Hyperbolographe de Delaunay

%@DATE: 31 mai 2005
 
input fichierps;
 
InitFichierPS(-120,-190,120,190);
 
u = 1cm;
 
 
% La longueur du bras AM.
l = 4;
 
% La longueur du bras AB.
L = 4.2; % L > l
 
% Angle des deux glissières;
a = 40;
ca = cosd(a);
sa = sind(a);
 
 
vardef Point(expr p) =
    draw p withpen pencircle scaled 4;
    draw p withpen pencircle scaled 3 withcolor white;
enddef;
 
% Les deux branches de l'hyperbole.
path hg,hd;
 
for i=0 upto 200:
  beginfig(i+1);
 
    pair A,B,C,D,M;
 
    if i<=50:
	M = (sa,ca) scaled (i*l/50) scaled u;
    elseif i<=150:
	M = (sa,ca) scaled (2l-i*l/50) scaled u;
    else:
	M = (sa,ca) scaled (i*l/50-4l) scaled u;
    fi;
 
    y := (ypart M)/u;
    x := (xpart M)/u;   
 
    k := l*sqrt(1-(x/l)*(x/l));
    h := L*sqrt(1-(k/L)*(k/L));
 
    A = (0,y+k) scaled u;
    C = (0,y-k) scaled u;
    B = (-h,y) scaled u;
    D = (h,y) scaled u;
 
 
    FondImage((1,.87,.68));
    drawoptions(withcolor 0.6white);    
    draw ((0,-1.6l)--(0,1.6l)) scaled u;
    draw ((0,-1.1l)--(0,1.1l)) rotated -a  scaled u;
    drawoptions();
 
    drawarrow (0,0)--(M scaled 0.95) withpen pencircle scaled 1.25;
 
    if i=0: 
	hg := B;
	hd := D;
    else:
	hg := hg -- B;
	hd := hd -- D;
	draw hd withpen pencircle scaled 1 withcolor blue;
	draw hg withpen pencircle scaled 1 withcolor blue;
    fi
 
    drawoptions(withpen pensquare scaled 2 withcolor (.55,.35,.17));	
    draw A--B--C--D--A;
    draw A--M--C;
    drawoptions();
 
    Point(A);
    Point(B);
    Point(C);
    Point(D);
    Point(M); 
  endfig;
endfor;
 
end