前幾天本人遇到了一些難題，就是怎樣求曲線的交點，不過現在找到了一些源程序，和與我遇到相同問題的朋友們分享一下！

轉自《工程計算可視化與MATLAB實現》尚濤等編著 武漢大學出版社

兩直線相交

function [X,Y]=pll(X1,Y1,X2,Y2)

% 直線相交求交點

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;

調用格式：

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');

直線與多條直線相交

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

直線與曲線相交

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')

曲線與曲線相交

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.')

直線與曲面相交

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*');

平面與曲面相交

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(\'觀察曲面后，按任意鍵畫交線\');

pause

clf

plot3(xx(r0~=0),yy(r0~=0),zz(r0~=0),'k*');

%曲面與多個截平面相交

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('觀察曲面后，按任意鍵畫交線');

hold off

平面與曲面相交

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);

曲面與曲面求交

[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

[本帖最后由 dianxin05 于 2009-4-29 10:12 編輯]

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