Computer Science ›› 2018, Vol. 45 ›› Issue (3): 76-82.doi: 10.11896/j.issn.1002-137X.2018.03.013

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Selection of Control Points of Quadratic-trigonometric Hermite Interpolation Splines

LIU Cheng-zhi, HAN Xu-li and LI Jun-cheng   

  • Online:2018-03-15 Published:2018-11-13

Abstract: This paper studied the selection of the free control points of the C1 continuous quadratic-trigonometric Hermite interpolation curves.Firstly,this paper discussed the selection of the free control points when the conditions of midpoint were given.In order to obtain the most smooth or the shortest arc length interpolation curves,an optimization model for solving the optimal control points was established based on the energy optimization method.By solving the optimization model,the optimal control points were obtained to minimize energy value of the curve.Then,an optimization model was also established for solving the shortest arc length.Numerical examples show that the optimal control points can make the curves smooth or have the shortest arc length.

Key words: Hermite interpolation spline,Quadratic-trigonometric curve,Conditions of midpoint,Energy optimization,Shortest arc length

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