculated, and the shortest distance from the point to the topological edge is obtained to obtain the projection point corresponding to the shortest distance on the topological edge. ;

[0064] Step 3.10.2: Point list for step 3.8 Medium Other points outside , and then use the topological surface list after the migration in step 3.9 Index other points The corresponding topological edge is adjacent to the face, and then the intersection of the two adjacent faces is obtained. Then the shortest distance from the point to the intersection edge is calculated to obtain the projection point corresponding to the shortest distance on the intersection edge. ;

[0065] Step 3.10.3: Combine the results of steps 3.10.1 and 3.10.2 to obtain a list of projected points. .

[0066] Step 3.11 specifically includes the following steps:

[0067] Step 3.11.1. Simultaneously traverse the list of points calculated in step 3.10 and the topological surface list obtained in step 3.9 ,Pick Two adjacent points in 、 and Zhongyu 、 Corresponding topological surface , and then use the UV parameterization method to Expand and get the expanded 、 The corresponding two UV points finally construct a two-dimensional line segment from the two UV points;

[0068] Step 3.11.2: Map the two-dimensional line segment obtained in step 3.11.1 to the target surface A three-dimensional curve is obtained, and finally all the projection curves obtained by traversal are connected, which is a segment of a single steel bar.

[0069] The beneficial effects of the present invention are as follows: the present invention integrates graph theory and UV parameterized splicing surface reinforcement method, and targets the technical difficulties of splicing surface reinforcement in the BIM three-dimensional design process of complex structural engineering. By introducing graph theory, an edge and surface topological connectivity graph model is constructed, which effectively solves the problem of steel bar path planning in disordered splicing surfaces, and realizes the rapid path finding of steel bar arrangement paths in the surface topological network and the rapid positioning of numerous sampling points on the topological edge. At the same time, combined with the UV bidirectional parameterized mapping mechanism, it solves the problem of adaptive arrangement of steel bars in three-dimensional surfaces, thereby realizing efficient solution and precise control of complex splicing surface reinforcement, breaking through the traditional reinforcement mode dominated by manual experience, and significantly improving the automation level and engineering reliability of complex splicing surface reinforcement design, and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a flow chart of the reinforcement method for splicing curved surfaces that integrates graph theory and UV parameterization according to the present invention;

[0071] Figure 2 is the undirected graph of the present invention Application representation diagram;

[0072] Figure 3 is the directed graph of the present invention Application representation diagram;

[0073] Figure 4 This is a schematic diagram of input parameters for a spliced ​​curved surface reinforcement example of the present invention;

[0074] Figure 5 This is a schematic diagram of the reinforcement control points and reinforcement segments of an example of spliced ​​curved surface reinforcement of the present invention;

[0075] Figure 6 This is a single segment of the spliced ​​curved surface reinforcement example of the present invention and generate reinforcement segment description drawings;

[0076] Figure 7 This is a rendering of the local reinforcement arrangement of the spliced ​​curved surface reinforcement example of the present invention. DETAILED DESCRIPTION

[0077] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] Example 1

[0079] The present invention provides a splicing surface reinforcement method that integrates graph theory and UV parameterization. Based on the input of adjacent guide lines and a set of connected topological surfaces between them, graph theory is used to construct a topological mapping model, and the topological edges of the three-dimensional structure are mapped to graph theory vertices, and the topological surfaces are mapped to graph theory edges, forming a topological element relationship diagram. Based on this, the Dijkstra algorithm is used to calculate the shortest path for the steel bars to be arranged along the topological surfaces and edges, and the topological elements between the adjacent guide lines associated with the steel bar layout are quickly located. Combined with UV parameterization technology, a bidirectional mapping between three-dimensional surfaces and two-dimensional planes is established. According to the principle of the shortest path for the steel bar line to be arranged along the surface, the control points determined by the input guide lines are used as the beginning and end, and the steel bar path control points on the non-guide lines in between are calculated to ensure that one topological surface has two control points. Finally, on the final reinforcement surface after the input parameters are offset, UV parameterization technology is still used to convert the single three-dimensional surface reinforcement into a two-dimensional plane straight line layout problem. The three-dimensional steel bar segments are generated by reverse mapping the parameter domain reinforcement, and finally connected to generate complete steel bars. As Figure 1 As shown, the following steps are included:

[0080] Step 1: Create or import a BIM 3D model.

