Rebar arrangement logic optimization method for complex construction nodes

Abstract

This invention belongs to the field of electrical digital data processing technology and relates to a method for optimizing the logic of rebar arrangement in complex construction nodes. It extracts the geometric parameters of the rebar and their anchorage constraints, constructing a directed acyclic graph (DAG) with rebar segments as nodes, spatial intersections as edges, and construction sequence and structural specifications as weights. Spatial arrangement conflicts are transformed into a loop identification problem in the graph. Graph coloring is used to hierarchically divide conflicting edges and assign avoidance priorities. Based on topological sorting and traversal, the bending avoidance direction and offset rules are determined according to the coloring values. Offset compensation calculations are performed by reversing the topological order, propagating the offsets back along the edges to non-conflicting rebar segments, and outputting the arrangement coordinates and the logical sequence of bending nodes. This invention transforms serial collisions into graph structure operations, overcoming the chain collisions and local deadlocks caused by serial avoidance, and eliminating spatial encroachment caused by avoidance.

Description

Technical Field

[0001] This invention belongs to the field of electrical digital data processing technology and relates to a method for optimizing the logic of steel reinforcement arrangement in complex construction nodes. Background Technology

[0002] Existing methods for complex construction node rebar layout typically employ a serial collision detection and rule-driven local avoidance approach based on 3D bounding boxes. After establishing the 3D geometric model of the node, each rebar component is traversed sequentially along a defined path. The intersection volume of the component bounding boxes is calculated to determine if a spatial conflict has occurred. When a conflict is detected, a pre-defined fixed-priority rule table is invoked, forcing lower-priority rebars to shift or bend in a specific direction to make room for higher-priority rebars. This process is executed sequentially according to the component order until all components have been traversed.

[0003] The above-mentioned implementation method based on serial collision detection and local offset avoidance, when dealing with complex nodes where multiple steel bars intersect densely, the avoidance action executed first will change the local space occupancy state, which is very likely to encroach on the original space of the steel bars to be arranged later, causing secondary collisions. This chain collision is continuously transmitted in densely packed components, causing the arrangement logic to fall into a local deadlock and fail to converge to a feasible solution. Summary of the Invention

[0004] The purpose of this invention is to provide a logical optimization method for the arrangement of reinforcing bars in complex construction nodes, which can effectively solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] Methods for optimizing the reinforcement layout logic in complex construction nodes include:

[0007] Extract the geometric parameters and anchorage constraints of each steel reinforcement component in complex construction nodes, and construct a directed acyclic graph with steel reinforcement segments as nodes, spatial occupancy and intersection relationships as edges, and construction sequence and construction specifications as edge weights.

[0008] The conflict in the spatial arrangement of steel bars is transformed into a loop identification problem in the directed acyclic graph. Graph coloring is used to classify the conflicting edges in the directed acyclic graph into hierarchical levels, and different coloring values ​​are assigned to conflicting steel bars as avoidance priorities.

[0009] Based on the topological sorting traversal of the directed acyclic graph, the bending avoidance direction and offset calculation rules of the reinforcing bars are determined according to the coloring value. Among them, high-priority reinforcing bars maintain the original path, and low-priority reinforcing bars generate bending path control points according to spatial tolerance and anchorage length constraints.

[0010] By performing offset compensation calculations in reverse order of the topological sorting, the bending offset is transmitted in reverse along the edges of the directed acyclic graph to the non-conflicting rebar segments, eliminating the chain space encroachment caused by the avoidance action, and outputting the three-dimensional arrangement coordinates of each rebar and the logical sequence of bending nodes.

[0011] Preferably, the construction of a directed acyclic graph with rebar segments as nodes, spatial occupancy intersections as edges, and construction sequence and structural specifications as edge weights includes:

[0012] Each continuous straight or bent steel bar segment within the complex construction node is defined as a node of the directed acyclic graph.

[0013] Traverse all the three-dimensional bounding boxes corresponding to the nodes. When the three-dimensional bounding boxes of any two nodes have intersecting volumes, generate the edge of the directed acyclic graph between the two corresponding nodes.

[0014] The direction of the edge is determined based on the difference between the body center coordinates of the intersecting volume and the coordinates of the anchorage starting point of the node. The weight value of the direction is quantified by combining the preset priority of the rebar type and the anchorage length specification. The weight value is then assigned to the edge to complete the construction of the directed acyclic graph.

[0015] Preferably, the step of transforming the spatial arrangement conflict of reinforcing bars into a loop identification problem in the directed acyclic graph (DAG) involves using graph coloring to hierarchically divide the conflicting edges in the DAG, including:

[0016] In the directed acyclic graph, a directed closed loop structure consisting of edges and nodes is detected, and the set of nodes corresponding to the directed closed loop structure is marked as a conflict group.

[0017] Initialize the color set, select the node with the largest in-degree from the conflict group as the starting node, and assign the initial color from the color set to the starting node;

[0018] Traverse the adjacent nodes in the conflict group along the direction of the directed closed loop structure, determine the weight value of the edge between the adjacent nodes, assign a different color to the node pointed to by the edge with the smaller weight value, until all the nodes in the conflict group have been assigned a color, and the color represents the avoidance priority of the node.

[0019] Preferably, the step of traversing the directed acyclic graph based on topological sorting and determining the bending avoidance direction and offset calculation rules of the reinforcing bars according to the coloring values ​​includes:

[0020] Extract the current processing node sequentially according to the topological sorting sequence of the nodes in the directed acyclic graph;

[0021] Obtain the avoidance priority corresponding to the coloring value of the current processing node. If the avoidance priority is higher than a preset threshold, keep the original spatial coordinates of the current processing node unchanged.

[0022] If the avoidance priority is lower than the preset threshold, the spatial occupancy boundary of the high-priority node that has a conflict edge with the current processing node is obtained, the direction vector of the available space gap is determined according to the spatial occupancy boundary, the offset distance is calculated along the direction vector, and a bend path control point is inserted on the original path of the current processing node so that the path of the current processing node bypasses the spatial occupancy boundary of the high-priority node.

