四阶三次均匀B样条函数插值

%%三次B样条均匀插值函数 %输入：扩展型值点矩阵P，型值点数m %输出：插值后得到的矩阵 function inter_path=interpolation(P,m) % C=[1 3 5 7 9 11 13 15 17 19 21;%型值点10 % 1 2.5 4 5 7 4.5 4 6 4 8 4]; % P=[0 1 3 5 7 9 11 13 15 17 19 21 0;%型值点扩展12 % 0 1 2.5 4 5 7 4.5 4 6 4 8 4 0]; %m=11; % n=10; % k=3; V=zeros(m+2,3); A=zeros(m+2,m+2); A(1,1)=6;A(1,2)=-6; A(m+2,m+2)=-6;A(m+2,m+1)=6; for j=2:m+1 A(j,j)=4; A(j,j-1)=1; A(j,j+1)=1; end % A=[6 -6 0 0 0 0 0 0 0 0 0 0; % 1 4 1 0 0 0 0 0 0 0 0 0; % 0 1 4 1 0 0 0 0 0 0 0 0; % 0 0 1 4 1 0 0 0 0 0 0 0; % 0 0 0 1 4 1 0 0 0 0 0 0; % 0 0 0 0 1 4 1 0 0 0 0 0; % 0 0 0 0 0 1 4 1 0 0 0 0; % 0 0 0 0 0 0 1 4 1 0 0 0; % 0 0 0 0 0 0 0 1 4 1 0 0; % 0 0 0 0 0 0 0 0 1 4 1 0; % 0 0 0 0 0 0 0 0 0 1 4 1; % 0 0 0 0 0 0 0 0 0 0 6 -6]; B=[1 4 1 0;-3 0 3 0;3 -6 3 0;-1 3 -3 1]; V=inv(A)*(6*P)'; j=1; for i=1:1:m-1 for u=0:0.001:1 theta_i=1/6*[1 u u*u u*u*u]*B*[V(i,:);V(i+1,:);V(i+2,:);V(i+3,:)]; inter_path(j,1)=theta_i(1,1); inter_path(j,2)=theta_i(1,2); inter_path(j,3)=theta_i(1,3); j=j+1; end end %plot(inter_path(:,1),inter_path(:,2));