非均匀B样条拟合MATLAB程序

直接上代码，多的不再说了。

1、写一个Base函数

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);

2、B样条程序

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

参考文章

3次非均匀B样条拟合程序