[0023] Preferably, the offset compensation calculation is performed in reverse order of the topological sorting, and the buckling offset is propagated in reverse along the edges of the directed acyclic graph to the non-conflicting reinforcement segments, including:

[0024] After completing the forward traversal of the topological sort, obtain the bend offset vectors corresponding to all nodes that have been assigned bend path control points;

[0025] Extract the current compensation node in reverse order of the topological sort, and determine whether the current compensation node is directly connected to the upstream node that has the bend offset vector;

[0026] If directly connected, the bend offset vector of the upstream node is superimposed with the original coordinates of the current compensation node to generate the compensated coordinates of the current compensation node, and the bend offset vector of the current compensation node is updated to the superimposed composite offset vector. This process continues to propagate to the downstream nodes until the traversal is complete.

[0027] Preferably, the output of the three-dimensional arrangement coordinates and bend node logic sequence of each reinforcing bar includes:

[0028] Obtain the compensated coordinates of all nodes in the directed acyclic graph and the bend path control points after the offset compensation calculation is completed;

[0029] Based on the direction of the edges in the directed acyclic graph, the compensated coordinates and the bend path control points are sorted according to the entity connection order of the steel reinforcement members to generate the bend node logical sequence.

[0030] The connection vectors between adjacent nodes in the bend node logic sequence are extracted. Combined with the geometric parameters of the steel bar cross section, the connection vectors are reconstructed into a three-dimensional envelope surface to generate a spatial surface dataset corresponding to the three-dimensional arrangement coordinates of each steel bar. The spatial surface dataset is then bound to the bend node logic sequence for output.

[0031] Preferably, the step of quantifying the weight value of the pointing direction by combining the preset priority of rebar type and anchorage length specifications, and assigning the weight value to the edge, includes:

[0032] Extract the steel bar type attributes and diameter parameters corresponding to the node, obtain the type weight coefficient based on the steel bar type attributes, and calculate the anchorage weight coefficient based on the diameter parameters and the anchorage length specification.

[0033] Obtain the overlap depth value of the intersecting volumes along the direction in three-dimensional space, and normalize the overlap depth value to obtain the spatial overlap coefficient;

[0034] The variety weight coefficient, the anchoring weight coefficient, and the spatial overlap coefficient are weighted and summed. The summation result is used as the weight value and assigned to the edge. When there is a bidirectional edge between the same pair of nodes, the weight values ​​of the bidirectional edges are compared. The bidirectional edge with the smaller weight value is removed, and the unidirectional edge with the larger weight value is retained.

[0035] Preferably, determining the weight values ​​of edges between adjacent nodes and assigning a different color to the node pointed to by the edge with the smaller weight value compared to the current node further includes:

[0036] When a node in the conflict group is connected to multiple colored nodes by edges, and the multiple colored nodes have occupied all available colors in the color set, the node is marked as a color saturation node.

[0037] The color set is expanded to generate new extended colors, and the extended colors are assigned to the color saturation nodes;

[0038] The weight difference between the edges between the color saturated node and the plurality of colored nodes is recalculated. If the weight difference is less than a preset difference threshold, a local graph reconstruction instruction is triggered to split the color saturated node into a plurality of virtual child nodes. Each virtual child node inherits part of the space occupancy attribute of the original color saturated node and is respectively assigned color compatibility with the corresponding colored node.

[0039] Preferably, calculating the offset distance along the direction vector and inserting a bend path control point on the original path of the current processing node includes:

[0040] Obtain the angle between the original path tangent vector of the current processing node and the direction vector, and calculate the preliminary positions of the buckling start point and buckling end point based on the angle value and the minimum bending radius constraint of the reinforcing bar.

[0041] An arc transition path is generated between the initial positions. The difference between the arc length of the arc transition path and the length of the corresponding line segment of the original path is calculated to obtain the path stretching amount.

[0042] The path expansion amount is compared with the anchorage redundancy length of the current processing node. If the path expansion amount is less than the anchorage redundancy length, the bend start point, the arc transition path, and the bend end point are inserted as the bend path control points. If it is greater, the offset distance is increased along the direction vector and recalculated until the anchorage redundancy length limit is met.

[0043] Preferably, the process of superimposing the bend offset vector of the upstream node with the original coordinates of the current compensation node to generate the compensated coordinates of the current compensation node includes:

[0044] Obtain the spatial Euclidean distance between the current compensation node and the upstream node, and calculate the offset transmission attenuation factor based on the spatial Euclidean distance and a preset attenuation coefficient;

[0045] Multiply the bend offset vector of the upstream node by the offset propagation attenuation factor to obtain the attenuation offset vector;

[0046] Extract the original coordinates of the current compensation node, and add the attenuation offset vector to the original coordinates to generate the compensated coordinates of the current compensation node;

[0047] If the compensated coordinates cause new spatial interference with the adjacent non-conflicting nodes of the current compensated node, the offset transfer attenuation factor is reduced by a preset ratio and the vector addition is re-executed until the new spatial interference is eliminated.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] 1. This invention constructs a directed acyclic graph (DAG) with rebar segments as nodes and spatial occupancy intersections as edges. It transforms spatial arrangement conflicts into a loop identification problem within the graph. Graph coloring is used to hierarchically divide conflicting edges and assign avoidance priorities. Based on the coloring values, the bending avoidance direction and offset are determined during topological sorting traversal. Offset compensation calculations are then performed in reverse order through topological sorting, propagating the bending offset in reverse along the edges of the DAG to non-conflicting rebar segments. This processing logic transforms serial collision avoidance in three-dimensional space into hierarchical operations and reverse offset propagation within a graph structure. This overcomes the chain collision problem caused by serial avoidance actions, eliminates spatial encroachment caused by avoidance actions, and prevents the arrangement logic from falling into local deadlock.

[0050] 2. In this invention, the edge direction is determined by the difference between the coordinates of the intersection volume center and the coordinates of the anchorage starting point, and the weight value is calculated by combining the type and diameter of the reinforcing steel, thus eliminating bidirectional edge redundancy in graph construction; when encountering color-saturated nodes, virtual child nodes are split, eliminating the allocation deadlock phenomenon under extremely dense conflicts; when generating bend path control points, the minimum bending radius constraint of the reinforcing steel is compared with the anchorage redundancy length, ensuring the construction compliance boundary of the layout path; in the offset compensation transmission, an attenuation factor based on spatial Euclidean distance is introduced and new spatial interference is detected, limiting the excessive diffusion of offset and ensuring the stability of the overall spatial allocation of nodes. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating the construction process of a directed acyclic graph of reinforcement bars for complex construction nodes in this invention.

