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SplineKnots

SplineKnots
is an option for B-spline functions and graphics primitives that specifies the positions of knots.
  • The following settings can be given:
Automaticknots arranged uniformly (with clamping)
{u1,u2,...}knots at positions , , ...
{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, 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 yields knots that are uniform, but do not necessarily span from the first control point to the last.
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:
SplineKnots->Automatic generates knots in such a way that the curve is smooth overall:
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By repeating knots, one can decrease the smoothness of the curve:
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Uniform knots that do not go through the end points:
Unclamped knots combined with SplineClosed will make a uniform periodic B-spline curve:
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:
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