Total Positivity of the Cubic Trigonometric Bézier Basis
Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parameters λ and μ given in Han et al. (2009) forms an optimal normalized totally positive basis for λ,μ∈(-2,1]. Moreover, we show that for λ=-2 or μ=-2 the basis is not...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/198745 |
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| _version_ | 1849306713161728000 |
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| author | Xuli Han Yuanpeng Zhu |
| author_facet | Xuli Han Yuanpeng Zhu |
| author_sort | Xuli Han |
| collection | DOAJ |
| description | Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parameters λ and μ given in Han et al. (2009) forms an optimal normalized totally positive basis for λ,μ∈(-2,1]. Moreover, we show that for λ=-2 or μ=-2 the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm. |
| format | Article |
| id | doaj-art-2ca6a1c382924ef183b46d141515c8f4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2ca6a1c382924ef183b46d141515c8f42025-08-20T03:55:00ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/198745198745Total Positivity of the Cubic Trigonometric Bézier BasisXuli Han0Yuanpeng Zhu1School of Mathematics and Statistics, Central South University, Changsha 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410083, ChinaWithin the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parameters λ and μ given in Han et al. (2009) forms an optimal normalized totally positive basis for λ,μ∈(-2,1]. Moreover, we show that for λ=-2 or μ=-2 the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm.http://dx.doi.org/10.1155/2014/198745 |
| spellingShingle | Xuli Han Yuanpeng Zhu Total Positivity of the Cubic Trigonometric Bézier Basis Journal of Applied Mathematics |
| title | Total Positivity of the Cubic Trigonometric Bézier Basis |
| title_full | Total Positivity of the Cubic Trigonometric Bézier Basis |
| title_fullStr | Total Positivity of the Cubic Trigonometric Bézier Basis |
| title_full_unstemmed | Total Positivity of the Cubic Trigonometric Bézier Basis |
| title_short | Total Positivity of the Cubic Trigonometric Bézier Basis |
| title_sort | total positivity of the cubic trigonometric bezier basis |
| url | http://dx.doi.org/10.1155/2014/198745 |
| work_keys_str_mv | AT xulihan totalpositivityofthecubictrigonometricbezierbasis AT yuanpengzhu totalpositivityofthecubictrigonometricbezierbasis |