[0052] Figure 2 This is a flowchart of the rebar conflict group detection and image coloring priority allocation of the present invention;

[0053] Figure 3 This is a flowchart of the reinforcement bend avoidance path generation based on topology sorting of the present invention;

[0054] Figure 4 This is a flowchart of the topological reverse offset compensation calculation and chain interference elimination of the present invention;

[0055] Figure 5 This is a flowchart of the reconstruction output of the three-dimensional arrangement coordinates and bending sequence of the reinforcing bars according to the present invention;

[0056] Figure 6 This is a flowchart of the virtual splitting and local graph reconstruction of color saturation nodes according to the present invention. Detailed Implementation

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

[0058] Please refer to Figure 1This embodiment provides a method for optimizing the logic of rebar arrangement in complex construction nodes. It extracts the geometric parameters and anchorage constraints of each rebar component in the complex construction node, constructing a directed acyclic graph (DAG) with rebar segments as nodes, spatial occupancy intersections as edges, and construction sequence and structural specifications as edge weights. The method parses rebar component data in IFC format from the Building Information Model (BIM), extracting information such as the globally unique identifier, material properties, cross-sectional geometric parameters, axis control point coordinates, anchorage end position, anchorage length, protective layer thickness, and construction sequence markers for each rebar component. For each rebar component, its axis is segmented according to anchorage points and bend points, with each continuous axis segment corresponding to a rebar segment node. The attributes of each rebar segment node include the globally unique identifier of the rebar component to which it belongs, rebar type, diameter, start coordinates, end coordinates, axis length, anchorage start coordinates, anchorage length, protective layer thickness, and construction sequence priority.

[0059] Iterate through all rebar segment nodes, generating an axis-aligned bounding box for each node. The minimum coordinate of the axis-aligned bounding box is the minimum coordinate of all control points along the node's axis minus half the rebar diameter, and the maximum coordinate is the maximum coordinate of all control points along the node's axis plus half the rebar diameter. For any two distinct nodes i and j, calculate the intersection volume of their bounding boxes. The formula for calculating the intersection volume is:

[0060] (1)

[0061] in, , Let be the minimum and maximum coordinates of the bounding box of node i along the x-axis, respectively. , These are the minimum and maximum coordinates of the bounding box of node j in the x-axis direction, respectively. The parameters for the y-axis and z-axis directions are defined the same as those for the x-axis.

[0062] If the intersection volume is greater than zero, a temporary edge is generated between node i and node j. The volume center coordinates of the intersection volume are calculated using the following formula:

[0063] (2)

[0064] Calculate the Euclidean distance from the body center coordinates to the anchorage starting points of node i and node j. The formula for calculating the distance is:

[0065] (3)

[0066]

[0067] in, Let i be the coordinates of the anchorage start point. Let be the coordinates of the anchorage starting point of node j.

[0068] Compare the two distances and set the temporary edge to point from the node with the smaller distance to the node with the larger distance. Calculate the weight of the edge and assign it to the edge. Iterate through all temporary edges. For bidirectional temporary edges between the same pair of nodes, compare the weights of the two edges, keep the one-way edge with the larger weight, and discard the one-way edge with the smaller weight. After processing all edges, the final directed acyclic graph is obtained.

[0069] refer to Figure 2 The problem of rebar spatial arrangement conflict is transformed into a loop identification problem in the directed acyclic graph (DAG). Graph coloring is used to hierarchically divide the conflicting edges in the DAG, assigning different coloring values ​​to conflicting rebars as avoidance priorities. A depth-first search algorithm is used to traverse all nodes in the DAG. Each node is marked with a visit status flag, including unvisited, currently visited, and visited states. Starting from any unvisited node, the traversal is initiated, marking the node's state as currently visited and adding it to the current visit path list. All adjacent nodes of the current node are visited sequentially. If an adjacent node is unvisited, it is recursively visited. If an adjacent node is currently visited, a directed closed loop is detected. The current visit path list is backtracked, and all nodes from the current node to the current node are extracted, forming a conflict group. All nodes in the conflict group are marked as conflicting nodes. After the recursive visit is completed, the current node is marked as visited and removed from the current visit path list. The above process is repeated until all nodes have been visited.

[0070] Initialize the color set, which initially contains three color values: 0, 1, and 2. For each conflict group, calculate the in-degree of each node in the group. The formula for calculating the in-degree is:

[0071]

[0072] in, Given the set of nodes in a directed acyclic graph, This is an indicator function that takes a value of 1 when there is an edge pointing from node u to node v, and a value of 0 otherwise.

[0073] Select the node with the largest in-degree as the starting node. If multiple nodes have the same in-degree, select the node with the largest sum of the weights of the edges connecting it to other nodes. Assign the starting node the first color value (0) from the color set. Iterate through the adjacent nodes in the conflict group along the direction of the directed closed loop. For the current node u and its adjacent node v, obtain the weights of the edges connecting nodes u and v. .like If the color value is less than a preset weight threshold, node v has a lower avoidance priority than node u, and therefore node v is assigned a different color value than node u. If there are unused color values ​​in the color set, the smallest unused color value is selected and assigned to node v. Color value and avoidance priority are negatively correlated; the smaller the color value, the higher the avoidance priority.

[0074] refer to Figure 3 The directed acyclic graph (DAG) is traversed based on topological sorting. The bending avoidance direction and offset calculation rules for reinforcing bars are determined according to the coloring values. High-priority reinforcing bars maintain their original paths, while low-priority reinforcing bars generate bending path control points based on spatial tolerance and anchorage length constraints. The Kahn algorithm is used to generate the topological sorting sequence for the DAG. The in-degree of each node in the DAG is calculated. A priority queue is created, sorted by node color values ​​from smallest to largest, and nodes with the same color value are sorted by the sum of edge weights from largest to smallest. All nodes with an in-degree of 0 are added to the priority queue. When the priority queue is not empty, the head node is removed and added to the topological sorting sequence. All adjacent nodes of the current node are traversed, and the in-degree of each adjacent node is decremented by 1. If the in-degree of an adjacent node becomes 0, it is added to the priority queue. This process is repeated until the priority queue is empty. If the length of the topological sorting sequence is less than the total number of nodes in the DAG, it indicates the presence of an undetected directed closed cycle, triggering a graph reconstruction instruction to re-perform cycle detection and graph coloring.

