prologues:=2;
input constantes;
input geometriepoint;
%papier millimétré
vardef millimetre suffix co =
 color coul;
 numeric hauteur, largeur ;
 path p[];
 %ligne horizontale
 p1:=(x.so*cm, 0)--(x.ne*cm, 0);
 %ligne verticale
 p2:=(0,y.so*cm)--(0,y.ne*cm);
 %choix de la couleur
 if str co ="" :
 coul:= orange
 else :
 coul:=co
 fi;
 %grille centimétrique
 pickup pencircle scaled 0.5;%christ 0.7
 %lignes horizontales
 for i:=y.so step 1 until y.ne:
 draw p1 shifted (0,i*cm) withcolor coul;
 endfor;
 %lignes verticales
 for i:=x.so step 1 until x.ne :
 draw p2 shifted (i*cm,0) withcolor coul;
 endfor;
 %grille penta-centimétrique
 %lignes horizontales
%christ pickup pencircle scaled 0.5;%christ 1
%christ for i:=0 step -5 until y.so :
%christ draw p1 shifted (0,i*cm) withcolor coul;
%christ endfor;
%christ for i:=0 step 5 until y.ne :
%christ draw p1 shifted (0,i*cm) withcolor coul;
%christ endfor;
 %lignesverticales
%christ for i:=0 step -5 until x.so :
%christ draw p2 shifted (i*cm,0) withcolor coul;
%christ endfor;
%christ for i:=0 step 5 until x.ne :
%christ draw p2 shifted (i*cm,0) withcolor coul;
%christ endfor;
enddef;

vardef origine(expr p)=
  x.origine:=xpart(p);
  y.origine:=ypart(p);
enddef;

vardef papiermillimetre(expr m,n,p,q,r)suffix col=
  origine(m);
  x.u:=n*cm;
  y.u:=p*cm;
  z.so=q;
  z.ne=r;
  millimetre col;
enddef;
beginfig(0);
  papiermillimetre((0,0),1,1,(0,0),(18,18))bleu;
  affixed.A(u*(3,13))o;
  affixed.B(z.A shifted (u*(2,4)))ne;
  drawarrow z.A--z.B;
  affixed.O(u*(8,9))no;
  affixed.E(u*(7,6))se;
  affixed.F(u*(12,11))no;
  draw droite(E,F,2);
  drawarrow (u*(2,12))..(u*(1.3,11))..(u*(1,10)) withpen pencircle scaled 2bp;
  path poisson;
  poisson=(u*(3,7))--(u*(4,8))--(u*(6,8))--(u*(7,9))--(u*(6,10))--(u*(5,10))--(u*(4,9))--(u*(3,10))--cycle;
  draw poisson withpen pencircle scaled 2bp;
  draw poisson rotatedabout(z.O,180) withpen pencircle scaled 2bp withcolor red;
  draw poisson reflectedabout(z.E,z.F) withpen pencircle scaled 2bp withcolor vert;
  draw poisson shifted (z.B-z.A) withpen pencircle scaled 2bp withcolor orange;
  draw poisson rotatedabout(z.E,90) withpen pencircle scaled 2bp withcolor violet;
  label.lrt(btex $\cal P$ etex,(u*(5,9)));
  label.lrt(btex ${\cal P}_1$ etex,((u*(5,9)) rotatedabout(z.O,180)));
  label.lrt(btex ${\cal P}_2$ etex,((u*(5,9)) reflectedabout(z.E,z.F)));
  label.lrt(btex ${\cal P}_3$ etex,((u*(5,9)) shifted (z.B-z.A)));
  label.lrt(btex ${\cal P}_4$ etex,((u*(5,9)) rotatedabout(z.E,90)));
endfig;
end