标题： 受肥皂膜启发的细分晶格结构构造 显示英文标题

标题： Soap Film-inspired Subdivisional Lattice Structure Construction

摘要： 具有可定制微观几何结构和卓越力学性能的晶格结构已在各个行业得到广泛应用。 其设计与制造中的一个基本过程是构建边界表示（B-rep）模型，这对于运行诸如模拟、优化和工艺规划等高级应用至关重要。 然而，由于晶格结构的高复杂性，这一构建过程面临重大挑战，尤其是在生成节点形状时，由于斜撑之间的复杂交叉，可能会出现健壮性和平滑性问题。 为了解决这些挑战，本文提出了一种通过切割斜撑并在空隙区域填充细分节点形状来构建晶格结构的新方法。 受肥皂膜的启发，该方法使用拉普拉斯平滑生成平滑且保形的控制网格，并通过点法线循环（PN-循环）细分方案对其进行细分以获得细分节点形状。 所提出的这种方法确保了构建鲁棒模型的同时减少了形状偏差，提高了表面光顺度，并实现了细分节点形状与保留斜撑之间的平滑过渡。 一系列示例和对比验证了该方法的有效性。 代码将在发表后开源。 显示英文摘要

摘要： 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.