%
% MATLAB for DUMMIES 10-11
% Exercice 4
%
%

function matlab4()
clear all; close all;

p = 2;
c = 1/sqrt(2);
T =  [0 0 0 1 1 2 2 3 3 4 4 4];
X = [1  1  0 -1 -1 -1  0  1  1]; 
Y = [0  1  1  1  0 -1 -1 -1  0];
W = [1 c 1 c 1 c 1 c 1 ];
L = computeLength(T,X,Y,W,p)

T =  [0 0 0 1 2 3 4 5 6 7 8 8 8];
X = [1  1  0 -6 -2 -1  7  1  1   -4]; 
Y = [0  1  4  1  4 -2 -2 -1  8 -6];
W = [1 1 1 1 3 1 2 1 1 4];
L = computeLength(T,X,Y,W,p)

nt = length(T) - 1;
dt = 0.005;
t = [T(p+1):dt:T(nt-p+1)];
for i=0:nt-p-1
  B(i+1,:) = b(t,T,i,p);
end

w = W * B;
x =(W .* X) * B ./ w;
y =(W .* Y) * B ./ w;

plot(x,y,'-r'); hold on;
plot(X,Y,'.r','MarkerSize',25);
axis equal
axis off


end



function u = b(t,T,j,p)
i = j+1;
if p==0
    u = (t>= T(i) & t < T(i+p+1)); return 
end

u = zeros(size(t));
if T(i) ~= T(i+p)
    u = u + ((t-T(i)) ./ (T(i+p) -T(i))) .* b(t,T,j,p-1);
end
if T(i+1) ~= T(i+p+1)
    u = u + ((T(i+p+1)-t) ./ (T(i+p+1) -T(i+1))) .* b(t,T,j+1,p-1);
end
end


function u = dbdt(t,T,j,p)
i = j+1;

u = zeros(size(t));
if T(i) ~= T(i+p)
    u = u + (p / (T(i+p) -T(i))) * b(t,T,j,p-1);
end
if T(i+1) ~= T(i+p+1)
    u = u - (p / (T(i+p+1) -T(i+1))) * b(t,T,j+1,p-1);
end
end