Total Positivity of the Cubic Trigonometric Bézier Basis

Xuli Han and Yuanpeng Zhu

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: 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.

Date: 2014
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https://doi.org/10.1155/2014/198745

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:198745

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