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|
%%%
% Diff\'erentes représentations graphiques
%%%
\def\filedateRepGraph{2024/08/20}%
\def\fileversionRepGraph{0.1a}%
\message{-- \filedateRepGraph\space v\fileversionRepGraph}%
%
\setKVdefault[TraceG]{Millimetre=false,Grille=false,Graduations=false,PasGradX=1,PasGradY=1,PasGrilleX=1,PasGrilleY=1,Xmin=-5.5,Xmax=5.5,Xstep=1,Ymin=-5.5,Ymax=5.5,Ystep=1,Bornea=-5.5,Borneb=5.5,LabelX={},LabelY={},LegendeX=false,LegendeY=false,LabelC=0.5,NomCourbe={},Origine={(5.5,5.5)},Fonction=false,Points=false,Invisible=false,CouleurPoint=red,CouleurTrace=black,Epaisseur=1,Relie=false,RelieSegment=false,Marque=dot,Code=false,Vide=false,NbPointsCourbe=100,Tiret=false,StyleTrace=0,Date=false}%
\defKV[TraceG]{Traces=\setKV[TraceG]{Code}}%
\defKV[TraceG]{LabelX=\setKV[TraceG]{LegendeX}}%
\defKV[TraceG]{LabelY=\setKV[TraceG]{LegendeY}}%
\newcommand\TraceGraphique[2][]{%
\useKVdefault[TraceG]%
\setKV[TraceG]{#1}%
\ifboolKV[TraceG]{Fonction}{%
\MPTraceFonction[#1]{#2}%
}{%
\setKV[TraceG]{Xmin=0,Ymin=0}
\setKV[TraceG]{#1}%
\readlist*\ListePointsPlaces{#2}%
\newtoks\toklistepoint%
\foreachitem\compteur\in\ListePointsPlaces{\expandafter\Updatetoks\compteur\nil}%
\MPPlacePoint[#1]{\the\toklistepoint}
}%
}%
\newcommand\MPPlacePoint[2][]{%
\ifluatex
\mplibforcehmode
\begin{mplibcode}
xmin=\useKV[TraceG]{Xmin};
xmax=\useKV[TraceG]{Xmax};
ymin=\useKV[TraceG]{Ymin};
ymax=\useKV[TraceG]{Ymax};
pasx=\useKV[TraceG]{Xstep};
pasy=\useKV[TraceG]{Ystep};
x.u=1cm/\useKV[TraceG]{Xstep};
y.u=1cm/\useKV[TraceG]{Ystep};
grillex=\useKV[TraceG]{PasGrilleX};
grilley=\useKV[TraceG]{PasGrilleY};
pasgradx=\useKV[TraceG]{PasGradX};
pasgrady=\useKV[TraceG]{PasGradY};
pos=\useKV[TraceG]{LabelC};
marque_p:=str \useKV[TraceG]{Marque};
m_c:=m_c*2;
color colorpoint,colortrace;
colorpoint=\useKV[TraceG]{CouleurPoint};
colortrace=\useKV[TraceG]{CouleurTrace};
boolean Grille,Graduations,LegendeX,LegendeY;
Grille=\useKV[TraceG]{Grille};
Graduations=\useKV[TraceG]{Graduations};
LegendeX:=\useKV[TraceG]{LegendeX};
LegendeY:=\useKV[TraceG]{LegendeY};
boolean Date;
Date=\useKV[TraceG]{Date};
boolean Relie;
Relie=\useKV[TraceG]{Relie};
boolean RelieSegment;
RelieSegment=\useKV[TraceG]{RelieSegment};
boolean Invisible;
Invisible=\useKV[TraceG]{Invisible};
pair Origine;
Origine=(0,0);
if Grille:
drawoptions(withcolor 0.75white);
for k=0 step grillex until (xmax-xmin):
trace (k*x.u,ypart(Origine))--(x.u*k,y.u*(ymax-ymin));
endfor;
for k=0 step grilley until (ymax-ymin):
trace (xpart(Origine),k*y.u)--(x.u*(xmax-xmin),y.u*k);
endfor;
drawoptions();
fi;
if Graduations:
for k=0 step pasgradx until (xmax-xmin):
trace ((0,-0.5mm)--(0,0.5mm)) shifted ((k*x.u,0) shifted Origine) withpen pencircle scaled1.25;
if Date:
label.bot(TEX(decimal(xmin+k)),(k*x.u,0) shifted Origine);
else:
