This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

BSplineFunction

 BSplineFunction represents a B-spline function for a curve defined by the control points . BSplineFunction[array]represents a B-spline function for a surface or high-dimensional manifold.
• 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 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 TensorRank[array]-1. The lengths of the lists that occur at the lowest level in the array define the embedding dimension.
• 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
• 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, all control points are chosen to have equal weights, corresponding to a polynomial B-spline function.
• With the setting SplineClosed, the boundaries are connected in directions i for which is True.
Construct a B-spline curve using a list of control points:
Apply the function to find a point on the curve:
Plot the B-spline curve with the control points:
Construct a B-spline surface closed in the u-direction:
Show the surface with the control points:
Construct a B-spline curve using a list of control points:
 Out[2]=
Apply the function to find a point on the curve:
 Out[3]=
Plot the B-spline curve with the control points:
 Out[4]=

Construct a B-spline surface closed in the u-direction:
 Out[2]=
Show the surface with the control points:
 Out[3]=
 Scope   (4)
Create a vector-valued function of dimension 2:
Create a vector-valued function of dimension 3:
Generate a two-variable function:
Generate a three-variable function:
SparseArray can be used with BSplineFunction:
 Options   (2)
Make line segments:
Make a quadratic B-spline curve:
Degrees can be specified in each parametric direction separately:
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