This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

BSplineBasis

 BSplineBasisgives the zeroth uniform B-spline basis function of degree d at x. BSplineBasisgives the n uniform B-spline basis function of degree d. BSplineBasis[{d, {u1, u2, ...}}, n, x] gives the n non-uniform B-spline basis function of degree d with knots at positions .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• BSplineBasis gives B-spline basis functions that have nonzero values only within the x interval between and .
• BSplineBasis gives B-spline basis functions that have nonzero values only within the x interval between and .
• The knot positions must form a non-decreasing sequence.
• Possible values of n range from 0 to .
Evaluate a uniform cubic B-spline basis numerically:
Plot it:
Evaluate the second cubic B-spline basis with given knots:
Plot all the cubic basis functions with given knots:
Symbolic derivative of B-spline basis:
Plot of the derivatives:
Evaluate a uniform cubic B-spline basis numerically:
 Out[1]=

Plot it:
 Out[1]=

Evaluate the second cubic B-spline basis with given knots:
 Out[2]=
Plot all the cubic basis functions with given knots:
 Out[3]=

Symbolic derivative of B-spline basis:
 Out[2]=
Plot of the derivatives:
 Out[3]=
 Scope   (1)
The nonzero part of a B-spline basis function is given by the range of knots:
The sum of all B-spline bases at points within the support is always one:
At most d+1 basis functions contribute the sum where d is the degree:
BSplineBasis can be used to build up BSplineCurve:
New in 7