[0081] Step 2: Based on the model obtained in step 1, input reinforcement parameters. This includes the following steps:

[0082] Step 2.1: Input the continuous splicing surface to be reinforced by picking, and record it as the reinforcement surface.

[0083] Step 2.2: Input several guide lines by picking them up for sampling to obtain the reinforcement line control points. One of them is the reference guide line and needs to be marked. The guide line is only valid when it is connected to the reinforcement surface.

[0084] Step 2.3: Enter the steel bar specifications, including steel bar grade and diameter.

[0085] Step 2.4: Enter the offset value from the model surface to the outer surface of the reinforcement.

[0086] Step 2.5. Enter the reinforcement array parameters, including reinforcement spacing, start distance, and end distance.

[0087] Step 3: Based on the reinforcement parameters in step 2, search for the layout path and generate reinforcement. This includes the following steps:

[0088] Step 3.1: Combine the array parameters and arrange the distribution points along the reference guide line input in step 2.2, and establish the association between the distribution points and the reference guide line.

[0089] Step 3.2: Following the same principle as the number of distribution points obtained in step 3.1, evenly arrange the distribution points on the guide line input in step 2.2, and establish an association relationship with the corresponding guide line.

[0090] Step 3.3: With the goal of ensuring that adjacent guide lines are connected by surfaces, the reinforcement surfaces input in step 2.1 and the guide lines input in step 2.2 are serially arranged. It should be noted that there can be multiple connecting surfaces between adjacent guide lines.

[0091] Step 3.4: Based on the distribution points obtained in steps 3.1 and 3.2, and the reinforcement surface data obtained in step 3.3, group them according to the requirements for creating a single steel bar, that is, each group of data corresponds to generating one steel bar.

[0092] Step 3.5, traverse the results obtained by grouping in step 3.4 in sequence, and define a segment list in the current group obtained. A segment in the list corresponds to one section of a single steel bar, which is recorded as a steel bar segment.

[0093]

[0094] Where, is a list of segments; Representative i segments; l is the total number of segments;

[0095] Among them, the data of a segment contains the guide line a Point on , adjacent guide lines b Point on , and a set of reinforcement surfaces connecting these two adjacent guide lines:

[0096]

[0097] Where, for A set of reinforced surfaces between adjacent guide lines.

[0098] Step 3.6: Traverse the segment list in step 3.5 , for the currenti Segments , from which , based on which we create an undirected graph, see Figure 2 :

[0099]

[0100]

[0101] ,

[0102] Where, is an undirected graph; is the set of vertices in an undirected graph; For the vertices, is the total number of vertices; It is an adjacency matrix that represents the relationship between edges and vertices in an undirected graph and has symmetry; Indicates the connection Vertex and The connectivity weight of all edges between vertices is 1, and ;

[0103] It should be noted that A topological surface in the graph corresponds to an undirected edge, and a topological edge on the topological surface corresponds to a vertex in the graph. It can be seen that all topological edges of the same topological surface are connected in pairs.

[0104] if , indicating that there is no edge connection between the two vertices, that is, there is no topological surface connection between the two topological edges; when hour, .

[0105] Step 3.7: The undirected graph in step 3.6 Find step 3.5 middle The two vertices corresponding to the guide line (topological edge) , using Dijkstra algorithm to search and get The shortest path between ;

[0106]

[0107]

[0108] In the formula, the vertex ,for The starting point; ,for The end point of 、 express Any adjacent item in ; for A list of edges between adjacent vertices in , for The first edge of for The last edge of express Any item in , and satisfies .

