| 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 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 on plot(x2,y2,\'b\'); plot(x,y,\'ko\'); 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 on x1=[1 5];y1=[4 5];line(x1,y1); x=zeros(size(xi)); y=x; for i=1:5-1 x2=xi([i i+1]);y2=yi([i i+1]); [x,y]=pll(x1,y1,x2,y2); plot(x,y,\'ro\') end 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 on c=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\') 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 on r0=abs(y2-sin(pi*x))<=0.02; yy=r0.*y1;xx=r0.*x;plot(xx(r0~=0),yy(r0~=0),\'r.\') 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 on x=[-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*\'); 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 on mesh(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*\') clc disp(\'观察曲面后，按任意键画交线\'); pause clf plot3(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 on mesh(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 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 on mesh(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); 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 on mesh(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 |
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