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The construction of λμ-B-spline curves and its application to rotational surfaces

Author

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  • Hu, Gang
  • Qin, Xinqiang
  • Ji, Xiaomin
  • Wei, Guo
  • Zhang, Suxia

Abstract

In order to provide more flexible approaches for designers, the λμ-B-spline curves are constructed as a generalization of the traditional cubic uniform B-spline curves. Possessing multiple local shape control parameters, λμ-B-spline curves not only inherit the properties of cubic uniform B-spline curves, but also exhibit better performance when adjusting its local shapes through two local shape control parameters. Particularly, to adjust and control the shapes of rotational surfaces more elegantly, the λμ-B-spline rotational surfaces with two local shape parameters are presented and utilized. A rotational surface is produced by combining λμ-B-spline with a transfinite vector valued rational interpolation function. Further, the properties of rotational surfaces, as well as its applications in rotational surface designs, are explored. Finally, the modeling examples are supplied to illustrate the proposed method in admitting the easy control of the shape of a surface, which suggest the much wider applications to the pattern design system of apparel CAD/CAM.

Suggested Citation

  • Hu, Gang & Qin, Xinqiang & Ji, Xiaomin & Wei, Guo & Zhang, Suxia, 2015. "The construction of λμ-B-spline curves and its application to rotational surfaces," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 194-211.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:194-211
    DOI: 10.1016/j.amc.2015.05.056
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    Cited by:

    1. Hu, Gang & Bo, Cuicui & Wei, Guo & Qin, Xinqiang, 2020. "Shape-adjustable generalized Bézier surfaces: Construction and it is geometric continuity conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    2. Abdul Majeed & Muhammad Abbas & Faiza Qayyum & Kenjiro T. Miura & Md Yushalify Misro & Tahir Nazir, 2020. "Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter," Mathematics, MDPI, vol. 8(12), pages 1-25, November.
    3. Abdul Majeed & Mehwish Naureen & Muhammad Abbas & Kenjiro T. Miura, 2022. "Construction of Cubic Trigonometric Curves with an Application of Curve Modelling," Mathematics, MDPI, vol. 10(7), pages 1-22, March.

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