An improvement on the upper bounds of the partial derivatives of NURBS surfaces

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 deriv...

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Main Authors:	Tian, Ye, Ning, Tao, Li, Jixing, Zheng, Jianmin, Chen, Zhitong
Other Authors:	School of Computer Science and Engineering
Format:	Article
Language:	English
Published:	2021
Subjects:	Engineering::Computer science and engineering NURBS Surfaces B-spline Basis Function
Online Access:	https://hdl.handle.net/10356/146177
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Institution:	Nanyang Technological University
Language:	English

id	sg-ntu-dr.10356-146177
record_format	dspace
spelling	sg-ntu-dr.10356-1461772021-01-29T03:41:31Z An improvement on the upper bounds of the partial derivatives of NURBS surfaces Tian, Ye Ning, Tao Li, Jixing Zheng, Jianmin Chen, Zhitong School of Computer Science and Engineering Engineering::Computer science and engineering NURBS Surfaces B-spline Basis Function 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. Published version 2021-01-29T03:41:31Z 2021-01-29T03:41:31Z 2020 Journal Article 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 2227-7390 0000-0002-6999-1098 0000-0002-6678-3672 0000-0001-7136-2234 https://hdl.handle.net/10356/146177 10.3390/math8081382 2-s2.0-85090207535 8 8 en Mathematics © 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 (http://creativecommons.org/licenses/by/4.0/). application/pdf
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	Engineering::Computer science and engineering NURBS Surfaces B-spline Basis Function
spellingShingle	Engineering::Computer science and engineering NURBS Surfaces B-spline Basis Function Tian, Ye Ning, Tao Li, Jixing Zheng, Jianmin Chen, Zhitong An improvement on the upper bounds of the partial derivatives of NURBS surfaces
description	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.
author2	School of Computer Science and Engineering
author_facet	School of Computer Science and Engineering Tian, Ye Ning, Tao Li, Jixing Zheng, Jianmin Chen, Zhitong
format	Article
author	Tian, Ye Ning, Tao Li, Jixing Zheng, Jianmin Chen, Zhitong
author_sort	Tian, Ye
title	An improvement on the upper bounds of the partial derivatives of NURBS surfaces
title_short	An improvement on the upper bounds of the partial derivatives of NURBS surfaces
title_full	An improvement on the upper bounds of the partial derivatives of NURBS surfaces
title_fullStr	An improvement on the upper bounds of the partial derivatives of NURBS surfaces
title_full_unstemmed	An improvement on the upper bounds of the partial derivatives of NURBS surfaces
title_sort	improvement on the upper bounds of the partial derivatives of nurbs surfaces
publishDate	2021
url	https://hdl.handle.net/10356/146177
_version_	1690658505030107136

An improvement on the upper bounds of the partial derivatives of NURBS surfaces

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