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Built-in Mathematica Symbol

SplineKnots

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

	Automatic	knots 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.

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

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

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

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

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: