import graph_pi;
import patterns;
usepackage("mathrsfs");

size(10cm,0);

graphicrules(xunit=1cm, yunit=1cm,
             xmin=-1, xmax=4,
             ymin=-3, ymax=3  //, crop=Crop
             );
// Définition et tracé de la grille
grid(xStep=1, xstep=.5,
     yStep=1, ystep=.5,
     pTick=.7bp+.7white, 
     ptick=.7bp+dotted+.7white,
     above=false
     );
// Définition et tracé des axes
cartesianaxis(
    xticks=Ticks(Label(Fill(white)),
                 Step=1, step=.5,
                 NoZero,
				 ptick=grey),
    yticks=Ticks(Label(Fill(white)),
                 Step=2, step=1,
                 NoZero,
                 ptick=grey),
    Arrow
    );
// Définition des fonctions
real f(real x) {return 2x-x^2;}
real g(real x) {return x;}
 
// Les hachures.
path zonehachuree=buildcycle(graph(f,0,3),(3,-5)--(3,5),graph(g,3,0));
add("hachure",hatch(H=1mm,dir=SE,lightgray));
fill(zonehachuree,pattern("hachure"));

// Tracé de courbe
path Cf=graph(f,-1.5,4.5,n=400);
path Cg=graph(g,-1.5,4.5,n=400);
draw(Cf,1bp+blue);
draw(Cg,dashed+1bp+red);
xlimits(-1.5,4.5,Crop);
ylimits(-3.5,3.5,Crop);
label("$\mathscr{C}_f$",(2.5,f(2.5)),SW,blue);
label("$\mathscr{C}_g$",(2.5,g(2.5)),NW,red);  

labeloij(p=1.4bp+.5*red,
         arrow=Arrow(SimpleHead,8bp),
         dot
         );