基于LSPIA的带能量项B样条曲线拟合  

B-spline curve fitting with energy term based on LSPIA

作　　者：王越 邓重阳[1] 李亚娟[1] WANG Yue;DENG Chongyang;LI Yajuan(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2022年第6期60-65,共6页Journal of Hangzhou Dianzi University：Natural Sciences

摘　　要：为了使B样条曲线在满足拟合误差精度的条件下能量最小,提出一种基于最小二乘渐进迭代逼近(Least Squares Progressive Iterative Approximation, LSPIA)的带能量项B样条曲线拟合算法。首先,用LSPIA算法得到一条满足拟合误差精度的B样条曲线,并作为初始拟合曲线;然后,添加能量项,将M.S.Floater提出的能量系数作为初值,用带能量LSPIA算法生成新的拟合曲线;最后,根据得到的拟合误差,用二分法调整能量系数,并用带能量LSPIA算法得到新的B样条曲线,直至找到满足拟合误差精度且能量系数尽可能大的B样条曲线。实验结果表明,提出算法具有较好的鲁棒性,并降低了拟合曲线的能量。In order to minimize the energy of B-spline curve under the fitting error accuracy, a B-spline fitting algorithm with energy term based on least squares progressive and iterative approximation(LSPIA) is proposed. Firstly, LSPIA is used to obtain a B-spline curve that meets the accuracy of fitting error as the initial fitting curve. Then, the energy term is added and the energy coefficient proposed by M. S. Floater is used as the initial value, a new fitting curve is generated by the LSPIA method with energy term. Finally, according to the fitting error, the energy coefficient is adjusted by dichotomy method, and continue to use the LSPIA method with energy term to obtain a new B-spline curve, until a B-spline curve with the largest possible energy coefficient is found that meets the precision of the fitting error. The example shows that the algorithm has good robustness and can also reduce the energy of the fitting curve.

关 键 词：B样条 能量 曲线拟合 渐进迭代逼近 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]