三次NURBS曲线的Obrechkoff参数化插值算法

董本志; 张小燕; 于鸣; 任洪娥

doi:10.13433/j.cnki.1003-8728.2016.1114

三次NURBS曲线的Obrechkoff参数化插值算法

doi: 10.13433/j.cnki.1003-8728.2016.1114

董本志^1,2,
张小燕¹,
于鸣^1,2,
任洪娥^1,2, ,

1.
东北林业大学信息与计算机工程学院, 哈尔滨 150040;
2.
黑龙江省林业智能装备工程研究中心, 哈尔滨 150040

基金项目:

国家“948”项目（2014-4-77）与国家科技支撑计划课题（2014BAF11B01）资助

详细信息

作者简介:
董本志(1975-),副教授,博士,研究方向为模式识别与智能控制和计算机可视化仿真,nefu_dbz@163.com

通讯作者:
任洪娥(联系人),教授,博士,nefu_rhe@163.com

计量
- 文章访问数: 188
- HTML全文浏览量: 35
- PDF下载量: 9
- 被引次数: 0
出版历程
- 收稿日期: 2014-12-14
- 刊出日期: 2016-11-05

A Third-order NURBS Interpolation Algorithm Based on Obrechkoff Parameterization

Dong Benzhi^1,2,
Zhang Xiaoyan¹,
Yu Ming^1,2,
Ren Hong'e^{1,2
, ,}

1.
School of Information and Computer Engineering, Northeast Forestry University, Harbin 150040, China;
2.
Forestry Intelligent Equipment Engineering Research Center, Harbin 150040, China

摘要

摘要: 针对工程实践中对复杂曲线曲面零件高精度加工的要求，提出一种基于单步四阶Obrechkoff参数化法的三次非均匀有理B样条（NURBS）曲线的插值算法。该算法通过后向差分代替微分的方法，对Obrechkoff法求解微分方程的参数化插值算法进行了合理的简化，降低了计算复杂度，有效地保证了计算的精度和插值的实时性。考虑参数化算法对插值曲线的光顺性影响，在MATLAB上与累计弦长参数化法和阿当姆斯参数化法进行仿真比较。结果表明，该算法对应的插值曲线平均曲率最小，光顺性最好。
- 参数化 /
- NURBS /
- 计算复杂度 /
- 实时性
Abstract: A third-order non-uniform rational B-spline (NURBS) interpolation algorithm based on Obrechkoff parameterization was proposed to satisfy the requirements of the high-precision machining of complex curve surface in the engineering practice. For furthermore ensuring the high-precision of calculation and real time control of interpolation, the parametric interpolation algorithm based on Obrechkoff was predigested by using rearward difference in place of differential to reduce the computational complexity of the algorithm. Considering the fairness effect of different parameterization, then compared the proposed algorithm with the accumulative chord length parameterization and the Adams parameterization in MATLAB, the computer simulation experiments indicate that the interpolation curve which simulated by the algorithm is more fairness because its average curvature is lowest.
- parameterization /
- computational complexity /
- real time control /
- computer simulation

HTML全文

参考文献(15)

[1]	Jahanpour J, Tsai M C, Cheng M Y. High-speed contouring control with NURBS-based C2 PH spline curves[J]. The International Journal of Advanced Manufacturing Technology, 2010,49(5-8):663-674
[2]	Baek D K, Yang S H, Ko T J. Precision NURBS interpolator based on recursive characteristics of NURBS[J]. The International Journal of Advanced Manufacturing Technology, 2013,65(1-4):403-410
[3]	王允森,盖荣丽,孙一兰,等.基于牛顿迭代法的NURBS曲线插补算法[J].组合机床与自动化加工技术,2013,(4):13-17 Wang Y S, Gai R L, Sun Y L, et al. NURBS interpolation algorithm based on Newton iteration method[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2013,(4):13-17(in Chinese)
[4]	Maekawa T, Matsumoto Y, Namiki K. Interpolation by geometric algorithm[J]. Computer-Aided Design, 2007,39(4):313-323
[5]	Fang J J, Hung C L. An improved parameterization method for B-spline curve and surface interpolation[J]. Computer-Aided Design, 2013,45(6):1005-1028
[6]	罗福源,游有鹏,尹涓.NURBS曲线泰勒展开插补法的平稳性与改进研究[J].中国机械工程,2012,23(4):383-388,434 Luo F Y, You Y P, Yin J. Research on stability and improvement of Taylor-expansion-based approach for NURBS curve interpolation[J]. China Mechanical Engineering, 2012,23(4):383-388,434(in Chinese)
[7]	贾庆祥,徐知行,刘新山.基于阿当姆斯算法的NURBS曲线插补[J].吉林大学学报(工学版),2009,39(S1):215-218 Jia Q X, Xu Z X, Liu X S. NURBS interpolation based on Adams algorithm[J]. Journal of Jilin University (Engineering and Technology Edition), 2009,39(S1):215-218(in Chinese)
[8]	盖荣丽,王允森,孙一兰,等.样条曲线插补方法综述[J].小型微型计算机系统,2012,33(12):2744-2748 Gai R L, Wang Y S, Sun Y L, et al. Survey on spline curve interpolation methods[J]. Journal of Chinese Computer Systems, 2012,33(12):2744-2748(in Chinese)
[9]	Baek D K, Ko T J, Yang S H. Fast and precision NURBS interpolator for CNC systems[J]. International Journal of Precision Engineering and Manufacturing, 2012,13(6):955-961
[10]	彭小军,宋绪丁.不同参数化法对多项式NURBS插值曲线的影响[J].机械制造,2013,51(2):33-37 Peng X J, Song X D. The effect of different parameterization method for NURBS interpolator[J]. Machinery, 2013,51(2):33-37(in Chinese)
[11]	韩江,江本赤,夏链,等.基于递归特征分析的NURBS曲线插补算法[J].中国机械工程,2015,26(1):107-111,119 Han J, Jiang B C, Xia L, et al. NURBS curve interpolation algorithm based on recursive feature analysis[J]. China Mechanical Engineering, 2015,26(1):107-111,119(in Chinese)
[12]	王允森,盖荣丽,孙一兰,等.面向高质量加工的NURBS曲线插补算法[J].计算机辅助设计与图形学学报,2013,25(10):1549-1556 Wang Y S, Gai R L, Sun Y L, et al. NURBS interpolation algorithm for high-quality machining[J]. Journal of Computer-Aided Design & Computer Graphics, 2013,25(10):1549-1556(in Chinese)
[13]	叶丽,谢明红.采用积累弦长法拟合3次NURBS曲线[J].华侨大学学报(自然科学版),2010,31(4):383-387 Ye L, Xie M H. Third-order non-uniform rational b-spline curve fitting based on method of accumulating chord length[J]. Journal of Huaqiao University (Natural Science), 2010,31(4):383-387(in Chinese)
[14]	张智丰,张亚荣.细分曲线参数化与累加弦长参数化的数值比较[J].湘潭师范学院学报(自然科学版),2009,31(4):13-16 Zhang Z F, Zhang Y R. The numerical comparision between subdivision curve parametrization and the accumulative chord length parametrization[J]. Journal of Xiangtan Normal University (Natural Science Edition), 2009,31(4):13-16(in Chinese)
[15]	Emami M M, Arezoo B. A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length[J]. Computer-Aided Design, 2010,42(7):625-632