[0109] Step 3.8: The shortest path obtained based on step 3.7 and corresponding , combined with step 3.5 , using graph theory and UV parameterization technology in Medium Search and calculate the other vertices (i.e. topological edges) outside the , so that from , in turn 、 arrive 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, two adjacent points 、 The lines between The projection curve on the corresponding topological surface;

[0110]

[0111] Where, is a list of points on the topological edges represented by the vertices on the shortest path calculated based on the above objectives; , , 、 express Any adjacent item in .

[0112] Step 3.9: Based on the data obtained in step 3.7 , offset each topological surface by the offset value entered in step 2.4; obtain:

[0113]

[0114] Where, for The list of topological faces after offset, for The topological surface after offset, for The topological surface after offset, express Any item in .

[0115] Step 3.10: With the offset of the topological surface in step 3.9, according to the principle of shortest projection distance, the shortest path in step 3.8 is The first and last points of the list are projected onto On the edge of the first and last faces, The other points in the list are projected onto On the intersection line of the two adjacent faces, we get the projected point list:

[0116]

[0117] Where, for The projected point list, for The projected point, for The projected point, 、 express Any adjacent item in .

[0118] Step 3.11: Simultaneously traverse the values ​​calculated in step 3.10 and the offset obtained in step 3.9 ,Pick Two adjacent points in 、 , while taking Zhongyu 、 Corresponding topological surface Based on this, the UV parameterization method is used to obtain the topological surface Connection on 、 Finally, all the projection curves obtained by traversing are connected to form a segment of a single steel bar.

[0119] Step 3.12: Repeat steps 3.6 to 3.11 to calculate all segments of a single steel bar, and then connect them to generate a complete steel bar.

[0120] Step 3.13: Repeat steps 3.5 to 3.12 to calculate and generate all the reinforcement bars to complete the layout.

[0121] Example 2

[0122] The present invention provides a method for reinforcement of a spliced ​​curved surface that integrates graph theory and UV parameterization. Based on Example 1, step 3.4 is preferably the following steps:

[0123] Step 3.4.1: With the goal of having a set of topological surfaces connected between two adjacent guide lines, group the splicing surfaces input in step 2.1 to obtain a list consisting of a data structure consisting of two guide lines and a set of topological surfaces.

[0124] Step 3.4.2: Assume that there are w Based on the order of the data structure list of two guide lines sandwiching a set of topological surfaces obtained in step 3.4.1, the distribution points of the same order on each guide line are combined into a point sequence, and finally the distribution points obtained in steps 3.1 and 3.2 are formed. w A sequence of such points.

[0125] Step 3.4.3. Take out the point sequence consisting of the distribution points of the same order on each guide line obtained in step 3.4.2 in turn, and associate the point sequence with the list consisting of the data structure of two guide lines and a group of topological surfaces obtained in step 3.4.1 according to the association relationship between the distribution points and the guide lines. Finally, a list consisting of two guide lines and the two control points above them and a group of topological surfaces is formed.

[0126] Step 3.4.4: Repeat step 3.4.3 to finally group the reinforcement input data, where each group of data generates a corresponding steel bar.

[0127] Example 3

[0128] The present invention provides a method for reinforcement of a spliced ​​curved surface that integrates graph theory and UV parameterization. Based on Example 1, step 3.8 is preferably the following steps:

[0129] Step 3.8.1. Set the number of iterations iter and number of sampling points s , the larger the value, the more accurate the calculated value.

[0130] Step 3.8.2, the shortest path in step 3.7 The topological edges represented by the vertices other than the first and last vertices are uniformly sampled. s sample points, where a topological edge is defined as a sampling layer, with a total of layer, The sampling area is determined by the result of the previous iteration and will gradually shrink. The first iteration area is the parameter space of the topological edge ends.

[0131] Step 3.8.3. Create a directed graph ,See Figure 3 , where in step 3.5 All sampling points obtained in step 3.8.2 are used as vertices, and the sampling points between adjacent layers are connected unidirectionally as edges. The weight of the edge is the length of the projected curve on the surface.

[0132]

[0133]

[0134] Where, is a directed graph; is the vertex set, corresponding to the shortest path in step 3.7 Total m layer, vertices; is an edge, and only one-way connection is allowed between vertices of adjacent layers; is the weight of the edge, corresponding to the length of the projected curve between two vertices on the surface, where the surface is based on and The corresponding relationship is Index in.

