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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 ui.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • BSplineBasis[d, n, x] gives B-spline basis functions that have nonzero values only within the x interval between n/(d+1) and (d+n+1)/(d+1).
  • BSplineBasis[{d, {u1, u2, ..., um}}, n, x] gives B-spline basis functions that have nonzero values only within the x interval between u1 and um.
  • The knot positions ui must form a non-decreasing sequence.
  • Possible values of n range from 0 to m-d-2.
EXAMPLESCLOSE ALL
Basic Examples   (4)
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:
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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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Scope   (1)
TraditionalForm formatting:
Properties & Relations   (3)
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:
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