SOLUTIONS

Mathematica
>
Data Manipulation
>
Numerical Data
>
Curve Fitting & Approximate Functions
>
Splines
>
BSplineFunction
BUILTIN MATHEMATICA SYMBOL
BSplineFunction
BSplineFunction[{pt_{1}, pt_{2}, ...}]
represents a Bspline function for a curve defined by the control points .
BSplineFunction[array]
represents a Bspline function for a surface or highdimensional manifold.
Details and OptionsDetails and Options
 BSplineFunction[...][u] gives the point on a Bspline curve corresponding to parameter u.
 BSplineFunction[...][u, v, ...] gives the point on a general Bspline manifold corresponding to the parameters u, v, ....
 The embedding dimension for the curve represented by BSplineFunction[{pt_{1}, pt_{2}, ...}] 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 Bspline 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 Bspline function.
 With the setting SplineClosed>{c_{1}, c_{2}, ...}, the boundaries are connected in directions i for which is True.
ExamplesExamplesopen allclose all
Basic Examples (2)Basic Examples (2)
Construct a Bspline curve using a list of control points:
In[1]:= 
In[2]:= 
Out[2]= 
Apply the function to find a point on the curve:
In[3]:= 
Out[3]= 
Plot the Bspline curve with the control points:
In[4]:= 
Out[4]= 
Construct a Bspline surface closed in the udirection:
In[1]:= 
In[2]:= 
Out[2]= 
Show the surface with the control points:
In[3]:= 
Out[3]= 
New in 7
Mathematica 9 is now available!
New to Mathematica?
Find your learning path »
Have a question?
Ask support »