luamplibAnimate/mplibanimate.tex

   1 \documentclass{article}
   2 \usepackage{animate}
   3 \usepackage{luamplib}
   4
   5 \begin{document}
   6
   7
   8 \mplibcodeinherit{enable} % pour permettre la mémoire entre les
   9                           % biginfig(i) produites
  10 \newcommand{\lemniscate}[1]{% #1: l'angle en degres
  11   \begin{mplibcode}
  12     if(#1=0):
  13     u:=4cm;%
  14     a:=2u;%
  15     h:=a/4;%
  16     s:=1.3;%
  17     path lemn;%
  18     path carre;%
  19     carre = (0,0)--(1,0)--(1,1)--(0,1)--cycle;
  20     fi;
  21     beginfig(#1);
  22     pickup pencircle scaled 0.6pt;
  23     drawarrow (0,-s*u)--(0,s*u);
  24     drawarrow (-s*u,0)--(s*u,0);
  25     path cercle,hori,verti;
  26     pair O,P,Q,R,M;
  27     O:=(0,0);
  28     cercle := fullcircle scaled (a);
  29     pickup pencircle scaled 0.4pt;
  30     draw cercle dashed evenly withcolor blue;
  31     P:=(a/2*cosd(#1),a/2*sind(#1)); % chemin qui parcourt le cercle
  32     Q:=(a/2*cosd(#1),0); %projection sur (Ox)
  33     % projection de Q sur [O,P]
  34     R = cosd(#1)*cosd(#1)*(a/2*cosd(#1),a/2*sind(#1));
  35     % M sur [PQ] tel que QM = QR
  36     QR := abs(R-Q);
  37     if(sind(#1)>0.0):
  38     M = Q + (0,QR);
  39     else:
  40     M = Q - (0,QR);
  41     fi;
  42
  43     if #1=0:
  44     lemn:=M;
  45     else:
  46     lemn:= lemn--M;
  47     fi;
  48
  49     if ((#1>0) and (#1<90)) or ((#1>180) and (#1<270)):
  50     draw carre scaled 6 rotated (angle(Q-P)+180) shifted Q;
  51     draw carre scaled 6 rotated (angle(R-P)) shifted R;
  52     fi;
  53     if((#1>=90) and (#1<180)) or ((#1>=270) and (#1<360)):
  54     draw carre scaled 6 rotated (angle(Q-P)+180) shifted Q;
  55     draw carre scaled 6 rotated (angle(R-P)+180) shifted R;
  56     fi;
  57
  58     draw O--P dashed evenly withcolor blue;
  59     draw P--Q dashed evenly withcolor blue;
  60     draw R--Q--M withcolor green;
  61
  62     label.lrt(btex $a$ etex, (a/2,0));
  63     label.llft(btex $x$ etex, (s*u,0));
  64     label.llft(btex $y$ etex, (0,s*u));
  65     label(btex \itshape Lemniscate \par de Gerono etex, (-0.7u,1.15u));
  66     label(btex $x^4=a^2(x^2-y^2)$ etex, (0.7u,-1.15u));
  67
  68
  69     dotlabel.llft(btex $O$ etex, O);
  70     dotlabel.urt(btex $M$ etex, M);
  71     dotlabel.urt(btex $P$ etex, P);
  72     dotlabel.urt(btex $Q$ etex, Q);
  73     dotlabel.urt(btex $R$ etex, R);
  74
  75     pickup pencircle scaled 1pt;
  76     draw lemn withcolor red;
  77
  78     clip currentpicture to (-s*u,-s*u)--(s*u,-s*u)--(s*u,s*u)--(-s*u,s*u)--cycle;
  79     endfig;
  80   \end{mplibcode}
  81 }
  82
  83
  84 \begin{center}
  85   \begin{animateinline}[poster=last, controls]{24}
  86     %
  87     \multiframe{360}{i=0+1}{\lemniscate{\i}}
  88   \end{animateinline}
  89 \end{center}
  90
  91 Le PDF produit est à télécharger dans la liste plus haut.
  92 \end{document}