Question

MATLAB由隐函数确定的两个曲面如何求其交线?

Answer 1

MATLAB由隐函数确定的两个曲面如何求其交线?
可以按下列思路来求解：
1、确定两个曲面函数，f1(x1,y1,z1)和f2(x2,y2,z2)
2、确定交线方程的大致范围，即x,y,z的范围
3、固定某两点求第三点
4、使用mesh函数绘制两个曲面图形，使用plot3函数绘制交线曲线

Answer 2

d=0.05;
[x,y,z]=meshgrid(0:d:4,-2:d:2,-2:d:3);
v=x.^2/4+y.^2/4+z.^2/4-x;
p=isosurface(x,y,z,v,0);

fz=@(x,y) (307620*x)/2908093 + (10070*y)/28793 + 671042474/363511625;
[xx yy]=meshgrid(0:d:4,-2:d:2);
zz=fz(xx,yy);

f=@(x,y) x.^2/4+y.^2/4+(fz(x,y)).^2/4-x;
c=contours(xx,yy,f(xx,yy),[0 0]);
xxx=c(1,2:end);yyy=c(2,2:end);
zzz=fz(xxx,yyy);

mesh(xx,yy,zz,'edgecolor','none','facecolor','r','facealpha',0.3);hold on
patch(p,'edgecolor','none','facecolor','b','facealpha',0.3);
plot3(xxx,yyy,zzz,'k','linewidth',1);hold off
axis equal;

Answer 3

d=0.05;
[x,y,z]=meshgrid(0:d:4,-2:d:2,-2:d:3);
v=x.^2/4+y.^2/4+z.^2/4-x;
p=isosurface(x,y,z,v,0);

fz=@(x,y) (307620*x)/2908093 + (10070*y)/28793 + 671042474/363511625;
[xx yy]=meshgrid(0:d:4,-2:d:2);
zz=fz(xx,yy);

f=@(x,y) x.^2/4+y.^2/4+(fz(x,y)).^2/4-x;
c=contours(xx,yy,f(xx,yy),[0 0]);
xxx=c(1,2:end);yyy=c(2,2:end);
zzz=fz(xxx,yyy);

mesh(xx,yy,zz,'edgecolor','none','facecolor','r','facealpha',0.3);hold on
patch(p,'edgecolor','none','facecolor','b','facealpha',0.3);
plot3(xxx,yyy,zzz,'k','linewidth',1);hold off
axis equal;