Cubic spline

Summary

A cubic spline is a spline of degree $3$. It is made of cubic polynomial pieces whose values, first derivatives and second derivatives agree at the knots. It is the most used spline, because it is the lowest degree whose graph looks smooth to the eye, with continuous curvature. A natural cubic spline also has zero second derivative at both ends. In spline interpolation, the natural cubic spline is the interpolant with the least total squared second derivative, the mathematical form of the bent draftsman's strip.