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%% repere.mp %%
%% Macros pour la construction de figures dans un repère %%
%% o.peault@gmail.com %%
%% Version 13.12 (Décembre 2013) %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% This work may be distributed and/or modified under the conditions of
% the LaTeX Project Public License, either version 1.3 of this license
% or (at your option) any later version. The latest version of this
% license is in http://www.latex-project.org/lppl.txt
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
input format;
warningcheck:=0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% REPERE %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
numeric _nfig,_nbaxes,theta,taillegrad,taillepoint,taillecroix,facteurx,facteury;
boolean flecheaxe,displayfrac,coupe;
_nfig:=1;
path cadre;
numeric _diag,_largcadre,_hautcadre,_tfig;
pair _O,_I,_J;
transform _T;
picture _axorlab; pair poslabO;
string marque_p,fraction;
facteury:=1;
boolean rep_groupe;
rep_groupe:=false;
let oldbeginfig=beginfig;
let oldendfig=endfig;
def beginfig(expr c)=
oldbeginfig(c);
_nfig:=c;
rep_groupe:=true
enddef;
def endfig=
oldendfig;
_nfig:=_nfig+1;
rep_groupe:=false
enddef;
vardef repere@#(text t)=
if (str @#="") or (str @#="larg") or (str @#="orth") or (str @#="prop"):
% _nfig:=_nfig+1;definitionrepere@#(t)
definitionrepere@#(t)
else:
reperenum@#(t)
fi
enddef;
vardef reperenum[]@#(text t)=
_nfig:=@;
definitionrepere@#(t)
enddef;
boolean bf;
bf:=false;
vardef definitionrepere@#(text t) =
save i,_def;
if not rep_groupe: oldbeginfig(_nfig);bf:=true fi;
numeric _def[],i,unitex,unitey,unite;
_def[7]:=90;i:=1;
for _i=t: _def[i]:=_i; i:=i+1; endfor;
Xmin:=_def1; Xmax:=_def2; Ymin:=_def4; Ymax:=_def5; theta:=_def7;
if str @#="larg": _def3:=(_def3-_def6*cosd(theta)/sind(theta))/(Xmax-Xmin);_def6:=_def6/((Ymax-Ymin)*sind(theta))
elseif str @#="orth": _def3:=_def3/(Xmax-Xmin); _def6:=_def3;theta:=90
elseif str @#="prop": _def3:=_def3/(Xmax-Xmin); _def6:=_def6*_def3;theta:=90
fi;
Ux:=_def3;Uy:=_def6;
_T:=identity xscaled Ux yscaled Uy slanted cosd(theta) yscaled sind(theta);
_defcadre;
settout(Xmin,Xmax,Ymin,Ymax);
_O:=_c(0,0); xO:=0 ; yO:=0;
_I:=_c(1,0); _J:=_c(0,1);
taillegrad:=0.8mm;taillepoint:=3;taillecroix:=1mm;_nbaxes:=0;_axorlab:=nullpicture;poslabO:=(0,0);
marque_p := "plein";displayfrac:=false;flecheaxe:=true;coupe:=true;
defaultscale:=1;
unitex:=abs(_I);unitey:=abs(_J);unite:=unitex;
facteurx:=1;facteury:=1;
string extranumx,extranumy;
extranumx=extranumy="";
enddef;
def setaxes(expr a,b,c,d)=
AxeXmin:=a;AxeXmax:=b;AxeYmin:=c;AxeYmax:=d
enddef;
def setgrad(expr a,b,c,d)=
GradXmin:=a;GradXmax:=b;GradYmin:=c;GradYmax:=d
enddef;
def setval(expr a,b,c,d)=
ValXmin:=a;ValXmax:=b;ValYmin:=c;ValYmax:=d
enddef;
def setquad(expr a,b,c,d)=
QuadXmin:=a;QuadXmax:=b;QuadYmin:=c;QuadYmax:=d
enddef;
def settout(expr a,b,c,d)=
setaxes(a,b,c,d);
setgrad(a,b,c,d);
setval(a,b,c,d);
setquad(a,b,c,d);
enddef;
let setall=settout;
def fin =
if _nbaxes=1: draw _axorlab fi;
if coupe: clip currentpicture to cadre fi;
if bf: oldendfig; bf:=false;_nfig:=_nfig+1 fi;
enddef;
def _defcadre=
cadre:=_c(Xmin,Ymin)--_c(Xmin,Ymax)--_c(Xmax,Ymax)--_c(Xmax,Ymin)--cycle;
_diag:=abs(llcorner cadre - urcorner cadre);
_largcadre:=abs(llcorner cadre - lrcorner cadre);
_hautcadre:=abs(llcorner cadre - ulcorner cadre);
_tfig:=max(_largcadre,_hautcadre); % compatibilité geometriesyr
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% ORIGINE %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
def interaxes(expr a,b) =
_O:=_c(a,b);
xO:=a;
yO:=b;
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% AXES %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pair _posgradx, _posgradx.lft, _posgradx.rt, _posgradx.ulft, _posgradx.top, _posgradx.urt, _posgradx.llft, _posgradx.bot, _posgradx.lrt;
_posgradx=_posgradx.bot=_posgradx.lft=_posgradx.rt=-_posgradx.top=(0,-1);
-_posgradx.llft=_posgradx.urt=(0.5,0.5);_posgradx.lrt=-_posgradx.ulft=(0.5,-0.5);
pair _posgrady, _posgrady.lft, _posgrady.rt, _posgrady.ulft, _posgrady.top, _posgrady.urt, _posgrady.llft, _posgrady.bot, _posgrady.lrt;
_posgrady=_posgrady.bot=_posgrady.lft=_posgrady.top=-_posgrady.rt=(-1,0);
-_posgrady.llft=_posgrady.urt=(0.5,0.5);_posgrady.lrt=-_posgrady.ulft=(0.5,-0.5);
vardef _etiqx_@#(expr ab,dec,st)= %étiquettes axe des abscisses
save pic;
picture pic;
if numeric st: pic:=LaTeX("$\num{" & decimal(st) & extranumx & "}$")
elseif string st: pic:=LaTeX(st)
else: pic:=st fi;
thelabel.@#(pic,_c(ab,yO) shifted (dec*_posgradx@#))
enddef;
vardef _etiqy_@#(expr ro,dec,st)= %étiquettes axe des ordonnées
save pic;
picture pic;
if numeric st: pic:=LaTeX("$\num{" & decimal(st) & extranumy & "}$")
elseif string st: pic:=LaTeX(st)
else: pic:=st fi;
thelabel.@#(pic,_c(xO,ro) shifted (dec*_posgrady@#))
enddef;
vardef graduationx(expr x)= %%%%%%% graduation axe des abscisses
((0,taillegrad)--(0,-taillegrad)) rotated (theta-90) shifted _c(x,yO)
enddef;
vardef graduationy(expr y)= %%%%%%% graduation axe des ordonnées
((taillegrad,0)--(-taillegrad,0)) shifted _c(xO,y)
enddef;
vardef etiquettex@#(expr x)=
_etiqx_@#(x,taillegrad,x*facteurx)
enddef;
vardef etiquettey@#(expr y)=
_etiqy_@#(y,taillegrad,y*facteury)
enddef;
vardef dessinaxex=_c(AxeXmin,yO)--_c(AxeXmax,yO) enddef;
vardef dessinaxey=_c(xO,AxeYmin)--_c(xO,AxeYmax) enddef;
vardef graduationsaxex(expr grad)= %%%% ensemble des graduations abscisses
save $;picture $;
$=image(%
imax:=floor((GradXmax-xO)/grad);imin:=ceiling((GradXmin-xO)/grad);
for i=imin upto imax-1:
draw graduationx(arrondimil(i*grad)+xO) withpen pencircle scaled 0.5bp;
endfor
% dernière graduation
if AxeXmax*Ux-(imax*grad+xO)*Ux>ahlength: draw graduationx(arrondimil(imax*grad)+xO) withpen pencircle scaled 0.5bp fi);
$
enddef;
vardef graduationsaxey(expr grad)= %%%% ensemble des graduations ordonnées
save $;picture $;
$=image(%
imax:=floor((GradYmax-yO)/grad);imin:=ceiling((GradYmin-yO)/grad);
for i=imin upto imax-1:
