Parametric modeling method for cableway bridge based on geometric shape finding and spatial topology mapping

Abstract

The application provides a cableway bridge parameterized modeling method based on geometric form finding and space topology mapping, relates to the technical field of bridge engineering digital design and modeling, and the technology comprises the following steps: constructing a calculation domain, analyzing form finding, constructing an assembly reference, component topology mapping and full model generation. The application establishes a full parameterized driving dynamic model: all geometric features of the model are driven by input design parameters and topology relations. Through preset parameter dependence relations and update sequences, the system can automatically and orderly update the whole three-dimensional model when the parameters are changed, realizes "one modification, everywhere update", significantly improves the design iteration and scheme comparison and selection efficiency, and solves the core problem of parameter and model disconnection.

Description

Technical Field

[0001] This invention relates to the field of digital design and modeling technology for bridge engineering, and in particular to a parametric modeling method for cableway bridges based on geometric form finding and spatial topology mapping. Background Technology

[0002] In the fields of water conservancy, hydropower, and transportation engineering, projects involving flexible cable-stayed structures are increasing, such as construction and transportation cableways spanning canyons, pedestrian cableway bridges in reservoir areas, and large suspension bridges. The core of designing these structures lies in determining their initial shape (i.e., "form finding"), because the geometry of a flexible cable under its own weight and loads is coupled with its internal force distribution; the accuracy of the shape directly affects the structure's safety and economy. Traditional design methods typically rely on simplified calculations combined with empirical formulas for initial form finding, followed by iterative finite element analysis for correction. This process is not only time-consuming and labor-intensive but also heavily reliant on the engineer's personal experience, making it difficult to achieve rapid and accurate parametric design and scheme comparison.

[0003] With the popularization of Building Information Modeling (BIM) technology, engineering design is developing towards a full lifecycle and fully parametric approach. However, existing mainstream BIM modeling platforms and their conventional parametric tools have significant shortcomings when dealing with flexible cable structures with complex spatial curves and dynamic topological relationships: 1. Low level of automation in form finding: Existing tools lack embedded form finding engines based on mechanical analytical equations. Engineers often need to rely on external professional analysis software to complete form finding calculations, and then manually import the results (usually a series of discrete point coordinates) into the BIM environment for fitting and modeling. This data flow method disconnects design and analysis, resulting in delayed model updates, and any modification to design parameters may lead to tedious repetitive work.

[0004] 2. Difficulty in Spatial Topology Following: Flexible cable structures contain various components attached to the spatial curves of the main cable, such as cable clamps, suspenders (rods), and bridge deck units. The position, orientation, and dimensions of these components are strictly controlled by the geometric characteristics of the main cable curve (such as tangent direction and normal plane). Existing BIM tools' arraying and lofting functions are usually based on a fixed global coordinate system or simple paths, making it difficult to achieve automatic, accurate, and dynamic association (i.e., "topology mapping") between component geometric properties (such as direction axes) and curve local geometric properties (such as Frenet frames). For example, the length of the suspenders needs to respond in real time to changes in the distance between the two main cables, and the bridge deck needs to be arranged strictly along the curve normal, which is difficult to achieve efficiently and accurately using conventional modeling methods.

[0005] 3. Poor model versatility and reusability: For different structural forms (such as suspension bridges with separated cables and belt bridges with coplanar decks) or different form-finding algorithms (catenches and parabolas), existing modeling methods often require writing different, customized scripts or processes, lacking a unified, configurable modeling framework. This makes it difficult to quickly port and adapt technical solutions to different projects, increasing learning costs and development redundancy.

[0006] Furthermore, existing technical solutions lack mechanisms for achieving dynamic and interconnected updates of parametric models. Even when some tools support parameter-driven operations, they often lack effective management of complex dependency chains. When upstream design parameters (such as span and sag) change, downstream model components (such as cable length and bridge deck orientation) cannot be updated automatically and reliably, or the update order may be disordered, leading to model errors and preventing the achievement of true "fully parametric dynamic response." This makes model maintenance and scheme adjustments inefficient.

[0007] Therefore, there is an urgent need in this field for a three-dimensional parametric modeling method and system that can deeply integrate analytical form-finding calculation, intelligent spatial topology mapping and has a reliable dynamic response mechanism, so as to overcome the defects of existing technologies such as low degree of automation, weak topological association, poor universality and unreliable model linkage update, and realize the efficient, accurate and fully automatic generation of flexible cable structure from design parameters to complete BIM model. Summary of the Invention

[0008] This invention aims to solve the following problems existing in current 3D modeling technology for cableway bridges: 1. The modeling process is cumbersome and relies on human experience: Traditional methods usually require engineers to manually draw and position each component in general 3D modeling software, which is inefficient and makes it difficult to ensure the mechanical rationality of the model.