label.bot(TEX("\num{"&decimal(xmin+k)&"}"),(k*x.u,0) shifted Origine);
fi;
endfor;
label.ulft(TEX("\num{"&decimal(ymin)&"}"),(0,0) shifted Origine);
for k=pasgrady step pasgrady until (ymax-ymin):
trace ((-0.5mm,0)--(0.5mm,0)) shifted ((0,k*y.u) shifted Origine) withpen pencircle scaled1.25;
label.lft(TEX("\num{"&decimal(ymin+k)&"}"),(0,k*y.u) shifted Origine);
endfor;
fi;
drawoptions(withpen pencircle scaled1.5);
drawarrow Origine--(xpart(Origine),y.u*(ymax-ymin));
drawarrow Origine--((xmax-xmin)*x.u,ypart(Origine));
drawoptions();
% On relie éventuellement les points
if Relie:
pair N[];
nbpoint=0;
for p_=#2:
nbpoint:=nbpoint+1;
N[nbpoint]=(x.u*(xpart(p_)-xmin),y.u*(ypart(p_)-ymin));
endfor;
draw N[1] for k=2 upto nbpoint:
..N[k]
endfor withcolor colortrace;
fi;
if RelieSegment:
pair N[];
nbpoint=0;
for p_=#2:
nbpoint:=nbpoint+1;
N[nbpoint]=(x.u*(xpart(p_)-xmin),y.u*(ypart(p_)-ymin));
endfor;
draw N[1] for k=2 upto nbpoint:
--N[k]
endfor withcolor colortrace;
fi;
% On place les points
if Invisible=false:
drawoptions(withcolor colorpoint);
for p_=#2:
if marque_p="dot":
dotlabel("",(x.u*(xpart(p_)-xmin),y.u*(ypart(p_)-ymin)));
elseif marque_p="croix":
pointe((x.u*(xpart(p_)-xmin),y.u*(ypart(p_)-ymin)));
fi;
endfor;
drawoptions();
fi;
% on labelise les axes
if LegendeX:
label.urt(btex \useKV[TraceG]{LabelX} etex,(x.u*(xmax-xmin),ypart(Origine)));
fi;
if LegendeY:
label.urt(btex \useKV[TraceG]{LabelY} etex,(xpart(Origine),y.u*(ymax-ymin)));
fi;
\end{mplibcode}
\else
\mpxcommands{%
\usepackage{ProfCollege}
\setKV[TraceG]{#1}
}
\begin{mpost}[mpsettings={xmin=\useKV[TraceG]{Xmin};xmax=\useKV[TraceG]{Xmax};ymin=\useKV[TraceG]{Ymin};ymax=\useKV[TraceG]{Ymax};pasx=\useKV[TraceG]{Xstep};pasy=\useKV[TraceG]{Ystep};xu=1cm/\useKV[TraceG]{Xstep};yu=1cm/\useKV[TraceG]{Ystep};grillex=\useKV[TraceG]{PasGrilleX};grilley=\useKV[TraceG]{PasGrilleY};pos=\useKV[TraceG]{LabelC};color colorpoint,colortrace;colorpoint=\useKV[TraceG]{CouleurPoint};colortrace=\useKV[TraceG]{CouleurTrace};boolean Grille;Grille=\useKV[TraceG]{Grille};boolean Graduations;Graduations=\useKV[TraceG]{Graduations};boolean Relie;Relie=\useKV[TraceG]{Relie};boolean RelieSegment;RelieSegment=\useKV[TraceG]{RelieSegment};boolean Invisible;Invisible=\useKV[TraceG]{Invisible};}]
pair Origine;
Origine=(0,0);
if Grille:
drawoptions(withcolor 0.75white);
for k=0 step grillex until (xmax-xmin):
trace (k*xu,ypart(Origine))--(xu*k,yu*(ymax-ymin));
endfor;
for k=0 step grilley until (ymax-ymin):
trace (xpart(Origine),k*yu)--(xu*(xmax-xmin),yu*k);
endfor;
drawoptions();
fi;
if Graduations:
for k=0 step grillex until (xmax-xmin):
trace ((0,-0.5mm)--(0,0.5mm)) shifted ((k*xu,0) shifted Origine) withpen pencircle scaled1.25;
label.bot(LATEX("\num{"&decimal(xmin+k)&"}"),(k*xu,0) shifted Origine);
endfor;
label.ulft(LATEX("\num{"&decimal(ymin)&"}"),(0,0) shifted Origine);
