CurveFitting
BSpline
compute a Bspline basis function
Calling Sequence
Parameters
Description
Examples
BSpline(k, v, opt)
k

positive integer; order
v
name
opt
(optional) equation of the form knots=knotlist where knotlist is a list of $k+1$ elements of type algebraic
The BSpline routine computes a piecewise function representing the Bspline of order k in the symbol v. The nonzero portions of this function are polynomials of degree k1. If the knots option is not provided, then the uniform knot list $\[0,1,...,k\]$ is used.
The knot list must contain exactly k+1 elements. These elements must be in nondecreasing order; otherwise, unexpected results may be produced. The knots can have a multiplicity up to k1. If the multiplicity of a knot is m, then the continuity at that knot is $C\left(km1\right)$.
This procedure returns a Bspline basis function. Use the CurveFitting[BSplineCurve] procedure to create a Bspline curve.
This function is part of the CurveFitting package, and so it can be used in the form BSpline(..) only after executing the command with(CurveFitting). However, it can always be accessed through the long form of the command by using CurveFitting[BSpline](..).
$\mathrm{with}\left(\mathrm{CurveFitting}\right)\:$
$\mathrm{BSpline}\left(2\,u\right)$
$\left\{\begin{array}{cc}{0}& {u}{<}{0}\\ {u}& {u}{<}{1}\\ {2}{}{u}& {u}{<}{2}\\ {0}& {2}{\le}{u}\end{array}\right.$
$\mathrm{BSpline}\left(2\,u\,\mathrm{knots}=\left[0\,a\,2\right]\right)$
$\left\{\begin{array}{cc}{0}& {u}{<}{0}\\ \frac{{u}}{{a}}& {u}{<}{a}\\ \frac{{}{u}{+}{a}}{{2}{}{a}}{+}{1}& {u}{<}{2}\\ {0}& {2}{\le}{u}\end{array}\right.$
See Also
CurveFitting[BSplineCurve]
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