[0009] 2. Disconnect between model and design parameters: Existing models are mostly static geometry. When design parameters (such as main cable tension, sag, span, etc.) change, they cannot be updated in a coordinated manner, resulting in a large amount of repetitive modeling work.

[0010] 3. Difficulty in balancing model accuracy and versatility: There is a lack of unified parametric modeling logic for different structural forms (such as suspension bridges, cableways, and belt bridges) and different form-finding algorithms (such as catenary and parabola), resulting in poor versatility of the schemes, or sacrificing the modeling accuracy of specific structures in pursuit of versatility.

[0011] 4. Software functions are too tightly bound to the underlying logic: The modeling methods of existing software tools are often deeply coupled with specific software operations (such as clicking, dragging, and running specific scripts). Their protection scope is limited to specific software implementations, making it difficult to form effective patent protection for the underlying modeling logic.

[0012] To address the aforementioned technical problems, this invention provides a method and system for three-dimensional parametric modeling of cableway bridges based on analytical geometry form finding and spatial topology mapping. The core idea is to decompose the complex cableway bridge structure into abstract geometric and topological relationships, generate accurate spatial curves for the main cable through analytical mechanics form finding, construct dynamic assembly datums using differential geometry, and finally drive the automatic generation of a complete three-dimensional model from predefined parametric components through a unified set of topology mapping rules.

[0013] A three-dimensional parametric modeling method for cableway bridges based on analytical geometry form finding and spatial topological mapping includes the following steps: S1: Construct the computational domain: Input the planar axis, design parameters, and structural topology of the cableway bridge; the structural topology is used to define the spatial hierarchy between the first and second topological boundaries, including separate hierarchical forms or coplanar hierarchical forms; S2: Analytical Form Finding: Based on the design parameters, mechanical form finding calculations are performed in the local vertical plane defined by the plane axis using the analytical equation of cable shape to generate the main cable skeleton curve in three-dimensional space; S3: Construct assembly benchmark: Calculate differential geometric properties along the main cable skeleton curve, and construct a dynamic frame that varies with the main cable skeleton curve; S4: Component Topology Mapping: Based on the structural topology, the predefined parameterized components are spatially associated and mapped with the main cable skeleton curve and the dynamic frame, wherein: The point-following unit's spatial positioning depends on a point on the curve of the main cable skeleton, and its central axis is constrained to be collinear with the tangential axis of the dynamic frame at that point. The length of the linear connection unit is driven by the spatial distance between the projection point on the first topological boundary and the projection point on the second topological boundary; The along-line functional units are swept or arrayed along the curve of the main cable skeleton. S5: Full Model Generation: Based on mapping relationships, it drives the update of all parametric components to generate a fully parametric 3D model containing geometric and engineering properties.

[0014] Preferably, in step S3, the dynamic frame is a Frenet frame, including a tangential axis T, a principal normal axis N, and a secondary normal axis B.

[0015] Preferably, in step S2, the analytical equation of the cable shape is a catenary equation or a parabola equation.

[0016] Preferably, in the separated hierarchical form, the first topological boundary and the second topological boundary are located on spatially separated hierarchical skeletons.

[0017] Preferably, in the coplanar hierarchical form, the first topological boundary and the second topological boundary are located on the same hierarchical skeleton or on a spatially coplanar skeleton.

[0018] A three-dimensional parametric modeling system for cableway bridges to implement the above modeling method includes: The driver interface module is used to receive user input of the plane axis, design parameters, and structural topology selection; The analytical shape-finding module, connected to the driving interface module, is used to perform mechanical calculations in a local vertical plane based on the design parameters and the selected cable alignment analytical equation, and generate a three-dimensional main cable skeleton curve. The topology assembly module is connected to the analytical shape-finding module and the driving interface module respectively. It is used to call a predefined parameterized component library according to the structural topology form, and to perform spatial topology mapping and assembly logic based on the main cable skeleton curve and its dynamic frame. The dynamic response mechanism module is connected to the analytical shape-finding module and the topology assembly module respectively. When the input parameters change, it updates the main cable skeleton curve and all associated parameterized components in real time according to the preset parameter dependency relationship and update sequence, thus refreshing the 3D model in real time.

[0019] Preferably, the topology assembly module further includes a terrain interaction unit, used to perform Boolean operations on the generated model and the digital terrain model to automatically generate an excavation model.

[0020] Preferably, the system further includes a data output module for extracting and outputting a bill of quantities from the fully parameterized 3D model generated by the dynamic response mechanism module.

[0021] Compared with the prior art, the present invention has the following beneficial effects: 1. The modeling process has been automated and made intelligent: Through the automated process of "input parameters - analytical shape finding - topological mapping", engineers are freed from tedious manual modeling, which greatly improves modeling efficiency and ensures the accuracy of the model based on mechanical principles.

