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Non-uniform interpolatory subdivision surface

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  • Li, Xin
  • Chang, Yubo

Abstract

This paper presents an interpolatory subdivision scheme with non-uniform parametrization for arbitrary polygon meshes with arbitrary manifold topology. This is the first attempt to generalize the non-uniform four point interpolatory curve subdivision to surface with extraordinary points. The scheme is constructed from the inspiration of the relation between the non-uniform four-point interpolatory subdivision scheme and the non-uniform B-spline refinement rule. Numerical examples and comparisons with the uniform interpolatory subdivision schemes indicate that the quality of the limit surface can be improved by using non-uniform parameter values for non-uniform initial data.

Suggested Citation

  • Li, Xin & Chang, Yubo, 2018. "Non-uniform interpolatory subdivision surface," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 239-253.
    • Handle: RePEc:eee:apmaco:v:324:y:2018:i:c:p:239-253
    DOI: 10.1016/j.amc.2017.11.035
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    References listed on IDEAS

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    1. Riffnaller-Schiefer, A. & Augsdörfer, U.H. & Fellner, D.W., 2016. "Isogeometric shell analysis with NURBS compatible subdivision surfaces," Applied Mathematics and Computation, Elsevier, vol. 272(P1), pages 139-147.
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    Cited by:

    1. Samir, Chafik & Adouani, Ines, 2019. "C1 interpolating Bézier path on Riemannian manifolds, with applications to 3D shape space," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 371-384.
    2. Samir, Chafik & Huang, Wen, 2021. "Coordinate descent optimization for one-to-one correspondence and supervised classification of 3D shapes," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    3. Mustafa, Ghulam & Hameed, Rabia, 2019. "Families of non-linear subdivision schemes for scattered data fitting and their non-tensor product extensions," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 214-240.
    4. 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.
    5. Baotao Chi & Shengmin Bai & Qianjian Guo & Yaoming Zhang & Wei Yuan & Can Li, 2023. "A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing," Mathematics, MDPI, vol. 11(16), pages 1-19, August.

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