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 ui.
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 ui.
Details
- 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 u1 and um.
- The knot positions ui must form a non-decreasing sequence.
- Possible values of n range from 0 to m-d-2.
- PiecewiseExpand can be used to expand symbolic BSplineBasis functions into explicit piecewise polynomials.
Examples
open all close allBasic Examples (4)
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 to the sum where d is the degree:
BSplineBasis can be used to build up BSplineCurve:
Text
Wolfram Research (2008), BSplineBasis, Wolfram Language function, https://reference.wolfram.com/language/ref/BSplineBasis.html.
CMS
Wolfram Language. 2008. "BSplineBasis." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BSplineBasis.html.
APA
Wolfram Language. (2008). BSplineBasis. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BSplineBasis.html