[0022] 2. A fully parameter-driven dynamic model was established: all geometric features of the model are driven by the input design parameters and topological relationships. Through preset parameter dependencies and update sequences, the system can automatically and orderly update the entire 3D model when parameters change, achieving "one modification, everywhere updated," significantly improving the efficiency of design iteration and scheme comparison, and solving the core problem of parameter and model disconnect.

[0023] 3. By employing abstraction and general design principles, the applicability of the solution has been broadened: Algorithm versatility: By adopting the concept of "analytical equations for cable lines", the method is compatible with various high-precision shape-finding algorithms such as catenary and parabola, and can adapt to different engineering accuracy requirements.

[0024] Structural versatility: By abstracting component types with clear geometric constraints, such as "point-following units," "linear connection units," and "functional units along the route," as well as topological forms with clearly defined spatial relationships, such as "separated hierarchies" and "coplanar hierarchies," the same set of modeling logic can be clearly and consistently applied to various flexible cable structures such as suspension bridges, construction cableways, and belt-type pedestrian bridges, overcoming the shortcomings of existing technologies that make it difficult to balance versatility and accuracy.

[0025] 4. By employing a "de-software-based" logical description, the patent protection is strengthened: the method claims focus on the underlying mathematical logic and geometric relationships such as "constructing a dynamic framework," "establishing vector constraints," and "driving spatial distances," rather than specific software operation steps. This ensures that the scope of patent protection is not limited to a particular software platform or user interface, but can cover all modeling behaviors based on this core logic, effectively expanding the scope of protection of the claims.

[0026] 5. Through a "black-box" system design, an anti-piracy barrier is constructed for software products: The system claims emphasize the feature of a "minimalist driver interface," meaning users only need to input the most basic axes, parameters, and topology selections, without needing to understand the complex internal implementation process. In particular, the system automatically manages complex update logic through a built-in dynamic response mechanism, ensuring that infringing software that achieves the functional loop of "minimalist input - automatic generation of a complete model" may fall within the protection scope of this patent, providing strong support for the commercial protection of software products.

[0027] 6. Enhanced engineering application value of the model: The generated model is not only a geometric model, but also a BIM model containing engineering attributes. The system can automatically extract the bill of quantities and interact with digital terrain to generate construction excavation models, directly applying design results to engineering quantity calculation and construction guidance, realizing data integration from design to construction. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of an engineering case illustrating the application of the cableway bridge formwork design in this invention. Figure 1 ; Figure 2 This is a schematic diagram of an engineering case illustrating the application of the cableway bridge formwork design in this invention. Figure 2 ; Figure 3 This is a schematic diagram of the overall structure of the parametric template for the cableway bridge of the present invention; Figure 4 This is a partial structural diagram of the parametric template for the cableway bridge of the present invention; Figure 5 This is a schematic diagram of the steel crossbeam component in the cableway bridge formwork of the present invention; Figure 6 This is a schematic diagram showing the comparison of multiple design schemes for the cableway bridge of the present invention; Figure 7 This is a schematic diagram of the planar axis of the cableway bridge of the present invention; Figure 8 This is a schematic diagram illustrating the use of a large template in this invention; Figure 9 This is a schematic diagram of the cableway bridge template after loading according to the present invention; Figure 10 This is a schematic diagram of parameter adjustment after loading in this invention; Figure 11 The present invention relates to the adjustment of the bridge deck width of the cableway bridge; Figure 12 This is a schematic diagram comparing multiple schemes of the cableway bridge of the present invention. Detailed Implementation

[0029] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0030] Technical Principle Explanation: Frenet Frame and Dynamic Coordinate System The core spatial positioning logic of this invention is based on the Frenet frame theory in differential geometry. For a smooth spatial curve (in this invention, the main cable skeleton curve), any point on it can define a unique local Cartesian coordinate system that varies with the curvature of the curve, i.e., the Frenet frame. This frame consists of three mutually perpendicular unit vectors: Tangential axis (T): Its direction is consistent with the tangent direction of the curve at that point, and it represents the instantaneous extension direction of the curve.

[0031] Principal normal axis (N): Its direction points to the center of curvature of the curve at that point, representing the direction of curvature of the curve in that plane.

[0032] The secondary normal axis (B) is defined by the cross product of the tangential axis (T) and the principal normal axis (N) (B = T × N), and it is perpendicular to the osculating plane of the curve at that point.

[0033] By continuously calculating the Frenet frame along the main cable skeleton curve, this invention constructs a "flying coordinate system." This dynamic frame provides precise spatial references and constraint directions for the assembly of all subsequent parametric components. For example, components that need to slide along the cable (point-following units) must align their direction of motion with the tangential axis (T); components that need to be mounted perpendicular to the cable surface (such as certain friction-adhesive functional units) can use the normal axis (N or B) as their normal direction. This mapping relationship based on differential geometric properties ensures that the spatial attitude of each component can automatically and accurately follow and adjust regardless of the complexity of the cable profile, achieving true full parametric drive.

