Constructing Planar C~1 Cubic Hermite Interpolation Curves Via Approximate Energy Minimization

英文篇名：Constructing Planar C~1 Cubic Hermite Interpolation Curves Via Approximate Energy Minimization
作者：Juncheng ; LI
英文作者：Juncheng LI;College of Mathematics and Finance, Hunan University of Humanities,Science and Technology;
英文关键词：Hermite interpolation;;strain energy;;curvature variation;;minimization
中文刊名：SXYJ
英文刊名：数学研究及应用(英文版)
机构：College of Mathematics and Finance, Hunan University of Humanities,Science and Technology;
出版日期：2019-05-09 11:00
出版单位：Journal of Mathematical Research with Applications
年：2019
期：v.39;No.177
基金：Supported by the Natural Science Foundation of Hunan Province(Grant No.2017JJ3124);; the Scientific Research Fund of Hunan Provincial Education Department(Grant No.18A415)
语种：英文;
页：SXYJ201904009
页数：8
CN：04
ISSN：21-1579/O1
分类号：107-114

摘要

The methods for constructing planar C~1 cubic Hermite interpolation curves via approximate energy minimization are studied. The main purpose of the proposed methods are to obtain the optimal tangent vectors of the C~1 cubic Hermite interpolation curves. By minimizing the appropriate approximate functions of the strain energy, the curvature variation energy and the combined energy, the linear equation systems for solving the optimal tangent vectors are obtained. It is found that there is no unique solution for the minimization of approximate curvature variation energy minimization, while there is unique solution for the minimization of approximate strain energy and the minimization of approximate combination energy because the coeffcient matrix of the equation system is strictly diagonally dominant. Some examples are provided to illustrate the effectiveness of the proposed method in constructing planar C~1 cubic Hermite interpolation curves.
The methods for constructing planar C~1 cubic Hermite interpolation curves via approximate energy minimization are studied. The main purpose of the proposed methods are to obtain the optimal tangent vectors of the C~1 cubic Hermite interpolation curves. By minimizing the appropriate approximate functions of the strain energy, the curvature variation energy and the combined energy, the linear equation systems for solving the optimal tangent vectors are obtained. It is found that there is no unique solution for the minimization of approximate curvature variation energy minimization, while there is unique solution for the minimization of approximate strain energy and the minimization of approximate combination energy because the coeffcient matrix of the equation system is strictly diagonally dominant. Some examples are provided to illustrate the effectiveness of the proposed method in constructing planar C~1 cubic Hermite interpolation curves.

引文

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