draw graduationy(arrondimil(i*grad)+yO) withpen pencircle scaled 0.5bp;
endfor;
% dernière graduation
if AxeYmax*Uy-(imax*grad+yO)*Uy>ahlength: draw graduationy(arrondimil(imax*grad)+yO) withpen pencircle scaled 0.5bp fi);
$
enddef;
vardef etiquettesaxex@#(expr val)= %%% ensemble des étiquettes abscisses
save $,imin,imax,labmin,labmax;
picture $,labmin,labmax;
numeric imin,imax;
$=image(%
imin:=ceiling((ValXmin-xO)/val);imax:=floor((ValXmax-xO)/val);
% définition première étiquette
if (imin<>0):
labmin:= etiquettex.@#(arrondimil(imin*val)+xO)
else: labmin:=nullpicture
fi;
% définition dernière étiquette
if (imax<>0):
labmax:= etiquettex.@#(arrondimil(imax*val)+xO)
else: labmax:=nullpicture
fi;
% tracé première étiquette
if xpart ((ulcorner labmin) transformed inverse _T)>=Xmin: draw labmin fi;
% tracé autres étiquettes
for i=imin+1 upto imax-1:
if (i<>0):
draw etiquettex.@#(arrondimil(i*val)+xO)
fi;
endfor;
% tracé dernière étiquette
if xpart ((lrcorner labmax) transformed inverse _T)<=Xmax: draw labmax fi;
);
$
enddef;
vardef etiquettesaxey@#(expr val)= %%% ensemble des étiquettes ordonnées
save $,imin,imax,labmin,labmax;
picture $,labmin,labmax;
numeric imin,imax;
$=image(%
imin:=ceiling((ValYmin-yO)/val);imax:=floor((ValYmax-yO)/val);
% définition première étiquette
if (imin<>0):
labmin:= etiquettey.@#(arrondimil(imin*val)+yO)
else: labmin:=nullpicture
fi;
% définition dernière étiquette
if (imax<>0):
labmax:= etiquettey.@#(arrondimil(imax*val)+yO)
else: labmax:=nullpicture
fi;
% tracé première étiquette
if ypart (llcorner labmin) >=ypart _c(Xmin,Ymin): draw labmin fi;
% tracé autres étiquettes
for i=imin+1 upto imax-1:
if (i<>0):
draw etiquettey.@#(arrondimil(i*val)+yO)
fi;
endfor;
% tracé dernière étiquette
if ypart (ulcorner labmax) <=ypart _c(Xmax,Ymax): draw labmax fi
);
$
enddef;
vardef _axex_@#(expr grad,val,nn)=
save $;
picture $;
$=image(
% axe
if flecheaxe: drawarrow else: draw fi dessinaxex;
% graduations
if grad>0: draw graduationsaxex(grad) fi;
% étiquettes
if val>0:
if nn=1:
if str @#<>"":
draw etiquettesaxex@#(val);
_axorlab:=etiquettex@#(xO)
else:
draw etiquettesaxex.bot(val);
_axorlab:=etiquettex.bot(xO)
fi;
poslabO:=poslabO + unitvector(0,ypart _posgradx@#);
if xO<>yO:
draw _axorlab
elseif _nbaxes=2:
draw _etiqx_(xO,0,xO) shifted (0.7*abs(llcorner _axorlab - urcorner _axorlab)*poslabO)
fi
elseif nn=2:
if str @#<>"":
draw etiquettesaxex@#(val);
draw etiquettex@#(xO)
else:
draw etiquettesaxex.bot(val);
draw etiquettex.bot(xO)
fi
else:
if str @#<>"":
draw etiquettesaxex@#(val)
else:
draw etiquettesaxex.bot(val)
fi
fi
fi
);
$
enddef;
vardef _axey_@#(expr grad,val,nn)=
save $;
picture $;
$=image(
% axe
if flecheaxe: drawarrow else: draw fi dessinaxey;
% graduations
if grad>0: draw graduationsaxey(grad) fi;
% étiquettes
if val>0:
if nn=1:
if str @#<>"":
draw etiquettesaxey@#(val);
_axorlab:=etiquettey@#(yO)
else:
draw etiquettesaxey.lft(val);
_axorlab:=etiquettey.lft(yO)
fi;
poslabO:=poslabO + unitvector(xpart _posgrady@#,0);
if xO<>yO:
draw _axorlab
elseif _nbaxes=2:
draw _etiqy_(yO,0,yO) shifted (0.7*abs(llcorner _axorlab - urcorner _axorlab)*poslabO)
fi
elseif nn=2:
if str @#<>"":
draw etiquettesaxey@#(val);
draw etiquettey@#(yO)
else:
draw etiquettesaxey.lft(val);
draw etiquettey.lft(yO)
fi
else:
if str @#<>"":
draw etiquettesaxey@#(val)
else:
draw etiquettesaxey.lft(val)
fi
fi
fi
);
$
enddef;
vardef axex@# (expr grad,val)= %%%%%%axe des abscisses avec gestion graduation origine
_nbaxes:=_nbaxes+1;
_axex_@#(grad,val,1)
enddef;
vardef axey@# (expr grad,val)= %%%%%%axe des ordonnées avec gestion graduation origine
_nbaxes:=_nbaxes+1;
_axey_@#(grad,val,1)
enddef;
vardef axexo@#(expr grad,val)= %%%%%%axe des abscisses avec graduation origine
_axex_@#(grad,val,2)
enddef;
vardef axeyo@#(expr grad,val)= %%%%%%axe des ordonnées avec graduation origine
_axey_@#(grad,val,2)
enddef;
vardef axexn@#(expr grad,val)= %%%%%%axe des abscisses sans graduation origine
_axex_@#(grad,val,3)
enddef;
vardef axeyn@#(expr grad,val)= %%%%%%axe des ordonnées sans graduation origine
_axey_@#(grad,val,3)
enddef;
vardef axes@# (expr grad,val)= %%%% les deux axes
save $,posx,posy;
picture $;
numeric posx,posy;
posx:=ypart (_posgradx@#+_posgrady@#);
posy:=xpart (_posgradx@#+_posgrady@#);
$=image(%
if posx>0: draw axex.top(grad,val) else: draw axex.bot(grad,val) fi;
if posy>0: draw axey.rt(grad,val) else: draw axey.lft(grad,val) fi
);
$
enddef;
vardef axeso@# (expr grad,val)= %%%% les deux axes avec origine
save $,posx,posy;
picture $;
numeric posx,posy;
posx:=ypart (_posgradx@#+_posgrady@#);
posy:=xpart (_posgradx@#+_posgrady@#);
$=image(%
if posx>0: draw axexo.top(grad,val) else: draw axexo.bot(grad,val) fi;
if posy>0: draw axeyo.rt(grad,val) else: draw axeyo.lft(grad,val) fi
);
$
enddef;
vardef axesn@# (expr grad,val)= %%%% les deux axes sans origine
save $,posx,posy;
picture $;
numeric posx,posy;
posx:=ypart (_posgradx@#+_posgrady@#);
posy:=xpart (_posgradx@#+_posgrady@#);
$=image(%
if posx>0: draw axexn.top(grad,val) else: draw axexn.bot(grad,val) fi;
if posy>0: draw axeyn.rt(grad,val) else: draw axeyn.lft(grad,val) fi
);
$
enddef;
% axes gradués avec multiples de pi
vardef fracmulttext(expr n,d,tt)= %%%% construction de la fraction n*tt/d
save nn,dd,s,fr,$,fraction;
string s,fr,fraction;
picture $;
numeric nn,dd;
nn:=abs((n)/pgcd(n,d));dd:=d/pgcd(n,d);
if displayfrac:
fraction:="d"
else: fraction:=""
fi;
if dd=1:
if nn=1:
fr:=tt
else: fr:=decimal nn & tt
fi
else:
if nn=1:
fr:="\" & fraction & "frac{" & tt & "}{" & decimal dd & "}"
else: fr:="\" & fraction & "frac{" & decimal nn & tt & "}{" & decimal dd & "}"
fi
fi;
if n<0:
s:="-"
else: s:="";
if n=0:
fr:= "0"
fi
fi;
$=LaTeX("$" & s & fr & "$");
$
enddef;
vardef fracmultpi(expr n,d)=
fracmulttext(n,d,"\pi")
enddef;
vardef etiquettexpi@#(expr n,d)=
_etiqx_@#(n*pi/d,taillegrad,fracmultpi(n,d))
enddef;
vardef etiquetteypi@#(expr n,d)=
_etiqy_@#(n*pi/d,taillegrad,fracmultpi(n,d))
enddef;