[0034] Core component unit definition and mapping rules In the specific implementation of the method of this invention, the key parameterized components involved can be abstracted and defined into the following three types of units based on their spatial behavior characteristics and parameter dependencies, and their mapping rules constitute the core logic of topology assembly: (1) Point-following unit: This refers to a component whose spatial positioning depends on a specific driving point on the main cable skeleton curve, and whose orientation (at least one direction axis, such as the central axis, axis of symmetry, or normal to the mounting surface) needs to maintain a preset vector constraint relationship with the local geometric properties of the curve at that driving point (especially a certain axis of the Frenet frame). Its technical feature is that the position of the unit is uniquely determined by curve parameters (such as arc length parameter s), and its orientation is driven by the dynamic frame at that point, thereby realizing the precise following of the unit's posture to the curve geometry. Typical mapping constraints include forcing the unit's central axis to be collinear with the tangential axis (T), or forcing the unit's mounting plane normal to be parallel to the principal normal axis (N).

[0035] (2) Linear connection unit: This refers to a component whose core dimensional parameter (usually length) is uniquely determined by the relative positional relationship between two specified discrete points (defined as the first topological boundary and the second topological boundary, respectively) that may be located on different components or curves in space. Its technical feature is that the length of this unit is not an independent input value, but is automatically driven by calculating the Euclidean distance between the two topological boundary points in real time. When the boundary points move due to changes in the position of the curves or components they are attached to, the length of the unit is automatically updated, thus maintaining the established connection relationship.

[0036] (3) Along-the-line functional unit: refers to a component that needs to be continuously swept or discretely arrayed along the main cable skeleton curve path to provide a continuous functional surface or repetitive functional structure. Its technical feature is that its distribution path is defined by the skeleton curve, and the local coordinate system of each distribution instance (for array) or section (for sweep) at each point on the path can be associated with the Frenet frame at the corresponding point according to preset rules. For example, controlling the torsion angle of the sweep section, or constraining the orientation of the array instance to align with a certain normal axis of the frame, to ensure that the unit can conform to the spatial orientation of the curve.

[0037] Definition of structural topology The "structural topology" is a predefined classification model used to describe the spatial hierarchy between the main load-bearing cables and main functional components of a cableway bridge. Its core function is to clarify the spatial context of the two "topological boundaries" connected by the "linear connection unit". This invention mainly defines and supports two basic forms: Separate hierarchical form: This refers to a structure where the first and second topological boundaries are located on spatially separated hierarchical frameworks. The most common scenario is that the first topological boundary is located on the upper main cable framework curve, while the second topological boundary is located on the lower bridge deck or another lower cable. This form corresponds to structures such as traditional suspension bridges.

[0038] Coplanar hierarchical form: This refers to a situation where the first and second topological boundaries are located on the same hierarchical framework, or although they are located on different frameworks, they are spatially coplanar or approximately coplanar. For example, two boundary points may both be located on the same main cable (such as the point connecting the pulley and the traction cable in a cableway), or they may be located on two spatially adjacent and almost parallel cables. This form corresponds to structures such as cableways and belt bridges.

[0039] Dynamic response and linkage update mechanism To achieve the fully parameterized driving and dynamic response described in the claims, the system of this invention implements a linkage update mechanism based on a parameter dependency graph and an ordered update sequence. This mechanism ensures that the entire model can be automatically and correctly updated when any input design parameter changes. Its core process is as follows: 1. Dependency Construction: During system initialization, based on predefined engineering logic, an explicit dependency graph is established from input parameters to all intermediate calculation data (such as main cable curve coordinates, Frenet frame, component positioning point coordinates, etc.). For example, the suspender length depends on the coordinates of the cable clamp point on the main cable and the coordinates of the suspension point on the bridge deck, and these two coordinates depend on the main cable curve parameters and the bridge deck positioning parameters, respectively.

[0040] 2. Change Triggering and Dirty Mark Propagation: When a user modifies an input parameter (such as sag f) through the interface, the system marks that parameter as "changed." Subsequently, based on the dependency graph, all computational nodes that directly or indirectly depend on that parameter are automatically and recursively marked as "dirty," meaning that the values ​​of these nodes are invalid and need to be recalculated. This includes the main cable curve, the Frenet frames of all points on the curve, and components located based on these frames.

[0041] 3. Ordered Update Sequence Execution: The system performs recalculation and update operations according to the topological order of dependencies, ensuring that parent nodes are updated before child nodes. A typical update sequence is as follows: a. Analytical shape-finding engine recalculation: Based on the new input parameters, the analytical equation of the cable alignment is resolved, and the three-dimensional coordinate data of the main cable skeleton curve is updated.

[0042] b. Geometric attribute recalculation: Recalculate the Frenet frame (tangential T, normal N, subnormal B) at each point along the updated main cable curve.