[0075] Each node is processed sequentially according to the topological sorting sequence. The color value of the currently processed node is obtained, and its avoidance priority is determined based on this value. If the avoidance priority of the currently processed node is higher than a preset priority threshold, the original spatial coordinates of that node remain unchanged. If the avoidance priority of the currently processed node is lower than the preset priority threshold, the spatial occupancy boundaries of all high-priority nodes with conflicting edges with that node are obtained. High-priority nodes are those with color values ​​lower than the color value of the currently processed node. For each high-priority node, the intersection point of its spatial occupancy boundary and the original path of the currently processed node is calculated. If multiple intersection points exist, the intersection point closest to the starting point of the currently processed node is selected as the valid intersection point. The outward normal vector of the spatial occupancy boundary of the high-priority node at the valid intersection point is calculated. The cross product of the outward normal vector and the tangent vector of the original path of the currently processed node is performed to obtain a direction vector perpendicular to the original path. The direction vector with the smallest angle to the tangent vector of the original path is selected as the bend avoidance direction vector. The direction vector is normalized to obtain a unit direction vector.

[0076] Calculate the offset distance using the following formula:

[0077] (6)

[0078] in, The diameter of the reinforcing bars for high-priority nodes. The diameter of the reinforcing bar at the currently processed node. This is the preset gap value.

[0079] Based on the offset distance and unit direction vector, calculate the coordinates of the bend initiation point, the center of the circular arc transition, and the bend termination point. Calculate the arc length of the circular arc transition path and the length of the corresponding line segment of the original path to obtain the path expansion. Obtain the anchorage redundancy length of the current processing node, which is equal to the actual anchorage length minus the minimum anchorage length required by the specification. If the path expansion is less than the anchorage redundancy length, insert the bend initiation point, the circular arc transition path, and the bend termination point as bend path control points into the original path of the current processing node. If the path expansion is greater than or equal to the anchorage redundancy length, increase the offset distance along the unit direction vector and recalculate the bend path control points until the path expansion is less than the anchorage redundancy length.

[0080] refer to Figure 4 The offset compensation calculation is performed in reverse order of the topological sorting, propagating the bend offset backward along the edges of the directed acyclic graph to the non-conflicting rebar segments. This eliminates the chain reaction of spatial encroachment caused by avoidance actions and outputs the three-dimensional arrangement coordinates of each rebar and the logical sequence of bend nodes. After completing the forward traversal of the topological sorting, all nodes with inserted bend path control points are collected. For each such node, its bend offset vector is calculated, which is equal to the coordinates of the bend termination point minus the coordinates of the original path endpoint. The topological sorting sequence is reversed to obtain the reverse topological sorting sequence. Each node is processed sequentially according to the reverse topological sorting sequence as the current compensation node.

[0081] Obtain all upstream nodes of the current compensation node. An upstream node is a node that precedes the current compensation node in the original topological sorting sequence and has an edge pointing from it to the current compensation node. If at least one upstream node has a non-zero bend offset vector, calculate the spatial Euclidean distance between the current compensation node and each upstream node. Based on the spatial Euclidean distance and a preset attenuation coefficient, calculate the offset propagation attenuation factor corresponding to each upstream node. Multiply the bend offset vector of each upstream node by the corresponding offset propagation attenuation factor to obtain the attenuated offset vector for each upstream node. Vector sum all attenuated offset vectors to obtain the comprehensive attenuated offset vector. Vector sum the comprehensive attenuated offset vector with the original coordinates of the current compensation node to obtain the preliminary compensated coordinates of the current compensation node.

[0082] Calculate the new axis-aligned bounding box corresponding to the preliminary compensated coordinates of the current compensated node. Iterate through all adjacent non-conflicting nodes of the current compensated node (nodes without conflicting edges with the current compensated node). Calculate the intersection volume between the new bounding box of the current compensated node and the bounding boxes of each adjacent non-conflicting node. If all intersection volumes are zero, use the preliminary compensated coordinates as the final compensated coordinates of the current compensated node. If any intersection volume is greater than zero, reduce the offset transfer attenuation factor of all offsets by a preset percentage, recalculate the comprehensive attenuation offset vector and the preliminary compensated coordinates, until all intersection volumes are zero. Update the bend offset vector of the current compensated node to the comprehensive attenuation offset vector and continue processing the next node.

[0083] refer to Figure 5 After offset compensation calculation, obtain the final compensated coordinates and bend path control points of all nodes. Based on the direction of edges in the directed acyclic graph, sort all nodes belonging to the same reinforcing member according to their connection order. For each reinforcing member, arrange the start coordinates, end coordinates, and bend path control points of all its nodes in spatial order to generate the bend node logical sequence of that reinforcing member. Extract the connection vectors between adjacent nodes in the bend node logical sequence. For each connection vector, generate a cylindrical envelope surface with the connection vector as the axis and half the diameter of the reinforcing bar as the radius. Combine the vertex coordinates, normal vectors, texture coordinates, and other data of all cylindrical envelope surfaces into a spatial surface dataset. Bind the globally unique identifier, type, diameter, bend node logical sequence, and spatial surface dataset of each reinforcing member to generate the final output data.

[0084] This embodiment fully implements the core process of logical optimization of reinforcement layout in complex construction nodes. By constructing a directed acyclic graph, spatial conflicts are transformed into graph structure problems. Graph coloring is used to determine avoidance priorities. Bending paths are generated in the forward direction through topological sorting, and offset compensation is performed in the reverse order, eliminating the cascading collision problem. The geometric parameters of the reinforcement members at beam-column nodes and the relationship between anchorage constraints are shown in Table 1.

[0085] Table 1. Relationship between geometric parameters and anchorage constraints of reinforced members in beam-column joints.

[0086]

[0087] Table 1 shows the geometric parameters and anchorage constraints of 12 main reinforcing steel members in a typical beam-column joint. These parameters were extracted from the BIM model and used to construct the node attributes of the directed acyclic graph. Among them, steel bars starting with R are the longitudinal reinforcing bars of the column, arranged along the z-axis; steel bars starting with B are the longitudinal reinforcing bars of the beam, arranged along the x-axis.

