clear all
P = [1 0;1 1;0 1];
w = [1 1 1];
w2 = [1 1 0.5];

t=[0:0.01:1];
%hyperbole
x=(1-(t.^2));
y=t;
%plot(x,y,'Color',"blue");

hold on
for i = 1:1:length(P)
    plot(P(i,1),P(i,2),'O');
end
hold off
bases_rationelles(P,w,100,'O');
%bases_rationelles(P,w2,100,'.');






function nb = Binomial(n,k)
    nb = factorial(n)/(factorial(k)*factorial(n-k));
end

%exists function "bernstein" which does almost the same thing
function polynome = Bernstein(i,n,t)

    for j = 1:1:length(t)
        polynome(1,j) = (Binomial(n,i))*((t(1,j))^i)*((1-(t(1,j)))^(n-i));
    end
end

function polynome = Rational(i,n,w,t)
    tmp = zeros(1,length(t));
    for j = 1:1:n
        tmp = tmp + w(j) * Bernstein(j-1,n-1,t);
    end
    polynome = (w(i)*Bernstein(i-1,n-1,t))./tmp;
end

function courbe = bases_rationelles(P,w,nb,forme)
    t = linspace(0,1,nb);
    n = length(P);
    courbeX = zeros(1,length(t));
    courbeY = zeros(1,length(t));

    for i = 1:1:n
        courbeX = courbeX + (P(i,1) * Rational(i,n,w,t));
        courbeY = courbeY + (P(i,2) * Rational(i,n,w,t));
    end
    courbe = [courbeX;courbeY];
    hold on
    for i = 1:1:length(courbe)
        plot(courbe(1,i),courbe(2,i),forme);
    end
    hold off
end