import hs_entete;
import animate;
animation A;
size(10cm);

zfct2 Ylm=Y(7,4);
real F(real phi, real theta)
{
  return 0.75+0.25*xpart(Ylm(phi,theta));
}
pen surfacepen(real t, real p)
{
  return interp(yellow,red, (F(t,p)-0.63)/(0.87-0.63));
}

// Mettre ŕ true pour sortir en pdf.
// Dans ce cas la compilation nécessite beaucoup plus de RAM.
bool pdf=false;

if(pdf) settings.outformat="pdf"; else A.global=false;

int da=10;
transform3 T;
triple adir=(0,0,4);
currentlight=(0,0,4);

currentlight=(4,4,2);
currentprojection=orthographic((4,2,2));


real M=0.210769451275276;
int n=20;
real step=1/n;

picture hs(int i)
{
  real l=i*step;
  real F(real phi, real theta)
  {
    real c=l+(1-l)*xpart(Ylm(phi,theta))^2/M;
    return c;
  }
  return sphericalsurface(F,(0,0),(pi,2pi), 60, surfacepen);
}

void fillsquare()
{
  if(!pdf) fill(shift(-1.1,-1.1)*scale(2.2)*unitsquare,black);
}

picture pic;
for(int i=0; i <= n; ++i) {
  save();
  fillsquare();
  pic=hs(i);
  add(pic);
  A.add();
  restore();
}

for (int i=0; i < 5; ++i) {
  save();
  fillsquare();
  add(pic);
  A.add();
  restore();
}

for(int i=n; i >= 0; --i) {
  real l=i*step;
  save();
  fillsquare();
  pic=hs(i);
  add(pic);
  A.add();
  restore();
}

A.movie(BBox(3mm,FillDraw(black)),keep=true);