[0088] In a preferred embodiment, each continuous straight or bent rebar segment within the complex construction node is defined as a node in the directed acyclic graph. A continuous straight rebar refers to the portion of the rebar that is not bent between two adjacent anchorage points; a bent rebar refers to the portion of the rebar between two adjacent bend points, where the bend angle at each bend point does not exceed 90 degrees and the bend radius meets the specifications. For rebars with multiple bends, they are divided into multiple continuous straight or bent segments, each segment serving as an independent node. The axial parametric equation for each node is:

[0089] (7)

[0090] in, Let be the starting coordinates of the node. The coordinates of the endpoint of the node.

[0091] Traverse all the 3D bounding boxes corresponding to the nodes. When the 3D bounding boxes of any two nodes intersect, generate an edge between the two corresponding nodes in the directed acyclic graph. The method for generating the 3D bounding boxes is as follows: for each node, the coordinates of all control points of its axis constitute a point set, and the minimum coordinate of the point set is... The maximum coordinate is The cross-section of the reinforcing bar is circular with a diameter of d. Therefore, the minimum coordinates of the three-dimensional bounding box of this node are: The maximum coordinate is For bent reinforcing bars, the bounding box is the smallest axis-aligned bounding box that includes the axes and sections of all bent segments.

[0092] The direction of an edge is determined based on the difference between the body center coordinates of the intersecting volumes and the coordinates of the anchorage starting point of the node. The weight of this direction is then quantified using preset rebar type priorities and anchorage length specifications, and assigned to the edge to complete the construction of the directed acyclic graph. The method for determining the edge direction is as follows: when the bounding boxes of two nodes intersect, the body center coordinates of the intersecting volumes are calculated. For node i, its anchoring starting point This refers to the starting coordinates of the anchorage end of the reinforcing steel member where the node is located, i.e., the starting point where the reinforcing steel extends into the support or other member. Calculation vector. Its mold length This represents the distance from the center of the intersecting volume to the anchorage point of node i. The direction of the edge is from... Smaller node points to For larger nodes, since nodes closer to the anchoring starting point are constructed earlier, the direction of the edge represents the order of construction.

[0093] Extract the rebar type attributes and diameter parameters corresponding to the nodes. Map the rebar type attributes to obtain a type weight coefficient, and calculate the anchorage weight coefficient based on the diameter parameters and the anchorage length specification. The mapping rule for the type weight coefficient is as follows: the preset type priority from high to low is prestressed rebar, HRB500, HRB400, HRB335, and HPB300, with corresponding weight coefficients of 1.0, 0.8, 0.6, 0.4, and 0.2, respectively. The calculation formula for the anchorage weight coefficient is:

[0094] (8)

[0095] in, This is the anchorage length of the reinforcing steel at that node. This is the maximum anchorage length among all nodes.

[0096] Obtain the overlap depth value of the intersecting volumes along the direction in three-dimensional space, and normalize the overlap depth value to obtain the spatial overlap coefficient. (Overlap depth value) This refers to the projection length of the intersecting volume onto the edge pointing vector, and its calculation formula is:

[0097] (9)

[0098] in, Let be the unit vector to which the edge points. The formula for calculating the spatial overlap coefficient is:

[0099] (10)

[0100] in, This is the maximum overlap depth value among all intersecting edges.

[0101] The weighted sum of the variety weight coefficient, the anchoring weight coefficient, and the spatial overlap coefficient is then used as the weight value assigned to the edge. The formula for calculating the edge weight is:

[0102] (11)

[0103] in, , , These are preset weighting coefficients that satisfy... ; This is the variety weighting coefficient. This is the anchorage weight coefficient. This is the spatial overlap coefficient.

[0104] When there is a bidirectional edge between the same pair of nodes, the weight values ​​of the bidirectional edges are compared. The bidirectional edge with the smaller weight value is removed, and the unidirectional edge with the larger weight value is retained. This eliminates the redundancy of bidirectional edges in the graph, ensuring that the graph is a directed acyclic graph.

[0105] In the directed acyclic graph, directed closed-loop structures formed by edges and nodes are detected, and the set of nodes corresponding to the directed closed-loop structures is marked as a conflict group. An improved depth-first search algorithm is used for directed closed-loop detection, recording the visit timestamp and completion timestamp of each node during traversal. When a node is encountered whose visit timestamp is less than the current node's visit timestamp and whose completion timestamp is greater than the current node's visit timestamp, a directed closed loop is detected. The current path is backtracked, and all nodes from that node to the current node are extracted, forming a conflict group.

[0106] Initialize the color set by selecting the node with the largest in-degree from the conflict group as the starting node and assigning it an initial color from the color set. The size of the initial color set is dynamically adjusted according to the size of the conflict group, with an initial size of 3. The node with the largest in-degree is usually the core node of the conflict, and assigning it the highest priority color can reduce conflicts in subsequent color assignments.

[0107] Traverse the adjacent nodes in the conflict group along the direction of the directed closed-loop structure, determine the weight of the edges between adjacent nodes, and assign a different color to the node pointed to by the edge with the smaller weight, until all nodes in the conflict group have been assigned a color, which represents the avoidance priority of the node. For the current node u and its adjacent node v, if the edge... The weight value is less than the edge If the weight value is less than that of node u, then node v has a lower avoidance priority than node u, therefore node v must be assigned a different color than node u. If the edge The weight value is greater than the edge If the weight value is determined, then node v has a higher avoidance priority than node u. Therefore, node v can be assigned the same color as node u. If the same color is already occupied, then a different color can be assigned.

[0108] refer to Figure 6 When a node in the conflict group is connected to multiple colored nodes via edges, and the multiple colored nodes have occupied all available colors in the color set, the node is marked as a color-saturated node. The color set is then expanded to generate new extended colors, which are assigned to the color-saturated nodes. The numbers of the extended colors increment sequentially, starting from the maximum number in the initial color set plus 1.

