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 
.
- 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.
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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New in 7
