Constructing planar C1 cubic Hermite interpolation curves via approximate energy minimization
Received:September 04, 2018  Revised:November 05, 2018
Key Word: Hermite interpolation, strain energy, curvature variation, minimization  
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Juncheng Li Hunan University of Humanities, Science and Technology lijuncheng82@126.com 
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Abstract:
      In this paper, the methods for constructing planar C1 cubic Hermite interpolation curves via approximate energy minimization are studied. The methods are to obtain the optimal tangent vectors of the interpolation. By minimizing the appropriate approximate functions of the strain energy, the curvature variation energy and the combined energy, the linear equation systems of the tangent vectors are obtained. We find that the approximate curvature variation energy minimization has no unique solution, while both the approximate strain energy minimization and the approximate combined minimization have the unique solutions due to the strictly diagonally dominant property of the obtained systems. Some examples are provided to illustrate the effects of the interpolation curves.
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