[0109] The weight differences between the edges of the saturated color node and the plurality of colored nodes are recalculated. If the weight difference is less than a preset difference threshold, a local graph reconstruction instruction is triggered, splitting the saturated color node into multiple virtual child nodes. The formula for calculating the weight difference is:

[0110] (12)

[0111] in, and These are the weights of the edges between the saturated color node u and the colored nodes v and w, respectively. If the difference is less than the preset difference threshold, it means that the color saturated node and multiple colored nodes have similar conflict levels, which cannot be resolved by a single color assignment. Therefore, virtual child node splitting is required.

[0112] Each virtual child node inherits a portion of the space-occupying attributes of the original color-saturated node and is color-compatiblely allocated with its corresponding colored node. The spatial partitioning method for the virtual child nodes is as follows: the axis of the original color-saturated node is divided into n equal segments, where n equals the number of colored nodes connected to that node. The bounding box corresponding to each segment is... ( ), each virtual child node inherit The spatial occupancy attributes, as well as the original node's rebar type, diameter, anchorage length, and other attributes, are determined. The edges between the original saturated color nodes and the colored nodes are replaced with the edges between the corresponding virtual child nodes and the colored nodes, while maintaining the edge weights. The original saturated color nodes are deleted, and all virtual child nodes are added to a conflict group. All nodes in the conflict group are then recolored, ensuring that the color value of each virtual child node is different from the color value of its corresponding colored node.

[0113] This embodiment details the construction of a directed acyclic graph (DAG). It eliminates bidirectional edge redundancy by quantizing edge weights and resolves color saturation issues under extremely dense conflicts through virtual child node splitting, thereby improving the stability of the graph structure and the success rate of color assignment. The edge weight calculation parameters for the DAG are shown in Table 2.

[0114] Table 2. Parameters for calculating edge weights in directed acyclic graphs.

[0115]

[0116] Table 2 shows the weight calculation parameters for the 12 main edges in the directed acyclic graph corresponding to the beam-column nodes in Table 1. The weighting coefficients α, β, and γ are set to 0.3, 0.4, and 0.3, respectively, reflecting that the anchorage length has the greatest impact on the construction sequence, followed by the priority of the type of work and the degree of spatial overlap. The larger the final weight value, the later the construction sequence of the node pointed to by the edge is, and the lower the avoidance priority.

[0117] In another preferred embodiment, the currently processed node is extracted sequentially according to the topological sorting sequence of the nodes in the directed acyclic graph. The topological sorting sequence is generated using an improved Kahn algorithm, which considers both the color value of the node and the sum of the edge weights in the priority queue. The smaller the color value, the higher the priority of the node; when color values ​​are the same, the larger the sum of the edge weights, the higher the priority of the node. This ensures that high-priority rebars are arranged first, reducing the complexity of subsequent avoidance.

[0118] The avoidance priority corresponding to the color value of the currently processed node is obtained. If the avoidance priority is higher than a preset threshold, the original spatial coordinates of the currently processed node are kept unchanged. The preset threshold is dynamically adjusted according to the complexity of the construction node. For nodes of general complexity, the threshold is set to 2, that is, nodes with color values ​​of 0 and 1 have an avoidance priority higher than the threshold and the original path is kept unchanged; nodes with color values ​​greater than or equal to 2 have an avoidance priority lower than the threshold and need to bend and avoid.

[0119] If the avoidance priority is lower than the preset threshold, the spatial occupancy boundary of the high-priority node that has a conflicting edge with the current processing node is obtained. The direction vector of the available space gap is determined based on the spatial occupancy boundary. The offset distance is calculated along the direction vector, and a bend path control point is inserted on the original path of the current processing node, causing the path of the current processing node to bypass the spatial occupancy boundary of the high-priority node. The spatial occupancy boundary of the high-priority node is the six surfaces of its axis-aligned bounding box. The method for determining the direction vector of the available space gap is as follows: calculate all intersection points between the original path of the current processing node and the bounding box of the high-priority node. For each intersection point, calculate the outward normal vector of the bounding box at that point. Perform a cross product between the outward normal vector and the tangent vector of the original path to obtain two candidate direction vectors perpendicular to the original path. Calculate the available space size in the direction of each candidate direction vector, and select the candidate direction vector with the largest available space as the bend avoidance direction vector.

[0120] Obtain the angle between the original path tangent vector of the current processing node and the direction vector. Calculate the preliminary positions of the buckling start and end points based on the angle and the minimum bending radius constraint of the reinforcing steel. The formula for calculating the original path tangent vector is:

[0121] (13)

[0122] in, and These are the start and end coordinates of the original path of the current processing node, respectively. The direction vector, after normalization, is... The angle between the original path tangent vector and the direction vector. The calculation formula is:

[0123] (14)

[0124] Minimum bending radius of reinforcing bars According to the specifications, for HRB400 steel bars, , where d is the diameter of the reinforcing bar.

[0125] inflection starting point The preliminary position calculation formula is:

[0126] (15)

[0127] inflection end point The preliminary position calculation formula is:

[0128] (16)

[0129] in, The intersection of the original path and the bounding box of the high-priority node. This represents the offset distance.

[0130] An arc transition path is generated between the initial positions. The difference between the arc length of the arc transition path and the length of the corresponding line segment of the original path is calculated to obtain the path scaling. The center coordinates of the arc transition path are:

[0131] (17)

[0132] The parametric equations for the circular arc transition path are:

[0133] (18)

[0134] The arc length of the circular transition path is:

[0135] (19)

[0136] The length of the line segment corresponding to the original path is:

[0137] (20)

[0138] The path scaling is:

[0139] (twenty one)

[0140] The path expansion / contraction amount is compared with the anchorage redundancy length of the current processing node. If the path expansion / contraction amount is less than the anchorage redundancy length, the bend start point, the arc transition path, and the bend end point are inserted as bend path control points. If it is greater, the offset distance is increased along the direction vector and recalculated until the anchorage redundancy length limit is met. The formula for calculating the anchorage redundancy length is:

[0141] (twenty two)

[0142] in, This represents the actual anchorage length of the reinforcing steel member at the currently processed node. This refers to the minimum anchorage length required by the standard.

[0143] After completing the forward traversal of the topological sort, obtain the bend offset vectors corresponding to all nodes that have been assigned bend path control points. The formula for calculating the bend offset vector is:

[0144] (twenty three)

[0145] in, This represents the coordinates of the endpoint of the original path of the currently processed node.

