B-spline

In the mathematical subfield of numerical analysis, a B-spline, or basis spline, is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expressed as a linear combination of B-splines of that degree. Cardinal B-splines have knots that are equidistant from each other. B-splines can be used for curve-fitting and numerical differentiation of experimental data.

In the computer-aided design and computer graphics, spline functions are constructed as linear combinations of B-splines with a set of control points.

The term "B-spline" was coined by Isaac Jacob Schoenberg and is short for basis spline. A spline function is a piecewise polynomial function of degree <k in a variable x. The places where the pieces meet are known as knots. The number of internal knots must be equal to, or greater than k-1. Thus the spline function has limited support. The key property of spline functions is that they are continuous at the knots. Some derivatives of the spline function may also be continuous, depending on whether the knots are distinct or not. A fundamental theorem states that every spline function of a given degree, smoothness, and domain partition, can be uniquely represented as a linear combination of B-splines of that same degree and smoothness, and over that same partition.

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