BSplineFunction—Wolfram Mathematica 9 Documentation

Details and Options Details and Options

BSplineFunction[...][u] gives the point on a B-spline curve corresponding to parameter u.
BSplineFunction[...][u, v, ...] gives the point on a general B-spline manifold corresponding to the parameters u, v, ....
The embedding dimension for the curve represented by BSplineFunction[{pt₁, pt₂, ...}] is given by the length of the lists .
BSplineFunction[array] can handle arrays of any depth, representing manifolds of any dimension.
The dimension of the manifold represented by BSplineFunction[array] is given by ArrayDepth[array]-1. The lengths of the lists that occur at the lowest level in the array define the embedding dimension.
BSplineFunction[array, d] creates a B-spline function of d variables.
The parameters u, v, ... by default run from 0 to 1 over the domain of the curve or other manifold.
The following options can be given:

SplineDegree	Automatic	degree of polynomial basis
SplineKnots	Automatic	knot sequence for spline
SplineWeights	Automatic	control point weights
SplineClosed	False	whether to make the spline closed

By default, BSplineFunction gives cubic splines.
The option setting SplineDegree->d specifies that the underlying polynomial basis should have maximal degree d.
By default, knots are chosen uniformly in parameter space, with additional knots added so that the curve starts at the first control point and ends at the last one.
With an explicit setting for SplineKnots, the degree of the polynomial basis is determined from the number of knots specified and the number of control points.
With the default setting SplineWeights->Automatic, all control points are chosen to have equal weights, corresponding to a polynomial B-spline function.
With the setting SplineClosed->{c₁, c₂, ...}, the boundaries are connected in directions i for which is True.