for k=grilley step grilley until (ymax-ymin):
trace ((-0.5mm,0)--(0.5mm,0)) shifted ((0,k*yu) shifted Origine) withpen pencircle scaled1.25;
label.lft(LATEX("\num{"&decimal(ymin+k)&"}"),(0,k*yu) shifted Origine);
endfor;
fi;
drawoptions(withpen pencircle scaled1.5);
drawarrow Origine--(xpart(Origine),yu*(ymax-ymin));
drawarrow Origine--((xmax-xmin)*xu,ypart(Origine));
drawoptions();
% On relie éventuellement les points
if Relie:
pair N[];
nbpoint=0;
for p_=#2:
nbpoint:=nbpoint+1;
N[nbpoint]=(xu*(xpart(p_)-xmin),yu*(ypart(p_)-ymin));
endfor;
draw N[1] for k=2 upto nbpoint:
..N[k]
endfor withcolor colortrace;
fi;
if RelieSegment:
pair N[];
nbpoint=0;
for p_=#2:
nbpoint:=nbpoint+1;
N[nbpoint]=(xu*(xpart(p_)-xmin),yu*(ypart(p_)-ymin));
endfor;
draw N[1] for k=2 upto nbpoint:
--N[k]
endfor withcolor colortrace;
fi;
% On place les points
if Invisible=false:
drawoptions(withcolor colorpoint);
for p_=#2:
dotlabel("",(xu*(xpart(p_)-xmin),yu*(ypart(p_)-ymin)));
endfor;
drawoptions();
fi;
%on labelise les axes
label.urt(btex \unexpanded{\useKV[TraceG]{LabelX}} etex,(xu*(xmax-xmin),ypart(Origine)));
label.urt(btex \unexpanded{\useKV[TraceG]{LabelY}} etex,(xpart(Origine),yu*(ymax-ymin)));
\end{mpost}
\fi
}
\newcommand\MPTraceFonction[2][]{%
\ifluatex
\mplibforcehmode
\begin{mplibcode}
borneinf=\useKV[TraceG]{Bornea};
bornesup=\useKV[TraceG]{Borneb};
nbpointsCourbe:=\useKV[TraceG]{NbPointsCourbe};
xmin=\useKV[TraceG]{Xmin};
xmax=\useKV[TraceG]{Xmax};
ymin=\useKV[TraceG]{Ymin};
ymax=\useKV[TraceG]{Ymax};
pasx=\useKV[TraceG]{Xstep};
pasy=\useKV[TraceG]{Ystep};
x.u=1cm/\useKV[TraceG]{Xstep};
y.u=1cm/\useKV[TraceG]{Ystep};
grillex=\useKV[TraceG]{PasGrilleX};
grilley=\useKV[TraceG]{PasGrilleY};
gradx=\useKV[TraceG]{PasGradX};
grady=\useKV[TraceG]{PasGradY};
pos=\useKV[TraceG]{LabelC};
Epaisseur:=\useKV[TraceG]{Epaisseur};
color colortrace;
colortrace=\useKV[TraceG]{CouleurTrace};
pair Origine;
Origine=(xmin,ymin)+\useKV[TraceG]{Origine};
boolean Grille,Vide,Graduations,LegendeX,LegendeY;
Grille=\useKV[TraceG]{Grille};
Vide=\useKV[TraceG]{Vide};
Graduations=\useKV[TraceG]{Graduations};
LegendeX:=\useKV[TraceG]{LegendeX};
LegendeY:=\useKV[TraceG]{LegendeY};
vardef sin(expr t) = sind(c*t) enddef;
vardef cos(expr t) = cosd(c*t) enddef;
vardef tan(expr t) = sin(t)/cos(t) enddef;
vardef exp(expr t) = e**t enddef;
vardef ch(expr x)=(exp(x)+exp(-x))/2 enddef;
vardef sh(expr x)=(exp(x)-exp(-x))/2 enddef;
vardef ln(expr t) = mlog(t)/256 enddef;
vardef arcsin(expr x)=%Définition mathématique en radian
pi*angle((sqrt(1-x**2),x))/180
enddef;
vardef arccos(expr x)=%Définition mathématique en radian
pi*angle((x,sqrt(1-x**2)))/180
enddef;
def enplace=
xscaled x.u yscaled y.u shifted (Origine*cm)
enddef;
vardef placepoint(expr q,r)=
(q,r) enplace
enddef;
path Cb[];
vardef courbe[](expr a,b,nb)(text texte)=