[0135] Step 3.8.4: Use Dijkstra algorithm to calculate the value in step 3.5 The shortest path between , and the points included in the shortest path of each layer of sampling points are recorded as .

[0136] Step 3.8.5, obtain the The area between two adjacent sampling points is defined as the new sampling area of ​​the sampling layer.

[0137] Step 3.8.6, repeat steps 3.8.2 to 3.8.5 for the next iteration. iter When they are equal, the iteration terminates.

[0138] Example 4

[0139] The present invention provides a method for reinforcement of a spliced ​​surface that integrates graph theory and UV parameterization. Based on Example 1, step 3.10 is preferably the following steps:

[0140] Step 3.10.1, for step 3.8 The beginning and end points ,Right now , and then offset by step 3.9 Index their corresponding topological edges, then calculate the shortest distance from the point to the topological edge, and finally get the projection point corresponding to the distance on the topological edge .

[0141] Step 3.10.2: For step 3.8 remove Other points outside , and then offset by step 3.9 Index the topological edge adjacent to the corresponding face, then intersect the two adjacent faces to get the intersection edge, and then calculate the shortest distance from the point to the intersection line, and finally get the projection point corresponding to the distance on the intersection edge. .

[0142] Step 3.10.3: Combine the results of steps 3.10.1 and 3.10.2 to obtain .

[0143] Example 5

[0144] The present invention provides a method for reinforcement of a spliced ​​curved surface that integrates graph theory and UV parameterization. Based on Example 1, step 3.11 is preferably the following steps:

[0145] Step 3.11.1, while traversing step 3.10 calculated and the offset obtained in step 3.9 ,Pick Two adjacent points in 、 and Zhongyu 、 Corresponding topological surface Then the UV parameterization method is used to Expand, and get the expanded 、 The corresponding two UV points are finally used to construct a two-dimensional line segment.

[0146] Step 3.11.2: Map the two-dimensional line segment obtained in step 3.11.1 to the target surface , get a three-dimensional curve, and finally connect all the projection curves obtained by traversal to form a steel bar segment.

[0147] Example 6

[0148] The present invention provides a method for reinforcement of spliced ​​curved surfaces that integrates graph theory and UV parameterization, which can be implemented in the following steps:

[0149] S1: Select a BIM platform based on the open source modeling engine OpenCASCADE (hereinafter referred to as "Occ") as the modeling engine, and choose to create or import a Figure 4 The tailwater pipe model shown is used as an example. Because the model contains too many topological elements, the reinforcement is arranged in a local area while ensuring that the application can be explained.

[0150] S2: Select Figure 4Use surfaces 1 to 6 as reinforcement surfaces. Select the baseline guide line and the other three guide lines shown in the figure, set the reinforcement array parameters (see Table 1), and finally unify them as input parameters.

[0151] Table 1 Steel bar distribution parameters (unit: cm)

[0152]

[0153] S3: According to the array parameters of steel bar spacing, starting distance, and ending distance, the distribution points are arranged in sequence along the reference guide line input in step S2, and then the distribution points on other guide lines are arranged in sequence while ensuring that the number of distribution points on each guide line is equal. Figure 5 .

[0154] S4: Based on the underlying topological relationship network, the input parameters are sorted in series. Figure 4 The identification of the middle guide line and the reinforcement surface, the corresponding sorting result is: base guide line → surface 1 and surface 2 → guide line 1 → surface 3 and surface 4 → guide line 2 → surface 5 and surface 6 → guide line 3.

[0155] S5: Group the sorting results obtained in S4, and generate a corresponding steel bar for each group of data.

[0156] S6: Traverse the grouping results of step S5 in sequence, and the current group obtained contains a segment list, and each segment corresponds to a section of a single steel bar. Figure 5 The steel bar segment represented in .

