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Copyright © 2014 Xuli Han and Yuanpeng Zhu. Xuli Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.

Details

Title
Total Positivity of the Cubic Trigonometric Bézier Basis
Author
Han, Xuli; Zhu, Yuanpeng
Publication year
2014
Publication date
2014
Publisher
John Wiley & Sons, Inc.
ISSN
1110757X
e-ISSN
16870042
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
1561763777
Copyright
Copyright © 2014 Xuli Han and Yuanpeng Zhu. Xuli Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.