B-Splines

Abstract

A spline is a piecewise polynomial2 whose pieces meet with continuity as high as possible given the degree. The abscissa values at which consecutive pieces meet are called the knots. A B-spline is a spline expressed with respect to a particular basis, in which the basis functions are each non-zero over as small a number of consecutive pieces as possible, given the degree and the continuity, and the basis functions sum to unity.