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.
Highlights
With the development of geometric design industry, the shapes of curves often need to be changed freely
The cubic Catmull-Rom spline [22] has been widely used in geometric design [23,24] and engineering applications [25,26] because it can automatically interpolate the given control points without solving equation systems
Shapes of the standard cubic Catmull-Rom spline would be modified if the control points are changed, and the control points can be adapted during a learning procedure [25,26]
Summary
With the development of geometric design industry, the shapes of curves often need to be changed freely. The corresponding cubic α-Catmull-Rom spline curves and interpolation function are defined on the basis of the cubic α-Catmull-Rom spline basis functions. The proposed cubic α-Catmull-Rom spline curves have the same properties as the standard cubic Catmull-Rom spline curves, and have one degree of freedom in the interpolation curves even if the control points are fixed.
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