function result = Bbase(i,k,u,t)

%第i段k次B样条基,Deboor递推递归算法

%t为变量,u(i)<=t<u(i+),k=0时result=;

if(k==)

    if(u(i)<=t && t<u(i+))%注意1=u(i)<=t<u(i+)=1时的情况,这里要用t<=u(i+);

        result=;

        return;

    else

        result=;

        return;

    end

else

    if(u(i+k)-u(i)==)

        alpha=;

    else

        alpha=(t-u(i))/(u(i+k)-u(i));

    end

    if(u(i+k+)-u(i+)==)

         beta=;

    else

        beta=(u(i+k+)-t)/(u(i+k+)-u(i+));

    end

end

result=alpha*Bbase(i,k-,u,t)+beta*Bbase(i+,k-,u,t);

%------------------非均匀B样条拟合MATLAB程序-----------------

clear

k=;

x=load('data.txt');

[n,m]=size(x);

%-----------弦长参数化--------------------------------------

u(k+n)=;

for i=:n-

 u(k+i+)=u(k+i)+sqrt((x(i+,)-x(i,))^+(x(i+,)-x(i,))^);

end;

L=u(n+k);

for i=:n

u(k+i)=u(k+i)/L;

end;

for i=:

u(k+i+n)=;

end

%控制多边线

plot(x(:,),x(:,),'o');

hold on

%------------反求n+2个控制点--------------------

%首位重节点v1=v2

%首位与控制多边形相切

A=zeros(n+);

A(,)=;A(,)=-;

A(,)=;

A(n+,n+)=-;A(n+,n+)=;

A(n+,n+)=;

for i=:n

  for j=:

    A(i,i+j-)=Base(i+j-,k,u,u(i+));

   end

end

%e:方程右边.

e=;

for i=:m

    e(n+,i)=;

end

for i=:n

    e(i+,:)=x(i,:);

end

%求出控制点d

d=inv(A)*e;

plot(d(:,),d(:,),'g');

hold on

%------------插值并作出样条曲线-----------------

x=;y=;down=;

for j=:(n-)

    uu=(u(j+)):0.0005:u(j+);

    for kk=:length(uu)

       down=down+;

        x(down)=d(j,)*Base(j,,u,uu(kk))+d(j+,)*Base(j+,,u,uu(kk))+d(j+,)*Base(j+,,u,uu(kk))+d(j+,)*Base(j+,,u,uu(kk));

        y(down)=d(j,)*Base(j,,u,uu(kk))+d(j+,)*Base(j+,,u,uu(kk))+d(j+,)*Base(j+,,u,uu(kk))+d(j+,)*Base(j+,,u,uu(kk));

    end

end

axis('equal');

plot(x,y,'red');

xlabel('x');ylabel('y');

grid on