几何迭代法的加速-计算机辅助设计与图形学学报.PDFVIP

第28 卷 第 11 期 计算机辅助设计与图形学学报 Vol. 28 No.11 2016 年 11 月 Journal of Computer-Aided Design Computer Graphics Nov. 2016 几何迭代法的加速 1) 1) 2) 1)* 1) 1) 刘 超 , 辛士庆 , 舒振宇 , 陈双敏 , 张 荣 , 赵杰煜 1) ( 宁波大学信息科学与工程学院 宁波 315211) 2) (浙江大学宁波理工学院信息科学与工程学院 宁波 315211) (chenshuangmin@nbu.edu.cn) : 考虑到传统的几何迭代法仅有一阶的收敛性, 提出一个二阶可导的能量函数来刻画当前曲线与目标点集之 间的差异. 首先根据初始的控制顶点和相应的基函数生成初始的样条曲线, 然后求差异函数关于各个控制顶点的梯 度, 最后采用 L-BFGS 算法快速寻找最优的插值或者逼近曲线. 实验结果表明, 文中算法具有超线性的收敛速度, 在 同样的精度要求下比原来的几何迭代法快出数十倍甚至上百倍; 既可用于插值问题, 也可用于逼近问题; 甚至也能 适用于数据点参数可变的情形. ：几何迭代法; L-BFGS 算法; 插值; 逼近 ：TP391.41 Accelerated Geometric Iteration Method Liu Chao1), Xin Shiqing1), Shu Zhenyu2), Chen Shuangmin1)*, Zhang Rong1), and Zhao Jieyu1) 1) (Faculty of Electrical Engineering and Computer Science, Ningbo University, Ningbo 315211) 2) (School of Information Science and Engineering, Ningbo Institute of Technology, Zhejiang University, Ningbo 315211) Abstract: Considering that the conventional geometric iteration method (GIM) has only 1-order convergence, this paper proposes an energy function with second-order smoothness that characterizes the difference between the up-to-date curve and the given data points. In numerical implementation, we initialize the spline curve ac- cording to the initial control points and the associated basis functions, then compute the difference function as well as the gradients with regard to the moveable control points, and finally use the L-BFGS technique to find the optimal interpolation/approximation curve. Experimental results show that our accelerated algorithm has a su- per-linear rate of convergence. With the same accuracy requirement, th