input geometrie2d;
input courbes;

picture pict;

O = Point(0,0);

pict = image(
	Repere(20,7,10,1,5,5);
	remplis fullcircle
		shifted (0,0.5)
		withcolor (0.5,0.7,0.7);
	trace fullcircle 
		shifted (0,0.5)
		withcolor (0.3,0.5,0.5);
	Axes;
	Debut;
	    trace Droite((-3,1),(3,1));
	    
	    marque.llft "O";
	Fin;
    );


vardef f(expr t) = 1 / ( 1 + t*t) enddef;
n = 95;

for i=0 upto n:
    beginfig(i+1);
	draw pict;
	Repere(20,7,10,1,5,5);
	Debut;
	    x := -2+4*i/n;
	    a := angle((x,1));
	    xb := sind(a)*cosd(a);
	    yb := sind(a)*sind(a); 
	    trace Droite((0,0),(x,1)) withcolor 0.6white;
	    trace Droite((x,0),(x,1)) withcolor 0.6white;
	    trace Droite((-2,yb),(2,yb)) withcolor 0.6white;
	    trace Representation(f,-2,x,floor((x+2)*5+2))
		withcolor red;
	    A := Point(x,1);	
	    if x < 0: marque.urt "A" else: marque.ulft "A" fi;
	    pointe (xb,yb);
	    pointe (x,yb);
	    pointe O;
	Fin;
    endfig;
endfor;

end