[0146] Extract the current compensation node sequentially in reverse order of the topological sort, and determine whether the current compensation node is directly connected to an upstream node with the bend offset vector. An upstream node is a node that precedes the current compensation node in the original topological sort sequence and has an edge pointing from it to the current compensation node. Direct connection means that there is an edge between the two nodes, and no other nodes in between.

[0147] If directly connected, the bend offset vector of the upstream node is superimposed with the original coordinates of the current compensation node to generate the compensated coordinates of the current compensation node. The bend offset vector of the current compensation node is then updated to the superimposed composite offset vector, and this process continues to propagate to the downstream nodes until traversal is complete. The formula for calculating the offset propagation attenuation factor is:

[0148] (twenty four)

[0149] Where k is the preset attenuation coefficient, and d is the spatial Euclidean distance between the current compensation node and the upstream node.

[0150] The formula for calculating the attenuation offset vector is:

[0151] (25)

[0152] The formula for calculating the compensated coordinates is:

[0153] (26)

[0154] The system detects whether the compensated coordinates create new spatial interference with the adjacent non-conflicting nodes of the current compensated node. If new spatial interference occurs, the offset transfer attenuation factor is reduced by a preset ratio, and vector addition is re-executed until the new spatial interference is eliminated. The method for detecting new spatial interference is as follows: calculate the intersection volume between the new bounding box of the current compensated node and the bounding boxes of the adjacent non-conflicting nodes. If the intersection volume is greater than zero, new spatial interference has occurred. The calculation method for the intersection volume is the same as before.

[0155] After completing the offset compensation calculation, obtain the compensated coordinates and bend path control points of all nodes in the directed acyclic graph. Based on the orientation of the edges in the directed acyclic graph, sort the compensated coordinates and bend path control points according to the entity connection order of the reinforcing steel members to generate the logical sequence of bend nodes. The entity connection order refers to the continuous sequence of the reinforcing steel members in actual construction, i.e., the order from one end of the reinforcing steel to the other.

[0156] The connection vectors between adjacent nodes in the bend node logic sequence are extracted. Combined with the geometric parameters of the rebar cross-section, a three-dimensional envelope surface is reconstructed from the connection vectors to generate a spatial surface dataset corresponding to the three-dimensional arrangement coordinates of each rebar. This spatial surface dataset is then bound to the bend node logic sequence for output. The method for reconstructing the three-dimensional envelope surface is as follows: for adjacent nodes... and The connection vector is Generate two orthogonal elements. unit vector and ,satisfy and and The parametric equations for the cylindrical envelope are:

[0157] (27)

[0158] Where d is the diameter of the reinforcing bar. The vertex coordinates, normal vectors, texture coordinates, and other data of all cylindrical envelope surfaces are combined into a spatial surface dataset.

[0159] This embodiment details the graph coloring process, the method for generating bend path control points, the transfer logic of offset compensation, and the output format. By introducing minimum bending radius constraints, anchorage redundancy length limits, and offset transfer attenuation factors, the construction compliance and spatial stability of the layout results are ensured. The bend path control point parameters are shown in Table 3.

[0160] Table 3. Parameters of Control Points for Bending Path

[0161]

[0162] Table 3 shows the bending path control point parameters for longitudinal reinforcement bars B001, B002, and B004 in Table 1. The minimum bending radius of all reinforcement bars is set to 5 times the diameter, and the gap value is set to 20 mm. The path expansion and contraction are all less than the corresponding anchorage redundancy length, meeting the requirements of the structural code. The coordinates of the bending path control points are used to generate a three-dimensional arrangement model of the reinforcement bars, which can be directly imported into CNC reinforcement bar processing equipment for processing.

Claims

1. A method for optimizing the logic of rebar arrangement in complex construction nodes, characterized in that, include: Extract the geometric parameters and anchorage constraints of each steel reinforcement component in complex construction nodes, and construct a directed acyclic graph with steel reinforcement segments as nodes, spatial occupancy and intersection relationships as edges, and construction sequence and construction specifications as edge weights. The conflict in the spatial arrangement of steel bars is transformed into a loop identification problem in the directed acyclic graph. Graph coloring is used to classify the conflicting edges in the directed acyclic graph into hierarchical levels, and different coloring values ​​are assigned to conflicting steel bars as avoidance priorities. Based on the topological sorting traversal of the directed acyclic graph, the bending avoidance direction and offset calculation rules of the reinforcing bars are determined according to the coloring value. Among them, high-priority reinforcing bars maintain the original path, and low-priority reinforcing bars generate bending path control points according to spatial tolerance and anchorage length constraints. By performing offset compensation calculation in reverse order of the topological sorting, the bend offset is transmitted in reverse along the edge of the directed acyclic graph to the non-conflicting rebar segment, and the three-dimensional arrangement coordinates of each rebar and the logical sequence of bend nodes are output. Offset compensation calculations are performed in reverse order of the topological sorting, propagating the buckling offset in reverse along the edges of the directed acyclic graph to the non-conflicting reinforcement segments, including: After completing the forward traversal of the topological sort, obtain the bend offset vectors corresponding to all nodes that have been assigned bend path control points; Extract the current compensation node in reverse order of the topological sort, and determine whether the current compensation node is directly connected to the upstream node that has the bend offset vector; If directly connected, the bend offset vector of the upstream node is superimposed with the original coordinates of the current compensation node to generate the compensated coordinates of the current compensation node, and the bend offset vector of the current compensation node is updated to the superimposed composite offset vector. This process continues to propagate to the downstream nodes until the traversal is complete. The process of superimposing the bend offset vector of the upstream node with the original coordinates of the current compensated node to generate the compensated coordinates of the current compensated node includes: Obtain the spatial Euclidean distance between the current compensation node and the upstream node, and calculate the offset transmission attenuation factor based on the spatial Euclidean distance and a preset attenuation coefficient; Multiply the bend offset vector of the upstream node by the offset propagation attenuation factor to obtain the attenuation offset vector; Extract the original coordinates of the current compensation node, and add the attenuation offset vector to the original coordinates to generate the compensated coordinates of the current compensation node; If the compensated coordinates cause new spatial interference with the adjacent non-conflicting nodes of the current compensated node, the offset transfer attenuation factor is reduced by a preset ratio and the vector addition is re-executed.

