Constructing Planar $C^1$ Cubic Hermite Interpolation Curves Via Approximate Energy Minimization
Received:September 04, 2018  Revised:October 26, 2018
Key Words: Hermite interpolation   strain energy   curvature variation   minimization  
Fund Project:Supported by the Natural Science Foundation of Hunan Province (Grant No.2017JJ3124) and the Scientific Research Fund of Hunan Provincial Education Department (Grant No.18A415).
Author NameAffiliation
Juncheng LI College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Hunan 417000, P. R. China 
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      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 coefficient 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.
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