[0157]

[0158] Where, is a list of segments; Representative i segments; l is the total number of segments;

[0159] Each segment consists of two adjacent guide lines and a set of reinforcement surfaces connected between them. If the points on the defined guide lines are ,and ,but:

[0160]

[0161] Where, for A set of reinforced surfaces between adjacent guide lines.

[0162] by Figure 5 For example, the group represented by the reinforcement line (sample reinforcement) in the figure contains three segments, namely l=3; among them, combined Figure 4 We can get: 、 、 .

[0163] S7: Traverse the segment list in step S6 , get the first i Segments , and then get from the segment , and create an undirected graph from this:

[0164]

[0165]

[0166] ,

[0167] Where, is an undirected graph; is the set of vertices in an undirected graph, For the vertices, is the total number of vertices; It is a symmetric adjacency matrix that represents the relationship between edges and vertices in an undirected graph, where Indicates the connection Vertex and The connectivity weight of all edges between vertices is 1, and ;

[0168] by For example, for the convenience of explanation, it is abstracted as Figure 6 As shown in the illustration. From this, we can see that the number of vertices ,Right now:

[0169]

[0170] Then you can get E The upper triangular matrix expression of is:

[0171]

[0172] S8: The undirected graph obtained in step S7 Find the i Segments middle The two vertices corresponding to the guide line (topological edge) , using Dijkstra algorithm to search and get The shortest path between ;

[0173]

[0174]

[0175] In the formula, the vertex ,for The starting point; ,for The end point of 、 express Any adjacent item in ; for A list of edges between adjacent vertices in , for The first edge of for The last edge of express Any item in , and satisfies .

[0176] Combine Figure 6 ,by Take this as an example to illustrate, That is the ,and Corresponding to Edge1 and Edge7 in the figure, the shortest path found by Dijkstra algorithm is:

[0177]

[0178]

[0179] S9: Set the number of iterations iter= 10; Number of sampling points s =6, then start iteration;

[0180] S10: The shortest path in step S8 Except for the first and last vertices, other vertices are uniformly sampled. s sample points, where a topological edge is defined as a sampling layer, with a total of layer, The sampling area is determined by the result of the previous iteration and will gradually shrink. The first iteration area is the parameter space of the topological edge ends.

[0181] Continue with Take the following example to illustrate the Figure 6 The shortest path In the example, all vertices except the first and last vertices are considered, i.e., there is only one topological edge, Edge4. A sampling layer is defined based on Edge4, and six samples are evenly sampled on it. The sampling region is defined by the results of the previous iteration, and the region for the first iteration is the parameter space of the first and last edges of Edge4. Specifically, in platform implementation, based on the parameterized topological curve functionality provided by Occ, Edge4 is used as input to initialize the BRepAdaptor_Curve object. The sampling region for the first iteration can be set between the FirstParameter and LastParameter of the BRepAdaptor_Curve object.

[0182] S11: According to step S8 All the sampling points obtained in step S10 are used as vertices, and the sampling points between adjacent layers are connected unidirectionally as edges to create a directed graph ,See Figure 3 ; The edge weight is the length of the projected curve on the surface;

[0183]

[0184]

[0185] Where, is a directed graph; is the vertex set, corresponding to the shortest path in step S8 Total m layer, vertices; is an edge, and only one-way connection is allowed between vertices of adjacent layers; is the weight of the edge, corresponding to the length of the projected curve between two vertices on the surface, where the surface is based on and The corresponding relationship is Index in.

[0186] according to Figure 6 middle For example, the vertices of the directed graph obtained are:

[0187]

[0188] The directed graph edges are:

[0189]

[0190] Where, Cv g-f Represents the first and last vertices (in According to the subscript index, here is and ), the weight is its length; 0 means there is no connectivity between the vertices.

