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Math. Comput. Appl. 2016, 21(3), 33;

The Cubic α-Catmull-Rom Spline

College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000, China
College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Author to whom correspondence should be addressed.
Academic Editor: Gözde Sarı
Received: 6 May 2016 / Revised: 25 July 2016 / Accepted: 1 August 2016 / Published: 9 August 2016
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By extending the definition interval of the standard cubic Catmull-Rom spline basis functions from [0,1] to [0,α], a class of cubic Catmull-Rom spline basis functions with a shape parameter α, named cubic α-Catmull-Rom spline basis functions, is constructed. Then, the corresponding cubic α-Catmull-Rom spline curves are generated based on the introduced basis functions. The cubic α-Catmull-Rom spline curves not only have the same properties as the standard cubic Catmull-Rom spline curves, but also can be adjusted by altering the value of the shape parameter α even if the control points are fixed. Furthermore, the cubic α-Catmull-Rom spline interpolation function is discussed, and a method for determining the optimal interpolation function is presented. View Full-Text
Keywords: Catmull-Rom spline; interpolation spline; shape parameter; shape adjustment Catmull-Rom spline; interpolation spline; shape parameter; shape adjustment

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Li, J.; Chen, S. The Cubic α-Catmull-Rom Spline. Math. Comput. Appl. 2016, 21, 33.

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