BUILT-IN MATHEMATICA SYMBOL

BSplineBasis

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

BSplineBasis[d, n, x]
gives 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 .

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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