[0043] c. Topology Boundary Point Update: Based on the updated curves and frames, recalculate the spatial coordinates of the topology boundary points on which all "point-following elements" and "linear connection elements" depend.

[0044] d. Component parameter-driven updates: For the "point-following unit", vector constraints are applied to update its spatial position and attitude based on its new positioning point coordinates and the new frame axis of that point.

[0045] For a “linear connection element”, the Euclidean distance is recalculated based on the new coordinates of its two topological boundary points, and this distance value is assigned to the length parameter of the element to drive its geometric model update.

[0046] For “functional units along the path”, based on the new path curve and the new frame field, sweep or array operations are re-executed to update their distribution pattern and orientation.

[0047] 4. Model Rendering Refresh: After all components have been updated, the system notifies the 3D graphics engine to refresh the view and present the updated complete model. The entire update process is completed automatically by the system without any manual intervention from the user, achieving a dynamic response effect of "one change, global linkage".

[0048] Example 1: Modeling of a Separated-Level Suspension Bridge Based on the Catenary Algorithm This embodiment demonstrates the application of the present invention in the modeling of a traditional double-main-cable suspension bridge (separate hierarchical form), and uses the catenary equation for accurate shape finding.

[0049] 1. Input: Users input the plane axis of the suspension bridge (usually the center line of the bridge deck), design parameters (including main cable span L, design sag f, main cable horizontal tension H0, suspender spacing, etc.) and select the "separate hierarchy" structural topology through the simplified driver interface.

[0050] 2. Analytical Shape Finding (S2): The analytical shape finding module uses the catenary equation based on the input parameters such as L, f, and H0. (Where q is the uniformly distributed load intensity of the main cable) Calculations are performed in the local vertical planes on both sides of the axis. Two precise three-dimensional catenary curves are obtained, serving as the skeleton curves of the left and right main cables.

[0051] 3. Constructing Assembly Datum (S3): The system calculates the Frenet frame along the two main cable skeleton curves respectively. For the main cable, which is approximately located in the vertical plane, its tangential axis (T) points to the tangent direction of the cable, the principal normal axis (N) points approximately to the center of curvature at that point (in the vertical plane), and the secondary normal axis (B) points horizontally to the transverse direction of the bridge.

[0052] 4. Component topology mapping (S4): Point-following unit mapping: The cable clamp is defined as a point-following unit. The system creates a positioning point on the main cable skeleton curve at the designed location of each sling. The center axis of the cable clamp (i.e., its fastening direction) is vector-constrained to be collinear with the tangential axis (T) of the Frenet frame at the location, ensuring that the cable clamp tightly "hugs" the main cable.

[0053] Linear Connector Unit Mapping: Suspensions are defined as linear connector units. The system uses the bottom connection point of the cable clamp as the "first topological boundary" and the corresponding suspension point on the bridge deck crossbeam as the "second topological boundary." The topology assembly module calculates the three-dimensional Euclidean distance between these two boundary points and directly drives the length parameter of the corresponding sling. When the main cable alignment changes due to parameter modifications, the cable clamp position moves accordingly, thereby automatically recalculating and updating the length of all slings.

[0054] Along-path functional unit mapping: Bridge deck blocks are defined as along-path functional units. The system performs a sweep operation using the bridge deck centerline as the path and the crossbeam cross section as the contour to generate a continuous bridge deck volume. The attitude of the bridge deck crossbeams can be indirectly constrained by their connection relationship with the anchor points under the suspension cables.

[0055] 5. Full Model Generation and Dynamic Response (S5): The dynamic response mechanism module operates based on the aforementioned "linked update mechanism." Any change in input parameters (such as sag f) will trigger an update chain: catenary recalculation → skeleton curve update → Frenet frame reconstruction → cable clamp repositioning (point-following unit update) → automatic adjustment of cable length (linear connection unit update) → bridge deck follow-up changes (along-line functional unit update), ultimately updating the entire suspension bridge's BIM model in real time. The data output module can synchronously update the bill of quantities, such as main cable length and cable specifications.

[0056] Example 2: Modeling of a Separated Hierarchical Suspension Bridge Based on Parabolic Algorithm The main difference between this embodiment and Embodiment 1 is that it uses a parabolic equation for shape finding, which is suitable for suspension bridges with uniform load distribution and small span-to-span ratio, and the calculation is more efficient.

[0057] 1. Input: The user inputs the plane axis, design parameters (span L, sag f, etc.), and selects the "separate hierarchy" mode.

[0058] 2. Analytical Shape Finding (S2): The analytical shape finding module uses the parabola equation. Perform main cable alignment calculations to generate parabolic skeleton curves for the left and right main cables.

[0059] 3. Construct assembly datum (S3): Similarly, construct the Frenet dynamic frame along the parabolic skeleton curve.

