Animations

Développante d'un cercle

%@AUTEUR: Maxime Chupin
%@DATE: 18 octobre 2009
 
verbatimtex
%&latex
\documentclass{minimal}
\usepackage[utf8]{inputenc}
\usepackage[garamond]{mathdesign}
\begin{document}
etex
 
u:=1cm;
 
%% === style.mp --------------------------------------------------------(JMS)
picture UnBeauPoint;
UnBeauPoint := image(
    fill fullcircle scaled 3pt;
    fill fullcircle scaled 2pt withcolor white;
);
vardef pointe expr p = draw UnBeauPoint shifted p; enddef;
%% =
 
numeric pi;
pi:=3.14159;
 
path arc, cercle,dev;
 
 
for i:=0 upto 360:
  beginfig(i);
    pair P,M,vecTan;
    color gris;
    gris:=0.7*white;
    draw fullcircle scaled 2u withcolor gris;
    % P parcourant le cercle
    P:=u*(cosd(i),sind(i));
    if i=0:
      arc:=P;
    else:
      arc:=arc--P
    fi;
    %on calcul la longueur de l'arc
    numeric longueurArc;
    longueurArc:= arclength(arc);
    %vecteur normal
    vecTan:=(sind(i),-cosd(i));
    %le point de la developpante
    M:=P+longueurArc*(vecTan);
    if i=0:
      dev:=M;
    else:
      dev:=dev--M;
    fi;
    draw arc withcolor blue;
    draw (0,0)--P dashed evenly withcolor gris;
    draw P--M dashed evenly withcolor blue;
    draw dev withpen pencircle scaled 1pt withcolor red;
    pointe (0,0);
    pointe (u,0);
    pointe P;
    pointe M;
    label.urt(btex $P$ etex, P);
    label.urt(btex $M$ etex,M);
    label.urt(btex \textit{Développante de cercle} etex,(-1.7*pi*u,-2*pi*u));
    draw (2u,-2.1*pi*u)--(2u,1.2pi*u)--(-1.8*pi*u,1.2pi*u)--(-1.8*pi*u,-2.1*pi*u)--cycle withcolor white;
  endfig;
endfor;
end.