clear;clf;
pas=0.01;

// Cercle de base

y=[0:pas:1]';
NY=size(y); ny=NY(1,1);

for i=1:ny
   x(i)=sqrt(1-y(i)^2);
end

// Cercles méridiens

for j=1:8
   r1=cos(j*%pi/18); // décalage de 10°
   r2=sin(j*%pi/18);
   for i=1:ny
      Xm(i,j)=x(i)*r1; // coordonnées des points du cercle incliné
      Ym(i,j)=y(i);
      Zm(i,j)=x(i)*r2;
   end
end

// Cercles parallèles

for j=1:8
   r1=cos(j*%pi/18); // décalage de 10°
   r2=sin(j*%pi/18);
   for i=1:ny
      Xp(i,j)=y(i)*r2; // coordonnées des points du cercle parallèle
      Yp(i,j)=r1;
      Zp(i,j)=x(i)*r2;
   end
end

// Projection stéréographique

// Pôle Sud S(0,0,-1), pôle P(X1,Y,Z)
// Droite : S + m*SP = (m*X1)i + (m*Y)j + (-1+m*(Z+1))k

for j=1:8
   for i=1:ny
      m = 1/(1+Zm(i,j)); // z=0
      Xm1(i,j)=m*Xm(i,j);
      Ym1(i,j)=m*Ym(i,j);
   end
end

for j=1:8
   for i=1:ny
      m = 1/(1+Zp(i,j)); // z=0
      Xp1(i,j)=m*Xp(i,j);
      Yp1(i,j)=m*Yp(i,j);
   end
end

// Tracé

angle=['10','20','30','40','50','60','70','80'];

for j=1:8
   plot2d(Xm1(:,j),Ym1(:,j),style=2)
   plot2d(-Xm1(:,j),Ym1(:,j),style=2)
   plot2d(Xm1(:,j),-Ym1(:,j),style=2)
   plot2d(-Xm1(:,j),-Ym1(:,j),style=2)
  
   plot2d(Xp1(:,j),Yp1(:,j),style=2)
   plot2d(-Xp1(:,j),Yp1(:,j),style=2)
   plot2d(Xp1(:,j),-Yp1(:,j),style=2)
   plot2d(-Xp1(:,j),-Yp1(:,j),style=2)
end

plot2d(x,y)
plot2d(-x,y)
plot2d(x,-y)
plot2d(-x,-y)

xpoly([0,0],[-1,1])
xpoly([-1,1],[0,0])

axe=get('current_axes');
axe.axes_visible=['off','off'];
axe.isoview='on';
axe.box='off';