Soap Film-inspired Subdivisional Lattice Structure Construction
Guoyue Luo, Qiang Zou
TL;DR
This paper tackles the challenge of robust boundary representation construction for lattice structures by introducing a soap film-inspired framework that builds smooth, subdivisional nodal shapes. It combines minimum cutting to avoid strut intersections, a nodal soap-film construction guided by a spherical Voronoi film geometry and Laplacian fairing, and a PN-Loop subdivision to ensure $C^1$ continuity and cylinder-preserving transitions with retained struts. The approach reduces shape deviations, improves surface fairness, and yields robust, topology-flexible B-rep models, as demonstrated across multiple case studies and comparisons to existing subdivision methods; code will be open-sourced upon publication. The work advances lattice design for additive manufacturing by providing a principled, geometry-driven method to integrate nodal regions with preserving struts while maintaining smooth, manufacturable surfaces.
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.