Abstract
A new interpolation spline with two parameters, called EH interpolation spline, is presented in this paper, which is the extension of the standard cubic Hermite interpolation spline, and inherits the same properties of the standard cubic Hermite interpolation spline. Given the fixed interpolation conditions, the shape of the proposed splines can be adjusted by changing the values of the parameters. Also, the introduced spline could approximate to the interpolated function better than the standard cubic Hermite interpolation spline and the quartic Hermite interpolation splines with single parameter by a new algorithm.
Highlights
Spline interpolation is a useful and powerful tool for curves and surfaces modeling
For given knots a = x0 < x1 < ⋅ ⋅ ⋅ < xn = b and data {(xi, yi, di), i = 0, 1, . . . , n}, where yi and di are the values of the function value and the first-order derivative value of the function being interpolated, let hi = xi+1 − xi, t = (x − xi)/hi and the standard cubic Hermite spline in the interval
In order to overcome the disadvantage of the standard cubic Hermite spline, we extend its basis functions firstly
Summary
Spline interpolation is a useful and powerful tool for curves and surfaces modeling. Standard cubic Hermite spline is one of those interpolation functions. For the given interpolation condition, the cubic Hermite interpolation spline is fixed; that is to say, the shape of the interpolation curve or surface is fixed for the given interpolation data [1– 6]. Many authors have presented some new method to modify the shape of the interpolation curve to satisfy the industrial product design with several kinds of new interpolation splines with parameters [7–20]. These new splines all have similar properties of the standard cubic Hermite spline. Several kinds of rational splines with a single parameter were presented in the papers [18, 19], which is simple to compute, but its approximation accuracy is not good for the given curves and surfaces.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
