Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Data Manipulation > Numerical Data > Curve Fitting & Approximate Functions > Splines > SplineKnots >
Mathematica > Data Manipulation > Statistical Data Analysis > Curve Fitting & Approximate Functions > Splines > SplineKnots >
Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Curve Fitting & Approximate Functions > Splines > SplineKnots >
BUILT-IN MATHEMATICA SYMBOLSee Also »|More About »

SplineKnots

SplineKnots
is an option for B-spline functions and graphics primitives that specifies the positions of knots.
MORE INFORMATION
  • 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.
EXAMPLESCLOSE ALL
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:
SplineKnots->Automatic generates knots in such a way that the curve is smooth overall:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=
 
By repeating knots, one can decrease the smoothness of the curve:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=
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:
New in 7
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF