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An Improvement on the Upper Bounds of the Partial Derivatives of NURBS Surfaces

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Listed:
  • Ye Tian

    (School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China)

  • Tao Ning

    (School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China)

  • Jixing Li

    (The Aviation Industry Corporation of China-Digital, Beijing 100028, China)

  • Jianmin Zheng

    (School of Computer Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 63979, Singapore)

  • Zhitong Chen

    (School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China)

Abstract

The Non-Uniform Rational B-spline (NURBS) surface not only has the characteristics of the rational Bézier surface, but also has changeable knot vectors and weights, which can express the quadric surface accurately. In this paper, we investigated new bounds of the first- and second-order partial derivatives of NURBS surfaces. A pilot study was performed using inequality theorems and degree reduction of B-spline basis functions. Theoretical analysis provides simple forms of the new bounds. Numerical examples are performed to illustrate that our method has sharper bounds than the existing ones.

Suggested Citation

  • Ye Tian & Tao Ning & Jixing Li & Jianmin Zheng & Zhitong Chen, 2020. "An Improvement on the Upper Bounds of the Partial Derivatives of NURBS Surfaces," Mathematics, MDPI, vol. 8(8), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1382-:d:400367
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    References listed on IDEAS

    as
    1. Zhang, Ren-Jiang, 2015. "Improved derivative bounds of the rational quadratic Bézier curves," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 492-496.
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