Other splines
Local control: it is convenient if each control point influences only a finite part of the curve; this is not true for natural splines: each control point affects the whole curve.
Problem: we want 1st and 2nd derivative continuity, interpolation of control points and local control. We cannot have all with cubic polynomials.
Why not increase the degree? High-degree polynomials often are are wiggly. Cubics are the most natural.
Choices: give up second derivative continuity or give up interpolation.