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Stretch-Energy-Minimizing B-Spline Interpolation Curves and Their Applications

Author

Listed:
  • Qian Ni

    (School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, China
    KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China)

  • Chen Xie

    (School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, China)

Abstract

In this paper, we propose a new method to construct energy-minimizing cubic B-spline interpolation curves by minimizing the approximated stretch energy. The construction of a B-spline interpolation curve with a minimal approximated stretch energy can be addressed by solving a sparse linear system. The proof of both the existence and uniqueness of the solution for the linear system is provided. In addition, we analyze the computational cost of cubic B-spline curves with an approximated stretch energy, which is close to that of the ordinary interpolation method with cubic B-splines without the requirement of stretch energy.

Suggested Citation

  • Qian Ni & Chen Xie, 2023. "Stretch-Energy-Minimizing B-Spline Interpolation Curves and Their Applications," Mathematics, MDPI, vol. 11(21), pages 1-9, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4534-:d:1273757
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    References listed on IDEAS

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    1. Johnson, Michael J. & Johnson, Hakim S., 2016. "A constructive framework for minimal energy planar curves," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 172-181.
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