%@ Maxime Chupin
%@ 14 janvier 2017

prologues := 3;
outputtemplate := "%j/%j-%c.svg";
outputformat := "svg";

verbatimtex
%&latex
  \documentclass{article}
  \usepackage{amsmath}
  \usepackage[charter]{mathdesign}
  \begin{document}
  etex

% unité
u:=1.5cm;
%rayon cercle
r:=1.5u;
% marge pour le clip
marge := 0.4u;
% le cercle
path cercle;
cercle := fullcircle scaled 2r;

% les points
pair C,B,D,M,P;

C := (3u, 0);
B := (-r,0);

% fonction qui retourne une droite à partir de deux points
vardef droite(expr A,B) =
  save d;
  path d;
  d := 20[A,B]--20[B,A];
  d
enddef;
% droite parallele à (A,B) passant par C
vardef parallele(expr A, B, C) =
  save dir,D,droite;
  path droite;
  pair dir,D;
  dir := B-A;
  D := C+dir;
  droite := 10[C,D]--10[D,C];
  droite
enddef;

% la droite parallèle à (C,P)
path para;
% perpendiculaire à (Ox) passant par D
path perp;
% la droite (CP)
path CP;
% l'axe Ox
path Ox;
Ox := droite (C,(-r,0));
% path du clip
path clipPath;
clipPath := (-r-marge, -r-marge)--(xpart C+marge,-r-marge)--(xpart C+marge,r+marge)--(-r-marge,r+marge)--cycle;

% la courbe
path rosillo;

% la boucle pour faire les images de l'animation
for i:=0 upto 359:
  beginfig(i);
    % construtsion des differents points
    P := r*(cosd(i),sind(i));
    CP := droite(C,P);
    D := (xpart P,0);
    para := parallele(C,P,B);
    perp := droite(D,P);
    M := para intersectionpoint perp;
    if(i=0):
      rosillo := M;
    else:
      rosillo := rosillo -- M;
    fi;

    draw cercle dashed evenly withcolor (0.1,0.7,0.1);
    draw CP dashed evenly;
    draw Ox dashed evenly;
    draw perp dashed evenly;
    draw para dashed evenly;

    draw C--P withcolor (0.1,0.1,0.7);
    draw B--M withcolor (0.1,0.1,0.7);
    draw D--P withcolor (0.1,0.1,0.7);
    draw D--M withcolor (0.1,0.1,0.7);

    % la courbe
    draw rosillo withpen pencircle scaled 1pt withcolor (0.7,0.1,0.1);
    % les labels
    dotlabel.lrt(btex $C$ etex, C);
    dotlabel.llft(btex $B$ etex, B);
    dotlabel.bot(btex $P$ etex, P);
    dotlabel.lrt(btex $D$ etex, D);
    dotlabel.bot(btex $M$ etex, M);
    label.urt(btex $\mathcal C$ etex, r*(cosd(50),sind(50)));
    label.ulft(btex \itshape La courbe de Rosillo etex, (xpart C+0.5marge,-r-0.5marge));
    % le clip
    draw clipPath withcolor white;
    clip currentpicture to clipPath;
  endfig;
endfor;
end.