size(12cm,0,false);
import graph3;
import contour;
texpreamble("\usepackage{icomma}");

real f(pair z) {
  return z.x*z.y*exp(-z.x);
}

bbox3 b=limits((0,0,0),(5,10,4.5));
currentprojection=orthographic(-2.5,-5,1);
currentlight=(1,-1,2);

aspect(b,1,1,1);

xaxis(rotate(X)*Label("$x$",align=project(-b.Y())),b,Ticks(), dir=-b.Y());
yaxis(Label("$y$",align=project(-b.X())),b,Ticks(Step=2), dir=-b.X());
zaxis(Label("$z=xye^{-x}$",align=2E,relative(1.1)),b.Y(),b.YZ(),LeftTicks());

layer();
pen p=rgb(0.2,0.5,0.7);

add(surface(f,(0,0),(5,10),100,100,meshpen=nullpen));
layer();
add(surface(f,5,(0,0),(5,10),20,20,nullpen,meshpen=p));

real[] datumz={.5,1,1.5,2,2.5,3,3.5};
pen[] p=sequence(new pen(int i) {
    return datumz[i]/3.5*red;
  },7);

Label [] L=sequence(new Label(int i) {
    return scale(0.75)*Label(format("$z=%g$",datumz[i]),align=E,BeginPoint);
  },7);

Label [] legend=sequence(new Label(int i) {
    return format("$z=%g$",datumz[i]);
  },7);

draw(L,lift(f,contour(f,(0,0),(5,10),datumz)),p,legend);
attach(legend(),project((4,6,2)),2E,UnFill);