[0060] 4. Component Topology Mapping (S4): The mapping logic is exactly the same as in Example 1. The cable clamp (point-following unit) axis is constrained to the tangential axis (T); the length of the suspension cable (linear connection unit) is driven by the spatial distance between the cable clamp point and the bridge deck suspension point; the bridge deck (along-distance functional unit) is generated by sweeping.

[0061] 5. Full model generation (S5): When the sag f is modified, the system recalculates the parabola based on the new parameters. Through the same dynamic response mechanism, the entire model, from the main cable and cable clamps to the suspenders, is automatically updated, realizing rapid scheme comparison and parametric design.

[0062] Example 3: Modeling of a Coplanar Hierarchical Double-Main-Cable Pedestrian / Lightweight Suspension Bridge Based on the Catenary Algorithm. This example demonstrates the application of the present invention in modeling a coplanar hierarchical suspension bridge structure where the main cables are coplanar with the bridge deck and the left and right main cables are arranged parallel to each other on both sides of the bridge deck. This structural form is commonly found in pedestrian suspension bridges, landscape suspension bridges, and lightweight functional bridges, such as... Figures 1 to 6 As shown.

[0063] 1. Input Users input the bridge's planar axis (usually the bridge deck centerline) through a simplified driver interface, and input design parameters, including but not limited to: Span L, design sag f; Lateral offset of the left and right main cables relative to the centerline of the bridge deck; Uniformly distributed load parameters or equivalent line load of the main cable ; Bridge deck unit length, connection construction parameters, etc.; and select the "coplanar hierarchy" structural topology.

[0064] 2. Analytical shape finding (S2) The analytical form-finding module performs catenary form-finding calculations for the main cables located on the left and right sides of the bridge deck within the same vertical plane. The system uses the bridge deck centerline as the reference axis and, based on the input lateral offset, generates calculation planes for the left and right main cables on both sides of this axis, applying the catenary equation within each plane: Solve for the spatial skeleton curves of the left and right main cables separately. The two resulting catenary lines have consistent linear characteristics in the vertical projection, are coplanar with the bridge deck in space but are separated laterally, forming the geometric basis for the coplanar arrangement of the two main cables.

[0065] 3. Establish assembly datum (S3) The system calculates the Frenet dynamic frame along the skeleton curves of the left and right main cables respectively. For each main cable, its: The tangential axis (T) is along the tangential direction of the cable; The principal normal axis (N) points to the center of curvature of the catenary and lies in the vertical plane of the bridge; The secondary normal axis (B) is along the transverse direction of the bridge.

[0066] Although the left and right main cables are located in different lateral positions, their Frenet frame construction logic remains consistent, providing a unified geometric reference system for the subsequent assembly of components on their respective main cables.

[0067] 4. Component Topology Mapping (S4) (1) Point-based following unit mapping Lateral connection components on the bridge deck (such as cable clamps, lateral support nodes, or bridge deck edge beam connection nodes) are defined as point-following units. At the design segment locations of the left and right main cables, the system generates positioning points on the respective main cable skeleton curves and constrains the critical installation axes of the corresponding components to align with the tangential axis (T) or secondary normal axis (B) of the Frenet frame at that point, ensuring that the components always maintain consistent geometric orientation with the main cables.

[0068] (2) Linear connection unit mapping The connecting cables or rods between the bridge deck and the left and right main cables are defined as linear connection units. The system uses the cable clamp positioning points on the main cables as the first topological boundary and the connection points on the bridge deck or side beams as the second topological boundary. It calculates the three-dimensional Euclidean distance between the two points in real time and uses this distance parameter to drive the length of the corresponding connection member. When the alignment of the main cables changes, the length and spatial orientation of the connection members are automatically updated.

[0069] (3) Mapping of functional units along the process The bridge deck unit is defined as a friction-dependent functional unit. The system uses the bridge deck centerline as a path and arranges the parameterized bridge deck units in an array along this path. The local coordinate system of each bridge deck can be constrained by its topological relationship with the left and right connecting units, and its attitude can be indirectly controlled by the normal axis (N) or sub-normal axis (B) in the Frenet frame of the left and right main cables, thereby ensuring that the overall bridge deck is geometrically consistent with the dual main cable system.

[0070] 5. Full Model Generation and Dynamic Response (S5) The dynamic response mechanism module operates based on the above topology mapping relationship. When the user modifies parameters such as sag f, span L, or main cable lateral offset, the system triggers the following update chain: Catenary recalculation → Update left and right main cable skeleton curves → Frenet frame reconstruction → Point-type following unit repositioning → Automatic adjustment of linear connection unit length and attitude → Overall linkage update of bridge deck along-line units.

[0071] Ultimately, it enables real-time updating of the BIM model of a double-main-cable coplanar hierarchical cable-stayed bridge, and can simultaneously output engineering data such as main cable length, connecting component specifications, and bridge deck component layout.

