import solids;

picture pic;
unitsize(pic,1.5cm);

currentlight=light(gray(0.25),specularfactor=3,viewport=false,
                  (0.5,-0.5,-0.25),(0.5,0.5,0.25),(0.5,0.5,1),(-0.5,-0.5,-1));
settings.outformat="pdf";
settings.render=4;
viewportmargin=(.5cm,.5cm);

triple f(pair p){
  real x=1+cos(p.x);
  real y=sin(p.x);
  real z=p.y*sqrt(4.000001-x^2-y^2);
  return (x,y,z);
}
triple g(pair p, real k){
  real x=1+cos(p.x);
  real y=p.y*sin(p.x);
  real z=k*sqrt(4.000001-x^2-y^2);
  return (x,y,z);
}
triple g1(pair p){ return g(p,1); }
triple gm1(pair p){ return g(p,-1); }

int n=100;
pen stylo = paleblue, stylo2 = palered;
draw(pic,surface(f,(0,-1),(2pi,1),n),stylo);
draw(pic,surface(g1,(0,-1),(2pi,1),n),stylo2);
draw(pic,surface(gm1,(0,-1),(2pi,1),n),stylo2);

addViews(pic,ThreeViewsFR);