Fichier limites.mp (figure 2) — Modifié le 20 Juin 2008 à 22 h 50
Source
prologues:=2;
verbatimtex %\input Modele%
% \documentclass{article}
% \usepackage[latin1]{inputenc}
% \usepackage[frenchb]{babel}
% \usepackage{amsmath}
% \begin{document}
etex
%input constantes;
%input papiers;
% color vert_e, turquoise, orange, vert_fonce, rose, vert_mer, bleu_ciel, or, rouge_v,bleu_m,bleu,bleu_f;
% vert_e:=(0,0.790002,0.340007);
% turquoise:=(0.250999,0.878399,0.815699);
% orange:=(0.589999,0.269997,0.080004);
% vert_fonce:=(0,1.4*0.392193,0);
% rose:=(1.0, 0.752907, 0.796106);
% bleu_ciel:=(1.2*0.529405,1.2*0.807794,1);%.2*0.921598);
% or:=(1,0.843104,0);
% rouge_v:=(0.829997,0.099994,0.119999);
% bleu_m:=(0.7*0.529405,0.7*0.807794,0.7);%*0.921598);
% bleu_f:=(0.211762,0.3231176,0.3686392);
% bleu:=(0.529405,0.807794,1);
u := 1cm; v=u; % Unité
pi:=3.14159265859;
%
def axes(expr xmin,xmax,ymin,ymax) =
pickup pencircle scaled 0.5pt;
draw ( (xmin,0) -- (xmax,0) ) scaled u ;
draw ( (0,ymin) -- (0,ymax) ) scaled v;
enddef;
def axesfleches(expr xmin,xmax,ymin,ymax) =
pickup pencircle scaled 0.5pt;
drawarrow ( (xmin,0) -- (xmax,0) ) scaled u ;
drawarrow ( (0,ymin) -- (0,ymax) ) scaled v;
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def grad(expr xscl,yscl,xmin,xmax,ymin,ymax)=
pickup pencircle scaled 0.5pt;
%% grad sur Ox
for i=0 step xscl until xmax:
draw (i*u,1/15cm)--(i*u,-1/15cm);
endfor;
for i=0 step -xscl until xmin:
draw (i*u,1/15cm)--(i*u,-1/15cm);
endfor;
%% grad sur Oy
for i=0 step yscl until ymax:
draw (1/15cm,i*v)--(-1/15cm,i*v);
endfor;
for i=0 step -yscl until ymin:
draw (1/15cm,i*v)--(-1/15cm,i*v);
endfor;
enddef;
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def vecunit =
pickup pencircle scaled 1pt;
ahangle:=30; %angle au sommet de la flèche
ahlength:=0.9*ahlength; %longueur de la pointe de flèche
drawarrow (( 0,0) -- (1,0) ) scaled u ; % vecteur i
drawarrow (( 0,0) -- (0,1) ) scaled v ; % vecteurj
label.llft(btex $O$ etex, (0,0)); % Place la lettre O en bas à gauche de (0,0)
%label.bot(btex $\vec{\imath}$ etex, (0.35,0)*u);
%label.lft(btex $\overrightarrow{j}$ etex, (-0.15,0.5)*v);
label.bot(btex $i$ etex, (0.35,0)*u);
label.lft(btex $j$ etex, (-0.15,0.5)*v);
%On colle ensuite dans le .tex:
%\psfrag{O}{$O$} \psfrag{i}{$\vi$} \psfrag{j}{$\vj$}
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def vecunitaire = %pareil mais sans les psfrag
pickup pencircle scaled 0.7pt;
ahangle:=30; %angle au sommet de la flèche
ahlength:=0.8*ahlength; %longueur de la pointe de flèche
drawarrow (( 0,0) -- (1,0) ) scaled u ; % vecteur i
drawarrow (( 0,0) -- (0,1) ) scaled v ; % vecteurj
label.llft(btex $O$ etex, (0,0)); % Place la lettre O en bas à gauche de (0,0)
