基于无网格局部Petrov-Galerkin法的曲面修复算法  

Surface Repairing Strategy Based on Meshless Local Petrov-Galerkin Method

作　　者：吴雪梅[1] 李瑰贤[1] 赵伟民[2] 郭峰[1] 

机构地区：[1]哈尔滨工业大学机电工程学院,哈尔滨150001 [2]大庆石油学院机械工程系,大庆163318

出　　处：《机械工程学报》2009年第1期94-100,共7页Journal of Mechanical Engineering

基　　金：黑龙江省国际合作(WB06A06);黑龙江省科技攻关(GC03A513);黑龙江省自然科学基金(F2004-15);高等学校学科创新引智计划(B07018)资助项目。

摘　　要：针对三维残缺数据曲面重构的困难,提出残缺点云或有孔洞网格曲面数据修复的新算法,该方法通过拟合进行曲面重构,大大减小了边界节点误差的影响:同时采用基于板壳理论的无网格法,使孔洞曲面修复更光滑,尤其可以更真实地修补出锻压制造的薄板零件。首先应用移动最小二乘法插值对残缺点云进行边界提取,然后给出逐层节点布置算法,最后应用基于最小势能原理的无网格法进行曲面修复,并将通常无网格法中积分圆域改进为多边形域。编写相应程序,经简单二次曲面缺损网格修补验证算法的有效性,结果分析表明误差很小,曲面修复结果理想。为进一步证明算法实用性,对实际薄壳产品的孔洞进行算法应用,修补效果理想。In view of the difficulty in surfaces reconstruction from 3D incomplete data, an innovative holes repairing algorithm for triangle mesh or incomplete points data is put forward： Meshless Local Petrov-Galerkin （MLPG） method is employed. Moving least square method （MLSM） is applied for boundary extraction of incomplete points cloud. The algorithm of layer-by-layer nodal arrangement is proposed. 3D incomplete data repairing strategy is proposed based on least energy principle and MLPG method. Corresponding computer program is compiled, repairing experiments to holes of conicoid and thin shell production have been done employing strategy hereinbefore. Moreover, the integral circular region in general MLPG method is improved to integral polygon region. The experimental results demonstrate the effectiveness of this proposed algorithm. Error is very little, and surface repair result is ideal.

关 键 词：三维残缺数据 孔洞修补 移动最小二乘法 无网格局部Petrov-Galerkin法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]