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Math. Comput. Appl. 2016, 21(3), 33; doi:10.3390/mca21030033

The Cubic α-Catmull-Rom Spline

1
College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000, China
2
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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Abstract

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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