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, {u_{1}, u_{2}, ...}}, 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, {u
_{1}, u_{2}, ..., u_{m}}}, 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:

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]= | |

New in 7