NURBS曲线曲率极值点快速分析与定位算法研究

尹涓; 罗福源; 游有鹏

doi:10.13433/j.cnki.1003-8728.2015.1016

NURBS曲线曲率极值点快速分析与定位算法研究

doi: 10.13433/j.cnki.1003-8728.2015.1016

1.
南京航空航天大学金城学院, 南京 211156;
2.
南京航空航天大学机电学院, 南京 210016

基金项目:

国家自然科学基金项目(501205200)、江苏省自然科学基金项目(BK2012388)及江苏省高校自然科学研究项目(14KJB460017)资助

详细信息

作者简介:
尹涓(1976-),讲师,硕士,研究方向为数控系统及其仿真、智能机器人,juany@nuaa.edu.cn

计量
- 文章访问数: 158
- HTML全文浏览量: 19
- PDF下载量: 12
- 被引次数: 0
出版历程
- 收稿日期: 2014-07-08
- 刊出日期: 2015-10-05

Study on Algorithm of Fast Analysis and Location Curvature Extremes for Nurbs Curves

1.
Jincheng College, Nanjing University of Aeronautics and Astronautics, Nanjing 211156, China;
2.
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

摘要

摘要: 在分析和加工具有NURBS曲线定义的轮廓的机械零件时,由于NURBS曲线基于基函数的分段构造与有理式表示形式,曲率极值点的计算十分复杂耗时。为此,提出一种以微邻域分析为核心手段的快速数值计算方法。该方法分成粗定位与精搜索两个阶段,粗定位阶段通过各个节点区间两端的微邻域采样点的分析去推断曲线曲率变化类型,进而确定曲率极值点的数量及其所在的单峰位置范围;精搜索阶段基于每次搜索范围中点左右微邻域采样点的曲率分析进行快速折半查找,实现极值点的精确定位。算例表明所提出的算法完备性好、收敛性强、计算效率高。
- NURBS /
- 曲率极值点 /
- 邻域分析 /
- 计算效率
Abstract: In analyzing and machining the mechanical parts whose profiles are defined by non-uniform rational B-splines(NURBS) curves, generally NURBS curves is piecewise constructed and represented in rational function form, the computation of curvature extremes is very complex and time-consuming. Therefore, a fast computation algorithm based on the micro-neighborhood analysis is proposed. The algorithm is consisted of the rough location stage and the precise search stage. In the rough location stage, the curvature variation type is deduced by analyzing the sampling points in the micro-neighborhood of the two endpoints of every knot section, then the amount of the curvature extremes and their single peak boundaries are determined. In the precise search stage, according to the analyzing the curvatures of the sampling points in the left and right micro-neighborhood of the midpoint of each search range, the fast binary search is done and the precise position of curvature extremes are located. The computation experiment demonstrated the good integrity, strong convergence and high computational efficiency of the present algorithm.
- algorithms /
- calculations /
- computational efficiency /
- convergence of numerical methods

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参考文献(15)

[1]	Rajab K, Piegl L A, Smarodzinava V. CAD model repair using knowledge-guided NURBS[J]. Engineering with Computers, 2013,29(4):477-486
[2]	Baek D K, Yang S H, Ko T J. Precision NURBS interpolator based on recursive characteristics of NURBS[J]. International Journal of Advanced Manufacturing Technology, 2013,65(1-4):403-410
[3]	Grove O, Rajab K, Piegl L A, et al. From CT to NURBS:bio-modeling with B-spline curves[J]. Computer-Aided Design and Applications, 2011,8(1):3-21
[4]	刘宇,赵波,戴丽,等.基于传动系统动力学的NURBS 曲线插补算法[J]. 机械工程学报,2009,45(12):187-197 Liu Y, Zhao B, Dai L, et al. Feedrate system dynamics based interpolator for NURBS curve[J]. Chinese Journal of Mechanical Engineering, 2009,45(12):187-197(in Chinese)
[5]	Conway J R, Darling A L, Ernesto C A, et al. Experimental study of contouring accuracy for CNC machines executing curved paths with constant and curvature-dependent feedrates[J]. Robotics and Computer Integrated Manufacturing, 2013,29(2):357-369
[6]	王世勇.高性能激光加工控制关键技术研究[D]. 广州:华南理工大学,2010 Wang S Y. Study of key technologies of control for high-performance laser processing[D]. Guangzhou:South China University of Technology, 2010(in Chinese)
[7]	罗福源,游有鹏,尹涓.NURBS曲线S形加减速双向寻优插补算法研究[J]. 机械工程学报,2012,48(5):147-156 Luo F Y, You Y P, Yin J. Research on the algorithm of NURBS curve bidirectional optimization interpolation with S-type acceleration and deceleration control[J]. Chinese Journal of Mechanical Engineering, 2012,48(5):147-156(in Chinese)
[8]	陈良骥,冯宪章.五轴NURBS插补中的速度前瞻控制方法[J]. 计算机集成制造系统,2009,15(12):2399-2404 Chen L J, Feng X Z. Look-ahead controlling method of feedrate in 5-axis NURBS interpolation[J]. Computer Integrated Manufacturing Systems, 2009,15(12):2399-2404(in Chinese)
[9]	林峰,张正红,陈胜.基于进给速度敏感点识别的NURBS曲线平滑插补算法研究[J]. 中国机械工程,2012,23(9):1060-1064 Lin F, Zhang Z H, Chen S. Research on smooth NURBS interpolation algorithm based on feedrate sensitive point identification[J]. China Mechanical Engineering, 2012,23(9):1060-1064(in Chinese)
[10]	彭芳瑜,何莹,李斌.NURBS曲线高速插补中的前瞻控制[J]. 计算机辅助设计与图形学学报,2006,18(5):625-629 Peng F Y, He Y, Li B. Look-ahead control in high feed rate NURBS curve interpolation[J]. Journal of Computer-Aided Design & Computer Graphics, 2006,18(5):625-629(in Chinese)
[11]	Piegl L A, Rajab K, Smarodzinava V, et al. Using a biarc filter to compute curvature extremes of NURBS curves[J]. Engineering with Computers, 2009,25(4):379-387
[12]	Piegl L A, Tiller W. Biarc approximation of NURBS curves[J]. Computer-Aided Design, 2002,34(11):807-814
[13]	Piegl L A, Tiller W. The NURBS book[M]. New York:Springer-Verlag, 1997
[14]	刘萍,王民权,范进桢,等.FANUC 系统中实时前瞻的NURBS插补研究与实现[J]. 机械科学与技术,2012,31(5):791-795 Liu P, Wang M Q, Fan J Z, et al. Realizing real-time look-ahead nurbs interpolation in FANUC system[J]. Mechanical Science and Technology for Aerospace Engineering, 2012,31(5):791-795(in Chinese)
[15]	严蔚敏.数据结构[M]. 北京:清华大学出版社,1999 Yan W M. Data structures[M]. Beijing:Tsinghua University Press, 1999(in Chinese)