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...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/146177 |
| _version_ | 1824455817668067328 |
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| author | Tian, Ye Ning, Tao Li, Jixing Zheng, Jianmin Chen, Zhitong |
| 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 |
| author_sort | Tian, Ye |
| collection | NTU |
| 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. |
| first_indexed | 2025-02-19T03:44:14Z |
| format | Journal Article |
| id | ntu-10356/146177 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:44:14Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-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 |
| 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 |
| title | 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_short | 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 |
| topic | Engineering::Computer science and engineering NURBS Surfaces B-spline Basis Function |
| url | https://hdl.handle.net/10356/146177 |
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