vardef etiquettesaxexpi@#(expr n,d)= %%% ensemble des étiquettes multiples de pi abscisses
save $,imin,imax,labmin,labmax,val;
picture $,labmin,labmax;
numeric imin,imax,val;
val:=n*pi/d;
$=image(%
imin:=ceiling((ValXmin-xO)/val);imax:=floor((ValXmax-xO)/val);
% définition première étiquette
if (imin<>0):
labmin:= etiquettexpi.@#(imin*n,d)
else: labmin:=nullpicture
fi;
% définition dernière étiquette
if (imax<>0):
labmax:= etiquettexpi.@#(imax*n,d)
else: labmax:=nullpicture
fi;
% tracé première étiquette
if xpart ((ulcorner labmin) transformed inverse _T)>=Xmin: draw labmin fi;
% tracé autres étiquettes
for i=imin+1 upto imax-1:
if (i<>0):
draw etiquettexpi.@#(i*n,d)
fi;
endfor;
% tracé dernière étiquette
if xpart ((lrcorner labmax) transformed inverse _T)<=Xmax: draw labmax fi;
);
$
enddef;
vardef etiquettesaxeypi@#(expr n,d)= %%% ensemble des étiquettes multiples de pi ordonnées
save $,imin,imax,labmin,labmax,val;
picture $,labmin,labmax;
numeric imin,imax,val;
val:=n*pi/d;
$=image(%
imin:=ceiling((ValYmin-yO)/val);imax:=floor((ValYmax-yO)/val);
% définition première étiquette
if (imin<>0):
labmin:= etiquetteypi.@#(imin*n,d)
else: labmin:=nullpicture
fi;
% définition dernière étiquette
if (imax<>0):
labmax:= etiquetteypi.@#(imax*n,d)
else: labmax:=nullpicture
fi;
% tracé première étiquette
if ypart (llcorner labmin) >=ypart _c(Xmin,Ymin): draw labmin fi;
% tracé autres étiquettes
for i=imin+1 upto imax-1:
if (i<>0):
draw etiquetteypi.@#(i*n,d)
fi;
endfor;
% tracé dernière étiquette
if ypart (ulcorner labmax) <=ypart _c(Xmax,Ymax): draw labmax fi
);
$
enddef;
vardef _axexpi_@#(expr num,den,nn)=
save $,grad;
numeric grad;
picture $;
grad:=num*pi/den;
$=image(
% axe
if flecheaxe: drawarrow else: draw fi dessinaxex;
% graduations
if grad>0: draw graduationsaxex(grad) fi;
% étiquettes
if nn=1:
if str @#<>"":
draw etiquettesaxexpi@#(num,den);
_axorlab:=etiquettexpi@#(xO/pi,1)
else:
draw etiquettesaxexpi.bot(num,den);
_axorlab:=etiquettexpi.bot(xO/pi,1)
fi;
poslabO:=poslabO + unitvector(0,ypart _posgradx@#);
if xO<>yO:
draw _axorlab
elseif _nbaxes=2:
draw _etiqx_(xO,0,fracmultpi(xO/pi,1)) shifted (0.7*abs(llcorner _axorlab - urcorner _axorlab)*poslabO)
fi
elseif nn=2:
if str @#<>"":
draw etiquettesaxexpi@#(num,den);
draw etiquettexpi@#(xO/pi,1)
else:
draw etiquettesaxexpi.bot(num,den);
draw etiquettexpi.bot(xO/pi,1)
fi
else:
if str @#<>"":
draw etiquettesaxexpi@#(num,den)
else:
draw etiquettesaxexpi.bot(num,den)
fi
fi
);
$
enddef;
vardef _axeypi_@#(expr num,den,nn)=
save $,grad;
numeric grad;
picture $;
grad:=num*pi/den;
$=image(
% axe
if flecheaxe: drawarrow else: draw fi dessinaxey;
% graduations
if grad>0: draw graduationsaxey(grad) fi;
% étiquettes
if nn=1:
if str @#<>"":
draw etiquettesaxeypi@#(num,den);
_axorlab:=etiquetteypi@#(yO/pi,1)
else:
draw etiquettesaxeypi.lft(num,den);
_axorlab:=etiquetteypi.lft(yO/pi,1)
fi;
poslabO:=poslabO + unitvector(xpart _posgrady@#,0);
if xO<>yO:
draw _axorlab
elseif _nbaxes=2:
draw _etiqy_(yO,0,fracmultpi(yO/pi,1)) shifted (0.7*abs(llcorner _axorlab - urcorner _axorlab)*poslabO)
% draw _etiqy_(yO,0,yO) shifted (0.7*abs(llcorner _axorlab - urcorner _axorlab)*poslabO)
fi
elseif nn=2:
if str @#<>"":
draw etiquettesaxeypi@#(num,den);
draw etiquetteypi@#(yO/pi,1)
else:
draw etiquettesaxeypi.lft(num,den);
draw etiquetteypi.lft(yO/pi,1)
fi
else:
if str @#<>"":
draw etiquettesaxeypi@#(num,den)
else:
draw etiquettesaxeypi.lft(num,den)
fi
fi
);
$
enddef;
vardef axexpi@# (expr n,d)= %%%%%%axe des abscisses avec gestion graduation origine mult pi
_nbaxes:=_nbaxes+1;
_axexpi_@#(n,d,1)
enddef;
vardef axeypi@# (expr n,d)= %%%%%%axe des ordonnées avec gestion graduation origine mult pi
_nbaxes:=_nbaxes+1;
_axeypi_@#(n,d,1)
enddef;
vardef axexpio@#(expr n,d)= %%%%%%axe des abscisses avec graduation origine mult pi
_axexpi_@#(n,d,2)
enddef;
vardef axeypio@#(expr n,d)= %%%%%%axe des ordonnées avec graduation origine mult pi
_axeypi_@#(n,d,2)
enddef;
vardef axexpin@#(expr n,d)= %%%%%%axe des abscisses sans graduation origine mult pi
_axexpi_@#(n,d,3)
enddef;
vardef axeypin@#(expr grad,val)= %%%%%%axe des ordonnées sans graduation origine mult pi
_axeypi_@#(n,d,3)
enddef;
vardef axespi@# (expr n,d)= %%%% les deux axes mult pi
save $,posx,posy;
picture $;
numeric posx,posy;
posx:=ypart (_posgradx@#+_posgrady@#);
posy:=xpart (_posgradx@#+_posgrady@#);
$=image(%
if posx>0: draw axexpi.top(n,d) else: draw axexpi.bot(n,d) fi;
if posy>0: draw axeypi.rt(n,d) else: draw axeypi.lft(n,d) fi
);
$
enddef;
vardef axespio@# (expr n,d)= %%%% les deux axes avec origine mult pi
save $,posx,posy;
picture $;
numeric posx,posy;
posx:=ypart (_posgradx@#+_posgrady@#);
posy:=xpart (_posgradx@#+_posgrady@#);
$=image(%
if posx>0: draw axexpio.top(n,d) else: draw axexpio.bot(n,d) fi;
if posy>0: draw axeypio.rt(n,d) else: draw axeypio.lft(n,d) fi
);
$
enddef;
vardef axespin@# (expr n,d)= %%%% les deux axes sans origine mult pi
save $,posx,posy;
picture $;
numeric posx,posy;
posx:=ypart (_posgradx@#+_posgrady@#);
posy:=xpart (_posgradx@#+_posgrady@#);
$=image(%
if posx>0: draw axexpin.top(n,d) else: draw axexpin.bot(n,d) fi;
if posy>0: draw axeypin.rt(n,d) else: draw axeypin.lft(n,d) fi
);
$
enddef;
%%%%%%%% graduations isolées
vardef axexpart@#(text t)=
save $,tmp,var;
picture $;
numeric tmp;
boolean var;
var:=false;
$=image(%
for _i=t:
if numeric _i:
if var: if str @#="": draw _etiqx_.bot(tmp,taillegrad,tmp) else: draw _etiqx_@#(tmp,taillegrad,tmp) fi fi;
% draw ((0,taillegrad)--(0,-taillegrad)) shifted _c(_i,yO) withpen pencircle scaled 0.8bp;
draw graduationx(_i) withpen pencircle scaled 0.8bp;
tmp:=_i;
var:=true
else:
if str @#="": draw _etiqx_.bot(tmp,taillegrad,_i) else: draw _etiqx_@#(tmp,taillegrad,_i) fi;
var:=false
fi;
endfor;
if var: if str @#="": draw _etiqx_.bot(tmp,taillegrad,tmp) else: draw _etiqx_@#(tmp,taillegrad,tmp) fi fi);
$
enddef;
vardef axeypart@#(text t)=
save $,tmp,var;
picture $;
numeric tmp;
boolean var;
var:=false;
$=image(%
for _i=t:
if numeric _i:
if var: if str @#="": draw _etiqy_.lft(tmp,taillegrad,tmp) else: draw _etiqy_@#(tmp,taillegrad,tmp) fi fi;
draw ((taillegrad,0)--(-taillegrad,0)) shifted _c(xO,_i) withpen pencircle scaled 0.8bp;
tmp:=_i;
var:=true
else:
if str @#="": draw _etiqy_.lft(tmp,taillegrad,_i) else: draw _etiqy_@#(tmp,taillegrad,_i) fi;
var:=false
fi;
endfor;
if var: if str @#="": draw _etiqy_.lft(tmp,taillegrad,tmp) else: draw _etiqy_@#(tmp,taillegrad,tmp) fi fi);
$
enddef;
vardef axesunit=
save $;
picture $;
$=image(%
draw axes(0,0);
draw axexpart(1);
draw axeypart(1);
label.llft(LaTeX("$0$"),_c(0,0));
% label.llft("0",_c(0,0));
);
$
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% POINTS - VECTEURS %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef _ccoord(expr xA,yA)=
(xA,yA) transformed _T
enddef;
vardef _cobjet(expr obj)=
obj transformed _T
enddef;
vardef _c(text t)=
if long_texte(t)=2: _ccoord(t)
else: _cobjet(t)
fi
enddef;
vardef pol(expr r,theta)=
_c(r*cos(theta),r*sin(theta))
enddef;
vardef pold(expr r,theta)=
_c(r*cosd(theta),r*sind(theta))
enddef;
color coulpoint,coullabel,coullabelfonc;
coulpoint:=black;coullabel:=black;coullabelfonc:=black;
vardef MarquePointFig(expr pp)= % compatibilité geometriesyr15
save $;
picture $;
if marque_p = "plein":
$:=image(fill fullcircle scaled taillepoint shifted pp withcolor coulpoint);
elseif marque_p = "creux":
$:=image(%
fill fullcircle scaled taillepoint shifted pp withcolor background;
draw fullcircle scaled taillepoint shifted pp withcolor coulpoint);
elseif marque_p = "croix":
$:=image(%
draw ((-taillecroix,0)--(taillecroix,0)) shifted pp withcolor coulpoint;
draw ((0,-taillecroix)--(0,taillecroix)) shifted pp withcolor coulpoint)
else: $:=nullpicture
fi;
$
enddef;
def MarquePoint(expr pp)= % compatibilité geometriesyr15
draw MarquePointFig(pp)
enddef;
vardef pointe(text t) = %geometriesyr15
for p_ = t: if pair p_: MarquePoint(p_); fi endfor;
enddef;
vardef nommepoint@#(text t)=
save $,ch,dess,latch;
pair $;
string ch,latch;
picture dess;
if long_texte(t)=1:
dess:=image(draw MarquePointFig(t);
ch:=_chaine(t);
label@#(LaTeX("$" & ch & "$"),t) withcolor coullabel)
else:
dess:=image(%
for PP=t:
if pair PP: MarquePoint(PP); $:=PP
else: if string PP: label@#(PP,$) else: label@#(PP scaled defaultscale,$) fi withcolor coullabel
fi;
endfor)
fi;
dess
enddef;
vardef nommecourbe@#(suffix p)(text t)=
save A,ch,dess;
pair A;
string ch;
picture dess;
if long_texte(t)=1:
dess:=image(ch:=_chaine(p);
A:=_c(t,fonccourbe.p(t));
label@#(LaTeX("$" & ch & "$"),A) withcolor coullabelfonc)
else:
dess:=image(%
for _a=t:
if numeric _a: A:=_c(_a,fonccourbe.p(_a))
else: if string _a: label@#(_a,A) else: label@#(_a scaled defaultscale,A) fi withcolor coullabelfonc
fi;
endfor)
fi;
dess
enddef;
vardef nommeobj@#(text t)=
save $;
picture $;
for i=t:
if pair i: $:=nommepoint@#(t)
else: $:=nommecourbe@#(t)
fi;
exitif true;
endfor
$
enddef;
def nomme = draw nommeobj enddef;
vardef vecteur@#(expr A)(text t)=
save $,ch,m;
picture $;
pair m;
string ch;
$=image(%
if long_texte(t)=1: drawarrow A--A+t;ch:=_chaine(t);label@#(LaTeX("$\vect{" & ijmath(ch) & "}$"),A+t/2)
else:
for u=t:
if pair u: drawarrow A--A+u; m:=A+u/2
else: if string u: if u<>"": label@#(LaTeX("$\vect{" & u & "}$"),m) fi else: label@#(u,m) fi
fi;
endfor
fi);
$
enddef;
vardef marquepointcourbefig(suffix p)(text t)=
save $;
picture $;
$=image(%
for i=t:
MarquePoint(_c(i,fonccourbe.p(i)));
endfor);
$
enddef;
def marquepointcourbe= draw marquepointcourbefig enddef;
vardef marquepointcheminfig(suffix p)(text t)=
save $;
picture $;
$=image(%
for i=t:
MarquePoint(point i of p);
endfor);
$
enddef;
def marquepointchemin= draw marquepointcheminfig enddef;
vardef marquecheminouvertdroitefig(expr p)=
halfcircle shifted (0,-0.5)
scaled (2*taillepoint)
rotated (90+angle(direction infinity of p))
shifted (point infinity of p)
enddef;
def marquecheminouvertdroite= draw marquecheminouvertdroitefig enddef;
vardef marquecheminouvertgauchefig(expr p)=
halfcircle shifted (0,-0.5)
scaled (2*taillepoint)
rotated (-90+angle(direction 0 of p))
shifted (point 0 of p)
enddef;
def marquecheminouvertgauche= draw marquecheminouvertgauchefig enddef;
vardef marquecheminouvert(expr p)=
marquecheminouvertdroite(p);
marquecheminouvertgauche(p)
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% BASE %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef ijmath(suffix s)=
if (substring (0,1) of s)="i": s:="\imath" & substring (1,infinity) of s fi;
if (substring (0,1) of s)="j": s:="\jmath" & substring (1,infinity) of s fi;
s
enddef;
color coulbase;
coulbase:=black;
vardef base(suffix a,b,c)=
save O,I,J,$;
string O,I,J;
picture $;
O:=_chaine(a); I:=_chaine(b); J:=_chaine(c);
$:=image(%
draw vecteur.bot(_O,_c(1,0),ijmath(I)) withpen pencircle scaled 0.8 withcolor coulbase;
draw vecteur.lft(_O,_c(0,1),ijmath(J)) withpen pencircle scaled 0.8 withcolor coulbase;
nomme.llft(_O,LaTeX("$" & O & "$")) withcolor coulbase
);
$
enddef;
vardef basep(suffix a,b,c)=
save O,I,J,$;
string O,I,J;
picture $;
O:=_chaine(a); I:=_chaine(b); J:=_chaine(c);
$:=image(%
nomme.llft(_O,LaTeX("$" & O & "$")) withcolor coulbase;
draw axexpart(1,LaTeX("$" & I & "$")) withcolor coulbase;
draw axeypart(1,LaTeX("$" & J & "$")) withcolor coulbase;
);
$
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% QUADRILLAGE %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
numeric ep; color coul;
ep:= .2bp; %%%%%%%% épaisseur du trait
coul := .7white; %%%%%%%% couleur du trait
def quadstyle= enddef;
vardef quadrillage(expr quadx,quady) =
save $;
picture $;
$=image(if quadx>0:
for i=ceiling((QuadXmin-xO)/quadx) upto floor((QuadXmax-xO)/quadx):
draw _c(arrondimil(i*quadx)+xO,QuadYmin)--_c(arrondimil(i*quadx)+xO,QuadYmax) quadstyle withpen pencircle scaled ep withcolor coul;
endfor;
fi;
if quady>0:
for i=ceiling((QuadYmin-yO)/quady) upto floor((QuadYmax-yO)/quady):
draw _c(QuadXmin,arrondimil(i*quady)+yO)--_c(QuadXmax,arrondimil(i*quady)+yO) withpen pencircle scaled ep withcolor coul quadstyle;
