Spline Toolbox™

Provide knot averages

Syntax

• tstar = aveknt(t,k)
  

Description

tstar = aveknt(t,k) returns the averages of successive k-1 knots, i.e., the sites

which are recommended as good interpolation site choices when interpolating from splines of order k with knot sequence .

Examples

aveknt([1 2 3 3 3],3) returns the vector [2.5000 3.0000], while aveknt([1 2 3],3) returns the empty vector.

With k and the strictly increasing sequence breaks given, the statements

• t = augknt(breaks,k); x = aveknt(t);
  sp = spapi(t,x,sin(x));
  

provide a spline interpolant to the sine function on the interval [breaks(1)..breaks(end)].

For sp the B-form of a scalar-valued univariate spline function, and with tstar and a computed as

• tstar = aveknt(fnbrk(sp,'knots'),fnbrk(sp,'order'));
  a = fnbrk(sp,'coefs');
  

the points constitute the control points of the spline, i.e., the vertices of the spline's control polygon.

See Also

aptknt, chbpnt, optknt

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