I try to demonstrate the use of splines in Bform. Nevertheless I am not sure about Bspline implementation in Matlab. In summary, for me there are 3 points:
- a spline looks like a hat-function, but smooth "spline".
- A family of splines tends to show maximum of weight sliding right as index of spline increases.
- multiplicity of end knots affect the slope and other derivatives, until, when a knot has multiplicity=order-1, to start at 1.0
This was the result below of "B-form" knots examples in Mathworks. Does anybody have experience with a ppform or break form ?
(Ich kann Deutsch lesen, aber mein Schreib ist eher begrenzt)
Code:
figure(2);
t = [.1 .4 .5 .80.9];
a = 1;
fnplt(spmak(t,a),2.5);
sp1=fnbrk(spmak(t,a),1:2)
t = [.1 .1 .4 .5 .8];
a = 1;
hold on; fnplt(spmak(t,a),2.5);
t = [.1 .1 .1 .4 .5];
a = 1;
hold on; fnplt(spmak(t,a),2.5);
t = [.1 .1 .1 .1 .4];
a = 1;
hold on; fnplt(spmak(t,a),2.5);
t = [0.40.50.80.90.9];
a = 1;
hold on; fnplt(spmak(t,a),2.5);
t = [0.50.80.90.90.9];
a = 1;
hold on; fnplt(spmak(t,a),2.5);
t = [0.80.90.90.90.9];
a = 1;
hold on; fnplt(spmak(t,a),2.5);
When using interp1 with option 'spline' (not sure whether that's a B-spline), I notice and dislike a tendency towards overshooting and thus introducing artificial minima and maxima. Thus, I often prefer 'makima' as it looks quite smooth (e.g., smoother than 'pchip') but avoids what I just wrote.
MATLAB Answers is a larger forum and English is the main language there, so you may be better served posting English-language questions there.
Best wishes,
Harald
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