endfor;
fi);
$
enddef;
vardef papierpointe(expr quadx,quady) =
save $;
picture $;
$=image(if (quadx>0) and (quady>0):
for i=ceiling(QuadXmin/quadx) upto floor(QuadXmax/quadx):
for j=ceiling(QuadYmin/quady) upto floor(QuadYmax/quady):
draw (0,0) shifted _c(i*quadx,j*quady) withpen pencircle scaled 2;
endfor;
endfor;
fi);
$
enddef;
numeric pm_epa, pm_epb, pm_epc;
color pm_coula, pm_coulb, pm_coulc;
pm_epa := .2bp; pm_epb := .3bp; pm_epc := .4bp; %%%%%%%%%% épaisseurs des traits
pm_coula := .6*white; pm_coulb := .4*white; pm_coulc := black; %%%%%%%%%% couleurs des traits
vardef papiermillimetre =
save $;
picture $;
$=image(%
for i= ceiling(QuadXmin*Ux*10/cm) upto floor(QuadXmax*Ux*10/cm):
if i mod 5 <> 0: draw (i*cm/10,QuadYmin*Uy)--(i*cm/10,QuadYmax*Uy) withpen pencircle scaled pm_epa withcolor pm_coula fi;
endfor
for i= ceiling(QuadYmin*Uy*10/cm) upto floor(QuadYmax*Uy*10/cm):
if i mod 5<> 0: draw (QuadXmin*Ux,i*cm/10)--(QuadXmax*Ux,i*cm/10) withpen pencircle scaled pm_epa withcolor pm_coula fi;
endfor
%
for i= ceiling(QuadXmin*Ux/cm)*2+1 step 2 until floor(QuadXmax*Ux/cm)*2-1:
draw (i*cm/2,QuadYmin*Uy)--(i*cm/2,QuadYmax*Uy) withpen pencircle scaled pm_epb withcolor pm_coulb;
endfor
for i= ceiling(QuadYmin*Uy/cm)*2+1 step 2 until floor(QuadYmax*Uy/cm)*2-1:
draw (QuadXmin*Ux,i*cm/2)--(QuadXmax*Ux,i*cm/2) withpen pencircle scaled pm_epb withcolor pm_coulb;
endfor
%
for i= ceiling(QuadXmin*Ux/cm) upto floor(QuadXmax*Ux/cm):
draw (i*cm,QuadYmin*Uy)--(i*cm,QuadYmax*Uy) withpen pencircle scaled pm_epc withcolor pm_coulc;
endfor
for i= ceiling(QuadYmin*Uy/cm) upto floor(QuadYmax*Uy/cm):
draw (QuadXmin*Ux,i*cm)--(QuadXmax*Ux,i*cm) withpen pencircle scaled pm_epc withcolor pm_coulc;
endfor);
$
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% FONCTIONS - COURBES %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef courbefonc(suffix f)(expr xmin, xmax, n) = %Courbe représentative d'une fonction
save $,x;
path $;
$=( _c(xmin,f(xmin))
for i=1 upto n-1:
.._c(xmin+i*(xmax-xmin)/(n-1),f(xmin+i*(xmax-xmin)/(n-1)))
endfor );
$
enddef;
%%%%%%%%%% TEST %%%%%%%%%%%%%
vardef courbefonct@#(expr xmin, xmax, n) = %Courbe représentative d'une fonction
save $,x;
path $;
$=( _c(xmin,@#(xmin))
for i=1 upto n-1:
.._c(xmin+i*(xmax-xmin)/(n-1),@#(xmin+i*(xmax-xmin)/(n-1)))
endfor );
$
enddef;
%%%%%%%%%% FINTEST %%%%%%%%%%%%%
vardef courbepoints(suffix f)(expr xmin, xmax, n) = %Points non reliés
save $,x;
picture $;
$=image(MarquePoint(_c(xmin,f(xmin)));
for i=1 upto n-1:
MarquePoint(_c(xmin+i*(xmax-xmin)/(n-1),f(xmin+i*(xmax-xmin)/(n-1))));
endfor );
$
enddef;
vardef fonccourbe@#(expr x)= %Ordonnée du point de la courbe @# d'abscisse x (dans le repère utilisateur)
ypart ((pointcourbe@#(x)) transformed inverse _T)
enddef;
vardef pointcourbe@#(expr x)= %Point de la courbe @# d'abscisse x dans le repère utilisateur
save _P_,t;
numeric t; pair _P_;
(t,whatever)=@# intersectiontimes (_c(x,2*Ymin-Ymax)--_c(x,2*Ymax-Ymin));
if t=-1: _P_:=_c(x,0)
else: _P_:=point t of @#
fi;
_P_
enddef;
vardef der@#(expr x)= %Fonction dérivée
save pp,t,v,w,d;
path pp;
pair v,w;
pp:=@#;
(t,whatever) = pp intersectiontimes (_c(x,2*Ymin-Ymax)--_c(x,2*Ymax-Ymin));
v:=direction t of pp;
w:=unitvector(v transformed inverse _T);
if xpart w = 0: d:=0 else: d:= (ypart w)/(xpart w) fi;
d
enddef;
vardef intercourbes(suffix P)(expr p,q)= %renvoie les points d'intersections de p et q dans P[]
save i,pp;
numeric i;
path pp;
pp:=p;
i:=1;
forever:
exitif xpart(pp intersectiontimes q)=-1;
P[i]:=point xpart(pp intersectiontimes q) of pp;
pp:=subpath(xpart(pp intersectiontimes q)+0.01,length pp) of pp;
%0.01(?!) pour que le point trouvé ne soit pas dans le sous-chemin...
i:=i+1;
endfor;
enddef;
vardef ptantecedents(suffix P)(expr y,p)=
intercourbes(P,_c(Xmin,y)--_c(Xmax,y),p)
enddef;
vardef antecedents(suffix P)(expr y,p)=
pair PP[];
ptantecedents(PP,y,p);
for i=1 upto 10: P[i]:=xpart (PP[i] transformed inverse _T); endfor
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% TANGENTES %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
numeric longtan;
longtan:=20;
vardef tangentefleche@# (suffix p)(text tt) =
save t,$,pp,i,N;
pair senstan.gauche,senstan.droite,senstan.double;
senstan.gauche=(1,0);senstan.droite=(0,1);senstan.double=(1,1);
numeric N[],i;
i:=0;
pair _v,M;
picture $;
for n=tt: i:=incr i ; N[i]:=n; endfor;
if i=1: N2:=longtan fi;
(t,whatever) = p intersectiontimes (_c(N1,Ymin)--_c(N1,Ymax));
M:=point t of p;
_v:=N2*unitvector(direction t of p);
$=image(%
MarquePoint(M);
if (xpart senstan@#) <> 0: drawarrow M--M-_v*(xpart senstan@#) fi;
if (ypart senstan@#) <> 0: drawarrow M--M+_v*(ypart senstan@#) fi;
);
$
enddef;
vardef tangentedroite(expr p,a) =
save $,m,M,t;
path $;
numeric m,t;
pair M;
(t,whatever) = p intersectiontimes (_c(a,Ymin)--_c(a,Ymax));
M:=point t of p;
$=M-_diag*unitvector(direction t of p)--M+_diag*unitvector(direction t of p);
$
enddef;
vardef tangente@#(suffix p)(text tt) =
if str @#="": tangentedroite(p)(tt)
else: tangentefleche@#(p)(tt)
fi
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% CALCUL INTÉGRAL %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef entrecourbes(expr p,q,xmin,xmax)=
buildcycle(droiteeqx(xmax),p,droiteeqx(xmin),q)
enddef;
vardef souscourbe(expr p,xmin,xmax)=
buildcycle(droiteeqx(xmax),p,droiteeqx(xmin),_c(Xmin,0)--_c(Xmax,0))
enddef;
vardef rectangles@#(suffix p)(expr a,b,n)= %Riemann, renvoie un chemin fermé
save pas,_rect_;
numeric pas;
path _rect_;
pas=(b-a)/n;
_rect_ =
for i=0 upto n-1:
_c(a+i*pas,yO)--_segmrect_@#(p,a+i*pas,pas)--
endfor
_c(b,yO)--cycle;
_rect_
enddef;
numeric _typerect.min,_typerect.max,_typerect.droite,_typerect.gauche;
_typerect.min=1;_typerect.max=2;_typerect.droite=3;_typerect.gauche=4;
vardef _segmrect_@#(suffix p)(expr a,pas)=
save _sousp;
path _sousp;
_sousp=subpath (xpart(p intersectiontimes droiteeqx(a)),xpart(p intersectiontimes droiteeqx(a+pas))) of p;
if _typerect@#=1: llcorner _sousp -- lrcorner _sousp
