Natural Cubic splines

This applet shows the natural cubic spline through a sequence of
control points.

You can move a control point by dragging it with the mouse,
add a new one by clicking the mouse, and delete one by holding
down the Shift key while clicking on it.

Between each pair of control points there is a cubic curve.
To make sure that curves join together smoothly, the first and
second derivative at the end of one curve must equal the the
first and second derivative start of the next one. Computing
the natural cubic spline essentially involves solving a system
of simultaneous equations to make sure this happens. It is
also possible to create a closed
natural cubic spline.

Unfortunately, while the curve is mathematically smooth, it
can wriggle in quite unexpected ways (try moving one control
point close to another one in the applet above). Furthermore,
we do not have local control - moving one control
point causs the entire curve to change, not just the part
near the control point.