B-Spline Basis Functions

order

3

number

2

B-splines of polynomial order

d

are the unique functions that are globally in

d-2

C

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.)