Spline

Summary

A spline is a function made of polynomial pieces on consecutive intervals. The pieces are joined at points called knots, so that the whole function is as smooth as the pieces allow. A spline of degree $n$ is usually required to have $n - 1$ continuous derivatives. Splines combine the flexibility of piecewise functions with the simplicity of polynomials, and they avoid the oscillations of high-degree polynomial interpolation. They are central in spline interpolation, in approximation theory and in computer-aided design, where B-splines give a convenient basis.