三次非均匀B样条曲面的绘制

1、%三次非均匀B样条曲面的绘制clcclfclearA=input(请输入控制点：)%16个控制顶点要求以列向量表示点的坐标2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5;2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5;1 2 3 1 3 4 6 2 7 5 6 2 9 1 3 4;n=input(请输入所需绘制B样条曲线的次数：);Vx=A(1,1:4);A(1,5:8);A(1,9:12);A(1,13:16);%将控制顶点的x坐标放到维数为4的方阵中Vy=A(2,1:4);A(2,5:8);A(2,9:12);A(2,13:16);%将控制顶点的y坐标放到维

2、数为4的方阵中Vz=A(3,1:4);A(3,5:8);A(3,9:12);A(3,13:16);%将控制顶点的z坐标放到维数为4的方阵中plot3(A(1,:),A(2,:),A(3,:),o);%输出控制顶点hold onsyms usyms w P_uwx=0;P_uwy=0;P_uwz=0;for i=1:1:4; for j=1:1:4u0=0;u1=0;u2=0;u3=0;u4=1;u5=1;u6=1;u7=1;%给定4个控制顶点所取的节点矢量B1=(u4-u3-u)3/(u4-u3)*(u4-u2)*(u4-u1);B2=(u3-u1+u)*(u4-u3-u)2)/(u4-u3)

3、*(u4-u2)*(u4-u1)+(u5-u3-u)*(u4-u3-u)*(u3-u2+u)/(u5-u2)*(u4-u3)*(u4-u2)+(u5-u3-u)2*u)/(u5-u3)*(u5-u2)*(u4-u2);B3=(u4-u3-u)*(u3-u2+u)2)/(u5-u2)*(u4-u3)*(u4-u2)+(u5-u3-u)*u*(u3-u2+u)/(u5-u3)*(u5-u2)*(u4-u3)+(u6-u3-u)*u2)/(u6-u3)*(u5-u3)*(u4-u3);B4=u3/(u6-u3)*(u5-u3)*(u4-u3);B=B1;B2;B3;B4;%三次非均匀B样条基函数矩阵

4、（自由曲线曲面造型技术139页）w0=0;w1=0;w2=0;w3=0;w4=1;w5=1;w6=1;w7=1;%给定4个控制顶点所取的节点矢量C1=(w4-w3-w)3/(w4-w3)*(w4-w2)*(w4-w1);C2=(w3-w1+w)*(w4-w3-w)2)/(w4-w3)*(w4-w2)*(w4-w1)+(w5-w3-w)*(w4-w3-w)*(w3-w2+w)/(w5-w2)*(w4-w3)*(w4-w2)+(w5-w3-w)2*w)/(w5-w3)*(w5-w2)*(w4-w2);C3=(w4-w3-w)*(w3-w2+w)2)/(w5-w2)*(w4-w3)*(w4-w2)+

5、(w5-w3-w)*w*(w3-w2+w)/(w5-w3)*(w5-w2)*(w4-w3)+(w6-w3-w)*w2)/(w6-w3)*(w5-w3)*(w4-w3);C4=w3/(w6-w3)*(w5-w3)*(w4-w3);C=C1;C2;C3;C4;%三次非均匀B样条基函数矩阵Puwx=Vx(i,j)* B(i)*C(j);%控制顶点的x坐标与两个方向的基函数做乘积Puwy=Vy(i,j)* B(i)*C(j);Puwz=Vz(i,j)* B(i)*C(j);P_uwx=P_uwx+Puwx;%得到曲面的x坐表关于u,w的表达式（自由曲线曲面造型技术146页）P_uwy=P_uwy+Puwy;%得到曲面的y坐表关于u,w的表达式P_uwz=P_uwz+Puwz;%得到曲面的z坐表关于u,w的表达式 endend%曲面的绘制X1=zeros(11);Y1=zeros(11);Z1=zeros(11);%形成11维0矩阵i=1;j=1;for m=0:1/10:1; for n=0:1/10:1;X=subs(P_uwx,u,w,m,n);%P=subs(P,u,w,m,n)就是把P表达式中所有u,w都用具体的m,n值代替Y=subs(P_uwy,u,w,m,n);Z=subs(P_uwz,u,w,m,n);X1(i,j)=X;%将X的值放入1