elseif _typerect@#=2: ulcorner _sousp -- urcorner _sousp
elseif _typerect@#=3: (pointcourbe.p(a))--(pointcourbe.p(a) shifted _c(pas,0))
elseif _typerect@#=4: (pointcourbe.p(a+pas) shifted _c(-pas,0))--(pointcourbe.p(a+pas))
fi
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% DROITES %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef droiteeqred(expr a,b)=
save $;
path $;
if (-(Ymax-Ymin)/(Xmax-Xmin)<a) and ((Ymax-Ymin)/(Xmax-Xmin)>a):
$:=_c(Xmin,a*Xmin+b)--_c(Xmax,a*Xmax+b);
else:
$:=_c(Ymin/a-b/a,Ymin)--_c(Ymax/a-b/a,Ymax);
fi;
$
enddef;
vardef droiteeqx(expr c)=
_c(c,2*Ymin-Ymax)--_c(c,2*Ymax-Ymin)
enddef;
vardef droiteeqcart(expr a,b,c)=
save $;
path $;
if b=0:
$=droiteeqx(-c/a)
else:
$:=droiteeqred(-a/b,-c/b)
fi;
$
enddef;
vardef droiteeq(text t)=
save $;
path $;
if long_texte(t)=1: $:= droiteeqx(t) fi;
if long_texte(t)=2: $:= droiteeqred(t) fi;
if long_texte(t)=3: $:= droiteeqcart(t) fi;
$
enddef;
vardef droitept(expr A,B)= %geometrie15syr
(_diag/abs(A-B))[B,A]--(_diag/abs(A-B))[A,B]
enddef;
vardef droite(text t)=
save $;
path $;
for i=t:
if pair i: $:=droitept(t) else: $:=droiteeq(t) fi;
exitif true;
endfor;
$
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% DEMI-PLANS %%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef demiplaninf(expr d)=
save $,A,B;
path $;
pair A,B;
if (point 0 of d) yscaled -1 < (point infinity of d) yscaled -1:
A:=point 0 of d; B:= point infinity of d
else: B:=point 0 of d; A:= point infinity of d
fi;
$=A--
if ypart A>=ypart _c(Xmin,Ymax): _c(Xmin,Ymax)-- fi
if ypart A>ypart _c(Xmin,Ymin): _c(Xmin,Ymin)-- fi
if ypart B>ypart _c(Xmax,Ymin): _c(Xmax,Ymin)-- fi
if ypart B>=ypart _c(Xmax,Ymax): _c(Xmax,Ymax)-- fi
B--cycle;
$
enddef;
vardef demiplansup(expr d)=
save $,A,B;
path $;
pair A,B;
if (point 0 of d) yscaled -1 < (point infinity of d) yscaled -1:
A:=point 0 of d; B:= point infinity of d
else: B:=point 0 of d; A:= point infinity of d
fi;
$=A--
if ypart A<=ypart _c(Xmin,Ymin): _c(Xmin,Ymin)-- fi
if ypart A<ypart _c(Xmin,Ymax): _c(Xmin,Ymax)-- fi
if ypart B<ypart _c(Xmax,Ymax): _c(Xmax,Ymax)-- fi
if ypart B<=ypart _c(Xmax,Ymin): _c(Xmax,Ymin)-- fi
B--cycle;
$
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% PROJECTIONS %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef projetex(expr A)=
_c(xpart (A transformed inverse _T),yO)
enddef;
vardef projetey(expr A)=
_c(xO,ypart (A transformed inverse _T))
enddef;
vardef projectionx@#(text t)=
save $,_a,_fg,dec;
picture $,_fg;_fg:=nullpicture;
numeric dec;dec=0;
pair _a;
$=image(%
for i=t:
if pair i: draw i--projetex(i);_a:=i elseif numeric i: dec:=i else: _fg:=thelabel.@#(i,projetex(_a)) fi;
endfor;
draw _fg shifted (0,dec));
$
enddef;
vardef projectiony@#(text t)=
save $,_a,_fg,dec;
picture $,_fg;_fg:=nullpicture;
numeric dec;dec=0;
pair _a;
$=image(%
for i=t:
if pair i: draw i--projetey(i);_a:=i elseif numeric i: dec:=i else: _fg:=thelabel.@#(i,projetey(_a)) fi;
endfor;
draw _fg shifted (dec,0));
$
enddef;
vardef projectionaxes(text t)=
save $,_A,n;
picture $,_fg[];_fg1=_fg2=nullpicture;
pair _A;
numeric n,dd;n=1;dd=0;
$=image(%
for i=t: if numeric i: dd:=i fi; endfor
for i=t:
if not numeric i:
if pair i: _A:=i;
elseif n=1: if ypart _A > ypart _O: draw projectionx.bot(_A,i,-dd) else: draw projectionx.top(_A,i,dd) fi;n:=n+1
else: if xpart _A > xpart _O: draw projectiony.lft(_A,i,-dd) else: draw projectiony.rt(_A,i,dd) fi;n:=n+1
fi;
fi;
endfor;
if n<=2: draw projectiony(_A) fi; if n=1: draw projectionx(_A) fi);
$
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% SUITES %%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef suite(suffix u)(expr deb,fin)=
save $;
picture $;
$=courbepoints(u,deb,fin,fin-deb+1);
$
enddef;
vardef _suiterecfonc_(expr x)=0 enddef;
numeric _suiterecdeb_, _suiterecfin_, _suiterecinit_;
vardef suiterec(suffix f)(expr deb,fin,init)= %escalier un+1=f(un), u_deb=init
vardef _suiterecfonc_(expr x)=f(x) enddef;
_suiterecdeb_:=deb;_suiterecfin_:=fin;_suiterecinit_:=init; %stocke les valeurs pour réutilisation
save $,un;
path $;
numeric un;
un=init;
$=_c(un,yO)
for i=deb upto fin-1:
--_c(un,f(un))--_c(f(un),f(un))
hide(un:=f(un))
endfor;
$
enddef;
vardef suiterecprojx@#(text t)= %projections et étiquettes sur axe x, utilise les valeurs de suiterec
save $,deb,fin,nom,_qw_,un;
picture $,lab;
string nom;
numeric deb,fin,_qw_,un,_prec;
deb:=_suiterecdeb_;fin:=_suiterecfin_;un:=_suiterecinit_;
_qw_:=1;
for i=t: %récupère les éventuelles nouvelles valeurs pour deb et fin
if _qw_ =1: if string i: nom:=i else: nom:="_val";_prec:=i fi;
elseif _qw_=2:
deb:=i;
for j=_suiterecdeb_ upto i-1:
un:=_suiterecfonc_(un);
endfor
elseif _qw_=3: fin:=i
fi;
_qw_:=_qw_+1;
endfor;
$=image(%
if nom="":
if deb=_suiterecdeb_:
deb:=deb+1;un:=_suiterecfonc_(un)
fi;
for i=deb upto fin:
draw projectionx.@#(_c(un,un));
un:=_suiterecfonc_(un);
endfor
elseif nom="_val":
if deb=_suiterecdeb_:
% label.@#(format("%10f",arrondi(10**_prec,un)),_c(un,yO));
draw etiquettex.@#(arrondi(10**_prec,un));
deb:=deb+1;un:=_suiterecfonc_(un)
fi;
for i=deb upto fin:
% draw projectionx.@#(_c(un,un),format("%10f",arrondi(10**_prec,un)));
lab:=LaTeX("$\num{" & decimal(arrondi(10**_prec,un)) & "}$");
draw projectionx.@#(_c(un,un),lab,-taillegrad);
un:=_suiterecfonc_(un);
endfor
else:
if deb=_suiterecdeb_:
label.@#(LaTeX("$" & nom & "_{" & decimal(deb) & "}" & "$"),_c(un,yO));
deb:=deb+1;un:=_suiterecfonc_(un)
fi;
for i=deb upto fin:
lab:=LaTeX("$" & nom & "_{" & decimal(i) & "}" & "$");
draw projectionx.@#(_c(un,un),lab);
un:=_suiterecfonc_(un);
endfor
fi);
$
enddef;
vardef suiterecprojy@#(text t)= %projections et étiquettes sur axe y, utilise les valeurs de suiterec
save $,deb,fin,nom,_qw_,un;
picture $,lab;
string nom;
numeric deb,fin,_qw_,un,_prec;
deb:=_suiterecdeb_;fin:=_suiterecfin_;un:=_suiterecinit_;
_qw_:=1;
for i=t: %récupère les éventuelles nouvelles valeurs pour deb et fin
if _qw_ =1: if string i: nom:=i else: nom:="_val";_prec:=i fi;
elseif _qw_=2:
deb:=i;