[0072] Example 4: Modeling of a Coplanar Hierarchical Strip Pedestrian Suspension Bridge Based on Parabolic Algorithm This embodiment demonstrates the application of the present invention in modeling cable-stayed bridges, such as stress band bridges, where the thin strip structure is coplanar with the main cable.

[0073] 1. Input: The user inputs the centerline of the bridge deck as the plane axis, design parameters (span, sag of the completed bridge alignment, etc.), and selects the "coplanar level" format.

[0074] 2. Analytical Form Finding (S2): The analytical form finding engine uses the parabolic equation to calculate the line shape of the prestressed strip main cable (which is integrated with or closely attached to the bridge deck) as the main load-bearing component, and generates the skeleton curve.

[0075] 3. Construct assembly datum (S3): Calculate the Frenet frame along the skeleton curve.

[0076] 4. Component topology mapping (S4): Along-path functional unit mapping: Bridge deck units are defined as along-path functional units. The system uses prefabricated bridge decks as parametric components, arrayed along the skeleton curve path. A key constraint is that the local coordinate system Z-axis of each bridge deck (usually defined as the thickness direction or normal direction) is constrained to align with the primary normal axis (N) or secondary normal axis (B) of the Frenet frame at that point (the specific alignment depends on design conventions; for example, constraining to the N-axis makes the deck surface perpendicular to the bending plane). This constraint ensures that the bridge decks can precisely conform to the varying cable (strip) surface.

[0077] Point-following unit mapping: Connecting components between bridge decks (such as hinges and shear keys) can be defined as point-following units, and their installation direction can be constrained by referring to the tangential axis (T) or the normal axis.

[0078] 5. Full Model Generation (S5): By changing the sag or span, the shape of the main cable strip is updated. Through a dynamic response mechanism, the normal direction of all bridge decks is automatically rotated by the normal axis constraint of the Frenet frame to keep it perpendicular to the cable surface, and a new bridge deck arrangement model is automatically generated.

[0079] Terminology Explanation and Description In the context of this invention, to maintain the breadth of the claims, the specification uses highly generalized terms whose specific meanings cover, but are not limited to, the following examples: "Point-following unit": refers to components that are primarily characterized as points in space, and whose orientation must strictly follow the local geometric properties of the cable curve. Specific embodiments include, but are not limited to: cable clamps in suspension bridges, pulleys or transport trolleys in cableways, anchorage connectors for various cables, and maintenance facility supports on suspension bridges that require positioning along the cable.

[0080] "Linear connection unit": refers to a component whose main function is to connect two discrete topological boundaries, and whose core dimensional parameters (especially length) are determined by the spatial relationship between these two boundary points. Specific embodiments include, but are not limited to: suspenders or rods connecting the main cable and the bridge deck in a suspension bridge, transverse wind-resistant cables connecting different cables, and tie rods connecting anchor points and load-bearing cables in a tension structure.

[0081] "Functional units along the cable frame": refers to components that need to be arranged continuously or discretely along the curved path of the cable frame to provide the main function or coverage. Specific examples include, but are not limited to: bridge decks of suspension bridges or belt bridges, bridge deck stiffening girders, protective sleeves on cables, and lighting or cable supports installed along the cables.

[0082] "Separate hierarchical form" and "coplanar hierarchical form": This dichotomy summarizes two basic spatial topologies of flexible cable-stayed structures. "Separate hierarchical form" refers to a structure where the main load-bearing cables and the main functional surfaces (such as the bridge deck) are clearly separated in space and connected by vertical or diagonal components, as in traditional suspension bridges. "Coplanar hierarchical form" refers to a structure where the load-bearing cables and the main functional surfaces are closely integrated in space or coplanar, as in cableways, stress-band pedestrian bridges, and certain cable-stayed membrane structures.

[0083] The specific implementation process of this invention in the 3DE platform is as follows: Step 1: Create the "Cableway Bridge Plane Axis" for this project, such as... Figure 7 As shown; Step 2: In the Civil 3D Design module of the 3DE platform, click the "Tools" button and then the "Installate from Display" icon. Next, click the "Super Copy" structure tree under the "Cableway Bridge Template V1.0" that you have already created. Then, 3DE will pop up a dialog box; enter the created "Cableway Bridge Plane Axis" as shown below. Figure 8 As shown; Step 3: Select the "Cableway Bridge Planar Axis" created in Step 1, and then click the "OK" button. This completes the initial creation of the cableway bridge's 3D model. Figure 9 As shown; Step 4: Modify design parameters. Simply edit the relevant "Cableway Bridge Design Parameters" in the parameter structure tree to make adjustments. For example, to move the left bank abutment of the cableway bridge downwards, double-click the design parameter "Left Bank Bridge Deck Elevation," modify the value in the dialog box, and the 3D model of the cableway bridge will update and adjust accordingly. Figure 10 As shown; Step 5: Designing the cableway bridge's structural dimensions. Simply modify the relevant structural dimension parameters of the cableway bridge in the parameter structure tree. For example, to adjust the cableway bridge deck width from 4.7 meters to 5 meters, double-click "Bridge Deck Width," modify the corresponding value in the dialog box, and the cableway bridge deck width will be updated accordingly. Figure 11 As shown; Step 6: Users perform 3D visualization design of the cableway bridge based on the 3D model of the cableway bridge and the terrain surface model. Real-time adjustments are possible, and multiple design schemes can be completed in 3D modeling, such as... Figure 12 As shown; Step 7: Users edit the 3D model of the cableway bridge for subsequent design scheme comparison, and extract geometric information from the 3D model for other engineering applications, such as quantity calculation.