path Courbe;
for i:=0 upto nb :
x@[i]:=(a+i*(b-a)/nb);
x:=x@[i];
y@[i]:=texte;
endfor ;
Cb@:=(x@.0*x.u,y@.0*y.u)
for i:=1 upto nb :
..(x@[i]*x.u,y@[i]*y.u)
endfor;
Cb@:=Cb@ shifted (Origine*cm);
Courbe=Cb@;
Courbe
enddef;
if Grille:
drawoptions(withcolor 0.75white);
for k=xpart(Origine) step grillex until xmax:
trace u*(k,ymin)--u*(k,ymax);
endfor;
for k=xpart(Origine) step -grillex until xmin:
trace u*(k,ymin)--u*(k,ymax);
endfor;
for k=ypart(Origine) step grilley until ymax:
trace u*(xmin,k)--u*(xmax,k);
endfor;
for k=ypart(Origine) step -grilley until ymin:
trace u*(xmin,k)--u*(xmax,k);
endfor;
drawoptions();
fi;
if Graduations:
for k=gradx step gradx until bornesup:%xmax*gradx/grillex:
dotlabel.bot(TEX("\num{"&decimal(k)&"}"),(k*x.u+xpart(Origine*cm),ypart(Origine*cm)));
endfor;
for k=-gradx step -gradx until borneinf:%xmin*gradx/grillex:
dotlabel.bot(TEX("\num{"&decimal(k)&"}"),(k*x.u+xpart(Origine*cm),ypart(Origine*cm)));
endfor;
for k=grady step grady until ymax*grady/grilley:
dotlabel.lft(TEX("\num{"&decimal(k)&"}"),(xpart(Origine*cm),k*y.u+ypart(Origine*cm)));
endfor;
for k=-grady step -grady until ymin*grady/grilley:
dotlabel.lft(TEX("\num{"&decimal(k)&"}"),(xpart(Origine*cm),k*y.u+ypart(Origine*cm)));
endfor;
fi;
drawoptions(withpen pencircle scaled(1));
drawarrow (u*(0,ymin)--u*(0,ymax)) shifted (u*(xpart(Origine),0));
drawarrow (u*(xmin,0)--u*(xmax,0)) shifted (u*(0,ypart(Origine)));
label.llft(btex 0 etex,u*Origine);
drawoptions();
if Vide:
clip currentpicture to polygone(u*(xmin,ymin),u*(xmax,ymin),u*(xmax,ymax),u*(xmin,ymax));
else:
draw courbe1(borneinf,bornesup,nbpointsCourbe)(#2) withpen (pencircle scaled Epaisseur) withcolor colortrace;
% labelisation
numeric t;
t=pos*length Cb1;
pair PT,Tangente;
PT:=point (pos*length Cb1) of Cb1;
Tangente:=unitvector(direction t of Cb1);
label(TEX("\useKV[TraceG]{NomCourbe}") rotated angle(Tangente),PT+2mm*(Tangente rotated 90));
% fin labelisation
if \useKV[TraceG]{Code}:
\useKV[TraceG]{Traces}
fi;
clip currentpicture to polygone(u*(xmin,ymin),u*(xmax,ymin),u*(xmax,ymax),u*(xmin,ymax));
if LegendeX:
label.rt(btex \useKV[TraceG]{LabelX} etex,u*(xmax,ypart(Origine)));
fi;
if LegendeY:
label.top(btex \useKV[TraceG]{LabelY} etex,u*(xpart(Origine),ymax));
fi;
fi;
\end{mplibcode}
\else
\mpxcommands{%
\usepackage{ProfCollege}
\setKV[TraceG]{#1}
}
\begin{mpost}[mpsettings={borneinf=\useKV[TraceG]{Bornea};bornesup=\useKV[TraceG]{Borneb};nbpointsCourbe:=\useKV[TraceG]{NbPointsCourbe};xmin=\useKV[TraceG]{Xmin};xmax=\useKV[TraceG]{Xmax};ymin=\useKV[TraceG]{Ymin};ymax=\useKV[TraceG]{Ymax};pasx=\useKV[TraceG]{Xstep};pasy=\useKV[TraceG]{Ystep};xu=1cm/\useKV[TraceG]{Xstep};yu=1cm/\useKV[TraceG]{Ystep};grillex=\useKV[TraceG]{PasGrilleX};grilley=\useKV[TraceG]{PasGrilleY};pos=\useKV[TraceG]{LabelC};Epaisseur=\useKV[TraceG]{Epaisseur}; color colortrace;colortrace=\useKV[TraceG]{CouleurTrace};boolean Grille,Vide;Grille=\useKV[TraceG]{Grille};Vide=\useKV[TraceG]{Vide};boolean Graduations;Graduations=\useKV[TraceG]{Graduations};
