基于轮廓关键点的B样条曲线拟合算法

韩江; 江本赤; 夏链; 李大柱

doi:10.3879/j.issn.1000-0887.2015.04.010

基于轮廓关键点的B样条曲线拟合算法

doi: 10.3879/j.issn.1000-0887.2015.04.010

合肥工业大学 CIMS研究所,合肥 230009

基金项目: 国家自然科学基金（51275147）

详细信息

作者简介:
韩江（1963—），男，河南洛阳人，教授，博士，博士生导师(E-mail: hanjiang626@126.com);江本赤（1979—），男，安徽六安人，讲师，博士生;夏链（1964—），女，四川乐山人，教授，博士，博士生导师(通讯作者. E-mail: xia_nian@126.com).

中图分类号: TP391.72
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出版历程
- 收稿日期: 2014-09-11
- 修回日期: 2015-01-12
- 刊出日期: 2015-04-15

A B-Spline Curve Fitting Algorithm Based on Contour Key Points

Institute of CIMS, Hefei University of Technology, Hefei 230009, P.R.China

Funds: The National Natural Science Foundation of China（51275147）

摘要

摘要: 针对逆向工程中的点云切片轮廓数据点列，提出一种基于轮廓关键点的B样条曲线拟合算法.在确保扫描线点列形状保真度的前提下，首先对其进行等距重采样等预处理，并遴选出曲线轮廓关键点，生成初始插值曲线；再利用邻域点比较法求出初始曲线与各采样点间的偏差值，在超过拟合允差处增加新的关键点，并生成新的插值曲线，重复该步骤至拟合曲线满足预定精度要求.实验表明，在对稠密的二维断面数据点进行B样条逼近时，该算法能有效压缩控制顶点数目，并具有较高的计算效率.同时，由于所得控制顶点的分布能准确反映曲线的曲率变化，该方法还可作为误差约束的曲线逼近中的迭代步骤之一.
- 轮廓关键点 /
- B样条 /
- 曲线拟合 /
- 偏差约束
Abstract: Aimed at the sliced contour data points of point cloud in the reverse engineering, a B-spline curve fitting method based on contour key points was presented. Under the premise of keeping the shape fidelity, first, the scanned strip point set was resampled with an equidistance method and the contour key points were selected, in turn an initial interpolation curve was built. Next, the curve deviation values were calculated with a neighborhood point comparison method, and a new key point was added where the curve deviation value exceeded the specified tolerance, then a new interpolation curve was gained. The above procedure was repeated until the fitting curve reached expected accuracy. The numerical experiments show that, for the B-spline fitting of dense sectional scanned points, the proposed algorithm effectively compresses the number of key points and bears high computational efficiency. At the same time, since the distribution of key points accurately reflects the fitting curve’s curvature changes, this method also makes one promising iteration step in the curve approximation under deviation constraints.
- contour key point /
- B-spline /
- curve fitting /
- deviation constraint

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参考文献(16)

[1]	Piegl L A, Tiller W. Least-square B-spline curve approximation with arbitrary end derivatives[J].Engineering With Computers,2000,16(2): 109-116.
[2]	WEN Wei-bin, JIAN Kai-lin, LUO Shao-ming. 2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending[J].Applied Mathematics and Mechanics(English Edition),2013,34(8): 1017-1030.
[3]	徐进, 柯映林, 曲巍崴. 基于特征点自动识别的B样条曲线逼近技术[J]. 机械工程学报, 2009,45(11): 212-217.(XU Jin, KE Yin-lin, QU Wei-wei. B-spline curve approximation based on feature points’automatic recognition[J].Journal of Mechanical Engineering,2009, 45(11): 212-217.（(in Chinese)）
[4]	Gofuku S, Tamura S, Maekawa T. Point-tangent/point-normal B-spline curve interpolation by geometric algorithms[J].Computer-Aided Design,2009,41(6): 412-422.
[5]	Greiner G, Kolb A, Riepl A. Scattered data interpolation using data dependent optimization techniques[J].Graphical Models, 2002，64(1): 1-18.
[6]	Park H, Kim K, Lee S C. A method for approximate NURBS curve compatibility based on multiple curves refitting[J].Computer-Aided Design,2000,32(4): 237-252.
[7]	Yoshimoto F, Harada T, Yoshimoto Y. Data fitting with a spline using a real-coded genetic algorithm[J].Computer-Aided Design,2003,35(8): 751-760.
[8]	Park H, Lee J H. B-spline curve fitting based on adaptive curve refinement using dominant points[J].Computer-Aided Design,2007,39(6): 439-451.
[9]	李水进, 周艳红, 周云飞, 何沛霖. B样条曲线的局部自动光顺算法[J]. 中国机械工程, 1998,9(10):44-45.(LI Shui-jin, ZHOU Yan-hong, ZHOU Yun-fei , HE Pei-lin. Local automatically smoothing algorithm of B-spline curve[J].China Mechanical Engineering,1998,9(10):44-45.(in Chinese)）
[10]	赵世田, 赵东标, 付莹莹. 测量数据点的高精度B样条曲线拟合算法[J]. 计算机集成制造系统, 2010,16(8): 1708-1713.(ZHAO Shi-tian, ZHAO Dong-biao, FU Ying-ying. High precision B-spline curve fitting algorithm of measure points[J].Computer Integrated Manufacturing Systems,2010,16(8):1708-1713.(in Chinese)）
[11]	程仙国, 刘伟军, 张鸣. 特征点的Ｂ样条曲线逼近技术[J]. 计算机辅助设计与图形学学报, 2011,23(10): 1714-1718.(CHENG Xian-guo, LIU Wei-jun, ZHANG Ming. Approximation of B-spline curve of feature points[J].Journal of Computer-Aided Design & Computer Graphic,2011,23(10): 1714-1718.（in Chinese)）
[12]	吴世雄, 王成勇. 散乱噪声点云的数据分割[J]. 机械工程学报, 2007,43(2): 230-233.(WU Shi-xiong, WANG Cheng-yong. Scattered noise segmentation of point cloud data[J].Journal of Mechanical Engineering,2007,43(2): 230-233.(in Chinese)）
[13]	梁新合, 梁晋, 郭成, 曹巨明. 基于自适应最优邻域的散乱点云降噪技术研究[J]. 中国机械工程, 2010,21(6): 639-643.(LIANG Xin-he, LIANG Jin, GUO Cheng, CAO Ju-ming. Study on scatter point cloud denoising technology based on self-adaptive optimal neighborhood[J].China Mechanical Engineering,2010,21(6): 639-643.（in Chinese)）
[14]	皮尔 L, 特莱尔 W. 非均匀有理B样条[M]. 第二版. 赵罡, 穆国旺, 王拉柱译. 北京: 清华大学出版社, 2010: 60-61.(Piegl L, Tiller W.Non Uniform Rational B Spline [M]. 2nd ed. ZHAO Gang, MU Guo-wang, WANG La-zhu transl. Beijing: Tsinghua University Press, 2010: 60-61.(Chinese version))
[15]	刘晶, 林大钧. 一种图像轮廓数据的控制点检测算法[J]. 机械科学与技术, 2011,30(2): 283-285.(LIU Jing, LIN Da-jun. An algorithm of dominant point detection for image contour[J].Mechanical Science and Technology for Aerospace Engineering,2011,30(2): 283-285.（in Chinese)）
[16]	ZHOU Kai, WANG Guan-jun, JIN Hou-zhong, TAN Zhong-yi. NURBS interpolation based on exponential smoothing forecasting[J].The International Journal of Advanced Manufacturing Technology,2008,39(11/12): 1190-1196.