[0084] Obviously, the above description is only a part of the embodiments of the present invention, and not all of the embodiments. The above embodiments are not intended to limit the present invention, and various modifications and variations can be made to the present invention by those skilled in the art. Any combination, modification, equivalent substitution, improvement, and all other embodiments that can be made by those skilled in the art within the spirit and principles of the present invention should be within the protection scope of the present invention.

Claims

1. A parametric modeling method for cableway bridges based on geometric form finding and spatial topological mapping, characterized in that, Includes the following steps: S1: Construct the computational domain: Input the plane axis, design parameters, and structural topology of the cableway bridge. The structural topology is used to define the spatial hierarchy between the first topological boundary and the second topological boundary, including a separate hierarchy or a coplanar hierarchy. S2: Analytical Form Finding: Based on the design parameters, mechanical form finding calculations are performed in the local vertical plane defined by the plane axis using the analytical equation of cable shape to generate the main cable skeleton curve in three-dimensional space; S3: Construct assembly benchmark: Calculate differential geometric properties along the main cable skeleton curve, and construct a dynamic frame that varies with the main cable skeleton curve; S4: Component Topology Mapping: Based on the structural topology, the predefined parameterized components are spatially associated and mapped with the main cable skeleton curve and the dynamic frame, wherein: The point-following unit's spatial positioning depends on a point on the curve of the main cable skeleton, and its central axis is constrained to be collinear with the tangential axis of the dynamic frame at that point. The length of the linear connection unit is driven by the spatial distance between the projection point on the first topological boundary and the projection point on the second topological boundary; The along-line functional units are swept or arrayed along the curve of the main cable skeleton. S5: Full Model Generation: Based on mapping relationships, it drives the update of all parametric components to generate a fully parametric 3D model containing geometric and engineering properties.

2. The modeling method according to claim 1, characterized in that, In step S4, the center axis vector of the point-following unit is constrained to be collinear with the tangential axis T of the dynamic frame.

3. The modeling method according to claim 1, characterized in that, In step S4, the length of the linear connection unit is driven by calculating the Euclidean distance between the projection point on the first topological boundary and the projection point on the second topological boundary.

4. The modeling method according to claim 1, characterized in that, In the separated hierarchical form, the first topological boundary and the second topological boundary are located on different spatially separated hierarchical skeletons.

5. The modeling method according to claim 1, characterized in that, In the coplanar hierarchical form, the first topological boundary and the second topological boundary are located on the same hierarchical skeleton or on a spatially coplanar skeleton.

6. The modeling method according to claim 1, characterized in that, In step S3, the dynamic frame is a Frenet frame, which includes a tangential axis T, a principal normal axis N, and a secondary normal axis B.

7. The modeling method according to claim 1, characterized in that, In step S2, the analytical equation for the cable shape is either the catenary equation or the parabola equation.

8. A three-dimensional parametric modeling system for cableway bridges used to implement the modeling method according to any one of claims 1 to 7, characterized in that, include: The driver interface module is used to receive user input of the plane axis, design parameters, and structural topology selection; The analytical shape-finding module, connected to the driving interface module, is used to perform mechanical calculations in a local vertical plane based on the design parameters and the selected cable alignment analytical equation, and generate a three-dimensional main cable skeleton curve. The topology assembly module is connected to the analytical shape-finding module and the driving interface module respectively. It is used to call a predefined parameterized component library according to the structural topology form, and to perform spatial topology mapping and assembly logic based on the main cable skeleton curve and its dynamic frame. The dynamic response mechanism module is connected to the analytical shape-finding module and the topology assembly module respectively. When the input parameters change, it updates the main cable skeleton curve and all associated parameterized components in real time according to the preset parameter dependency relationship and update sequence, thus refreshing the 3D model in real time.

9. The modeling system according to claim 8, characterized in that, The topology assembly module also includes a terrain interaction unit, which performs Boolean operations on the generated model and the digital terrain model to automatically generate an excavation model.

10. The modeling system according to claim 8, characterized in that, The system also includes a data output module for extracting and outputting a bill of quantities from the fully parameterized 3D model generated by the dynamic response mechanism module.

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