pair Origine;
Origine=(xmin,ymin)+\useKV[TraceG]{Origine};}]
vardef sin(expr t) = sind(c*t) enddef;
vardef cos(expr t) = cosd(c*t) enddef;
vardef tan(expr t) = sin(t)/cos(t) enddef;
vardef exp(expr t) = e**t enddef;
vardef ch(expr x)=(exp(x)+exp(-x))/2 enddef;
vardef sh(expr x)=(exp(x)-exp(-x))/2 enddef;
vardef ln(expr t) = mlog(t)/256 enddef;
vardef arcsin(expr x)=%Définition mathématique en radian
pi*angle((sqrt(1-x**2),x))/180
enddef;
vardef arccos(expr x)=%Définition mathématique en radian
pi*angle((x,sqrt(1-x**2)))/180
enddef;
path Cb[];
vardef courbe[](expr a,b,nb)(text texte)=
path Courbe;
for i:=0 upto nb :
x@[i]:=(a+i*(b-a)/nb);
x:=x@[i];
y@[i]:=texte;
endfor ;
Cb@:=(x@.0*xu,y@.0*yu)
for i:=1 upto nb :
..(x@[i]*xu,y@[i]*yu)
endfor;
Cb@:=Cb@ shifted (Origine*cm);
Courbe=Cb@;
Courbe
enddef;
if Grille:
drawoptions(withcolor 0.75white);
for k=xpart(Origine) step grillex until xmax:
trace u*(k,ymin)--u*(k,ymax);
endfor;
for k=xpart(Origine) step -grillex until xmin:
trace u*(k,ymin)--u*(k,ymax);
endfor;
for k=ypart(Origine) step grilley until ymax:
trace u*(xmin,k)--u*(xmax,k);
endfor;
for k=ypart(Origine) step -grilley until ymin:
trace u*(xmin,k)--u*(xmax,k);
endfor;
drawoptions();
fi;
if Graduations:
for k=1 upto xmax/grillex:
dotlabel.bot(LATEX("\num{"&decimal(k)&"}"),(k*xu+xpart(Origine*cm),ypart(Origine*cm)));
endfor;
for k=-1 downto xmin/grillex:
dotlabel.bot(LATEX("\num{"&decimal(k)&"}"),(k*xu+xpart(Origine*cm),ypart(Origine*cm)));
endfor;
for k=1 upto ymax/grilley:
dotlabel.lft(LATEX("\num{"&decimal(k)&"}"),(xpart(Origine*cm),k*yu+ypart(Origine*cm)));
endfor;
for k=-1 downto ymin/grilley:
dotlabel.lft(LATEX("\num{"&decimal(k)&"}"),(xpart(Origine*cm),k*yu+ypart(Origine*cm)));
endfor;
fi;
drawoptions(withpen pencircle scaled1.5);
drawarrow (u*(0,ymin)--u*(0,ymax)) shifted (u*(xpart(Origine),0));
drawarrow (u*(xmin,0)--u*(xmax,0)) shifted (u*(0,ypart(Origine)));
drawoptions();
if Vide:
else:
draw courbe1(borneinf,bornesup,nbpointsCourbe)(#2) withpen (pencircle scaled Epaisseur) withcolor colortrace;
% % labelisation
numeric t;
t=pos*length Cb1;
pair PT,Tangente;
PT:=point (pos*length Cb1) of Cb1;
Tangente:=unitvector(direction t of Cb1);
label(btex \noexpand\useKV[TraceG]{NomCourbe} etex rotated angle(Tangente),PT+2mm*(Tangente rotated 90));
% % fin labelisation
clip currentpicture to polygone(u*(xmin,ymin),u*(xmax,ymin),u*(xmax,ymax),u*(xmin,ymax));
label.rt(btex \useKV[TraceG]{LabelX} etex,u*(xmax,ypart(Origine)));
label.top(btex \useKV[TraceG]{LabelY} etex,u*(xpart(Origine),ymax));
fi;
\end{mpost}
\fi
}%
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