Cubic Spline Interpolation

Function: - Cubic Spline Interpolation 2

This is a quite interesting function. Max amplitude is always a constant of 1.0 with a constant period of between a maximum and a minimum. The function rapidly changes - from down to up at points where the sine function equals one ( ).This where any Spline interpolations has problems. At the trough 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 number of points.

Graph 3. Function: - Cubic Spline Interpolation. For x=Pi = 3.14 the interpolation should be equal to zero. There were not enough nodes in these points for a Cubic Spline (red curve), therefore the Spline interpolation has produced a mismatch of approximately 0.09

Graph 4 Zoomed Graph 3 Showing a mismatch at ( ). The Cubic Spline has missed some troughs as some nodes are too far from each other. In these troughs the function changes it's first differential from -1 to +1