- Journal Home
- Volume 18 - 2025
- Volume 17 - 2024
- Volume 16 - 2023
- Volume 15 - 2022
- Volume 14 - 2021
- Volume 13 - 2020
- Volume 12 - 2019
- Volume 11 - 2018
- Volume 10 - 2017
- Volume 9 - 2016
- Volume 8 - 2015
- Volume 7 - 2014
- Volume 6 - 2013
- Volume 5 - 2012
- Volume 4 - 2011
- Volume 3 - 2010
- Volume 2 - 2009
- Volume 1 - 2008
Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 374-398.
Published online: 2014-07
Cited by
- BibTex
- RIS
- TXT
In this paper, the $G^2$ interpolation by Pythagorean-hodograph (PH) quintic curves in $\mathbb{R}^d$, $d ≥2$, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension $d$, they supply a $G^2$ quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the interpolating curve as unknowns. Although several solutions might exist, the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data case. The numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation method. Numerical examples confirm the efficiency of the proposed method.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.1314nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5880.html} }In this paper, the $G^2$ interpolation by Pythagorean-hodograph (PH) quintic curves in $\mathbb{R}^d$, $d ≥2$, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension $d$, they supply a $G^2$ quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the interpolating curve as unknowns. Although several solutions might exist, the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data case. The numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation method. Numerical examples confirm the efficiency of the proposed method.