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BSplineFunction

BSplineFunction[{pt1, pt2, ...}]
represents a B-spline function for a curve defined by the control points pti;
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[{pt1, pt2, ...}] is given by the length of the lists pti.
  • 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.
  • 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:
SplineDegreeAutomaticdegree of polynomial basis
SplineKnotsAutomaticknot sequence for spline
SplineWeightsAutomaticcontrol point weights
SplineClosedFalsewhether 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->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 ci 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 u-direction:
Show the surface with the control points:
Construct a B-spline curve using a list of control points:
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Apply the function to find a point on the curve:
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Plot the B-spline curve with the control points:
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Construct a B-spline surface closed in u-direction:
In[1]:=
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In[2]:=
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Out[2]=
Show the surface with the control points:
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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:
Make line segments:
Make a quadratic B-spline curve:
Degrees can be specified in each parametric direction separately:
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