Total Positivity of the Cubic Trigonometric Bézier Basis | Zendy

Xuli Han | Zendy; Yuanpeng Zhu | Zendy

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Total Positivity of the Cubic Trigonometric Bézier Basis

Author(s) -

Xuli Han,

Yuanpeng Zhu

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/198745

Subject(s) - algorithm , basis (linear algebra) , computer science , artificial intelligence , mathematics , geometry

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

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