Matlab里的直线、曲线、平面、曲面相交问题.doc

转自工程计算可视化与MATLAB实现尚涛等编著 武汉大学出版社（1）两直线相交function X,Y=pll(X1,Y1,X2,Y2)% 直线相交求交点A1=Y1(1)-Y1(2);B1=X1(2)-X1(1);C1=Y1(2)*X1(1)-Y1(1)*X1(2);A2=Y2(1)-Y2(2);B2=X2(2)-X2(1);C2=Y2(2)*X2(1)-Y2(1)*X2(2);D=det(A1,B1;A2,B2);X=det(-C1 B1;-C2 B2)/D;Y=det(A1 -C1;A2,-C2)/D;调用格式：x1=1 5;y1=1 5;x2=1 5;y2=5,1;x,y=pll(x1,y1,x2,y2);plot(x1,y1,r);hold onplot(x2,y2,b);plot(x,y,ko);（2）直线与多条直线相交xi=1 2 3 4 5;yi=2 6 3 6 1;plot(xi,yi);hold onx1=1 5;y1=4 5;line(x1,y1);x=zeros(size(xi);y=x;for i=1:5-1x2=xi(i i+1);y2=yi(i i+1);x,y=pll(x1,y1,x2,y2);plot(x,y,ro)end（3）直线与曲线相交x=-8:0.1:8;y=x;X,Y=meshgrid(x,y);R=sqrt(X.2+Y.2)+eps;Z=sin(R)./R;contour(Z,3);hold onc=contour(Z,3);x=0 360;y=0 400;y=(y(2)-y(1)/(x(2)-x(1)*(x-x(1)+y(1);z=0 0;line(x,y,z);c=c;X=c(:,1);Y=c(:,2);r0=abs(Y-(y(2)-y(1)/(x(2)-x(1)*(X-x(1)+y(1)=.93;zz=0;yy=r0.*Y;xx=r0.*X;plot(xx(r0=0),yy(r0=0),r)（4）曲线与曲线相交x=0:pi/400:2*pi;x=x;y1=sin(pi*x);y2=cos(pi*x);plot(x,y1,x,y2);hold onr0=abs(y2-sin(pi*x)=0.02;yy=r0.*y1;xx=r0.*x;plot(xx(r0=0),yy(r0=0),r.)（5）直线与曲面相交x=-8:0.3:8;y=x;X,Y=meshgrid(x,y);Z=X.2+Y.2;mesh(X,Y,Z);hold onx=-10 10;y=-10 3;z=30 35;line(x,y,z);r0=(abs(Y-y(1)-(y(2)-y(1)/(x(2)-x(1)*(X-x(1)=0.45)&.(abs(Z-z(1)-(z(2)-z(1)/(x(2)-x(1)*(X-x(1)0.45)&.(abs(Y-y(1)-(y(2)-y(1)/(z(2)-z(1)*(Z-z(1)=0.45);zz=r0.*Z;yy=r0.*Y;xx=r0.*X;plot3(xx(r0=0),yy(r0=0),zz(r0=0),r*);（6）平面与曲面相交x=-8:0.1:8;y=x;X,Y=meshgrid(x,y);Z1=2*ones(size(X);Z2=X.2-Y.2;mesh(X,Y,Z1);hold onmesh(X,Y,Z2);r0=(abs(Z1-Z2)=.65);zz=r0.*Z1;yy=r0.*Y;xx=r0.*X;plot3(xx(r0=0),yy(r0=0),zz(r0=0),k*)clcdisp(观察曲面后，按任意键画交线);pauseclfplot3(xx(r0=0),yy(r0=0),zz(r0=0),k*);%曲面与多个截平面相交y=-10:0.5:10;z=y;Z,Y=meshgrid(z,y);X=Z;X1=0*ones(size(Z);X2=3*ones(size(Z);X3=-3*ones(size(Z);Z4=(X.2-Y.2)/10;mesh(X1,Y,Z);hold onmesh(X2,Y,Z)mesh(X3,Y,Z);mesh(X,Y,Z4);r1=(abs(X1-X)0.05);r2=(abs(X2-X)0.05);r3=(abs(X3-X)0.05);zz1=r1.*Z4;yy1=r1.*Y;xx1=r1.*X;zz2=r2.*Z4;yy2=r1.*Y;xx2=r1.*X;zz3=r3.*Z4;yy3=r1.*Y;xx3=r1.*X;plot3(xx1(r1=0),yy1(r1=0),zz1(r1=0),k*);plot3(xx2(r2=0),yy2(r2=0),zz2(r2=0),k*);plot3(xx3(r3=0),yy3(r3=0),zz3(r3=0),k*);colormap(hsv)clc;disp(观察曲面后，按任意键画交线);hold off（7）平面与曲面相交y=-8:0.4:8;z=y;Z,Y=meshgrid(z,y);X=Z;X1=zeros(size(Z);Z2=zeros(size(Z);Z3=(X.2-Y.2)/10;mesh(X1,Y,Z);hold onmesh(X,Y,Z2);mesh(X,Y,Z3);r1=(abs(X1-X)0.05);r2=(abs(Z3-Z2)0.05);r3=(abs(X1-X)0.05)&(abs(Z-Z2)=0.05);zz1=r1.*Z3;yy1=r1.*Y;xx1=r1.*X;zz2=r2.*Z3;yy2=r2.*Y;xx2=r2.*X;zz3=r3.*Z;yy1=r3.*Y;xx1=r3.*X1;plot3(xx1(r1=0),yy1(r1=0),zz1(r1=0),k*);plot3(xx2(r2=0),yy2(r2=0),zz2(r2=0),k*);plot3(xx3(r3=0),yy3(r3=0),zz3(r3=0),k*);colormap(hsv);（8）曲面与曲面求交x,y=meshgrid(-2:.1:2);z1=x.2-2*y.2;z2=x.2+y.2-5;mesh(x,y,z1);hold onmesh(x,y,z2);r0=(abs(z1-z2)=.1);zz=r0.*z1;yy=r0.*y;xx=r0.*x;plot3(xx(r0=0),yy(r0=0),zz(r0=0),k*)colormap(cool)hold off