# B-spline

 related topics {math, number, function} {@card@, make, design}

In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. B-splines were investigated as early as the nineteenth century by Nikolai Lobachevsky from Kazan State University, Russia. A fundamental theorem states that every spline function of a given degree, smoothness, and domain partition, can be represented as a linear combination of B-splines of that same degree and smoothness, and over that same partition.[1] The term B-spline was coined by Isaac Jacob Schoenberg and is short for basis spline.[2] B-splines can be evaluated in a numerically stable way by the de Boor algorithm. Simplified, potentially faster variants of the de Boor algorithm have been created but they suffer from comparatively lower stability.[3][4]

In the computer science subfields of computer-aided design and computer graphics, the term B-spline frequently refers to a spline curve parametrized by spline functions that are expressed as linear combinations of B-splines (in the mathematical sense above). A B-spline is simply a generalisation of a Bézier curve, and it can avoid the Runge phenomenon without increasing the degree of the B-spline.