Akima Spline Interpolation

Function: - Akima Spline Interpolation 1

This is quite an interesting function. Max amplitude is always constant with a value of 1.0 and a constant period between maximum and minimum. The function has rapid changes, from down to up, at the point where the sine function equals one ( ).This is where any Spline interpolation has a problem. At the points, where the function should be equal to zero, the interpolation has a different value. The only way to improve the interpolation is to increase the number of points. On the next graph we compare Cubic Spline, Hermite and Akima Spline interpolations. It is very clear that the Akima will give the best results for this type of function with sharp edges.

Graph 20. Function: - Akima Spline (orange), Cubic Spline (blue), Hermite Spline (red) Interpolation. At the points the function should be equal to zero. The Akima Spline (orange) represents the best solution for sharp edges of the minimums.

Graph 21. It is a magnified Graph 20. Function: - Akima Spline (orange), Hermite Spline (red) Cubic Spline (blue), Interpolation. The function should be equal zero at the points . Akima Spline (orange) gives the best solution for sharp minimums.