for j=_suiterecdeb_ upto i-2:
un:=_suiterecfonc_(un);
endfor
elseif _qw_=3: fin:=i
fi;
_qw_:=_qw_+1;
endfor;
$=image(%
if nom="":
if deb=_suiterecdeb_:
deb:=deb+1;
fi;
for i=deb-1 upto fin-1:
draw projectiony.@#(_c(un,_suiterecfonc_(un)));
un:=_suiterecfonc_(un);
endfor
elseif nom="_val":
if deb=_suiterecdeb_:
deb:=deb+1;
fi;
for i=deb-1 upto fin-1:
lab:=LaTeX("$\num{" & decimal(arrondi(10**_prec,un)) & "}$");
draw projectiony.@#(_c(un,_suiterecfonc_(un)),lab,-taillegrad);
un:=_suiterecfonc_(un);
endfor
else:
if deb=_suiterecdeb_:
deb:=deb+1;
fi;
for i=deb-1 upto fin-1:
lab:=LaTeX("$" & nom & "_{" & decimal(i+1) & "}" & "$");
draw projectiony.@#(_c(un,_suiterecfonc_(un)),lab);
un:=_suiterecfonc_(un);
endfor
fi);
$
enddef;
vardef suiterecproj(text t)=
save $;
picture $;
$=image(%
draw suiterecprojx.bot(t);
draw suiterecprojy.lft(t));
$
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% INTERVALLES %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
vardef bornex[](expr val)=
((1mm,-2mm)--(0,-2mm)--(0,2mm)--(1mm,2mm)) if @<0: xscaled -1 fi shifted _c(val,xO)
enddef;
vardef borney[](expr val)=
((2mm,1mm)--(2mm,0)--(-2mm,0)--(-2mm,1mm)) if @<0: yscaled -1 fi shifted _c(yO,val)
enddef;
pair sensborne.FF,sensborne.FO,sensborne.OF,sensborne.OO;
sensborne.FF=-sensborne.OO=(1,-1);sensborne.FO=-sensborne.OF=(1,1);
vardef intervallex@#(expr vmin,vmax)=
save $;
picture $;
$=image(%
draw _c(vmin,xO)--_c(vmax,xO) withpen pencircle scaled 2pt;
draw bornex[xpart sensborne@#](vmin) withpen pencircle scaled 2pt;
draw bornex[ypart sensborne@#](vmax) withpen pencircle scaled 2pt);
$
enddef;
vardef intervalley@#(expr vmin,vmax)=
save $;
picture $;
$=image(%
draw _c(yO,vmin)--_c(yO,vmax) withpen pencircle scaled 2pt;
draw borney[xpart sensborne@#](vmin) withpen pencircle scaled 2pt;
draw borney[ypart sensborne@#](vmax) withpen pencircle scaled 2pt);
$
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%% STATISTIQUES %%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
numeric _decboitemoustache_,_largboitemoustache_;
vardef boitemoustache(text t)=
_decboitemoustache_:=1.5cm;
_largboitemoustache_:=1cm;
save $,n;
picture $;
numeric n,_valeursboitemoustache_[];
n:=1;
for i=t:
_valeursboitemoustache_[n]:=i;
n:=n+1;
endfor;
if known _valeursboitemoustache_[6]: _decboitemoustache_:=_valeursboitemoustache_[6] fi;
if known _valeursboitemoustache_[7]: _largboitemoustache_:=_valeursboitemoustache_[7] fi;
$=image(%
fill fullcircle scaled 3 shifted _c(_valeursboitemoustache_[1],yO);
draw _c(_valeursboitemoustache_[1],yO)--_c(_valeursboitemoustache_[2],yO);
draw _c(_valeursboitemoustache_[2],yO) shifted (0,-_largboitemoustache_/2)--_c(_valeursboitemoustache_[2],yO) shifted (0,_largboitemoustache_/2)--_c(_valeursboitemoustache_[4],yO) shifted (0,_largboitemoustache_/2)--_c(_valeursboitemoustache_[4],yO) shifted (0,-_largboitemoustache_/2)--cycle;
draw _c(_valeursboitemoustache_[3],yO) shifted (0,-_largboitemoustache_/2)--_c(_valeursboitemoustache_[3],yO) shifted (0,_largboitemoustache_/2);
draw _c(_valeursboitemoustache_[4],yO)--_c(_valeursboitemoustache_[5],yO);
fill fullcircle scaled 3 shifted _c(_valeursboitemoustache_[5],yO)%
) shifted (0,_decboitemoustache_);
$
enddef;
vardef projboitemoustache@#(text t)=
save $,n,_lab_,_comp_,A,tmp;
pair A;
picture $,_lab_[];
numeric n_comp_,tmp;
n:=long_texte(t);
if n=0:
_lab_[1]:=LaTeX("$X_{min}$");
_lab_[2]:=LaTeX("$Q_1$");
_lab_[3]:=LaTeX("$M_e$");
_lab_[4]:=LaTeX("$Q_3$");
_lab_[5]:=LaTeX("$X_{max}$");
elseif n=1:
if t=0: for i=1 upto 5: _lab_[i]:=nullpicture; endfor
else:
tmp:=floor(t);
for i=1 upto 5:
_lab_[i]:=LaTeX("\num{" & decimal(arrondi(10**tmp,_valeursboitemoustache_[i])) & "}");
endfor
fi
else: _comp_:=1; for i=t:
if numeric i: _lab_[_comp_]:=LaTeX("\num{" & decimal(i) & "}")
elseif string i: _lab_[_comp_]:=LaTeX(i)
else: _lab_[_comp_]:=i
fi;
_comp_:=_comp_+1;
endfor
fi;
$=image(%
for i=1 upto 5:
if (i=1) or (i=5):
A:=_c(_valeursboitemoustache_[i],yO) shifted(0,_decboitemoustache_)
else: A:=_c(_valeursboitemoustache_[i],yO) shifted(0,_decboitemoustache_-_largboitemoustache_/2)
fi;
draw projectionx@#(A,_lab_[i]);
endfor);
$
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% FONCTIONS USUELLES %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pi:=3.141592654;
e:=2.718281828;
vardef sin(expr x) = sind(180*x/pi) enddef;
vardef cos(expr x) = cosd(180*x/pi) enddef;
vardef tan(expr x) = sin(x)/cos(x) enddef;
vardef exp(expr x) = mexp(x*256) enddef;
vardef ln(expr x) = mlog(x)/256 enddef;
vardef ch(expr x)=(exp(x)+exp(-x))/2 enddef;
vardef sh(expr x)=(exp(x)-exp(-x))/2 enddef;
vardef Arctan(expr x)= pi*angle(1,x)/180 enddef;
vardef Arcsin(expr x)= Arctan(x/sqrt(1-x**2)) enddef;
vardef Arccos(expr x)= pi/2-Arcsin(x) enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% REMPLISSAGE %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
let _fill_ = fill;
def fill expr c=
if path c: _fill_ c else: draw c fi
enddef;
numeric largbriques,hautbriques,decbriques;
largbriques=12;hautbriques=6;decbriques=6;
vardef briques(text t)=
if long_texte(t)=0:
repbriques(largbriques,hautbriques,decbriques)
else:
repbriques(t)
fi
enddef;
vardef repbriques(expr larg,haut,dec)=
numeric d;d=0;
image(%
for j=0 upto _hautcadre/haut:
draw ((0,0)--(_largcadre,0)) shifted (0,j*haut);
d:=d+dec;if d>larg: d:=d-larg fi;
for i=0 upto _largcadre/larg:
draw ((0,0)--(0,haut)) shifted (i*larg+d,j*haut);
endfor;
endfor) shifted llcorner cadre
enddef;
numeric pashach,anglehach;
pashach=5;anglehach=60;
vardef hachures(text t)=
if long_texte(t)=0:
rephachures(pashach,anglehach)
else:
rephachures(t)
fi
enddef;
vardef rephachures(expr pas,angle)=
image(%
for i=floor(-_diag/(2*pas)) upto ceiling(_diag/(2*pas)):
draw ((-_diag/2,0)--(_diag/2,0)) shifted (0,i*pas);
endfor) rotated angle shifted center cadre
enddef;
numeric pervagues,ampvagues,decvagues;
pervagues=20;ampvagues=3;decvagues=10;
vardef vagues(text t)=
if long_texte(t)=0:
repvagues(pervagues,ampvagues,decvagues)
