cscvn of a function, coefficients and breaks

Hey all together,

I have another question concerning the cscvn function. When I create a spline for a function with cscvn

yy =  cscvn(xges)

and take a look at yy.coefs and yy.breaks

      form: 'pp'
    breaks: [1x25 double]
     coefs: [48x4 double]
    pieces: 24
     order: 4
       dim: 2

then I have nearly twice as much coefs as breaks. How is this possible and what does that mean? How can I create the piecewise polynomial functions out of my coefs? At the end I want to calculate the curvature of the function, but first I have to understand what this coefs mean, and how I can create the piecewise polynoms.

Thank you in advance,

David

[Lucie]

Hello, I am facing the same issue. Did you receive an answer regarding the meaning of the coefficients?

[Mathieu NOE]

everything is in the doc

Constructing and Working with ppform Splines - MATLAB & Simulink - MathWorks France

Answer 1

[Bruno Luong]

This is how to use pp

m = 2;
n = 5; % 25 in the original question
points = rand(m,n);

pp = cscvn(points)

pp = struct with fields:
      form: 'pp'
    breaks: [0 0.8735 1.5529 2.4191 3.2527]
     coefs: [8×4 double]
    pieces: 4
     order: 4
       dim: 2

m = pp.dim;
p = pp.pieces;

% https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/INT-APP/PARA-centripetal.html
%D = diff(points,1,2);
%d = sqrt(sqrt(sum(D.^2,1)));
%t = cumsum([0 d]); % Eugene Lee's, equal to pp.breaks, see https://www.mathworks.com/help/curvefit/cscvn.html
t = pp.breaks;

ni = 200;
ti = linspace(t(1),t(end), ni);
loc = discretize(ti, t);
x = zeros(length(ti), m);
coefs = reshape(pp.coefs, m, p, []);
for k=1:p
    ink = loc == k;
    tik = ti(ink);
    dti = tik - t(k);
    for d=1:m
        P = coefs(d, k, :);
        x(ink,d) = polyval(P(:), dti);
    end
end
close all
hold on
if m == 2
    plot(points(1,:),points(2,:),'or'),
    plot(x(:,1), x(:,2),'b.')
elseif m == 3
    plot3(points(1,:),points(2,:),points(3,:),'or'),
    plot3(x(:,1), x(:,2), x(:,3), 'b.')
else
    warning('plotting not supported')
end