[0191] The calculation process of the projection curve: relying on the interface provided by Occ, first according to the vertex of the directed graph The relevant topological surface is indexed and passed to the initialized topology-to-geometry adapter object BRepAdaptor_Surface, which then obtains the parameterized surface object Geom_Surface. The coordinate data of the two vertices of the projected curve to be generated is then extracted from the directed graph structure. The GeomAPI_ProjectPointOnSurf projection tool class is then instantiated based on each vertex coordinate and the parameterized surface to complete the initial configuration of the geometric projection algorithm. The tool class's LowerDistanceParameters method is then called to obtain the two-dimensional points in the surface's corresponding UV space for the two input vertices. The final reverse mapping process includes: 1) constructing a topological line using the BRepBuilderAPI_MakeEdge edge tool class and two UV points; 2) geometrically parameterizing this topological line using the CurveOnSurface method of the BRepTool tool class, while also geometrically parameterizing the surface using the Surface method; 3) After obtaining the two geometrically parameterized objects, the resulting objects are passed to the BRepBuilderAPI_MakeEdge tool class to construct a topological edge, which is the reverse mapping curve.

[0192] S12: The result obtained in step S11 , calculated using Dijkstra algorithm The shortest path between , and the points included in the shortest path of each layer of sampling points are recorded as .

[0193] Where, is a list of points on the topological edges represented by the vertices on the shortest path calculated based on the above objectives; , , 、 express Any adjacent item in .

[0194] correspond Example, get .

[0195] S13: Get the result in step S12 The area between two adjacent sampling points is defined as the new sampling area of ​​the sampling layer.

[0196] correspond For example, the sampling area for the second iteration is .

[0197] S14: Repeat steps S10 to S13 for the next iteration. The iteration is terminated after 10 iterations to obtain the final reinforcement control point. , from which we can get ,like Figure 5 and Figure 6 shown.

[0198] S15: Based on the result obtained in step S8 , offset each topological surface, the offset distance is the offset value from the model surface to the outer surface of the steel bar input in step S2; get:

[0199]

[0200] Where, for The list of topological faces after offset, for The topological surface after offset, for The topological surface after offset, express Any item in .

[0201] correspond Example, .

[0202] S16: With the offset of the topological surface in step S15, the shortest path in step S12 is converted according to the principle of shortest projection distance. The first and last points of the list are projected onto On the edge of the first and last faces, The other points in the list are projected onto On the intersection line of the two adjacent faces, we get the projected point list:

[0203]

[0204] Where, for The projected point list, for The projected point, for The projected point, 、 express Any adjacent item in .

[0205] correspond Example, The beginning and end points is projected onto the topological edge after the offset of Edge1 and Edge7; is projected onto and On the intersection line, we get .

[0206] To address the shortest distance principle, we rely on the Occ-provided tool class BRepExtrema_DistShapeShape, which calculates the shortest distance between two shapes. Once initialized, calling the PointOnShape1 method yields the projection point based on the shortest distance principle. Intersection calculations are performed using the Occ-provided Boolean intersection tool class BRepAlgoAPI_Section.

[0207] S17: Simultaneously traverse the results calculated in step S16 and the offset obtained in step S15 ,Pick Two adjacent points in 、 , while taking Zhongyu 、 Corresponding topological surface Based on this, the UV parameterization method is used to obtain the topological surface Connection on 、 Finally, all the projection curves obtained by traversing are connected to form a segment of a single steel bar.

[0208] correspond Examples, such as Figure 6 As shown, adjacent points 、 Corresponding topological surface , adjacent points 、 Corresponding topological surface The method for calculating the projection curve based on UV parameterization described in step S11 is used to obtain the steel bar curve, and finally the steel bar segments shown in the figure are obtained by connecting them.

[0209] S18. Repeat steps S7 to S17 to calculate all segments of a single steel bar, and then connect them to generate a complete steel bar.

[0210] S19, repeat steps S6 to S18, calculate and generate all the steel bars, and complete the layout, such as Figure 7 shown.

Claims

1. A method for reinforcement of spliced ​​surfaces that integrates graph theory and UV parameterization, characterized in that: The following steps are involved: Step 1: Create a component BIM 3D model; Step 2: Based on the model obtained in step 1, input reinforcement parameters; specifically, the following steps are included: Step 2.1: Input the continuous splicing surface to be reinforced by picking, and record it as the reinforcement surface; Step 2.2: Input several guide lines by picking them up for sampling to obtain the reinforcement line control points and mark the reference guide lines; Step 2.3, enter the steel bar specifications; Step 2.4, enter the offset value from the model surface to the outer surface of the steel bar; Step 2.

