BSplineFunction

• 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 pt_i.

• 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 TensorRank[array]-1. The lengths of the lists that occur at the lowest level in 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:

• 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 c_i is True.