SplineKnots

SplineKnots

is an option for B-spline functions and graphics primitives that specifies the positions of knots.

Details

  • The following settings can be given:
  • Automaticknots arranged uniformly (with clamping)
    {u1,u2,}knots at positions u1, u2,
    {list1,list2,}knot positions in several dimensions
    "Clamped"uniform with clamping
    "Unclamped"uniform without clamping
  • Knots indicate breakpoints in the piecewise parametrization of B-spline functions.
  • For a B-spline function with n control points in a particular dimension and a polynomial basis of degree d, n+d+1 knots must be specified.
  • SplineKnots->Automatic specifies that knots should be chosen uniformly, but with additional knots added so that the function spans from the first control point to the last.
  • SplineKnots->"Unclamped" yields knots that are uniform, but do not necessarily span from the first control point to the last.

Examples

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Basic Examples  (2)

SplineKnots->Automatic generates knots in such a way that the curve is smooth overall:

By repeating knots, one can decrease the smoothness of the curve:

Scope  (1)

Uniform knots that do not go through the end points:

Generalizations & Extensions  (1)

Unclamped knots combined with SplineClosed will make a uniform periodic B-spline curve:

Properties & Relations  (2)

Using clamped knots will force interpolation of the first and last control points:

Explicit knots corresponding to clamped knots:

Using unclamped knots, typically used for closed curves:

Explicit knots corresponding to unclamped knots:

Introduced in 2008
 (7.0)