else:
repvagues(t)
fi
enddef;
vardef repvagues(expr per,amp,dec)= %D'après le manuel de l'utilisateur de MetaPost
image(%
for j=0 upto _hautcadre/dec:
for i=0 upto _largcadre/amp:
draw ((0,0){curl 0}..(per/4,-amp)..(per/2,0){curl 0}..(3*per/4,amp)..(per,0){curl 0}) shifted (i*per,j*dec);
endfor;
endfor) shifted llcorner cadre
enddef;
primarydef p avec c =
begingroup
save _des_;
picture _des_;
_des_:=c;
clip _des_ to p;
_des_
endgroup
enddef;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% DIVERS %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
string LaTeX_packages[],LaTeX_preamble,LaTeX_inputenc;
LaTeX_preamble:="";LaTeX_inputenc:="";
numeric n_packages;
n_packages:=0;
def LaTeX_AjoutPackage(expr t)=
if known latexmp_module:
latexmp_packages:=latexmp_packages & "," & t
else:
n_packages:=n_packages+1;
LaTeX_packages[n_packages]:=t
fi
enddef;
def LaTeX_AjoutCommande(expr t)=
LaTeX_preamble:=LaTeX_preamble & t
enddef;
def LaTeX_Encodage(expr t)=
LaTeX_inputenc:= t
enddef;
boolean LaTeXprem;
LaTeXprem:=true;
def LaTeXsetup =
if LaTeXprem:
LaTeXprem:=false;
latexmp_preamble:=LaTeX_preamble;
latexmp_inputenc:=LaTeX_inputenc;
if latexmp_inputenc="": latexmp_inputenc:="utf8" fi;
if latexmp_packages="": latexmp_packages:="fourier" fi;
latexmp_packages:=latexmp_packages & ",textcomp,mathtools,mathrsfs,esvect[e],siunitx[output-decimal-marker={,}],babel[frenchb]";
latexmp_preamble:=latexmp_preamble & "\newcommand{\vect}[1]{\vv{#1}}" & "\newcommand{\calc}{\mathscr{C}}" & "\newcommand{\calp}{\mathscr{P}}" & "\DecimalMathComma" ;
fi
enddef;
vardef LaTeX primary sc = %D'après TEX.mp
if known latexmp_module: LaTeXsetup; textext(sc) scaled defaultscale
else:
save n_p;
numeric n_p;
write "verbatimtex" to "mptextmp.mp";
write "%&latex" to "mptextmp.mp";
write "\documentclass[10pt]{article}" to "mptextmp.mp";
if LaTeX_inputenc="":
write "\usepackage[utf8]{inputenc}" to "mptextmp.mp"
else:
write "\usepackage[" & LaTeX_inputenc &"]{inputenc}" to "mptextmp.mp"
fi;
write "\usepackage[T1]{fontenc}" to "mptextmp.mp";
if known LaTeX_packages[1]:
n_p:=1;
forever: exitunless known LaTeX_packages[n_p];
write "\usepackage{" & LaTeX_packages[n_p] &"}" to "mptextmp.mp";
n_p:=n_p+1;
endfor
else:
write "\usepackage{fourier}" to "mptextmp.mp"
fi;
write "\usepackage{amsmath}" to "mptextmp.mp";
write "\usepackage{mathrsfs}" to "mptextmp.mp";
write "\usepackage[e]{esvect}" to "mptextmp.mp";
write "\usepackage[output-decimal-marker={,}]{siunitx}" to "mptextmp.mp";
write "\usepackage[frenchb]{babel}" to "mptextmp.mp";
write LaTeX_preamble to "mptextmp.mp";
write "\newcommand{\vect}[1]{\vv{#1}}" to "mptextmp.mp";
write "\newcommand{\calc}{\mathscr{C}}" to "mptextmp.mp";
write "\newcommand{\calp}{\mathscr{P}}" to "mptextmp.mp";
write "\begin{document}" to "mptextmp.mp";
write "etex" to "mptextmp.mp";
write "btex "& sc &" etex" to "mptextmp.mp";
write EOF to "mptextmp.mp";
scantokens "input mptextmp" scaled defaultscale
fi
enddef;
%%%%%%%%%%%%%%%Figure intermédiaire%%%%%%%%%%%%%%%%%%%
def figureinter=
clip currentpicture to cadre;
shipit;
_nfig:=_nfig+1;
charcode:=charcode+1;
enddef;
vardef arrowhead expr p = %redéfinition flèches
save q,e; path q; pair e;
e = point length p of p;
q = gobble(p shifted -e cutafter makepath(pencircle scaled 2ahlength))
cuttings;
(q rotated .5ahangle & reverse q rotated -.5ahangle -- 0.5*(point 0 of q)-- cycle) shifted e
enddef;
def epaisseur=withpen pencircle scaled enddef;
def couleur=withcolor enddef;
vardef long_texte(text t)=
save i;
numeric i;
i:=0;
for n=t: i:=i+1; endfor
i
enddef;
vardef _chaine(suffix s)= %met les termes en indice si le 2e est un chiffre
save c,d;
string c,d;
d:= str s;
if length(d)=1:
c:=d
elseif isdigit (substring (1,2) of d):
c:= (substring (0,1) of d) & "_{" & substring (1,infinity) of d & "}"
else: c:=str s
fi;
c
enddef;
vardef arrondi(expr p,x)= %arrondi de x au p-ième
round((x-floor(x))*p)/p+floor(x)
enddef;
vardef arrondimil(expr x)=
arrondi(1000,x)
enddef;
vardef pgcd(expr a,b)=
save r_,a_,b_;
numeric r_,a_,b_;
a_=a;b_=b;
forever:
r_:=a_ mod b_;
exitif r_=0;
a_:=b_;
b_:=r_;
endfor;
b_
enddef;
%%%%%%%%%%%%%%% COULEURS %%%%%%%%%%%%%%%%%%%
cmykcolor Rouge,Vert,Bleu,Marron,Lime,Orange,Rose,Pourpre,Violet,Cyan,Magenta,Jaune,Olive,Noir,Grisfonce,Gris,Grisclair,Blanc,Beige,Marine,Moutarde,Vertfonce;
Rouge:=(0,1,1,0);
Vert:=(1,0,1,0);
Bleu:=(1,1,0,0);
Marron:=(0,0.53,1,0.65);
Lime:=(0.38,0,0.78,0.01);
Orange:=(0,0.5,1,0);
Rose:=(0,0.57,0.38,0.01);
Pourpre:=(0,0.91,0.59,0.38);
Violet:=(0.5,1,0,0.4);
Cyan:=(1,0,0,0);
Magenta:=(0,1,0,0);
Jaune:=(0,0,1,0);
Olive:=(0.21,0,0.75,0.45);
Noir:=(0,0,0,1);
Grisfonce:=(0,0,0,0.75);
Gris:=(0,0,0,0.5);
Grisclair:=(0,0,0,0.25);
Blanc:=(0,0,0,0);
Beige:=(0,0.14,0.37,0.22);
Marine:=(1,1,0,0.5);
Moutarde:=(0.04,0,1,0.19);
Vertfonce:=(1,0,1,0.5);
vardef conversion_cmyn_rvb(expr coul)=
((1-cyanpart coul)*(1-blackpart coul),(1-magentapart coul)*(1-blackpart coul),(1-yellowpart coul)*(1-blackpart coul))
enddef;
color rouge,vert,bleu,marron,lime,orange,rose,pourpre,violet,cyan,magenta,jaune,olive,noir,grisfonce,gris,grisclair,blanc,beige,marine,moutarde,vertfonce;
rouge:=conversion_cmyn_rvb(Rouge);
vert:=conversion_cmyn_rvb(Vert);
bleu:=conversion_cmyn_rvb(Bleu);
marron:=conversion_cmyn_rvb(Marron);
lime:=conversion_cmyn_rvb(Lime);
orange:=conversion_cmyn_rvb(Orange);
rose:=conversion_cmyn_rvb(Rose);
pourpre:=conversion_cmyn_rvb(Pourpre);
violet:=conversion_cmyn_rvb(Violet);
cyan:=conversion_cmyn_rvb(Cyan);
magenta:=conversion_cmyn_rvb(Magenta);
jaune:=conversion_cmyn_rvb(Jaune);
olive:=conversion_cmyn_rvb(Olive);
noir:=conversion_cmyn_rvb(Noir);
grisfonce:=conversion_cmyn_rvb(Grisfonce);
gris:=conversion_cmyn_rvb(Gris);
grisclair:=conversion_cmyn_rvb(Grisclair);
blanc:=conversion_cmyn_rvb(Blanc);
beige:=conversion_cmyn_rvb(Beige);
marine:=conversion_cmyn_rvb(Marine);
moutarde:=conversion_cmyn_rvb(Moutarde);
vertfonce:=conversion_cmyn_rvb(Vertfonce);
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