面向增材制造点阵结构的直接切片方法研究

doi:10.11996/JG.j.2095-302X.2026051148

摘要/Abstract

摘要：

由于当下增材制造中的点阵结构设计与后续切片流程存在割裂，传统方法依赖基于STL模型的通用切片算法，需将完整点阵结构离散为三角面片网格，再通过面片与切平面求交生成轮廓。然而，点阵结构中杆件数量庞大，STL模型数据量巨大，且三角面片近似表达易引入几何误差，导致切片精度下降；同时，面片求交需遍历大量冗余三角面片，计算效率低下，难以满足大规模点阵结构快速预处理的需求。针对上述问题，提出一种面向点阵结构的直接切片方法，避免STL模型的中间转换。首先将每根连杆抽象为圆柱或圆锥几何体，直接利用设计阶段生成的杆件拓扑位置数据，建立切平面与杆件之间的解析几何关系，通过空间直线与二次曲面求交的封闭公式，直接计算杆件与切平面的相交轮廓，获得精确截面形状，有效规避了三角面片离散带来的几何失真，提升了轮廓精度。在计算效率优化方面，引入数据映射技术，将圆锥曲线轮廓的解析求解转化为基于单位圆的线性映射与矩阵运算，并通过预计算变换矩阵，使各切片层仅需更新杆件中心坐标即可实现轮廓重构，有效消除了冗余计算，提升了大规模点阵的处理速度。此外，针对节点处多杆交汇形成的复杂轮廓，采用多边形融合操作进行后处理，消除轮廓交叉与冗余边，生成连续、无自交的切片轮廓。实验结果表明，该算法具有良好的可行性与有效性，能够提升点阵结构增材制造模型预处理的效率与精度。

关键词: 点阵结构, 直接切片, 增材制造, 数据映射, 设计制造一体化

Abstract:

Currently, the design of lattice structures for additive manufacturing is disconnected from the subsequent slicing. Traditional methods rely on generic slicing algorithms based on STL (Standard Triangle Language) models, in which the entire lattice structure must first be discretized into a triangular mesh, and contours are then generated by intersecting the mesh with slicing plane. However, lattice structures contain a large number of members, resulting in massive STL model data volumes. Furthermore, the approximate representation of triangular patches is prone to introducing geometric errors, leading to reduced slicing accuracy. At the same time, the intersection calculation requires traversing a large number of redundant triangular patches, resulting in low computational efficiency and making it difficult to meet the demand for rapid preprocessing of large-scale lattice structures. To address these issues, a direct slicing method tailored for lattice structures was proposed to avoid the intermediate conversion to an STL model. This method first abstracted each connecting rod into a cylindrical or conical geometric shape and directly utilized the topological position data of the members generated during the design phase. to establish an analytical geometric relationship between the cutting plane and the members. By applying the closed-form formula for the intersection of a spatial line and a quadratic surface, the method directly calculated the intersection contour between the members and the cutting plane, yielding precise cross-sectional shapes. Geometric distortion caused by triangular-mesh discretization was thereby avoided, and improves contour accuracy was improved. To optimize computational efficiency, data-mapping technology was introduced to transform the analytical solution of conic-section contours into linear mappings and matrix operations based on the unit circle. By pre-computing transformation matrices, this method enabled contour reconstruction for each slice layer by simply updating the member center coordinates, effectively eliminating redundant calculations and accelerating the processing of large-scale grids. Furthermore, for complex contours formed by the intersection of multiple members at nodes, a polygon merging operation was employed for post-processing to eliminate contour intersections and redundant edges, thereby generating continuous, self-intersection-free slice contours. Experimental results demonstrated that the proposed algorithm exhibited good feasibility and effectiveness, capable of improving the efficiency and accuracy of preprocessing for additive manufacturing models of lattice structures.

Key words: lattice structures, direct slicing, additive manufacturing, data mapping, design-manufacturing integration

中图分类号:

原伟琦, 陆旭浩, 肖文磊. 面向增材制造点阵结构的直接切片方法研究[J]. 图学学报, 2026, 47(5): 1148-1155.

YUAN Weiqi, LU Xuhao, XIAO Wenlei. Research on direct slicing methods for additive manufacturing lattice structures[J]. Journal of Graphics, 2026, 47(5): 1148-1155.

图/表 16

图1 点阵结构STL模型常见问题

Fig. 1 Frequently asked questions about STL models

图2 不同表示方法连杆求交差异示意图

Fig. 2 Schematic diagram of the differences in intersection of connecting rods represented by different methods

图3 切平面表构建示意图

Fig. 3 Schematic diagram of cutting plane table construction

图4 连杆与平面相交情况示意图

Fig. 4 Schematic diagram of linkage intersecting a plane

图5 轮廓映射过程图

Fig. 5 Schematic diagram of the contour mapping process

图6 圆锥曲线映射原理图((a) 双曲线；(b) 抛物线)

Fig. 6 Schematic diagram of conic section mapping ((a) Hyperbola; (b) Parabola)

图7 Clipper库轮廓融合过程

Fig. 7 Clipper library profile fusion process

图8 节点填充前后对比图

Fig. 8 Before and after node filling comparison

图9 等半径模型单一切片层轮廓展示

Fig. 9 Equidistant model single-slice layer profile display

表1 加工案例模型信息

Table 1 Machining case study model information

模型名称	加工参数		模型参数
模型名称	工艺	模型材料	连杆数	节点数
复杂立方	SLM	铝合金	2 550	434
兔子	SLA	光敏材料	5 597	1 032
猫	SLS	尼龙	9 160	3 629

图10 模型实际加工效果图

Fig. 10 Rendering of the model’s actual machining results

表2 测试案例信息

Table 2 Test case information

模型名称	模型参数
模型名称	尺寸/mm	连杆数	节点数
简化机翼	112.80×40.00×4.49	689	2 550
花瓶	170.00×170.00×102.00	4 539	5 597
长方形	42.00×162.00×42.00	4 700	9 160

图11 测试案例示意图

Fig. 11 Test case diagram

表3 模型切片效率对比

Table 3 Comparison of model slicing efficiency

模型名称	总时间/s		效率提升/%
模型名称	STL切片	直接切片	效率提升/%
复杂立方	20.83	12.74	38.83
兔	18.72	10.88	41.88
猫	22.76	15.28	32.86
简化机翼	11.48	7.30	36.41
花瓶	26.08	16.95	35.01
长方形	24.21	14.38	40.60

图12 参数化直接切片算法效果比较图

Fig. 12 Comparison of height-1 parametric direct slicing algorithms

图13 轮廓精度对比图

Fig. 13 Contour accuracy comparison chart

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