label.bot(btex $\vec{\imath}$ etex, (0.35,0)*u);
label.lft(btex $\vec{\jmath}$ etex, (-0.15,0.5)*v);
enddef;
%%%%%%%%%%%%%
def courbe(suffix f)(expr xmin, xmax, M) =
draw ( ( xmin*u, (f(xmin))*v )
for i=1 upto M:
..( (xmin + (i/M)*(xmax - xmin))*u, (f( xmin + (i/M)*(xmax - xmin) ))*v)
endfor ) ;
enddef;
%%%%
%%%
def relie_pts(suffix f)(expr xmin, xscl, N) =
draw ( ( xmin*u, (f(xmin))*v )%
for i=1 upto N:%
--( (xmin + i*xscl)*u, (f( xmin + i*xscl) )*v)
endfor ) dashed evenly ;
for i=0 upto N:%
dotlabel(btex $$ etex ,((xmin + i*xscl)*u, (f( xmin + i*xscl) )*v));
%(xmin + i*xscl)*u, (f( xmin + i*xscl) ))*v);
endfor;
enddef;
%%
%%###########################################################
%%
beginfig(1)
%vardef est nécéssaire pour pouvoir passer f en argument
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef f(expr x) = mexp(-256*x)-1 enddef; % Ici on définit f(x)
vardef g(expr x) = cosd(x/pi*180) enddef; % Ici on définit g(x)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Def des fonctions usuelles en metapost %%
%% %%
%% mexp(x)=exp(x/256) %%
%% mlog(x)=ln(x/256) %%
%% cosd(x)=cos(x) x en degrés x/pi*180 %%
%% sind(x)=sin(x) x en degrés %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% On règle la fenêtre ici %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
i=1;
xmin=-2; %
xmax=6.3; %
xscl=1; %
ymin=-1; %
ymax=7; %
yscl=1; %
Nb_de_pts=50; %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
axes(xmin,xmax,ymin,ymax);
grad(xscl,yscl,xmin,xmax,ymin,ymax);
courbe(f,xmin,xmax,Nb_de_pts );
courbe(g,xmin,xmax,Nb_de_pts);
vecunit;
endfig;
beginfig(1)
% Illustre la convergence d'une suite vers l avec un tube l+/-epsilon
%vardef est nécéssaire pour pouvoir passer f en argument
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%vardef g(expr x) = mexp(-256*x)-1 enddef; % Ici on définit f(x)
vardef f(expr x) := 1.5*sind(x/pi*700)/x+0.7 enddef; % Ici on définit g(x)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Def des fonctions usuelles en metapost %%
%% %%
%% mexp(x)=exp(x/256) %%
%% mlog(x)=ln(x/256) %%
%% cosd(x)=cos(x) x en degrés x/pi*180 %%
%% sind(x)=sin(x) x en degrés %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% On règle la fenêtre ici %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
u:=0.8cm;
i:=1;
xmin:=-0.2; %
xmax:=8; %
xscl:=0.3; %
ymin:=-0.1; %
ymax:=1.9; %
yscl:=2; %
Nb_de_pts:=10; %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pair A[];
axesfleches(xmin,xmax+xscl,ymin,2);
grad(xscl,yscl,xmin,xmax,ymin,ymax);
%reliepts(f,0.1,xmax,Nb_de_pts );
% relie_pts(f,1,xscl,Nb_de_pts);
relie_pts(f,3*xscl,xscl,((xmax-3*xscl)/xscl));
A0=(0,0.7*v);
A1=(0.3*u,1.8*v);
A2=(0.6*u,1.5*v);
