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[1]刘子奕,陈绪兵,彭伊丽*,等. 面向刀路计算的参数曲面几何自适应网格生成算法 [J].武汉工程大学学报,2026,48(02):193-200.[doi:10.19843/j.cnki.CN42-1779/TQ.202503011]
　LIU Ziyi,CHEN Xubing,PENG Yili*,et al. Geometry-adaptive mesh generation algorithm for parametric curves oriented to tool path calculation [J].Journal of Wuhan Institute of Technology,2026,48(02):193-200.[doi:10.19843/j.cnki.CN42-1779/TQ.202503011]
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面向刀路计算的参数曲面几何自适应网格生成算法
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《武汉工程大学学报》[ISSN:1674-2869/CN:42-1779/TQ]

卷:
48
期数:
2026年02期
页码:
193-200
栏目:
智能制造
出版日期:
2026-04-30

文章信息/Info

Title:
Geometry-adaptive mesh generation algorithm for parametric curves oriented to tool path calculation
文章编号:
1674 - 2869（2026）02 - 0193 - 08
作者:
刘子奕1; 2; 陈绪兵1; 2; 彭伊丽*1; 2; 郭中扬1; 2
1.武汉工程大学机电工程学院，湖北 武汉 430205；
2.智能焊接装备与软件工程技术湖北省研究中心（武汉工程大学），湖北 武汉 430205
Author(s):
LIU Ziyi1; 2;  CHEN Xubing1; 2;  PENG Yili*1; 2;  GUO Zhongyang1; 2
1. School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China；
2. Hubei Research Center of Intelligent Welding Equipment and Software Engineering Technology （Wuhan Institute of Technology）, Wuhan 430205, China
关键词:
曲面网格生成; 自适应; 映射法; Delaunay三角化; 数控加工
Keywords:
curve mesh generation;  adaption;  mapping method;  Delaunay triangulation;  numerical control machining
分类号:
TP391
DOI:
10.19843/j.cnki.CN42-1779/TQ.202503011
文献标志码:
A
摘要:
针对数控加工中复杂参数曲面刀路计算效率低下的问题，提出了一种参数曲面几何自适应网格生成算法。该算法基于参数曲线的几何特性，构建了差异化离散策略：针对直线和圆弧，采用等距和等角度策略对参数曲线进行离散；针对 NURBS 曲线，提出了一种基于弦高差与角度差双精度指标的动态步长调整方法，通过精确控制离散点的分布密度，确保了曲率变化敏感区域的几何精度。在曲面网格生成阶段，结合映射法与Delaunay三角化法生成曲面网格，并采用均匀缩放优化方法改善三角形单元的形状与质量。为满足数控加工对网格几何精度的更高要求，进一步提出基于三角形三边中点和重心的自适应加密策略，通过局部网格细化增强高曲率区域的解析能力。实验结果表明，该算法在保证几何逼近精度的同时，使曲面网格生成效率相比某商用软件平均提升约3%，且网格顶点数和三角面片数分别减少约4.57%和5.60%。该结果验证了本文算法在网格规模和计算效率方面均表现出优异的性能，为复杂曲面加工的刀路计算提供了高效的网格预处理方法，具有重要的理论意义和工程应用价值。
Abstract:
To address the issue of low computational efficiency in tool path computation for complex parametric curves in numerical control machining, a geometric adaptive mesh generation algorithm for parametric curves was proposed. The algorithm employed a differentiated discretization strategy based on the geometric characteristics of parametric curves.? For lines and circular arcs, constant-distance and equal-angle strategies were applied to discretize the curves. For NURBS curves, a dynamic step size adjustment method using dual-precision criteria—chord height error and angular deviation—was developed to precisely control the density distribution of discrete points, ensuring geometric accuracy in curvature-sensitive regions. During the curve meshing phase, the algorithm combined the mapping method with Delaunay triangulation to generate curve meshes and employed uniform scaling optimization to enhance the shape and quality of triangular elements. To meet the stringent geometric accuracy requirements of numerical control machining, an adaptive refinement strategy based on triangle edge midpoints and centroids was further proposed, enabling local mesh refinement to improve resolution in high-curvature regions. Experimental results demonstrated that the proposed algorithm achieves an average improvement of approximately 3% in mesh generation efficiency compared to commercial software while maintaining geometric accuracy. Additionally, it reduces the number of mesh vertices and triangular facets by 4.57% and 5.60%, respectively. These results confirmed the algorithm’s superior performance in balancing mesh scale and computational efficiency, providing an effective preprocessing solution for tool path computation in complex curve machining. This work holds significant theoretical and practical value for advancing high-precision numerical control machining.

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备注/Memo

备注/Memo:
收稿日期：2025-03-14
基金项目：国家自然科学基金（52205536）
作者简介：刘子奕，硕士研究生。Email：1191184523@qq.com
*通信作者：彭伊丽，博士，讲师。Email：21040301@wit.edu.cn
更新日期/Last Update: 2026-05-07