Curve fitting and optimal interpolation on CNC machines based on quadratic B-splines  

作　　者：ZHANG Mei YANWei YUAN ChunMing WANG DingKang GAO XiaoShan 

机构地区：[1]Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing 100190, China [2]Research Institute of Petroleum Exploration and Development, Beijing 100083, China

出　　处：《Science China(Information Sciences)》2011年第7期1407-1418,共12页中国科学（信息科学）（英文版）

基　　金：supported by the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No.KGCX2-YW-119-1);the National Natural Science Foundation of China (Grant No.608210021/F02)

摘　　要：In this paper, curve fitting of 3-D points generated by C01 codes and interpolation based on quadratic B-splines are studied. Feature points of G01 codes are selected using an adaptive method. Next, quadratic B-splines are obtained as the fitting curve by interpolating these feature points. Computations re- quired in implementing the velocity planning algorithm mentioned by Timer et al. are very complicated because of the appearance of high-order curves. An improved time-optimal method for the quadratic B-spline curves is presented to circumvent this issue. The algorithms are verified with simulations as well as on real CNC machines.In this paper, curve fitting of 3-D points generated by C01 codes and interpolation based on quadratic B-splines are studied. Feature points of G01 codes are selected using an adaptive method. Next, quadratic B-splines are obtained as the fitting curve by interpolating these feature points. Computations re- quired in implementing the velocity planning algorithm mentioned by Timer et al. are very complicated because of the appearance of high-order curves. An improved time-optimal method for the quadratic B-spline curves is presented to circumvent this issue. The algorithms are verified with simulations as well as on real CNC machines.

关 键 词：quadratic B-spline GO1 codes feature point velocity planning INTERPOLATION 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] TU31[自动化与计算机技术—计算机科学与技术]