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S-λ Bases and S-λ Curves
Fan Feilong ,Zeng Xiaoming
Department of Mathematics, University of Xiamen
*Correspondence author
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Funding: National Defense Basic Scientific Research program of China （No.Grant No. B1420110155）, Natural Science Foundation of Fujian Province of China（No.Grant No. 2010J01012）
Opened online:27 May 2011
Accepted by: none
Citation: Fan Feilong ,Zeng Xiaoming .S-λ Bases and S-λ Curves [OL]. [27 May 2011] http://en.paper.edu.cn/en_releasepaper/content/4428911
 
 
In this paper the S-λ distributions are presented and the S-λ basis functions are constructed from the S-λ distributions by means of the technique of generating functions and transform factors. These basis functions generate S-λ curves. We show that S-λ curves include Bezier curves, Poisson curves, rational Bezier curves and a lot of other curves. Therefore the researches of this paper provide a unified scheme for dealing with these famous curves. We study the important properties and identities of the S-λ basis functions and S-λ curves. Furthermore, by means of the technique of the generating function, a new convenient and practical method for local changes of S-λ curves is proposed.
Keywords:S-λ distributions; Basis functions; S-λ curves; generating functions; convolution
 
 
 

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