How to build polynomial with cscvn function coeffs?

Hello, could you tell please how to restore the polynomial of a spline segment obtained by the cscvn function? I took the code from the help and now I want to get polynomials, how can I compose them correctly? Thank you

npts = 13;
t = linspace(0,8*pi,npts);
z = linspace(-1,1,npts);
omz = sqrt(1-z.^2);
xyz = [cos(t).*omz; sin(t).*omz; z];
plot3(xyz(1,:),xyz(2,:),xyz(3,:),'ro','LineWidth',2);
text(xyz(1,:),xyz(2,:),xyz(3,:),[repmat('  ',npts,1), num2str((1:npts)')]);
ax = gca;
ax.XTick = [];
ax.YTick = [];
ax.ZTick = [];
box on;
hold on;
fnplt(cscvn(xyz(:,[1:end 1])),'r',2);
s = cscvn(xyz(:,[1:end 1])),'r',2;

%----------------------------------------------------------

figure;
t1 = s.breaks(1):0.02:s.breaks(2);
x1 = s.coefs(1, 1) * t1.^3 + s.coefs(1, 2) * t1.^2 + s.coefs(1, 3)* t1 + s.coefs(1, 4);
y1 = s.coefs(2, 1) * t1.^3 + s.coefs(2, 2) * t1.^2 + s.coefs(2, 3) * t1 + s.coefs(2, 4);
z1 = s.coefs(3, 1) * t1.^3 + s.coefs(3, 2) * t1.^2 + s.coefs(3, 3) * t1 + s.coefs(3, 4);

t2 = s.breaks(2):0.02:s.breaks(3);
x2 = s.coefs(4, 1) * t2.^3	+ s.coefs(4, 2) * t2.^2	+ s.coefs(4, 3) * t2 + s.coefs(4, 4);
y2 = s.coefs(5, 1) * t2.^3	+ s.coefs(5, 2) * t2.^2	+ s.coefs(5, 3) * t2 + s.coefs(5, 4);
z2 = s.coefs(6, 1) * t2.^3	+ s.coefs(6, 2) * t2.^2 + s.coefs(6, 3) * t2 + s.coefs(6, 4);

t3 = s.breaks(3):0.02:s.breaks(4);
x3 = s.coefs(7, 1) * t3.^3 + s.coefs(7, 2) * t3.^2 + s.coefs(7, 3) * t3 + s.coefs(7, 4);
y3 = s.coefs(8, 1) * t3.^3 + s.coefs(8, 2) * t3.^2 + s.coefs(8, 3) * t3 + s.coefs(8, 4);
z3 = s.coefs(9, 1) * t3.^3 + s.coefs(9, 2) * t3.^2 + s.coefs(9, 3) * t3 + s.coefs(9, 4);

t4 = s.breaks(4):0.02:s.breaks(5);
x4 = s.coefs(10, 1) * t4.^3 + s.coefs(10, 2) * t4.^2 + s.coefs(10, 3) * t4 + s.coefs(10, 4);
y4 = s.coefs(11, 1) * t4.^3 + s.coefs(11, 2) * t4.^2 + s.coefs(11, 3) * t4 + s.coefs(11, 4);
z4 = s.coefs(12, 1) * t4.^3 + s.coefs(12, 2) * t4.^2 + s.coefs(12, 3) * t4 + s.coefs(12, 4);

plot3(x1, y1, z1, "Color", 'r', 'LineWidth', 4);
box on;
hold on;
plot3(x2, y2, z2, "Color", 'b', 'LineWidth', 4);
plot3(x3, y3, z3, "Color", 'g', 'LineWidth', 4);
plot3(x4, y4, z4, "Color", 'b', 'LineWidth', 4);

hold off;

Answer 1

[Steven Lord]

If you want to evaluate the spline, don't try to make polynomials. Just use the output argument from your call to cscvn with the ppval function.

points=[0 1 1 0 -1 -1 0 0; 0 0 1 2 1 0 -1 -2]; 
S = cscvn(points);
% Plot the spline
fnplt(S);

% Evaluate the spline at certain points and plot them
x = 0:0.5:7;
values = ppval(S, x);
hold on
plot(values(1, :), values(2, :), 'o')

If you are required to create polynomials, remember that the output of cscvn is in ppform. See the definition of ppform on that page. You need to subtract off the breaks before evaluating your polynomials. But I wouldn't make the polynomials myself, I'd just use polyval as shown on that documentation page.

[Kennedy]

Thanks for answer. I am looking for exactly polynomial form because I need to build those splines in other program.