Soap Film-inspired Subdivisional Lattice Structure Construction

2025-04-11

AI Summary

To address poor nodal shape robustness and surface discontinuities caused by strut overlap in complex lattice B-rep modeling, this paper proposes a soap-film-inspired subdivision-based nodal construction method. First, struts are trimmed and topological holes filled; then, a smooth, conformal control mesh is constructed; finally, high-continuity nodal surfaces are generated via PN-Loop subdivision. This work pioneers the integration of the soap-film minimal-energy principle into lattice node modeling, synergistically combining Laplacian smoothing with PN-Loop subdivision to achieve geometric adaptivity, C²-continuous nodal surfaces, and seamless strut–node transitions. Experiments demonstrate that our method significantly reduces shape deviation, enhances surface fairness and modeling robustness, and consistently outperforms state-of-the-art approaches across diverse complex junction configurations. The implementation will be made publicly available.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Lattice structures, distinguished by their customizable geometries at the microscale and outstanding mechanical performance, have found widespread application across various industries. One fundamental process in their design and manufacturing is constructing boundary representation (B-rep) models, which are essential for running advanced applications like simulation, optimization, and process planning. However, this construction process presents significant challenges due to the high complexity of lattice structures, particularly in generating nodal shapes where robustness and smoothness issues can arise from the complex intersections between struts. To address these challenges, this paper proposes a novel approach for lattice structure construction by cutting struts and filling void regions with subdivisional nodal shapes. Inspired by soap films, the method generates smooth, shape-preserving control meshes using Laplacian fairing and subdivides them through the point-normal Loop (PN-Loop) subdivision scheme to obtain subdivisional nodal shapes. The proposed method ensures robust model construction with reduced shape deviations, enhanced surface fairness, and smooth transitions between subdivisional nodal shapes and retained struts. The effectiveness of the method has been demonstrated by a series of examples and comparisons. The code will be open-sourced upon publication.

Problem

• Constructing robust B-rep models for complex lattice structures
• Ensuring smooth nodal shapes at strut intersections
• Reducing shape deviations in lattice structure design

Innovation

• Cutting struts and filling voids with subdivisional nodal shapes
• Using Laplacian fairing for smooth control meshes
• Applying PN-Loop subdivision for robust nodal shapes