B-spline

Summary

A B-spline is a spline of given degree on a given knot sequence that is nonnegative and nonzero only on a few consecutive knot intervals. The B-splines of degree $p$ on a knot sequence form a basis of the corresponding spline space. So every such spline is a unique combination of them. They are computed by a stable recursion, they sum to $1$, and each one is local. This makes them the standard representation of splines in numerical work and in computer-aided design. Curves built from them, including NURBS, are evaluated with de Boor's algorithm.