BSplineBasis

BSplineBasis[d,x]
gives the zeroth uniform B-spline basis function of degree d at x.

BSplineBasis[d,n,x]
gives the n^(th) uniform B-spline basis function of degree d.

BSplineBasis[{d,{u1,u2,}},n,x]
gives the n^(th) non-uniform B-spline basis function of degree d with knots at positions .

DetailsDetails

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • BSplineBasis[d,x] is equivalent to BSplineBasis[d,0,x].
  • BSplineBasis[d,n,x] gives B-spline basis functions that have nonzero values only within the x interval between and .
  • BSplineBasis[{d,{u1,u2,,um}},n,x] 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 .
  • PiecewiseExpand can be used to expand symbolic BSplineBasis functions into explicit piecewise polynomials.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Evaluate a uniform cubic B-spline basis numerically:

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Plot it:

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Evaluate the second cubic B-spline basis with given knots:

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Plot all the cubic basis functions with given knots:

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Symbolic derivative of B-spline basis:

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Plot of the derivatives:

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Introduced in 2008
(7.0)