# Drawing the Reeb foliation

I am trying to draw the Reeb foliation. So far I have the code and image below. The problem is that one surface is very slightly bulging out through the one in front of it (through the very front surface). They should be nested each one entirely inside the previous, like curved flower pots.

``````settings.outformat="pdf";
settings.prc=false;
settings.render=4;

import graph;
import graph3;
import three;

size(12cm,0);

real rcutoff=.8;
real rinner=1;
real router=2;

currentprojection=orthographic(1,-2,1);
currentlight=(1,-1,0.5);

real f(pair z) {return 1/(1-abs(z)^2);}

// We change variables so that the unit cylinder x^2+y^2<1 gets mapped to the torus.
triple changevariables(triple X)
{
return (
(router+rinner*X.x)*cos(X.z),
(router+rinner*X.x)*sin(X.z),
rinner*X.y
);
}

// g returns the location of a point on a ``paraboloid'' inside the unit cylinder with given angle and radius above the unit disk in the (x,y) plane.
triple g(pair p){
real x=p.x*cos(p.y), y=p.x*sin(p.y);
return (x,y,f((x,y)));
}

triple h(pair p){
return changevariables(g(p));
}

real anglestep=10;

for (int z = 0; z <= 20; ++z) {
draw(
rotate(-anglestep*z,Z)*surface(
h,
(0,0),
(rcutoff,2*pi),Spline
),lightgray+opacity(1)
);
//  real zz=f((rcutoff,0));
//  triple cent=changevariables((0,0,zz));
//  draw(
//      rotate(-anglestep,Z)*
//      circle(c=cent, r=rcutoff,normal=(-router*sin(zz),router*cos(zz),0)),
//      white
//  );
}
`````` Perhaps the problem is even clearer if I only draw the final two surfaces, in different colours: • Thank you for adding the second image. I had no idea what you were asking about when I looked at this earlier ;). – cfr Dec 23 '14 at 19:50

``````draw(