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Title: An improvement on the upper bounds of the partial derivatives of NURBS surfaces
Authors: Tian, Ye
Ning, Tao
Li, Jixing
Zheng, Jianmin
Chen, Zhitong
Keywords: Engineering::Computer science and engineering
Issue Date: 2020
Source: Tian, Y., Ning, T., Li, J., Zheng, J., & Chen, Z. (2020). An improvement on the upper bounds of the partial derivatives of NURBS surfaces. Mathematics, 8(8), 1382-. doi:10.3390/math8081382
Journal: Mathematics 
Abstract: The Non-Uniform Rational B-spline (NURBS) surface not only has the characteristics of the rational Bezier 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.
ISSN: 2227-7390
DOI: 10.3390/math8081382
Schools: School of Computer Science and Engineering 
Rights: © 2020 The Authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SCSE Journal Articles

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