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

Ye Tian, Tao Ning, Jixing Li, Jianmin Zheng and Zhitong Chen
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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

Mathematics, 2020, vol. 8, issue 8, 1-15

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.

Keywords: NURBS surfaces; B-spline basis function; upper bounds; derivatives (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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