B样条的学习

clc;clear;close;

Point = [9.036145, 21.084337, 37.607573, 51.893287, 61.187608;
    51.779661, 70.084746, 50.254237, 69.745763, 49.576271];
n=size(Point,2)-1;

p=4;

NodeVector = linspace(0, 1, n+p+2); % 均匀B样条的节点矢量
Base = zeros(n+1, 1);

 plot(Point(1, 1:n+1), Point(2, 1:n+1),...
                        'o','LineWidth',1,...
                        'MarkerEdgeColor','k',...
                        'MarkerFaceColor','g',...
                        'MarkerSize',6);
        line(Point(1, 1:n+1), Point(2, 1:n+1));
        
for u = p/(n+p+1) :0.001: (n+1)/(n+p+1)
  
    for k=1:n+p+1
       if u>=NodeVector(k) && u<NodeVector(k+1)
            i=k;
       end
    end
    
    B= MyBaseFun(i, p , u, NodeVector);
    Base(1:size(B,2),1)=B';
    C = Point * Base;
    line(C(1,1), C(2,1), 'Marker','.','LineStyle','-', 'Color',[.3 .6 .9]);
end

 

function [ B ,F] = MyBaseFun(k,p,u,U)%%进入这个条件的默认条件，是u是属于该区间的，且k表示区间在第几个序号，从1开始算的，p表示阶次，u是自变量，U是节点
%%B的存储方式是按基函数的序号进行存储的，在那基础上加上1的
if p==0
   if U(k)<=u&&u<U(k+1)
       B(k)=1;
       return;
   else
       B(k)=0;
       return;
   end
end
    B(k)=1;
    for i=1:p
        B(k-i)=((U(i+1+k-i)-u)/(U(i+1+k-i)-U(1+k-i)))*B(k-i+1);
        D(k-i,i)= B(k-i);
        %%B(k-i)=((U(k+1)-u)/(U(k+1)-U(1+k-i)))*B(k-i+1);
        for j=k-i+1:k-1
            B(j)=((u-U(j))/(U(j+i)-U(j)))*B(j)+((U(i+1+j)-u)/(U(i+1+j)-U(1+j)))*B(j+1);
            D(j,i)= B(j);
        end
        
         B(k)=((u-U(k))/(U(i+k)-U(k)))*B(k);
         D(k,i)= B(k);
    end
    
    if size(B,2)>size(U,2)-p-1
       B=B(size(B,2)-(size(U,2)-p-1)+1:size(B,2));
    end
    
    F(:,2:size(D,2)+1)=D
    F(k,1)=1;
end