B-spline

A Dictionary of Computing | 2004 | 588 words | Copyright

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 x_i_–_n < x_i_–_n₊₁ < … < x_i

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.

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JOHN DAINTITH. "B-spline." A Dictionary of Computing. 2004. Encyclopedia.com. 27 May. 2012 <http://www.encyclopedia.com>.

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