A8=(xmax*u,0.7*v);
draw A1--A2--(0.9*u,(f(0.9))*v) dashed evenly ;
dotlabel(btex $$ etex ,A1);
dotlabel(btex $$ etex ,A2);
draw A0--A8;
draw ((A0--A8) shifted (0,0.28*v)) dashed evenly ;
draw ((A0--A8) shifted (0,-0.28*v)) dashed evenly ;
label.lft(btex $\ell+\varepsilon$ etex ,A0 shifted (0,0.28*v));
label.lft(btex $\ell$ etex ,A0);
label.lft(btex $\ell-\varepsilon$ etex ,A0 shifted (0,-0.28*v));
draw (((0,0)--(0,0.98*v)) shifted (16*xscl*u,0));
label.bot(btex $p$ etex ,(16*xscl*u,0));
label.bot(btex $n$ etex ,(xmax*u,0));
label.lft(btex $u_n$ etex ,(0,ymax*v));
%courbe(f,xmin,xmax,Nb_de_pts);
%vecunit;
endfig;
beginfig(2)
% Illustre le th des gendarmes pour fct avec un tube l+/-epsilon
%vardef est nécéssaire pour pouvoir passer f en argument
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef g(expr x) = 1/(0.7*x)+0.72 enddef; % Ici on définit f(x)
vardef f(expr x) := 70*sind(x/pi*700)/(12*x*x)+0.7 enddef; % Ici on définit g(x)
vardef h(expr x) := -1/(1.5*x)+0.62 enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Def des fonctions usuelles en metapost %%
%% %%
%% mexp(x)=exp(x/256) %%
%% mlog(x)=ln(x/256) %%
%% cosd(x)=cos(x) x en degrés x/pi*180 %%
%% sind(x)=sin(x) x en degrés %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% On règle la fenêtre ici %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
u:=1.2cm;
v:=1.8cm;
i:=1;
xmin:=-0.2; %
xmax:=10; %
xscl:=0.3; %
ymin:=-0.1; %
ymax:=1.9; %
yscl:=2; %
Nb_de_pts:=20; %
M:=20;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pair A[];path p[];
axesfleches(xmin,xmax+xscl,ymin,2.3);
grad(xscl,yscl,xmin,xmax,ymin,ymax);
%reliepts(f,0.1,xmax,Nb_de_pts );
% relie_pts(f,1,xscl,Nb_de_pts);
%relie_pts(f,3*xscl,xscl,((xmax-3*xscl)/xscl));
% courbe(f,3*xscl,xscl,((xmax-3*xscl)/xscl));
courbe(f,1.8,xmax,100 );
%courbe(g,1.1,xmax,Nb_de_pts );
courbe(h,0.6,xmax,Nb_de_pts );
xmin:=2;
p1=( (0.6u,0.6v){dir 60}..( xmin*u, (g(xmin))*v )
for i=1 upto M:
..( (xmin + (i/M)*(xmax - xmin))*u, (g( xmin + (i/M)*(xmax - xmin) ))*v)
endfor ) ;
draw p1;
A0=(0,0.7*v);
%A1=(0.3*u,1.8*v);
%A2=(0.6*u,1.5*v);
A8=(xmax*u,0.7*v);
%draw A1--A2--(0.9*u,(f(0.9))*v) dashed evenly ;
%dotlabel(btex $$ etex ,A1);
%dotlabel(btex $$ etex ,A2);
draw A0--A8;
draw ((A0--A8) shifted (0,0.28*v)) dashed evenly ;
draw ((A0--A8) shifted (0,-0.28*v)) dashed evenly ;
label.lft(btex $\ell+\varepsilon$ etex ,A0 shifted (0,0.28*v));
label.lft(btex $\ell$ etex ,A0);
label.lft(btex $\ell-\varepsilon$ etex ,A0 shifted (0,-0.28*v));
label.bot(btex $x$ etex ,(xmax*u,0));
label.lft(btex $y$ etex ,(0,ymax*v));
label.rt(btex $C_g$ etex ,(2.1*u,2v));
label.top(btex $C_f$ etex ,(0.9*u,1.2v));
label.lft(btex $C_h$ etex ,(0.7*u,-0.3v));
endfig;
end