B-spline (basis spline) is a kind of spline generated by so-called basis functions. The advantage of B-splines over Bezier curves (which are a special case of B-splines) is that the control vertices (CVs) of a B-spline affect only their local region of the curve or surface.

a mathematical, parametric definition of a series of connected geometric curve segments

a parametric curve (a curve defined by coordinates derived from functions sharing a common parameter) whose shape is determined by a series of control points whose influence is described by basis functions

Parametric function built by the summation of polynomes connected by knots. The polynoms are calculated by recurring equations. A B-Spline surface in 3D is obtained by calculating 2D curves along two different directions, but in accordance with a set of common parameters.

This is class of piecewise polynomials that is used for curve and surface definition. The B stands for basis. B-splines are mathematically defined using vertex control points, which do not lie on the curve or surface.

B-splines are a formulation (Barsky and Beatty, 1983) of B-spline curve segments. Barsky introduced two new degrees of freedom- bias and tension- which cab be applied either uniformly to the whole curve or non-uniformly by varying their values along the curve.