Ellipsographes

Ellipsographe de L'Hospital

%@DATE: 31 mai 2005
 
input fichierps;
 
InitFichierPS(-160,-150,160,150);
 
u = 1.2cm;
 
 
% La longueur de la tige.
l = 4;
 
% Angle des deux glissières;
a = 70;
ca = cosd(a);
sa = sind(a);
lx = l/sa;
 
% La position du point décrivant l'ellipse sur la tige.
f := 0.6;
 
vardef Point(expr p) =
    draw p withpen pencircle scaled 4;
    draw p withpen pencircle scaled 3 withcolor white;
enddef;
 
% L'ellipse;
path e;
 
for i=0 upto 200:
  beginfig(i+1);
 
    pair A,B,E;
    if i<=50:
	A = (i*lx/50,0) scaled u;
    elseif i<=150:
	A = (2lx-i*lx/50,0) scaled u;
    else:
	A = (i*lx/50-4lx,0) scaled u;
    fi;
    x := (xpart A)/u;    
    k := l*sqrt(1-(x/lx)*(x/lx));
 
    if (i>50) and (i<150):
	h := ca*x - k;
    else:
	h := ca*x + k;
    fi;
    B = (ca,sa) scaled (h*u);
 
    E = f[B,A];
 
    drawoptions(withcolor 0.6white);    
    draw ((-1.1l,0)--(1.1l,0))  scaled u;
    draw ((-1.1l,0)--(1.1l,0)) rotated a  scaled u;
    drawoptions();
 
    drawarrow (0,0)--(A scaled 0.95) withpen pencircle scaled 1.25;
 
    if i=0: 
	e := E;
    else:
	e := e -- E;
	draw e withpen pencircle scaled 1 withcolor blue;
    fi
 
    drawoptions(withpen pensquare scaled 2 withcolor (1,0.08,0.58));	
    draw A--B;
    drawoptions();
 
    Point(A);
    Point(B);
    Point(E); 
  endfig;
endfor;
 
end