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Polynomial-Based Non-Uniform Ternary Interpolation Surface Subdivision on Quadrilateral Mesh

Author

Listed:
  • Kaijun Peng

    (School of Computer and Information, Hefei University of Technology, Hefei 230601, China
    School of Mathematics, Hefei University of Technology, Hefei 230601, China)

  • Jieqing Tan

    (School of Computer and Information, Hefei University of Technology, Hefei 230601, China
    School of Mathematics, Hefei University of Technology, Hefei 230601, China)

  • Li Zhang

    (School of Mathematics, Hefei University of Technology, Hefei 230601, China)

Abstract

For non-uniform control polygons, a parameterized four-point interpolation curve ternary subdivision scheme is proposed, and its convergence and continuity are demonstrated. Following curve subdivision, a non-uniform interpolation surface ternary subdivision on regular quadrilateral meshes is proposed by applying the tensor product method. Analyses were conducted on the updating rules of parameters, proving that the limit surface is continuous. In this paper, we present a novel interpolation subdivision method to generate new virtual edge points and new face points of the extraordinary points of quadrilateral mesh. We also provide numerical examples to assess the validity of various interpolation methods.

Suggested Citation

  • Kaijun Peng & Jieqing Tan & Li Zhang, 2023. "Polynomial-Based Non-Uniform Ternary Interpolation Surface Subdivision on Quadrilateral Mesh," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:486-:d:1037772
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    References listed on IDEAS

    as
    1. Sooyoung Jung & Yong Tae Yoon & Jun-Ho Huh, 2020. "An Efficient Micro Grid Optimization Theory," Mathematics, MDPI, vol. 8(4), pages 1-21, April.
    2. Li, Xin & Chang, Yubo, 2018. "Non-uniform interpolatory subdivision surface," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 239-253.
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