基于平面路径的扫掠面高精度重建  

High-precision reconstruction of swept surfaces with a planar path

作　　者：刘圣军[1] 陶珊珊 王海波 李钦松 刘新儒[1] LIU Shengjun;TAO Shanshan;WANG Haibo;LI Qinsong;LIU Xinru(School of Mathematics and Statistics,Central South University,Changsha Hunan 410083,China;Big Data Institute,Central South University,Changsha Hunan 410083,China)

机构地区：[1]中南大学数学与统计学院,湖南长沙410083 [2]中南大学大数据研究院,湖南长沙410083

出　　处：《图学学报》2025年第2期425-436,共12页Journal of Graphics

基　　金：国家自然科学基金(62172447,62302530);湖南省自然科学基金(2023JJ40769)。

摘　　要：从三角网格数据重建CAD建模过程是逆向工程中的研究重点之一,高效、高精的曲面重建具有重要的工程价值。针对由直线段和圆弧段组成的平面路径扫掠生成的三角网格表示曲面,提出了基于轮廓和路径曲线自动提取的扫掠过程重建,实现扫掠曲面的高精度重建。首先,基于统一三角网格模型曲率矢量场自动获得初始路径,再利用高斯映射迭代和配准拟合的方法生成了扫掠的轮廓曲线;然后,逆向计算扫掠路径的离散有序点集,通过引入切空间表示方法来识别路径中的直线段和圆弧段,并基于相切几何约束条件建立了拟合的优化模型,对初始路径进一步优化;最后,由计算得到的轮廓曲线和路径曲线执行扫掠操作,以获得重建的扫掠曲面。实验结果表明,该方法实现了自动提取轮廓曲线和路径曲线,进而重建扫掠模型的建模过程,减少了繁琐的人工交互,提取的轮廓和路径有效地避免了离散误差累积,使得最终重建的扫掠曲面精度更高,且适用于有噪声的数据和存在缺失数据的扫掠曲面。The reconstruction of CAD modeling process from triangular mesh is a key focus in reverse engineering,and efficient,high-precision swept surface reconstruction is of great engineering value.Targeting the mesh representation surface generated by planar path sweeping composed of line and arc segments,sweeping reconstruction based on profile and path automatic extraction was proposed to achieve high-precision reconstruction of swept surfaces.Firstly,the initial path was automatically obtained based on the unified curvature vector field of the triangular mesh,and the profile was generated using Gaussian mapping iteration,registration,and fitting.Then,the scattered point set of the path was computed inversely.The straight line and arc segments in the path were identified using a tangent space representation,and the fitting optimization model was established based on the tangent geometric constraints to optimize the initial path.Finally,the swept surface was reconstructed by performing a sweeping operation with the calculated profile and path.Experimental results demonstrated that the proposed method achieved automatic extraction of profile and path curves,thereby reconstructing the modeling process of the sweeping model.This approach reduced tedious manual interactions,and the extracted profiles and paths effectively avoided the accumulation of discrete errors,resulting in a higher precision in the final reconstructed sweeping surface.The method was also applicable to models with noisy data and those with missing data.

关 键 词：逆向工程 曲面重建 扫掠曲面 高斯映射 几何约束 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]