5. Enter the reinforcement array parameters, including reinforcement spacing, start distance, and end distance; Step 3: Based on the reinforcement parameters in step 2, search for the layout path and generate reinforcement. Specifically, the following steps are included: Step 3.1: Based on the array parameters, distribute the distribution points along the reference guide line input in step 2.2, and establish the association between the distribution points and the reference guide line; Step 3.2: Evenly distribute distribution points on all guide lines other than the baseline guide line input in step 2.

2. The number of distribution points on all other guide lines is equal to the number of distribution points on the baseline guide line. Establish associations between the distribution points on all other guide lines and the guide lines to which they belong. Step 3.3, arranging the reinforcement surface input in step 2.1 and the guide line input in step 2.2 in series; Step 3.4: Based on the distribution points obtained in Steps 3.1 and 3.2, and the reinforcement surface data obtained in Step 3.3, group them 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: Traverse the results of the grouping in step 3.4 and define a segment list in the current group. , segment list A segment in the diagram corresponds to a section of a single steel bar, namely a steel bar segment: Where, l is the total number of segments; Representative i segments, The data contains guide lines a Point on , adjacent guide lines b Point on ,and a 、 b A set of reinforcement surfaces connected between two adjacent guide lines : Step 3.6: Traverse the segment list obtained in step 3.5 , for the i Segments Take from it , creating an undirected graph : ， Where, is the set of vertices in an undirected graph; For the vertices, is the total number of vertices; It is the adjacency matrix that represents the relationship between edges and vertices in an undirected graph; Indicates the connection Vertex and The connectivity weight of all edges between vertices is 1, and ; Step 3.7: The undirected graph obtained in step 3.6 Find step 3.5 middle The two vertices corresponding to the guide line , using Dijkstra algorithm to search and get The shortest path between ; In the formula, the vertex ,for The starting point; ,for The end point of 、 express Any adjacent item in ; for A list of edges between adjacent vertices in , for The first edge of for The last edge of express Any item 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 , using graph theory and UV parameterization method in Medium Search and calculate the other vertices to get a point , so that from Pass in sequence 、 arrive 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, two adjacent points 、 The lines between The projection curve on the corresponding topological surface; calculate the list of points on the topological edge represented by the vertex on the shortest path : Where, , , 、 express Any adjacent item in ; Step 3.9: Offset the edge list obtained in step 3.7 For each topological surface in , the offset distance is the offset value entered in step 2.4, and the offset topological surface list is obtained. : Where, for The topological surface after offset, for The topological surface after offset, express Any item in ; Step 3.10: With the offset of the topological surface in step 3.9, the shortest path point list obtained in step 3.8 is The first and last points are projected onto On the edge lines of the first and last faces, list the points Other points are projected onto On the intersection line of two adjacent faces, we get the projected point list : Where, for The projected point, for The projected point, 、 express Any adjacent item in ; Step 3.11: Traverse the point list obtained in step 3.10 at the same time and the topological surface list obtained in step 3.9 ,Pick Two adjacent points in 、 , while taking Zhongyu 、 Corresponding topological surface , using UV parameterization method to obtain topological surface Connection on 、 The projection curve of the steel bar is finally connected to form a segment of a single steel bar. Step 3.12: Repeat steps 3.6 to 3.11 to calculate all segments of a single steel bar, and then connect all segments to form a complete steel bar. Step 3.13: Repeat steps 3.5 to 3.12 to calculate and generate all the reinforcement bars to complete the layout.

2. The method for reinforcement of a spliced ​​surface integrating graph theory and UV parameterization according to claim 1, characterized in that: The steel bar specifications entered in step 2.3 include steel bar grade and diameter.

