基于稀疏表示的G^(1)圆弧样条自动逼近方法  

Automatic G^(1) arc spline approximation via sparse representation

作　　者：徐琳琳 Linlin XU(School of Computer Information Management,Inner Mongolia University of Finance and Economics,Hohhot 010070,China)

机构地区：[1]内蒙古财经大学计算机信息管理学院,呼和浩特010070

出　　处：《中国科学：信息科学》2021年第8期1255-1269,共15页Scientia Sinica(Informationis)

基　　金：内蒙古自治区高等学校科学研究项目(批准号:NJZY21282)资助。

摘　　要：圆弧样条普遍用于数控机床的刀具轨迹设计中,希望用尽可能少的圆弧段逼近曲线.现有方法大多是启发式的,圆弧样条曲率的分段常值性质还没有引起足够的重视.本文基于这个内在的稀疏性质,提出基于稀疏表示的G^(1)圆弧样条自动逼近方法,主要分两步:稀疏优化问题自动检测圆弧间连接点的全局初始化和重新调整连接点位置保证G^(1)连续性的局部修正.实验结果显示新方法对对称性比较敏感,部分尖锐特征、自交数据也可以逼近得很好,充分说明了新方法的优越性.Arc spline is popularized in describing the tool path for a certain CNC machine, and it is desirable to approximate curves with as few arcs as possible. Most of existing methods are heuristic;researchers have seldom paid attention to the piecewise constant property of the curvature of arc spline. Based on the intrinsic sparse property, this paper proposes an automatic G^(1) arc spline approximation method via sparse representation. There are two main steps: global initialization using a sparse optimization problem for automatically detecting the joint points between adjacent arcs, and local modification by readjusting the positions of joint points to ensure the G^(1) continuity. The experimental results show that the new method is sensitive to symmetry. Some sharp features and self-intersecting data can be approximated well, which fully shows the advantages of the new method.

关 键 词：圆弧样条 稀疏表示 逼近 G^(1)连续 

分 类 号：TG659[金属学及工艺—金属切削加工及机床]