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A note on curvature variation minimizing cubic Hermite interpolants

Author

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  • Lu, Lizheng

Abstract

In the paper [1], Jaklič and Žagar studied curvature variation minimizing cubic Hermite interpolants. To match planar two-point G1 Hermite data, they obtained the optimal cubic curve by minimizing an approximate form of the curvature variation energy. In this paper, we present a simple method for this problem by minimizing the jerk energy, which is also an approximate form of the curvature variation energy. The unique solution can be easily obtained since the jerk energy is represented as a quadratic polynomial of two unknowns and is strictly convex. Finally, we prove that our method is equivalent to their method.

Suggested Citation

  • Lu, Lizheng, 2015. "A note on curvature variation minimizing cubic Hermite interpolants," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 596-599.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:596-599
    DOI: 10.1016/j.amc.2014.11.113
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    Cited by:

    1. Jiaoyue Zheng & Gang Hu & Liuxin Chen & Xiaomin Ji, 2023. "Combined SGC-Ball Interpolation Curves: Construction and IGEO-Based Shape Optimization," Mathematics, MDPI, vol. 11(16), pages 1-25, August.

    More about this item

    Keywords

    G1 Hermite interpolation; Cubic curve; Curvature; Jerk energy; Minimization;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets

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