B样条和贝塞尔曲线曲面的拼接.docx

实验二 曲线曲面的拼接贝塞尔曲线的拼接P=-1 2 3.5 4 4.5 6 7;7 5 6 6.5 7 3 9;2 6 4 4.5 5 11 9;plot3(P(1,1:4),P(2,1:4),P(3,1:4),o)hold onplot3(P(1,4:7),P(2,4:7),P(3,4:7),+);hold onB=-1 3 -3 1;3 -6 3 0;-3 3 0 0;1 0 0 0;for t=0:0.05:1 T=t3 t2 t 1; P1=T*B*P(1,1:4); P2=T*B*P(2,1:4); P3=T*B*P(3,1:4); plot3(P1,P2,P3,r.) hold on Q1=T*B*P(1,4:7); Q2=T*B*P(2,4:7); Q3=T*B*P(3,4:7); plot3(Q1,Q2,Q3,b*)endtitle(贝塞尔曲线的拼接);xlabel(x);ylabel(y);zlabel(z);B样条曲线的拼接P=1 2 3 4 5;1.5 7 6 6.5 7;3 1.5 3.5 5.5 4.5;plot3(P(1,1:4),P(2,1:4),P(3,1:4),o)hold onplot3(P(1,2:5),P(2,2:5),P(3,2:5),+)hold onB=-1 3 -3 1;3 -6 3 0;-3 0 3 0;1 4 1 0;for t=0:0.05:1 T=t3 t2 t 1; P1=1/6*T*B*P(1,1:4); P2=1/6*T*B*P(2,1:4); P3=1/6*T*B*P(3,1:4); plot3(P1,P2,P3,r.) hold on Q1=1/6*T*B*P(1,2:5); Q2=1/6*T*B*P(2,2:5); Q3=1/6*T*B*P(3,2:5); plot3(Q1,Q2,Q3,b*);endtitle(B样条曲线的拼接);xlabel(x);ylabel(y);zlabel(z);双三次贝塞尔曲面的拼接X1,Y1=meshgrid(0:1/3:1,1:1/3:2);X2,Y2=meshgrid(1:1/3:2,0:1/3:1);Z1=sin(X1+Y1).3;B(:,:,1)=X1; B(:,:,2)=Y1; B(:,:,3)=Z1;X,Y=meshgrid(0:1/3:1);Z=sin(X+Y).3;C(:,:,1)=X; C(:,:,2)=Y; C(:,:,3)=Z;M=-1 3 -3 1;3 -6 3 0;-3 3 0 0;1 0 0 0;for i=1:3 Q(:,:,i)=M*B(:,:,i)*M; P(:,:,i)=M*C(:,:,i)*M; for u=0:1:10 for w=0:1:10 u3=(u/10)3; u2=(u/10)2; u1=(u/10); w3=(w/10)3; w2=(w/10)2; w1=(w/10); S1(u+1,w+1,i)=u3,u2,u1 1*Q(:,:,i)*w3,w2,w1,1; S2(u+1,w+1,i)=u3,u2,u1 1*P(:,:,i)*w3,w2,w1,1; end endendplot3(B(:,:,1),B(:,:,2),B(:,:,3),o);hold onplot3(C(:,:,1),C(:,:,2),C(:,:,3),.);hold onplot3(X1,Y1,Z1)hold on plot3(Y2,X2,Z1)hold onplot3(X,Y,Z)hold on plot3(Y,X,Z)surf(S1(:,:,1),S1(:,:,2),S1(:,:,3)surf(S2(:,:,1),S2(:,:,2),S2(:,:,3)title(双三次贝塞尔曲面的拼接);xlabel(x);ylabel(y);zlabel(z);双三次B样条曲面的拼接X1,Y1=meshgrid(0:1/3:1,1/3:1/3:4/3);X2,Y2=meshgrid(1/3:1/3:4/3,0:1/3:1);Z1=sin(X1+Y1);B(:,:,1)=X1;B(:,:,2)=Y1;B(:,:,3)=Z1;X,Y=meshgrid(0:1/3:1);Z=sin(X+Y);C(:,:,1)=X;C(:,:,2)=Y;C(:,:,3)=Z;M=-1 3 -3 1;3 -6 3 0;-3 0 3 0;1 4 1 0/6;for i=1:3 Q(:,:,i)=M*B(:,:,i)*M; P(:,:,i)=M*C(:,:,i)*M; for u=0:1:10 for w=0:1:10 u3=(u/10)3; u2=(u/10)2; u1=(u/10); w3=(w/10)3; w2=(w/10)2; w1=(w/10); S1(u+1,w+1,i)=u3,u2,u1 1*Q(:,:,i)*w3,w2,w1,1; S2(u+1,w+1,i)=u3,u2,u1 1*P(:,:,i)*w3,w2,w1,1; end endendplot3(B(:,:,1),B(:,:,2),B(:,:,3),.);hold onplot3(X1,Y1,Z1)hold on plot3(Y2,X2,Z1)plot3(C(:,:,1),C(:,:,2),C(:,:,3),o);hold onplot3(X,Y,Z)hold on plot3(Y,X,Z)