B-Spline Basis Functions

B-splines of polynomial order d are the unique functions that are globally in (C^(d-2)) and piecewise polynomial of degree d-1. A B-spline of order d is fixed when d+1 knots are given: the conditions generate a set of equations that is uniquely solved, up to normalization. The normalization is such that all B-splines with respect to a knot sequence form a partition of unity: they sum up to 1. (On the boundaries of the knot sequence, this does not hold.)

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Contributed by: Tammo Jan Dijkema

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