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B-spline A piecewise polynomial function, defined over a knot sequence, that has local support and is nonnegative (see spline). The B-spline of order n (degree n–1) is zero everywhere except over the n successive spans xin < xin+1 < … < xi

The importance of B-splines is that any spline can be expressed as a sum of multiples of B-splines, and if a spline of degree n–1 is expressed in terms of B-splines, then changing the coefficient of one of the B-splines alters precisely n spans of the curve without affecting its continuity properties.