I recently had an interesting query from Georg, a geography student in Germany regarding the use of cubic splines to fit a smooth curve to experimental data. The graph he sent me is shown below:
The cubic spline has produced a nice smooth curve, but the problem is that it is supposed to be a cumulative frequency curve, and cumulative frequency curves are not supposed to slope downwards, let along pass below the zero line. Unfortunately cubic splines don’t know that, and will just adopt the shape dictated bt the given points.
One solution is to insert additional points in the areas with problems as illustrated below:
Which gives us the result we want!