This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# SplineKnots

 SplineKnots is an option for B-spline functions and graphics primitives that specifies the positions of knots.
• The following settings can be given:
 Automatic knots 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 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 generates knots in such a way that the curve is smooth overall:
By repeating knots, one can decrease the smoothness of the curve:
SplineKnots generates knots in such a way that the curve is smooth overall:
 Out[2]=

By repeating knots, one can decrease the smoothness of the curve:
 Out[2]=
 Scope   (1)
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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