A B-spline curve differs from a Hermite or B zier curve in that it usually consists of more than one curve segment. Each segment is defined and influenced by only a few control points, which are the coefficients of the B-spline basis function polynomials. The degree of the curve is independent of the total number of control points. These characteristics allow changes in shape that do not propagate beyond one or only a few local segments. Most curve-defining techniques do not provide for local control of shape. Consequently, local changes (for example, a small change in the position of a point on a spline curve or of a vertex of a characteristic polygon of a B zier curve) tend to be strongly propagated throughout the entire curve. This is sometimes described as a global propagation of local change. The B-spline curve avoids this problem by using a special set of basis functions that has only local influence and depends on only a few neighboring control points. Connecting the control points pi (Equation 5.1) in the order of their numbering with straight lines produces the Bspline control polygon. The B-spline curve is contained within the convex hull of its control polygon. In general, B-splines do not necessarily interpolate their end points. However, the nonuniform B-spline basis functions allow this. We consider here both nonrational and rational forms of the B-spline basis functions.