空间曲线的拟插值重建

doi:10.12288/szjs.s2021-0810

数值计算与计算机应用 ›› 2023, Vol. 44 ›› Issue (1): 68-80.DOI: 10.12288/szjs.s2021-0810

• 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. 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.

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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 Xinru^1,2, Ren Yan³, Wang Haibo¹, Liu Shengjun^1,2

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.

关键词： 拟插值, 空间曲线, Multiquadric (MQ), 多项式再生性

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.

Key words: quasi-interpolation, space curve, multiquadric(MQ), polynomial reproducibility

MR(2010)主题分类:

65D10

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空间曲线的拟插值重建

QUASI-INTERPOLATION RECONSTRUCTION FOR SPACE CURVES

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