Animations

Épicycloïde

%@AUTEUR: Maxime Chupin
%@DATE: 28 mars 2007
 
verbatimtex
%&latex
\documentclass{article}
\usepackage{amsmath}
\begin{document}
etex
 
u:=1cm;
a:=3u;
m:=3;
q:=5/m;
pair O,O',M;
O:=(0,0);
path gcercle,pcercle,rayon,epi;
 
for i:=0 upto (m*180):
 beginfig(i+1);
  pickup pencircle scaled 0.8pt;
  drawarrow (-1.2*a-(2*a/q),0)--(1.2*a+(2*a/q),0);
  drawarrow (0,-1.2*a-(2*a/q))--(0,1.2*a+(2*a/q));  
  gcercle:=fullcircle scaled (2*a);
  O':=((a+(a/q))*cosd(i*2),(a+(a/q))*sind(i*2));
  pcercle := fullcircle scaled ((2*a)/q) shifted O';
  rayon:= (0,0)--(12*u*cosd((q+1)*i*2),12*u*sind((q+1)*i*2));
  rayon := rayon shifted O';
  M := rayon intersectionpoint pcercle;
 if i=0:
  epi := M;
 else:
  epi := epi--M;
 fi;
  pickup pencircle scaled 0.7pt;
  draw gcercle dashed evenly withcolor blue;
  draw pcercle dashed evenly withcolor green;
  draw O'--M dashed evenly;
  pickup pencircle scaled 1pt;
  draw epi withcolor red;
  label.top(btex $a$ etex , (a/2,0));
  label.urt(btex $\frac{a}{q}$ etex, 
	    ((xpart O'+xpart M)/2,(ypart O'+ypart M)/2));
  dotlabel.urt(btex $M$ etex, M);
  dotlabel.urt(btex $O'$ etex, O');
  dotlabel.urt(btex $O$ etex, O);
  clip currentpicture to (-1.2*a-(2*a/q),-1.2*a-(2*a/q))
	    --(1.2*a+(2*a/q),-1.2*a-(2*a/q))
	    --(1.2*a+(2*a/q),1.2*a+(2*a/q))
	    --(-1.2*a-(2*a/q),1.2*a+(2*a/q))--cycle;
 endfig;
endfor;
end