3. The method for reinforcement of spliced ​​curved surfaces integrating graph theory and UV parameterization according to claim 1, characterized in that: The step 3.4 specifically includes the following steps: Step 3.4.1: With a set of topological surfaces connected between two adjacent guide lines as the goal, group the splicing surfaces input in step 2.1 to obtain a list consisting of a data structure consisting of two guide lines and a set of topological surfaces; Step 3.4.2: Assume that there are w Based on the order of the data structure list of two guide lines sandwiching a set of topological surfaces obtained in step 3.4.1, the distribution points of the same order on each guide line are combined into a point sequence, and finally the distribution points obtained in steps 3.1 and 3.2 are formed. w A sequence of points; Step 3.4.

3. Sequentially extract the point sequence consisting of the distributed points of the same order on each guide line obtained in step 3.4.

2. Based on the association between the distributed points and the guide lines, associate the point sequence with the list consisting of the data structure of two guide lines and a group of topological surfaces obtained in step 3.4.1, thereby forming a list consisting of two guide lines and two control points on them, each of which is a group of topological surfaces. Step 3.4.4: Repeat step 3.4.3 to group the reinforcement input data, where each group of data generates a corresponding steel bar.

4. The method for reinforcement of a spliced ​​surface integrating graph theory and UV parameterization according to claim 1, characterized in that: The step 3.8 specifically includes the following steps: Step 3.8.

1. Set the number of iterations iter and number of sampling points s ; Step 3.8.2, the shortest path in step 3.7 The topological edges represented by the vertices other than the first and last vertices are uniformly sampled. s sample points, where a topological edge is defined as a sampling layer, with a total of layer, Sampling points, the sampling area is determined by the result of the previous iteration, and the first iteration area is the parameter space of the topological edge head and tail; Step 3.8.

3. Create a directed graph , change the point in step 3.5 to All sampling points obtained in step 3.8.2 are used as vertices, and the sampling points between adjacent layers are connected unidirectionally as edges. The weight of the edge is the length of the projected curve on the surface. Where, is the vertex set, corresponding to the shortest path in step 3.7 Total m layer, vertices; is an edge, and only one-way connection is allowed between vertices of adjacent layers; is the weight of the edge, corresponding to the length of the projected curve between two vertices on the surface, where the surface is based on With the shortest path The corresponding relationship is in the corresponding edge list Middle Index; Step 3.8.4: Use Dijkstra's algorithm to calculate the midpoint of step 3.5 The shortest path between , and the points included in the shortest path of each layer of sampling points are recorded as ; Step 3.8.5: Get the midpoint of step 3.8.4 The two adjacent sampling points are defined 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 reaches the value set in step 3.8.

1. iter When they are equal, the iteration terminates.

5. The method for reinforcement of spliced ​​curved surfaces integrating graph theory and UV parameterization according to claim 1, characterized in that: The step 3.10 specifically includes the following steps: Step 3.10.1: Point list in step 3.8 The beginning and end points ,Right now , and then use the topological surface list after the migration in step 3.9 Index start and end points The corresponding topological edges are then calculated, and the shortest distance from the point to the topological edge is obtained to obtain the projection point corresponding to the shortest distance on the topological edge. ; Step 3.10.2: Point list for step 3.8 Medium Other points outside , and then use the topological surface list after the migration in step 3.9 Index other points The corresponding topological edge is adjacent to the face, and then the intersection of the two adjacent faces is obtained. Then the shortest distance from the point to the intersection edge is calculated to obtain the projection point corresponding to the shortest distance on the intersection edge. ; Step 3.10.3: Combine the results of steps 3.10.1 and 3.10.2 to obtain a list of projected points. .

6. The method for reinforcement of spliced ​​curved surfaces integrating graph theory and UV parameterization according to claim 1, characterized in that: The step 3.11 specifically includes the following steps: Step 3.11.

1. Simultaneously traverse the list of points calculated in step 3.10 and the topological surface list obtained in step 3.9 ,Pick Two adjacent points in 、 and Zhongyu 、 Corresponding topological surface , and then use the UV parameterization method to Expand and get the expanded 、 The corresponding two UV points 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 A three-dimensional curve is obtained, and finally all the projection curves obtained by traversal are connected, which is a segment of a single steel bar.

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