• 论文 • 上一篇    

空间曲线的拟插值重建

刘新儒1,2, 任燕3, 王海波1, 刘圣军1,2   

  1. 1. 中南大学数学与统计学院, 长沙 410083;
    2. 中南大学工程建模与科学计算研究所, 长沙 410083;
    3. 重庆市机械高级技工学校, 重庆 400055
  • 收稿日期:2021-12-05 发布日期:2023-03-16
  • 通讯作者: 刘圣军,Email:shjliu.cg@gmail.com.
  • 基金资助:
    国家自然科学基金(62172447)资助.

刘新儒, 任燕, 王海波, 刘圣军. 空间曲线的拟插值重建[J]. 数值计算与计算机应用, 2023, 44(1): 68-80.

Liu Xinru, Ren Yan, Wang Haibo, Liu Shengjun. QUASI-INTERPOLATION RECONSTRUCTION FOR SPACE CURVES[J]. Journal on Numerica Methods and Computer Applications, 2023, 44(1): 68-80.

QUASI-INTERPOLATION RECONSTRUCTION FOR SPACE CURVES

Liu Xinru1,2, Ren Yan3, Wang Haibo1, Liu Shengjun1,2   

  1. 1. School of Mathematics and Statistics, Central South University, Changsha 410083, China;
    2. Institute of Engineering Modeling and Scientific Computing, Central South University, Changsha 410083, China;
    3. Chongqing Mechanical Senior Technician School, Chongqing 400055, China
  • Received:2021-12-05 Published:2023-03-16
在一元Multiquadric拟插值算子的基础上,将一元基函数扩展到多元,并重新定义了空间点之间的距离,提出了一种新的多元拟插值算子,并分析了其任意阶多项式再生性及逼近性.数值实验表明,新的多元拟插值算子可直接使用空间点集的坐标实现曲线的高精度拟插值重建.
Based on the univariate multiquadric quasi-interpolation operator, the univariate basis function is extended to multivariate basis function, and the distance between spatial points is redefined, and a new multivariate quasi-interpolation operator is proposed. We analyzed any degree polynomial reproduction property and the approximation of the quasi-interpolation operator. Numerical experiments showed that the new multivariate quasi-interpolation operator can achieve high-precision quasi-interpolation reconstruction of the space curve by using the coordinates of the spatial point set directly.

MR(2010)主题分类: 

()
[1] 张继红, 王瑞林. 一种新的MQ径向基函数拟插值格式[J]. 大连交通大学学报, 2017, 38(5):118-120.
[2] Beatson R, Powell M. Univariate multiquadric approximation:quasi-interpolation to scattered data[J]. Constructive Approximation, 1992, 8(3):275-288.
[3] Wu Z, Robert S. Shape preserving properties and convergence of univariate multiquadric quasiinterpolation[J]. Acta Mathematicae Applicatae Sinica, 1994, 10(4):441-446.
[4] Wang R H, Xu M, Fang Q. A kind of improved univariate multiquadric quasi-interpolation operators[J]. Computers & mathematics with applications, 2010, 59(1):451-456.
[5] Ling L. A univariate quasi-multiquadric interpolationwith better smoothness[J]. Computers & Mathematics with Applications, 2004, 48(5-6):897-912.
[6] Chen R, Han X, Wu Z. A multiquadric quasi-interpolation with linear reproducing and preserving monotonicity[J]. Journal of computational and applied mathematics, 2009, 231(2):517-525.
[7] Feng R, Li F. A quasi-interpolation satisfying quadratic polynomial reproduction property and shape-preserving property to scattered data[J]. Journal of Computational and Applied Mathematics, 2009, 225:594-601.
[8] 陈荣华, 韩旭里, 吴宗敏. 一种新的Multiquadric拟插值[J]. 工程图学学报, 2010, 31(3):117-121.
[9] Gao W, Wu Z. Quasi-interpolation for linear functional data[J]. Journal of Computational and Applied Mathematics, 2012, 236(13):3256-3264.
[10] 陈荣荣. MQ拟插值算子的构造及其相关性质[D]. Master's thesis, 东北师范大学, 2015.
[11] Feng R, Zhou X. A kind of multiquadric quasi-interpolation operator satisfying any degree polynomial reproduction property to scattered data[J]. Journal of computational and applied mathematics, 2011, 235(5):1502-1514.
[12] Ling L. Multivariate quasi-interpolation schemes for dimension-splitting multiquadric[J]. Applied mathematics and computation, 2005, 161(1):195-209.
[13] Wu R, Wu T, Li H. A family of multivariate multiquadric quasi-interpolation operators with higher degree polynomial reproduction[J]. Journal of Computational and Applied Mathematics, 2015, 274:88-108.
[14] Feng R, Peng S. Quasi-interpolation scheme for arbitrary dimensional scattered data approximation based on natural neighbors and RBF interpolation[J]. Journal of Computational and Applied Mathematics, 2018, 329:95-105.
[15] 丛伟. 拟合任意空间曲线曲面的三角函数法[J]. 沈阳航空工业学院学报, 2001, 1:69-70.
[16] 吴暐, 罗良玲, 田华. 空间曲线拟合算法的研究[J]. 南昌大学学报:工科版, 2004, 26(3):38-40.
[17] Zhao X, Zhu X, Fan H. Research of space curve fitting based on FBG sensor technology[J]. Procedia Engineering, 2011, 15:1764-1770.
[18] Di H. Space curve fitting method based on fiber-optic curvature gages[J]. Optics & Laser Technology, 2012, 44(1):290-294.
[19] Liu X, Wang Y. Research of automatically piecewise polynomial curve-fitting method based on least-square principle[J]. Science Technology and Engineering, 2014, 14(3):55-58.
[20] Xue L. Piecewise Curve Fitting Based on Least Square Method in 3D Space[J]. International Journal of Mathematical Physics, 2020, 3(1):7-11.
[21] 凌海雅, 赵仕卿, 陆利正, 汪国昭. 空间曲线基于内在几何量的高质量采样和B样条拟合[J]. 计算机辅助设计与图形学学报, 2020, 32(2):255-261.
[22] 刘明慧. 径向基函数基本理论及其应用[D]. Master's thesis, 东北师范大学, 2015.
[23] Feng R, Li F. A shape-preserving quasi-interpolation operator satisfying quadratic polynomial reproduction property to scattered data[J]. Journal of computational and applied mathematics, 2009, 225(2):594-601.
No related articles found!
阅读次数
全文


摘要