[1]郑峰松,朱达欣,罗仙仙.多层次非均匀B样条曲线重建[J].泉州师范学院学报,2020,(06):28-33.
　ZHENG Fengsong,ZHU Daxin,LUO Xianxian.On the Multilevel Nonuniform B-Spline Curve Reconstruction[J].,2020,(06):28-33.
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多层次非均匀B样条曲线重建()
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《泉州师范学院学报》[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2020年06期
页码:
28-33
栏目:
数理科学
出版日期:
2020-12-15

文章信息/Info

Title:
On the Multilevel Nonuniform B-Spline Curve Reconstruction
文章编号:
1009-8224(2020)06-0028-06
作者:
郑峰松1; 2; 3; 朱达欣1; 2; 3; 罗仙仙1; 2; 3
重点实验室,福建 泉州 362000; 3.智能计算与信息处理福建省高等学校重点实验室,福建 泉州 362000
Author(s):
ZHENG Fengsong1; 2; 3; ZHU Daxin1; 2; 3; LUO Xianxian1; 2; 3
1.College of Mathematics and Computer Science,Quanzhou Normal University,Quanzhou Fujian362000,China; 2.Fujian Provincial Key Laboratory of Data Intensive Computing, Quanzhou Fujian362000,China; 3.Key Laboratory of Intelligent Computing and Information Processing,Fujian ProvinceUniversity, Quanzhou Fujian 362000,China
关键词:
多层次B样条;  非均匀B样条;  曲线重建
Keywords:
multilevel B-spline;  nonuniform B-spline;  curve reconstruction
分类号:
TP391
文献标志码:
A
摘要:
提出了一种快速有效的B样条曲线重建算法.该算法利用多层次B样条技术,通过在误差超限节点区间插入新节点,从而生成一系列多层次B样条曲线来逐渐逼近给定的数据点集.当层数足够多时,多层次B样条曲线可以达到用户指定的精度,最后输出的多层次B样条曲线用一个等价的B样条函数表示.该算法在计算每层B样条曲线的控制顶点时不用求解一个关于控制顶点的线性方程组,而且从第二层开始,控制顶点的计算是基于超限的误差,因此可以显著减少计算量.实验结果表明该算法可以快速有效重建用户指定精度的B样条曲线.
Abstract:
A fast and effective B-spline curve reconstruction algorithm is proposed. In thisalgorithm, a series of multilevel B-spline curves are generated to approach the given datapoint set gradually by inserting new nodes in node intervals where the error exceeds thelimit using multilevel B-spline technology. When the number of levels is large enough, themultilevel B-spline curve can reach the precision specified by the user, and the finaloutput multilevel B-spline curve is represented by one equivalent B-spline function. Thisalgorithm does not need to solve a set of linear equations about control points whencalculating the control points of B-spline curves at each level, and starting from thesecond level, the calculation of control points is based on the over-limit error, so it cansignificantly reduce the amount of computation. Experimental results show that thisalgorithm can quickly and effectively reconstruct B-spline curves with user-specifiedprecision.

参考文献/References:

[1] ROGERS D F,FOG N G.Constrained B-spline curve and surfacefitting[J]. Computer-Aided Design,1989,21(10):641-648.
[2] 张毓华,曹娟,陈中贵,等.几何信息均分的B样条曲线节点设置[J].计算机辅助设计与图形学学报,2017,29(2):304-311.
[3] 孙越泓,魏建香,夏德深.基于自适应遗传算法的B样条曲线拟合的参数优化[J].计算机应用,2010,30(7): 1878-1882.
[4] 高茂庭,冯莉.基于遗传算法的B样条曲线拟合改进算法[J].计算机应用研究,2019,36(10):2840-2844.
[5] 潘日晶,姚志强.基于动态参数化的二次B样条插值曲线[J].计算机学报,2005(3):334-342.
[6] 星蓉生,潘日晶.三次均匀 B 样条曲线插值数据点及其切矢的PIA算法[J].福建师范大学学报(自然科学版),2014,30(1):25-32.
[7] 蔺宏伟.几何迭代法及其应用综述[J].计算机辅助设计与图形学学报,2015(4):582-589.
[8] 李莎莎,徐惠霞,邓重阳. 数据点加权最小二乘渐进迭代逼近及其B样条曲线拟合[J].计算机辅助设计与图形学学报,2019,31(9):1574-1580.
[9] LEE S,WOLBERG G,SHIN S Y. Scattered data interpolation with multilevel B-splines[J].IEEE Trans on Visualization and Computer Graphics,1997,3(3):228-244.
[10] 施法中.计算机辅助几何设计与非均匀有理B样条[M].北京:高等教育出版社,2001.

备注/Memo

备注/Memo:
收稿日期:2020-09-09
作者简介:郑峰松(1982-),男,福建泉州人,助教,硕士,从事计算机辅助几何设计等研究.
基金项目:福建省中青年教师教育科研项目(JT180358); 福建省教育厅教育科研项目(JAT170475)
更新日期/Last Update: 2020-12-15