2. The method for optimizing the logic of reinforcement arrangement in complex construction nodes according to claim 1, characterized in that, The construction of a directed acyclic graph, with rebar segments as nodes, spatial intersection relationships as edges, and construction sequence and structural specifications as edge weights, includes: Each continuous straight or bent steel bar segment within the complex construction node is defined as a node of the directed acyclic graph. Traverse all the three-dimensional bounding boxes corresponding to the nodes. When the three-dimensional bounding boxes of any two nodes have intersecting volumes, generate the edge of the directed acyclic graph between the two corresponding nodes. The direction of the edge is determined based on the difference between the body center coordinates of the intersecting volume and the coordinates of the anchorage starting point of the node. The weight value of the direction is quantified by combining the preset priority of the rebar type and the anchorage length specification. The weight value is then assigned to the edge to complete the construction of the directed acyclic graph.

3. The method for optimizing the logic of reinforcement arrangement in complex construction nodes according to claim 2, characterized in that, The process of transforming the spatial arrangement conflict of reinforcing bars into a loop identification problem in the directed acyclic graph (DAG) involves using graph coloring to hierarchically partition the conflict edges in the DAG, including: In the directed acyclic graph, a directed closed loop structure consisting of edges and nodes is detected, and the set of nodes corresponding to the directed closed loop structure is marked as a conflict group. Initialize the color set, select the node with the largest in-degree from the conflict group as the starting node, and assign the initial color from the color set to the starting node; Traverse the adjacent nodes in the conflict group along the direction of the directed closed loop structure, determine the weight value of the edge between the adjacent nodes, and assign a different color to the node pointed to by the edge with the smaller weight value, until all the nodes in the conflict group have been assigned a color, and the color represents the avoidance priority of the node.

4. The method for optimizing the logic of reinforcement arrangement in complex construction nodes according to claim 1, characterized in that, The rule for calculating the bending avoidance direction and offset of the reinforcing bars based on the coloring value by traversing the directed acyclic graph using topological sorting includes: Extract the current processing node sequentially according to the topological sorting sequence of the nodes in the directed acyclic graph; Obtain the avoidance priority corresponding to the coloring value of the current processing node. If the avoidance priority is higher than a preset threshold, keep the original spatial coordinates of the current processing node unchanged. If the avoidance priority is lower than the preset threshold, the spatial occupancy boundary of the high-priority node that has a conflict edge with the current processing node is obtained, the direction vector of the available space gap is determined according to the spatial occupancy boundary, the offset distance is calculated along the direction vector, and a bend path control point is inserted on the original path of the current processing node so that the path of the current processing node bypasses the spatial occupancy boundary of the high-priority node.

5. The method for optimizing the logic of reinforcement arrangement in complex construction nodes according to claim 1, characterized in that, The output of the three-dimensional arrangement coordinates and bend node logic sequence of each reinforcing bar includes: Obtain the compensated coordinates of all nodes in the directed acyclic graph and the bend path control points after the offset compensation calculation is completed; Based on the direction of the edges in the directed acyclic graph, the compensated coordinates and the bend path control points are sorted according to the entity connection order of the steel reinforcement members to generate the bend node logical sequence. The connection vectors between adjacent nodes in the bend node logic sequence are extracted. Combined with the geometric parameters of the steel bar cross section, the connection vectors are reconstructed into a three-dimensional envelope surface to generate a spatial surface dataset corresponding to the three-dimensional arrangement coordinates of each steel bar. The spatial surface dataset is then bound to the bend node logic sequence for output.

6. The method for optimizing the logic of reinforcement arrangement in complex construction nodes according to claim 2, characterized in that, The step of quantifying the weight value of the pointing direction by combining the preset priority of steel bar type and anchorage length specifications, and assigning the weight value to the edge, includes: Extract the steel bar type attributes and diameter parameters corresponding to the node, obtain the type weight coefficient based on the steel bar type attributes, and calculate the anchorage weight coefficient based on the diameter parameters and the anchorage length specification. Obtain the overlap depth value of the intersecting volumes along the direction in three-dimensional space, and normalize the overlap depth value to obtain the spatial overlap coefficient; The variety weight coefficient, the anchoring weight coefficient, and the spatial overlap coefficient are weighted and summed. The summation result is used as the weight value and assigned to the edge. When there is a bidirectional edge between the same pair of nodes, the weight values ​​of the bidirectional edges are compared. The bidirectional edge with the smaller weight value is removed, and the unidirectional edge with the larger weight value is retained.

7. The method for optimizing the logic of reinforcement arrangement in complex construction nodes according to claim 3, characterized in that, Determine the weight values ​​of the edges between adjacent nodes, and assign a different color to the node pointed to by the edge with the smaller weight value than the current node. This also includes: When a node in the conflict group is connected to multiple colored nodes by edges, and the multiple colored nodes have occupied all available colors in the color set, the node is marked as a color saturation node. The color set is expanded to generate new extended colors, and the extended colors are assigned to the color saturation nodes; The weight difference between the edges between the color saturated node and the plurality of colored nodes is recalculated. If the weight difference is less than a preset difference threshold, a local graph reconstruction instruction is triggered to split the color saturated node into a plurality of virtual child nodes. Each virtual child node inherits part of the space occupancy attribute of the original color saturated node and is respectively assigned color compatibility with the corresponding colored node.

8. The method for optimizing the logic of reinforcement arrangement in complex construction nodes according to claim 4, characterized in that, Calculate the offset distance along the direction vector and insert a bend path control point on the original path of the current processing node, including: Obtain the angle between the original path tangent vector of the current processing node and the direction vector, and calculate the preliminary positions of the buckling start point and buckling end point based on the angle value and the minimum bending radius constraint of the reinforcing bar. An arc transition path is generated between the initial positions. The difference between the arc length of the arc transition path and the length of the corresponding line segment of the original path is calculated to obtain the path stretching amount. The path expansion amount is compared with the anchorage redundancy length of the current processing node. If the path expansion amount is less than the anchorage redundancy length, the bend start point, the arc transition path, and the bend end point are inserted as the bend path control points. If it is greater, the offset distance is increased along the direction vector and recalculated until the anchorage redundancy length limit is met.

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