// Pseudosphere:
// x = a sin(u) cos(v);
// y = a sin(u) sin(v);
// z = a (ln(tg(u/2))+cos(u));

import three;
import solids;
import graph3;
import palette;

triple pseudosphere(real x) {
  return (sin(x),0,cos(x)+log(tan(x/2)));
}

size(20cm,IgnoreAspect);
currentprojection=orthographic(160,40,100);
currentlight=(50,50,50);

path3 G=graph(pseudosphere,0.5pi,0.965pi,10,Spline);

revolution r=revolution(O,G,Z);

draw(r,1,longitudinalpen=nullpen);
surface s=surface(r);
s.colors(palette(s.map(zpart),Gradient(cyan+white+opacity(0.9),
                                       magenta+white+opacity(0.9))));
draw(s);

draw(r,6,backpen=linetype("10 10",10),longitudinalpen=nullpen);

int n=10;
for(int i=0; i < n; ++i)
  draw(rotate(i*360/n,O,Z)*G);