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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[2345234523452345;2222333344445555;1231346275629134];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)];
2、%将控制顶点的y坐标放到维数为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holdonsymsusymswP_uwx=[0];P_uwy=[0];P_uwz=[0];fori=1:1:4;forj=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/
3、((u4-u3)*(u4-u2)*(u4-u1));B2=((u3-u1+u)*(u4-u3-u)^2)/((u4-u3)*(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-
4、u3)*(u5-u2)*(u4-u3))+((u6-u3-u)*u^2)/((u6-u3)*(u5-u3)*(u4-u3));B4=u^3/((u6-u3)*(u5-u3)*(u4-u3));B=[B1;B2;B3;B4];%三次非均匀B样条基函数矩阵（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
5、)^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))+((w5-w3-w)*w*(w3-w2+w))/((w5-w3)*(w5-w2)*(w4-w3))+((w6-w3-w)*w^2)/((w6-w3)*(w
6、5-w3)*(w4-w3));C4=w^3/((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
7、_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;form=0:1/10:1;forn=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,
8、w},{m,n});X1(i,j)=X;%将X的值放入11维的方阵Y1(i,j)=Y;Z1(i,j)=Z;j=j+1;endj=1;i=i+1;endgrid;surf(X1,Y1,Z1);holdon输出结果：图1.三次非均匀曲面图
